Finite Group Databasebeta

← #29648807

Subgroups — #29648807

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459695C211yesmaximal, characteristic
2#21454936C211yesmaximal, characteristic, complemented
3#21444552C211yesmaximal, characteristic, complemented
4#21444550C211yesmaximal, characteristic, complemented
5#21444539C211yesmaximal, characteristic, complemented
6#21444532C211yesmaximal, characteristic, complemented
7#21444527C211yesmaximal, characteristic, complemented
8#21444525C211yesmaximal, characteristic, complemented
9#21444515C211yesmaximal, characteristic, complemented
10#21444512C211yesmaximal, characteristic, complemented
11#21444494C211yesmaximal, characteristic, complemented
12#21444486C211yesmaximal, characteristic, complemented
13#21444479C211yesmaximal, characteristic, complemented
14#21444466C211yesmaximal, characteristic, complemented
15C61×#2925C211yesmaximal, characteristic, complemented
16#16840497—21no—
17#16840497C412yes—
18#16840433—21no—
19#16840433C412yes—
20#16840408—21no—
21#16840408—21no—
22#16840408C412yes—
23#16840408C412yes—
24#16840367—21no—
25#16840367—21no—
26#16840326—21no—
27#16840319C2211yescharacteristic
28#16840312C2211yescharacteristic
29#16840312C2211yescharacteristic
30#16840312C2211yescharacteristic
31#16840312C2211yescharacteristic
32C2×#14519774C2211yescharacteristic
33#16840236—21no—
34#16839893—21no—
35#16839840—21no—
36#16839834—21no—
37#16839834—21no—
38#16839819C2211yescharacteristic
39#16839819C2211yescharacteristic, complemented
40#16839815C2211yescharacteristic, complemented
41#16839786C2211yescharacteristic
42#16839786C2211yescharacteristic, complemented
43C2×C4⋊#92418C2211yescharacteristic, complemented
44#16839510C2211yescharacteristic, complemented
45#16839510C2211yescharacteristic, complemented
46#16839510C2211yescharacteristic, complemented
47#16839510C2211yescharacteristic, 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×#433—21no—
62C61×#433—21no—
63C61×#432C2211yescharacteristic
64C61×#432C2211yescharacteristic, complemented
65C61×#431C2211yescharacteristic
66C61×#431C2211yescharacteristic, complemented
67C61×#423C2211yescharacteristic, complemented
68C2×C4⋊C8×C61C2211yescharacteristic, complemented
69C61×#408—21no—
70C61×#405—21no—
71C2×#11758222—21no—
72C2×#11758222—21no—
73C2×#11758222C2×C412yes—
74C2×#11758222C2×C412yes—
75C22×D244—21no—
76C22×D244—21no—
77C22×D244C2×C412yes—
78C2×#11758194—21no—
79C2×#11758194—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#14519769—21no—
90#14519766—22no—
91#14519765—21no—
92#14519765—21no—
93#14519765C2×C412yes—
94#14519765C2×C412yes—
95#14519762—22no—
96#14519762—22no—
97#14519762—22no—
98#14519762—22no—
99#14519756—21no—
100#14519756C2×C412yes—
101#14519751—21no—
102#14519751—21no—
103#14519751—21no—
104#14519751—21no—
105#14519751—21no—
106#14519751—21no—
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×Dic122C2×C412yes—
117C4×D244—21no—
118C4×D244—21no—
119C4×D244—21no—
120C4×D244—21no—
121C4×D244—21no—
122C4×D244—21no—
123C4×D244C2×C412yes—
124C4×D244C2×C412yes—
125#14519739—22no—
126#14519739—22no—
127#14519736—21no—
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×C61D411yescharacteristic
144C2×M16×C61—21no—
145C22×C8×C61—21no—
146C4×Q8×C61C2×C411yescharacteristic
147C4×Q8×C61D411yescharacteristic
148C4×D4×C61C2×C411yescharacteristic
149C4×D4×C61C2×C411yescharacteristic
150C4×D4×C61C2×C411yescharacteristic
151C4×D4×C61D411yescharacteristic
152C4×D4×C61D411yescharacteristic
153C4×D4×C61D411yescharacteristic
154#117×C61D411yescharacteristic
155#117×C61D411yescharacteristic
156#117×C61D411yescharacteristic
157C2×C42×C61C2311yescharacteristic
158C2×C42×C61C2311yescharacteristic
159C2×C42×C61C2311yescharacteristic
160C4⋊C8×C61—21no—
161C4⋊C8×C61—21no—
162C4⋊C8×C61C2311yescharacteristic
163C4⋊C8×C61C2311yescharacteristic
164C4⋊C8×C61C2311yescharacteristic
165C4⋊C8×C61C2311yescharacteristic
166C22⋊C8×C61—21no—
167C22⋊C8×C61—21no—
168C22⋊C8×C61—21no—
169C22⋊C8×C61—21no—
170#97×C61—21no—
171#97×C61—21no—
172C4×C8×C61—21no—
173C4×C8×C61—21no—
174C23×D61—22no—
175#41×C61—41no—
176#41×C61—41no—
177C2×Q8×C61C22⋊C411yescharacteristic
178C2×D4×C61C22⋊C411yescharacteristic
179C2×D4×C61C22⋊C411yescharacteristic
180C2×D4×C61C22⋊C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—22no—
194#11758222—81no—
195#11758222—81no—
196#11758222—81no—
197#11758222—81no—
198#11758222—82no—
199#11758222—82no—
200C2×D244—22no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—22no—
206C2×D244—22no—
207C2×D244—42no—
208C2×D244—42no—
209C2×D244—81no—
210C2×D244—81no—
211C2×D244—82no—
212C2×D244C22×C412yes—
213C2×D244C22×C412yes—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×Dic122—21no—
219C2×Dic122C22×C412yes—
220M16×C61—42no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—42no—
226C4⋊C4×C61C22⋊C411yescharacteristic
227C4⋊C4×C61C22⋊C411yescharacteristic
228C4⋊C4×C61C22⋊C411yescharacteristic
229C4⋊C4×C61C22⋊C411yescharacteristic
230C4⋊C4×C61C22⋊C411yescharacteristic
231C4⋊C4×C61C22⋊C411yescharacteristic
232C22⋊C4×C61C22⋊C411yescharacteristic
233C22⋊C4×C61C22⋊C411yescharacteristic
234C22⋊C4×C61C22⋊C411yescharacteristic
235C22⋊C4×C61C22⋊C411yescharacteristic
236C22⋊C4×C61C22⋊C411yescharacteristic
237C22⋊C4×C61C22⋊C411yescharacteristic
238C42×C61C22×C411yescharacteristic
239C42×C61C22×C411yescharacteristic
240C42×C61C22×C411yescharacteristic
241C42×C61C2×D411yescharacteristic
242C42×C61C2×D411yescharacteristic
243C42×C61C2×D411yescharacteristic
244C42×C61C2×D411yescharacteristic
245C42×C61C2×D411yescharacteristic
246C42×C61C2×D411yescharacteristic
247C42×C61C2411yescharacteristic
248C22⋊Dic61—22no—
249#11758198—22no—
250#11758198—22no—
251#11758198—22no—
252#11758198—22no—
253#11758198—22no—
254#11758198—22no—
255#11758198—22no—
256#11758198—22no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61C22×C412yes—
261#11758196—22no—
262#11758196—22no—
263C4×Dic61—22no—
264#11758194—81no—
265#11758194—81no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—81no—
271C23×C61C2×C22⋊C411yescharacteristic
272C23×C61C2×C22⋊C411yescharacteristic
273C23×C61C2×C22⋊C411yescharacteristic
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—44no—
277C22×D61—82no—
278C22×D61—82no—
279Q8×C61—41no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
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—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C2×C4×C61C2×C22⋊C411yescharacteristic
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×C61C23×C411yescharacteristic
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C22×D411yescharacteristic
310C22⋊D61—82no—
311C22⋊D61—82no—
312C22⋊D61—82no—
313C22⋊D61—82no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316D244—42no—
317D244—42no—
318D244—44no—
319D244—41no—
320D244—41no—
321D244—41no—
322D244—41no—
323D244—41no—
324D244—41no—
325D244—41no—
326D244—41no—
327D244—82no—
328D244—82no—
329C4×D61—82no—
330C4×D61—82no—
331C4×D61—82no—
332C4×D61—82no—
333Dic122—41no—
334Dic122—41no—
335Dic122—42no—
336C8×C61—41no—
337C8×C61—41no—
338C8×C61—41no—
339C8×C61—41no—
340#92418—41no—
341#92418—41no—
342#92418—41no—
343#92418—41no—
344#17766—611nomaximal, Sylow
345C22×C61—21no—
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—21no—
354C22×C61C22×C22⋊C411yescharacteristic
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—164no—
362C4×C61—21no—
363C4×C61—21no—
364C4×C61—21no—
365C4×C61—21no—
366C4×C61—21no—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61#57511yescharacteristic
373C4×C61#57511yescharacteristic
374C4×C61#57611yescharacteristic
375C4×C61#57711yescharacteristic
376Dic61—42no—
377Dic61—42no—
378#3508—611no—
379#2989—611no—
380#2925D6111yescharacteristic, complemented
381#1560—611no—
382#1559—611no—
383#1557—611no—
384#1555—611no—
385#1554—611no—
386#1553—611no—
387#1551—611no—
388#1551—611no—
389#1547—611no—
390#1545—611no—
391#1543—611no—
392#1540—611no—
393C2×C61—41no—
394C2×C61—41no—
395C2×C61—41no—
396C2×C61#288811yescharacteristic
397C2×C61#289611yescharacteristic
398C2×C61#289711yescharacteristic
399D61—82no—
400D61—82no—
401#559—612no—
402#559—1221no—
403#550—612no—
404#550—1221no—
405#546—612no—
406#546—612no—
407#546—1221no—
408#546—1221no—
409#540—1221no—
410#540—1221no—
411#535—1221no—
412#533—611no—
413#532—611no—
414#532—611no—
415#532—611no—
416#532—611no—
417C2×#127—611no—
418#518—1221no—
419C4×#41C2×D6111yescharacteristic
420#446—1221no—
421#436—1221no—
422#435—1221no—
423#435—1221no—
424#433—21no—
425#433—21no—
426#432—611no—
427#432—611no—
428#432C2×D6111yescharacteristic
429#432C2×D6111yescharacteristic, complemented
430#431—611no—
431#431C2×D6111yescharacteristic
432#431C2×D6111yescharacteristic, complemented
433#423—611no—
434#423—611no—
435#423C2×D6111yescharacteristic, complemented
436C2×C4⋊C8—611no—
437C2×C4⋊C8C2×D6111yescharacteristic, complemented
438#408—21no—
439#405—21no—
440#333—611no—
441#333—611no—
442#333—611no—
443#333—611no—
444#332—611no—
445#332—611no—
446#332—611no—
447#332—611no—
448#331—611no—
449#331—611no—
450#331—611no—
451#331—611no—
452#331—611no—
453#331—611no—
454#331—611no—
455#331—611no—
456C61#1776611yescharacteristic, complemented, Sylow
457C2×#41—612no—
458C2×#41—612no—
459C2×#41—1221no—
460C2×#41—1221no—
461C2×#41C22⋊D6111yescharacteristic
462C22×D4—612no—
463C22×D4—1221no—
464C22×D4—1221no—
465C2×M16—21no—
466C2×M16—1221no—
467C2×M16—1221no—
468C22×C8—21no—
469C22×C8—1221no—
470C4⋊Q8—611no—
471C4⋊Q8—611no—
472#127—612no—
473#127—611no—
474#127—611no—
475#127—1222no—
476#127—1221no—
477#127—1221no—
478#125—1221no—
479#124—612no—
480#124—612no—
481#124—1222no—
482#124—1221no—
483#124—1221no—
484#123—1222no—
485#123—1222no—
486#123—1222no—
487#123—1222no—
488C22⋊Q8—612no—
489C22⋊Q8—1221no—
490#121—612no—
491#121—612no—
492#121—1221no—
493#121—1221no—
494#121—1221no—
495#121—1221no—
496#121—1221no—
497#121—1221no—
498#121—1222no—
499#121—1222no—
500#121—1222no—
501#121—1222no—
502#120—1222no—
503#120—1222no—
504C4×Q8—612no—
505C4×Q8—1221no—
506C4×Q8C4×D6111yescharacteristic
507C4×Q8D24411yescharacteristic
508C4×D4—612no—
509C4×D4—612no—
510C4×D4—1222no—
511C4×D4—1222no—
512C4×D4—1221no—
513C4×D4—1221no—
514C4×D4—1221no—
515C4×D4—1221no—
516C4×D4—1221no—
517C4×D4—1221no—
518C4×D4C4×D6111yescharacteristic
519C4×D4C4×D6111yescharacteristic
520C4×D4C4×D6111yescharacteristic
521C4×D4D24411yescharacteristic
522C4×D4D24411yescharacteristic
523C4×D4D24411yescharacteristic
524#117—1221no—
525#117C22⋊D6111yescharacteristic
526#117C22⋊D6111yescharacteristic
527#117C22⋊D6111yescharacteristic
528C2×C22⋊C4—1222no—
529C2×C22⋊C4—1222no—
530C2×C42C22×D6111yescharacteristic
531C2×C42C22×D6111yescharacteristic
532C2×C42C22×D6111yescharacteristic
533C4⋊C8—21no—
534C4⋊C8—21no—
535C4⋊C8—611no—
536C4⋊C8—611no—
537C4⋊C8—611no—
538C4⋊C8—611no—
539C4⋊C8—1221no—
540C4⋊C8—1221no—
541C4⋊C8—1221no—
542C4⋊C8C22×D6111yescharacteristic
543C4⋊C8C22×D6111yescharacteristic
544C4⋊C8C22×D6111yescharacteristic
545C4⋊C8C22×D6111yescharacteristic
546C22⋊C8—21no—
547C22⋊C8—21no—
548C22⋊C8—21no—
549C22⋊C8—21no—
550C22⋊C8—1221no—
551C22⋊C8—1221no—
552C22⋊C8—1221no—
553#97—21no—
554#97—21no—
555#97—1221no—
556#97—1221no—
557C4×C8—21no—
558C4×C8—21no—
559C4×C8—1221no—
560C24—1222no—
561#41—41no—
562#41—41no—
563#41—4881no—
564#41—4881no—
565#41—4881no—
566#41—4881no—
567#41—4882no—
568#41—4882no—
569C2×Q8—612no—
570C2×Q8—1221no—
571C2×Q8#1175819811yescharacteristic
572C2×D4—612no—
573C2×D4—612no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1222no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—4881no—
586C2×D4—4881no—
587C2×D4—4882no—
588C2×D4—2442no—
589C2×D4—2442no—
590C2×D4#1175819811yescharacteristic
591C2×D4#1175819811yescharacteristic
592C2×D4#1175819811yescharacteristic
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4C2×C4×D6111yescharacteristic
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4C2×D24411yescharacteristic
601C22×C4C2×D24411yescharacteristic
602C22×C4C2×D24411yescharacteristic
603C22×C4C2×C22⋊D6111yescharacteristic
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C2×C22⋊D6111yescharacteristic
606M16—42no—
607M16—4881no—
608M16—4881no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—42no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—4881no—
619C4⋊C4—612no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1222no—
624C4⋊C4—1222no—
625C4⋊C4#1175819811yescharacteristic
626C4⋊C4#1175819811yescharacteristic
627C4⋊C4#1175819811yescharacteristic
628C4⋊C4#1175819811yescharacteristic
629C4⋊C4#1175819811yescharacteristic
630C4⋊C4#1175819811yescharacteristic
631C22⋊C4—1222no—
632C22⋊C4—1222no—
633C22⋊C4—1222no—
634C22⋊C4—1222no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C22⋊C4—1222no—
639C22⋊C4—1222no—
640C22⋊C4#1175819811yescharacteristic
641C22⋊C4#1175819811yescharacteristic
642C22⋊C4#1175819811yescharacteristic
643C22⋊C4#1175819811yescharacteristic
644C22⋊C4#1175819811yescharacteristic
645C22⋊C4#1175819811yescharacteristic
646C42—1222no—
647C42C2×C4×D6111yescharacteristic
648C42C2×C4×D6111yescharacteristic
649C42C2×C4×D6111yescharacteristic
650C42C2×D24411yescharacteristic
651C42C2×D24411yescharacteristic
652C42C2×D24411yescharacteristic
653C42C2×C22⋊D6111yescharacteristic
654C42C2×C22⋊D6111yescharacteristic
655C42C2×C22⋊D6111yescharacteristic
656C42C23×D6111yescharacteristic
657C23—1222no—
658C23—1222no—
659C23—4882no—
660C23—4882no—
661C23—2444no—
662C23C2×#1175819811yescharacteristic
663C23C2×#1175819811yescharacteristic
664C23C2×#1175819811yescharacteristic
665Q8—41no—
666Q8—2442no—
667Q8—2441no—
668Q8—2441no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—4882no—
673D4—4882no—
674D4—4882no—
675D4—4882no—
676D4—4882no—
677D4—4882no—
678D4—2442no—
679D4—2442no—
680D4—2444no—
681D4—2441no—
682D4—2441no—
683D4—2441no—
684D4—2441no—
685D4—2441no—
686D4—2441no—
687D4—2441no—
688D4—2441no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—4882no—
707C2×C4—4882no—
708C2×C4—4882no—
709C2×C4—4882no—
710C2×C4C2×#1175819811yescharacteristic
711C2×C4C2×#1175819811yescharacteristic
712C2×C4C2×#1175819811yescharacteristic
713C2×C4C2×#1175819811yescharacteristic
714C2×C4C2×#1175819811yescharacteristic
715C2×C4C2×#1175819811yescharacteristic
716C2×C4C2×#1175819811yescharacteristic
717C2×C4C2×#1175819811yescharacteristic
718C2×C4C2×#1175819811yescharacteristic
719C2×C4C22×C4×D6111yescharacteristic
720C2×C4C22×C22⋊D6111yescharacteristic
721C2×C4C22×D24411yescharacteristic
722C8—41no—
723C8—41no—
724C8—41no—
725C8—41no—
726C8—2441no—
727C8—2441no—
728C8—2441no—
729C8—2441no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—9764no—
740C22—2442no—
741C22—2442no—
742C22—2442no—
743C22—2442no—
744C22—2442no—
745C22—2442no—
746C22C22×#1175819811yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—2442no—
758C4—2442no—
759C4#1684056011yescharacteristic
760C4#1684056011yescharacteristic
761C4#1684056711yescharacteristic
762C4#1684057411yescharacteristic
763C2—41no—
764C2—41no—
765C2—41no—
766C2—4882no—
767C2—4882no—
768C2#2145429711yescharacteristic
769C2#2145433611yescharacteristic
770C2#2145434611yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2925C2
socleC22×C61C22×C22⋊C4
prime radical#21459695C2
cosocleC42×C61C24
hypercenter#2925D61
hypocenterC61#17766
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #21454936C2semidirect
3. #21444552C2semidirect
4. #21444550C2semidirect
5. #21444539C2semidirect
6. #21444532C2semidirect
7. #21444527C2semidirect
8. #21444525C2semidirect
9. #21444515C2semidirect
10. #21444512C2semidirect
11. #21444494C2semidirect
12. #21444486C2semidirect
13. #21444479C2semidirect
14. #21444466C2semidirect
15. C61×#2925C2semidirect
39. #16839819C22semidirect
40. #16839815C22semidirect
42. #16839786C22semidirect
43. C2×C4⋊#92418C22semidirect
44. #16839510C22semidirect
45. #16839510C22semidirect
46. #16839510C22semidirect
47. #16839510C22semidirect
48. #16839507C22semidirect
49. #16839507C22semidirect
50. #16839507C22semidirect
51. #16839507C22semidirect
64. C61×#432C22semidirect
66. C61×#431C22semidirect
67. C61×#423C22semidirect
68. C2×C4⋊C8×C61C22semidirect
380. #2925D61semidirect
429. #432C2×D61semidirect
432. #431C2×D61semidirect
435. #423C2×D61semidirect
437. C2×C4⋊C8C2×D61semidirect
456. C61#17766semidirect

Maximal subgroups

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

subgroupindex
#214596952
#214549362
#214445522
#214445502
#214445392
#214445322
#214445272
#214445252
#214445152
#214445122
#214444942
#214444862
#214444792
#214444662
C61×#29252
#1776661