Finite Group Databasebeta

← #30602567

Subgroups — #30602567

Order 15616.

1350 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840831C211yesmaximal, characteristic
2C2×#16840753C211yesmaximal, characteristic
3C2×#16840641C211yesmaximal, characteristic, complemented
4#21461507C211yesmaximal, characteristic, complemented
5C2×#16840633C211yesmaximal, characteristic, complemented
6#21460997C211yesmaximal, characteristic, complemented
7C2×#104×D61C211yesmaximal, characteristic
8C2×D61⋊M16C2211yescharacteristic
9#16840831—22no—
10#16840831—22no—
11#16840831—22no—
12#16840831C414yescomplemented
13C2×Q8×#6923—21no—
14C2×D4×#6923—22no—
15C2×D4×#6923—21no—
16C2×#14519856—21no—
17C2×#14519856C2211yescharacteristic
18C22×C4⋊#6923—21no—
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21#16840753—22no—
22#16840753C414yescomplemented
23C2×#14519840—21no—
24C2×#14519839—21no—
25C2×(C2×#6923)⋊C4—22no—
26#16840641—22no—
27#16840636—21no—
28#16840636—21no—
29#16840633—22no—
30C2×#41×D61C2211yescharacteristic
31C2×M16×D61C2211yescharacteristic
32C2×C42×D61C2211yescharacteristic
33C2×#14519705C411yescharacteristic, complemented
34C2×#14519704C411yescharacteristic, complemented
35C2×#14519703C411yescharacteristic, complemented
36#104×D61—22no—
37#104×D61—22no—
38C2×#104×C61C411yescharacteristic, complemented
39C23×#6923—22no—
40C23×#6923—21no—
41C23×#6923D412yes—
42C2×#11758213—21no—
43D61⋊M16—21no—
44D61⋊M16—21no—
45D61⋊M16—21no—
46D61⋊M16C2×C412yescomplemented
47C2×#11758217—21no—
48C2×D61⋊C8—21no—
49Q8×#6923—24no—
50Q8×#6923—24no—
51D4×#6923—28no—
52D4×#6923—24no—
53D4×#6923—28no—
54D4×#6923—24no—
55#14519856—24no—
56#14519856—21no—
57#14519856—21no—
58#14519856—24no—
59#14519856C2×C412yes—
60#14519856D412yes—
61C2×C4⋊#6923—22no—
62C2×C4⋊#6923—24no—
63C2×C4⋊#6923—21no—
64C2×C4⋊#6923—21no—
65C2×C4⋊#6923—21no—
66C2×C4⋊#6923—21no—
67C2×C4⋊#6923—24no—
68C2×C4⋊#6923—21no—
69C2×C4⋊#6923—21no—
70C2×C4⋊#6923—21no—
71C2×C4⋊#6923—21no—
72C2×C4⋊#6923—21no—
73C2×C4⋊#6923C2×C412yes—
74C2×C4⋊#6923C2×C412yescomplemented
75C2×C4⋊#6923D412yes—
76C2×C4⋊#6923D411yescharacteristic
77C2×C4⋊#6923D411yescharacteristic
78C2×C22⋊#6923—22no—
79C2×C22⋊#6923—21no—
80C2×C4×#6923—22no—
81C2×C4×#6923—21no—
82#14519840—24no—
83#14519839—24no—
84(C2×#6923)⋊C4—44no—
85C2×#11758226Q811yescharacteristic
86C2×#11758222—21no—
87C2×#11758222C2×C411yescharacteristic
88C2×#11758224—21no—
89C2×#11758224Q811yescharacteristic
90#41×D61—21no—
91#41×D61—21no—
92#41×D61—21no—
93#41×D61—21no—
94#41×D61C2×C412yes—
95#41×D61C2×C412yes—
96#41×D61D412yes—
97#41×D61D412yes—
98C2×Q8×D61D411yescharacteristic
99C2×D4×D61—21no—
100C2×D4×D61D411yescharacteristic
101C22×C4×D61—21no—
102C22×C4×D61—21no—
103C22×C4×D61C2311yescharacteristic
104C2×#11758194C2×C411yescharacteristic, complemented
105C2×#11758189—21no—
106M16×D61—21no—
107M16×D61—21no—
108M16×D61—21no—
109M16×D61—21no—
110C2×C8×D61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61C2×C411yescharacteristic, complemented
113C42×D61—21no—
114C42×D61—21no—
115C42×D61—21no—
116C42×D61—21no—
117#14519705—22no—
118#14519704—22no—
119#14519703—22no—
120C2×#41×C61C2×C411yescharacteristic
121C2×M16×C61C2×C411yescharacteristic, complemented
122C2×C42×C61C2×C411yescharacteristic, complemented
123#104×C61—22no—
124C23×D61—21no—
125C23×D61C2×D411yescharacteristic
126C22×#6923—21no—
127C22×#6923—22no—
128C22×#6923—21no—
129C22×#6923—28no—
130C22×#6923—22no—
131C22×#6923—22no—
132C22×#6923—42no—
133C22×#6923—42no—
134C22×#6923—42no—
135C22×#6923—42no—
136C22×#6923—41no—
137C22×#6923—41no—
138C22×#6923—82no—
139C22×#6923—82no—
140C22×#6923C22⋊C414yes—
141#41×C61—21no—
142#41×C61—21no—
143#41×C61C4212yes—
144#41×C61C22⋊C412yes—
145C2×Q8×C61C4⋊C411yescharacteristic
146C2×D4×C61—21no—
147C2×D4×C61C4⋊C411yescharacteristic
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61C22×C411yescharacteristic
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C2×C22⋊D61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61#4111yescharacteristic
157#11758226—21no—
158#11758226—21no—
159#11758226C4⋊C412yes—
160#11758226C4⋊C412yes—
161Q8×D61—21no—
162Q8×D61—21no—
163Q8×D61C22⋊C412yes—
164Q8×D61C22⋊C412yes—
165#11758224—22no—
166#11758224—22no—
167#11758224—22no—
168#11758224—22no—
169#11758224—21no—
170#11758224—21no—
171#11758224C4⋊C412yes—
172#11758224C4⋊C412yes—
173D4×D61—22no—
174D4×D61—22no—
175D4×D61—22no—
176D4×D61—22no—
177D4×D61—21no—
178D4×D61—21no—
179D4×D61C22⋊C412yes—
180D4×D61C22⋊C412yes—
181#11758222—21no—
182#11758222—21no—
183#11758222—22no—
184#11758222—22no—
185#11758222—22no—
186#11758222—22no—
187#11758222C4212yes—
188#11758222C22⋊C412yes—
189C2×D244—21no—
190C2×D244C4⋊C411yescharacteristic
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—22no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—41no—
201C2×C4×D61—41no—
202C2×C4×D61—41no—
203C2×C4×D61—41no—
204C2×C4×D61C22×C411yescharacteristic
205C2×C4×D61C22×C411yescharacteristic
206C2×C4×D61C2×D411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×Q811yescharacteristic
213C2×C4×D61#4111yescharacteristic
214C2×C4×D61#4111yescharacteristic
215C2×C4×D61#4111yescharacteristic
216C2×Dic122—21no—
217C2×Dic122C4⋊C411yescharacteristic
218C22⋊#6923—28no—
219C22⋊#6923—22no—
220C22⋊#6923—22no—
221#11758217—22no—
222#11758217—41no—
223C2×#92420—41no—
224C4⋊#6923—28no—
225C4⋊#6923—22no—
226C4⋊#6923—22no—
227C4⋊#6923—22no—
228C4⋊#6923—22no—
229C4⋊#6923—22no—
230C4⋊#6923—21no—
231C4⋊#6923—22no—
232C4⋊#6923—21no—
233C4⋊#6923—41no—
234C4⋊#6923—41no—
235C4⋊#6923C22⋊C412yes—
236C4⋊#6923C22⋊C412yes—
237C4×#6923—28no—
238C4×#6923—22no—
239C4×#6923—22no—
240#11758213—22no—
241#11758213—41no—
242D61⋊C8—22no—
243D61⋊C8—41no—
244M16×C61—21no—
245M16×C61—21no—
246C2×C8×C61—21no—
247C42×C61—21no—
248C42×C61—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61—41no—
252C4×Dic61—41no—
253#11758194—21no—
254#11758194—21no—
255C2×#92418—21no—
256#11758189—41no—
257#11758189—41no—
258C8×D61—41no—
259C8×D61—41no—
260C23×C61—21no—
261C23×C61C4×D411yescharacteristic
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61C2×C22⋊C411yescharacteristic
274C22×D61C4×D411yescharacteristic
275C22×D61#12011yescharacteristic
276C22×D61#12011yescharacteristic
277C22×D61#12111yescharacteristic
278C22×D61C22⋊Q811yescharacteristic
279C2×#6923—22no—
280C2×#6923—24no—
281C2×#6923—22no—
282C2×#6923—42no—
283C2×#6923—41no—
284C2×#6923—41no—
285C2×#6923—42no—
286C2×#6923—41no—
287C2×#6923—41no—
288C2×#6923—44no—
289C2×#6923—44no—
290C2×#6923—42no—
291C2×#6923—82no—
292C2×#6923—88no—
293C2×#6923—82no—
294C2×#6923—81no—
295C2×#6923—81no—
296Q8×C61—21no—
297Q8×C61#9512yescomplemented
298D4×C61—22no—
299D4×C61—22no—
300D4×C61—21no—
301D4×C61#9512yescomplemented
302C2×C4×C61—21no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61C2×C4211yescharacteristic
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C2×C4⋊C411yescharacteristic
311C2×C4×C61C4×D411yescharacteristic
312C2×C4×C61C4×D411yescharacteristic
313C2×C4×C61C4×D411yescharacteristic
314C22⋊D61—22no—
315C22⋊D61—22no—
316C22⋊D61—22no—
317C22⋊D61—22no—
318C22⋊D61—22no—
319C22⋊D61—22no—
320C2×Dic61—21no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61#11711yescharacteristic
327C2×Dic61C4×D411yescharacteristic
328C2×Dic61#12111yescharacteristic
329C2×Dic61C22⋊Q811yescharacteristic
330C2×Dic61#12311yescharacteristic
331C2×Dic61#12311yescharacteristic
332D244—22no—
333D244—22no—
334D244—21no—
335D244#9512yescomplemented
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—42no—
343C4×D61—42no—
344C4×D61—42no—
345C4×D61—42no—
346C4×D61C2×C22⋊C411yescharacteristic
347C4×D61C2×C22⋊C411yescharacteristic
348C4×D61C2×C22⋊C411yescharacteristic
349C4×D61C2×C4⋊C411yescharacteristic
350C4×D61C2×C4⋊C411yescharacteristic
351C4×D61#11711yescharacteristic
352C4×D61C4×D411yescharacteristic
353C4×D61C4×D411yescharacteristic
354C4×D61#12011yescharacteristic
355C4×D61#12011yescharacteristic
356C4×D61#12111yescharacteristic
357C4×D61#12111yescharacteristic
358C4×D61C22⋊Q811yescharacteristic
359C4×D61C22⋊Q811yescharacteristic
360C4×D61#12311yescharacteristic
361C4×D61#12311yescharacteristic
362Dic122—21no—
363Dic122—22no—
364Dic122—22no—
365Dic122#9512yescomplemented
366#92420—42no—
367C8×C61—41no—
368#92418—41no—
369#10781—611nomaximal, Sylow
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—22no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61C4×C22⋊C411yescharacteristic
376C22×C61#38511yescharacteristic
377C22×C61#38611yescharacteristic
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—22no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61#37911yescharacteristic
396C2×D61#38011yescharacteristic
397C2×D61#38511yescharacteristic
398C2×D61#38611yescharacteristic
399C2×D61#45311yescharacteristic
400C2×D61#45411yescharacteristic
401C2×D61#45511yescharacteristic
402C2×D61#45611yescharacteristic
403#6923—44no—
404#6923—42no—
405#6923—42no—
406#6923—82no—
407C4×C61—22no—
408C4×C61—42no—
409C4×C61C2×#9511yescharacteristic
410C4×C61C4×C22⋊C411yescharacteristic
411C4×C61#38511yescharacteristic
412C4×C61#38611yescharacteristic
413Dic61—22no—
414Dic61—42no—
415Dic61#38011yescharacteristic
416Dic61#38111yescharacteristic
417Dic61#38511yescharacteristic
418Dic61#38611yescharacteristic
419C2×#520—611no—
420C22×#104—611no—
421C2×#417—611no—
422C2×#343—611no—
423#1736—611no—
424C2×#339—611no—
425C4⋊#95—611no—
426C2×C61—21no—
427C2×C61—21no—
428C2×C61—42no—
429C2×C61C22⋊#9511yescharacteristic
430C2×C61#185911yescharacteristic
431C2×C61#186011yescharacteristic
432D61—21no—
433D61—21no—
434D61—42no—
435D61#179211yescharacteristic
436D61#179311yescharacteristic
437D61#188211yescharacteristic
438D61#188311yescharacteristic
439C22×#41—611no—
440C22×M16—611no—
441C22×M16—611no—
442#520—614no—
443#520—1222no—
444#520—1222no—
445#520—1222no—
446C2×C4×Q8—1221no—
447C2×C4×D4—1222no—
448C2×C4×D4—1221no—
449C2×#117—611no—
450C2×#117—1221no—
451C22×C4⋊C4—611no—
452C22×C4⋊C4—611no—
453C22×C4⋊C4—1221no—
454C22×C42—611no—
455C2×#104—611no—
456C2×#104—611no—
457C2×#104—611no—
458C2×#104—1222no—
459C2×#104—1222no—
460C2×#104#692311yescharacteristic, complemented
461#417—614no—
462#417—1222no—
463C2×#103—1221no—
464C2×#102—1221no—
465C2×#95—1222no—
466#343—1222no—
467#340—1221no—
468#340—1221no—
469#339—1222no—
470C61#1078111yescharacteristic, complemented, Sylow
471C2×#41—612no—
472C2×#41—612no—
473C2×#41—612no—
474C2×#41—612no—
475C2×#41—611no—
476C2×#41—611no—
477C2×#41—611no—
478C2×#41—1221no—
479C2×#41—1221no—
480C2×#41—1221no—
481C2×#41—1221no—
482C2×#41—1221no—
483C2×#41—1221no—
484C2×#41C2×#692311yescharacteristic
485C22×Q8—611no—
486C22×D4—611no—
487C22×D4—1221no—
488C23×C4—611no—
489C23×C4—612no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4—1222no—
493C23×C4—1221no—
494C2×M16—612no—
495C2×M16—611no—
496C2×M16—1221no—
497C2×M16—1221no—
498C2×M16—1221no—
499C2×M16—1221no—
500C2×M16—1221no—
501C2×M16—1221no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C2×M16—1221no—
506C2×M16C2×#692311yescharacteristic, complemented
507C22×C8—1221no—
508C22×C8—1221no—
509C4×Q8—1224no—
510C4×Q8—1224no—
511C4×D4—1228no—
512C4×D4—1224no—
513C4×D4—1224no—
514C4×D4—1228no—
515#117—612no—
516#117—612no—
517#117—1224no—
518#117—1221no—
519#117—1221no—
520#117—1224no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—612no—
524C2×C4⋊C4—612no—
525C2×C4⋊C4—612no—
526C2×C4⋊C4—1224no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1222no—
532C2×C4⋊C4—1224no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1222no—
540C2×C42—611no—
541C2×C42—1221no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42—1221no—
545C2×C42—1221no—
546C2×C42—1222no—
547C2×C42—1221no—
548C2×C42C2×#692311yescharacteristic, complemented
549#104—22no—
550#104—1222no—
551#104—1222no—
552#104—1222no—
553#103—1224no—
554#102—1224no—
555#95—2444no—
556C24—611no—
557C24—1221no—
558#41—21no—
559#41—21no—
560#41—612no—
561#41—612no—
562#41—612no—
563#41—612no—
564#41—612no—
565#41—612no—
566#41—1222no—
567#41—1222no—
568#41—1222no—
569#41—1222no—
570#41—1222no—
571#41—1222no—
572#41—1222no—
573#41—1222no—
574#41—1221no—
575#41—1221no—
576#41—1221no—
577#41—1221no—
578#41—1221no—
579#41—1221no—
580#41C4×#692312yes—
581#41C22⋊#692312yes—
582C2×Q8—612no—
583C2×Q8—612no—
584C2×Q8—611no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8C4⋊#692311yescharacteristic
589C2×D4—21no—
590C2×D4—612no—
591C2×D4—612no—
592C2×D4—611no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—1221no—
597C2×D4—1222no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—1222no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4C4⋊#692311yescharacteristic
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—614no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1221no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1221no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1222no—
631C22×C4—1228no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1222no—
635C22×C4—1221no—
636C22×C4—1222no—
637C22×C4—4882no—
638C22×C4—4882no—
639C22×C4—2441no—
640C22×C4—2441no—
641C22×C4—2441no—
642C22×C4—2441no—
643C22×C4—2441no—
644C22×C4—2441no—
645C22×C4—2442no—
646C22×C4—2442no—
647C22×C4—2442no—
648C22×C4—2442no—
649C22×C4C22×#692311yescharacteristic
650M16—21no—
651M16—21no—
652M16—1222no—
653M16—1222no—
654M16—1221no—
655M16—1221no—
656M16—2441no—
657M16—2441no—
658M16—2441no—
659M16—2441no—
660C2×C8—21no—
661C2×C8—1222no—
662C2×C8—1221no—
663C2×C8—2441no—
664C2×C8—2441no—
665C2×C8—2441no—
666C2×C8—2441no—
667C4⋊C4—612no—
668C4⋊C4—612no—
669C4⋊C4—1221no—
670C4⋊C4—1222no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—1221no—
675C4⋊C4—1222no—
676C4⋊C4—1222no—
677C4⋊C4—1228no—
678C4⋊C4—2441no—
679C4⋊C4—2441no—
680C22⋊C4—1222no—
681C22⋊C4—1222no—
682C22⋊C4—1228no—
683C42—21no—
684C42—21no—
685C42—1222no—
686C42—1222no—
687C42—1228no—
688C42—1221no—
689C42—1221no—
690C42—2441no—
691C42—2441no—
692C23—21no—
693C23—611no—
694C23—611no—
695C23—611no—
696C23—611no—
697C23—611no—
698C23—611no—
699C23—1221no—
700C23—1221no—
701C23—1221no—
702C23—1221no—
703C23—1222no—
704C23—1222no—
705C23—1221no—
706C23—2441no—
707C23—2441no—
708C23—2441no—
709C23—2441no—
710C23D4×#692311yescharacteristic
711Q8—21no—
712Q8—612no—
713Q8—1222no—
714Q8—1222no—
715Q8—1221no—
716Q8(C2×#6923)⋊C412yescomplemented
717D4—22no—
718D4—22no—
719D4—21no—
720D4—612no—
721D4—1222no—
722D4—1222no—
723D4—1222no—
724D4—1222no—
725D4—1222no—
726D4—1222no—
727D4—1222no—
728D4—1222no—
729D4—1221no—
730D4(C2×#6923)⋊C412yescomplemented
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—611no—
738C2×C4—611no—
739C2×C4—611no—
740C2×C4—611no—
741C2×C4—611no—
742C2×C4—611no—
743C2×C4—611no—
744C2×C4—611no—
745C2×C4—611no—
746C2×C4—611no—
747C2×C4—611no—
748C2×C4—611no—
749C2×C4—611no—
750C2×C4—611no—
751C2×C4—611no—
752C2×C4—611no—
753C2×C4—611no—
754C2×C4—611no—
755C2×C4—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—611no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1221no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1224no—
772C2×C4—4881no—
773C2×C4—4881no—
774C2×C4—4882no—
775C2×C4—4882no—
776C2×C4—4888no—
777C2×C4—2442no—
778C2×C4—2442no—
779C2×C4—2442no—
780C2×C4—2442no—
781C2×C4—2442no—
782C2×C4—2444no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2442no—
789C2×C4—2442no—
790C2×C4—2441no—
791C2×C4—2444no—
792C2×C4C2×C4×#692311yescharacteristic
793C2×C4C2×C22⋊#692311yescharacteristic
794C2×C4C2×C4⋊#692311yescharacteristic
795C2×C4D4×#692311yescharacteristic
796C2×C4D4×#692311yescharacteristic
797C2×C4D4×#692311yescharacteristic
798C8—41no—
799C8—2442no—
800C8—2441no—
801C22—21no—
802C22—21no—
803C22—22no—
804C22—41no—
805C22—41no—
806C22—611no—
807C22—611no—
808C22—611no—
809C22—611no—
810C22—611no—
811C22—611no—
812C22—611no—
813C22—611no—
814C22—1221no—
815C22—1221no—
816C22—1221no—
817C22—1221no—
818C22—1221no—
819C22—1221no—
820C22—1221no—
821C22—1221no—
822C22—1221no—
823C22—1221no—
824C22—1222no—
825C22—2442no—
826C22—2442no—
827C22—2442no—
828C22—2442no—
829C22—2441no—
830C22—2441no—
831C22C22⋊C4×#692311yescharacteristic
832C22#1684070911yescharacteristic
833C22#1684071011yescharacteristic
834C4—22no—
835C4—42no—
836C4—611no—
837C4—611no—
838C4—611no—
839C4—611no—
840C4—1222no—
841C4—4882no—
842C4—2442no—
843C4—2442no—
844C4—2444no—
845C4—2442no—
846C4C2×(C2×#6923)⋊C411yescharacteristic
847C4C22⋊C4×#692311yescharacteristic
848C4#1684070911yescharacteristic
849C4#1684071011yescharacteristic
850C2—21no—
851C2—21no—
852C2—42no—
853C2—611no—
854C2—611no—
855C2—611no—
856C2—611no—
857C2—1221no—
858C2—1221no—
859C2—2442no—
860C2#2146099211yescharacteristic
861C2#2146177811yescharacteristic
862C2#2146177911yescharacteristic
subgroupG/H
centerC22#16840709
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×#104×C61C4
socleC22×C61#385
prime radicalC2×#41×D61C22
cosocleC22×C4×D61C23
hypercenterC2×#104#6923
hypocenterC61#10781
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
3. C2×#16840641C2semidirect
4. #21461507C2semidirect
5. C2×#16840633C2semidirect
6. #21460997C2semidirect
12. #16840831C4semidirect
22. #16840753C4semidirect
33. C2×#14519705C4semidirect
34. C2×#14519704C4semidirect
35. C2×#14519703C4semidirect
38. C2×#104×C61C4semidirect
46. D61⋊M16C2×C4semidirect
74. C2×C4⋊#6923C2×C4semidirect
104. C2×#11758194C2×C4semidirect
112. C2×C4×Dic61C2×C4semidirect
121. C2×M16×C61C2×C4semidirect
122. C2×C42×C61C2×C4semidirect
297. Q8×C61#95semidirect
301. D4×C61#95semidirect
335. D244#95semidirect
365. Dic122#95semidirect
460. C2×#104#6923semidirect
470. C61#10781semidirect
506. C2×M16C2×#6923semidirect
548. C2×C42C2×#6923semidirect
716. Q8(C2×#6923)⋊C4semidirect
730. D4(C2×#6923)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#168408312
C2×#168407532
C2×#168406412
#214615072
C2×#168406332
#214609972
C2×#104×D612
#1078161