Finite Group Databasebeta

← C2×#21460160 #30587696

Subgroups — C2×#21460160 #30587696

Order 15616.

7086 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460160C2132yesmaximal, direct product factor
2C2×#16840513C214yesmaximal, complemented
3C2×Q8×Dic122C211yesmaximal, characteristic, complemented
4C2×#16840477C211yesmaximal, characteristic, complemented
5C2×#16840473C211yesmaximal, characteristic, complemented
6C2×#16840450C212yesmaximal, complemented
7C2×#16840446C212yesmaximal, complemented
8C2×#16840417C212yesmaximal, complemented
9C2×#16840413C212yesmaximal, complemented
10C2×#16840393C212yesmaximal, complemented
11C2×#16840392C212yesmaximal, complemented
12C2×#16840385C212yesmaximal, complemented
13C2×#16840377C212yesmaximal, complemented
14C2×#16840335C214yesmaximal, complemented
15C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
16C2×#16840299C211yesmaximal, characteristic, complemented
17C2×#16840294C211yesmaximal, characteristic, complemented
18C2×C61×#554C211yesmaximal, characteristic, complemented
19C22×#11758222C2214yes—
20C22×Q8×D61C2212yes—
21#16840513C22164yescomplemented
22Q8×Dic122C22116yescomplemented
23#16840477C22116yescomplemented
24#16840473C22116yescomplemented
25#16840450C22132yescomplemented
26#16840446C22132yescomplemented
27#16840417C22132yescomplemented
28#16840413C22132yescomplemented
29#16840393C22132yescomplemented
30#16840392C22132yescomplemented
31#16840385C22132yescomplemented
32#16840377C22132yescomplemented
33#16840335C22164yescomplemented
34C2×#14519777C2212yes—
35C2×#14519777C2211yescharacteristic
36C2×#14519776C2214yes—
37C2×#14519776C2212yes—
38C2×#14519776C2212yes—
39C2×#14519776C2212yes—
40C2×#14519776C2214yes—
41C2×#14519775C2212yes—
42C4⋊Q8×D61C22116yescomplemented
43#16840299C22116yescomplemented
44#16840294C22116yescomplemented
45C2×#14519772C2214yes—
46C2×#14519772C2212yes—
47C2×#14519770C2214yes—
48C2×#14519770C2212yes—
49C2×#14519768C2211yescharacteristic
50C2×#14519768C2211yescharacteristic
51C2×#14519768C2212yes—
52C2×#14519768C2214yes—
53C2×#14519767C2214yes—
54C2×#14519766C2211yescharacteristic
55C2×#14519764C2211yescharacteristic
56C2×#14519763C2214yes—
57C2×#14519763C2214yes—
58C2×#14519762C2214yes—
59C2×#14519762C2212yes—
60C2×#14519760C2214yes—
61C2×#14519759C2214yes—
62C2×#14519759C2214yes—
63C2×#14519759C2212yes—
64C2×#14519757C2214yes—
65C2×#14519757C2211yescharacteristic
66C2×#14519757C2212yes—
67C2×#14519756C2214yes—
68C2×#14519756C2214yes—
69C2×#14519755C2214yes—
70C2×#14519753C2211yescharacteristic
71C2×#14519753C2214yes—
72C2×#14519752C2211yescharacteristic
73C2×#14519751C2212yes—
74C2×#14519748C2211yescharacteristic
75C2×#14519748C2212yes—
76C2×Q8×Dic61C2212yes—
77C2×C4×Dic122C2212yes—
78C2×C4×Dic122C2211yescharacteristic
79C2×C4×D244C2212yes—
80C2×C4×D244C2211yescharacteristic
81C2×#14519739C2212yes—
82C2×C4×C22⋊D61C2212yes—
83C2×#14519736C2212yes—
84C2×#14519736C2212yes—
85C2×#14519735C2212yes—
86C2×#14519735C2214yes—
87C2×#14519734C2212yes—
88C2×C4⋊C4×D61C2212yes—
89C2×C4⋊C4×D61C2212yes—
90C2×C4⋊C4×D61C2212yes—
91C2×C42×D61C2211yescharacteristic
92C61×#554C22116yescomplemented
93C2×C4⋊Q8×C61C2211yescharacteristic
94C2×#125×C61C2212yes—
95C2×C22⋊Q8×C61C2212yes—
96C2×C22⋊Q8×C61C2214yes—
97C2×C4×Q8×C61C2211yescharacteristic
98C2×C4×D4×C61C2212yes—
99C2×C4×D4×C61C2211yescharacteristic
100C22×C4⋊C4×C61C2212yes—
101C2×#11758222—416no—
102C2×#11758222C23132yes—
103C22×Dic122C2311yescharacteristic
104C22×Dic122C2314yes—
105C22×Dic122C2314yes—
106C22×Dic122C2312yes—
107C2×Q8×D61—48no—
108C2×Q8×D61C23116yes—
109C22×D244C2311yescharacteristic
110C22×D244C2312yes—
111C22×C22⋊D61C2312yes—
112C22×C22⋊D61C2314yes—
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2314yes—
117C22×C4×D61C2312yes—
118C22×C4×D61C2314yes—
119#14519777C2318yes—
120#14519777C23116yes—
121#14519776C23132yes—
122#14519776C23116yes—
123#14519776C23116yes—
124#14519776C23116yes—
125#14519776C23132yes—
126#14519775C23116yes—
127#14519772C23132yes—
128#14519772C23116yes—
129#14519770C23116yes—
130#14519770C23132yes—
131#14519768C23132yes—
132#14519768C23116yes—
133#14519768C2318yes—
134#14519768C2318yes—
135#14519767C23132yes—
136#14519766C2318yes—
137#14519764C2318yes—
138#14519763C23132yes—
139#14519763C23132yes—
140#14519762C23132yes—
141#14519762C23116yes—
142#14519760C23132yes—
143#14519759C23132yes—
144#14519759C23116yes—
145#14519759C23132yes—
146#14519757C2318yes—
147#14519757C23116yes—
148#14519757C23132yes—
149#14519756C23132yes—
150#14519756C23132yes—
151#14519755C23132yes—
152#14519753C23132yes—
153#14519753C2318yes—
154#14519752C2318yes—
155#14519751C23116yes—
156#14519748C23116yes—
157#14519748C2318yes—
158Q8×Dic61C23116yes—
159C4×Dic122C23116yes—
160C4×Dic122C2318yes—
161C4×D244C23116yes—
162C4×D244C2318yes—
163#14519739C23116yes—
164C4×C22⋊D61C23116yes—
165#14519736C23116yes—
166#14519736C23116yes—
167#14519735C23116yes—
168#14519735C23132yes—
169#14519734C23116yes—
170C2×C4⋊Dic61C2311yescharacteristic
171C2×C4⋊Dic61C2312yes—
172C2×C4⋊Dic61C2312yes—
173C2×C4⋊Dic61C2314yes—
174C2×C4⋊Dic61C2311yescharacteristic
175C2×C4⋊Dic61C2312yes—
176C2×C4⋊Dic61C2312yes—
177C2×C4⋊Dic61C2312yes—
178C2×C4⋊Dic61C2314yes—
179C2×#11758196C2314yes—
180C2×#11758196C2314yes—
181C2×#11758196C2314yes—
182C2×#11758196C2312yes—
183C2×#11758196C2312yes—
184C2×#11758196C2312yes—
185C2×#11758196C2312yes—
186C2×#11758196C2314yes—
187C4⋊C4×D61C23116yes—
188C4⋊C4×D61C23116yes—
189C4⋊C4×D61C23116yes—
190C2×C22⋊Dic61C2312yes—
191C2×C22⋊Dic61C2314yes—
192C2×C22⋊Dic61C2312yes—
193C2×C22⋊Dic61C2312yes—
194C2×#11758198C2312yes—
195C2×#11758198C2312yes—
196C2×#11758198C2312yes—
197C2×#11758198C2312yes—
198C2×#11758198C2314yes—
199C2×#11758198C2314yes—
200C2×#11758198C2312yes—
201C2×#11758198C2312yes—
202C2×C4×Dic61C2311yescharacteristic
203C2×C4×Dic61C2311yescharacteristic
204C2×C4×Dic61C2311yescharacteristic
205C2×C4×Dic61C2314yes—
206C2×C4×Dic61C2314yes—
207C2×C4×Dic61C2312yes—
208C42×D61C2318yes—
209C22×Q8×C61C2311yescharacteristic
210C22×Q8×C61C2312yes—
211C22×D4×C61C2311yescharacteristic
212C23×C4×C61C2312yes—
213C23×C4×C61C2314yes—
214C4⋊Q8×C61C2318yes—
215#125×C61C23116yes—
216C22⋊Q8×C61C23132yes—
217C22⋊Q8×C61C23116yes—
218C4×Q8×C61C2318yes—
219C4×D4×C61C2318yes—
220C4×D4×C61C23116yes—
221C2×C4⋊C4×C61C2312yes—
222C2×C4⋊C4×C61C2312yes—
223C2×C4⋊C4×C61C23116yes—
224C2×C4⋊C4×C61C2311yescharacteristic
225C2×C4⋊C4×C61C2314yes—
226C2×C4⋊C4×C61C2311yescharacteristic
227C2×C4⋊C4×C61C2314yes—
228C2×C4⋊C4×C61C2312yes—
229C2×C22⋊C4×C61C2314yes—
230C2×C22⋊C4×C61C2312yes—
231C2×C42×C61C2311yescharacteristic
232C2×C42×C61C2312yes—
233C24×C61C2412yes—
234C23×D61C2412yes—
235C23×D61C2411yescharacteristic
236C2×Q8×C61—24no—
237C2×Q8×C61—44no—
238C2×Q8×C61C2414yes—
239C2×Q8×C61C2418yes—
240C2×D4×C61—24no—
241C2×D4×C61C2414yes—
242C22×C4×C61—28no—
243C22×C4×C61—48no—
244C22×C4×C61C2414yes—
245C22×C4×C61C2411yescharacteristic
246C22×C4×C61C2412yes—
247C22×C4×C61C2412yes—
248C22×C4×C61C2412yes—
249C22×C4×C61C2418yes—
250C22×C4×C61C24116yes—
251C22×C4×C61C2411yescharacteristic
252C22×C4×C61C2411yescharacteristic
253C2×C22⋊D61—28no—
254C2×C22⋊D61—48no—
255C2×C22⋊D61C2418yes—
256C2×C22⋊D61C24116yes—
257C22×Dic61C2412yes—
258C22×Dic61C2414yes—
259C22×Dic61C2411yescharacteristic
260C22×Dic61C2411yescharacteristic
261C22×Dic61C2411yescharacteristic
262C22×Dic61C2412yes—
263C22×Dic61C2412yes—
264Q8×D61—432no—
265#11758222—464no—
266C2×D244—28no—
267C2×D244—24no—
268C2×D244C2418yes—
269C2×D244C2414yes—
270C2×C4×D61—24no—
271C2×C4×D61—216no—
272C2×C4×D61—24no—
273C2×C4×D61—24no—
274C2×C4×D61—28no—
275C2×C4×D61—48no—
276C2×C4×D61C2414yes—
277C2×C4×D61C24116yes—
278C2×C4×D61C2414yes—
279C2×C4×D61C2414yes—
280C2×C4×D61C2418yes—
281C2×C4×D61C24116yes—
282C2×Dic122—24no—
283C2×Dic122—48no—
284C2×Dic122—44no—
285C2×Dic122—48no—
286C2×Dic122C2414yes—
287C2×Dic122C24116yes—
288C2×Dic122C2418yes—
289C2×Dic122C24116yes—
290C4⋊C4×C61C2414yes—
291C4⋊C4×C61C24116yes—
292C4⋊C4×C61C2418yes—
293C4⋊C4×C61C2414yes—
294C4⋊C4×C61C2418yes—
295C4⋊C4×C61C2418yes—
296C4⋊C4×C61C24116yes—
297C22⋊C4×C61C24116yes—
298C22⋊C4×C61C2418yes—
299C42×C61C2418yes—
300C42×C61C2414yes—
301C22⋊Dic61C2418yes—
302C22⋊Dic61C24116yes—
303C22⋊Dic61C2418yes—
304C22⋊Dic61C2418yes—
305#11758198C2418yes—
306#11758198C2418yes—
307#11758198C2418yes—
308#11758198C2418yes—
309#11758198C24116yes—
310#11758198C24116yes—
311#11758198C2418yes—
312#11758198C2418yes—
313C4⋊Dic61C2414yes—
314C4⋊Dic61C2418yes—
315C4⋊Dic61C2418yes—
316C4⋊Dic61C24116yes—
317C4⋊Dic61C2414yes—
318C4⋊Dic61C2418yes—
319C4⋊Dic61C2418yes—
320C4⋊Dic61C2418yes—
321C4⋊Dic61C24116yes—
322#11758196C24116yes—
323#11758196C24116yes—
324#11758196C24116yes—
325#11758196C2418yes—
326#11758196C2418yes—
327#11758196C2418yes—
328#11758196C2418yes—
329#11758196C24116yes—
330C4×Dic61C2414yes—
331C4×Dic61C2414yes—
332C4×Dic61C2414yes—
333C4×Dic61C24116yes—
334C4×Dic61C24116yes—
335C4×Dic61C2418yes—
336C23×C61—24no—
337C23×C61—24no—
338C23×C61—24no—
339C23×C61C2514yes—
340C23×C61C2511yescharacteristic
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—24no—
344C22×D61—24no—
345C22×D61—24no—
346C22×D61H(5,𝔽2)14yes—
347C22×D61C2514yes—
348C22×D61C2512yes—
349Q8×C61—28no—
350Q8×C61—48no—
351D4×C61—28no—
352C2×C4×C61—22no—
353C2×C4×C61—24no—
354C2×C4×C61—28no—
355C2×C4×C61—24no—
356C2×C4×C61—24no—
357C2×C4×C61—216no—
358C2×C4×C61—416no—
359C2×C4×C612−1+414yes—
360C2×C4×C612−1+414yes—
361C2×C4×C61C2514yes—
362C2×C4×C61C2514yes—
363C2×C4×C61C2512yes—
364C2×C4×C61C2514yes—
365C2×C4×C61C2518yes—
366C2×C4×C61C2512yes—
367C2×C4×C61C2512yes—
368C22⋊D61—216no—
369C22⋊D61—416no—
370C2×Dic61—22no—
371C2×Dic61—28no—
372C2×Dic61—24no—
373C2×Dic61—24no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—24no—
377C2×Dic61C2514yes—
378C2×Dic61C2512yes—
379C2×Dic61C2512yes—
380C2×Dic61C2514yes—
381C2×Dic61C2518yes—
382C2×Dic61C2512yes—
383C2×Dic61C2514yes—
384D244—216no—
385D244—28no—
386C4×D61—232no—
387C4×D61—28no—
388C4×D61—28no—
389C4×D61—28no—
390C4×D61—216no—
391C4×D61—416no—
392Dic122—28no—
393Dic122—416no—
394Dic122—416no—
395Dic122—48no—
396C2×#3544—611nomaximal, Sylow
397C22×C61—24no—
398C22×C61—24no—
399C22×C61—24no—
400C22×C61—48no—
401C22×C61C2×H(5,𝔽2)12yes—
402C22×C61C2×2−1+412yes—
403C22×C61C2×2−1+412yes—
404C22×C61C2611yescharacteristic
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—28no—
408C2×D61—24no—
409C2×D61—24no—
410C2×D61—24no—
411C2×D61—48no—
412C2×D61C2×H(5,𝔽2)14yes—
413C4×C61—22no—
414C4×C61—24no—
415C4×C61—28no—
416C4×C61—24no—
417C4×C61—24no—
418C4×C61C2×2−1+414yes—
419C4×C61C2×2−1+414yes—
420Dic61—22no—
421Dic61—28no—
422Dic61—24no—
423Dic61—24no—
424Dic61—22no—
425Dic61—22no—
426Dic61—24no—
427#3544—6132no—
428C2×#563—614no—
429C2×Q82—611no—
430C2×#555—611no—
431C2×#554—611no—
432C2×#554D6111yescharacteristic, complemented
433C2×#552—612no—
434C2×#552—612no—
435C2×#547—612no—
436C2×#547—612no—
437C2×#544—612no—
438C2×#544—612no—
439C2×#542—612no—
440C2×#542—612no—
441C2×#536—614no—
442C22×C4⋊Q8—611no—
443C2×#529—611no—
444C2×#529—611no—
445C2×C61—44no—
446C2×C61#354414yescomplemented
447C2×C61C22×H(5,𝔽2)11yescharacteristic
448C2×C61C22×2−1+411yescharacteristic
449C2×C61C22×2−1+411yescharacteristic
450D61—24no—
451D61—44no—
452C22×#41—614no—
453C23×Q8—612no—
454#563—6164no—
455Q82—6116no—
456#555—6116no—
457#554—6116no—
458#554C2×D61116yescomplemented
459#552—6132no—
460#552—6132no—
461#547—6132no—
462#547—6132no—
463#544—6132no—
464#544—6132no—
465#542—6132no—
466#542—6132no—
467#536—6164no—
468C2×C4⋊Q8—612no—
469C2×C4⋊Q8—6116no—
470C2×C4⋊Q8—612no—
471C2×C4⋊Q8—612no—
472C2×C4⋊Q8—614no—
473C2×C4⋊Q8—614no—
474C2×C4⋊Q8—612no—
475C2×C4⋊Q8—611no—
476C2×C4⋊Q8—612no—
477C2×C4⋊Q8C2×D6111yescharacteristic
478#529—6116no—
479#529—6116no—
480C2×#126—612no—
481C2×#126—614no—
482C2×#126—612no—
483C2×#126—614no—
484C2×#125—614no—
485C2×#125—611no—
486C2×#125—611no—
487C2×#125—612no—
488C2×#125—614no—
489C2×#125C2×D6112yes—
490C2×#124—611no—
491C2×#124—611no—
492C2×#124—614no—
493C2×#124—614no—
494C2×#123—614no—
495C2×#123—612no—
496C2×#123—614no—
497C2×#123—612no—
498C2×#123—614no—
499C2×#123—614no—
500C2×C22⋊Q8—611no—
501C2×C22⋊Q8—614no—
502C2×C22⋊Q8—614no—
503C2×C22⋊Q8—614no—
504C2×C22⋊Q8—614no—
505C2×C22⋊Q8—611no—
506C2×C22⋊Q8—614no—
507C2×C22⋊Q8—612no—
508C2×C22⋊Q8C2×D6114yes—
509C2×C22⋊Q8C2×D6112yes—
510C2×#121—611no—
511C2×#121—612no—
512C2×#121—612no—
513C2×#121—611no—
514C2×C4×Q8—612no—
515C2×C4×Q8—611no—
516C2×C4×Q8—612no—
517C2×C4×Q8C2×D6111yescharacteristic
518C2×C4×D4—612no—
519C2×C4×D4—612no—
520C2×C4×D4—612no—
521C2×C4×D4—611no—
522C2×C4×D4C2×D6111yescharacteristic
523C2×C4×D4C2×D6112yes—
524C2×#117—612no—
525C2×#117—612no—
526C2×#117—614no—
527C2×#117—612no—
528C2×#117—612no—
529C22×C4⋊C4—612no—
530C22×C4⋊C4—612no—
531C22×C4⋊C4—612no—
532C22×C4⋊C4C2×D6112yes—
533C22×C42—611no—
534C61C2×#354411yescharacteristic, complemented, Sylow
535C2×#41—6132no—
536C2×#41—24416no—
537C22×Q8—6116no—
538C22×Q8—611no—
539C22×Q8—614no—
540C22×Q8—614no—
541C22×Q8—612no—
542C22×Q8—2448no—
543C22×Q8C22×D6111yescharacteristic
544C22×Q8C22×D6112yes—
545C22×D4—612no—
546C22×D4—614no—
547C22×D4—611no—
548C22×D4—612no—
549C22×D4C22×D6111yescharacteristic
550C23×C4—614no—
551C23×C4—611no—
552C23×C4—611no—
553C23×C4—612no—
554C23×C4—611no—
555C23×C4—614no—
556C23×C4C22×D6112yes—
557C23×C4C22×D6114yes—
558C4⋊Q8—6116no—
559C4⋊Q8—6116no—
560C4⋊Q8—6116no—
561C4⋊Q8—6132no—
562C4⋊Q8—6132no—
563C4⋊Q8—6116no—
564C4⋊Q8—618no—
565C4⋊Q8—6116no—
566C4⋊Q8C22×D6118yes—
567#126—6116no—
568#126—6132no—
569#126—6116no—
570#126—6132no—
571#125—618no—
572#125—618no—
573#125—6116no—
574#125—6132no—
575#125—6132no—
576#125C22×D61116yes—
577#124—618no—
578#124—618no—
579#124—6132no—
580#124—6132no—
581#123—6132no—
582#123—6116no—
583#123—6132no—
584#123—6116no—
585#123—6132no—
586#123—6132no—
587C22⋊Q8—618no—
588C22⋊Q8—6132no—
589C22⋊Q8—6132no—
590C22⋊Q8—6132no—
591C22⋊Q8—618no—
592C22⋊Q8—6132no—
593C22⋊Q8—6116no—
594C22⋊Q8—6132no—
595C22⋊Q8C22×D61132yes—
596C22⋊Q8C22×D61116yes—
597#121—618no—
598#121—6116no—
599#121—6116no—
600#121—618no—
601C4×Q8—6116no—
602C4×Q8—618no—
603C4×Q8—6116no—
604C4×Q8C22×D6118yes—
605C4×D4—6116no—
606C4×D4—6116no—
607C4×D4—6116no—
608C4×D4—618no—
609C4×D4C22×D6118yes—
610C4×D4C22×D61116yes—
611#117—6116no—
612#117—6116no—
613#117—6132no—
614#117—6116no—
615#117—6116no—
616C2×C4⋊C4—611no—
617C2×C4⋊C4—612no—
618C2×C4⋊C4—612no—
619C2×C4⋊C4—614no—
620C2×C4⋊C4—614no—
621C2×C4⋊C4—614no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—614no—
624C2×C4⋊C4—612no—
625C2×C4⋊C4—612no—
626C2×C4⋊C4—612no—
627C2×C4⋊C4—612no—
628C2×C4⋊C4—612no—
629C2×C4⋊C4—612no—
630C2×C4⋊C4—612no—
631C2×C4⋊C4—614no—
632C2×C4⋊C4—614no—
633C2×C4⋊C4—6116no—
634C2×C4⋊C4—6116no—
635C2×C4⋊C4—6116no—
636C2×C4⋊C4C22×D6112yes—
637C2×C4⋊C4C22×D6112yes—
638C2×C4⋊C4C22×D6111yescharacteristic
639C2×C4⋊C4C22×D6114yes—
640C2×C4⋊C4C22×D61116yes—
641C2×C4⋊C4C22×D6111yescharacteristic
642C2×C4⋊C4C22×D6114yes—
643C2×C4⋊C4C22×D6112yes—
644C2×C22⋊C4—612no—
645C2×C22⋊C4—614no—
646C2×C22⋊C4—612no—
647C2×C22⋊C4—612no—
648C2×C22⋊C4—612no—
649C2×C22⋊C4—612no—
650C2×C22⋊C4—612no—
651C2×C22⋊C4—614no—
652C2×C22⋊C4—612no—
653C2×C22⋊C4—614no—
654C2×C22⋊C4—612no—
655C2×C22⋊C4—612no—
656C2×C22⋊C4C22×D6114yes—
657C2×C22⋊C4C22×D6112yes—
658C2×C42—614no—
659C2×C42—611no—
660C2×C42—611no—
661C2×C42—612no—
662C2×C42—614no—
663C2×C42—611no—
664C2×C42—618no—
665C2×C42C22×D6112yes—
666C2×C42C22×D6111yescharacteristic
667C24—611no—
668C24—612no—
669C24C23×D6112yes—
670#41—24464no—
671C2×Q8—24no—
672C2×Q8—44no—
673C2×Q8—614no—
674C2×Q8—6116no—
675C2×Q8—6116no—
676C2×Q8—618no—
677C2×Q8—1224no—
678C2×Q8—2448no—
679C2×Q8—2444no—
680C2×Q8—2448no—
681C2×Q8—24432no—
682C2×Q8C23×D6114yes—
683C2×Q8C23×D6118yes—
684C2×D4—24no—
685C2×D4—618no—
686C2×D4—6116no—
687C2×D4—614no—
688C2×D4—618no—
689C2×D4—1228no—
690C2×D4—1228no—
691C2×D4—1224no—
692C2×D4—2448no—
693C2×D4C23×D6114yes—
694C22×C4—28no—
695C22×C4—48no—
696C22×C4—612no—
697C22×C4—611no—
698C22×C4—612no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—614no—
702C22×C4—612no—
703C22×C4—614no—
704C22×C4—614no—
705C22×C4—614no—
706C22×C4—6116no—
707C22×C4—618no—
708C22×C4—6116no—
709C22×C4—1224no—
710C22×C4—12216no—
711C22×C4—1224no—
712C22×C4—1224no—
713C22×C4—1228no—
714C22×C4—2448no—
715C22×C4C23×D6118yes—
716C22×C4C23×D6112yes—
717C22×C4C23×D6112yes—
718C22×C4C23×D6111yescharacteristic
719C22×C4C23×D6112yes—
720C22×C4C23×D6114yes—
721C22×C4C23×D61116yes—
722C22×C4C23×D6111yescharacteristic
723C22×C4C23×D6111yescharacteristic
724C4⋊C4—614no—
725C4⋊C4—6116no—
726C4⋊C4—6116no—
727C4⋊C4—6116no—
728C4⋊C4—618no—
729C4⋊C4—618no—
730C4⋊C4—618no—
731C4⋊C4—618no—
732C4⋊C4—618no—
733C4⋊C4—618no—
734C4⋊C4—6116no—
735C4⋊C4—614no—
736C4⋊C4—6116no—
737C4⋊C4—618no—
738C4⋊C4—618no—
739C4⋊C4—618no—
740C4⋊C4—6116no—
741C4⋊C4C23×D6118yes—
742C4⋊C4C23×D6118yes—
743C4⋊C4C23×D6114yes—
744C4⋊C4C23×D61116yes—
745C4⋊C4C23×D6114yes—
746C4⋊C4C23×D61116yes—
747C4⋊C4C23×D6118yes—
748C22⋊C4—618no—
749C22⋊C4—6116no—
750C22⋊C4—618no—
751C22⋊C4—618no—
752C22⋊C4—618no—
753C22⋊C4—618no—
754C22⋊C4—618no—
755C22⋊C4—6116no—
756C22⋊C4—618no—
757C22⋊C4—6116no—
758C22⋊C4—618no—
759C22⋊C4—618no—
760C22⋊C4C23×D61116yes—
761C22⋊C4C23×D6118yes—
762C42—614no—
763C42—614no—
764C42—614no—
765C42—6116no—
766C42—618no—
767C42—6116no—
768C42C23×D6114yes—
769C42C23×D6118yes—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—614no—
774C23—612no—
775C23—614no—
776C23—1222no—
777C23—1222no—
778C23—1224no—
779C23—1224no—
780C23—1224no—
781C23C24×D6114yes—
782C23C24×D6111yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—1228no—
786Q8—24416no—
787Q8—2448no—
788Q8—24416no—
789D4—28no—
790D4—12216no—
791D4—12216no—
792D4—1228no—
793D4—24416no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—216no—
800C2×C4—416no—
801C2×C4—614no—
802C2×C4—612no—
803C2×C4—612no—
804C2×C4—614no—
805C2×C4—612no—
806C2×C4—618no—
807C2×C4—614no—
808C2×C4—1228no—
809C2×C4—12232no—
810C2×C4—1228no—
811C2×C4—1222no—
812C2×C4—1224no—
813C2×C4—1222no—
814C2×C4—1224no—
815C2×C4—1222no—
816C2×C4—1224no—
817C2×C4—1228no—
818C2×C4—1228no—
819C2×C4—12216no—
820C2×C4—24416no—
821C2×C4#1451982414yes—
822C2×C4#1451982514yes—
823C2×C4C24×D6114yes—
824C2×C4C24×D6114yes—
825C2×C4C24×D6112yes—
826C2×C4C24×D6114yes—
827C2×C4C24×D6118yes—
828C2×C4C24×D6112yes—
829C2×C4C24×D6112yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—614no—
835C22—1222no—
836C22—1222no—
837C22—1228no—
838C22—1224no—
839C22—1224no—
840C22—1224no—
841C22—2448no—
842C22H(5,𝔽2)×D6112yes—
843C22C2×#1451982412yes—
844C22C2×#1451982512yes—
845C22C25×D6111yescharacteristic
846C4—24no—
847C4—28no—
848C4—22no—
849C4—24no—
850C4—24no—
851C4—1228no—
852C4—1222no—
853C4—1224no—
854C4—1222no—
855C4—1222no—
856C4—1224no—
857C4—1224no—
858C4C2×#1451982414yes—
859C4C2×#1451982514yes—
860C2—44no—
861C2—1224no—
862C2—2444no—
863C2#2146016014yesdirect product factor
864C2C2×H(5,𝔽2)×D6111yescharacteristic
865C2C22×#1451982411yescharacteristic
866C2C22×#1451982511yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#554C2
socleC23×C61C25
hypercenterC2×#554D61
hypocenterC61C2×#3544
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #21460160C2direct (N × H)
2. C2×#16840513C2semidirect
3. C2×Q8×Dic122C2semidirect
4. C2×#16840477C2semidirect
5. C2×#16840473C2semidirect
6. C2×#16840450C2semidirect
7. C2×#16840446C2semidirect
8. C2×#16840417C2semidirect
9. C2×#16840413C2semidirect
10. C2×#16840393C2semidirect
11. C2×#16840392C2semidirect
12. C2×#16840385C2semidirect
13. C2×#16840377C2semidirect
14. C2×#16840335C2semidirect
15. C2×C4⋊Q8×D61C2semidirect
16. C2×#16840299C2semidirect
17. C2×#16840294C2semidirect
18. C2×C61×#554C2semidirect
21. #16840513C22semidirect
22. Q8×Dic122C22semidirect
23. #16840477C22semidirect
24. #16840473C22semidirect
25. #16840450C22semidirect
26. #16840446C22semidirect
27. #16840417C22semidirect
28. #16840413C22semidirect
29. #16840393C22semidirect
30. #16840392C22semidirect
31. #16840385C22semidirect
32. #16840377C22semidirect
33. #16840335C22semidirect
42. C4⋊Q8×D61C22semidirect
43. #16840299C22semidirect
44. #16840294C22semidirect
92. C61×#554C22semidirect
432. C2×#554D61semidirect
446. C2×C61#3544semidirect
458. #554C2×D61semidirect
534. C61C2×#3544semidirect
863. C2#21460160direct (N × H)

Maximal subgroups

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

subgroupindex
#214601602
C2×#168405132
C2×Q8×Dic1222
C2×#168404772
C2×#168404732
C2×#168404502
C2×#168404462
C2×#168404172
C2×#168404132
C2×#168403932
C2×#168403922
C2×#168403852
C2×#168403772
C2×#168403352
C2×C4⋊Q8×D612
C2×#168402992
C2×#168402942
C2×C61×#5542
C2×#354461