Finite Group Databasebeta

← C2×#21462637 #30625563

Subgroups — C2×#21462637 #30625563

Order 15616.

2070 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462637C2116yesmaximal, direct product factor
2C2×#16840814C211yesmaximal, characteristic, complemented
3C2×#16840811C211yesmaximal, characteristic, complemented
4C2×#16840795C211yesmaximal, characteristic, complemented
5C2×#16840794C211yesmaximal, characteristic, complemented
6C2×#16840792C211yesmaximal, characteristic, complemented
7C2×#16840790C211yesmaximal, characteristic, complemented
8C2×#16840789C211yesmaximal, characteristic, complemented
9C2×#16840789C211yesmaximal, characteristic, complemented
10C2×#16840787C211yesmaximal, characteristic, complemented
11C2×#16840786C211yesmaximal, characteristic, complemented
12C2×#16840785C211yesmaximal, characteristic, complemented
13C2×#16840727C211yesmaximal, characteristic, complemented
14C2×#16840726C211yesmaximal, characteristic, complemented
15C2×C4×D61⋊C8C211yesmaximal, characteristic, complemented
16C2×#16840295C211yesmaximal, characteristic
17C22×#11758213C2211yescharacteristic
18C22×#11758217C2211yescharacteristic
19C22×D61⋊C8C2211yescharacteristic
20C22×D61⋊C8C2211yescharacteristic
21C22×D61⋊C8C2211yescharacteristic
22C23×#92420C2211yescharacteristic
23#16840814C2218yescomplemented
24#16840811C2218yescomplemented
25#16840795C2218yescomplemented
26#16840794C2218yescomplemented
27#16840792C2218yescomplemented
28#16840790C2218yescomplemented
29#16840789C2218yescomplemented
30#16840789C2218yescomplemented
31#16840787C2218yescomplemented
32#16840786C2218yescomplemented
33#16840785C2218yescomplemented
34C2×#14519844C2211yescharacteristic
35C2×#14519844C2211yescharacteristic
36C2×#14519844C2211yescharacteristic
37C2×#14519844C2211yescharacteristic
38C2×C4⋊#92420C2211yescharacteristic
39C2×C4⋊#92420C2211yescharacteristic
40C2×#14519834C2211yescharacteristic
41C2×#14519834C2211yescharacteristic
42C2×#14519834C2211yescharacteristic
43C2×#14519834C2211yescharacteristic
44C2×C22⋊#92420C2211yescharacteristic
45C2×C22⋊#92420C2211yescharacteristic
46#16840727C2218yescomplemented
47#16840726C2218yescomplemented
48C2×#14519832C2211yescharacteristic
49C2×#14519832C2211yescharacteristic
50C2×#14519832C2211yescharacteristic
51C2×#14519832C2211yescharacteristic
52C4×D61⋊C8C2218yescomplemented
53C2×C4×#92420C2211yescharacteristic
54C2×C4×#92420C2211yescharacteristic
55C2×C4×#92420C2211yescharacteristic
56C2×C4×#92420C2211yescharacteristic
57C2×C4×#92420C2211yescharacteristic
58C2×C4×#92420C2211yescharacteristic
59#16840295C418yes—
60#16840295C2218yes—
61C2×#14519771C411yescharacteristic
62C2×#14519767C411yescharacteristic
63C2×#14519763C411yescharacteristic
64C2×#14519762C411yescharacteristic
65C2×#14519759C411yescharacteristic
66C2×#14519755C411yescharacteristic
67C2×#14519750C411yescharacteristic
68C2×#14519742C2211yescharacteristic
69C2×#14519739C2211yescharacteristic
70C2×#14519737C2211yescharacteristic
71C2×#14519737C2211yescharacteristic
72C2×#14519735C2211yescharacteristic
73C2×#14519733C2211yescharacteristic
74C2×C42×D61C2211yescharacteristic
75C2×#126×C61C411yescharacteristic
76C2×#11758213—24no—
77C2×#11758213C2314yes—
78C2×#11758217—24no—
79C2×#11758217C2314yes—
80C2×D61⋊C8—24no—
81C2×D61⋊C8—24no—
82C2×D61⋊C8—24no—
83C2×D61⋊C8C2314yes—
84C2×D61⋊C8C2314yes—
85C2×D61⋊C8C2314yes—
86C22×#92420—24no—
87C22×#92420C2311yescharacteristic
88C22×#92420C2311yescharacteristic
89C22×#92420C2311yescharacteristic
90C22×#92420C2311yescharacteristic
91C22×#92420C2311yescharacteristic
92C22×#92420C2311yescharacteristic
93C22×#92420C2314yes—
94C22×#92420C2311yescharacteristic
95C22×#92420C2311yescharacteristic
96#14519844C2314yes—
97#14519844C2314yes—
98#14519844C2314yes—
99#14519844C2314yes—
100C4⋊#92420C2314yes—
101C4⋊#92420C2314yes—
102#14519834C2314yes—
103#14519834C2314yes—
104#14519834C2314yes—
105#14519834C2314yes—
106C22⋊#92420C2314yes—
107C22⋊#92420C2314yes—
108#14519832C2314yes—
109#14519832C2314yes—
110#14519832C2314yes—
111#14519832C2314yes—
112C4×#92420C2314yes—
113C4×#92420C2314yes—
114C4×#92420C2314yes—
115C4×#92420C2314yes—
116C4×#92420C2314yes—
117C4×#92420C2314yes—
118C22×Dic122C2×C411yescharacteristic
119C22×D244C2×C411yescharacteristic
120C22×C22⋊D61C2×C411yescharacteristic
121C22×C22⋊D61C2×C411yescharacteristic
122C23×Dic61C2311yescharacteristic
123C22×C4×D61C2×C411yescharacteristic
124C22×C4×D61C2×C411yescharacteristic
125C22×C4×D61C2311yescharacteristic
126C22×C4×D61C2311yescharacteristic
127#14519771C2×C418yes—
128#14519767C2×C418yes—
129#14519763C2×C418yes—
130#14519762C2×C418yes—
131#14519759C2×C418yes—
132#14519755C2×C418yes—
133#14519750C2×C418yes—
134#14519742C2×C414yes—
135#14519742C2314yes—
136#14519739C2×C414yes—
137#14519739C2314yes—
138#14519737C2×C414yes—
139#14519737C2×C414yes—
140#14519737C2314yes—
141#14519737C2314yes—
142#14519735C2×C414yes—
143#14519735C2314yes—
144#14519733C2×C414yes—
145#14519733C2314yes—
146C2×C4⋊Dic61C2×C411yescharacteristic
147C2×#11758196C2×C411yescharacteristic
148C2×#11758196C2×C411yescharacteristic
149C2×#11758196C2×C411yescharacteristic
150C2×#11758196C2×C411yescharacteristic
151C2×#11758196C2×C411yescharacteristic
152C2×#11758196C2×C411yescharacteristic
153C2×C22⋊Dic61C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2×C411yescharacteristic
156C2×#11758198C2×C411yescharacteristic
157C2×#11758198C2×C411yescharacteristic
158C2×#11758198C2×C411yescharacteristic
159C2×#11758198C2×C411yescharacteristic
160C2×C4×Dic61C2×C411yescharacteristic
161C2×C4×Dic61C2311yescharacteristic
162C2×C4×Dic61C2311yescharacteristic
163C2×C4×Dic61C2311yescharacteristic
164C2×C4×Dic61C2311yescharacteristic
165C42×D61C2×C414yes—
166C42×D61C2314yes—
167#126×C61C2×C418yes—
168C2×C4⋊C4×C61C2×C411yescharacteristic
169C2×C4⋊C4×C61C2×C411yescharacteristic
170C2×C4⋊C4×C61C2×C411yescharacteristic
171C2×C22⋊C4×C61C2×C411yescharacteristic
172C2×C22⋊C4×C61C2×C411yescharacteristic
173C2×C22⋊C4×C61C2×C411yescharacteristic
174C2×C42×C61C2×C411yescharacteristic
175C24×C61C22×C411yescharacteristic
176C23×D61C22×C411yescharacteristic
177C23×D61C22×C411yescharacteristic
178C22×C4×C61C22×C411yescharacteristic
179C22×C4×C61C22×C411yescharacteristic
180C22×C4×C61C22×C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C22×C411yescharacteristic
184C2×C22⋊D61—24no—
185C2×C22⋊D61—24no—
186C2×C22⋊D61C22×C414yes—
187C2×C22⋊D61C22×C414yes—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C22×C412yes—
193C22×Dic61C22×C411yescharacteristic
194C22×Dic61C22×C411yescharacteristic
195C22×Dic61C22×C411yescharacteristic
196C22×Dic61C2412yes—
197C22×Dic61C2411yescharacteristic
198C2×D244—24no—
199C2×D244C22×C414yes—
200C2×C4×D61—24no—
201C2×C4×D61—24no—
202C2×C4×D61—22no—
203C2×C4×D61—22no—
204C2×C4×D61—22no—
205C2×C4×D61—22no—
206C2×C4×D61C22×C414yes—
207C2×C4×D61C22×C414yes—
208C2×C4×D61C22×C412yes—
209C2×C4×D61C22×C412yes—
210C2×C4×D61C2412yes—
211C2×C4×D61C2412yes—
212C2×Dic122—24no—
213C2×Dic122C22×C414yes—
214#11758217—28no—
215C2×#92420—22no—
216C2×#92420—22no—
217C2×#92420—22no—
218C2×#92420—22no—
219C2×#92420—22no—
220C2×#92420—22no—
221C2×#92420—28no—
222C2×#92420#4114yes—
223C2×#92420#4114yes—
224C2×#92420C2412yes—
225C2×#92420C2412yes—
226C2×#92420C2412yes—
227C2×#92420C2412yes—
228C2×#92420C2412yes—
229C2×#92420C2412yes—
230C2×#92420C2412yes—
231C2×#92420C2412yes—
232#11758213—28no—
233D61⋊C8—28no—
234D61⋊C8—28no—
235D61⋊C8—28no—
236C4⋊C4×C61C22×C414yes—
237C4⋊C4×C61C22×C414yes—
238C4⋊C4×C61C22×C414yes—
239C22⋊C4×C61C22×C414yes—
240C22⋊C4×C61C22×C414yes—
241C22⋊C4×C61C22×C414yes—
242C42×C61C22×C414yes—
243C22⋊Dic61C22×C414yes—
244#11758198C22×C414yes—
245#11758198C22×C414yes—
246#11758198C22×C414yes—
247#11758198C22×C414yes—
248#11758198C22×C414yes—
249#11758198C22×C414yes—
250C4⋊Dic61C22×C414yes—
251#11758196C22×C414yes—
252#11758196C22×C414yes—
253#11758196C22×C414yes—
254#11758196C22×C414yes—
255#11758196C22×C414yes—
256#11758196C22×C414yes—
257C4×Dic61C22×C412yes—
258C4×Dic61C22×C412yes—
259C4×Dic61C22×C414yes—
260C4×Dic61C22×C412yes—
261C4×Dic61C22×C412yes—
262C4×Dic61C2412yes—
263C4×Dic61C2412yes—
264C4×Dic61C2412yes—
265C4×Dic61C2412yes—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61C23×C412yes—
270C23×C61C23×C411yescharacteristic
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61#13114yes—
277C22×D61C23×C412yes—
278C22×D61C23×C412yes—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61C23×C412yes—
286C2×C4×C61C23×C412yes—
287C2×C4×C61C23×C412yes—
288C2×C4×C61C23×C412yes—
289C2×C4×C61C23×C412yes—
290C2×C4×C61C23×C412yes—
291C22⋊D61—28no—
292C22⋊D61—28no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—24no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61#13114yes—
301C2×Dic61C23×C412yes—
302C2×Dic61C23×C412yes—
303C2×Dic61C23×C412yes—
304C2×Dic61C23×C412yes—
305C2×Dic61C23×C411yescharacteristic
306C2×Dic61C23×C412yes—
307C2×Dic61C2×#4112yes—
308C2×Dic61C2×#4112yes—
309C2×Dic61C2511yescharacteristic
310D244—28no—
311C4×D61—28no—
312C4×D61—24no—
313C4×D61—24no—
314C4×D61—28no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319Dic122—28no—
320#92420—22no—
321#92420—22no—
322#92420—22no—
323#92420—22no—
324#92420—22no—
325#92420—22no—
326#92420C2×#4114yes—
327#92420C2×#4114yes—
328C2×#2966—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—44no—
333C22×C61C4×#4112yes—
334C22×C61C2×#13112yes—
335C22×C61C2×#13112yes—
336C22×C61C24×C411yescharacteristic
337C2×D61—22no—
338C2×D61—28no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—44no—
344C2×D61C2×#13114yes—
345C4×C61—22no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—22no—
350C4×C61—22no—
351Dic61—22no—
352Dic61—22no—
353Dic61—22no—
354Dic61—22no—
355Dic61C4×#4112yes—
356Dic61C2×#13114yes—
357Dic61C22×#4111yescharacteristic
358Dic61C22×#4111yescharacteristic
359C2×#529—611no—
360#2966—6116no—
361C2×#446—611no—
362C2×C8×Q8—611no—
363C2×#436—611no—
364C2×#435—611no—
365C2×#435—611no—
366C2×C8×D4—611no—
367C2×C8×D4—611no—
368C2×C8×D4—611no—
369C2×#433—611no—
370C2×#433—611no—
371C2×#432—611no—
372C2×#405—611no—
373C2×#405—611no—
374C22×C4×C8—611no—
375C2×C61—42no—
376C2×C61#296614yescomplemented
377C2×C61C2×C4×#4111yescharacteristic
378C2×C61C22×#13111yescharacteristic
379C2×C61C22×#13111yescharacteristic
380D61—24no—
381D61—42no—
382C22×M16—611no—
383C22×M16—611no—
384C23×C8—611no—
385C23×C8—611no—
386C23×C8—611no—
387C23×C8—611no—
388#529—618no—
389#529—618no—
390C2×#126—611no—
391C2×#126#692311yescharacteristic
392C2×#125—611no—
393C2×#124—611no—
394C2×#123—611no—
395C2×#123—611no—
396C2×C22⋊Q8—611no—
397C2×#121—611no—
398C2×C4×Q8—611no—
399C2×C4×D4—611no—
400C2×C4×D4—611no—
401C2×C4×D4—611no—
402C2×#117—611no—
403C2×#117—611no—
404C22×C42—611no—
405#446—618no—
406C8×Q8—618no—
407#436—618no—
408#435—618no—
409#435—618no—
410C8×D4—618no—
411C8×D4—618no—
412C8×D4—618no—
413#433—618no—
414#433—618no—
415#432—618no—
416C2×C4⋊C8—611no—
417C2×C4⋊C8—611no—
418C2×C4⋊C8—611no—
419C2×C4⋊C8—611no—
420C2×C4⋊C8—611no—
421C2×C4⋊C8—611no—
422C2×C22⋊C8—611no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C2×C22⋊C8—611no—
426C2×C22⋊C8—611no—
427C2×C22⋊C8—611no—
428#405—618no—
429#405—618no—
430C2×#97—611no—
431C2×#97—611no—
432C2×#97—611no—
433C2×#97—611no—
434C2×C4×C8—611no—
435C2×C4×C8—611no—
436C2×C4×C8—611no—
437C2×C4×C8—611no—
438C2×C4×C8—611no—
439C2×C4×C8—611no—
440C2×C4×C8—618no—
441C61C2×#296611yescharacteristic, complemented, Sylow
442C22×Q8—611no—
443C22×D4—611no—
444C22×D4—611no—
445C22×D4—611no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C2×M16—614no—
452C2×M16—614no—
453C2×M16—1224no—
454C2×M16—1224no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—614no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—614no—
465C22×C8—614no—
466C22×C8—614no—
467C22×C8—1224no—
468C22×C8—1224no—
469C22×C8—1224no—
470C22×C8—1224no—
471#126—618no—
472#126C2×#692318yes—
473#125—618no—
474#124—618no—
475#123—618no—
476#123—618no—
477C22⋊Q8—618no—
478#121—618no—
479C4×Q8—614no—
480C4×Q8—614no—
481C4×D4—614no—
482C4×D4—614no—
483C4×D4—614no—
484C4×D4—614no—
485C4×D4—614no—
486C4×D4—614no—
487#117—614no—
488#117—614no—
489#117—614no—
490#117—614no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4C2×#692311yescharacteristic
499C2×C4⋊C4C2×#692311yescharacteristic
500C2×C4⋊C4C2×#692311yescharacteristic
501C2×C22⋊C4—611no—
502C2×C22⋊C4—611no—
503C2×C22⋊C4—611no—
504C2×C22⋊C4—611no—
505C2×C22⋊C4—611no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—611no—
508C2×C22⋊C4C2×#692311yescharacteristic
509C2×C22⋊C4C2×#692311yescharacteristic
510C2×C22⋊C4C2×#692311yescharacteristic
511C2×C42—611no—
512C2×C42—611no—
513C2×C42—611no—
514C2×C42—611no—
515C2×C42—611no—
516C2×C42—614no—
517C2×C42—614no—
518C2×C42C2×#692311yescharacteristic
519C4⋊C8—614no—
520C4⋊C8—614no—
521C4⋊C8—614no—
522C4⋊C8—614no—
523C4⋊C8—614no—
524C4⋊C8—614no—
525C22⋊C8—614no—
526C22⋊C8—614no—
527C22⋊C8—614no—
528C22⋊C8—614no—
529C22⋊C8—614no—
530C22⋊C8—614no—
531#97—614no—
532#97—614no—
533#97—614no—
534#97—614no—
535C4×C8—614no—
536C4×C8—614no—
537C4×C8—614no—
538C4×C8—614no—
539C4×C8—614no—
540C4×C8—614no—
541C24—611no—
542C24—611no—
543C24C22×#692311yescharacteristic
544C2×Q8—614no—
545C2×Q8—1224no—
546C2×D4—614no—
547C2×D4—614no—
548C2×D4—614no—
549C2×D4—1224no—
550C2×D4—1224no—
551C2×D4—1224no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—612no—
555C22×C4—612no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—614no—
564C22×C4—614no—
565C22×C4—612no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1224no—
571C22×C4—1224no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4C22×#692311yescharacteristic
575C22×C4C22×#692311yescharacteristic
576C22×C4C22×#692311yescharacteristic
577C22×C4C22×#692311yescharacteristic
578C22×C4C22×#692311yescharacteristic
579C22×C4C22×#692311yescharacteristic
580M16—1228no—
581M16—1228no—
582C2×C8—612no—
583C2×C8—612no—
584C2×C8—614no—
585C2×C8—614no—
586C2×C8—612no—
587C2×C8—612no—
588C2×C8—612no—
589C2×C8—612no—
590C2×C8—612no—
591C2×C8—612no—
592C2×C8—1228no—
593C2×C8—1228no—
594C2×C8—1228no—
595C2×C8—1228no—
596C2×C8—1222no—
597C2×C8—1222no—
598C2×C8—1222no—
599C2×C8—1222no—
600C2×C8—1222no—
601C2×C8—1222no—
602C4⋊C4—614no—
603C4⋊C4—614no—
604C4⋊C4—614no—
605C4⋊C4—614no—
606C4⋊C4—614no—
607C4⋊C4—614no—
608C4⋊C4—614no—
609C4⋊C4C22×#692314yes—
610C4⋊C4C22×#692314yes—
611C4⋊C4C22×#692314yes—
612C22⋊C4—614no—
613C22⋊C4—614no—
614C22⋊C4—614no—
615C22⋊C4—614no—
616C22⋊C4—614no—
617C22⋊C4—614no—
618C22⋊C4—614no—
619C22⋊C4C22×#692314yes—
620C22⋊C4C22×#692314yes—
621C22⋊C4C22×#692314yes—
622C42—612no—
623C42—612no—
624C42—612no—
625C42—612no—
626C42—612no—
627C42—612no—
628C42—614no—
629C42—612no—
630C42—612no—
631C42C22×#692314yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—614no—
636C23—612no—
637C23—612no—
638C23—1222no—
639C23—1222no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23C23×#692312yes—
644C23C23×#692311yescharacteristic
645Q8—1228no—
646D4—1228no—
647D4—1228no—
648D4—1228no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—612no—
656C2×C4—612no—
657C2×C4—614no—
658C2×C4—611no—
659C2×C4—612no—
660C2×C4—611no—
661C2×C4—612no—
662C2×C4—612no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1224no—
670C2×C4—1224no—
671C2×C4—1228no—
672C2×C4—1228no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1224no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4C23×#692312yes—
681C2×C4C23×#692312yes—
682C2×C4C23×#692312yes—
683C2×C4C23×#692312yes—
684C2×C4C23×#692312yes—
685C2×C4C23×#692312yes—
686C8—614no—
687C8—614no—
688C8—1222no—
689C8—1222no—
690C8—1222no—
691C8—1222no—
692C8—1222no—
693C8—1222no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—614no—
699C22—1222no—
700C22—1222no—
701C22—1228no—
702C22—1222no—
703C22—1222no—
704C22—1222no—
705C22—2444no—
706C22#41×#692312yes—
707C22D61⋊#13112yes—
708C22D61⋊#13112yes—
709C22C24×#692311yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—612no—
717C4—611no—
718C4—611no—
719C4—614no—
720C4—1222no—
721C4—1222no—
722C4—1222no—
723C4—1222no—
724C2—42no—
725C2—1224no—
726C2—2442no—
727C2#2146263714yesdirect product factor
728C2C2×#41×#692311yescharacteristic
729C2C2×D61⋊#13111yescharacteristic
730C2C2×D61⋊#13111yescharacteristic
subgroupG/H
centerC23C23×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC2×#126×C61C4
socleC23×C61C23×C4
prime radicalC2×#14519750C4
cosocleC2×Dic61C25
hypercenterC2×#126#6923
hypocenterC61C2×#2966
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #21462637C2direct (N × H)
2. C2×#16840814C2semidirect
3. C2×#16840811C2semidirect
4. C2×#16840795C2semidirect
5. C2×#16840794C2semidirect
6. C2×#16840792C2semidirect
7. C2×#16840790C2semidirect
8. C2×#16840789C2semidirect
9. C2×#16840789C2semidirect
10. C2×#16840787C2semidirect
11. C2×#16840786C2semidirect
12. C2×#16840785C2semidirect
13. C2×#16840727C2semidirect
14. C2×#16840726C2semidirect
15. C2×C4×D61⋊C8C2semidirect
23. #16840814C22semidirect
24. #16840811C22semidirect
25. #16840795C22semidirect
26. #16840794C22semidirect
27. #16840792C22semidirect
28. #16840790C22semidirect
29. #16840789C22semidirect
30. #16840789C22semidirect
31. #16840787C22semidirect
32. #16840786C22semidirect
33. #16840785C22semidirect
46. #16840727C22semidirect
47. #16840726C22semidirect
52. C4×D61⋊C8C22semidirect
376. C2×C61#2966semidirect
441. C61C2×#2966semidirect
727. C2#21462637direct (N × H)

Maximal subgroups

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

subgroupindex
#214626372
C2×#168408142
C2×#168408112
C2×#168407952
C2×#168407942
C2×#168407922
C2×#168407902
C2×#168407892
C2×#168407872
C2×#168407862
C2×#168407852
C2×#168407272
C2×#168407262
C2×C4×D61⋊C82
C2×#168402952
C2×#296661