Finite Group Databasebeta

← #35197140

Subgroups — #35197140

Order 20224.

6528 conjugacy classes of subgroups.

The subgroup lattice has 1718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778037C214yesmaximal, complemented
2#23778024C214yesmaximal, complemented
3#23777902C214yesmaximal, complemented
4#23777890C212yesmaximal, complemented
5#23777873C212yesmaximal, complemented
6#23777845C212yesmaximal, complemented
7#23777740C212yesmaximal, complemented
8#23777613C214yesmaximal, complemented
9#23777494C212yesmaximal, complemented
10#23777483C212yesmaximal, complemented
11#23777449C214yesmaximal, complemented
12#23777415C212yesmaximal, complemented
13#23777380C212yesmaximal, complemented
14#23777366C214yesmaximal, complemented
15#23777294C212yesmaximal, complemented
16#23777265C211yesmaximal, characteristic, complemented
17#23777256C214yesmaximal, complemented
18#23777252C211yesmaximal, characteristic, complemented
19#23777224C212yesmaximal, complemented
20#23777210C211yesmaximal, characteristic, complemented
21#23777203C211yesmaximal, characteristic, complemented
22#23777152C214yesmaximal, complemented
23#23777146C212yesmaximal, complemented
24#23777129C212yesmaximal, complemented
25#23776696C211yesmaximal, characteristic, complemented
26C2×#19099120C211yesmaximal, characteristic, complemented
27C2×#529×C79C211yesmaximal, characteristic, complemented
28#19099316C2218yescomplemented
29#19099315C2218yescomplemented
30#19099315C2218yescomplemented
31#19099310C2218yescomplemented
32#19099298C2212yescomplemented
33#19099296C2214yescomplemented
34#19099295C2214yescomplemented
35#19099295C2214yescomplemented
36Q8×Dic158C2212yescomplemented
37Q8×Dic158C2212yescomplemented
38#19099292C2212yescomplemented
39#19099292C2212yescomplemented
40#19099291C2212yescomplemented
41#19099290C2214yescomplemented
42#19099290C2214yescomplemented
43#19099289C2214yescomplemented
44#19099289C2214yescomplemented
45#19099286C2212yescomplemented
46#19099285C2214yescomplemented
47#19099284C2214yescomplemented
48#19099283C2214yescomplemented
49#19099283C2212yescomplemented
50#19099282C2214yescomplemented
51#19099282C2214yescomplemented
52#19099281C2218yescomplemented
53#19099280C2218yescomplemented
54#19099278C2212yescomplemented
55#19099277C2214yes—
56#19099273C2212yescomplemented
57#19099272C2214yescomplemented
58#19099272C2214yescomplemented
59#19099271C2214yescomplemented
60#19099270C2212yescomplemented
61#19099270C2212yescomplemented
62#19099269C2214yescomplemented
63#19099269C2214yescomplemented
64#19099268C2218yes—
65#19099268C2218yes—
66#19099265C2214yes—
67#19099263C2214yescomplemented
68#19099260C2214yes—
69#19099255C2214yescomplemented
70#19099254C2214yescomplemented
71#19099253C2214yescomplemented
72#19099253C2214yescomplemented
73#19099252C2218yescomplemented
74#19099250C2218yescomplemented
75#19099249C2218yescomplemented
76#19099248C2218yes—
77#19099247C2214yescomplemented
78#19099246C2218yescomplemented
79#19099246C2218yescomplemented
80#19099239C2218yes—
81#19099239C2218yes—
82#19099239C2218yes—
83#19099239C2218yes—
84#19099234C2212yescomplemented
85D4×Dic158C2212yescomplemented
86D4×Dic158C2214yescomplemented
87D4×Dic158C2212yescomplemented
88#19099222C2214yescomplemented
89#19099222C2214yescomplemented
90#19099218C2212yescomplemented
91#19099218C2214yescomplemented
92#19099217C2214yescomplemented
93#19099213C2214yes—
94#19099211C2218yescomplemented
95#19099207C2218yes—
96#19099194C2214yes—
97#19099194C2212yes—
98#19099194C2212yes—
99#19099193C2214yescomplemented
100#19099193C2214yescomplemented
101#19099191C2214yescomplemented
102#19099189C2214yes—
103#19099186C2214yescomplemented
104#19099184C2214yescomplemented
105#19099184C2214yescomplemented
106#19099182C2214yescomplemented
107#19099182C2214yescomplemented
108#19099181C2218yescomplemented
109#19099180C2214yes—
110#19099179C2218yescomplemented
111#19099178C2218yescomplemented
112#19099175C2214yescomplemented
113#19099175C2214yescomplemented
114#19099173C2214yescomplemented
115#19099170C2218yescomplemented
116#19099170C2218yescomplemented
117#19099166C2214yes—
118#19099160C2214yes—
119#19099157C2218yescomplemented
120#19099156C2218yescomplemented
121#19099155C2218yescomplemented
122#19099155C2218yescomplemented
123#19099154C2218yescomplemented
124#19099151C2214yes—
125#19099139C2214yescomplemented
126#19099137C2212yes—
127#19099135C2218yescomplemented
128#19099130C2212yes—
129#19099120C2212yes—
130#19099120C2212yes—
131#19099120C2214yes—
132#19099120C2211yescharacteristic
133#19099120C2211yescharacteristic
134#19099120C2212yes—
135#19099120C2211yescharacteristic
136#19099120C2212yescomplemented
137#19099120C2211yescharacteristic, complemented
138#19099120C2211yescharacteristic, complemented
139#19099120C2212yescomplemented
140#19099120C2211yescharacteristic, complemented
141#19099120C2212yescomplemented
142#19099120C2211yescharacteristic, complemented
143#19099119C2214yescomplemented
144#19099115C2214yescomplemented
145#19099113C2211yescharacteristic
146#19099113C2211yescharacteristic, complemented
147#19099113C2211yescharacteristic, complemented
148#19099108C2214yes—
149C2×#14579161C2211yescharacteristic, complemented
150C2×#14579161C2211yescharacteristic, complemented
151#19099099C2214yescomplemented
152#19099097C2212yes—
153#19099097C2214yes—
154#19099097C2212yes—
155#19099097C2212yescomplemented
156#19099097C2212yescomplemented
157#19099097C2212yescomplemented
158#19099097C2212yescomplemented
159#19099094C2214yes—
160#19099092C2214yescomplemented
161#19099092C2214yescomplemented
162C2×#14579153C2212yescomplemented
163#125×D79C2214yescomplemented
164#19099074C2212yes—
165#19099074C2212yes—
166#19099074C2214yes—
167#19099074C2212yes—
168C2×#14579140C2212yes—
169C2×#14579140C2214yes—
170C2×#14579140C2212yes—
171#19099044C2212yes—
172#19099044C2212yes—
173#19099043C2214yescomplemented
174#19099042C2218yescomplemented
175#19099041C2212yes—
176#19099040C2214yescomplemented
177#19099038C2212yes—
178C4×#11929624C2212yes—
179C4×#11929624C2212yescomplemented
180C4×#11929624C2212yescomplemented
181C2×C4×Dic158C2212yescomplemented
182C2×C4×Dic158C2212yescomplemented
183C2×#14579120C2212yes—
184#529×C79C2212yes—
185#529×C79C2212yes—
186#529×C79C2212yes—
187#529×C79C2212yes—
188#529×C79C2212yes—
189#529×C79C2212yes—
190#529×C79C2212yes—
191#529×C79C2212yes—
192C2×#126×C79C2212yes—
193C2×#125×C79C2211yescharacteristic
194C2×#124×C79C2211yescharacteristic
195C2×#123×C79C2212yes—
196C2×C22⋊Q8×C79C2211yescharacteristic
197C2×#121×C79C2211yescharacteristic
198C2×C4×Q8×C79C2211yescharacteristic
199C2×C4×D4×C79C2212yes—
200C2×C4×D4×C79C2211yescharacteristic
201C2×#117×C79C2212yes—
202C22×C42×C79C2211yescharacteristic
203C2×#11929624C2312yes—
204C2×#11929624C2314yes—
205C2×#11929624C2312yes—
206C2×#11929624C2312yes—
207C2×#11929623C2318yes—
208C22×Dic158C2314yes—
209C22×Dic158C2312yes—
210C22×Dic158C2312yes—
211#14579161C2312yes—
212#14579161C2314yes—
213#14579161C2312yes—
214#14579161C2312yes—
215#14579161C2312yes—
216#14579161C2314yes—
217#14579161C2311yescharacteristic
218#14579161C2311yescharacteristic
219#14579161C2311yescharacteristic
220#14579161C2311yescharacteristic
221#14579161C2311yescharacteristic
222#14579161C2311yescharacteristic
223#14579161C2311yescharacteristic
224#14579161C2312yes—
225#14579161C2312yes—
226#14579160C2318yes—
227#14579160C2318yes—
228#14579160C2314yes—
229#14579160C2318yes—
230#14579160C2314yes—
231#14579160C2318yes—
232#14579160C2314yes—
233#14579160C2314yes—
234#14579159C2314yes—
235#14579158C2311yescharacteristic
236#14579157C2314yes—
237#14579156C2318yes—
238#14579156C2318yes—
239#14579156C2318yes—
240#14579155C2318yes—
241#14579155C2314yes—
242#14579155C2314yes—
243#14579154C2318yes—
244#14579154C2318yes—
245#14579154C2318yes—
246#14579154C2318yes—
247#14579154C2318yes—
248#14579154C2318yes—
249#14579154C2318yes—
250#14579154C2318yes—
251#14579154C2318yes—
252#14579153C2314yes—
253#14579153C2318yes—
254#14579153C2312yes—
255#14579153C2312yes—
256#14579153C2314yes—
257#14579153C2314yes—
258#14579153C2312yes—
259#14579153C2312yes—
260#14579153C2312yes—
261#14579153C2312yes—
262#14579153C2312yes—
263#14579152C2318yes—
264#14579152C2318yes—
265#14579152C2314yes—
266#14579152C2318yes—
267#14579152C2314yes—
268#14579152C2314yes—
269#14579152C2314yes—
270#14579151C2318yes—
271#14579151C2318yes—
272#14579151C2318yes—
273#14579151C2318yes—
274#14579151C2318yes—
275#14579151C2318yes—
276#14579151C2318yes—
277#14579150C2314yes—
278#14579149C2312yes—
279#14579149C2314yes—
280#14579149C2312yes—
281#14579149C2312yes—
282#14579148C2318yes—
283#14579148C2314yes—
284#14579147C2318yes—
285#14579147C2318yes—
286#14579147C2318yes—
287#14579147C2318yes—
288#14579147C2318yes—
289#14579146C2318yes—
290#14579145C2318yes—
291#14579145C2318yes—
292#14579145C2318yes—
293#14579145C2318yes—
294#14579144C2318yes—
295#14579144C2314yes—
296#14579144C2318yes—
297#14579144C2314yes—
298#14579144C2314yes—
299#14579143C2318yes—
300#14579143C2318yes—
301#14579143C2318yes—
302#14579143C2318yes—
303#14579143C2318yes—
304#14579142C2318yes—
305#14579142C2318yes—
306#14579141C2318yes—
307#14579141C2318yes—
308#14579141C2318yes—
309#14579140C2312yes—
310#14579140C2314yes—
311#14579140C2318yes—
312#14579140C2312yes—
313#14579140C2312yes—
314#14579140C2312yes—
315#14579140C2314yes—
316#14579140C2314yes—
317#14579140C2314yes—
318#14579140C2312yes—
319#14579140C2312yes—
320#14579140C2318yes—
321#14579140C2318yes—
322#14579140C2312yes—
323#14579140C2312yes—
324#14579140C2312yes—
325#14579140C2314yes—
326#14579140C2314yes—
327#14579140C2314yes—
328#14579140C2312yes—
329#14579140C2312yes—
330#14579140C2312yes—
331#14579140C2312yes—
332#14579140C2312yes—
333#14579139C2318yes—
334#14579139C2318yes—
335#14579139C2318yes—
336#14579139C2318yes—
337#14579139C2318yes—
338#14579138C2318yes—
339#14579138C2318yes—
340#14579138C2318yes—
341#14579138C2318yes—
342#14579138C2318yes—
343#14579138C2318yes—
344#14579138C2318yes—
345#14579138C2318yes—
346#14579137C2314yes—
347#14579137C2314yes—
348#14579135C2312yes—
349#14579135C2312yes—
350#14579135C2314yes—
351#14579135C2312yes—
352#14579135C2312yes—
353#14579135C2312yes—
354#14579135C2312yes—
355#14579134C2318yes—
356#14579133C2318yes—
357#14579133C2318yes—
358#14579132C2318yes—
359#14579132C2314yes—
360#14579132C2314yes—
361#14579130C2318yes—
362#14579130C2314yes—
363Q8×Dic79C2314yes—
364Q8×Dic79C2314yes—
365Q8×Dic79C2314yes—
366Q8×Dic79C2314yes—
367C4×Dic158C2312yes—
368C4×Dic158C2314yes—
369C4×Dic158C2312yes—
370C4×Dic158C2312yes—
371C4×Dic158C2314yes—
372C4×Dic158C2314yes—
373C4×Dic158C2318yes—
374C4×Dic158C2312yes—
375C4×Dic158C2314yes—
376C4×Dic158C2312yes—
377C4×Dic158C2312yes—
378C4×Dic158C2312yes—
379C4×Dic158C2314yes—
380C4×Dic158C2312yes—
381C4×Dic158C2314yes—
382C4×Dic158C2314yes—
383C4×Dic158C2312yes—
384C4×Dic158C2312yes—
385C4×Dic158C2312yes—
386C4×Dic158C2312yes—
387C4×Dic158C2312yes—
388C4×Dic158C2312yes—
389#14579126C2318yes—
390#14579126C2318yes—
391#14579126C2314yes—
392#14579126C2314yes—
393#14579126C2318yes—
394C4×D316C2312yes—
395C4×D316C2312yes—
396C4×D316C2314yes—
397C4×D316C2312yes—
398C4×D316C2312yes—
399C4×D316C2312yes—
400C4×D316C2312yes—
401D4×Dic79C2318yes—
402D4×Dic79C2314yes—
403D4×Dic79C2314yes—
404D4×Dic79C2314yes—
405D4×Dic79C2314yes—
406#14579123C2314yes—
407#14579123C2314yes—
408C4×C22⋊D79C2318yes—
409C4×C22⋊D79C2314yes—
410C4×C22⋊D79C2318yes—
411C4×C22⋊D79C2314yes—
412C4×C22⋊D79C2318yes—
413C4×C22⋊D79C2314yes—
414C4×C22⋊D79C2314yes—
415C4×C22⋊D79C2314yes—
416C4×C22⋊D79C2314yes—
417(C22⋊D79)⋊C4C2318yes—
418(C22⋊D79)⋊C4C2318yes—
419(C22⋊D79)⋊C4C2318yes—
420(C22⋊D79)⋊C4C2318yes—
421#14579120C2312yes—
422#14579120C2314yes—
423#14579120C2314yes—
424#14579120C2312yes—
425#14579120C2318yes—
426#14579120C2312yes—
427#14579120C2314yes—
428#14579120C2312yes—
429#14579120C2312yes—
430#14579120C2312yes—
431#14579120C2312yes—
432#14579119C2318yes—
433#14579119C2314yes—
434#14579119C2314yes—
435#14579118C2318yes—
436#14579118C2314yes—
437#14579118C2314yes—
438#14579118C2314yes—
439#14579117C2318yes—
440#14579117C2318yes—
441#14579117C2318yes—
442#14579117C2318yes—
443C2×C4⋊Dic79C2312yes—
444C2×C4⋊Dic79C2314yes—
445C2×C4⋊Dic79C2312yes—
446C2×C4⋊Dic79C2312yes—
447C2×C4⋊Dic79C2312yes—
448C2×Dic79⋊C4C2314yes—
449C2×Dic79⋊C4C2318yes—
450C2×Dic79⋊C4C2314yes—
451C4⋊C4×D79C2318yes—
452C4⋊C4×D79C2318yes—
453C4⋊C4×D79C2314yes—
454C4⋊C4×D79C2314yes—
455C2×C22⋊Dic79C2318yes—
456C2×C22⋊Dic79C2314yes—
457C2×C4×Dic79C2314yes—
458C42×D79C2314yes—
459C22×Q8×C79C2311yescharacteristic
460C22×D4×C79C2311yescharacteristic
461C22×D4×C79C2312yes—
462C23×C4×C79C2311yescharacteristic
463C23×C4×C79C2311yescharacteristic
464C23×C4×C79C2311yescharacteristic
465C23×C4×C79C2312yes—
466#126×C79C2314yes—
467#126×C79C2314yes—
468#126×C79C2314yes—
469#126×C79C2314yes—
470#125×C79C2312yes—
471#125×C79C2312yes—
472#125×C79C2312yes—
473#125×C79C2312yes—
474#124×C79C2312yes—
475#124×C79C2312yes—
476#124×C79C2312yes—
477#124×C79C2312yes—
478#123×C79C2314yes—
479#123×C79C2314yes—
480#123×C79C2314yes—
481#123×C79C2314yes—
482C22⋊Q8×C79C2312yes—
483C22⋊Q8×C79C2312yes—
484C22⋊Q8×C79C2312yes—
485C22⋊Q8×C79C2312yes—
486#121×C79C2312yes—
487#121×C79C2312yes—
488#121×C79C2312yes—
489#121×C79C2312yes—
490C4×Q8×C79C2312yes—
491C4×Q8×C79C2312yes—
492C4×Q8×C79C2312yes—
493C4×Q8×C79C2312yes—
494C4×D4×C79C2314yes—
495C4×D4×C79C2314yes—
496C4×D4×C79C2314yes—
497C4×D4×C79C2314yes—
498C4×D4×C79C2312yes—
499C4×D4×C79C2312yes—
500C4×D4×C79C2312yes—
501C4×D4×C79C2312yes—
502#117×C79C2314yes—
503#117×C79C2314yes—
504#117×C79C2314yes—
505#117×C79C2314yes—
506C2×C4⋊C4×C79C2312yes—
507C2×C4⋊C4×C79C2311yescharacteristic
508C2×C4⋊C4×C79C2311yescharacteristic
509C2×C4⋊C4×C79C2312yes—
510C2×C4⋊C4×C79C2312yes—
511C2×C4⋊C4×C79C2312yes—
512C2×C22⋊C4×C79C2312yes—
513C2×C22⋊C4×C79C2312yes—
514C2×C22⋊C4×C79C2312yes—
515C2×C22⋊C4×C79C2312yes—
516C2×C22⋊C4×C79C2312yes—
517C2×C42×C79C2311yescharacteristic
518C2×C42×C79C2311yescharacteristic
519C2×C42×C79C2311yescharacteristic
520C2×C42×C79C2311yescharacteristic
521C2×C42×C79C2311yescharacteristic
522C2×C42×C79C2311yescharacteristic
523C2×C42×C79C2311yescharacteristic
524C2×C42×C79C2311yescharacteristic
525C2×C42×C79C2311yescharacteristic
526C2×C42×C79C2311yescharacteristic
527C2×C42×C79C2311yescharacteristic
528C2×C42×C79C2311yescharacteristic
529C2×C42×C79C2312yes—
530#11929624—28no—
531#11929624—44no—
532#11929624—48no—
533#11929624—44no—
534#11929623—416no—
535C2×Dic158—44no—
536C2×Dic158—48no—
537C2×Dic158—44no—
538C2×Dic158C2412yes—
539C2×Dic158C2412yes—
540C2×Dic158C2412yes—
541C2×Dic158C2412yes—
542C2×Dic158C2418yes—
543C2×Dic158C2412yes—
544C2×Dic158C2414yes—
545C2×Dic158C2414yes—
546C2×Dic158C2412yes—
547C2×Dic158C2418yes—
548C2×Dic158C2412yes—
549C2×D316C2412yes—
550C2×D316C2412yes—
551C2×D316C2412yes—
552C2×C22⋊D79C2414yes—
553C2×C22⋊D79C2414yes—
554C2×C22⋊D79C2418yes—
555C2×C22⋊D79C2418yes—
556C2×C22⋊D79C2414yes—
557C22×Dic79C2414yes—
558C22×Dic79C2414yes—
559C22×Dic79C2418yes—
560C22×Dic79C2418yes—
561C2×C4×D79C2414yes—
562C2×C4×D79C2418yes—
563C2×C4×D79C2414yes—
564C2×C4×D79C2414yes—
565C2×C4×D79C2418yes—
566C4⋊Dic79C2412yes—
567C4⋊Dic79C2412yes—
568C4⋊Dic79C2418yes—
569C4⋊Dic79C2418yes—
570C4⋊Dic79C2412yes—
571C4⋊Dic79C2412yes—
572C4⋊Dic79C2412yes—
573C4⋊Dic79C2412yes—
574C4⋊Dic79C2412yes—
575C4⋊Dic79C2414yes—
576C4⋊Dic79C2414yes—
577C4⋊Dic79C2412yes—
578C4⋊Dic79C2414yes—
579C4⋊Dic79C2414yes—
580C4⋊Dic79C2412yes—
581C4⋊Dic79C2412yes—
582C4⋊Dic79C2412yes—
583C4⋊Dic79C2412yes—
584C4⋊Dic79C2412yes—
585C4⋊Dic79C2412yes—
586C4⋊Dic79C2418yes—
587C4⋊Dic79C2418yes—
588Dic79⋊C4C2414yes—
589Dic79⋊C4C2414yes—
590Dic79⋊C4C2418yes—
591Dic79⋊C4C2418yes—
592Dic79⋊C4C2418yes—
593Dic79⋊C4C2418yes—
594Dic79⋊C4C2414yes—
595Dic79⋊C4C2414yes—
596Dic79⋊C4C2414yes—
597Dic79⋊C4C2414yes—
598Dic79⋊C4C2418yes—
599Dic79⋊C4C2414yes—
600Dic79⋊C4C2414yes—
601Dic79⋊C4C2414yes—
602Dic79⋊C4C2414yes—
603Dic79⋊C4C2418yes—
604Dic79⋊C4C2418yes—
605Dic79⋊C4C2418yes—
606Dic79⋊C4C2414yes—
607Dic79⋊C4C2414yes—
608Dic79⋊C4C2414yes—
609Dic79⋊C4C2414yes—
610C22⋊Dic79C2414yes—
611C22⋊Dic79C2414yes—
612C22⋊Dic79C2414yes—
613C22⋊Dic79C2414yes—
614C22⋊Dic79C2414yes—
615C22⋊Dic79C2418yes—
616C22⋊Dic79C2418yes—
617C22⋊Dic79C2414yes—
618C22⋊Dic79C2418yes—
619C22⋊Dic79C2418yes—
620C22⋊Dic79C2414yes—
621(C2×D79)⋊C4C2414yes—
622(C2×D79)⋊C4C2414yes—
623(C2×D79)⋊C4C2418yes—
624(C2×D79)⋊C4C2414yes—
625(C2×D79)⋊C4C2414yes—
626(C2×D79)⋊C4C2414yes—
627(C2×D79)⋊C4C2414yes—
628(C2×D79)⋊C4C2418yes—
629(C2×D79)⋊C4C2418yes—
630(C2×D79)⋊C4C2418yes—
631C4×Dic79C2414yes—
632C4×Dic79C2414yes—
633C4×Dic79C2414yes—
634C4×Dic79C2414yes—
635C4×Dic79C2414yes—
636C4×Dic79C2414yes—
637C4×Dic79C2414yes—
638C4×Dic79C2418yes—
639C4×Dic79C2418yes—
640C4×Dic79C2418yes—
641C4×Dic79C2418yes—
642C24×C79C2411yescharacteristic
643C24×C79C2412yes—
644C2×Q8×C79—24no—
645C2×Q8×C79C2412yes—
646C2×Q8×C79C2412yes—
647C2×D4×C79—24no—
648C2×D4×C79—44no—
649C2×D4×C79C2414yes—
650C2×D4×C79C2412yes—
651C2×D4×C79C2412yes—
652C2×D4×C79C2414yes—
653C22×C4×C79—24no—
654C22×C4×C79—42no—
655C22×C4×C79—44no—
656C22×C4×C79—42no—
657C22×C4×C79C2411yescharacteristic
658C22×C4×C79C2411yescharacteristic
659C22×C4×C79C2414yes—
660C22×C4×C79C2411yescharacteristic
661C22×C4×C79C2411yescharacteristic
662C22×C4×C79C2411yescharacteristic
663C22×C4×C79C2411yescharacteristic
664C22×C4×C79C2411yescharacteristic
665C22×C4×C79C2411yescharacteristic
666C22×C4×C79C2411yescharacteristic
667C22×C4×C79C2411yescharacteristic
668C22×C4×C79C2412yes—
669C22×C4×C79C2411yescharacteristic
670C22×C4×C79C2411yescharacteristic
671C22×C4×C79C2411yescharacteristic
672C22×C4×C79C2411yescharacteristic
673C22×C4×C79C2411yescharacteristic
674C22×C4×C79C2411yescharacteristic
675C22×C4×C79C2411yescharacteristic
676C22×C4×C79C2412yes—
677C22×C4×C79C2412yes—
678C22×C4×C79C2414yes—
679C22×C4×C79C2411yescharacteristic
680C4⋊C4×C79C2414yes—
681C4⋊C4×C79C2414yes—
682C4⋊C4×C79C2414yes—
683C4⋊C4×C79C2414yes—
684C4⋊C4×C79C2412yes—
685C4⋊C4×C79C2412yes—
686C4⋊C4×C79C2414yes—
687C4⋊C4×C79C2414yes—
688C4⋊C4×C79C2412yes—
689C4⋊C4×C79C2412yes—
690C4⋊C4×C79C2414yes—
691C4⋊C4×C79C2414yes—
692C22⋊C4×C79C2414yes—
693C22⋊C4×C79C2414yes—
694C22⋊C4×C79C2414yes—
695C22⋊C4×C79C2414yes—
696C22⋊C4×C79C2414yes—
697C22⋊C4×C79C2414yes—
698C22⋊C4×C79C2414yes—
699C22⋊C4×C79C2414yes—
700C22⋊C4×C79C2414yes—
701C22⋊C4×C79C2414yes—
702C42×C79C2411yescharacteristic
703C42×C79C2411yescharacteristic
704C42×C79C2411yescharacteristic
705C42×C79C2411yescharacteristic
706C42×C79C2411yescharacteristic
707C42×C79C2411yescharacteristic
708C42×C79C2411yescharacteristic
709C42×C79C2411yescharacteristic
710C42×C79C2411yescharacteristic
711C42×C79C2411yescharacteristic
712C42×C79C2411yescharacteristic
713C42×C79C2411yescharacteristic
714C42×C79C2411yescharacteristic
715C42×C79C2411yescharacteristic
716C42×C79C2411yescharacteristic
717C42×C79C2411yescharacteristic
718C42×C79C2414yes—
719C42×C79C2414yes—
720C23×C79—22no—
721C23×C79—22no—
722C23×C79—24no—
723C23×C79—41no—
724C23×C79—42no—
725C23×C79—42no—
726C23×C79C2511yescharacteristic
727C23×C79C2514yes—
728C23×C79C2511yescharacteristic
729C23×C79C2511yescharacteristic
730C22×D79C2514yes—
731Q8×C79—24no—
732Q8×C79—24no—
733D4×C79—28no—
734D4×C79—24no—
735D4×C79—24no—
736D4×C79—44no—
737C2×C4×C79—22no—
738C2×C4×C79—24no—
739C2×C4×C79—22no—
740C2×C4×C79—22no—
741C2×C4×C79—22no—
742C2×C4×C79—22no—
743C2×C4×C79—22no—
744C2×C4×C79—22no—
745C2×C4×C79—22no—
746C2×C4×C79—28no—
747C2×C4×C79—22no—
748C2×C4×C79—22no—
749C2×C4×C79—41no—
750C2×C4×C79—44no—
751C2×C4×C79—41no—
752C2×C4×C79—41no—
753C2×C4×C79—41no—
754C2×C4×C79—41no—
755C2×C4×C79—41no—
756C2×C4×C79—41no—
757C2×C4×C79—42no—
758C2×C4×C79—42no—
759C2×C4×C792−1+414yes—
760C2×C4×C79C2511yescharacteristic
761C2×C4×C79C2514yes—
762C2×C4×C79C2511yescharacteristic
763C2×C4×C79C2511yescharacteristic
764C2×C4×C79C2514yes—
765C2×C4×C79C2514yes—
766C2×C4×C79C2511yescharacteristic
767C2×C4×C79C2511yescharacteristic
768C2×C4×C79C2511yescharacteristic
769C2×C4×C79C2511yescharacteristic
770C2×C4×C79C2511yescharacteristic
771C2×C4×C79C2511yescharacteristic
772C2×C4×C79C2511yescharacteristic
773C2×C4×C79C2511yescharacteristic
774C2×C4×C79C2511yescharacteristic
775C22⋊D79—28no—
776C22⋊D79—28no—
777C22⋊D79—48no—
778C22⋊D79—48no—
779C22⋊D79—44no—
780C2×Dic79—28no—
781C2×Dic79—44no—
782C2×Dic79—48no—
783C2×Dic79—48no—
784C2×Dic79C2514yes—
785C2×Dic79C2514yes—
786C2×Dic79C2514yes—
787C2×Dic79C2514yes—
788C2×Dic79C2514yes—
789C2×Dic79C2514yes—
790C2×Dic79C2514yes—
791D316—24no—
792D316—24no—
793D316—42no—
794C4×D79—28no—
795C4×D79—48no—
796C4×D79—44no—
797C4×D79—48no—
798C4×D79—44no—
799Dic158—24no—
800Dic158—24no—
801Dic158—24no—
802Dic158—24no—
803Dic158—44no—
804Dic158—42no—
805Dic158—44no—
806Dic158—48no—
807Dic158—42no—
808Dic158—48no—
809Dic158—42no—
810C22×C79—21no—
811C22×C79—21no—
812C22×C79—21no—
813C22×C79—21no—
814C22×C79—21no—
815C22×C79—24no—
816C22×C79—21no—
817C22×C79—24no—
818C22×C79—24no—
819C22×C79—21no—
820C22×C79—44no—
821C22×C79—84no—
822C22×C79C2×2−1+412yes—
823C22×C79#58512yes—
824C22×C79C2611yescharacteristic
825C2×D79—24no—
826C2×D79—24no—
827C2×D79—24no—
828C4×C79—21no—
829C4×C79—21no—
830C4×C79—24no—
831C4×C79—21no—
832C4×C79—21no—
833C4×C79—21no—
834C4×C79—21no—
835C4×C79—24no—
836C4×C79—21no—
837C4×C79—21no—
838C4×C79—21no—
839C4×C79—24no—
840C4×C79C2×2−1+412yes—
841C4×C79C2×2−1+412yes—
842C4×C79#58512yes—
843Dic79—24no—
844Dic79—24no—
845Dic79—24no—
846Dic79—24no—
847Dic79—24no—
848Dic79—24no—
849Dic79—24no—
850#62831—791nomaximal, Sylow
851C2×C79—22no—
852C2×C79—22no—
853C2×C79—41no—
854C2×C79—44no—
855C2×C79C22×2−1+411yescharacteristic
856C2×C79C2×#58511yescharacteristic
857C2×C79C2×#58511yescharacteristic
858D79—44no—
859#3565—794no—
860#3564—794no—
861#3557—794no—
862#3555—792no—
863#3554—792no—
864#3552—792no—
865#3544—792no—
866#3535—794no—
867#3523—792no—
868#3522—792no—
869#3520—794no—
870#3518—792no—
871#3515—794no—
872#3515—792no—
873#3510—792no—
874#3507—794no—
875#3507—791no—
876#3506—791no—
877#3504—792no—
878#3502—791no—
879#3501—791no—
880#3495—792no—
881#3495—794no—
882#3494—792no—
883#3444—791no—
884C2×#533—791no—
885C2×#529D7911yescharacteristic, complemented
886C79#6283111yescharacteristic, complemented, Sylow
887#563—798no—
888#563—798no—
889#563—798no—
890#562—798no—
891#559—794no—
892#559—794no—
893#559—792no—
894#559—794no—
895Q82—792no—
896Q82—792no—
897#557—794no—
898#557—794no—
899#557—794no—
900#557—794no—
901#557—792no—
902#557—792no—
903#557—792no—
904#556—798no—
905#556—794no—
906#556—794no—
907#556—794no—
908#556—794no—
909#556—792no—
910#556—792no—
911#556—794no—
912#556—798no—
913#555—794no—
914#555—792no—
915#554—794no—
916#554—794no—
917#554—794no—
918#554—792no—
919#554—792no—
920#554—792no—
921#554—794no—
922#554—794no—
923#554—798no—
924#554—798no—
925#553—794no—
926#553—794no—
927#553—794no—
928#552—798no—
929#552—798no—
930#552—794no—
931#552—794no—
932#552—794no—
933#552—794no—
934#552—794no—
935#552—798no—
936#552—798no—
937#552—798no—
938#552—798no—
939#551—798no—
940#551—798no—
941#551—798no—
942#551—798no—
943#550—792no—
944D4×Q8—792no—
945D4×Q8—792no—
946D4×Q8—794no—
947#548—794no—
948#548—794no—
949#547—798no—
950#547—794no—
951#547—794no—
952#547—792no—
953#547—794no—
954#546—798no—
955#544—794no—
956#544—794no—
957#544—794no—
958#544—792no—
959#544—792no—
960#544—794no—
961#543—794no—
962#542—798no—
963#542—794no—
964#542—794no—
965#542—798no—
966#542—794no—
967#542—794no—
968#542—798no—
969#542—794no—
970#542—794no—
971#541—798no—
972#541—798no—
973#541—794no—
974#541—794no—
975#541—794no—
976#540—794no—
977#539—798no—
978#539—798no—
979#539—798no—
980#539—798no—
981#539—798no—
982#539—794no—
983#538—794no—
984#536—792no—
985#536—798no—
986#536—794no—
987#535—792no—
988#533—794no—
989#533—794no—
990#533—792no—
991#533—791no—
992#533—791no—
993#533—792no—
994#533—791no—
995#533—791no—
996#533—792no—
997#533—792no—
998#533—792no—
999#533—792no—
1000#533—791no—
1001#533—791no—
1002#533—791no—
1003#533—794no—
1004#532—794no—
1005#532—791no—
1006#532—791no—
1007#532—791no—
1008C2×C4⋊Q8—791no—
1009C2×C4⋊Q8—791no—
1010#529—794no—
1011#529—794no—
1012#529—794no—
1013#529—794no—
1014#529—792no—
1015#529—792no—
1016#529—792no—
1017#529—792no—
1018#529—792no—
1019#529—792no—
1020#529—794no—
1021#529C2×D7912yes—
1022#529C2×D7912yes—
1023#529C2×D7912yes—
1024#529C2×D7912yes—
1025#529C2×D7912yes—
1026#529C2×D7912yes—
1027#529C2×D7912yes—
1028#529C2×D7912yes—
1029C2×#126C2×D7912yes—
1030C2×#125—794no—
1031C2×#125—792no—
1032C2×#125C2×D7911yescharacteristic
1033C2×#124C2×D7911yescharacteristic
1034#525—792no—
1035#525—792no—
1036#525—792no—
1037#525—794no—
1038C2×#123C2×D7912yes—
1039C2×C22⋊Q8—792no—
1040C2×C22⋊Q8—792no—
1041C2×C22⋊Q8—794no—
1042C2×C22⋊Q8C2×D7911yescharacteristic
1043C2×#121C2×D7911yescharacteristic
1044#520—798no—
1045#520—794no—
1046#520—792no—
1047#520—792no—
1048#519—792no—
1049#519—794no—
1050#518—792no—
1051C4×#41—792no—
1052C4×#41—792no—
1053C4×#41—792no—
1054C2×C4×Q8—792no—
1055C2×C4×Q8—792no—
1056C2×C4×Q8C2×D7911yescharacteristic
1057C2×C4×D4C2×D7911yescharacteristic
1058C2×C4×D4C2×D7912yes—
1059C2×#117—792no—
1060C2×#117C2×D7912yes—
1061C22×C42C2×D7911yescharacteristic
1062C2×#41—798no—
1063C2×#41—792no—
1064C2×#41—792no—
1065C2×#41—794no—
1066C2×#41—792no—
1067C22×Q8—792no—
1068C22×Q8—792no—
1069C22×Q8—794no—
1070C22×Q8C22×D7911yescharacteristic
1071C22×D4C22×D7911yescharacteristic
1072C22×D4C22×D7912yes—
1073C23×C4C22×D7911yescharacteristic
1074C23×C4C22×D7912yes—
1075C23×C4C22×D7911yescharacteristic
1076C23×C4C22×D7911yescharacteristic
1077C4⋊Q8—794no—
1078C4⋊Q8—794no—
1079C4⋊Q8—794no—
1080C4⋊Q8—794no—
1081C4⋊Q8—794no—
1082C4⋊Q8—798no—
1083C4⋊Q8—798no—
1084C4⋊Q8—798no—
1085C4⋊Q8—798no—
1086C4⋊Q8—792no—
1087C4⋊Q8—792no—
1088C4⋊Q8—792no—
1089C4⋊Q8—792no—
1090C4⋊Q8—791no—
1091C4⋊Q8—791no—
1092C4⋊Q8—791no—
1093C4⋊Q8—791no—
1094C4⋊Q8—792no—
1095C4⋊Q8—792no—
1096C4⋊Q8—791no—
1097C4⋊Q8—791no—
1098C4⋊Q8—791no—
1099C4⋊Q8—794no—
1100C4⋊Q8—794no—
1101#127—794no—
1102#127—791no—
1103#126—798no—
1104#126—798no—
1105#126—798no—
1106#126—798no—
1107#126—798no—
1108#126—798no—
1109#126—798no—
1110#126—798no—
1111#126—798no—
1112#126—798no—
1113#126—798no—
1114#126—798no—
1115#126—794no—
1116#126—794no—
1117#126—798no—
1118#126C22×D7914yes—
1119#126C22×D7914yes—
1120#126C22×D7914yes—
1121#126C22×D7914yes—
1122#125—798no—
1123#125—798no—
1124#125—794no—
1125#125—794no—
1126#125—794no—
1127#125—794no—
1128#125—798no—
1129#125—798no—
1130#125—798no—
1131#125—798no—
1132#125—798no—
1133#125—798no—
1134#125—798no—
1135#125—798no—
1136#125—792no—
1137#125—792no—
1138#125—794no—
1139#125—794no—
1140#125—792no—
1141#125—792no—
1142#125—792no—
1143#125—792no—
1144#125—792no—
1145#125—794no—
1146#125—798no—
1147#125C22×D7912yes—
1148#125C22×D7912yes—
1149#125C22×D7912yes—
1150#125C22×D7912yes—
1151#124—794no—
1152#124—794no—
1153#124—798no—
1154#124—798no—
1155#124—798no—
1156#124—798no—
1157#124—798no—
1158#124—798no—
1159#124—792no—
1160#124—792no—
1161#124—792no—
1162#124—794no—
1163#124C22×D7912yes—
1164#124C22×D7912yes—
1165#124C22×D7912yes—
1166#124C22×D7912yes—
1167#123—798no—
1168#123—798no—
1169#123—794no—
1170#123—794no—
1171#123—794no—
1172#123—798no—
1173#123—798no—
1174#123—798no—
1175#123—798no—
1176#123—798no—
1177#123—798no—
1178#123—798no—
1179#123—798no—
1180#123—798no—
1181#123—798no—
1182#123—798no—
1183#123—798no—
1184#123C22×D7914yes—
1185#123C22×D7914yes—
1186#123C22×D7914yes—
1187#123C22×D7914yes—
1188C22⋊Q8—794no—
1189C22⋊Q8—794no—
1190C22⋊Q8—792no—
1191C22⋊Q8—792no—
1192C22⋊Q8—792no—
1193C22⋊Q8—792no—
1194C22⋊Q8—792no—
1195C22⋊Q8—794no—
1196C22⋊Q8—792no—
1197C22⋊Q8—792no—
1198C22⋊Q8—792no—
1199C22⋊Q8—792no—
1200C22⋊Q8—794no—
1201C22⋊Q8—794no—
1202C22⋊Q8—794no—
1203C22⋊Q8—798no—
1204C22⋊Q8—794no—
1205C22⋊Q8—794no—
1206C22⋊Q8—798no—
1207C22⋊Q8—792no—
1208C22⋊Q8—792no—
1209C22⋊Q8—792no—
1210C22⋊Q8—792no—
1211C22⋊Q8—792no—
1212C22⋊Q8—794no—
1213C22⋊Q8—798no—
1214C22⋊Q8—798no—
1215C22⋊Q8—798no—
1216C22⋊Q8—798no—
1217C22⋊Q8—798no—
1218C22⋊Q8—798no—
1219C22⋊Q8—798no—
1220C22⋊Q8—798no—
1221C22⋊Q8—798no—
1222C22⋊Q8—798no—
1223C22⋊Q8—798no—
1224C22⋊Q8—798no—
1225C22⋊Q8—798no—
1226C22⋊Q8—798no—
1227C22⋊Q8—798no—
1228C22⋊Q8—798no—
1229C22⋊Q8—798no—
1230C22⋊Q8C22×D7912yes—
1231C22⋊Q8C22×D7912yes—
1232C22⋊Q8C22×D7912yes—
1233C22⋊Q8C22×D7912yes—
1234#121—794no—
1235#121—794no—
1236#121—798no—
1237#121—798no—
1238#121—798no—
1239#121—792no—
1240#121—792no—
1241#121—792no—
1242#121—792no—
1243#121—792no—
1244#121—792no—
1245#121—794no—
1246#121—798no—
1247#121C22×D7912yes—
1248#121C22×D7912yes—
1249#121C22×D7912yes—
1250#121C22×D7912yes—
1251#120—794no—
1252#120—798no—
1253C4×Q8—794no—
1254C4×Q8—794no—
1255C4×Q8—794no—
1256C4×Q8—794no—
1257C4×Q8—798no—
1258C4×Q8—798no—
1259C4×Q8—794no—
1260C4×Q8—798no—
1261C4×Q8—794no—
1262C4×Q8—792no—
1263C4×Q8—792no—
1264C4×Q8—794no—
1265C4×Q8—792no—
1266C4×Q8—792no—
1267C4×Q8—792no—
1268C4×Q8—794no—
1269C4×Q8—792no—
1270C4×Q8—794no—
1271C4×Q8—794no—
1272C4×Q8—792no—
1273C4×Q8—792no—
1274C4×Q8—792no—
1275C4×Q8—792no—
1276C4×Q8—792no—
1277C4×Q8—792no—
1278C4×Q8—792no—
1279C4×Q8—792no—
1280C4×Q8—794no—
1281C4×Q8—794no—
1282C4×Q8—794no—
1283C4×Q8—798no—
1284C4×Q8C22×D7912yes—
1285C4×Q8C22×D7912yes—
1286C4×Q8C22×D7912yes—
1287C4×Q8C22×D7912yes—
1288C4×D4—794no—
1289C4×D4—794no—
1290C4×D4—794no—
1291C4×D4—794no—
1292C4×D4—798no—
1293C4×D4—794no—
1294C4×D4—794no—
1295C4×D4—794no—
1296C4×D4—794no—
1297C4×D4—794no—
1298C4×D4—794no—
1299C4×D4—798no—
1300C4×D4—798no—
1301C4×D4—798no—
1302C4×D4—794no—
1303C4×D4—794no—
1304C4×D4—798no—
1305C4×D4—798no—
1306C4×D4—798no—
1307C4×D4—798no—
1308C4×D4—792no—
1309C4×D4—792no—
1310C4×D4—792no—
1311C4×D4—792no—
1312C4×D4—792no—
1313C4×D4—792no—
1314C4×D4—794no—
1315C4×D4C22×D7914yes—
1316C4×D4C22×D7914yes—
1317C4×D4C22×D7914yes—
1318C4×D4C22×D7914yes—
1319C4×D4C22×D7912yes—
1320C4×D4C22×D7912yes—
1321C4×D4C22×D7912yes—
1322C4×D4C22×D7912yes—
1323#117—792no—
1324#117—792no—
1325#117—794no—
1326#117—794no—
1327#117—792no—
1328#117—792no—
1329#117—792no—
1330#117—792no—
1331#117—792no—
1332#117—794no—
1333#117—798no—
1334#117—798no—
1335#117—794no—
1336#117—794no—
1337#117—798no—
1338#117—798no—
1339#117—798no—
1340#117—798no—
1341#117—794no—
1342#117—794no—
1343#117—794no—
1344#117—798no—
1345#117C22×D7914yes—
1346#117C22×D7914yes—
1347#117C22×D7914yes—
1348#117C22×D7914yes—
1349C2×C4⋊C4—792no—
1350C2×C4⋊C4—792no—
1351C2×C4⋊C4—794no—
1352C2×C4⋊C4—794no—
1353C2×C4⋊C4—792no—
1354C2×C4⋊C4—792no—
1355C2×C4⋊C4—798no—
1356C2×C4⋊C4—794no—
1357C2×C4⋊C4—798no—
1358C2×C4⋊C4—798no—
1359C2×C4⋊C4—794no—
1360C2×C4⋊C4—794no—
1361C2×C4⋊C4C22×D7912yes—
1362C2×C4⋊C4C22×D7912yes—
1363C2×C4⋊C4C22×D7911yescharacteristic
1364C2×C4⋊C4C22×D7912yes—
1365C2×C4⋊C4C22×D7911yescharacteristic
1366C2×C4⋊C4C22×D7912yes—
1367C2×C22⋊C4—794no—
1368C2×C22⋊C4—798no—
1369C2×C22⋊C4C22×D7912yes—
1370C2×C22⋊C4C22×D7912yes—
1371C2×C22⋊C4C22×D7912yes—
1372C2×C22⋊C4C22×D7912yes—
1373C2×C22⋊C4C22×D7912yes—
1374C2×C42—794no—
1375C2×C42—794no—
1376C2×C42C22×D7911yescharacteristic
1377C2×C42C22×D7912yes—
1378C2×C42C22×D7911yescharacteristic
1379C2×C42C22×D7911yescharacteristic
1380C2×C42C22×D7911yescharacteristic
1381C2×C42C22×D7911yescharacteristic
1382C2×C42C22×D7911yescharacteristic
1383C2×C42C22×D7911yescharacteristic
1384C2×C42C22×D7911yescharacteristic
1385C2×C42C22×D7911yescharacteristic
1386C2×C42C22×D7911yescharacteristic
1387C2×C42C22×D7911yescharacteristic
1388C2×C42C22×D7911yescharacteristic
1389C24C23×D7911yescharacteristic
1390C24C23×D7912yes—
1391#41—3168no—
1392#41—3164no—
1393#41—3164no—
1394#41—31616no—
1395#41—1588no—
1396C2×Q8—24no—
1397C2×Q8—3164no—
1398C2×Q8—3168no—
1399C2×Q8—3164no—
1400C2×Q8—792no—
1401C2×Q8—798no—
1402C2×Q8—794no—
1403C2×Q8—794no—
1404C2×Q8—792no—
1405C2×Q8—798no—
1406C2×Q8—792no—
1407C2×Q8—792no—
1408C2×Q8—792no—
1409C2×Q8—792no—
1410C2×Q8—792no—
1411C2×Q8C23×D7912yes—
1412C2×Q8C23×D7912yes—
1413C2×D4—24no—
1414C2×D4—44no—
1415C2×D4—794no—
1416C2×D4—798no—
1417C2×D4—798no—
1418C2×D4—794no—
1419C2×D4—794no—
1420C2×D4—792no—
1421C2×D4—792no—
1422C2×D4—792no—
1423C2×D4C23×D7912yes—
1424C2×D4C23×D7912yes—
1425C2×D4C23×D7914yes—
1426C2×D4C23×D7914yes—
1427C22×C4—24no—
1428C22×C4—42no—
1429C22×C4—44no—
1430C22×C4—42no—
1431C22×C4—794no—
1432C22×C4—798no—
1433C22×C4—798no—
1434C22×C4—794no—
1435C22×C4—794no—
1436C22×C4—798no—
1437C22×C4—798no—
1438C22×C4—794no—
1439C22×C4—794no—
1440C22×C4C23×D7911yescharacteristic
1441C22×C4C23×D7911yescharacteristic
1442C22×C4C23×D7911yescharacteristic
1443C22×C4C23×D7911yescharacteristic
1444C22×C4C23×D7911yescharacteristic
1445C22×C4C23×D7911yescharacteristic
1446C22×C4C23×D7911yescharacteristic
1447C22×C4C23×D7911yescharacteristic
1448C22×C4C23×D7911yescharacteristic
1449C22×C4C23×D7911yescharacteristic
1450C22×C4C23×D7912yes—
1451C22×C4C23×D7914yes—
1452C22×C4C23×D7911yescharacteristic
1453C22×C4C23×D7911yescharacteristic
1454C22×C4C23×D7911yescharacteristic
1455C22×C4C23×D7911yescharacteristic
1456C22×C4C23×D7911yescharacteristic
1457C22×C4C23×D7911yescharacteristic
1458C22×C4C23×D7911yescharacteristic
1459C22×C4C23×D7912yes—
1460C22×C4C23×D7912yes—
1461C22×C4C23×D7914yes—
1462C22×C4C23×D7911yescharacteristic
1463C4⋊C4—794no—
1464C4⋊C4—794no—
1465C4⋊C4—794no—
1466C4⋊C4—794no—
1467C4⋊C4—798no—
1468C4⋊C4—794no—
1469C4⋊C4—794no—
1470C4⋊C4—794no—
1471C4⋊C4—798no—
1472C4⋊C4—798no—
1473C4⋊C4—798no—
1474C4⋊C4—798no—
1475C4⋊C4—794no—
1476C4⋊C4—794no—
1477C4⋊C4—794no—
1478C4⋊C4—798no—
1479C4⋊C4—794no—
1480C4⋊C4—794no—
1481C4⋊C4—794no—
1482C4⋊C4—794no—
1483C4⋊C4—798no—
1484C4⋊C4—798no—
1485C4⋊C4—792no—
1486C4⋊C4—792no—
1487C4⋊C4—792no—
1488C4⋊C4—792no—
1489C4⋊C4—798no—
1490C4⋊C4—792no—
1491C4⋊C4—792no—
1492C4⋊C4—792no—
1493C4⋊C4—794no—
1494C4⋊C4—794no—
1495C4⋊C4—798no—
1496C4⋊C4—792no—
1497C4⋊C4—794no—
1498C4⋊C4—794no—
1499C4⋊C4—792no—
1500C4⋊C4—792no—
1501C4⋊C4—792no—
1502C4⋊C4—792no—
1503C4⋊C4—792no—
1504C4⋊C4—792no—
1505C4⋊C4—798no—
1506C4⋊C4—798no—
1507C4⋊C4C23×D7912yes—
1508C4⋊C4C23×D7912yes—
1509C4⋊C4C23×D7914yes—
1510C4⋊C4C23×D7914yes—
1511C4⋊C4C23×D7914yes—
1512C4⋊C4C23×D7914yes—
1513C4⋊C4C23×D7914yes—
1514C4⋊C4C23×D7912yes—
1515C4⋊C4C23×D7912yes—
1516C4⋊C4C23×D7914yes—
1517C4⋊C4C23×D7914yes—
1518C4⋊C4C23×D7914yes—
1519C22⋊C4—794no—
1520C22⋊C4—794no—
1521C22⋊C4—794no—
1522C22⋊C4—794no—
1523C22⋊C4—794no—
1524C22⋊C4—798no—
1525C22⋊C4—798no—
1526C22⋊C4—794no—
1527C22⋊C4—798no—
1528C22⋊C4—798no—
1529C22⋊C4—794no—
1530C22⋊C4—794no—
1531C22⋊C4—794no—
1532C22⋊C4—798no—
1533C22⋊C4—798no—
1534C22⋊C4—794no—
1535C22⋊C4—794no—
1536C22⋊C4—794no—
1537C22⋊C4—794no—
1538C22⋊C4—798no—
1539C22⋊C4—798no—
1540C22⋊C4C23×D7914yes—
1541C22⋊C4C23×D7914yes—
1542C22⋊C4C23×D7914yes—
1543C22⋊C4C23×D7914yes—
1544C22⋊C4C23×D7914yes—
1545C22⋊C4C23×D7914yes—
1546C22⋊C4C23×D7914yes—
1547C22⋊C4C23×D7914yes—
1548C22⋊C4C23×D7914yes—
1549C22⋊C4C23×D7914yes—
1550C42—794no—
1551C42—794no—
1552C42—794no—
1553C42—794no—
1554C42—794no—
1555C42—794no—
1556C42—794no—
1557C42—798no—
1558C42—798no—
1559C42—798no—
1560C42—798no—
1561C42C23×D7911yescharacteristic
1562C42C23×D7911yescharacteristic
1563C42C23×D7911yescharacteristic
1564C42C23×D7911yescharacteristic
1565C42C23×D7911yescharacteristic
1566C42C23×D7911yescharacteristic
1567C42C23×D7911yescharacteristic
1568C42C23×D7911yescharacteristic
1569C42C23×D7911yescharacteristic
1570C42C23×D7911yescharacteristic
1571C42C23×D7911yescharacteristic
1572C42C23×D7911yescharacteristic
1573C42C23×D7911yescharacteristic
1574C42C23×D7911yescharacteristic
1575C42C23×D7911yescharacteristic
1576C42C23×D7911yescharacteristic
1577C42C23×D7914yes—
1578C42C23×D7914yes—
1579C23—22no—
1580C23—22no—
1581C23—24no—
1582C23—41no—
1583C23—42no—
1584C23—42no—
1585C23—794no—
1586C23C24×D7911yescharacteristic
1587C23C24×D7914yes—
1588C23C24×D7911yescharacteristic
1589C23C24×D7911yescharacteristic
1590Q8—24no—
1591Q8—24no—
1592Q8—3168no—
1593Q8—3162no—
1594Q8—3164no—
1595Q8—3164no—
1596Q8—3162no—
1597Q8—3162no—
1598Q8—3168no—
1599Q8—1584no—
1600Q8—1584no—
1601Q8—1584no—
1602Q8—1584no—
1603D4—28no—
1604D4—24no—
1605D4—24no—
1606D4—44no—
1607D4—3162no—
1608D4—3168no—
1609D4—3164no—
1610D4—3168no—
1611D4—1588no—
1612D4—1588no—
1613D4—1584no—
1614D4—1584no—
1615C2×C4—22no—
1616C2×C4—24no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—28no—
1626C2×C4—22no—
1627C2×C4—41no—
1628C2×C4—44no—
1629C2×C4—41no—
1630C2×C4—41no—
1631C2×C4—41no—
1632C2×C4—41no—
1633C2×C4—42no—
1634C2×C4—41no—
1635C2×C4—41no—
1636C2×C4—42no—
1637C2×C4—3164no—
1638C2×C4—3164no—
1639C2×C4—3168no—
1640C2×C4—3168no—
1641C2×C4—3164no—
1642C2×C4—3168no—
1643C2×C4—3168no—
1644C2×C4—794no—
1645C2×C4—794no—
1646C2×C4—794no—
1647C2×C4—794no—
1648C2×C4—794no—
1649C2×C4—794no—
1650C2×C4—794no—
1651C2×C4—1588no—
1652C2×C4—1588no—
1653C2×C4#1457920814yes—
1654C2×C4C24×D7911yescharacteristic
1655C2×C4C24×D7911yescharacteristic
1656C2×C4C24×D7911yescharacteristic
1657C2×C4C24×D7914yes—
1658C2×C4C24×D7914yes—
1659C2×C4C24×D7914yes—
1660C2×C4C24×D7911yescharacteristic
1661C2×C4C24×D7911yescharacteristic
1662C2×C4C24×D7911yescharacteristic
1663C2×C4C24×D7911yescharacteristic
1664C2×C4C24×D7911yescharacteristic
1665C2×C4C24×D7911yescharacteristic
1666C2×C4C24×D7911yescharacteristic
1667C2×C4C24×D7911yescharacteristic
1668C2×C4C24×D7911yescharacteristic
1669C22—21no—
1670C22—21no—
1671C22—21no—
1672C22—21no—
1673C22—21no—
1674C22—24no—
1675C22—24no—
1676C22—21no—
1677C22—21no—
1678C22—24no—
1679C22—44no—
1680C22—84no—
1681C22—1584no—
1682C22—1584no—
1683C22—1584no—
1684C22C2×#1457920812yes—
1685C22#1909939912yes—
1686C22C25×D7911yescharacteristic
1687C4—21no—
1688C4—21no—
1689C4—24no—
1690C4—21no—
1691C4—21no—
1692C4—21no—
1693C4—24no—
1694C4—21no—
1695C4—21no—
1696C4—21no—
1697C4—21no—
1698C4—24no—
1699C4—1584no—
1700C4—1584no—
1701C4—1584no—
1702C4—1584no—
1703C4—1584no—
1704C4—1584no—
1705C4—1584no—
1706C4C2×#1457920812yes—
1707C4C2×#1457920812yes—
1708C4#1909939912yes—
1709C2—22no—
1710C2—22no—
1711C2—41no—
1712C2—44no—
1713C2—3164no—
1714C2C22×#1457920811yescharacteristic
1715C2C2×#1909939911yescharacteristic
1716C2C2×#1909939911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC2×#529×C79C2
hypercenterC2×#529D79
hypocenterC79#62831
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #23778037C2semidirect
2. #23778024C2semidirect
3. #23777902C2semidirect
4. #23777890C2semidirect
5. #23777873C2semidirect
6. #23777845C2semidirect
7. #23777740C2semidirect
8. #23777613C2semidirect
9. #23777494C2semidirect
10. #23777483C2semidirect
11. #23777449C2semidirect
12. #23777415C2semidirect
13. #23777380C2semidirect
14. #23777366C2semidirect
15. #23777294C2semidirect
16. #23777265C2semidirect
17. #23777256C2semidirect
18. #23777252C2semidirect
19. #23777224C2semidirect
20. #23777210C2semidirect
21. #23777203C2semidirect
22. #23777152C2semidirect
23. #23777146C2semidirect
24. #23777129C2semidirect
25. #23776696C2semidirect
26. C2×#19099120C2semidirect
27. C2×#529×C79C2semidirect
28. #19099316C22semidirect
29. #19099315C22semidirect
30. #19099315C22semidirect
31. #19099310C22semidirect
32. #19099298C22semidirect
33. #19099296C22semidirect
34. #19099295C22semidirect
35. #19099295C22semidirect
36. Q8×Dic158C22semidirect
37. Q8×Dic158C22semidirect
38. #19099292C22semidirect
39. #19099292C22semidirect
40. #19099291C22semidirect
41. #19099290C22semidirect
42. #19099290C22semidirect
43. #19099289C22semidirect
44. #19099289C22semidirect
45. #19099286C22semidirect
46. #19099285C22semidirect
47. #19099284C22semidirect
48. #19099283C22semidirect
49. #19099283C22semidirect
50. #19099282C22semidirect
51. #19099282C22semidirect
52. #19099281C22semidirect
53. #19099280C22semidirect
54. #19099278C22semidirect
56. #19099273C22semidirect
57. #19099272C22semidirect
58. #19099272C22semidirect
59. #19099271C22semidirect
60. #19099270C22semidirect
61. #19099270C22semidirect
62. #19099269C22semidirect
63. #19099269C22semidirect
67. #19099263C22semidirect
69. #19099255C22semidirect
70. #19099254C22semidirect
71. #19099253C22semidirect
72. #19099253C22semidirect
73. #19099252C22semidirect
74. #19099250C22semidirect
75. #19099249C22semidirect
77. #19099247C22semidirect
78. #19099246C22semidirect
79. #19099246C22semidirect
84. #19099234C22semidirect
85. D4×Dic158C22semidirect
86. D4×Dic158C22semidirect
87. D4×Dic158C22semidirect
88. #19099222C22semidirect
89. #19099222C22semidirect
90. #19099218C22semidirect
91. #19099218C22semidirect
92. #19099217C22semidirect
94. #19099211C22semidirect
99. #19099193C22semidirect
100. #19099193C22semidirect
101. #19099191C22semidirect
103. #19099186C22semidirect
104. #19099184C22semidirect
105. #19099184C22semidirect
106. #19099182C22semidirect
107. #19099182C22semidirect
108. #19099181C22semidirect
110. #19099179C22semidirect
111. #19099178C22semidirect
112. #19099175C22semidirect
113. #19099175C22semidirect
114. #19099173C22semidirect
115. #19099170C22semidirect
116. #19099170C22semidirect
119. #19099157C22semidirect
120. #19099156C22semidirect
121. #19099155C22semidirect
122. #19099155C22semidirect
123. #19099154C22semidirect
125. #19099139C22semidirect
127. #19099135C22semidirect
136. #19099120C22semidirect
137. #19099120C22semidirect
138. #19099120C22semidirect
139. #19099120C22semidirect
140. #19099120C22semidirect
141. #19099120C22semidirect
142. #19099120C22semidirect
143. #19099119C22semidirect
144. #19099115C22semidirect
146. #19099113C22semidirect
147. #19099113C22semidirect
149. C2×#14579161C22semidirect
150. C2×#14579161C22semidirect
151. #19099099C22semidirect
155. #19099097C22semidirect
156. #19099097C22semidirect
157. #19099097C22semidirect
158. #19099097C22semidirect
160. #19099092C22semidirect
161. #19099092C22semidirect
162. C2×#14579153C22semidirect
163. #125×D79C22semidirect
173. #19099043C22semidirect
174. #19099042C22semidirect
176. #19099040C22semidirect
179. C4×#11929624C22semidirect
180. C4×#11929624C22semidirect
181. C2×C4×Dic158C22semidirect
182. C2×C4×Dic158C22semidirect
885. C2×#529D79semidirect
886. C79#62831semidirect

Maximal subgroups

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

subgroupindex
#237780372
#237780242
#237779022
#237778902
#237778732
#237778452
#237777402
#237776132
#237774942
#237774832
#237774492
#237774152
#237773802
#237773662
#237772942
#237772652
#237772562
#237772522
#237772242
#237772102
#237772032
#237771522
#237771462
#237771292
#237766962
C2×#190991202
C2×#529×C792
#6283179