Finite Group Databasebeta

← #29733282

Subgroups — #29733282

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840452C211yesmaximal, characteristic, complemented
2C2×#16840116C211yesmaximal, characteristic, complemented
3C2×#16839981C211yesmaximal, characteristic, complemented
4#21446827C211yesmaximal, characteristic, complemented
5#21446827C211yesmaximal, characteristic, complemented
6#21446822C211yesmaximal, characteristic, complemented
7#21446822C211yesmaximal, characteristic, complemented
8#21446776C211yesmaximal, characteristic, complemented
9#21446614C211yesmaximal, characteristic, complemented
10#21446142C211yesmaximal, characteristic, complemented
11#21446137C211yesmaximal, characteristic, complemented
12#21446132C211yesmaximal, characteristic, complemented
13#21446127C211yesmaximal, characteristic, complemented
14C4×#14519700C211yesmaximal, characteristic, complemented
15C61×#2540C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18#16840452—24no—
19#16840452—24no—
20C2×#14519770—21no—
21C2×#14519769C2211yescharacteristic
22C2×#14519767—21no—
23C2×#14519758—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519756C2211yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×#14519736C2211yescharacteristic
28C2×#14519733—21no—
29C22×C4⋊Dic61C2211yescharacteristic
30#16840116—24no—
31#16839981—24no—
32C2×C4⋊#92418C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×C4×#92418C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×#124×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×#121×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C61×#399—21no—
59C61×#392—21no—
60C61×#390—21no—
61C61×#390—21no—
62C4×C4⋊C4×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C23×Dic61—21no—
65C2×#11758202—22no—
66C2×#11758202—41no—
67C2×#11758202—41no—
68C2×#11758200—22no—
69C2×#11758200—41no—
70C2×#11758200—41no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519770—28no—
76#14519769—22no—
77#14519769D414yescomplemented
78#14519767—28no—
79#14519758—28no—
80#14519756—22no—
81#14519756—22no—
82#14519756—22no—
83#14519756—22no—
84C4×Dic122—22no—
85C4×Dic122D414yescomplemented
86#14519736—22no—
87#14519736—22no—
88#14519733—28no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C4⋊#92418—22no—
106#14519701—22no—
107#14519701—22no—
108#14519701—22no—
109#14519700—22no—
110#14519700—22no—
111#14519698—22no—
112#14519698—22no—
113#14519698—22no—
114C22⋊#92418—41no—
115C22⋊#92418—41no—
116C22⋊#92418—41no—
117C22⋊#92418—41no—
118C4×#92418—22no—
119C22×Q8×C61C2311yescharacteristic
120C22×D4×C61—21no—
121C22×D4×C61—21no—
122C22×D4×C61D411yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126#124×C61—22no—
127#124×C61—22no—
128C22⋊Q8×C61—22no—
129C22⋊Q8×C61—22no—
130C22⋊Q8×C61—41no—
131C22⋊Q8×C61—41no—
132#121×C61—22no—
133#121×C61—22no—
134#121×C61—41no—
135#121×C61—41no—
136C4×D4×C61—22no—
137C4×D4×C61—22no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61D411yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61D411yescharacteristic
150C2×C22⋊C4×C61D411yescharacteristic
151C2×C42×C61—21no—
152C2×C42×C61C2311yescharacteristic
153#95×C61—21no—
154C24×C61—21no—
155C24×C61C2×D411yescharacteristic
156C24×C61C2×D411yescharacteristic
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—41no—
172C2×D4×C61—42no—
173C2×D4×C61—42no—
174C2×D4×C61—42no—
175C2×D4×C61—42no—
176C2×D4×C61—81no—
177C2×D4×C61—81no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
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—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2411yescharacteristic
198C22×Dic61—24no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—42no—
204C22×Dic61—42no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122C2×D412yes—
211C4⋊C4×C61—22no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—42no—
215C4⋊C4×C61—42no—
216C4⋊C4×C61#4112yes—
217C4⋊C4×C61#4112yes—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—42no—
223C22⋊C4×C61—42no—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—42no—
226C42×C61—81no—
227C42×C61C2×D412yes—
228C42×C61C2×D412yes—
229C22⋊Dic61—24no—
230C22⋊Dic61—24no—
231C22⋊Dic61—24no—
232#11758202—44no—
233#11758200—44no—
234C4⋊Dic61—24no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61C2×D412yes—
239C4⋊Dic61C2×D412yes—
240C4⋊Dic61C2×D412yes—
241#11758196—24no—
242#11758196—24no—
243#11758196—24no—
244#11758196—24no—
245#11758196—24no—
246C4×Dic61—24no—
247C4×Dic61—24no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61#13512yes—
281C23×C61C22×D411yescharacteristic
282Q8×C61—41no—
283Q8×C61—41no—
284Q8×C61—41no—
285Q8×C61—41no—
286D4×C61—44no—
287D4×C61—41no—
288D4×C61—41no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—84no—
292D4×C61—84no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
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×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61#12012yes—
321C2×C4×C61#12012yes—
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C2×#4111yescharacteristic
325C2×C4×C61C2×#4111yescharacteristic
326C2×C4×C61H(5,𝔽2)11yescharacteristic
327C2×C4×C61H(5,𝔽2)11yescharacteristic
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—48no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341Dic122—22no—
342Dic122—22no—
343Dic122—41no—
344Dic122—41no—
345#92418—41no—
346#92418—41no—
347#92418—41no—
348#92418—41no—
349#25576—611nomaximal, Sylow
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61C2×#12011yescharacteristic
372C22×C61#54611yescharacteristic
373C22×C61#54611yescharacteristic
374C22×C61C2×#13511yescharacteristic
375C22×C61#57511yescharacteristic
376C22×C61#57711yescharacteristic
377C22×C61#57811yescharacteristic
378C4×C61—22no—
379C4×C61—22no—
380C4×C61—41no—
381C4×C61—41no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61—81no—
385C4×C61#53211yescharacteristic
386C4×C61#53511yescharacteristic
387C4×C61#55011yescharacteristic
388C4×C61#55011yescharacteristic
389Dic61—42no—
390Dic61—42no—
391Dic61—42no—
392Dic61—42no—
393C2×#552—611no—
394C2×#488—611no—
395C2×#464—611no—
396#2540D6111yescharacteristic
397#2001—611no—
398#2001—611no—
399#2000—611no—
400#2000—611no—
401#1989—611no—
402#1954—611no—
403#1875—611no—
404#1874—611no—
405#1873—611no—
406#1872—611no—
407C4×#103—611no—
408C2×C61—42no—
409C2×C61—81no—
410C2×C61—161no—
411C2×C61#243111yescharacteristic
412C2×C61#300211yescharacteristic
413C2×C61#301311yescharacteristic
414C2×C61#329611yescharacteristic
415C2×C61#330011yescharacteristic
416C2×C61#332311yescharacteristic
417C2×C61#332711yescharacteristic
418C22×Q16—611no—
419C22×SD16—611no—
420#552—1224no—
421#552—1224no—
422C2×#126—1221no—
423C2×#125—611no—
424C2×#125—1221no—
425C2×#124C2×D6111yescharacteristic
426C2×#123—1221no—
427C2×C22⋊Q8—611no—
428C2×C22⋊Q8—611no—
429C2×C22⋊Q8C2×D6111yescharacteristic
430C2×C22⋊Q8C2×D6111yescharacteristic
431C2×#121C2×D6111yescharacteristic
432C2×#121C2×D6111yescharacteristic
433C2×C4×Q8—611no—
434C2×C4×D4C2×D6111yescharacteristic
435C2×#117—611no—
436C2×#117—1221no—
437C22×C4⋊C4—611no—
438#488—1224no—
439#464—1224no—
440C2×C4⋊C8—611no—
441C2×#103—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#103—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×C22⋊C8—611no—
450C2×C22⋊C8—611no—
451C2×C22⋊C8—611no—
452C2×C22⋊C8—611no—
453C2×C4×C8—611no—
454#399—21no—
455#392—21no—
456#390—21no—
457#390—21no—
458C4×C4⋊C4C2×D6111yescharacteristic
459#340—611no—
460#340—611no—
461#340—611no—
462#340—611no—
463#340—611no—
464#340—611no—
465C61#2557611yescharacteristic, complemented, Sylow
466C22×Q8—611no—
467C22×Q8C22×D6111yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4C22⋊D6111yescharacteristic
471C22×D4C22×D6111yescharacteristic
472C23×C4—1221no—
473C23×C4C22×D6111yescharacteristic
474C23×C4C22×D6111yescharacteristic
475C2×Q16—1222no—
476C2×Q16—2441no—
477C2×Q16—2441no—
478C2×SD16—1222no—
479C2×SD16—2441no—
480C2×SD16—2441no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8—611no—
485#126—1228no—
486#125—614no—
487#125—1228no—
488#125—1222no—
489#124—22no—
490#124—22no—
491#123—1228no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—41no—
495C22⋊Q8—41no—
496C22⋊Q8—1222no—
497C22⋊Q8—1222no—
498C22⋊Q8—1222no—
499C22⋊Q8—1222no—
500#121—22no—
501#121—22no—
502#121—41no—
503#121—41no—
504C4×Q8—614no—
505C4×Q8—1222no—
506C4×D4—22no—
507C4×D4—22no—
508#117—1228no—
509#117—1222no—
510#117—1222no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—1222no—
517C2×C4⋊C4—1222no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4C22⋊D6111yescharacteristic
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4C22⋊D6111yescharacteristic
537C2×C22⋊C4C22⋊D6111yescharacteristic
538C2×C42—21no—
539C2×C42—1221no—
540C2×C42—1221no—
541C2×C42C22×D6111yescharacteristic
542C4⋊C8—1222no—
543#103—1222no—
544#103—1222no—
545#103—1222no—
546#103—1222no—
547#103—1222no—
548#102—1222no—
549#102—1222no—
550#102—1222no—
551C22⋊C8—2441no—
552C22⋊C8—2441no—
553C22⋊C8—2441no—
554C22⋊C8—2441no—
555C4×C8—1222no—
556#95—21no—
557C24—21no—
558C24C2×C22⋊D6111yescharacteristic
559C24C2×C22⋊D6111yescharacteristic
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—612no—
567C2×Q8—1221no—
568C2×Q8—1221no—
569C2×Q8—1221no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—41no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—1224no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—2442no—
608C22×C4—2442no—
609C22×C4C2×C22⋊D6111yescharacteristic
610C22×C4C2×C22⋊D6111yescharacteristic
611C22×C4C2×C22⋊D6111yescharacteristic
612C22×C4C2×C22⋊D6111yescharacteristic
613C22×C4C23×D6111yescharacteristic
614Q16—2444no—
615SD16—2444no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—22no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—612no—
634C4⋊C4—612no—
635C4⋊C4—612no—
636C4⋊C4—1224no—
637C4⋊C4—1224no—
638C4⋊C4—1224no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1224no—
643C4⋊C4—1224no—
644C4⋊C4—1224no—
645C4⋊C4#1175822412yes—
646C4⋊C4#1175822412yes—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C22⋊C4—1224no—
658C42—81no—
659C42—1224no—
660C42—1224no—
661C42D4×D6112yes—
662C42D4×D6112yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23#1451979712yes—
684C23C22×C22⋊D6111yescharacteristic
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689Q8—1222no—
690Q8—1222no—
691Q8—2441no—
692Q8—2441no—
693D4—44no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—2448no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4#1451974512yes—
741C2×C4#1451974512yes—
742C2×C4C2×D4×D6111yescharacteristic
743C2×C4C2×D4×D6111yescharacteristic
744C2×C4C2×#1175822411yescharacteristic
745C2×C4C2×#1175822411yescharacteristic
746C2×C4#1451982211yescharacteristic
747C2×C4#1451982211yescharacteristic
748C8—2441no—
749C8—2441no—
750C8—2441no—
751C8—2441no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22C2×#1451974511yescharacteristic
774C22#1684040611yescharacteristic
775C22#1684040611yescharacteristic
776C22C2×#1451979711yescharacteristic
777C22#1684056011yescharacteristic
778C22#1684057311yescharacteristic
779C22#1684057711yescharacteristic
780C4—22no—
781C4—22no—
782C4—42no—
783C4—41no—
784C4—41no—
785C4—42no—
786C4—81no—
787C4—2442no—
788C4—2442no—
789C4—2442no—
790C4—2442no—
791C4#1684031011yescharacteristic
792C4#1684032511yescharacteristic
793C4#1684043211yescharacteristic
794C4#1684043211yescharacteristic
795C2—42no—
796C2—81no—
797C2—161no—
798C2#2144943511yescharacteristic
799C2#2145503511yescharacteristic
800C2#2145513111yescharacteristic
801C2#2145765411yescharacteristic
802C2#2145770611yescharacteristic
803C2#2145803511yescharacteristic
804C2#2145808711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2540C2
socleC23×C61C22×D4
hypercenter#2540D61
hypocenterC61#25576
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#16840452C2semidirect
2. C2×#16840116C2semidirect
3. C2×#16839981C2semidirect
4. #21446827C2semidirect
5. #21446827C2semidirect
6. #21446822C2semidirect
7. #21446822C2semidirect
8. #21446776C2semidirect
9. #21446614C2semidirect
10. #21446142C2semidirect
11. #21446137C2semidirect
12. #21446132C2semidirect
13. #21446127C2semidirect
14. C4×#14519700C2semidirect
77. #14519769D4semidirect
85. C4×Dic122D4semidirect
465. C61#25576semidirect

Maximal subgroups

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

subgroupindex
C2×#168404522
C2×#168401162
C2×#168399812
#214468272
#214468222
#214467762
#214466142
#214461422
#214461372
#214461322
#214461272
C4×#145197002
C61×#25402
#2557661