Finite Group Databasebeta

← #35197382

Subgroups — #35197382

Order 20224.

11222 conjugacy classes of subgroups.

The subgroup lattice has 1646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099399C211yesmaximal, characteristic, complemented
2C2×#19099398C211yesmaximal, characteristic, complemented
3#23777168C212yesmaximal, complemented
4#23777165C212yesmaximal, complemented
5#23777160C216yesmaximal, complemented
6#23777156C216yesmaximal, complemented
7#23777081C211yesmaximal, characteristic, complemented
8#23777080C211yesmaximal, characteristic, complemented
9#23777079C212yesmaximal, complemented
10#23777075C213yesmaximal, complemented
11#23777072C213yesmaximal, complemented
12#23777071C216yesmaximal, complemented
13#23777068C212yesmaximal, complemented
14#23777067C213yesmaximal, complemented
15#23777065C213yesmaximal, complemented
16#23777062C211yesmaximal, characteristic, complemented
17#23777060C216yesmaximal, complemented
18#23776731C213yesmaximal, complemented
19#23776730C213yesmaximal, complemented
20C2×#19099142C213yesmaximal, complemented
21#537×D79C213yesmaximal, complemented
22#520×D79C211yesmaximal, characteristic, complemented
23C79×#3488C211yesmaximal, characteristic, complemented
24#19099399—216no—
25#19099398—216no—
26C2×#14579209C2211yescharacteristic, complemented
27C2×#14579209C2211yescharacteristic, complemented
28C2×#14579208C2213yescomplemented
29C2×#14579208C2213yescomplemented
30C2×#14579208C2211yescharacteristic, complemented
31C2×#14579208C2211yescharacteristic, complemented
32C2×#14579208C2212yescomplemented
33C2×#14579207C2211yescharacteristic, complemented
34C2×#14579207C2213yescomplemented
35C2×#14579206C2213yescomplemented
36C2×#14579206C2213yescomplemented
37C2×#14579206C2213yescomplemented
38C2×#14579206C2216yescomplemented
39C22×#11929624C2213yescomplemented
40C22×#11929624C2213yescomplemented
41C22×#11929623C2216yescomplemented
42C22×#11929623C2213yescomplemented
43C2×#41×D79C2211yescharacteristic
44C2×#41×D79C2211yescharacteristic, complemented
45C2×#41×D79C2213yescomplemented
46C2×#41×D79C2212yescomplemented
47C2×#41×D79C2213yescomplemented
48C2×#41×D79C2213yescomplemented
49#19099233C2216yescomplemented
50#19099232C2212yescomplemented
51#19099231C2216yescomplemented
52Q8×D316C2212yescomplemented
53D4×Dic158C2216yescomplemented
54Q8×C22⋊D79C2212yescomplemented
55#19099226C2216yescomplemented
56#19099225C2212yescomplemented
57#19099222C2216yescomplemented
58#19099221C2216yescomplemented
59#19099220C2212yescomplemented
60#19099220C2212yescomplemented
61#19099219C2216yescomplemented
62#19099219C2216yescomplemented
63#19099218C2216yescomplemented
64#19099217C2216yescomplemented
65#19099215C2216yescomplemented
66#19099213C22112yescomplemented
67#19099212C2216yescomplemented
68#19099211C22112yescomplemented
69#19099210C2216yescomplemented
70#19099210C2216yescomplemented
71#19099209C2216yescomplemented
72#19099208C2216yescomplemented
73#19099207C2216yescomplemented
74#19099207C2216yescomplemented
75#19099206C2216yescomplemented
76#19099203C22112yescomplemented
77#19099202C22112yescomplemented
78#19099200C22112yescomplemented
79#19099200C22112yescomplemented
80#19099198C2216yescomplemented
81#19099197C2216yescomplemented
82D4×C22⋊D79C2216yescomplemented
83D4×C22⋊D79C22112yescomplemented
84#19099195C22112yescomplemented
85#19099144C2213yescomplemented
86#19099143C2216yescomplemented
87#19099143C2213yescomplemented
88#19099143C2211yescharacteristic, complemented
89#19099142C2216yescomplemented
90#19099142C2216yescomplemented
91#19099142C2216yescomplemented
92#19099142C2216yescomplemented
93#19099142C2216yescomplemented
94#19099142C2216yescomplemented
95#19099142C2216yescomplemented
96#19099142C2216yescomplemented
97#19099142C2213yescomplemented
98#19099142C2213yescomplemented
99#19099141C2213yescomplemented
100#19099141C2213yescomplemented
101#19099140C22112yescomplemented
102#19099139C2213yescomplemented
103#19099136C2213yescomplemented
104#19099136C2213yescomplemented
105#19099135C2216yescomplemented
106#19099134C2213yescomplemented
107#19099133C2216yescomplemented
108#19099130C2213yescomplemented
109#19099129C2213yescomplemented
110#19099129C2213yescomplemented
111#19099128C2216yescomplemented
112#19099126C2216yescomplemented
113#19099124C2216yescomplemented
114#19099123C2216yescomplemented
115#19099123C22112yescomplemented
116#19099112C2216yescomplemented
117#19099111C2216yescomplemented
118#19099110C2216yescomplemented
119#19099110C2216yescomplemented
120#19099075C2213yescomplemented
121#19099074C2213yescomplemented
122#19099073C2216yescomplemented
123#19099073C2216yescomplemented
124#19099072C2216yescomplemented
125#19099072C2216yescomplemented
126#19099070C2213yescomplemented
127#19099069C22112yescomplemented
128C2×#14579141C2213yescomplemented
129C2×#14579140C2213yescomplemented
130C2×#14579138C2216yescomplemented
131C22⋊Q8×D79C2216yescomplemented
132C22⋊Q8×D79C2216yescomplemented
133C2×#14579134C2216yescomplemented
134C2×#14579133C2216yescomplemented
135C2×#14579132C2213yescomplemented
136C2×#14579132C2216yescomplemented
137#121×D79C2216yescomplemented
138#121×D79C2216yescomplemented
139#121×D79C22112yescomplemented
140#19099046C2211yescharacteristic, complemented
141#19099045C2212yescomplemented
142#19099044C2213yescomplemented
143#19099043C2213yescomplemented
144#19099042C2216yescomplemented
145C4×Q8×D79C2212yescomplemented
146C4×D4×D79C2216yescomplemented
147#117×D79C2213yescomplemented
148C2×C4⋊C4×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
160#14579209—28no—
161#14579209—28no—
162#14579208—28no—
163#14579208—224no—
164#14579208—224no—
165#14579208—216no—
166#14579208—28no—
167#14579207—28no—
168#14579207—224no—
169#14579206—224no—
170#14579206—224no—
171#14579206—248no—
172#14579206—224no—
173C2×#11929625C2313yes—
174C2×#11929625C2313yes—
175C2×#11929625C2311yescharacteristic
176C2×#11929625C2311yescharacteristic
177C2×#11929625C2311yescharacteristic
178C2×#11929624—224no—
179C2×#11929624—224no—
180C2×#11929624C2313yes—
181C2×#11929624C2313yes—
182C2×#11929624C2313yes—
183C2×#11929624C2316yes—
184C2×#11929624C2316yes—
185C2×#11929624C2313yes—
186C2×#11929624C2313yes—
187C2×#11929624C2313yes—
188C2×#11929624C2313yes—
189C2×#11929624C2313yes—
190C2×#11929624C2313yes—
191C2×#11929624C2316yes—
192C2×#11929624C2313yes—
193C2×#11929624C2313yes—
194C2×#11929624C2311yescharacteristic
195C2×#11929624C2313yes—
196C2×#11929623—248no—
197C2×#11929623—224no—
198C2×#11929623C2316yes—
199C2×#11929623C2316yes—
200C2×#11929623C2313yes—
201C2×#11929623C2316yes—
202C2×#11929623C2316yes—
203C2×#11929623C23112yes—
204C2×#11929623C2313yes—
205C2×#11929623C2316yes—
206C2×#11929623C2313yes—
207C2×#11929623C2316yes—
208C2×#11929623C2316yes—
209C2×#11929623C2313yes—
210C2×#11929623C2316yes—
211C2×#11929623C2313yes—
212#41×D79—28no—
213#41×D79—216no—
214#41×D79—224no—
215#41×D79—224no—
216#41×D79—224no—
217#41×D79D4116yescomplemented
218C22×Dic158C2313yes—
219C22×Dic158C2313yes—
220C22×Dic158C2316yes—
221C22×Dic158C2313yes—
222C2×Q8×D79C2313yes—
223C2×Q8×D79C2312yes—
224C2×Q8×D79C2311yescharacteristic
225C2×Q8×D79C2313yes—
226C2×Q8×D79C2313yes—
227C2×Q8×D79C2311yescharacteristic
228C22×D316C2313yes—
229C22×D316C2313yes—
230C22×C22⋊D79C23112yes—
231C22×C22⋊D79C2316yes—
232C22×C22⋊D79C2313yes—
233C22×C22⋊D79C2316yes—
234C22×C22⋊D79C2313yes—
235C22×C22⋊D79C2316yes—
236C2×D4×D79C2316yes—
237C2×D4×D79C2316yes—
238C2×D4×D79C2313yes—
239C2×D4×D79C2316yes—
240C2×D4×D79C2313yes—
241C2×D4×D79C2313yes—
242C2×D4×D79C2316yes—
243C2×D4×D79C2313yes—
244C2×D4×D79C23112yes—
245C2×D4×D79C2313yes—
246C23×Dic79C2316yes—
247C22×C4×D79C2316yes—
248C22×C4×D79C2316yes—
249C22×C4×D79C2313yes—
250C22×C4×D79C2316yes—
251C22×C4×D79C2313yes—
252#14579161C2316yes—
253#14579160C2316yes—
254#14579160C2316yes—
255#14579159C2316yes—
256#14579157C2316yes—
257#14579157C2316yes—
258#14579157C2316yes—
259#14579149C2316yes—
260#14579148C2316yes—
261#14579148C2316yes—
262#14579147C2316yes—
263#14579147C2316yes—
264#14579147C2316yes—
265#14579147C2316yes—
266#14579146C2316yes—
267#14579146C2316yes—
268#14579145C23112yes—
269#14579145C2316yes—
270#14579144C2316yes—
271#14579143C2316yes—
272#14579143C2316yes—
273#14579143C23112yes—
274#14579143C23112yes—
275#14579142C23112yes—
276#14579142C2316yes—
277#14579141C2313yes—
278#14579141C2313yes—
279#14579141C2316yes—
280#14579141C2316yes—
281#14579141C2316yes—
282#14579141C2316yes—
283#14579140C2313yes—
284#14579140C2313yes—
285#14579140C2316yes—
286#14579140C2316yes—
287#14579140C2316yes—
288#14579140C2316yes—
289#14579139C2316yes—
290#14579139C23112yes—
291#14579139C2312yes—
292#14579138C23112yes—
293#14579138C23112yes—
294#14579138C2316yes—
295#14579138C23112yes—
296#14579138C23112yes—
297#14579138C2316yes—
298#14579137C2311yescharacteristic
299#14579137C2313yes—
300#14579137C2316yes—
301#14579136C2316yes—
302#14579136C2313yes—
303#14579136C2316yes—
304#14579136C2311yescharacteristic
305#14579136C2312yes—
306#14579135C23112yes—
307#14579135C2313yes—
308#14579135C2316yes—
309#14579135C2311yescharacteristic
310#14579134C2316yes—
311#14579134C23112yes—
312#14579134C2316yes—
313#14579134C2316yes—
314#14579134C23112yes—
315#14579134C23112yes—
316#14579134C23112yes—
317#14579134C2316yes—
318#14579134C2312yes—
319#14579134C2312yes—
320#14579133C23112yes—
321#14579133C23112yes—
322#14579133C23112yes—
323#14579133C23112yes—
324#14579133C2316yes—
325#14579133C23112yes—
326#14579133C23112yes—
327#14579133C2316yes—
328#14579132C2316yes—
329#14579132C2316yes—
330#14579132C23112yes—
331#14579132C2313yes—
332#14579132C2316yes—
333#14579132C23112yes—
334#14579132C2316yes—
335#14579132C23112yes—
336#14579132C2316yes—
337#14579132C2313yes—
338#14579132C2316yes—
339#14579131C2316yes—
340#14579131C2316yes—
341#14579131C2316yes—
342#14579130C23112yes—
343#14579130C2316yes—
344#14579129C23112yes—
345#14579129C2316yes—
346#14579129C2316yes—
347#14579129C23112yes—
348#14579129C2316yes—
349Q8×Dic79C2312yes—
350C4×Dic158C2316yes—
351#14579126C2316yes—
352C4×D316C2316yes—
353C4×D316C2316yes—
354C4×D316C2316yes—
355D4×Dic79C2316yes—
356D4×Dic79C23112yes—
357D4×Dic79C23112yes—
358#14579123C2316yes—
359C4×C22⋊D79C23112yes—
360C4×C22⋊D79C2316yes—
361C4×C22⋊D79C2316yes—
362C4×C22⋊D79C2316yes—
363C4×C22⋊D79C2316yes—
364(C22⋊D79)⋊C4C23112yes—
365(C22⋊D79)⋊C4C23112yes—
366(C22⋊D79)⋊C4C23112yes—
367#14579120C2313yes—
368#14579119C2313yes—
369#14579119C2313yes—
370#14579118C2316yes—
371#14579117C2316yes—
372C2×C4⋊Dic79C2313yes—
373C2×C4⋊Dic79C2316yes—
374C2×Dic79⋊C4C2316yes—
375C2×Dic79⋊C4C2316yes—
376C4⋊C4×D79C2313yes—
377C4⋊C4×D79C2316yes—
378C4⋊C4×D79C2311yescharacteristic
379C4⋊C4×D79C2316yes—
380C4⋊C4×D79C2316yes—
381C4⋊C4×D79C23112yes—
382C2×C22⋊Dic79C2316yes—
383C2×C22⋊Dic79C2316yes—
384C2×(C2×D79)⋊C4C2316yes—
385C22⋊C4×D79C23112yes—
386C22⋊C4×D79C23112yes—
387C22⋊C4×D79C2316yes—
388C42×D79C2316yes—
389H(5,𝔽2)×C79—28no—
390C2×#41×C79—28no—
391C2×#41×C79C2313yes—
392C2×#41×C79C2311yescharacteristic
393C2×#41×C79C2313yes—
394C2×#41×C79C2312yes—
395C2×#41×C79C2313yes—
396C2×#41×C79C2311yescharacteristic
397C22×Q8×C79C2311yescharacteristic
398C22×D4×C79C2313yes—
399C22×D4×C79C2316yes—
400C22×D4×C79C2313yes—
401C22×D4×C79C2316yes—
402C23×C4×C79C2313yes—
403#127×C79C2316yes—
404#124×C79C2316yes—
405#123×C79C2316yes—
406C22⋊Q8×C79C2311yescharacteristic
407C22⋊Q8×C79C2313yes—
408C22⋊Q8×C79C2316yes—
409#121×C79C23112yes—
410#121×C79C2313yes—
411#121×C79C2316yes—
412#121×C79C2316yes—
413#121×C79C2316yes—
414#121×C79C2316yes—
415#121×C79C2313yes—
416#120×C79C23112yes—
417#120×C79C2316yes—
418C4×Q8×C79C2312yes—
419C4×D4×C79C2316yes—
420C4×D4×C79C2316yes—
421C4×D4×C79C2316yes—
422#117×C79C2313yes—
423C2×C4⋊C4×C79C2313yes—
424C2×C22⋊C4×C79C2316yes—
425C23×D79C2416yes—
426C23×D79C2416yes—
427C23×D79C2413yes—
428C23×D79C2413yes—
429#11929625—212no—
430#11929625—24no—
431#11929625—212no—
432#11929625—24no—
433#11929625C2×D418yescomplemented
434#11929624—224no—
435#11929624—212no—
436#11929624—212no—
437#11929624—212no—
438#11929624—224no—
439#11929624—212no—
440#11929624—24no—
441#11929624—212no—
442#11929624—212no—
443#11929624—212no—
444#11929624—212no—
445#11929624—212no—
446#11929624—212no—
447#11929624—212no—
448#11929624—224no—
449#11929624C2×D4124yescomplemented
450#11929623—224no—
451#11929623—224no—
452#11929623—224no—
453#11929623—212no—
454#11929623—212no—
455#11929623—224no—
456#11929623—224no—
457#11929623—212no—
458#11929623—224no—
459#11929623—212no—
460#11929623—224no—
461#11929623—224no—
462#11929623—248no—
463#11929623C2×D4124yescomplemented
464C2×Dic158—212no—
465C2×Dic158—224no—
466C2×Dic158—212no—
467C2×Dic158—212no—
468C2×Dic158C2413yes—
469C2×Dic158C2413yes—
470C2×Dic158C2413yes—
471C2×Dic158C2416yes—
472C2×Dic158C2413yes—
473C2×Dic158C2416yes—
474C2×Dic158C2411yescharacteristic
475C2×Dic158C2413yes—
476C2×Dic158C2413yes—
477Q8×D79—212no—
478Q8×D79—212no—
479Q8×D79—212no—
480Q8×D79—28no—
481Q8×D79—24no—
482Q8×D79C2×D418yescomplemented
483C2×D316—212no—
484C2×D316—212no—
485C2×D316C2413yes—
486C2×D316C2411yescharacteristic
487C2×D316C2412yes—
488C2×D316C2411yescharacteristic
489C2×D316C2413yes—
490C2×D316C2413yes—
491C2×D316C2413yes—
492C2×D316C2412yes—
493C2×D316C2416yes—
494C2×D316C2413yes—
495C2×C22⋊D79—212no—
496C2×C22⋊D79—224no—
497C2×C22⋊D79—212no—
498C2×C22⋊D79—248no—
499C2×C22⋊D79—224no—
500C2×C22⋊D79—86no—
501C2×C22⋊D79C24112yes—
502C2×C22⋊D79C2416yes—
503C2×C22⋊D79C2416yes—
504C2×C22⋊D79C2416yes—
505C2×C22⋊D79C2413yes—
506C2×C22⋊D79C2416yes—
507C2×C22⋊D79C2413yes—
508C2×C22⋊D79C2413yes—
509C2×C22⋊D79C2413yes—
510C2×C22⋊D79C2413yes—
511C2×C22⋊D79C2411yescharacteristic
512C2×C22⋊D79C2411yescharacteristic
513C2×C22⋊D79C2413yes—
514C2×C22⋊D79C2416yes—
515C2×C22⋊D79C24112yes—
516C2×C22⋊D79C2412yes—
517C2×C22⋊D79C2416yes—
518C2×C22⋊D79C2416yes—
519C2×C22⋊D79C2416yes—
520D4×D79—224no—
521D4×D79—212no—
522D4×D79—212no—
523D4×D79—212no—
524D4×D79—224no—
525D4×D79—224no—
526D4×D79—212no—
527D4×D79—224no—
528D4×D79—812no—
529D4×D79C2×D4124yescomplemented
530C22×Dic79—224no—
531C22×Dic79C2416yes—
532C22×Dic79C2413yes—
533C22×Dic79C24112yes—
534C22×Dic79C2416yes—
535C22×Dic79C2416yes—
536C22×Dic79C2416yes—
537C22×Dic79C2413yes—
538C2×C4×D79—224no—
539C2×C4×D79—224no—
540C2×C4×D79—212no—
541C2×C4×D79—86no—
542C2×C4×D79C2×D4124yescomplemented
543C2×C4×D79C2416yes—
544C2×C4×D79C2416yes—
545C2×C4×D79C2416yes—
546C2×C4×D79C2416yes—
547C2×C4×D79C2413yes—
548C2×C4×D79C2413yes—
549C2×C4×D79C2412yes—
550C2×C4×D79C2411yescharacteristic
551C2×C4×D79C2413yes—
552C2×C4×D79C2412yes—
553C2×C4×D79C2416yes—
554C2×C4×D79C24112yes—
555C2×C4×D79C2413yes—
556C2×C4×D79C2413yes—
557C2×C4×D79C2413yes—
558C2×C4×D79C2411yescharacteristic
559C4⋊Dic79C2413yes—
560C4⋊Dic79C2416yes—
561C4⋊Dic79C24112yes—
562C4⋊Dic79C2411yescharacteristic
563C4⋊Dic79C2416yes—
564C4⋊Dic79C2416yes—
565Dic79⋊C4C2416yes—
566Dic79⋊C4C24112yes—
567Dic79⋊C4C2416yes—
568Dic79⋊C4C24112yes—
569Dic79⋊C4C2412yes—
570Dic79⋊C4C2416yes—
571Dic79⋊C4C2416yes—
572Dic79⋊C4C2412yes—
573C22⋊Dic79C24112yes—
574C22⋊Dic79C24112yes—
575C22⋊Dic79C2416yes—
576C22⋊Dic79C2416yes—
577C22⋊Dic79C2416yes—
578C22⋊Dic79C2416yes—
579C22⋊Dic79C2416yes—
580(C2×D79)⋊C4C2416yes—
581(C2×D79)⋊C4C2416yes—
582(C2×D79)⋊C4C2416yes—
583(C2×D79)⋊C4C24112yes—
584(C2×D79)⋊C4C2416yes—
585(C2×D79)⋊C4C2416yes—
586(C2×D79)⋊C4C2416yes—
587(C2×D79)⋊C4C2416yes—
588(C2×D79)⋊C4C2412yes—
589(C2×D79)⋊C4C2412yes—
590(C2×D79)⋊C4C2412yes—
591C4×Dic79C2416yes—
592C4×Dic79C2416yes—
593C4×Dic79C2416yes—
594C24×C79C2416yes—
595C24×C79C2413yes—
596#41×C79—28no—
597#41×C79—24no—
598#41×C79—212no—
599#41×C79—212no—
600#41×C79—212no—
601#41×C79C2×D418yescomplemented
602C2×Q8×C79—24no—
603C2×Q8×C79C2411yescharacteristic
604C2×Q8×C79C2413yes—
605C2×Q8×C79C2411yescharacteristic
606C2×D4×C79—224no—
607C2×D4×C79—212no—
608C2×D4×C79—212no—
609C2×D4×C79—86no—
610C2×D4×C79C2416yes—
611C2×D4×C79C2413yes—
612C2×D4×C79C2416yes—
613C2×D4×C79C2416yes—
614C2×D4×C79C2413yes—
615C2×D4×C79C2416yes—
616C2×D4×C79C2416yes—
617C2×D4×C79C24112yes—
618C2×D4×C79C2413yes—
619C22×C4×C79—212no—
620C22×C4×C79C2413yes—
621C22×C4×C79C2413yes—
622C22×C4×C79C2416yes—
623C22×C4×C79C2413yes—
624C22×C4×C79C2411yescharacteristic
625C22×C4×C79C2413yes—
626C22×C4×C79C2416yes—
627C22×C4×C79C2413yes—
628C4⋊C4×C79C2413yes—
629C4⋊C4×C79C2416yes—
630C4⋊C4×C79C2411yescharacteristic
631C4⋊C4×C79C2412yes—
632C4⋊C4×C79C2416yes—
633C22⋊C4×C79C2416yes—
634C22⋊C4×C79C24112yes—
635C22⋊C4×C79C2416yes—
636C22⋊C4×C79C2412yes—
637C22⋊C4×C79C2416yes—
638C22⋊C4×C79C2416yes—
639C42×C79C2416yes—
640C23×C79—212no—
641C23×C79—26no—
642C23×C79—46no—
643C23×C79—43no—
644C23×C79—43no—
645C23×C79—46no—
646C23×C79C2513yes—
647C23×C79C2511yescharacteristic
648C23×C79C2516yes—
649C23×C79C2513yes—
650C22×D79—26no—
651C22×D79—212no—
652C22×D79—212no—
653C22×D79—43no—
654C22×D79—43no—
655C22×D79—46no—
656C22×D79—46no—
657C22×D79—43no—
658C22×D79—46no—
659C22×D79—46no—
660C22×D79—43no—
661C22×D79C22×D4112yes—
662C22×D79C2512yes—
663C22×D79C2511yescharacteristic
664C22×D79C2513yes—
665C22×D79C2513yes—
666C22×D79C2511yescharacteristic
667Q8×C79—22no—
668Q8×C79—26no—
669Q8×C79C22×D414yes—
670D4×C79—212no—
671D4×C79—212no—
672D4×C79—26no—
673D4×C79—26no—
674D4×C79—212no—
675D4×C79—412no—
676D4×C79—46no—
677D4×C79—46no—
678D4×C79C22×D4112yes—
679C2×C4×C79—26no—
680C2×C4×C79—26no—
681C2×C4×C79—212no—
682C2×C4×C79—26no—
683C2×C4×C79—22no—
684C2×C4×C79—26no—
685C2×C4×C79—46no—
686C2×C4×C79C22×D4112yes—
687C2×C4×C79C2512yes—
688C2×C4×C79C2516yes—
689C2×C4×C79C2512yes—
690C2×C4×C79C2513yes—
691C2×C4×C79C2511yescharacteristic
692C2×C4×C79C2513yes—
693C2×C4×C79C2511yescharacteristic
694C22⋊D79—212no—
695C22⋊D79—212no—
696C22⋊D79—26no—
697C22⋊D79—26no—
698C22⋊D79—212no—
699C22⋊D79—224no—
700C22⋊D79—22no—
701C22⋊D79—26no—
702C22⋊D79—26no—
703C22⋊D79—26no—
704C22⋊D79—212no—
705C22⋊D79—26no—
706C22⋊D79—22no—
707C22⋊D79—46no—
708C22⋊D79—412no—
709C22⋊D79—46no—
710C22⋊D79—46no—
711C22⋊D79—42no—
712C22⋊D79C22×D4124yes—
713C2×Dic79—26no—
714C2×Dic79—212no—
715C2×Dic79—212no—
716C2×Dic79—212no—
717C2×Dic79—224no—
718C2×Dic79—46no—
719C2×Dic79C22×D4112yes—
720C2×Dic79C2512yes—
721C2×Dic79C2516yes—
722C2×Dic79C2516yes—
723C2×Dic79C2513yes—
724C2×Dic79C2511yescharacteristic
725C2×Dic79C2513yes—
726C2×Dic79C2511yescharacteristic
727D316—24no—
728D316—26no—
729D316—26no—
730D316—22no—
731D316—26no—
732D316—22no—
733D316—26no—
734D316—46no—
735D316—42no—
736D316C22×D4112yes—
737C4×D79—212no—
738C4×D79—212no—
739C4×D79—26no—
740C4×D79—22no—
741C4×D79—212no—
742C4×D79—26no—
743C4×D79—26no—
744C4×D79—24no—
745C4×D79—212no—
746C4×D79—46no—
747C4×D79—412no—
748C4×D79—42no—
749C4×D79C22×D4112yes—
750C4×D79C22×D4112yes—
751C4×D79C22×D414yes—
752C4×D79C22×D4112yes—
753Dic158—26no—
754Dic158—26no—
755Dic158—212no—
756Dic158—26no—
757Dic158—26no—
758Dic158—212no—
759Dic158—26no—
760Dic158—22no—
761Dic158C22×D4112yes—
762C22×C79—23no—
763C22×C79—23no—
764C22×C79—21no—
765C22×C79—23no—
766C22×C79—26no—
767C22×C79—26no—
768C22×C79—23no—
769C22×C79—21no—
770C22×C79—21no—
771C22×C79—26no—
772C22×C79—23no—
773C22×C79—86no—
774C22×C79—812no—
775C22×C79C23×D416yes—
776C22×C79C2611yescharacteristic
777C2×D79—23no—
778C2×D79—21no—
779C2×D79—23no—
780C2×D79—21no—
781C2×D79—22no—
782C2×D79—23no—
783C2×D79—21no—
784C2×D79—21no—
785C2×D79—23no—
786C2×D79—22no—
787C2×D79—23no—
788C2×D79—22no—
789C2×D79—21no—
790C2×D79—412no—
791C2×D79—812no—
792C2×D79—812no—
793C2×D79—86no—
794C2×D79C23×D412yes—
795C2×D79C23×D416yes—
796C4×C79—21no—
797C4×C79—22no—
798C4×C79—23no—
799C4×C79—26no—
800C4×C79—22no—
801C4×C79C23×D412yes—
802C4×C79C23×D416yes—
803Dic79—23no—
804Dic79—21no—
805Dic79—26no—
806Dic79—26no—
807Dic79—22no—
808Dic79C23×D416yes—
809Dic79C23×D412yes—
810#62853—791nomaximal, Sylow
811C2×C79—26no—
812C2×C79—43no—
813C2×C79—46no—
814C2×C79—41no—
815C2×C79C24×D411yescharacteristic
816C2×C79H(7,𝔽2)11yescharacteristic
817C2×C792−1+611yescharacteristic
818D79—22no—
819D79—26no—
820D79—42no—
821D79—41no—
822D79—43no—
823C2×#585—791no—
824C2×#585—791no—
825#3497—792no—
826#3497—792no—
827#3496—796no—
828#3496—796no—
829#3489—791no—
830#3489—792no—
831#3489—796no—
832#3489—793no—
833#3489—793no—
834#3489—791no—
835#3488—791no—
836#3488—792no—
837#3488—796no—
838#3488—793no—
839#3488—793no—
840#3488D7911yescharacteristic, complemented
841#3449—793no—
842#3449—793no—
843C2×#537—793no—
844C2×#537—793no—
845C2×#520—791no—
846C79#6285311yescharacteristic, complemented, Sylow
847#585—15816no—
848#585—15816no—
849C2×2−1+4—793no—
850C2×2−1+4—793no—
851C2×2−1+4—791no—
852C2×2−1+4—791no—
853C2×2−1+4—792no—
854C2×2−1+4—791no—
855C2×2−1+4—791no—
856C2×H(5,𝔽2)—791no—
857C2×H(5,𝔽2)—793no—
858C2×H(5,𝔽2)—793no—
859C2×H(5,𝔽2)—793no—
860C2×H(5,𝔽2)—796no—
861C2×H(5,𝔽2)—793no—
862C2×H(5,𝔽2)C2×D7911yescharacteristic, complemented
863C22×#41—791no—
864C22×#41—793no—
865C22×#41—793no—
866C22×#41—792no—
867C22×#41—793no—
868C22×#41—791no—
869C22×#41—793no—
870C22×#41—796no—
871C22×#41—793no—
872C22×#41—793no—
873C22×#41C2×D7911yescharacteristic, complemented
874#550—792no—
875#550—796no—
876#550—796no—
877#550C2×D7912yescomplemented
878D4×Q8—792no—
879D4×Q8—796no—
880D4×Q8—792no—
881D4×Q8—796no—
882#548—792no—
883#548—792no—
884#548—796no—
885#548—796no—
886#548—796no—
887#548—792no—
888#548—796no—
889#548C2×D7912yescomplemented
890#547—796no—
891#547—7912no—
892#547—796no—
893#547—7912no—
894#547—796no—
895#547—796no—
896#546—796no—
897#546—796no—
898#546—796no—
899#546—7912no—
900#546—796no—
901#546—796no—
902#546—7912no—
903#546—7912no—
904#546—796no—
905#546—796no—
906#546—7912no—
907#546C2×D7916yescomplemented
908D42—796no—
909D42—7912no—
910D42—796no—
911D42—796no—
912D42—7912no—
913D42C2×D7916yescomplemented
914#537—793no—
915#537—793no—
916#537—793no—
917#537—796no—
918#537—791no—
919#537—7912no—
920#537—796no—
921#537—793no—
922#537—796no—
923#537—796no—
924#537—796no—
925#537—796no—
926#537—796no—
927#537—796no—
928#537—796no—
929#537—793no—
930#537—793no—
931#537C2×D7913yescomplemented
932#536—793no—
933#536—796no—
934#536—796no—
935#536—793no—
936#536—793no—
937#536—793no—
938#535—793no—
939#535—796no—
940#535—793no—
941#535—793no—
942#535—796no—
943#535C2×D7913yescomplemented
944#534—796no—
945#534—7912no—
946#534—796no—
947#532—796no—
948#532—796no—
949#532—796no—
950#532—796no—
951#525—793no—
952#525—793no—
953#525—796no—
954#525—796no—
955#525—7912no—
956#525—796no—
957#525—796no—
958#525—793no—
959#525C2×D7913yescomplemented
960C2×C22⋊Q8—793no—
961C2×C22⋊Q8—796no—
962C2×C22⋊Q8—796no—
963C2×C22⋊Q8—793no—
964C2×C22⋊Q8—796no—
965C2×#121—793no—
966C2×#121—796no—
967C2×#121—796no—
968C2×#121—796no—
969C2×#121—796no—
970C2×#121—7912no—
971C2×#121—796no—
972C2×#121C2×D7913yescomplemented
973#520—791no—
974#520—792no—
975#520—796no—
976#520—793no—
977#520—793no—
978#520C2×D7911yescharacteristic, complemented
979C2×C4×Q8—792no—
980C2×C4×D4—796no—
981C2×#117—793no—
982C22×C4⋊C4—793no—
9832−1+4—1588no—
9842−1+4—1588no—
9852−1+4—1588no—
9862−1+4—15816no—
9872−1+4—15824no—
9882−1+4—15824no—
9892−1+4—1588no—
990H(5,𝔽2)—28no—
991H(5,𝔽2)—15824no—
992H(5,𝔽2)—15848no—
993H(5,𝔽2)—15824no—
994H(5,𝔽2)—15824no—
995H(5,𝔽2)—15824no—
996H(5,𝔽2)—1588no—
997C2×#41—28no—
998C2×#41—7916no—
999C2×#41—791no—
1000C2×#41—793no—
1001C2×#41—791no—
1002C2×#41—793no—
1003C2×#41—791no—
1004C2×#41—793no—
1005C2×#41—796no—
1006C2×#41—796no—
1007C2×#41—793no—
1008C2×#41—796no—
1009C2×#41—796no—
1010C2×#41—796no—
1011C2×#41—793no—
1012C2×#41—793no—
1013C2×#41—796no—
1014C2×#41—7912no—
1015C2×#41—796no—
1016C2×#41—793no—
1017C2×#41—796no—
1018C2×#41—793no—
1019C2×#41—793no—
1020C2×#41—793no—
1021C2×#41—793no—
1022C2×#41—796no—
1023C2×#41—793no—
1024C2×#41—793no—
1025C2×#41—793no—
1026C2×#41—793no—
1027C2×#41—793no—
1028C2×#41—793no—
1029C2×#41—791no—
1030C2×#41—796no—
1031C2×#41—793no—
1032C2×#41—796no—
1033C2×#41—793no—
1034C2×#41—15824no—
1035C2×#41—15824no—
1036C2×#41—15824no—
1037C2×#41—15824no—
1038C2×#41—15824no—
1039C2×#41—15848no—
1040C2×#41—15816no—
1041C2×#41—15824no—
1042C2×#41—1588no—
1043C2×#41C22×D7913yes—
1044C2×#41C22×D7913yes—
1045C2×#41C22×D7913yes—
1046C2×#41C22×D7911yescharacteristic
1047C2×#41C22×D7912yes—
1048C2×#41C22×D7911yescharacteristic
1049C22×Q8—791no—
1050C22×Q8—793no—
1051C22×Q8—793no—
1052C22×Q8—793no—
1053C22×Q8—792no—
1054C22×Q8—791no—
1055C22×Q8—793no—
1056C22×Q8—793no—
1057C22×Q8—796no—
1058C22×Q8—793no—
1059C22×Q8C22×D7911yescharacteristic
1060C22×D4—793no—
1061C22×D4—796no—
1062C22×D4—793no—
1063C22×D4—796no—
1064C22×D4—793no—
1065C22×D4—796no—
1066C22×D4—7912no—
1067C22×D4—7912no—
1068C22×D4—796no—
1069C22×D4—796no—
1070C22×D4—793no—
1071C22×D4—793no—
1072C22×D4—796no—
1073C22×D4—793no—
1074C22×D4—796no—
1075C22×D4—793no—
1076C22×D4—793no—
1077C22×D4—793no—
1078C22×D4C22×D7913yes—
1079C22×D4C22×D7916yes—
1080C22×D4C22×D7913yes—
1081C22×D4C22×D7916yes—
1082C23×C4—793no—
1083C23×C4—796no—
1084C23×C4—796no—
1085C23×C4—796no—
1086C23×C4—796no—
1087C23×C4—793no—
1088C23×C4C22×D7913yes—
1089C4⋊Q8—796no—
1090C4⋊Q8—796no—
1091C4⋊Q8—796no—
1092C4⋊Q8—796no—
1093#127—796no—
1094#127—796no—
1095#127—796no—
1096#127C22×D7916yes—
1097#124—796no—
1098#124—796no—
1099#124—796no—
1100#124—796no—
1101#124—796no—
1102#124—796no—
1103#124—796no—
1104#124C22×D7916yes—
1105#123—796no—
1106#123—7912no—
1107#123—796no—
1108#123—796no—
1109#123—796no—
1110#123—7912no—
1111#123—796no—
1112#123—796no—
1113#123—7912no—
1114#123—7912no—
1115#123—796no—
1116#123C22×D7916yes—
1117C22⋊Q8—793no—
1118C22⋊Q8—796no—
1119C22⋊Q8—791no—
1120C22⋊Q8—796no—
1121C22⋊Q8—793no—
1122C22⋊Q8—796no—
1123C22⋊Q8—796no—
1124C22⋊Q8—796no—
1125C22⋊Q8—793no—
1126C22⋊Q8—796no—
1127C22⋊Q8—796no—
1128C22⋊Q8—793no—
1129C22⋊Q8—7912no—
1130C22⋊Q8—796no—
1131C22⋊Q8—796no—
1132C22⋊Q8—796no—
1133C22⋊Q8—792no—
1134C22⋊Q8—793no—
1135C22⋊Q8—7912no—
1136C22⋊Q8—796no—
1137C22⋊Q8—7912no—
1138C22⋊Q8—7912no—
1139C22⋊Q8—7912no—
1140C22⋊Q8—796no—
1141C22⋊Q8C22×D7913yes—
1142C22⋊Q8C22×D7916yes—
1143C22⋊Q8C22×D7911yescharacteristic
1144#121—793no—
1145#121—796no—
1146#121—7912no—
1147#121—796no—
1148#121—7912no—
1149#121—796no—
1150#121—7912no—
1151#121—7912no—
1152#121—7912no—
1153#121—7912no—
1154#121—796no—
1155#121—796no—
1156#121—796no—
1157#121—7912no—
1158#121—7912no—
1159#121—7912no—
1160#121—793no—
1161#121—796no—
1162#121—796no—
1163#121—793no—
1164#121—7912no—
1165#121—796no—
1166#121—791no—
1167#121—793no—
1168#121—796no—
1169#121—796no—
1170#121—791no—
1171#121—792no—
1172#121—796no—
1173#121—796no—
1174#121—7912no—
1175#121—796no—
1176#121—7912no—
1177#121—7912no—
1178#121—7912no—
1179#121—792no—
1180#121—796no—
1181#121—792no—
1182#121C22×D7916yes—
1183#121C22×D79112yes—
1184#121C22×D7916yes—
1185#121C22×D7913yes—
1186#121C22×D7916yes—
1187#121C22×D7916yes—
1188#121C22×D7913yes—
1189#120—796no—
1190#120—7912no—
1191#120—7912no—
1192#120—796no—
1193#120—796no—
1194#120—7912no—
1195#120—796no—
1196#120—796no—
1197#120—796no—
1198#120—796no—
1199#120C22×D79112yes—
1200#120C22×D7916yes—
1201C4×Q8—792no—
1202C4×Q8—796no—
1203C4×Q8—796no—
1204C4×Q8C22×D7912yes—
1205C4×D4—796no—
1206C4×D4—7912no—
1207C4×D4—7912no—
1208C4×D4—7912no—
1209C4×D4—796no—
1210C4×D4—796no—
1211C4×D4—796no—
1212C4×D4—796no—
1213C4×D4—796no—
1214C4×D4—7912no—
1215C4×D4—7912no—
1216C4×D4—7912no—
1217C4×D4—796no—
1218C4×D4—796no—
1219C4×D4—796no—
1220C4×D4C22×D7916yes—
1221C4×D4C22×D7916yes—
1222C4×D4C22×D7916yes—
1223#117—793no—
1224#117—793no—
1225#117—793no—
1226#117—796no—
1227#117—796no—
1228#117C22×D7913yes—
1229C2×C4⋊C4—796no—
1230C2×C4⋊C4—793no—
1231C2×C4⋊C4—796no—
1232C2×C4⋊C4—796no—
1233C2×C4⋊C4—793no—
1234C2×C4⋊C4—796no—
1235C2×C4⋊C4—796no—
1236C2×C4⋊C4—796no—
1237C2×C4⋊C4—791no—
1238C2×C4⋊C4—7912no—
1239C2×C4⋊C4C22×D7913yes—
1240C2×C22⋊C4—796no—
1241C2×C22⋊C4—796no—
1242C2×C22⋊C4—796no—
1243C2×C22⋊C4—796no—
1244C2×C22⋊C4—7912no—
1245C2×C22⋊C4—7912no—
1246C2×C22⋊C4C22×D7916yes—
1247C2×C42—796no—
1248C24—793no—
1249C24—796no—
1250C24—796no—
1251C24—793no—
1252C24C23×D7913yes—
1253C24C23×D7916yes—
1254#41—24no—
1255#41—28no—
1256#41—212no—
1257#41—212no—
1258#41—212no—
1259#41—798no—
1260#41—7924no—
1261#41—7924no—
1262#41—1584no—
1263#41—15812no—
1264#41—15812no—
1265#41—15812no—
1266#41—15812no—
1267#41—15812no—
1268#41—15812no—
1269#41—15812no—
1270#41—15824no—
1271#41—15824no—
1272#41—15812no—
1273#41—15824no—
1274#41—15812no—
1275#41—15824no—
1276#41—15812no—
1277#41—15824no—
1278#41—15824no—
1279#41—15824no—
1280#41—15824no—
1281#41—15812no—
1282#41—1584no—
1283#41—15812no—
1284#41—15848no—
1285#41—15824no—
1286#41—15824no—
1287#41—15812no—
1288#41—15812no—
1289#41—1584no—
1290#41—15812no—
1291#41—15824no—
1292#41—15812no—
1293#41—15812no—
1294#41D4×D7918yescomplemented
1295C2×Q8—24no—
1296C2×Q8—798no—
1297C2×Q8—793no—
1298C2×Q8—793no—
1299C2×Q8—791no—
1300C2×Q8—793no—
1301C2×Q8—796no—
1302C2×Q8—793no—
1303C2×Q8—793no—
1304C2×Q8—793no—
1305C2×Q8—796no—
1306C2×Q8—15812no—
1307C2×Q8—15812no—
1308C2×Q8—15824no—
1309C2×Q8—15812no—
1310C2×Q8—15812no—
1311C2×Q8—15812no—
1312C2×Q8—1588no—
1313C2×Q8—1584no—
1314C2×Q8—15812no—
1315C2×Q8C23×D7911yescharacteristic
1316C2×Q8C23×D7913yes—
1317C2×Q8C23×D7911yescharacteristic
1318C2×D4—212no—
1319C2×D4—224no—
1320C2×D4—212no—
1321C2×D4—86no—
1322C2×D4—792no—
1323C2×D4—796no—
1324C2×D4—796no—
1325C2×D4—7912no—
1326C2×D4—796no—
1327C2×D4—796no—
1328C2×D4—7924no—
1329C2×D4—793no—
1330C2×D4—793no—
1331C2×D4—7912no—
1332C2×D4—796no—
1333C2×D4—796no—
1334C2×D4—793no—
1335C2×D4—791no—
1336C2×D4—793no—
1337C2×D4—791no—
1338C2×D4—796no—
1339C2×D4—793no—
1340C2×D4—793no—
1341C2×D4—796no—
1342C2×D4—792no—
1343C2×D4—796no—
1344C2×D4—793no—
1345C2×D4—793no—
1346C2×D4—793no—
1347C2×D4—792no—
1348C2×D4—793no—
1349C2×D4—791no—
1350C2×D4—791no—
1351C2×D4—793no—
1352C2×D4—63212no—
1353C2×D4—6326no—
1354C2×D4—15812no—
1355C2×D4—15812no—
1356C2×D4—15812no—
1357C2×D4—15812no—
1358C2×D4—15812no—
1359C2×D4—15824no—
1360C2×D4—15824no—
1361C2×D4—15812no—
1362C2×D4—15824no—
1363C2×D4—15824no—
1364C2×D4—15824no—
1365C2×D4—15848no—
1366C2×D4—15812no—
1367C2×D4—15824no—
1368C2×D4—15812no—
1369C2×D4C23×D7916yes—
1370C2×D4C23×D7916yes—
1371C2×D4C23×D7913yes—
1372C2×D4C23×D7913yes—
1373C2×D4C23×D7916yes—
1374C2×D4C23×D7916yes—
1375C2×D4C23×D79112yes—
1376C2×D4C23×D7916yes—
1377C2×D4C23×D7913yes—
1378C22×C4—212no—
1379C22×C4—796no—
1380C22×C4—792no—
1381C22×C4—796no—
1382C22×C4—7912no—
1383C22×C4—793no—
1384C22×C4—793no—
1385C22×C4—791no—
1386C22×C4—793no—
1387C22×C4—793no—
1388C22×C4—7924no—
1389C22×C4—796no—
1390C22×C4—793no—
1391C22×C4—796no—
1392C22×C4—7912no—
1393C22×C4—796no—
1394C22×C4—796no—
1395C22×C4—796no—
1396C22×C4—796no—
1397C22×C4—796no—
1398C22×C4—793no—
1399C22×C4—793no—
1400C22×C4—792no—
1401C22×C4—791no—
1402C22×C4—793no—
1403C22×C4—6326no—
1404C22×C4—15824no—
1405C22×C4—15824no—
1406C22×C4—15824no—
1407C22×C4—15812no—
1408C22×C4C23×D7913yes—
1409C22×C4C23×D7916yes—
1410C22×C4C23×D7913yes—
1411C22×C4C23×D7913yes—
1412C22×C4C23×D7913yes—
1413C22×C4C23×D7911yescharacteristic
1414C22×C4C23×D7916yes—
1415C22×C4C23×D7913yes—
1416C4⋊C4—796no—
1417C4⋊C4—7912no—
1418C4⋊C4—796no—
1419C4⋊C4—7912no—
1420C4⋊C4—796no—
1421C4⋊C4—792no—
1422C4⋊C4—792no—
1423C4⋊C4—796no—
1424C4⋊C4—793no—
1425C4⋊C4—796no—
1426C4⋊C4—7912no—
1427C4⋊C4—796no—
1428C4⋊C4—791no—
1429C4⋊C4—796no—
1430C4⋊C4C23×D7913yes—
1431C4⋊C4C23×D7916yes—
1432C4⋊C4C23×D7916yes—
1433C4⋊C4C23×D7911yescharacteristic
1434C4⋊C4C23×D7912yes—
1435C22⋊C4—7912no—
1436C22⋊C4—796no—
1437C22⋊C4—7912no—
1438C22⋊C4—796no—
1439C22⋊C4—796no—
1440C22⋊C4—796no—
1441C22⋊C4—796no—
1442C22⋊C4—796no—
1443C22⋊C4—796no—
1444C22⋊C4—796no—
1445C22⋊C4—7912no—
1446C22⋊C4—796no—
1447C22⋊C4—796no—
1448C22⋊C4—796no—
1449C22⋊C4—792no—
1450C22⋊C4—792no—
1451C22⋊C4—796no—
1452C22⋊C4—792no—
1453C22⋊C4C23×D7916yes—
1454C22⋊C4C23×D79112yes—
1455C22⋊C4C23×D7916yes—
1456C22⋊C4C23×D7916yes—
1457C22⋊C4C23×D7916yes—
1458C22⋊C4C23×D7912yes—
1459C42—796no—
1460C42—796no—
1461C42—796no—
1462C42C23×D7916yes—
1463C23—26no—
1464C23—212no—
1465C23—43no—
1466C23—46no—
1467C23—43no—
1468C23—46no—
1469C23—3163no—
1470C23—3163no—
1471C23—3163no—
1472C23—3166no—
1473C23—3166no—
1474C23—3163no—
1475C23—3166no—
1476C23—3166no—
1477C23—7912no—
1478C23—793no—
1479C23—791no—
1480C23—793no—
1481C23—792no—
1482C23—791no—
1483C23—15812no—
1484C23—15812no—
1485C23—1586no—
1486C23C24×D7913yes—
1487C23C24×D7911yescharacteristic
1488C23C24×D7916yes—
1489C23C24×D7913yes—
1490Q8—26no—
1491Q8—22no—
1492Q8—7912no—
1493Q8—1582no—
1494Q8—1586no—
1495Q8—15812no—
1496Q8—1586no—
1497Q8—1586no—
1498Q8—1586no—
1499Q8—1586no—
1500Q8—15812no—
1501Q8C2×D4×D7914yes—
1502D4—212no—
1503D4—212no—
1504D4—26no—
1505D4—212no—
1506D4—26no—
1507D4—46no—
1508D4—412no—
1509D4—46no—
1510D4—3166no—
1511D4—3162no—
1512D4—3166no—
1513D4—3162no—
1514D4—3166no—
1515D4—31612no—
1516D4—3166no—
1517D4—7924no—
1518D4—7912no—
1519D4—1582no—
1520D4—1586no—
1521D4—1584no—
1522D4—1586no—
1523D4—1586no—
1524D4—1582no—
1525D4—1586no—
1526D4—1586no—
1527D4—1586no—
1528D4—15812no—
1529D4—1582no—
1530D4—1586no—
1531D4—1586no—
1532D4—1586no—
1533D4—15812no—
1534D4—15824no—
1535D4—15812no—
1536D4—15812no—
1537D4—1582no—
1538D4—1586no—
1539D4C2×D4×D79112yes—
1540C2×C4—26no—
1541C2×C4—22no—
1542C2×C4—26no—
1543C2×C4—26no—
1544C2×C4—26no—
1545C2×C4—212no—
1546C2×C4—46no—
1547C2×C4—3166no—
1548C2×C4—31612no—
1549C2×C4—3162no—
1550C2×C4—3166no—
1551C2×C4—793no—
1552C2×C4—791no—
1553C2×C4—7912no—
1554C2×C4—794no—
1555C2×C4—7912no—
1556C2×C4—7912no—
1557C2×C4—7912no—
1558C2×C4—792no—
1559C2×C4—796no—
1560C2×C4—791no—
1561C2×C4—793no—
1562C2×C4—796no—
1563C2×C4—1584no—
1564C2×C4—15812no—
1565C2×C4—15812no—
1566C2×C4—15812no—
1567C2×C4—15812no—
1568C2×C4—15812no—
1569C2×C4—15824no—
1570C2×C4—15812no—
1571C2×C4—1586no—
1572C2×C4—1586no—
1573C2×C4—1582no—
1574C2×C4—15812no—
1575C2×C4—1586no—
1576C2×C4—1586no—
1577C2×C4C2×D4×D79112yes—
1578C2×C4C24×D7912yes—
1579C2×C4C24×D7916yes—
1580C2×C4C24×D7912yes—
1581C2×C4C24×D7913yes—
1582C2×C4C24×D7911yescharacteristic
1583C2×C4C24×D7913yes—
1584C2×C4C24×D7911yescharacteristic
1585C22—23no—
1586C22—23no—
1587C22—21no—
1588C22—23no—
1589C22—26no—
1590C22—21no—
1591C22—23no—
1592C22—26no—
1593C22—23no—
1594C22—26no—
1595C22—21no—
1596C22—86no—
1597C22—812no—
1598C22—31612no—
1599C22—792no—
1600C22—796no—
1601C22—6326no—
1602C22—63212no—
1603C22—63212no—
1604C22—1582no—
1605C22—1583no—
1606C22—1581no—
1607C22—1582no—
1608C22—1583no—
1609C22—1581no—
1610C22—1581no—
1611C22—1582no—
1612C22—1583no—
1613C22—1581no—
1614C22—1583no—
1615C22—1581no—
1616C22—1583no—
1617C22C22×D4×D7916yes—
1618C22C25×D7911yescharacteristic
1619C4—21no—
1620C4—22no—
1621C4—23no—
1622C4—26no—
1623C4—22no—
1624C4—792no—
1625C4—796no—
1626C4—1583no—
1627C4—1586no—
1628C4—1581no—
1629C4—1586no—
1630C4—1582no—
1631C4C22×D4×D7912yes—
1632C4C22×D4×D7916yes—
1633C2—26no—
1634C2—41no—
1635C2—46no—
1636C2—43no—
1637C2—3161no—
1638C2—3163no—
1639C2—3162no—
1640C2—1582no—
1641C2—1586no—
1642C2C23×D4×D7911yescharacteristic
1643C2#2377821011yescharacteristic
1644C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3488C2
hypercenter#3488D79
hypocenterC79#62853
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×#19099398C2semidirect
3. #23777168C2semidirect
4. #23777165C2semidirect
5. #23777160C2semidirect
6. #23777156C2semidirect
7. #23777081C2semidirect
8. #23777080C2semidirect
9. #23777079C2semidirect
10. #23777075C2semidirect
11. #23777072C2semidirect
12. #23777071C2semidirect
13. #23777068C2semidirect
14. #23777067C2semidirect
15. #23777065C2semidirect
16. #23777062C2semidirect
17. #23777060C2semidirect
18. #23776731C2semidirect
19. #23776730C2semidirect
20. C2×#19099142C2semidirect
21. #537×D79C2semidirect
22. #520×D79C2semidirect
23. C79×#3488C2semidirect
26. C2×#14579209C22semidirect
27. C2×#14579209C22semidirect
28. C2×#14579208C22semidirect
29. C2×#14579208C22semidirect
30. C2×#14579208C22semidirect
31. C2×#14579208C22semidirect
32. C2×#14579208C22semidirect
33. C2×#14579207C22semidirect
34. C2×#14579207C22semidirect
35. C2×#14579206C22semidirect
36. C2×#14579206C22semidirect
37. C2×#14579206C22semidirect
38. C2×#14579206C22semidirect
39. C22×#11929624C22semidirect
40. C22×#11929624C22semidirect
41. C22×#11929623C22semidirect
42. C22×#11929623C22semidirect
44. C2×#41×D79C22semidirect
45. C2×#41×D79C22semidirect
46. C2×#41×D79C22semidirect
47. C2×#41×D79C22semidirect
48. C2×#41×D79C22semidirect
49. #19099233C22semidirect
50. #19099232C22semidirect
51. #19099231C22semidirect
52. Q8×D316C22semidirect
53. D4×Dic158C22semidirect
54. Q8×C22⋊D79C22semidirect
55. #19099226C22semidirect
56. #19099225C22semidirect
57. #19099222C22semidirect
58. #19099221C22semidirect
59. #19099220C22semidirect
60. #19099220C22semidirect
61. #19099219C22semidirect
62. #19099219C22semidirect
63. #19099218C22semidirect
64. #19099217C22semidirect
65. #19099215C22semidirect
66. #19099213C22semidirect
67. #19099212C22semidirect
68. #19099211C22semidirect
69. #19099210C22semidirect
70. #19099210C22semidirect
71. #19099209C22semidirect
72. #19099208C22semidirect
73. #19099207C22semidirect
74. #19099207C22semidirect
75. #19099206C22semidirect
76. #19099203C22semidirect
77. #19099202C22semidirect
78. #19099200C22semidirect
79. #19099200C22semidirect
80. #19099198C22semidirect
81. #19099197C22semidirect
82. D4×C22⋊D79C22semidirect
83. D4×C22⋊D79C22semidirect
84. #19099195C22semidirect
85. #19099144C22semidirect
86. #19099143C22semidirect
87. #19099143C22semidirect
88. #19099143C22semidirect
89. #19099142C22semidirect
90. #19099142C22semidirect
91. #19099142C22semidirect
92. #19099142C22semidirect
93. #19099142C22semidirect
94. #19099142C22semidirect
95. #19099142C22semidirect
96. #19099142C22semidirect
97. #19099142C22semidirect
98. #19099142C22semidirect
99. #19099141C22semidirect
100. #19099141C22semidirect
101. #19099140C22semidirect
102. #19099139C22semidirect
103. #19099136C22semidirect
104. #19099136C22semidirect
105. #19099135C22semidirect
106. #19099134C22semidirect
107. #19099133C22semidirect
108. #19099130C22semidirect
109. #19099129C22semidirect
110. #19099129C22semidirect
111. #19099128C22semidirect
112. #19099126C22semidirect
113. #19099124C22semidirect
114. #19099123C22semidirect
115. #19099123C22semidirect
116. #19099112C22semidirect
117. #19099111C22semidirect
118. #19099110C22semidirect
119. #19099110C22semidirect
120. #19099075C22semidirect
121. #19099074C22semidirect
122. #19099073C22semidirect
123. #19099073C22semidirect
124. #19099072C22semidirect
125. #19099072C22semidirect
126. #19099070C22semidirect
127. #19099069C22semidirect
128. C2×#14579141C22semidirect
129. C2×#14579140C22semidirect
130. C2×#14579138C22semidirect
131. C22⋊Q8×D79C22semidirect
132. C22⋊Q8×D79C22semidirect
133. C2×#14579134C22semidirect
134. C2×#14579133C22semidirect
135. C2×#14579132C22semidirect
136. C2×#14579132C22semidirect
137. #121×D79C22semidirect
138. #121×D79C22semidirect
139. #121×D79C22semidirect
140. #19099046C22semidirect
141. #19099045C22semidirect
142. #19099044C22semidirect
143. #19099043C22semidirect
144. #19099042C22semidirect
145. C4×Q8×D79C22semidirect
146. C4×D4×D79C22semidirect
147. #117×D79C22semidirect
148. C2×C4⋊C4×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
217. #41×D79D4semidirect
433. #11929625C2×D4semidirect
449. #11929624C2×D4semidirect
463. #11929623C2×D4semidirect
482. Q8×D79C2×D4semidirect
529. D4×D79C2×D4semidirect
542. C2×C4×D79C2×D4semidirect
601. #41×C79C2×D4semidirect
840. #3488D79semidirect
846. C79#62853semidirect
862. C2×H(5,𝔽2)C2×D79semidirect
873. C22×#41C2×D79semidirect
877. #550C2×D79semidirect
889. #548C2×D79semidirect
907. #546C2×D79semidirect
913. D42C2×D79semidirect
931. #537C2×D79semidirect
943. #535C2×D79semidirect
959. #525C2×D79semidirect
972. C2×#121C2×D79semidirect
978. #520C2×D79semidirect
1294. #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×#190993982
#237771682
#237771652
#237771602
#237771562
#237770812
#237770802
#237770792
#237770752
#237770722
#237770712
#237770682
#237770672
#237770652
#237770622
#237770602
#237767312
#237767302
C2×#190991422
#537×D792
#520×D792
C79×#34882
#6285379