Finite Group Databasebeta

← C2×#21462754 #30625977

Subgroups — C2×#21462754 #30625977

Order 15616.

1938 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#21462754C2116yesmaximal, direct product factor
2C2×#16840814C211yesmaximal, characteristic, complemented
3C2×#16840812C211yesmaximal, characteristic, complemented
4C2×#16840794C211yesmaximal, characteristic, complemented
5C2×#16840793C211yesmaximal, characteristic, complemented
6C2×#16840791C211yesmaximal, characteristic, complemented
7C2×#16840791C211yesmaximal, characteristic, complemented
8C2×#16840789C211yesmaximal, characteristic, complemented
9C2×D4×#92420C211yesmaximal, characteristic, complemented
10C2×#16840787C211yesmaximal, characteristic, complemented
11C2×#16840786C211yesmaximal, characteristic, complemented
12C2×#16840782C211yesmaximal, characteristic, complemented
13C2×#16840769C211yesmaximal, characteristic, complemented
14C2×#16840768C211yesmaximal, characteristic, complemented
15C22×C4⋊#92420C211yesmaximal, characteristic, complemented
16C2×#16840289C211yesmaximal, characteristic
17C22×#11758213C2211yescharacteristic
18C22×#11758217C2211yescharacteristic
19C22×D61⋊C8C2211yescharacteristic
20C23×#92420C2211yescharacteristic
21C23×#92420C2211yescharacteristic
22C23×#92420C2211yescharacteristic
23#16840814C2218yescomplemented
24#16840812C2218yescomplemented
25#16840794C2218yescomplemented
26#16840793C2218yescomplemented
27#16840791C2218yescomplemented
28#16840791C2218yescomplemented
29#16840789C2218yescomplemented
30D4×#92420C2218yescomplemented
31#16840787C2218yescomplemented
32#16840786C2218yescomplemented
33#16840782C2218yescomplemented
34#16840769C2218yescomplemented
35#16840768C2218yescomplemented
36C2×#14519844C2211yescharacteristic
37C2×#14519844C2211yescharacteristic
38C2×#14519844C2211yescharacteristic
39C2×#14519844C2211yescharacteristic
40C2×C4⋊#92420C2211yescharacteristic
41C2×C4⋊#92420C2211yescharacteristic
42C2×C4⋊#92420C2211yescharacteristic
43C2×C4⋊#92420C2211yescharacteristic
44C2×C4⋊#92420C2211yescharacteristic
45C2×C4⋊#92420C2211yescharacteristic
46C2×C4⋊#92420C2218yescomplemented
47C2×#14519834C2211yescharacteristic
48C2×#14519834C2211yescharacteristic
49C2×C22⋊#92420C2211yescharacteristic
50C2×C22⋊#92420C2211yescharacteristic
51C2×C22⋊#92420C2211yescharacteristic
52C2×C22⋊#92420C2211yescharacteristic
53C2×#14519832C2211yescharacteristic
54C2×#14519832C2211yescharacteristic
55C2×#14519832C2211yescharacteristic
56C2×#14519832C2211yescharacteristic
57C2×C4×#92420C2211yescharacteristic
58C2×C4×#92420C2211yescharacteristic
59#16840289C418yes—
60#16840289C2218yes—
61C2×#14519772C411yescharacteristic
62C2×#14519770C411yescharacteristic
63C2×#14519767C411yescharacteristic
64C2×#14519763C411yescharacteristic
65C2×#14519760C411yescharacteristic
66C2×#14519754C411yescharacteristic
67C2×#14519749C411yescharacteristic
68C2×#14519742C2211yescharacteristic
69C2×D4×Dic61C2211yescharacteristic
70C2×#14519737C2211yescharacteristic
71C2×#14519737C2211yescharacteristic
72C2×#14519735C2211yescharacteristic
73C2×#14519733C2211yescharacteristic
74C22×C4×Dic61C2211yescharacteristic
75C2×#123×C61C411yescharacteristic
76C2×#11758213—42no—
77C2×#11758213C2314yes—
78C2×#11758217—42no—
79C2×#11758217C2314yes—
80C2×D61⋊C8—42no—
81C2×D61⋊C8C2314yes—
82C22×#92420—42no—
83C22×#92420—42no—
84C22×#92420—42no—
85C22×#92420C2311yescharacteristic
86C22×#92420C2311yescharacteristic
87C22×#92420C2311yescharacteristic
88C22×#92420C2311yescharacteristic
89C22×#92420C2311yescharacteristic
90C22×#92420C2311yescharacteristic
91C22×#92420C2311yescharacteristic
92C22×#92420C2311yescharacteristic
93C22×#92420C2314yes—
94C22×#92420C2314yes—
95C22×#92420C2314yes—
96#14519844C2314yes—
97#14519844C2314yes—
98#14519844C2314yes—
99#14519844C2314yes—
100C4⋊#92420C2314yes—
101C4⋊#92420C2314yes—
102C4⋊#92420C2314yes—
103C4⋊#92420C2314yes—
104C4⋊#92420C2314yes—
105C4⋊#92420C2314yes—
106#14519834C2314yes—
107#14519834C2314yes—
108C22⋊#92420C2314yes—
109C22⋊#92420C2314yes—
110C22⋊#92420C2314yes—
111C22⋊#92420C2314yes—
112#14519832C2314yes—
113#14519832C2314yes—
114#14519832C2314yes—
115#14519832C2314yes—
116C4×#92420C2314yes—
117C4×#92420C2314yes—
118C22×Dic122C2×C411yescharacteristic
119C22×C22⋊D61C2×C411yescharacteristic
120C22×C22⋊D61C2×C411yescharacteristic
121C23×Dic61C2×C411yescharacteristic
122C23×Dic61C2311yescharacteristic
123C23×Dic61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125#14519772C2×C418yes—
126#14519770C2×C418yes—
127#14519767C2×C418yes—
128#14519763C2×C418yes—
129#14519760C2×C418yes—
130#14519754C2×C418yes—
131#14519749C2×C418yes—
132#14519742C2×C414yes—
133#14519742C2314yes—
134D4×Dic61C2×C414yes—
135D4×Dic61C2314yes—
136#14519737C2×C414yes—
137#14519737C2×C414yes—
138#14519737C2314yes—
139#14519737C2314yes—
140#14519735C2×C414yes—
141#14519735C2314yes—
142#14519733C2×C414yes—
143#14519733C2314yes—
144C2×C4⋊Dic61C2×C411yescharacteristic
145C2×C4⋊Dic61C2×C411yescharacteristic
146C2×#11758196C2×C411yescharacteristic
147C2×#11758196C2×C411yescharacteristic
148C2×#11758196C2×C411yescharacteristic
149C2×#11758196C2×C411yescharacteristic
150C2×#11758196C2×C411yescharacteristic
151C2×#11758196C2×C411yescharacteristic
152C2×C22⋊Dic61C2×C411yescharacteristic
153C2×C22⋊Dic61C2×C411yescharacteristic
154C2×C22⋊Dic61C2×C411yescharacteristic
155C2×#11758198C2×C411yescharacteristic
156C2×#11758198C2×C411yescharacteristic
157C2×#11758198C2×C411yescharacteristic
158C2×#11758198C2×C411yescharacteristic
159C2×C4×Dic61C2×C411yescharacteristic
160C2×C4×Dic61C2×C411yescharacteristic
161C2×C4×Dic61C2×C414yes—
162C2×C4×Dic61C2311yescharacteristic
163C2×C4×Dic61C2311yescharacteristic
164C2×C4×Dic61C2311yescharacteristic
165C2×C4×Dic61C2311yescharacteristic
166C2×C4×Dic61C2314yes—
167C22×D4×C61C2×C411yescharacteristic
168C23×C4×C61C2×C411yescharacteristic
169#123×C61C2×C418yes—
170C2×C4⋊C4×C61C2×C411yescharacteristic
171C2×C4⋊C4×C61C2×C411yescharacteristic
172C2×C22⋊C4×C61C2×C411yescharacteristic
173C2×C22⋊C4×C61C2×C411yescharacteristic
174C2×C22⋊C4×C61C2×C411yescharacteristic
175C24×C61C22×C411yescharacteristic
176C24×C61C22×C411yescharacteristic
177C23×D61C22×C411yescharacteristic
178C2×D4×C61—24no—
179C2×D4×C61C22×C414yes—
180C22×C4×C61—24no—
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C22×C414yes—
187C2×C22⋊D61—24no—
188C2×C22⋊D61—42no—
189C2×C22⋊D61C22×C414yes—
190C2×C22⋊D61C22×C414yes—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—42no—
196C22×Dic61C22×C411yescharacteristic
197C22×Dic61C22×C411yescharacteristic
198C22×Dic61C22×C411yescharacteristic
199C22×Dic61C22×C412yes—
200C22×Dic61C22×C411yescharacteristic
201C22×Dic61C22×C412yes—
202C22×Dic61C22×C411yescharacteristic
203C22×Dic61C22×C411yescharacteristic
204C22×Dic61C22×C414yes—
205C22×Dic61C2412yes—
206C22×Dic61C2412yes—
207C22×Dic61C2411yescharacteristic
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61C22×C412yes—
211C2×C4×D61C2412yes—
212C2×Dic122—42no—
213C2×Dic122C22×C414yes—
214#11758217—44no—
215C2×#92420—22no—
216C2×#92420—22no—
217C2×#92420—22no—
218C2×#92420—22no—
219C2×#92420—22no—
220C2×#92420—22no—
221C2×#92420—22no—
222C2×#92420—22no—
223C2×#92420—44no—
224C2×#92420—44no—
225C2×#92420—44no—
226C2×#92420C2412yes—
227C2×#92420C2412yes—
228C2×#92420C2412yes—
229C2×#92420C2412yes—
230C2×#92420C2412yes—
231C2×#92420C2412yes—
232C2×#92420C2412yes—
233C2×#92420C2412yes—
234#11758213—44no—
235D61⋊C8—44no—
236C4⋊C4×C61C22×C414yes—
237C4⋊C4×C61C22×C414yes—
238C22⋊C4×C61C22×C414yes—
239C22⋊C4×C61C22×C414yes—
240C22⋊C4×C61C22×C414yes—
241C22⋊Dic61C22×C414yes—
242C22⋊Dic61C22×C414yes—
243C22⋊Dic61C22×C414yes—
244#11758198C22×C414yes—
245#11758198C22×C414yes—
246#11758198C22×C414yes—
247#11758198C22×C414yes—
248C4⋊Dic61C22×C414yes—
249C4⋊Dic61C22×C414yes—
250#11758196C22×C414yes—
251#11758196C22×C414yes—
252#11758196C22×C414yes—
253#11758196C22×C414yes—
254#11758196C22×C414yes—
255#11758196C22×C414yes—
256C4×Dic61C22×C412yes—
257C4×Dic61C22×C412yes—
258C4×Dic61C22×C414yes—
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×C61—22no—
270C23×C61—22no—
271C23×C61#13114yes—
272C23×C61C23×C412yes—
273C23×C61C23×C412yes—
274C23×C61C23×C411yescharacteristic
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61C23×C412yes—
279D4×C61—28no—
280C2×C4×C61—22no—
281C2×C4×C61—28no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
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—44no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—24no—
300C2×Dic61—24no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—44no—
306C2×Dic61C23×C412yes—
307C2×Dic61C23×C412yes—
308C2×Dic61C23×C412yes—
309C2×Dic61C23×C412yes—
310C2×Dic61C23×C412yes—
311C2×Dic61C23×C412yes—
312C2×Dic61C23×C411yescharacteristic
313C2×Dic61H(5,𝔽2)12yes—
314C2×Dic612−1+412yes—
315C2×Dic61C2511yescharacteristic
316C4×D61—24no—
317C4×D61—22no—
318C4×D61—22no—
319Dic122—44no—
320#92420—22no—
321#92420—22no—
322#92420—22no—
323#92420—22no—
324#92420—22no—
325#92420—22no—
326#92420—22no—
327#92420—22no—
328C2×#2992—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—28no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—44no—
336C22×C61#52012yes—
337C22×C61C2×#13114yes—
338C22×C61C2×#13112yes—
339C22×C61#56812yes—
340C22×C61C24×C411yescharacteristic
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—44no—
345C4×C61—22no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—22no—
350Dic61—22no—
351Dic61—22no—
352Dic61—22no—
353Dic61—22no—
354Dic61—22no—
355Dic61—22no—
356Dic61#52012yes—
357Dic61C2×H(5,𝔽2)11yescharacteristic
358Dic61C2×2−1+411yescharacteristic
359C2×#529—611no—
360#2992—6116no—
361C2×#446—611no—
362C2×#446—611no—
363C2×#435—611no—
364C2×#435—611no—
365C2×#435—611no—
366C2×#435—611no—
367C2×C8×D4—611no—
368C2×C8×D4—611no—
369C2×#433—611no—
370C2×#433—611no—
371C2×#432—611no—
372C2×#424—611no—
373C2×#424—611no—
374C22×C4⋊C8—611no—
375C2×C61—24no—
376C2×C61—42no—
377C2×C61#299214yescomplemented
378C2×C61C2×#52011yescharacteristic
379C2×C61C22×#13111yescharacteristic
380C2×C61C2×#56811yescharacteristic
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—611no—
392C2×#125—611no—
393C2×#124—611no—
394C2×#123—611no—
395C2×#123#692311yescharacteristic
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—
406#446—618no—
407#435—618no—
408#435—618no—
409#435—618no—
410#435—618no—
411C8×D4—618no—
412C8×D4—618no—
413#433—618no—
414#433—618no—
415#432—618no—
416#424—618no—
417#424—618no—
418C2×C4⋊C8—611no—
419C2×C4⋊C8—611no—
420C2×C4⋊C8—611no—
421C2×C4⋊C8—611no—
422C2×C4⋊C8—611no—
423C2×C4⋊C8—611no—
424C2×C4⋊C8—618no—
425C2×C4⋊C8—611no—
426C2×C4⋊C8—611no—
427C2×C4⋊C8—611no—
428C2×C4⋊C8—611no—
429C2×C22⋊C8—611no—
430C2×C22⋊C8—611no—
431C2×C22⋊C8—611no—
432C2×C22⋊C8—611no—
433C2×C22⋊C8—611no—
434C2×C22⋊C8—611no—
435C2×#97—611no—
436C2×#97—611no—
437C2×#97—611no—
438C2×#97—611no—
439C2×C4×C8—611no—
440C2×C4×C8—611no—
441C61C2×#299211yescharacteristic, complemented, Sylow
442C22×Q8—611no—
443C22×D4—611no—
444C22×D4—611no—
445C22×D4C2×#692311yescharacteristic
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4C2×#692311yescharacteristic
451C2×M16—614no—
452C2×M16—614no—
453C2×M16—2442no—
454C2×M16—2442no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8—614no—
464C22×C8—614no—
465C22×C8—614no—
466C22×C8—614no—
467C22×C8—2442no—
468C22×C8—2442no—
469C22×C8—2442no—
470C22×C8—2442no—
471#126—618no—
472#126—618no—
473#125—618no—
474#124—618no—
475#123—618no—
476#123C2×#692318yes—
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⋊C4—611no—
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—611no—
517C2×C42—614no—
518C2×C42—614no—
519C4⋊C8—614no—
520C4⋊C8—614no—
521C4⋊C8—614no—
522C4⋊C8—614no—
523C4⋊C8—614no—
524C4⋊C8—614no—
525C4⋊C8—614no—
526C4⋊C8—614no—
527C4⋊C8—614no—
528C4⋊C8—614no—
529C22⋊C8—614no—
530C22⋊C8—614no—
531C22⋊C8—614no—
532C22⋊C8—614no—
533C22⋊C8—614no—
534C22⋊C8—614no—
535#97—614no—
536#97—614no—
537#97—614no—
538#97—614no—
539C4×C8—614no—
540C4×C8—614no—
541C24—611no—
542C24C22×#692311yescharacteristic
543C24C22×#692311yescharacteristic
544C2×Q8—614no—
545C2×Q8—2442no—
546C2×D4—24no—
547C2×D4—614no—
548C2×D4—614no—
549C2×D4—1224no—
550C2×D4—2442no—
551C2×D4C22×#692314yes—
552C22×C4—24no—
553C22×C4—611no—
554C22×C4—612no—
555C22×C4—612no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—614no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—2442no—
574C22×C4C22×#692314yes—
575C22×C4C22×#692311yescharacteristic
576C22×C4C22×#692311yescharacteristic
577C22×C4C22×#692311yescharacteristic
578C22×C4C22×#692311yescharacteristic
579C22×C4C22×#692311yescharacteristic
580M16—2444no—
581M16—2444no—
582C2×C8—612no—
583C2×C8—612no—
584C2×C8—612no—
585C2×C8—612no—
586C2×C8—612no—
587C2×C8—612no—
588C2×C8—612no—
589C2×C8—612no—
590C2×C8—1222no—
591C2×C8—1222no—
592C2×C8—1222no—
593C2×C8—1222no—
594C2×C8—1222no—
595C2×C8—1222no—
596C2×C8—1222no—
597C2×C8—1222no—
598C2×C8—2444no—
599C2×C8—2444no—
600C2×C8—2444no—
601C2×C8—2444no—
602C4⋊C4—614no—
603C4⋊C4—614no—
604C4⋊C4—614no—
605C4⋊C4—614no—
606C4⋊C4—614no—
607C4⋊C4—614no—
608C4⋊C4—614no—
609C4⋊C4—614no—
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—614no—
630C42—612no—
631C42—612no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—612no—
638C23—1222no—
639C23—1222no—
640C23—1222no—
641C23#1451986414yes—
642C23C23×#692312yes—
643C23C23×#692312yes—
644C23C23×#692311yescharacteristic
645Q8—2444no—
646D4—28no—
647D4—1228no—
648D4—2444no—
649C2×C4—22no—
650C2×C4—28no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—612no—
656C2×C4—612no—
657C2×C4—611no—
658C2×C4—611no—
659C2×C4—612no—
660C2×C4—612no—
661C2×C4—612no—
662C2×C4—612no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—1222no—
666C2×C4—1224no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1224no—
671C2×C4—1224no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—2444no—
681C2×C4C23×#692312yes—
682C2×C4C23×#692312yes—
683C2×C4C23×#692312yes—
684C2×C4C23×#692312yes—
685C2×C4C23×#692312yes—
686C8—1222no—
687C8—1222no—
688C8—1222no—
689C8—1222no—
690C8—1222no—
691C8—1222no—
692C8—1222no—
693C8—1222no—
694C22—22no—
695C22—22no—
696C22—28no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—1222no—
702C22—1222no—
703C22—1222no—
704C22—2444no—
705C22#1684083112yes—
706C22C2×#1451986414yes—
707C22C2×#1451986412yes—
708C22#1684084112yes—
709C22C24×#692311yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—612no—
716C4—611no—
717C4—611no—
718C4—1222no—
719C4—1222no—
720C4—1222no—
721C4—1222no—
722C4—1222no—
723C4—1222no—
724C2—24no—
725C2—42no—
726C2—2442no—
727C2#2146275414yesdirect product factor
728C2C2×#1684083111yescharacteristic
729C2C22×#1451986411yescharacteristic
730C2C2×#1684084111yescharacteristic
subgroupG/H
centerC23C23×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC2×#123×C61C4
socleC23×C61C23×C4
prime radicalC2×#14519749C4
cosocleC2×Dic61C25
hypercenterC2×#123#6923
hypocenterC61C2×#2992
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #21462754C2direct (N × H)
2. C2×#16840814C2semidirect
3. C2×#16840812C2semidirect
4. C2×#16840794C2semidirect
5. C2×#16840793C2semidirect
6. C2×#16840791C2semidirect
7. C2×#16840791C2semidirect
8. C2×#16840789C2semidirect
9. C2×D4×#92420C2semidirect
10. C2×#16840787C2semidirect
11. C2×#16840786C2semidirect
12. C2×#16840782C2semidirect
13. C2×#16840769C2semidirect
14. C2×#16840768C2semidirect
15. C22×C4⋊#92420C2semidirect
23. #16840814C22semidirect
24. #16840812C22semidirect
25. #16840794C22semidirect
26. #16840793C22semidirect
27. #16840791C22semidirect
28. #16840791C22semidirect
29. #16840789C22semidirect
30. D4×#92420C22semidirect
31. #16840787C22semidirect
32. #16840786C22semidirect
33. #16840782C22semidirect
34. #16840769C22semidirect
35. #16840768C22semidirect
46. C2×C4⋊#92420C22semidirect
377. C2×C61#2992semidirect
441. C61C2×#2992semidirect
727. C2#21462754direct (N × H)

Maximal subgroups

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

subgroupindex
#214627542
C2×#168408142
C2×#168408122
C2×#168407942
C2×#168407932
C2×#168407912
C2×#168407892
C2×D4×#924202
C2×#168407872
C2×#168407862
C2×#168407822
C2×#168407692
C2×#168407682
C22×C4⋊#924202
C2×#168402892
C2×#299261