Finite Group Databasebeta

← #29685772

Subgroups — #29685772

Order 15616.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840241C211yesmaximal, characteristic
2C2×#16839925C211yesmaximal, characteristic
3C2×#16839868C211yesmaximal, characteristic, complemented
4C2×#16839853C211yesmaximal, characteristic, complemented
5#21448499C211yesmaximal, characteristic, complemented
6#21446159C211yesmaximal, characteristic, complemented
7#21446153C211yesmaximal, characteristic, complemented
8#21446125C211yesmaximal, characteristic, complemented
9#21446086C211yesmaximal, characteristic, complemented
10#21446010C211yesmaximal, characteristic, complemented
11#21445756C211yesmaximal, characteristic
12#21445646C211yesmaximal, characteristic, complemented
13#21445638C211yesmaximal, characteristic, complemented
14#21445584C211yesmaximal, characteristic, complemented
15C61×#1864C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×Dic244C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C2×#14519757C2211yescharacteristic
20#16840241—24no—
21#16840241—24no—
22C2×C4×Dic122C2211yescharacteristic
23C2×#14519742C2211yescharacteristic
24C2×#14519742C2211yescharacteristic
25C2×D4×Dic61C2211yescharacteristic
26C2×C4×C22⋊D61—21no—
27C2×#14519737—21no—
28C2×#14519734C2211yescharacteristic
29C2×#14519733—21no—
30C22×#11758196—21no—
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839925C418yescomplemented
33#16839868—24no—
34#16839853—24no—
35C2×#14519708C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519687C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic
46#16839668C2211yescharacteristic
47#16839658—21no—
48#16839652—21no—
49#16839651—21no—
50#16839645—21no—
51#16839619C2211yescharacteristic
52C4⋊C4×Dic61C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839517C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×#106×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#389C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#336C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224C2×C414yes—
70C22×Dic122C2311yescharacteristic
71C22×Dic122C2311yescharacteristic
72C22×C22⋊D61—21no—
73C23×Dic61—21no—
74C23×Dic61—21no—
75C22×C4×D61—21no—
76C22×C4×D61C2311yescharacteristic
77C2×Dic244—22no—
78C2×Dic244—22no—
79C2×Dic244C2×C414yescomplemented
80C2×#11758200—22no—
81C2×#11758200—22no—
82C2×#11758200C2×C414yescomplemented
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519757—22no—
86#14519757C2×C414yescomplemented
87C4×Dic122—22no—
88C4×Dic122—22no—
89#14519742—22no—
90#14519742—22no—
91#14519742—22no—
92#14519742D414yes—
93D4×Dic61—22no—
94D4×Dic61D414yes—
95C4×C22⋊D61—28no—
96#14519737—28no—
97#14519734—22no—
98#14519734—22no—
99#14519733—28no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758196—28no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196D411yescharacteristic
109C2×#11758196D411yescharacteristic
110C4⋊C4×D61—22no—
111C4⋊C4×D61—22no—
112C2×C22⋊Dic61—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198D411yescharacteristic
116C2×#11758198D411yescharacteristic
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122#14519708—22no—
123#14519702—22no—
124#14519702—22no—
125#14519700—22no—
126#14519700—22no—
127#14519700C2×C414yescomplemented
128#14519698—22no—
129#14519689—22no—
130#14519689C2×C414yescomplemented
131#14519687—22no—
132C8×Dic61—22no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137C22×D4×C61C2311yescharacteristic
138C23×C4×C61—21no—
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C4×D4×C61—22no—
142C4×D4×C61—22no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C22⋊C4×C61—21no—
148C2×C42×C61C2311yescharacteristic
149#106×C61—22no—
150#102×C61—22no—
151#102×C61C2×C414yescomplemented
152#95×C61—21no—
153C24×C61—21no—
154C23×D61C2×D411yescharacteristic
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61C22×C412yes—
159C2×D4×C61C2×D412yes—
160C2×D4×C61#4112yes—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—24no—
164C22×C4×C61—21no—
165C22×C4×C61—81no—
166C22×C4×C61—81no—
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2411yescharacteristic
170C2×C22⋊D61—24no—
171C2×C22⋊D61—24no—
172C2×C22⋊D61—24no—
173C22×Dic61—24no—
174C22×Dic61—24no—
175C22×Dic61—21no—
176C22×Dic61—24no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—24no—
180C22×Dic61—21no—
181C22×Dic61—81no—
182C22×Dic61—81no—
183C22×Dic61C2×D411yescharacteristic
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186#11758224—28no—
187#11758224—28no—
188#11758224—28no—
189#11758224—28no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—24no—
195C2×C4×D61—81no—
196C2×C4×D61—81no—
197C2×C4×D61C22×C412yes—
198C2×C4×D61#4112yes—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122C22×C412yes—
208C2×Dic122C22×C412yes—
209C2×Dic122C2×D412yes—
210C2×Dic122#4112yes—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61C22×C412yes—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—81no—
222C4⋊C4×C61C22×C412yes—
223C4⋊C4×C61C2×D412yes—
224C22⋊C4×C61—24no—
225C42×C61—21no—
226C42×C61—21no—
227C22⋊Dic61—24no—
228#11758200—28no—
229#11758198—24no—
230#11758198—22no—
231#11758198—22no—
232#11758198—81no—
233C4⋊Dic61—21no—
234C4⋊Dic61—24no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61C2×D412yes—
238#11758196—24no—
239#11758196—24no—
240#11758196—22no—
241#11758196—24no—
242#11758196—22no—
243#11758196—42no—
244C4×Dic61—24no—
245C4×Dic61—24no—
246C4×Dic61—42no—
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—
256Dic244—28no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61C22×D411yescharacteristic
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61C4×D412yes—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—22no—
275D4×C61C4×D414yes—
276C2×C4×C61—22no—
277C2×C4×C61—21no—
278C2×C4×C61—22no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—84no—
292C2×C4×C61C23×C411yescharacteristic
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C22⋊D61—216no—
299C2×Dic61—216no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—21no—
303C2×Dic61—22no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—84no—
319C2×Dic61C4×D412yes—
320C2×Dic61#12012yes—
321C2×Dic61#12012yes—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—84no—
327Dic122—22no—
328Dic122—22no—
329Dic122—22no—
330Dic122—22no—
331Dic122—22no—
332Dic122—41no—
333Dic122—41no—
334Dic122C4×D414yes—
335C8×C61—22no—
336C8×C61—41no—
337#92418—22no—
338#92418—41no—
339#21461—611nomaximal, Sylow
340C22×C61—24no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61C2×C4×D411yescharacteristic
348C22×C61C2×#12011yescharacteristic
349C22×C61#52511yescharacteristic
350C22×C61#57711yescharacteristic
351C22×C61#57711yescharacteristic
352C22×C61#57711yescharacteristic
353C22×C61#57811yescharacteristic
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—41no—
361C4×C61—42no—
362C4×C61—42no—
363C4×C61—41no—
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—24no—
373Dic61—22no—
374Dic61—42no—
375Dic61—42no—
376Dic61—81no—
377C2×#520—611no—
378C2×#452—611no—
379C2×#441—611no—
380C2×C4×SD16—611no—
381#2323—611no—
382#1878—611no—
383#1877—611no—
384#1872—611no—
385#1865—611no—
386#1864D6111yescharacteristic, complemented
387#1853—611no—
388#1788—611no—
389#1762—611no—
390C4×#103—611no—
391#1750—611no—
392C2×C61—44no—
393C2×C61C4×#12011yescharacteristic
394C2×C61#294711yescharacteristic
395C2×C61#295211yescharacteristic
396C2×C61#300911yescharacteristic
397C2×C61#301311yescharacteristic
398C2×C61#312011yescharacteristic
399C2×C61#312511yescharacteristic
400D61—42no—
401C22×#41—611no—
402C22×Q16—611no—
403C22×SD16—611no—
404C2×C22⋊Q8—611no—
405#520—1224no—
406#520—1224no—
407C2×C4×Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—611no—
410C2×C4×D4—611no—
411C2×C4×D4—1221no—
412C2×C4×D4—1221no—
413C2×C4×D4C2×D6111yescharacteristic
414C2×#117—611no—
415C2×#117—1221no—
416C22×C4⋊C4—611no—
417C22×C4⋊C4—1221no—
418#452—618no—
419#441—1224no—
420C4×SD16—1224no—
421C2×#106—611no—
422C2×#106C2×D6111yescharacteristic
423C2×#103—611no—
424C2×#103—611no—
425C2×#103—611no—
426C2×#103—611no—
427C2×#103—611no—
428C2×#102—611no—
429C2×#102C2×D6111yescharacteristic
430C2×#102C2×D6111yescharacteristic
431C2×C22⋊C8—611no—
432C2×C22⋊C8—611no—
433C2×#97—611no—
434C2×C4×C8—611no—
435#391—611no—
436#389—1221no—
437#389C2×D6111yescharacteristic
438#388—1221no—
439#388—1221no—
440#387—1221no—
441#380—611no—
442C4×C4⋊C4—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340C2×D6111yescharacteristic
447#336—611no—
448#336C2×D6111yescharacteristic
449C61#2146111yescharacteristic, complemented, Sylow
450C2×#41—614no—
451C2×#41—1222no—
452C2×#41—1222no—
453C2×#41—1222no—
454C2×#41—1222no—
455C2×#41—1222no—
456C22×Q8—611no—
457C22×Q8—611no—
458C22×D4—1221no—
459C22×D4C22×D6111yescharacteristic
460C23×C4—21no—
461C23×C4—611no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4—1221no—
465C2×Q16—614no—
466C2×Q16—1222no—
467C2×Q16—1222no—
468C2×SD16—614no—
469C2×SD16—1222no—
470C2×SD16—1222no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C22⋊Q8—614no—
476C22⋊Q8—1222no—
477C4×Q8—614no—
478C4×Q8—1222no—
479C4×Q8—1222no—
480C4×Q8—1222no—
481C4×Q8—1222no—
482C4×Q8—1222no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—614no—
486C4×D4—1222no—
487C4×D4—1228no—
488C4×D4—1228no—
489#117—1222no—
490#117—1222no—
491#117—1228no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—1222no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1228no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1222no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—611no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C42—611no—
515C2×C42—1221no—
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42C22×D6111yescharacteristic
520#106—22no—
521#106—1222no—
522#103—614no—
523#103—1222no—
524#103—1222no—
525#103—1222no—
526#103—1222no—
527#102—22no—
528#102—1222no—
529#102C4×D6114yescomplemented
530C22⋊C8—614no—
531C22⋊C8—1222no—
532#97—1222no—
533C4×C8—1222no—
534#95—21no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—21no—
540C24—611no—
541#41—1228no—
542#41—1228no—
543#41—1228no—
544#41—1228no—
545C2×Q8—612no—
546C2×Q8—612no—
547C2×Q8—612no—
548C2×Q8—612no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—1224no—
561C2×D4—1224no—
562C2×D4—1224no—
563C2×D4C2×C4×D6112yes—
564C2×D4D4×D6112yes—
565C2×D4#1175822612yes—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—81no—
571C22×C4—81no—
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—1224no—
581C22×C4—1224no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—4881no—
591C22×C4—4881no—
592C22×C4—4881no—
593C22×C4—4881no—
594C22×C4D4×D6111yescharacteristic
595C22×C4D4×D6111yescharacteristic
596C22×C4C23×D6111yescharacteristic
597Q16—1228no—
598SD16—1228no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—612no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8C2×C4×D6112yes—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—81no—
616C4⋊C4—612no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C4⋊C4—1224no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—2442no—
627C4⋊C4C2×C4×D6112yes—
628C4⋊C4D4×D6112yes—
629C22⋊C4—24no—
630C22⋊C4—1222no—
631C22⋊C4—1222no—
632C22⋊C4—1224no—
633C22⋊C4—1224no—
634C22⋊C4—4881no—
635C42—21no—
636C42—21no—
637C42—612no—
638C42—612no—
639C42—1224no—
640C42—1224no—
641C42—4881no—
642C42—2442no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—612no—
651C23—1221no—
652C23—1221no—
653C23—1221no—
654C23—1221no—
655C23—1221no—
656C23—1221no—
657C23C2×D4×D6111yescharacteristic
658Q8—614no—
659Q8—1222no—
660Q8—1222no—
661Q8—1222no—
662Q8—1222no—
663Q8—1222no—
664Q8—2441no—
665Q8—2441no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—12216no—
670D4#1451973914yes—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—84no—
687C2×C4—612no—
688C2×C4—612no—
689C2×C4—612no—
690C2×C4—12216no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1222no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—4884no—
707C2×C4—4884no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4C22×C4×D6111yescharacteristic
716C2×C4C2×D4×D6111yescharacteristic
717C2×C4C2×D4×D6111yescharacteristic
718C2×C4#41×D6111yescharacteristic
719C2×C4#41×D6111yescharacteristic
720C2×C4C2×#1175822611yescharacteristic
721C8—22no—
722C8—41no—
723C8—1222no—
724C8—2441no—
725C22—24no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—1222no—
733C22—1222no—
734C22—1222no—
735C22—2441no—
736C22—2441no—
737C22—2441no—
738C22—2441no—
739C22C4×D4×D6111yescharacteristic
740C22#120×D6111yescharacteristic
741C22#1684027511yescharacteristic
742C22#1684056811yescharacteristic
743C22#1684057211yescharacteristic
744C22#1684057211yescharacteristic
745C22#1684057611yescharacteristic
746C4—41no—
747C4—42no—
748C4—41no—
749C4—42no—
750C4—81no—
751C4—1222no—
752C4—1222no—
753C4—1224no—
754C4—1222no—
755C4—4881no—
756C4—2442no—
757C4—2442no—
758C4C4×D4×D6111yescharacteristic
759C4C2×#1451973911yescharacteristic
760C4#1684027011yescharacteristic
761C4#1684027511yescharacteristic
762C2—44no—
763C2—2442no—
764C2#2144832011yescharacteristic
765C2#2145465511yescharacteristic
766C2#2145470111yescharacteristic
767C2#2145509111yescharacteristic
768C2#2145513211yescharacteristic
769C2#2145603811yescharacteristic
770C2#2145610111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1864C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
cosocleC22×C4×C61C24
hypercenter#1864D61
hypocenterC61#21461
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
3. C2×#16839868C2semidirect
4. C2×#16839853C2semidirect
5. #21448499C2semidirect
6. #21446159C2semidirect
7. #21446153C2semidirect
8. #21446125C2semidirect
9. #21446086C2semidirect
10. #21446010C2semidirect
12. #21445646C2semidirect
13. #21445638C2semidirect
14. #21445584C2semidirect
15. C61×#1864C2semidirect
32. #16839925C4semidirect
79. C2×Dic244C2×C4semidirect
82. C2×#11758200C2×C4semidirect
86. #14519757C2×C4semidirect
127. #14519700C2×C4semidirect
130. #14519689C2×C4semidirect
151. #102×C61C2×C4semidirect
386. #1864D61semidirect
449. C61#21461semidirect
529. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402412
C2×#168399252
C2×#168398682
C2×#168398532
#214484992
#214461592
#214461532
#214461252
#214460862
#214460102
#214457562
#214456462
#214456382
#214455842
C61×#18642
#2146161