Finite Group Databasebeta

← #29648866

Subgroups — #29648866

Order 15616.

990 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459695C211yesmaximal, characteristic
2#21454944C211yesmaximal, characteristic, complemented
3#21444542C211yesmaximal, characteristic, complemented
4#21444539C211yesmaximal, characteristic, complemented
5#21444532C211yesmaximal, characteristic, complemented
6#21444525C211yesmaximal, characteristic, complemented
7#21444522C211yesmaximal, characteristic, complemented
8#21444520C211yesmaximal, characteristic, complemented
9#21444517C211yesmaximal, characteristic, complemented
10#21444497C211yesmaximal, characteristic, complemented
11#21444494C211yesmaximal, characteristic, complemented
12#21444469C211yesmaximal, characteristic, complemented
13#21444466C211yesmaximal, characteristic, complemented
14C2×#16839505C211yesmaximal, characteristic, complemented
15C61×#2990C211yesmaximal, characteristic, complemented
16#16840497—21no—
17#16840497—21no—
18#16840433—21no—
19#16840433—21no—
20#16840408—21no—
21#16840408—21no—
22#16840408—21no—
23#16840408—21no—
24#16840367C412yes—
25#16840367C412yes—
26#16840326C412yes—
27#16840319C2211yescharacteristic
28#16840312C2211yescharacteristic
29#16840312C2211yescharacteristic
30#16840312C2211yescharacteristic
31#16840312C2211yescharacteristic
32C2×#14519774C2211yescharacteristic
33#16840236C412yes—
34#16839893—21no—
35#16839834—21no—
36#16839834—21no—
37D4×#92418—21no—
38#16839819C2211yescharacteristic
39#16839819C2211yescharacteristic, complemented
40#16839815C2211yescharacteristic, complemented
41#16839786C2211yescharacteristic, complemented
42C2×C4⋊#92418C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic, complemented
44#16839509C2211yescharacteristic, complemented
45#16839509C2211yescharacteristic, complemented
46#16839509C2211yescharacteristic, complemented
47#16839509C2211yescharacteristic, complemented
48#16839507C2211yescharacteristic, complemented
49#16839507C2211yescharacteristic, complemented
50#16839507C2211yescharacteristic, complemented
51#16839507C2211yescharacteristic, complemented
52#16839505C2211yescharacteristic
53#16839505C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
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, complemented
67C61×#431C2211yescharacteristic, complemented
68C61×#423C2211yescharacteristic, complemented
69C2×C4⋊C8×C61C2211yescharacteristic
70C2×C4⋊C8×C61C2211yescharacteristic, complemented
71C2×#11758222—21no—
72C2×#11758222—21no—
73C2×#11758222—21no—
74C2×#11758222—21no—
75C22×D244—21no—
76C22×D244—21no—
77C22×D244C2×C412yes—
78C2×#11758194—21no—
79C22×#92418—21no—
80C22×#92418—21no—
81#14519777C2311yescharacteristic
82#14519777C2311yescharacteristic
83#14519774—21no—
84#14519774—21no—
85#14519774C2×C412yes—
86#14519774C2311yescharacteristic
87#14519774C2311yescharacteristic
88#14519773—22no—
89#14519769C2×C412yes—
90#14519766—22no—
91#14519765—21no—
92#14519765—21no—
93#14519765—21no—
94#14519765—21no—
95#14519762—22no—
96#14519762—22no—
97#14519762—22no—
98#14519762—22no—
99#14519756—21no—
100#14519756—21no—
101#14519751—21no—
102#14519751—21no—
103#14519751—21no—
104#14519751—21no—
105#14519751C2×C412yes—
106#14519751C2×C412yes—
107#14519751C2×C412yes—
108#14519751C2×C412yes—
109#14519750—22no—
110#14519750—22no—
111#14519750—22no—
112#14519750—22no—
113#14519745—22no—
114#14519745—22no—
115C4×Dic122—21no—
116C4×Dic122—21no—
117C4×D244—21no—
118C4×D244—21no—
119C4×D244—21no—
120C4×D244—21no—
121C4×D244C2×C412yes—
122C4×D244C2×C412yes—
123C4×D244C2×C412yes—
124C4×D244C2×C412yes—
125#14519739—22no—
126#14519739—22no—
127#14519736C2×C412yes—
128C22⋊C4×D61—22no—
129C22⋊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—
174C23×D61—22no—
175#41×C61—42no—
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—
192C2×C22⋊D61—22no—
193#11758222—81no—
194#11758222—81no—
195#11758222—81no—
196#11758222—81no—
197#11758222—81no—
198#11758222—81no—
199#11758222—81no—
200#11758222—81no—
201C2×D244—22no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—22no—
207C2×D244—22no—
208C2×D244—44no—
209C2×D244—81no—
210C2×D244—81no—
211C2×D244—81no—
212C2×D244—81no—
213C2×D244C22×C412yes—
214C2×D244C22×C412yes—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221M16×C61—81no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—81no—
227C2×C8×C61—81no—
228C4⋊C4×C61C22⋊C411yescharacteristic
229C4⋊C4×C61C22⋊C411yescharacteristic
230C4⋊C4×C61C22⋊C411yescharacteristic
231C4⋊C4×C61C22⋊C411yescharacteristic
232C4⋊C4×C61C22⋊C411yescharacteristic
233C4⋊C4×C61C22⋊C411yescharacteristic
234C22⋊C4×C61C22⋊C411yescharacteristic
235C22⋊C4×C61C22⋊C411yescharacteristic
236C22⋊C4×C61C22⋊C411yescharacteristic
237C22⋊C4×C61C22⋊C411yescharacteristic
238C22⋊C4×C61C22⋊C411yescharacteristic
239C22⋊C4×C61C22⋊C411yescharacteristic
240C42×C61C22×C411yescharacteristic
241C42×C61C22×C411yescharacteristic
242C42×C61C22×C411yescharacteristic
243C42×C61C2×D411yescharacteristic
244C42×C61C2×D411yescharacteristic
245C42×C61C2×D411yescharacteristic
246C42×C61C2×D411yescharacteristic
247C42×C61C2×D411yescharacteristic
248C42×C61C2×D411yescharacteristic
249C42×C61C2411yescharacteristic
250C22⋊Dic61—22no—
251#11758198—22no—
252#11758198—22no—
253#11758198—22no—
254#11758198—22no—
255#11758198—22no—
256#11758198—22no—
257#11758198—22no—
258#11758198—22no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61C22×C412yes—
262C4⋊Dic61C22×C412yes—
263#11758196—22no—
264#11758196—22no—
265C4×Dic61—22no—
266#11758194—81no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—81no—
272C2×#92418—81no—
273C23×C61C2×C22⋊C411yescharacteristic
274C23×C61C2×C22⋊C411yescharacteristic
275C23×C61C2×C22⋊C411yescharacteristic
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—44no—
279C22×D61—82no—
280C22×D61—82no—
281Q8×C61—41no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61—41no—
285C2×C4×C61—22no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61C2×C22⋊C411yescharacteristic
301C2×C4×C61C2×C22⋊C411yescharacteristic
302C2×C4×C61C2×C22⋊C411yescharacteristic
303C2×C4×C61C2×C22⋊C411yescharacteristic
304C2×C4×C61C2×C22⋊C411yescharacteristic
305C2×C4×C61C2×C22⋊C411yescharacteristic
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C23×C411yescharacteristic
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C22⋊D61—82no—
313C22⋊D61—82no—
314C22⋊D61—82no—
315C22⋊D61—82no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318D244—42no—
319D244—42no—
320D244—44no—
321D244—41no—
322D244—41no—
323D244—41no—
324D244—41no—
325D244—41no—
326D244—41no—
327D244—41no—
328D244—41no—
329D244—82no—
330D244—82no—
331C4×D61—82no—
332C4×D61—82no—
333C4×D61—82no—
334C4×D61—82no—
335Dic122—41no—
336Dic122—41no—
337Dic122—41no—
338Dic122—41no—
339C8×C61—41no—
340C8×C61—41no—
341C8×C61—41no—
342C8×C61—41no—
343#92418—41no—
344#92418—41no—
345#92418—41no—
346#92418—41no—
347#17771—611nomaximal, Sylow
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61#41312yes—
357C22×C61C22×C22⋊C411yescharacteristic
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—164no—
365C4×C61—21no—
366C4×C61—21no—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—21no—
375C4×C61#57611yescharacteristic
376C4×C61#57611yescharacteristic
377C4×C61#57711yescharacteristic
378C4×C61#57711yescharacteristic
379Dic61—42no—
380Dic61—42no—
381#3508—611no—
382#2990—611no—
383#2990D6111yescharacteristic, complemented
384#1557—611no—
385#1557—611no—
386#1555—611no—
387#1553—611no—
388#1553—611no—
389#1552—611no—
390#1552—611no—
391#1547—611no—
392#1547—611no—
393#1540—611no—
394#1540—611no—
395C2×#331—611no—
396C2×C61—22no—
397C2×C61—41no—
398C2×C61—41no—
399C2×C61C2×#41311yescharacteristic
400C2×C61#289711yescharacteristic
401C2×C61#289711yescharacteristic
402D61—82no—
403D61—82no—
404#559—1221no—
405#559—1221no—
406#550—1221no—
407#550—1221no—
408#546—1221no—
409#546—1221no—
410#546—1221no—
411#546—1221no—
412#540—612no—
413#540—612no—
414#535—612no—
415#533—611no—
416#532—611no—
417#532—611no—
418#532—611no—
419#532—611no—
420C2×#127—611no—
421#518—612no—
422C4×#41C2×D6111yescharacteristic
423#446—21no—
424#446—1221no—
425#435—21no—
426#435—21no—
427#435—1221no—
428#435—1221no—
429C8×D4—21no—
430C8×D4—1221no—
431#432—611no—
432#432—611no—
433#432C2×D6111yescharacteristic
434#432C2×D6111yescharacteristic, complemented
435#431—611no—
436#431C2×D6111yescharacteristic, complemented
437#423—611no—
438#423C2×D6111yescharacteristic, complemented
439C2×C4⋊C8—611no—
440C2×C4⋊C8—611no—
441C2×C4⋊C8C2×D6111yescharacteristic
442C2×C4⋊C8C2×D6111yescharacteristic, complemented
443#332—611no—
444#332—611no—
445#332—611no—
446#332—611no—
447#332—611no—
448#332—611no—
449#332—611no—
450#332—611no—
451#331—611no—
452#331—611no—
453#331—611no—
454#331—611no—
455#331—611no—
456#331—611no—
457#331—611no—
458#331—611no—
459C61#1777111yescharacteristic, complemented, Sylow
460C2×#41—1221no—
461C2×#41—1221no—
462C2×#41—1221no—
463C2×#41—1221no—
464C2×#41C4×D6111yescharacteristic
465C22×D4—612no—
466C22×D4—1221no—
467C22×D4—1221no—
468C2×M16—21no—
469C2×M16—1221no—
470C22×C8—21no—
471C22×C8—21no—
472C22×C8—1221no—
473C22×C8—1221no—
474C4⋊Q8—611no—
475C4⋊Q8—611no—
476#127—612no—
477#127—611no—
478#127—611no—
479#127—1222no—
480#127—1221no—
481#127—1221no—
482#125—612no—
483#124—1222no—
484#124—1221no—
485#124—1221no—
486#124—1221no—
487#124—1221no—
488#123—1222no—
489#123—1222no—
490#123—1222no—
491#123—1222no—
492C22⋊Q8—1221no—
493C22⋊Q8—1221no—
494#121—612no—
495#121—612no—
496#121—612no—
497#121—612no—
498#121—1221no—
499#121—1221no—
500#121—1221no—
501#121—1221no—
502#121—1222no—
503#121—1222no—
504#121—1222no—
505#121—1222no—
506#120—1222no—
507#120—1222no—
508C4×Q8—1221no—
509C4×Q8—1221no—
510C4×Q8D24411yescharacteristic
511C4×Q8C22⋊D6111yescharacteristic
512C4×D4—612no—
513C4×D4—612no—
514C4×D4—612no—
515C4×D4—612no—
516C4×D4—1222no—
517C4×D4—1222no—
518C4×D4—1221no—
519C4×D4—1221no—
520C4×D4—1221no—
521C4×D4—1221no—
522C4×D4D24411yescharacteristic
523C4×D4D24411yescharacteristic
524C4×D4D24411yescharacteristic
525C4×D4C22⋊D6111yescharacteristic
526C4×D4C22⋊D6111yescharacteristic
527C4×D4C22⋊D6111yescharacteristic
528#117—612no—
529#117C4×D6111yescharacteristic
530#117C4×D6111yescharacteristic
531#117C4×D6111yescharacteristic
532C2×C22⋊C4—1222no—
533C2×C22⋊C4—1222no—
534C2×C42C22×D6111yescharacteristic
535C2×C42C22×D6111yescharacteristic
536C2×C42C22×D6111yescharacteristic
537C4⋊C8—21no—
538C4⋊C8—21no—
539C4⋊C8—21no—
540C4⋊C8—611no—
541C4⋊C8—611no—
542C4⋊C8—611no—
543C4⋊C8—611no—
544C4⋊C8—1221no—
545C4⋊C8—1221no—
546C4⋊C8—1221no—
547C4⋊C8C22×D6111yescharacteristic
548C4⋊C8C22×D6111yescharacteristic
549C4⋊C8C22×D6111yescharacteristic
550C4⋊C8C22×D6111yescharacteristic
551C22⋊C8—21no—
552C22⋊C8—21no—
553C22⋊C8—21no—
554C22⋊C8—1221no—
555C22⋊C8—1221no—
556C22⋊C8—1221no—
557#97—21no—
558#97—21no—
559#97—1221no—
560#97—1221no—
561C4×C8—21no—
562C4×C8—1221no—
563C24—1222no—
564#41—42no—
565#41—4881no—
566#41—4881no—
567#41—4881no—
568#41—4881no—
569#41—4881no—
570#41—4881no—
571#41—4881no—
572#41—4881no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8#1175819811yescharacteristic
576C2×D4—612no—
577C2×D4—612no—
578C2×D4—1222no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—1222no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—4881no—
590C2×D4—4881no—
591C2×D4—4881no—
592C2×D4—4881no—
593C2×D4—2444no—
594C2×D4#1175819811yescharacteristic
595C2×D4#1175819811yescharacteristic
596C2×D4#1175819811yescharacteristic
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4C2×C4×D6111yescharacteristic
602C22×C4C2×C4×D6111yescharacteristic
603C22×C4C2×C4×D6111yescharacteristic
604C22×C4C2×D24411yescharacteristic
605C22×C4C2×D24411yescharacteristic
606C22×C4C2×D24411yescharacteristic
607C22×C4C2×C22⋊D6111yescharacteristic
608C22×C4C2×C22⋊D6111yescharacteristic
609C22×C4C2×C22⋊D6111yescharacteristic
610M16—81no—
611M16—4881no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—81no—
617C2×C8—81no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—4881no—
623C2×C8—4881no—
624C4⋊C4—612no—
625C4⋊C4—612no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1222no—
629C4⋊C4—1222no—
630C4⋊C4#1175819811yescharacteristic
631C4⋊C4#1175819811yescharacteristic
632C4⋊C4#1175819811yescharacteristic
633C4⋊C4#1175819811yescharacteristic
634C4⋊C4#1175819811yescharacteristic
635C4⋊C4#1175819811yescharacteristic
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C22⋊C4—1222no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C22⋊C4—1222no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4#1175819811yescharacteristic
646C22⋊C4#1175819811yescharacteristic
647C22⋊C4#1175819811yescharacteristic
648C22⋊C4#1175819811yescharacteristic
649C22⋊C4#1175819811yescharacteristic
650C22⋊C4#1175819811yescharacteristic
651C42—1222no—
652C42C2×C4×D6111yescharacteristic
653C42C2×C4×D6111yescharacteristic
654C42C2×C4×D6111yescharacteristic
655C42C2×D24411yescharacteristic
656C42C2×D24411yescharacteristic
657C42C2×D24411yescharacteristic
658C42C2×C22⋊D6111yescharacteristic
659C42C2×C22⋊D6111yescharacteristic
660C42C2×C22⋊D6111yescharacteristic
661C42C23×D6111yescharacteristic
662C23—1222no—
663C23—1222no—
664C23—4882no—
665C23—4882no—
666C23—2444no—
667C23C2×#1175819811yescharacteristic
668C23C2×#1175819811yescharacteristic
669C23C2×#1175819811yescharacteristic
670Q8—41no—
671Q8—2441no—
672Q8—2441no—
673Q8—2441no—
674Q8—2441no—
675D4—22no—
676D4—22no—
677D4—41no—
678D4—4882no—
679D4—4882no—
680D4—4882no—
681D4—4882no—
682D4—4882no—
683D4—4882no—
684D4—2442no—
685D4—2442no—
686D4—2444no—
687D4—2441no—
688D4—2441no—
689D4—2441no—
690D4—2441no—
691D4—2441no—
692D4—2441no—
693D4—2441no—
694D4—2441no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—4882no—
713C2×C4—4882no—
714C2×C4—4882no—
715C2×C4—4882no—
716C2×C4C2×#1175819811yescharacteristic
717C2×C4C2×#1175819811yescharacteristic
718C2×C4C2×#1175819811yescharacteristic
719C2×C4C2×#1175819811yescharacteristic
720C2×C4C2×#1175819811yescharacteristic
721C2×C4C2×#1175819811yescharacteristic
722C2×C4C2×#1175819811yescharacteristic
723C2×C4C2×#1175819811yescharacteristic
724C2×C4C2×#1175819811yescharacteristic
725C2×C4C22×C4×D6111yescharacteristic
726C2×C4C22×C22⋊D6111yescharacteristic
727C2×C4C22×D24411yescharacteristic
728C8—41no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—2441no—
733C8—2441no—
734C8—2441no—
735C8—2441no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—9764no—
745C22—2442no—
746C22—2442no—
747C22—2442no—
748C22—2442no—
749C22—2442no—
750C22—2442no—
751C22#1683974412yes—
752C22C22×#1175819811yescharacteristic
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—2442no—
764C4—2442no—
765C4#1684056511yescharacteristic
766C4#1684056711yescharacteristic
767C4#1684057011yescharacteristic
768C4#1684057411yescharacteristic
769C2—22no—
770C2—41no—
771C2—41no—
772C2—4882no—
773C2—4882no—
774C2C2×#1683974411yescharacteristic
775C2#2145434211yescharacteristic
776C2#2145434611yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2990C2
socleC22×C61C22×C22⋊C4
prime radical#21459695C2
cosocleC42×C61C24
hypercenter#2990D61
hypocenterC61#17771
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. #21444542C2semidirect
4. #21444539C2semidirect
5. #21444532C2semidirect
6. #21444525C2semidirect
7. #21444522C2semidirect
8. #21444520C2semidirect
9. #21444517C2semidirect
10. #21444497C2semidirect
11. #21444494C2semidirect
12. #21444469C2semidirect
13. #21444466C2semidirect
14. C2×#16839505C2semidirect
15. C61×#2990C2semidirect
39. #16839819C22semidirect
40. #16839815C22semidirect
41. #16839786C22semidirect
43. C2×C4⋊#92418C22semidirect
44. #16839509C22semidirect
45. #16839509C22semidirect
46. #16839509C22semidirect
47. #16839509C22semidirect
48. #16839507C22semidirect
49. #16839507C22semidirect
50. #16839507C22semidirect
51. #16839507C22semidirect
66. C61×#432C22semidirect
67. C61×#431C22semidirect
68. C61×#423C22semidirect
70. C2×C4⋊C8×C61C22semidirect
383. #2990D61semidirect
434. #432C2×D61semidirect
436. #431C2×D61semidirect
438. #423C2×D61semidirect
442. C2×C4⋊C8C2×D61semidirect
459. C61#17771semidirect

Maximal subgroups

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

subgroupindex
#214596952
#214549442
#214445422
#214445392
#214445322
#214445252
#214445222
#214445202
#214445172
#214444972
#214444942
#214444692
#214444662
C2×#168395052
C61×#29902
#1777161