Finite Group Databasebeta

← C2×#21459685 #30588094

Subgroups — C2×#21459685 #30588094

Order 15616.

7130 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459685C2132yesmaximal, direct product factor
2C2×#16840497C211yesmaximal, characteristic, complemented
3C2×#16840497C211yesmaximal, characteristic, complemented
4C2×#16840487C211yesmaximal, characteristic, complemented
5C2×#16840486C212yesmaximal, complemented
6C2×#16840484C212yesmaximal, complemented
7C2×#16840484C212yesmaximal, complemented
8C2×#16840468C212yesmaximal, complemented
9C2×#16840444C214yesmaximal, complemented
10C2×#16840360C214yesmaximal, complemented
11C2×#16840337C212yesmaximal, complemented
12C2×#16840316C211yesmaximal, characteristic, complemented
13C2×#16840313C211yesmaximal, characteristic
14C2×#16840299C212yesmaximal, complemented
15C2×#16840297C212yesmaximal, complemented
16C2×#16840244C212yesmaximal, complemented
17C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
18C2×C61×#557C211yesmaximal, characteristic, complemented
19C22×#11758226C2212yes—
20C22×Q8×D61C2211yescharacteristic
21#16840497C22116yescomplemented
22#16840497C22116yescomplemented
23#16840487C22116yescomplemented
24#16840486C22132yescomplemented
25#16840484C22132yescomplemented
26#16840484C22132yescomplemented
27#16840468C22132yescomplemented
28#16840444C22164yescomplemented
29#16840360C22164yescomplemented
30#16840337C22132yescomplemented
31#16840316C22116yescomplemented
32#16840313C22116yes—
33C2×#14519776C2211yescharacteristic
34C2×#14519775C2211yescharacteristic
35C2×#14519775C2212yes—
36C2×#14519774C2211yescharacteristic
37#16840299C22132yescomplemented
38#16840297C22132yescomplemented
39C2×#14519772C2214yes—
40C2×#14519772C2214yes—
41C2×#14519772C2214yes—
42C2×#14519771C2214yes—
43C2×#14519768C2212yes—
44C2×#14519767C2212yes—
45C2×#14519767C2214yes—
46C2×#14519766C2212yes—
47C2×#14519766C2212yes—
48C2×#14519766C2212yes—
49C2×#14519765C2212yes—
50C2×#14519765C2212yes—
51C2×#14519762C2214yes—
52C2×#14519762C2214yes—
53C2×#14519762C2214yes—
54C2×#14519762C2214yes—
55C2×#14519757C2211yescharacteristic
56C2×#14519757C2214yes—
57C2×#14519755C2214yes—
58C2×#14519755C2214yes—
59C2×#14519755C2214yes—
60C2×#14519755C2212yes—
61C2×#14519753C2211yescharacteristic
62C2×#14519752C2212yes—
63C2×#14519752C2212yes—
64#16840244C22132yescomplemented
65C2×Q8×Dic61C2211yescharacteristic
66C2×Q8×Dic61C2212yes—
67C2×C4×Dic122C2212yes—
68C2×C4×Dic122C2211yescharacteristic
69C2×C4×Dic122C2212yes—
70C2×C4×Dic122C2211yescharacteristic
71C2×#14519742C2212yes—
72C2×#14519742C2211yescharacteristic
73C2×#14519742C2212yes—
74C4×Q8×D61C22116yescomplemented
75C2×C4×D244C2214yes—
76C2×C4×D244C2212yes—
77C2×C4×D244C2212yes—
78C2×#14519739C2214yes—
79C2×#14519739C2212yes—
80C2×#14519739C2212yes—
81C2×#14519739C2212yes—
82C2×#14519739C2212yes—
83C2×#14519735C2214yes—
84C2×#14519734C2214yes—
85C2×#14519734C2212yes—
86C2×#14519734C2214yes—
87C2×C4⋊C4×D61C2211yescharacteristic
88C2×C4⋊C4×D61C2212yes—
89C2×C4⋊C4×D61C2214yes—
90C2×C42×D61C2212yes—
91C2×C42×D61C2211yescharacteristic
92C61×#557C22116yescomplemented
93C2×C4⋊Q8×C61C2211yescharacteristic
94C2×C4⋊Q8×C61C2212yes—
95C2×#125×C61C2214yes—
96C2×#125×C61C2212yes—
97C2×C4×Q8×C61C2211yescharacteristic
98C2×C4×Q8×C61C2212yes—
99C2×C4×Q8×C61C2212yes—
100C2×C4×Q8×C61C2211yescharacteristic
101C2×#11758226—216no—
102C2×#11758226C23116yes—
103C22×Dic122C2311yescharacteristic
104C22×Dic122C2312yes—
105C22×Dic122C2311yescharacteristic
106C22×Dic122C2312yes—
107C2×Q8×D61—28no—
108C2×Q8×D61C2318yes—
109C22×D244C2312yes—
110C22×D244C2314yes—
111C22×D244C2312yes—
112C22×D244C2312yes—
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2312yes—
115C22×C4×D61C2314yes—
116C22×C4×D61C2312yes—
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2314yes—
119C22×C4×D61C2314yes—
120C22×C4×D61C2311yescharacteristic
121#14519776C2318yes—
122#14519775C2318yes—
123#14519775C23116yes—
124#14519774C2318yes—
125#14519772C23132yes—
126#14519772C23132yes—
127#14519772C23132yes—
128#14519771C23132yes—
129#14519768C23116yes—
130#14519767C23132yes—
131#14519767C23116yes—
132#14519766C23116yes—
133#14519766C23116yes—
134#14519766C23116yes—
135#14519765C23116yes—
136#14519765C23116yes—
137#14519762C23132yes—
138#14519762C23132yes—
139#14519762C23132yes—
140#14519762C23132yes—
141#14519757C23132yes—
142#14519757C2318yes—
143#14519755C23132yes—
144#14519755C23132yes—
145#14519755C23132yes—
146#14519755C23116yes—
147#14519753C2318yes—
148#14519752C23116yes—
149#14519752C23116yes—
150Q8×Dic61C2318yes—
151Q8×Dic61C23116yes—
152C4×Dic122C23116yes—
153C4×Dic122C2318yes—
154C4×Dic122C23116yes—
155C4×Dic122C2318yes—
156#14519742C2318yes—
157#14519742C23116yes—
158#14519742C23116yes—
159C4×D244C23116yes—
160C4×D244C23116yes—
161C4×D244C23132yes—
162#14519739C23116yes—
163#14519739C23116yes—
164#14519739C23116yes—
165#14519739C23132yes—
166#14519739C23116yes—
167#14519735C23132yes—
168#14519734C23132yes—
169#14519734C23132yes—
170#14519734C23116yes—
171C2×C4⋊Dic61C2311yescharacteristic
172C2×C4⋊Dic61C2314yes—
173C2×C4⋊Dic61C2312yes—
174C2×C4⋊Dic61C2312yes—
175C2×C4⋊Dic61C2311yescharacteristic
176C2×#11758196C2312yes—
177C2×#11758196C2312yes—
178C2×#11758196C2312yes—
179C2×#11758196C2312yes—
180C2×#11758196C2312yes—
181C2×#11758196C2312yes—
182C2×#11758196C2314yes—
183C2×#11758196C2314yes—
184C2×#11758196C2312yes—
185C2×#11758196C2312yes—
186C4⋊C4×D61C23132yes—
187C4⋊C4×D61C2318yes—
188C4⋊C4×D61C23116yes—
189C2×#11758198C2314yes—
190C2×#11758198C2312yes—
191C2×#11758198C2314yes—
192C2×#11758198C2312yes—
193C2×#11758198C2314yes—
194C2×#11758198C2314yes—
195C2×#11758198C2314yes—
196C2×#11758198C2314yes—
197C2×#11758198C2314yes—
198C2×#11758198C2314yes—
199C2×C4×Dic61C2312yes—
200C2×C4×Dic61C2312yes—
201C2×C4×Dic61C2311yescharacteristic
202C2×C4×Dic61C2311yescharacteristic
203C2×C4×Dic61C2312yes—
204C2×C4×Dic61C2311yescharacteristic
205C2×C4×Dic61C2314yes—
206C2×C4×Dic61C2312yes—
207C42×D61C23116yes—
208C42×D61C2318yes—
209C22×Q8×C61C2311yescharacteristic
210C22×Q8×C61C2312yes—
211C22×Q8×C61C2311yescharacteristic
212C4⋊Q8×C61C23116yes—
213C4⋊Q8×C61C2318yes—
214#125×C61C23116yes—
215#125×C61C23132yes—
216C4×Q8×C61C2318yes—
217C4×Q8×C61C23116yes—
218C4×Q8×C61C23116yes—
219C4×Q8×C61C2318yes—
220C2×C4⋊C4×C61C2314yes—
221C2×C4⋊C4×C61C2312yes—
222C2×C4⋊C4×C61C2312yes—
223C2×C4⋊C4×C61C2314yes—
224C2×C4⋊C4×C61C2311yescharacteristic
225C2×C4⋊C4×C61C2314yes—
226C2×C4⋊C4×C61C2312yes—
227C2×C4⋊C4×C61C2311yescharacteristic
228C2×C4⋊C4×C61C2312yes—
229C2×C42×C61C2311yescharacteristic
230C2×C42×C61C2312yes—
231C2×C42×C61C2312yes—
232C2×C42×C61C2314yes—
233C23×D61C2414yes—
234C23×D61C2411yescharacteristic
235C2×Q8×C61—24no—
236C2×Q8×C61—28no—
237C2×Q8×C61—24no—
238C2×Q8×C61C2414yes—
239C2×Q8×C61C2418yes—
240C2×Q8×C61C2414yes—
241C22×C4×C61C2412yes—
242C22×C4×C61C2412yes—
243C22×C4×C61C2411yescharacteristic
244C22×C4×C61C2414yes—
245C22×C4×C61C2412yes—
246C22×C4×C61C2412yes—
247C22×C4×C61C2411yescharacteristic
248C22×C4×C61C2411yescharacteristic
249C22×Dic61C2412yes—
250C22×Dic61C2412yes—
251C22×Dic61C2412yes—
252C22×Dic61C2411yescharacteristic
253C22×Dic61C2411yescharacteristic
254C22×Dic61C2412yes—
255C22×Dic61C2411yescharacteristic
256#11758226—264no—
257Q8×D61—232no—
258C2×D244—216no—
259C2×D244—28no—
260C2×D244—28no—
261C2×D244—44no—
262C2×D244C24116yes—
263C2×D244C2418yes—
264C2×D244C2418yes—
265C2×D244C2418yes—
266C2×C4×D61—28no—
267C2×C4×D61—24no—
268C2×C4×D61—216no—
269C2×C4×D61—42no—
270C2×C4×D61—48no—
271C2×C4×D61—48no—
272C2×C4×D61—44no—
273C2×C4×D61#4118yes—
274C2×C4×D61C2418yes—
275C2×C4×D61C24116yes—
276C2×C4×D61C2414yes—
277C2×C4×D61C2418yes—
278C2×C4×D61C2414yes—
279C2×C4×D61C24116yes—
280C2×C4×D61C24116yes—
281C2×C4×D61C2414yes—
282C2×Dic122—24no—
283C2×Dic122—24no—
284C2×Dic122—28no—
285C2×Dic122—44no—
286C2×Dic122C2418yes—
287C2×Dic122C2414yes—
288C2×Dic122C2414yes—
289C2×Dic122C2418yes—
290C4⋊C4×C61C2414yes—
291C4⋊C4×C61C24116yes—
292C4⋊C4×C61C2418yes—
293C4⋊C4×C61C2414yes—
294C4⋊C4×C61C2418yes—
295C4⋊C4×C61C2418yes—
296C4⋊C4×C61C24116yes—
297C4⋊C4×C61C24116yes—
298C4⋊C4×C61C2418yes—
299C42×C61C2418yes—
300C42×C61C24116yes—
301C42×C61C2414yes—
302C42×C61C2418yes—
303#11758198C24116yes—
304#11758198C2418yes—
305#11758198C24116yes—
306#11758198C2418yes—
307#11758198C24116yes—
308#11758198C24116yes—
309#11758198C24116yes—
310#11758198C24116yes—
311#11758198C24116yes—
312#11758198C24116yes—
313C4⋊Dic61C2414yes—
314C4⋊Dic61C24116yes—
315C4⋊Dic61C2418yes—
316C4⋊Dic61C2418yes—
317C4⋊Dic61C2414yes—
318#11758196C2418yes—
319#11758196C2418yes—
320#11758196C2418yes—
321#11758196C2418yes—
322#11758196C2418yes—
323#11758196C2418yes—
324#11758196C24116yes—
325#11758196C24116yes—
326#11758196C2418yes—
327#11758196C2418yes—
328C4×Dic61C2418yes—
329C4×Dic61C2418yes—
330C4×Dic61C2414yes—
331C4×Dic61C2414yes—
332C4×Dic61C2418yes—
333C4×Dic61C2414yes—
334C4×Dic61C24116yes—
335C4×Dic61C2418yes—
336C23×C61C2511yescharacteristic
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—28no—
340C22×D61—28no—
341C22×D61—28no—
342C22×D61C2×#4114yes—
343C22×D61C2518yes—
344C22×D61C2512yes—
345Q8×C61—28no—
346Q8×C61—216no—
347Q8×C61—28no—
348C2×C4×C61—24no—
349C2×C4×C61—28no—
350C2×C4×C61—24no—
351C2×C4×C61—24no—
352C2×C4×C61—24no—
353C2×C4×C61—22no—
354C2×C4×C61C2×#4114yes—
355C2×C4×C612−1+414yes—
356C2×C4×C61C2512yes—
357C2×C4×C61C2518yes—
358C2×C4×C61C2514yes—
359C2×C4×C61C2514yes—
360C2×C4×C61C2514yes—
361C2×C4×C61C2514yes—
362C2×C4×C61C2512yes—
363C2×C4×C61C2512yes—
364C2×Dic61—24no—
365C2×Dic61—24no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—24no—
369C2×Dic61—24no—
370C2×Dic61C2×#4114yes—
371C2×Dic61C2512yes—
372C2×Dic61C2514yes—
373C2×Dic61C2514yes—
374C2×Dic61C2514yes—
375C2×Dic61C2512yes—
376C2×Dic61C2514yes—
377C2×Dic61C2512yes—
378D244—232no—
379D244—216no—
380D244—216no—
381D244—48no—
382C4×D61—216no—
383C4×D61—28no—
384C4×D61—232no—
385C4×D61—44no—
386C4×D61—416no—
387C4×D61—416no—
388C4×D61—48no—
389C4×D61C2×#41116yes—
390Dic122—28no—
391Dic122—28no—
392Dic122—216no—
393Dic122—48no—
394C2×#3507—611nomaximal, Sylow
395C22×C61C22×#4112yes—
396C22×C61C2×2−1+412yes—
397C22×C61#58512yes—
398C22×C61C2611yescharacteristic
399C2×D61—22no—
400C2×D61—22no—
401C2×D61—28no—
402C2×D61—28no—
403C2×D61—28no—
404C2×D61—28no—
405C2×D61—416no—
406C2×D61C22×#4114yes—
407C4×C61—24no—
408C4×C61—28no—
409C4×C61—24no—
410C4×C61—24no—
411C4×C61—24no—
412C4×C61—22no—
413C4×C61C22×#4114yes—
414C4×C61C2×2−1+414yes—
415Dic61—24no—
416Dic61—24no—
417Dic61—22no—
418Dic61—22no—
419Dic61—24no—
420Dic61—24no—
421Dic61C22×#4114yes—
422#3507—6132no—
423C2×#559—611no—
424C2×#559—611no—
425C2×#557—611no—
426C2×#557D6111yescharacteristic, complemented
427C2×#556—612no—
428C2×#556—612no—
429C2×#556—612no—
430C2×#554—612no—
431C2×#552—614no—
432C2×#539—614no—
433C2×#536—612no—
434C2×#533—611no—
435C2×#532—611no—
436C2×#529—612no—
437C2×#529—612no—
438C2×#520—612no—
439C22×C4×Q8—611no—
440C2×C61#350714yescomplemented
441C2×C61C23×#4111yescharacteristic
442C2×C61C22×2−1+411yescharacteristic
443C2×C61C2×#58511yescharacteristic
444D61—24no—
445D61—48no—
446C22×#41—612no—
447C23×Q8—611no—
448#559—6116no—
449#559—6116no—
450#557—6116no—
451#557C2×D61116yescomplemented
452#556—6132no—
453#556—6132no—
454#556—6132no—
455#554—6132no—
456#552—6164no—
457#539—6164no—
458#536—6132no—
459#533—6116no—
460#532—6116no—
461C2×C4⋊Q8—611no—
462C2×C4⋊Q8—612no—
463C2×C4⋊Q8—611no—
464C2×C4⋊Q8C2×D6111yescharacteristic
465C2×C4⋊Q8C2×D6112yes—
466C2×#127—611no—
467#529—6132no—
468#529—6132no—
469C2×#126—614no—
470C2×#126—614no—
471C2×#126—614no—
472C2×#126—614no—
473C2×#125—612no—
474C2×#125—614no—
475C2×#125—612no—
476C2×#125C2×D6112yes—
477C2×#125C2×D6114yes—
478C2×#124—612no—
479C2×#124—612no—
480C2×#124—612no—
481C2×#124—612no—
482C2×#124—612no—
483C2×#123—614no—
484C2×#123—614no—
485C2×#123—614no—
486C2×#123—614no—
487C2×C22⋊Q8—611no—
488C2×C22⋊Q8—612no—
489C2×C22⋊Q8—614no—
490C2×C22⋊Q8—614no—
491C2×C22⋊Q8—614no—
492C2×C22⋊Q8—611no—
493C2×C22⋊Q8—614no—
494C2×#121—612no—
495C2×#121—612no—
496#520—6132no—
497C2×C4×Q8—611no—
498C2×C4×Q8—612no—
499C2×C4×Q8—6116no—
500C2×C4×Q8—612no—
501C2×C4×Q8—611no—
502C2×C4×Q8—612no—
503C2×C4×Q8—612no—
504C2×C4×Q8—611no—
505C2×C4×Q8—612no—
506C2×C4×Q8—611no—
507C2×C4×Q8C2×D6111yescharacteristic
508C2×C4×Q8C2×D6112yes—
509C2×C4×Q8C2×D6112yes—
510C2×C4×Q8C2×D6111yescharacteristic
511C2×C4×D4—614no—
512C2×C4×D4—612no—
513C2×C4×D4—612no—
514C2×C4×D4—612no—
515C2×C4×D4—612no—
516C2×C4×D4—614no—
517C2×C4×D4—612no—
518C2×C4×D4—612no—
519C2×#117—614no—
520C2×#117—612no—
521C2×#117—614no—
522C2×#117—614no—
523C22×C4⋊C4—611no—
524C22×C4⋊C4—612no—
525C22×C4⋊C4—614no—
526C22×C42—612no—
527C22×C42—611no—
528C61C2×#350711yescharacteristic, complemented, Sylow
529C2×#41—6116no—
530C2×#41—12216no—
531C22×Q8—618no—
532C22×Q8—611no—
533C22×Q8—612no—
534C22×Q8—611no—
535C22×Q8—612no—
536C22×Q8—1228no—
537C22×Q8C22×D6111yescharacteristic
538C22×Q8C22×D6112yes—
539C22×Q8C22×D6111yescharacteristic
540C22×D4—612no—
541C22×D4—614no—
542C22×D4—612no—
543C22×D4—612no—
544C23×C4—611no—
545C23×C4—614no—
546C23×C4—612no—
547C23×C4—611no—
548C23×C4—612no—
549C23×C4—611no—
550C23×C4—614no—
551C23×C4—614no—
552C4⋊Q8—618no—
553C4⋊Q8—6116no—
554C4⋊Q8—618no—
555C4⋊Q8C22×D6118yes—
556C4⋊Q8C22×D61116yes—
557#127—618no—
558#126—6132no—
559#126—6132no—
560#126—6132no—
561#126—6132no—
562#125—6116no—
563#125—6116no—
564#125—6132no—
565#125C22×D61116yes—
566#125C22×D61132yes—
567#124—6116no—
568#124—6116no—
569#124—6116no—
570#124—6116no—
571#124—6116no—
572#123—6132no—
573#123—6132no—
574#123—6132no—
575#123—6132no—
576C22⋊Q8—618no—
577C22⋊Q8—618no—
578C22⋊Q8—6116no—
579C22⋊Q8—6132no—
580C22⋊Q8—6132no—
581C22⋊Q8—6132no—
582C22⋊Q8—6132no—
583#121—6116no—
584#121—6116no—
585C4×Q8—618no—
586C4×Q8—6116no—
587C4×Q8—6116no—
588C4×Q8—618no—
589C4×Q8—6116no—
590C4×Q8—6116no—
591C4×Q8—618no—
592C4×Q8—6116no—
593C4×Q8—618no—
594C4×Q8C22×D6118yes—
595C4×Q8C22×D61116yes—
596C4×Q8C22×D61116yes—
597C4×Q8C22×D6118yes—
598C4×D4—6132no—
599C4×D4—6116no—
600C4×D4—6116no—
601C4×D4—6116no—
602C4×D4—6116no—
603C4×D4—6132no—
604C4×D4—6116no—
605C4×D4—6116no—
606#117—6132no—
607#117—6116no—
608#117—6132no—
609#117—6132no—
610C2×C4⋊C4—612no—
611C2×C4⋊C4—612no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—614no—
614C2×C4⋊C4—612no—
615C2×C4⋊C4—612no—
616C2×C4⋊C4—612no—
617C2×C4⋊C4—612no—
618C2×C4⋊C4—612no—
619C2×C4⋊C4—612no—
620C2×C4⋊C4—614no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—612no—
623C2×C4⋊C4—614no—
624C2×C4⋊C4—612no—
625C2×C4⋊C4—618no—
626C2×C4⋊C4—6116no—
627C2×C4⋊C4—6132no—
628C2×C4⋊C4C22×D6111yescharacteristic
629C2×C4⋊C4C22×D6114yes—
630C2×C4⋊C4C22×D6112yes—
631C2×C4⋊C4C22×D6114yes—
632C2×C4⋊C4C22×D6111yescharacteristic
633C2×C4⋊C4C22×D6112yes—
634C2×C4⋊C4C22×D6112yes—
635C2×C4⋊C4C22×D6112yes—
636C2×C4⋊C4C22×D6114yes—
637C2×C22⋊C4—614no—
638C2×C22⋊C4—612no—
639C2×C22⋊C4—612no—
640C2×C22⋊C4—614no—
641C2×C22⋊C4—614no—
642C2×C22⋊C4—614no—
643C2×C22⋊C4—614no—
644C2×C22⋊C4—614no—
645C2×C22⋊C4—614no—
646C2×C22⋊C4—614no—
647C2×C42—614no—
648C2×C42—612no—
649C2×C42—612no—
650C2×C42—612no—
651C2×C42—611no—
652C2×C42—611no—
653C2×C42—612no—
654C2×C42—611no—
655C2×C42—6116no—
656C2×C42—618no—
657C2×C42C22×D6114yes—
658C2×C42C22×D6112yes—
659C2×C42C22×D6112yes—
660C2×C42C22×D6111yescharacteristic
661C24—611no—
662C24—614no—
663#41—12264no—
664C2×Q8—24no—
665C2×Q8—28no—
666C2×Q8—24no—
667C2×Q8—614no—
668C2×Q8—618no—
669C2×Q8—614no—
670C2×Q8—618no—
671C2×Q8—1228no—
672C2×Q8—12232no—
673C2×Q8—1224no—
674C2×Q8—1224no—
675C2×Q8—2444no—
676C2×Q8C23×D6114yes—
677C2×Q8C23×D6118yes—
678C2×Q8C23×D6114yes—
679C2×D4—618no—
680C2×D4—6116no—
681C2×D4—618no—
682C2×D4—618no—
683C2×D4—12216no—
684C2×D4—1228no—
685C2×D4—1228no—
686C2×D4—2444no—
687C22×C4—611no—
688C22×C4—618no—
689C22×C4—614no—
690C22×C4—611no—
691C22×C4—612no—
692C22×C4—612no—
693C22×C4—612no—
694C22×C4—611no—
695C22×C4—612no—
696C22×C4—614no—
697C22×C4—618no—
698C22×C4—6116no—
699C22×C4—618no—
700C22×C4—614no—
701C22×C4—6116no—
702C22×C4—6116no—
703C22×C4—12216no—
704C22×C4—1228no—
705C22×C4—1224no—
706C22×C4—2444no—
707C22×C4—2448no—
708C22×C4—2448no—
709C22×C4—2442no—
710C22×C4C23×D6112yes—
711C22×C4C23×D6112yes—
712C22×C4C23×D6114yes—
713C22×C4C23×D6111yescharacteristic
714C22×C4C23×D6112yes—
715C22×C4C23×D6112yes—
716C22×C4C23×D6111yescharacteristic
717C22×C4C23×D6111yescharacteristic
718C4⋊C4—618no—
719C4⋊C4—618no—
720C4⋊C4—618no—
721C4⋊C4—618no—
722C4⋊C4—614no—
723C4⋊C4—6116no—
724C4⋊C4—618no—
725C4⋊C4—618no—
726C4⋊C4—618no—
727C4⋊C4—6116no—
728C4⋊C4—618no—
729C4⋊C4—6116no—
730C4⋊C4—618no—
731C4⋊C4—618no—
732C4⋊C4—614no—
733C4⋊C4C23×D6114yes—
734C4⋊C4C23×D61116yes—
735C4⋊C4C23×D6118yes—
736C4⋊C4C23×D61116yes—
737C4⋊C4C23×D6114yes—
738C4⋊C4C23×D6118yes—
739C4⋊C4C23×D6118yes—
740C4⋊C4C23×D6118yes—
741C4⋊C4C23×D61116yes—
742C22⋊C4—6116no—
743C22⋊C4—618no—
744C22⋊C4—618no—
745C22⋊C4—6116no—
746C22⋊C4—6116no—
747C22⋊C4—6116no—
748C22⋊C4—6116no—
749C22⋊C4—6116no—
750C22⋊C4—6116no—
751C22⋊C4—6116no—
752C42—618no—
753C42—618no—
754C42—614no—
755C42—614no—
756C42—618no—
757C42—614no—
758C42—6116no—
759C42—618no—
760C42C23×D6118yes—
761C42C23×D6114yes—
762C42C23×D61116yes—
763C42C23×D6118yes—
764C23—614no—
765C23—612no—
766C23—618no—
767C23—1222no—
768C23—1222no—
769C23—1228no—
770C23—1228no—
771C23—1228no—
772C23C24×D6111yescharacteristic
773Q8—28no—
774Q8—216no—
775Q8—28no—
776Q8—12216no—
777Q8—1228no—
778Q8—1228no—
779Q8—2448no—
780D4—12232no—
781D4—12216no—
782D4—12216no—
783D4—2448no—
784C2×C4—28no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—614no—
791C2×C4—612no—
792C2×C4—6116no—
793C2×C4—612no—
794C2×C4—614no—
795C2×C4—614no—
796C2×C4—614no—
797C2×C4—612no—
798C2×C4—614no—
799C2×C4—12232no—
800C2×C4—12216no—
801C2×C4—1224no—
802C2×C4—1222no—
803C2×C4—1224no—
804C2×C4—1224no—
805C2×C4—1224no—
806C2×C4—1222no—
807C2×C4—1228no—
808C2×C4—2448no—
809C2×C4—24416no—
810C2×C4—24416no—
811C2×C4—2444no—
812C2×C4#41×D6114yes—
813C2×C4#1451982514yes—
814C2×C4C24×D6114yes—
815C2×C4C24×D6114yes—
816C2×C4C24×D6118yes—
817C2×C4C24×D6112yes—
818C2×C4C24×D6114yes—
819C2×C4C24×D6114yes—
820C2×C4C24×D6112yes—
821C2×C4C24×D6112yes—
822C22—614no—
823C22—1222no—
824C22—1222no—
825C22—1228no—
826C22—1228no—
827C22—1228no—
828C22—1228no—
829C22—24416no—
830C22C2×#41×D6112yes—
831C22C2×#1451982512yes—
832C22#1684059912yes—
833C22C25×D6111yescharacteristic
834C4—28no—
835C4—24no—
836C4—24no—
837C4—24no—
838C4—24no—
839C4—22no—
840C4—614no—
841C4—1224no—
842C4—1222no—
843C4—1224no—
844C4—1224no—
845C4—1224no—
846C4—1222no—
847C4C2×#41×D6114yes—
848C4C2×#1451982514yes—
849C2—1224no—
850C2—2448no—
851C2#2145968514yesdirect product factor
852C2C22×#41×D6111yescharacteristic
853C2C22×#1451982511yescharacteristic
854C2C2×#1684059911yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#557C2
socleC23×C61C25
prime radicalC2×#16840313C2
hypercenterC2×#557D61
hypocenterC61C2×#3507
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #21459685C2direct (N × H)
2. C2×#16840497C2semidirect
3. C2×#16840497C2semidirect
4. C2×#16840487C2semidirect
5. C2×#16840486C2semidirect
6. C2×#16840484C2semidirect
7. C2×#16840484C2semidirect
8. C2×#16840468C2semidirect
9. C2×#16840444C2semidirect
10. C2×#16840360C2semidirect
11. C2×#16840337C2semidirect
12. C2×#16840316C2semidirect
14. C2×#16840299C2semidirect
15. C2×#16840297C2semidirect
16. C2×#16840244C2semidirect
17. C2×C4×Q8×D61C2semidirect
18. C2×C61×#557C2semidirect
21. #16840497C22semidirect
22. #16840497C22semidirect
23. #16840487C22semidirect
24. #16840486C22semidirect
25. #16840484C22semidirect
26. #16840484C22semidirect
27. #16840468C22semidirect
28. #16840444C22semidirect
29. #16840360C22semidirect
30. #16840337C22semidirect
31. #16840316C22semidirect
37. #16840299C22semidirect
38. #16840297C22semidirect
64. #16840244C22semidirect
74. C4×Q8×D61C22semidirect
92. C61×#557C22semidirect
426. C2×#557D61semidirect
440. C2×C61#3507semidirect
451. #557C2×D61semidirect
528. C61C2×#3507semidirect
851. C2#21459685direct (N × H)

Maximal subgroups

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

subgroupindex
#214596852
C2×#168404972
C2×#168404872
C2×#168404862
C2×#168404842
C2×#168404682
C2×#168404442
C2×#168403602
C2×#168403372
C2×#168403162
C2×#168403132
C2×#168402992
C2×#168402972
C2×#168402442
C2×C4×Q8×D612
C2×C61×#5572
C2×#350761