Finite Group Databasebeta

← #30622710

Subgroups — #30622710

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840796C211yesmaximal, characteristic, complemented
2C2×#16840795C211yesmaximal, characteristic, complemented
3C2×#16840794C211yesmaximal, characteristic, complemented
4C2×#16840792C211yesmaximal, characteristic, complemented
5#21461945C211yesmaximal, characteristic, complemented
6#21461944C211yesmaximal, characteristic, complemented
7#21461942C211yesmaximal, characteristic, complemented
8#21461941C211yesmaximal, characteristic, complemented
9#21461799C211yesmaximal, characteristic, complemented
10#21461798C211yesmaximal, characteristic, complemented
11#21461797C211yesmaximal, characteristic, complemented
12#21461795C211yesmaximal, characteristic, complemented
13#21461607C211yesmaximal, characteristic, complemented
14#21461607C211yesmaximal, characteristic, complemented
15#21449099C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×#11758213C2211yescharacteristic
18C22×#11758217C2211yescharacteristic
19C22×D61⋊C8C2211yescharacteristic
20#16840796—24no—
21#16840795—24no—
22#16840794—24no—
23#16840792—24no—
24C2×#14519844C2211yescharacteristic
25C2×#14519844C2211yescharacteristic
26C2×C4⋊#92420C2211yescharacteristic
27C2×C4⋊#92420C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×#14519834C2211yescharacteristic
32C2×#14519834C2211yescharacteristic
33C2×#14519834C2211yescharacteristic
34C2×#14519834C2211yescharacteristic
35C2×#14519834C2211yescharacteristic
36C2×#14519834C2211yescharacteristic
37C2×C22⋊#92420C2211yescharacteristic
38C2×C22⋊#92420C2211yescharacteristic
39C2×C22⋊#92420C2211yescharacteristic
40C2×#14519832C2211yescharacteristic
41C2×#14519832C2211yescharacteristic
42C2×C4×#92420C2211yescharacteristic
43C2×C4×#92420C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48C2×#14519739C2211yescharacteristic
49C2×#14519739C2211yescharacteristic
50C2×#14519739C2211yescharacteristic
51C2×#14519737C2211yescharacteristic
52C2×#14519737C2211yescharacteristic
53C2×#14519737C2211yescharacteristic
54#16839697C411yescharacteristic
55#16839697C411yescharacteristic
56#16839697C411yescharacteristic
57#16839672C411yescharacteristic
58#16839671C411yescharacteristic
59#16839671C411yescharacteristic
60#16839671C411yescharacteristic
61#16839607C2211yescharacteristic
62C61×#399C411yescharacteristic
63C2×#11758213—22no—
64C2×#11758213—22no—
65C2×#11758213—22no—
66C2×#11758213—22no—
67C2×#11758213—41no—
68C2×#11758213—41no—
69C2×#11758217—22no—
70C2×#11758217—22no—
71C2×#11758217—41no—
72C2×D61⋊C8—22no—
73C2×D61⋊C8—22no—
74C2×D61⋊C8—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—22no—
92#14519834—22no—
93#14519834—41no—
94#14519834—41no—
95#14519834—41no—
96C22⋊#92420—22no—
97C22⋊#92420—22no—
98C22⋊#92420—41no—
99#14519832—22no—
100#14519832—22no—
101C4×#92420—22no—
102C4×#92420—22no—
103C22×D244C2×C411yescharacteristic
104C22×D244C2×C411yescharacteristic
105C22×D244C2×C411yescharacteristic
106C22×C22⋊D61C2×C411yescharacteristic
107C22×C22⋊D61C2×C411yescharacteristic
108C22×C22⋊D61C2×C411yescharacteristic
109C23×Dic61C2311yescharacteristic
110C22×C4×D61C2311yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113#14519739—22no—
114#14519739—22no—
115#14519739—22no—
116#14519739—22no—
117#14519739—41no—
118#14519739—41no—
119#14519737—22no—
120#14519737—22no—
121#14519737—22no—
122#14519737—22no—
123#14519737—41no—
124#14519737—41no—
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×#11758198C2×C411yescharacteristic
130C2×#11758198C2×C411yescharacteristic
131C2×#11758198C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×#11758198C2×C411yescharacteristic
136C2×#11758198C2×C411yescharacteristic
137C2×C4×Dic61C2311yescharacteristic
138C2×C4×Dic61C2311yescharacteristic
139C2×C4×Dic61C2311yescharacteristic
140#14519684C2×C411yescharacteristic
141#14519684C2×C411yescharacteristic
142#14519684C2×C411yescharacteristic
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
148C2×C22⋊C4×C61C2×C411yescharacteristic
149#95×C61C2×C411yescharacteristic
150C24×C61C22×C411yescharacteristic
151C23×D61C22×C411yescharacteristic
152C23×D61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—41no—
164C2×C22⋊D61—41no—
165C2×C22⋊D61—41no—
166C2×C22⋊D61—41no—
167C2×C22⋊D61—41no—
168C2×C22⋊D61—41no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C2411yescharacteristic
180C2×D244—22no—
181C2×D244—22no—
182C2×D244—22no—
183C2×D244—22no—
184C2×D244—41no—
185C2×D244—41no—
186C2×D244—41no—
187C2×D244—41no—
188C2×D244—41no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
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—
207#11758217—44no—
208C2×#92420—21no—
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×#92420C2×D412yes—
229C2×#92420C2×D412yes—
230C2×#92420C2×D412yes—
231C2×#92420C2×D412yes—
232#11758213—44no—
233#11758213—44no—
234D61⋊C8—44no—
235C4⋊C4×C61—22no—
236C4⋊C4×C61—22no—
237C4⋊C4×C61—41no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—41no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244#11758198—22no—
245#11758198—22no—
246#11758198—22no—
247#11758198—41no—
248#11758198—41no—
249#11758198—41no—
250#11758196—22no—
251#11758196—22no—
252#11758196—41no—
253C4×Dic61—21no—
254C4×Dic61—21no—
255C4×Dic61C2×D412yes—
256C4×Dic61C2×D412yes—
257C4×Dic61#4112yes—
258C4×Dic61#4112yes—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61C23×C411yescharacteristic
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
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#13112yes—
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—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61C4×D412yes—
305C2×C4×C61C4×D412yes—
306C22⋊D61—44no—
307C22⋊D61—44no—
308C22⋊D61—44no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61C4×D412yes—
324C2×Dic61C4×D412yes—
325C2×Dic61C22×D411yescharacteristic
326C2×Dic61C22×D411yescharacteristic
327C2×Dic61C2×#4111yescharacteristic
328C2×Dic61C2×#4111yescharacteristic
329C2×Dic61H(5,𝔽2)11yescharacteristic
330C2×Dic61H(5,𝔽2)11yescharacteristic
331D244—44no—
332D244—44no—
333D244—44no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61—41no—
344C4×D61—41no—
345C4×D61—41no—
346#92420—22no—
347#92420—22no—
348#92420—22no—
349#92420—22no—
350#92420—41no—
351#92420—41no—
352#92420—41no—
353#92420—41no—
354#23178—611nomaximal, Sylow
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61C2×C4×D411yescharacteristic
363C22×C61C2×C4×D411yescharacteristic
364C22×C61#51811yescharacteristic
365C22×C61C2×#13111yescharacteristic
366C22×C61#56811yescharacteristic
367C22×C61#56811yescharacteristic
368C22×C61#56811yescharacteristic
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C4×C61—22no—
391C4×C61—22no—
392C4×C61—41no—
393C4×C61—41no—
394C4×C61—41no—
395C4×C61—41no—
396Dic61—22no—
397Dic61—22no—
398Dic61—41no—
399Dic61—41no—
400Dic61D4211yescharacteristic
401Dic61#55011yescharacteristic
402Dic61#55011yescharacteristic
403Dic61#55911yescharacteristic
404C2×#436—611no—
405C2×#436—611no—
406C2×#435—611no—
407C2×#435—611no—
408#2397—611no—
409#1955—611no—
410#1955—611no—
411#1954—611no—
412#1954—611no—
413#1870—611no—
414#1870—611no—
415#1870—611no—
416#1869—611no—
417#1768—611no—
418#1768—611no—
419C2×C61—81no—
420C2×C61#236611yescharacteristic
421C2×C61#293011yescharacteristic
422C2×C61#293011yescharacteristic
423C2×C61#293311yescharacteristic
424C2×C61#293311yescharacteristic
425C2×C61#297611yescharacteristic
426C2×C61#297811yescharacteristic
427D61—42no—
428D61—81no—
429D61—81no—
430C22×M16—611no—
431C22×M16—611no—
432C22×M16—611no—
433C23×C8—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×C4×D4—611no—
438C2×C4×D4—611no—
439C2×C4×D4—611no—
440#436—1224no—
441#436—1224no—
442#435—1224no—
443#435—1224no—
444C2×C4⋊C8—611no—
445C2×C4⋊C8—611no—
446C2×C4⋊C8—611no—
447C2×C4⋊C8—611no—
448C2×C22⋊C8—611no—
449C2×C22⋊C8—611no—
450C2×C22⋊C8—611no—
451C2×C22⋊C8—611no—
452C2×C22⋊C8—611no—
453C2×C22⋊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×#97—611no—
461C2×#97—611no—
462C2×C4×C8—611no—
463C2×C4×C8—611no—
464#399—611no—
465#399—611no—
466#399—611no—
467#399#692311yescharacteristic
468#392—611no—
469#392—611no—
470#392—611no—
471#392—611no—
472#376—611no—
473#336—611no—
474#336—611no—
475#336—611no—
476#336—611no—
477C61#2317811yescharacteristic, complemented, Sylow
478C22×D4—611no—
479C22×D4—611no—
480C22×D4—611no—
481C22×D4—611no—
482C22×D4—611no—
483C22×D4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C2×M16—1222no—
489C2×M16—1222no—
490C2×M16—1222no—
491C2×M16—1222no—
492C2×M16—1222no—
493C2×M16—1222no—
494C2×M16—2441no—
495C2×M16—2441no—
496C2×M16—2441no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8—611no—
500C22×C8—611no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—611no—
505C22×C8—1222no—
506C22×C8—1222no—
507C22×C8—2441no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—1222no—
511C4×D4—1222no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1222no—
515C4×D4—1222no—
516C4×D4—2441no—
517C4×D4—2441no—
518C4×D4—2441no—
519C4×D4—2441no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4C2×#692311yescharacteristic
524C2×C4⋊C4C2×#692311yescharacteristic
525C2×C4⋊C4C2×#692311yescharacteristic
526C2×C22⋊C4—611no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—611no—
533C2×C22⋊C4—611no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4C2×#692311yescharacteristic
536C2×C22⋊C4C2×#692311yescharacteristic
537C2×C22⋊C4C2×#692311yescharacteristic
538C2×C42—611no—
539C2×C42—611no—
540C2×C42—611no—
541C4⋊C8—614no—
542C4⋊C8—614no—
543C4⋊C8—1222no—
544C4⋊C8—1222no—
545C22⋊C8—1222no—
546C22⋊C8—1222no—
547C22⋊C8—1222no—
548C22⋊C8—1222no—
549C22⋊C8—1222no—
550C22⋊C8—1222no—
551C22⋊C8—1222no—
552C22⋊C8—1222no—
553C22⋊C8—2441no—
554C22⋊C8—2441no—
555C22⋊C8—2441no—
556C22⋊C8—2441no—
557#97—1222no—
558#97—1222no—
559C4×C8—1222no—
560C4×C8—1222no—
561#95—611no—
562#95—611no—
563#95—611no—
564#95C2×#692311yescharacteristic
565C24—611no—
566C24—611no—
567C24—611no—
568C24C22×#692311yescharacteristic
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—2441no—
577C2×D4—2441no—
578C2×D4—2441no—
579C2×D4—2441no—
580C2×D4—2441no—
581C2×D4—2441no—
582C2×D4—2441no—
583C2×D4—2441no—
584C2×D4—2441no—
585C2×D4—2441no—
586C2×D4—2441no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
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×C4C22×#692311yescharacteristic
617C22×C4C22×#692311yescharacteristic
618C22×C4C22×#692311yescharacteristic
619C22×C4C22×#692311yescharacteristic
620C22×C4C22×#692311yescharacteristic
621C22×C4C22×#692311yescharacteristic
622M16—2444no—
623M16—2444no—
624M16—2444no—
625C2×C8—612no—
626C2×C8—612no—
627C2×C8—612no—
628C2×C8—612no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
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—2444no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—41no—
653C4⋊C4—1222no—
654C4⋊C4—1222no—
655C4⋊C4—2441no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—41no—
659C22⋊C4—1222no—
660C22⋊C4—1222no—
661C22⋊C4—1222no—
662C22⋊C4—1222no—
663C22⋊C4—1222no—
664C22⋊C4—1222no—
665C22⋊C4—2441no—
666C22⋊C4—2441no—
667C22⋊C4—2441no—
668C42—612no—
669C42—612no—
670C42—612no—
671C42—612no—
672C42—1221no—
673C42—1221no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—612no—
682C23—1221no—
683C23—1221no—
684C23—1221no—
685C23—1221no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1221no—
691C23—1221no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23—1221no—
698C23—1221no—
699C23—1221no—
700C23—1221no—
701C23—1221no—
702C23C23×#692311yescharacteristic
703D4—2444no—
704D4—2444no—
705D4—2444no—
706D4—2444no—
707D4—2444no—
708D4—2444no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—611no—
728C2×C4—611no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—612no—
732C2×C4—612no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4D4×#692312yes—
760C2×C4D4×#692312yes—
761C8—1222no—
762C8—1222no—
763C8—1222no—
764C8—1222no—
765C8—2441no—
766C8—2441no—
767C8—2441no—
768C8—2441no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—1222no—
777C22—1222no—
778C22—1222no—
779C22—2441no—
780C22—2441no—
781C22—2441no—
782C22—2441no—
783C22—2441no—
784C22—2441no—
785C22—2441no—
786C22—2441no—
787C22—2441no—
788C22—2441no—
789C22—2441no—
790C22—2441no—
791C22—2441no—
792C22—2441no—
793C22—2441no—
794C22—2441no—
795C22—2441no—
796C22—2441no—
797C22C2×D4×#692311yescharacteristic
798C22C2×D4×#692311yescharacteristic
799C22#1684082911yescharacteristic
800C22D61⋊#13111yescharacteristic
801C22#1684084111yescharacteristic
802C22#1684084111yescharacteristic
803C22#1684084211yescharacteristic
804C4—22no—
805C4—22no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—611no—
811C4—611no—
812C4—611no—
813C4—611no—
814C4—1222no—
815C4—1222no—
816C4—2441no—
817C4—2441no—
818C2—81no—
819C2—4881no—
820C2—4881no—
821C2—2442no—
822C2#2146234911yescharacteristic
823C2#2146253911yescharacteristic
824C2#2146254011yescharacteristic
825C2#2146255311yescharacteristic
826C2#2146255411yescharacteristic
827C2#2146268711yescharacteristic
828C2#2146269811yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#399C4
prime radical#21449099C2
cosocleC22×Dic61C24
hypercenter#399#6923
hypocenterC61#23178
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#16840796C2semidirect
2. C2×#16840795C2semidirect
3. C2×#16840794C2semidirect
4. C2×#16840792C2semidirect
5. #21461945C2semidirect
6. #21461944C2semidirect
7. #21461942C2semidirect
8. #21461941C2semidirect
9. #21461799C2semidirect
10. #21461798C2semidirect
11. #21461797C2semidirect
12. #21461795C2semidirect
13. #21461607C2semidirect
14. #21461607C2semidirect
84. #14519844D4semidirect
86. C4⋊#92420D4semidirect
477. C61#23178semidirect

Maximal subgroups

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

subgroupindex
C2×#168407962
C2×#168407952
C2×#168407942
C2×#168407922
#214619452
#214619442
#214619422
#214619412
#214617992
#214617982
#214617972
#214617952
#214616072
#214490992
#2317861