Finite Group Databasebeta

← C2×#21460291 #30587637

Subgroups — C2×#21460291 #30587637

Order 15616.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460291C2132yesmaximal, direct product factor
2C2×#16840508C214yesmaximal, complemented
3C2×#16840497C211yesmaximal, characteristic, complemented
4C2×#16840495C212yesmaximal, complemented
5C2×#16840487C211yesmaximal, characteristic, complemented
6C2×#16840473C212yesmaximal, complemented
7C2×#16840433C211yesmaximal, characteristic, complemented
8C2×#16840423C212yesmaximal, complemented
9C2×#16840414C212yesmaximal, complemented
10C2×#16840386C212yesmaximal, complemented
11C2×#16840385C212yesmaximal, complemented
12C2×#16840363C212yesmaximal, complemented
13C2×#16840358C214yesmaximal, complemented
14C2×#16840336C212yesmaximal, complemented
15C2×#16840316C211yesmaximal, characteristic, complemented
16C2×#16840313C211yesmaximal, characteristic, complemented
17C2×#16840294C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C61C211yesmaximal, characteristic, complemented
19C22×#11758226C2212yes—
20C22×#11758222C2212yes—
21#16840508C22164yescomplemented
22#16840497C22116yescomplemented
23#16840495C22132yescomplemented
24#16840487C22116yescomplemented
25#16840473C22132yescomplemented
26#16840433C22116yescomplemented
27#16840423C22132yescomplemented
28#16840414C22132yescomplemented
29#16840386C22132yescomplemented
30#16840385C22132yescomplemented
31#16840363C22132yescomplemented
32#16840358C22164yescomplemented
33#16840336C22132yescomplemented
34#16840316C22116yescomplemented
35#16840313C22116yescomplemented
36C2×#14519776C2211yescharacteristic
37C2×#14519775C2212yes—
38C2×#14519775C2211yescharacteristic
39C2×#14519774C2211yescharacteristic
40C2×#14519773C2212yes—
41#16840294C22116yescomplemented
42C2×#14519772C2214yes—
43C2×#14519770C2212yes—
44C2×#14519768C2211yescharacteristic
45C2×#14519768C2212yes—
46C2×#14519767C2212yes—
47C2×#14519767C2214yes—
48C2×#14519766C2214yes—
49C2×#14519766C2212yes—
50C2×#14519766C2212yes—
51C2×#14519765C2212yes—
52C2×#14519764C2211yescharacteristic
53C2×#14519763C2214yes—
54C2×#14519762C2214yes—
55C2×#14519762C2214yes—
56C2×#14519760C2214yes—
57C2×#14519760C2214yes—
58C2×#14519759C2214yes—
59C2×#14519759C2212yes—
60C2×#14519759C2214yes—
61C2×#14519757C2211yescharacteristic
62C2×#14519757C2211yescharacteristic
63C2×#14519757C2214yes—
64C2×#14519755C2212yes—
65C2×#14519753C2214yes—
66C2×#14519753C2211yescharacteristic
67C2×#14519753C2214yes—
68C2×#14519753C2214yes—
69C2×#14519752C2212yes—
70C2×#14519752C2212yes—
71C2×#14519751C2212yes—
72C2×#14519751C2214yes—
73C2×#14519750C2214yes—
74C2×#14519750C2214yes—
75C2×#14519748C2211yescharacteristic
76C2×Q8×Dic61C2212yes—
77C2×C4×Dic122C2211yescharacteristic
78C2×C4×Dic122C2211yescharacteristic
79C2×C4×Dic122C2212yes—
80C2×#14519742C2212yes—
81C2×C4×D244C2212yes—
82C2×#14519739C2212yes—
83C2×#14519739C2212yes—
84C2×#14519739C2212yes—
85C2×#14519739C2212yes—
86C2×C4×C22⋊D61C2212yes—
87C2×C4×C22⋊D61C2214yes—
88C2×#14519736C2212yes—
89C2×#14519734C2212yes—
90C2×C4⋊C4×D61C2214yes—
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×#11758226—48no—
102C2×#11758226C23116yes—
103C2×#11758222—48no—
104C2×#11758222C23116yes—
105C22×Dic122C2311yescharacteristic
106C22×Dic122C2311yescharacteristic
107C22×Dic122C2312yes—
108C22×D244C2312yes—
109C22×D244C2312yes—
110C22×D244C2312yes—
111C22×D244C2314yes—
112C22×C22⋊D61C2312yes—
113C22×C22⋊D61C2314yes—
114C22×C22⋊D61C2314yes—
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2314yes—
119C22×C4×D61C2314yes—
120C22×C4×D61C2314yes—
121#14519776C2318yes—
122#14519775C23116yes—
123#14519775C2318yes—
124#14519774C2318yes—
125#14519773C23116yes—
126#14519772C23132yes—
127#14519770C23116yes—
128#14519768C2318yes—
129#14519768C23116yes—
130#14519767C23132yes—
131#14519767C23116yes—
132#14519766C23116yes—
133#14519766C23132yes—
134#14519766C23116yes—
135#14519765C23116yes—
136#14519764C2318yes—
137#14519763C23132yes—
138#14519762C23132yes—
139#14519762C23132yes—
140#14519760C23132yes—
141#14519760C23132yes—
142#14519759C23132yes—
143#14519759C23116yes—
144#14519759C23132yes—
145#14519757C23132yes—
146#14519757C2318yes—
147#14519757C2318yes—
148#14519755C23116yes—
149#14519753C23132yes—
150#14519753C23132yes—
151#14519753C2318yes—
152#14519753C23132yes—
153#14519752C23116yes—
154#14519752C23116yes—
155#14519751C23132yes—
156#14519751C23116yes—
157#14519750C23132yes—
158#14519750C23132yes—
159#14519748C2318yes—
160Q8×Dic61C23116yes—
161C4×Dic122C23116yes—
162C4×Dic122C2318yes—
163C4×Dic122C2318yes—
164#14519742C23116yes—
165C4×D244C23116yes—
166#14519739C23116yes—
167#14519739C23116yes—
168#14519739C23116yes—
169#14519739C23116yes—
170C4×C22⋊D61C23132yes—
171C4×C22⋊D61C23116yes—
172#14519736C23116yes—
173#14519734C23116yes—
174C2×C4⋊Dic61C2312yes—
175C2×C4⋊Dic61C2312yes—
176C2×C4⋊Dic61C2312yes—
177C2×C4⋊Dic61C2311yescharacteristic
178C2×C4⋊Dic61C2311yescharacteristic
179C2×C4⋊Dic61C2314yes—
180C2×#11758196C2312yes—
181C2×#11758196C2314yes—
182C2×#11758196C2312yes—
183C2×#11758196C2312yes—
184C2×#11758196C2312yes—
185C2×#11758196C2314yes—
186C2×#11758196C2312yes—
187C2×#11758196C2312yes—
188C2×#11758196C2312yes—
189C4⋊C4×D61C23132yes—
190C2×C22⋊Dic61C2312yes—
191C2×C22⋊Dic61C2312yes—
192C2×C22⋊Dic61C2312yes—
193C2×#11758198C2312yes—
194C2×#11758198C2312yes—
195C2×#11758198C2314yes—
196C2×#11758198C2312yes—
197C2×#11758198C2314yes—
198C2×#11758198C2314yes—
199C2×#11758198C2314yes—
200C2×#11758198C2314yes—
201C2×#11758198C2314yes—
202C2×C4×Dic61C2311yescharacteristic
203C2×C4×Dic61C2311yescharacteristic
204C2×C4×Dic61C2311yescharacteristic
205C2×C4×Dic61C2312yes—
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×C61C2314yes—
227C2×C4⋊C4×C61C2312yes—
228C2×C4⋊C4×C61C2311yescharacteristic
229C2×C4⋊C4×C61C2312yes—
230C2×C22⋊C4×C61C2312yes—
231C2×C22⋊C4×C61C2314yes—
232C2×C42×C61C2311yescharacteristic
233C2×C42×C61C2312yes—
234C24×C61C2412yes—
235C23×D61C2411yescharacteristic
236C23×D61C2414yes—
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×C61C2412yes—
250C22×C4×C61C2411yescharacteristic
251C22×C4×C61C2414yes—
252C22×C4×C61C2418yes—
253C22×C4×C61C2412yes—
254C22×C4×C61C24116yes—
255C22×C4×C61C2411yescharacteristic
256C22×C4×C61C2411yescharacteristic
257C2×C22⋊D61—48no—
258C2×C22⋊D61—44no—
259C2×C22⋊D61—48no—
260C2×C22⋊D61C24116yes—
261C2×C22⋊D61C2418yes—
262C2×C22⋊D61C24116yes—
263C22×Dic61C2411yescharacteristic
264C22×Dic61C2412yes—
265C22×Dic61C2412yes—
266C22×Dic61C2411yescharacteristic
267C22×Dic61C2411yescharacteristic
268C22×Dic61C2412yes—
269C22×Dic61C2412yes—
270#11758226—432no—
271#11758222—432no—
272C2×D244—28no—
273C2×D244—28no—
274C2×D244—44no—
275C2×D244—48no—
276C2×D244C2418yes—
277C2×D244C2418yes—
278C2×D244C24116yes—
279C2×D244C2418yes—
280C2×C4×D61—24no—
281C2×C4×D61—24no—
282C2×C4×D61—42no—
283C2×C4×D61—48no—
284C2×C4×D61—48no—
285C2×C4×D61—48no—
286C2×C4×D61C2414yes—
287C2×C4×D61C2414yes—
288C2×C4×D61C24116yes—
289C2×C4×D61C24116yes—
290C2×C4×D61C2414yes—
291C2×C4×D61C24116yes—
292C2×Dic122—24no—
293C2×Dic122—24no—
294C2×Dic122—44no—
295C2×Dic122C2414yes—
296C2×Dic122C2414yes—
297C2×Dic122C2418yes—
298C4⋊C4×C61C2414yes—
299C4⋊C4×C61C2418yes—
300C4⋊C4×C61C2414yes—
301C4⋊C4×C61C2418yes—
302C4⋊C4×C61C24116yes—
303C4⋊C4×C61C2418yes—
304C22⋊C4×C61C2418yes—
305C22⋊C4×C61C24116yes—
306C42×C61C2414yes—
307C42×C61C2418yes—
308C22⋊Dic61C2418yes—
309C22⋊Dic61C2418yes—
310C22⋊Dic61C2418yes—
311#11758198C2418yes—
312#11758198C2418yes—
313#11758198C24116yes—
314#11758198C2418yes—
315#11758198C24116yes—
316#11758198C24116yes—
317#11758198C24116yes—
318#11758198C24116yes—
319#11758198C24116yes—
320C4⋊Dic61C2418yes—
321C4⋊Dic61C2418yes—
322C4⋊Dic61C2418yes—
323C4⋊Dic61C2414yes—
324C4⋊Dic61C2414yes—
325C4⋊Dic61C24116yes—
326#11758196C2418yes—
327#11758196C24116yes—
328#11758196C2418yes—
329#11758196C2418yes—
330#11758196C2418yes—
331#11758196C24116yes—
332#11758196C2418yes—
333#11758196C2418yes—
334#11758196C2418yes—
335C4×Dic61C2414yes—
336C4×Dic61C2414yes—
337C4×Dic61C2414yes—
338C4×Dic61C2418yes—
339C4×Dic61C2418yes—
340C4×Dic61C24116yes—
341C23×C61—24no—
342C23×C61—24no—
343C23×C61—24no—
344C23×C61C2514yes—
345C23×C61C2511yescharacteristic
346C22×D61—22no—
347C22×D61—28no—
348C22×D61—22no—
349C22×D61—28no—
350C22×D61—28no—
351C22×D61—22no—
352C22×D61C2512yes—
353C22×D61C2518yes—
354Q8×C61—216no—
355Q8×C61—28no—
356Q8×C61—416no—
357D4×C61—28no—
358C2×C4×C61—24no—
359C2×C4×C61—28no—
360C2×C4×C61—24no—
361C2×C4×C61—24no—
362C2×C4×C61—22no—
363C2×C4×C61—216no—
364C2×C4×C61—416no—
365C2×C4×C61H(5,𝔽2)14yes—
366C2×C4×C612−1+414yes—
367C2×C4×C61C2512yes—
368C2×C4×C61C2518yes—
369C2×C4×C61C2514yes—
370C2×C4×C61C2514yes—
371C2×C4×C61C2514yes—
372C2×C4×C61C2512yes—
373C2×C4×C61C2512yes—
374C22⋊D61—416no—
375C22⋊D61—416no—
376C22⋊D61—48no—
377C2×Dic61—24no—
378C2×Dic61—22no—
379C2×Dic61—24no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—24no—
383C2×Dic61—24no—
384C2×Dic61C2514yes—
385C2×Dic61C2514yes—
386C2×Dic61C2512yes—
387C2×Dic61C2512yes—
388C2×Dic61C2512yes—
389C2×Dic61C2514yes—
390C2×Dic61C2514yes—
391D244—216no—
392D244—216no—
393D244—48no—
394D244—416no—
395C4×D61—28no—
396C4×D61—28no—
397C4×D61—44no—
398C4×D61—416no—
399C4×D61—416no—
400C4×D61—416no—
401Dic122—28no—
402Dic122—28no—
403Dic122—48no—
404C2×#3554—611nomaximal, Sylow
405C22×C61—24no—
406C22×C61—24no—
407C22×C61—24no—
408C22×C61—48no—
409C22×C61C2×H(5,𝔽2)12yes—
410C22×C61C2×2−1+412yes—
411C22×C61#58512yes—
412C22×C61C2611yescharacteristic
413C2×D61—22no—
414C2×D61—28no—
415C2×D61—22no—
416C2×D61—28no—
417C2×D61—28no—
418C2×D61—22no—
419C2×D61—44no—
420C2×D61—416no—
421C4×C61—24no—
422C4×C61—28no—
423C4×C61—24no—
424C4×C61—24no—
425C4×C61—22no—
426C4×C61C2×H(5,𝔽2)14yes—
427C4×C61C2×2−1+414yes—
428Dic61—24no—
429Dic61—22no—
430Dic61—24no—
431Dic61—22no—
432Dic61—22no—
433Dic61—24no—
434Dic61—24no—
435#3554—6132no—
436C2×#562—614no—
437C2×#559—611no—
438C2×#559—612no—
439C2×#557—611no—
440C2×#554—612no—
441C2×#550—611no—
442C2×D4×Q8D6111yescharacteristic, complemented
443C2×#548—612no—
444C2×#547—612no—
445C2×#542—612no—
446C2×#542—612no—
447C2×#540—612no—
448C2×#539—614no—
449C2×#536—612no—
450C2×#533—611no—
451C2×#532—611no—
452C2×#529—611no—
453C2×C61—44no—
454C2×C61#355414yescomplemented
455C2×C61C22×H(5,𝔽2)11yescharacteristic
456C2×C61C22×2−1+411yescharacteristic
457C2×C61C2×#58511yescharacteristic
458D61—42no—
459D61—48no—
460C22×#41—612no—
461C22×#41—612no—
462C23×Q8C2×D6112yes—
463#562—6164no—
464#559—6116no—
465#559—6132no—
466#557—6116no—
467#554—6132no—
468#550—6116no—
469D4×Q8C2×D61116yescomplemented
470#548—6132no—
471#547—6132no—
472#542—6132no—
473#542—6132no—
474#540—6132no—
475#539—6164no—
476#536—6132no—
477#533—6116no—
478#532—6116no—
479C2×C4⋊Q8—611no—
480C2×C4⋊Q8—612no—
481C2×C4⋊Q8—611no—
482C2×C4⋊Q8C2×D6111yescharacteristic
483C2×C4⋊Q8C2×D6112yes—
484C2×#127—612no—
485C2×#127—611no—
486#529—6116no—
487C2×#126—614no—
488C2×#126—612no—
489C2×#125—612no—
490C2×#125—614no—
491C2×#125—611no—
492C2×#125—612no—
493C2×#124—612no—
494C2×#124—612no—
495C2×#124—614no—
496C2×#124—611no—
497C2×#124—614no—
498C2×#124—612no—
499C2×#123—614no—
500C2×#123—614no—
501C2×#123—614no—
502C2×#123—614no—
503C2×#123—612no—
504C2×#123—614no—
505C2×#123—614no—
506C2×C22⋊Q8—611no—
507C2×C22⋊Q8—614no—
508C2×C22⋊Q8—614no—
509C2×C22⋊Q8—614no—
510C2×C22⋊Q8—612no—
511C2×C22⋊Q8—611no—
512C2×C22⋊Q8—611no—
513C2×C22⋊Q8—614no—
514C2×C22⋊Q8C2×D6114yes—
515C2×C22⋊Q8C2×D6112yes—
516C2×#121—611no—
517C2×#121—614no—
518C2×#121—612no—
519C2×#121—612no—
520C2×#121—612no—
521C2×#121—614no—
522C2×#121—614no—
523C2×C4×Q8—612no—
524C2×C4×Q8—612no—
525C2×C4×Q8—611no—
526C2×C4×Q8—611no—
527C2×C4×Q8—612no—
528C2×C4×Q8C2×D6111yescharacteristic
529C2×C4×D4—612no—
530C2×C4×D4—614no—
531C2×C4×D4—612no—
532C2×C4×D4—612no—
533C2×C4×D4—612no—
534C2×C4×D4—612no—
535C2×C4×D4—612no—
536C2×C4×D4C2×D6111yescharacteristic
537C2×C4×D4C2×D6112yes—
538C2×#117—612no—
539C2×#117—612no—
540C22×C4⋊C4—614no—
541C22×C42—611no—
542C61C2×#355411yescharacteristic, complemented, Sylow
543C2×#41—6116no—
544C2×#41—6116no—
545C2×#41—2448no—
546C2×#41—2448no—
547C22×Q8—48no—
548C22×Q8—611no—
549C22×Q8—611no—
550C22×Q8—612no—
551C22×Q8C22×D6112yes—
552C22×Q8C22×D6111yescharacteristic
553C22×Q8C22×D6114yes—
554C22×Q8C22×D61116yes—
555C22×D4—612no—
556C22×D4—614no—
557C22×D4—614no—
558C22×D4—612no—
559C22×D4—612no—
560C22×D4—612no—
561C22×D4—614no—
562C22×D4C22×D6111yescharacteristic
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—614no—
566C23×C4—614no—
567C23×C4—614no—
568C23×C4—611no—
569C23×C4C22×D6112yes—
570C23×C4C22×D6114yes—
571C4⋊Q8—618no—
572C4⋊Q8—6116no—
573C4⋊Q8—618no—
574C4⋊Q8C22×D6118yes—
575C4⋊Q8C22×D61116yes—
576#127—6116no—
577#127—618no—
578#126—6132no—
579#126—6116no—
580#125—618no—
581#125—6116no—
582#125—6132no—
583#125—6116no—
584#124—6116no—
585#124—6116no—
586#124—6132no—
587#124—618no—
588#124—6132no—
589#124—6116no—
590#123—6132no—
591#123—6132no—
592#123—6132no—
593#123—6132no—
594#123—6116no—
595#123—6132no—
596#123—6132no—
597C22⋊Q8—618no—
598C22⋊Q8—6132no—
599C22⋊Q8—6132no—
600C22⋊Q8—6132no—
601C22⋊Q8—618no—
602C22⋊Q8—618no—
603C22⋊Q8—6116no—
604C22⋊Q8—6132no—
605C22⋊Q8C22×D61132yes—
606C22⋊Q8C22×D61116yes—
607#121—618no—
608#121—6132no—
609#121—6116no—
610#121—6116no—
611#121—6116no—
612#121—6132no—
613#121—6132no—
614C4×Q8—6116no—
615C4×Q8—6116no—
616C4×Q8—618no—
617C4×Q8—618no—
618C4×Q8—6116no—
619C4×Q8C22×D6118yes—
620C4×D4—6116no—
621C4×D4—6132no—
622C4×D4—6116no—
623C4×D4—6116no—
624C4×D4—6116no—
625C4×D4—6116no—
626C4×D4—6116no—
627C4×D4C22×D6118yes—
628C4×D4C22×D61116yes—
629#117—6116no—
630#117—6116no—
631C2×C4⋊C4—612no—
632C2×C4⋊C4—612no—
633C2×C4⋊C4—614no—
634C2×C4⋊C4—612no—
635C2×C4⋊C4—612no—
636C2×C4⋊C4—612no—
637C2×C4⋊C4—612no—
638C2×C4⋊C4—611no—
639C2×C4⋊C4—612no—
640C2×C4⋊C4—611no—
641C2×C4⋊C4—612no—
642C2×C4⋊C4—614no—
643C2×C4⋊C4—612no—
644C2×C4⋊C4—614no—
645C2×C4⋊C4—612no—
646C2×C4⋊C4—6132no—
647C2×C4⋊C4C22×D6114yes—
648C2×C4⋊C4C22×D6111yescharacteristic
649C2×C4⋊C4C22×D6111yescharacteristic
650C2×C4⋊C4C22×D6112yes—
651C2×C4⋊C4C22×D6112yes—
652C2×C4⋊C4C22×D6112yes—
653C2×C22⋊C4—612no—
654C2×C22⋊C4—612no—
655C2×C22⋊C4—612no—
656C2×C22⋊C4—612no—
657C2×C22⋊C4—612no—
658C2×C22⋊C4—614no—
659C2×C22⋊C4—614no—
660C2×C22⋊C4—614no—
661C2×C22⋊C4—614no—
662C2×C22⋊C4—612no—
663C2×C22⋊C4—614no—
664C2×C22⋊C4—614no—
665C2×C22⋊C4C22×D6112yes—
666C2×C22⋊C4C22×D6114yes—
667C2×C42—611no—
668C2×C42—612no—
669C2×C42—612no—
670C2×C42—611no—
671C2×C42—611no—
672C2×C42—614no—
673C2×C42—618no—
674C2×C42C22×D6112yes—
675C2×C42C22×D6111yescharacteristic
676C24—611no—
677C24—614no—
678C24C23×D6112yes—
679#41—24432no—
680#41—24432no—
681C2×Q8—24no—
682C2×Q8—28no—
683C2×Q8—48no—
684C2×Q8—432no—
685C2×Q8—614no—
686C2×Q8—614no—
687C2×Q8—618no—
688C2×Q8—1224no—
689C2×Q8—1224no—
690C2×Q8—2444no—
691C2×Q8C23×D6118yes—
692C2×Q8C23×D6114yes—
693C2×Q8C23×D61116yes—
694C2×D4—24no—
695C2×D4—618no—
696C2×D4—6116no—
697C2×D4—6116no—
698C2×D4—618no—
699C2×D4—618no—
700C2×D4—618no—
701C2×D4—6116no—
702C2×D4—1228no—
703C2×D4—1228no—
704C2×D4—2448no—
705C2×D4—2444no—
706C2×D4—2448no—
707C2×D4—2444no—
708C2×D4—2448no—
709C2×D4C23×D6114yes—
710C22×C4—28no—
711C22×C4—48no—
712C22×C4—612no—
713C22×C4—612no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—612no—
718C22×C4—612no—
719C22×C4—614no—
720C22×C4—614no—
721C22×C4—614no—
722C22×C4—6116no—
723C22×C4—6116no—
724C22×C4—6116no—
725C22×C4—1224no—
726C22×C4—1224no—
727C22×C4—2448no—
728C22×C4—2442no—
729C22×C4—2448no—
730C22×C4—2448no—
731C22×C4C23×D6118yes—
732C22×C4C23×D6111yescharacteristic
733C22×C4C23×D6114yes—
734C22×C4C23×D6112yes—
735C22×C4C23×D6112yes—
736C22×C4C23×D6112yes—
737C22×C4C23×D61116yes—
738C22×C4C23×D6111yescharacteristic
739C22×C4C23×D6111yescharacteristic
740C4⋊C4—618no—
741C4⋊C4—618no—
742C4⋊C4—6116no—
743C4⋊C4—618no—
744C4⋊C4—618no—
745C4⋊C4—618no—
746C4⋊C4—618no—
747C4⋊C4—618no—
748C4⋊C4—6116no—
749C4⋊C4—618no—
750C4⋊C4—618no—
751C4⋊C4—618no—
752C4⋊C4—614no—
753C4⋊C4—614no—
754C4⋊C4—6116no—
755C4⋊C4C23×D61116yes—
756C4⋊C4C23×D6114yes—
757C4⋊C4C23×D6114yes—
758C4⋊C4C23×D6118yes—
759C4⋊C4C23×D6118yes—
760C4⋊C4C23×D6118yes—
761C22⋊C4—618no—
762C22⋊C4—618no—
763C22⋊C4—618no—
764C22⋊C4—618no—
765C22⋊C4—618no—
766C22⋊C4—6116no—
767C22⋊C4—6116no—
768C22⋊C4—6116no—
769C22⋊C4—6116no—
770C22⋊C4—618no—
771C22⋊C4—6116no—
772C22⋊C4—6116no—
773C22⋊C4C23×D6118yes—
774C22⋊C4C23×D61116yes—
775C42—614no—
776C42—614no—
777C42—614no—
778C42—618no—
779C42—618no—
780C42—6116no—
781C42C23×D6114yes—
782C42C23×D6118yes—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—612no—
787C23—618no—
788C23—1222no—
789C23—1228no—
790C23—1222no—
791C23—1228no—
792C23—1228no—
793C23—1222no—
794C23C24×D6114yes—
795C23C24×D6111yescharacteristic
796Q8—28no—
797Q8—216no—
798Q8—416no—
799Q8—1228no—
800Q8—1228no—
801Q8—2448no—
802D4—28no—
803D4—12216no—
804D4—12216no—
805D4—2448no—
806D4—24416no—
807D4—2448no—
808D4—24416no—
809D4—24416no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—216no—
816C2×C4—416no—
817C2×C4—614no—
818C2×C4—614no—
819C2×C4—612no—
820C2×C4—612no—
821C2×C4—612no—
822C2×C4—614no—
823C2×C4—614no—
824C2×C4—1222no—
825C2×C4—1224no—
826C2×C4—1222no—
827C2×C4—1224no—
828C2×C4—1224no—
829C2×C4—1222no—
830C2×C4—1224no—
831C2×C4—1228no—
832C2×C4—1228no—
833C2×C4—24416no—
834C2×C4—2444no—
835C2×C4—24416no—
836C2×C4—24416no—
837C2×C4#1451982214yes—
838C2×C4#1451982514yes—
839C2×C4C24×D6112yes—
840C2×C4C24×D6118yes—
841C2×C4C24×D6114yes—
842C2×C4C24×D6114yes—
843C2×C4C24×D6114yes—
844C2×C4C24×D6112yes—
845C2×C4C24×D6112yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—48no—
850C22—1222no—
851C22—1228no—
852C22—1222no—
853C22—1228no—
854C22—1228no—
855C22—1222no—
856C22—2444no—
857C22—24416no—
858C22C2×#1451982212yes—
859C22C2×#1451982512yes—
860C22#1684059912yes—
861C22C25×D6111yescharacteristic
862C4—24no—
863C4—24no—
864C4—28no—
865C4—24no—
866C4—22no—
867C4—1222no—
868C4—1224no—
869C4—1222no—
870C4—1224no—
871C4—1224no—
872C4—1222no—
873C4—1224no—
874C4C2×#1451982214yes—
875C4C2×#1451982514yes—
876C2—44no—
877C2—2442no—
878C2—2448no—
879C2#2146029114yesdirect product factor
880C2C22×#1451982211yescharacteristic
881C2C22×#1451982511yescharacteristic
882C2C2×#1684059911yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×D4×Q8×C61C2
socleC23×C61C25
hypercenterC2×D4×Q8D61
hypocenterC61C2×#3554
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #21460291C2direct (N × H)
2. C2×#16840508C2semidirect
3. C2×#16840497C2semidirect
4. C2×#16840495C2semidirect
5. C2×#16840487C2semidirect
6. C2×#16840473C2semidirect
7. C2×#16840433C2semidirect
8. C2×#16840423C2semidirect
9. C2×#16840414C2semidirect
10. C2×#16840386C2semidirect
11. C2×#16840385C2semidirect
12. C2×#16840363C2semidirect
13. C2×#16840358C2semidirect
14. C2×#16840336C2semidirect
15. C2×#16840316C2semidirect
16. C2×#16840313C2semidirect
17. C2×#16840294C2semidirect
18. C2×D4×Q8×C61C2semidirect
21. #16840508C22semidirect
22. #16840497C22semidirect
23. #16840495C22semidirect
24. #16840487C22semidirect
25. #16840473C22semidirect
26. #16840433C22semidirect
27. #16840423C22semidirect
28. #16840414C22semidirect
29. #16840386C22semidirect
30. #16840385C22semidirect
31. #16840363C22semidirect
32. #16840358C22semidirect
33. #16840336C22semidirect
34. #16840316C22semidirect
35. #16840313C22semidirect
41. #16840294C22semidirect
93. D4×Q8×C61C22semidirect
442. C2×D4×Q8D61semidirect
454. C2×C61#3554semidirect
469. D4×Q8C2×D61semidirect
542. C61C2×#3554semidirect
879. C2#21460291direct (N × H)

Maximal subgroups

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

subgroupindex
#214602912
C2×#168405082
C2×#168404972
C2×#168404952
C2×#168404872
C2×#168404732
C2×#168404332
C2×#168404232
C2×#168404142
C2×#168403862
C2×#168403852
C2×#168403632
C2×#168403582
C2×#168403362
C2×#168403162
C2×#168403132
C2×#168402942
C2×D4×Q8×C612
C2×#355461