Finite Group Databasebeta

← #35160910

Subgroups — #35160910

Order 20224.

1678 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777219C211yesmaximal, characteristic, complemented
2#23774662C214yesmaximal, complemented
3#23774647C214yesmaximal, complemented
4#23774636C212yesmaximal, complemented
5#23774636C212yesmaximal, complemented
6#23774627C212yesmaximal, complemented
7#23774618C212yesmaximal, complemented
8#23773949C211yesmaximal, characteristic, complemented
9C2×#19098973C211yesmaximal, characteristic, complemented
10#23773793C211yesmaximal, characteristic, complemented
11#23773745C211yesmaximal, characteristic, complemented
12#23773385C212yesmaximal, complemented
13#23773374C212yesmaximal, complemented
14#23773262C212yesmaximal, complemented
15#23773251C212yesmaximal, complemented
16#23772051C211yesmaximal, characteristic, complemented
17C79×#3512C211yesmaximal, characteristic
18Q8×Dic158—21no—
19#19099292—21no—
20#19099270—22no—
21#19099270—21no—
22D4×Dic158—22no—
23D4×Dic158—21no—
24#19099191C2212yes—
25#19099191C2214yes—
26#19099120C2211yescharacteristic
27#19099120C2212yes—
28C2×#14579161C2211yescharacteristic
29C2×#14579161C2212yes—
30#19099046C2212yes—
31#19098973C2212yes—
32#19098973C2212yes—
33#19098973C2212yes—
34#19098973C2212yes—
35#19098973C2214yes—
36#19098962C2214yes—
37#19098931C2212yes—
38#19098927C2212yes—
39#19098922C2211yescharacteristic
40#19098922C2211yescharacteristic
41#19098922C2211yescharacteristic
42#19098922C2211yescharacteristic
43#19098922C2212yes—
44#19098922C2212yes—
45#19098913C2212yes—
46#19098909C2212yes—
47#19098901C2214yes—
48#19098901C2214yes—
49#19098896C2214yes—
50#19098891C2214yes—
51#19098884C2214yes—
52#19098884C2214yes—
53#19098879C2214yes—
54#19098874C2214yes—
55#19098870C2214yes—
56#19098870C2214yes—
57#19098863C2214yes—
58#19098863C2214yes—
59#19098858C2214yes—
60#19098853C2214yes—
61#19098848C2214yes—
62#19098843C2214yes—
63#19098624C2214yes—
64#19098620C2212yes—
65#19098620C2212yes—
66#19098603C2212yes—
67#19098603C2212yes—
68C2×#14579094C2212yes—
69C2×#14579092C2212yes—
70#19098590C2212yes—
71#19098564C2212yes—
72#19098564C2212yes—
73#19098559C2212yes—
74#19098559C2212yes—
75#19098530C2212yes—
76C4×#11929608C2211yescharacteristic
77C2×#14579072C2211yescharacteristic
78#553×C79—22no—
79#553×C79—22no—
80#553×C79—21no—
81#553×C79—21no—
82#552×C79—21no—
83#552×C79—21no—
84#541×C79C2212yes—
85#540×C79C2212yes—
86#537×C79C2211yescharacteristic
87#537×C79C2211yescharacteristic
88#532×C79C2211yescharacteristic
89#529×C79C2212yes—
90#529×C79C2212yes—
91C2×#125×C79C2211yescharacteristic
92#520×C79C2211yescharacteristic
93#520×C79C2211yescharacteristic
94C4×#41×C79C2211yescharacteristic
95C22×Dic158—21no—
96C22×Dic158—22no—
97C2×#11929608C2312yes—
98C22×C79⋊C8C2312yes—
99#14579161—22no—
100#14579161—21no—
101#14579161—22no—
102#14579161—21no—
103#14579161C2312yes—
104#14579161C2311yescharacteristic
105#14579161C2312yes—
106#14579161C2311yescharacteristic
107#14579161C2314yes—
108#14579160—22no—
109#14579160—24no—
110#14579153C2312yes—
111#14579153C2314yes—
112#14579152—22no—
113#14579152—24no—
114#14579140—21no—
115#14579140—22no—
116#14579140—21no—
117#14579140—22no—
118#14579138—24no—
119#14579138—24no—
120#14579138—24no—
121Q8×Dic79—22no—
122C4×Dic158—22no—
123C4×Dic158—21no—
124C4×Dic158—22no—
125C4×Dic158—21no—
126D4×Dic79—24no—
127D4×Dic79—22no—
128#14579120C2314yes—
129#14579120C2312yes—
130C2×C4⋊Dic79—21no—
131C2×C4⋊Dic79—22no—
132C2×C4⋊Dic79C2314yes—
133C2×C4⋊Dic79C2312yes—
134#14579094C2314yes—
135#14579094C2314yes—
136#14579094C2314yes—
137#14579094C2314yes—
138#14579092C2314yes—
139#14579092C2314yes—
140#14579092C2314yes—
141#14579092C2314yes—
142C4⋊(C79⋊C8)C2314yes—
143C4⋊(C79⋊C8)C2314yes—
144#14579085C2312yes—
145#14579085C2314yes—
146#14579085C2312yes—
147#14579085C2314yes—
148#14579085C2312yes—
149#14579085C2312yes—
150#14579082C2312yes—
151#14579082C2312yes—
152#14579082C2314yes—
153#14579082C2314yes—
154#14579082C2312yes—
155#14579082C2312yes—
156C22⋊(C79⋊C8)C2314yes—
157C22⋊(C79⋊C8)C2314yes—
158#14579072C2312yes—
159#14579072C2311yescharacteristic
160#14579072C2311yescharacteristic
161#14579072C2312yes—
162C4×C79⋊C8C2312yes—
163C2×#41×C79C2311yescharacteristic
164C2×#41×C79C2311yescharacteristic
165C2×#41×C79C2311yescharacteristic
166C4⋊Q8×C79C2311yescharacteristic
167#127×C79C2311yescharacteristic
168#126×C79—22no—
169#126×C79—22no—
170#126×C79—22no—
171#126×C79—22no—
172#125×C79—22no—
173#125×C79—22no—
174#125×C79—21no—
175#125×C79—21no—
176#125×C79C2312yes—
177#125×C79C2312yes—
178#124×C79C2311yescharacteristic
179#124×C79C2311yescharacteristic
180#123×C79—22no—
181#123×C79—22no—
182#123×C79—22no—
183#123×C79—22no—
184C22⋊Q8×C79—21no—
185C22⋊Q8×C79—21no—
186C22⋊Q8×C79C2312yes—
187C22⋊Q8×C79C2312yes—
188#121×C79—21no—
189#121×C79—21no—
190#121×C79—22no—
191#121×C79—22no—
192#121×C79—21no—
193#121×C79—21no—
194#121×C79—22no—
195#121×C79—22no—
196#121×C79C2312yes—
197#121×C79C2312yes—
198C4×Q8×C79D411yescharacteristic
199C4×Q8×C79D411yescharacteristic
200C4×Q8×C79C2312yes—
201C4×Q8×C79C2312yes—
202C4×D4×C79—22no—
203C4×D4×C79—22no—
204C4×D4×C79—22no—
205C4×D4×C79—22no—
206C4×D4×C79—21no—
207C4×D4×C79—21no—
208C4×D4×C79D412yes—
209C4×D4×C79D411yescharacteristic
210C4×D4×C79D412yes—
211C4×D4×C79D411yescharacteristic
212C4×D4×C79C2312yes—
213C4×D4×C79C2312yes—
214#117×C79—21no—
215#117×C79—21no—
216#117×C79—22no—
217#117×C79—22no—
218#117×C79C2312yes—
219#117×C79C2311yescharacteristic
220C2×C4⋊C4×C79—21no—
221C2×C4⋊C4×C79—21no—
222C2×C4⋊C4×C79—21no—
223C2×C4⋊C4×C79—21no—
224C2×C4⋊C4×C79C2311yescharacteristic
225C2×C4⋊C4×C79C2311yescharacteristic
226C2×C42×C79C2311yescharacteristic
227C2×C42×C79C2312yes—
228C2×Dic158—22no—
229C2×Dic158—21no—
230C2×Dic158—21no—
231C2×Dic158—24no—
232C2×Dic158—22no—
233C2×Dic158—84no—
234C2×Dic158—82no—
235C22×Dic79—24no—
236C22×Dic79—22no—
237#11929608—24no—
238C2×C79⋊C8—24no—
239C2×C79⋊C8C2414yes—
240C2×C79⋊C8C2412yes—
241C2×C79⋊C8C2412yes—
242C4⋊Dic79—22no—
243C4⋊Dic79—21no—
244C4⋊Dic79—24no—
245C4⋊Dic79—22no—
246C4⋊Dic79—24no—
247C4⋊Dic79—22no—
248C4⋊Dic79—21no—
249C4⋊Dic79C2414yes—
250C4⋊Dic79C2412yes—
251C4⋊Dic79C2412yes—
252Dic79⋊C4—24no—
253Dic79⋊C4—22no—
254Dic79⋊C4—24no—
255Dic79⋊C4—22no—
256C22⋊Dic79—24no—
257C22⋊Dic79—22no—
258C4×Dic79—24no—
259C4×Dic79—22no—
260#41×C79—24no—
261#41×C79—24no—
262#41×C79—24no—
263C2×Q8×C79C2×D411yescharacteristic
264C2×Q8×C79C2411yescharacteristic
265C2×Q8×C79C2411yescharacteristic
266C2×D4×C79—21no—
267C2×D4×C79—21no—
268C2×D4×C79—22no—
269C2×D4×C79—22no—
270C2×D4×C79—21no—
271C2×D4×C79—21no—
272C2×D4×C79C2×D412yes—
273C2×D4×C79C2×D411yescharacteristic
274C2×D4×C79C2411yescharacteristic
275C2×D4×C79C2411yescharacteristic
276C22×C4×C79—21no—
277C22×C4×C79—21no—
278C22×C4×C79—21no—
279C22×C4×C79—21no—
280C22×C4×C79—22no—
281C22×C4×C79—22no—
282C22×C4×C79C2×D411yescharacteristic
283C22×C4×C79C2×D412yes—
284C22×C4×C79C2×D411yescharacteristic
285C22×C4×C79C2×D412yes—
286C22×C4×C79C2412yes—
287C22×C4×C79C2411yescharacteristic
288C4⋊C4×C79—21no—
289C4⋊C4×C79—21no—
290C4⋊C4×C79—22no—
291C4⋊C4×C79—22no—
292C4⋊C4×C79—22no—
293C4⋊C4×C79—22no—
294C4⋊C4×C79—22no—
295C4⋊C4×C79—22no—
296C4⋊C4×C79—22no—
297C4⋊C4×C79—22no—
298C4⋊C4×C79—21no—
299C4⋊C4×C79—21no—
300C4⋊C4×C79C2×D411yescharacteristic
301C4⋊C4×C79C2×D411yescharacteristic
302C4⋊C4×C79C2×D412yes—
303C4⋊C4×C79C2×D412yes—
304C4⋊C4×C79C2412yes—
305C4⋊C4×C79C2412yes—
306C22⋊C4×C79—22no—
307C22⋊C4×C79—22no—
308C22⋊C4×C79—21no—
309C22⋊C4×C79—21no—
310C22⋊C4×C79—22no—
311C22⋊C4×C79—22no—
312C22⋊C4×C79—22no—
313C22⋊C4×C79—22no—
314C22⋊C4×C79—21no—
315C22⋊C4×C79—21no—
316C22⋊C4×C79C2×D412yes—
317C22⋊C4×C79C2×D412yes—
318C22⋊C4×C79C2×D412yes—
319C42×C79—22no—
320C42×C79—22no—
321C42×C79C2×D412yes—
322C42×C79C2×D412yes—
323C42×C79C2×D411yescharacteristic
324C42×C79C2×D411yescharacteristic
325C42×C79C2411yescharacteristic
326C42×C79C2412yes—
327C42×C79C2411yescharacteristic
328C23×C79—21no—
329C23×C79—21no—
330C23×C79C22×D412yes—
331C23×C79C22×D411yescharacteristic
332Q8×C79—22no—
333Q8×C79—22no—
334Q8×C79—22no—
335D4×C79—24no—
336D4×C79—22no—
337D4×C79—22no—
338D4×C79—22no—
339D4×C79—42no—
340D4×C79—42no—
341D4×C79—81no—
342D4×C79—81no—
343D4×C79—82no—
344D4×C79—82no—
345C2×C4×C79—24no—
346C2×C4×C79—21no—
347C2×C4×C79—21no—
348C2×C4×C79—22no—
349C2×C4×C79—22no—
350C2×C4×C79—42no—
351C2×C4×C79—41no—
352C2×C4×C79—42no—
353C2×C4×C79—41no—
354C2×C4×C79—42no—
355C2×C4×C79—42no—
356C2×C4×C79—82no—
357C2×C4×C79—82no—
358C2×C4×C79—81no—
359C2×C4×C79—81no—
360C2×C4×C79C22×D412yes—
361C2×C4×C79C22×D412yes—
362C2×C4×C79C22×D411yescharacteristic
363C2×C4×C79C22×D412yes—
364C2×C4×C79C22×D411yescharacteristic
365C2×C4×C79C22×D411yescharacteristic
366C2×C4×C79C22×D411yescharacteristic
367C2×C4×C79C22×D411yescharacteristic
368C2×C4×C792−1+414yes—
369C2×C4×C79C2511yescharacteristic
370C2×Dic79—22no—
371C2×Dic79—24no—
372C2×Dic79—22no—
373C2×Dic79—82no—
374C2×Dic79—84no—
375Dic158—42no—
376Dic158—42no—
377Dic158—44no—
378Dic158—84no—
379Dic158—82no—
380C79⋊C8—22no—
381C79⋊C8—22no—
382C79⋊C8—24no—
383C22×C79—21no—
384C22×C79—21no—
385C22×C79—22no—
386C22×C79—22no—
387C22×C79—22no—
388C22×C79—41no—
389C22×C79—41no—
390C22×C79—41no—
391C22×C79—41no—
392C22×C79—41no—
393C22×C79—41no—
394C22×C79#53612yes—
395C22×C79C23×D411yescharacteristic
396C4×C79—21no—
397C4×C79—22no—
398C4×C79—21no—
399C4×C79—21no—
400C4×C79—22no—
401C4×C79—21no—
402C4×C79—22no—
403C4×C79—42no—
404C4×C79—42no—
405C4×C79—41no—
406C4×C79—41no—
407C4×C79#53612yes—
408C4×C79C2×2−1+412yes—
409Dic79—42no—
410Dic79—44no—
411Dic79—42no—
412#60887—791nomaximal, Sylow
413C2×C79—22no—
414C2×C79—42no—
415C2×C79—81no—
416C2×C79—81no—
417C2×C79C2×#53611yescharacteristic
418C2×C79#358511yescharacteristic
419C2×C79#358611yescharacteristic
420#3512D7911yescharacteristic
421#3503—791no—
422#3242—794no—
423#3241—794no—
424#3240—792no—
425#3240—792no—
426#3239—792no—
427#3238—792no—
428#3166—791no—
429C2×#501—791no—
430#3141—791no—
431#3135—791no—
432#3099—792no—
433#3098—792no—
434#3084—792no—
435#3083—792no—
436#2923—791no—
437C79#6088711yescharacteristic, complemented, Sylow
438Q82—1581no—
439#557—1581no—
440#554—1582no—
441#554—1581no—
442#553—22no—
443#553—22no—
444#553—21no—
445#553—21no—
446#552—21no—
447#552—21no—
448D4×Q8—1582no—
449D4×Q8—1581no—
450#544—792no—
451#544—794no—
452#541C2×D7912yes—
453#540C2×D7912yes—
454#537C2×D7911yescharacteristic
455#537C2×D7911yescharacteristic
456#533—791no—
457#533—792no—
458#532C2×D7911yescharacteristic
459C2×C4⋊Q8—791no—
460C2×C4⋊Q8—792no—
461#529C2×D7912yes—
462#529C2×D7912yes—
463C2×#125C2×D7911yescharacteristic
464#520—792no—
465#520C2×D7911yescharacteristic
466#520C2×D7911yescharacteristic
467C4×#41C2×D7911yescharacteristic
468#501—792no—
469#501—792no—
470#501—794no—
471#501—792no—
472#501—792no—
473#499—794no—
474#491—792no—
475#490—792no—
476#489—791no—
477#489—791no—
478#489—791no—
479#489—791no—
480#489—792no—
481#489—792no—
482#487—792no—
483#486—792no—
484#485—794no—
485#485—794no—
486#484—794no—
487#483—794no—
488#482—794no—
489#482—794no—
490#481—794no—
491#480—794no—
492#479—794no—
493#479—794no—
494#478—794no—
495#478—794no—
496#477—794no—
497#476—794no—
498#475—794no—
499#474—794no—
500#433—794no—
501#432—792no—
502#432—792no—
503#428—792no—
504#428—792no—
505C2×#107—792no—
506C2×#106—792no—
507#424—792no—
508#417—792no—
509#417—792no—
510#416—792no—
511#416—792no—
512#408—792no—
513C4×M16—791no—
514C2×#97—791no—
515C2×#41C22×D7911yescharacteristic
516C2×#41C22×D7911yescharacteristic
517C2×#41C22×D7911yescharacteristic
518C22×Q8—1581no—
519C22×Q8—1582no—
520C2×M16—792no—
521C22×C8—792no—
522C4⋊Q8—792no—
523C4⋊Q8—791no—
524C4⋊Q8—794no—
525C4⋊Q8—792no—
526C4⋊Q8—791no—
527C4⋊Q8—1582no—
528C4⋊Q8—1584no—
529C4⋊Q8—1582no—
530C4⋊Q8—1581no—
531C4⋊Q8—1582no—
532C4⋊Q8—1581no—
533C4⋊Q8C22×D7911yescharacteristic
534#127C22×D7911yescharacteristic
535#126—22no—
536#126—22no—
537#126—22no—
538#126—22no—
539#125—22no—
540#125—22no—
541#125—21no—
542#125—21no—
543#125—794no—
544#125—792no—
545#125—1582no—
546#125—1584no—
547#125C22×D7912yes—
548#125C22×D7912yes—
549#124C22×D7911yescharacteristic
550#124C22×D7911yescharacteristic
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—1581no—
558C22⋊Q8—1582no—
559C22⋊Q8—1581no—
560C22⋊Q8—1582no—
561C22⋊Q8—1584no—
562C22⋊Q8—1584no—
563C22⋊Q8—1584no—
564C22⋊Q8C22×D7912yes—
565C22⋊Q8C22×D7912yes—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—21no—
571#121—21no—
572#121—22no—
573#121—22no—
574#121C22×D7912yes—
575#121C22×D7912yes—
576C4×Q8—1582no—
577C4×Q8—1582no—
578C4×Q8—1581no—
579C4×Q8—1582no—
580C4×Q8—1581no—
581C4×Q8C22⋊D7911yescharacteristic
582C4×Q8C22⋊D7911yescharacteristic
583C4×Q8C22×D7912yes—
584C4×Q8C22×D7912yes—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—1584no—
592C4×D4—1582no—
593C4×D4C22⋊D7912yes—
594C4×D4C22⋊D7911yescharacteristic
595C4×D4C22⋊D7912yes—
596C4×D4C22⋊D7911yescharacteristic
597C4×D4C22×D7912yes—
598C4×D4C22×D7912yes—
599#117—21no—
600#117—21no—
601#117—22no—
602#117—22no—
603#117—792no—
604#117—794no—
605#117C22×D7911yescharacteristic
606#117C22×D7912yes—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—792no—
612C2×C4⋊C4—794no—
613C2×C4⋊C4—1581no—
614C2×C4⋊C4—1582no—
615C2×C4⋊C4C22×D7911yescharacteristic
616C2×C4⋊C4C22×D7911yescharacteristic
617C2×C42C22×D7911yescharacteristic
618C2×C42C22×D7912yes—
619#107—794no—
620#107—794no—
621#107—794no—
622#107—794no—
623#106—794no—
624#106—794no—
625#106—794no—
626#106—794no—
627C4⋊C8—794no—
628C4⋊C8—794no—
629#103—792no—
630#103—792no—
631#103—792no—
632#103—792no—
633#103—794no—
634#103—794no—
635#102—792no—
636#102—792no—
637#102—792no—
638#102—792no—
639#102—794no—
640#102—794no—
641C22⋊C8—794no—
642C22⋊C8—794no—
643#97—791no—
644#97—791no—
645#97—792no—
646#97—792no—
647C4×C8—792no—
648#41—24no—
649#41—24no—
650#41—24no—
651C2×Q8—6324no—
652C2×Q8—6322no—
653C2×Q8—1581no—
654C2×Q8—1582no—
655C2×Q8—1581no—
656C2×Q8—1584no—
657C2×Q8—1582no—
658C2×Q8C2×C22⋊D7911yescharacteristic
659C2×Q8C23×D7911yescharacteristic
660C2×Q8C23×D7911yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4C2×C22⋊D7912yes—
668C2×D4C2×C22⋊D7911yescharacteristic
669C2×D4C23×D7911yescharacteristic
670C2×D4C23×D7911yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—1584no—
678C22×C4—1582no—
679C22×C4C2×C22⋊D7911yescharacteristic
680C22×C4C2×C22⋊D7911yescharacteristic
681C22×C4C2×C22⋊D7912yes—
682C22×C4C2×C22⋊D7912yes—
683C22×C4C23×D7912yes—
684C22×C4C23×D7911yescharacteristic
685M16—1584no—
686C2×C8—794no—
687C2×C8—792no—
688C2×C8—792no—
689C2×C8—1584no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—792no—
703C4⋊C4—794no—
704C4⋊C4—792no—
705C4⋊C4—1584no—
706C4⋊C4—1582no—
707C4⋊C4—1584no—
708C4⋊C4—1582no—
709C4⋊C4—1584no—
710C4⋊C4—1582no—
711C4⋊C4—1582no—
712C4⋊C4—1581no—
713C4⋊C4—1584no—
714C4⋊C4—1582no—
715C4⋊C4—1581no—
716C4⋊C4C2×C22⋊D7911yescharacteristic
717C4⋊C4C2×C22⋊D7911yescharacteristic
718C4⋊C4C2×C22⋊D7912yes—
719C4⋊C4C2×C22⋊D7912yes—
720C4⋊C4C23×D7912yes—
721C4⋊C4C23×D7912yes—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—22no—
729C22⋊C4—22no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—1584no—
733C22⋊C4—1582no—
734C22⋊C4C2×C22⋊D7912yes—
735C22⋊C4C2×C22⋊D7912yes—
736C22⋊C4C2×C22⋊D7912yes—
737C42—22no—
738C42—22no—
739C42—1584no—
740C42—1582no—
741C42C2×C22⋊D7912yes—
742C42C2×C22⋊D7912yes—
743C42C2×C22⋊D7911yescharacteristic
744C42C2×C22⋊D7911yescharacteristic
745C42C23×D7911yescharacteristic
746C42C23×D7911yescharacteristic
747C42C23×D7912yes—
748C23—21no—
749C23—21no—
750C23C22×C22⋊D7912yes—
751C23C22×C22⋊D7911yescharacteristic
752Q8—22no—
753Q8—22no—
754Q8—22no—
755Q8—3164no—
756Q8—3162no—
757Q8—3162no—
758Q8—6324no—
759Q8—6322no—
760D4—24no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—42no—
765D4—42no—
766D4—81no—
767D4—81no—
768D4—82no—
769D4—82no—
770C2×C4—24no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—82no—
782C2×C4—82no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—6322no—
786C2×C4—6324no—
787C2×C4—1582no—
788C2×C4—1584no—
789C2×C4—1582no—
790C2×C4C22×C22⋊D7912yes—
791C2×C4C22×C22⋊D7912yes—
792C2×C4C22×C22⋊D7912yes—
793C2×C4C22×C22⋊D7911yescharacteristic
794C2×C4C22×C22⋊D7911yescharacteristic
795C2×C4C22×C22⋊D7911yescharacteristic
796C2×C4C22×C22⋊D7911yescharacteristic
797C2×C4C22×C22⋊D7911yescharacteristic
798C2×C4#1457920814yes—
799C2×C4C24×D7911yescharacteristic
800C8—1582no—
801C8—1582no—
802C8—1584no—
803C22—21no—
804C22—21no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22#1909913412yes—
815C22C23×C22⋊D7911yescharacteristic
816C4—21no—
817C4—22no—
818C4—21no—
819C4—21no—
820C4—22no—
821C4—21no—
822C4—22no—
823C4—42no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—3164no—
828C4—3162no—
829C4—3162no—
830C4#1909913412yes—
831C4C2×#1457920812yes—
832C2—22no—
833C2—42no—
834C2—81no—
835C2—81no—
836C2C2×#1909913411yescharacteristic
837C2#2377817911yescharacteristic
838C2#2377818611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
Fitting, prime radicalC79×#3512C2
socleC22×C79C23×D4
hypercenter#3512D79
hypocenterC79#60887
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3512

Complements

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

NH ≅ G/Ntype
1. #23777219C2semidirect
2. #23774662C2semidirect
3. #23774647C2semidirect
4. #23774636C2semidirect
5. #23774636C2semidirect
6. #23774627C2semidirect
7. #23774618C2semidirect
8. #23773949C2semidirect
9. C2×#19098973C2semidirect
10. #23773793C2semidirect
11. #23773745C2semidirect
12. #23773385C2semidirect
13. #23773374C2semidirect
14. #23773262C2semidirect
15. #23773251C2semidirect
16. #23772051C2semidirect
437. C79#60887semidirect

Maximal subgroups

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

subgroupindex
#237772192
#237746622
#237746472
#237746362
#237746272
#237746182
#237739492
C2×#190989732
#237737932
#237737452
#237733852
#237733742
#237732622
#237732512
#237720512
C79×#35122
#6088779