Finite Group Databasebeta

← #29695583

Subgroups — #29695583

Order 15616.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839834C211yesmaximal, characteristic
2C2×#16839771C211yesmaximal, characteristic, complemented
3C22×#14519701C211yesmaximal, characteristic, complemented
4#21448748C211yesmaximal, characteristic
5#21446743C211yesmaximal, characteristic, complemented
6#21446640C211yesmaximal, characteristic, complemented
7#21446253C211yesmaximal, characteristic, complemented
8#21446243C211yesmaximal, characteristic, complemented
9#21446132C211yesmaximal, characteristic, complemented
10#21446127C211yesmaximal, characteristic, complemented
11#21445834C211yesmaximal, characteristic, complemented
12#21445754C211yesmaximal, characteristic, complemented
13#21445754C211yesmaximal, characteristic, complemented
14#21445649C211yesmaximal, characteristic, complemented
15C2×D4×Q8×C61C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20#16839834—24no—
21C2×C4⋊#92418C2211yescharacteristic
22#16839771—24no—
23C2×#14519701—24no—
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×#14519688C2211yescharacteristic
39#16839655—21no—
40#16839648—21no—
41#16839642—21no—
42#16839628C2211yescharacteristic
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic
45C4×C4⋊Dic61C2211yescharacteristic
46C22⋊C4×Dic61—21no—
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51C23×Q8×C61C2211yescharacteristic
52C23×Q8×C61C2211yescharacteristic
53D4×Q8×C61—24no—
54D4×Q8×C61C418yescomplemented
55C2×C4⋊Q8×C61—21no—
56C2×C4⋊Q8×C61C2211yescharacteristic
57C2×C22⋊Q8×C61—21no—
58C2×C22⋊Q8×C61—21no—
59C2×C22⋊Q8×C61C2211yescharacteristic
60C2×C22⋊Q8×C61C2211yescharacteristic
61C2×C4×Q8×C61C2211yescharacteristic
62C2×C4×D4×C61—21no—
63C2×C4×D4×C61C2211yescharacteristic
64C23×Dic61—21no—
65C2×#11758194—22no—
66C2×#11758194—22no—
67C2×#11758194—41no—
68C22×#92418—22no—
69C22×#92418—22no—
70C22×#92418—41no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519736—22no—
76#14519736—41no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—41no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C4⋊#92418—22no—
90#14519701—22no—
91#14519701—22no—
92#14519701—22no—
93#14519701—22no—
94#14519701—22no—
95#14519701—22no—
96#14519701—22no—
97#14519701—41no—
98#14519701—41no—
99#14519701—41no—
100#14519701—41no—
101#14519701D414yescomplemented
102C22⋊#92418—22no—
103C22⋊#92418—22no—
104#14519688—22no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110C22×Q8×C61—21no—
111C22×Q8×C61—21no—
112C22×Q8×C61—22no—
113C22×Q8×C61—22no—
114C22×Q8×C61—22no—
115C22×Q8×C61—22no—
116C22×Q8×C61—22no—
117C22×Q8×C61—22no—
118C22×Q8×C61—41no—
119C22×Q8×C61—41no—
120C22×Q8×C61—41no—
121C22×Q8×C61—41no—
122C22×Q8×C61C2×C414yes—
123C22×Q8×C61C2×C414yescomplemented
124C22×Q8×C61C2311yescharacteristic
125C22×Q8×C61C2311yescharacteristic
126C22×Q8×C61C2311yescharacteristic
127C22×D4×C61D411yescharacteristic
128C23×C4×C61—21no—
129C23×C4×C61—21no—
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C4⋊Q8×C61—28no—
133C4⋊Q8×C61—22no—
134C4⋊Q8×C61C2×C414yescomplemented
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61—22no—
137C22⋊Q8×C61—28no—
138C22⋊Q8×C61—28no—
139C22⋊Q8×C61C2×C414yes—
140C22⋊Q8×C61C2×C414yescomplemented
141C4×Q8×C61—22no—
142C4×Q8×C61C2×C414yescomplemented
143C4×D4×C61—28no—
144C4×D4×C61C2×C414yes—
145C4×D4×C61D414yes—
146C2×C4⋊C4×C61—21no—
147C2×C4⋊C4×C61—21no—
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61—21no—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61D411yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61D411yescharacteristic
156C2×C22⋊C4×C61D411yescharacteristic
157C2×C42×C61—21no—
158C2×C42×C61C2311yescharacteristic
159C24×C61C2×D411yescharacteristic
160C24×C61C2×D411yescharacteristic
161C2×Q8×C61—24no—
162C2×Q8×C61—24no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—28no—
169C2×Q8×C61—28no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—42no—
179C2×Q8×C61—42no—
180C2×Q8×C61—42no—
181C2×Q8×C61—42no—
182C2×Q8×C61—44no—
183C2×Q8×C61—44no—
184C2×Q8×C61—44no—
185C2×Q8×C61—44no—
186C2×Q8×C61—44no—
187C2×Q8×C61—44no—
188C2×Q8×C61C22×C412yes—
189C2×Q8×C61C22×C412yes—
190C2×Q8×C61C22×C412yes—
191C2×Q8×C61C2×D412yes—
192C2×Q8×C61#4112yes—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61C22⋊C414yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—24no—
206C22×C4×C61—24no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—42no—
211C22×C4×C61—42no—
212C22×C4×C61—42no—
213C22×C4×C61—42no—
214C22×C4×C61C22×C412yes—
215C22×C4×C61C22×C412yes—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D412yes—
221C22×C4×C61C2×D412yes—
222C22×C4×C61C2411yescharacteristic
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—42no—
228C22×Dic61—42no—
229C22×Dic61—81no—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—24no—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61C22⋊C414yes—
237C4⋊C4×C61C22×C412yes—
238C22⋊C4×C61—24no—
239C22⋊C4×C61—24no—
240C22⋊C4×C61C22⋊C414yes—
241C22⋊C4×C61C22⋊C414yes—
242C42×C61—24no—
243C42×C61C22×C412yes—
244C42×C61C2×D412yes—
245C22⋊Dic61—42no—
246C22⋊Dic61—42no—
247C22⋊Dic61—81no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—42no—
256C4⋊Dic61C2×D412yes—
257C4×Dic61—42no—
258C4×Dic61—81no—
259#11758194—44no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—44no—
272C2×#92418C2×D412yes—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61C2×C22⋊C412yes—
284C23×C61C2×C22⋊C412yes—
285C23×C61#13712yes—
286C23×C61#13712yes—
287C23×C61C22×D411yescharacteristic
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61—48no—
296Q8×C61—48no—
297Q8×C61—41no—
298Q8×C61—41no—
299Q8×C61—41no—
300Q8×C61—41no—
301Q8×C61C4×D414yes—
302D4×C61—28no—
303C2×C4×C61—22no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—22no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—48no—
326C2×C4×C61—48no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61C2×C22⋊C412yes—
334C2×C4×C61C2×C22⋊C412yes—
335C2×C4×C61C2×C22⋊C412yes—
336C2×C4×C61C2×C22⋊C412yes—
337C2×C4×C61C23×C411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C2×Dic61—22no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—84no—
356#92418—22no—
357#92418—41no—
358#92418—41no—
359#92418—41no—
360#22425—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61#41914yescomplemented
375C22×C61C22×C22⋊C411yescharacteristic
376C22×C61D4211yescharacteristic
377C22×C61#54611yescharacteristic
378C22×C61C2×#13711yescharacteristic
379C22×C61C2×#13711yescharacteristic
380C22×C61#57711yescharacteristic
381C22×C61#57811yescharacteristic
382C4×C61—22no—
383C4×C61—22no—
384C4×C61—24no—
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61C2×C4×D411yescharacteristic
391C4×C61#51811yescharacteristic
392C4×C61D4211yescharacteristic
393C4×C61#54611yescharacteristic
394Dic61—42no—
395Dic61—81no—
396Dic61—81no—
397Dic61—81no—
398C2×D4×Q8D6111yescharacteristic
399C2×#435—611no—
400C2×#419—611no—
401C22×#103—611no—
402#2352—611no—
403#1981—611no—
404#1960—611no—
405#1894—611no—
406#1892—611no—
407#1873—611no—
408#1872—611no—
409#1805—611no—
410#1787—611no—
411#1787—611no—
412#1763—611no—
413C2×C61—24no—
414C2×C61—42no—
415C2×C61D4×C22⋊C411yescharacteristic
416C2×C61C2×#41911yescharacteristic
417C2×C61#289811yescharacteristic
418C2×C61#326611yescharacteristic
419C2×C61#327011yescharacteristic
420C2×C61#331211yescharacteristic
421C2×C61#332011yescharacteristic
422C23×Q8C2×D6111yescharacteristic
423C23×Q8C2×D6111yescharacteristic
424C22×M16—611no—
425C23×C8—611no—
426D4×Q8—24no—
427D4×Q8Dic6118yescomplemented
428C2×C4⋊Q8—21no—
429C2×C4⋊Q8C2×D6111yescharacteristic
430C2×C22⋊Q8—21no—
431C2×C22⋊Q8—21no—
432C2×C22⋊Q8C2×D6111yescharacteristic
433C2×C22⋊Q8C2×D6111yescharacteristic
434C2×C4×Q8C2×D6111yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C2×D6111yescharacteristic
437C2×#117—611no—
438C22×C4⋊C4—611no—
439#435—1224no—
440C2×C4⋊C8—611no—
441#419—1224no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#103—611no—
446C2×#103—611no—
447C2×#103—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#103—1224no—
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×#97—611no—
458#388—1221no—
459#387—1221no—
460#386—1221no—
461#382—611no—
462#380—611no—
463#380—611no—
464C4×C4⋊C4—611no—
465C4×C22⋊C4—1221no—
466#340—611no—
467#340—611no—
468#340—611no—
469#340—611no—
470C61#2242511yescharacteristic, complemented, Sylow
471C22×Q8—21no—
472C22×Q8—21no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8—22no—
477C22×Q8—22no—
478C22×Q8—22no—
479C22×Q8—41no—
480C22×Q8—41no—
481C22×Q8—41no—
482C22×Q8—41no—
483C22×Q8C2×Dic6114yes—
484C22×Q8C2×Dic6114yescomplemented
485C22×Q8C22×D6111yescharacteristic
486C22×Q8C22×D6111yescharacteristic
487C22×Q8C22×D6111yescharacteristic
488C22×D4C22⋊D6111yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—1221no—
492C23×C4C22×D6111yescharacteristic
493C23×C4C22×D6111yescharacteristic
494C2×M16—1222no—
495C2×M16—1222no—
496C2×M16—2441no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8—611no—
500C22×C8—611no—
501C22×C8—1222no—
502C22×C8—1222no—
503C22×C8—2441no—
504C4⋊Q8—28no—
505C4⋊Q8—22no—
506C4⋊Q8C2×Dic6114yescomplemented
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509C22⋊Q8—28no—
510C22⋊Q8—28no—
511C22⋊Q8C2×Dic6114yes—
512C22⋊Q8C2×Dic6114yescomplemented
513C4×Q8—22no—
514C4×Q8C2×Dic6114yescomplemented
515C4×D4—28no—
516C4×D4C2×Dic6114yes—
517C4×D4C22⋊D6114yes—
518#117—1222no—
519#117—2441no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—1222no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—2441no—
532C2×C4⋊C4C22⋊D6111yescharacteristic
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4C22⋊D6111yescharacteristic
540C2×C22⋊C4C22⋊D6111yescharacteristic
541C2×C42—21no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42C22×D6111yescharacteristic
545C4⋊C8—1222no—
546#103—614no—
547#103—1222no—
548#103—1222no—
549#103—1222no—
550#103—1222no—
551#103—1222no—
552#103—1222no—
553#103—1222no—
554#103—2441no—
555#103—2441no—
556#103—2441no—
557#103—2441no—
558C22⋊C8—1222no—
559C22⋊C8—1222no—
560#97—1222no—
561#95—1221no—
562#95—1221no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566C24C2×C22⋊D6111yescharacteristic
567C24C2×C22⋊D6111yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—24no—
574C2×Q8—24no—
575C2×Q8—28no—
576C2×Q8—28no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—42no—
586C2×Q8—42no—
587C2×Q8—42no—
588C2×Q8—42no—
589C2×Q8—44no—
590C2×Q8—44no—
591C2×Q8—44no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—44no—
595C2×Q8D4×D6112yes—
596C2×Q8#1175822412yes—
597C2×Q8C22×Dic6112yes—
598C2×Q8C22×Dic6112yes—
599C2×Q8C22×Dic6112yes—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4C22⋊Dic6114yes—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—4881no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4C22×Dic6112yes—
629C22×C4C22×Dic6112yes—
630C22×C4C2×C22⋊D6112yes—
631C22×C4C2×C22⋊D6112yes—
632C22×C4C2×C22⋊D6111yescharacteristic
633C22×C4C2×C22⋊D6111yescharacteristic
634C22×C4C2×C22⋊D6111yescharacteristic
635C22×C4C2×C22⋊D6111yescharacteristic
636C22×C4C23×D6111yescharacteristic
637M16—2444no—
638C2×C8—612no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—2444no—
651C4⋊C4—21no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—612no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—2442no—
666C4⋊C4C22⋊Dic6114yes—
667C4⋊C4C22×Dic6112yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—4881no—
671C22⋊C4—2442no—
672C22⋊C4—2442no—
673C22⋊C4C22⋊Dic6114yes—
674C22⋊C4C22⋊Dic6114yes—
675C42—24no—
676C42—4881no—
677C42—2442no—
678C42C22×Dic6112yes—
679C42C2×C22⋊D6112yes—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23C2×C22⋊Dic6112yes—
691C23C2×C22⋊Dic6112yes—
692C23#1451980812yes—
693C23#1451980812yes—
694C23C22×C22⋊D6111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—22no—
701Q8—22no—
702Q8—48no—
703Q8—48no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8D4×Dic6114yes—
709D4—28no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—1222no—
741C2×C4—4884no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4C2×C22⋊Dic6112yes—
754C2×C4C2×C22⋊Dic6112yes—
755C2×C4C2×C22⋊Dic6112yes—
756C2×C4C2×C22⋊Dic6112yes—
757C2×C4C23×Dic6111yescharacteristic
758C2×C4C2×D4×D6111yescharacteristic
759C2×C4C22×C22⋊D6111yescharacteristic
760C2×C4C2×#1175822411yescharacteristic
761C2×C4#1451982211yescharacteristic
762C2×C4#1451982211yescharacteristic
763C8—1222no—
764C8—2441no—
765C8—2441no—
766C8—2441no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22#1683977114yescomplemented
781C22C22×C22⋊Dic6111yescharacteristic
782C22D4×C22⋊D6111yescharacteristic
783C22#1684040611yescharacteristic
784C22C2×#1451980811yescharacteristic
785C22C2×#1451980811yescharacteristic
786C22#1684057011yescharacteristic
787C22#1684057711yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—24no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—4881no—
797C4—4881no—
798C4—4881no—
799C4—2442no—
800C4C2×D4×Dic6111yescharacteristic
801C4#1684023711yescharacteristic
802C4D4×C22⋊D6111yescharacteristic
803C4#1684040611yescharacteristic
804C2—24no—
805C2—42no—
806C2D4×C22⋊Dic6111yescharacteristic
807C2C2×#1683977111yescharacteristic
808C2#2145435211yescharacteristic
809C2#2145733011yescharacteristic
810C2#2145739011yescharacteristic
811C2#2145787011yescharacteristic
812C2#2145799011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×D4×Q8×C61C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
cosocleC22×C4×C61C24
hypercenterC2×D4×Q8D61
hypocenterC61#22425
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#16839771C2semidirect
3. C22×#14519701C2semidirect
5. #21446743C2semidirect
6. #21446640C2semidirect
7. #21446253C2semidirect
8. #21446243C2semidirect
9. #21446132C2semidirect
10. #21446127C2semidirect
11. #21445834C2semidirect
12. #21445754C2semidirect
13. #21445754C2semidirect
14. #21445649C2semidirect
54. D4×Q8×C61C4semidirect
101. #14519701D4semidirect
123. C22×Q8×C61C2×C4semidirect
134. C4⋊Q8×C61C2×C4semidirect
140. C22⋊Q8×C61C2×C4semidirect
142. C4×Q8×C61C2×C4semidirect
374. C22×C61#419semidirect
427. D4×Q8Dic61semidirect
470. C61#22425semidirect
484. C22×Q8C2×Dic61semidirect
506. C4⋊Q8C2×Dic61semidirect
512. C22⋊Q8C2×Dic61semidirect
514. C4×Q8C2×Dic61semidirect
780. C22#16839771semidirect

Maximal subgroups

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

subgroupindex
C2×#168398342
C2×#168397712
C22×#145197012
#214487482
#214467432
#214466402
#214462532
#214462432
#214461322
#214461272
#214458342
#214457542
#214456492
C2×D4×Q8×C612
#2242561