Finite Group Databasebeta

← #29648844

Subgroups — #29648844

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459730C211yesmaximal, characteristic
2#21454485C211yesmaximal, characteristic, complemented
3#21444556C211yesmaximal, characteristic, complemented
4#21444542C211yesmaximal, characteristic, complemented
5#21444539C211yesmaximal, characteristic, complemented
6#21444537C211yesmaximal, characteristic, complemented
7#21444525C211yesmaximal, characteristic, complemented
8#21444522C211yesmaximal, characteristic, complemented
9#21444520C211yesmaximal, characteristic, complemented
10#21444517C211yesmaximal, characteristic, complemented
11#21444497C211yesmaximal, characteristic, complemented
12#21444492C211yesmaximal, characteristic, complemented
13#21444483C211yesmaximal, characteristic, complemented
14#21444469C211yesmaximal, characteristic, complemented
15C61×#2989C211yesmaximal, characteristic, complemented
16#16840485—21no—
17#16840477C412yes—
18#16840472C412yes—
19#16840458C412yes—
20#16840458C412yes—
21#16840421—21no—
22#16840421—21no—
23#16840417—21no—
24#16840383—21no—
25#16840383—21no—
26#16840340—21no—
27#16840319C2211yescharacteristic
28#16840319C2211yescharacteristic
29#16840312C2211yescharacteristic
30#16840312C2211yescharacteristic
31#16840312C2211yescharacteristic
32C2×#14519777C2211yescharacteristic
33#16840242—21no—
34#16839823—21no—
35#16839823—21no—
36#16839819C2211yescharacteristic
37#16839819C2211yescharacteristic
38#16839815C2211yescharacteristic
39#16839815C2211yescharacteristic
40#16839786C2211yescharacteristic
41C2×C4⋊#92418C2211yescharacteristic
42#16839729—21no—
43#16839718—21no—
44#16839509C2211yescharacteristic
45#16839509C2211yescharacteristic
46#16839509C2211yescharacteristic
47#16839509C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839509C2211yescharacteristic
50#16839509C2211yescharacteristic
51#16839509C2211yescharacteristic
52#16839507C2211yescharacteristic
53#16839507C2211yescharacteristic
54#16839507C2211yescharacteristic
55#16839507C2211yescharacteristic
56#16839505C2211yescharacteristic
57#16839505C2211yescharacteristic
58#16839505C2211yescharacteristic
59#16839505C2211yescharacteristic
60C4×#41×C61C2211yescharacteristic
61C61×#446—21no—
62C61×#436—21no—
63C61×#435—21no—
64C61×#435—21no—
65C61×#432C2211yescharacteristic
66C61×#432C2211yescharacteristic
67C61×#431C2211yescharacteristic
68C61×#423C2211yescharacteristic
69C61×#423C2211yescharacteristic
70C2×C4⋊C8×C61C2211yescharacteristic
71C2×#11758222—21no—
72C2×#11758222—21no—
73C2×#11758222—21no—
74C22×Dic122—21no—
75C2×#11758194—21no—
76C22×#92418—21no—
77#14519777—21no—
78#14519777—21no—
79#14519777C2×C412yes—
80#14519777C2311yescharacteristic
81#14519777C2311yescharacteristic
82#14519777C2311yescharacteristic
83#14519774C2311yescharacteristic
84#14519772—22no—
85#14519772—22no—
86#14519769C2×C412yes—
87#14519769C2×C412yes—
88#14519765—21no—
89#14519765—21no—
90#14519765—21no—
91#14519763—22no—
92#14519763—22no—
93#14519759—22no—
94#14519759—22no—
95#14519756—21no—
96#14519756—21no—
97#14519756—21no—
98#14519756—21no—
99#14519755—22no—
100#14519755—22no—
101#14519753—22no—
102#14519751—21no—
103#14519751—21no—
104#14519751—21no—
105#14519751C2×C412yes—
106#14519751C2×C412yes—
107#14519751C2×C412yes—
108#14519749—22no—
109#14519749—22no—
110#14519748—22no—
111C4×Dic122—21no—
112C4×Dic122—21no—
113C4×Dic122—21no—
114C4×Dic122—21no—
115C4×D244—21no—
116C4×D244—21no—
117C4×D244—21no—
118C4×D244C2×C412yes—
119C4×D244C2×C412yes—
120C4×D244C2×C412yes—
121#14519737—22no—
122#14519737—22no—
123#14519736C2×C412yes—
124#14519736C2×C412yes—
125#14519735—22no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61C2×C412yes—
128C4⋊C4×D61—22no—
129C4⋊#92418—21no—
130C4⋊#92418—21no—
131C4⋊#92418C2311yescharacteristic
132C4⋊#92418C2311yescharacteristic
133C4⋊#92418C2311yescharacteristic
134C4⋊#92418C2311yescharacteristic
135C22⋊#92418—21no—
136C22⋊#92418—21no—
137C22⋊#92418—21no—
138C22⋊#92418—21no—
139#14519688—21no—
140#14519688—21no—
141C4×#92418—21no—
142C4×#92418—21no—
143C2×#41×C61D411yescharacteristic
144C2×M16×C61—21no—
145C2×M16×C61—21no—
146C22×C8×C61—21no—
147C4×Q8×C61C2×C411yescharacteristic
148C4×Q8×C61D411yescharacteristic
149C4×D4×C61C2×C411yescharacteristic
150C4×D4×C61C2×C411yescharacteristic
151C4×D4×C61C2×C411yescharacteristic
152C4×D4×C61D411yescharacteristic
153C4×D4×C61D411yescharacteristic
154C4×D4×C61D411yescharacteristic
155#117×C61D411yescharacteristic
156#117×C61D411yescharacteristic
157#117×C61D411yescharacteristic
158C2×C42×C61C2311yescharacteristic
159C2×C42×C61C2311yescharacteristic
160C2×C42×C61C2311yescharacteristic
161C4⋊C8×C61—21no—
162C4⋊C8×C61—21no—
163C4⋊C8×C61—21no—
164C4⋊C8×C61C2311yescharacteristic
165C4⋊C8×C61C2311yescharacteristic
166C4⋊C8×C61C2311yescharacteristic
167C4⋊C8×C61C2311yescharacteristic
168C22⋊C8×C61—21no—
169C22⋊C8×C61—21no—
170C22⋊C8×C61—21no—
171#97×C61—21no—
172#97×C61—21no—
173C4×C8×C61—21no—
174#41×C61—41no—
175#41×C61—41no—
176C2×Q8×C61C22⋊C411yescharacteristic
177C2×D4×C61C22⋊C411yescharacteristic
178C2×D4×C61C22⋊C411yescharacteristic
179C2×D4×C61C22⋊C411yescharacteristic
180C22×C4×C61C22×C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C22×Dic61—22no—
193#11758222—42no—
194#11758222—42no—
195#11758222—81no—
196#11758222—81no—
197#11758222—81no—
198#11758222—81no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244C22×C412yes—
202C2×C4×D61—22no—
203C2×C4×D61—22no—
204C2×C4×D61—22no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—22no—
209C2×Dic122—81no—
210C2×Dic122—81no—
211M16×C61—81no—
212M16×C61—81no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—81no—
218C4⋊C4×C61C22⋊C411yescharacteristic
219C4⋊C4×C61C22⋊C411yescharacteristic
220C4⋊C4×C61C22⋊C411yescharacteristic
221C4⋊C4×C61C22⋊C411yescharacteristic
222C4⋊C4×C61C22⋊C411yescharacteristic
223C4⋊C4×C61C22⋊C411yescharacteristic
224C22⋊C4×C61C22⋊C411yescharacteristic
225C22⋊C4×C61C22⋊C411yescharacteristic
226C22⋊C4×C61C22⋊C411yescharacteristic
227C22⋊C4×C61C22⋊C411yescharacteristic
228C22⋊C4×C61C22⋊C411yescharacteristic
229C22⋊C4×C61C22⋊C411yescharacteristic
230C42×C61C22×C411yescharacteristic
231C42×C61C22×C411yescharacteristic
232C42×C61C22×C411yescharacteristic
233C42×C61C2×D411yescharacteristic
234C42×C61C2×D411yescharacteristic
235C42×C61C2×D411yescharacteristic
236C42×C61C2×D411yescharacteristic
237C42×C61C2×D411yescharacteristic
238C42×C61C2×D411yescharacteristic
239C42×C61C2411yescharacteristic
240C22⋊Dic61—22no—
241C22⋊Dic61—22no—
242#11758198—22no—
243#11758198—22no—
244#11758198—22no—
245#11758198—22no—
246#11758198—22no—
247#11758198—22no—
248C4⋊Dic61—22no—
249C4⋊Dic61—22no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61C22×C412yes—
254C4⋊Dic61C22×C412yes—
255C4⋊Dic61C22×C412yes—
256#11758196—22no—
257#11758196—22no—
258#11758196—22no—
259#11758196—22no—
260C4×Dic61—22no—
261C4×Dic61—22no—
262#11758194—42no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—42no—
268C23×C61C2×C22⋊C411yescharacteristic
269C23×C61C2×C22⋊C411yescharacteristic
270C23×C61C2×C22⋊C411yescharacteristic
271C22×D61—22no—
272Q8×C61—41no—
273D4×C61—41no—
274D4×C61—41no—
275D4×C61—41no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C2×C4×C61C2×C22⋊C411yescharacteristic
300C2×C4×C61C23×C411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C22⋊D61—44no—
304C22⋊D61—82no—
305C22⋊D61—82no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—82no—
310D244—42no—
311D244—41no—
312D244—41no—
313D244—41no—
314D244—41no—
315C4×D61—44no—
316C4×D61—82no—
317C4×D61—82no—
318Dic122—41no—
319Dic122—41no—
320Dic122—41no—
321Dic122—41no—
322Dic122—41no—
323Dic122—41no—
324Dic122—82no—
325C8×C61—41no—
326C8×C61—41no—
327C8×C61—41no—
328C8×C61—41no—
329#92418—41no—
330#92418—41no—
331#92418—41no—
332#92418—41no—
333#17769—611nomaximal, Sylow
334C22×C61—21no—
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—21no—
343C22×C61C22×C22⋊C411yescharacteristic
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C4×C61—21no—
348C4×C61—21no—
349C4×C61—21no—
350C4×C61—21no—
351C4×C61—21no—
352C4×C61—21no—
353C4×C61—21no—
354C4×C61—21no—
355C4×C61—21no—
356C4×C61—21no—
357C4×C61#57511yescharacteristic
358C4×C61#57511yescharacteristic
359C4×C61#57611yescharacteristic
360C4×C61#57711yescharacteristic
361Dic61—42no—
362Dic61—42no—
363Dic61—42no—
364#3511—611no—
365#2989D6111yescharacteristic, complemented
366#2925—611no—
367#1561—611no—
368#1557—611no—
369#1557—611no—
370#1556—611no—
371#1553—611no—
372#1553—611no—
373#1552—611no—
374#1552—611no—
375#1547—611no—
376#1546—611no—
377#1544—611no—
378#1540—611no—
379C2×C61—41no—
380C2×C61—41no—
381C2×C61—41no—
382C2×C61#288911yescharacteristic
383C2×C61#289611yescharacteristic
384C2×C61#289711yescharacteristic
385D61—82no—
386#556—1221no—
387#555—612no—
388#554—612no—
389#553—612no—
390#553—612no—
391#548—1221no—
392#548—1221no—
393#547—1221no—
394#542—1221no—
395#542—1221no—
396#537—1221no—
397#533—611no—
398#533—611no—
399#532—611no—
400#532—611no—
401#532—611no—
402C2×C4⋊Q8—611no—
403#520—1221no—
404C4×#41C2×D6111yescharacteristic
405#446—21no—
406#436—21no—
407#435—21no—
408#435—21no—
409#433—1221no—
410#433—1221no—
411#432—611no—
412#432—611no—
413#432C2×D6111yescharacteristic
414#432C2×D6111yescharacteristic
415#431—611no—
416#431—611no—
417#431C2×D6111yescharacteristic
418#423—611no—
419#423C2×D6111yescharacteristic
420#423C2×D6111yescharacteristic
421C2×C4⋊C8—611no—
422C2×C4⋊C8C2×D6111yescharacteristic
423#408—1221no—
424#405—1221no—
425#332—611no—
426#332—611no—
427#332—611no—
428#332—611no—
429#332—611no—
430#332—611no—
431#332—611no—
432#332—611no—
433#332—611no—
434#332—611no—
435#332—611no—
436#332—611no—
437#331—611no—
438#331—611no—
439#331—611no—
440#331—611no—
441C61#1776911yescharacteristic, complemented, Sylow
442C2×#41—1221no—
443C2×#41—1221no—
444C2×#41—1221no—
445C2×#41D24411yescharacteristic
446C22×Q8—1221no—
447C2×M16—21no—
448C2×M16—21no—
449C2×M16—1221no—
450C22×C8—21no—
451C22×C8—1221no—
452C4⋊Q8—612no—
453C4⋊Q8—611no—
454C4⋊Q8—611no—
455C4⋊Q8—611no—
456C4⋊Q8—1221no—
457C4⋊Q8—1221no—
458#127—611no—
459#126—1222no—
460#126—1222no—
461#125—612no—
462#125—612no—
463#124—1222no—
464#124—1222no—
465#124—1221no—
466#124—1221no—
467#124—1221no—
468#123—1222no—
469#123—1222no—
470C22⋊Q8—1222no—
471C22⋊Q8—1221no—
472C22⋊Q8—1221no—
473C22⋊Q8—1221no—
474C22⋊Q8—1221no—
475C22⋊Q8—1222no—
476C22⋊Q8—1222no—
477#121—612no—
478#121—612no—
479#121—612no—
480#121—1222no—
481#121—1222no—
482#121—1222no—
483#121—1221no—
484#121—1221no—
485#121—1221no—
486C4×Q8—1221no—
487C4×Q8—1221no—
488C4×Q8—1221no—
489C4×Q8—1221no—
490C4×Q8C4×D6111yescharacteristic
491C4×Q8C22⋊D6111yescharacteristic
492C4×D4—612no—
493C4×D4—612no—
494C4×D4—612no—
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—1221no—
498C4×D4—1221no—
499C4×D4—1221no—
500C4×D4C4×D6111yescharacteristic
501C4×D4C4×D6111yescharacteristic
502C4×D4C4×D6111yescharacteristic
503C4×D4C22⋊D6111yescharacteristic
504C4×D4C22⋊D6111yescharacteristic
505C4×D4C22⋊D6111yescharacteristic
506#117—612no—
507#117—612no—
508#117—1222no—
509#117D24411yescharacteristic
510#117D24411yescharacteristic
511#117D24411yescharacteristic
512C2×C4⋊C4—612no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1222no—
515C2×C42C22×D6111yescharacteristic
516C2×C42C22×D6111yescharacteristic
517C2×C42C22×D6111yescharacteristic
518C4⋊C8—21no—
519C4⋊C8—21no—
520C4⋊C8—21no—
521C4⋊C8—611no—
522C4⋊C8—611no—
523C4⋊C8—611no—
524C4⋊C8—611no—
525C4⋊C8—1221no—
526C4⋊C8—1221no—
527C4⋊C8C22×D6111yescharacteristic
528C4⋊C8C22×D6111yescharacteristic
529C4⋊C8C22×D6111yescharacteristic
530C4⋊C8C22×D6111yescharacteristic
531C22⋊C8—21no—
532C22⋊C8—21no—
533C22⋊C8—21no—
534C22⋊C8—1221no—
535C22⋊C8—1221no—
536C22⋊C8—1221no—
537C22⋊C8—1221no—
538#97—21no—
539#97—21no—
540#97—1221no—
541#97—1221no—
542C4×C8—21no—
543C4×C8—1221no—
544C4×C8—1221no—
545#41—41no—
546#41—41no—
547#41—4881no—
548#41—4881no—
549#41—4881no—
550#41—4881no—
551#41—2442no—
552#41—2442no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1222no—
557C2×Q8—4881no—
558C2×Q8—4881no—
559C2×Q8#1175819811yescharacteristic
560C2×D4—612no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4#1175819811yescharacteristic
567C2×D4#1175819811yescharacteristic
568C2×D4#1175819811yescharacteristic
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4C2×C4×D6111yescharacteristic
574C22×C4C2×C4×D6111yescharacteristic
575C22×C4C2×C4×D6111yescharacteristic
576C22×C4C2×D24411yescharacteristic
577C22×C4C2×D24411yescharacteristic
578C22×C4C2×D24411yescharacteristic
579C22×C4C2×C22⋊D6111yescharacteristic
580C22×C4C2×C22⋊D6111yescharacteristic
581C22×C4C2×C22⋊D6111yescharacteristic
582M16—81no—
583M16—81no—
584M16—2442no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—81no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—2442no—
595C4⋊C4—612no—
596C4⋊C4—612no—
597C4⋊C4—612no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1222no—
602C4⋊C4—1222no—
603C4⋊C4—1222no—
604C4⋊C4—1222no—
605C4⋊C4—1222no—
606C4⋊C4—1222no—
607C4⋊C4#1175819811yescharacteristic
608C4⋊C4#1175819811yescharacteristic
609C4⋊C4#1175819811yescharacteristic
610C4⋊C4#1175819811yescharacteristic
611C4⋊C4#1175819811yescharacteristic
612C4⋊C4#1175819811yescharacteristic
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—1222no—
621C22⋊C4#1175819811yescharacteristic
622C22⋊C4#1175819811yescharacteristic
623C22⋊C4#1175819811yescharacteristic
624C22⋊C4#1175819811yescharacteristic
625C22⋊C4#1175819811yescharacteristic
626C22⋊C4#1175819811yescharacteristic
627C42—1222no—
628C42—1222no—
629C42C2×C4×D6111yescharacteristic
630C42C2×C4×D6111yescharacteristic
631C42C2×C4×D6111yescharacteristic
632C42C2×D24411yescharacteristic
633C42C2×D24411yescharacteristic
634C42C2×D24411yescharacteristic
635C42C2×C22⋊D6111yescharacteristic
636C42C2×C22⋊D6111yescharacteristic
637C42C2×C22⋊D6111yescharacteristic
638C42C23×D6111yescharacteristic
639C23—1222no—
640C23C2×#1175819811yescharacteristic
641C23C2×#1175819811yescharacteristic
642C23C2×#1175819811yescharacteristic
643Q8—41no—
644Q8—4882no—
645Q8—2441no—
646Q8—2441no—
647Q8—2441no—
648Q8—2441no—
649Q8—2441no—
650Q8—2441no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—4882no—
655D4—4882no—
656D4—2442no—
657D4—2444no—
658D4—2441no—
659D4—2441no—
660D4—2441no—
661D4—2441no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—4882no—
681C2×C4—4882no—
682C2×C4—4882no—
683C2×C4—2444no—
684C2×C4C2×#1175819811yescharacteristic
685C2×C4C2×#1175819811yescharacteristic
686C2×C4C2×#1175819811yescharacteristic
687C2×C4C2×#1175819811yescharacteristic
688C2×C4C2×#1175819811yescharacteristic
689C2×C4C2×#1175819811yescharacteristic
690C2×C4C2×#1175819811yescharacteristic
691C2×C4C2×#1175819811yescharacteristic
692C2×C4C2×#1175819811yescharacteristic
693C2×C4C22×C4×D6111yescharacteristic
694C2×C4C22×C22⋊D6111yescharacteristic
695C2×C4C22×D24411yescharacteristic
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C8—2441no—
701C8—2441no—
702C8—2441no—
703C8—2441no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—2442no—
714C22—2442no—
715C22—2442no—
716C22C22×#1175819811yescharacteristic
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—21no—
724C4—21no—
725C4—21no—
726C4—21no—
727C4—2442no—
728C4—2442no—
729C4—2442no—
730C4#1684056211yescharacteristic
731C4#1684056211yescharacteristic
732C4#1684056511yescharacteristic
733C4#1684057011yescharacteristic
734C2—41no—
735C2—41no—
736C2—41no—
737C2—4882no—
738C2#2145430111yescharacteristic
739C2#2145433911yescharacteristic
740C2#2145434211yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2989C2
socleC22×C61C22×C22⋊C4
prime radical#21459730C2
cosocleC42×C61C24
hypercenter#2989D61
hypocenterC61#17769
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2989

Complements

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

NH ≅ G/Ntype
2. #21454485C2semidirect
3. #21444556C2semidirect
4. #21444542C2semidirect
5. #21444539C2semidirect
6. #21444537C2semidirect
7. #21444525C2semidirect
8. #21444522C2semidirect
9. #21444520C2semidirect
10. #21444517C2semidirect
11. #21444497C2semidirect
12. #21444492C2semidirect
13. #21444483C2semidirect
14. #21444469C2semidirect
15. C61×#2989C2semidirect
365. #2989D61semidirect
441. C61#17769semidirect

Maximal subgroups

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

subgroupindex
#214597302
#214544852
#214445562
#214445422
#214445392
#214445372
#214445252
#214445222
#214445202
#214445172
#214444972
#214444922
#214444832
#214444692
C61×#29892
#1776961