Finite Group Databasebeta

← C2×#21460311 #30587848

Subgroups — C2×#21460311 #30587848

Order 15616.

6338 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460311C2132yesmaximal, direct product factor
2C2×C61⋊#564C214yesmaximal, complemented
3C2×#16840491C211yesmaximal, characteristic, complemented
4C2×#16840490C212yesmaximal, complemented
5C2×#16840490C211yesmaximal, characteristic, complemented
6C2×#16840489C212yesmaximal, complemented
7C2×#16840488C212yesmaximal, complemented
8C2×#16840487C211yesmaximal, characteristic, complemented
9C2×#16840487C212yesmaximal, complemented
10C2×#16840375C212yesmaximal
11C2×#16840373C212yesmaximal
12C2×#16840371C214yesmaximal
13C2×#16840370C212yesmaximal
14C2×#16840370C212yesmaximal
15C2×#16840317C211yesmaximal, characteristic
16C2×#16840316C211yesmaximal, characteristic
17C2×#16840316C211yesmaximal, characteristic
18C2×C61×#557C211yesmaximal, characteristic, complemented
19C61⋊#564C22164yescomplemented
20#16840491C22116yescomplemented
21#16840490C22116yescomplemented
22#16840490C22132yescomplemented
23#16840489C22132yescomplemented
24#16840488C22132yescomplemented
25#16840487C22116yescomplemented
26#16840487C22132yescomplemented
27#16840375C22132yes—
28#16840373C22132yes—
29#16840371C22164yes—
30#16840370C22132yes—
31#16840370C22132yes—
32#16840317C22116yes—
33#16840316C22116yes—
34#16840316C22116yes—
35C2×#14519777C2211yescharacteristic
36C2×#14519777C2212yes—
37C2×#14519776C2211yescharacteristic
38C2×#14519776C2211yescharacteristic
39C2×#14519776C2214yes—
40C2×#14519775C2211yescharacteristic
41C2×#14519775C2211yescharacteristic
42C2×#14519775C2212yes—
43C2×#14519775C2212yes—
44C2×#14519772C2214yes—
45C2×#14519772C2214yes—
46C2×#14519772C2214yes—
47C2×#14519771C2214yes—
48C2×#14519769C2212yes—
49C2×#14519769C2214yes—
50C2×#14519769C2214yes—
51C2×#14519768C2212yes—
52C2×#14519768C2212yes—
53C2×#14519768C2214yes—
54C2×#14519768C2212yes—
55C2×#14519768C2214yes—
56C2×#14519768C2214yes—
57C2×#14519767C2212yes—
58C2×#14519767C2212yes—
59C2×#14519767C2214yes—
60C2×#14519767C2214yes—
61C2×#14519767C2214yes—
62C2×#14519767C2214yes—
63C2×#14519767C2214yes—
64C2×#14519767C2214yes—
65C2×#14519767C2214yes—
66C2×#14519757C2211yescharacteristic
67C2×#14519757C2211yescharacteristic
68C2×#14519757C2212yes—
69C2×#14519755C2212yes—
70C2×#14519755C2212yes—
71C2×#14519753C2211yescharacteristic
72C2×#14519753C2211yescharacteristic
73C2×#14519753C2212yes—
74C2×Q8×Dic61C2212yes—
75C2×Q8×Dic61C2212yes—
76C2×Q8×Dic61C2212yes—
77C2×C4×Dic122C2212yes—
78C2×C4×Dic122C2211yescharacteristic
79C2×C4×Dic122C2211yescharacteristic
80C2×C4×Dic122C2212yes—
81C2×C4×Dic122C2212yes—
82C2×C4×Dic122C2214yes—
83C2×C4×Dic122C2212yes—
84C2×#14519742C2212yes—
85C2×#14519742C2214yes—
86C2×#14519742C2212yes—
87C2×#14519742C2212yes—
88C2×#14519735C2212yes—
89C2×#14519734C2212yes—
90C2×#14519734C2212yes—
91C2×C42×D61C2211yescharacteristic
92C61×#557C22116yescomplemented
93C2×C4⋊Q8×C61C2211yescharacteristic
94C2×C4⋊Q8×C61C2212yes—
95C2×#125×C61C2212yes—
96C2×#125×C61C2214yes—
97C2×C4×Q8×C61C2211yescharacteristic
98C2×C4×Q8×C61C2211yescharacteristic
99C2×C4×Q8×C61C2212yes—
100C2×C4×Q8×C61C2212yes—
101C22×Dic122C2312yes—
102C22×Dic122C2312yes—
103C22×Dic122C2311yescharacteristic
104C22×Dic122C2312yes—
105C22×Dic122C2311yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C22×C4×D61C2311yescharacteristic
108C22×C4×D61C2311yescharacteristic
109#14519777C2318yes—
110#14519777C23116yes—
111#14519776C2318yes—
112#14519776C23132yes—
113#14519776C2318yes—
114#14519775C2318yes—
115#14519775C23116yes—
116#14519775C2318yes—
117#14519775C23116yes—
118#14519772C23132yes—
119#14519772C23132yes—
120#14519772C23132yes—
121#14519771C23132yes—
122#14519769C23116yes—
123#14519769C23132yes—
124#14519769C23132yes—
125#14519768C23116yes—
126#14519768C23132yes—
127#14519768C23116yes—
128#14519768C23132yes—
129#14519768C23132yes—
130#14519768C23116yes—
131#14519767C23132yes—
132#14519767C23132yes—
133#14519767C23132yes—
134#14519767C23132yes—
135#14519767C23132yes—
136#14519767C23132yes—
137#14519767C23132yes—
138#14519767C23116yes—
139#14519767C23116yes—
140#14519757C2318yes—
141#14519757C2318yes—
142#14519757C23116yes—
143#14519755C23116yes—
144#14519755C23116yes—
145#14519753C2318yes—
146#14519753C2318yes—
147#14519753C23116yes—
148Q8×Dic61C23116yes—
149Q8×Dic61C23116yes—
150Q8×Dic61C23116yes—
151C4×Dic122C23116yes—
152C4×Dic122C2318yes—
153C4×Dic122C23116yes—
154C4×Dic122C2318yes—
155C4×Dic122C23132yes—
156C4×Dic122C23116yes—
157C4×Dic122C23116yes—
158#14519742C23132yes—
159#14519742C23116yes—
160#14519742C23116yes—
161#14519742C23116yes—
162#14519735C23116yes—
163#14519734C23116yes—
164#14519734C23116yes—
165C2×C4⋊Dic61C2312yes—
166C2×C4⋊Dic61C2311yescharacteristic
167C2×C4⋊Dic61C2312yes—
168C2×C4⋊Dic61C2311yescharacteristic
169C2×C4⋊Dic61C2312yes—
170C2×C4⋊Dic61C2312yes—
171C2×C4⋊Dic61C2314yes—
172C2×C4⋊Dic61C2314yes—
173C2×C4⋊Dic61C2314yes—
174C2×C4⋊Dic61C2314yes—
175C2×#11758196C2312yes—
176C2×#11758196C2312yes—
177C2×#11758196C2312yes—
178C2×#11758196C2312yes—
179C2×#11758196C2312yes—
180C2×#11758196C2314yes—
181C2×#11758196C2314yes—
182C2×#11758196C2314yes—
183C2×#11758196C2314yes—
184C2×#11758196C2312yes—
185C2×#11758196C2312yes—
186C2×#11758196C2312yes—
187C2×#11758196C2312yes—
188C2×#11758196C2312yes—
189C2×#11758196C2314yes—
190C2×#11758196C2314yes—
191C2×#11758196C2314yes—
192C2×#11758198C2312yes—
193C2×#11758198C2312yes—
194C2×#11758198C2312yes—
195C2×#11758198C2312yes—
196C2×#11758198C2314yes—
197C2×C4×Dic61C2311yescharacteristic
198C2×C4×Dic61C2311yescharacteristic
199C2×C4×Dic61C2311yescharacteristic
200C2×C4×Dic61C2312yes—
201C2×C4×Dic61C2312yes—
202C2×C4×Dic61C2314yes—
203C2×C4×Dic61C2314yes—
204C2×C4×Dic61C2314yes—
205C2×C4×Dic61C2314yes—
206C42×D61C2318yes—
207C22×Q8×C61C2312yes—
208C22×Q8×C61C2311yescharacteristic
209C22×Q8×C61C2311yescharacteristic
210C4⋊Q8×C61C2318yes—
211C4⋊Q8×C61C23116yes—
212#125×C61C23116yes—
213#125×C61C23132yes—
214C4×Q8×C61C23116yes—
215C4×Q8×C61C2318yes—
216C4×Q8×C61C23116yes—
217C4×Q8×C61C2318yes—
218C2×C4⋊C4×C61C2312yes—
219C2×C4⋊C4×C61C2312yes—
220C2×C4⋊C4×C61C2314yes—
221C2×C4⋊C4×C61C2314yes—
222C2×C4⋊C4×C61C2311yescharacteristic
223C2×C4⋊C4×C61C2312yes—
224C2×C4⋊C4×C61C2312yes—
225C2×C4⋊C4×C61C2311yescharacteristic
226C2×C4⋊C4×C61C2314yes—
227C2×C42×C61C2311yescharacteristic
228C2×C42×C61C2312yes—
229C2×C42×C61C2312yes—
230C2×C42×C61C2314yes—
231C23×D61C2411yescharacteristic
232C2×Q8×C61—28no—
233C2×Q8×C61—24no—
234C2×Q8×C61—24no—
235C2×Q8×C61C2414yes—
236C2×Q8×C61C2418yes—
237C2×Q8×C61C2414yes—
238C22×C4×C61C2411yescharacteristic
239C22×C4×C61C2412yes—
240C22×C4×C61C2412yes—
241C22×C4×C61C2412yes—
242C22×C4×C61C2412yes—
243C22×C4×C61C2414yes—
244C22×C4×C61C2411yescharacteristic
245C22×C4×C61C2411yescharacteristic
246C22×Dic61C2411yescharacteristic
247C22×Dic61C2411yescharacteristic
248C22×Dic61C2412yes—
249C22×Dic61C2412yes—
250C22×Dic61C2412yes—
251C22×Dic61C2412yes—
252C22×Dic61C2414yes—
253C22×Dic61C2411yescharacteristic
254C2×C4×D61—24no—
255C2×C4×D61—24no—
256C2×C4×D61—24no—
257C2×C4×D61C2414yes—
258C2×C4×D61C2414yes—
259C2×C4×D61C2414yes—
260C2×Dic122—24no—
261C2×Dic122—28no—
262C2×Dic122—24no—
263C2×Dic122—28no—
264C2×Dic122—28no—
265C2×Dic122C2418yes—
266C2×Dic122C2414yes—
267C2×Dic122C2418yes—
268C2×Dic122C2418yes—
269C2×Dic122C2414yes—
270C4⋊C4×C61C2414yes—
271C4⋊C4×C61C2414yes—
272C4⋊C4×C61C2418yes—
273C4⋊C4×C61C2418yes—
274C4⋊C4×C61C24116yes—
275C4⋊C4×C61C2418yes—
276C4⋊C4×C61C24116yes—
277C4⋊C4×C61C2418yes—
278C4⋊C4×C61C24116yes—
279C42×C61C2418yes—
280C42×C61C24116yes—
281C42×C61C2414yes—
282C42×C61C2418yes—
283#11758198C2418yes—
284#11758198C2418yes—
285#11758198C2418yes—
286#11758198C2418yes—
287#11758198C24116yes—
288C4⋊Dic61C2418yes—
289C4⋊Dic61C2414yes—
290C4⋊Dic61C2418yes—
291C4⋊Dic61C2414yes—
292C4⋊Dic61C2418yes—
293C4⋊Dic61C2418yes—
294C4⋊Dic61C24116yes—
295C4⋊Dic61C24116yes—
296C4⋊Dic61C24116yes—
297C4⋊Dic61C24116yes—
298#11758196C2418yes—
299#11758196C2418yes—
300#11758196C2418yes—
301#11758196C2418yes—
302#11758196C2418yes—
303#11758196C24116yes—
304#11758196C24116yes—
305#11758196C24116yes—
306#11758196C24116yes—
307#11758196C2418yes—
308#11758196C2418yes—
309#11758196C2418yes—
310#11758196C2418yes—
311#11758196C2418yes—
312#11758196C24116yes—
313#11758196C24116yes—
314#11758196C24116yes—
315C4×Dic61C2414yes—
316C4×Dic61C2414yes—
317C4×Dic61C2414yes—
318C4×Dic61C2418yes—
319C4×Dic61C2418yes—
320C4×Dic61C24116yes—
321C4×Dic61C24116yes—
322C4×Dic61C24116yes—
323C4×Dic61C24116yes—
324C23×C61C2511yescharacteristic
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61C2512yes—
329Q8×C61—216no—
330Q8×C61—28no—
331Q8×C61—28no—
332C2×C4×C61—24no—
333C2×C4×C61—24no—
334C2×C4×C61—22no—
335C2×C4×C61—24no—
336C2×C4×C61—28no—
337C2×C4×C61—24no—
338C2×C4×C612−1+414yes—
339C2×C4×C612−1+414yes—
340C2×C4×C61C2518yes—
341C2×C4×C61C2514yes—
342C2×C4×C61C2514yes—
343C2×C4×C61C2512yes—
344C2×C4×C61C2514yes—
345C2×C4×C61C2514yes—
346C2×C4×C61C2512yes—
347C2×C4×C61C2512yes—
348C2×Dic61—24no—
349C2×Dic61—24no—
350C2×Dic61—24no—
351C2×Dic61—24no—
352C2×Dic61—28no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic612−1+414yes—
356C2×Dic61C2514yes—
357C2×Dic61C2514yes—
358C2×Dic61C2514yes—
359C2×Dic61C2514yes—
360C2×Dic61C2518yes—
361C2×Dic61C2512yes—
362C2×Dic61C2512yes—
363C2×Dic61C2512yes—
364C4×D61—28no—
365C4×D61—28no—
366C4×D61—28no—
367Dic122—28no—
368Dic122—28no—
369Dic122—216no—
370Dic122—216no—
371Dic122—216no—
372C2×#3556—611nomaximal, Sylow
373C22×C61C2×2−1+412yes—
374C22×C61C2×2−1+412yes—
375C22×C61C2×2−1+412yes—
376C22×C61C2611yescharacteristic
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—44no—
381C4×C61—24no—
382C4×C61—24no—
383C4×C61—22no—
384C4×C61—28no—
385C4×C61—24no—
386C4×C61—24no—
387C4×C61C2×2−1+414yes—
388C4×C61C2×2−1+414yes—
389Dic61—24no—
390Dic61—24no—
391Dic61—24no—
392Dic61—24no—
393Dic61—28no—
394Dic61—22no—
395Dic61—22no—
396Dic61C2×2−1+414yes—
397#3556—6132no—
398C2×#564—614no—
399C2×#557—612no—
400C2×#557—611no—
401C2×#557—612no—
402C2×#557—612no—
403C2×#557—612no—
404C2×#557—611no—
405C2×#557—611no—
406C2×#557D6111yescharacteristic, complemented
407C2×#541—612no—
408C2×#541—614no—
409C2×#541—612no—
410C2×#541—612no—
411C2×#541—612no—
412C2×#533—611no—
413C2×#533—611no—
414C2×#533—611no—
415C2×C61#355614yescomplemented
416C2×C61C22×2−1+411yescharacteristic
417C2×C61C22×2−1+411yescharacteristic
418C2×C61C22×2−1+411yescharacteristic
419D61—42no—
420#564—6164no—
421#557—6132no—
422#557—6116no—
423#557—6132no—
424#557—6132no—
425#557—6132no—
426#557—6116no—
427#557—6116no—
428#557C2×D61116yescomplemented
429#541—6132no—
430#541—6164no—
431#541—6132no—
432#541—6132no—
433#541—6132no—
434#533—6116no—
435#533—6116no—
436#533—6116no—
437C2×C4⋊Q8—611no—
438C2×C4⋊Q8—611no—
439C2×C4⋊Q8—612no—
440C2×C4⋊Q8—612no—
441C2×C4⋊Q8—611no—
442C2×C4⋊Q8—611no—
443C2×C4⋊Q8—614no—
444C2×C4⋊Q8—611no—
445C2×C4⋊Q8—612no—
446C2×C4⋊Q8C2×D6111yescharacteristic
447C2×C4⋊Q8C2×D6112yes—
448C2×#126—614no—
449C2×#126—614no—
450C2×#126—614no—
451C2×#126—614no—
452C2×#125—612no—
453C2×#125—612no—
454C2×#125—614no—
455C2×#125—614no—
456C2×#125—614no—
457C2×#125—614no—
458C2×#125—614no—
459C2×#125—614no—
460C2×#125—614no—
461C2×#125—612no—
462C2×#125—612no—
463C2×#125—612no—
464C2×#125—614no—
465C2×#125—614no—
466C2×#125—614no—
467C2×#125—612no—
468C2×#125—614no—
469C2×#125—614no—
470C2×#125C2×D6112yes—
471C2×#125C2×D6114yes—
472C2×C22⋊Q8—611no—
473C2×C22⋊Q8—612no—
474C2×C22⋊Q8—611no—
475C2×C22⋊Q8—612no—
476C2×C22⋊Q8—612no—
477C2×C22⋊Q8—612no—
478C2×C22⋊Q8—611no—
479C2×C22⋊Q8—611no—
480C2×C4×Q8—612no—
481C2×C4×Q8—612no—
482C2×C4×Q8—612no—
483C2×C4×Q8—612no—
484C2×C4×Q8—614no—
485C2×C4×Q8—612no—
486C2×C4×Q8—612no—
487C2×C4×Q8—611no—
488C2×C4×Q8—611no—
489C2×C4×Q8—612no—
490C2×C4×Q8—612no—
491C2×C4×Q8—614no—
492C2×C4×Q8—612no—
493C2×C4×Q8—612no—
494C2×C4×Q8C2×D6111yescharacteristic
495C2×C4×Q8C2×D6111yescharacteristic
496C2×C4×Q8C2×D6112yes—
497C2×C4×Q8C2×D6112yes—
498C2×#117—612no—
499C2×#117—612no—
500C2×#117—612no—
501C22×C42—611no—
502C61C2×#355611yescharacteristic, complemented, Sylow
503C22×Q8—612no—
504C22×Q8—612no—
505C22×Q8—611no—
506C22×Q8—612no—
507C22×Q8—611no—
508C22×Q8C22×D6112yes—
509C22×Q8C22×D6111yescharacteristic
510C22×Q8C22×D6111yescharacteristic
511C23×C4—611no—
512C23×C4—611no—
513C23×C4—611no—
514C4⋊Q8—618no—
515C4⋊Q8—618no—
516C4⋊Q8—6116no—
517C4⋊Q8—6116no—
518C4⋊Q8—618no—
519C4⋊Q8—618no—
520C4⋊Q8—6132no—
521C4⋊Q8—618no—
522C4⋊Q8—6116no—
523C4⋊Q8C22×D6118yes—
524C4⋊Q8C22×D61116yes—
525#126—6132no—
526#126—6132no—
527#126—6132no—
528#126—6132no—
529#125—6116no—
530#125—6116no—
531#125—6116no—
532#125—6132no—
533#125—6116no—
534#125—6116no—
535#125—6132no—
536#125—6132no—
537#125—6132no—
538#125—6132no—
539#125—6132no—
540#125—6132no—
541#125—6132no—
542#125—6132no—
543#125—6132no—
544#125—6116no—
545#125—6132no—
546#125—6132no—
547#125C22×D61116yes—
548#125C22×D61132yes—
549C22⋊Q8—6116no—
550C22⋊Q8—618no—
551C22⋊Q8—618no—
552C22⋊Q8—6116no—
553C22⋊Q8—6116no—
554C22⋊Q8—6116no—
555C22⋊Q8—618no—
556C22⋊Q8—618no—
557C4×Q8—6116no—
558C4×Q8—6116no—
559C4×Q8—6116no—
560C4×Q8—6116no—
561C4×Q8—6132no—
562C4×Q8—6116no—
563C4×Q8—6116no—
564C4×Q8—6116no—
565C4×Q8—6116no—
566C4×Q8—618no—
567C4×Q8—618no—
568C4×Q8—6132no—
569C4×Q8—6116no—
570C4×Q8—6116no—
571C4×Q8C22×D6118yes—
572C4×Q8C22×D6118yes—
573C4×Q8C22×D61116yes—
574C4×Q8C22×D61116yes—
575#117—6116no—
576#117—6116no—
577#117—6116no—
578C2×C4⋊C4—612no—
579C2×C4⋊C4—612no—
580C2×C4⋊C4—612no—
581C2×C4⋊C4—612no—
582C2×C4⋊C4—612no—
583C2×C4⋊C4—612no—
584C2×C4⋊C4—612no—
585C2×C4⋊C4—612no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—612no—
589C2×C4⋊C4—612no—
590C2×C4⋊C4—614no—
591C2×C4⋊C4—612no—
592C2×C4⋊C4—612no—
593C2×C4⋊C4—614no—
594C2×C4⋊C4—612no—
595C2×C4⋊C4—612no—
596C2×C4⋊C4—614no—
597C2×C4⋊C4—614no—
598C2×C4⋊C4—614no—
599C2×C4⋊C4—614no—
600C2×C4⋊C4—614no—
601C2×C4⋊C4—614no—
602C2×C4⋊C4—614no—
603C2×C4⋊C4—614no—
604C2×C4⋊C4—614no—
605C2×C4⋊C4C22×D6112yes—
606C2×C4⋊C4C22×D6112yes—
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C4⋊C4C22×D6114yes—
609C2×C4⋊C4C22×D6111yescharacteristic
610C2×C4⋊C4C22×D6112yes—
611C2×C4⋊C4C22×D6112yes—
612C2×C4⋊C4C22×D6114yes—
613C2×C4⋊C4C22×D6114yes—
614C2×C22⋊C4—614no—
615C2×C22⋊C4—612no—
616C2×C22⋊C4—612no—
617C2×C22⋊C4—612no—
618C2×C22⋊C4—612no—
619C2×C42—614no—
620C2×C42—612no—
621C2×C42—612no—
622C2×C42—611no—
623C2×C42—611no—
624C2×C42—614no—
625C2×C42—614no—
626C2×C42—614no—
627C2×C42—611no—
628C2×C42—618no—
629C2×C42C22×D6112yes—
630C2×C42C22×D6112yes—
631C2×C42C22×D6111yescharacteristic
632C2×C42C22×D6114yes—
633C24—611no—
634C2×Q8—28no—
635C2×Q8—24no—
636C2×Q8—24no—
637C2×Q8—618no—
638C2×Q8—618no—
639C2×Q8—614no—
640C2×Q8—618no—
641C2×Q8—614no—
642C2×Q8—1228no—
643C2×Q8—1228no—
644C2×Q8—1224no—
645C2×Q8—1228no—
646C2×Q8—1224no—
647C2×Q8C23×D6118yes—
648C2×Q8C23×D6114yes—
649C2×Q8C23×D6114yes—
650C22×C4—611no—
651C22×C4—612no—
652C22×C4—612no—
653C22×C4—612no—
654C22×C4—612no—
655C22×C4—614no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—614no—
659C22×C4—614no—
660C22×C4—614no—
661C22×C4—1224no—
662C22×C4—1224no—
663C22×C4—1224no—
664C22×C4C23×D6114yes—
665C22×C4C23×D6112yes—
666C22×C4C23×D6112yes—
667C22×C4C23×D6111yescharacteristic
668C22×C4C23×D6112yes—
669C22×C4C23×D6112yes—
670C22×C4C23×D6111yescharacteristic
671C22×C4C23×D6111yescharacteristic
672C4⋊C4—618no—
673C4⋊C4—618no—
674C4⋊C4—618no—
675C4⋊C4—618no—
676C4⋊C4—618no—
677C4⋊C4—618no—
678C4⋊C4—618no—
679C4⋊C4—618no—
680C4⋊C4—6116no—
681C4⋊C4—618no—
682C4⋊C4—618no—
683C4⋊C4—6116no—
684C4⋊C4—6116no—
685C4⋊C4—6116no—
686C4⋊C4—6116no—
687C4⋊C4—6116no—
688C4⋊C4—6116no—
689C4⋊C4—618no—
690C4⋊C4—618no—
691C4⋊C4—614no—
692C4⋊C4—614no—
693C4⋊C4—6116no—
694C4⋊C4—618no—
695C4⋊C4—618no—
696C4⋊C4—6116no—
697C4⋊C4—6116no—
698C4⋊C4—6116no—
699C4⋊C4C23×D6118yes—
700C4⋊C4C23×D6118yes—
701C4⋊C4C23×D6114yes—
702C4⋊C4C23×D61116yes—
703C4⋊C4C23×D6114yes—
704C4⋊C4C23×D6118yes—
705C4⋊C4C23×D6118yes—
706C4⋊C4C23×D61116yes—
707C4⋊C4C23×D61116yes—
708C22⋊C4—6116no—
709C22⋊C4—618no—
710C22⋊C4—618no—
711C22⋊C4—618no—
712C22⋊C4—618no—
713C42—614no—
714C42—614no—
715C42—614no—
716C42—6116no—
717C42—618no—
718C42—618no—
719C42—6116no—
720C42—6116no—
721C42—6116no—
722C42C23×D6114yes—
723C42C23×D6118yes—
724C42C23×D6118yes—
725C42C23×D61116yes—
726C23—612no—
727C23—1222no—
728C23—1222no—
729C23—1222no—
730C23C24×D6111yescharacteristic
731Q8—216no—
732Q8—28no—
733Q8—28no—
734Q8—12216no—
735Q8—12216no—
736Q8—1228no—
737Q8—12216no—
738Q8—1228no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—614no—
746C2×C4—612no—
747C2×C4—614no—
748C2×C4—614no—
749C2×C4—614no—
750C2×C4—614no—
751C2×C4—618no—
752C2×C4—612no—
753C2×C4—612no—
754C2×C4—1228no—
755C2×C4—1224no—
756C2×C4—1224no—
757C2×C4—1222no—
758C2×C4—1224no—
759C2×C4—1222no—
760C2×C4—1224no—
761C2×C4—1228no—
762C2×C4—1228no—
763C2×C4—1228no—
764C2×C4#1451982414yes—
765C2×C4#1451982514yes—
766C2×C4C24×D6118yes—
767C2×C4C24×D6114yes—
768C2×C4C24×D6114yes—
769C2×C4C24×D6112yes—
770C2×C4C24×D6114yes—
771C2×C4C24×D6114yes—
772C2×C4C24×D6112yes—
773C2×C4C24×D6112yes—
774C22—1222no—
775C22—1222no—
776C22—1222no—
777C22—2444no—
778C222−1+4×D6112yes—
779C22C2×#1451982412yes—
780C22C2×#1451982512yes—
781C22C25×D6111yescharacteristic
782C4—22no—
783C4—24no—
784C4—24no—
785C4—28no—
786C4—24no—
787C4—24no—
788C4—614no—
789C4—1224no—
790C4—1224no—
791C4—1222no—
792C4—1224no—
793C4—1222no—
794C4—1224no—
795C4—1228no—
796C4C2×#1451982414yes—
797C4C2×#1451982514yes—
798C2—2442no—
799C2#2146031114yesdirect product factor
800C2C2×2−1+4×D6111yescharacteristic
801C2C22×#1451982411yescharacteristic
802C2C22×#1451982511yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#557C2
socleC23×C61C25
prime radicalC23×D61C24
hypercenterC2×#557D61
hypocenterC61C2×#3556
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #21460311C2direct (N × H)
2. C2×C61⋊#564C2semidirect
3. C2×#16840491C2semidirect
4. C2×#16840490C2semidirect
5. C2×#16840490C2semidirect
6. C2×#16840489C2semidirect
7. C2×#16840488C2semidirect
8. C2×#16840487C2semidirect
9. C2×#16840487C2semidirect
18. C2×C61×#557C2semidirect
19. C61⋊#564C22semidirect
20. #16840491C22semidirect
21. #16840490C22semidirect
22. #16840490C22semidirect
23. #16840489C22semidirect
24. #16840488C22semidirect
25. #16840487C22semidirect
26. #16840487C22semidirect
92. C61×#557C22semidirect
406. C2×#557D61semidirect
415. C2×C61#3556semidirect
428. #557C2×D61semidirect
502. C61C2×#3556semidirect
799. C2#21460311direct (N × H)

Maximal subgroups

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

subgroupindex
#214603112
C2×C61⋊#5642
C2×#168404912
C2×#168404902
C2×#168404892
C2×#168404882
C2×#168404872
C2×#168403752
C2×#168403732
C2×#168403712
C2×#168403702
C2×#168403172
C2×#168403162
C2×C61×#5572
C2×#355661