Finite Group Databasebeta

← #29647538

Subgroups — #29647538

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454854C211yesmaximal, characteristic, complemented
2#21448452C211yesmaximal, characteristic, complemented
3#21444396C211yesmaximal, characteristic, complemented
4#21444387C211yesmaximal, characteristic, complemented
5#21444379C211yesmaximal, characteristic, complemented
6#21444375C211yesmaximal, characteristic, complemented
7#21444366C211yesmaximal, characteristic, complemented
8#21444362C211yesmaximal, characteristic, complemented
9#21444357C211yesmaximal, characteristic, complemented
10#21444348C211yesmaximal, characteristic, complemented
11#21444335C211yesmaximal, characteristic, complemented
12#21444323C211yesmaximal, characteristic, complemented
13#21444310C211yesmaximal, characteristic, complemented
14C2×#16839496C211yesmaximal, characteristic, complemented
15C61×#3519C211yesmaximal, characteristic
16#16839840—21no—
17#16839834—21no—
18#16839834—21no—
19D4×#92418—21no—
20#16839819C2211yescharacteristic, complemented
21#16839815C2211yescharacteristic, complemented
22#16839726C2211yescharacteristic, complemented
23#16839726C2211yescharacteristic, complemented
24C2×C22⋊#92418C2211yescharacteristic, complemented
25C2×C22⋊#92418C2211yescharacteristic, complemented
26#16839655—21no—
27#16839648—21no—
28#16839642—21no—
29#16839637—21no—
30#16839630C2211yescharacteristic, complemented
31#16839628C2211yescharacteristic, complemented
32#16839625C2211yescharacteristic, complemented
33#16839622C2211yescharacteristic, complemented
34C4×C22⋊Dic61C2211yescharacteristic, complemented
35C2×#14519684C2211yescharacteristic, complemented
36#16839499C2211yescharacteristic, complemented
37#16839499C2211yescharacteristic, complemented
38#16839499C2211yescharacteristic, complemented
39#16839499C2211yescharacteristic, complemented
40#16839496C2211yescharacteristic
41#16839496C2211yescharacteristic
42#16839496C2211yescharacteristic
43#16839496C2211yescharacteristic
44#16839496C2211yescharacteristic, complemented
45#16839496C2211yescharacteristic, complemented
46#16839496C2211yescharacteristic, complemented
47#16839496C2211yescharacteristic, complemented
48#16839496C2211yescharacteristic, complemented
49#16839496C2211yescharacteristic, complemented
50#16839496C2211yescharacteristic, complemented
51#16839496C2211yescharacteristic, complemented
52C61×#555C411yescharacteristic, complemented
53C61×#554C411yescharacteristic, complemented
54C61×#553—21no—
55C61×#553C411yescharacteristic, complemented
56C61×#553C411yescharacteristic, complemented
57C61×#550C411yescharacteristic, complemented
58C61×#546—21no—
59C61×#546—21no—
60C61×#546C411yescharacteristic, complemented
61C61×#546C411yescharacteristic, complemented
62D42×C61—21no—
63D42×C61C411yescharacteristic, complemented
64C61×#540—21no—
65C61×#538—21no—
66C61×#538—21no—
67C61×#532C2211yescharacteristic
68C61×#529C2211yescharacteristic
69C61×#525C2211yescharacteristic
70C61×#525C2211yescharacteristic
71C2×#121×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#518—21no—
74C2×C4×D4×C61C2211yescharacteristic
75C23×Dic61—21no—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C22×#92418—21no—
79C22×#92418—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C4×Dic61—21no—
86C4⋊#92418—21no—
87C4⋊#92418—21no—
88C22⋊#92418—21no—
89C22⋊#92418—21no—
90C22⋊#92418—21no—
91C22⋊#92418—21no—
92C22⋊#92418C2311yescharacteristic
93C22⋊#92418C2311yescharacteristic
94C22⋊#92418C2311yescharacteristic
95C22⋊#92418C2311yescharacteristic
96#14519688—21no—
97C4×#92418—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684C2311yescharacteristic
104#14519684C2311yescharacteristic
105#14519684C2311yescharacteristic
106#14519684C2311yescharacteristic
107C2×#41×C61—21no—
108C2×#41×C61C2×C411yescharacteristic
109C2×#41×C61C2×C411yescharacteristic, complemented
110C22×D4×C61—21no—
111C22×D4×C61—21no—
112C22×D4×C61—21no—
113C22×D4×C61C2×C411yescharacteristic
114C22×D4×C61C2×C411yescharacteristic, complemented
115C22×D4×C61D411yescharacteristic
116C23×C4×C61C2311yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C4⋊Q8×C61C2×C411yescharacteristic, complemented
119#127×C61—21no—
120#127×C61C2×C411yescharacteristic, complemented
121#126×C61—21no—
122#126×C61—21no—
123#126×C61—21no—
124#125×C61—21no—
125#125×C61C2×C411yescharacteristic, complemented
126#124×C61—21no—
127#124×C61—21no—
128#124×C61—21no—
129#124×C61C2×C411yescharacteristic, complemented
130#123×C61—21no—
131#123×C61—21no—
132#123×C61—21no—
133#123×C61—21no—
134#123×C61—21no—
135#123×C61—21no—
136#123×C61—21no—
137C22⋊Q8×C61—21no—
138C22⋊Q8×C61—21no—
139C22⋊Q8×C61C2×C411yescharacteristic
140C22⋊Q8×C61C2×C411yescharacteristic, complemented
141C22⋊Q8×C61C2311yescharacteristic
142#121×C61—21no—
143#121×C61—21no—
144#121×C61—21no—
145#121×C61—21no—
146#121×C61—21no—
147#121×C61—21no—
148#121×C61—21no—
149#121×C61—21no—
150#121×C61—21no—
151#121×C61—21no—
152#121×C61—21no—
153#121×C61—21no—
154#121×C61—21no—
155#121×C61C2×C411yescharacteristic
156#121×C61C2×C411yescharacteristic
157#121×C61C2×C411yescharacteristic
158#121×C61C2×C411yescharacteristic, complemented
159#121×C61C2×C411yescharacteristic, complemented
160#121×C61C2×C411yescharacteristic, complemented
161#121×C61C2311yescharacteristic
162#121×C61C2311yescharacteristic
163#121×C61C2311yescharacteristic
164#120×C61—21no—
165#120×C61—21no—
166#120×C61—21no—
167#120×C61—21no—
168#120×C61—21no—
169#120×C61—21no—
170C4×Q8×C61C2×C411yescharacteristic, complemented
171C4×D4×C61—21no—
172C4×D4×C61—21no—
173C4×D4×C61—21no—
174C4×D4×C61—21no—
175C4×D4×C61—21no—
176C4×D4×C61—21no—
177C4×D4×C61—21no—
178C4×D4×C61—21no—
179C4×D4×C61—21no—
180C4×D4×C61—21no—
181C4×D4×C61C2×C411yescharacteristic
182C4×D4×C61C2×C411yescharacteristic
183C4×D4×C61C2×C411yescharacteristic
184C4×D4×C61C2×C411yescharacteristic
185C4×D4×C61C2×C411yescharacteristic, complemented
186C4×D4×C61C2×C411yescharacteristic, complemented
187C4×D4×C61C2×C411yescharacteristic, complemented
188C4×D4×C61D411yescharacteristic
189C4×D4×C61D411yescharacteristic
190C4×D4×C61D411yescharacteristic
191C4×D4×C61D411yescharacteristic
192#117×C61—21no—
193#117×C61—21no—
194#117×C61C2×C411yescharacteristic
195#117×C61C2×C411yescharacteristic, complemented
196C2×C4⋊C4×C61C2×C411yescharacteristic
197C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
198C2×C4⋊C4×C61D411yescharacteristic
199C2×C22⋊C4×C61—21no—
200C2×C22⋊C4×C61—21no—
201C2×C22⋊C4×C61—21no—
202C2×C22⋊C4×C61—21no—
203C2×C22⋊C4×C61D411yescharacteristic
204C2×C22⋊C4×C61D411yescharacteristic
205C2×C42×C61C2311yescharacteristic
206C24×C61—21no—
207C24×C61—21no—
208C24×C61C2×D411yescharacteristic
209C24×C61C2×D411yescharacteristic
210#41×C61—81no—
211#41×C61—81no—
212#41×C61—81no—
213#41×C61—81no—
214C2×Q8×C61—21no—
215C2×Q8×C61C22×C411yescharacteristic
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61—42no—
232C2×D4×C61—44no—
233C2×D4×C61—81no—
234C2×D4×C61—81no—
235C2×D4×C61—81no—
236C2×D4×C61—81no—
237C2×D4×C61—81no—
238C2×D4×C61—81no—
239C2×D4×C61C22⋊C411yescharacteristic
240C2×D4×C61C22⋊C411yescharacteristic
241C2×D4×C61C22⋊C411yescharacteristic
242C2×D4×C61C22⋊C411yescharacteristic
243C2×D4×C61C22×C411yescharacteristic
244C2×D4×C61C22×C411yescharacteristic
245C2×D4×C61C22×C411yescharacteristic
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—81no—
254C22×C4×C61—81no—
255C22×C4×C61C22×C411yescharacteristic
256C22×C4×C61C22×C411yescharacteristic
257C22×C4×C61C22×C411yescharacteristic
258C22×C4×C61C22×C411yescharacteristic
259C22×C4×C61C2×D411yescharacteristic
260C22×C4×C61C2×D411yescharacteristic
261C22×C4×C61C2×D411yescharacteristic
262C22×C4×C61C2×D411yescharacteristic
263C22×C4×C61C2×D411yescharacteristic
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2×D411yescharacteristic
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2411yescharacteristic
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—42no—
273C22×Dic61—81no—
274C22×Dic61—81no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61C22⋊C411yescharacteristic
285C4⋊C4×C61C22⋊C411yescharacteristic
286C4⋊C4×C61C22⋊C411yescharacteristic
287C4⋊C4×C61C22⋊C411yescharacteristic
288C4⋊C4×C61C22×C411yescharacteristic
289C4⋊C4×C61C22×C411yescharacteristic
290C4⋊C4×C61C22×C411yescharacteristic
291C4⋊C4×C61C22×C411yescharacteristic
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C22⋊C4×C61—21no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61—21no—
300C22⋊C4×C61—21no—
301C22⋊C4×C61—21no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—21no—
307C22⋊C4×C61—21no—
308C22⋊C4×C61—21no—
309C22⋊C4×C61—21no—
310C22⋊C4×C61—21no—
311C22⋊C4×C61C22⋊C411yescharacteristic
312C22⋊C4×C61C22⋊C411yescharacteristic
313C22⋊C4×C61C22⋊C411yescharacteristic
314C22⋊C4×C61C22⋊C411yescharacteristic
315C22⋊C4×C61C22⋊C411yescharacteristic
316C22⋊C4×C61C22⋊C411yescharacteristic
317C22⋊C4×C61C22⋊C411yescharacteristic
318C22⋊C4×C61C22⋊C411yescharacteristic
319C42×C61—21no—
320C42×C61—21no—
321C42×C61—21no—
322C42×C61C22×C411yescharacteristic
323C42×C61C22×C411yescharacteristic
324C42×C61C2×D411yescharacteristic
325C42×C61C2×D411yescharacteristic
326C22⋊Dic61—42no—
327C22⋊Dic61—81no—
328C22⋊Dic61—81no—
329C4⋊Dic61—81no—
330C4⋊Dic61—81no—
331C4×Dic61—81no—
332#11758194—81no—
333#11758194—81no—
334C2×#92418—21no—
335C2×#92418—21no—
336C2×#92418—21no—
337C2×#92418—21no—
338C2×#92418—81no—
339C2×#92418—81no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—22no—
343C23×C61—21no—
344C23×C61—21no—
345C23×C61—21no—
346C23×C61—21no—
347C23×C61—21no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—42no—
352C23×C61—42no—
353C23×C61—81no—
354C23×C61—81no—
355C23×C61—81no—
356C23×C61—81no—
357C23×C61C2×C22⋊C411yescharacteristic
358C23×C61C2×C22⋊C411yescharacteristic
359C23×C61C2×C22⋊C411yescharacteristic
360C23×C61C2×C22⋊C411yescharacteristic
361C23×C61C22×D411yescharacteristic
362Q8×C61—41no—
363Q8×C61—81no—
364D4×C61—22no—
365D4×C61—22no—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—41no—
369D4×C61—41no—
370D4×C61—41no—
371D4×C61—42no—
372D4×C61—42no—
373D4×C61—41no—
374D4×C61—41no—
375D4×C61—41no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—41no—
379D4×C61—42no—
380D4×C61—81no—
381D4×C61—81no—
382D4×C61—81no—
383D4×C61—81no—
384D4×C61—81no—
385D4×C61—81no—
386D4×C61—81no—
387D4×C61—81no—
388D4×C61—81no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—42no—
409C2×C4×C61—81no—
410C2×C4×C61—81no—
411C2×C4×C61—81no—
412C2×C4×C61—81no—
413C2×C4×C61—81no—
414C2×C4×C61—81no—
415C2×C4×C61C2×C22⋊C411yescharacteristic
416C2×C4×C61C2×C22⋊C411yescharacteristic
417C2×C4×C61C2×C22⋊C411yescharacteristic
418C2×C4×C61C2×C22⋊C411yescharacteristic
419C2×C4×C61C2×C22⋊C411yescharacteristic
420C2×C4×C61C2×C22⋊C411yescharacteristic
421C2×C4×C61C2×C22⋊C411yescharacteristic
422C2×C4×C61C2×C22⋊C411yescharacteristic
423C2×C4×C61C23×C411yescharacteristic
424C2×C4×C61C22×D411yescharacteristic
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431C2×Dic61—41no—
432C2×Dic61—41no—
433C2×Dic61—41no—
434C2×Dic61—41no—
435C2×Dic61—41no—
436C2×Dic61—41no—
437C2×Dic61—84no—
438#92418—41no—
439#92418—41no—
440#92418—41no—
441#92418—41no—
442#17597—611nomaximal, Sylow
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—21no—
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—42no—
457C22×C61—42no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61—41no—
461C22×C61—41no—
462C22×C61—41no—
463C22×C61—41no—
464C22×C61—41no—
465C22×C61—41no—
466C22×C61—41no—
467C22×C61—81no—
468C22×C61—81no—
469C22×C61—162no—
470C22×C61—162no—
471C22×C61#42112yes—
472C22×C61C22×C22⋊C411yescharacteristic
473C22×C61#57611yescharacteristic
474C22×C61#57711yescharacteristic
475C4×C61—21no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—21no—
483C4×C61—21no—
484C4×C61—21no—
485C4×C61—41no—
486C4×C61—41no—
487C4×C61—41no—
488C4×C61—41no—
489C4×C61—41no—
490Dic61—81no—
491Dic61—81no—
492Dic61—81no—
493Dic61—81no—
494#3519D6111yescharacteristic
495#2974—611no—
496#2318—611no—
497#1521—611no—
498#1519—611no—
499#1517—611no—
500#1516—611no—
501#1514—611no—
502#1513—611no—
503#1512—611no—
504#1510—611no—
505#1507—611no—
506#1504—611no—
507#1501—611no—
508C2×#327—611no—
509C2×C61—21no—
510C2×C61—21no—
511C2×C61—22no—
512C2×C61—41no—
513C2×C61—41no—
514C2×C61—41no—
515C2×C61—81no—
516C2×C61—81no—
517C2×C61—81no—
518C2×C61#288311yescharacteristic
519C2×C61#289711yescharacteristic
520C2×C61C2×#42111yescharacteristic
521#555Dic6111yescharacteristic, complemented
522#554Dic6111yescharacteristic, complemented
523#553—21no—
524#553Dic6111yescharacteristic, complemented
525#553Dic6111yescharacteristic, complemented
526#550Dic6111yescharacteristic, complemented
527#546—21no—
528#546—21no—
529#546Dic6111yescharacteristic, complemented
530#546Dic6111yescharacteristic, complemented
531D42—21no—
532D42Dic6111yescharacteristic, complemented
533#540—21no—
534#538—21no—
535#538—21no—
536#532C2×D6111yescharacteristic
537#529C2×D6111yescharacteristic
538#525C2×D6111yescharacteristic
539#525C2×D6111yescharacteristic
540C2×#121C2×D6111yescharacteristic
541C2×#121C2×D6111yescharacteristic
542#518—21no—
543C2×C4×D4C2×D6111yescharacteristic
544#436—1221no—
545#435—1221no—
546#435—1221no—
547C8×D4—1221no—
548#432—611no—
549#431—611no—
550#407—611no—
551#407—611no—
552C2×C22⋊C8—611no—
553C2×C22⋊C8—611no—
554#388—1221no—
555#387—1221no—
556#386—1221no—
557#385—1221no—
558#383—611no—
559#382—611no—
560#381—611no—
561#380—611no—
562C4×C22⋊C4—611no—
563C2×#95—611no—
564#328—611no—
565#328—611no—
566#328—611no—
567#328—611no—
568#327—611no—
569#327—611no—
570#327—611no—
571#327—611no—
572#327—611no—
573#327—611no—
574#327—611no—
575#327—611no—
576#327—611no—
577#327—611no—
578#327—611no—
579#327—611no—
580C61#1759711yescharacteristic, complemented, Sylow
581C2×#41—21no—
582C2×#41C2×Dic6111yescharacteristic
583C2×#41C2×Dic6111yescharacteristic, complemented
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4C2×Dic6111yescharacteristic
588C22×D4C2×Dic6111yescharacteristic, complemented
589C22×D4C22⋊D6111yescharacteristic
590C23×C4—1221no—
591C23×C4C22×D6111yescharacteristic
592C23×C4C22×D6111yescharacteristic
593C2×M16—1221no—
594C2×M16—1221no—
595C22×C8—1221no—
596C22×C8—1221no—
597C4⋊Q8C2×Dic6111yescharacteristic, complemented
598#127—21no—
599#127C2×Dic6111yescharacteristic, complemented
600#126—21no—
601#126—21no—
602#126—21no—
603#125—21no—
604#125C2×Dic6111yescharacteristic, complemented
605#124—21no—
606#124—21no—
607#124—21no—
608#124C2×Dic6111yescharacteristic, complemented
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8C2×Dic6111yescharacteristic
619C22⋊Q8C2×Dic6111yescharacteristic, complemented
620C22⋊Q8C22×D6111yescharacteristic
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121C2×Dic6111yescharacteristic
635#121C2×Dic6111yescharacteristic
636#121C2×Dic6111yescharacteristic
637#121C2×Dic6111yescharacteristic, complemented
638#121C2×Dic6111yescharacteristic, complemented
639#121C2×Dic6111yescharacteristic, complemented
640#121C22×D6111yescharacteristic
641#121C22×D6111yescharacteristic
642#121C22×D6111yescharacteristic
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648#120—21no—
649C4×Q8C2×Dic6111yescharacteristic, complemented
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4C2×Dic6111yescharacteristic
661C4×D4C2×Dic6111yescharacteristic
662C4×D4C2×Dic6111yescharacteristic
663C4×D4C2×Dic6111yescharacteristic
664C4×D4C2×Dic6111yescharacteristic, complemented
665C4×D4C2×Dic6111yescharacteristic, complemented
666C4×D4C2×Dic6111yescharacteristic, complemented
667C4×D4C22⋊D6111yescharacteristic
668C4×D4C22⋊D6111yescharacteristic
669C4×D4C22⋊D6111yescharacteristic
670C4×D4C22⋊D6111yescharacteristic
671#117—21no—
672#117—21no—
673#117C2×Dic6111yescharacteristic
674#117C2×Dic6111yescharacteristic, complemented
675C2×C4⋊C4—1221no—
676C2×C4⋊C4—1221no—
677C2×C4⋊C4C2×Dic6111yescharacteristic
678C2×C4⋊C4C2×Dic6111yescharacteristic, complemented
679C2×C4⋊C4C22⋊D6111yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4C22⋊D6111yescharacteristic
688C2×C22⋊C4C22⋊D6111yescharacteristic
689C2×C42—1221no—
690C2×C42C22×D6111yescharacteristic
691C4⋊C8—1221no—
692C4⋊C8—1221no—
693C22⋊C8—611no—
694C22⋊C8—611no—
695C22⋊C8—611no—
696C22⋊C8—611no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8—1221no—
700C22⋊C8—1221no—
701#97—1221no—
702C4×C8—1221no—
703#95—611no—
704#95—611no—
705#95—611no—
706#95—611no—
707#95—1221no—
708#95—1221no—
709#95—1221no—
710#95—1221no—
711#95—1221no—
712C24—21no—
713C24—21no—
714C24C2×C22⋊D6111yescharacteristic
715C24C2×C22⋊D6111yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719#41—81no—
720C2×Q8—21no—
721C2×Q8C22×Dic6111yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4C22⋊Dic6111yescharacteristic
746C2×D4C22⋊Dic6111yescharacteristic
747C2×D4C22⋊Dic6111yescharacteristic
748C2×D4C22⋊Dic6111yescharacteristic
749C2×D4C22×Dic6111yescharacteristic
750C2×D4C22×Dic6111yescharacteristic
751C2×D4C22×Dic6111yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—81no—
760C22×C4—81no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—4881no—
766C22×C4—4881no—
767C22×C4—2442no—
768C22×C4C22×Dic6111yescharacteristic
769C22×C4C22×Dic6111yescharacteristic
770C22×C4C22×Dic6111yescharacteristic
771C22×C4C22×Dic6111yescharacteristic
772C22×C4C2×C22⋊D6111yescharacteristic
773C22×C4C2×C22⋊D6111yescharacteristic
774C22×C4C2×C22⋊D6111yescharacteristic
775C22×C4C2×C22⋊D6111yescharacteristic
776C22×C4C2×C22⋊D6111yescharacteristic
777C22×C4C2×C22⋊D6111yescharacteristic
778C22×C4C2×C22⋊D6111yescharacteristic
779C22×C4C2×C22⋊D6111yescharacteristic
780C22×C4C23×D6111yescharacteristic
781M16—4881no—
782M16—4881no—
783C2×C8—1221no—
784C2×C8—1221no—
785C2×C8—1221no—
786C2×C8—1221no—
787C2×C8—4881no—
788C2×C8—4881no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—4881no—
799C4⋊C4—4881no—
800C4⋊C4C22⋊Dic6111yescharacteristic
801C4⋊C4C22⋊Dic6111yescharacteristic
802C4⋊C4C22⋊Dic6111yescharacteristic
803C4⋊C4C22⋊Dic6111yescharacteristic
804C4⋊C4C22×Dic6111yescharacteristic
805C4⋊C4C22×Dic6111yescharacteristic
806C4⋊C4C22×Dic6111yescharacteristic
807C4⋊C4C22×Dic6111yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—4881no—
828C22⋊C4—4881no—
829C22⋊C4—2442no—
830C22⋊C4C22⋊Dic6111yescharacteristic
831C22⋊C4C22⋊Dic6111yescharacteristic
832C22⋊C4C22⋊Dic6111yescharacteristic
833C22⋊C4C22⋊Dic6111yescharacteristic
834C22⋊C4C22⋊Dic6111yescharacteristic
835C22⋊C4C22⋊Dic6111yescharacteristic
836C22⋊C4C22⋊Dic6111yescharacteristic
837C22⋊C4C22⋊Dic6111yescharacteristic
838C42—21no—
839C42—21no—
840C42—21no—
841C42—4881no—
842C42C22×Dic6111yescharacteristic
843C42C22×Dic6111yescharacteristic
844C42C2×C22⋊D6111yescharacteristic
845C42C2×C22⋊D6111yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23C2×C22⋊Dic6111yescharacteristic
864C23C2×C22⋊Dic6111yescharacteristic
865C23C2×C22⋊Dic6111yescharacteristic
866C23C2×C22⋊Dic6111yescharacteristic
867C23C22×C22⋊D6111yescharacteristic
868Q8—41no—
869Q8—81no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—42no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—42no—
915C2×C4—81no—
916C2×C4—81no—
917C2×C4—81no—
918C2×C4—81no—
919C2×C4—81no—
920C2×C4—81no—
921C2×C4—4884no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4C2×C22⋊Dic6111yescharacteristic
935C2×C4C2×C22⋊Dic6111yescharacteristic
936C2×C4C2×C22⋊Dic6111yescharacteristic
937C2×C4C2×C22⋊Dic6111yescharacteristic
938C2×C4C2×C22⋊Dic6111yescharacteristic
939C2×C4C2×C22⋊Dic6111yescharacteristic
940C2×C4C2×C22⋊Dic6111yescharacteristic
941C2×C4C2×C22⋊Dic6111yescharacteristic
942C2×C4C23×Dic6111yescharacteristic
943C2×C4C22×C22⋊D6111yescharacteristic
944C8—2441no—
945C8—2441no—
946C8—2441no—
947C8—2441no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—81no—
973C22—81no—
974C22—162no—
975C22—162no—
976C22#1683977912yes—
977C22C22×C22⋊Dic6111yescharacteristic
978C22#1684056511yescharacteristic
979C22#1684057311yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—4881no—
996C4—4881no—
997C4—4881no—
998C4—4881no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—81no—
1006C2—81no—
1007C2—81no—
1008C2#2145428011yescharacteristic
1009C2#2145434511yescharacteristic
1010C2C2×#1683977911yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#3519C2
socleC22×C61C22×C22⋊C4
cosocleC22×C4×C61C24
hypercenter#3519D61
hypocenterC61#17597
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3519

Complements

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

NH ≅ G/Ntype
1. #21454854C2semidirect
2. #21448452C2semidirect
3. #21444396C2semidirect
4. #21444387C2semidirect
5. #21444379C2semidirect
6. #21444375C2semidirect
7. #21444366C2semidirect
8. #21444362C2semidirect
9. #21444357C2semidirect
10. #21444348C2semidirect
11. #21444335C2semidirect
12. #21444323C2semidirect
13. #21444310C2semidirect
14. C2×#16839496C2semidirect
20. #16839819C22semidirect
21. #16839815C22semidirect
22. #16839726C22semidirect
23. #16839726C22semidirect
24. C2×C22⋊#92418C22semidirect
25. C2×C22⋊#92418C22semidirect
30. #16839630C22semidirect
31. #16839628C22semidirect
32. #16839625C22semidirect
33. #16839622C22semidirect
34. C4×C22⋊Dic61C22semidirect
35. C2×#14519684C22semidirect
36. #16839499C22semidirect
37. #16839499C22semidirect
38. #16839499C22semidirect
39. #16839499C22semidirect
44. #16839496C22semidirect
45. #16839496C22semidirect
46. #16839496C22semidirect
47. #16839496C22semidirect
48. #16839496C22semidirect
49. #16839496C22semidirect
50. #16839496C22semidirect
51. #16839496C22semidirect
52. C61×#555C4semidirect
53. C61×#554C4semidirect
55. C61×#553C4semidirect
56. C61×#553C4semidirect
57. C61×#550C4semidirect
60. C61×#546C4semidirect
61. C61×#546C4semidirect
63. D42×C61C4semidirect
109. C2×#41×C61C2×C4semidirect
114. C22×D4×C61C2×C4semidirect
118. C4⋊Q8×C61C2×C4semidirect
120. #127×C61C2×C4semidirect
125. #125×C61C2×C4semidirect
129. #124×C61C2×C4semidirect
140. C22⋊Q8×C61C2×C4semidirect
158. #121×C61C2×C4semidirect
159. #121×C61C2×C4semidirect
160. #121×C61C2×C4semidirect
170. C4×Q8×C61C2×C4semidirect
185. C4×D4×C61C2×C4semidirect
186. C4×D4×C61C2×C4semidirect
187. C4×D4×C61C2×C4semidirect
195. #117×C61C2×C4semidirect
197. C2×C4⋊C4×C61C2×C4semidirect
521. #555Dic61semidirect
522. #554Dic61semidirect
524. #553Dic61semidirect
525. #553Dic61semidirect
526. #550Dic61semidirect
529. #546Dic61semidirect
530. #546Dic61semidirect
532. D42Dic61semidirect
580. C61#17597semidirect
583. C2×#41C2×Dic61semidirect
588. C22×D4C2×Dic61semidirect
597. C4⋊Q8C2×Dic61semidirect
599. #127C2×Dic61semidirect
604. #125C2×Dic61semidirect
608. #124C2×Dic61semidirect
619. C22⋊Q8C2×Dic61semidirect
637. #121C2×Dic61semidirect
638. #121C2×Dic61semidirect
639. #121C2×Dic61semidirect
649. C4×Q8C2×Dic61semidirect
664. C4×D4C2×Dic61semidirect
665. C4×D4C2×Dic61semidirect
666. C4×D4C2×Dic61semidirect
674. #117C2×Dic61semidirect
678. C2×C4⋊C4C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
#214548542
#214484522
#214443962
#214443872
#214443792
#214443752
#214443662
#214443622
#214443572
#214443482
#214443352
#214443232
#214443102
C2×#168394962
C61×#35192
#1759761