Finite Group Databasebeta

← #29646033

Subgroups — #29646033

Order 15616.

1080 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840350C211yesmaximal, characteristic
2#21454845C211yesmaximal, characteristic, complemented
3#21454841C211yesmaximal, characteristic, complemented
4#21444185C212yesmaximal, complemented
5#21444177C212yesmaximal, complemented
6#21444169C212yesmaximal, complemented
7#21444164C212yesmaximal, complemented
8#21444135C211yesmaximal, characteristic, complemented
9#21444135C211yesmaximal, characteristic, complemented
10C2×#16839486C211yesmaximal, characteristic, complemented
11C2×C61×#323C211yesmaximal, characteristic, complemented
12#16840350—22no—
13#16840350—22no—
14#16840350—22no—
15#16840350—22no—
16C2×#14519770C411yescharacteristic
17C2×#14519770C2211yescharacteristic
18C2×#14519763C411yescharacteristic
19C2×#14519763C2211yescharacteristic
20C2×#14519759C411yescharacteristic
21C2×#14519759C2211yescharacteristic
22C2×#14519756C411yescharacteristic
23C2×#14519751C411yescharacteristic
24C2×#14519750C411yescharacteristic
25C2×#14519750C2211yescharacteristic
26C2×#14519746C411yescharacteristic
27C2×#14519746C411yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C4×C22⋊D61C2211yescharacteristic
30#16839833—22no—
31#16839830—22no—
32C8×C22⋊D61—22no—
33#16839825—22no—
34#16839816C2212yescomplemented
35#16839812C2212yescomplemented
36#16839724C2212yescomplemented
37C2×C22⋊#92418C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C22⋊C8×D61C2212yescomplemented
40#16839487C2212yescomplemented
41#16839487C2212yescomplemented
42#16839486C2212yes—
43#16839486C2212yes—
44#16839485C2212yescomplemented
45#16839485C2212yescomplemented
46C22×C22⋊C4×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C2×C22⋊C8×C61C2211yescharacteristic
49C61×#323C2212yes—
50C61×#323C2212yes—
51C22×Dic122C2×C411yescharacteristic
52C22×D244C2×C411yescharacteristic
53C22×C22⋊D61C2×C411yescharacteristic
54C22×C22⋊D61C2×C411yescharacteristic
55C22×C22⋊D61C2×C411yescharacteristic
56C22×C22⋊D61C2×C411yescharacteristic
57C22×C22⋊D61C2×C411yescharacteristic
58C22×C22⋊D61C2×C411yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2311yescharacteristic
61C2×#11758189—22no—
62C22×#92418—21no—
63C22×#92418—21no—
64C2×C8×D61—22no—
65#14519770—22no—
66#14519770—22no—
67#14519770—22no—
68#14519770—22no—
69#14519763—22no—
70#14519763—22no—
71#14519763—22no—
72#14519763—22no—
73#14519759—22no—
74#14519759—22no—
75#14519759—22no—
76#14519759—22no—
77#14519756—22no—
78#14519756—22no—
79#14519751—22no—
80#14519751—22no—
81#14519750—22no—
82#14519750—22no—
83#14519750—22no—
84#14519750—22no—
85#14519746—22no—
86#14519746—22no—
87#14519746—22no—
88#14519746—22no—
89C4×C22⋊D61—21no—
90C4×C22⋊D61—21no—
91C4×C22⋊D61—21no—
92C4×C22⋊D61—21no—
93C4×C22⋊D61D412yes—
94C4×C22⋊D61D412yes—
95C4×C22⋊D61D412yes—
96C4×C22⋊D61D412yes—
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2311yescharacteristic
103C2×C22⋊Dic61C2×C411yescharacteristic
104C2×C22⋊Dic61C2×C411yescharacteristic
105C2×C22⋊Dic61C2×C411yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×C22⋊Dic61C2×C411yescharacteristic
108C2×C22⋊Dic61C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2311yescharacteristic
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418—21no—
118C22⋊#92418—21no—
119C22⋊#92418C2312yes—
120C22⋊#92418C2312yes—
121#14519689—22no—
122#14519689—22no—
123#14519687—22no—
124C8×Dic61—22no—
125C25×C61C2×C411yescharacteristic
126C23×C4×C61C2×C411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C22×C8×C61—21no—
129C22×C8×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139C22⋊C8×C61—21no—
140C22⋊C8×C61C2312yes—
141C22⋊C8×C61C2312yes—
142C24×C61—21no—
143C24×C61—21no—
144C24×C61—22no—
145C24×C61—22no—
146C24×C61—81no—
147C24×C61—81no—
148C24×C61C22×C411yescharacteristic
149C24×C61C22×C411yescharacteristic
150C24×C61C22×C411yescharacteristic
151C23×D61C22×C411yescharacteristic
152C23×D61C22×C411yescharacteristic
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—81no—
156C22×C4×C61—81no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2411yescharacteristic
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—21no—
168C2×C22⋊D61—21no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—81no—
176C2×C22⋊D61—81no—
177C2×C22⋊D61—81no—
178C2×C22⋊D61—81no—
179C2×C22⋊D61C22⋊C412yes—
180C2×C22⋊D61C22⋊C412yes—
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C2×D244—22no—
188C2×D244—81no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—81no—
192C2×C4×D61—81no—
193C2×C4×D61C2×D412yes—
194C2×C4×D61C2×D412yes—
195C2×Dic122—22no—
196C2×Dic122—81no—
197C2×C8×C61—22no—
198C2×C8×C61—22no—
199C2×C8×C61—81no—
200C2×C8×C61—81no—
201C22⋊C4×C61—21no—
202C22⋊C4×C61—21no—
203C22⋊C4×C61—21no—
204C22⋊C4×C61—21no—
205C22⋊C4×C61—21no—
206C22⋊C4×C61—21no—
207C22⋊C4×C61—21no—
208C22⋊C4×C61—21no—
209C22⋊Dic61—21no—
210C22⋊Dic61—21no—
211C22⋊Dic61—22no—
212C22⋊Dic61—22no—
213C22⋊Dic61—22no—
214C22⋊Dic61—22no—
215C22⋊Dic61C22⋊C412yes—
216C22⋊Dic61C22⋊C412yes—
217#11758198—22no—
218#11758198—21no—
219#11758198—21no—
220#11758198—22no—
221#11758198C22⋊C412yes—
222#11758198C22⋊C412yes—
223C4⋊Dic61—22no—
224C4⋊Dic61—22no—
225#11758196—21no—
226#11758196—21no—
227#11758196—22no—
228#11758196—22no—
229#11758196C22⋊C412yes—
230#11758196C22⋊C412yes—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61C2×D412yes—
234C4×Dic61C2×D412yes—
235C2×#92418—22no—
236C2×#92418—22no—
237C2×#92418—81no—
238C2×#92418—81no—
239#11758189—82no—
240C8×D61—82no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—42no—
254C23×C61—42no—
255C23×C61—81no—
256C23×C61—81no—
257C23×C61—81no—
258C23×C61—81no—
259C23×C61—84no—
260C23×C61—84no—
261C23×C61C2×C22⋊C411yescharacteristic
262C23×C61C2×C22⋊C411yescharacteristic
263C23×C61#13112yes—
264C23×C61#13112yes—
265C23×C61C23×C411yescharacteristic
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61C2×C22⋊C412yes—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—81no—
287C2×C4×C61—81no—
288C2×C4×C61C2×C22⋊C411yescharacteristic
289C2×C4×C61C2×C22⋊C411yescharacteristic
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C22×D411yescharacteristic
292C22⋊D61—24no—
293C22⋊D61—24no—
294C22⋊D61—42no—
295C22⋊D61—42no—
296C22⋊D61—82no—
297C22⋊D61—82no—
298C22⋊D61—82no—
299C22⋊D61—82no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61C2×C22⋊C412yes—
312C2×Dic61C2×C22⋊C412yes—
313C2×Dic61C2×C22⋊C412yes—
314D244—82no—
315C4×D61—42no—
316C4×D61—42no—
317C4×D61—81no—
318C4×D61—81no—
319Dic122—82no—
320C8×C61—42no—
321C8×C61—42no—
322#92418—42no—
323#92418—42no—
324#17386—611nomaximal, Sylow
325C22×C61—21no—
326C22×C61—21no—
327C22×C61—21no—
328C22×C61—21no—
329C22×C61—21no—
330C22×C61—21no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61—84no—
344C22×C61—84no—
345C22×C61#40812yes—
346C22×C61#40812yes—
347C22×C61C22×C22⋊C411yescharacteristic
348C22×C61C2×#13111yescharacteristic
349C22×C61C2×#13111yescharacteristic
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—41no—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C4×C61—21no—
361C4×C61—21no—
362C4×C61—21no—
363C4×C61—21no—
364C4×C61—41no—
365C4×C61—41no—
366Dic61—22no—
367Dic61—22no—
368Dic61—22no—
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372C2×#538—611no—
373#2973—611no—
374#2972—611no—
375#1473—612no—
376#1471—612no—
377#1469—612no—
378#1468—612no—
379#1459—611no—
380#1459—611no—
381C2×#323—611no—
382C2×#323D6111yescharacteristic, complemented
383C2×C61—21no—
384C2×C61—21no—
385C2×C61—22no—
386C2×C61—22no—
387C2×C61—81no—
388C2×C61—81no—
389C2×C61C2×#40811yescharacteristic
390C2×C61#288311yescharacteristic
391C2×C61#288811yescharacteristic
392D61—42no—
393D61—81no—
394#538—1222no—
395#538—1222no—
396#538—1222no—
397#538—1222no—
398C2×#126—611no—
399C2×#126—611no—
400C2×#124—611no—
401C2×#124—611no—
402C2×#123—611no—
403C2×#123—611no—
404C2×C22⋊Q8—611no—
405C2×#121—611no—
406C2×#121—611no—
407C2×#121—611no—
408C2×#120—611no—
409C2×#120—611no—
410C2×C4×D4—611no—
411C2×C4×D4—611no—
412C22×C22⋊C4C2×D6111yescharacteristic
413#435—1222no—
414#435—1222no—
415C8×D4—1222no—
416C8×D4—1222no—
417#432—612no—
418#431—612no—
419#407—612no—
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422C2×C22⋊C8—612no—
423C2×C22⋊C8C2×D6111yescharacteristic
424C2×C22⋊C8C2×D6111yescharacteristic
425#324—612no—
426#324—612no—
427#323—612no—
428#323—612no—
429#323—612no—
430#323—612no—
431#323C2×D6112yes—
432#323C2×D6112yes—
433C61#1738611yescharacteristic, complemented, Sylow
434C25C4×D6111yescharacteristic
435C22×Q8—611no—
436C22×D4—611no—
437C22×D4—611no—
438C22×D4—611no—
439C22×D4—611no—
440C22×D4—611no—
441C22×D4—611no—
442C22×D4—611no—
443C23×C4—611no—
444C23×C4—611no—
445C23×C4C4×D6111yescharacteristic
446C23×C4C22×D6111yescharacteristic
447C2×M16—1222no—
448C22×C8—21no—
449C22×C8—21no—
450C22×C8—1222no—
451C22×C8—1221no—
452C22×C8—1221no—
453#126—1222no—
454#126—1222no—
455#126—1222no—
456#126—1222no—
457#124—1222no—
458#124—1222no—
459#124—1222no—
460#124—1222no—
461#123—1222no—
462#123—1222no—
463#123—1222no—
464#123—1222no—
465C22⋊Q8—1222no—
466C22⋊Q8—1222no—
467#121—1222no—
468#121—1222no—
469#121—1222no—
470#121—1222no—
471#121—1222no—
472#121—1222no—
473#120—1222no—
474#120—1222no—
475#120—1222no—
476#120—1222no—
477C4×D4—612no—
478C4×D4—612no—
479C4×D4—612no—
480C4×D4—612no—
481C4×D4—1221no—
482C4×D4—1221no—
483C4×D4—1221no—
484C4×D4—1221no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—611no—
496C2×C22⋊C4—611no—
497C2×C22⋊C4—611no—
498C2×C22⋊C4—611no—
499C2×C22⋊C4—611no—
500C2×C22⋊C4—611no—
501C2×C22⋊C4—611no—
502C2×C22⋊C4—611no—
503C2×C22⋊C4—611no—
504C2×C22⋊C4—611no—
505C2×C22⋊C4C4×D6111yescharacteristic
506C2×C22⋊C4C4×D6111yescharacteristic
507C2×C22⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4C22×D6111yescharacteristic
509C2×C42—611no—
510C2×C42—611no—
511C4⋊C8—1222no—
512C4⋊C8—1222no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—612no—
516C22⋊C8—612no—
517C22⋊C8—1222no—
518C22⋊C8—1222no—
519C22⋊C8—1221no—
520C22⋊C8—1221no—
521C22⋊C8C22×D6112yes—
522C22⋊C8C22×D6112yes—
523#97—1222no—
524C4×C8—1222no—
525C24—21no—
526C24—21no—
527C24—22no—
528C24—22no—
529C24—81no—
530C24—81no—
531C24—611no—
532C24—611no—
533C24C2×C4×D6111yescharacteristic
534C24C2×C4×D6111yescharacteristic
535C24C2×C4×D6111yescharacteristic
536C2×Q8—1222no—
537C2×Q8—4881no—
538C2×D4—612no—
539C2×D4—612no—
540C2×D4—1222no—
541C2×D4—1222no—
542C2×D4—1222no—
543C2×D4—1222no—
544C2×D4—1222no—
545C2×D4—1222no—
546C2×D4—1222no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—1222no—
550C2×D4—1222no—
551C2×D4—4881no—
552C2×D4—4881no—
553C2×D4—4881no—
554C2×D4—4881no—
555C2×D4—4881no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—4881no—
571C22×C4—4881no—
572C22×C4C2×C4×D6111yescharacteristic
573C22×C4C2×C4×D6111yescharacteristic
574C22×C4C2×C4×D6111yescharacteristic
575C22×C4D4×D6111yescharacteristic
576C22×C4D4×D6111yescharacteristic
577C22×C4D4×D6111yescharacteristic
578C22×C4D4×D6111yescharacteristic
579C22×C4C23×D6111yescharacteristic
580M16—4882no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—81no—
584C2×C8—81no—
585C2×C8—1222no—
586C2×C8—1222no—
587C2×C8—4882no—
588C2×C8—4881no—
589C2×C8—4881no—
590C4⋊C4—612no—
591C4⋊C4—612no—
592C4⋊C4—1222no—
593C4⋊C4—1222no—
594C4⋊C4—1222no—
595C4⋊C4—1222no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—612no—
607C22⋊C4—612no—
608C22⋊C4—612no—
609C22⋊C4—612no—
610C22⋊C4—1222no—
611C22⋊C4—1222no—
612C22⋊C4—1222no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4—1221no—
617C22⋊C4—1221no—
618C22⋊C4—1221no—
619C22⋊C4—1221no—
620C42—612no—
621C42—612no—
622C42—1221no—
623C42—1221no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—42no—
637C23—42no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—84no—
643C23—84no—
644C23—612no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23—1221no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23C22⋊C4×D6111yescharacteristic
655C23C22⋊C4×D6111yescharacteristic
656C23#1451978312yes—
657C23#1451978512yes—
658C23C22×C4×D6111yescharacteristic
659Q8—4882no—
660D4—1224no—
661D4—1224no—
662D4—4882no—
663D4—4882no—
664D4—4882no—
665D4—4882no—
666D4—4882no—
667D4—2442no—
668D4—2442no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—81no—
680C2×C4—81no—
681C2×C4—612no—
682C2×C4—612no—
683C2×C4—612no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—4881no—
692C2×C4—4881no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4C22⋊C4×D6111yescharacteristic
700C2×C4C22⋊C4×D6111yescharacteristic
701C2×C4C2×D4×D6111yescharacteristic
702C2×C4C2×D4×D6111yescharacteristic
703C8—42no—
704C8—42no—
705C8—2442no—
706C8—2442no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—42no—
714C22—42no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—84no—
726C22—84no—
727C22—1222no—
728C22—1222no—
729C22—1222no—
730C22—4881no—
731C22—4881no—
732C22—4881no—
733C22—4881no—
734C22—2441no—
735C22—2441no—
736C22—2441no—
737C22#1683972712yes—
738C22#1683972712yes—
739C22C2×C22⋊C4×D6111yescharacteristic
740C22C2×#1451978311yescharacteristic
741C22C2×#1451978511yescharacteristic
742C4—21no—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—41no—
747C4—41no—
748C4—1222no—
749C4—1222no—
750C4—1222no—
751C4—2441no—
752C4—2441no—
753C4—2441no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—22no—
758C2—81no—
759C2—81no—
760C2—4881no—
761C2—2442no—
762C2C2×#1683972711yescharacteristic
763C2#2145427711yescharacteristic
764C2#2145429511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#323C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840350C2
cosocleC22×C4×C61C24
hypercenterC2×#323D61
hypocenterC61#17386
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. #21454845C2semidirect
3. #21454841C2semidirect
4. #21444185C2semidirect
5. #21444177C2semidirect
6. #21444169C2semidirect
7. #21444164C2semidirect
8. #21444135C2semidirect
9. #21444135C2semidirect
10. C2×#16839486C2semidirect
11. C2×C61×#323C2semidirect
34. #16839816C22semidirect
35. #16839812C22semidirect
36. #16839724C22semidirect
39. C22⋊C8×D61C22semidirect
40. #16839487C22semidirect
41. #16839487C22semidirect
44. #16839485C22semidirect
45. #16839485C22semidirect
382. C2×#323D61semidirect
433. C61#17386semidirect

Maximal subgroups

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

subgroupindex
C2×#168403502
#214548452
#214548412
#214441852
#214441772
#214441692
#214441642
#214441352
C2×#168394862
C2×C61×#3232
#1738661