Finite Group Databasebeta

← #29656356

Subgroups — #29656356

Order 15616.

1190 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456533C211yesmaximal, characteristic, complemented
2#21455981C211yesmaximal, characteristic, complemented
3#21455616C211yesmaximal, characteristic, complemented
4#21445068C211yesmaximal, characteristic, complemented
5#21445054C211yesmaximal, characteristic, complemented
6#21445012C211yesmaximal, characteristic, complemented
7#21444998C211yesmaximal, characteristic, complemented
8#21444984C211yesmaximal, characteristic, complemented
9#21444970C211yesmaximal, characteristic, complemented
10#21444946C211yesmaximal, characteristic, complemented
11#21444935C211yesmaximal, characteristic, complemented
12#21444541C211yesmaximal, characteristic, complemented
13#21444262C211yesmaximal, characteristic, complemented
14#21444258C211yesmaximal, characteristic, complemented
15D4×#41×C61C211yesmaximal, characteristic
16#16840319C2211yescharacteristic, complemented
17#16840165C2211yescharacteristic, complemented
18#16840134C2211yescharacteristic, complemented
19#16840114C2211yescharacteristic, complemented
20#16840108C2211yescharacteristic, complemented
21#16840103—21no—
22#16840062—21no—
23#16840062—21no—
24#16840057C2211yescharacteristic, complemented
25#16840052C2211yescharacteristic
26#16840052C2211yescharacteristic, complemented
27#16840052C2211yescharacteristic, complemented
28#16840042C2211yescharacteristic
29#16840042C2211yescharacteristic, complemented
30#16840006—22no—
31#16839972C2211yescharacteristic, complemented
32#16839967C2211yescharacteristic, complemented
33#16839924—21no—
34#16839867—21no—
35#16839862—21no—
36#16839862—22no—
37#16839819C2211yescharacteristic, complemented
38#16839802—21no—
39#16839786C2211yescharacteristic, complemented
40#16839767—21no—
41C4×#11758194C2211yescharacteristic, complemented
42#16839508C2211yescharacteristic, complemented
43#16839508C2211yescharacteristic, complemented
44#16839506C2211yescharacteristic, complemented
45#16839506C2211yescharacteristic, complemented
46Q8⋊#92418C2211yescharacteristic, complemented
47Q8⋊#92418C2211yescharacteristic, complemented
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50D4⋊#92418C2211yescharacteristic, complemented
51D4⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54C22×#41×C61—21no—
55C61×#550C2211yescharacteristic
56D4×Q8×C61C2211yescharacteristic
57C61×#548—21no—
58C61×#547—21no—
59C61×#547C2211yescharacteristic
60C61×#546—22no—
61C61×#546—21no—
62D42×C61—21no—
63D42×C61C2211yescharacteristic
64C61×#532—21no—
65C61×#532C2211yescharacteristic
66C61×#525—22no—
67C61×#525—21no—
68C4×#41×C61C2211yescharacteristic
69C2×C4×D4×C61—21no—
70C2×C4×D4×C61C2211yescharacteristic
71C2×#11758202—21no—
72C2×#11758200—21no—
73C2×#11758200—22no—
74C2×#11758194—21no—
75C2×#11758194—21no—
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519769—21no—
79#14519756—21no—
80#14519756—21no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83#14519736—21no—
84#14519710—22no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519708—21no—
89#14519708—21no—
90#14519708—21no—
91C4⋊#92418—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519701—21no—
97#14519700—21no—
98#14519700—21no—
99#14519700—22no—
100#14519698—22no—
101#14519698—21no—
102#14519698—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106C22⋊#92418—21no—
107#14519688—21no—
108#14519688—21no—
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C2×#41×C61—22no—
112C2×#41×C61—22no—
113C2×#41×C61—21no—
114C2×#41×C61—21no—
115C2×#41×C61—21no—
116C2×#41×C61—44no—
117C2×#41×C61—44no—
118C2×#41×C61D411yescharacteristic
119C22×Q8×C61—21no—
120C22×D4×C61—22no—
121C22×D4×C61—21no—
122C22×D4×C61—21no—
123C22×D4×C61D411yescharacteristic
124C23×C4×C61—22no—
125C23×C4×C61—21no—
126C4⋊Q8×C61—21no—
127C4⋊Q8×C61C2311yescharacteristic
128#127×C61—21no—
129#127×C61C2311yescharacteristic
130#124×C61—22no—
131#124×C61—21no—
132#123×C61—22no—
133#123×C61—22no—
134#123×C61—22no—
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61—21no—
137C22⋊Q8×C61—22no—
138C22⋊Q8×C61—21no—
139#121×C61—22no—
140#121×C61—22no—
141#121×C61—21no—
142#121×C61—22no—
143#121×C61—21no—
144#121×C61—21no—
145#121×C61—21no—
146#121×C61—21no—
147#121×C61D412yes—
148#120×C61—22no—
149#120×C61—22no—
150#120×C61—22no—
151C4×Q8×C61D411yescharacteristic
152C4×Q8×C61C2311yescharacteristic
153C4×D4×C61—22no—
154C4×D4×C61—22no—
155C4×D4×C61—22no—
156C4×D4×C61—21no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61—21no—
161C4×D4×C61—21no—
162C4×D4×C61—21no—
163C4×D4×C61D411yescharacteristic
164C4×D4×C61D412yes—
165C4×D4×C61D411yescharacteristic
166C4×D4×C61D411yescharacteristic
167C4×D4×C61C2311yescharacteristic
168C4×D4×C61C2311yescharacteristic
169C4×D4×C61C2311yescharacteristic
170#117×C61—21no—
171#117×C61D411yescharacteristic
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61D411yescharacteristic
174C2×C22⋊C4×C61—22no—
175C2×C22⋊C4×C61—21no—
176C2×C42×C61—21no—
177C2×C42×C61C2311yescharacteristic
178C24×C61—22no—
179C24×C61—21no—
180#41×C61—22no—
181#41×C61—22no—
182#41×C61—48no—
183#41×C61—42no—
184#41×C61—42no—
185#41×C61—48no—
186#41×C61—42no—
187#41×C61—42no—
188#41×C61—42no—
189#41×C61—42no—
190C2×Q8×C61—22no—
191C2×Q8×C61—21no—
192C2×Q8×C61—42no—
193C2×Q8×C61—42no—
194C2×Q8×C61C2×D411yescharacteristic
195C2×D4×C61—21no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—41no—
207C2×D4×C61—42no—
208C2×D4×C61—48no—
209C2×D4×C61—42no—
210C2×D4×C61—42no—
211C2×D4×C61—42no—
212C2×D4×C61C2×D411yescharacteristic
213C2×D4×C61C2×D411yescharacteristic
214C2×D4×C61C2×D411yescharacteristic
215C2×D4×C61C2×D412yes—
216C22×C4×C61—21no—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—22no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—22no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—48no—
229C22×C4×C61—42no—
230C22×C4×C61—42no—
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C2×Dic122—21no—
235C2×Dic122—21no—
236C4⋊C4×C61—22no—
237C4⋊C4×C61—22no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2×D411yescharacteristic
243C4⋊C4×C61C2×D411yescharacteristic
244C4⋊C4×C61C2×D411yescharacteristic
245C4⋊C4×C61C2×D411yescharacteristic
246C4⋊C4×C61C2×D412yes—
247C22⋊C4×C61—22no—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—22no—
250C22⋊C4×C61—22no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—21no—
255C22⋊C4×C61—21no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—21no—
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C42×C61—21no—
261C42×C61—21no—
262C42×C61—21no—
263C42×C61C2×D411yescharacteristic
264C42×C61C2×D411yescharacteristic
265C42×C61C2×D411yescharacteristic
266C42×C61C2411yescharacteristic
267C22⋊Dic61—41no—
268#11758202—42no—
269#11758200—44no—
270#11758200—42no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275#11758196—41no—
276#11758196—41no—
277C4×Dic61—41no—
278#11758194—42no—
279#11758194—42no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—22no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61—44no—
293C23×C61—44no—
294C23×C61—81no—
295C23×C61—82no—
296C23×C61#12011yescharacteristic
297Q8×C61—21no—
298Q8×C61—44no—
299Q8×C61—41no—
300Q8×C61—41no—
301Q8×C61AGL(1,ℤ/8)12yes—
302D4×C61—24no—
303D4×C61—21no—
304D4×C61—21no—
305D4×C61—21no—
306D4×C61—21no—
307D4×C61—42no—
308D4×C61—42no—
309D4×C61—44no—
310D4×C61—44no—
311D4×C61—44no—
312D4×C61—44no—
313D4×C61—44no—
314D4×C61—41no—
315D4×C61—41no—
316D4×C61—41no—
317D4×C61—41no—
318D4×C61—82no—
319D4×C61AGL(1,ℤ/8)12yes—
320D4×C61#13712yes—
321C2×C4×C61—24no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—22no—
331C2×C4×C61—21no—
332C2×C4×C61—41no—
333C2×C4×C61—42no—
334C2×C4×C61—44no—
335C2×C4×C61—44no—
336C2×C4×C61—42no—
337C2×C4×C61—44no—
338C2×C4×C61—42no—
339C2×C4×C61—44no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—81no—
347C2×C4×C61#12011yescharacteristic
348C2×C4×C61#12011yescharacteristic
349C2×C4×C61#12011yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×Dic61—41no—
354C2×Dic61—41no—
355Dic122—42no—
356Dic122—41no—
357Dic122—41no—
358#92418—22no—
359#92418—41no—
360#92418—41no—
361#92418—41no—
362#92418—41no—
363#92418—41no—
364#18555—611nomaximal, Sylow
365C22×C61—21no—
366C22×C61—22no—
367C22×C61—21no—
368C22×C61—22no—
369C22×C61—21no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—42no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—41no—
380C22×C61—84no—
381C22×C61—88no—
382C22×C61C2×#12011yescharacteristic
383C4×C61—21no—
384C4×C61—22no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—41no—
389C4×C61—42no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
394C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
395C4×C61C2×#13711yescharacteristic
396C4×C61#57511yescharacteristic
397Dic61—81no—
398Dic61—81no—
399D4×#41D6111yescharacteristic
400#3182—611no—
401#3116—611no—
402#3077—611no—
403#1649—611no—
404#1647—611no—
405#1641—611no—
406#1639—611no—
407#1637—611no—
408#1635—611no—
409#1631—611no—
410#1629—611no—
411#1557—611no—
412#1490—611no—
413#1489—611no—
414C2×C61—41no—
415C2×C61—42no—
416C2×C61—42no—
417C2×C61—81no—
418C2×C61—82no—
419C2×C61#300311yescharacteristic
420C2×C61#300711yescharacteristic
421C2×C61#301811yescharacteristic
422C22×#41—21no—
423#550C2×D6111yescharacteristic
424D4×Q8C2×D6111yescharacteristic
425#548—21no—
426#547—21no—
427#547C2×D6111yescharacteristic
428#546—22no—
429#546—21no—
430D42—21no—
431D42C2×D6111yescharacteristic
432#533—611no—
433#532—21no—
434#532C2×D6111yescharacteristic
435#525—22no—
436#525—21no—
437C4×#41C2×D6111yescharacteristic
438C2×C4×D4—21no—
439C2×C4×D4C2×D6111yescharacteristic
440#500—611no—
441#492—611no—
442#487—611no—
443#486—611no—
444#485—1221no—
445#478—1221no—
446#478—1221no—
447#477—611no—
448#476—611no—
449#476—611no—
450#476—611no—
451#474—611no—
452#474—611no—
453#468—1222no—
454#462—611no—
455#461—611no—
456#452—1221no—
457#441—1221no—
458#440—1221no—
459#440—1222no—
460#432—611no—
461#428—1221no—
462#423—611no—
463#418—1221no—
464C4×M16—611no—
465#332—611no—
466#332—611no—
467#331—611no—
468#331—611no—
469Q8⋊C8—611no—
470Q8⋊C8—611no—
471D4⋊C8—611no—
472D4⋊C8—611no—
473D4⋊C8—611no—
474D4⋊C8—611no—
475D4⋊C8—611no—
476D4⋊C8—611no—
477C61#1855511yescharacteristic, complemented, Sylow
478C2×#41—22no—
479C2×#41—22no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—44no—
484C2×#41—44no—
485C2×#41C22⋊D6111yescharacteristic
486C22×Q8—21no—
487C22×D4—22no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C22⋊D6111yescharacteristic
491C23×C4—22no—
492C23×C4—21no—
493C2×Q16—1221no—
494C2×SD16—1221no—
495C2×SD16—1222no—
496C2×M16—1221no—
497C2×M16—1221no—
498C4⋊Q8—21no—
499C4⋊Q8—611no—
500C4⋊Q8—611no—
501C4⋊Q8C22×D6111yescharacteristic
502#127—21no—
503#127C22×D6111yescharacteristic
504#125—1221no—
505#124—22no—
506#124—21no—
507#123—22no—
508#123—22no—
509#123—22no—
510C22⋊Q8—22no—
511C22⋊Q8—21no—
512C22⋊Q8—22no—
513C22⋊Q8—21no—
514C22⋊Q8—1221no—
515C22⋊Q8—1221no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121C22⋊D6112yes—
525#120—22no—
526#120—22no—
527#120—22no—
528C4×Q8—1221no—
529C4×Q8—1221no—
530C4×Q8C22⋊D6111yescharacteristic
531C4×Q8C22×D6111yescharacteristic
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4C22⋊D6111yescharacteristic
543C4×D4C22⋊D6111yescharacteristic
544C4×D4C22⋊D6111yescharacteristic
545C4×D4C22⋊D6112yes—
546C4×D4C22×D6111yescharacteristic
547C4×D4C22×D6111yescharacteristic
548C4×D4C22×D6111yescharacteristic
549#117—21no—
550#117—1221no—
551#117C22⋊D6111yescharacteristic
552C2×C4⋊C4—21no—
553C2×C4⋊C4C22⋊D6111yescharacteristic
554C2×C22⋊C4—22no—
555C2×C22⋊C4—21no—
556C2×C42—21no—
557C2×C42C22×D6111yescharacteristic
558#107—1221no—
559#107—1221no—
560#107—1222no—
561#107—1221no—
562#106—1221no—
563#106—1221no—
564#106—1221no—
565C4⋊C8—611no—
566C4⋊C8—611no—
567C4⋊C8—611no—
568C4⋊C8—611no—
569C4⋊C8—1221no—
570#103—1221no—
571#103—1221no—
572#103—1222no—
573#103—1221no—
574#102—1221no—
575#102—1221no—
576#102—1221no—
577#102—1221no—
578#102—1221no—
579#102—1222no—
580C22⋊C8—1221no—
581#97—1221no—
582#97—1221no—
583C4×C8—611no—
584C4×C8—611no—
585C24—22no—
586C24—21no—
587#41—22no—
588#41—22no—
589#41—48no—
590#41—42no—
591#41—42no—
592#41—48no—
593#41—42no—
594#41—42no—
595#41—42no—
596#41—42no—
597C2×Q8—22no—
598C2×Q8—21no—
599C2×Q8—42no—
600C2×Q8—42no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×Q8C2×C22⋊D6111yescharacteristic
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—41no—
616C2×D4—48no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4C2×C22⋊D6111yescharacteristic
622C2×D4C2×C22⋊D6111yescharacteristic
623C2×D4C2×C22⋊D6111yescharacteristic
624C2×D4C2×C22⋊D6112yes—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—48no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4C2×C22⋊D6111yescharacteristic
641C22×C4C2×C22⋊D6111yescharacteristic
642C22×C4C2×C22⋊D6111yescharacteristic
643Q16—2442no—
644SD16—2444no—
645SD16—2442no—
646M16—2442no—
647M16—2442no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—2441no—
665C4⋊C4—2441no—
666C4⋊C4C2×C22⋊D6111yescharacteristic
667C4⋊C4C2×C22⋊D6111yescharacteristic
668C4⋊C4C2×C22⋊D6112yes—
669C4⋊C4C2×C22⋊D6111yescharacteristic
670C4⋊C4C2×C22⋊D6111yescharacteristic
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—22no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—22no—
684C22⋊C4—2441no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—2441no—
689C42C2×C22⋊D6111yescharacteristic
690C42C2×C22⋊D6111yescharacteristic
691C42C2×C22⋊D6111yescharacteristic
692C42C23×D6111yescharacteristic
693C23—21no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—42no—
698C23—42no—
699C23—44no—
700C23—44no—
701C23—81no—
702C23—82no—
703C23#1451974611yescharacteristic
704Q8—21no—
705Q8—44no—
706Q8—41no—
707Q8—41no—
708Q8—2442no—
709Q8—2441no—
710Q8—2441no—
711Q8#1451980312yes—
712D4—24no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—21no—
717D4—42no—
718D4—42no—
719D4—44no—
720D4—44no—
721D4—44no—
722D4—44no—
723D4—44no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—82no—
729D4#1451980312yes—
730D4#1451980712yes—
731C2×C4—24no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—81no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4#1451974611yescharacteristic
760C2×C4#1451974611yescharacteristic
761C2×C4#1451974611yescharacteristic
762C2×C4C22×C22⋊D6111yescharacteristic
763C2×C4C22×C22⋊D6111yescharacteristic
764C2×C4C22×C22⋊D6111yescharacteristic
765C8—1222no—
766C8—2441no—
767C8—2441no—
768C8—2441no—
769C8—2441no—
770C8—2441no—
771C22—21no—
772C22—21no—
773C22—22no—
774C22—21no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—41no—
784C22—41no—
785C22—42no—
786C22—84no—
787C22—88no—
788C22C2×#1451974611yescharacteristic
789C4—21no—
790C4—21no—
791C4—21no—
792C4—22no—
793C4—21no—
794C4—41no—
795C4—41no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—4881no—
800C4—4881no—
801C4C2×#1451980311yescharacteristic
802C4C2×#1451980311yescharacteristic
803C4C2×#1451980711yescharacteristic
804C4#1684056011yescharacteristic
805C2—41no—
806C2—42no—
807C2—42no—
808C2—82no—
809C2—81no—
810C2#2145504611yescharacteristic
811C2#2145507911yescharacteristic
812C2#2145516811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalD4×#41×C61C2
socleC22×C61C2×#120
hypercenterD4×#41D61
hypocenterC61#18555
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. #21456533C2semidirect
2. #21455981C2semidirect
3. #21455616C2semidirect
4. #21445068C2semidirect
5. #21445054C2semidirect
6. #21445012C2semidirect
7. #21444998C2semidirect
8. #21444984C2semidirect
9. #21444970C2semidirect
10. #21444946C2semidirect
11. #21444935C2semidirect
12. #21444541C2semidirect
13. #21444262C2semidirect
14. #21444258C2semidirect
16. #16840319C22semidirect
17. #16840165C22semidirect
18. #16840134C22semidirect
19. #16840114C22semidirect
20. #16840108C22semidirect
24. #16840057C22semidirect
26. #16840052C22semidirect
27. #16840052C22semidirect
29. #16840042C22semidirect
31. #16839972C22semidirect
32. #16839967C22semidirect
37. #16839819C22semidirect
39. #16839786C22semidirect
41. C4×#11758194C22semidirect
42. #16839508C22semidirect
43. #16839508C22semidirect
44. #16839506C22semidirect
45. #16839506C22semidirect
46. Q8⋊#92418C22semidirect
47. Q8⋊#92418C22semidirect
50. D4⋊#92418C22semidirect
51. D4⋊#92418C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
477. C61#18555semidirect

Maximal subgroups

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

subgroupindex
#214565332
#214559812
#214556162
#214450682
#214450542
#214450122
#214449982
#214449842
#214449702
#214449462
#214449352
#214445412
#214442622
#214442582
D4×#41×C612
#1855561