Finite Group Databasebeta

← #29696972

Subgroups — #29696972

Order 15616.

1018 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839812C211yesmaximal, characteristic, complemented
2#21448310C211yesmaximal, characteristic
3#21446435C211yesmaximal, characteristic, complemented
4#21446428C211yesmaximal, characteristic, complemented
5#21446422C211yesmaximal, characteristic, complemented
6#21446422C211yesmaximal, characteristic, complemented
7#21446002C211yesmaximal, characteristic, complemented
8#21445997C211yesmaximal, characteristic, complemented
9#21445885C211yesmaximal, characteristic, complemented
10#21445801C211yesmaximal, characteristic, complemented
11#21445731C211yesmaximal, characteristic
12#21445600C211yesmaximal, characteristic, complemented
13C8×C22⋊Dic61C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C2×C61×#408C211yesmaximal, characteristic
16C2×#14519736C2211yescharacteristic
17C22×C4×Dic61C2211yescharacteristic
18#16839812—24no—
19C2×#14519706C2211yescharacteristic
20C2×#14519706C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24C2×C22⋊#92418C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×#14519687C2211yescharacteristic
30C2×C8×Dic61C2211yescharacteristic
31C2×C8×Dic61C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839669C411yescharacteristic
34#16839669C411yescharacteristic
35#16839665C411yescharacteristic
36#16839665C411yescharacteristic
37#16839642C411yescharacteristic
38#16839642C411yescharacteristic
39#16839642C411yescharacteristic
40#16839642C411yescharacteristic
41C4×C22⋊Dic61C2211yescharacteristic
42C4×C22⋊Dic61C2211yescharacteristic
43C4×C22⋊Dic61C2211yescharacteristic
44C4×C22⋊Dic61C2211yescharacteristic
45#16839516C2211yescharacteristic
46#16839516C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C22×#41×C61C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C61×#408—24no—
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C23×Dic61C2×C411yescharacteristic
62C23×Dic61C2×C411yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519736—41no—
68#14519736—41no—
69C2×C4⋊Dic61C2×C411yescharacteristic
70C2×C4⋊Dic61C2×C411yescharacteristic
71C2×C22⋊Dic61C2×C411yescharacteristic
72C2×C22⋊Dic61C2×C411yescharacteristic
73C2×C22⋊Dic61C2×C411yescharacteristic
74C2×C22⋊Dic61C2×C411yescharacteristic
75C2×C22⋊Dic61C2×C411yescharacteristic
76C2×C22⋊Dic61C2×C411yescharacteristic
77C2×C22⋊Dic61C2×C411yescharacteristic
78C2×C22⋊Dic61C2×C411yescharacteristic
79C2×C22⋊Dic61C2×C411yescharacteristic
80C2×C22⋊Dic61C2×C411yescharacteristic
81C2×C4×Dic61—22no—
82C2×C4×Dic61—22no—
83C2×C4×Dic61C2×C411yescharacteristic
84C2×C4×Dic61C2×C411yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89#14519706—22no—
90#14519706—22no—
91#14519706—41no—
92#14519706—41no—
93C22⋊#92418—22no—
94C22⋊#92418—22no—
95C22⋊#92418—22no—
96C22⋊#92418—22no—
97C22⋊#92418—41no—
98C22⋊#92418—41no—
99#14519687—41no—
100C8×Dic61—22no—
101C8×Dic61—22no—
102C8×Dic61—41no—
103#14519684C2×C411yescharacteristic
104#14519684C2×C411yescharacteristic
105#14519684C2×C411yescharacteristic
106#14519684C2×C411yescharacteristic
107#14519684C2×C411yescharacteristic
108#14519684C2×C411yescharacteristic
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111C2×#41×C61—22no—
112C2×#41×C61—22no—
113C2×#41×C61—22no—
114C2×#41×C61—22no—
115C2×#41×C61—41no—
116C2×#41×C61—41no—
117C22×Q8×C61C2×C411yescharacteristic
118C22×D4×C61C2×C411yescharacteristic
119C22×D4×C61C2×C411yescharacteristic
120C22×D4×C61C2×C411yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C2×M16×C61—22no—
125C2×M16×C61—22no—
126C2×M16×C61—41no—
127C22×C8×C61—22no—
128C22×C8×C61—22no—
129C22×C8×C61—41no—
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22⋊C8×C61—22no—
135C22⋊C8×C61—22no—
136C22⋊C8×C61—22no—
137C22⋊C8×C61D414yes—
138C24×C61C22×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C24×C61C22×C411yescharacteristic
141#41×C61—44no—
142#41×C61—44no—
143#41×C61—44no—
144#41×C61—44no—
145C2×Q8×C61—22no—
146C2×Q8×C61—22no—
147C2×Q8×C61—41no—
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—22no—
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61—22no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61—41no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C22×C411yescharacteristic
174C22×C4×C61C2×D412yes—
175C22×C4×C61#4112yes—
176C22×C4×C61#4112yes—
177C22×C4×C61#4112yes—
178C22×C4×C61C2411yescharacteristic
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—41no—
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C22×C411yescharacteristic
193M16×C61—44no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—44no—
205C2×C8×C61C2×D412yes—
206C2×C8×C61C2×D412yes—
207C22⋊Dic61—22no—
208C22⋊Dic61—22no—
209C22⋊Dic61—22no—
210C22⋊Dic61—22no—
211C22⋊Dic61—22no—
212C22⋊Dic61—22no—
213C22⋊Dic61—41no—
214C22⋊Dic61—41no—
215C22⋊Dic61—41no—
216C22⋊Dic61—41no—
217C4⋊Dic61—41no—
218C4⋊Dic61—41no—
219C4×Dic61—22no—
220C4×Dic61—22no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61#11712yes—
261C23×C61C4×D412yes—
262C23×C61C23×C411yescharacteristic
263Q8×C61—44no—
264D4×C61—44no—
265D4×C61—44no—
266D4×C61—44no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61#11712yes—
287C2×C4×C61C4×D412yes—
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×Dic61—28no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—44no—
317C2×Dic61#13112yes—
318C2×Dic61#13112yes—
319C2×Dic61#13112yes—
320C8×C61—22no—
321C8×C61—22no—
322C8×C61—41no—
323C8×C61—41no—
324#92418—41no—
325#92418—41no—
326#92418—41no—
327#92418—41no—
328#22556—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61C2×#11711yescharacteristic
351C22×C61C2×C4×D411yescharacteristic
352C22×C61#51811yescharacteristic
353C22×C61C2×#13111yescharacteristic
354C22×C61C2×#13111yescharacteristic
355C22×C61C2×#13111yescharacteristic
356C22×C61#56811yescharacteristic
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—41no—
360C4×C61#54611yescharacteristic
361C4×C61#54611yescharacteristic
362C4×C61#55111yescharacteristic
363C4×C61#55111yescharacteristic
364Dic61—22no—
365Dic61—22no—
366Dic61—22no—
367Dic61—41no—
368Dic61—41no—
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372C2×#431—611no—
373C2×#408D6111yescharacteristic
374#2297—611no—
375#1924—611no—
376#1923—611no—
377#1923—611no—
378#1923—611no—
379#1851—611no—
380#1850—611no—
381#1817—611no—
382#1798—611no—
383#1780—611no—
384#1753—611no—
385C8×C22⋊C4—611no—
386#1750—611no—
387C2×C61—42no—
388C2×C61—42no—
389C2×C61—81no—
390C2×C61#234211yescharacteristic
391C2×C61#292211yescharacteristic
392C2×C61#292511yescharacteristic
393C2×C61#292911yescharacteristic
394C2×C61#293311yescharacteristic
395C2×C61#297911yescharacteristic
396C2×C61#298111yescharacteristic
397C22×#41C2×D6111yescharacteristic
398C22×M16C2×D6111yescharacteristic
399C23×C8C2×D6111yescharacteristic
400C2×#117—611no—
401C22×C42—611no—
402#431—1224no—
403C2×C4⋊C8—611no—
404C2×C4⋊C8—611no—
405C2×C4⋊C8—611no—
406C2×C4⋊C8—611no—
407#408—24no—
408C2×C22⋊C8—611no—
409C2×C22⋊C8—611no—
410C2×C22⋊C8—611no—
411C2×C22⋊C8—611no—
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8C2×D6111yescharacteristic
415C2×C22⋊C8C2×D6111yescharacteristic
416C2×C22⋊C8C2×D6111yescharacteristic
417C2×C22⋊C8C2×D6111yescharacteristic
418C2×#97—611no—
419C2×C4×C8—611no—
420C2×C4×C8—611no—
421C2×C4×C8—611no—
422#391—611no—
423#391—611no—
424#390—611no—
425#390—611no—
426#386—611no—
427#386—611no—
428#386—611no—
429#386—611no—
430C4×C22⋊C4—611no—
431C4×C22⋊C4—611no—
432C4×C22⋊C4—611no—
433C4×C22⋊C4—611no—
434#336—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438#336—611no—
439#336—611no—
440#336—611no—
441#336—611no—
442C61#2255611yescharacteristic, complemented, Sylow
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C22×Q8C4×D6111yescharacteristic
450C22×D4C4×D6111yescharacteristic
451C22×D4C4×D6111yescharacteristic
452C22×D4C4×D6111yescharacteristic
453C23×C4—611no—
454C23×C4—611no—
455C23×C4C22×D6111yescharacteristic
456C23×C4C22×D6111yescharacteristic
457C23×C4C22×D6111yescharacteristic
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—41no—
461C22×C8—22no—
462C22×C8—22no—
463C22×C8—41no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8C22×D6111yescharacteristic
469C22×C8C22×D6111yescharacteristic
470C22×C8C22×D6111yescharacteristic
471C22×C8C22×D6111yescharacteristic
472#117—2441no—
473#117—2441no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C22⋊C4—611no—
477C2×C22⋊C4—611no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—611no—
481C2×C22⋊C4—611no—
482C2×C22⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—611no—
489C2×C42—611no—
490C2×C42—611no—
491C2×C42—611no—
492C2×C42—1222no—
493C2×C42—1222no—
494C4⋊C8—1222no—
495C4⋊C8—1222no—
496C4⋊C8—2441no—
497C4⋊C8—2441no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501C22⋊C8—1222no—
502C22⋊C8—1222no—
503C22⋊C8—1222no—
504C22⋊C8—1222no—
505C22⋊C8—2441no—
506C22⋊C8—2441no—
507C22⋊C8C22⋊D6114yes—
508#97—2441no—
509C4×C8—1222no—
510C4×C8—1222no—
511C4×C8—2441no—
512#95—611no—
513#95—611no—
514#95—611no—
515#95—611no—
516#95—611no—
517#95—611no—
518#95—611no—
519#95—611no—
520C24C2×C4×D6111yescharacteristic
521C24C2×C4×D6111yescharacteristic
522C24C2×C4×D6111yescharacteristic
523#41—44no—
524#41—44no—
525#41—44no—
526#41—44no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—41no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—2441no—
567C22×C4C2×C4×D6111yescharacteristic
568C22×C4C2×C4×D6111yescharacteristic
569C22×C4C2×C4×D6111yescharacteristic
570C22×C4#1175822212yes—
571C22×C4#1175822412yes—
572C22×C4#1175822412yes—
573C22×C4C2×C22⋊D6112yes—
574C22×C4C23×D6111yescharacteristic
575M16—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—44no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8C2×C22⋊D6112yes—
600C2×C8C2×C22⋊D6112yes—
601C4⋊C4—2441no—
602C4⋊C4—2441no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—2441no—
610C22⋊C4—2441no—
611C22⋊C4—2441no—
612C22⋊C4—2441no—
613C42—1221no—
614C42—1221no—
615C42—1221no—
616C42—1221no—
617C42—1221no—
618C42—1221no—
619C42—1221no—
620C42—1221no—
621C42—1222no—
622C42—1222no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23#1451973312yes—
643C23C4×C22⋊D6112yes—
644C23C22×C4×D6111yescharacteristic
645Q8—44no—
646D4—44no—
647D4—44no—
648D4—44no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—1228no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—2444no—
694C2×C4#1451973312yes—
695C2×C4C4×C22⋊D6112yes—
696C2×C4C22×C22⋊D6111yescharacteristic
697C2×C4C2×#1175822411yescharacteristic
698C2×C4C2×#1175822411yescharacteristic
699C2×C4C2×#1175822211yescharacteristic
700C2×C4#1451982211yescharacteristic
701C2×C4#1451982211yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C8—2441no—
707C8—2441no—
708C8—2441no—
709C8—2441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22C2×#1451973311yescharacteristic
732C22C2×C4×C22⋊D6111yescharacteristic
733C22#1684023511yescharacteristic
734C22#131×D6111yescharacteristic
735C22#131×D6111yescharacteristic
736C22#131×D6111yescharacteristic
737C22#1684052711yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—1222no—
742C4—1222no—
743C4—1222no—
744C4—2441no—
745C4—2441no—
746C4—2441no—
747C4—2441no—
748C4—2441no—
749C4#1684040611yescharacteristic
750C4#1684040611yescharacteristic
751C4#1684043811yescharacteristic
752C4#1684043811yescharacteristic
753C2—42no—
754C2—42no—
755C2—81no—
756C2#2144866411yescharacteristic
757C2#2145445911yescharacteristic
758C2#2145448111yescharacteristic
759C2#2145451111yescharacteristic
760C2#2145454111yescharacteristic
761C2#2145488311yescharacteristic
762C2#2145489211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC2×C61×#408C2
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#408D61
hypocenterC61#22556
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C2×#16839812C2semidirect
3. #21446435C2semidirect
4. #21446428C2semidirect
5. #21446422C2semidirect
6. #21446422C2semidirect
7. #21446002C2semidirect
8. #21445997C2semidirect
9. #21445885C2semidirect
10. #21445801C2semidirect
12. #21445600C2semidirect
13. C8×C22⋊Dic61C2semidirect
14. #21445587C2semidirect
442. C61#22556semidirect

Maximal subgroups

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

subgroupindex
C2×#168398122
#214483102
#214464352
#214464282
#214464222
#214460022
#214459972
#214458852
#214458012
#214457312
#214456002
C8×C22⋊Dic612
#214455872
C2×C61×#4082
#2255661