Finite Group Databasebeta

← #29695457

Subgroups — #29695457

Order 15616.

1498 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840419C211yesmaximal, characteristic
2C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#103×D61C211yesmaximal, characteristic, complemented
4#21448749C211yesmaximal, characteristic, complemented
5#21446750C211yesmaximal, characteristic, complemented
6#21446629C211yesmaximal, characteristic, complemented
7#21446244C211yesmaximal, characteristic, complemented
8#21446242C211yesmaximal, characteristic, complemented
9#21446133C211yesmaximal, characteristic, complemented
10#21446131C211yesmaximal, characteristic, complemented
11#21445832C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#103×Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#416C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#16840419—24no—
19#16840419C418yescomplemented
20C2×#14519764—21no—
21C2×#14519764C2211yescharacteristic
22C2×#14519756—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519748—21no—
25C2×#14519748C2211yescharacteristic
26C2×Q8×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61—21no—
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C8×C22⋊D61—24no—
31C2×#14519706C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38#103×D61—24no—
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×C8×Dic61C2211yescharacteristic
44#16839656—21no—
45#16839646—21no—
46#16839638—21no—
47#16839627C2211yescharacteristic
48#16839622C2211yescharacteristic
49#16839619C2211yescharacteristic
50C4⋊C4×Dic61C2211yescharacteristic
51C4×#11758198—21no—
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C22×#41×C61C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic
58C2×#117×C61C2211yescharacteristic
59C61×#416—24no—
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×#102×C61C2211yescharacteristic
64C22×Dic122—21no—
65C22×Dic122C2311yescharacteristic
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—41no—
70C2×Q8×D61—41no—
71C2×Q8×D61C2×C414yes—
72C22×C22⋊D61—21no—
73C22×C22⋊D61D411yescharacteristic
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C2×C8×D61—22no—
80C2×C8×D61—22no—
81C2×C8×D61—41no—
82#14519764—28no—
83#14519764—22no—
84#14519764C2×C414yescomplemented
85#14519756—22no—
86#14519756—28no—
87#14519756C2×C414yescomplemented
88#14519748—28no—
89#14519748—22no—
90#14519748C2×C414yes—
91Q8×Dic61—22no—
92Q8×Dic61C2×C414yescomplemented
93C4×C22⋊D61—28no—
94C4×C22⋊D61C2×C414yes—
95C4×C22⋊D61D414yes—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196D411yescharacteristic
103C4⋊C4×D61—22no—
104C4⋊C4×D61—41no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61D411yescharacteristic
111C2×#11758198—21no—
112C2×#11758198D411yescharacteristic
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61C2311yescharacteristic
116#14519706—22no—
117#14519702—22no—
118#14519702—41no—
119#14519701—22no—
120#14519701—22no—
121#14519700—22no—
122#14519700—41no—
123#14519698—41no—
124#14519698—41no—
125C22⋊#92418—22no—
126#14519689—22no—
127C8×Dic61—22no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131#14519684—21no—
132#14519684—21no—
133C2×#41×C61—22no—
134C2×#41×C61—22no—
135C2×#41×C61—22no—
136C2×#41×C61—41no—
137C2×#41×C61—41no—
138C2×#41×C61C2×C414yescomplemented
139C22×Q8×C61C2311yescharacteristic
140C22×D4×C61—21no—
141C22×D4×C61C2311yescharacteristic
142C23×C4×C61—21no—
143C23×C4×C61C2311yescharacteristic
144C22×C8×C61—22no—
145C22×C8×C61—22no—
146C22×C8×C61—41no—
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149#117×C61—22no—
150#117×C61—41no—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—21no—
154C2×C42×C61—21no—
155#103×C61—22no—
156#103×C61D414yescomplemented
157#102×C61—22no—
158#102×C61—22no—
159C24×C61—21no—
160C24×C61C2×D411yescharacteristic
161C23×D61C2×D411yescharacteristic
162#41×C61—28no—
163#41×C61—44no—
164#41×C61—44no—
165#41×C61—44no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61C22×C412yes—
170C2×Q8×C61C2×D412yes—
171C2×Q8×C61#4112yes—
172C2×D4×C61—24no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—42no—
179C2×D4×C61—42no—
180C2×D4×C61C22×C412yes—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—24no—
188C22×C4×C61—21no—
189C22×C4×C61—42no—
190C22×C4×C61—42no—
191C22×C4×C61C22×C412yes—
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2411yescharacteristic
195C2×C22⋊D61—22no—
196C2×C22⋊D61—22no—
197C2×C22⋊D61—24no—
198C2×C22⋊D61—42no—
199C2×C22⋊D61—42no—
200C2×C22⋊D61C22⋊C414yes—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208Q8×D61—28no—
209Q8×D61—44no—
210Q8×D61—44no—
211Q8×D61—44no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—24no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61—81no—
222C2×C4×D61C22×C412yes—
223C2×C4×D61C2×D412yes—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—24no—
230C2×Dic122—42no—
231C2×Dic122—42no—
232C2×Dic122C22×C412yes—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—44no—
239C2×C8×C61C2×D412yes—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61C2×D412yes—
244C22⋊C4×C61—42no—
245C42×C61—42no—
246C22⋊Dic61—24no—
247C22⋊Dic61—24no—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61—81no—
251C22⋊Dic61C22⋊C414yes—
252#11758198—42no—
253#11758198C22⋊C414yes—
254C4⋊Dic61—21no—
255C4⋊Dic61—24no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61C22×C412yes—
261#11758196—24no—
262#11758196—42no—
263#11758196C22⋊C414yes—
264C4×Dic61—24no—
265C4×Dic61—81no—
266C4×Dic61C22×C412yes—
267C4×Dic61C2×D412yes—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C8×D61—44no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—22no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61C2×C22⋊C412yes—
289C23×C61C22×D411yescharacteristic
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61C2×C22⋊C412yes—
295C22×D61#13512yes—
296C22×D61#13512yes—
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—22no—
300Q8×C61C4×D414yes—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—48no—
304D4×C61—41no—
305D4×C61—41no—
306C2×C4×C61—22no—
307C2×C4×C61—21no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—21no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—48no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61C2×C22⋊C412yes—
323C2×C4×C61C23×C411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C2×#4111yescharacteristic
327C2×C4×C61H(5,𝔽2)11yescharacteristic
328C2×C4×C61H(5,𝔽2)11yescharacteristic
329C22⋊D61—28no—
330C22⋊D61—48no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61C2×C22⋊C412yes—
350C2×Dic61C2×C22⋊C412yes—
351C2×Dic61C2×C22⋊C412yes—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—48no—
357C4×D61—84no—
358Dic122—22no—
359Dic122—22no—
360Dic122—48no—
361Dic122—41no—
362Dic122—41no—
363C8×C61—22no—
364C8×C61—41no—
365#92418—41no—
366#92418—41no—
367#22416—611nomaximal, Sylow
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61—81no—
382C22×C61C22×C22⋊C411yescharacteristic
383C22×C61D4211yescharacteristic
384C22×C61#54611yescharacteristic
385C22×C61C2×#13511yescharacteristic
386C22×C61C2×#13511yescharacteristic
387C22×C61#57711yescharacteristic
388C22×C61#57811yescharacteristic
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—22no—
395C2×D61#41614yescomplemented
396C4×C61—24no—
397C4×C61—22no—
398C4×C61—42no—
399C4×C61—81no—
400C4×C61C2×C4×D411yescharacteristic
401C4×C61#51811yescharacteristic
402C4×C61D4211yescharacteristic
403C4×C61#54611yescharacteristic
404Dic61—22no—
405Dic61—22no—
406Dic61—22no—
407Dic61—42no—
408Dic61—42no—
409Dic61—81no—
410Dic61—81no—
411C2×#548—611no—
412C2×C8×D4—611no—
413C2×#416D6111yescharacteristic, complemented
414C22×#103—611no—
415#2352—611no—
416#1983—611no—
417#1958—611no—
418#1893—611no—
419#1892—611no—
420#1874—611no—
421#1873—611no—
422#1805—611no—
423#1788—611no—
424#1787—611no—
425C4×#103—611no—
426C2×C61—42no—
427C2×C61—82no—
428C2×C61D4×C22⋊C411yescharacteristic
429C2×C61C2×#41611yescharacteristic
430C2×C61#289811yescharacteristic
431C2×C61#328211yescharacteristic
432C2×C61#328511yescharacteristic
433C2×C61#330011yescharacteristic
434C2×C61#330111yescharacteristic
435D61—24no—
436C22×#41C2×D6111yescharacteristic
437C23×Q8—611no—
438C23×C8—611no—
439C23×C8C2×D6111yescharacteristic
440#548—618no—
441#548—1224no—
442C2×#124—611no—
443C2×#124—1221no—
444C2×C22⋊Q8—611no—
445C2×C22⋊Q8—1221no—
446C2×#121—611no—
447C2×#121—1221no—
448C2×C4×Q8—611no—
449C2×C4×D4—611no—
450C2×C4×D4—1221no—
451C2×#117C2×D6111yescharacteristic
452C22×C4⋊C4—611no—
453C8×D4—1224no—
454C2×C4⋊C8—611no—
455#416—24no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—1224no—
463C2×#103C2×D6111yescharacteristic
464C2×#103C2×D6111yescharacteristic
465C2×#102—611no—
466C2×#102—611no—
467C2×#102C2×D6111yescharacteristic
468C2×#102C2×D6111yescharacteristic
469C2×C22⋊C8—611no—
470C2×C22⋊C8—611no—
471C2×C4×C8—611no—
472#388—1221no—
473#387—1221no—
474#386—1221no—
475#382—611no—
476#380—611no—
477#380—611no—
478C4×C4⋊C4—611no—
479C4×C22⋊C4—1221no—
480#340—611no—
481#340—611no—
482#340—611no—
483#340—611no—
484C61#2241611yescharacteristic, complemented, Sylow
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41C4×D6114yescomplemented
491C22×Q8—614no—
492C22×Q8—611no—
493C22×Q8—1221no—
494C22×Q8—1222no—
495C22×Q8—1222no—
496C22×Q8—1222no—
497C22×Q8—2441no—
498C22×Q8—2441no—
499C22×Q8C22×D6111yescharacteristic
500C22×D4—21no—
501C22×D4—611no—
502C22×D4—1221no—
503C22×D4C22×D6111yescharacteristic
504C23×C4—21no—
505C23×C4—611no—
506C23×C4—1221no—
507C23×C4—1221no—
508C23×C4C22×D6111yescharacteristic
509C22×C8—22no—
510C22×C8—22no—
511C22×C8—41no—
512C22×C8—611no—
513C22×C8—611no—
514C22×C8—1222no—
515C22×C8—1222no—
516C22×C8—2441no—
517C22×C8C22×D6111yescharacteristic
518C22×C8C22×D6111yescharacteristic
519#124—614no—
520#124—1222no—
521#124—1228no—
522C22⋊Q8—614no—
523C22⋊Q8—1228no—
524C22⋊Q8—1222no—
525#121—614no—
526#121—1222no—
527#121—1228no—
528C4×Q8—614no—
529C4×Q8—1222no—
530C4×D4—614no—
531C4×D4—614no—
532C4×D4—1228no—
533#117—22no—
534#117—41no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1222no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—2441no—
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C4⋊C4C22×D6111yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—611no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C42—21no—
556C2×C42—611no—
557C2×C42—1221no—
558C2×C42—1221no—
559C4⋊C8—1222no—
560#103—22no—
561#103—1222no—
562#103—1222no—
563#103—1222no—
564#103—1222no—
565#103—2441no—
566#103—2441no—
567#103C22⋊D6114yescomplemented
568#102—22no—
569#102—22no—
570#102—2441no—
571#102—2441no—
572C22⋊C8—1222no—
573C22⋊C8—1222no—
574C4×C8—1222no—
575#95—1221no—
576#95—1221no—
577#95—1221no—
578#95—1221no—
579#95—1221no—
580C24—21no—
581C24—611no—
582C24D4×D6111yescharacteristic
583#41—28no—
584#41—44no—
585#41—44no—
586#41—44no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—612no—
591C2×Q8—1224no—
592C2×Q8—1221no—
593C2×Q8—1228no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—2442no—
599C2×Q8—2442no—
600C2×Q8—2444no—
601C2×Q8—2444no—
602C2×Q8—2444no—
603C2×Q8C2×C4×D6112yes—
604C2×Q8#1175822212yes—
605C2×Q8C2×C22⋊D6112yes—
606C2×D4—24no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—614no—
615C2×D4—1222no—
616C2×D4—1222no—
617C2×D4—1224no—
618C2×D4—2442no—
619C2×D4—2442no—
620C2×D4C2×C4×D6112yes—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—21no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—612no—
635C22×C4—612no—
636C22×C4—1224no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—4881no—
646C22×C4—2442no—
647C22×C4—2442no—
648C22×C4—2442no—
649C22×C4—2442no—
650C22×C4C2×C4×D6112yes—
651C22×C4D4×D6112yes—
652C22×C4D4×D6111yescharacteristic
653C22×C4C23×D6111yescharacteristic
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—44no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—2444no—
667C2×C8C2×C22⋊D6112yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—614no—
672C4⋊C4—612no—
673C4⋊C4—1224no—
674C4⋊C4—1221no—
675C4⋊C4—1224no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—2442no—
681C4⋊C4C2×C22⋊D6112yes—
682C22⋊C4—42no—
683C22⋊C4—614no—
684C22⋊C4—614no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—4881no—
690C22⋊C4—2442no—
691C42—42no—
692C42—612no—
693C42—612no—
694C42—1224no—
695C42—4881no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—22no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—612no—
710C23—612no—
711C23—612no—
712C23—1221no—
713C23—1221no—
714C23—1221no—
715C23—1221no—
716C23C22⋊C4×D6112yes—
717C23C2×D4×D6111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—1222no—
722Q8—1222no—
723Q8—2448no—
724Q8—2441no—
725Q8—2441no—
726Q8C4×C22⋊D6114yes—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—1228no—
733D4—2448no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—48no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—612no—
751C2×C4—612no—
752C2×C4—612no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—4884no—
766C2×C4—2448no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4—2441no—
777C2×C4C22⋊C4×D6112yes—
778C2×C4C22×C4×D6111yescharacteristic
779C2×C4C2×D4×D6111yescharacteristic
780C2×C4C22×C22⋊D6111yescharacteristic
781C2×C4C2×#1175822211yescharacteristic
782C2×C4#1451982211yescharacteristic
783C2×C4#1451982211yescharacteristic
784C8—22no—
785C8—41no—
786C8—2441no—
787C8—2441no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—614no—
803C22—1222no—
804C22—1222no—
805C22—1222no—
806C22—1222no—
807C22—1222no—
808C22—1222no—
809C22C2×C22⋊C4×D6111yescharacteristic
810C22D4×C22⋊D6111yescharacteristic
811C22#1684040211yescharacteristic
812C22#135×D6111yescharacteristic
813C22#135×D6111yescharacteristic
814C22#1684056911yescharacteristic
815C22#1684057611yescharacteristic
816C4—22no—
817C4—24no—
818C4—42no—
819C4—81no—
820C4—1222no—
821C4—1222no—
822C4—1222no—
823C4—4881no—
824C4—4881no—
825C4—2442no—
826C4—2442no—
827C4C2×C4×C22⋊D6111yescharacteristic
828C4#1684023511yescharacteristic
829C4D4×C22⋊D6111yescharacteristic
830C4#1684040211yescharacteristic
831C2—42no—
832C2—82no—
833C2—1224no—
834C2C22⋊C4×C22⋊D6111yescharacteristic
835C2#416×D6111yescharacteristic
836C2#2145434811yescharacteristic
837C2#2145752011yescharacteristic
838C2#2145755411yescharacteristic
839C2#2145770711yescharacteristic
840C2#2145772211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#416C2
socleC23×C61C22×D4
prime radicalC2×#16840419C2
cosocleC22×C4×C61C24
hypercenterC2×#416D61
hypocenterC61#22416
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D61C2semidirect
3. C2×#103×D61C2semidirect
4. #21448749C2semidirect
5. #21446750C2semidirect
6. #21446629C2semidirect
7. #21446244C2semidirect
8. #21446242C2semidirect
9. #21446133C2semidirect
10. #21446131C2semidirect
11. #21445832C2semidirect
12. #21445759C2semidirect
13. #21445752C2semidirect
14. #103×Dic61C2semidirect
15. C2×C61×#416C2semidirect
19. #16840419C4semidirect
84. #14519764C2×C4semidirect
87. #14519756C2×C4semidirect
92. Q8×Dic61C2×C4semidirect
138. C2×#41×C61C2×C4semidirect
156. #103×C61D4semidirect
395. C2×D61#416semidirect
413. C2×#416D61semidirect
484. C61#22416semidirect
490. C2×#41C4×D61semidirect
567. #103C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404192
C2×C8×C22⋊D612
C2×#103×D612
#214487492
#214467502
#214466292
#214462442
#214462422
#214461332
#214461312
#214458322
#214457592
#214457522
#103×Dic612
C2×C61×#4162
#2241661