Finite Group Databasebeta

← C2×#21460265 #30587623

Subgroups — C2×#21460265 #30587623

Order 15616.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460265C2132yesmaximal, direct product factor
2C2×#16840516C214yesmaximal, complemented
3C2×#16840485C211yesmaximal, characteristic, complemented
4C2×#16840472C212yesmaximal, complemented
5C2×#16840465C212yesmaximal, complemented
6C2×Q8×D244C211yesmaximal, characteristic, complemented
7C2×#16840427C212yesmaximal, complemented
8C2×#16840424C212yesmaximal, complemented
9C2×#16840415C211yesmaximal, characteristic, complemented
10C2×#16840392C212yesmaximal, complemented
11C2×#16840384C212yesmaximal, complemented
12C2×#16840370C212yesmaximal, complemented
13C2×#16840360C214yesmaximal, complemented
14C2×#16840337C212yesmaximal, complemented
15C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
16C2×#16840299C211yesmaximal, characteristic, complemented
17C2×#16840299C211yesmaximal, characteristic, complemented
18C2×C61×#557C211yesmaximal, characteristic, complemented
19C22×#11758226C2212yes—
20C22×Q8×D61C2212yes—
21C22×Q8×D61C2212yes—
22#16840516C22164yescomplemented
23#16840485C22116yescomplemented
24#16840472C22132yescomplemented
25#16840465C22132yescomplemented
26Q8×D244C22116yescomplemented
27#16840427C22132yescomplemented
28#16840424C22132yescomplemented
29#16840415C22116yescomplemented
30#16840392C22132yescomplemented
31#16840384C22132yescomplemented
32#16840370C22132yescomplemented
33#16840360C22164yescomplemented
34#16840337C22132yescomplemented
35C2×#14519777C2212yes—
36C2×#14519777C2211yescharacteristic
37C2×#14519776C2214yes—
38C2×#14519776C2212yes—
39C2×#14519776C2212yes—
40C2×#14519775C2212yes—
41C4⋊Q8×D61C22116yescomplemented
42#16840299C22116yescomplemented
43#16840299C22116yescomplemented
44C2×#14519772C2212yes—
45C2×#14519772C2212yes—
46C2×#14519772C2214yes—
47C2×#14519772C2214yes—
48C2×#14519771C2214yes—
49C2×#14519769C2214yes—
50C2×#14519768C2211yescharacteristic
51C2×#14519768C2211yescharacteristic
52C2×#14519767C2214yes—
53C2×#14519766C2211yescharacteristic
54C2×#14519766C2211yescharacteristic
55C2×#14519765C2212yes—
56C2×#14519765C2214yes—
57C2×#14519762C2214yes—
58C2×#14519762C2212yes—
59C2×#14519762C2212yes—
60C2×#14519762C2214yes—
61C2×#14519762C2214yes—
62C2×#14519757C2214yes—
63C2×#14519757C2212yes—
64C2×#14519757C2214yes—
65C2×#14519755C2214yes—
66C2×#14519755C2214yes—
67C2×#14519755C2214yes—
68C2×#14519755C2214yes—
69C2×#14519753C2212yes—
70C2×#14519753C2211yescharacteristic
71C2×#14519753C2211yescharacteristic
72C2×#14519753C2212yes—
73C2×#14519752C2212yes—
74C2×#14519752C2211yescharacteristic
75C2×#14519752C2214yes—
76C2×#14519752C2211yescharacteristic
77C2×C4×Dic122C2212yes—
78C2×C4×D244C2211yescharacteristic
79C2×C4×D244C2211yescharacteristic
80C2×C4×D244C2212yes—
81C2×C4×D244C2214yes—
82C2×C4×D244C2212yes—
83C2×C4×D244C2212yes—
84C2×#14519739C2214yes—
85C2×#14519735C2212yes—
86C2×#14519734C2212yes—
87C2×#14519734C2212yes—
88C2×C4⋊C4×D61C2212yes—
89C2×C4⋊C4×D61C2212yes—
90C2×C4⋊C4×D61C2212yes—
91C2×C42×D61C2211yescharacteristic
92C61×#557C22116yescomplemented
93C2×C4⋊Q8×C61C2211yescharacteristic
94C2×C4⋊Q8×C61C2212yes—
95C2×#125×C61C2212yes—
96C2×#125×C61C2214yes—
97C2×C4×Q8×C61C2212yes—
98C2×C4×Q8×C61C2211yescharacteristic
99C2×C4×Q8×C61C2211yescharacteristic
100C2×C4×Q8×C61C2212yes—
101C2×#11758226—48no—
102C2×#11758226C23116yes—
103C22×Dic122C2312yes—
104C22×Dic122C2314yes—
105C22×Dic122C2314yes—
106C2×Q8×D61—48no—
107C2×Q8×D61—48no—
108C2×Q8×D61C23116yes—
109C2×Q8×D61C23116yes—
110C22×D244C2312yes—
111C22×D244C2312yes—
112C22×D244C2311yescharacteristic
113C22×D244C2311yescharacteristic
114C22×D244C2314yes—
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2312yes—
119C22×C4×D61C2312yes—
120C22×C4×D61C2314yes—
121C22×C4×D61C2314yes—
122C22×C4×D61C2314yes—
123#14519777C23116yes—
124#14519777C2318yes—
125#14519776C23116yes—
126#14519776C23132yes—
127#14519776C23116yes—
128#14519775C23116yes—
129#14519772C23132yes—
130#14519772C23132yes—
131#14519772C23116yes—
132#14519772C23116yes—
133#14519771C23132yes—
134#14519769C23132yes—
135#14519768C2318yes—
136#14519768C2318yes—
137#14519767C23132yes—
138#14519766C2318yes—
139#14519766C2318yes—
140#14519765C23116yes—
141#14519765C23132yes—
142#14519762C23132yes—
143#14519762C23132yes—
144#14519762C23116yes—
145#14519762C23116yes—
146#14519762C23132yes—
147#14519757C23132yes—
148#14519757C23132yes—
149#14519757C23116yes—
150#14519755C23132yes—
151#14519755C23132yes—
152#14519755C23132yes—
153#14519755C23132yes—
154#14519753C2318yes—
155#14519753C23116yes—
156#14519753C2318yes—
157#14519753C23116yes—
158#14519752C2318yes—
159#14519752C23132yes—
160#14519752C23116yes—
161#14519752C2318yes—
162C4×Dic122C23116yes—
163C4×D244C23116yes—
164C4×D244C23116yes—
165C4×D244C23132yes—
166C4×D244C2318yes—
167C4×D244C2318yes—
168C4×D244C23116yes—
169#14519739C23132yes—
170#14519735C23116yes—
171#14519734C23116yes—
172#14519734C23116yes—
173C2×C4⋊Dic61C2311yescharacteristic
174C2×C4⋊Dic61C2312yes—
175C2×C4⋊Dic61C2312yes—
176C2×C4⋊Dic61C2311yescharacteristic
177C2×C4⋊Dic61C2314yes—
178C2×C4⋊Dic61C2312yes—
179C2×C4⋊Dic61C2312yes—
180C2×#11758196C2314yes—
181C2×#11758196C2314yes—
182C2×#11758196C2314yes—
183C2×#11758196C2312yes—
184C2×#11758196C2312yes—
185C2×#11758196C2312yes—
186C2×#11758196C2312yes—
187C2×#11758196C2314yes—
188C4⋊C4×D61C23116yes—
189C4⋊C4×D61C23116yes—
190C4⋊C4×D61C23116yes—
191C2×#11758198C2312yes—
192C2×#11758198C2312yes—
193C2×#11758198C2312yes—
194C2×#11758198C2312yes—
195C2×#11758198C2314yes—
196C2×#11758198C2312yes—
197C2×#11758198C2314yes—
198C2×#11758198C2312yes—
199C2×#11758198C2314yes—
200C2×#11758198C2314yes—
201C2×#11758198C2312yes—
202C2×#11758198C2312yes—
203C2×#11758198C2312yes—
204C2×#11758198C2312yes—
205C2×C4×Dic61C2311yescharacteristic
206C2×C4×Dic61C2311yescharacteristic
207C2×C4×Dic61C2311yescharacteristic
208C2×C4×Dic61C2314yes—
209C42×D61C2318yes—
210C22×Q8×C61C2311yescharacteristic
211C22×Q8×C61C2312yes—
212C22×Q8×C61C2311yescharacteristic
213C4⋊Q8×C61C2318yes—
214C4⋊Q8×C61C23116yes—
215#125×C61C23116yes—
216#125×C61C23132yes—
217C4×Q8×C61C23116yes—
218C4×Q8×C61C2318yes—
219C4×Q8×C61C2318yes—
220C4×Q8×C61C23116yes—
221C2×C4⋊C4×C61C2312yes—
222C2×C4⋊C4×C61C2312yes—
223C2×C4⋊C4×C61C2314yes—
224C2×C4⋊C4×C61C2314yes—
225C2×C4⋊C4×C61C2311yescharacteristic
226C2×C4⋊C4×C61C2311yescharacteristic
227C2×C4⋊C4×C61C2314yes—
228C2×C4⋊C4×C61C2312yes—
229C2×C4⋊C4×C61C2312yes—
230C2×C42×C61C2311yescharacteristic
231C2×C42×C61C2312yes—
232C2×C42×C61C2312yes—
233C2×C42×C61C2314yes—
234C23×D61C2412yes—
235C23×D61C2412yes—
236C23×D61C2411yescharacteristic
237C2×Q8×C61—24no—
238C2×Q8×C61—28no—
239C2×Q8×C61—24no—
240C2×Q8×C61C2414yes—
241C2×Q8×C61C2418yes—
242C2×Q8×C61C2414yes—
243C22×C4×C61C2414yes—
244C22×C4×C61C2412yes—
245C22×C4×C61C2411yescharacteristic
246C22×C4×C61C2412yes—
247C22×C4×C61C2412yes—
248C22×C4×C61C2412yes—
249C22×C4×C61C2411yescharacteristic
250C22×C4×C61C2411yescharacteristic
251C22×Dic61C2412yes—
252C22×Dic61C2414yes—
253C22×Dic61C2411yescharacteristic
254C22×Dic61C2411yescharacteristic
255C22×Dic61C2411yescharacteristic
256C22×Dic61C2412yes—
257#11758226—432no—
258Q8×D61—432no—
259Q8×D61—432no—
260C2×D244—28no—
261C2×D244—28no—
262C2×D244—24no—
263C2×D244—24no—
264C2×D244—48no—
265C2×D244C2414yes—
266C2×D244C2418yes—
267C2×D244C2418yes—
268C2×D244C2414yes—
269C2×D244C24116yes—
270C2×C4×D61—24no—
271C2×C4×D61—24no—
272C2×C4×D61—28no—
273C2×C4×D61—24no—
274C2×C4×D61—28no—
275C2×C4×D61—48no—
276C2×C4×D61—48no—
277C2×C4×D61—48no—
278C2×C4×D61C2414yes—
279C2×C4×D61C2418yes—
280C2×C4×D61C2414yes—
281C2×C4×D61C2414yes—
282C2×C4×D61C2418yes—
283C2×C4×D61C24116yes—
284C2×C4×D61C24116yes—
285C2×C4×D61C24116yes—
286C2×Dic122—28no—
287C2×Dic122—48no—
288C2×Dic122—48no—
289C2×Dic122C2418yes—
290C2×Dic122C24116yes—
291C2×Dic122C24116yes—
292C4⋊C4×C61C2414yes—
293C4⋊C4×C61C2414yes—
294C4⋊C4×C61C24116yes—
295C4⋊C4×C61C2418yes—
296C4⋊C4×C61C2418yes—
297C4⋊C4×C61C2418yes—
298C4⋊C4×C61C24116yes—
299C4⋊C4×C61C2418yes—
300C4⋊C4×C61C24116yes—
301C42×C61C2418yes—
302C42×C61C24116yes—
303C42×C61C2414yes—
304C42×C61C2418yes—
305#11758198C2418yes—
306#11758198C2418yes—
307#11758198C2418yes—
308#11758198C2418yes—
309#11758198C24116yes—
310#11758198C2418yes—
311#11758198C24116yes—
312#11758198C2418yes—
313#11758198C24116yes—
314#11758198C24116yes—
315#11758198C2418yes—
316#11758198C2418yes—
317#11758198C2418yes—
318#11758198C2418yes—
319C4⋊Dic61C2414yes—
320C4⋊Dic61C2418yes—
321C4⋊Dic61C2418yes—
322C4⋊Dic61C2414yes—
323C4⋊Dic61C24116yes—
324C4⋊Dic61C2418yes—
325C4⋊Dic61C2418yes—
326#11758196C24116yes—
327#11758196C24116yes—
328#11758196C24116yes—
329#11758196C2418yes—
330#11758196C2418yes—
331#11758196C2418yes—
332#11758196C2418yes—
333#11758196C24116yes—
334C4×Dic61C2414yes—
335C4×Dic61C2414yes—
336C4×Dic61C2414yes—
337C4×Dic61C24116yes—
338C23×C61C2511yescharacteristic
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—24no—
342C22×D61—24no—
343C22×D61—24no—
344C22×D61—24no—
345C22×D61—24no—
346C22×D61—24no—
347C22×D612−1+414yes—
348C22×D61C2514yes—
349C22×D61C2514yes—
350C22×D61C2512yes—
351Q8×C61—28no—
352Q8×C61—216no—
353Q8×C61—28no—
354C2×C4×C61—24no—
355C2×C4×C61—28no—
356C2×C4×C61—22no—
357C2×C4×C61—24no—
358C2×C4×C61—24no—
359C2×C4×C61—24no—
360C2×C4×C61H(5,𝔽2)14yes—
361C2×C4×C612−1+414yes—
362C2×C4×C61C2514yes—
363C2×C4×C61C2512yes—
364C2×C4×C61C2514yes—
365C2×C4×C61C2518yes—
366C2×C4×C61C2514yes—
367C2×C4×C61C2514yes—
368C2×C4×C61C2512yes—
369C2×C4×C61C2512yes—
370C2×Dic61—28no—
371C2×Dic61—22no—
372C2×Dic61—24no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—24no—
376C2×Dic61C2512yes—
377C2×Dic61C2512yes—
378C2×Dic61C2514yes—
379C2×Dic61C2512yes—
380C2×Dic61C2518yes—
381C2×Dic61C2514yes—
382D244—216no—
383D244—216no—
384D244—28no—
385D244—28no—
386D244—416no—
387C4×D61—28no—
388C4×D61—28no—
389C4×D61—216no—
390C4×D61—28no—
391C4×D61—216no—
392C4×D61—416no—
393C4×D61—416no—
394C4×D61—416no—
395Dic122—216no—
396Dic122—416no—
397Dic122—416no—
398C2×#3552—611nomaximal, Sylow
399C22×C61C2×H(5,𝔽2)12yes—
400C22×C61C2×2−1+412yes—
401C22×C61C2×2−1+412yes—
402C22×C61C2611yescharacteristic
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—28no—
406C2×D61—24no—
407C2×D61—24no—
408C2×D61—24no—
409C2×D61—24no—
410C2×D61—24no—
411C2×D61—24no—
412C2×D61—48no—
413C2×D61—48no—
414C2×D61C2×2−1+414yes—
415C4×C61—24no—
416C4×C61—28no—
417C4×C61—22no—
418C4×C61—24no—
419C4×C61—24no—
420C4×C61—24no—
421C4×C61C2×H(5,𝔽2)14yes—
422C4×C61C2×2−1+414yes—
423Dic61—28no—
424Dic61—22no—
425Dic61—24no—
426Dic61—22no—
427Dic61—22no—
428Dic61—24no—
429#3552—6132no—
430C2×#563—614no—
431C2×#557D6111yescharacteristic, complemented
432C2×#556—611no—
433C2×#554—612no—
434C2×#553—612no—
435C2×D4×Q8—612no—
436C2×D4×Q8—611no—
437C2×#548—612no—
438C2×#547—611no—
439C2×#544—612no—
440C2×#542—612no—
441C2×#541—612no—
442C2×#539—614no—
443C2×#536—612no—
444C22×C4⋊Q8—611no—
445C2×#529—611no—
446C2×#529—611no—
447C2×C61#355214yescomplemented
448C2×C61C22×H(5,𝔽2)11yescharacteristic
449C2×C61C22×2−1+411yescharacteristic
450C2×C61C22×2−1+411yescharacteristic
451D61—24no—
452D61—44no—
453D61—44no—
454C22×#41—612no—
455C23×Q8—612no—
456C23×Q8—612no—
457#563—6164no—
458#557C2×D61116yescomplemented
459#556—6116no—
460#554—6132no—
461#553—6132no—
462D4×Q8—6132no—
463D4×Q8—6116no—
464#548—6132no—
465#547—6116no—
466#544—6132no—
467#542—6132no—
468#541—6132no—
469#539—6164no—
470#536—6132no—
471C2×C4⋊Q8—612no—
472C2×C4⋊Q8—6116no—
473C2×C4⋊Q8—612no—
474C2×C4⋊Q8—612no—
475C2×C4⋊Q8—614no—
476C2×C4⋊Q8—611no—
477C2×C4⋊Q8—612no—
478C2×C4⋊Q8C2×D6111yescharacteristic
479C2×C4⋊Q8C2×D6112yes—
480#529—6116no—
481#529—6116no—
482C2×#126—612no—
483C2×#126—612no—
484C2×#126—614no—
485C2×#126—614no—
486C2×#126—614no—
487C2×#125—614no—
488C2×#125—611no—
489C2×#125—611no—
490C2×#125—614no—
491C2×#125C2×D6114yes—
492C2×#125C2×D6112yes—
493C2×#124—611no—
494C2×#124—611no—
495C2×#124—612no—
496C2×#124—614no—
497C2×#123—612no—
498C2×#123—612no—
499C2×#123—614no—
500C2×#123—614no—
501C2×#123—614no—
502C2×C22⋊Q8—611no—
503C2×C22⋊Q8—611no—
504C2×C22⋊Q8—612no—
505C2×C22⋊Q8—612no—
506C2×C22⋊Q8—614no—
507C2×C22⋊Q8—614no—
508C2×C22⋊Q8—614no—
509C2×C22⋊Q8—614no—
510C2×C22⋊Q8—614no—
511C2×C22⋊Q8—612no—
512C2×C22⋊Q8—614no—
513C2×#121—611no—
514C2×#121—611no—
515C2×#121—614no—
516C2×#121—612no—
517C2×C4×Q8—612no—
518C2×C4×Q8C2×D6111yescharacteristic
519C2×C4×Q8C2×D6111yescharacteristic
520C2×C4×Q8C2×D6112yes—
521C2×C4×Q8C2×D6112yes—
522C2×C4×D4—614no—
523C2×C4×D4—611no—
524C2×C4×D4—611no—
525C2×C4×D4—612no—
526C2×C4×D4—612no—
527C2×C4×D4—614no—
528C2×C4×D4—612no—
529C2×#117—612no—
530C2×#117—612no—
531C2×#117—612no—
532C22×C4⋊C4—612no—
533C22×C4⋊C4—612no—
534C22×C4⋊C4—612no—
535C22×C42—611no—
536C61C2×#355211yescharacteristic, complemented, Sylow
537C2×#41—6116no—
538C2×#41—2448no—
539C22×Q8—6116no—
540C22×Q8—6116no—
541C22×Q8—612no—
542C22×Q8—614no—
543C22×Q8—614no—
544C22×Q8—2448no—
545C22×Q8—2448no—
546C22×Q8C22×D6111yescharacteristic
547C22×Q8C22×D6111yescharacteristic
548C22×Q8C22×D6112yes—
549C22×D4—612no—
550C22×D4—612no—
551C22×D4—611no—
552C22×D4—611no—
553C22×D4—614no—
554C23×C4—611no—
555C23×C4—611no—
556C23×C4—612no—
557C23×C4—612no—
558C23×C4—611no—
559C23×C4—614no—
560C23×C4—614no—
561C23×C4—614no—
562C4⋊Q8—6116no—
563C4⋊Q8—6116no—
564C4⋊Q8—6116no—
565C4⋊Q8—6132no—
566C4⋊Q8—618no—
567C4⋊Q8—6116no—
568C4⋊Q8C22×D6118yes—
569C4⋊Q8C22×D61116yes—
570#126—6116no—
571#126—6116no—
572#126—6132no—
573#126—6132no—
574#126—6132no—
575#125—618no—
576#125—618no—
577#125—6132no—
578#125—6132no—
579#125C22×D61132yes—
580#125C22×D61116yes—
581#124—618no—
582#124—618no—
583#124—6116no—
584#124—6132no—
585#123—6116no—
586#123—6116no—
587#123—6132no—
588#123—6132no—
589#123—6132no—
590C22⋊Q8—618no—
591C22⋊Q8—618no—
592C22⋊Q8—6116no—
593C22⋊Q8—6116no—
594C22⋊Q8—6132no—
595C22⋊Q8—6132no—
596C22⋊Q8—6132no—
597C22⋊Q8—6132no—
598C22⋊Q8—6116no—
599C22⋊Q8—6132no—
600C22⋊Q8—6132no—
601#121—618no—
602#121—618no—
603#121—6132no—
604#121—6116no—
605C4×Q8—6116no—
606C4×Q8C22×D6118yes—
607C4×Q8C22×D6118yes—
608C4×Q8C22×D61116yes—
609C4×Q8C22×D61116yes—
610C4×D4—6132no—
611C4×D4—618no—
612C4×D4—618no—
613C4×D4—6116no—
614C4×D4—6116no—
615C4×D4—6132no—
616C4×D4—6116no—
617#117—6116no—
618#117—6116no—
619#117—6116no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—612no—
622C2×C4⋊C4—614no—
623C2×C4⋊C4—612no—
624C2×C4⋊C4—614no—
625C2×C4⋊C4—614no—
626C2×C4⋊C4—612no—
627C2×C4⋊C4—612no—
628C2×C4⋊C4—612no—
629C2×C4⋊C4—612no—
630C2×C4⋊C4—611no—
631C2×C4⋊C4—614no—
632C2×C4⋊C4—612no—
633C2×C4⋊C4—612no—
634C2×C4⋊C4—614no—
635C2×C4⋊C4—6116no—
636C2×C4⋊C4—6116no—
637C2×C4⋊C4—6116no—
638C2×C4⋊C4C22×D6112yes—
639C2×C4⋊C4C22×D6112yes—
640C2×C4⋊C4C22×D6111yescharacteristic
641C2×C4⋊C4C22×D6114yes—
642C2×C4⋊C4C22×D6111yescharacteristic
643C2×C4⋊C4C22×D6114yes—
644C2×C4⋊C4C22×D6114yes—
645C2×C4⋊C4C22×D6112yes—
646C2×C4⋊C4C22×D6112yes—
647C2×C22⋊C4—614no—
648C2×C22⋊C4—612no—
649C2×C22⋊C4—612no—
650C2×C22⋊C4—612no—
651C2×C22⋊C4—612no—
652C2×C22⋊C4—612no—
653C2×C22⋊C4—612no—
654C2×C22⋊C4—614no—
655C2×C22⋊C4—614no—
656C2×C22⋊C4—612no—
657C2×C22⋊C4—612no—
658C2×C22⋊C4—614no—
659C2×C22⋊C4—612no—
660C2×C22⋊C4—612no—
661C2×C42—611no—
662C2×C42—611no—
663C2×C42—614no—
664C2×C42—611no—
665C2×C42—618no—
666C2×C42C22×D6112yes—
667C2×C42C22×D6112yes—
668C2×C42C22×D6111yescharacteristic
669C2×C42C22×D6114yes—
670C24—611no—
671C24—612no—
672C24—612no—
673#41—24432no—
674C2×Q8—24no—
675C2×Q8—28no—
676C2×Q8—24no—
677C2×Q8—618no—
678C2×Q8—6116no—
679C2×Q8—6116no—
680C2×Q8—1228no—
681C2×Q8—2448no—
682C2×Q8—2448no—
683C2×Q8—24432no—
684C2×Q8—24432no—
685C2×Q8C23×D6114yes—
686C2×Q8C23×D6114yes—
687C2×Q8C23×D6118yes—
688C2×D4—618no—
689C2×D4—618no—
690C2×D4—614no—
691C2×D4—614no—
692C2×D4—6116no—
693C2×D4—1228no—
694C2×D4—1228no—
695C2×D4—1224no—
696C2×D4—1224no—
697C2×D4—2448no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—612no—
701C22×C4—611no—
702C22×C4—614no—
703C22×C4—612no—
704C22×C4—614no—
705C22×C4—614no—
706C22×C4—614no—
707C22×C4—618no—
708C22×C4—618no—
709C22×C4—6116no—
710C22×C4—6116no—
711C22×C4—6116no—
712C22×C4—1224no—
713C22×C4—1224no—
714C22×C4—1228no—
715C22×C4—1224no—
716C22×C4—1228no—
717C22×C4—2448no—
718C22×C4—2448no—
719C22×C4—2448no—
720C22×C4C23×D6112yes—
721C22×C4C23×D6111yescharacteristic
722C22×C4C23×D6112yes—
723C22×C4C23×D6112yes—
724C22×C4C23×D6112yes—
725C22×C4C23×D6114yes—
726C22×C4C23×D6111yescharacteristic
727C22×C4C23×D6111yescharacteristic
728C4⋊C4—614no—
729C4⋊C4—6116no—
730C4⋊C4—6116no—
731C4⋊C4—6116no—
732C4⋊C4—618no—
733C4⋊C4—618no—
734C4⋊C4—618no—
735C4⋊C4—618no—
736C4⋊C4—618no—
737C4⋊C4—618no—
738C4⋊C4—6116no—
739C4⋊C4—614no—
740C4⋊C4—6116no—
741C4⋊C4—618no—
742C4⋊C4—618no—
743C4⋊C4C23×D6118yes—
744C4⋊C4C23×D6118yes—
745C4⋊C4C23×D6114yes—
746C4⋊C4C23×D61116yes—
747C4⋊C4C23×D6114yes—
748C4⋊C4C23×D61116yes—
749C4⋊C4C23×D61116yes—
750C4⋊C4C23×D6118yes—
751C4⋊C4C23×D6118yes—
752C22⋊C4—6116no—
753C22⋊C4—618no—
754C22⋊C4—618no—
755C22⋊C4—618no—
756C22⋊C4—618no—
757C22⋊C4—618no—
758C22⋊C4—618no—
759C22⋊C4—6116no—
760C22⋊C4—6116no—
761C22⋊C4—618no—
762C22⋊C4—618no—
763C22⋊C4—6116no—
764C22⋊C4—618no—
765C22⋊C4—618no—
766C42—614no—
767C42—614no—
768C42—614no—
769C42—6116no—
770C42C23×D6114yes—
771C42C23×D6118yes—
772C42C23×D6118yes—
773C42C23×D61116yes—
774C23—614no—
775C23—612no—
776C23—614no—
777C23—614no—
778C23—1222no—
779C23—1222no—
780C23—1224no—
781C23—1224no—
782C23—1224no—
783C23—1224no—
784C23—1224no—
785C23—1224no—
786C23C24×D6111yescharacteristic
787Q8—28no—
788Q8—216no—
789Q8—28no—
790Q8—12216no—
791Q8—24416no—
792Q8—24416no—
793D4—12216no—
794D4—12216no—
795D4—1228no—
796D4—1228no—
797D4—24416no—
798C2×C4—28no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—612no—
805C2×C4—612no—
806C2×C4—614no—
807C2×C4—612no—
808C2×C4—618no—
809C2×C4—614no—
810C2×C4—1228no—
811C2×C4—1224no—
812C2×C4—1222no—
813C2×C4—1228no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1224no—
817C2×C4—1228no—
818C2×C4—12216no—
819C2×C4—1228no—
820C2×C4—12216no—
821C2×C4—24416no—
822C2×C4—24416no—
823C2×C4—24416no—
824C2×C4#1451982314yes—
825C2×C4#1451982514yes—
826C2×C4C24×D6114yes—
827C2×C4C24×D6112yes—
828C2×C4C24×D6114yes—
829C2×C4C24×D6114yes—
830C2×C4C24×D6114yes—
831C2×C4C24×D6118yes—
832C2×C4C24×D6112yes—
833C2×C4C24×D6112yes—
834C22—614no—
835C22—1228no—
836C22—1222no—
837C22—1222no—
838C22—1224no—
839C22—1224no—
840C22—1224no—
841C22—1224no—
842C22—1224no—
843C22—1224no—
844C22—2448no—
845C22—2448no—
846C22C2×#1451982312yes—
847C222−1+4×D6112yes—
848C22C2×#1451982512yes—
849C22C25×D6111yescharacteristic
850C4—28no—
851C4—24no—
852C4—22no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—1224no—
857C4—1222no—
858C4—1228no—
859C4—1222no—
860C4—1222no—
861C4—1224no—
862C4C2×#1451982314yes—
863C4C2×#1451982514yes—
864C2—1224no—
865C2—2444no—
866C2—2444no—
867C2#2146026514yesdirect product factor
868C2C22×#1451982311yescharacteristic
869C2C2×2−1+4×D6111yescharacteristic
870C2C22×#1451982511yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#557C2
socleC23×C61C25
hypercenterC2×#557D61
hypocenterC61C2×#3552
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #21460265C2direct (N × H)
2. C2×#16840516C2semidirect
3. C2×#16840485C2semidirect
4. C2×#16840472C2semidirect
5. C2×#16840465C2semidirect
6. C2×Q8×D244C2semidirect
7. C2×#16840427C2semidirect
8. C2×#16840424C2semidirect
9. C2×#16840415C2semidirect
10. C2×#16840392C2semidirect
11. C2×#16840384C2semidirect
12. C2×#16840370C2semidirect
13. C2×#16840360C2semidirect
14. C2×#16840337C2semidirect
15. C2×C4⋊Q8×D61C2semidirect
16. C2×#16840299C2semidirect
17. C2×#16840299C2semidirect
18. C2×C61×#557C2semidirect
22. #16840516C22semidirect
23. #16840485C22semidirect
24. #16840472C22semidirect
25. #16840465C22semidirect
26. Q8×D244C22semidirect
27. #16840427C22semidirect
28. #16840424C22semidirect
29. #16840415C22semidirect
30. #16840392C22semidirect
31. #16840384C22semidirect
32. #16840370C22semidirect
33. #16840360C22semidirect
34. #16840337C22semidirect
41. C4⋊Q8×D61C22semidirect
42. #16840299C22semidirect
43. #16840299C22semidirect
92. C61×#557C22semidirect
431. C2×#557D61semidirect
447. C2×C61#3552semidirect
458. #557C2×D61semidirect
536. C61C2×#3552semidirect
867. C2#21460265direct (N × H)

Maximal subgroups

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

subgroupindex
#214602652
C2×#168405162
C2×#168404852
C2×#168404722
C2×#168404652
C2×Q8×D2442
C2×#168404272
C2×#168404242
C2×#168404152
C2×#168403922
C2×#168403842
C2×#168403702
C2×#168403602
C2×#168403372
C2×C4⋊Q8×D612
C2×#168402992
C2×C61×#5572
C2×#355261