Finite Group Databasebeta

← #29679543

Subgroups — #29679543

Order 15616.

1462 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840244C211yesmaximal, characteristic
2C2×#16839787C211yesmaximal, characteristic, complemented
3C2×#16839762C211yesmaximal, characteristic
4C2×#16839757C211yesmaximal, characteristic
5#21448444C211yesmaximal, characteristic, complemented
6#21445832C211yesmaximal, characteristic, complemented
7#21445828C211yesmaximal, characteristic, complemented
8#21445826C211yesmaximal, characteristic, complemented
9#21445824C211yesmaximal, characteristic, complemented
10#21445822C211yesmaximal, characteristic, complemented
11#21445820C211yesmaximal, characteristic, complemented
12#21445818C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#1805C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840244—24no—
20#16840244C418yescomplemented
21C2×Q8×Dic61C2211yescharacteristic
22C2×C4×D244—21no—
23C2×C4×D244C2211yescharacteristic
24C2×#14519739—21no—
25C2×#14519739C2211yescharacteristic
26C2×#14519735C2211yescharacteristic
27C2×#14519734—21no—
28C2×#14519734C2211yescharacteristic
29C2×C4⋊C4×D61—21no—
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839787—24no—
33C2×C4⋊#92418C2211yescharacteristic
34C2×#14519706C2211yescharacteristic
35C2×#14519706C2211yescharacteristic
36#16839762—24no—
37#16839757—24no—
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44#16839659—21no—
45#16839659—21no—
46#16839636—21no—
47#16839636—21no—
48#16839632C2211yescharacteristic
49#16839631C2211yescharacteristic
50#16839627C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#382C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226C2×C414yes—
68C2×#11758226D414yes—
69C2×#11758226Q814yes—
70C22×D244—21no—
71C22×D244C2311yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758189—22no—
79C2×#11758189—22no—
80C2×#11758189—22no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C2×C8×D61—22no—
84C2×C8×D61—22no—
85C2×C8×D61—22no—
86Q8×Dic61—22no—
87Q8×Dic61C2×C414yescomplemented
88C4×D244—22no—
89C4×D244—28no—
90C4×D244C2×C414yescomplemented
91#14519739—28no—
92#14519739—22no—
93#14519739C2×C414yescomplemented
94#14519735—22no—
95#14519735—22no—
96#14519734—28no—
97#14519734C2×C414yes—
98#14519734D414yes—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196D411yescharacteristic
110C2×#11758196D411yescharacteristic
111C4⋊C4×D61—22no—
112C4⋊C4×D61—28no—
113C4⋊C4×D61—22no—
114C4⋊C4×D61—22no—
115C4⋊C4×D61C2×C414yes—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198D411yescharacteristic
120C2×#11758198D411yescharacteristic
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61C2311yescharacteristic
124C4⋊#92418—22no—
125#14519706—22no—
126#14519706—22no—
127#14519701—22no—
128#14519701—22no—
129#14519699—22no—
130#14519699—22no—
131#14519697—22no—
132#14519697—22no—
133#14519684—21no—
134#14519684—21no—
135C22×Q8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C4×Q8×C61—22no—
139C4×Q8×C61C2×C414yescomplemented
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C42×C61—21no—
145C2×C42×C61C2311yescharacteristic
146C4⋊C8×C61—22no—
147#103×C61—22no—
148#103×C61—22no—
149#95×C61—21no—
150#95×C61—21no—
151C23×D61—21no—
152C23×D61C2×D411yescharacteristic
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61C22×C412yes—
157C2×Q8×C61C2×D412yes—
158C2×Q8×C61C2×Q812yes—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2411yescharacteristic
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172#11758226—28no—
173#11758226—28no—
174#11758226—28no—
175#11758226C4⋊C4116yescomplemented
176C2×D244—24no—
177C2×D244—24no—
178C2×D244—24no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244C22×C412yes—
183C2×D244C2×D412yes—
184C2×D244C2×Q812yes—
185C2×C4×D61—24no—
186C2×C4×D61—24no—
187C2×C4×D61—24no—
188C2×C4×D61—24no—
189C2×C4×D61—24no—
190C2×C4×D61—24no—
191C2×C4×D61—42no—
192C2×C4×D61—81no—
193C2×C4×D61—81no—
194C2×C4×D61—81no—
195C2×C4×D61—81no—
196C2×C4×D61—81no—
197C2×C4×D61—81no—
198C2×C4×D61—81no—
199C2×C4×D61—81no—
200C2×C4×D61C22×C412yes—
201C2×C4×D61C2×D412yes—
202C2×C4×D61C2×D412yes—
203C2×C4×D61C2×Q812yes—
204C2×C4×D61#4112yes—
205C2×C4×D61#4112yes—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C4⋊C4×C61—24no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61C22×C412yes—
219C42×C61—24no—
220C42×C61C22×C412yes—
221C42×C61C2×D412yes—
222#11758198—24no—
223#11758198—24no—
224#11758198—42no—
225#11758198C22⋊C414yes—
226#11758198C22⋊C414yes—
227C4⋊Dic61—21no—
228C4⋊Dic61—24no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—81no—
234C4⋊Dic61—81no—
235C4⋊Dic61C22×C412yes—
236#11758196—24no—
237#11758196—42no—
238#11758196—81no—
239#11758196—81no—
240#11758196C22⋊C414yes—
241#11758196C22⋊C414yes—
242C4×Dic61—24no—
243C4×Dic61—42no—
244C4×Dic61C22×C412yes—
245C4×Dic61C2×D412yes—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252#11758189—44no—
253C8×D61—44no—
254C23×C61C22×D411yescharacteristic
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61C2×C22⋊C412yes—
267C22×D61#12112yes—
268C22×D61C22⋊Q812yes—
269Q8×C61—22no—
270Q8×C61—22no—
271Q8×C61—22no—
272Q8×C61C2×C4⋊C414yes—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—22no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61C2×C22⋊C412yes—
290C2×C4×C61C2×C22⋊C412yes—
291C2×C4×C61C23×C411yescharacteristic
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61C22×Q811yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—22no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61C2×C22⋊C412yes—
311C2×Dic61C2×C22⋊C412yes—
312C2×Dic61C2×C22⋊C412yes—
313C2×Dic61#12112yes—
314C2×Dic61C22⋊Q812yes—
315D244—216no—
316D244—22no—
317D244—22no—
318D244—22no—
319D244C2×C4⋊C414yes—
320C4×D61—216no—
321C4×D61—84no—
322C4×D61—84no—
323C4×D61—84no—
324C4×D61—84no—
325C4×D61C2×C4⋊C414yes—
326C4×D61#11714yes—
327C4×D61#12114yes—
328C4×D61C22⋊Q814yes—
329C8×C61—41no—
330C8×C61—41no—
331#92418—41no—
332#92418—41no—
333#20652—611nomaximal, Sylow
334C22×C61C22×C22⋊C411yescharacteristic
335C22×C61C2×#12111yescharacteristic
336C22×C61C2×C22⋊Q811yescharacteristic
337C22×C61#57611yescharacteristic
338C22×C61#57711yescharacteristic
339C22×C61#57711yescharacteristic
340C22×C61#57811yescharacteristic
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—24no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61#38014yes—
355C4×C61—22no—
356C4×C61—22no—
357C4×C61—24no—
358C4×C61—42no—
359C4×C61—81no—
360C4×C61—81no—
361C4×C61C22×C4⋊C411yescharacteristic
362C4×C61C2×#11711yescharacteristic
363C4×C61C2×#12111yescharacteristic
364C4×C61C2×C22⋊Q811yescharacteristic
365Dic61—22no—
366Dic61—22no—
367Dic61—42no—
368Dic61—81no—
369Dic61—81no—
370Dic61#38014yes—
371C2×#520—611no—
372C2×#424—611no—
373C2×#417—611no—
374C2×#416—611no—
375#2317—611no—
376#1805—611no—
377#1805D6111yescharacteristic, complemented
378#1804—611no—
379#1804—611no—
380#1803—611no—
381#1803—611no—
382#1802—611no—
383#1802—611no—
384#1736—611no—
385C2×#340—611no—
386C2×C61C2×#38011yescharacteristic
387C2×C61#289711yescharacteristic
388C2×C61#289811yescharacteristic
389C2×C61#304511yescharacteristic
390C2×C61#304611yescharacteristic
391C2×C61#308311yescharacteristic
392C2×C61#308411yescharacteristic
393D61—24no—
394D61—44no—
395C22×#41—611no—
396C22×M16—611no—
397C23×C8—611no—
398#520—618no—
399#520—1224no—
400C2×C4×Q8—611no—
401C2×C4×Q8C2×D6111yescharacteristic
402C2×C4×D4—611no—
403C2×C4×D4—611no—
404C2×C4×D4—1221no—
405C2×C4×D4—1221no—
406C2×#117—611no—
407C2×#117—611no—
408C2×#117—1221no—
409C22×C4⋊C4—611no—
410C22×C4⋊C4—611no—
411C22×C4⋊C4—1221no—
412#424—1224no—
413C2×C4⋊C8—611no—
414C2×C4⋊C8—611no—
415C2×C4⋊C8—611no—
416C2×C4⋊C8C2×D6111yescharacteristic
417#417—1224no—
418#416—1224no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103C2×D6111yescharacteristic
422C2×#103C2×D6111yescharacteristic
423C2×#102—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#102—611no—
427#389—1221no—
428#389—1221no—
429#385—1221no—
430#385—1221no—
431#384—611no—
432#384—611no—
433#382—611no—
434#382C2×D6111yescharacteristic
435#340—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#340—611no—
441#340C2×D6111yescharacteristic
442#340C2×D6111yescharacteristic
443C61#2065211yescharacteristic, complemented, Sylow
444C2×#41—614no—
445C2×#41—614no—
446C2×#41—614no—
447C2×#41—1222no—
448C2×#41—1222no—
449C2×#41—1222no—
450C22×Q8C22×D6111yescharacteristic
451C22×D4—611no—
452C22×D4—1221no—
453C23×C4—611no—
454C23×C4—1221no—
455C23×C4—1221no—
456C23×C4—1221no—
457C23×C4—1221no—
458C23×C4—1221no—
459C2×M16—1222no—
460C2×M16—1222no—
461C2×M16—1222no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—1222no—
465C22×C8—1222no—
466C22×C8—1222no—
467C22×C8C22×D6111yescharacteristic
468C22×C8C22×D6111yescharacteristic
469C4×Q8—22no—
470C4×Q8—614no—
471C4×Q8—1222no—
472C4×Q8C4×D6114yescomplemented
473C4×D4—614no—
474C4×D4—614no—
475C4×D4—1228no—
476C4×D4—1222no—
477C4×D4—1228no—
478C4×D4—1222no—
479#117—614no—
480#117—614no—
481#117—1228no—
482#117—1222no—
483#117—1222no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—614no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—1228no—
492C2×C4⋊C4—1222no—
493C2×C4⋊C4—1222no—
494C2×C4⋊C4—1222no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4C22×D6111yescharacteristic
503C2×C4⋊C4C22×D6111yescharacteristic
504C2×C4⋊C4C22×D6111yescharacteristic
505C2×C22⋊C4—611no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C42—21no—
511C2×C42—611no—
512C2×C42—1221no—
513C2×C42—1221no—
514C2×C42C22×D6111yescharacteristic
515C4⋊C8—22no—
516C4⋊C8—1222no—
517C4⋊C8—1222no—
518C4⋊C8—1222no—
519#103—22no—
520#103—22no—
521#103—1222no—
522#103—1222no—
523#102—1222no—
524#102—1222no—
525#102—1222no—
526#102—1222no—
527#95—21no—
528#95—21no—
529#95—1221no—
530#95—1221no—
531C24—611no—
532C24—1221no—
533#41—6116no—
534#41—1228no—
535#41—1228no—
536#41—1228no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8C2×C4×D6112yes—
541C2×Q8D4×D6112yes—
542C2×Q8Q8×D6112yes—
543C2×D4—612no—
544C2×D4—612no—
545C2×D4—612no—
546C2×D4—1224no—
547C2×D4—1224no—
548C2×D4—1224no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—1221no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—611no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—1224no—
566C22×C4—1224no—
567C22×C4—1224no—
568C22×C4—1224no—
569C22×C4—1224no—
570C22×C4—1221no—
571C22×C4—1224no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—4881no—
575C22×C4—4881no—
576C22×C4—4881no—
577C22×C4—4881no—
578C22×C4—4881no—
579C22×C4—4881no—
580C22×C4—4881no—
581C22×C4—4881no—
582C22×C4—2442no—
583C22×C4D4×D6111yescharacteristic
584C22×C4D4×D6111yescharacteristic
585C22×C4C23×D6111yescharacteristic
586M16—2444no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—2444no—
600C4⋊C4—21no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—614no—
607C4⋊C4—614no—
608C4⋊C4—612no—
609C4⋊C4—1224no—
610C4⋊C4—1224no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—4881no—
617C4⋊C4—4881no—
618C4⋊C4—4881no—
619C4⋊C4—4881no—
620C4⋊C4—2442no—
621C4⋊C4C2×C4×D6112yes—
622C22⋊C4—614no—
623C22⋊C4—614no—
624C22⋊C4—1224no—
625C22⋊C4—1224no—
626C22⋊C4—2442no—
627C42—24no—
628C42—612no—
629C42—612no—
630C42—1224no—
631C42—2442no—
632C42C2×C4×D6112yes—
633C42D4×D6112yes—
634C23—612no—
635C23—612no—
636C23—612no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23C2×D4×D6111yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8C4⋊C4×D6114yes—
653D4—614no—
654D4—12216no—
655D4—1222no—
656D4—1222no—
657D4—1222no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—612no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—614no—
678C2×C4—614no—
679C2×C4—614no—
680C2×C4—614no—
681C2×C4—612no—
682C2×C4—612no—
683C2×C4—12216no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1222no—
689C2×C4—4884no—
690C2×C4—4884no—
691C2×C4—4884no—
692C2×C4—4884no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4C22⋊C4×D6112yes—
702C2×C4C22⋊C4×D6112yes—
703C2×C4C22×C4×D6111yescharacteristic
704C2×C4C2×D4×D6111yescharacteristic
705C2×C4C2×D4×D6111yescharacteristic
706C2×C4C2×Q8×D6111yescharacteristic
707C2×C4#41×D6111yescharacteristic
708C2×C4#41×D6111yescharacteristic
709C8—41no—
710C8—41no—
711C8—2441no—
712C8—2441no—
713C22—614no—
714C22—1222no—
715C22—1222no—
716C22—1222no—
717C22—1222no—
718C22—1222no—
719C22—1222no—
720C22—1224no—
721C22—2442no—
722C22—2442no—
723C22—2442no—
724C22—2442no—
725C22—2442no—
726C22—2442no—
727C22C2×C22⋊C4×D6111yescharacteristic
728C22#121×D6111yescharacteristic
729C22C22⋊Q8×D6111yescharacteristic
730C22#1684056411yescharacteristic
731C22#1684056911yescharacteristic
732C22#1684057111yescharacteristic
733C22#1684057811yescharacteristic
734C4—22no—
735C4—22no—
736C4—24no—
737C4—42no—
738C4—81no—
739C4—81no—
740C4—614no—
741C4—1222no—
742C4—1222no—
743C4—4881no—
744C4—4881no—
745C4—2442no—
746C4C2×C4⋊C4×D6111yescharacteristic
747C4#117×D6111yescharacteristic
748C4#121×D6111yescharacteristic
749C4C22⋊Q8×D6111yescharacteristic
750C2—1224no—
751C2—2444no—
752C2#380×D6111yescharacteristic
753C2#2145434111yescharacteristic
754C2#2145435111yescharacteristic
755C2#2145536111yescharacteristic
756C2#2145537211yescharacteristic
757C2#2145567311yescharacteristic
758C2#2145568411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1805C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
cosocleC22×C4×C61C24
hypercenter#1805D61
hypocenterC61#20652
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
2. C2×#16839787C2semidirect
5. #21448444C2semidirect
6. #21445832C2semidirect
7. #21445828C2semidirect
8. #21445826C2semidirect
9. #21445824C2semidirect
10. #21445822C2semidirect
11. #21445820C2semidirect
12. #21445818C2semidirect
13. #21445537C2semidirect
14. #340×D61C2semidirect
15. C61×#1805C2semidirect
20. #16840244C4semidirect
87. Q8×Dic61C2×C4semidirect
90. C4×D244C2×C4semidirect
93. #14519739C2×C4semidirect
139. C4×Q8×C61C2×C4semidirect
175. #11758226C4⋊C4semidirect
377. #1805D61semidirect
443. C61#20652semidirect
472. C4×Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402442
C2×#168397872
C2×#168397622
C2×#168397572
#214484442
#214458322
#214458282
#214458262
#214458242
#214458222
#214458202
#214458182
#214455372
#340×D612
C61×#18052
#2065261