Finite Group Databasebeta

← #29733638

Subgroups — #29733638

Order 15616.

1158 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840144C211yesmaximal, characteristic, complemented
2C2×#16840124C211yesmaximal, characteristic, complemented
3#21451576C211yesmaximal, characteristic, complemented
4#21446827C211yesmaximal, characteristic, complemented
5#21446822C211yesmaximal, characteristic, complemented
6#21446820C211yesmaximal, characteristic, complemented
7#21446815C211yesmaximal, characteristic
8#21446781C211yesmaximal, characteristic, complemented
9#21446636C211yesmaximal, characteristic, complemented
10#21446174C211yesmaximal, characteristic, complemented
11#21446167C211yesmaximal, characteristic, complemented
12#21446160C211yesmaximal, characteristic, complemented
13#21446153C211yesmaximal, characteristic, complemented
14#21445585C211yesmaximal, characteristic, complemented
15C2×C61×#542C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C2×#14519765C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23#16840144—24no—
24#16840124—24no—
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519700C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×#14519688C2211yescharacteristic
36C2×C4×#92418C2211yescharacteristic
37#16839684—21no—
38#16839684—21no—
39#16839678—21no—
40#16839678—21no—
41#16839668C2211yescharacteristic
42#16839664C2211yescharacteristic
43#16839632C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C61×#542—24no—
51C61×#542—24no—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×#126×C61—21no—
54C2×#124×C61—21no—
55C2×#124×C61C2211yescharacteristic
56C2×#123×C61—21no—
57C2×C22⋊Q8×C61—21no—
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#121×C61C2211yescharacteristic
60C2×C4×Q8×C61C2211yescharacteristic
61C2×C4×D4×C61C2211yescharacteristic
62C2×#117×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C2×#11758202—22no—
67C2×#11758202—22no—
68C2×#11758202—41no—
69C2×#11758200—22no—
70C2×#11758200—22no—
71C2×#11758200—41no—
72C2×#11758201—22no—
73C2×#11758201—22no—
74C2×#11758201—41no—
75C2×#11758199—22no—
76C2×#11758199—22no—
77C2×#11758199—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82#14519765—22no—
83#14519765—22no—
84#14519756—41no—
85#14519756—41no—
86#14519751—41no—
87#14519751—41no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×#11758196—21no—
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99#14519701—41no—
100#14519701—41no—
101#14519700—22no—
102#14519700—22no—
103#14519698—41no—
104#14519698—41no—
105#14519697—22no—
106#14519697—22no—
107C22⋊#92418—22no—
108C22⋊#92418—22no—
109#14519688—22no—
110C4×#92418—22no—
111#14519684—21no—
112#14519684—21no—
113C22×Q8×C61—21no—
114C22×Q8×C61C2311yescharacteristic
115C22×D4×C61—21no—
116C22×D4×C61C2311yescharacteristic
117C23×C4×C61—21no—
118C23×C4×C61C2311yescharacteristic
119C4⋊Q8×C61—22no—
120C4⋊Q8×C61D414yescomplemented
121#126×C61—28no—
122#124×C61—28no—
123#124×C61—22no—
124#124×C61D414yescomplemented
125#123×C61—28no—
126C22⋊Q8×C61—28no—
127C22⋊Q8×C61—22no—
128C22⋊Q8×C61—22no—
129#121×C61—22no—
130#121×C61—22no—
131C4×Q8×C61—22no—
132C4×Q8×C61—22no—
133C4×D4×C61—22no—
134C4×D4×C61—22no—
135#117×C61—22no—
136#117×C61—22no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61D411yescharacteristic
141C2×C4⋊C4×C61D411yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
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
153C2×C42×C61C2311yescharacteristic
154C24×C61—21no—
155C24×C61C2×D411yescharacteristic
156C23×D61—21no—
157C2×Q8×C61—24no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—81no—
164C2×Q8×C61—81no—
165C2×Q8×C61C2×D412yes—
166C2×D4×C61—24no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—81no—
173C2×D4×C61—81no—
174C2×D4×C61C2×D412yes—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—24no—
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—81no—
186C22×C4×C61—81no—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2411yescharacteristic
193C2×C22⋊D61—42no—
194C2×C22⋊D61—81no—
195C2×C22⋊D61—81no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C4⋊C4×C61—24no—
212C4⋊C4×C61—24no—
213C4⋊C4×C61—24no—
214C4⋊C4×C61—22no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61C2×D412yes—
219C4⋊C4×C61C2×D412yes—
220C22⋊C4×C61—24no—
221C22⋊C4×C61—24no—
222C22⋊C4×C61—24no—
223C22⋊C4×C61—24no—
224C22⋊C4×C61—24no—
225C22⋊C4×C61—22no—
226C22⋊C4×C61—22no—
227C42×C61—24no—
228C42×C61—21no—
229C42×C61—21no—
230C42×C61C2×D412yes—
231C42×C61C2×D412yes—
232C22⋊Dic61—42no—
233#11758202—44no—
234#11758201—44no—
235#11758200—44no—
236#11758199—44no—
237#11758198—42no—
238#11758198—42no—
239#11758198—42no—
240#11758198—81no—
241#11758198—81no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—81no—
247C4⋊Dic61—81no—
248#11758196—42no—
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#4112yes—
260C2×#92418#4112yes—
261C23×C61—21no—
262C23×C61—22no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61C22×D411yescharacteristic
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283Q8×C61—22no—
284Q8×C61—22no—
285Q8×C61—41no—
286Q8×C61—41no—
287Q8×C61—84no—
288D4×C61—22no—
289D4×C61—22no—
290D4×C61—41no—
291D4×C61—41no—
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—22no—
299C2×C4×C61—21no—
300C2×C4×C61—22no—
301C2×C4×C61—21no—
302C2×C4×C61—22no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
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—84no—
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
328C22⋊D61—84no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338D244—41no—
339D244—41no—
340D244—41no—
341D244—41no—
342Dic122—41no—
343Dic122—41no—
344Dic122—41no—
345Dic122—41no—
346#92418—22no—
347#92418—22no—
348#92418—41no—
349#92418—41no—
350#25610—611nomaximal, Sylow
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—42no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—42no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—42no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61C2×#12011yescharacteristic
366C22×C61#53211yescharacteristic
367C22×C61#53511yescharacteristic
368C22×C61#57611yescharacteristic
369C22×C61#57711yescharacteristic
370C22×C61#57711yescharacteristic
371C22×C61#57811yescharacteristic
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C2×D61—81no—
377C2×D61—81no—
378C2×D61—81no—
379C4×C61—22no—
380C4×C61—22no—
381C4×C61—41no—
382C4×C61—42no—
383C4×C61—41no—
384C4×C61—42no—
385C4×C61—42no—
386C4×C61—41no—
387C4×C61#54611yescharacteristic
388C4×C61#54611yescharacteristic
389C4×C61#55011yescharacteristic
390C4×C61#55011yescharacteristic
391Dic61—81no—
392Dic61—81no—
393Dic61—81no—
394C2×#542D6111yescharacteristic, complemented
395C2×#495—611no—
396C2×#489—611no—
397#2620—611no—
398#2001—611no—
399#2000—611no—
400#2000—611no—
401#1999—611no—
402#1990—611no—
403#1959—611no—
404#1880—611no—
405#1879—611no—
406#1878—611no—
407#1877—611no—
408#1750—611no—
409C2×C61—81no—
410C2×C61—82no—
411C2×C61#243111yescharacteristic
412C2×C61#301211yescharacteristic
413C2×C61#301311yescharacteristic
414C2×C61#317311yescharacteristic
415C2×C61#317511yescharacteristic
416C2×C61#322411yescharacteristic
417C2×C61#322511yescharacteristic
418D61—161no—
419C22×Q16—611no—
420C22×SD16—611no—
421C22×SD16—611no—
422C22×D8—611no—
423#542—24no—
424#542—24no—
425C2×C4⋊Q8C2×D6111yescharacteristic
426C2×#126—21no—
427C2×#124—21no—
428C2×#124—611no—
429C2×#124C2×D6111yescharacteristic
430C2×#123—21no—
431C2×C22⋊Q8—21no—
432C2×C22⋊Q8—611no—
433C2×C22⋊Q8C2×D6111yescharacteristic
434C2×#121—611no—
435C2×#121C2×D6111yescharacteristic
436C2×C4×Q8C2×D6111yescharacteristic
437C2×C4×D4C2×D6111yescharacteristic
438C2×#117C2×D6111yescharacteristic
439#495—1224no—
440#489—1224no—
441C2×#103—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×C22⋊C8—611no—
450C2×C22⋊C8—611no—
451C2×#97—611no—
452C2×C4×C8—611no—
453#396—1221no—
454#396—1221no—
455#394—1221no—
456#394—1221no—
457#391—611no—
458#390—611no—
459#384—611no—
460#340—611no—
461#340—611no—
462#340—611no—
463#340—611no—
464#336—611no—
465#336—611no—
466C61#2561011yescharacteristic, complemented, Sylow
467C22×Q8—21no—
468C22×Q8—611no—
469C22×Q8C22×D6111yescharacteristic
470C22×D4—21no—
471C22×D4—611no—
472C22×D4—1221no—
473C22×D4C22×D6111yescharacteristic
474C23×C4—21no—
475C23×C4C22×D6111yescharacteristic
476C2×Q16—1222no—
477C2×Q16—1222no—
478C2×Q16—2441no—
479C2×SD16—1222no—
480C2×SD16—1222no—
481C2×SD16—1222no—
482C2×SD16—1222no—
483C2×SD16—2441no—
484C2×SD16—2441no—
485C2×D8—1222no—
486C2×D8—1222no—
487C2×D8—2441no—
488C22×C8—611no—
489C22×C8—611no—
490C22×C8—611no—
491C22×C8—611no—
492C4⋊Q8—22no—
493C4⋊Q8C22⋊D6114yescomplemented
494#126—28no—
495#124—28no—
496#124—22no—
497#124—1222no—
498#124—1222no—
499#124C22⋊D6114yescomplemented
500#123—28no—
501C22⋊Q8—28no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8—2441no—
505C22⋊Q8—2441no—
506#121—22no—
507#121—22no—
508#121—2441no—
509#121—2441no—
510C4×Q8—22no—
511C4×Q8—22no—
512C4×D4—22no—
513C4×D4—22no—
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
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×C4⋊C4C22×D6111yescharacteristic
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⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4C22⋊D6111yescharacteristic
540C2×C22⋊C4C22⋊D6111yescharacteristic
541C2×C42—21no—
542C2×C42C22×D6111yescharacteristic
543C2×C42C22×D6111yescharacteristic
544#103—1222no—
545#103—1222no—
546#103—2441no—
547#103—2441no—
548#102—1222no—
549#102—1222no—
550#102—2441no—
551#102—2441no—
552C22⋊C8—1222no—
553C22⋊C8—1222no—
554#97—1222no—
555C4×C8—1222no—
556#95—1221no—
557#95—1221no—
558C24—21no—
559C24—1221no—
560C24C2×C22⋊D6111yescharacteristic
561C2×Q8—21no—
562C2×Q8—24no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—81no—
568C2×Q8—81no—
569C2×Q8—1221no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8C2×C22⋊D6112yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—4881no—
591C2×D4—4881no—
592C2×D4—2442no—
593C2×D4C2×C22⋊D6112yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—24no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4C2×C22⋊D6111yescharacteristic
610C22×C4C2×C22⋊D6111yescharacteristic
611C22×C4C2×C22⋊D6111yescharacteristic
612C22×C4C2×C22⋊D6111yescharacteristic
613C22×C4C2×C22⋊D6111yescharacteristic
614C22×C4C23×D6111yescharacteristic
615Q16—2444no—
616SD16—2444no—
617SD16—2444no—
618D8—2444no—
619C2×C8—612no—
620C2×C8—612no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—24no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—4881no—
643C4⋊C4—4881no—
644C4⋊C4—2442no—
645C4⋊C4C2×C22⋊D6112yes—
646C4⋊C4C2×C22⋊D6112yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—4881no—
655C22⋊C4—4881no—
656C22⋊C4—2442no—
657C22⋊C4—2442no—
658C22⋊C4—2442no—
659C22⋊C4—2442no—
660C42—24no—
661C42—21no—
662C42—21no—
663C42C2×C22⋊D6112yes—
664C42C2×C22⋊D6112yes—
665C23—21no—
666C23—22no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23C22×C22⋊D6111yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—41no—
690Q8—41no—
691Q8—84no—
692Q8—2441no—
693Q8—2441no—
694Q8—2441no—
695Q8—2441no—
696D4—22no—
697D4—22no—
698D4—41no—
699D4—41no—
700D4—84no—
701D4—4884no—
702D4—2441no—
703D4—2441no—
704D4—2441no—
705D4—2441no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—84no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4#1451974612yes—
743C2×C4#1451974612yes—
744C2×C4C22×C22⋊D6111yescharacteristic
745C2×C4C22×C22⋊D6111yescharacteristic
746C2×C4#41×D6111yescharacteristic
747C2×C4#41×D6111yescharacteristic
748C2×C4#1451982311yescharacteristic
749C2×C4#1451982311yescharacteristic
750C8—1222no—
751C8—1222no—
752C8—2441no—
753C8—2441no—
754C22—41no—
755C22—42no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—4881no—
769C22—4881no—
770C22—4881no—
771C22—4881no—
772C22—4881no—
773C22—4881no—
774C22—4881no—
775C22C2×#1451974611yescharacteristic
776C22#1684030811yescharacteristic
777C22#1684032611yescharacteristic
778C22#1684056511yescharacteristic
779C22#1684057011yescharacteristic
780C22#1684057311yescharacteristic
781C22#1684057711yescharacteristic
782C4—22no—
783C4—22no—
784C4—41no—
785C4—42no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—42no—
790C4—4881no—
791C4—4881no—
792C4—4881no—
793C4#1684040011yescharacteristic
794C4#1684040011yescharacteristic
795C4#1684043111yescharacteristic
796C4#1684043111yescharacteristic
797C2—81no—
798C2—82no—
799C2—9761no—
800C2#2144943411yescharacteristic
801C2#2145512311yescharacteristic
802C2#2145513411yescharacteristic
803C2#2145643011yescharacteristic
804C2#2145645211yescharacteristic
805C2#2145690711yescharacteristic
806C2#2145692211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#542C2
socleC23×C61C22×D4
prime radical#21446815C2
hypercenterC2×#542D61
hypocenterC61#25610
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16840144C2semidirect
2. C2×#16840124C2semidirect
3. #21451576C2semidirect
4. #21446827C2semidirect
5. #21446822C2semidirect
6. #21446820C2semidirect
8. #21446781C2semidirect
9. #21446636C2semidirect
10. #21446174C2semidirect
11. #21446167C2semidirect
12. #21446160C2semidirect
13. #21446153C2semidirect
14. #21445585C2semidirect
15. C2×C61×#542C2semidirect
120. C4⋊Q8×C61D4semidirect
124. #124×C61D4semidirect
394. C2×#542D61semidirect
466. C61#25610semidirect
493. C4⋊Q8C22⋊D61semidirect
499. #124C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168401442
C2×#168401242
#214515762
#214468272
#214468222
#214468202
#214468152
#214467812
#214466362
#214461742
#214461672
#214461602
#214461532
#214455852
C2×C61×#5422
#2561061