Finite Group Databasebeta

← #29733089

Subgroups — #29733089

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840075C211yesmaximal, characteristic, complemented
2C2×#16840010C211yesmaximal, characteristic, complemented
3#21449237C211yesmaximal, characteristic
4#21447144C211yesmaximal, characteristic, complemented
5#21447019C211yesmaximal, characteristic, complemented
6#21446952C211yesmaximal, characteristic, complemented
7#21446820C211yesmaximal, characteristic, complemented
8#21446174C211yesmaximal, characteristic, complemented
9#21446136C211yesmaximal, characteristic, complemented
10#21446132C211yesmaximal, characteristic, complemented
11#21446117C211yesmaximal, characteristic, complemented
12#21446073C211yesmaximal, characteristic, complemented
13#21446007C211yesmaximal, characteristic, complemented
14#21445538C211yesmaximal, characteristic, complemented
15C2×C61×#554C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21#16840075—24no—
22#16840010—24no—
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35#16839677—21no—
36#16839670—21no—
37#16839664C2211yescharacteristic
38#16839662—21no—
39#16839660C2211yescharacteristic
40#16839652—21no—
41#16839622C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C61×#554—24no—
51C61×#554—24no—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×#125×C61—21no—
54C2×C22⋊Q8×C61—21no—
55C2×C22⋊Q8×C61—21no—
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×C4×Q8×C61C2211yescharacteristic
59C2×C4×D4×C61—21no—
60C2×C4×D4×C61C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C2×#11758201—22no—
67C2×#11758201—22no—
68C2×#11758201—41no—
69C2×#11758194—22no—
70C2×#11758194—22no—
71C2×#11758194—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519751—22no—
77#14519751—22no—
78#14519751—22no—
79#14519751—41no—
80#14519736—22no—
81#14519736—41no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×C4×Dic61—21no—
93#14519710—22no—
94#14519710—22no—
95#14519710—22no—
96#14519701—22no—
97#14519701—22no—
98#14519701—41no—
99#14519697—22no—
100#14519697—22no—
101#14519697—22no—
102C22⋊#92418—22no—
103C22⋊#92418—22no—
104C22⋊#92418—41no—
105#14519684—21no—
106#14519684—21no—
107C22×Q8×C61—21no—
108C22×Q8×C61C2311yescharacteristic
109C22×D4×C61D411yescharacteristic
110C23×C4×C61—21no—
111C23×C4×C61—21no—
112C23×C4×C61C2311yescharacteristic
113C23×C4×C61C2311yescharacteristic
114C4⋊Q8×C61—22no—
115C4⋊Q8×C61—22no—
116#125×C61—28no—
117C22⋊Q8×C61—28no—
118C22⋊Q8×C61—28no—
119C22⋊Q8×C61—22no—
120C22⋊Q8×C61—22no—
121C22⋊Q8×C61—22no—
122C22⋊Q8×C61D414yescomplemented
123C4×Q8×C61—22no—
124C4×Q8×C61—22no—
125C4×D4×C61—28no—
126C4×D4×C61—22no—
127C4×D4×C61—22no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—22no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—22no—
136C2×C4⋊C4×C61—22no—
137C2×C4⋊C4×C61D411yescharacteristic
138C2×C4⋊C4×C61D414yescomplemented
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C42×C61—21no—
147C2×C42×C61C2311yescharacteristic
148C24×C61C2×D411yescharacteristic
149C24×C61C2×D411yescharacteristic
150C23×D61—21no—
151C2×Q8×C61—24no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—81no—
158C2×Q8×C61—81no—
159C2×Q8×C61C2×D412yes—
160C2×D4×C61—22no—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C22×C4×C61—21no—
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—24no—
172C22×C4×C61—24no—
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—81no—
180C22×C4×C61—81no—
181C22×C4×C61—81no—
182C22×C4×C61—81no—
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D412yes—
187C22×C4×C61C2×D412yes—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—81no—
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—
205C4⋊C4×C61—24no—
206C4⋊C4×C61—24no—
207C4⋊C4×C61—24no—
208C4⋊C4×C61—24no—
209C4⋊C4×C61—24no—
210C4⋊C4×C61—24no—
211C4⋊C4×C61—22no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61C2×D412yes—
216C4⋊C4×C61C2×D412yes—
217C4⋊C4×C61C2×D412yes—
218C22⋊C4×C61—24no—
219C22⋊C4×C61—24no—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—22no—
222C42×C61—24no—
223C42×C61—21no—
224C42×C61—21no—
225C22⋊Dic61—42no—
226C22⋊Dic61—81no—
227#11758201—44no—
228#11758198—42no—
229#11758198—42no—
230#11758198—42no—
231#11758198—81no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61#4112yes—
238#11758196—81no—
239C4×Dic61—42no—
240#11758194—44no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418#4112yes—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61#12012yes—
266C23×C61#13712yes—
267C23×C61C22×D411yescharacteristic
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61—41no—
278Q8×C61—41no—
279Q8×C61—84no—
280D4×C61—28no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—21no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
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—84no—
312C2×C4×C61—84no—
313C2×C4×C61#12012yes—
314C2×C4×C61#13712yes—
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C2×C4×C612−1+411yescharacteristic
321C22⋊D61—84no—
322C22⋊D61—84no—
323C2×Dic61—22no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332D244—41no—
333D244—41no—
334D244—41no—
335D244—41no—
336#92418—22no—
337#92418—41no—
338#92418—41no—
339#92418—41no—
340#25559—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61C2×#12011yescharacteristic
356C22×C61#54611yescharacteristic
357C22×C61#54711yescharacteristic
358C22×C61C2×#13711yescharacteristic
359C22×C61C2×#13711yescharacteristic
360C22×C61#57611yescharacteristic
361C22×C61#57611yescharacteristic
362C2×D61—81no—
363C2×D61—81no—
364C2×D61—81no—
365C2×D61—81no—
366C2×D61—81no—
367C2×D61—81no—
368C2×D61—81no—
369C4×C61—22no—
370C4×C61—22no—
371C4×C61—41no—
372C4×C61—42no—
373C4×C61—41no—
374C4×C61—42no—
375C4×C61—42no—
376C4×C61—42no—
377C4×C61#53211yescharacteristic
378C4×C61#53711yescharacteristic
379C4×C61#54611yescharacteristic
380C4×C61#54711yescharacteristic
381Dic61—42no—
382Dic61—81no—
383Dic61—81no—
384C2×#554D6111yescharacteristic, complemented
385C2×#480—611no—
386C2×#468—611no—
387#2414—611no—
388#2057—611no—
389#2036—611no—
390#2023—611no—
391#2000—611no—
392#1880—611no—
393#1874—611no—
394#1873—611no—
395#1870—611no—
396#1863—611no—
397#1852—611no—
398#1736—611no—
399C2×C61—42no—
400C2×C61—42no—
401C2×C61#243011yescharacteristic
402C2×C61#300411yescharacteristic
403C2×C61#300811yescharacteristic
404C2×C61#331411yescharacteristic
405C2×C61#333311yescharacteristic
406C2×C61#334611yescharacteristic
407C2×C61#335711yescharacteristic
408D61—161no—
409C22×SD16—611no—
410C22×M16—611no—
411#554—24no—
412#554—24no—
413C2×C4⋊Q8C2×D6111yescharacteristic
414C2×#125—21no—
415C2×C22⋊Q8—21no—
416C2×C22⋊Q8—21no—
417C2×C22⋊Q8C2×D6111yescharacteristic
418C2×C22⋊Q8C2×D6111yescharacteristic
419C2×#121—611no—
420C2×#121—611no—
421C2×C4×Q8C2×D6111yescharacteristic
422C2×C4×D4—21no—
423C2×C4×D4C2×D6111yescharacteristic
424C2×#117—611no—
425C22×C4⋊C4C2×D6111yescharacteristic
426C22×C4⋊C4C2×D6111yescharacteristic
427#480—1224no—
428#468—1224no—
429C2×#107—611no—
430C2×#107—611no—
431C2×#107—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441#394—1221no—
442#392—1221no—
443#390—611no—
444#390—1221no—
445#389—611no—
446#388—1221no—
447#380—611no—
448#340—611no—
449#340—611no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454#336—611no—
455#336—611no—
456C61#2555911yescharacteristic, complemented, Sylow
457C22×Q8—21no—
458C22×Q8C22×D6111yescharacteristic
459C22×D4—611no—
460C22×D4—1221no—
461C22×D4—1221no—
462C22×D4C22⋊D6111yescharacteristic
463C23×C4—21no—
464C23×C4—21no—
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467C2×SD16—1222no—
468C2×SD16—1222no—
469C2×SD16—2441no—
470C2×M16—1222no—
471C2×M16—1222no—
472C2×M16—2441no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8—611no—
477C4⋊Q8—22no—
478C4⋊Q8—22no—
479#125—28no—
480C22⋊Q8—28no—
481C22⋊Q8—28no—
482C22⋊Q8—22no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8C22⋊D6114yescomplemented
486#121—1222no—
487#121—1222no—
488#121—1222no—
489#121—2441no—
490C4×Q8—22no—
491C4×Q8—22no—
492C4×D4—28no—
493C4×D4—22no—
494C4×D4—22no—
495#117—1222no—
496#117—2441no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4C22⋊D6111yescharacteristic
511C2×C4⋊C4C22⋊D6114yescomplemented
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4C22⋊D6111yescharacteristic
524C2×C22⋊C4C22⋊D6111yescharacteristic
525C2×C42—21no—
526C2×C42—1221no—
527C2×C42C22×D6111yescharacteristic
528#107—1222no—
529#107—1222no—
530#107—1222no—
531#103—1222no—
532#103—1222no—
533#103—2441no—
534#102—1222no—
535#102—1222no—
536#102—1222no—
537C22⋊C8—1222no—
538C22⋊C8—1222no—
539C22⋊C8—2441no—
540#95—1221no—
541#95—1221no—
542C24—1221no—
543C24C2×C22⋊D6111yescharacteristic
544C24C2×C22⋊D6111yescharacteristic
545C2×Q8—24no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—81no—
552C2×Q8—81no—
553C2×Q8C2×C22⋊D6112yes—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—1221no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4—1221no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—4881no—
564C2×D4—4881no—
565C2×D4—4881no—
566C2×D4—2442no—
567C2×D4—2442no—
568C2×D4—2442no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4C2×C22⋊D6111yescharacteristic
593C22×C4C2×C22⋊D6111yescharacteristic
594C22×C4C2×C22⋊D6111yescharacteristic
595C22×C4C2×C22⋊D6112yes—
596C22×C4C2×C22⋊D6112yes—
597C22×C4C2×C22⋊D6111yescharacteristic
598C22×C4C23×D6111yescharacteristic
599SD16—2444no—
600M16—2444no—
601C2×C8—612no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—22no—
623C4⋊C4—612no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—4881no—
630C4⋊C4C2×C22⋊D6112yes—
631C4⋊C4C2×C22⋊D6112yes—
632C4⋊C4C2×C22⋊D6112yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—4881no—
638C22⋊C4—4881no—
639C22⋊C4—2442no—
640C22⋊C4—2442no—
641C22⋊C4—2442no—
642C22⋊C4—2442no—
643C42—24no—
644C42—21no—
645C42—21no—
646C42—2442no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—2441no—
660C23—2441no—
661C23—2441no—
662C23—2441no—
663C23—2441no—
664C23—2441no—
665C23—2441no—
666C23#1451974612yes—
667C23#1451980812yes—
668C23C22×C22⋊D6111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673Q8—84no—
674D4—28no—
675D4—4884no—
676D4—4884no—
677D4—2441no—
678D4—2441no—
679D4—2441no—
680D4—2441no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—84no—
712C2×C4—84no—
713C2×C4—1222no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4#1451974612yes—
723C2×C4#1451980812yes—
724C2×C4C22×C22⋊D6111yescharacteristic
725C2×C4C22×C22⋊D6111yescharacteristic
726C2×C4#41×D6111yescharacteristic
727C2×C4#41×D6111yescharacteristic
728C2×C4#1451982311yescharacteristic
729C2×C4#1451982411yescharacteristic
730C8—1222no—
731C8—2441no—
732C8—2441no—
733C8—2441no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—4881no—
749C22—4881no—
750C22—4881no—
751C22—4881no—
752C22—4881no—
753C22—4881no—
754C22—4881no—
755C22C2×#1451974611yescharacteristic
756C22#1684040011yescharacteristic
757C22#1684041111yescharacteristic
758C22C2×#1451980811yescharacteristic
759C22C2×#1451980811yescharacteristic
760C22#1684056511yescharacteristic
761C22#1684056511yescharacteristic
762C4—22no—
763C4—22no—
764C4—41no—
765C4—42no—
766C4—41no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—4881no—
771C4—4881no—
772C4—2442no—
773C4#1684030811yescharacteristic
774C4#1684034011yescharacteristic
775C4#1684040011yescharacteristic
776C4#1684041111yescharacteristic
777C2—42no—
778C2—42no—
779C2—9761no—
780C2#2144942311yescharacteristic
781C2#2145505311yescharacteristic
782C2#2145508711yescharacteristic
783C2#2145789411yescharacteristic
784C2#2145815111yescharacteristic
785C2#2145829811yescharacteristic
786C2#2145844511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#554C2
socleC23×C61C22×D4
prime radical#21449237C2
hypercenterC2×#554D61
hypocenterC61#25559
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16840075C2semidirect
2. C2×#16840010C2semidirect
4. #21447144C2semidirect
5. #21447019C2semidirect
6. #21446952C2semidirect
7. #21446820C2semidirect
8. #21446174C2semidirect
9. #21446136C2semidirect
10. #21446132C2semidirect
11. #21446117C2semidirect
12. #21446073C2semidirect
13. #21446007C2semidirect
14. #21445538C2semidirect
15. C2×C61×#554C2semidirect
122. C22⋊Q8×C61D4semidirect
138. C2×C4⋊C4×C61D4semidirect
384. C2×#554D61semidirect
456. C61#25559semidirect
485. C22⋊Q8C22⋊D61semidirect
511. C2×C4⋊C4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400752
C2×#168400102
#214492372
#214471442
#214470192
#214469522
#214468202
#214461742
#214461362
#214461322
#214461172
#214460732
#214460072
#214455382
C2×C61×#5542
#2555961