Finite Group Databasebeta

← #30622698

Subgroups — #30622698

Order 15616.

1116 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840794C211yesmaximal, characteristic, complemented
2C2×#16840793C211yesmaximal, characteristic, complemented
3C2×#16840792C211yesmaximal, characteristic, complemented
4C2×#16840791C211yesmaximal, characteristic, complemented
5#21461945C211yesmaximal, characteristic, complemented
6#21461944C211yesmaximal, characteristic, complemented
7#21461944C211yesmaximal, characteristic, complemented
8#21461943C211yesmaximal, characteristic, complemented
9#21461798C211yesmaximal, characteristic, complemented
10#21461797C211yesmaximal, characteristic, complemented
11#21461794C211yesmaximal, characteristic, complemented
12#21461793C211yesmaximal, characteristic, complemented
13#21461605C211yesmaximal, characteristic, complemented
14#21461604C211yesmaximal, characteristic, complemented
15#21448383C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×#11758217C2211yescharacteristic
18C22×D61⋊C8C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840794—24no—
21#16840793—24no—
22#16840792—24no—
23#16840791—24no—
24C2×#14519844C2211yescharacteristic
25C2×#14519844C2211yescharacteristic
26C2×C4⋊#92420C2211yescharacteristic
27C2×C4⋊#92420C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×#14519834C2211yescharacteristic
32C2×#14519834C2211yescharacteristic
33C2×#14519834C2211yescharacteristic
34C2×C22⋊#92420C2211yescharacteristic
35C2×C22⋊#92420C2211yescharacteristic
36C2×C22⋊#92420C2211yescharacteristic
37C2×C22⋊#92420C2211yescharacteristic
38C2×C22⋊#92420C2211yescharacteristic
39C2×C22⋊#92420C2211yescharacteristic
40C2×#14519832C2211yescharacteristic
41C2×#14519832C2211yescharacteristic
42C2×#14519832C2211yescharacteristic
43C2×#14519832C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48C2×#14519773C411yescharacteristic
49C2×D4×Dic61C2211yescharacteristic
50C2×#14519739C2211yescharacteristic
51C2×#14519737C2211yescharacteristic
52C2×#14519737C2211yescharacteristic
53C2×#14519737C2211yescharacteristic
54C2×#14519737C2211yescharacteristic
55#16839664C411yescharacteristic
56#16839662C411yescharacteristic
57#16839662C411yescharacteristic
58#16839662C411yescharacteristic
59#16839662C411yescharacteristic
60#16839631C411yescharacteristic
61C42×Dic61C2211yescharacteristic
62C61×#390C411yescharacteristic
63C2×#11758213—22no—
64C2×#11758213—22no—
65C2×#11758213—41no—
66C2×#11758217—22no—
67C2×#11758217—22no—
68C2×#11758217—41no—
69C2×D61⋊C8—22no—
70C2×D61⋊C8—22no—
71C2×D61⋊C8—41no—
72C22×#92420—22no—
73C22×#92420—22no—
74C22×#92420—41no—
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83#14519844—22no—
84#14519844D414yescomplemented
85C4⋊#92420—22no—
86C4⋊#92420D414yescomplemented
87#14519834—22no—
88#14519834—22no—
89#14519834—22no—
90#14519834—22no—
91#14519834—41no—
92#14519834—41no—
93C22⋊#92420—22no—
94C22⋊#92420—22no—
95C22⋊#92420—22no—
96C22⋊#92420—22no—
97C22⋊#92420—41no—
98C22⋊#92420—41no—
99#14519832—22no—
100#14519832—22no—
101#14519832—22no—
102#14519832—22no—
103C22×D244C2×C411yescharacteristic
104C22×C22⋊D61C2×C411yescharacteristic
105C22×C22⋊D61C2×C411yescharacteristic
106C22×C22⋊D61C2×C411yescharacteristic
107C22×C22⋊D61C2×C411yescharacteristic
108C23×Dic61C2311yescharacteristic
109C23×Dic61C2311yescharacteristic
110C22×C4×D61C2311yescharacteristic
111C22×C4×D61C2311yescharacteristic
112#14519773—24no—
113D4×Dic61—22no—
114D4×Dic61—22no—
115#14519739—22no—
116#14519739—22no—
117#14519737—22no—
118#14519737—22no—
119#14519737—22no—
120#14519737—22no—
121#14519737—41no—
122#14519737—41no—
123#14519737—41no—
124#14519737—41no—
125C2×C4⋊Dic61C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758196C2×C411yescharacteristic
129C2×#11758196C2×C411yescharacteristic
130C2×C22⋊Dic61C2×C411yescharacteristic
131C2×C22⋊Dic61C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×#11758198C2×C411yescharacteristic
136C2×#11758198C2×C411yescharacteristic
137C2×#11758198C2×C411yescharacteristic
138C2×C4×Dic61C2×C411yescharacteristic
139C2×C4×Dic61C2×C411yescharacteristic
140C2×C4×Dic61C2×C411yescharacteristic
141C2×C4×Dic61C2311yescharacteristic
142C2×C4×Dic61C2311yescharacteristic
143C2×C4×Dic61C2311yescharacteristic
144C22×D4×C61C2×C411yescharacteristic
145C2×C4⋊C4×C61C2×C411yescharacteristic
146C2×C22⋊C4×C61C2×C411yescharacteristic
147C2×C22⋊C4×C61C2×C411yescharacteristic
148C2×C22⋊C4×C61C2×C411yescharacteristic
149C2×C22⋊C4×C61C2×C411yescharacteristic
150C2×C42×C61C2×C411yescharacteristic
151C24×C61C22×C411yescharacteristic
152C24×C61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—41no—
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—41no—
169C2×C22⋊D61—41no—
170C2×C22⋊D61—41no—
171C2×C22⋊D61—41no—
172C2×C22⋊D61—41no—
173C2×C22⋊D61—41no—
174C2×C22⋊D61M1614yescomplemented
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C2411yescharacteristic
193C2×D244—22no—
194C2×D244—22no—
195C2×D244—41no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208#11758217—44no—
209C2×#92420—21no—
210C2×#92420—21no—
211C2×#92420—21no—
212C2×#92420—21no—
213C2×#92420—21no—
214C2×#92420—21no—
215C2×#92420—21no—
216C2×#92420—21no—
217C2×#92420—21no—
218C2×#92420—21no—
219C2×#92420—21no—
220C2×#92420—21no—
221C2×#92420—21no—
222C2×#92420—21no—
223C2×#92420—21no—
224C2×#92420—21no—
225C2×#92420—21no—
226C2×#92420—21no—
227C2×#92420—21no—
228C2×#92420—21no—
229C2×#92420—44no—
230C2×#92420C2×D412yes—
231C2×#92420C2×D412yes—
232C2×#92420C2×D412yes—
233C2×#92420C2×D412yes—
234#11758213—44no—
235D61⋊C8—44no—
236C4⋊C4×C61—22no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—41no—
240C22⋊C4×C61—41no—
241C42×C61—41no—
242C22⋊Dic61—22no—
243C22⋊Dic61—22no—
244#11758198—22no—
245#11758198—22no—
246#11758198—22no—
247#11758198—22no—
248#11758198—41no—
249#11758198—41no—
250C4⋊Dic61—22no—
251#11758196—22no—
252#11758196—22no—
253#11758196—41no—
254#11758196—41no—
255C4×Dic61—22no—
256C4×Dic61—21no—
257C4×Dic61—21no—
258C4×Dic61—41no—
259C4×Dic61—41no—
260C4×Dic61C2×D412yes—
261C4×Dic61C2×D412yes—
262C4×Dic61#4112yes—
263C4×Dic61#4112yes—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61C2×M1612yes—
278C23×C61C23×C411yescharacteristic
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61C2×M1612yes—
293D4×C61—44no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61C4×D412yes—
308C2×C4×C61C4×D412yes—
309C22⋊D61—44no—
310C22⋊D61—44no—
311C22⋊D61—44no—
312C22⋊D61—44no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61C4×D412yes—
334C2×Dic61C4×D412yes—
335C2×Dic61C2×M1612yes—
336C2×Dic61C22×D411yescharacteristic
337C2×Dic61C22×D411yescharacteristic
338C2×Dic61C2×#4111yescharacteristic
339C2×Dic61C2×#4111yescharacteristic
340C2×Dic61H(5,𝔽2)11yescharacteristic
341C2×Dic61H(5,𝔽2)11yescharacteristic
342D244—44no—
343C4×D61—41no—
344C4×D61—41no—
345C4×D61—41no—
346C4×D61—41no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351#92420—22no—
352#92420—22no—
353#92420—22no—
354#92420—22no—
355#92420—41no—
356#92420—41no—
357#92420—41no—
358#92420—41no—
359#23175—611nomaximal, Sylow
360C22×C61—22no—
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61C2×C4×D411yescharacteristic
375C22×C61C2×C4×D411yescharacteristic
376C22×C61#51811yescharacteristic
377C22×C61C22×M1611yescharacteristic
378C22×C61#56811yescharacteristic
379C22×C61#56811yescharacteristic
380C22×C61#56811yescharacteristic
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C4×C61—22no—
396C4×C61—22no—
397C4×C61—41no—
398C4×C61—41no—
399C4×C61—41no—
400Dic61—22no—
401Dic61—22no—
402Dic61—22no—
403Dic61—41no—
404Dic61—41no—
405Dic61D4211yescharacteristic
406Dic61#55011yescharacteristic
407Dic61#55011yescharacteristic
408Dic61#55911yescharacteristic
409C2×#435—611no—
410C2×#435—611no—
411C2×#435—611no—
412C2×#435—611no—
413C4×#127—611no—
414#1955—611no—
415#1955—611no—
416#1955—611no—
417#1955—611no—
418#1870—611no—
419#1870—611no—
420#1869—611no—
421#1869—611no—
422#1767—611no—
423#1767—611no—
424C2×C61—42no—
425C2×C61—81no—
426C2×C61#236611yescharacteristic
427C2×C61#293211yescharacteristic
428C2×C61#293211yescharacteristic
429C2×C61D4×M1611yescharacteristic
430C2×C61D4×M1611yescharacteristic
431C2×C61#297311yescharacteristic
432C2×C61#298011yescharacteristic
433D61—42no—
434D61—81no—
435C22×M16—611no—
436C22×M16—611no—
437C23×C8—611no—
438C23×C8—611no—
439C2×#127—611no—
440C2×C4×D4—611no—
441C2×C4×D4—611no—
442C2×C4×D4—611no—
443C2×C4×D4—611no—
444C2×C4×D4—611no—
445C2×C4×D4—611no—
446#435—1224no—
447#435—1224no—
448#435—1224no—
449#435—1224no—
450C2×C4⋊C8—611no—
451C2×C4⋊C8—611no—
452C2×C4⋊C8—611no—
453C2×C4⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×C22⋊C8—611no—
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461C2×C22⋊C8—611no—
462C2×C22⋊C8—611no—
463C2×C22⋊C8—611no—
464C2×C22⋊C8—611no—
465C2×C22⋊C8—611no—
466C2×#97—611no—
467C2×#97—611no—
468C2×#97—611no—
469C2×#97—611no—
470#390—611no—
471#390—611no—
472#390—611no—
473#390—611no—
474#390—611no—
475#390#692311yescharacteristic
476#384—611no—
477C43—611no—
478#336—611no—
479#336—611no—
480#336—611no—
481#336—611no—
482C61#2317511yescharacteristic, complemented, Sylow
483C22×D4—611no—
484C22×D4—611no—
485C22×D4—611no—
486C22×D4—611no—
487C22×D4—611no—
488C22×D4C2×#692311yescharacteristic
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C2×M16—1222no—
494C2×M16—1222no—
495C2×M16—1222no—
496C2×M16—1222no—
497C2×M16—2441no—
498C2×M16—2441no—
499C22×C8—611no—
500C22×C8—611no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—611no—
505C22×C8—611no—
506C22×C8—611no—
507C22×C8—1222no—
508C22×C8—1222no—
509C22×C8—1222no—
510C22×C8—1222no—
511C22×C8—2441no—
512C22×C8—2441no—
513#127—1224no—
514C4×D4—1222no—
515C4×D4—1222no—
516C4×D4—1222no—
517C4×D4—1222no—
518C4×D4—1222no—
519C4×D4—1222no—
520C4×D4—1222no—
521C4×D4—1222no—
522C4×D4—2441no—
523C4×D4—2441no—
524C4×D4—2441no—
525C4×D4—2441no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4C2×#692311yescharacteristic
532C2×C22⋊C4—611no—
533C2×C22⋊C4—611no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—611no—
539C2×C22⋊C4—611no—
540C2×C22⋊C4C2×#692311yescharacteristic
541C2×C22⋊C4C2×#692311yescharacteristic
542C2×C22⋊C4C2×#692311yescharacteristic
543C2×C22⋊C4C2×#692311yescharacteristic
544C2×C42—611no—
545C2×C42—611no—
546C2×C42—611no—
547C2×C42—611no—
548C2×C42—611no—
549C2×C42—611no—
550C2×C42C2×#692311yescharacteristic
551C4⋊C8—614no—
552C4⋊C8—614no—
553C4⋊C8—1222no—
554C4⋊C8—1222no—
555C22⋊C8—1222no—
556C22⋊C8—1222no—
557C22⋊C8—1222no—
558C22⋊C8—1222no—
559C22⋊C8—1222no—
560C22⋊C8—1222no—
561C22⋊C8—1222no—
562C22⋊C8—1222no—
563C22⋊C8—2441no—
564C22⋊C8—2441no—
565C22⋊C8—2441no—
566C22⋊C8—2441no—
567#97—1222no—
568#97—1222no—
569#97—1222no—
570#97—1222no—
571C24—611no—
572C24—611no—
573C24C22×#692311yescharacteristic
574C24C22×#692311yescharacteristic
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—41no—
578C2×D4—614no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—1222no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—2441no—
587C2×D4—2441no—
588C2×D4—2441no—
589C2×D4—2441no—
590C2×D4—2441no—
591C2×D4—2441no—
592C2×D4—2441no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4C22×#692311yescharacteristic
624C22×C4C22×#692311yescharacteristic
625C22×C4C22×#692311yescharacteristic
626C22×C4C22×#692311yescharacteristic
627C22×C4C22×#692311yescharacteristic
628M16—2444no—
629M16—2444no—
630C2×C8—612no—
631C2×C8—612no—
632C2×C8—612no—
633C2×C8—612no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—2444no—
655C2×C8—2444no—
656C4⋊C4—22no—
657C4⋊C4—1222no—
658C4⋊C4—1222no—
659C4⋊C4—1222no—
660C4⋊C4—2441no—
661C4⋊C4—2441no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—1222no—
667C22⋊C4—1222no—
668C22⋊C4—1222no—
669C22⋊C4—1222no—
670C22⋊C4—1222no—
671C22⋊C4—1222no—
672C22⋊C4—2441no—
673C22⋊C4—2441no—
674C42—41no—
675C42—612no—
676C42—612no—
677C42—612no—
678C42—612no—
679C42—1221no—
680C42—1221no—
681C42—1222no—
682C42—2441no—
683C42—2441no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—612no—
698C23—1221no—
699C23—1221no—
700C23—1221no—
701C23—1221no—
702C23—1221no—
703C23—1221no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1221no—
710C23—1221no—
711C23D61⋊M1612yes—
712C23C23×#692311yescharacteristic
713D4—44no—
714D4—2444no—
715D4—2444no—
716D4—2444no—
717D4—2444no—
718D4—2444no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—611no—
733C2×C4—611no—
734C2×C4—611no—
735C2×C4—611no—
736C2×C4—611no—
737C2×C4—611no—
738C2×C4—612no—
739C2×C4—612no—
740C2×C4—612no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4D4×#692312yes—
770C2×C4D4×#692312yes—
771C8—1222no—
772C8—1222no—
773C8—1222no—
774C8—1222no—
775C8—2441no—
776C8—2441no—
777C8—2441no—
778C8—2441no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—1222no—
794C22—1222no—
795C22—1222no—
796C22—2441no—
797C22—2441no—
798C22—2441no—
799C22—2441no—
800C22—2441no—
801C22—2441no—
802C22—2441no—
803C22—2441no—
804C22—2441no—
805C22—2441no—
806C22—2441no—
807C22C2×D4×#692311yescharacteristic
808C22C2×D4×#692311yescharacteristic
809C22#1684082911yescharacteristic
810C22C2×D61⋊M1611yescharacteristic
811C22#1684084011yescharacteristic
812C22#1684084111yescharacteristic
813C22#1684084111yescharacteristic
814C4—22no—
815C4—22no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—611no—
820C4—611no—
821C4—611no—
822C4—611no—
823C4—1222no—
824C4—1222no—
825C4—1222no—
826C4—2441no—
827C4—2441no—
828C2—42no—
829C2—81no—
830C2—4881no—
831C2—2442no—
832C2#2146234911yescharacteristic
833C2#2146254511yescharacteristic
834C2#2146254711yescharacteristic
835C2#2146255711yescharacteristic
836C2#2146255811yescharacteristic
837C2#2146267111yescharacteristic
838C2#2146270311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#390C4
prime radicalC2×#14519773C4
cosocleC22×Dic61C24
hypercenter#390#6923
hypocenterC61#23175
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#16840794C2semidirect
2. C2×#16840793C2semidirect
3. C2×#16840792C2semidirect
4. C2×#16840791C2semidirect
5. #21461945C2semidirect
6. #21461944C2semidirect
7. #21461944C2semidirect
8. #21461943C2semidirect
9. #21461798C2semidirect
10. #21461797C2semidirect
11. #21461794C2semidirect
12. #21461793C2semidirect
13. #21461605C2semidirect
14. #21461604C2semidirect
84. #14519844D4semidirect
86. C4⋊#92420D4semidirect
174. C2×C22⋊D61M16semidirect
482. C61#23175semidirect

Maximal subgroups

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

subgroupindex
C2×#168407942
C2×#168407932
C2×#168407922
C2×#168407912
#214619452
#214619442
#214619432
#214617982
#214617972
#214617942
#214617932
#214616052
#214616042
#214483832
#2317561