Finite Group Databasebeta

← #29685787

Subgroups — #29685787

Order 15616.

1400 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840238C211yesmaximal, characteristic, complemented
2C2×#16839902C211yesmaximal, characteristic
3C2×#16839861C211yesmaximal, characteristic, complemented
4C2×#16839847C211yesmaximal, characteristic, complemented
5#21448510C211yesmaximal, characteristic
6#21446174C211yesmaximal, characteristic, complemented
7#21446173C211yesmaximal, characteristic, complemented
8#21446140C211yesmaximal, characteristic
9#21446086C211yesmaximal, characteristic, complemented
10#21446015C211yesmaximal, characteristic, complemented
11#21445752C211yesmaximal, characteristic, complemented
12#21445651C211yesmaximal, characteristic, complemented
13#21445638C211yesmaximal, characteristic, complemented
14#21445584C211yesmaximal, characteristic, complemented
15C61×#1863C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C2×#14519752C2211yescharacteristic
20#16840238—24no—
21#16840238—24no—
22C2×Q8×Dic61C2211yescharacteristic
23C2×C4×Dic122—21no—
24C2×C4×Dic122C2211yescharacteristic
25C2×#14519742—21no—
26C2×#14519742C2211yescharacteristic
27C2×#14519739C2211yescharacteristic
28C2×#14519735—21no—
29C2×#14519735C2211yescharacteristic
30C2×#14519734—21no—
31C2×#14519734C2211yescharacteristic
32#16839902C418yescomplemented
33#16839861—24no—
34#16839847—24no—
35C2×#14519708C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519687C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic
46#16839664C2211yescharacteristic
47#16839663—21no—
48#16839651—21no—
49#16839640—21no—
50#16839633—21no—
51#16839619C2211yescharacteristic
52C4⋊C4×Dic61C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839517C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×#107×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#389C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#336C2211yescharacteristic
64C22×Dic122—21no—
65C22×Dic122C2311yescharacteristic
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—22no—
71C2×Q8×D61C2×C414yescomplemented
72C22×D244—21no—
73C22×D244C2311yescharacteristic
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61C2311yescharacteristic
77C2×#11758190—22no—
78C2×#11758190—22no—
79C2×#11758190C2×C414yes—
80C2×#11758201—22no—
81C2×#11758201—22no—
82C2×#11758201C2×C414yes—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519752—22no—
86#14519752C2×C414yes—
87Q8×Dic61—22no—
88Q8×Dic61D414yescomplemented
89C4×Dic122—28no—
90C4×Dic122—22no—
91C4×Dic122—22no—
92#14519742—28no—
93#14519742—22no—
94#14519742D414yescomplemented
95#14519739—22no—
96#14519739—22no—
97#14519735—28no—
98#14519735—22no—
99#14519735—22no—
100#14519734—28no—
101#14519734—22no—
102#14519734—22no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196D411yescharacteristic
109C2×#11758196D411yescharacteristic
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198D411yescharacteristic
117C2×#11758198D411yescharacteristic
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519708—22no—
125#14519702—22no—
126#14519701—22no—
127#14519700—22no—
128#14519700C2×C414yescomplemented
129#14519699—22no—
130#14519697—22no—
131#14519689—22no—
132#14519689C2×C414yescomplemented
133#14519687—22no—
134C8×Dic61—22no—
135#14519684—21no—
136#14519684—21no—
137C22×Q8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C4×Q8×C61—22no—
141C4×Q8×C61—22no—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C42×C61—21no—
148C2×C42×C61C2311yescharacteristic
149#107×C61—22no—
150#103×C61—22no—
151#103×C61C2×C414yescomplemented
152#95×C61—21no—
153C23×D61—21no—
154C23×D61C2×D411yescharacteristic
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61C22×C412yes—
159C2×Q8×C61C2×D412yes—
160C2×Q8×C61#4112yes—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174Q8×D61—28no—
175Q8×D61—28no—
176Q8×D61—28no—
177Q8×D61—28no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—24no—
184C2×D244—81no—
185C2×D244—81no—
186C2×D244C22×C412yes—
187C2×C4×D61—24no—
188C2×C4×D61—24no—
189C2×C4×D61—24no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—42no—
195C2×C4×D61—81no—
196C2×C4×D61—81no—
197C2×C4×D61C22×C412yes—
198C2×C4×D61#4112yes—
199C2×Dic122—24no—
200C2×Dic122—24no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—24no—
205C2×Dic122C22×C412yes—
206C2×Dic122C2×D412yes—
207C2×Dic122#4112yes—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61C22×C412yes—
214C4⋊C4×C61—24no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—81no—
220C4⋊C4×C61C22×C412yes—
221C4⋊C4×C61C2×D412yes—
222C42×C61—24no—
223C42×C61—21no—
224C42×C61—21no—
225#11758201—28no—
226#11758198—24no—
227#11758198—24no—
228#11758198—22no—
229#11758198—22no—
230#11758198—42no—
231#11758198—81no—
232#11758198—81no—
233#11758198—81no—
234C4⋊Dic61—21no—
235C4⋊Dic61—24no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61C2×D412yes—
239#11758196—24no—
240#11758196—24no—
241#11758196—22no—
242#11758196—22no—
243C4×Dic61—24no—
244C4×Dic61—24no—
245C4×Dic61—24no—
246C4×Dic61—24no—
247C4×Dic61—81no—
248C4×Dic61C2×D412yes—
249C4×Dic61C2×D412yes—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418C22×C412yes—
256#11758190—28no—
257C23×C61C22×D411yescharacteristic
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—22no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61C4×D412yes—
272Q8×C61—22no—
273Q8×C61—22no—
274Q8×C61—22no—
275Q8×C61C4×D414yes—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—21no—
281C2×C4×C61—22no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61C23×C411yescharacteristic
295C2×C4×C61C22×D411yescharacteristic
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×Dic61—22no—
301C2×Dic61—21no—
302C2×Dic61—22no—
303C2×Dic61—21no—
304C2×Dic61—22no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—22no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61C4×D412yes—
316C2×Dic61#12012yes—
317C2×Dic61#12012yes—
318D244—22no—
319D244—22no—
320D244—41no—
321D244—41no—
322D244—84no—
323C4×D61—216no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—84no—
329Dic122—216no—
330Dic122—22no—
331Dic122—22no—
332Dic122—22no—
333Dic122C4×D414yes—
334C8×C61—22no—
335C8×C61—41no—
336#92418—22no—
337#92418—41no—
338#21462—611nomaximal, Sylow
339C22×C61C2×C4×D411yescharacteristic
340C22×C61C2×#12011yescharacteristic
341C22×C61#52511yescharacteristic
342C22×C61#57711yescharacteristic
343C22×C61#57711yescharacteristic
344C22×C61#57711yescharacteristic
345C22×C61#57811yescharacteristic
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C4×C61—24no—
361C4×C61—42no—
362C4×C61—41no—
363C4×C61—42no—
364C4×C61—41no—
365C4×C61—81no—
366C4×C61C2×C4×D411yescharacteristic
367C4×C61C2×C4×D411yescharacteristic
368C4×C61#52511yescharacteristic
369C4×C61#52511yescharacteristic
370Dic61—22no—
371Dic61—22no—
372Dic61—22no—
373Dic61—24no—
374Dic61—42no—
375Dic61—81no—
376C2×#519—611no—
377C2×#448—611no—
378C2×#440—611no—
379C2×C4×SD16—611no—
380#2324—611no—
381#1880—611no—
382#1880—611no—
383#1875—611no—
384#1865—611no—
385#1863D6111yescharacteristic, complemented
386#1854—611no—
387#1787—611no—
388#1763—611no—
389C4×#103—611no—
390#1750—611no—
391C2×C61C4×#12011yescharacteristic
392C2×C61#294711yescharacteristic
393C2×C61#294911yescharacteristic
394C2×C61#301011yescharacteristic
395C2×C61#301311yescharacteristic
396C2×C61#312111yescharacteristic
397C2×C61#312611yescharacteristic
398D61—42no—
399D61—82no—
400C23×Q8—611no—
401C22×SD16—611no—
402C22×SD16—611no—
403C2×#121—611no—
404#519—1224no—
405#519—1224no—
406C2×C4×Q8—611no—
407C2×C4×Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—1221no—
410C2×C4×Q8—1221no—
411C2×C4×Q8C2×D6111yescharacteristic
412C2×C4×D4—611no—
413C2×#117—611no—
414C2×#117—611no—
415C2×#117—1221no—
416C2×#117—1221no—
417#448—618no—
418#440—1224no—
419C4×SD16—1224no—
420C2×#107C2×D6111yescharacteristic
421C2×#106—611no—
422C2×#103—611no—
423C2×#103—611no—
424C2×#103—611no—
425C2×#103—611no—
426C2×#103C2×D6111yescharacteristic
427C2×#103C2×D6111yescharacteristic
428C2×#102—611no—
429C2×#102—611no—
430C2×C22⋊C8—611no—
431C2×C22⋊C8—611no—
432C2×#97—611no—
433C2×C4×C8—611no—
434#390—611no—
435#390—1221no—
436#389C2×D6111yescharacteristic
437#388—1221no—
438#386—1221no—
439#385—1221no—
440#380—611no—
441C4×C4⋊C4—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340C2×D6111yescharacteristic
446#336—611no—
447#336C2×D6111yescharacteristic
448C61#2146211yescharacteristic, complemented, Sylow
449C22×Q8—614no—
450C22×Q8—611no—
451C22×Q8—1221no—
452C22×Q8—1222no—
453C22×Q8—1222no—
454C22×Q8—1222no—
455C22×Q8—1222no—
456C22×Q8—1222no—
457C22×Q8C22×D6111yescharacteristic
458C22×D4—611no—
459C22×D4—1221no—
460C23×C4—611no—
461C23×C4—1221no—
462C23×C4—1221no—
463C2×SD16—614no—
464C2×SD16—614no—
465C2×SD16—1222no—
466C2×SD16—1222no—
467C2×SD16—1222no—
468C2×SD16—1222no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8C22×D6111yescharacteristic
472C22×C8C22×D6111yescharacteristic
473#121—614no—
474#121—1222no—
475C4×Q8—22no—
476C4×Q8—22no—
477C4×Q8—614no—
478C4×Q8—614no—
479C4×Q8—1222no—
480C4×Q8—1222no—
481C4×Q8—1228no—
482C4×Q8—1222no—
483C4×Q8—1222no—
484C4×Q8—1228no—
485C4×D4—1222no—
486C4×D4—1222no—
487#117—1222no—
488#117—1222no—
489#117—1228no—
490#117—1222no—
491#117—1228no—
492#117—1222no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
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×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C42—21no—
514C2×C42—611no—
515C2×C42—1221no—
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42—1221no—
520C2×C42C22×D6111yescharacteristic
521#107—22no—
522#106—1222no—
523#103—22no—
524#103—614no—
525#103—1222no—
526#103—1222no—
527#103—1222no—
528#103C4×D6114yescomplemented
529#102—1222no—
530#102—1222no—
531C22⋊C8—614no—
532C22⋊C8—1222no—
533#97—1222no—
534C4×C8—1222no—
535#95—21no—
536#95—1221no—
537#95—1221no—
538C24—611no—
539C24—1221no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—612no—
544C2×Q8—612no—
545C2×Q8—612no—
546C2×Q8—1224no—
547C2×Q8—1224no—
548C2×Q8—1224no—
549C2×Q8—1228no—
550C2×Q8—1228no—
551C2×Q8—1228no—
552C2×Q8—1228no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8C2×C4×D6112yes—
557C2×Q8D4×D6112yes—
558C2×Q8#1175822612yes—
559C2×D4—612no—
560C2×D4—1224no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—4881no—
567C2×D4—4881no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—612no—
576C22×C4—612no—
577C22×C4—1224no—
578C22×C4—1224no—
579C22×C4—1224no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—4881no—
588C22×C4—4881no—
589C22×C4—2442no—
590C22×C4D4×D6111yescharacteristic
591C22×C4D4×D6111yescharacteristic
592C22×C4C23×D6111yescharacteristic
593SD16—1228no—
594SD16—1228no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—612no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8C2×C4×D6112yes—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—81no—
613C4⋊C4—612no—
614C4⋊C4—1222no—
615C4⋊C4—1222no—
616C4⋊C4—1224no—
617C4⋊C4—1224no—
618C4⋊C4—1224no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4C2×C4×D6112yes—
623C4⋊C4D4×D6112yes—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1224no—
627C22⋊C4—1224no—
628C22⋊C4—4881no—
629C22⋊C4—4881no—
630C22⋊C4—4881no—
631C22⋊C4—2442no—
632C42—24no—
633C42—21no—
634C42—21no—
635C42—612no—
636C42—612no—
637C42—1224no—
638C42—1224no—
639C42—1224no—
640C42—1224no—
641C42—4881no—
642C23—612no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23—1222no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655C23—2441no—
656C23C2×D4×D6111yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—614no—
661Q8—12216no—
662Q8—1222no—
663Q8—1222no—
664Q8—1222no—
665Q8#1451973914yes—
666D4—1222no—
667D4—1222no—
668D4—4884no—
669D4—2441no—
670D4—2441no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—612no—
690C2×C4—612no—
691C2×C4—612no—
692C2×C4—12216no—
693C2×C4—1222no—
694C2×C4—1221no—
695C2×C4—1222no—
696C2×C4—1221no—
697C2×C4—1222no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—4884no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4C22×C4×D6111yescharacteristic
714C2×C4C2×D4×D6111yescharacteristic
715C2×C4C2×D4×D6111yescharacteristic
716C2×C4#41×D6111yescharacteristic
717C2×C4#41×D6111yescharacteristic
718C2×C4C2×#1175822611yescharacteristic
719C8—22no—
720C8—41no—
721C8—1222no—
722C8—2441no—
723C22—1222no—
724C22—1222no—
725C22—1222no—
726C22—4881no—
727C22—4881no—
728C22—4881no—
729C22—4881no—
730C22—2442no—
731C22—2442no—
732C22—2442no—
733C22—2441no—
734C22—2441no—
735C22—2441no—
736C22—2441no—
737C22C4×D4×D6111yescharacteristic
738C22#120×D6111yescharacteristic
739C22#1684027511yescharacteristic
740C22#1684056911yescharacteristic
741C22#1684057111yescharacteristic
742C22#1684057211yescharacteristic
743C22#1684057511yescharacteristic
744C4—24no—
745C4—41no—
746C4—42no—
747C4—41no—
748C4—42no—
749C4—81no—
750C4—1222no—
751C4—1222no—
752C4—1224no—
753C4—1222no—
754C4—4881no—
755C4—2442no—
756C4C4×D4×D6111yescharacteristic
757C4C2×#1451973911yescharacteristic
758C4#1684027011yescharacteristic
759C4#1684027511yescharacteristic
760C2—4882no—
761C2—2442no—
762C2#2144832011yescharacteristic
763C2#2145465711yescharacteristic
764C2#2145467511yescharacteristic
765C2#2145510211yescharacteristic
766C2#2145513511yescharacteristic
767C2#2145605311yescharacteristic
768C2#2145611211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1863C2
socleC23×C61C22×D4
prime radicalC2×#14519752C22
cosocleC22×C4×C61C24
hypercenter#1863D61
hypocenterC61#21462
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
1. C2×#16840238C2semidirect
3. C2×#16839861C2semidirect
4. C2×#16839847C2semidirect
6. #21446174C2semidirect
7. #21446173C2semidirect
9. #21446086C2semidirect
10. #21446015C2semidirect
11. #21445752C2semidirect
12. #21445651C2semidirect
13. #21445638C2semidirect
14. #21445584C2semidirect
15. C61×#1863C2semidirect
32. #16839902C4semidirect
71. C2×Q8×D61C2×C4semidirect
88. Q8×Dic61D4semidirect
94. #14519742D4semidirect
128. #14519700C2×C4semidirect
132. #14519689C2×C4semidirect
151. #103×C61C2×C4semidirect
385. #1863D61semidirect
448. C61#21462semidirect
528. #103C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402382
C2×#168399022
C2×#168398612
C2×#168398472
#214485102
#214461742
#214461732
#214461402
#214460862
#214460152
#214457522
#214456512
#214456382
#214455842
C61×#18632
#2146261