Finite Group Databasebeta

← #29696578

Subgroups — #29696578

Order 15616.

1014 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840468C211yesmaximal, characteristic
2M16×Dic122C211yesmaximal, characteristic, complemented
3#21454770C211yesmaximal, characteristic, complemented
4#21446813C211yesmaximal, characteristic, complemented
5#21446810C211yesmaximal, characteristic, complemented
6#21446810C211yesmaximal, characteristic, complemented
7#21446806C211yesmaximal, characteristic, complemented
8#21446806C211yesmaximal, characteristic, complemented
9#21445810C211yesmaximal, characteristic
10#21445810C211yesmaximal, characteristic
11#21445808C211yesmaximal, characteristic
12C4×#14519693C211yesmaximal, characteristic
13#21445610C211yesmaximal, characteristic
14#21445610C211yesmaximal, characteristic
15C61×#1998C211yesmaximal, characteristic, complemented
16#16840468—21no—
17#16840468—21no—
18#16840468—21no—
19#16840468—21no—
20#16840468—21no—
21#16840468—21no—
22#16840468—21no—
23#16840468—21no—
24C2×#14519776C2211yescharacteristic
25C2×#14519768C2211yescharacteristic
26C2×#14519757C412yes—
27C2×#14519755C412yes—
28C2×#14519755C412yes—
29C2×C4×Dic122C2211yescharacteristic
30C2×C4×D244C2211yescharacteristic
31C2×#14519739C2211yescharacteristic
32C2×#14519739C2211yescharacteristic
33C2×C4⋊C4×D61C412yes—
34#16839892—21no—
35#16839891—21no—
36#16839891—21no—
37#16839890—21no—
38#16839890—21no—
39#16839889—21no—
40C8×Dic122—21no—
41#16839886—21no—
42#16839786C2211yescharacteristic
43#16839785C2211yescharacteristic
44#16839785C2211yescharacteristic
45#16839785C2211yescharacteristic
46#16839785C2211yescharacteristic
47C2×#14519693C2211yescharacteristic
48C2×#14519693C2211yescharacteristic
49C2×#14519693C2211yescharacteristic
50C2×#14519693C2211yescharacteristic
51C4×#11758194C2211yescharacteristic
52M16×Dic61C2211yescharacteristic
53M16×Dic61C2211yescharacteristic
54M16×Dic61C2211yescharacteristic
55M16×Dic61C2211yescharacteristic
56#16839531C2211yescharacteristic
57#16839531C2211yescharacteristic
58#16839531C2211yescharacteristic
59#16839531C2211yescharacteristic
60#16839530C2211yescharacteristic
61#16839530C2211yescharacteristic
62#16839530C2211yescharacteristic
63#16839530C2211yescharacteristic
64C2×#125×C61C2211yescharacteristic
65C61×#423C2211yescharacteristic
66C4×M16×C61C2211yescharacteristic
67C61×#343C2211yescharacteristic
68C61×#343C2211yescharacteristic
69C61×#343C2211yescharacteristic
70C61×#343C2211yescharacteristic
71C22×Dic122C2×C412yes—
72C22×Dic122C2×C411yescharacteristic
73C22×D244C2311yescharacteristic
74C22×C4×D61C2×C412yes—
75C22×C4×D61C2×C412yes—
76C22×C4×D61C2×C412yes—
77C2×#11758194C2311yescharacteristic
78C2×#11758194C2311yescharacteristic
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81#14519776—21no—
82#14519776—21no—
83#14519776—21no—
84#14519776—21no—
85#14519768—21no—
86#14519768—21no—
87#14519768—21no—
88#14519768—21no—
89#14519757—22no—
90#14519757—22no—
91#14519757—22no—
92#14519757—22no—
93#14519755—22no—
94#14519755—22no—
95#14519755—22no—
96#14519755—22no—
97#14519755—22no—
98#14519755—22no—
99#14519755—22no—
100#14519755—22no—
101C4×Dic122D411yescharacteristic
102C4×Dic122D411yescharacteristic
103C4×Dic122D411yescharacteristic
104C4×Dic122D411yescharacteristic
105C4×Dic122D411yescharacteristic
106C4×Dic122D411yescharacteristic
107C4×Dic122D411yescharacteristic
108C4×Dic122D411yescharacteristic
109C4×D244—21no—
110C4×D244—21no—
111C4×D244—21no—
112C4×D244—21no—
113#14519739—21no—
114#14519739—21no—
115#14519739—21no—
116#14519739—21no—
117#14519739—21no—
118#14519739—21no—
119#14519739—21no—
120#14519739—21no—
121C2×C4⋊Dic61C2×C412yes—
122C2×C4⋊Dic61C2×C411yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×#11758196C2×C412yes—
125C2×#11758196C2×C412yes—
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C4⋊C4×D61—22no—
129C4⋊C4×D61—22no—
130C4⋊C4×D61—22no—
131C4⋊C4×D61—22no—
132C2×#11758198C2×C412yes—
133C2×#11758198C2×C412yes—
134C2×#11758198C2×C412yes—
135C2×C4×Dic61C2311yescharacteristic
136C2×C4×Dic61C2311yescharacteristic
137C4⋊#92418—21no—
138C4⋊#92418—21no—
139#14519706—21no—
140#14519706—21no—
141#14519706—21no—
142#14519706—21no—
143#14519706—21no—
144#14519706—21no—
145#14519706—21no—
146#14519706—21no—
147#14519693—22no—
148#14519693—22no—
149#14519693—22no—
150#14519693Q814yescomplemented
151#14519688—21no—
152#14519687—21no—
153#14519687—21no—
154#14519687—21no—
155#14519687—21no—
156C4×#92418—21no—
157C8×Dic61—21no—
158C8×Dic61—21no—
159C8×Dic61—21no—
160C8×Dic61—21no—
161C2×M16×C61C2311yescharacteristic
162C2×M16×C61C2311yescharacteristic
163C2×M16×C61C2311yescharacteristic
164C2×M16×C61C2311yescharacteristic
165#125×C61—21no—
166#125×C61—21no—
167#125×C61—21no—
168#125×C61—21no—
169C2×C4⋊C4×C61C2×C412yes—
170C2×C4⋊C4×C61C2×C412yes—
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C42×C61C2311yescharacteristic
174C4⋊C8×C61—21no—
175C4⋊C8×C61—21no—
176#97×C61—21no—
177C4×C8×C61—21no—
178C23×D61C22×C412yes—
179C22×C4×C61C22×C412yes—
180C22×C4×C61C22×C412yes—
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C2411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C412yes—
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244C2×Q812yes—
194C2×D244#4112yes—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—44no—
202C2×C4×D61—82no—
203C2×C4×D61—82no—
204C2×Dic122—22no—
205C2×Dic122—22no—
206C2×Dic122—42no—
207C2×Dic122—82no—
208C2×Dic122C22⋊C411yescharacteristic
209C2×Dic122C22⋊C411yescharacteristic
210C2×Dic122C22⋊C411yescharacteristic
211C2×Dic122C22⋊C411yescharacteristic
212M16×C61—21no—
213M16×C61—21no—
214M16×C61—21no—
215M16×C61—21no—
216M16×C61—21no—
217M16×C61—21no—
218M16×C61—21no—
219M16×C61C2×Q812yes—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—22no—
226C4⋊C4×C61—22no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C42×C61C2×D411yescharacteristic
233C42×C61C2×D411yescharacteristic
234C42×C61C2×D411yescharacteristic
235C42×C61C2×D411yescharacteristic
236#11758198—22no—
237#11758198—22no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241#11758198—22no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—22no—
245C4⋊Dic61—22no—
246C4⋊Dic61C22⋊C411yescharacteristic
247C4⋊Dic61C22⋊C411yescharacteristic
248C4⋊Dic61C22⋊C411yescharacteristic
249C4⋊Dic61C22⋊C411yescharacteristic
250#11758196—22no—
251#11758196—22no—
252#11758196—22no—
253#11758196—22no—
254#11758196C22⋊C411yescharacteristic
255#11758196C22⋊C411yescharacteristic
256#11758196C22⋊C411yescharacteristic
257#11758196C22⋊C411yescharacteristic
258#11758196C22⋊C411yescharacteristic
259#11758196C22⋊C411yescharacteristic
260#11758196C22⋊C411yescharacteristic
261#11758196C22⋊C411yescharacteristic
262C4×Dic61C2×D411yescharacteristic
263C4×Dic61C2×D411yescharacteristic
264C4×Dic61C2×D411yescharacteristic
265C4×Dic61C2×D411yescharacteristic
266C4×Dic61C2×D411yescharacteristic
267C4×Dic61C2×D411yescharacteristic
268C4×Dic61C2×D411yescharacteristic
269C4×Dic61C2×D411yescharacteristic
270#11758194—21no—
271#11758194—21no—
272#11758194—21no—
273#11758194—21no—
274#11758194—21no—
275#11758194—21no—
276#11758194—21no—
277#11758194C2×Q812yes—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C23×C61C23×C411yescharacteristic
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—42no—
286C22×D61—42no—
287C22×D61C4×Q814yes—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×Q811yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C612−1+411yescharacteristic
303C2×C4×C612−1+411yescharacteristic
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—42no—
310C2×Dic61C2×C22⋊C411yescharacteristic
311C2×Dic61C2×C22⋊C411yescharacteristic
312C2×Dic61C2×C22⋊C411yescharacteristic
313C2×Dic61C2×C22⋊C411yescharacteristic
314C2×Dic61C2×C22⋊C411yescharacteristic
315C2×Dic61C2×C22⋊C411yescharacteristic
316C2×Dic61C2×C22⋊C411yescharacteristic
317C2×Dic61C2×C22⋊C411yescharacteristic
318D244—22no—
319D244—22no—
320D244—22no—
321D244—22no—
322C4×D61—44no—
323C4×D61—44no—
324C4×D61—82no—
325C4×D61—82no—
326C4×D61—82no—
327C4×D61—82no—
328Dic122—22no—
329Dic122—22no—
330Dic122—41no—
331Dic122—41no—
332Dic122—82no—
333Dic122—82no—
334C8×C61—22no—
335C8×C61—41no—
336C8×C61—41no—
337C8×C61—41no—
338#92418—22no—
339#92418—41no—
340#92418—41no—
341#92418—41no—
342#22515—611nomaximal, Sylow
343C22×C61—21no—
344C22×C61—21no—
345C22×C61C22×C22⋊C411yescharacteristic
346C22×C61C2×C4×Q811yescharacteristic
347C22×C61#51911yescharacteristic
348C2×D61—24no—
349C2×D61—44no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—44no—
353C4×C61—21no—
354C4×C61—21no—
355C4×C61—21no—
356C4×C61—21no—
357C4×C61—42no—
358C4×C61—42no—
359C4×C61#54811yescharacteristic
360C4×C61#54811yescharacteristic
361C4×C61D4×Q811yescharacteristic
362C4×C61D4×Q811yescharacteristic
363Dic61—21no—
364Dic61—21no—
365Dic61—21no—
366Dic61—21no—
367Dic61—21no—
368Dic61—21no—
369Dic61—21no—
370Dic61—42no—
371Dic61#41312yes—
372C2×#554—611no—
373Q8×M16—611no—
374Q8×M16—611no—
375#1998—611no—
376#1998—611no—
377#1998—611no—
378#1998D6111yescharacteristic, complemented
379#1997—611no—
380#1997—611no—
381#1800—611no—
382#1800—611no—
383#1800—611no—
384C4×#100—611no—
385C4×#100—611no—
386C4×#100—611no—
387C2×C61—21no—
388C2×C61—21no—
389C2×C61Q8×C22⋊C411yescharacteristic
390C2×C61C2×#41311yescharacteristic
391C2×C61#288811yescharacteristic
392D61—44no—
393#554—1221no—
394#554—1221no—
395#554—1221no—
396#554—1221no—
397#554—1221no—
398#554—1221no—
399#554—1221no—
400#554—1221no—
401C2×C4⋊Q8—611no—
402C2×#125—611no—
403C2×#125C2×D6111yescharacteristic
404C2×C22⋊Q8—612no—
405C2×C22⋊Q8—612no—
406C2×C22⋊Q8—612no—
407C2×C4×Q8—611no—
408C2×C4×D4—611no—
409C2×C4×D4—611no—
410C2×C4×D4—611no—
411C22×C4⋊C4—612no—
412#446—1221no—
413#446—1221no—
414#446—1221no—
415#446—1221no—
416#446—1221no—
417#446—1221no—
418C8×Q8—1221no—
419C8×Q8—1221no—
420#423—611no—
421#423—611no—
422#423—611no—
423#423—611no—
424#423—611no—
425#423C2×D6111yescharacteristic
426C2×#100—611no—
427C2×#100—611no—
428C2×#100—611no—
429C2×#100—611no—
430C4×M16—611no—
431C4×M16—611no—
432C4×M16—611no—
433C4×M16—611no—
434C4×M16—611no—
435C4×M16C2×D6111yescharacteristic
436#343—611no—
437#343—611no—
438#343—611no—
439#343—611no—
440#343—611no—
441#343—611no—
442#343—611no—
443#343—611no—
444#343C2×D6111yescharacteristic
445#343C2×D6111yescharacteristic
446#343C2×D6111yescharacteristic
447#343C2×D6111yescharacteristic
448C61#2251511yescharacteristic, complemented, Sylow
449C22×Q8—611no—
450C22×Q8—612no—
451C22×D4—611no—
452C23×C4—612no—
453C23×C4—612no—
454C23×C4—612no—
455C2×M16—611no—
456C2×M16—611no—
457C2×M16—611no—
458C2×M16—611no—
459C2×M16C22×D6111yescharacteristic
460C2×M16C22×D6111yescharacteristic
461C2×M16C22×D6111yescharacteristic
462C2×M16C22×D6111yescharacteristic
463C4⋊Q8—1221no—
464C4⋊Q8—1221no—
465C4⋊Q8—1221no—
466C4⋊Q8—1221no—
467#125—21no—
468#125—21no—
469#125—21no—
470#125—21no—
471#125—1221no—
472#125—1221no—
473#125—1221no—
474#125—1221no—
475C22⋊Q8—1222no—
476C22⋊Q8—1222no—
477C22⋊Q8—1222no—
478C22⋊Q8—1222no—
479C22⋊Q8—1222no—
480C22⋊Q8—1222no—
481C22⋊Q8—1222no—
482C22⋊Q8—1222no—
483C22⋊Q8—1222no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C4×Q8—611no—
488C4×Q8—611no—
489C4×Q8—611no—
490C4×Q8—611no—
491C4×Q8—611no—
492C4×Q8—611no—
493C4×Q8—611no—
494C4×Q8—611no—
495C4×D4—1221no—
496C4×D4—1221no—
497C4×D4—1221no—
498C4×D4—1221no—
499C4×D4—1221no—
500C4×D4—1221no—
501C4×D4—1221no—
502C4×D4—1221no—
503C4×D4—1221no—
504C4×D4—1221no—
505C4×D4—1221no—
506C4×D4—1221no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—612no—
511C2×C4⋊C4—612no—
512C2×C4⋊C4—612no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—1222no—
515C2×C4⋊C4—1222no—
516C2×C4⋊C4—1222no—
517C2×C4⋊C4—1222no—
518C2×C4⋊C4C4×D6112yes—
519C2×C4⋊C4C4×D6112yes—
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C4⋊C4C22×D6111yescharacteristic
522C2×C22⋊C4—612no—
523C2×C22⋊C4—612no—
524C2×C22⋊C4—612no—
525C2×C42—611no—
526C2×C42—611no—
527C2×C42C22×D6111yescharacteristic
528C4⋊C8—21no—
529C4⋊C8—21no—
530C4⋊C8—1221no—
531C4⋊C8—1221no—
532C4⋊C8—1221no—
533C4⋊C8—1221no—
534C4⋊C8—1221no—
535C4⋊C8—1221no—
536C4⋊C8—1221no—
537C4⋊C8—1221no—
538C4⋊C8—1221no—
539C4⋊C8—1221no—
540#100—614no—
541#100—1222no—
542#100—1222no—
543#100—1222no—
544#97—21no—
545#97—1221no—
546#97—1221no—
547#97—1221no—
548#97—1221no—
549#97—1221no—
550C4×C8—21no—
551C4×C8—1221no—
552C4×C8—1221no—
553C4×C8—1221no—
554C4×C8—1221no—
555C4×C8—1221no—
556C24—612no—
557C2×Q8—611no—
558C2×Q8—611no—
559C2×Q8—611no—
560C2×Q8—611no—
561C2×Q8—1222no—
562C2×Q8—1222no—
563C2×Q8—4882no—
564C2×Q8—2442no—
565C2×D4—612no—
566C2×D4—612no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1221no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—612no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—4882no—
583C22×C4—4882no—
584C22×C4—2444no—
585C22×C4C2×C4×D6112yes—
586C22×C4C2×C4×D6112yes—
587C22×C4C2×C4×D6111yescharacteristic
588C22×C4C2×C4×D6111yescharacteristic
589C22×C4C23×D6111yescharacteristic
590M16—21no—
591M16—21no—
592M16—21no—
593M16—21no—
594M16—21no—
595M16—21no—
596M16—21no—
597M16—612no—
598M16—1221no—
599M16—1221no—
600M16—1221no—
601M16—1221no—
602M16—1221no—
603M16—1221no—
604M16—1221no—
605M16Q8×D6112yes—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—611no—
623C4⋊C4—611no—
624C4⋊C4—611no—
625C4⋊C4—611no—
626C4⋊C4—611no—
627C4⋊C4—611no—
628C4⋊C4—611no—
629C4⋊C4—611no—
630C4⋊C4—611no—
631C4⋊C4—611no—
632C4⋊C4—611no—
633C4⋊C4—611no—
634C4⋊C4—1222no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C4⋊C4—1222no—
639C4⋊C4—1222no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C42—611no—
649C42—611no—
650C42—611no—
651C42—611no—
652C42—611no—
653C42—611no—
654C42—611no—
655C42—611no—
656C42D4×D6111yescharacteristic
657C42D4×D6111yescharacteristic
658C42D4×D6111yescharacteristic
659C42D4×D6111yescharacteristic
660C23—614no—
661C23—1222no—
662C23—1222no—
663C23—2442no—
664C23—2442no—
665C23C22×C4×D6111yescharacteristic
666Q8—1222no—
667Q8—1222no—
668Q8—4882no—
669Q8—4882no—
670Q8—2441no—
671Q8—2441no—
672D4—1222no—
673D4—1222no—
674D4—1222no—
675D4—1222no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—611no—
683C2×C4—611no—
684C2×C4—611no—
685C2×C4—611no—
686C2×C4—611no—
687C2×C4—611no—
688C2×C4—611no—
689C2×C4—611no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—4882no—
693C2×C4—4882no—
694C2×C4—4882no—
695C2×C4—4882no—
696C2×C4—2444no—
697C2×C4—2444no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2442no—
702C2×C4C22⋊C4×D6111yescharacteristic
703C2×C4C22⋊C4×D6111yescharacteristic
704C2×C4C22⋊C4×D6111yescharacteristic
705C2×C4C22⋊C4×D6111yescharacteristic
706C2×C4C2×D4×D6111yescharacteristic
707C2×C4C2×D4×D6111yescharacteristic
708C2×C4C2×Q8×D6111yescharacteristic
709C2×C4#41×D6111yescharacteristic
710C2×C4#1451982411yescharacteristic
711C2×C4#1451982511yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—1222no—
717C8—2441no—
718C8—2441no—
719C8—2441no—
720C22—21no—
721C22—21no—
722C22—1224no—
723C22—2444no—
724C22—2444no—
725C22—2442no—
726C22—2442no—
727C22C2×C22⋊C4×D6111yescharacteristic
728C22C4×Q8×D6111yescharacteristic
729C22#1684023811yescharacteristic
730C4—21no—
731C4—21no—
732C4—21no—
733C4—21no—
734C4—42no—
735C4—42no—
736C4—612no—
737C4—1221no—
738C4—1221no—
739C4—1221no—
740C4—1221no—
741C4—1221no—
742C4—1221no—
743C4—1221no—
744C4—2442no—
745C4#1684042011yescharacteristic
746C4#1684042211yescharacteristic
747C4#1684042511yescharacteristic
748C4#1684042711yescharacteristic
749C2—21no—
750C2—21no—
751C2—2444no—
752C2#2144865311yescharacteristic
753C2#413×D6111yescharacteristic
754C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1998C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenter#1998D61
hypocenterC61#22515
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1998

Complements

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

NH ≅ G/Ntype
2. M16×Dic122C2semidirect
3. #21454770C2semidirect
4. #21446813C2semidirect
5. #21446810C2semidirect
6. #21446810C2semidirect
7. #21446806C2semidirect
8. #21446806C2semidirect
15. C61×#1998C2semidirect
150. #14519693Q8semidirect
378. #1998D61semidirect
448. C61#22515semidirect

Maximal subgroups

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

subgroupindex
C2×#168404682
M16×Dic1222
#214547702
#214468132
#214468102
#214468062
#214458102
#214458082
C4×#145196932
#214456102
C61×#19982
#2251561