Finite Group Databasebeta

← C2×#21460261 #30587619

Subgroups — C2×#21460261 #30587619

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#21460261C2132yesmaximal, direct product factor
2C2×#16840513C214yesmaximal, complemented
3C2×#16840490C211yesmaximal, characteristic, complemented
4C2×#16840486C211yesmaximal, characteristic, complemented
5C2×#16840473C212yesmaximal, complemented
6C2×#16840462C212yesmaximal, complemented
7C2×Q8×C22⋊D61C212yesmaximal, complemented
8C2×#16840422C212yesmaximal, complemented
9C2×#16840417C211yesmaximal, characteristic, complemented
10C2×#16840389C212yesmaximal, complemented
11C2×#16840377C212yesmaximal, complemented
12C2×#16840372C212yesmaximal, complemented
13C2×#16840358C214yesmaximal, complemented
14C2×#16840336C212yesmaximal, complemented
15C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
16C2×#16840299C211yesmaximal, characteristic, complemented
17C2×#16840294C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C61C211yesmaximal, characteristic, complemented
19C22×#11758222C2212yes—
20C22×Q8×D61C2212yes—
21#16840513C22164yescomplemented
22#16840490C22116yescomplemented
23#16840486C22116yescomplemented
24#16840473C22132yescomplemented
25#16840462C22132yescomplemented
26Q8×C22⋊D61C22132yescomplemented
27#16840422C22132yescomplemented
28#16840417C22116yescomplemented
29#16840389C22132yescomplemented
30#16840377C22132yescomplemented
31#16840372C22132yescomplemented
32#16840358C22164yescomplemented
33#16840336C22132yescomplemented
34C2×#14519777C2211yescharacteristic
35C2×#14519776C2212yes—
36C2×#14519776C2212yes—
37C2×#14519775C2214yes—
38C2×#14519775C2212yes—
39C2×#14519775C2212yes—
40C4⋊Q8×D61C22116yescomplemented
41#16840299C22116yescomplemented
42#16840294C22116yescomplemented
43C2×#14519772C2212yes—
44C2×#14519772C2214yes—
45C2×#14519770C2212yes—
46C2×#14519770C2214yes—
47C2×#14519770C2214yes—
48C2×#14519769C2212yes—
49C2×#14519768C2211yescharacteristic
50C2×#14519768C2211yescharacteristic
51C2×#14519768C2214yes—
52C2×#14519767C2214yes—
53C2×#14519767C2214yes—
54C2×#14519766C2212yes—
55C2×#14519766C2211yescharacteristic
56C2×#14519764C2211yescharacteristic
57C2×#14519763C2214yes—
58C2×#14519762C2212yes—
59C2×#14519760C2214yes—
60C2×#14519760C2214yes—
61C2×#14519759C2214yes—
62C2×#14519759C2212yes—
63C2×#14519757C2211yescharacteristic
64C2×#14519757C2212yes—
65C2×#14519756C2212yes—
66C2×#14519756C2214yes—
67C2×#14519755C2214yes—
68C2×#14519753C2214yes—
69C2×#14519753C2211yescharacteristic
70C2×#14519753C2214yes—
71C2×#14519753C2214yes—
72C2×#14519752C2211yescharacteristic
73C2×#14519750C2214yes—
74C2×#14519748C2212yes—
75C2×#14519748C2211yescharacteristic
76C2×Q8×Dic61C2212yes—
77C2×C4×Dic122C2211yescharacteristic
78C2×C4×Dic122C2212yes—
79C2×#14519742C2212yes—
80C2×C4×D244C2211yescharacteristic
81C2×C4×D244C2212yes—
82C2×#14519739C2214yes—
83C2×C4×C22⋊D61C2212yes—
84C2×C4×C22⋊D61C2214yes—
85C2×#14519736C2212yes—
86C2×#14519735C2212yes—
87C2×#14519734C2212yes—
88C2×C4⋊C4×D61C2212yes—
89C2×C4⋊C4×D61C2212yes—
90C2×C4⋊C4×D61C2212yes—
91C2×C42×D61C2211yescharacteristic
92C23×Q8×C61C2212yes—
93D4×Q8×C61C22116yescomplemented
94C2×C4⋊Q8×C61C2212yes—
95C2×C4⋊Q8×C61C2211yescharacteristic
96C2×C22⋊Q8×C61C2212yes—
97C2×C22⋊Q8×C61C2214yes—
98C2×C4×Q8×C61C2211yescharacteristic
99C2×C4×D4×C61C2211yescharacteristic
100C2×C4×D4×C61C2212yes—
101C2×#11758222—48no—
102C2×#11758222C23116yes—
103C22×Dic122C2312yes—
104C22×Dic122C2311yescharacteristic
105C22×Dic122C2314yes—
106C2×Q8×D61—48no—
107C2×Q8×D61C23116yes—
108C22×D244C2312yes—
109C22×D244C2311yescharacteristic
110C22×C22⋊D61C2312yes—
111C22×C22⋊D61C2314yes—
112C22×C4×D61C2311yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2312yes—
116C22×C4×D61C2314yes—
117C22×C4×D61C2314yes—
118#14519777C2318yes—
119#14519776C23116yes—
120#14519776C23116yes—
121#14519775C23116yes—
122#14519775C23132yes—
123#14519775C23116yes—
124#14519772C23132yes—
125#14519772C23116yes—
126#14519770C23132yes—
127#14519770C23116yes—
128#14519770C23132yes—
129#14519769C23116yes—
130#14519768C23132yes—
131#14519768C2318yes—
132#14519768C2318yes—
133#14519767C23132yes—
134#14519767C23132yes—
135#14519766C23116yes—
136#14519766C2318yes—
137#14519764C2318yes—
138#14519763C23132yes—
139#14519762C23116yes—
140#14519760C23132yes—
141#14519760C23132yes—
142#14519759C23132yes—
143#14519759C23116yes—
144#14519757C2318yes—
145#14519757C23116yes—
146#14519756C23132yes—
147#14519756C23116yes—
148#14519755C23132yes—
149#14519753C23132yes—
150#14519753C23132yes—
151#14519753C2318yes—
152#14519753C23132yes—
153#14519752C2318yes—
154#14519750C23132yes—
155#14519748C2318yes—
156#14519748C23116yes—
157Q8×Dic61C23116yes—
158C4×Dic122C23116yes—
159C4×Dic122C2318yes—
160#14519742C23116yes—
161C4×D244C23116yes—
162C4×D244C2318yes—
163#14519739C23132yes—
164C4×C22⋊D61C23132yes—
165C4×C22⋊D61C23116yes—
166#14519736C23116yes—
167#14519735C23116yes—
168#14519734C23116yes—
169C2×C4⋊Dic61C2312yes—
170C2×C4⋊Dic61C2312yes—
171C2×C4⋊Dic61C2311yescharacteristic
172C2×C4⋊Dic61C2312yes—
173C2×C4⋊Dic61C2312yes—
174C2×C4⋊Dic61C2311yescharacteristic
175C2×C4⋊Dic61C2312yes—
176C2×C4⋊Dic61C2314yes—
177C2×#11758196C2314yes—
178C2×#11758196C2314yes—
179C2×#11758196C2314yes—
180C2×#11758196C2312yes—
181C2×#11758196C2312yes—
182C2×#11758196C2314yes—
183C2×#11758196C2312yes—
184C2×#11758196C2314yes—
185C2×#11758196C2314yes—
186C2×#11758196C2312yes—
187C4⋊C4×D61C23116yes—
188C4⋊C4×D61C23116yes—
189C4⋊C4×D61C23116yes—
190C2×C22⋊Dic61C2312yes—
191C2×C22⋊Dic61C2312yes—
192C2×C22⋊Dic61C2314yes—
193C2×C22⋊Dic61C2312yes—
194C2×#11758198C2312yes—
195C2×#11758198C2312yes—
196C2×#11758198C2314yes—
197C2×#11758198C2312yes—
198C2×#11758198C2312yes—
199C2×#11758198C2314yes—
200C2×#11758198C2312yes—
201C2×#11758198C2312yes—
202C2×C4×Dic61C2311yescharacteristic
203C2×C4×Dic61C2311yescharacteristic
204C2×C4×Dic61C2311yescharacteristic
205C2×C4×Dic61C2314yes—
206C2×C4×Dic61C2312yes—
207C2×C4×Dic61C2314yes—
208C42×D61C2318yes—
209C22×Q8×C61—48no—
210C22×Q8×C61C2312yes—
211C22×Q8×C61C2311yescharacteristic
212C22×Q8×C61C2314yes—
213C22×Q8×C61C23116yes—
214C22×D4×C61C2311yescharacteristic
215C23×C4×C61C2312yes—
216C23×C4×C61C2314yes—
217C4⋊Q8×C61C23116yes—
218C4⋊Q8×C61C2318yes—
219C22⋊Q8×C61C23132yes—
220C22⋊Q8×C61C23116yes—
221C4×Q8×C61C2318yes—
222C4×D4×C61C23116yes—
223C4×D4×C61C2318yes—
224C2×C4⋊C4×C61C2311yescharacteristic
225C2×C4⋊C4×C61C2312yes—
226C2×C4⋊C4×C61C2312yes—
227C2×C4⋊C4×C61C2314yes—
228C2×C4⋊C4×C61C2311yescharacteristic
229C2×C4⋊C4×C61C2312yes—
230C2×C22⋊C4×C61C2314yes—
231C2×C22⋊C4×C61C2312yes—
232C2×C42×C61C2311yescharacteristic
233C2×C42×C61C2312yes—
234C24×C61C2412yes—
235C23×D61C2412yes—
236C23×D61C2411yescharacteristic
237C2×Q8×C61—28no—
238C2×Q8×C61—24no—
239C2×Q8×C61—48no—
240C2×Q8×C61—432no—
241C2×Q8×C61C2418yes—
242C2×Q8×C61C2414yes—
243C2×Q8×C61C24116yes—
244C2×D4×C61—24no—
245C2×D4×C61C2414yes—
246C22×C4×C61—28no—
247C22×C4×C61—48no—
248C22×C4×C61C2412yes—
249C22×C4×C61C2414yes—
250C22×C4×C61C2411yescharacteristic
251C22×C4×C61C2412yes—
252C22×C4×C61C2418yes—
253C22×C4×C61C2412yes—
254C22×C4×C61C24116yes—
255C22×C4×C61C2411yescharacteristic
256C22×C4×C61C2411yescharacteristic
257C2×C22⋊D61—28no—
258C2×C22⋊D61—48no—
259C2×C22⋊D61C2418yes—
260C2×C22⋊D61C24116yes—
261C22×Dic61C2414yes—
262C22×Dic61C2411yescharacteristic
263C22×Dic61C2411yescharacteristic
264C22×Dic61C2411yescharacteristic
265C22×Dic61C2412yes—
266C22×Dic61C2412yes—
267C22×Dic61C2412yes—
268Q8×D61—432no—
269#11758222—432no—
270C2×D244—28no—
271C2×D244—24no—
272C2×D244C2414yes—
273C2×D244C2418yes—
274C2×C4×D61—24no—
275C2×C4×D61—24no—
276C2×C4×D61—24no—
277C2×C4×D61—28no—
278C2×C4×D61—48no—
279C2×C4×D61—48no—
280C2×C4×D61C2414yes—
281C2×C4×D61C2414yes—
282C2×C4×D61C2414yes—
283C2×C4×D61C2418yes—
284C2×C4×D61C24116yes—
285C2×C4×D61C24116yes—
286C2×Dic122—28no—
287C2×Dic122—24no—
288C2×Dic122—48no—
289C2×Dic122C2418yes—
290C2×Dic122C2414yes—
291C2×Dic122C24116yes—
292C4⋊C4×C61C2414yes—
293C4⋊C4×C61C2418yes—
294C4⋊C4×C61C2414yes—
295C4⋊C4×C61C2418yes—
296C4⋊C4×C61C2418yes—
297C4⋊C4×C61C24116yes—
298C22⋊C4×C61C24116yes—
299C22⋊C4×C61C2418yes—
300C42×C61C2414yes—
301C42×C61C2418yes—
302C22⋊Dic61C2418yes—
303C22⋊Dic61C2418yes—
304C22⋊Dic61C24116yes—
305C22⋊Dic61C2418yes—
306#11758198C2418yes—
307#11758198C2418yes—
308#11758198C24116yes—
309#11758198C2418yes—
310#11758198C2418yes—
311#11758198C24116yes—
312#11758198C2418yes—
313#11758198C2418yes—
314C4⋊Dic61C2418yes—
315C4⋊Dic61C2418yes—
316C4⋊Dic61C2414yes—
317C4⋊Dic61C2418yes—
318C4⋊Dic61C2418yes—
319C4⋊Dic61C2414yes—
320C4⋊Dic61C2418yes—
321C4⋊Dic61C24116yes—
322#11758196C24116yes—
323#11758196C24116yes—
324#11758196C24116yes—
325#11758196C2418yes—
326#11758196C2418yes—
327#11758196C24116yes—
328#11758196C2418yes—
329#11758196C24116yes—
330#11758196C24116yes—
331#11758196C2418yes—
332C4×Dic61C2414yes—
333C4×Dic61C2414yes—
334C4×Dic61C2414yes—
335C4×Dic61C24116yes—
336C4×Dic61C2418yes—
337C4×Dic61C24116yes—
338C23×C61—24no—
339C23×C61—24no—
340C23×C61—24no—
341C23×C61C2514yes—
342C23×C61C2511yescharacteristic
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—24no—
346C22×D61—24no—
347C22×D61—24no—
348C22×D612−1+414yes—
349C22×D61C2514yes—
350C22×D61C2512yes—
351Q8×C61—216no—
352Q8×C61—28no—
353Q8×C61—416no—
354D4×C61—28no—
355C2×C4×C61—28no—
356C2×C4×C61—24no—
357C2×C4×C61—24no—
358C2×C4×C61—22no—
359C2×C4×C61—24no—
360C2×C4×C61—216no—
361C2×C4×C61—416no—
362C2×C4×C61H(5,𝔽2)14yes—
363C2×C4×C612−1+414yes—
364C2×C4×C61C2514yes—
365C2×C4×C61C2512yes—
366C2×C4×C61C2518yes—
367C2×C4×C61C2514yes—
368C2×C4×C61C2514yes—
369C2×C4×C61C2512yes—
370C2×C4×C61C2512yes—
371C22⋊D61—216no—
372C22⋊D61—416no—
373C2×Dic61—28no—
374C2×Dic61—22no—
375C2×Dic61—24no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—24no—
379C2×Dic61—24no—
380C2×Dic61C2514yes—
381C2×Dic61C2514yes—
382C2×Dic61C2512yes—
383C2×Dic61C2512yes—
384C2×Dic61C2514yes—
385C2×Dic61C2512yes—
386C2×Dic61C2518yes—
387D244—216no—
388D244—28no—
389C4×D61—28no—
390C4×D61—28no—
391C4×D61—28no—
392C4×D61—216no—
393C4×D61—416no—
394C4×D61—416no—
395Dic122—216no—
396Dic122—28no—
397Dic122—416no—
398C2×#3552—611nomaximal, Sylow
399C22×C61—24no—
400C22×C61—24no—
401C22×C61—24no—
402C22×C61—48no—
403C22×C61C2×H(5,𝔽2)12yes—
404C22×C61C2×2−1+412yes—
405C22×C61C2×2−1+412yes—
406C22×C61C2611yescharacteristic
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—28no—
410C2×D61—24no—
411C2×D61—24no—
412C2×D61—24no—
413C2×D61—48no—
414C2×D61C2×2−1+414yes—
415C4×C61—28no—
416C4×C61—24no—
417C4×C61—24no—
418C4×C61—22no—
419C4×C61—24no—
420C4×C61C2×H(5,𝔽2)14yes—
421C4×C61C2×2−1+414yes—
422Dic61—28no—
423Dic61—22no—
424Dic61—24no—
425Dic61—22no—
426Dic61—22no—
427Dic61—24no—
428Dic61—24no—
429#3552—6132no—
430C2×#563—614no—
431C2×#557—611no—
432C2×#556—611no—
433C2×#554—612no—
434C2×#553—612no—
435C2×D4×Q8—612no—
436C2×D4×Q8D6111yescharacteristic, complemented
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—44no—
448C2×C61#355214yescomplemented
449C2×C61C22×H(5,𝔽2)11yescharacteristic
450C2×C61C22×2−1+411yescharacteristic
451C2×C61C22×2−1+411yescharacteristic
452D61—24no—
453D61—44no—
454C22×#41—612no—
455C23×Q8—612no—
456C23×Q8C2×D6112yes—
457#563—6164no—
458#557—6116no—
459#556—6116no—
460#554—6132no—
461#553—6132no—
462D4×Q8—6132no—
463D4×Q8C2×D61116yescomplemented
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—612no—
473C2×C4⋊Q8—614no—
474C2×C4⋊Q8—6116no—
475C2×C4⋊Q8—612no—
476C2×C4⋊Q8—612no—
477C2×C4⋊Q8—611no—
478C2×C4⋊Q8C2×D6111yescharacteristic
479C2×C4⋊Q8C2×D6112yes—
480#529—6116no—
481#529—6116no—
482C2×#126—612no—
483C2×#126—614no—
484C2×#126—612no—
485C2×#126—614no—
486C2×#126—614no—
487C2×#125—614no—
488C2×#125—614no—
489C2×#125—611no—
490C2×#125—611no—
491C2×#125—614no—
492C2×#125—612no—
493C2×#124—611no—
494C2×#124—612no—
495C2×#124—611no—
496C2×#124—614no—
497C2×#123—614no—
498C2×#123—614no—
499C2×#123—612no—
500C2×#123—612no—
501C2×#123—614no—
502C2×C22⋊Q8—611no—
503C2×C22⋊Q8—614no—
504C2×C22⋊Q8—614no—
505C2×C22⋊Q8—614no—
506C2×C22⋊Q8—612no—
507C2×C22⋊Q8—614no—
508C2×C22⋊Q8—614no—
509C2×C22⋊Q8—611no—
510C2×C22⋊Q8—612no—
511C2×C22⋊Q8C2×D6114yes—
512C2×C22⋊Q8C2×D6112yes—
513C2×#121—611no—
514C2×#121—612no—
515C2×#121—611no—
516C2×#121—614no—
517C2×C4×Q8—612no—
518C2×C4×Q8—612no—
519C2×C4×Q8—611no—
520C2×C4×Q8—612no—
521C2×C4×Q8C2×D6111yescharacteristic
522C2×C4×D4—612no—
523C2×C4×D4—614no—
524C2×C4×D4—614no—
525C2×C4×D4—611no—
526C2×C4×D4—612no—
527C2×C4×D4C2×D6111yescharacteristic
528C2×C4×D4C2×D6112yes—
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—48no—
540C22×Q8—6116no—
541C22×Q8—611no—
542C22×Q8—612no—
543C22×Q8—614no—
544C22×Q8—2448no—
545C22×Q8C22×D6112yes—
546C22×Q8C22×D6111yescharacteristic
547C22×Q8C22×D6114yes—
548C22×Q8C22×D61116yes—
549C22×D4—612no—
550C22×D4—614no—
551C22×D4—612no—
552C22×D4—611no—
553C22×D4C22×D6111yescharacteristic
554C23×C4—611no—
555C23×C4—611no—
556C23×C4—612no—
557C23×C4—611no—
558C23×C4—614no—
559C23×C4—614no—
560C23×C4C22×D6112yes—
561C23×C4C22×D6114yes—
562C4⋊Q8—6116no—
563C4⋊Q8—6116no—
564C4⋊Q8—6132no—
565C4⋊Q8—6116no—
566C4⋊Q8—6116no—
567C4⋊Q8—618no—
568C4⋊Q8C22×D6118yes—
569C4⋊Q8C22×D61116yes—
570#126—6116no—
571#126—6132no—
572#126—6116no—
573#126—6132no—
574#126—6132no—
575#125—618no—
576#125—618no—
577#125—6132no—
578#125—6132no—
579#125—6132no—
580#125—6116no—
581#124—618no—
582#124—6116no—
583#124—618no—
584#124—6132no—
585#123—6132no—
586#123—6132no—
587#123—6116no—
588#123—6116no—
589#123—6132no—
590C22⋊Q8—618no—
591C22⋊Q8—6132no—
592C22⋊Q8—6132no—
593C22⋊Q8—6132no—
594C22⋊Q8—6116no—
595C22⋊Q8—6132no—
596C22⋊Q8—618no—
597C22⋊Q8—6116no—
598C22⋊Q8—6132no—
599C22⋊Q8C22×D61132yes—
600C22⋊Q8C22×D61116yes—
601#121—618no—
602#121—6116no—
603#121—618no—
604#121—6132no—
605C4×Q8—6116no—
606C4×Q8—6116no—
607C4×Q8—618no—
608C4×Q8—6116no—
609C4×Q8C22×D6118yes—
610C4×D4—6116no—
611C4×D4—6132no—
612C4×D4—6132no—
613C4×D4—618no—
614C4×D4—6116no—
615C4×D4C22×D6118yes—
616C4×D4C22×D61116yes—
617#117—6116no—
618#117—6116no—
619#117—6116no—
620C2×C4⋊C4—612no—
621C2×C4⋊C4—614no—
622C2×C4⋊C4—614no—
623C2×C4⋊C4—614no—
624C2×C4⋊C4—612no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—612no—
627C2×C4⋊C4—612no—
628C2×C4⋊C4—612no—
629C2×C4⋊C4—612no—
630C2×C4⋊C4—611no—
631C2×C4⋊C4—612no—
632C2×C4⋊C4—614no—
633C2×C4⋊C4—612no—
634C2×C4⋊C4—614no—
635C2×C4⋊C4—614no—
636C2×C4⋊C4—614no—
637C2×C4⋊C4—612no—
638C2×C4⋊C4—6116no—
639C2×C4⋊C4—6116no—
640C2×C4⋊C4—6116no—
641C2×C4⋊C4C22×D6111yescharacteristic
642C2×C4⋊C4C22×D6112yes—
643C2×C4⋊C4C22×D6112yes—
644C2×C4⋊C4C22×D6114yes—
645C2×C4⋊C4C22×D6111yescharacteristic
646C2×C4⋊C4C22×D6112yes—
647C2×C22⋊C4—612no—
648C2×C22⋊C4—612no—
649C2×C22⋊C4—614no—
650C2×C22⋊C4—612no—
651C2×C22⋊C4—614no—
652C2×C22⋊C4—612no—
653C2×C22⋊C4—612no—
654C2×C22⋊C4—612no—
655C2×C22⋊C4—612no—
656C2×C22⋊C4—612no—
657C2×C22⋊C4—614no—
658C2×C22⋊C4—612no—
659C2×C22⋊C4C22×D6114yes—
660C2×C22⋊C4C22×D6112yes—
661C2×C42—611no—
662C2×C42—611no—
663C2×C42—612no—
664C2×C42—614no—
665C2×C42—614no—
666C2×C42—611no—
667C2×C42—618no—
668C2×C42C22×D6112yes—
669C2×C42C22×D6111yescharacteristic
670C24—611no—
671C24—612no—
672C24C23×D6112yes—
673#41—24432no—
674C2×Q8—24no—
675C2×Q8—28no—
676C2×Q8—48no—
677C2×Q8—432no—
678C2×Q8—614no—
679C2×Q8—618no—
680C2×Q8—6116no—
681C2×Q8—1228no—
682C2×Q8—1224no—
683C2×Q8—2448no—
684C2×Q8—24432no—
685C2×Q8C23×D6118yes—
686C2×Q8C23×D6114yes—
687C2×Q8C23×D61116yes—
688C2×D4—24no—
689C2×D4—618no—
690C2×D4—6116no—
691C2×D4—618no—
692C2×D4—614no—
693C2×D4—1228no—
694C2×D4—1228no—
695C2×D4—1224no—
696C2×D4—2448no—
697C2×D4C23×D6114yes—
698C22×C4—28no—
699C22×C4—48no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—611no—
703C22×C4—611no—
704C22×C4—612no—
705C22×C4—611no—
706C22×C4—614no—
707C22×C4—614no—
708C22×C4—614no—
709C22×C4—614no—
710C22×C4—618no—
711C22×C4—6116no—
712C22×C4—6116no—
713C22×C4—1224no—
714C22×C4—1224no—
715C22×C4—1224no—
716C22×C4—1228no—
717C22×C4—2448no—
718C22×C4—2448no—
719C22×C4C23×D6118yes—
720C22×C4C23×D6112yes—
721C22×C4C23×D6111yescharacteristic
722C22×C4C23×D6114yes—
723C22×C4C23×D6112yes—
724C22×C4C23×D6112yes—
725C22×C4C23×D61116yes—
726C22×C4C23×D6111yescharacteristic
727C22×C4C23×D6111yescharacteristic
728C4⋊C4—618no—
729C4⋊C4—6116no—
730C4⋊C4—6116no—
731C4⋊C4—6116no—
732C4⋊C4—618no—
733C4⋊C4—618no—
734C4⋊C4—618no—
735C4⋊C4—618no—
736C4⋊C4—6116no—
737C4⋊C4—6116no—
738C4⋊C4—6116no—
739C4⋊C4—618no—
740C4⋊C4—614no—
741C4⋊C4—618no—
742C4⋊C4—618no—
743C4⋊C4—614no—
744C4⋊C4—618no—
745C4⋊C4—6116no—
746C4⋊C4C23×D6114yes—
747C4⋊C4C23×D6118yes—
748C4⋊C4C23×D6118yes—
749C4⋊C4C23×D61116yes—
750C4⋊C4C23×D6114yes—
751C4⋊C4C23×D6118yes—
752C22⋊C4—618no—
753C22⋊C4—618no—
754C22⋊C4—6116no—
755C22⋊C4—618no—
756C22⋊C4—6116no—
757C22⋊C4—618no—
758C22⋊C4—618no—
759C22⋊C4—618no—
760C22⋊C4—618no—
761C22⋊C4—618no—
762C22⋊C4—6116no—
763C22⋊C4—618no—
764C22⋊C4C23×D61116yes—
765C22⋊C4C23×D6118yes—
766C42—614no—
767C42—614no—
768C42—614no—
769C42—618no—
770C42—6116no—
771C42—6116no—
772C42C23×D6114yes—
773C42C23×D6118yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—614no—
778C23—612no—
779C23—614no—
780C23—1222no—
781C23—1222no—
782C23—1224no—
783C23—1224no—
784C23—1224no—
785C23C24×D6114yes—
786C23C24×D6111yescharacteristic
787Q8—28no—
788Q8—216no—
789Q8—416no—
790Q8—12216no—
791Q8—1228no—
792Q8—24416no—
793D4—28no—
794D4—12216no—
795D4—12216no—
796D4—1228no—
797D4—24416no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—216no—
804C2×C4—416no—
805C2×C4—614no—
806C2×C4—614no—
807C2×C4—612no—
808C2×C4—612no—
809C2×C4—614no—
810C2×C4—612no—
811C2×C4—618no—
812C2×C4—1228no—
813C2×C4—1222no—
814C2×C4—1228no—
815C2×C4—1222no—
816C2×C4—1224no—
817C2×C4—1222no—
818C2×C4—1224no—
819C2×C4—1224no—
820C2×C4—1228no—
821C2×C4—1228no—
822C2×C4—12216no—
823C2×C4—24416no—
824C2×C4—24416no—
825C2×C4#1451982214yes—
826C2×C4#1451982514yes—
827C2×C4C24×D6114yes—
828C2×C4C24×D6112yes—
829C2×C4C24×D6118yes—
830C2×C4C24×D6114yes—
831C2×C4C24×D6114yes—
832C2×C4C24×D6112yes—
833C2×C4C24×D6112yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—48no—
838C22—614no—
839C22—1228no—
840C22—1222no—
841C22—1222no—
842C22—1224no—
843C22—1224no—
844C22—1224no—
845C22—2448no—
846C22C2×#1451982212yes—
847C222−1+4×D6112yes—
848C22C2×#1451982512yes—
849C22C25×D6111yescharacteristic
850C4—24no—
851C4—24no—
852C4—28no—
853C4—22no—
854C4—24no—
855C4—1222no—
856C4—1228no—
857C4—1222no—
858C4—1224no—
859C4—1222no—
860C4—1224no—
861C4—1224no—
862C4C2×#1451982214yes—
863C4C2×#1451982514yes—
864C2—44no—
865C2—1224no—
866C2—2444no—
867C2#2146026114yesdirect product factor
868C2C22×#1451982211yescharacteristic
869C2C2×2−1+4×D6111yescharacteristic
870C2C22×#1451982511yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×D4×Q8×C61C2
socleC23×C61C25
hypercenterC2×D4×Q8D61
hypocenterC61C2×#3552
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #21460261C2direct (N × H)
2. C2×#16840513C2semidirect
3. C2×#16840490C2semidirect
4. C2×#16840486C2semidirect
5. C2×#16840473C2semidirect
6. C2×#16840462C2semidirect
7. C2×Q8×C22⋊D61C2semidirect
8. C2×#16840422C2semidirect
9. C2×#16840417C2semidirect
10. C2×#16840389C2semidirect
11. C2×#16840377C2semidirect
12. C2×#16840372C2semidirect
13. C2×#16840358C2semidirect
14. C2×#16840336C2semidirect
15. C2×C4⋊Q8×D61C2semidirect
16. C2×#16840299C2semidirect
17. C2×#16840294C2semidirect
18. C2×D4×Q8×C61C2semidirect
21. #16840513C22semidirect
22. #16840490C22semidirect
23. #16840486C22semidirect
24. #16840473C22semidirect
25. #16840462C22semidirect
26. Q8×C22⋊D61C22semidirect
27. #16840422C22semidirect
28. #16840417C22semidirect
29. #16840389C22semidirect
30. #16840377C22semidirect
31. #16840372C22semidirect
32. #16840358C22semidirect
33. #16840336C22semidirect
40. C4⋊Q8×D61C22semidirect
41. #16840299C22semidirect
42. #16840294C22semidirect
93. D4×Q8×C61C22semidirect
436. C2×D4×Q8D61semidirect
448. C2×C61#3552semidirect
463. D4×Q8C2×D61semidirect
536. C61C2×#3552semidirect
867. C2#21460261direct (N × H)

Maximal subgroups

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

subgroupindex
#214602612
C2×#168405132
C2×#168404902
C2×#168404862
C2×#168404732
C2×#168404622
C2×Q8×C22⋊D612
C2×#168404222
C2×#168404172
C2×#168403892
C2×#168403772
C2×#168403722
C2×#168403582
C2×#168403362
C2×C4⋊Q8×D612
C2×#168402992
C2×#168402942
C2×D4×Q8×C612
C2×#355261