Finite Group Databasebeta

← #29658557

Subgroups — #29658557

Order 15616.

1042 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456752C211yesmaximal, characteristic, complemented
2#21455970C211yesmaximal, characteristic, complemented
3#21455274C211yesmaximal, characteristic, complemented
4#21445033C211yesmaximal, characteristic, complemented
5#21445026C211yesmaximal, characteristic, complemented
6#21445005C211yesmaximal, characteristic, complemented
7#21444998C211yesmaximal, characteristic, complemented
8#21444891C211yesmaximal, characteristic, complemented
9#21444891C211yesmaximal, characteristic, complemented
10#21444878C211yesmaximal, characteristic, complemented
11#21444873C211yesmaximal, characteristic, complemented
12#21444514C211yesmaximal, characteristic, complemented
13#21444253C211yesmaximal, characteristic, complemented
14#21444206C211yesmaximal, characteristic, complemented
15C61×#3481C211yesmaximal, characteristic, complemented
16C2×#14519797—21no—
17#16840312C2211yescharacteristic, complemented
18#16840138C2211yescharacteristic
19#16840136C2211yescharacteristic, complemented
20#16840112C2211yescharacteristic, complemented
21#16840108C2211yescharacteristic
22#16840086—21no—
23#16840047C2211yescharacteristic, complemented
24#16840042C2211yescharacteristic
25#16839984—21no—
26#16839977—21no—
27#16839974—22no—
28#16839972C2211yescharacteristic, complemented
29#16839967C2211yescharacteristic
30#16839962C2211yescharacteristic, complemented
31#16839962C2211yescharacteristic, complemented
32#16839957C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839907—21no—
35#16839907—22no—
36#16839872—21no—
37#16839860—21no—
38#16839819C2211yescharacteristic, complemented
39#16839815C2211yescharacteristic, complemented
40C2×C4⋊#92418C2211yescharacteristic, complemented
41#16839756—21no—
42#16839511C2211yescharacteristic, complemented
43#16839511C2211yescharacteristic, complemented
44#16839506C2211yescharacteristic
45#16839506C2211yescharacteristic
46Q8⋊#92418C2211yescharacteristic, complemented
47Q8⋊#92418C2211yescharacteristic, complemented
48Q8⋊#92418C2211yescharacteristic, complemented
49Q8⋊#92418C2211yescharacteristic, complemented
50D4⋊#92418C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54C61×#559C2211yescharacteristic
55C61×#554C2211yescharacteristic
56C61×#554C2211yescharacteristic
57C61×#553—21no—
58C61×#553—21no—
59C61×#551—22no—
60C61×#546—21no—
61C61×#546—21no—
62D42×C61C2211yescharacteristic
63C61×#532C2211yescharacteristic
64C61×#529—21no—
65C61×#529—21no—
66C61×#525—22no—
67C4×#41×C61C2211yescharacteristic
68C4×#41×C61C2211yescharacteristic
69C2×C4×D4×C61—21no—
70C2×C4×D4×C61—21no—
71C2×#11758222—21no—
72#14519797—44no—
73C2×#11758202—21no—
74C2×#11758200—21no—
75C2×#11758201—21no—
76C2×#11758201—21no—
77C2×#11758201—22no—
78C2×#11758199—21no—
79C2×#11758199—21no—
80C2×#11758199—22no—
81C22×#92418—21no—
82#14519777C2311yescharacteristic
83#14519774C2311yescharacteristic
84#14519765—21no—
85#14519751—21no—
86#14519751—21no—
87C4×D244—21no—
88C4×D244—21no—
89#14519710—21no—
90#14519708—21no—
91C4⋊#92418—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—22no—
98#14519701—21no—
99#14519700—21no—
100#14519700—21no—
101#14519698—22no—
102#14519698—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107C22⋊#92418—21no—
108C22⋊#92418—21no—
109#14519688—21no—
110C4×#92418C2311yescharacteristic
111C4×#92418C2311yescharacteristic
112C2×#41×C61D411yescharacteristic
113C2×#41×C61D411yescharacteristic
114C2×#41×C61D412yes—
115C22×D4×C61—21no—
116C22×D4×C61—21no—
117C23×C4×C61—22no—
118C4⋊Q8×C61C2311yescharacteristic
119#127×C61C2311yescharacteristic
120#126×C61—22no—
121#126×C61—22no—
122#125×C61—21no—
123#125×C61—21no—
124#124×C61—21no—
125#124×C61—21no—
126#124×C61D412yes—
127#123×C61—22no—
128#123×C61—22no—
129#123×C61—22no—
130#123×C61—22no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C22⋊Q8×C61—22no—
134C22⋊Q8×C61—22no—
135#121×C61—22no—
136#121×C61—22no—
137#121×C61—21no—
138#121×C61—21no—
139#121×C61—21no—
140#121×C61—21no—
141#120×C61—22no—
142#120×C61—22no—
143C4×Q8×C61D411yescharacteristic
144C4×Q8×C61D411yescharacteristic
145C4×Q8×C61C2311yescharacteristic
146C4×Q8×C61C2311yescharacteristic
147C4×D4×C61—22no—
148C4×D4×C61—22no—
149C4×D4×C61—22no—
150C4×D4×C61—22no—
151C4×D4×C61—21no—
152C4×D4×C61—21no—
153C4×D4×C61—21no—
154C4×D4×C61—21no—
155C4×D4×C61—21no—
156C4×D4×C61—21no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61—21no—
161C4×D4×C61D411yescharacteristic
162C4×D4×C61D411yescharacteristic
163C4×D4×C61C2311yescharacteristic
164C4×D4×C61C2311yescharacteristic
165#117×C61—22no—
166#117×C61—21no—
167#117×C61—21no—
168#117×C61D411yescharacteristic
169#117×C61D411yescharacteristic
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C22⋊C4×C61—22no—
173C2×C22⋊C4×C61—22no—
174C2×C42×C61—21no—
175C2×C42×C61—21no—
176C2×C42×C61C2311yescharacteristic
177C24×C61—22no—
178#41×C61—22no—
179#41×C61—22no—
180#41×C61—41no—
181#41×C61—41no—
182#41×C61—82no—
183C2×Q8×C61C2×D411yescharacteristic
184C2×Q8×C61C2×D411yescharacteristic
185C2×Q8×C61C2×D412yes—
186C2×D4×C61—22no—
187C2×D4×C61—22no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—22no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—42no—
194C2×D4×C61—42no—
195C2×D4×C61—42no—
196C2×D4×C61—42no—
197C2×D4×C61C2×D411yescharacteristic
198C2×D4×C61C2×D411yescharacteristic
199C2×D4×C61C2×D412yes—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—22no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—84no—
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C2×C22⋊D61—41no—
215#11758222—42no—
216#11758222—42no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×C4×D61—41no—
221C2×Dic122—21no—
222C4⋊C4×C61—22no—
223C4⋊C4×C61—22no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—22no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61C2×D411yescharacteristic
233C4⋊C4×C61C2×D411yescharacteristic
234C4⋊C4×C61C2×D411yescharacteristic
235C4⋊C4×C61C2×D411yescharacteristic
236C22⋊C4×C61—22no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—21no—
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—22no—
248C22⋊C4×C61—21no—
249C22⋊C4×C61—21no—
250C42×C61—21no—
251C42×C61—21no—
252C42×C61—21no—
253C42×C61—21no—
254C42×C61—21no—
255C42×C61—21no—
256C42×C61C2×D411yescharacteristic
257C42×C61C2×D411yescharacteristic
258C42×C61C2×D411yescharacteristic
259C42×C61C2411yescharacteristic
260#11758202—42no—
261#11758201—42no—
262#11758201—42no—
263#11758201—82no—
264#11758200—42no—
265#11758199—42no—
266#11758199—42no—
267#11758199—82no—
268#11758198—41no—
269#11758198—41no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—42no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—22no—
282C23×C61—44no—
283C23×C61—44no—
284C23×C61—82no—
285C23×C61#12011yescharacteristic
286C22×D61—41no—
287Q8×C61—21no—
288Q8×C61—21no—
289Q8×C61—21no—
290Q8×C61—21no—
291Q8×C61—42no—
292D4×C61—21no—
293D4×C61—21no—
294D4×C61—42no—
295D4×C61—42no—
296D4×C61—42no—
297D4×C61—44no—
298D4×C61—44no—
299D4×C61—41no—
300D4×C61—41no—
301D4×C61—41no—
302D4×C61—41no—
303D4×C61—82no—
304D4×C61#13512yescomplemented
305D4×C61AGL(1,ℤ/8)12yes—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—22no—
317C2×C4×C61—41no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—44no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—82no—
328C2×C4×C61—82no—
329C2×C4×C61—82no—
330C2×C4×C61#12011yescharacteristic
331C2×C4×C61#12011yescharacteristic
332C2×C4×C61#12011yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C22⋊D61—82no—
337C2×Dic61—41no—
338D244—42no—
339D244—41no—
340D244—41no—
341D244—41no—
342D244—41no—
343C4×D61—82no—
344Dic122—41no—
345Dic122—41no—
346#92418—41no—
347#92418—41no—
348#92418—41no—
349#92418—41no—
350#92418—41no—
351#92418—41no—
352#18754—611nomaximal, Sylow
353C22×C61—21no—
354C22×C61—22no—
355C22×C61—21no—
356C22×C61—22no—
357C22×C61—21no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—88no—
366C22×C61C2×#12011yescharacteristic
367C2×D61—81no—
368C2×D61—81no—
369C2×D61—81no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—41no—
375C4×C61—41no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61—42no—
381C4×C61C2×#13511yescharacteristic
382C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
383C4×C61#57511yescharacteristic
384C4×C61#57511yescharacteristic
385Dic61—81no—
386#3481D6111yescharacteristic, complemented
387#3207—611no—
388#3115—611no—
389#3035—611no—
390#1644—611no—
391#1643—611no—
392#1640—611no—
393#1639—611no—
394#1622—611no—
395#1622—611no—
396#1620—611no—
397#1619—611no—
398#1551—611no—
399#1488—611no—
400#1477—611no—
401C2×C61—41no—
402C2×C61—42no—
403C2×C61—42no—
404C2×C61—82no—
405C2×C61#300211yescharacteristic
406C2×C61#300611yescharacteristic
407C2×C61#301911yescharacteristic
408D61—161no—
409C2×#135—1221no—
410#559C2×D6111yescharacteristic
411#554C2×D6111yescharacteristic
412#554C2×D6111yescharacteristic
413#553—21no—
414#553—21no—
415#551—22no—
416#546—21no—
417#546—21no—
418D42C2×D6111yescharacteristic
419#532—611no—
420#532C2×D6111yescharacteristic
421#529—21no—
422#529—21no—
423#525—22no—
424C4×#41C2×D6111yescharacteristic
425C4×#41C2×D6111yescharacteristic
426C2×C4×D4—21no—
427C2×C4×D4—21no—
428#493—611no—
429#492—611no—
430#487—611no—
431#486—611no—
432#482—1221no—
433#475—611no—
434#474—611no—
435#464—1221no—
436#463—1222no—
437#463—1221no—
438#462—611no—
439#461—611no—
440#460—611no—
441#460—611no—
442#459—611no—
443#459—611no—
444#449—1221no—
445#449—1222no—
446#442—1221no—
447#440—1221no—
448#432—611no—
449#431—611no—
450C2×C4⋊C8—611no—
451#416—1221no—
452#333—611no—
453#333—611no—
454#331—611no—
455#331—611no—
456Q8⋊C8—611no—
457Q8⋊C8—611no—
458Q8⋊C8—611no—
459Q8⋊C8—611no—
460D4⋊C8—611no—
461D4⋊C8—611no—
462D4⋊C8—611no—
463D4⋊C8—611no—
464C61#1875411yescharacteristic, complemented, Sylow
465C2×#41—1221no—
466C2×#41C22⋊D6111yescharacteristic
467C2×#41C22⋊D6111yescharacteristic
468C2×#41C22⋊D6112yes—
469C22×D4—21no—
470C22×D4—21no—
471C23×C4—22no—
472#135—2444no—
473C2×Q16—1221no—
474C2×SD16—1222no—
475C2×SD16—1221no—
476C2×SD16—1221no—
477C2×SD16—1221no—
478C2×D8—1222no—
479C2×D8—1221no—
480C2×D8—1221no—
481C22×C8—1221no—
482C4⋊Q8—611no—
483C4⋊Q8C22×D6111yescharacteristic
484#127—611no—
485#127C22×D6111yescharacteristic
486#126—22no—
487#126—22no—
488#125—21no—
489#125—21no—
490#124—21no—
491#124—21no—
492#124—1221no—
493#124C22⋊D6112yes—
494#123—22no—
495#123—22no—
496#123—22no—
497#123—22no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—1221no—
509#121—1221no—
510#120—22no—
511#120—22no—
512C4×Q8C22⋊D6111yescharacteristic
513C4×Q8C22⋊D6111yescharacteristic
514C4×Q8C22×D6111yescharacteristic
515C4×Q8C22×D6111yescharacteristic
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4C22⋊D6111yescharacteristic
533C4×D4C22⋊D6111yescharacteristic
534C4×D4C22×D6111yescharacteristic
535C4×D4C22×D6111yescharacteristic
536#117—22no—
537#117—21no—
538#117—21no—
539#117C22⋊D6111yescharacteristic
540#117C22⋊D6111yescharacteristic
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C42—21no—
546C2×C42—21no—
547C2×C42C22×D6111yescharacteristic
548#107—1221no—
549#106—1221no—
550C4⋊C8—611no—
551C4⋊C8—611no—
552C4⋊C8—611no—
553C4⋊C8—611no—
554C4⋊C8—1221no—
555C4⋊C8—1221no—
556#103—1221no—
557#103—1222no—
558#103—1221no—
559#103—1221no—
560#102—1221no—
561#102—1222no—
562#102—1221no—
563#102—1221no—
564#102—1221no—
565#102—1221no—
566C22⋊C8—1221no—
567C22⋊C8—1221no—
568#97—1221no—
569C4×C8—611no—
570C4×C8—611no—
571C24—22no—
572#41—22no—
573#41—22no—
574#41—41no—
575#41—41no—
576#41—82no—
577#41—2442no—
578#41—2442no—
579C2×Q8—1221no—
580C2×Q8C2×C22⋊D6111yescharacteristic
581C2×Q8C2×C22⋊D6111yescharacteristic
582C2×Q8C2×C22⋊D6112yes—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—1221no—
597C2×D4—2441no—
598C2×D4C2×C22⋊D6111yescharacteristic
599C2×D4C2×C22⋊D6111yescharacteristic
600C2×D4C2×C22⋊D6112yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—84no—
612C22×C4—2441no—
613C22×C4C2×C22⋊D6111yescharacteristic
614C22×C4C2×C22⋊D6111yescharacteristic
615C22×C4C2×C22⋊D6111yescharacteristic
616Q16—2442no—
617SD16—4882no—
618SD16—2442no—
619SD16—2442no—
620SD16—2442no—
621D8—4882no—
622D8—2442no—
623D8—2442no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—2442no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4C2×C22⋊D6111yescharacteristic
644C4⋊C4C2×C22⋊D6111yescharacteristic
645C4⋊C4C2×C22⋊D6111yescharacteristic
646C4⋊C4C2×C22⋊D6111yescharacteristic
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—2441no—
662C22⋊C4—2441no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42C2×C22⋊D6111yescharacteristic
670C42C2×C22⋊D6111yescharacteristic
671C42C2×C22⋊D6111yescharacteristic
672C42C23×D6111yescharacteristic
673C23—21no—
674C23—21no—
675C23—22no—
676C23—44no—
677C23—44no—
678C23—82no—
679C23—2441no—
680C23#1451974611yescharacteristic
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—42no—
686Q8—2441no—
687Q8—2441no—
688D4—21no—
689D4—21no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—44no—
694D4—44no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—82no—
700D4—4882no—
701D4—2442no—
702D4—2441no—
703D4—2441no—
704D4—2441no—
705D4—2441no—
706D4#1451979712yescomplemented
707D4#1451980212yes—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—4882no—
733C2×C4—2441no—
734C2×C4#1451974611yescharacteristic
735C2×C4#1451974611yescharacteristic
736C2×C4#1451974611yescharacteristic
737C2×C4C22×C22⋊D6111yescharacteristic
738C2×C4C22×C22⋊D6111yescharacteristic
739C2×C4C22×C22⋊D6111yescharacteristic
740C8—2441no—
741C8—2441no—
742C8—2441no—
743C8—2441no—
744C8—2441no—
745C8—2441no—
746C22—21no—
747C22—21no—
748C22—22no—
749C22—21no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—88no—
759C22—4881no—
760C22—4881no—
761C22—4881no—
762C22C2×#1451974611yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—4881no—
775C4C2×#1451979711yescharacteristic
776C4C2×#1451980211yescharacteristic
777C4#1684056011yescharacteristic
778C4#1684056011yescharacteristic
779C2—41no—
780C2—42no—
781C2—42no—
782C2—82no—
783C2—9761no—
784C2#2145503711yescharacteristic
785C2#2145507111yescharacteristic
786C2#2145517611yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3481C2
socleC22×C61C2×#120
hypercenter#3481D61
hypocenterC61#18754
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3481

Complements

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

NH ≅ G/Ntype
1. #21456752C2semidirect
2. #21455970C2semidirect
3. #21455274C2semidirect
4. #21445033C2semidirect
5. #21445026C2semidirect
6. #21445005C2semidirect
7. #21444998C2semidirect
8. #21444891C2semidirect
9. #21444891C2semidirect
10. #21444878C2semidirect
11. #21444873C2semidirect
12. #21444514C2semidirect
13. #21444253C2semidirect
14. #21444206C2semidirect
15. C61×#3481C2semidirect
17. #16840312C22semidirect
19. #16840136C22semidirect
20. #16840112C22semidirect
23. #16840047C22semidirect
28. #16839972C22semidirect
30. #16839962C22semidirect
31. #16839962C22semidirect
38. #16839819C22semidirect
39. #16839815C22semidirect
40. C2×C4⋊#92418C22semidirect
42. #16839511C22semidirect
43. #16839511C22semidirect
46. Q8⋊#92418C22semidirect
47. Q8⋊#92418C22semidirect
48. Q8⋊#92418C22semidirect
49. Q8⋊#92418C22semidirect
304. D4×C61#135semidirect
386. #3481D61semidirect
464. C61#18754semidirect
706. D4#14519797semidirect

Maximal subgroups

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

subgroupindex
#214567522
#214559702
#214552742
#214450332
#214450262
#214450052
#214449982
#214448912
#214448782
#214448732
#214445142
#214442532
#214442062
C61×#34812
#1875461