Finite Group Databasebeta

← #29733280

Subgroups — #29733280

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×#16840119C211yesmaximal, characteristic, complemented
2C2×#16839984C211yesmaximal, characteristic, complemented
3#21450758C211yesmaximal, characteristic
4#21446827C211yesmaximal, characteristic, complemented
5#21446827C211yesmaximal, characteristic, complemented
6#21446820C211yesmaximal, characteristic, complemented
7#21446820C211yesmaximal, characteristic, complemented
8#21446777C211yesmaximal, characteristic, complemented
9#21446614C211yesmaximal, characteristic, complemented
10#21446141C211yesmaximal, characteristic, complemented
11#21446136C211yesmaximal, characteristic, complemented
12#21446131C211yesmaximal, characteristic, complemented
13#21446126C211yesmaximal, characteristic, complemented
14C4×#14519701C211yesmaximal, characteristic, complemented
15C2×C61×#552C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C2×#14519765C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23#16840119—24no—
24#16839984—24no—
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×C4×#92418C2211yescharacteristic
39#16839697—21no—
40#16839670—21no—
41#16839662—21no—
42#16839662—21no—
43C4×C4⋊Dic61C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C61×#552—24no—
51C61×#552—24no—
52C2×#126×C61—21no—
53C2×#125×C61—21no—
54C2×#125×C61C2211yescharacteristic
55C2×#123×C61—21no—
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×C4×Q8×C61C2211yescharacteristic
59C2×C4×D4×C61C2211yescharacteristic
60C2×#117×C61—21no—
61C2×#117×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C22⋊D61—21no—
67C2×#11758202—22no—
68C2×#11758202—41no—
69C2×#11758202—41no—
70C2×#11758201—22no—
71C2×#11758201—41no—
72C2×#11758201—41no—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519765—22no—
78#14519765—22no—
79#14519756—22no—
80#14519756—22no—
81#14519756—41no—
82#14519756—41no—
83#14519751—22no—
84#14519751—22no—
85#14519751—41no—
86#14519751—41no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×C4×Dic61—21no—
98C4⋊#92418—22no—
99#14519701—22no—
100#14519701—22no—
101#14519700—22no—
102#14519700—22no—
103#14519700—22no—
104#14519697—22no—
105#14519697—22no—
106#14519697—22no—
107C22⋊#92418—41no—
108C22⋊#92418—41no—
109C22⋊#92418—41no—
110C22⋊#92418—41no—
111C4×#92418—22no—
112#14519684—21no—
113C22×Q8×C61C2311yescharacteristic
114C22×D4×C61D411yescharacteristic
115C23×C4×C61—21no—
116C23×C4×C61C2311yescharacteristic
117C23×C4×C61C2311yescharacteristic
118#126×C61—28no—
119#125×C61—28no—
120#125×C61—22no—
121#125×C61D414yescomplemented
122#123×C61—28no—
123C22⋊Q8×C61—22no—
124C22⋊Q8×C61—22no—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61—22no—
127C4×Q8×C61—22no—
128C4×Q8×C61D414yescomplemented
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131#117×C61—28no—
132#117×C61—22no—
133#117×C61—22no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61—22no—
141C2×C4⋊C4×C61—22no—
142C2×C4⋊C4×C61D411yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
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×C61—21no—
153C2×C42×C61C2311yescharacteristic
154C24×C61C2×D411yescharacteristic
155C24×C61C2×D411yescharacteristic
156C23×D61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61C2×D412yes—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—41no—
166C22×C4×C61—24no—
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×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—42no—
184C22×C4×C61—42no—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
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—24no—
215C4⋊C4×C61—24no—
216C4⋊C4×C61—24no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61C2×D412yes—
222C4⋊C4×C61C2×D412yes—
223C4⋊C4×C61C2×D412yes—
224C22⋊C4×C61—24no—
225C22⋊C4×C61—24no—
226C22⋊C4×C61—24no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C42×C61—24no—
230C42×C61—24no—
231C42×C61C2×D412yes—
232C42×C61C2×D412yes—
233C22⋊Dic61—42no—
234C22⋊Dic61—42no—
235#11758202—44no—
236#11758201—44no—
237#11758198—42no—
238#11758198—42no—
239#11758198—42no—
240#11758198—42no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61#4112yes—
244C4⋊Dic61#4112yes—
245#11758196—42no—
246#11758196—42no—
247C4×Dic61—81no—
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#13512yes—
274C23×C61C22×D411yescharacteristic
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282Q8×C61—22no—
283Q8×C61—22no—
284Q8×C61—41no—
285Q8×C61—41no—
286D4×C61—44no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—22no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—48no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
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#12012yes—
319C2×C4×C61#12012yes—
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C2×#4111yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C2×C4×C61H(5,𝔽2)11yescharacteristic
325C2×C4×C61H(5,𝔽2)11yescharacteristic
326C22⋊D61—84no—
327C22⋊D61—84no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337D244—41no—
338D244—41no—
339D244—41no—
340D244—41no—
341Dic122—41no—
342Dic122—41no—
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×C61C2×#12011yescharacteristic
365C22×C61#54611yescharacteristic
366C22×C61#54611yescharacteristic
367C22×C61C2×#13511yescharacteristic
368C22×C61#57511yescharacteristic
369C22×C61#57711yescharacteristic
370C22×C61#57811yescharacteristic
371C2×D61—81no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C2×D61—81no—
377C2×D61—81no—
378C4×C61—22no—
379C4×C61—22no—
380C4×C61—41no—
381C4×C61—41no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61—42no—
385C4×C61—42no—
386C4×C61#53211yescharacteristic
387C4×C61#53511yescharacteristic
388C4×C61#55011yescharacteristic
389C4×C61#55011yescharacteristic
390Dic61—42no—
391Dic61—42no—
392Dic61—81no—
393C2×#552D6111yescharacteristic, complemented
394C2×#488—611no—
395C2×#464—611no—
396#2540—611no—
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#243111yescharacteristic
411C2×C61#300211yescharacteristic
412C2×C61#301311yescharacteristic
413C2×C61#329611yescharacteristic
414C2×C61#330011yescharacteristic
415C2×C61#332311yescharacteristic
416C2×C61#332711yescharacteristic
417D61—161no—
418C22×Q16—611no—
419C22×SD16—611no—
420#552—24no—
421#552—24no—
422C2×#126—21no—
423C2×#125—21no—
424C2×#125C2×D6111yescharacteristic
425C2×#124—611no—
426C2×#123—21no—
427C2×C22⋊Q8—611no—
428C2×C22⋊Q8—611no—
429C2×C22⋊Q8C2×D6111yescharacteristic
430C2×C22⋊Q8C2×D6111yescharacteristic
431C2×#121—611no—
432C2×#121—611no—
433C2×C4×Q8C2×D6111yescharacteristic
434C2×C4×D4C2×D6111yescharacteristic
435C2×#117—21no—
436C2×#117C2×D6111yescharacteristic
437C22×C4⋊C4C2×D6111yescharacteristic
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—1221no—
455#392—1221no—
456#390—1221no—
457#390—1221no—
458C4×C4⋊C4—611no—
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—611no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4C22⋊D6111yescharacteristic
472C23×C4—21no—
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—28no—
486#125—28no—
487#125—22no—
488#125C22⋊D6114yescomplemented
489#124—1222no—
490#124—1222no—
491#123—28no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—22no—
496C22⋊Q8—1222no—
497C22⋊Q8—1222no—
498C22⋊Q8—2441no—
499C22⋊Q8—2441no—
500#121—1222no—
501#121—1222no—
502#121—2441no—
503#121—2441no—
504C4×Q8—22no—
505C4×Q8C22⋊D6114yescomplemented
506C4×D4—22no—
507C4×D4—22no—
508#117—28no—
509#117—22no—
510#117—22no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4C22⋊D6111yescharacteristic
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—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
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—21no—
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—1221no—
557C24—1221no—
558C24C2×C22⋊D6111yescharacteristic
559C24C2×C22⋊D6111yescharacteristic
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—1221no—
566C2×Q8—1221no—
567C2×Q8—1221no—
568C2×Q8—1221no—
569C2×Q8—1221no—
570C2×Q8—1221no—
571C2×Q8C2×C22⋊D6112yes—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—41no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—4881no—
582C2×D4—4881no—
583C2×D4—2442no—
584C2×D4—2442no—
585C2×D4—2442no—
586C2×D4—2442no—
587C22×C4—24no—
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—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
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×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—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—612no—
639C4⋊C4—612no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—2442no—
643C4⋊C4—2442no—
644C4⋊C4C2×C22⋊D6112yes—
645C4⋊C4C2×C22⋊D6112yes—
646C4⋊C4C2×C22⋊D6112yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—2442no—
653C22⋊C4—2442no—
654C22⋊C4—2442no—
655C22⋊C4—2442no—
656C22⋊C4—2442no—
657C22⋊C4—2442no—
658C42—24no—
659C42—24no—
660C42—4881no—
661C42C2×C22⋊D6112yes—
662C42C2×C22⋊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—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23#1451979712yes—
684C23C22×C22⋊D6111yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—41no—
688Q8—41no—
689Q8—2441no—
690Q8—2441no—
691Q8—2441no—
692Q8—2441no—
693D4—44no—
694D4—4884no—
695D4—4884no—
696D4—2441no—
697D4—2441no—
698D4—2441no—
699D4—2441no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—48no—
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—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4#1451974612yes—
741C2×C4#1451974612yes—
742C2×C4C22×C22⋊D6111yescharacteristic
743C2×C4C22×C22⋊D6111yescharacteristic
744C2×C4#41×D6111yescharacteristic
745C2×C4#41×D6111yescharacteristic
746C2×C4#1451982311yescharacteristic
747C2×C4#1451982311yescharacteristic
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—4881no—
767C22—4881no—
768C22—4881no—
769C22—4881no—
770C22—4881no—
771C22—4881no—
772C22—4881no—
773C22C2×#1451974611yescharacteristic
774C22#1684040011yescharacteristic
775C22#1684040011yescharacteristic
776C22C2×#1451979711yescharacteristic
777C22#1684056011yescharacteristic
778C22#1684057011yescharacteristic
779C22#1684057711yescharacteristic
780C4—22no—
781C4—22no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—41no—
786C4—41no—
787C4—42no—
788C4—4881no—
789C4—2442no—
790C4—2442no—
791C4#1684030811yescharacteristic
792C4#1684032611yescharacteristic
793C4#1684043111yescharacteristic
794C4#1684043111yescharacteristic
795C2—42no—
796C2—81no—
797C2—9761no—
798C2#2144943411yescharacteristic
799C2#2145503711yescharacteristic
800C2#2145513411yescharacteristic
801C2#2145764811yescharacteristic
802C2#2145770011yescharacteristic
803C2#2145802911yescharacteristic
804C2#2145808111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#552C2
socleC23×C61C22×D4
prime radical#21450758C2
hypercenterC2×#552D61
hypocenterC61#25576
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#16840119C2semidirect
2. C2×#16839984C2semidirect
4. #21446827C2semidirect
5. #21446827C2semidirect
6. #21446820C2semidirect
7. #21446820C2semidirect
8. #21446777C2semidirect
9. #21446614C2semidirect
10. #21446141C2semidirect
11. #21446136C2semidirect
12. #21446131C2semidirect
13. #21446126C2semidirect
14. C4×#14519701C2semidirect
15. C2×C61×#552C2semidirect
121. #125×C61D4semidirect
128. C4×Q8×C61D4semidirect
393. C2×#552D61semidirect
465. C61#25576semidirect
488. #125C22⋊D61semidirect
505. C4×Q8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168401192
C2×#168399842
#214507582
#214468272
#214468202
#214467772
#214466142
#214461412
#214461362
#214461312
#214461262
C4×#145197012
C2×C61×#5522
#2557661