Finite Group Databasebeta

← #30622090

Subgroups — #30622090

Order 15616.

850 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462352C211yesmaximal, characteristic, complemented
2#21462332C211yesmaximal, characteristic
3#21462003C211yesmaximal, characteristic, complemented
4#21461932C211yesmaximal, characteristic, complemented
5#21461924C211yesmaximal, characteristic, complemented
6#21461923C211yesmaximal, characteristic, complemented
7#21461883C211yesmaximal, characteristic, complemented
8#21461880C211yesmaximal, characteristic, complemented
9#21461784C211yesmaximal, characteristic
10#21461782C211yesmaximal, characteristic
11#21461620C211yesmaximal, characteristic, complemented
12#21461590C211yesmaximal, characteristic
13#21461589C211yesmaximal, characteristic
14#102×#6923C211yesmaximal, characteristic
15#474×D61C211yesmaximal, characteristic
16C2×D4×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519846C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20C2×#14519839C2211yescharacteristic
21C2×#14519839C2211yescharacteristic
22#16840721C2211yescharacteristic
23C2×#14519831C2211yescharacteristic
24C2×C8×#6923C2211yescharacteristic
25(C2×#6923)⋊Q8—21no—
26(C2×#6923)⋊Q8—21no—
27#16840713—21no—
28#16840713C2211yescharacteristic
29#16840713C2211yescharacteristic
30#16840713C2211yescharacteristic
31#16840713C2211yescharacteristic
32#16840709—21no—
33#16840709—21no—
34#16840706C2211yescharacteristic
35#16840704—21no—
36C4⋊C4×#6923—21no—
37C4⋊C4×#6923C2211yescharacteristic
38C4⋊C4×#6923C2211yescharacteristic
39C4×C4⋊#6923C2211yescharacteristic
40C4×C4⋊#6923C2211yescharacteristic
41C2×(C2×#6923)⋊C4—21no—
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C4⋊Q8×D61C2211yescharacteristic
53C4×D4×D61C2211yescharacteristic
54#16840043C411yescharacteristic, complemented
55#16840042C411yescharacteristic, complemented
56#16840041C411yescharacteristic, complemented
57#16840041C411yescharacteristic, complemented
58#16840040C411yescharacteristic, complemented
59#16840040C411yescharacteristic, complemented
60#16840039C411yescharacteristic, complemented
61#107×D61C2211yescharacteristic
62#107×D61C2211yescharacteristic
63C4⋊C8×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#474C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73D4×#6923—41no—
74D4×#6923—41no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923D411yescharacteristic
80C2×C4⋊#6923D411yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923C2311yescharacteristic
91C2×C4×#6923C2311yescharacteristic
92#14519846—41no—
93#14519845—41no—
94#14519839—22no—
95#14519839Q814yescomplemented
96#14519832—21no—
97#14519832—21no—
98#14519831—41no—
99C8×#6923—41no—
100(C2×#6923)⋊C4—21no—
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
111C2×Q8×D61—21no—
112C2×D4×D61C2311yescharacteristic
113C22×C4×D61—21no—
114C2×C8×D61C2311yescharacteristic
115C2×C8×D61C2311yescharacteristic
116#14519777C2×C411yescharacteristic, complemented
117#14519776—21no—
118#14519776C2×C411yescharacteristic, complemented
119#14519776C2×C411yescharacteristic, complemented
120#14519775—21no—
121C4×D244C2×C411yescharacteristic
122D4×Dic61C2×C411yescharacteristic
123#14519739C2×C411yescharacteristic
124C4×C22⋊D61—21no—
125#14519737—21no—
126C4⋊C4×D61—21no—
127C4⋊C4×D61C2311yescharacteristic
128C4⋊C4×D61C2311yescharacteristic
129C4⋊C4×D61C2311yescharacteristic
130C22⋊C4×D61—21no—
131C42×D61C2311yescharacteristic
132#14519711C2×C411yescharacteristic, complemented
133#14519711C2×C411yescharacteristic, complemented
134#14519710C2×C411yescharacteristic, complemented
135#14519710C2×C411yescharacteristic, complemented
136#14519710C2×C411yescharacteristic, complemented
137#14519710C2×C411yescharacteristic, complemented
138C4⋊#92418C2×C411yescharacteristic, complemented
139#14519706C2×C411yescharacteristic, complemented
140#14519706C2×C411yescharacteristic, complemented
141#14519699C2×C411yescharacteristic
142#14519699C2×C411yescharacteristic
143#14519698C2×C411yescharacteristic
144#14519698C2×C411yescharacteristic
145#14519697C2×C411yescharacteristic
146#14519697C2×C411yescharacteristic
147C4⋊Q8×C61C2×C411yescharacteristic, complemented
148C4×D4×C61C2×C411yescharacteristic
149#107×C61C2×C411yescharacteristic, complemented
150#107×C61C2×C411yescharacteristic, complemented
151C4⋊C8×C61C2×C411yescharacteristic, complemented
152#102×C61C2×C411yescharacteristic
153#102×C61C2×C411yescharacteristic
154C23×D61—21no—
155C22×#6923—21no—
156C22×#6923—21no—
157C22×#6923—21no—
158C22×#6923—21no—
159C22×#6923—42no—
160C22×#6923—42no—
161C22×#6923—42no—
162C22×#6923—42no—
163C22×#6923—81no—
164C22×#6923—81no—
165C22×#6923C2×D411yescharacteristic
166C22×#6923C2×D411yescharacteristic
167C22×#6923C2×D411yescharacteristic
168C22×#6923C2×D411yescharacteristic
169C2×Q8×C61—21no—
170C2×D4×C61C22×C411yescharacteristic
171C22×C4×C61—21no—
172C2×C22⋊D61—21no—
173C22×Dic61—21no—
174Q8×D61—81no—
175Q8×D61—81no—
176D4×D61—21no—
177D4×D61—21no—
178D4×D61C2×Q812yes—
179D4×D61#4112yes—
180C2×D244C22×C411yescharacteristic
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—81no—
187C2×C4×D61—81no—
188C2×C4×D61C2×D411yescharacteristic
189C2×C4×D61C2×D411yescharacteristic
190C2×C4×D61C2411yescharacteristic
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C22⋊#6923—42no—
195C22⋊#6923—42no—
196C2×#92420—21no—
197C2×#92420—21no—
198C4⋊#6923—22no—
199C4⋊#6923—21no—
200C4⋊#6923—21no—
201C4⋊#6923—21no—
202C4⋊#6923—21no—
203C4⋊#6923—21no—
204C4⋊#6923—21no—
205C4⋊#6923—21no—
206C4⋊#6923—41no—
207C4⋊#6923—81no—
208C4⋊#6923—81no—
209C4⋊#6923—81no—
210C4⋊#6923—81no—
211C4⋊#6923C2×Q812yes—
212C4×#6923—21no—
213C4×#6923—21no—
214C4×#6923—21no—
215C4×#6923—21no—
216C4×#6923—42no—
217C4×#6923—81no—
218C4×#6923—81no—
219D61⋊C8—21no—
220D61⋊C8—21no—
221D61⋊C8—21no—
222D61⋊C8C2×Q812yes—
223C2×C8×C61C22×C411yescharacteristic
224C2×C8×C61C22×C411yescharacteristic
225C4⋊C4×C61—21no—
226C4⋊C4×C61C22×C411yescharacteristic
227C4⋊C4×C61C22×C411yescharacteristic
228C4⋊C4×C61C22×C411yescharacteristic
229C22⋊C4×C61—21no—
230C42×C61C22×C411yescharacteristic
231C22⋊Dic61—21no—
232#11758198—21no—
233#11758198—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61C22×C411yescharacteristic
236C4⋊Dic61C22×C411yescharacteristic
237C4⋊Dic61C22×C411yescharacteristic
238#11758196—21no—
239#11758196—21no—
240#11758196—21no—
241#11758196—21no—
242#11758196—21no—
243C4×Dic61C22×C411yescharacteristic
244C4×Dic61#4111yescharacteristic
245C4×Dic61#4111yescharacteristic
246C2×#92418C22×C411yescharacteristic
247C2×#92418C22×C411yescharacteristic
248C8×D61—21no—
249C8×D61—21no—
250C8×D61—21no—
251C8×D61—21no—
252C23×C61—21no—
253C22×D61—21no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61C22×D411yescharacteristic
261C2×#6923—21no—
262C2×#6923—21no—
263C2×#6923—21no—
264C2×#6923—21no—
265C2×#6923—21no—
266C2×#6923—22no—
267C2×#6923—21no—
268C2×#6923—21no—
269C2×#6923—21no—
270C2×#6923—21no—
271C2×#6923—21no—
272C2×#6923—21no—
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—84no—
286C2×#6923#13712yes—
287Q8×C61—81no—
288D4×C61—21no—
289D4×C61C4×Q812yes—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—81no—
294C2×C4×C61C4×D411yescharacteristic
295C2×C4×C61C4×D411yescharacteristic
296C2×C4×C61C23×C411yescharacteristic
297C22⋊D61—22no—
298C22⋊D61—22no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—81no—
303C2×Dic61C4×D411yescharacteristic
304C2×Dic61C4×D411yescharacteristic
305C2×Dic61C2×#4111yescharacteristic
306D244—21no—
307D244C4×Q812yes—
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×D61—81no—
319C4×D61—81no—
320C4×D61C22×Q811yescharacteristic
321C4×D61C2×#4111yescharacteristic
322C4×D61H(5,𝔽2)11yescharacteristic
323C4×D612−1+411yescharacteristic
324Dic122—81no—
325Dic122—81no—
326Dic122—81no—
327#92420—22no—
328#92420—41no—
329C8×C61—21no—
330C8×C61—21no—
331#92418—21no—
332#92418—21no—
333#22979—611nomaximal, Sylow
334C22×C61—22no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61C2×C4×D411yescharacteristic
338C2×D61—22no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—42no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61#54611yescharacteristic
346C2×D61D4×Q811yescharacteristic
347C2×D61C2×#13711yescharacteristic
348C2×D61#57511yescharacteristic
349C2×D61#57611yescharacteristic
350C2×D61#57611yescharacteristic
351#6923—22no—
352#6923—42no—
353#6923—41no—
354#6923—41no—
355#6923—41no—
356#6923—81no—
357#6923—81no—
358#6923—81no—
359C4×C61—21no—
360C4×C61—21no—
361C4×C61—41no—
362C4×C61—41no—
363C4×C61—41no—
364C4×C61C2×C4×Q811yescharacteristic
365C4×C61#52011yescharacteristic
366Dic61—21no—
367Dic61—21no—
368Dic61—41no—
369Dic61—41no—
370Dic61—41no—
371Dic61#55211yescharacteristic
372Dic61#55411yescharacteristic
373C2×#474—611no—
374#2369—611no—
375#2349—611no—
376#1993—611no—
377#1949—611no—
378#1943—611no—
379#1942—611no—
380#1921—611no—
381#1918—611no—
382#1864—611no—
383#1862—611no—
384#1771—611no—
385#1762—611no—
386#1762—611no—
387C4×#102—611no—
388C2×C61—42no—
389C2×C61#236011yescharacteristic
390C2×C61C4×#13711yescharacteristic
391C2×C61#294811yescharacteristic
392D61—42no—
393D61#331411yescharacteristic
394D61#331911yescharacteristic
395D61#338511yescharacteristic
396D61#338911yescharacteristic
397C2×C4⋊Q8—611no—
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C2×C4×D4—611no—
401#474—611no—
402#474—611no—
403#474—611no—
404#474—611no—
405#474—611no—
406#474—611no—
407#474—611no—
408#474#692311yescharacteristic, complemented
409C2×#107—611no—
410C2×#107—611no—
411C2×#107—611no—
412C2×#106—611no—
413C2×C4⋊C8—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×#97—611no—
419C2×#97—611no—
420C2×C4×C8—611no—
421#391—1221no—
422#391—1221no—
423#389—611no—
424#389—611no—
425#389—611no—
426#389—611no—
427#389—1221no—
428#385—1221no—
429#385—1221no—
430#382—611no—
431#380—1221no—
432C4×C4⋊C4—611no—
433C4×C4⋊C4—611no—
434C4×C4⋊C4—611no—
435C4×C4⋊C4—611no—
436C4×C4⋊C4—1221no—
437C2×#95—1221no—
438#340—611no—
439#340—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#336—611no—
447#336—611no—
448C61#2297911yescharacteristic, complemented, Sylow
449C22×Q8—1221no—
450C22×D4—611no—
451C23×C4—1221no—
452C23×C4—1221no—
453C23×C4—1221no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458C4⋊Q8—611no—
459C4⋊Q8—611no—
460C4⋊Q8—611no—
461C4⋊Q8—1221no—
462C4⋊Q8—1221no—
463C4⋊Q8C2×#692311yescharacteristic, complemented
464C4×D4—611no—
465C4×D4—611no—
466C4×D4—611no—
467C4×D4—1221no—
468C4×D4—1221no—
469C4×D4—1222no—
470C4×D4—1222no—
471C4×D4—2441no—
472C4×D4—2441no—
473C4×D4C2×#692311yescharacteristic
474C2×C4⋊C4—611no—
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—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C42—611no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—1221no—
495C2×C42—1221no—
496C2×C42—1221no—
497#107—611no—
498#107—611no—
499#107—611no—
500#107—611no—
501#107—611no—
502#107—611no—
503#107—2441no—
504#107C2×#692311yescharacteristic, complemented
505#107C2×#692311yescharacteristic, complemented
506#106—2441no—
507C4⋊C8—611no—
508C4⋊C8—611no—
509C4⋊C8—611no—
510C4⋊C8C2×#692311yescharacteristic, complemented
511#102—614no—
512#102—611no—
513#102—611no—
514#102—611no—
515#102—611no—
516#102—611no—
517#102—611no—
518#102—1222no—
519#102C2×#692311yescharacteristic
520#102C2×#692311yescharacteristic
521#97—1221no—
522#97—1221no—
523#97—2441no—
524C4×C8—2441no—
525#95—611no—
526#95—611no—
527#95—1221no—
528#95—1221no—
529#95—1221no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533#95—1221no—
534#95—1221no—
535#95—1221no—
536C24—1221no—
537C2×Q8—21no—
538C2×Q8—1221no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×Q8—4881no—
542C2×Q8—4881no—
543C2×D4—612no—
544C2×D4—612no—
545C2×D4—611no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4C22×#692311yescharacteristic
550C22×C4—21no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—4881no—
569C22×C4—4881no—
570C22×C4—4881no—
571C22×C4—4881no—
572C22×C4—2442no—
573C22×C4—2442no—
574C22×C4—2442no—
575C22×C4—2442no—
576C2×C8—612no—
577C2×C8—611no—
578C2×C8—611no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8C22×#692311yescharacteristic
589C2×C8C22×#692311yescharacteristic
590C4⋊C4—21no—
591C4⋊C4—612no—
592C4⋊C4—611no—
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—1222no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—4881no—
610C4⋊C4—4881no—
611C4⋊C4—4881no—
612C4⋊C4—4881no—
613C4⋊C4—2441no—
614C4⋊C4C22×#692311yescharacteristic
615C4⋊C4C22×#692311yescharacteristic
616C4⋊C4C22×#692311yescharacteristic
617C22⋊C4—21no—
618C22⋊C4—1221no—
619C22⋊C4—1221no—
620C22⋊C4—1221no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C42—611no—
624C42—611no—
625C42—611no—
626C42—1221no—
627C42—1221no—
628C42—1221no—
629C42—1221no—
630C42—4881no—
631C42—4881no—
632C42—2442no—
633C42C22×#692311yescharacteristic
634C23—21no—
635C23—611no—
636C23—1222no—
637C23—1222no—
638C23—1221no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643Q8—81no—
644Q8—4881no—
645Q8—4881no—
646Q8—4881no—
647D4—21no—
648D4—612no—
649D4—1222no—
650D4—1222no—
651D4—1221no—
652D4Q8×#692312yes—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—81no—
657C2×C4—611no—
658C2×C4—611no—
659C2×C4—611no—
660C2×C4—611no—
661C2×C4—611no—
662C2×C4—612no—
663C2×C4—611no—
664C2×C4—611no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1222no—
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—4881no—
685C2×C4—4881no—
686C2×C4—4884no—
687C2×C4—4881no—
688C2×C4—4884no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
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×C4D4×#692311yescharacteristic
707C2×C4D4×#692311yescharacteristic
708C2×C4C23×#692311yescharacteristic
709C8—21no—
710C8—21no—
711C8—1222no—
712C8—1221no—
713C8—1221no—
714C8—2441no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—611no—
719C22—611no—
720C22—611no—
721C22—611no—
722C22—611no—
723C22—611no—
724C22—1222no—
725C22—2442no—
726C22—2442no—
727C22—2442no—
728C22—2442no—
729C22—2441no—
730C22—2441no—
731C22C2×D4×#692311yescharacteristic
732C4—21no—
733C4—21no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—611no—
738C4—611no—
739C4—1222no—
740C4—1221no—
741C4—1221no—
742C4—4881no—
743C4—4881no—
744C4—4881no—
745C4—2441no—
746C4—2441no—
747C4—2441no—
748C4—2442no—
749C4—2441no—
750C4—2441no—
751C4—2441no—
752C4C2×Q8×#692311yescharacteristic
753C4#1684083111yescharacteristic
754C2—42no—
755C2—611no—
756C2—611no—
757C2—611no—
758C2—611no—
759C2—2442no—
760C2#2146234311yescharacteristic
761C2#137×#692311yescharacteristic
762C2#2146257811yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#474C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#474#6923
hypocenterC61#22979
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #21462352C2semidirect
3. #21462003C2semidirect
4. #21461932C2semidirect
5. #21461924C2semidirect
6. #21461923C2semidirect
7. #21461883C2semidirect
8. #21461880C2semidirect
11. #21461620C2semidirect
54. #16840043C4semidirect
55. #16840042C4semidirect
56. #16840041C4semidirect
57. #16840041C4semidirect
58. #16840040C4semidirect
59. #16840040C4semidirect
60. #16840039C4semidirect
66. C61×#474C4semidirect
95. #14519839Q8semidirect
116. #14519777C2×C4semidirect
118. #14519776C2×C4semidirect
119. #14519776C2×C4semidirect
132. #14519711C2×C4semidirect
133. #14519711C2×C4semidirect
134. #14519710C2×C4semidirect
135. #14519710C2×C4semidirect
136. #14519710C2×C4semidirect
137. #14519710C2×C4semidirect
138. C4⋊#92418C2×C4semidirect
139. #14519706C2×C4semidirect
140. #14519706C2×C4semidirect
147. C4⋊Q8×C61C2×C4semidirect
149. #107×C61C2×C4semidirect
150. #107×C61C2×C4semidirect
151. C4⋊C8×C61C2×C4semidirect
408. #474#6923semidirect
448. C61#22979semidirect
463. C4⋊Q8C2×#6923semidirect
504. #107C2×#6923semidirect
505. #107C2×#6923semidirect
510. C4⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623522
#214623322
#214620032
#214619322
#214619242
#214619232
#214618832
#214618802
#214617842
#214617822
#214616202
#214615902
#214615892
#102×#69232
#474×D612
#2297961