Finite Group Databasebeta

← #29695576

Subgroups — #29695576

Order 15616.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D61C211yesmaximal, characteristic
2C2×#16839836C211yesmaximal, characteristic
3C2×#16839771C211yesmaximal, characteristic, complemented
4C2×#103×D61C211yesmaximal, characteristic, complemented
5#21448741C211yesmaximal, characteristic
6#21446740C211yesmaximal, characteristic, complemented
7#21446637C211yesmaximal, characteristic, complemented
8#21446250C211yesmaximal, characteristic, complemented
9#21446239C211yesmaximal, characteristic, complemented
10#21446129C211yesmaximal, characteristic, complemented
11#21446123C211yesmaximal, characteristic, complemented
12#21445832C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445651C211yesmaximal, characteristic, complemented
15C61×#1787C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19Q8×C22⋊D61—24no—
20Q8×C22⋊D61C418yescomplemented
21C2×#14519775—21no—
22C2×#14519775C2211yescharacteristic
23C2×#14519756—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519753—21no—
26C2×#14519753C2211yescharacteristic
27C2×Q8×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519736C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839836—24no—
33C2×#14519706C2211yescharacteristic
34#16839771—24no—
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43#103×D61—24no—
44C2×#14519689C2211yescharacteristic
45C2×#14519687C2211yescharacteristic
46#16839650—21no—
47#16839644—21no—
48#16839638—21no—
49#16839627C2211yescharacteristic
50#16839619C2211yescharacteristic
51C4⋊C4×Dic61C2211yescharacteristic
52#16839609—21no—
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C23×Q8×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
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⋊D61D411yescharacteristic
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61C2311yescharacteristic
76C2×#11758194—22no—
77C2×#11758194—22no—
78C2×#11758194—41no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83C2×C8×D61—41no—
84#14519775—28no—
85#14519775—22no—
86#14519775C2×C414yescomplemented
87#14519756—22no—
88#14519756—28no—
89#14519756C2×C414yescomplemented
90#14519753—22no—
91#14519753—28no—
92#14519753C2×C414yes—
93Q8×Dic61—22no—
94Q8×Dic61C2×C414yescomplemented
95C4×C22⋊D61—28no—
96C4×C22⋊D61C2×C414yes—
97C4×C22⋊D61D414yes—
98#14519736—22no—
99#14519736—41no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196D411yescharacteristic
110C4⋊C4×D61—22no—
111C4⋊C4×D61—41no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61D411yescharacteristic
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198D411yescharacteristic
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122#14519706—22no—
123#14519702—22no—
124#14519702—41no—
125#14519701—22no—
126#14519701—22no—
127#14519701—22no—
128#14519701D414yescomplemented
129#14519700—22no—
130#14519700—41no—
131#14519689—22no—
132#14519687—22no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137C22×Q8×C61—21no—
138C22×Q8×C61—22no—
139C22×Q8×C61—22no—
140C22×Q8×C61—22no—
141C22×Q8×C61—41no—
142C22×Q8×C61—41no—
143C22×Q8×C61C2×C414yescomplemented
144C22×Q8×C61C2311yescharacteristic
145C22×Q8×C61C2311yescharacteristic
146C23×C4×C61—21no—
147C23×C4×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153#103×C61—22no—
154#103×C61—22no—
155#103×C61—41no—
156#103×C61—41no—
157C22⋊C8×C61—22no—
158#95×C61—21no—
159C24×C61C2×D411yescharacteristic
160C23×D61C2×D411yescharacteristic
161C2×Q8×C61—24no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—28no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—42no—
172C2×Q8×C61—42no—
173C2×Q8×C61—44no—
174C2×Q8×C61—44no—
175C2×Q8×C61—44no—
176C2×Q8×C61C22×C412yes—
177C2×Q8×C61C22×C412yes—
178C2×Q8×C61C2×D412yes—
179C2×Q8×C61#4112yes—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—24no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
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⋊D61C22⋊C414yes—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205Q8×D61—28no—
206Q8×D61—44no—
207Q8×D61—44no—
208Q8×D61—44no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—24no—
214C2×C4×D61—42no—
215C2×C4×D61—42no—
216C2×C4×D61—42no—
217C2×C4×D61—42no—
218C2×C4×D61—81no—
219C2×C4×D61C22×C412yes—
220C2×C4×D61C2×D412yes—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—24no—
227C2×Dic122—42no—
228C2×Dic122—42no—
229C2×Dic122C22×C412yes—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C22⋊C4×C61—81no—
241C22⋊Dic61—24no—
242C22⋊Dic61—42no—
243C22⋊Dic61C22⋊C414yes—
244#11758198—24no—
245#11758198—42no—
246#11758198C22⋊C414yes—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—24no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61C22×C412yes—
253C4⋊Dic61C2×D412yes—
254#11758196—24no—
255#11758196—24no—
256#11758196—24no—
257#11758196—24no—
258#11758196—42no—
259#11758196C22⋊C414yes—
260C4×Dic61—24no—
261C4×Dic61—42no—
262C4×Dic61—81no—
263C4×Dic61C22×C412yes—
264C4×Dic61C2×D412yes—
265#11758194—44no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418C2×D412yes—
272C8×D61—44no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61C2×C22⋊C412yes—
280C23×C61C22×D411yescharacteristic
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61C2×C22⋊C412yes—
286C22×D61#13712yes—
287C22×D61#13712yes—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—22no—
293Q8×C61—48no—
294Q8×C61—41no—
295Q8×C61—41no—
296Q8×C61C4×D414yes—
297C2×C4×C61—22no—
298C2×C4×C61—21no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—21no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—48no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61C2×C22⋊C412yes—
317C2×C4×C61C23×C411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C22⋊D61—28no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61C2×C22⋊C412yes—
343C2×Dic61C2×C22⋊C412yes—
344C2×Dic61C2×C22⋊C412yes—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—48no—
350C4×D61—84no—
351Dic122—22no—
352Dic122—22no—
353Dic122—48no—
354Dic122—41no—
355Dic122—41no—
356C8×C61—41no—
357C8×C61—41no—
358#92418—22no—
359#92418—41no—
360#22425—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61C22×C22⋊C411yescharacteristic
369C22×C61D4211yescharacteristic
370C22×C61#54611yescharacteristic
371C22×C61C2×#13711yescharacteristic
372C22×C61C2×#13711yescharacteristic
373C22×C61#57711yescharacteristic
374C22×C61#57811yescharacteristic
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61#41914yescomplemented
382C4×C61—24no—
383C4×C61—22no—
384C4×C61—42no—
385C4×C61—81no—
386C4×C61—81no—
387C4×C61C2×C4×D411yescharacteristic
388C4×C61#51811yescharacteristic
389C4×C61D4211yescharacteristic
390C4×C61#54611yescharacteristic
391Dic61—22no—
392Dic61—22no—
393Dic61—22no—
394Dic61—42no—
395Dic61—42no—
396Dic61—42no—
397Dic61—81no—
398C2×D4×Q8—611no—
399C2×#435—611no—
400C2×#419—611no—
401C22×#103—611no—
402#2352—611no—
403#1981—611no—
404#1960—611no—
405#1894—611no—
406#1892—611no—
407#1873—611no—
408#1872—611no—
409#1805—611no—
410#1787—611no—
411#1787D6111yescharacteristic, complemented
412#1763—611no—
413C2×C61—42no—
414C2×C61D4×C22⋊C411yescharacteristic
415C2×C61C2×#41911yescharacteristic
416C2×C61#289811yescharacteristic
417C2×C61#326611yescharacteristic
418C2×C61#327011yescharacteristic
419C2×C61#331211yescharacteristic
420C2×C61#332011yescharacteristic
421D61—24no—
422C23×Q8—611no—
423C23×Q8C2×D6111yescharacteristic
424C22×M16—611no—
425C23×C8—611no—
426D4×Q8—618no—
427D4×Q8—1224no—
428C2×C4⋊Q8—611no—
429C2×C4⋊Q8—1221no—
430C2×C22⋊Q8—611no—
431C2×C22⋊Q8—611no—
432C2×C22⋊Q8—1221no—
433C2×C22⋊Q8—1221no—
434C2×C4×Q8—611no—
435C2×C4×D4—611no—
436C2×C4×D4—1221no—
437C2×#117—611no—
438C22×C4⋊C4—611no—
439#435—1224no—
440C2×C4⋊C8—611no—
441#419—1224no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#103—611no—
446C2×#103—611no—
447C2×#103—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—1224no—
451C2×#103C2×D6111yescharacteristic
452C2×#103C2×D6111yescharacteristic
453C2×#103C2×D6111yescharacteristic
454C2×#103C2×D6111yescharacteristic
455C2×C22⋊C8—611no—
456C2×C22⋊C8C2×D6111yescharacteristic
457C2×#97—611no—
458#388—1221no—
459#387—1221no—
460#386—1221no—
461#382—611no—
462#380—611no—
463#380C2×D6111yescharacteristic
464C4×C4⋊C4—611no—
465C4×C22⋊C4—1221no—
466#340—611no—
467#340—611no—
468#340—611no—
469#340—611no—
470C61#2242511yescharacteristic, complemented, Sylow
471C22×Q8—21no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8—41no—
476C22×Q8—41no—
477C22×Q8—614no—
478C22×Q8—611no—
479C22×Q8—1221no—
480C22×Q8—1222no—
481C22×Q8—1222no—
482C22×Q8—1222no—
483C22×Q8—2441no—
484C22×Q8—2441no—
485C22×Q8C4×D6114yescomplemented
486C22×Q8C22×D6111yescharacteristic
487C22×Q8C22×D6111yescharacteristic
488C22×D4—611no—
489C23×C4—21no—
490C23×C4—611no—
491C23×C4—1221no—
492C23×C4—1221no—
493C23×C4C22×D6111yescharacteristic
494C2×M16—1222no—
495C2×M16—1222no—
496C2×M16—2441no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8—1222no—
500C22×C8—1222no—
501C22×C8—2441no—
502C22×C8C22×D6111yescharacteristic
503C22×C8C22×D6111yescharacteristic
504C4⋊Q8—614no—
505C4⋊Q8—1222no—
506C4⋊Q8—1228no—
507C22⋊Q8—614no—
508C22⋊Q8—614no—
509C22⋊Q8—1228no—
510C22⋊Q8—1228no—
511C22⋊Q8—1222no—
512C22⋊Q8—1222no—
513C4×Q8—614no—
514C4×Q8—1222no—
515C4×D4—614no—
516C4×D4—614no—
517C4×D4—1228no—
518#117—1222no—
519#117—2441no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—1222no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—2441no—
532C2×C4⋊C4C22×D6111yescharacteristic
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C42—611no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42—1221no—
545C4⋊C8—1222no—
546#103—22no—
547#103—22no—
548#103—41no—
549#103—41no—
550#103—614no—
551#103—1222no—
552#103—1222no—
553#103—1222no—
554#103—1222no—
555#103—1222no—
556#103—2441no—
557#103—2441no—
558C22⋊C8—22no—
559C22⋊C8—1222no—
560#97—1222no—
561#95—21no—
562#95—1221no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566C24—611no—
567C24D4×D6111yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—24no—
573C2×Q8—28no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8—42no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—44no—
583C2×Q8—612no—
584C2×Q8—1224no—
585C2×Q8—1221no—
586C2×Q8—1228no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—1221no—
590C2×Q8—1221no—
591C2×Q8—2442no—
592C2×Q8—2442no—
593C2×Q8—2444no—
594C2×Q8—2444no—
595C2×Q8—2444no—
596C2×Q8C2×C4×D6112yes—
597C2×Q8C2×C4×D6112yes—
598C2×Q8D4×D6112yes—
599C2×Q8#1175822412yes—
600C2×D4—614no—
601C2×D4—1222no—
602C2×D4—1222no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—24no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—612no—
618C22×C4—612no—
619C22×C4—1224no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—4881no—
629C22×C4—2442no—
630C22×C4—2442no—
631C22×C4—2442no—
632C22×C4—2442no—
633C22×C4C2×C4×D6112yes—
634C22×C4D4×D6112yes—
635C22×C4D4×D6111yescharacteristic
636C22×C4C23×D6111yescharacteristic
637M16—2444no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—612no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—2444no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—614no—
656C4⋊C4—612no—
657C4⋊C4—612no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1224no—
665C4⋊C4—1221no—
666C4⋊C4—1221no—
667C4⋊C4—2442no—
668C22⋊C4—81no—
669C22⋊C4—614no—
670C22⋊C4—614no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4—2442no—
674C22⋊C4—2442no—
675C42—612no—
676C42—612no—
677C42—1224no—
678C42—4881no—
679C42—2442no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—612no—
687C23—612no—
688C23—612no—
689C23—1221no—
690C23—1221no—
691C23—1221no—
692C23—1221no—
693C23C22⋊C4×D6112yes—
694C23C2×D4×D6111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—48no—
701Q8—41no—
702Q8—41no—
703Q8—1222no—
704Q8—1222no—
705Q8—2448no—
706Q8—2441no—
707Q8—2441no—
708Q8#1451973714yes—
709D4—1228no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—612no—
730C2×C4—612no—
731C2×C4—612no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—4884no—
746C2×C4—2448no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4C22⋊C4×D6112yes—
757C2×C4C22×C4×D6111yescharacteristic
758C2×C4C2×D4×D6111yescharacteristic
759C2×C4C2×D4×D6111yescharacteristic
760C2×C4C2×#1175822411yescharacteristic
761C2×C4#1451982211yescharacteristic
762C2×C4#1451982211yescharacteristic
763C8—41no—
764C8—41no—
765C8—1222no—
766C8—2441no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—614no—
775C22—1222no—
776C22—1222no—
777C22—1222no—
778C22—1222no—
779C22—1222no—
780C22—1222no—
781C22C2×C22⋊C4×D6111yescharacteristic
782C22#1684039411yescharacteristic
783C22#1684039911yescharacteristic
784C22#137×D6111yescharacteristic
785C22#137×D6111yescharacteristic
786C22#1684056811yescharacteristic
787C22#1684057511yescharacteristic
788C4—22no—
789C4—24no—
790C4—42no—
791C4—81no—
792C4—81no—
793C4—1222no—
794C4—1222no—
795C4—1222no—
796C4—4881no—
797C4—2442no—
798C4—2442no—
799C4—2442no—
800C4C2×#1451973711yescharacteristic
801C4#1684023511yescharacteristic
802C4#1684039411yescharacteristic
803C4#1684039911yescharacteristic
804C2—42no—
805C2—1224no—
806C2#2144863511yescharacteristic
807C2#419×D6111yescharacteristic
808C2#2145434711yescharacteristic
809C2#2145733211yescharacteristic
810C2#2145739211yescharacteristic
811C2#2145786311yescharacteristic
812C2#2145798311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1787C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
cosocleC22×C4×C61C24
hypercenter#1787D61
hypocenterC61#22425
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
3. C2×#16839771C2semidirect
4. C2×#103×D61C2semidirect
6. #21446740C2semidirect
7. #21446637C2semidirect
8. #21446250C2semidirect
9. #21446239C2semidirect
10. #21446129C2semidirect
11. #21446123C2semidirect
12. #21445832C2semidirect
13. #21445752C2semidirect
14. #21445651C2semidirect
15. C61×#1787C2semidirect
20. Q8×C22⋊D61C4semidirect
86. #14519775C2×C4semidirect
89. #14519756C2×C4semidirect
94. Q8×Dic61C2×C4semidirect
128. #14519701D4semidirect
143. C22×Q8×C61C2×C4semidirect
381. C2×D61#419semidirect
411. #1787D61semidirect
470. C61#22425semidirect
485. C22×Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D612
C2×#168398362
C2×#168397712
C2×#103×D612
#214487412
#214467402
#214466372
#214462502
#214462392
#214461292
#214461232
#214458322
#214457522
#214456512
C61×#17872
#2242561