Finite Group Databasebeta

← #29648911

Subgroups — #29648911

Order 15616.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459730C211yesmaximal, characteristic
2#21454944C211yesmaximal, characteristic, complemented
3#21444547C211yesmaximal, characteristic, complemented
4#21444542C211yesmaximal, characteristic, complemented
5#21444537C211yesmaximal, characteristic, complemented
6#21444530C211yesmaximal, characteristic, complemented
7#21444522C211yesmaximal, characteristic, complemented
8#21444515C211yesmaximal, characteristic, complemented
9#21444512C211yesmaximal, characteristic, complemented
10#21444507C211yesmaximal, characteristic, complemented
11#21444497C211yesmaximal, characteristic, complemented
12#21444474C211yesmaximal, characteristic, complemented
13#21444469C211yesmaximal, characteristic, complemented
14C2×#16839509C211yesmaximal, characteristic, complemented
15C61×#2990C211yesmaximal, characteristic, complemented
16#16840485—21no—
17#16840477—21no—
18#16840472—21no—
19#16840458—21no—
20#16840458—21no—
21#16840421—21no—
22#16840421—21no—
23#16840417—21no—
24#16840383C412yes—
25#16840383C412yes—
26#16840340C412yes—
27#16840319C2211yescharacteristic
28#16840319C2211yescharacteristic
29#16840312C2211yescharacteristic
30#16840312C2211yescharacteristic
31#16840312C2211yescharacteristic
32C2×#14519777C2211yescharacteristic
33#16840242C412yes—
34#16839893—21no—
35#16839834—21no—
36#16839834—21no—
37D4×#92418—21no—
38#16839819C2211yescharacteristic
39#16839819C2211yescharacteristic
40#16839815C2211yescharacteristic
41#16839786C2211yescharacteristic
42C2×C4⋊#92418C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44#16839510C2211yescharacteristic
45#16839510C2211yescharacteristic
46#16839510C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839509C2211yescharacteristic
50#16839509C2211yescharacteristic
51#16839509C2211yescharacteristic
52#16839509C2211yescharacteristic
53#16839509C2211yescharacteristic
54#16839509C2211yescharacteristic
55#16839509C2211yescharacteristic
56#16839505C2211yescharacteristic
57#16839505C2211yescharacteristic
58#16839505C2211yescharacteristic
59#16839505C2211yescharacteristic
60C4×#41×C61C2211yescharacteristic
61C61×#446—21no—
62C61×#435—21no—
63C61×#435—21no—
64C8×D4×C61—21no—
65C61×#432C2211yescharacteristic
66C61×#432C2211yescharacteristic
67C61×#431C2211yescharacteristic
68C61×#423C2211yescharacteristic
69C2×C4⋊C8×C61C2211yescharacteristic
70C2×C4⋊C8×C61C2211yescharacteristic
71C2×#11758222—21no—
72C2×#11758222—21no—
73C2×#11758222C2×C412yes—
74C22×Dic122—21no—
75C2×#11758194—21no—
76C22×#92418—21no—
77C22×#92418—21no—
78#14519777—21no—
79#14519777—21no—
80#14519777C2×C412yes—
81#14519777C2311yescharacteristic
82#14519777C2311yescharacteristic
83#14519777C2311yescharacteristic
84#14519774C2311yescharacteristic
85#14519772—22no—
86#14519772—22no—
87#14519769—21no—
88#14519769—21no—
89#14519765—21no—
90#14519765—21no—
91#14519765C2×C412yes—
92#14519763—22no—
93#14519763—22no—
94#14519759—22no—
95#14519759—22no—
96#14519756—21no—
97#14519756—21no—
98#14519756C2×C412yes—
99#14519756C2×C412yes—
100#14519755—22no—
101#14519755—22no—
102#14519753—22no—
103#14519751—21no—
104#14519751—21no—
105#14519751—21no—
106#14519751—21no—
107#14519751C2×C412yes—
108#14519751C2×C412yes—
109#14519749—22no—
110#14519749—22no—
111#14519748—22no—
112C4×Dic122—21no—
113C4×Dic122—21no—
114C4×Dic122C2×C412yes—
115C4×Dic122C2×C412yes—
116C4×D244—21no—
117C4×D244—21no—
118C4×D244—21no—
119C4×D244—21no—
120C4×D244C2×C412yes—
121C4×D244C2×C412yes—
122#14519737—22no—
123#14519737—22no—
124#14519736—21no—
125#14519736—21no—
126#14519735—22no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61C2×C412yes—
129C4⋊C4×D61—22no—
130C4⋊#92418—21no—
131C4⋊#92418—21no—
132C4⋊#92418—21no—
133C4⋊#92418C2311yescharacteristic
134C4⋊#92418C2311yescharacteristic
135C4⋊#92418C2311yescharacteristic
136C4⋊#92418C2311yescharacteristic
137C22⋊#92418—21no—
138C22⋊#92418—21no—
139C22⋊#92418—21no—
140#14519688—21no—
141#14519688—21no—
142C4×#92418—21no—
143C2×#41×C61C2×C411yescharacteristic
144C2×M16×C61—21no—
145C22×C8×C61—21no—
146C22×C8×C61—21no—
147C4×Q8×C61D411yescharacteristic
148C4×Q8×C61D411yescharacteristic
149C4×D4×C61D411yescharacteristic
150C4×D4×C61D411yescharacteristic
151C4×D4×C61D411yescharacteristic
152C4×D4×C61D411yescharacteristic
153C4×D4×C61D411yescharacteristic
154C4×D4×C61D411yescharacteristic
155#117×C61C2×C411yescharacteristic
156#117×C61C2×C411yescharacteristic
157#117×C61C2×C411yescharacteristic
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—42no—
175C2×Q8×C61C22⋊C411yescharacteristic
176C2×D4×C61C22⋊C411yescharacteristic
177C2×D4×C61C22⋊C411yescharacteristic
178C2×D4×C61C22⋊C411yescharacteristic
179C22×C4×C61C22×C411yescharacteristic
180C22×C4×C61C22×C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C22×Dic61—22no—
192#11758222—44no—
193#11758222—81no—
194#11758222—81no—
195#11758222—81no—
196#11758222—81no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244C22×C412yes—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122—22no—
206C2×Dic122—81no—
207C2×Dic122—81no—
208C2×Dic122C22×C412yes—
209M16×C61—81no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—81no—
215C2×C8×C61—81no—
216C4⋊C4×C61C22⋊C411yescharacteristic
217C4⋊C4×C61C22⋊C411yescharacteristic
218C4⋊C4×C61C22⋊C411yescharacteristic
219C4⋊C4×C61C22⋊C411yescharacteristic
220C4⋊C4×C61C22⋊C411yescharacteristic
221C4⋊C4×C61C22⋊C411yescharacteristic
222C22⋊C4×C61C22⋊C411yescharacteristic
223C22⋊C4×C61C22⋊C411yescharacteristic
224C22⋊C4×C61C22⋊C411yescharacteristic
225C22⋊C4×C61C22⋊C411yescharacteristic
226C22⋊C4×C61C22⋊C411yescharacteristic
227C22⋊C4×C61C22⋊C411yescharacteristic
228C42×C61C22×C411yescharacteristic
229C42×C61C22×C411yescharacteristic
230C42×C61C22×C411yescharacteristic
231C42×C61C2×D411yescharacteristic
232C42×C61C2×D411yescharacteristic
233C42×C61C2×D411yescharacteristic
234C42×C61C2×D411yescharacteristic
235C42×C61C2×D411yescharacteristic
236C42×C61C2×D411yescharacteristic
237C42×C61C2411yescharacteristic
238C22⋊Dic61—22no—
239C22⋊Dic61—22no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244#11758198—22no—
245#11758198—22no—
246C4⋊Dic61—22no—
247C4⋊Dic61—22no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61C22×C412yes—
253C4⋊Dic61C22×C412yes—
254#11758196—22no—
255#11758196—22no—
256#11758196—22no—
257#11758196—22no—
258C4×Dic61—22no—
259C4×Dic61—22no—
260#11758194—81no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—81no—
266C2×#92418—81no—
267C23×C61C2×C22⋊C411yescharacteristic
268C23×C61C2×C22⋊C411yescharacteristic
269C23×C61C2×C22⋊C411yescharacteristic
270C22×D61—22no—
271Q8×C61—41no—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—41no—
275C2×C4×C61—22no—
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×C61C2×C22⋊C411yescharacteristic
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×C61C23×C411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C22⋊D61—44no—
303C22⋊D61—82no—
304C22⋊D61—82no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—82no—
309D244—42no—
310D244—41no—
311D244—41no—
312D244—41no—
313D244—41no—
314C4×D61—44no—
315C4×D61—82no—
316C4×D61—82no—
317Dic122—41no—
318Dic122—41no—
319Dic122—41no—
320Dic122—41no—
321Dic122—42no—
322Dic122—82no—
323C8×C61—41no—
324C8×C61—41no—
325C8×C61—41no—
326C8×C61—41no—
327#92418—41no—
328#92418—41no—
329#92418—41no—
330#92418—41no—
331#17775—611nomaximal, Sylow
332C22×C61—21no—
333C22×C61—21no—
334C22×C61—21no—
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61#41312yes—
341C22×C61C22×C22⋊C411yescharacteristic
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C4×C61—21no—
346C4×C61—21no—
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#57611yescharacteristic
356C4×C61#57711yescharacteristic
357C4×C61#57711yescharacteristic
358C4×C61#57811yescharacteristic
359Dic61—42no—
360Dic61—42no—
361Dic61—42no—
362#3511—611no—
363#2990—611no—
364#2990D6111yescharacteristic, complemented
365#1559—611no—
366#1557—611no—
367#1556—611no—
368#1554—611no—
369#1553—611no—
370#1551—611no—
371#1551—611no—
372#1550—611no—
373#1547—611no—
374#1542—611no—
375#1540—611no—
376C2×#332—611no—
377C2×C61—22no—
378C2×C61—41no—
379C2×C61—41no—
380C2×C61C2×#41311yescharacteristic
381C2×C61#289711yescharacteristic
382C2×C61#289811yescharacteristic
383D61—82no—
384#556—1221no—
385#555—1221no—
386#554—1221no—
387#553—1221no—
388#553—1221no—
389#548—1221no—
390#548—1221no—
391#547—1221no—
392#542—612no—
393#542—612no—
394#537—612no—
395#533—611no—
396#533—611no—
397#532—611no—
398#532—611no—
399#532—611no—
400C2×C4⋊Q8—611no—
401#520—612no—
402C4×#41C2×D6111yescharacteristic
403#446—21no—
404#446—1221no—
405#435—21no—
406#435—21no—
407#435—1221no—
408#435—1221no—
409C8×D4—21no—
410C8×D4—1221no—
411#432—611no—
412#432—611no—
413#432C2×D6111yescharacteristic
414#432C2×D6111yescharacteristic
415#431—611no—
416#431C2×D6111yescharacteristic
417#423—611no—
418#423C2×D6111yescharacteristic
419C2×C4⋊C8—611no—
420C2×C4⋊C8—611no—
421C2×C4⋊C8C2×D6111yescharacteristic
422C2×C4⋊C8C2×D6111yescharacteristic
423#333—611no—
424#333—611no—
425#333—611no—
426#333—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#331—611no—
436#331—611no—
437#331—611no—
438#331—611no—
439C61#1777511yescharacteristic, complemented, Sylow
440C2×#41—612no—
441C2×#41—1221no—
442C2×#41—1221no—
443C2×#41C4×D6111yescharacteristic
444C22×Q8—1221no—
445C2×M16—21no—
446C2×M16—1221no—
447C22×C8—21no—
448C22×C8—21no—
449C22×C8—1221no—
450C22×C8—1221no—
451C4⋊Q8—612no—
452C4⋊Q8—611no—
453C4⋊Q8—611no—
454C4⋊Q8—611no—
455C4⋊Q8—1221no—
456C4⋊Q8—1221no—
457#127—611no—
458#126—1222no—
459#126—1222no—
460#125—1221no—
461#125—1221no—
462#124—612no—
463#124—1222no—
464#124—1222no—
465#124—1221no—
466#124—1221no—
467#123—1222no—
468#123—1222no—
469C22⋊Q8—612no—
470C22⋊Q8—612no—
471C22⋊Q8—1222no—
472C22⋊Q8—1221no—
473C22⋊Q8—1221no—
474C22⋊Q8—1222no—
475C22⋊Q8—1222no—
476#121—612no—
477#121—612no—
478#121—1222no—
479#121—1222no—
480#121—1222no—
481#121—1221no—
482#121—1221no—
483#121—1221no—
484#121—1221no—
485C4×Q8—612no—
486C4×Q8—612no—
487C4×Q8—1221no—
488C4×Q8—1221no—
489C4×Q8D24411yescharacteristic
490C4×Q8C22⋊D6111yescharacteristic
491C4×D4—612no—
492C4×D4—612no—
493C4×D4—1222no—
494C4×D4—1222no—
495C4×D4—1221no—
496C4×D4—1221no—
497C4×D4—1221no—
498C4×D4—1221no—
499C4×D4D24411yescharacteristic
500C4×D4D24411yescharacteristic
501C4×D4D24411yescharacteristic
502C4×D4C22⋊D6111yescharacteristic
503C4×D4C22⋊D6111yescharacteristic
504C4×D4C22⋊D6111yescharacteristic
505#117—1221no—
506#117—1221no—
507#117—1222no—
508#117C4×D6111yescharacteristic
509#117C4×D6111yescharacteristic
510#117C4×D6111yescharacteristic
511C2×C4⋊C4—612no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1222no—
514C2×C42C22×D6111yescharacteristic
515C2×C42C22×D6111yescharacteristic
516C2×C42C22×D6111yescharacteristic
517C4⋊C8—21no—
518C4⋊C8—21no—
519C4⋊C8—21no—
520C4⋊C8—611no—
521C4⋊C8—611no—
522C4⋊C8—611no—
523C4⋊C8—611no—
524C4⋊C8—1221no—
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—
537#97—21no—
538#97—21no—
539#97—1221no—
540#97—1221no—
541C4×C8—21no—
542C4×C8—1221no—
543#41—42no—
544#41—4881no—
545#41—4881no—
546#41—4881no—
547#41—4881no—
548#41—2444no—
549C2×Q8—612no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8—1222no—
553C2×Q8—4881no—
554C2×Q8—4881no—
555C2×Q8#1175819811yescharacteristic
556C2×D4—612no—
557C2×D4—1222no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1221no—
561C2×D4—1221no—
562C2×D4#1175819811yescharacteristic
563C2×D4#1175819811yescharacteristic
564C2×D4#1175819811yescharacteristic
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4C2×C4×D6111yescharacteristic
570C22×C4C2×C4×D6111yescharacteristic
571C22×C4C2×C4×D6111yescharacteristic
572C22×C4C2×D24411yescharacteristic
573C22×C4C2×D24411yescharacteristic
574C22×C4C2×D24411yescharacteristic
575C22×C4C2×C22⋊D6111yescharacteristic
576C22×C4C2×C22⋊D6111yescharacteristic
577C22×C4C2×C22⋊D6111yescharacteristic
578M16—81no—
579M16—4881no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—81no—
585C2×C8—81no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—4881no—
591C2×C8—4881no—
592C4⋊C4—612no—
593C4⋊C4—612no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1222no—
599C4⋊C4—1222no—
600C4⋊C4—1222no—
601C4⋊C4—1222no—
602C4⋊C4—1222no—
603C4⋊C4—1222no—
604C4⋊C4#1175819811yescharacteristic
605C4⋊C4#1175819811yescharacteristic
606C4⋊C4#1175819811yescharacteristic
607C4⋊C4#1175819811yescharacteristic
608C4⋊C4#1175819811yescharacteristic
609C4⋊C4#1175819811yescharacteristic
610C22⋊C4—1222no—
611C22⋊C4—1222no—
612C22⋊C4—1222no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4#1175819811yescharacteristic
619C22⋊C4#1175819811yescharacteristic
620C22⋊C4#1175819811yescharacteristic
621C22⋊C4#1175819811yescharacteristic
622C22⋊C4#1175819811yescharacteristic
623C22⋊C4#1175819811yescharacteristic
624C42—1222no—
625C42—1222no—
626C42C2×C4×D6111yescharacteristic
627C42C2×C4×D6111yescharacteristic
628C42C2×C4×D6111yescharacteristic
629C42C2×D24411yescharacteristic
630C42C2×D24411yescharacteristic
631C42C2×D24411yescharacteristic
632C42C2×C22⋊D6111yescharacteristic
633C42C2×C22⋊D6111yescharacteristic
634C42C2×C22⋊D6111yescharacteristic
635C42C23×D6111yescharacteristic
636C23—1222no—
637C23C2×#1175819811yescharacteristic
638C23C2×#1175819811yescharacteristic
639C23C2×#1175819811yescharacteristic
640Q8—41no—
641Q8—4882no—
642Q8—2442no—
643Q8—2441no—
644Q8—2441no—
645Q8—2441no—
646Q8—2441no—
647D4—22no—
648D4—22no—
649D4—41no—
650D4—4882no—
651D4—4882no—
652D4—2442no—
653D4—2444no—
654D4—2441no—
655D4—2441no—
656D4—2441no—
657D4—2441no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
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—41no—
672C2×C4—41no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—4882no—
677C2×C4—4882no—
678C2×C4—4882no—
679C2×C4—2444no—
680C2×C4C2×#1175819811yescharacteristic
681C2×C4C2×#1175819811yescharacteristic
682C2×C4C2×#1175819811yescharacteristic
683C2×C4C2×#1175819811yescharacteristic
684C2×C4C2×#1175819811yescharacteristic
685C2×C4C2×#1175819811yescharacteristic
686C2×C4C2×#1175819811yescharacteristic
687C2×C4C2×#1175819811yescharacteristic
688C2×C4C2×#1175819811yescharacteristic
689C2×C4C22×C4×D6111yescharacteristic
690C2×C4C22×C22⋊D6111yescharacteristic
691C2×C4C22×D24411yescharacteristic
692C8—41no—
693C8—41no—
694C8—41no—
695C8—41no—
696C8—2441no—
697C8—2441no—
698C8—2441no—
699C8—2441no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—2442no—
709C22—2442no—
710C22—2442no—
711C22#1683974412yes—
712C22C22×#1175819811yescharacteristic
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—2442no—
724C4—2442no—
725C4—2442no—
726C4#1684056511yescharacteristic
727C4#1684057011yescharacteristic
728C4#1684057411yescharacteristic
729C4#1684057911yescharacteristic
730C2—22no—
731C2—41no—
732C2—41no—
733C2—4882no—
734C2C2×#1683974411yescharacteristic
735C2#2145434211yescharacteristic
736C2#2145435311yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2990C2
socleC22×C61C22×C22⋊C4
prime radical#21459730C2
cosocleC42×C61C24
hypercenter#2990D61
hypocenterC61#17775
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #21454944C2semidirect
3. #21444547C2semidirect
4. #21444542C2semidirect
5. #21444537C2semidirect
6. #21444530C2semidirect
7. #21444522C2semidirect
8. #21444515C2semidirect
9. #21444512C2semidirect
10. #21444507C2semidirect
11. #21444497C2semidirect
12. #21444474C2semidirect
13. #21444469C2semidirect
14. C2×#16839509C2semidirect
15. C61×#2990C2semidirect
364. #2990D61semidirect
439. C61#17775semidirect

Maximal subgroups

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

subgroupindex
#214597302
#214549442
#214445472
#214445422
#214445372
#214445302
#214445222
#214445152
#214445122
#214445072
#214444972
#214444742
#214444692
C2×#168395092
C61×#29902
#1777561