Finite Group Databasebeta

← #35197372

Subgroups — #35197372

Order 20224.

11618 conjugacy classes of subgroups.

The subgroup lattice has 1670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099399C211yesmaximal, characteristic, complemented
2C2×H(5,𝔽2)×D79C211yesmaximal, characteristic, complemented
3#23777191C212yesmaximal, complemented
4#23777186C216yesmaximal, complemented
5#23777177C212yesmaximal, complemented
6#23777172C216yesmaximal, complemented
7#23777070C211yesmaximal, characteristic, complemented
8#23777069C211yesmaximal, characteristic, complemented
9#23777067C213yesmaximal, complemented
10#23777065C213yesmaximal, complemented
11#23777064C213yesmaximal, complemented
12#23777062C211yesmaximal, characteristic, complemented
13#23777061C213yesmaximal, complemented
14#23777057C212yesmaximal, complemented
15#23777053C212yesmaximal, complemented
16#23777030C216yesmaximal, complemented
17#23777028C216yesmaximal, complemented
18#23776730C213yesmaximal, complemented
19#23776728C213yesmaximal, complemented
20C2×#19099129C213yesmaximal, complemented
21#535×D79C213yesmaximal, complemented
22#23776600C211yesmaximal, characteristic, complemented
23C79×#3488C211yesmaximal, characteristic, complemented
24#19099399—216no—
25C2×#14579209C2211yescharacteristic, complemented
26C2×#14579209C2211yescharacteristic, complemented
27C2×#14579208C2211yescharacteristic, complemented
28C2×#14579208C2213yescomplemented
29C2×#14579207C2213yescomplemented
30C2×#14579207C2211yescharacteristic, complemented
31C2×#14579207C2212yescomplemented
32C2×#14579207C2213yescomplemented
33C2×#14579207C2211yescharacteristic, complemented
34C2×#14579206C2213yescomplemented
35C2×#14579206C2216yescomplemented
36C2×#14579206C2213yescomplemented
37C2×#14579206C2213yescomplemented
38H(5,𝔽2)×D79—216no—
39C22×#11929624C2213yescomplemented
40C22×#11929624C2213yescomplemented
41C2×#41×D79C2211yescharacteristic
42C2×#41×D79C2212yescomplemented
43C2×#41×D79C2213yescomplemented
44C2×#41×D79C2213yescomplemented
45C2×#41×D79C2213yescomplemented
46C2×#41×D79C2211yescharacteristic, complemented
47C22×D4×D79C2216yescomplemented
48C22×D4×D79C2213yescomplemented
49#19099235C2212yescomplemented
50#19099234C2216yescomplemented
51#19099233C2216yescomplemented
52#19099232C2212yescomplemented
53#19099232C2212yescomplemented
54#19099231C2216yescomplemented
55#19099231C2216yescomplemented
56#19099225C2212yescomplemented
57#19099224C2212yescomplemented
58#19099223C2216yescomplemented
59#19099222C2216yescomplemented
60#19099221C2216yescomplemented
61#19099220C2212yescomplemented
62#19099219C2216yescomplemented
63#19099210C2216yescomplemented
64#19099209C2216yescomplemented
65#19099208C2216yescomplemented
66#19099207C2216yescomplemented
67#19099206C2216yescomplemented
68#19099205C22112yescomplemented
69#19099204C2216yescomplemented
70#19099203C22112yescomplemented
71#19099202C22112yescomplemented
72#19099201C2216yescomplemented
73#19099200C22112yescomplemented
74D4×D316C2216yescomplemented
75D4×D316C2216yescomplemented
76#19099198C2216yescomplemented
77#19099197C22112yescomplemented
78#19099197C2216yescomplemented
79#19099197C2216yescomplemented
80D4×C22⋊D79C2216yescomplemented
81D4×C22⋊D79C2216yescomplemented
82D4×C22⋊D79C22112yescomplemented
83#19099195C22112yescomplemented
84#19099195C22112yescomplemented
85#19099144C2213yescomplemented
86#19099143C2213yescomplemented
87#19099143C2213yescomplemented
88#19099142C2213yescomplemented
89#19099142C2213yescomplemented
90#19099141C2213yescomplemented
91#19099141C2213yescomplemented
92#19099136C2213yescomplemented
93#19099136C2211yescharacteristic, complemented
94#19099136C2216yescomplemented
95#19099135C2216yescomplemented
96#19099132C2213yescomplemented
97#19099131C2216yescomplemented
98#19099130C2213yescomplemented
99#19099129C2216yescomplemented
100#19099129C2216yescomplemented
101#19099129C2213yescomplemented
102#19099129C2216yescomplemented
103#19099129C2213yescomplemented
104#19099129C2216yescomplemented
105#19099129C2216yescomplemented
106#19099129C2216yescomplemented
107#19099129C2216yescomplemented
108#19099129C2216yescomplemented
109#19099128C2216yescomplemented
110#19099128C22112yescomplemented
111#19099127C2213yescomplemented
112#19099126C2216yescomplemented
113#19099124C2216yescomplemented
114#19099123C2216yescomplemented
115#19099121C22112yescomplemented
116#19099110C2216yescomplemented
117#19099110C2216yescomplemented
118#19099108C22112yescomplemented
119C2×#14579157C2216yescomplemented
120#127×D79C2216yescomplemented
121C2×#14579147C2216yescomplemented
122#124×D79C2216yescomplemented
123#19099076C2216yescomplemented
124#19099076C2216yescomplemented
125#19099075C2213yescomplemented
126#19099074C2213yescomplemented
127#19099073C2216yescomplemented
128#19099073C2216yescomplemented
129#19099072C2216yescomplemented
130#19099072C2216yescomplemented
131#19099070C2213yescomplemented
132C2×#14579136C2213yescomplemented
133C2×#14579135C2213yescomplemented
134C2×#14579132C2213yescomplemented
135#121×D79C2216yescomplemented
136#121×D79C2216yescomplemented
137C2×#14579131C2216yescomplemented
138C2×#14579129C2216yescomplemented
139#120×D79C22112yescomplemented
140#19099046C2211yescharacteristic, complemented
141#19099044C2213yescomplemented
142#19099043C2213yescomplemented
143#19099039C2212yescomplemented
144#19099035C2216yescomplemented
145C4×#11929625C2212yescomplemented
146C4×#11929623C2216yescomplemented
147C2×#14579119C2213yescomplemented
148#117×D79C2213yescomplemented
149C2×H(5,𝔽2)×C79C2211yescharacteristic, complemented
150C22×#41×C79C2211yescharacteristic, complemented
151#550×C79C2212yescomplemented
152#548×C79C2212yescomplemented
153#546×C79C2216yescomplemented
154D42×C79C2216yescomplemented
155#537×C79C2213yescomplemented
156#535×C79C2213yescomplemented
157#525×C79C2213yescomplemented
158C2×#121×C79C2213yescomplemented
159#520×C79C2211yescharacteristic, complemented
160C24×D79C2316yes—
161#14579209—28no—
162#14579209—28no—
163#14579208—224no—
164#14579208—28no—
165#14579207—28no—
166#14579207—216no—
167#14579207—28no—
168#14579207—224no—
169#14579207—224no—
170#14579206—224no—
171#14579206—248no—
172#14579206—224no—
173#14579206—224no—
174C2×#11929625C2313yes—
175C2×#11929625C2312yes—
176C2×#11929625C2313yes—
177C2×#11929625C2311yescharacteristic
178C2×#11929625C2313yescomplemented
179C2×#11929625C2311yescharacteristic, complemented
180C2×#11929624—224no—
181C2×#11929624—224no—
182C2×#11929624C2316yes—
183C2×#11929624C2313yes—
184C2×#11929624C2311yescharacteristic
185C2×#11929624C2313yes—
186C2×#11929624C2316yes—
187C2×#11929624C2313yes—
188C2×#11929624C2313yes—
189C2×#11929624C2313yes—
190C2×#11929624C2313yescomplemented
191C2×#11929624C2313yescomplemented
192C2×#11929624C2313yescomplemented
193C2×#11929624C2316yescomplemented
194C2×#11929624C2313yescomplemented
195C2×#11929624C2313yescomplemented
196C2×#11929624C2313yescomplemented
197C2×#11929624C2313yescomplemented
198C2×#11929623C2313yes—
199C2×#11929623C2316yes—
200C2×#11929623C2316yes—
201C2×#11929623C2313yes—
202C2×#11929623C2313yes—
203C2×#11929623C2316yescomplemented
204C2×#11929623C2313yescomplemented
205C2×#11929623C2313yescomplemented
206C2×#11929623C2316yescomplemented
207#41×D79—28no—
208#41×D79—224no—
209#41×D79—216no—
210#41×D79—224no—
211#41×D79—224no—
212#41×D79D4116yescomplemented
213C22×Dic158C2313yescomplemented
214C22×Dic158C2313yescomplemented
215C2×Q8×D79C2311yescharacteristic
216C2×Q8×D79C2311yescharacteristic
217C2×Q8×D79C2313yescomplemented
218C2×Q8×D79C2311yescharacteristic, complemented
219C2×Q8×D79C2313yescomplemented
220C22×D316C2316yes—
221C22×D316C2313yes—
222C22×D316C2313yes—
223C22×D316C2313yescomplemented
224C22×D316C2316yescomplemented
225C22×C22⋊D79C23112yes—
226C22×C22⋊D79C2313yes—
227C22×C22⋊D79C2316yes—
228C22×C22⋊D79C2316yescomplemented
229C22×C22⋊D79C2313yescomplemented
230C22×C22⋊D79C2316yescomplemented
231C22×C22⋊D79C2316yescomplemented
232C2×D4×D79—248no—
233C2×D4×D79—224no—
234C2×D4×D79C23112yes—
235C2×D4×D79C2316yes—
236C2×D4×D79C2316yes—
237C2×D4×D79C2316yes—
238C2×D4×D79C2316yes—
239C2×D4×D79C2316yes—
240C2×D4×D79C2316yes—
241C2×D4×D79C2316yes—
242C2×D4×D79C2313yes—
243C2×D4×D79C2313yes—
244C2×D4×D79C2316yescomplemented
245C2×D4×D79C2313yescomplemented
246C2×D4×D79C2313yescomplemented
247C2×D4×D79C2313yescomplemented
248C2×D4×D79C23112yescomplemented
249C2×D4×D79C23112yescomplemented
250C22×C4×D79C2316yes—
251C22×C4×D79C2313yes—
252C22×C4×D79C2316yescomplemented
253C22×C4×D79C2313yescomplemented
254#14579160C2316yescomplemented
255#14579160C2312yescomplemented
256#14579158C2316yescomplemented
257#14579157C23112yescomplemented
258#14579157C23112yescomplemented
259#14579157C2316yescomplemented
260#14579157C2316yescomplemented
261#14579157C2316yescomplemented
262#14579157C23112yescomplemented
263#14579157C2316yescomplemented
264#14579150C2316yescomplemented
265#14579149C2316yescomplemented
266#14579148C2316yescomplemented
267#14579147C23112yescomplemented
268#14579147C2316yescomplemented
269#14579147C2312yescomplemented
270#14579147C23112yescomplemented
271#14579147C23112yescomplemented
272#14579147C2316yescomplemented
273#14579147C2316yescomplemented
274#14579146C2312yes—
275#14579146C2316yes—
276#14579146C23112yescomplemented
277#14579145C2316yescomplemented
278#14579144C2316yescomplemented
279#14579143C2312yes—
280#14579143C2316yes—
281#14579143C23112yescomplemented
282#14579142C2316yescomplemented
283#14579141C2311yescharacteristic, complemented
284#14579141C2313yescomplemented
285#14579141C2316yescomplemented
286#14579140C2313yescomplemented
287#14579140C2316yescomplemented
288#14579140C2311yescharacteristic, complemented
289#14579139C2316yescomplemented
290#14579139C2316yescomplemented
291#14579138C2316yescomplemented
292#14579138C2316yescomplemented
293#14579137C2313yescomplemented
294#14579137C2316yescomplemented
295#14579137C2311yescharacteristic, complemented
296#14579136C2316yescomplemented
297#14579136C2316yescomplemented
298#14579136C2313yescomplemented
299#14579136C2313yescomplemented
300#14579136C2316yescomplemented
301#14579136C2316yescomplemented
302#14579136C2316yescomplemented
303#14579136C2316yescomplemented
304#14579135C2316yescomplemented
305#14579135C2316yescomplemented
306#14579135C2313yescomplemented
307#14579135C2313yescomplemented
308#14579135C23112yescomplemented
309#14579135C2316yescomplemented
310#14579135C2316yescomplemented
311#14579134C2316yescomplemented
312#14579134C2316yescomplemented
313#14579134C2316yescomplemented
314#14579134C2316yescomplemented
315#14579134C2316yescomplemented
316#14579134C2316yescomplemented
317#14579134C23112yescomplemented
318#14579134C23112yescomplemented
319#14579133C23112yescomplemented
320#14579133C23112yescomplemented
321#14579133C2316yescomplemented
322#14579133C2316yescomplemented
323#14579133C23112yescomplemented
324#14579133C23112yescomplemented
325#14579132C2316yescomplemented
326#14579132C2316yescomplemented
327#14579132C2316yescomplemented
328#14579132C2316yescomplemented
329#14579132C2313yescomplemented
330#14579132C2313yescomplemented
331#14579132C2316yescomplemented
332#14579132C2316yescomplemented
333#14579131C2316yes—
334#14579131C23112yes—
335#14579131C2316yes—
336#14579131C2316yescomplemented
337#14579131C23112yescomplemented
338#14579131C23112yescomplemented
339#14579131C23112yescomplemented
340#14579131C23112yescomplemented
341#14579130C2316yescomplemented
342#14579130C23112yescomplemented
343#14579129C2316yes—
344#14579129C23112yes—
345#14579129C2316yes—
346#14579129C23112yescomplemented
347#14579129C23112yescomplemented
348#14579129C2316yescomplemented
349#14579129C23112yescomplemented
350#14579129C23112yescomplemented
351Q8×Dic79C2312yescomplemented
352C4×Dic158C2316yescomplemented
353#14579126C2316yescomplemented
354C4×D316C2316yescomplemented
355C4×D316C2316yescomplemented
356C4×D316C2316yescomplemented
357D4×Dic79C2316yescomplemented
358D4×Dic79C23112yescomplemented
359#14579123C2316yescomplemented
360#14579123C23112yescomplemented
361C4×C22⋊D79C23112yescomplemented
362C4×C22⋊D79C2316yescomplemented
363C4×C22⋊D79C2316yescomplemented
364C4×C22⋊D79C2316yescomplemented
365C4×C22⋊D79C2316yescomplemented
366(C22⋊D79)⋊C4C23112yescomplemented
367(C22⋊D79)⋊C4C23112yescomplemented
368(C22⋊D79)⋊C4C23112yescomplemented
369#14579120C2313yescomplemented
370#14579119C2311yescharacteristic
371#14579119C2313yes—
372#14579119C2316yes—
373#14579119C2316yescomplemented
374#14579119C2316yescomplemented
375#14579118C2316yes—
376#14579117C2316yescomplemented
377C2×C4⋊Dic79C2313yescomplemented
378C4⋊C4×D79C2313yescomplemented
379C4⋊C4×D79C2313yescomplemented
380C2×C22⋊Dic79C2316yescomplemented
381C2×(C2×D79)⋊C4C2316yes—
382C2×(C2×D79)⋊C4C2316yescomplemented
383C2×(C2×D79)⋊C4C2316yescomplemented
384C22⋊C4×D79C2316yes—
385C22⋊C4×D79C23112yescomplemented
386C22⋊C4×D79C23112yescomplemented
387C2×C4×Dic79C2316yescomplemented
388C42×D79C2316yescomplemented
389H(5,𝔽2)×C79—28no—
390C2×#41×C79—28no—
391C2×#41×C79C2313yes—
392C2×#41×C79C2312yes—
393C2×#41×C79C2311yescharacteristic
394C2×#41×C79C2313yescomplemented
395C2×#41×C79C2311yescharacteristic, complemented
396C2×#41×C79C2313yescomplemented
397C22×Q8×C79C2311yescharacteristic, complemented
398C22×D4×C79C2316yes—
399C22×D4×C79C2313yes—
400C22×D4×C79C2313yescomplemented
401C22×D4×C79C2316yescomplemented
402C23×C4×C79C2313yescomplemented
403#127×C79C2316yescomplemented
404#124×C79C2316yescomplemented
405#123×C79C2316yescomplemented
406C22⋊Q8×C79C2311yescharacteristic, complemented
407C22⋊Q8×C79C2313yescomplemented
408C22⋊Q8×C79C2316yescomplemented
409#121×C79C2313yescomplemented
410#121×C79C2313yescomplemented
411#121×C79C23112yescomplemented
412#121×C79C2316yescomplemented
413#121×C79C2316yescomplemented
414#121×C79C2316yescomplemented
415#121×C79C2316yescomplemented
416#120×C79C2316yescomplemented
417#120×C79C23112yescomplemented
418C4×Q8×C79C2312yescomplemented
419C4×D4×C79C2316yescomplemented
420C4×D4×C79C2316yescomplemented
421C4×D4×C79C2316yescomplemented
422#117×C79C2313yescomplemented
423C2×C4⋊C4×C79C2313yescomplemented
424C2×C22⋊C4×C79C2316yescomplemented
425C23×D79—224no—
426C23×D79—86no—
427C23×D79—86no—
428C23×D79C2416yes—
429C23×D79C24112yes—
430C23×D79C2416yes—
431C23×D79C2416yes—
432C23×D79C2413yes—
433C23×D79C2413yes—
434#11929625—212no—
435#11929625—212no—
436#11929625—212no—
437#11929625—28no—
438#11929625—24no—
439#11929625C2×D418yescomplemented
440#11929624—212no—
441#11929624—212no—
442#11929624—212no—
443#11929624—224no—
444#11929624—24no—
445#11929624—212no—
446#11929624—212no—
447#11929624—212no—
448#11929624—212no—
449#11929624—212no—
450#11929624—224no—
451#11929624—212no—
452#11929624—212no—
453#11929624—212no—
454#11929624—224no—
455#11929624C2×D4124yescomplemented
456#11929623—224no—
457#11929623—224no—
458#11929623—212no—
459#11929623—212no—
460#11929623—224no—
461#11929623—212no—
462#11929623—212no—
463#11929623—224no—
464#11929623C2×D4124yescomplemented
465C2×Dic158—212no—
466C2×Dic158—212no—
467C2×Dic158C2411yescharacteristic
468C2×Dic158C2412yes—
469C2×Dic158C2413yes—
470C2×Dic158C2413yes—
471C2×Dic158C2413yes—
472C2×Dic158C2413yes—
473C2×Dic158C2411yescharacteristic
474C2×Dic158C2413yes—
475Q8×D79—24no—
476Q8×D79—212no—
477Q8×D79—212no—
478Q8×D79—24no—
479Q8×D79C2×D418yescomplemented
480C2×D316—212no—
481C2×D316—224no—
482C2×D316—212no—
483C2×D316—212no—
484C2×D316—86no—
485C2×D316C2411yescharacteristic
486C2×D316C2413yes—
487C2×D316C2416yes—
488C2×D316C2413yes—
489C2×D316C2416yes—
490C2×D316C2413yes—
491C2×D316C2413yes—
492C2×D316C2413yes—
493C2×D316C24112yes—
494C2×D316C2416yes—
495C2×D316C2416yes—
496C2×D316C2413yes—
497C2×C22⋊D79—212no—
498C2×C22⋊D79—224no—
499C2×C22⋊D79—212no—
500C2×C22⋊D79—224no—
501C2×C22⋊D79—248no—
502C2×C22⋊D79—86no—
503C2×C22⋊D79—86no—
504C2×C22⋊D79C2413yes—
505C2×C22⋊D79C2416yes—
506C2×C22⋊D79C2416yes—
507C2×C22⋊D79C24112yes—
508C2×C22⋊D79C2416yes—
509C2×C22⋊D79C2413yes—
510C2×C22⋊D79C2413yes—
511C2×C22⋊D79C2413yes—
512C2×C22⋊D79C2416yes—
513C2×C22⋊D79C2411yescharacteristic
514C2×C22⋊D79C2413yes—
515C2×C22⋊D79C2411yescharacteristic
516C2×C22⋊D79C2413yes—
517C2×C22⋊D79C24112yes—
518C2×C22⋊D79C24112yes—
519C2×C22⋊D79C2416yes—
520C2×C22⋊D79C2416yes—
521C2×C22⋊D79C2416yes—
522C2×C22⋊D79C2416yes—
523C2×C22⋊D79C2416yes—
524D4×D79—212no—
525D4×D79—224no—
526D4×D79—212no—
527D4×D79—224no—
528D4×D79—212no—
529D4×D79—224no—
530D4×D79—224no—
531D4×D79—224no—
532D4×D79—224no—
533D4×D79—212no—
534D4×D79—224no—
535D4×D79—224no—
536D4×D79—248no—
537D4×D79—812no—
538D4×D79—812no—
539D4×D79C2×D4124yescomplemented
540C22×Dic79C2416yes—
541C22×Dic79C2413yes—
542C22×Dic79C2416yes—
543C22×Dic79C2416yes—
544C22×Dic79C2413yes—
545C2×C4×D79—224no—
546C2×C4×D79—224no—
547C2×C4×D79—212no—
548C2×C4×D79C2×D4124yescomplemented
549C2×C4×D79C2412yes—
550C2×C4×D79C2413yes—
551C2×C4×D79C2413yes—
552C2×C4×D79C2416yes—
553C2×C4×D79C2416yes—
554C2×C4×D79C2416yes—
555C2×C4×D79C2416yes—
556C2×C4×D79C2413yes—
557C2×C4×D79C2411yescharacteristic
558C2×C4×D79C2416yes—
559C2×C4×D79C2416yes—
560C2×C4×D79C2413yes—
561C2×C4×D79C2411yescharacteristic
562C2×C4×D79C2413yes—
563C2×C4×D79C2413yes—
564C4⋊Dic79C2411yescharacteristic
565C4⋊Dic79C2413yes—
566C4⋊Dic79C2416yes—
567C4⋊Dic79C2416yes—
568C4⋊Dic79C2412yes—
569Dic79⋊C4C2416yes—
570Dic79⋊C4C2416yes—
571Dic79⋊C4C2416yes—
572Dic79⋊C4C2416yes—
573Dic79⋊C4C2412yes—
574Dic79⋊C4C2412yes—
575C22⋊Dic79C2416yes—
576C22⋊Dic79C2416yes—
577C22⋊Dic79C24112yes—
578C22⋊Dic79C2416yes—
579C22⋊Dic79C2412yes—
580C22⋊Dic79C2416yes—
581(C2×D79)⋊C4C2412yes—
582(C2×D79)⋊C4C2416yes—
583(C2×D79)⋊C4C2416yes—
584(C2×D79)⋊C4C2416yes—
585(C2×D79)⋊C4C24112yes—
586(C2×D79)⋊C4C24112yes—
587(C2×D79)⋊C4C24112yes—
588(C2×D79)⋊C4C2416yes—
589(C2×D79)⋊C4C2416yes—
590(C2×D79)⋊C4C2416yes—
591(C2×D79)⋊C4C2412yes—
592(C2×D79)⋊C4C2416yes—
593(C2×D79)⋊C4C2412yes—
594C4×Dic79C2412yes—
595C4×Dic79C2416yes—
596C4×Dic79C2416yes—
597C4×Dic79C24112yes—
598C24×C79C2416yes—
599C24×C79C2413yes—
600#41×C79—28no—
601#41×C79—24no—
602#41×C79—212no—
603#41×C79—212no—
604#41×C79—212no—
605#41×C79C2×D418yescomplemented
606C2×Q8×C79—24no—
607C2×Q8×C79C2411yescharacteristic
608C2×Q8×C79C2413yes—
609C2×Q8×C79C2411yescharacteristic
610C2×D4×C79—212no—
611C2×D4×C79—224no—
612C2×D4×C79—212no—
613C2×D4×C79—86no—
614C2×D4×C79C2413yes—
615C2×D4×C79C2416yes—
616C2×D4×C79C2413yes—
617C2×D4×C79C2416yes—
618C2×D4×C79C2416yes—
619C2×D4×C79C2416yes—
620C2×D4×C79C2416yes—
621C2×D4×C79C24112yes—
622C2×D4×C79C2413yes—
623C22×C4×C79—212no—
624C22×C4×C79C2413yes—
625C22×C4×C79C2413yes—
626C22×C4×C79C2416yes—
627C22×C4×C79C2413yes—
628C22×C4×C79C2411yescharacteristic
629C22×C4×C79C2413yes—
630C22×C4×C79C2416yes—
631C22×C4×C79C2413yes—
632C4⋊C4×C79C2413yes—
633C4⋊C4×C79C2416yes—
634C4⋊C4×C79C2411yescharacteristic
635C4⋊C4×C79C2412yes—
636C4⋊C4×C79C2416yes—
637C22⋊C4×C79C2416yes—
638C22⋊C4×C79C24112yes—
639C22⋊C4×C79C2416yes—
640C22⋊C4×C79C2412yes—
641C22⋊C4×C79C2416yes—
642C22⋊C4×C79C2416yes—
643C42×C79C2416yes—
644C23×C79—26no—
645C23×C79—212no—
646C23×C79—43no—
647C23×C79—46no—
648C23×C79—46no—
649C23×C79—43no—
650C23×C79C2516yes—
651C23×C79C2513yes—
652C23×C79C2511yescharacteristic
653C23×C79C2513yes—
654C22×D79—26no—
655C22×D79—212no—
656C22×D79—212no—
657C22×D79—212no—
658C22×D79—224no—
659C22×D79—43no—
660C22×D79—43no—
661C22×D79—46no—
662C22×D79—46no—
663C22×D79—46no—
664C22×D79—46no—
665C22×D79—412no—
666C22×D79—412no—
667C22×D79—43no—
668C22×D79—46no—
669C22×D79—43no—
670C22×D79—46no—
671C22×D79—848no—
672C22×D79C22×D4112yes—
673C22×D79C2516yes—
674C22×D79C2511yescharacteristic
675C22×D79C2513yes—
676C22×D79C2511yescharacteristic
677C22×D79C2513yes—
678Q8×C79—26no—
679Q8×C79—22no—
680Q8×C79C22×D414yes—
681D4×C79—212no—
682D4×C79—212no—
683D4×C79—26no—
684D4×C79—212no—
685D4×C79—26no—
686D4×C79—46no—
687D4×C79—412no—
688D4×C79—46no—
689D4×C79C22×D4112yes—
690C2×C4×C79—26no—
691C2×C4×C79—26no—
692C2×C4×C79—212no—
693C2×C4×C79—26no—
694C2×C4×C79—22no—
695C2×C4×C79—26no—
696C2×C4×C79—46no—
697C2×C4×C79C22×D4112yes—
698C2×C4×C79C2516yes—
699C2×C4×C79C2512yes—
700C2×C4×C79C2513yes—
701C2×C4×C79C2511yescharacteristic
702C2×C4×C79C2512yes—
703C2×C4×C79C2513yes—
704C2×C4×C79C2511yescharacteristic
705C22⋊D79—212no—
706C22⋊D79—212no—
707C22⋊D79—212no—
708C22⋊D79—26no—
709C22⋊D79—26no—
710C22⋊D79—26no—
711C22⋊D79—22no—
712C22⋊D79—212no—
713C22⋊D79—224no—
714C22⋊D79—26no—
715C22⋊D79—26no—
716C22⋊D79—22no—
717C22⋊D79—26no—
718C22⋊D79—46no—
719C22⋊D79—46no—
720C22⋊D79—412no—
721C22⋊D79—412no—
722C22⋊D79—46no—
723C22⋊D79—46no—
724C22⋊D79C22×D4124yes—
725C2×Dic79—26no—
726C2×Dic79—212no—
727C2×Dic79—212no—
728C2×Dic79—46no—
729C2×Dic79C22×D4112yes—
730C2×Dic79C2516yes—
731C2×Dic79C2512yes—
732C2×Dic79C2513yes—
733C2×Dic79C2511yescharacteristic
734C2×Dic79C2512yes—
735C2×Dic79C2511yescharacteristic
736C2×Dic79C2513yes—
737D316—212no—
738D316—26no—
739D316—26no—
740D316—26no—
741D316—22no—
742D316—26no—
743D316—212no—
744D316—26no—
745D316—46no—
746D316—412no—
747D316—46no—
748D316C22×D4112yes—
749C4×D79—24no—
750C4×D79—212no—
751C4×D79—26no—
752C4×D79—22no—
753C4×D79—212no—
754C4×D79—26no—
755C4×D79—26no—
756C4×D79—212no—
757C4×D79—212no—
758C4×D79—46no—
759C4×D79—46no—
760C4×D79C22×D4112yes—
761C4×D79C22×D4112yes—
762C4×D79C22×D414yes—
763C4×D79C22×D4112yes—
764Dic158—26no—
765Dic158—22no—
766Dic158—26no—
767Dic158—26no—
768Dic158—24no—
769Dic158—22no—
770Dic158—26no—
771Dic158C22×D4112yes—
772C22×C79—23no—
773C22×C79—23no—
774C22×C79—21no—
775C22×C79—23no—
776C22×C79—26no—
777C22×C79—21no—
778C22×C79—23no—
779C22×C79—26no—
780C22×C79—23no—
781C22×C79—26no—
782C22×C79—21no—
783C22×C79—812no—
784C22×C79—86no—
785C22×C79C23×D416yes—
786C22×C79C2611yescharacteristic
787C2×D79—21no—
788C2×D79—21no—
789C2×D79—23no—
790C2×D79—23no—
791C2×D79—26no—
792C2×D79—23no—
793C2×D79—21no—
794C2×D79—21no—
795C2×D79—23no—
796C2×D79—26no—
797C2×D79—23no—
798C2×D79—26no—
799C2×D79—21no—
800C2×D79—412no—
801C2×D79—424no—
802C2×D79—812no—
803C2×D79—824no—
804C2×D79—86no—
805C2×D79—812no—
806C2×D79C23×D416yes—
807C2×D79C23×D412yes—
808C4×C79—21no—
809C4×C79—22no—
810C4×C79—23no—
811C4×C79—26no—
812C4×C79—22no—
813C4×C79C23×D412yes—
814C4×C79C23×D416yes—
815Dic79—22no—
816Dic79—23no—
817Dic79—21no—
818Dic79—22no—
819Dic79—26no—
820Dic79C23×D412yes—
821Dic79C23×D416yes—
822#62852—791nomaximal, Sylow
823C2×C79—26no—
824C2×C79—46no—
825C2×C79—43no—
826C2×C79—41no—
827C2×C79C24×D411yescharacteristic
828C2×C79H(7,𝔽2)11yescharacteristic
829C2×C79H(7,𝔽2)11yescharacteristic
830D79—22no—
831D79—26no—
832D79—46no—
833D79—41no—
834D79—43no—
835C2×#585—791no—
836C22×H(5,𝔽2)—791no—
837#3500—792no—
838#3500—796no—
839#3498—792no—
840#3498—796no—
841#3488—791no—
842#3488—791no—
843#3488—793no—
844#3488—793no—
845#3488—793no—
846#3488—793no—
847#3488—791no—
848#3488D7911yescharacteristic, complemented
849#3487—792no—
850#3487—792no—
851#3484—796no—
852#3484—796no—
853#3449—793no—
854#3449—793no—
855C2×#535—793no—
856C2×#535—793no—
857#3428—791no—
858C79#6285211yescharacteristic, complemented, Sylow
859#585—15816no—
860C2×2−1+4—791no—
861C2×2−1+4—793no—
862C2×2−1+4—791no—
863C2×2−1+4—791no—
864C2×H(5,𝔽2)—793no—
865C2×H(5,𝔽2)—791no—
866C2×H(5,𝔽2)—792no—
867C2×H(5,𝔽2)—793no—
868C2×H(5,𝔽2)—791no—
869C2×H(5,𝔽2)—793no—
870C2×H(5,𝔽2)—796no—
871C2×H(5,𝔽2)—793no—
872C2×H(5,𝔽2)—793no—
873C2×H(5,𝔽2)—15816no—
874C2×H(5,𝔽2)C2×D7911yescharacteristic, complemented
875C22×#41—791no—
876C22×#41—793no—
877C22×#41—792no—
878C22×#41—791no—
879C22×#41—793no—
880C22×#41—793no—
881C22×#41—793no—
882C22×#41—793no—
883C22×#41C2×D7911yescharacteristic, complemented
884C23×D4—793no—
885C23×D4—796no—
886#550—792no—
887#550—792no—
888#550—796no—
889#550—796no—
890#550—796no—
891#550—792no—
892#550—796no—
893#550C2×D7912yescomplemented
894#548—792no—
895#548—792no—
896#548—796no—
897#548—796no—
898#548—796no—
899#548—792no—
900#548—796no—
901#548C2×D7912yescomplemented
902#546—796no—
903#546—796no—
904#546—796no—
905#546—7912no—
906#546—796no—
907#546—7912no—
908#546—796no—
909#546—7912no—
910#546—796no—
911#546—796no—
912#546—7912no—
913#546C2×D7916yescomplemented
914D42—796no—
915D42—796no—
916D42—7912no—
917D42—796no—
918D42—7912no—
919D42—796no—
920D42—796no—
921D42—7912no—
922D42—7912no—
923D42—796no—
924D42—796no—
925D42C2×D7916yescomplemented
926#537—793no—
927#537—793no—
928#537—793no—
929#537—793no—
930#537—793no—
931#537—793no—
932#537—793no—
933#537C2×D7913yescomplemented
934#536—796no—
935#536—793no—
936#536—791no—
937#536—796no—
938#535—793no—
939#535—793no—
940#535—796no—
941#535—796no—
942#535—793no—
943#535—796no—
944#535—793no—
945#535—796no—
946#535—796no—
947#535—796no—
948#535—796no—
949#535—796no—
950#535—796no—
951#535—796no—
952#535—7912no—
953#535—796no—
954#535—793no—
955#535C2×D7913yescomplemented
956#534—796no—
957#534—7912no—
958#534—796no—
959#532—7912no—
960#532—796no—
961#532—796no—
962C2×#127—796no—
963C2×#127—796no—
964C2×#124—796no—
965C2×#124—796no—
966#525—793no—
967#525—793no—
968#525—796no—
969#525—796no—
970#525—796no—
971#525—796no—
972#525—796no—
973#525—796no—
974#525—793no—
975#525C2×D7913yescomplemented
976C2×#121—793no—
977C2×#121—793no—
978C2×#121—796no—
979C2×#121—796no—
980C2×#121—793no—
981C2×#121C2×D7913yescomplemented
982C2×#120—796no—
983C2×#120—7912no—
984C2×#120—796no—
985#520—791no—
986#520—793no—
987#520—793no—
988#520C2×D7911yescharacteristic, complemented
989#519—792no—
990#518—796no—
991C4×#41—792no—
992C4×#41—796no—
993C2×#117—793no—
994C2×#117—793no—
995C25—796no—
9962−1+4—1588no—
9972−1+4—1588no—
9982−1+4—1588no—
9992−1+4—15824no—
1000H(5,𝔽2)—28no—
1001H(5,𝔽2)—15824no—
1002H(5,𝔽2)—15848no—
1003H(5,𝔽2)—15824no—
1004H(5,𝔽2)—15824no—
1005H(5,𝔽2)—15824no—
1006H(5,𝔽2)—15816no—
1007H(5,𝔽2)—15824no—
1008H(5,𝔽2)—1588no—
1009H(5,𝔽2)—1588no—
1010C2×#41—28no—
1011C2×#41—7916no—
1012C2×#41—791no—
1013C2×#41—793no—
1014C2×#41—793no—
1015C2×#41—792no—
1016C2×#41—793no—
1017C2×#41—791no—
1018C2×#41—793no—
1019C2×#41—793no—
1020C2×#41—793no—
1021C2×#41—796no—
1022C2×#41—796no—
1023C2×#41—796no—
1024C2×#41—793no—
1025C2×#41—796no—
1026C2×#41—793no—
1027C2×#41—793no—
1028C2×#41—793no—
1029C2×#41—793no—
1030C2×#41—793no—
1031C2×#41—796no—
1032C2×#41—793no—
1033C2×#41—791no—
1034C2×#41—796no—
1035C2×#41—793no—
1036C2×#41—793no—
1037C2×#41—793no—
1038C2×#41—793no—
1039C2×#41—793no—
1040C2×#41—793no—
1041C2×#41—796no—
1042C2×#41—793no—
1043C2×#41—15824no—
1044C2×#41—15824no—
1045C2×#41—15824no—
1046C2×#41—15824no—
1047C2×#41—15816no—
1048C2×#41—15824no—
1049C2×#41—1588no—
1050C2×#41C22×D7913yes—
1051C2×#41C22×D7912yes—
1052C2×#41C22×D7911yescharacteristic
1053C2×#41C22×D7913yescomplemented
1054C2×#41C22×D7913yescomplemented
1055C2×#41C22×D7911yescharacteristic, complemented
1056C22×Q8—791no—
1057C22×Q8—791no—
1058C22×Q8—793no—
1059C22×Q8—793no—
1060C22×Q8—791no—
1061C22×Q8—793no—
1062C22×Q8—793no—
1063C22×Q8C22×D7911yescharacteristic, complemented
1064C22×D4—793no—
1065C22×D4—796no—
1066C22×D4—796no—
1067C22×D4—793no—
1068C22×D4—796no—
1069C22×D4—793no—
1070C22×D4—796no—
1071C22×D4—7912no—
1072C22×D4—7912no—
1073C22×D4—7912no—
1074C22×D4—796no—
1075C22×D4—796no—
1076C22×D4—796no—
1077C22×D4—793no—
1078C22×D4—796no—
1079C22×D4—796no—
1080C22×D4—793no—
1081C22×D4—796no—
1082C22×D4—793no—
1083C22×D4—793no—
1084C22×D4—7912no—
1085C22×D4—796no—
1086C22×D4—796no—
1087C22×D4—796no—
1088C22×D4—793no—
1089C22×D4—793no—
1090C22×D4—793no—
1091C22×D4—796no—
1092C22×D4—15824no—
1093C22×D4—15848no—
1094C22×D4C22×D7913yes—
1095C22×D4C22×D7916yes—
1096C22×D4C22×D7913yescomplemented
1097C22×D4C22×D7916yescomplemented
1098C23×C4—793no—
1099C23×C4—796no—
1100C23×C4—793no—
1101C23×C4—796no—
1102C23×C4C22×D7913yescomplemented
1103C4⋊Q8—796no—
1104C4⋊Q8—792no—
1105#127—7912no—
1106#127—796no—
1107#127—796no—
1108#127—796no—
1109#127—796no—
1110#127—7912no—
1111#127—7912no—
1112#127—796no—
1113#127C22×D7916yescomplemented
1114#124—796no—
1115#124—796no—
1116#124—796no—
1117#124—7912no—
1118#124—796no—
1119#124—7912no—
1120#124—7912no—
1121#124—796no—
1122#124—792no—
1123#124—796no—
1124#124C22×D7916yescomplemented
1125#123—796no—
1126#123—796no—
1127#123—796no—
1128#123—792no—
1129#123—7912no—
1130#123—796no—
1131#123—792no—
1132#123—7912no—
1133#123—796no—
1134#123C22×D7916yescomplemented
1135C22⋊Q8—791no—
1136C22⋊Q8—793no—
1137C22⋊Q8—796no—
1138C22⋊Q8—793no—
1139C22⋊Q8—791no—
1140C22⋊Q8—796no—
1141C22⋊Q8—791no—
1142C22⋊Q8—793no—
1143C22⋊Q8—796no—
1144C22⋊Q8—796no—
1145C22⋊Q8—796no—
1146C22⋊Q8—796no—
1147C22⋊Q8—796no—
1148C22⋊Q8C22×D7913yescomplemented
1149C22⋊Q8C22×D7916yescomplemented
1150C22⋊Q8C22×D7911yescharacteristic, complemented
1151#121—793no—
1152#121—796no—
1153#121—793no—
1154#121—796no—
1155#121—796no—
1156#121—7912no—
1157#121—7912no—
1158#121—796no—
1159#121—796no—
1160#121—796no—
1161#121—796no—
1162#121—796no—
1163#121—7912no—
1164#121—7912no—
1165#121—796no—
1166#121—793no—
1167#121—793no—
1168#121—796no—
1169#121—796no—
1170#121—796no—
1171#121—7912no—
1172#121—793no—
1173#121—796no—
1174#121—793no—
1175#121—796no—
1176#121—796no—
1177#121—796no—
1178#121—796no—
1179#121—796no—
1180#121—7912no—
1181#121—7912no—
1182#121—796no—
1183#121—796no—
1184#121—796no—
1185#121—796no—
1186#121—796no—
1187#121—796no—
1188#121C22×D7913yescomplemented
1189#121C22×D7916yescomplemented
1190#121C22×D7913yescomplemented
1191#121C22×D7916yescomplemented
1192#121C22×D7916yescomplemented
1193#121C22×D7916yescomplemented
1194#121C22×D79112yescomplemented
1195#120—7912no—
1196#120—796no—
1197#120—7912no—
1198#120—796no—
1199#120—796no—
1200#120—7912no—
1201#120—7912no—
1202#120—7912no—
1203#120—796no—
1204#120—7912no—
1205#120—796no—
1206#120—7912no—
1207#120—796no—
1208#120—7912no—
1209#120—7912no—
1210#120—7912no—
1211#120—7912no—
1212#120—796no—
1213#120C22×D79112yescomplemented
1214#120C22×D7916yescomplemented
1215C4×Q8—792no—
1216C4×Q8—796no—
1217C4×Q8—796no—
1218C4×Q8C22×D7912yescomplemented
1219C4×D4—796no—
1220C4×D4—7912no—
1221C4×D4—7912no—
1222C4×D4—796no—
1223C4×D4—796no—
1224C4×D4—796no—
1225C4×D4—796no—
1226C4×D4—796no—
1227C4×D4—7912no—
1228C4×D4—7912no—
1229C4×D4—7912no—
1230C4×D4—7912no—
1231C4×D4—796no—
1232C4×D4—796no—
1233C4×D4—796no—
1234C4×D4C22×D7916yescomplemented
1235C4×D4C22×D7916yescomplemented
1236C4×D4C22×D7916yescomplemented
1237#117—793no—
1238#117—791no—
1239#117—793no—
1240#117—796no—
1241#117—796no—
1242#117—796no—
1243#117—796no—
1244#117—796no—
1245#117C22×D7913yescomplemented
1246C2×C4⋊C4—793no—
1247C2×C4⋊C4—793no—
1248C2×C4⋊C4—793no—
1249C2×C4⋊C4C22×D7913yescomplemented
1250C2×C22⋊C4—796no—
1251C2×C22⋊C4—796no—
1252C2×C22⋊C4—796no—
1253C2×C22⋊C4—796no—
1254C2×C22⋊C4—796no—
1255C2×C22⋊C4—7912no—
1256C2×C22⋊C4—7912no—
1257C2×C22⋊C4C22×D7916yescomplemented
1258C2×C42—796no—
1259C2×C42—796no—
1260C24—793no—
1261C24—7912no—
1262C24—796no—
1263C24—796no—
1264C24—796no—
1265C24—793no—
1266C24—6326no—
1267C24—6326no—
1268C24—15824no—
1269C24C23×D7916yes—
1270C24C23×D7913yes—
1271#41—24no—
1272#41—28no—
1273#41—212no—
1274#41—212no—
1275#41—212no—
1276#41—798no—
1277#41—7924no—
1278#41—7924no—
1279#41—1584no—
1280#41—15812no—
1281#41—15812no—
1282#41—15812no—
1283#41—15824no—
1284#41—15812no—
1285#41—15812no—
1286#41—15812no—
1287#41—15812no—
1288#41—15824no—
1289#41—15812no—
1290#41—15824no—
1291#41—15812no—
1292#41—15824no—
1293#41—15812no—
1294#41—15824no—
1295#41—15812no—
1296#41—15812no—
1297#41—15812no—
1298#41—15824no—
1299#41—15824no—
1300#41—15812no—
1301#41—15812no—
1302#41—1588no—
1303#41—1584no—
1304#41—15812no—
1305#41—15812no—
1306#41—15812no—
1307#41D4×D7918yescomplemented
1308C2×Q8—24no—
1309C2×Q8—798no—
1310C2×Q8—793no—
1311C2×Q8—791no—
1312C2×Q8—793no—
1313C2×Q8—793no—
1314C2×Q8—793no—
1315C2×Q8—793no—
1316C2×Q8—791no—
1317C2×Q8—792no—
1318C2×Q8—15812no—
1319C2×Q8—15812no—
1320C2×Q8—1584no—
1321C2×Q8—15812no—
1322C2×Q8—15812no—
1323C2×Q8—1584no—
1324C2×Q8C23×D7911yescharacteristic
1325C2×Q8C23×D7913yes—
1326C2×Q8C23×D7911yescharacteristic
1327C2×D4—224no—
1328C2×D4—212no—
1329C2×D4—212no—
1330C2×D4—86no—
1331C2×D4—7912no—
1332C2×D4—796no—
1333C2×D4—796no—
1334C2×D4—7912no—
1335C2×D4—796no—
1336C2×D4—796no—
1337C2×D4—796no—
1338C2×D4—7924no—
1339C2×D4—793no—
1340C2×D4—791no—
1341C2×D4—793no—
1342C2×D4—793no—
1343C2×D4—796no—
1344C2×D4—796no—
1345C2×D4—796no—
1346C2×D4—7912no—
1347C2×D4—793no—
1348C2×D4—793no—
1349C2×D4—796no—
1350C2×D4—793no—
1351C2×D4—791no—
1352C2×D4—7912no—
1353C2×D4—796no—
1354C2×D4—796no—
1355C2×D4—793no—
1356C2×D4—793no—
1357C2×D4—791no—
1358C2×D4—793no—
1359C2×D4—793no—
1360C2×D4—796no—
1361C2×D4—793no—
1362C2×D4—796no—
1363C2×D4—793no—
1364C2×D4—6326no—
1365C2×D4—63212no—
1366C2×D4—63212no—
1367C2×D4—6326no—
1368C2×D4—6326no—
1369C2×D4—15824no—
1370C2×D4—15812no—
1371C2×D4—15812no—
1372C2×D4—15812no—
1373C2×D4—15824no—
1374C2×D4—15824no—
1375C2×D4—15824no—
1376C2×D4—15812no—
1377C2×D4—15824no—
1378C2×D4—15812no—
1379C2×D4—15848no—
1380C2×D4—15824no—
1381C2×D4—15824no—
1382C2×D4—15812no—
1383C2×D4—15824no—
1384C2×D4—15824no—
1385C2×D4—15848no—
1386C2×D4—15824no—
1387C2×D4—15812no—
1388C2×D4—15824no—
1389C2×D4—15812no—
1390C2×D4—15812no—
1391C2×D4C23×D7916yes—
1392C2×D4C23×D7916yes—
1393C2×D4C23×D7913yes—
1394C2×D4C23×D7916yes—
1395C2×D4C23×D7913yes—
1396C2×D4C23×D79112yes—
1397C2×D4C23×D7916yes—
1398C2×D4C23×D7916yes—
1399C2×D4C23×D7913yes—
1400C22×C4—212no—
1401C22×C4—796no—
1402C22×C4—796no—
1403C22×C4—796no—
1404C22×C4—793no—
1405C22×C4—793no—
1406C22×C4—793no—
1407C22×C4—791no—
1408C22×C4—793no—
1409C22×C4—7924no—
1410C22×C4—793no—
1411C22×C4—796no—
1412C22×C4—796no—
1413C22×C4—796no—
1414C22×C4—796no—
1415C22×C4—793no—
1416C22×C4—793no—
1417C22×C4—796no—
1418C22×C4—796no—
1419C22×C4—791no—
1420C22×C4—793no—
1421C22×C4—792no—
1422C22×C4—15824no—
1423C22×C4—15824no—
1424C22×C4—15812no—
1425C22×C4C23×D7913yes—
1426C22×C4C23×D7913yes—
1427C22×C4C23×D7913yes—
1428C22×C4C23×D7916yes—
1429C22×C4C23×D7913yes—
1430C22×C4C23×D7911yescharacteristic
1431C22×C4C23×D7916yes—
1432C22×C4C23×D7913yes—
1433C4⋊C4—796no—
1434C4⋊C4—796no—
1435C4⋊C4—796no—
1436C4⋊C4—792no—
1437C4⋊C4—796no—
1438C4⋊C4—792no—
1439C4⋊C4—791no—
1440C4⋊C4—793no—
1441C4⋊C4—796no—
1442C4⋊C4—796no—
1443C4⋊C4—792no—
1444C4⋊C4C23×D7911yescharacteristic
1445C4⋊C4C23×D7913yes—
1446C4⋊C4C23×D7916yes—
1447C4⋊C4C23×D7916yes—
1448C4⋊C4C23×D7912yes—
1449C22⋊C4—796no—
1450C22⋊C4—7912no—
1451C22⋊C4—796no—
1452C22⋊C4—796no—
1453C22⋊C4—796no—
1454C22⋊C4—792no—
1455C22⋊C4—796no—
1456C22⋊C4—792no—
1457C22⋊C4—796no—
1458C22⋊C4—7912no—
1459C22⋊C4—796no—
1460C22⋊C4—7912no—
1461C22⋊C4—796no—
1462C22⋊C4—796no—
1463C22⋊C4—7912no—
1464C22⋊C4—792no—
1465C22⋊C4—796no—
1466C22⋊C4—796no—
1467C22⋊C4—792no—
1468C22⋊C4C23×D7916yes—
1469C22⋊C4C23×D79112yes—
1470C22⋊C4C23×D7916yes—
1471C22⋊C4C23×D7916yes—
1472C22⋊C4C23×D7916yes—
1473C22⋊C4C23×D7912yes—
1474C42—796no—
1475C42—792no—
1476C42—7912no—
1477C42—796no—
1478C42C23×D7916yes—
1479C23—26no—
1480C23—212no—
1481C23—43no—
1482C23—46no—
1483C23—43no—
1484C23—46no—
1485C23—3163no—
1486C23—3163no—
1487C23—3166no—
1488C23—3166no—
1489C23—3163no—
1490C23—3163no—
1491C23—3166no—
1492C23—3166no—
1493C23—3166no—
1494C23—3166no—
1495C23—31612no—
1496C23—31612no—
1497C23—7912no—
1498C23—791no—
1499C23—793no—
1500C23—796no—
1501C23—793no—
1502C23—791no—
1503C23—63248no—
1504C23—15812no—
1505C23—15812no—
1506C23—15824no—
1507C23—1586no—
1508C23—15812no—
1509C23C24×D7916yes—
1510C23C24×D7913yes—
1511C23C24×D7911yescharacteristic
1512C23C24×D7913yes—
1513Q8—26no—
1514Q8—22no—
1515Q8—7912no—
1516Q8—1582no—
1517Q8—1586no—
1518Q8—1586no—
1519Q8—1586no—
1520Q8—1584no—
1521Q8—1586no—
1522Q8—1582no—
1523Q8C2×D4×D7914yes—
1524D4—212no—
1525D4—212no—
1526D4—26no—
1527D4—212no—
1528D4—26no—
1529D4—46no—
1530D4—412no—
1531D4—46no—
1532D4—3166no—
1533D4—31612no—
1534D4—3166no—
1535D4—3166no—
1536D4—3166no—
1537D4—31612no—
1538D4—31612no—
1539D4—3166no—
1540D4—3166no—
1541D4—7924no—
1542D4—7912no—
1543D4—15812no—
1544D4—1582no—
1545D4—1586no—
1546D4—1586no—
1547D4—1586no—
1548D4—15812no—
1549D4—15824no—
1550D4—1582no—
1551D4—1586no—
1552D4—1586no—
1553D4—1586no—
1554D4—15812no—
1555D4—1582no—
1556D4—1586no—
1557D4—1586no—
1558D4—1586no—
1559D4—15812no—
1560D4—15812no—
1561D4—1586no—
1562D4—15812no—
1563D4—1586no—
1564D4C2×D4×D79112yes—
1565C2×C4—26no—
1566C2×C4—22no—
1567C2×C4—26no—
1568C2×C4—26no—
1569C2×C4—26no—
1570C2×C4—212no—
1571C2×C4—46no—
1572C2×C4—3166no—
1573C2×C4—3166no—
1574C2×C4—3166no—
1575C2×C4—791no—
1576C2×C4—793no—
1577C2×C4—7912no—
1578C2×C4—794no—
1579C2×C4—7912no—
1580C2×C4—7912no—
1581C2×C4—7912no—
1582C2×C4—792no—
1583C2×C4—796no—
1584C2×C4—791no—
1585C2×C4—793no—
1586C2×C4—792no—
1587C2×C4—15812no—
1588C2×C4—15812no—
1589C2×C4—1584no—
1590C2×C4—15812no—
1591C2×C4—15812no—
1592C2×C4—15812no—
1593C2×C4—1586no—
1594C2×C4—1586no—
1595C2×C4—1582no—
1596C2×C4—15812no—
1597C2×C4—1586no—
1598C2×C4—1586no—
1599C2×C4C2×D4×D79112yes—
1600C2×C4C24×D7916yes—
1601C2×C4C24×D7912yes—
1602C2×C4C24×D7913yes—
1603C2×C4C24×D7911yescharacteristic
1604C2×C4C24×D7912yes—
1605C2×C4C24×D7913yes—
1606C2×C4C24×D7911yescharacteristic
1607C22—23no—
1608C22—23no—
1609C22—21no—
1610C22—23no—
1611C22—26no—
1612C22—21no—
1613C22—23no—
1614C22—26no—
1615C22—23no—
1616C22—26no—
1617C22—21no—
1618C22—812no—
1619C22—86no—
1620C22—31612no—
1621C22—31624no—
1622C22—792no—
1623C22—796no—
1624C22—63212no—
1625C22—6326no—
1626C22—63224no—
1627C22—63212no—
1628C22—1583no—
1629C22—1581no—
1630C22—1586no—
1631C22—1581no—
1632C22—1583no—
1633C22—1586no—
1634C22—1583no—
1635C22—1581no—
1636C22—1586no—
1637C22—1583no—
1638C22—1581no—
1639C22—1583no—
1640C22—1581no—
1641C22C22×D4×D7916yes—
1642C22C25×D7911yescharacteristic
1643C4—21no—
1644C4—22no—
1645C4—23no—
1646C4—26no—
1647C4—22no—
1648C4—792no—
1649C4—796no—
1650C4—1582no—
1651C4—1583no—
1652C4—1581no—
1653C4—1582no—
1654C4—1586no—
1655C4C22×D4×D7912yes—
1656C4C22×D4×D7916yes—
1657C2—26no—
1658C2—41no—
1659C2—46no—
1660C2—43no—
1661C2—3166no—
1662C2—3161no—
1663C2—3163no—
1664C2—1582no—
1665C2—1586no—
1666C2C23×D4×D7911yescharacteristic
1667C2#2377821011yescharacteristic
1668C2#2377821111yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3488C2
hypercenter#3488D79
hypocenterC79#62852
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3488

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#19099399C2semidirect
2. C2×H(5,𝔽2)×D79C2semidirect
3. #23777191C2semidirect
4. #23777186C2semidirect
5. #23777177C2semidirect
6. #23777172C2semidirect
7. #23777070C2semidirect
8. #23777069C2semidirect
9. #23777067C2semidirect
10. #23777065C2semidirect
11. #23777064C2semidirect
12. #23777062C2semidirect
13. #23777061C2semidirect
14. #23777057C2semidirect
15. #23777053C2semidirect
16. #23777030C2semidirect
17. #23777028C2semidirect
18. #23776730C2semidirect
19. #23776728C2semidirect
20. C2×#19099129C2semidirect
21. #535×D79C2semidirect
22. #23776600C2semidirect
23. C79×#3488C2semidirect
25. C2×#14579209C22semidirect
26. C2×#14579209C22semidirect
27. C2×#14579208C22semidirect
28. C2×#14579208C22semidirect
29. C2×#14579207C22semidirect
30. C2×#14579207C22semidirect
31. C2×#14579207C22semidirect
32. C2×#14579207C22semidirect
33. C2×#14579207C22semidirect
34. C2×#14579206C22semidirect
35. C2×#14579206C22semidirect
36. C2×#14579206C22semidirect
37. C2×#14579206C22semidirect
39. C22×#11929624C22semidirect
40. C22×#11929624C22semidirect
42. C2×#41×D79C22semidirect
43. C2×#41×D79C22semidirect
44. C2×#41×D79C22semidirect
45. C2×#41×D79C22semidirect
46. C2×#41×D79C22semidirect
47. C22×D4×D79C22semidirect
48. C22×D4×D79C22semidirect
49. #19099235C22semidirect
50. #19099234C22semidirect
51. #19099233C22semidirect
52. #19099232C22semidirect
53. #19099232C22semidirect
54. #19099231C22semidirect
55. #19099231C22semidirect
56. #19099225C22semidirect
57. #19099224C22semidirect
58. #19099223C22semidirect
59. #19099222C22semidirect
60. #19099221C22semidirect
61. #19099220C22semidirect
62. #19099219C22semidirect
63. #19099210C22semidirect
64. #19099209C22semidirect
65. #19099208C22semidirect
66. #19099207C22semidirect
67. #19099206C22semidirect
68. #19099205C22semidirect
69. #19099204C22semidirect
70. #19099203C22semidirect
71. #19099202C22semidirect
72. #19099201C22semidirect
73. #19099200C22semidirect
74. D4×D316C22semidirect
75. D4×D316C22semidirect
76. #19099198C22semidirect
77. #19099197C22semidirect
78. #19099197C22semidirect
79. #19099197C22semidirect
80. D4×C22⋊D79C22semidirect
81. D4×C22⋊D79C22semidirect
82. D4×C22⋊D79C22semidirect
83. #19099195C22semidirect
84. #19099195C22semidirect
85. #19099144C22semidirect
86. #19099143C22semidirect
87. #19099143C22semidirect
88. #19099142C22semidirect
89. #19099142C22semidirect
90. #19099141C22semidirect
91. #19099141C22semidirect
92. #19099136C22semidirect
93. #19099136C22semidirect
94. #19099136C22semidirect
95. #19099135C22semidirect
96. #19099132C22semidirect
97. #19099131C22semidirect
98. #19099130C22semidirect
99. #19099129C22semidirect
100. #19099129C22semidirect
101. #19099129C22semidirect
102. #19099129C22semidirect
103. #19099129C22semidirect
104. #19099129C22semidirect
105. #19099129C22semidirect
106. #19099129C22semidirect
107. #19099129C22semidirect
108. #19099129C22semidirect
109. #19099128C22semidirect
110. #19099128C22semidirect
111. #19099127C22semidirect
112. #19099126C22semidirect
113. #19099124C22semidirect
114. #19099123C22semidirect
115. #19099121C22semidirect
116. #19099110C22semidirect
117. #19099110C22semidirect
118. #19099108C22semidirect
119. C2×#14579157C22semidirect
120. #127×D79C22semidirect
121. C2×#14579147C22semidirect
122. #124×D79C22semidirect
123. #19099076C22semidirect
124. #19099076C22semidirect
125. #19099075C22semidirect
126. #19099074C22semidirect
127. #19099073C22semidirect
128. #19099073C22semidirect
129. #19099072C22semidirect
130. #19099072C22semidirect
131. #19099070C22semidirect
132. C2×#14579136C22semidirect
133. C2×#14579135C22semidirect
134. C2×#14579132C22semidirect
135. #121×D79C22semidirect
136. #121×D79C22semidirect
137. C2×#14579131C22semidirect
138. C2×#14579129C22semidirect
139. #120×D79C22semidirect
140. #19099046C22semidirect
141. #19099044C22semidirect
142. #19099043C22semidirect
143. #19099039C22semidirect
144. #19099035C22semidirect
145. C4×#11929625C22semidirect
146. C4×#11929623C22semidirect
147. C2×#14579119C22semidirect
148. #117×D79C22semidirect
149. C2×H(5,𝔽2)×C79C22semidirect
150. C22×#41×C79C22semidirect
151. #550×C79C22semidirect
152. #548×C79C22semidirect
153. #546×C79C22semidirect
154. D42×C79C22semidirect
155. #537×C79C22semidirect
156. #535×C79C22semidirect
157. #525×C79C22semidirect
158. C2×#121×C79C22semidirect
159. #520×C79C22semidirect
178. C2×#11929625C23semidirect
179. C2×#11929625C23semidirect
190. C2×#11929624C23semidirect
191. C2×#11929624C23semidirect
192. C2×#11929624C23semidirect
193. C2×#11929624C23semidirect
194. C2×#11929624C23semidirect
195. C2×#11929624C23semidirect
196. C2×#11929624C23semidirect
197. C2×#11929624C23semidirect
203. C2×#11929623C23semidirect
204. C2×#11929623C23semidirect
205. C2×#11929623C23semidirect
206. C2×#11929623C23semidirect
212. #41×D79D4semidirect
213. C22×Dic158C23semidirect
214. C22×Dic158C23semidirect
217. C2×Q8×D79C23semidirect
218. C2×Q8×D79C23semidirect
219. C2×Q8×D79C23semidirect
223. C22×D316C23semidirect
224. C22×D316C23semidirect
228. C22×C22⋊D79C23semidirect
229. C22×C22⋊D79C23semidirect
230. C22×C22⋊D79C23semidirect
231. C22×C22⋊D79C23semidirect
244. C2×D4×D79C23semidirect
245. C2×D4×D79C23semidirect
246. C2×D4×D79C23semidirect
247. C2×D4×D79C23semidirect
248. C2×D4×D79C23semidirect
249. C2×D4×D79C23semidirect
252. C22×C4×D79C23semidirect
253. C22×C4×D79C23semidirect
254. #14579160C23semidirect
255. #14579160C23semidirect
256. #14579158C23semidirect
257. #14579157C23semidirect
258. #14579157C23semidirect
259. #14579157C23semidirect
260. #14579157C23semidirect
261. #14579157C23semidirect
262. #14579157C23semidirect
263. #14579157C23semidirect
264. #14579150C23semidirect
265. #14579149C23semidirect
266. #14579148C23semidirect
267. #14579147C23semidirect
268. #14579147C23semidirect
269. #14579147C23semidirect
270. #14579147C23semidirect
271. #14579147C23semidirect
272. #14579147C23semidirect
273. #14579147C23semidirect
276. #14579146C23semidirect
277. #14579145C23semidirect
278. #14579144C23semidirect
281. #14579143C23semidirect
282. #14579142C23semidirect
283. #14579141C23semidirect
284. #14579141C23semidirect
285. #14579141C23semidirect
286. #14579140C23semidirect
287. #14579140C23semidirect
288. #14579140C23semidirect
289. #14579139C23semidirect
290. #14579139C23semidirect
291. #14579138C23semidirect
292. #14579138C23semidirect
293. #14579137C23semidirect
294. #14579137C23semidirect
295. #14579137C23semidirect
296. #14579136C23semidirect
297. #14579136C23semidirect
298. #14579136C23semidirect
299. #14579136C23semidirect
300. #14579136C23semidirect
301. #14579136C23semidirect
302. #14579136C23semidirect
303. #14579136C23semidirect
304. #14579135C23semidirect
305. #14579135C23semidirect
306. #14579135C23semidirect
307. #14579135C23semidirect
308. #14579135C23semidirect
309. #14579135C23semidirect
310. #14579135C23semidirect
311. #14579134C23semidirect
312. #14579134C23semidirect
313. #14579134C23semidirect
314. #14579134C23semidirect
315. #14579134C23semidirect
316. #14579134C23semidirect
317. #14579134C23semidirect
318. #14579134C23semidirect
319. #14579133C23semidirect
320. #14579133C23semidirect
321. #14579133C23semidirect
322. #14579133C23semidirect
323. #14579133C23semidirect
324. #14579133C23semidirect
325. #14579132C23semidirect
326. #14579132C23semidirect
327. #14579132C23semidirect
328. #14579132C23semidirect
329. #14579132C23semidirect
330. #14579132C23semidirect
331. #14579132C23semidirect
332. #14579132C23semidirect
336. #14579131C23semidirect
337. #14579131C23semidirect
338. #14579131C23semidirect
339. #14579131C23semidirect
340. #14579131C23semidirect
341. #14579130C23semidirect
342. #14579130C23semidirect
346. #14579129C23semidirect
347. #14579129C23semidirect
348. #14579129C23semidirect
349. #14579129C23semidirect
350. #14579129C23semidirect
351. Q8×Dic79C23semidirect
352. C4×Dic158C23semidirect
353. #14579126C23semidirect
354. C4×D316C23semidirect
355. C4×D316C23semidirect
356. C4×D316C23semidirect
357. D4×Dic79C23semidirect
358. D4×Dic79C23semidirect
359. #14579123C23semidirect
360. #14579123C23semidirect
361. C4×C22⋊D79C23semidirect
362. C4×C22⋊D79C23semidirect
363. C4×C22⋊D79C23semidirect
364. C4×C22⋊D79C23semidirect
365. C4×C22⋊D79C23semidirect
366. (C22⋊D79)⋊C4C23semidirect
367. (C22⋊D79)⋊C4C23semidirect
368. (C22⋊D79)⋊C4C23semidirect
369. #14579120C23semidirect
373. #14579119C23semidirect
374. #14579119C23semidirect
376. #14579117C23semidirect
377. C2×C4⋊Dic79C23semidirect
378. C4⋊C4×D79C23semidirect
379. C4⋊C4×D79C23semidirect
380. C2×C22⋊Dic79C23semidirect
382. C2×(C2×D79)⋊C4C23semidirect
383. C2×(C2×D79)⋊C4C23semidirect
385. C22⋊C4×D79C23semidirect
386. C22⋊C4×D79C23semidirect
387. C2×C4×Dic79C23semidirect
388. C42×D79C23semidirect
394. C2×#41×C79C23semidirect
395. C2×#41×C79C23semidirect
396. C2×#41×C79C23semidirect
397. C22×Q8×C79C23semidirect
400. C22×D4×C79C23semidirect
401. C22×D4×C79C23semidirect
402. C23×C4×C79C23semidirect
403. #127×C79C23semidirect
404. #124×C79C23semidirect
405. #123×C79C23semidirect
406. C22⋊Q8×C79C23semidirect
407. C22⋊Q8×C79C23semidirect
408. C22⋊Q8×C79C23semidirect
409. #121×C79C23semidirect
410. #121×C79C23semidirect
411. #121×C79C23semidirect
412. #121×C79C23semidirect
413. #121×C79C23semidirect
414. #121×C79C23semidirect
415. #121×C79C23semidirect
416. #120×C79C23semidirect
417. #120×C79C23semidirect
418. C4×Q8×C79C23semidirect
419. C4×D4×C79C23semidirect
420. C4×D4×C79C23semidirect
421. C4×D4×C79C23semidirect
422. #117×C79C23semidirect
423. C2×C4⋊C4×C79C23semidirect
424. C2×C22⋊C4×C79C23semidirect
439. #11929625C2×D4semidirect
455. #11929624C2×D4semidirect
464. #11929623C2×D4semidirect
479. Q8×D79C2×D4semidirect
539. D4×D79C2×D4semidirect
548. C2×C4×D79C2×D4semidirect
605. #41×C79C2×D4semidirect
848. #3488D79semidirect
858. C79#62852semidirect
874. C2×H(5,𝔽2)C2×D79semidirect
883. C22×#41C2×D79semidirect
893. #550C2×D79semidirect
901. #548C2×D79semidirect
913. #546C2×D79semidirect
925. D42C2×D79semidirect
933. #537C2×D79semidirect
955. #535C2×D79semidirect
975. #525C2×D79semidirect
981. C2×#121C2×D79semidirect
988. #520C2×D79semidirect
1053. C2×#41C22×D79semidirect
1054. C2×#41C22×D79semidirect
1055. C2×#41C22×D79semidirect
1063. C22×Q8C22×D79semidirect
1096. C22×D4C22×D79semidirect
1097. C22×D4C22×D79semidirect
1102. C23×C4C22×D79semidirect
1113. #127C22×D79semidirect
1124. #124C22×D79semidirect
1134. #123C22×D79semidirect
1148. C22⋊Q8C22×D79semidirect
1149. C22⋊Q8C22×D79semidirect
1150. C22⋊Q8C22×D79semidirect
1188. #121C22×D79semidirect
1189. #121C22×D79semidirect
1190. #121C22×D79semidirect
1191. #121C22×D79semidirect
1192. #121C22×D79semidirect
1193. #121C22×D79semidirect
1194. #121C22×D79semidirect
1213. #120C22×D79semidirect
1214. #120C22×D79semidirect
1218. C4×Q8C22×D79semidirect
1234. C4×D4C22×D79semidirect
1235. C4×D4C22×D79semidirect
1236. C4×D4C22×D79semidirect
1245. #117C22×D79semidirect
1249. C2×C4⋊C4C22×D79semidirect
1257. C2×C22⋊C4C22×D79semidirect
1307. #41D4×D79semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#190993992
C2×H(5,𝔽2)×D792
#237771912
#237771862
#237771772
#237771722
#237770702
#237770692
#237770672
#237770652
#237770642
#237770622
#237770612
#237770572
#237770532
#237770302
#237770282
#237767302
#237767282
C2×#190991292
#535×D792
#237766002
C79×#34882
#6285279