Finite Group Databasebeta

← #30617413

Subgroups — #30617413

Order 15616.

826 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462314C211yesmaximal, characteristic, complemented
2#21462309C211yesmaximal, characteristic
3#21462000C211yesmaximal, characteristic, complemented
4#21461948C211yesmaximal, characteristic
5#21461911C211yesmaximal, characteristic
6#21461910C211yesmaximal, characteristic, complemented
7#21461909C211yesmaximal, characteristic
8#21461908C211yesmaximal, characteristic, complemented
9#21461742C211yesmaximal, characteristic, complemented
10#21461592C211yesmaximal, characteristic, complemented
11#21461590C211yesmaximal, characteristic
12#103×#6923C211yesmaximal, characteristic, complemented
13#102×#6923C211yesmaximal, characteristic
14#21461477C211yesmaximal, characteristic, complemented
15#489×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519840C2211yescharacteristic
19C2×#14519840C2211yescharacteristic
20C2×#14519839C2211yescharacteristic
21C2×#14519839C2211yescharacteristic
22C2×#14519831C2211yescharacteristic
23C2×#14519831C2211yescharacteristic
24C4×D61⋊C8C2211yescharacteristic
25C2×C8×#6923C2211yescharacteristic
26C2×C8×#6923C2211yescharacteristic
27(C2×#6923)⋊Q8—21no—
28(C2×#6923)⋊Q8—21no—
29(C2×#6923)⋊Q8C2211yescharacteristic
30#16840714C2211yescharacteristic
31#16840713C2211yescharacteristic
32#16840713C2211yescharacteristic
33#16840712—21no—
34#16840712—21no—
35#16840711—21no—
36#16840711—21no—
37#16840709—21no—
38#16840709—21no—
39#16840708C2211yescharacteristic
40#16840706C2211yescharacteristic
41C4⋊C4×#6923C2211yescharacteristic
42C4⋊C4×#6923C2211yescharacteristic
43#16840698C2211yescharacteristic
44#16840636C2211yescharacteristic
45#16840636C2211yescharacteristic
46#16840636C2211yescharacteristic
47#16840636C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52C4⋊Q8×D61C2211yescharacteristic
53#124×D61C2211yescharacteristic
54#16840124C411yescharacteristic, complemented
55#16840123C411yescharacteristic, complemented
56#16840123C411yescharacteristic, complemented
57#16840122C411yescharacteristic, complemented
58#16840121C411yescharacteristic, complemented
59#16840120C411yescharacteristic, complemented
60#16840120C411yescharacteristic, complemented
61#103×D61C2211yescharacteristic
62#103×D61C2211yescharacteristic
63#102×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#97×D61C2211yescharacteristic
66C61×#489C411yescharacteristic, complemented
67C23×#6923—21no—
68C2×D61⋊C8C2311yescharacteristic
69C2×D61⋊C8C2311yescharacteristic
70Q8×#6923—22no—
71Q8×#6923—22no—
72D4×#6923—22no—
73D4×#6923—22no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923C2311yescharacteristic
90C2×C4×#6923C2311yescharacteristic
91#14519840—22no—
92#14519840—22no—
93#14519839—22no—
94#14519839—22no—
95#14519831—22no—
96#14519831—22no—
97C4×#92420—21no—
98C4×#92420—21no—
99C8×#6923—22no—
100C8×#6923—22no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4D411yescharacteristic
110(C2×#6923)⋊C4D411yescharacteristic
111(C2×#6923)⋊C4D411yescharacteristic
112(C2×#6923)⋊C4D411yescharacteristic
113C2×Q8×D61—21no—
114C2×Q8×D61C2311yescharacteristic
115C2×D4×D61C2311yescharacteristic
116C2×C8×D61C2311yescharacteristic
117C2×C8×D61C2311yescharacteristic
118#14519777C2×C411yescharacteristic, complemented
119#14519776—21no—
120#14519776C2×C411yescharacteristic, complemented
121#14519776C2×C411yescharacteristic, complemented
122#14519775—21no—
123#14519766C2×C411yescharacteristic
124#14519765C2×C411yescharacteristic
125#14519764C2×C411yescharacteristic
126#14519763—21no—
127#14519763—21no—
128C4⋊C4×D61—21no—
129C4⋊C4×D61C2311yescharacteristic
130C4⋊C4×D61C2311yescharacteristic
131C22⋊C4×D61—21no—
132C22⋊C4×D61—21no—
133C42×D61C2311yescharacteristic
134#14519702C2×C411yescharacteristic, complemented
135#14519702C2×C411yescharacteristic, complemented
136#14519701C2×C411yescharacteristic, complemented
137#14519701C2×C411yescharacteristic, complemented
138#14519700C2×C411yescharacteristic, complemented
139#14519700C2×C411yescharacteristic, complemented
140#14519699C2×C411yescharacteristic
141#14519699C2×C411yescharacteristic
142#14519698C2×C411yescharacteristic
143#14519698C2×C411yescharacteristic
144#14519697C2×C411yescharacteristic
145#14519697C2×C411yescharacteristic
146#14519688C2×C411yescharacteristic, complemented
147#14519687C2×C411yescharacteristic, complemented
148#14519687C2×C411yescharacteristic, complemented
149C4⋊Q8×C61C2×C411yescharacteristic, complemented
150#124×C61C2×C411yescharacteristic
151#103×C61C2×C411yescharacteristic, complemented
152#103×C61C2×C411yescharacteristic, complemented
153#102×C61C2×C411yescharacteristic
154#102×C61C2×C411yescharacteristic
155#97×C61C2×C411yescharacteristic, complemented
156C23×D61—21no—
157C22×#6923—21no—
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923—42no—
162C22×#6923—81no—
163C22×#6923—81no—
164C22×#6923C2×D411yescharacteristic
165C22×#6923C2×D411yescharacteristic
166C22×#6923C2×D411yescharacteristic
167C22×#6923C2×D411yescharacteristic
168C2×Q8×C61—21no—
169C2×Q8×C61C22×C411yescharacteristic
170C2×D4×C61C22×C411yescharacteristic
171C2×C22⋊D61—21no—
172Q8×D61—21no—
173Q8×D61—21no—
174Q8×D61—21no—
175Q8×D61—21no—
176Q8×D61—81no—
177Q8×D61—81no—
178D4×D61—21no—
179D4×D61—21no—
180D4×D61—21no—
181D4×D61—21no—
182C2×D244C22×C411yescharacteristic
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61C2×D411yescharacteristic
187C2×C4×D61C2×D411yescharacteristic
188C2×C4×D61C2411yescharacteristic
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122C22×C411yescharacteristic
194C22⋊#6923—42no—
195C22⋊#6923—81no—
196C22⋊#6923—81no—
197C2×#92420—21no—
198C2×#92420—21no—
199C4⋊#6923—21no—
200C4⋊#6923—21no—
201C4⋊#6923—21no—
202C4⋊#6923—21no—
203C4⋊#6923—21no—
204C4⋊#6923—21no—
205C4⋊#6923—21no—
206C4⋊#6923—21no—
207C4⋊#6923—42no—
208C4⋊#6923—81no—
209C4⋊#6923—81no—
210C4⋊#6923—81no—
211C4⋊#6923—81no—
212C4×#6923—21no—
213C4×#6923—21no—
214C4×#6923—42no—
215C4×#6923—81no—
216C4×#6923—81no—
217C4×#6923#4112yes—
218C4×#6923#4112yes—
219D61⋊C8—21no—
220D61⋊C8—21no—
221D61⋊C8#4112yes—
222D61⋊C8#4112yes—
223C2×C8×C61C22×C411yescharacteristic
224C2×C8×C61C22×C411yescharacteristic
225C4⋊C4×C61—21no—
226C4⋊C4×C61C22×C411yescharacteristic
227C4⋊C4×C61C22×C411yescharacteristic
228C22⋊C4×C61—21no—
229C22⋊C4×C61—21no—
230C42×C61C22×C411yescharacteristic
231C22⋊Dic61—21no—
232C22⋊Dic61—21no—
233#11758198—21no—
234#11758198—21no—
235#11758198—21no—
236#11758198—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61C22×C411yescharacteristic
239C4⋊Dic61C22×C411yescharacteristic
240#11758196—21no—
241#11758196—21no—
242#11758196—21no—
243#11758196—21no—
244C4×Dic61C22×C411yescharacteristic
245C4×Dic61#4111yescharacteristic
246C4×Dic61#4111yescharacteristic
247C2×#92418C22×C411yescharacteristic
248C2×#92418C22×C411yescharacteristic
249C8×D61—21no—
250C8×D61—21no—
251C8×D61—21no—
252C8×D61—21no—
253C23×C61—21no—
254C22×D61—21no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61C22×D411yescharacteristic
262C2×#6923—21no—
263C2×#6923—21no—
264C2×#6923—21no—
265C2×#6923—21no—
266C2×#6923—21no—
267C2×#6923—21no—
268C2×#6923—21no—
269C2×#6923—21no—
270C2×#6923—21no—
271C2×#6923—21no—
272C2×#6923—41no—
273C2×#6923—41no—
274C2×#6923—41no—
275C2×#6923—41no—
276C2×#6923—41no—
277C2×#6923—41no—
278C2×#6923—41no—
279C2×#6923—41no—
280C2×#6923—41no—
281C2×#6923—41no—
282C2×#6923—41no—
283C2×#6923—41no—
284C2×#6923—84no—
285C2×#6923#12412yes—
286C2×#6923#12412yes—
287Q8×C61—21no—
288Q8×C61—21no—
289Q8×C61—81no—
290D4×C61—21no—
291D4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61C4×D411yescharacteristic
296C2×C4×C61C4×D411yescharacteristic
297C2×C4×C61C23×C411yescharacteristic
298C22⋊D61—41no—
299C22⋊D61—41no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61C4×D411yescharacteristic
304C2×Dic61C4×D411yescharacteristic
305C2×Dic61C2×#4111yescharacteristic
306D244—21no—
307D244—21no—
308C4×D61—21no—
309C4×D61—21no—
310C4×D61—21no—
311C4×D61—21no—
312C4×D61—41no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61C2×#4111yescharacteristic
319C4×D61C2×#4111yescharacteristic
320C4×D61C2×#4111yescharacteristic
321C4×D61C2×#4111yescharacteristic
322Dic122—21no—
323Dic122—21no—
324Dic122—41no—
325Dic122—41no—
326Dic122—81no—
327Dic122—81no—
328Dic122—81no—
329#92420—22no—
330#92420—22no—
331C8×C61—21no—
332C8×C61—21no—
333#92418—21no—
334#92418—21no—
335#21654—611nomaximal, Sylow
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61C2×C4×D411yescharacteristic
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—41no—
343C2×D61—81no—
344C2×D61—81no—
345C2×D61—81no—
346C2×D61—81no—
347C2×D61C2×#12411yescharacteristic
348C2×D61#53211yescharacteristic
349C2×D61#57611yescharacteristic
350C2×D61#57711yescharacteristic
351C2×D61#57711yescharacteristic
352C2×D61#57811yescharacteristic
353#6923—22no—
354#6923—22no—
355#6923—41no—
356#6923—41no—
357#6923—81no—
358#6923—81no—
359#6923—81no—
360#6923—81no—
361C4×C61—21no—
362C4×C61—21no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61C4×#4111yescharacteristic
367C4×C61C4×#4111yescharacteristic
368Dic61—21no—
369Dic61—21no—
370Dic61—41no—
371Dic61—41no—
372Dic61—41no—
373Dic61#52911yescharacteristic
374Dic61#52911yescharacteristic
375C2×#489—611no—
376#2331—611no—
377#2326—611no—
378#1990—611no—
379#1958—611no—
380#1936—611no—
381#1935—611no—
382#1934—611no—
383#1933—611no—
384#1836—611no—
385#1763—611no—
386#1762—611no—
387C4×#103—611no—
388C4×#102—611no—
389#1726—611no—
390C2×C61—81no—
391C2×C61C4×#12411yescharacteristic
392C2×C61#294611yescharacteristic
393C2×C61#294711yescharacteristic
394D61—81no—
395D61#313611yescharacteristic
396D61#313711yescharacteristic
397D61#317311yescharacteristic
398D61#317511yescharacteristic
399C2×C4⋊Q8—611no—
400C2×#124—611no—
401C2×C4×Q8—611no—
402C2×C4×D4—611no—
403#489—611no—
404#489—611no—
405#489—611no—
406#489—611no—
407#489—611no—
408#489—611no—
409#489—611no—
410#489#692311yescharacteristic, complemented
411C2×#103—611no—
412C2×#103—611no—
413C2×#103—611no—
414C2×#103—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#97—611no—
420C2×#97—611no—
421C2×#97—611no—
422C2×C4×C8—611no—
423C2×C4×C8—611no—
424C2×C4×C8—611no—
425#391—611no—
426#391—1221no—
427#391—1221no—
428#390—611no—
429#389—611no—
430#389—611no—
431#388—1221no—
432#388—1221no—
433#387—1221no—
434#387—1221no—
435#385—1221no—
436#385—1221no—
437#384—611no—
438#382—611no—
439C4×C4⋊C4—611no—
440C4×C4⋊C4—611no—
441#376—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#340—611no—
448#340—611no—
449#340—611no—
450C61#2165411yescharacteristic, complemented, Sylow
451C22×Q8—611no—
452C22×Q8—1221no—
453C22×D4—611no—
454C23×C4—1221no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—611no—
459C4⋊Q8—611no—
460C4⋊Q8—611no—
461C4⋊Q8—611no—
462C4⋊Q8—1221no—
463C4⋊Q8—1221no—
464C4⋊Q8C2×#692311yescharacteristic, complemented
465#124—611no—
466#124—611no—
467#124—611no—
468#124—1221no—
469#124—1221no—
470#124C2×#692311yescharacteristic
471C4×Q8—1222no—
472C4×Q8—1222no—
473C4×D4—1222no—
474C4×D4—1222no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—1221no—
496C2×C42—1221no—
497C2×C42—1221no—
498#103—611no—
499#103—611no—
500#103—611no—
501#103—611no—
502#103—611no—
503#103—611no—
504#103—1222no—
505#103—1222no—
506#103C2×#692311yescharacteristic, complemented
507#103C2×#692311yescharacteristic, complemented
508#102—611no—
509#102—611no—
510#102—611no—
511#102—611no—
512#102—611no—
513#102—611no—
514#102—1222no—
515#102—1222no—
516#102C2×#692311yescharacteristic
517#102C2×#692311yescharacteristic
518#97—611no—
519#97—611no—
520#97—611no—
521#97—1222no—
522#97—1222no—
523#97C2×#692311yescharacteristic, complemented
524C4×C8—1222no—
525C4×C8—1221no—
526C4×C8—1221no—
527C4×C8—1222no—
528#95—611no—
529#95—611no—
530#95—611no—
531#95—611no—
532#95—1221no—
533#95—1221no—
534#95—1221no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539#95—1221no—
540C24—1221no—
541C2×Q8—21no—
542C2×Q8—611no—
543C2×Q8—1221no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8—4881no—
552C2×Q8—4881no—
553C2×Q8C22×#692311yescharacteristic
554C2×D4—611no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4C22×#692311yescharacteristic
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—4881no—
576C22×C4—4881no—
577C22×C4—2442no—
578C2×C8—612no—
579C2×C8—612no—
580C2×C8—611no—
581C2×C8—611no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8C22×#692311yescharacteristic
591C2×C8C22×#692311yescharacteristic
592C4⋊C4—21no—
593C4⋊C4—611no—
594C4⋊C4—611no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—4881no—
609C4⋊C4—4881no—
610C4⋊C4—4881no—
611C4⋊C4—4881no—
612C4⋊C4—2442no—
613C4⋊C4C22×#692311yescharacteristic
614C4⋊C4C22×#692311yescharacteristic
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—1221no—
618C22⋊C4—1221no—
619C22⋊C4—1221no—
620C22⋊C4—1221no—
621C22⋊C4—1221no—
622C22⋊C4—1221no—
623C22⋊C4—4881no—
624C22⋊C4—4881no—
625C22⋊C4—2442no—
626C42—612no—
627C42—612no—
628C42—611no—
629C42—611no—
630C42—611no—
631C42—1221no—
632C42—1221no—
633C42—4881no—
634C42—4881no—
635C42—2442no—
636C42C22×#692311yescharacteristic
637C23—21no—
638C23—611no—
639C23—1221no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23—2441no—
646Q8—21no—
647Q8—21no—
648Q8—81no—
649Q8—1221no—
650Q8—1221no—
651Q8—4881no—
652Q8—4881no—
653Q8—4881no—
654Q8—2441no—
655Q8—2441no—
656D4—21no—
657D4—21no—
658D4—1221no—
659D4—1221no—
660D4—2441no—
661D4—2441no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—611no—
666C2×C4—611no—
667C2×C4—611no—
668C2×C4—611no—
669C2×C4—611no—
670C2×C4—612no—
671C2×C4—612no—
672C2×C4—611no—
673C2×C4—611no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—4884no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4D4×#692311yescharacteristic
711C2×C4D4×#692311yescharacteristic
712C2×C4C23×#692311yescharacteristic
713C8—21no—
714C8—21no—
715C8—1222no—
716C8—1222no—
717C8—1221no—
718C8—1221no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—611no—
723C22—611no—
724C22—611no—
725C22—611no—
726C22—611no—
727C22—611no—
728C22—4881no—
729C22—4881no—
730C22—4881no—
731C22—4881no—
732C22—2441no—
733C22—2441no—
734C22—2441no—
735C22C2×D4×#692311yescharacteristic
736C4—21no—
737C4—21no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—611no—
742C4—611no—
743C4—1222no—
744C4—1222no—
745C4—1221no—
746C4—1221no—
747C4—4881no—
748C4—4881no—
749C4—4881no—
750C4—4881no—
751C4—2441no—
752C4—2441no—
753C4—2441no—
754C4—2441no—
755C4—2441no—
756C4#41×#692311yescharacteristic
757C4#41×#692311yescharacteristic
758C2—81no—
759C2—611no—
760C2—611no—
761C2—611no—
762C2—611no—
763C2—4881no—
764C2#124×#692311yescharacteristic
765C2#2146257611yescharacteristic
766C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#489C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#489#6923
hypocenterC61#21654
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #21462314C2semidirect
3. #21462000C2semidirect
6. #21461910C2semidirect
8. #21461908C2semidirect
9. #21461742C2semidirect
10. #21461592C2semidirect
12. #103×#6923C2semidirect
14. #21461477C2semidirect
54. #16840124C4semidirect
55. #16840123C4semidirect
56. #16840123C4semidirect
57. #16840122C4semidirect
58. #16840121C4semidirect
59. #16840120C4semidirect
60. #16840120C4semidirect
66. C61×#489C4semidirect
118. #14519777C2×C4semidirect
120. #14519776C2×C4semidirect
121. #14519776C2×C4semidirect
134. #14519702C2×C4semidirect
135. #14519702C2×C4semidirect
136. #14519701C2×C4semidirect
137. #14519701C2×C4semidirect
138. #14519700C2×C4semidirect
139. #14519700C2×C4semidirect
146. #14519688C2×C4semidirect
147. #14519687C2×C4semidirect
148. #14519687C2×C4semidirect
149. C4⋊Q8×C61C2×C4semidirect
151. #103×C61C2×C4semidirect
152. #103×C61C2×C4semidirect
155. #97×C61C2×C4semidirect
410. #489#6923semidirect
450. C61#21654semidirect
464. C4⋊Q8C2×#6923semidirect
506. #103C2×#6923semidirect
507. #103C2×#6923semidirect
523. #97C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623142
#214623092
#214620002
#214619482
#214619112
#214619102
#214619092
#214619082
#214617422
#214615922
#214615902
#103×#69232
#102×#69232
#214614772
#489×D612
#2165461