Finite Group Databasebeta

← #35197385

Subgroups — #35197385

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×#19099400C211yesmaximal, characteristic, complemented
2C2×#19099399C211yesmaximal, characteristic, complemented
3#23777170C212yesmaximal, complemented
4#23777168C212yesmaximal, complemented
5#23777160C216yesmaximal, complemented
6#23777158C216yesmaximal, complemented
7#23777078C213yesmaximal, complemented
8#23777077C212yesmaximal, complemented
9#23777076C213yesmaximal, complemented
10#23777074C216yesmaximal, complemented
11#23777073C211yesmaximal, characteristic, complemented
12#23777070C211yesmaximal, characteristic, complemented
13#23777069C211yesmaximal, characteristic, complemented
14#23777066C212yesmaximal, complemented
15#23777064C213yesmaximal, complemented
16#23777063C216yesmaximal, complemented
17#23777061C213yesmaximal, complemented
18#23776732C213yesmaximal, complemented
19#23776730C213yesmaximal, complemented
20C2×#19099143C213yesmaximal, complemented
21#537×D79C213yesmaximal, complemented
22#520×D79C211yesmaximal, characteristic, complemented
23C79×#3489C211yesmaximal, characteristic, complemented
24#19099400—216no—
25#19099399—216no—
26C2×#14579209C2213yescomplemented
27C2×#14579209C2211yescharacteristic, complemented
28C2×#14579209C2212yescomplemented
29C2×#14579209C2211yescharacteristic, complemented
30C2×#14579208C2213yescomplemented
31C2×#14579208C2211yescharacteristic, complemented
32C2×#14579207C2213yescomplemented
33C2×#14579207C2211yescharacteristic, complemented
34C2×#14579207C2211yescharacteristic, complemented
35C2×#14579207C2213yescomplemented
36C2×#14579207C2216yescomplemented
37C2×#14579206C2213yescomplemented
38C2×#14579206C2213yescomplemented
39C22×#11929625C2212yescomplemented
40C22×#11929625C2213yescomplemented
41C22×#11929624C2213yescomplemented
42C22×#11929624C2213yescomplemented
43C2×#41×D79C2211yescharacteristic
44C2×#41×D79C2216yescomplemented
45C2×#41×D79C2213yescomplemented
46C2×#41×D79C2211yescharacteristic, complemented
47C2×#41×D79C2213yescomplemented
48C2×#41×D79C2213yescomplemented
49#19099235C2212yescomplemented
50#19099234C2216yescomplemented
51#19099232C2212yescomplemented
52#19099231C2216yescomplemented
53#19099228C2216yescomplemented
54Q8×C22⋊D79C2212yescomplemented
55#19099226C2216yescomplemented
56#19099225C2212yescomplemented
57#19099224C2212yescomplemented
58#19099224C2212yescomplemented
59#19099223C2216yescomplemented
60#19099223C2216yescomplemented
61#19099222C2216yescomplemented
62#19099221C2216yescomplemented
63#19099216C2216yescomplemented
64#19099215C2216yescomplemented
65#19099214C22112yescomplemented
66#19099212C2216yescomplemented
67#19099211C22112yescomplemented
68#19099209C2216yescomplemented
69#19099208C2216yescomplemented
70#19099206C2216yescomplemented
71#19099205C22112yescomplemented
72#19099205C22112yescomplemented
73#19099204C2216yescomplemented
74#19099204C2216yescomplemented
75#19099203C22112yescomplemented
76#19099202C22112yescomplemented
77#19099201C2216yescomplemented
78#19099201C2216yescomplemented
79D4×D316C2216yescomplemented
80D4×D316C2216yescomplemented
81#19099197C22112yescomplemented
82#19099197C2216yescomplemented
83D4×C22⋊D79C2216yescomplemented
84#19099195C22112yescomplemented
85#19099144C2213yescomplemented
86#19099143C2216yescomplemented
87#19099143C2216yescomplemented
88#19099143C2216yescomplemented
89#19099143C2216yescomplemented
90#19099143C2216yescomplemented
91#19099143C2216yescomplemented
92#19099143C2216yescomplemented
93#19099143C2216yescomplemented
94#19099143C2213yescomplemented
95#19099143C2213yescomplemented
96#19099142C2216yescomplemented
97#19099142C2213yescomplemented
98#19099142C2211yescharacteristic, complemented
99#19099141C2213yescomplemented
100#19099141C2213yescomplemented
101#19099140C22112yescomplemented
102#19099138C2216yescomplemented
103#19099137C2213yescomplemented
104#19099136C2213yescomplemented
105#19099136C2213yescomplemented
106#19099135C2216yescomplemented
107#19099132C2213yescomplemented
108#19099131C2216yescomplemented
109#19099129C2213yescomplemented
110#19099129C2213yescomplemented
111#19099128C2216yescomplemented
112#19099127C2213yescomplemented
113#19099124C2216yescomplemented
114#19099124C22112yescomplemented
115#19099123C2216yescomplemented
116#19099114C2216yescomplemented
117#19099112C2216yescomplemented
118#19099110C2216yescomplemented
119#19099110C2216yescomplemented
120#19099076C2216yescomplemented
121#19099076C2216yescomplemented
122#19099075C2213yescomplemented
123#19099074C2213yescomplemented
124#19099072C2216yescomplemented
125#19099072C2216yescomplemented
126#19099071C22112yescomplemented
127#19099070C2213yescomplemented
128C2×#14579139C2216yescomplemented
129C2×#14579137C2213yescomplemented
130C22⋊Q8×D79C2216yescomplemented
131C22⋊Q8×D79C2216yescomplemented
132C2×#14579136C2213yescomplemented
133C2×#14579136C2216yescomplemented
134C2×#14579135C2213yescomplemented
135C2×#14579134C2216yescomplemented
136C2×#14579134C2216yescomplemented
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
149C2×2−1+4×C79C2211yescharacteristic, complemented
150C22×#41×C79C2211yescharacteristic, complemented
151D4×Q8×C79C2212yescomplemented
152#548×C79C2212yescomplemented
153#547×C79C2216yescomplemented
154#546×C79C2216yescomplemented
155#537×C79C2213yescomplemented
156#536×C79C2213yescomplemented
157#525×C79C2213yescomplemented
158C2×C22⋊Q8×C79C2213yescomplemented
159#520×C79C2211yescharacteristic, complemented
160#14579209—28no—
161#14579209—224no—
162#14579209—28no—
163#14579209—216no—
164#14579208—224no—
165#14579208—28no—
166#14579207—28no—
167#14579207—28no—
168#14579207—224no—
169#14579207—224no—
170#14579207—248no—
171#14579206—224no—
172#14579206—224no—
173C2×#11929625—216no—
174C2×#11929625—224no—
175C2×#11929625C2316yes—
176C2×#11929625C2316yes—
177C2×#11929625C2316yes—
178C2×#11929625C2313yes—
179C2×#11929625C2313yes—
180C2×#11929625C2316yes—
181C2×#11929625C2311yescharacteristic
182C2×#11929625C2312yes—
183C2×#11929625C2313yes—
184C2×#11929625C2311yescharacteristic
185C2×#11929624—224no—
186C2×#11929624—224no—
187C2×#11929624C2313yes—
188C2×#11929624C2313yes—
189C2×#11929624C2313yes—
190C2×#11929624C2313yes—
191C2×#11929624C2313yes—
192C2×#11929624C2313yes—
193C2×#11929624C2313yes—
194C2×#11929624C2313yes—
195C2×#11929624C2313yes—
196C2×#11929624C2316yes—
197C2×#11929624C2313yes—
198C2×#11929624C2316yes—
199C2×#11929624C23112yes—
200C2×#11929624C2316yes—
201C2×#11929624C2313yes—
202C2×#11929624C2311yescharacteristic
203C2×#11929624C2313yes—
204C2×#11929623C2316yes—
205C2×#11929623C2313yes—
206C2×#11929623C2316yes—
207C2×#11929623C2313yes—
208C2×#11929623C2313yes—
209C2×#11929623C2316yes—
210C2×#11929623C2311yescharacteristic
211C2×#11929623C2313yes—
212#41×D79—28no—
213#41×D79—224no—
214#41×D79—248no—
215#41×D79—224no—
216#41×D79—224no—
217#41×D79D4116yescomplemented
218C22×Dic158C2313yes—
219C22×Dic158C2313yes—
220C2×Q8×D79C2313yes—
221C2×Q8×D79C2313yes—
222C2×Q8×D79C2313yes—
223C2×Q8×D79C2311yescharacteristic
224C2×Q8×D79C2316yes—
225C2×Q8×D79C2311yescharacteristic
226C22×D316C2316yes—
227C22×D316C2313yes—
228C22×D316C2316yes—
229C22×D316C2313yes—
230C22×D316C2313yes—
231C22×D316C2316yes—
232C22×C22⋊D79C2316yes—
233C22×C22⋊D79C2313yes—
234C22×C22⋊D79C2313yes—
235C22×C22⋊D79C2316yes—
236C2×D4×D79C2316yes—
237C2×D4×D79C2313yes—
238C2×D4×D79C2313yes—
239C2×D4×D79C2316yes—
240C2×D4×D79C2313yes—
241C2×D4×D79C23112yes—
242C2×D4×D79C2316yes—
243C2×D4×D79C2316yes—
244C2×D4×D79C2313yes—
245C2×D4×D79C23112yes—
246C2×D4×D79C2313yes—
247C22×C4×D79C2316yes—
248C22×C4×D79C2316yes—
249C22×C4×D79C2316yes—
250C22×C4×D79C2313yes—
251C22×C4×D79C2316yes—
252C22×C4×D79C2313yes—
253#14579160C2316yes—
254#14579160C2316yes—
255#14579159C2316yes—
256#14579158C2316yes—
257#14579157C2316yes—
258#14579157C2316yes—
259#14579157C2316yes—
260#14579150C2316yes—
261#14579150C2316yes—
262#14579149C2316yes—
263#14579147C2316yes—
264#14579147C2316yes—
265#14579147C2316yes—
266#14579147C2316yes—
267#14579146C2316yes—
268#14579146C2316yes—
269#14579146C23112yes—
270#14579146C23112yes—
271#14579145C2316yes—
272#14579144C23112yes—
273#14579144C2316yes—
274#14579143C2316yes—
275#14579143C2316yes—
276#14579142C2316yes—
277#14579141C2311yescharacteristic
278#14579141C2313yes—
279#14579141C2316yes—
280#14579140C2311yescharacteristic
281#14579140C2313yes—
282#14579140C2316yes—
283#14579139C2316yes—
284#14579139C23112yes—
285#14579139C23112yes—
286#14579139C2316yes—
287#14579139C23112yes—
288#14579139C23112yes—
289#14579138C2316yes—
290#14579138C23112yes—
291#14579138C2312yes—
292#14579137C2313yes—
293#14579137C2313yes—
294#14579137C2316yes—
295#14579137C2316yes—
296#14579137C2316yes—
297#14579137C2316yes—
298#14579136C23112yes—
299#14579136C2313yes—
300#14579136C2316yes—
301#14579136C2316yes—
302#14579136C23112yes—
303#14579136C2316yes—
304#14579136C23112yes—
305#14579136C2316yes—
306#14579136C2316yes—
307#14579136C2313yes—
308#14579136C2316yes—
309#14579135C23112yes—
310#14579135C2316yes—
311#14579135C2316yes—
312#14579135C2313yes—
313#14579135C2316yes—
314#14579135C2316yes—
315#14579135C2313yes—
316#14579134C23112yes—
317#14579134C23112yes—
318#14579134C2316yes—
319#14579134C23112yes—
320#14579134C2312yes—
321#14579134C2316yes—
322#14579134C2316yes—
323#14579134C23112yes—
324#14579134C23112yes—
325#14579134C23112yes—
326#14579134C23112yes—
327#14579134C2316yes—
328#14579134C2316yes—
329#14579133C2316yes—
330#14579133C23112yes—
331#14579133C23112yes—
332#14579133C23112yes—
333#14579133C2312yes—
334#14579132C2313yes—
335#14579132C2316yes—
336#14579132C2316yes—
337#14579132C2311yescharacteristic
338#14579132C2312yes—
339#14579131C23112yes—
340#14579131C23112yes—
341#14579131C23112yes—
342#14579131C2316yes—
343#14579131C2316yes—
344#14579131C2316yes—
345#14579130C2316yes—
346#14579129C2316yes—
347#14579129C23112yes—
348#14579129C2316yes—
349#14579129C2316yes—
350Q8×Dic79C2312yes—
351C4×Dic158C2316yes—
352#14579126C2316yes—
353C4×D316C2316yes—
354C4×D316C2316yes—
355C4×D316C2316yes—
356D4×Dic79C2316yes—
357#14579123C2316yes—
358#14579123C23112yes—
359#14579123C23112yes—
360C4×C22⋊D79C2316yes—
361C4×C22⋊D79C23112yes—
362C4×C22⋊D79C2316yes—
363C4×C22⋊D79C2316yes—
364C4×C22⋊D79C2316yes—
365(C22⋊D79)⋊C4C23112yes—
366(C22⋊D79)⋊C4C23112yes—
367(C22⋊D79)⋊C4C23112yes—
368#14579120C2313yes—
369#14579119C2313yes—
370#14579119C2313yes—
371#14579118C2316yes—
372#14579117C2316yes—
373C2×C4⋊Dic79C2313yes—
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×(C2×D79)⋊C4C2316yes—
383C2×(C2×D79)⋊C4C2316yes—
384C2×(C2×D79)⋊C4C2316yes—
385C22⋊C4×D79C23112yes—
386C22⋊C4×D79C23112yes—
387C22⋊C4×D79C2316yes—
388C42×D79C2316yes—
3892−1+4×C79—28no—
390C2×#41×C79—28no—
391C2×#41×C79C2313yes—
392C2×#41×C79C2311yescharacteristic
393C2×#41×C79C2313yes—
394C2×#41×C79C2316yes—
395C2×#41×C79C2313yes—
396C2×#41×C79C2311yescharacteristic
397C22×Q8×C79C2313yes—
398C22×Q8×C79C2311yescharacteristic
399C22×Q8×C79C2312yes—
400C22×D4×C79C2313yes—
401C23×C4×C79C2313yes—
402C4⋊Q8×C79C2316yes—
403#124×C79C2316yes—
404#123×C79C2316yes—
405#123×C79C23112yes—
406C22⋊Q8×C79C2313yes—
407C22⋊Q8×C79C2313yes—
408C22⋊Q8×C79C2316yes—
409C22⋊Q8×C79C2316yes—
410C22⋊Q8×C79C2316yes—
411C22⋊Q8×C79C2316yes—
412#121×C79C23112yes—
413#121×C79C2316yes—
414#121×C79C2311yescharacteristic
415#121×C79C2313yes—
416#120×C79C2316yes—
417C4×Q8×C79C2312yes—
418C4×D4×C79C2316yes—
419C4×D4×C79C2316yes—
420C4×D4×C79C2316yes—
421#117×C79C2313yes—
422C2×C4⋊C4×C79C2313yes—
423C2×C4⋊C4×C79C2316yes—
424C2×C22⋊C4×C79C2316yes—
425C23×D79C2416yes—
426C23×D79C2416yes—
427C23×D79C2413yes—
428C23×D79C2416yes—
429C23×D79C2413yes—
430#11929625—212no—
431#11929625—224no—
432#11929625—224no—
433#11929625—212no—
434#11929625—212no—
435#11929625—224no—
436#11929625—224no—
437#11929625—24no—
438#11929625—28no—
439#11929625C2×D418yescomplemented
440#11929624—212no—
441#11929624—212no—
442#11929624—212no—
443#11929624—224no—
444#11929624—212no—
445#11929624—24no—
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—248no—
455#11929624—224no—
456#11929624C2×D4124yescomplemented
457#11929623—224no—
458#11929623—224no—
459#11929623—24no—
460#11929623—212no—
461#11929623—212no—
462#11929623—212no—
463#11929623—224no—
464#11929623C2×D4124yescomplemented
465C2×Dic158—212no—
466C2×Dic158—212no—
467C2×Dic158C2416yes—
468C2×Dic158C2411yescharacteristic
469C2×Dic158C2413yes—
470C2×Dic158C2413yes—
471C2×Dic158C2413yes—
472C2×Dic158C2411yescharacteristic
473C2×Dic158C2413yes—
474C2×Dic158C2413yes—
475Q8×D79—212no—
476Q8×D79—212no—
477Q8×D79—212no—
478Q8×D79—224no—
479Q8×D79—24no—
480Q8×D79C2×D418yescomplemented
481C2×D316—212no—
482C2×D316—224no—
483C2×D316—212no—
484C2×D316—224no—
485C2×D316—212no—
486C2×D316—86no—
487C2×D316C2413yes—
488C2×D316C2411yescharacteristic
489C2×D316C2413yes—
490C2×D316C2413yes—
491C2×D316C2413yes—
492C2×D316C24112yes—
493C2×D316C2416yes—
494C2×D316C2413yes—
495C2×D316C2416yes—
496C2×D316C2416yes—
497C2×D316C24112yes—
498C2×D316C2416yes—
499C2×D316C2413yes—
500C2×C22⋊D79—212no—
501C2×C22⋊D79—212no—
502C2×C22⋊D79—224no—
503C2×C22⋊D79—86no—
504C2×C22⋊D79C2413yes—
505C2×C22⋊D79C2416yes—
506C2×C22⋊D79C2413yes—
507C2×C22⋊D79C2413yes—
508C2×C22⋊D79C2413yes—
509C2×C22⋊D79C2416yes—
510C2×C22⋊D79C2412yes—
511C2×C22⋊D79C2416yes—
512C2×C22⋊D79C2413yes—
513C2×C22⋊D79C2411yescharacteristic
514C2×C22⋊D79C2411yescharacteristic
515C2×C22⋊D79C2413yes—
516C2×C22⋊D79C2416yes—
517C2×C22⋊D79C24112yes—
518C2×C22⋊D79C2412yes—
519C2×C22⋊D79C2416yes—
520C2×C22⋊D79C2416yes—
521C2×C22⋊D79C2416yes—
522D4×D79—212no—
523D4×D79—212no—
524D4×D79—212no—
525D4×D79—224no—
526D4×D79—224no—
527D4×D79—212no—
528D4×D79—224no—
529D4×D79—224no—
530D4×D79—248no—
531D4×D79—812no—
532D4×D79C2×D4124yescomplemented
533C22×Dic79C2413yes—
534C22×Dic79C2416yes—
535C22×Dic79C2412yes—
536C22×Dic79C2416yes—
537C22×Dic79C2413yes—
538C2×C4×D79—224no—
539C2×C4×D79—224no—
540C2×C4×D79—224no—
541C2×C4×D79—212no—
542C2×C4×D79—86no—
543C2×C4×D79C2×D4124yescomplemented
544C2×C4×D79C2416yes—
545C2×C4×D79C2413yes—
546C2×C4×D79C2413yes—
547C2×C4×D79C2416yes—
548C2×C4×D79C2416yes—
549C2×C4×D79C24112yes—
550C2×C4×D79C2416yes—
551C2×C4×D79C2416yes—
552C2×C4×D79C2411yescharacteristic
553C2×C4×D79C2413yes—
554C2×C4×D79C2412yes—
555C2×C4×D79C2416yes—
556C2×C4×D79C24112yes—
557C2×C4×D79C2413yes—
558C2×C4×D79C2413yes—
559C2×C4×D79C2413yes—
560C2×C4×D79C2411yescharacteristic
561C4⋊Dic79C2413yes—
562C4⋊Dic79C2416yes—
563C4⋊Dic79C2416yes—
564C4⋊Dic79C2411yescharacteristic
565C4⋊Dic79C2412yes—
566Dic79⋊C4C2416yes—
567Dic79⋊C4C24112yes—
568Dic79⋊C4C2416yes—
569Dic79⋊C4C24112yes—
570Dic79⋊C4C2412yes—
571Dic79⋊C4C2416yes—
572Dic79⋊C4C2416yes—
573Dic79⋊C4C2412yes—
574C22⋊Dic79C2416yes—
575C22⋊Dic79C2416yes—
576C22⋊Dic79C2416yes—
577C22⋊Dic79C2412yes—
578C22⋊Dic79C2412yes—
579(C2×D79)⋊C4C2416yes—
580(C2×D79)⋊C4C24112yes—
581(C2×D79)⋊C4C24112yes—
582(C2×D79)⋊C4C24112yes—
583(C2×D79)⋊C4C2416yes—
584(C2×D79)⋊C4C2416yes—
585(C2×D79)⋊C4C2416yes—
586(C2×D79)⋊C4C2416yes—
587(C2×D79)⋊C4C2416yes—
588(C2×D79)⋊C4C2416yes—
589(C2×D79)⋊C4C2416yes—
590(C2×D79)⋊C4C2416yes—
591(C2×D79)⋊C4C2412yes—
592C4×Dic79C2416yes—
593C4×Dic79C2416yes—
594C4×Dic79C2416yes—
595C24×C79C2413yes—
596#41×C79—24no—
597#41×C79—224no—
598#41×C79—212no—
599#41×C79—212no—
600#41×C79—212no—
601#41×C79C2×D418yescomplemented
602C2×Q8×C79—28no—
603C2×Q8×C79—24no—
604C2×Q8×C79—212no—
605C2×Q8×C79C2413yes—
606C2×Q8×C79C2413yes—
607C2×Q8×C79C2416yes—
608C2×Q8×C79C2411yescharacteristic
609C2×D4×C79—212no—
610C2×D4×C79C2416yes—
611C2×D4×C79C2413yes—
612C2×D4×C79C2416yes—
613C2×D4×C79C2411yescharacteristic
614C2×D4×C79C2412yes—
615C2×D4×C79C2416yes—
616C2×D4×C79C2413yes—
617C22×C4×C79—212no—
618C22×C4×C79C2413yes—
619C22×C4×C79C2413yes—
620C22×C4×C79C2413yes—
621C22×C4×C79C2411yescharacteristic
622C22×C4×C79C2416yes—
623C22×C4×C79C2416yes—
624C22×C4×C79C2413yes—
625C22×C4×C79C2416yes—
626C22×C4×C79C2413yes—
627C4⋊C4×C79C2413yes—
628C4⋊C4×C79C2416yes—
629C4⋊C4×C79C2416yes—
630C4⋊C4×C79C24112yes—
631C4⋊C4×C79C2411yescharacteristic
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—26no—
641C23×C79—43no—
642C23×C79—43no—
643C23×C79C2512yes—
644C23×C79C2513yes—
645C23×C79C2511yescharacteristic
646C23×C79C2513yes—
647C22×D79—26no—
648C22×D79—212no—
649C22×D79—212no—
650C22×D79—212no—
651C22×D79—43no—
652C22×D79—43no—
653C22×D79—46no—
654C22×D79—46no—
655C22×D79—46no—
656C22×D79—43no—
657C22×D79—46no—
658C22×D79—46no—
659C22×D79—43no—
660C22×D79—46no—
661C22×D79C22×D4112yes—
662C22×D79C2513yes—
663C22×D79C2511yescharacteristic
664C22×D79C2516yes—
665C22×D79C2513yes—
666C22×D79C2511yescharacteristic
667Q8×C79—26no—
668Q8×C79—26no—
669Q8×C79—212no—
670Q8×C79C22×D414yes—
671D4×C79—212no—
672D4×C79—212no—
673D4×C79—22no—
674D4×C79—26no—
675D4×C79—46no—
676D4×C79—42no—
677D4×C79C22×D4112yes—
678C2×C4×C79—212no—
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×C79C2513yes—
690C2×C4×C79C2511yescharacteristic
691C2×C4×C79C2516yes—
692C2×C4×C79C2513yes—
693C2×C4×C79C2511yescharacteristic
694C22⋊D79—212no—
695C22⋊D79—212no—
696C22⋊D79—24no—
697C22⋊D79—26no—
698C22⋊D79—26no—
699C22⋊D79—22no—
700C22⋊D79—26no—
701C22⋊D79—212no—
702C22⋊D79—26no—
703C22⋊D79—26no—
704C22⋊D79—26no—
705C22⋊D79—22no—
706C22⋊D79—46no—
707C22⋊D79—412no—
708C22⋊D79—46no—
709C22⋊D79—42no—
710C22⋊D79—46no—
711C22⋊D79C22×D4124yes—
712C2×Dic79—26no—
713C2×Dic79—24no—
714C2×Dic79—212no—
715C2×Dic79—46no—
716C2×Dic79C22×D4112yes—
717C2×Dic79C2512yes—
718C2×Dic79C2516yes—
719C2×Dic79C2513yes—
720C2×Dic79C2511yescharacteristic
721C2×Dic79C2512yes—
722C2×Dic79C2513yes—
723C2×Dic79C2511yescharacteristic
724D316—26no—
725D316—26no—
726D316—212no—
727D316—224no—
728D316—22no—
729D316—26no—
730D316—26no—
731D316—26no—
732D316—212no—
733D316—412no—
734D316—46no—
735D316—46no—
736D316C22×D4112yes—
737C4×D79—212no—
738C4×D79—212no—
739C4×D79—26no—
740C4×D79—22no—
741C4×D79—26no—
742C4×D79—26no—
743C4×D79—212no—
744C4×D79—212no—
745C4×D79—212no—
746C4×D79—224no—
747C4×D79—46no—
748C4×D79—412no—
749C4×D79—42no—
750C4×D79C22×D4112yes—
751C4×D79C22×D4112yes—
752C4×D79C22×D414yes—
753C4×D79C22×D4112yes—
754Dic158—22no—
755Dic158—26no—
756Dic158—212no—
757Dic158—26no—
758Dic158—26no—
759Dic158—26no—
760Dic158—22no—
761Dic158C22×D4112yes—
762C22×C79—23no—
763C22×C79—23no—
764C22×C79—21no—
765C22×C79—22no—
766C22×C79—23no—
767C22×C79—21no—
768C22×C79—23no—
769C22×C79—22no—
770C22×C79—23no—
771C22×C79—22no—
772C22×C79—21no—
773C22×C79—86no—
774C22×C79C23×D416yes—
775C22×C79C2611yescharacteristic
776C2×D79—23no—
777C2×D79—21no—
778C2×D79—23no—
779C2×D79—21no—
780C2×D79—23no—
781C2×D79—21no—
782C2×D79—26no—
783C2×D79—26no—
784C2×D79—23no—
785C2×D79—21no—
786C2×D79—21no—
787C2×D79—26no—
788C2×D79—23no—
789C2×D79—412no—
790C2×D79—812no—
791C2×D79—812no—
792C2×D79—86no—
793C2×D79—812no—
794C2×D79C23×D412yes—
795C2×D79C23×D416yes—
796C4×C79—21no—
797C4×C79—23no—
798C4×C79—26no—
799C4×C79—26no—
800C4×C79—22no—
801C4×C79C23×D412yes—
802C4×C79C23×D416yes—
803Dic79—22no—
804Dic79—23no—
805Dic79—21no—
806Dic79—26no—
807Dic79—22no—
808Dic79C23×D416yes—
809Dic79C23×D412yes—
810#62853—791nomaximal, Sylow
811C2×C79—26no—
812C2×C79—42no—
813C2×C79—43no—
814C2×C79—41no—
815C2×C79C24×D411yescharacteristic
816C2×C79H(7,𝔽2)11yescharacteristic
817C2×C792−1+611yescharacteristic
818D79—22no—
819D79—26no—
820D79—43no—
821D79—41no—
822D79—46no—
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#3489D7911yescharacteristic, complemented
835#3488—791no—
836#3488—792no—
837#3488—796no—
838#3488—793no—
839#3488—793no—
840#3488—791no—
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—791no—
851C2×2−1+4—791no—
852C2×2−1+4—793no—
853C2×2−1+4—791no—
854C2×2−1+4—792no—
855C2×2−1+4C2×D7911yescharacteristic, complemented
856C2×H(5,𝔽2)—791no—
857C2×H(5,𝔽2)—793no—
858C2×H(5,𝔽2)—791no—
859C2×H(5,𝔽2)—793no—
860C2×H(5,𝔽2)—796no—
861C2×H(5,𝔽2)—793no—
862C2×H(5,𝔽2)—793no—
863C22×#41—791no—
864C22×#41—793no—
865C22×#41—793no—
866C22×#41—796no—
867C22×#41—793no—
868C22×#41—791no—
869C22×#41—793no—
870C22×#41—792no—
871C22×#41—793no—
872C22×#41—793no—
873C22×#41C2×D7911yescharacteristic, complemented
874#550—792no—
875#550—796no—
876#550—792no—
877#550—796no—
878D4×Q8—792no—
879D4×Q8—796no—
880D4×Q8—796no—
881D4×Q8C2×D7912yescomplemented
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—796no—
892#547—7912no—
893#547—796no—
894#547—7912no—
895#547C2×D7916yescomplemented
896#546—796no—
897#546—796no—
898#546—796no—
899#546—7912no—
900#546—7912no—
901#546—796no—
902#546—796no—
903#546—7912no—
904#546—796no—
905#546—796no—
906#546—7912no—
907#546C2×D7916yescomplemented
908D42—796no—
909D42—7912no—
910D42—796no—
911D42—7912no—
912D42—796no—
913D42—796no—
914#537—793no—
915#537—793no—
916#537—796no—
917#537—793no—
918#537—796no—
919#537—796no—
920#537—796no—
921#537—796no—
922#537—796no—
923#537—796no—
924#537—796no—
925#537—793no—
926#537—7912no—
927#537—793no—
928#537—796no—
929#537—791no—
930#537—793no—
931#537C2×D7913yescomplemented
932#536—793no—
933#536—796no—
934#536—796no—
935#536—793no—
936#536—793no—
937#536C2×D7913yescomplemented
938#535—793no—
939#535—796no—
940#535—793no—
941#535—793no—
942#535—796no—
943#535—793no—
944#534—7912no—
945#534—796no—
946#534—796no—
947#532—796no—
948#532—796no—
949#532—796no—
950#532—796no—
951#525—793no—
952#525—793no—
953#525—7912no—
954#525—796no—
955#525—796no—
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—796no—
964C2×C22⋊Q8C2×D7913yescomplemented
965C2×#121—793no—
966C2×#121—796no—
967C2×#121—796no—
968C2×#121—7912no—
969C2×#121—793no—
970C2×#121—796no—
971C2×#121—796no—
972C2×#121—796no—
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—28no—
9842−1+4—1588no—
9852−1+4—15816no—
9862−1+4—1588no—
9872−1+4—15824no—
9882−1+4—1588no—
9892−1+4—15824no—
990H(5,𝔽2)—15824no—
991H(5,𝔽2)—15824no—
992H(5,𝔽2)—15824no—
993H(5,𝔽2)—15848no—
994H(5,𝔽2)—1588no—
995H(5,𝔽2)—15824no—
996H(5,𝔽2)—1588no—
997C2×#41—28no—
998C2×#41—7916no—
999C2×#41—791no—
1000C2×#41—796no—
1001C2×#41—793no—
1002C2×#41—796no—
1003C2×#41—796no—
1004C2×#41—793no—
1005C2×#41—793no—
1006C2×#41—796no—
1007C2×#41—791no—
1008C2×#41—792no—
1009C2×#41—793no—
1010C2×#41—796no—
1011C2×#41—793no—
1012C2×#41—796no—
1013C2×#41—791no—
1014C2×#41—793no—
1015C2×#41—796no—
1016C2×#41—793no—
1017C2×#41—793no—
1018C2×#41—793no—
1019C2×#41—793no—
1020C2×#41—793no—
1021C2×#41—793no—
1022C2×#41—793no—
1023C2×#41—796no—
1024C2×#41—793no—
1025C2×#41—793no—
1026C2×#41—793no—
1027C2×#41—793no—
1028C2×#41—791no—
1029C2×#41—793no—
1030C2×#41—796no—
1031C2×#41—7912no—
1032C2×#41—793no—
1033C2×#41—796no—
1034C2×#41—15824no—
1035C2×#41—15824no—
1036C2×#41—15824no—
1037C2×#41—15824no—
1038C2×#41—15824no—
1039C2×#41—15816no—
1040C2×#41—15848no—
1041C2×#41—15824no—
1042C2×#41—1588no—
1043C2×#41C22×D7913yes—
1044C2×#41C22×D7913yes—
1045C2×#41C22×D7913yes—
1046C2×#41C22×D7916yes—
1047C2×#41C22×D7911yescharacteristic
1048C2×#41C22×D7911yescharacteristic
1049C22×Q8—791no—
1050C22×Q8—793no—
1051C22×Q8—793no—
1052C22×Q8—793no—
1053C22×Q8—796no—
1054C22×Q8—791no—
1055C22×Q8—793no—
1056C22×Q8—793no—
1057C22×Q8C22×D7913yes—
1058C22×Q8C22×D7911yescharacteristic
1059C22×Q8C22×D7912yes—
1060C22×D4—793no—
1061C22×D4—796no—
1062C22×D4—793no—
1063C22×D4—793no—
1064C22×D4—796no—
1065C22×D4—7912no—
1066C22×D4—796no—
1067C22×D4—796no—
1068C22×D4—793no—
1069C22×D4—793no—
1070C22×D4—796no—
1071C22×D4—7912no—
1072C22×D4—793no—
1073C22×D4—796no—
1074C22×D4—793no—
1075C22×D4—796no—
1076C22×D4—793no—
1077C22×D4—796no—
1078C22×D4—793no—
1079C22×D4—793no—
1080C22×D4—796no—
1081C22×D4C22×D7913yes—
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⋊Q8C22×D7916yes—
1093#127—796no—
1094#127—796no—
1095#127—796no—
1096#127—796no—
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—796no—
1107#123—7912no—
1108#123—7912no—
1109#123—796no—
1110#123—7912no—
1111#123—796no—
1112#123—796no—
1113#123—796no—
1114#123—796no—
1115#123C22×D79112yes—
1116#123C22×D7916yes—
1117C22⋊Q8—793no—
1118C22⋊Q8—796no—
1119C22⋊Q8—796no—
1120C22⋊Q8—796no—
1121C22⋊Q8—796no—
1122C22⋊Q8—793no—
1123C22⋊Q8—793no—
1124C22⋊Q8—796no—
1125C22⋊Q8—791no—
1126C22⋊Q8—7912no—
1127C22⋊Q8—796no—
1128C22⋊Q8—793no—
1129C22⋊Q8—7912no—
1130C22⋊Q8—7912no—
1131C22⋊Q8—7912no—
1132C22⋊Q8—796no—
1133C22⋊Q8—796no—
1134C22⋊Q8—791no—
1135C22⋊Q8—796no—
1136C22⋊Q8—7912no—
1137C22⋊Q8—792no—
1138C22⋊Q8C22×D7916yes—
1139C22⋊Q8C22×D7916yes—
1140C22⋊Q8C22×D7913yes—
1141C22⋊Q8C22×D7916yes—
1142C22⋊Q8C22×D7916yes—
1143C22⋊Q8C22×D7913yes—
1144#121—793no—
1145#121—796no—
1146#121—796no—
1147#121—7912no—
1148#121—7912no—
1149#121—796no—
1150#121—7912no—
1151#121—791no—
1152#121—792no—
1153#121—792no—
1154#121—796no—
1155#121—793no—
1156#121—7912no—
1157#121—796no—
1158#121—796no—
1159#121—796no—
1160#121—793no—
1161#121—796no—
1162#121—793no—
1163#121—7912no—
1164#121—796no—
1165#121—7912no—
1166#121—7912no—
1167#121—796no—
1168#121—796no—
1169#121—796no—
1170#121—793no—
1171#121—796no—
1172#121—7912no—
1173#121—796no—
1174#121—796no—
1175#121—7912no—
1176#121—796no—
1177#121—7912no—
1178#121—7912no—
1179#121—7912no—
1180#121—7912no—
1181#121—7912no—
1182#121—796no—
1183#121—796no—
1184#121—792no—
1185#121C22×D7913yes—
1186#121C22×D79112yes—
1187#121C22×D7916yes—
1188#121C22×D7911yescharacteristic
1189#120—796no—
1190#120—796no—
1191#120—7912no—
1192#120—796no—
1193#120—796no—
1194#120—7912no—
1195#120—796no—
1196#120—7912no—
1197#120—796no—
1198#120—796no—
1199#120—7912no—
1200#120C22×D7916yes—
1201C4×Q8—792no—
1202C4×Q8—796no—
1203C4×Q8—796no—
1204C4×Q8C22×D7912yes—
1205C4×D4—796no—
1206C4×D4—7912no—
1207C4×D4—796no—
1208C4×D4—796no—
1209C4×D4—796no—
1210C4×D4—796no—
1211C4×D4—796no—
1212C4×D4—7912no—
1213C4×D4—7912no—
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—793no—
1233C2×C4⋊C4—796no—
1234C2×C4⋊C4—796no—
1235C2×C4⋊C4—796no—
1236C2×C4⋊C4—791no—
1237C2×C4⋊C4—7912no—
1238C2×C4⋊C4C22×D7913yes—
1239C2×C4⋊C4C22×D7916yes—
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—796no—
1252C24—793no—
1253C24C23×D7913yes—
1254#41—24no—
1255#41—212no—
1256#41—224no—
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—15848no—
1273#41—15812no—
1274#41—15812no—
1275#41—15824no—
1276#41—15824no—
1277#41—1584no—
1278#41—15824no—
1279#41—15812no—
1280#41—15812no—
1281#41—15824no—
1282#41—15824no—
1283#41—15824no—
1284#41—15812no—
1285#41—15824no—
1286#41—15812no—
1287#41—15824no—
1288#41—15812no—
1289#41—1584no—
1290#41—1588no—
1291#41—15812no—
1292#41—15812no—
1293#41—15812no—
1294#41D4×D7918yescomplemented
1295C2×Q8—24no—
1296C2×Q8—28no—
1297C2×Q8—212no—
1298C2×Q8—798no—
1299C2×Q8—793no—
1300C2×Q8—793no—
1301C2×Q8—791no—
1302C2×Q8—791no—
1303C2×Q8—793no—
1304C2×Q8—793no—
1305C2×Q8—796no—
1306C2×Q8—793no—
1307C2×Q8—15812no—
1308C2×Q8—15812no—
1309C2×Q8—15812no—
1310C2×Q8—15812no—
1311C2×Q8—15824no—
1312C2×Q8—15812no—
1313C2×Q8—1584no—
1314C2×Q8C23×D7913yes—
1315C2×Q8C23×D7913yes—
1316C2×Q8C23×D7916yes—
1317C2×Q8C23×D7911yescharacteristic
1318C2×D4—212no—
1319C2×D4—792no—
1320C2×D4—796no—
1321C2×D4—796no—
1322C2×D4—7912no—
1323C2×D4—796no—
1324C2×D4—796no—
1325C2×D4—7924no—
1326C2×D4—793no—
1327C2×D4—793no—
1328C2×D4—796no—
1329C2×D4—796no—
1330C2×D4—793no—
1331C2×D4—791no—
1332C2×D4—792no—
1333C2×D4—793no—
1334C2×D4—791no—
1335C2×D4—796no—
1336C2×D4—793no—
1337C2×D4—793no—
1338C2×D4—796no—
1339C2×D4—7912no—
1340C2×D4—796no—
1341C2×D4—793no—
1342C2×D4—793no—
1343C2×D4—793no—
1344C2×D4—7912no—
1345C2×D4—793no—
1346C2×D4—791no—
1347C2×D4—796no—
1348C2×D4—793no—
1349C2×D4—793no—
1350C2×D4—796no—
1351C2×D4—6326no—
1352C2×D4—63212no—
1353C2×D4—6326no—
1354C2×D4—15812no—
1355C2×D4—15824no—
1356C2×D4—15812no—
1357C2×D4—15824no—
1358C2×D4—15812no—
1359C2×D4—15812no—
1360C2×D4—15812no—
1361C2×D4—15824no—
1362C2×D4—15848no—
1363C2×D4—15812no—
1364C2×D4—15824no—
1365C2×D4—15824no—
1366C2×D4—15824no—
1367C2×D4—15812no—
1368C2×D4—15812no—
1369C2×D4—15824no—
1370C2×D4—15812no—
1371C2×D4C23×D7916yes—
1372C2×D4C23×D7916yes—
1373C2×D4C23×D7911yescharacteristic
1374C2×D4C23×D7913yes—
1375C2×D4C23×D7912yes—
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—793no—
1390C22×C4—796no—
1391C22×C4—792no—
1392C22×C4—796no—
1393C22×C4—796no—
1394C22×C4—796no—
1395C22×C4—7912no—
1396C22×C4—793no—
1397C22×C4—793no—
1398C22×C4—796no—
1399C22×C4—796no—
1400C22×C4—793no—
1401C22×C4—791no—
1402C22×C4—6326no—
1403C22×C4—15824no—
1404C22×C4—15824no—
1405C22×C4—15824no—
1406C22×C4—15812no—
1407C22×C4C23×D7913yes—
1408C22×C4C23×D7916yes—
1409C22×C4C23×D7913yes—
1410C22×C4C23×D7913yes—
1411C22×C4C23×D7916yes—
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—796no—
1427C4⋊C4—791no—
1428C4⋊C4—792no—
1429C4⋊C4C23×D7913yes—
1430C4⋊C4C23×D7916yes—
1431C4⋊C4C23×D79112yes—
1432C4⋊C4C23×D7911yescharacteristic
1433C4⋊C4C23×D7916yes—
1434C4⋊C4C23×D7916yes—
1435C22⋊C4—796no—
1436C22⋊C4—796no—
1437C22⋊C4—796no—
1438C22⋊C4—792no—
1439C22⋊C4—792no—
1440C22⋊C4—7912no—
1441C22⋊C4—796no—
1442C22⋊C4—7912no—
1443C22⋊C4—796no—
1444C22⋊C4—796no—
1445C22⋊C4—7912no—
1446C22⋊C4—796no—
1447C22⋊C4—796no—
1448C22⋊C4—796no—
1449C22⋊C4—796no—
1450C22⋊C4—796no—
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—43no—
1465C23—43no—
1466C23—3163no—
1467C23—3163no—
1468C23—3166no—
1469C23—3163no—
1470C23—3166no—
1471C23—3166no—
1472C23—3163no—
1473C23—3166no—
1474C23—3166no—
1475C23—3166no—
1476C23—7912no—
1477C23—793no—
1478C23—791no—
1479C23—791no—
1480C23—796no—
1481C23—793no—
1482C23—15812no—
1483C23—15812no—
1484C23—1586no—
1485C23—15812no—
1486C23C24×D7912yes—
1487C23C24×D7913yes—
1488C23C24×D7911yescharacteristic
1489C23C24×D7913yes—
1490Q8—26no—
1491Q8—212no—
1492Q8—26no—
1493Q8—7912no—
1494Q8—1582no—
1495Q8—1586no—
1496Q8—1586no—
1497Q8—1586no—
1498Q8—15812no—
1499Q8—1582no—
1500Q8—1586no—
1501Q8C2×D4×D7914yes—
1502D4—212no—
1503D4—212no—
1504D4—26no—
1505D4—22no—
1506D4—46no—
1507D4—42no—
1508D4—3166no—
1509D4—31612no—
1510D4—3166no—
1511D4—3162no—
1512D4—3166no—
1513D4—3166no—
1514D4—31612no—
1515D4—3166no—
1516D4—7924no—
1517D4—7912no—
1518D4—1582no—
1519D4—1586no—
1520D4—1586no—
1521D4—1586no—
1522D4—15812no—
1523D4—15824no—
1524D4—1582no—
1525D4—1586no—
1526D4—1586no—
1527D4—15812no—
1528D4—1586no—
1529D4—1582no—
1530D4—1586no—
1531D4—1584no—
1532D4—1586no—
1533D4—1586no—
1534D4—15812no—
1535D4—15812no—
1536D4—1586no—
1537D4—1586no—
1538D4—15812no—
1539D4C2×D4×D79112yes—
1540C2×C4—26no—
1541C2×C4—212no—
1542C2×C4—22no—
1543C2×C4—26no—
1544C2×C4—26no—
1545C2×C4—26no—
1546C2×C4—212no—
1547C2×C4—46no—
1548C2×C4—3166no—
1549C2×C4—31612no—
1550C2×C4—3162no—
1551C2×C4—3166no—
1552C2×C4—793no—
1553C2×C4—791no—
1554C2×C4—7912no—
1555C2×C4—794no—
1556C2×C4—7912no—
1557C2×C4—7912no—
1558C2×C4—7912no—
1559C2×C4—792no—
1560C2×C4—796no—
1561C2×C4—792no—
1562C2×C4—793no—
1563C2×C4—791no—
1564C2×C4—15812no—
1565C2×C4—15812no—
1566C2×C4—15824no—
1567C2×C4—15812no—
1568C2×C4—15812no—
1569C2×C4—1584no—
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×D7913yes—
1581C2×C4C24×D7911yescharacteristic
1582C2×C4C24×D7916yes—
1583C2×C4C24×D7913yes—
1584C2×C4C24×D7911yescharacteristic
1585C22—23no—
1586C22—23no—
1587C22—21no—
1588C22—22no—
1589C22—23no—
1590C22—22no—
1591C22—23no—
1592C22—21no—
1593C22—21no—
1594C22—22no—
1595C22—23no—
1596C22—86no—
1597C22—31612no—
1598C22—792no—
1599C22—796no—
1600C22—6326no—
1601C22—63212no—
1602C22—63212no—
1603C22—63212no—
1604C22—1586no—
1605C22—1583no—
1606C22—1581no—
1607C22—1581no—
1608C22—1583no—
1609C22—1586no—
1610C22—1583no—
1611C22—1586no—
1612C22—1581no—
1613C22—1581no—
1614C22—1583no—
1615C22—1581no—
1616C22—1583no—
1617C22C22×D4×D7916yes—
1618C22C25×D7911yescharacteristic
1619C4—21no—
1620C4—23no—
1621C4—26no—
1622C4—26no—
1623C4—22no—
1624C4—792no—
1625C4—796no—
1626C4—1582no—
1627C4—1583no—
1628C4—1581no—
1629C4—1586no—
1630C4—1582no—
1631C4C22×D4×D7912yes—
1632C4C22×D4×D7916yes—
1633C2—26no—
1634C2—41no—
1635C2—43no—
1636C2—42no—
1637C2—3161no—
1638C2—3166no—
1639C2—3163no—
1640C2—1582no—
1641C2—1586no—
1642C2C23×D4×D7911yescharacteristic
1643C2#2377821111yescharacteristic
1644C2#2377821211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3489C2
hypercenter#3489D79
hypocenterC79#62853
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. C2×#19099400C2semidirect
2. C2×#19099399C2semidirect
3. #23777170C2semidirect
4. #23777168C2semidirect
5. #23777160C2semidirect
6. #23777158C2semidirect
7. #23777078C2semidirect
8. #23777077C2semidirect
9. #23777076C2semidirect
10. #23777074C2semidirect
11. #23777073C2semidirect
12. #23777070C2semidirect
13. #23777069C2semidirect
14. #23777066C2semidirect
15. #23777064C2semidirect
16. #23777063C2semidirect
17. #23777061C2semidirect
18. #23776732C2semidirect
19. #23776730C2semidirect
20. C2×#19099143C2semidirect
21. #537×D79C2semidirect
22. #520×D79C2semidirect
23. C79×#3489C2semidirect
26. C2×#14579209C22semidirect
27. C2×#14579209C22semidirect
28. C2×#14579209C22semidirect
29. C2×#14579209C22semidirect
30. C2×#14579208C22semidirect
31. C2×#14579208C22semidirect
32. C2×#14579207C22semidirect
33. C2×#14579207C22semidirect
34. C2×#14579207C22semidirect
35. C2×#14579207C22semidirect
36. C2×#14579207C22semidirect
37. C2×#14579206C22semidirect
38. C2×#14579206C22semidirect
39. C22×#11929625C22semidirect
40. C22×#11929625C22semidirect
41. C22×#11929624C22semidirect
42. C22×#11929624C22semidirect
44. C2×#41×D79C22semidirect
45. C2×#41×D79C22semidirect
46. C2×#41×D79C22semidirect
47. C2×#41×D79C22semidirect
48. C2×#41×D79C22semidirect
49. #19099235C22semidirect
50. #19099234C22semidirect
51. #19099232C22semidirect
52. #19099231C22semidirect
53. #19099228C22semidirect
54. Q8×C22⋊D79C22semidirect
55. #19099226C22semidirect
56. #19099225C22semidirect
57. #19099224C22semidirect
58. #19099224C22semidirect
59. #19099223C22semidirect
60. #19099223C22semidirect
61. #19099222C22semidirect
62. #19099221C22semidirect
63. #19099216C22semidirect
64. #19099215C22semidirect
65. #19099214C22semidirect
66. #19099212C22semidirect
67. #19099211C22semidirect
68. #19099209C22semidirect
69. #19099208C22semidirect
70. #19099206C22semidirect
71. #19099205C22semidirect
72. #19099205C22semidirect
73. #19099204C22semidirect
74. #19099204C22semidirect
75. #19099203C22semidirect
76. #19099202C22semidirect
77. #19099201C22semidirect
78. #19099201C22semidirect
79. D4×D316C22semidirect
80. D4×D316C22semidirect
81. #19099197C22semidirect
82. #19099197C22semidirect
83. D4×C22⋊D79C22semidirect
84. #19099195C22semidirect
85. #19099144C22semidirect
86. #19099143C22semidirect
87. #19099143C22semidirect
88. #19099143C22semidirect
89. #19099143C22semidirect
90. #19099143C22semidirect
91. #19099143C22semidirect
92. #19099143C22semidirect
93. #19099143C22semidirect
94. #19099143C22semidirect
95. #19099143C22semidirect
96. #19099142C22semidirect
97. #19099142C22semidirect
98. #19099142C22semidirect
99. #19099141C22semidirect
100. #19099141C22semidirect
101. #19099140C22semidirect
102. #19099138C22semidirect
103. #19099137C22semidirect
104. #19099136C22semidirect
105. #19099136C22semidirect
106. #19099135C22semidirect
107. #19099132C22semidirect
108. #19099131C22semidirect
109. #19099129C22semidirect
110. #19099129C22semidirect
111. #19099128C22semidirect
112. #19099127C22semidirect
113. #19099124C22semidirect
114. #19099124C22semidirect
115. #19099123C22semidirect
116. #19099114C22semidirect
117. #19099112C22semidirect
118. #19099110C22semidirect
119. #19099110C22semidirect
120. #19099076C22semidirect
121. #19099076C22semidirect
122. #19099075C22semidirect
123. #19099074C22semidirect
124. #19099072C22semidirect
125. #19099072C22semidirect
126. #19099071C22semidirect
127. #19099070C22semidirect
128. C2×#14579139C22semidirect
129. C2×#14579137C22semidirect
130. C22⋊Q8×D79C22semidirect
131. C22⋊Q8×D79C22semidirect
132. C2×#14579136C22semidirect
133. C2×#14579136C22semidirect
134. C2×#14579135C22semidirect
135. C2×#14579134C22semidirect
136. C2×#14579134C22semidirect
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. C2×2−1+4×C79C22semidirect
150. C22×#41×C79C22semidirect
151. D4×Q8×C79C22semidirect
152. #548×C79C22semidirect
153. #547×C79C22semidirect
154. #546×C79C22semidirect
155. #537×C79C22semidirect
156. #536×C79C22semidirect
157. #525×C79C22semidirect
158. C2×C22⋊Q8×C79C22semidirect
159. #520×C79C22semidirect
217. #41×D79D4semidirect
439. #11929625C2×D4semidirect
456. #11929624C2×D4semidirect
464. #11929623C2×D4semidirect
480. Q8×D79C2×D4semidirect
532. D4×D79C2×D4semidirect
543. C2×C4×D79C2×D4semidirect
601. #41×C79C2×D4semidirect
834. #3489D79semidirect
846. C79#62853semidirect
855. C2×2−1+4C2×D79semidirect
873. C22×#41C2×D79semidirect
881. D4×Q8C2×D79semidirect
889. #548C2×D79semidirect
895. #547C2×D79semidirect
907. #546C2×D79semidirect
931. #537C2×D79semidirect
937. #536C2×D79semidirect
959. #525C2×D79semidirect
964. C2×C22⋊Q8C2×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×#190994002
C2×#190993992
#237771702
#237771682
#237771602
#237771582
#237770782
#237770772
#237770762
#237770742
#237770732
#237770702
#237770692
#237770662
#237770642
#237770632
#237770612
#237767322
#237767302
C2×#190991432
#537×D792
#520×D792
C79×#34892
#6285379