Finite Group Databasebeta

← #29730976

Subgroups — #29730976

Order 15616.

1120 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840010C211yesmaximal, characteristic, complemented
2C2×#16839993C211yesmaximal, characteristic, complemented
3C2×#16839962C211yesmaximal, characteristic, complemented
4C2×#16839834C211yesmaximal, characteristic, complemented
5#21450765C211yesmaximal, characteristic
6#21447008C211yesmaximal, characteristic, complemented
7#21447001C211yesmaximal, characteristic, complemented
8#21446820C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446642C211yesmaximal, characteristic, complemented
11#21446585C211yesmaximal, characteristic, complemented
12#21446255C211yesmaximal, characteristic, complemented
13#21446245C211yesmaximal, characteristic, complemented
14#21445649C211yesmaximal, characteristic, complemented
15C61×#2536C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519774C2211yescharacteristic
21C2×#14519773—21no—
22C2×#14519751C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519751C2211yescharacteristic
25C2×#14519751C2211yescharacteristic
26#16840010—24no—
27#16839993—24no—
28#16839962—24no—
29#16839834—24no—
30C2×#14519710C2211yescharacteristic
31C2×#14519708C2211yescharacteristic
32C2×C4⋊#92418C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×#14519688C2211yescharacteristic
44#16839671—21no—
45#16839671—21no—
46#16839663—21no—
47C4×C4⋊Dic61C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×C22⋊Q8×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#398—21no—
57C61×#394—21no—
58C61×#388—21no—
59C61×#388—21no—
60C61×#382C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic
63C22×D244—21no—
64C22×D244—21no—
65C22×D244C2311yescharacteristic
66C22×D244C2311yescharacteristic
67C22×C22⋊D61—21no—
68C22×C22⋊D61—21no—
69C22×C22⋊D61—21no—
70C22×C22⋊D61—21no—
71C2×#11758201—22no—
72C2×#11758201—22no—
73C2×#11758201—22no—
74C2×#11758201—22no—
75C2×#11758201—41no—
76C2×#11758201—41no—
77C2×#11758194—22no—
78C2×#11758194—22no—
79C2×#11758194—41no—
80C22×#92418—22no—
81C22×#92418—22no—
82C22×#92418—41no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87#14519774—22no—
88#14519774—22no—
89#14519773—44no—
90#14519751—22no—
91#14519751—22no—
92#14519751—22no—
93#14519751—22no—
94#14519751—41no—
95#14519751—41no—
96#14519751—41no—
97#14519751—41no—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—21no—
105#14519710—22no—
106#14519708—22no—
107C4⋊#92418D414yescomplemented
108#14519701—22no—
109#14519701D414yescomplemented
110#14519697—22no—
111#14519697—22no—
112#14519697—22no—
113#14519697—22no—
114#14519697—41no—
115#14519697—41no—
116C22⋊#92418—22no—
117C22⋊#92418—22no—
118#14519688—22no—
119#14519684—21no—
120C22×Q8×C61C2311yescharacteristic
121C22×D4×C61D411yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C22⋊Q8×C61—22no—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61—41no—
127C22⋊Q8×C61—41no—
128C4×Q8×C61—22no—
129C4×Q8×C61—22no—
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61D411yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C42×C61—21no—
146C2×C42×C61C2311yescharacteristic
147#95×C61—21no—
148#95×C61—21no—
149#95×C61—21no—
150#95×C61—21no—
151C24×C61C2×D411yescharacteristic
152C24×C61C2×D411yescharacteristic
153C23×D61—21no—
154C23×D61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61C2×D412yes—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—41no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2411yescharacteristic
185C2×C22⋊D61—42no—
186C2×C22⋊D61—42no—
187C2×C22⋊D61—42no—
188C2×C22⋊D61—42no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—81no—
194C2×C22⋊D61—81no—
195C2×C22⋊D61—81no—
196C2×C22⋊D61—81no—
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×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—42no—
212C2×D244—42no—
213C2×D244—42no—
214C2×D244—42no—
215C2×D244—81no—
216C2×D244—81no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—42no—
225C4⋊C4×C61—42no—
226C4⋊C4×C61—42no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—42no—
230C22⋊C4×C61—42no—
231C22⋊C4×C61—42no—
232C22⋊C4×C61—42no—
233C42×C61—42no—
234C42×C61C2×D412yes—
235C42×C61#4112yes—
236#11758201—44no—
237#11758201—44no—
238#11758198—42no—
239#11758198—42no—
240#11758198—42no—
241#11758198—42no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61C2×D412yes—
245C4⋊Dic61#4112yes—
246C4×Dic61—42no—
247#11758194—44no—
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—44no—
258C2×#92418C2×D412yes—
259C2×#92418C2×D412yes—
260C2×#92418C2×D412yes—
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—21no—
274C23×C61AGL(1,ℤ/8)12yes—
275C23×C61C22×D411yescharacteristic
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—41no—
293Q8×C61—41no—
294D4×C61—44no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—22no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
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—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61#12112yes—
326C2×C4×C61#12112yes—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×C4×C61C2×#4111yescharacteristic
331C2×C4×C61H(5,𝔽2)11yescharacteristic
332C2×C4×C61H(5,𝔽2)11yescharacteristic
333C22⋊D61—84no—
334C22⋊D61—84no—
335C22⋊D61—84no—
336C22⋊D61—84no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343D244—41no—
344D244—41no—
345D244—41no—
346D244—41no—
347D244—41no—
348D244—41no—
349D244—41no—
350D244—41no—
351D244—84no—
352D244—84no—
353#92418—22no—
354#92418—22no—
355#92418—22no—
356#92418—41no—
357#25402—611nomaximal, Sylow
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—22no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61C2×#12111yescharacteristic
373C22×C61D4211yescharacteristic
374C22×C61#54611yescharacteristic
375C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C61#57511yescharacteristic
377C22×C61#57711yescharacteristic
378C22×C61#57711yescharacteristic
379C2×D61—81no—
380C2×D61—81no—
381C2×D61—81no—
382C2×D61—81no—
383C2×D61—81no—
384C2×D61—81no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C2×D61—81no—
393C4×C61—22no—
394C4×C61—22no—
395C4×C61—41no—
396C4×C61—41no—
397C4×C61—42no—
398C4×C61—81no—
399C4×C61—81no—
400C4×C61—81no—
401C4×C61#53211yescharacteristic
402C4×C61#54011yescharacteristic
403C4×C61D4211yescharacteristic
404C4×C61#55011yescharacteristic
405Dic61—42no—
406Dic61—42no—
407C2×#468—611no—
408C2×#465—611no—
409C2×#460—611no—
410C2×#435—611no—
411#2541—611no—
412#2536D6111yescharacteristic, complemented
413#2034—611no—
414#2033—611no—
415#2000—611no—
416#2000—611no—
417#1961—611no—
418#1949—611no—
419#1895—611no—
420#1893—611no—
421#1763—611no—
422C2×C61—42no—
423C2×C61—81no—
424C2×C61#242811yescharacteristic
425C2×C61#305511yescharacteristic
426C2×C61#305711yescharacteristic
427C2×C61#326511yescharacteristic
428C2×C61#327111yescharacteristic
429C2×C61#331011yescharacteristic
430C2×C61#331711yescharacteristic
431D61—161no—
432D61—161no—
433C22×SD16—611no—
434C22×SD16—611no—
435C22×M16—611no—
436C23×C8—611no—
437C2×#127—611no—
438C2×#127—1221no—
439C2×C22⋊Q8C2×D6111yescharacteristic
440C2×C22⋊Q8C2×D6111yescharacteristic
441C2×#121—611no—
442C2×#121—611no—
443C2×#121—611no—
444C2×#121—611no—
445C2×C4×Q8C2×D6111yescharacteristic
446C2×C4×D4C2×D6111yescharacteristic
447#468—1224no—
448#465—1224no—
449#460—1224no—
450#435—1224no—
451C2×#107—611no—
452C2×#106—611no—
453C2×C4⋊C8—611no—
454C2×#103—611no—
455C2×#103—611no—
456C2×#102—611no—
457C2×#102—611no—
458C2×#102—611no—
459C2×#102—611no—
460C2×#102—611no—
461C2×#102—611no—
462C2×C22⋊C8—611no—
463C2×C22⋊C8—611no—
464C2×#97—611no—
465#398—21no—
466#394—21no—
467#392—1221no—
468#392—1221no—
469#390—1221no—
470#388—21no—
471#388—21no—
472#382C2×D6111yescharacteristic
473#380C2×D6111yescharacteristic
474#380C2×D6111yescharacteristic
475C4×C4⋊C4—611no—
476#340—611no—
477#340—611no—
478#340—611no—
479#340—611no—
480C61#2540211yescharacteristic, complemented, Sylow
481C22×Q8C22×D6111yescharacteristic
482C22×D4—611no—
483C22×D4—611no—
484C22×D4—1221no—
485C22×D4—1221no—
486C22×D4—1221no—
487C22×D4—1221no—
488C22×D4—1221no—
489C22×D4—1221no—
490C22×D4C22⋊D6111yescharacteristic
491C23×C4C22×D6111yescharacteristic
492C23×C4C22×D6111yescharacteristic
493C2×SD16—1222no—
494C2×SD16—1222no—
495C2×SD16—1222no—
496C2×SD16—1222no—
497C2×SD16—2441no—
498C2×SD16—2441no—
499C2×M16—1222no—
500C2×M16—1222no—
501C2×M16—2441no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—611no—
505C22×C8—611no—
506C22×C8—1222no—
507C22×C8—1222no—
508C22×C8—2441no—
509#127—1222no—
510#127—1222no—
511#127—2444no—
512C22⋊Q8—22no—
513C22⋊Q8—22no—
514C22⋊Q8—41no—
515C22⋊Q8—41no—
516#121—1222no—
517#121—1222no—
518#121—1222no—
519#121—1222no—
520#121—2441no—
521#121—2441no—
522#121—2441no—
523#121—2441no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×D4—22no—
527C4×D4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4C22⋊D6111yescharacteristic
534C2×C4⋊C4C22×D6111yescharacteristic
535C2×C4⋊C4C22×D6111yescharacteristic
536C2×C4⋊C4C22×D6111yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4C22⋊D6111yescharacteristic
546C2×C22⋊C4C22⋊D6111yescharacteristic
547C2×C42—21no—
548C2×C42—1221no—
549C2×C42C22×D6111yescharacteristic
550#107—1222no—
551#106—1222no—
552C4⋊C8—614no—
553#103—614no—
554#103—1222no—
555#102—1222no—
556#102—1222no—
557#102—1222no—
558#102—1222no—
559#102—2441no—
560#102—2441no—
561C22⋊C8—1222no—
562C22⋊C8—1222no—
563#97—1222no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—1221no—
569C24—1221no—
570C24—1221no—
571C24C2×C22⋊D6111yescharacteristic
572C24C2×C22⋊D6111yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8D4×D6112yes—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—41no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—4881no—
595C2×D4—4881no—
596C2×D4—4881no—
597C2×D4—4881no—
598C2×D4—4881no—
599C2×D4—4881no—
600C2×D4—2442no—
601C2×D4—2442no—
602C2×D4—2442no—
603C2×D4—2442no—
604C2×D4—2442no—
605C2×D4—2442no—
606C2×D4—2442no—
607C2×D4—2442no—
608C2×D4—2442no—
609C2×D4—2442no—
610C2×D4—2442no—
611C2×D4—2442no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4C2×C22⋊D6111yescharacteristic
631C22×C4C2×C22⋊D6111yescharacteristic
632C22×C4C2×C22⋊D6111yescharacteristic
633C22×C4C2×C22⋊D6111yescharacteristic
634C22×C4C23×D6111yescharacteristic
635SD16—2444no—
636SD16—2444no—
637M16—2444no—
638C2×C8—612no—
639C2×C8—612no—
640C2×C8—612no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—2444no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—612no—
662C4⋊C4—612no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—2442no—
672C22⋊C4—2442no—
673C22⋊C4—2442no—
674C22⋊C4—2442no—
675C42—42no—
676C42—2442no—
677C42D4×D6112yes—
678C42#1175822412yes—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—2441no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23#1451980212yes—
707C23C22×C22⋊D6111yescharacteristic
708Q8—22no—
709Q8—22no—
710Q8—41no—
711Q8—41no—
712D4—44no—
713D4—4884no—
714D4—4884no—
715D4—4884no—
716D4—4884no—
717D4—4884no—
718D4—4884no—
719D4—2441no—
720D4—2441no—
721D4—2441no—
722D4—2441no—
723D4—2441no—
724D4—2441no—
725D4—2441no—
726D4—2441no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4#1451974912yes—
764C2×C4#1451974912yes—
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4C2×D4×D6111yescharacteristic
767C2×C4#41×D6111yescharacteristic
768C2×C4C2×#1175822411yescharacteristic
769C2×C4#1451982211yescharacteristic
770C2×C4#1451982311yescharacteristic
771C8—1222no—
772C8—1222no—
773C8—1222no—
774C8—2441no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—4881no—
790C22—4881no—
791C22—4881no—
792C22—4881no—
793C22—4881no—
794C22—4881no—
795C22—4881no—
796C22—4881no—
797C22—4881no—
798C22—4881no—
799C22—4881no—
800C22—4881no—
801C22—4881no—
802C22—4881no—
803C22C2×#1451974911yescharacteristic
804C22D4×C22⋊D6111yescharacteristic
805C22#1684040011yescharacteristic
806C22C2×#1451980211yescharacteristic
807C22#1684056011yescharacteristic
808C22#1684057011yescharacteristic
809C22#1684057011yescharacteristic
810C4—22no—
811C4—22no—
812C4—41no—
813C4—41no—
814C4—42no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4—2442no—
819C4—2442no—
820C4#1684030711yescharacteristic
821C4#1684036511yescharacteristic
822C4#1684039611yescharacteristic
823C4#1684043011yescharacteristic
824C2—42no—
825C2—81no—
826C2—9761no—
827C2—9761no—
828C2#2144940911yescharacteristic
829C2#2145544011yescharacteristic
830C2#2145546011yescharacteristic
831C2#2145731511yescharacteristic
832C2#2145740511yescharacteristic
833C2#2145783411yescharacteristic
834C2#2145793911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2536C2
socleC23×C61C22×D4
prime radical#21450765C2
hypercenter#2536D61
hypocenterC61#25402
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2536

Complements

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

NH ≅ G/Ntype
1. C2×#16840010C2semidirect
2. C2×#16839993C2semidirect
3. C2×#16839962C2semidirect
4. C2×#16839834C2semidirect
6. #21447008C2semidirect
7. #21447001C2semidirect
8. #21446820C2semidirect
9. #21446820C2semidirect
10. #21446642C2semidirect
11. #21446585C2semidirect
12. #21446255C2semidirect
13. #21446245C2semidirect
14. #21445649C2semidirect
15. C61×#2536C2semidirect
107. C4⋊#92418D4semidirect
109. #14519701D4semidirect
412. #2536D61semidirect
480. C61#25402semidirect

Maximal subgroups

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

subgroupindex
C2×#168400102
C2×#168399932
C2×#168399622
C2×#168398342
#214507652
#214470082
#214470012
#214468202
#214466422
#214465852
#214462552
#214462452
#214456492
C61×#25362
#2540261