Finite Group Databasebeta

← #29696361

Subgroups — #29696361

Order 15616.

1390 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×#16839834C211yesmaximal, characteristic, complemented
2#21448748C211yesmaximal, characteristic, complemented
3#21446793C211yesmaximal, characteristic, complemented
4#21446768C211yesmaximal, characteristic, complemented
5#21446258C211yesmaximal, characteristic, complemented
6#21446248C211yesmaximal, characteristic, complemented
7#21446142C211yesmaximal, characteristic, complemented
8#21446137C211yesmaximal, characteristic, complemented
9#21445909C211yesmaximal, characteristic, complemented
10#21445905C211yesmaximal, characteristic, complemented
11#21445829C211yesmaximal, characteristic, complemented
12#21445644C211yesmaximal, characteristic, complemented
13#21445538C211yesmaximal, characteristic, complemented
14C2×#16839524C211yesmaximal, characteristic, complemented
15C2×C61×#547C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20#16839834—24no—
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×#14519688C2211yescharacteristic
29#16839655—21no—
30#16839648—21no—
31#16839642—21no—
32#16839628C2211yescharacteristic
33#16839622C2211yescharacteristic
34#16839622C2211yescharacteristic
35C4×C4⋊Dic61C2211yescharacteristic
36C22⋊C4×Dic61—21no—
37#16839524C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49C22×#41×C61—21no—
50C61×#547—24no—
51C61×#547C418yescomplemented
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×#123×C61—21no—
54C2×#123×C61—21no—
55C2×C22⋊Q8×C61—21no—
56C2×#121×C61C2211yescharacteristic
57C2×#121×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C2×C4×D4×C61C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C23×Dic61—21no—
63C2×#11758194—22no—
64C2×#11758194—22no—
65C2×#11758194—41no—
66C22×#92418—22no—
67C22×#92418—22no—
68C22×#92418—41no—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519736—22no—
74#14519736—41no—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—41no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C4⋊#92418—22no—
88#14519698—22no—
89#14519698—22no—
90#14519698—41no—
91#14519698—41no—
92C22⋊#92418—22no—
93C22⋊#92418—22no—
94#14519688—22no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100C2×#41×C61—28no—
101C2×#41×C61—44no—
102C2×#41×C61—44no—
103C22×Q8×C61—21no—
104C22×D4×C61—21no—
105C22×D4×C61—21no—
106C22×D4×C61D411yescharacteristic
107C22×D4×C61C2311yescharacteristic
108C23×C4×C61—21no—
109C23×C4×C61—21no—
110C23×C4×C61—21no—
111C23×C4×C61C2311yescharacteristic
112C23×C4×C61C2311yescharacteristic
113C4⋊Q8×C61—22no—
114C4⋊Q8×C61C2×C414yescomplemented
115#123×C61—28no—
116#123×C61—28no—
117C22⋊Q8×C61—28no—
118#121×C61—22no—
119#121×C61—22no—
120#121×C61C2×C414yes—
121#121×C61C2×C414yescomplemented
122C4×D4×C61—22no—
123C4×D4×C61C2×C414yes—
124C4×D4×C61C2×C414yescomplemented
125C4×D4×C61D414yes—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—22no—
128C2×C4⋊C4×C61—22no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2×C414yes—
132C2×C4⋊C4×C61C2×C414yescomplemented
133C2×C4⋊C4×C61D411yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61D411yescharacteristic
141C2×C22⋊C4×C61D411yescharacteristic
142C2×C42×C61C2311yescharacteristic
143C24×C61—21no—
144C24×C61C2×D411yescharacteristic
145C24×C61C2×D411yescharacteristic
146#41×C61—432no—
147C2×Q8×C61—24no—
148C2×Q8×C61—42no—
149C2×Q8×C61—42no—
150C2×D4×C61—22no—
151C2×D4×C61—22no—
152C2×D4×C61—24no—
153C2×D4×C61—24no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—42no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61C22⋊C414yes—
164C2×D4×C61C22×C412yes—
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×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—24no—
174C22×C4×C61—24no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—24no—
179C22×C4×C61—42no—
180C22×C4×C61—42no—
181C22×C4×C61—42no—
182C22×C4×C61—42no—
183C22×C4×C61—42no—
184C22×C4×C61—42no—
185C22×C4×C61C22×C412yes—
186C22×C4×C61C22×C412yes—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D412yes—
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2411yescharacteristic
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—42no—
199C22×Dic61—42no—
200C22×Dic61—81no—
201C4⋊C4×C61—24no—
202C4⋊C4×C61—24no—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61C22⋊C414yes—
208C4⋊C4×C61C22×C412yes—
209C4⋊C4×C61C22×C412yes—
210C4⋊C4×C61C22×C412yes—
211C22⋊C4×C61—24no—
212C22⋊C4×C61—24no—
213C22⋊C4×C61—24no—
214C22⋊C4×C61C22⋊C414yes—
215C22⋊C4×C61C22⋊C414yes—
216C42×C61C22×C412yes—
217C42×C61C2×D412yes—
218C22⋊Dic61—42no—
219C22⋊Dic61—42no—
220C22⋊Dic61—81no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—42no—
229C4⋊Dic61#4112yescomplemented
230C4×Dic61—42no—
231C4×Dic61—81no—
232#11758194—44no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—44no—
245C2×#92418#4112yescomplemented
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—22no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61C2×C22⋊C412yes—
264C23×C61C2×C22⋊C412yes—
265C23×C61AGL(1,ℤ/8)12yes—
266C23×C61AGL(1,ℤ/8)12yes—
267C23×C61C22×D411yescharacteristic
268Q8×C61—48no—
269D4×C61—28no—
270D4×C61—22no—
271D4×C61—22no—
272D4×C61—48no—
273D4×C61—48no—
274D4×C61—41no—
275D4×C61—41no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—48no—
296C2×C4×C61—48no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—48no—
304C2×C4×C61C2×C22⋊C412yes—
305C2×C4×C61C2×C22⋊C412yes—
306C2×C4×C61C2×C22⋊C412yes—
307C2×C4×C61C2×C22⋊C412yes—
308C2×C4×C61C23×C411yescharacteristic
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C2×C4×C612−1+411yescharacteristic
314C2×Dic61—22no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—84no—
327#92418—22no—
328#92418—41no—
329#92418—41no—
330#92418—41no—
331#22495—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61#41814yes—
353C22×C61C22×C22⋊C411yescharacteristic
354C22×C61#54611yescharacteristic
355C22×C61#54711yescharacteristic
356C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
358C22×C61#57711yescharacteristic
359C22×C61#57811yescharacteristic
360C4×C61—22no—
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—22no—
364C4×C61—42no—
365C4×C61—42no—
366C4×C61—42no—
367C4×C61C4×#4111yescharacteristic
368C4×C61#52011yescharacteristic
369C4×C61#54611yescharacteristic
370C4×C61#54711yescharacteristic
371Dic61—42no—
372Dic61—81no—
373Dic61—81no—
374Dic61—81no—
375C2×#547D6111yescharacteristic
376C2×#435—611no—
377#2352—611no—
378#1993—611no—
379#1987—611no—
380#1895—611no—
381#1893—611no—
382#1875—611no—
383#1874—611no—
384#1824—611no—
385#1823—611no—
386#1804—611no—
387#1762—611no—
388#1736—611no—
389C2×#340—611no—
390C2×C61—24no—
391C2×C61—42no—
392C2×C61—82no—
393C2×C61#233911yescharacteristic
394C2×C61C2×#41811yescharacteristic
395C2×C61#289811yescharacteristic
396C2×C61#330611yescharacteristic
397C2×C61#330811yescharacteristic
398C2×C61#334311yescharacteristic
399C2×C61#334511yescharacteristic
400C22×#41—21no—
401C22×M16—611no—
402C23×C8—611no—
403#547—24no—
404#547Dic6118yescomplemented
405C2×C4⋊Q8C2×D6111yescharacteristic
406C2×#123—21no—
407C2×#123—21no—
408C2×C22⋊Q8—21no—
409C2×#121C2×D6111yescharacteristic
410C2×#121C2×D6111yescharacteristic
411C2×C4×D4C2×D6111yescharacteristic
412C2×C4×D4C2×D6111yescharacteristic
413C2×#117—611no—
414C22×C4⋊C4—611no—
415C22×C4⋊C4C2×D6111yescharacteristic
416C22×C4⋊C4C2×D6111yescharacteristic
417#435—1224no—
418C2×C4⋊C8—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C2×#97—611no—
426#388—1221no—
427#387—1221no—
428#386—1221no—
429#382—611no—
430#380—611no—
431#380—611no—
432C4×C4⋊C4—611no—
433C4×C22⋊C4—1221no—
434#340—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446C61#2249511yescharacteristic, complemented, Sylow
447C2×#41—28no—
448C2×#41—44no—
449C2×#41—44no—
450C22×Q8—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4C22⋊D6111yescharacteristic
454C22×D4C22×D6111yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—1221no—
459C23×C4C22×D6111yescharacteristic
460C23×C4C22×D6111yescharacteristic
461C2×M16—1222no—
462C2×M16—1222no—
463C2×M16—2441no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8—1222no—
469C22×C8—1222no—
470C22×C8—2441no—
471C4⋊Q8—22no—
472C4⋊Q8C2×Dic6114yescomplemented
473#123—28no—
474#123—28no—
475C22⋊Q8—28no—
476#121—22no—
477#121—22no—
478#121C2×Dic6114yes—
479#121C2×Dic6114yescomplemented
480C4×D4—22no—
481C4×D4C2×Dic6114yes—
482C4×D4C2×Dic6114yescomplemented
483C4×D4C22⋊D6114yes—
484#117—1222no—
485#117—2441no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—1222no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—2441no—
498C2×C4⋊C4C2×Dic6114yes—
499C2×C4⋊C4C2×Dic6114yescomplemented
500C2×C4⋊C4C22⋊D6111yescharacteristic
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C4⋊C4C22×D6111yescharacteristic
503C2×C4⋊C4C22×D6111yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4C22⋊D6111yescharacteristic
511C2×C22⋊C4C22⋊D6111yescharacteristic
512C2×C42—1221no—
513C2×C42—1221no—
514C2×C42C22×D6111yescharacteristic
515C4⋊C8—1222no—
516#102—1222no—
517#102—1222no—
518#102—2441no—
519#102—2441no—
520C22⋊C8—1222no—
521C22⋊C8—1222no—
522#97—1222no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528C24—21no—
529C24C2×C22⋊D6111yescharacteristic
530C24C2×C22⋊D6111yescharacteristic
531#41—432no—
532C2×Q8—24no—
533C2×Q8—42no—
534C2×Q8—42no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4C22⋊Dic6114yes—
549C2×D4C22×Dic6112yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—4881no—
575C22×C4—2442no—
576C22×C4—2442no—
577C22×C4C22×Dic6112yes—
578C22×C4C22×Dic6112yes—
579C22×C4C2×C22⋊D6112yes—
580C22×C4C2×C22⋊D6112yes—
581C22×C4C2×C22⋊D6111yescharacteristic
582C22×C4C2×C22⋊D6111yescharacteristic
583C22×C4C2×C22⋊D6111yescharacteristic
584C22×C4C2×C22⋊D6111yescharacteristic
585C22×C4C23×D6111yescharacteristic
586M16—2444no—
587C2×C8—612no—
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×C8—2444no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—612no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—2442no—
615C4⋊C4C22⋊Dic6114yes—
616C4⋊C4C22×Dic6112yes—
617C4⋊C4C22×Dic6112yes—
618C4⋊C4C22×Dic6112yes—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—4881no—
623C22⋊C4—2442no—
624C22⋊C4—2442no—
625C22⋊C4C22⋊Dic6114yes—
626C22⋊C4C22⋊Dic6114yes—
627C42—4881no—
628C42—2442no—
629C42C22×Dic6112yes—
630C42C2×C22⋊D6112yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23C2×C22⋊Dic6112yes—
649C23C2×C22⋊Dic6112yes—
650C23#1451980312yes—
651C23#1451980312yes—
652C23C22×C22⋊D6111yescharacteristic
653Q8—48no—
654D4—28no—
655D4—22no—
656D4—22no—
657D4—48no—
658D4—48no—
659D4—41no—
660D4—41no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—48no—
681C2×C4—48no—
682C2×C4—48no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—1222no—
690C2×C4—4884no—
691C2×C4—2441no—
692C2×C4—2441no—
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×C4—2441no—
702C2×C4C2×C22⋊Dic6112yes—
703C2×C4C2×C22⋊Dic6112yes—
704C2×C4C2×C22⋊Dic6112yes—
705C2×C4C2×C22⋊Dic6112yes—
706C2×C4C23×Dic6111yescharacteristic
707C2×C4C22×C22⋊D6111yescharacteristic
708C2×C4#41×D6111yescharacteristic
709C2×C4#41×D6111yescharacteristic
710C2×C4#1451982311yescharacteristic
711C2×C4#1451982411yescharacteristic
712C8—1222no—
713C8—2441no—
714C8—2441no—
715C8—2441no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22#1683976714yes—
737C22C22×C22⋊Dic6111yescharacteristic
738C22#1684040011yescharacteristic
739C22#1684041111yescharacteristic
740C22C2×#1451980311yescharacteristic
741C22C2×#1451980311yescharacteristic
742C22#1684057011yescharacteristic
743C22#1684057711yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—4881no—
752C4—4881no—
753C4—4881no—
754C4—2442no—
755C4#41×Dic6111yescharacteristic
756C4#1684024511yescharacteristic
757C4#1684040011yescharacteristic
758C4#1684041111yescharacteristic
759C2—24no—
760C2—42no—
761C2—82no—
762C2#2144864911yescharacteristic
763C2C2×#1683976711yescharacteristic
764C2#2145435211yescharacteristic
765C2#2145777411yescharacteristic
766C2#2145780411yescharacteristic
767C2#2145825311yescharacteristic
768C2#2145828911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#547C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×#547D61
hypocenterC61#22495
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#16839834C2semidirect
2. #21448748C2semidirect
3. #21446793C2semidirect
4. #21446768C2semidirect
5. #21446258C2semidirect
6. #21446248C2semidirect
7. #21446142C2semidirect
8. #21446137C2semidirect
9. #21445909C2semidirect
10. #21445905C2semidirect
11. #21445829C2semidirect
12. #21445644C2semidirect
13. #21445538C2semidirect
14. C2×#16839524C2semidirect
51. C61×#547C4semidirect
114. C4⋊Q8×C61C2×C4semidirect
121. #121×C61C2×C4semidirect
124. C4×D4×C61C2×C4semidirect
132. C2×C4⋊C4×C61C2×C4semidirect
229. C4⋊Dic61#41semidirect
245. C2×#92418#41semidirect
404. #547Dic61semidirect
446. C61#22495semidirect
472. C4⋊Q8C2×Dic61semidirect
479. #121C2×Dic61semidirect
482. C4×D4C2×Dic61semidirect
499. C2×C4⋊C4C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398342
#214487482
#214467932
#214467682
#214462582
#214462482
#214461422
#214461372
#214459092
#214459052
#214458292
#214456442
#214455382
C2×#168395242
C2×C61×#5472
#2249561