Finite Group Databasebeta

← #30616447

Subgroups — #30616447

Order 15616.

1162 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840768C211yesmaximal, characteristic
2C2×#16840726C211yesmaximal, characteristic
3#21461993C211yesmaximal, characteristic, complemented
4#21461992C211yesmaximal, characteristic, complemented
5#21461992C211yesmaximal, characteristic, complemented
6#21461991C211yesmaximal, characteristic, complemented
7#21461990C211yesmaximal, characteristic, complemented
8#21461990C211yesmaximal, characteristic, complemented
9#21461989C211yesmaximal, characteristic, complemented
10#21461988C211yesmaximal, characteristic, complemented
11#21461485C211yesmaximal, characteristic
12#21461485C211yesmaximal, characteristic
13#21461482C211yesmaximal, characteristic
14C2×#16840628C211yesmaximal, characteristic
15C2×#16840314C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C22×#11758217C2211yescharacteristic
18C23×#92420C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840768—24no—
21C2×#14519844C2211yescharacteristic
22C2×#14519844C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×C4⋊#92420C2211yescharacteristic
25#16840726—24no—
26C2×#14519832C2211yescharacteristic
27C2×#14519832C2211yescharacteristic
28C2×C4×#92420C2211yescharacteristic
29C2×C4×#92420C2211yescharacteristic
30#16840628C2211yescharacteristic
31#16840628C2211yescharacteristic
32#16840628C2211yescharacteristic
33#16840628C2211yescharacteristic
34#16840628C2211yescharacteristic
35#16840628C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840314—24no—
47#16840314—24no—
48C2×#14519776C411yescharacteristic
49C2×#14519775C411yescharacteristic
50C2×#14519767C411yescharacteristic
51C2×#14519767C411yescharacteristic
52C2×#14519756C411yescharacteristic
53C2×#14519754C411yescharacteristic
54C2×#14519754C411yescharacteristic
55C2×Q8×Dic61C2211yescharacteristic
56C2×#14519742C2211yescharacteristic
57C2×#14519742C2211yescharacteristic
58C2×#14519742C2211yescharacteristic
59C2×#14519733C2211yescharacteristic
60C2×#14519733C2211yescharacteristic
61C22×C4×Dic61C2211yescharacteristic
62C2×C22⋊Q8×C61C411yescharacteristic
63C2×#11758217—22no—
64C2×#11758217—22no—
65C2×#11758217—22no—
66C2×#11758217—22no—
67C2×#11758217—22no—
68C2×#11758217Q814yescomplemented
69C22×#92420—22no—
70C22×#92420—22no—
71C22×#92420—22no—
72C22×#92420—22no—
73C22×#92420—22no—
74C22×#92420Q814yescomplemented
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83#14519844—22no—
84#14519844—22no—
85C4⋊#92420—22no—
86C4⋊#92420—22no—
87#14519832—22no—
88#14519832—22no—
89C4×#92420—22no—
90C4×#92420—22no—
91C22×Dic122C2×C411yescharacteristic
92C22×Dic122C2×C411yescharacteristic
93C22×Dic122C2×C411yescharacteristic
94C23×Dic61C2×C411yescharacteristic
95C23×Dic61C2311yescharacteristic
96#14519776—24no—
97#14519775—24no—
98#14519767—24no—
99#14519767—24no—
100#14519756—24no—
101#14519754—24no—
102#14519754—24no—
103Q8×Dic61—22no—
104Q8×Dic61—22no—
105#14519742—22no—
106#14519742—22no—
107#14519742—22no—
108#14519742—22no—
109#14519742—22no—
110#14519742—22no—
111#14519733—22no—
112#14519733—22no—
113#14519733D414yes—
114#14519733D414yes—
115C2×C4⋊Dic61C2×C411yescharacteristic
116C2×C4⋊Dic61C2×C411yescharacteristic
117C2×C4⋊Dic61C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C2×#11758196C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×C22⋊Dic61C2×C411yescharacteristic
129C2×C22⋊Dic61C2×C411yescharacteristic
130C2×C4×Dic61—22no—
131C2×C4×Dic61—22no—
132C2×C4×Dic61C2×C411yescharacteristic
133C2×C4×Dic61C2×C411yescharacteristic
134C2×C4×Dic61C2311yescharacteristic
135C2×C4×Dic61C2311yescharacteristic
136C2×C4×Dic61C2311yescharacteristic
137C2×C4×Dic61C2311yescharacteristic
138C2×C4×Dic61C2311yescharacteristic
139C2×C4×Dic61C2311yescharacteristic
140C22×Q8×C61C2×C411yescharacteristic
141C23×C4×C61C2×C411yescharacteristic
142C22⋊Q8×C61—24no—
143C2×C4⋊C4×C61C2×C411yescharacteristic
144C2×C4⋊C4×C61C2×C411yescharacteristic
145C2×C4⋊C4×C61C2×C411yescharacteristic
146C2×C22⋊C4×C61C2×C411yescharacteristic
147C2×C22⋊C4×C61C2×C411yescharacteristic
148C24×C61C22×C411yescharacteristic
149C2×Q8×C61—22no—
150C2×Q8×C61—22no—
151C2×Q8×C61—41no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—41no—
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—41no—
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C2×D412yes—
172C22×Dic61C2×D412yes—
173C22×Dic61C2×Q812yes—
174C22×Dic61C2×Q812yes—
175C22×Dic61#4112yes—
176C22×Dic61#4112yes—
177C22×Dic61C2411yescharacteristic
178C2×Dic122—22no—
179C2×Dic122—22no—
180C2×Dic122—22no—
181C2×Dic122—22no—
182C2×Dic122—22no—
183C2×Dic122—22no—
184C2×Dic122—41no—
185C2×Dic122—41no—
186C2×Dic122—41no—
187#11758217—28no—
188#11758217—44no—
189C2×#92420—28no—
190C2×#92420—21no—
191C2×#92420—21no—
192C2×#92420—21no—
193C2×#92420—21no—
194C2×#92420—21no—
195C2×#92420—21no—
196C2×#92420—21no—
197C2×#92420—21no—
198C2×#92420—21no—
199C2×#92420—21no—
200C2×#92420—21no—
201C2×#92420—21no—
202C2×#92420—21no—
203C2×#92420—21no—
204C2×#92420—21no—
205C2×#92420—21no—
206C2×#92420—21no—
207C2×#92420—21no—
208C2×#92420—21no—
209C2×#92420—21no—
210C2×#92420—44no—
211C2×#92420C2×Q812yes—
212C2×#92420C2×Q812yes—
213C2×#92420C2×Q812yes—
214C2×#92420C2×Q812yes—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61—22no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61C22⋊C414yes—
220C22⋊Dic61—22no—
221C22⋊Dic61C22⋊C414yes—
222C4⋊Dic61—22no—
223C4⋊Dic61—22no—
224C4⋊Dic61—22no—
225#11758196—22no—
226#11758196—22no—
227#11758196—22no—
228#11758196—22no—
229#11758196—22no—
230#11758196—22no—
231#11758196—22no—
232#11758196—22no—
233#11758196C22⋊C414yes—
234#11758196C22⋊C414yes—
235C4×Dic61—22no—
236C4×Dic61—22no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C4×Dic61—21no—
243C4×Dic61—21no—
244C4×Dic61—21no—
245C4×Dic61C2×D412yes—
246C4×Dic61C2×D412yes—
247C4×Dic61C2×D412yes—
248C4×Dic61C2×D412yes—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61C2×C22⋊C412yes—
254C23×C61C4×Q812yes—
255C23×C61C4×Q812yes—
256C23×C61C23×C411yescharacteristic
257Q8×C61—44no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—44no—
274C2×C4×C61C2×C22⋊C412yes—
275C2×C4×C61C2×C22⋊C412yes—
276C2×C4×C61#13112yes—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—44no—
293C2×Dic61C2×C22⋊C412yes—
294C2×Dic61C2×C22⋊C412yes—
295C2×Dic61C2×C22⋊C412yes—
296C2×Dic61C4×Q812yes—
297C2×Dic61C4×Q812yes—
298C2×Dic61C22⋊Q814yes—
299C2×Dic61C22⋊Q814yes—
300C2×Dic61#12414yes—
301C2×Dic61C4⋊Q814yes—
302C2×Dic61#13112yes—
303C2×Dic61C22×D411yescharacteristic
304C2×Dic61C22×D411yescharacteristic
305C2×Dic61C22×Q811yescharacteristic
306C2×Dic61C22×Q811yescharacteristic
307C2×Dic61C2×#4111yescharacteristic
308C2×Dic61C2×#4111yescharacteristic
309Dic122—44no—
310Dic122—44no—
311Dic122—44no—
312#92420—22no—
313#92420—22no—
314#92420—22no—
315#92420—22no—
316#92420—41no—
317#92420—41no—
318#92420—41no—
319#92420—41no—
320#21304—611nomaximal, Sylow
321C22×C61—22no—
322C22×C61—22no—
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61#39114yes—
328C22×C61C22×C22⋊C411yescharacteristic
329C22×C61C2×C4×Q811yescharacteristic
330C22×C61C2×C4×Q811yescharacteristic
331C22×C61C2×#13111yescharacteristic
332C22×C61C2×#13111yescharacteristic
333C22×C61#56811yescharacteristic
334C22×C61#56811yescharacteristic
335C4×C61—22no—
336C4×C61—22no—
337C4×C61—22no—
338C4×C61—41no—
339C4×C61—41no—
340C4×C61—41no—
341Dic61—22no—
342Dic61—22no—
343Dic61—22no—
344Dic61—41no—
345Dic61—41no—
346Dic61—41no—
347Dic61#39114yes—
348Dic61C2×C22⋊Q811yescharacteristic
349Dic61C2×C22⋊Q811yescharacteristic
350Dic61C2×#12411yescharacteristic
351Dic61C2×C4⋊Q811yescharacteristic
352C2×#533—611no—
353C2×#424—611no—
354C2×#405—611no—
355#1985—611no—
356#1985—611no—
357#1985—611no—
358#1985—611no—
359#1984—611no—
360#1984—611no—
361#1984—611no—
362#1984—611no—
363#1729—611no—
364#1729—611no—
365#1728—611no—
366C2×#336—611no—
367C2×C61—24no—
368C2×C61C2×#39111yescharacteristic
369C2×C61#288011yescharacteristic
370C2×C61#288011yescharacteristic
371C2×C61#296011yescharacteristic
372C2×C61#296111yescharacteristic
373C2×C61#296211yescharacteristic
374C2×C61#296211yescharacteristic
375C22×M16—611no—
376C22×M16—611no—
377C23×C8—611no—
378C23×C8—611no—
379#533—1224no—
380#533—1224no—
381C2×C4⋊Q8—611no—
382C2×C4⋊Q8—611no—
383C2×#125—611no—
384C2×#125—611no—
385C2×C22⋊Q8—611no—
386C2×C22⋊Q8—611no—
387C2×C22⋊Q8—611no—
388C2×C22⋊Q8#692311yescharacteristic
389C2×C4×Q8—611no—
390C2×C4×Q8—611no—
391C2×C4×Q8—611no—
392C2×C4×Q8—611no—
393C2×#117—611no—
394C2×#117—611no—
395C22×C42—611no—
396#424—1224no—
397C2×C4⋊C8—611no—
398C2×C4⋊C8—611no—
399C2×C4⋊C8—611no—
400C2×C4⋊C8—611no—
401#405—1224no—
402C2×#97—611no—
403C2×#97—611no—
404C2×C4×C8—611no—
405C2×C4×C8—611no—
406#336—611no—
407#336—611no—
408#336—611no—
409#336—611no—
410#336—611no—
411#336—611no—
412#336—611no—
413#336—611no—
414#336—611no—
415#336—611no—
416#336—611no—
417#336—611no—
418#336—611no—
419#336—611no—
420#336—611no—
421#336—611no—
422C61#2130411yescharacteristic, complemented, Sylow
423C22×Q8—611no—
424C22×Q8—611no—
425C22×Q8—611no—
426C22×Q8C2×#692311yescharacteristic
427C23×C4—611no—
428C23×C4—611no—
429C23×C4C2×#692311yescharacteristic
430C2×M16—614no—
431C2×M16—1222no—
432C2×M16—1222no—
433C2×M16—1222no—
434C2×M16—1222no—
435C2×M16—1222no—
436C22×C8—614no—
437C22×C8—611no—
438C22×C8—611no—
439C22×C8—611no—
440C22×C8—611no—
441C22×C8—611no—
442C22×C8—611no—
443C22×C8—611no—
444C22×C8—611no—
445C22×C8—1222no—
446C22×C8—1222no—
447C22×C8—1222no—
448C22×C8—1222no—
449C22×C8—1222no—
450C4⋊Q8—1224no—
451C4⋊Q8—1224no—
452#125—1224no—
453#125—1224no—
454C22⋊Q8—24no—
455C22⋊Q8—1224no—
456C22⋊Q8—1224no—
457C22⋊Q8—1224no—
458C4×Q8—1222no—
459C4×Q8—1222no—
460C4×Q8—1222no—
461C4×Q8—1222no—
462C4×Q8—1222no—
463C4×Q8—1222no—
464C4×Q8—1222no—
465C4×Q8—1222no—
466#117—614no—
467#117—614no—
468#117—1222no—
469#117—1222no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4C2×#692311yescharacteristic
484C2×C4⋊C4C2×#692311yescharacteristic
485C2×C4⋊C4C2×#692311yescharacteristic
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4C2×#692311yescharacteristic
489C2×C22⋊C4C2×#692311yescharacteristic
490C2×C42—611no—
491C2×C42—611no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—611no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42—1222no—
499C2×C42—1222no—
500C4⋊C8—1222no—
501C4⋊C8—1222no—
502C4⋊C8—1222no—
503C4⋊C8—1222no—
504#97—1222no—
505#97—1222no—
506C4×C8—1222no—
507C4×C8—1222no—
508C24C22×#692311yescharacteristic
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—41no—
512C2×Q8—1222no—
513C2×Q8—1222no—
514C2×Q8—1222no—
515C2×Q8—1222no—
516C2×Q8—1222no—
517C2×Q8—1222no—
518C2×Q8—2441no—
519C2×Q8—2441no—
520C2×Q8—2441no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—41no—
524C22×C4—612no—
525C22×C4—612no—
526C22×C4—612no—
527C22×C4—612no—
528C22×C4—612no—
529C22×C4—612no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—1222no—
539C22×C4—1222no—
540C22×C4—2441no—
541C22×C4C22×#692311yescharacteristic
542C22×C4C22×#692311yescharacteristic
543C22×C4C22×#692311yescharacteristic
544C22×C4C22×#692311yescharacteristic
545C22×C4C22×#692311yescharacteristic
546C22×C4C22×#692311yescharacteristic
547M16—1228no—
548M16—2444no—
549C2×C8—612no—
550C2×C8—612no—
551C2×C8—612no—
552C2×C8—612no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8—1221no—
557C2×C8—1228no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—2444no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—614no—
579C4⋊C4—614no—
580C4⋊C4—1222no—
581C4⋊C4—1222no—
582C4⋊C4—1222no—
583C4⋊C4—1222no—
584C4⋊C4—1222no—
585C4⋊C4—1222no—
586C4⋊C4—1222no—
587C4⋊C4—1222no—
588C4⋊C4—1222no—
589C4⋊C4—1222no—
590C4⋊C4—1222no—
591C22⋊C4—22no—
592C22⋊C4—614no—
593C22⋊C4—1222no—
594C22⋊C4C22⋊#692314yes—
595C42—612no—
596C42—612no—
597C42—612no—
598C42—612no—
599C42—1221no—
600C42—1221no—
601C42—1221no—
602C42—1221no—
603C42—1222no—
604C42—1222no—
605C42—1221no—
606C42—1221no—
607C42—1221no—
608C42—1221no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23C2×C22⋊#692312yes—
614C23Q8×#692312yes—
615C23Q8×#692312yes—
616C23C23×#692311yescharacteristic
617Q8—44no—
618Q8—2444no—
619Q8—2444no—
620Q8—2444no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—44no—
637C2×C4—614no—
638C2×C4—614no—
639C2×C4—614no—
640C2×C4—614no—
641C2×C4—612no—
642C2×C4—611no—
643C2×C4—611no—
644C2×C4—612no—
645C2×C4—612no—
646C2×C4—611no—
647C2×C4—611no—
648C2×C4—611no—
649C2×C4—611no—
650C2×C4—612no—
651C2×C4—612no—
652C2×C4—612no—
653C2×C4—1221no—
654C2×C4—1221no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—2444no—
669C2×C4C2×C22⋊#692312yes—
670C2×C4C2×C22⋊#692312yes—
671C2×C4#1451986412yes—
672C8—1222no—
673C8—1222no—
674C8—1222no—
675C8—1222no—
676C8—2441no—
677C8—2441no—
678C8—2441no—
679C8—2441no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22(C2×#6923)⋊Q814yes—
687C22C22×C22⋊#692311yescharacteristic
688C22C2×Q8×#692311yescharacteristic
689C22C2×Q8×#692311yescharacteristic
690C22C2×#1451986411yescharacteristic
691C22D61⋊#13111yescharacteristic
692C22#1684084011yescharacteristic
693C22#1684084111yescharacteristic
694C4—22no—
695C4—22no—
696C4—22no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—611no—
701C4—611no—
702C4—611no—
703C4—611no—
704C4—614no—
705C4—1222no—
706C4—1222no—
707C4—1222no—
708C4—2441no—
709C4—2441no—
710C4—2441no—
711C2—24no—
712C2C2×(C2×#6923)⋊Q811yescharacteristic
713C2#2146240711yescharacteristic
714C2#2146240911yescharacteristic
715C2#2146260711yescharacteristic
716C2#2146261011yescharacteristic
717C2#2146261411yescharacteristic
718C2#2146261611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×C22⋊Q8×C61C4
prime radicalC24×C61C22×C4
cosocleC22×Dic61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#21304
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21461993C2semidirect
4. #21461992C2semidirect
5. #21461992C2semidirect
6. #21461991C2semidirect
7. #21461990C2semidirect
8. #21461990C2semidirect
9. #21461989C2semidirect
10. #21461988C2semidirect
68. C2×#11758217Q8semidirect
74. C22×#92420Q8semidirect
422. C61#21304semidirect

Maximal subgroups

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

subgroupindex
C2×#168407682
C2×#168407262
#214619932
#214619922
#214619912
#214619902
#214619892
#214619882
#214614852
#214614822
C2×#168406282
C2×#168403142
#2130461