Finite Group Databasebeta

← #29648848

Subgroups — #29648848

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454936C211yesmaximal, characteristic, complemented
2#21454485C211yesmaximal, characteristic, complemented
3#21444557C211yesmaximal, characteristic, complemented
4#21444541C211yesmaximal, characteristic, complemented
5#21444541C211yesmaximal, characteristic, complemented
6#21444536C211yesmaximal, characteristic, complemented
7#21444524C211yesmaximal, characteristic, complemented
8#21444524C211yesmaximal, characteristic, complemented
9#21444519C211yesmaximal, characteristic, complemented
10#21444519C211yesmaximal, characteristic, complemented
11#21444496C211yesmaximal, characteristic, complemented
12#21444491C211yesmaximal, characteristic, complemented
13#21444484C211yesmaximal, characteristic, complemented
14#21444468C211yesmaximal, characteristic, complemented
15C61×#3511C211yesmaximal, characteristic
16#16839893—21no—
17#16839840—21no—
18#16839834—21no—
19#16839834—21no—
20#16839823—21no—
21#16839823—21no—
22#16839819C2211yescharacteristic
23#16839819C2211yescharacteristic
24#16839819C2211yescharacteristic
25#16839819C2211yescharacteristic
26#16839815C2211yescharacteristic
27#16839815C2211yescharacteristic
28#16839815C2211yescharacteristic
29#16839786C2211yescharacteristic
30#16839786C2211yescharacteristic
31#16839786C2211yescharacteristic
32C2×C4⋊#92418C2211yescharacteristic
33C2×C4⋊#92418C2211yescharacteristic
34#16839729—21no—
35#16839718—21no—
36#16839508C2211yescharacteristic
37#16839508C2211yescharacteristic
38#16839508C2211yescharacteristic
39#16839508C2211yescharacteristic
40#16839508C2211yescharacteristic
41#16839508C2211yescharacteristic
42#16839508C2211yescharacteristic
43#16839508C2211yescharacteristic
44#16839508C2211yescharacteristic
45#16839508C2211yescharacteristic
46#16839508C2211yescharacteristic
47#16839508C2211yescharacteristic
48#16839506C2211yescharacteristic
49#16839506C2211yescharacteristic
50#16839506C2211yescharacteristic
51#16839506C2211yescharacteristic
52C61×#556—21no—
53C61×#555C412yes—
54C61×#554C412yes—
55C61×#553C412yes—
56C61×#553C412yes—
57C61×#548—21no—
58C61×#548—21no—
59C61×#547—21no—
60C61×#542—21no—
61C61×#542—21no—
62C61×#537—21no—
63C61×#533C2211yescharacteristic
64C61×#533C2211yescharacteristic
65C61×#532C2211yescharacteristic
66C61×#532C2211yescharacteristic
67C61×#532C2211yescharacteristic
68C2×C4⋊Q8×C61C2211yescharacteristic
69C61×#520—21no—
70C4×#41×C61C2211yescharacteristic
71C2×#11758194—21no—
72C2×#11758194—21no—
73C2×#11758194—21no—
74C22×#92418—21no—
75C22×#92418—21no—
76C4⋊#92418—21no—
77C4⋊#92418—21no—
78C4⋊#92418—21no—
79C4⋊#92418—21no—
80C4⋊#92418—21no—
81C4⋊#92418C2311yescharacteristic
82C4⋊#92418C2311yescharacteristic
83C4⋊#92418C2311yescharacteristic
84C4⋊#92418C2311yescharacteristic
85C4⋊#92418C2311yescharacteristic
86C4⋊#92418C2311yescharacteristic
87C4⋊#92418C2311yescharacteristic
88C4⋊#92418C2311yescharacteristic
89C22⋊#92418—21no—
90C22⋊#92418—21no—
91C22⋊#92418—21no—
92C22⋊#92418—21no—
93C22⋊#92418—21no—
94C22⋊#92418—21no—
95C22⋊#92418—21no—
96#14519688—21no—
97#14519688—21no—
98#14519688—21no—
99#14519688—21no—
100C4×#92418—21no—
101C4×#92418—21no—
102C4×#92418—21no—
103C2×#41×C61—21no—
104C2×#41×C61—21no—
105C2×#41×C61—21no—
106C2×#41×C61D411yescharacteristic
107C22×Q8×C61—21no—
108C4⋊Q8×C61—21no—
109C4⋊Q8×C61—21no—
110C4⋊Q8×C61C2×C412yes—
111C4⋊Q8×C61C2311yescharacteristic
112C4⋊Q8×C61C2311yescharacteristic
113C4⋊Q8×C61C2311yescharacteristic
114#127×C61C2311yescharacteristic
115#126×C61—22no—
116#126×C61—22no—
117#125×C61C2×C412yes—
118#125×C61C2×C412yes—
119#124×C61—22no—
120#124×C61—22no—
121#124×C61—21no—
122#124×C61—21no—
123#124×C61—21no—
124#123×C61—22no—
125#123×C61—22no—
126C22⋊Q8×C61—22no—
127C22⋊Q8×C61—21no—
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—22no—
132C22⋊Q8×C61—22no—
133#121×C61—22no—
134#121×C61—22no—
135#121×C61—22no—
136#121×C61—21no—
137#121×C61—21no—
138#121×C61—21no—
139#121×C61C2×C412yes—
140#121×C61C2×C412yes—
141#121×C61C2×C412yes—
142C4×Q8×C61—21no—
143C4×Q8×C61—21no—
144C4×Q8×C61—21no—
145C4×Q8×C61—21no—
146C4×Q8×C61C2×C411yescharacteristic
147C4×Q8×C61D411yescharacteristic
148C4×D4×C61—22no—
149C4×D4×C61—22no—
150C4×D4×C61—21no—
151C4×D4×C61—21no—
152C4×D4×C61—21no—
153C4×D4×C61C2×C412yes—
154C4×D4×C61C2×C412yes—
155C4×D4×C61C2×C412yes—
156C4×D4×C61C2×C411yescharacteristic
157C4×D4×C61C2×C411yescharacteristic
158C4×D4×C61C2×C411yescharacteristic
159C4×D4×C61D411yescharacteristic
160C4×D4×C61D411yescharacteristic
161C4×D4×C61D411yescharacteristic
162#117×C61—22no—
163#117×C61C2×C412yes—
164#117×C61C2×C412yes—
165#117×C61D411yescharacteristic
166#117×C61D411yescharacteristic
167#117×C61D411yescharacteristic
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—22no—
170C2×C4⋊C4×C61C2×C412yes—
171C2×C42×C61C2311yescharacteristic
172C2×C42×C61C2311yescharacteristic
173C2×C42×C61C2311yescharacteristic
174#41×C61—41no—
175#41×C61—41no—
176#41×C61—42no—
177#41×C61—42no—
178#41×C61—81no—
179#41×C61—81no—
180#41×C61—81no—
181#41×C61—81no—
182C2×Q8×C61—22no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—81no—
187C2×Q8×C61—81no—
188C2×Q8×C61C22⋊C411yescharacteristic
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61C22⋊C411yescharacteristic
195C2×D4×C61C22⋊C411yescharacteristic
196C2×D4×C61C22⋊C411yescharacteristic
197C2×D4×C61C22×C412yes—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61C22×C411yescharacteristic
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C22×C411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C4⋊C4×C61—22no—
212C4⋊C4×C61—22no—
213C4⋊C4×C61—22no—
214C4⋊C4×C61—22no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61C22⋊C411yescharacteristic
221C4⋊C4×C61C22⋊C411yescharacteristic
222C4⋊C4×C61C22⋊C411yescharacteristic
223C4⋊C4×C61C22⋊C411yescharacteristic
224C4⋊C4×C61C22⋊C411yescharacteristic
225C4⋊C4×C61C22⋊C411yescharacteristic
226C4⋊C4×C61C22×C412yes—
227C4⋊C4×C61C22×C412yes—
228C4⋊C4×C61C22×C412yes—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—22no—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—22no—
237C22⋊C4×C61C22⋊C411yescharacteristic
238C22⋊C4×C61C22⋊C411yescharacteristic
239C22⋊C4×C61C22⋊C411yescharacteristic
240C22⋊C4×C61C22⋊C411yescharacteristic
241C22⋊C4×C61C22⋊C411yescharacteristic
242C22⋊C4×C61C22⋊C411yescharacteristic
243C42×C61—22no—
244C42×C61—22no—
245C42×C61C22×C411yescharacteristic
246C42×C61C22×C411yescharacteristic
247C42×C61C22×C411yescharacteristic
248C42×C61C2×D411yescharacteristic
249C42×C61C2×D411yescharacteristic
250C42×C61C2×D411yescharacteristic
251C42×C61C2×D411yescharacteristic
252C42×C61C2×D411yescharacteristic
253C42×C61C2×D411yescharacteristic
254C42×C61C2411yescharacteristic
255#11758194—42no—
256#11758194—81no—
257#11758194—81no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—42no—
267C2×#92418—81no—
268C23×C61—22no—
269C23×C61C2×C22⋊C411yescharacteristic
270C23×C61C2×C22⋊C411yescharacteristic
271C23×C61C2×C22⋊C411yescharacteristic
272Q8×C61—41no—
273Q8×C61—41no—
274Q8×C61—41no—
275Q8×C61—41no—
276Q8×C61—41no—
277Q8×C61—41no—
278Q8×C61—41no—
279Q8×C61—82no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—42no—
284D4×C61—44no—
285D4×C61—41no—
286D4×C61—41no—
287D4×C61—41no—
288D4×C61—41no—
289D4×C61—82no—
290D4×C61—82no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—44no—
310C2×C4×C61—82no—
311C2×C4×C61—82no—
312C2×C4×C61—82no—
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61C23×C411yescharacteristic
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325#92418—41no—
326#92418—41no—
327#92418—41no—
328#92418—41no—
329#92418—41no—
330#92418—41no—
331#92418—41no—
332#92418—41no—
333#17769—611nomaximal, Sylow
334C22×C61—21no—
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—21no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61C22×C22⋊C411yescharacteristic
347C4×C61—21no—
348C4×C61—21no—
349C4×C61—21no—
350C4×C61—21no—
351C4×C61—21no—
352C4×C61—21no—
353C4×C61—21no—
354C4×C61—21no—
355C4×C61—21no—
356C4×C61—21no—
357C4×C61—42no—
358C4×C61—42no—
359C4×C61—42no—
360C4×C61#57511yescharacteristic
361C4×C61#57511yescharacteristic
362C4×C61#57611yescharacteristic
363C4×C61#57711yescharacteristic
364#3511D6111yescharacteristic
365#2989—611no—
366#2925—611no—
367#1561—611no—
368#1557—611no—
369#1557—611no—
370#1556—611no—
371#1553—611no—
372#1553—611no—
373#1552—611no—
374#1552—611no—
375#1547—611no—
376#1546—611no—
377#1544—611no—
378#1540—611no—
379C2×C61—41no—
380C2×C61—41no—
381C2×C61—41no—
382C2×C61—82no—
383C2×C61#288911yescharacteristic
384C2×C61#289611yescharacteristic
385C2×C61#289711yescharacteristic
386#556—21no—
387#555Dic6112yes—
388#554Dic6112yes—
389#553Dic6112yes—
390#553Dic6112yes—
391#548—21no—
392#548—21no—
393#547—21no—
394#542—21no—
395#542—21no—
396#537—21no—
397#533C2×D6111yescharacteristic
398#533C2×D6111yescharacteristic
399#532C2×D6111yescharacteristic
400#532C2×D6111yescharacteristic
401#532C2×D6111yescharacteristic
402C2×C4⋊Q8C2×D6111yescharacteristic
403#520—21no—
404C4×#41C2×D6111yescharacteristic
405#446—1221no—
406#436—1221no—
407#435—1221no—
408#435—1221no—
409#433—1221no—
410#433—1221no—
411#432—611no—
412#432—611no—
413#432—611no—
414#432—611no—
415#431—611no—
416#431—611no—
417#431—611no—
418#423—611no—
419#423—611no—
420#423—611no—
421C2×C4⋊C8—611no—
422C2×C4⋊C8—611no—
423#408—1221no—
424#405—1221no—
425#332—611no—
426#332—611no—
427#332—611no—
428#332—611no—
429#332—611no—
430#332—611no—
431#332—611no—
432#332—611no—
433#332—611no—
434#332—611no—
435#332—611no—
436#332—611no—
437#331—611no—
438#331—611no—
439#331—611no—
440#331—611no—
441C61#1776911yescharacteristic, complemented, Sylow
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41C22⋊D6111yescharacteristic
446C22×Q8—21no—
447C2×M16—1221no—
448C2×M16—1221no—
449C2×M16—1221no—
450C22×C8—1221no—
451C22×C8—1221no—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454C4⋊Q8C2×Dic6112yes—
455C4⋊Q8C22×D6111yescharacteristic
456C4⋊Q8C22×D6111yescharacteristic
457C4⋊Q8C22×D6111yescharacteristic
458#127C22×D6111yescharacteristic
459#126—22no—
460#126—22no—
461#125C2×Dic6112yes—
462#125C2×Dic6112yes—
463#124—22no—
464#124—22no—
465#124—21no—
466#124—21no—
467#124—21no—
468#123—22no—
469#123—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121C2×Dic6112yes—
484#121C2×Dic6112yes—
485#121C2×Dic6112yes—
486C4×Q8—21no—
487C4×Q8—21no—
488C4×Q8—21no—
489C4×Q8—21no—
490C4×Q8C2×Dic6111yescharacteristic
491C4×Q8C22⋊D6111yescharacteristic
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4C2×Dic6112yes—
498C4×D4C2×Dic6112yes—
499C4×D4C2×Dic6112yes—
500C4×D4C2×Dic6111yescharacteristic
501C4×D4C2×Dic6111yescharacteristic
502C4×D4C2×Dic6111yescharacteristic
503C4×D4C22⋊D6111yescharacteristic
504C4×D4C22⋊D6111yescharacteristic
505C4×D4C22⋊D6111yescharacteristic
506#117—22no—
507#117C2×Dic6112yes—
508#117C2×Dic6112yes—
509#117C22⋊D6111yescharacteristic
510#117C22⋊D6111yescharacteristic
511#117C22⋊D6111yescharacteristic
512C2×C4⋊C4—21no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4C2×Dic6112yes—
515C2×C42C22×D6111yescharacteristic
516C2×C42C22×D6111yescharacteristic
517C2×C42C22×D6111yescharacteristic
518C4⋊C8—611no—
519C4⋊C8—611no—
520C4⋊C8—611no—
521C4⋊C8—611no—
522C4⋊C8—611no—
523C4⋊C8—611no—
524C4⋊C8—611no—
525C4⋊C8—611no—
526C4⋊C8—1221no—
527C4⋊C8—1221no—
528C4⋊C8—1221no—
529C4⋊C8—1221no—
530C4⋊C8—1221no—
531C22⋊C8—1221no—
532C22⋊C8—1221no—
533C22⋊C8—1221no—
534C22⋊C8—1221no—
535C22⋊C8—1221no—
536C22⋊C8—1221no—
537C22⋊C8—1221no—
538#97—1221no—
539#97—1221no—
540#97—1221no—
541#97—1221no—
542C4×C8—1221no—
543C4×C8—1221no—
544C4×C8—1221no—
545#41—41no—
546#41—41no—
547#41—42no—
548#41—42no—
549#41—81no—
550#41—81no—
551#41—81no—
552#41—81no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—81no—
558C2×Q8—81no—
559C2×Q8C22⋊Dic6111yescharacteristic
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4C22⋊Dic6111yescharacteristic
566C2×D4C22⋊Dic6111yescharacteristic
567C2×D4C22⋊Dic6111yescharacteristic
568C2×D4C22×Dic6112yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4C22×Dic6111yescharacteristic
574C22×C4C22×Dic6111yescharacteristic
575C22×C4C22×Dic6111yescharacteristic
576C22×C4C2×C22⋊D6111yescharacteristic
577C22×C4C2×C22⋊D6111yescharacteristic
578C22×C4C2×C22⋊D6111yescharacteristic
579C22×C4C2×C22⋊D6111yescharacteristic
580C22×C4C2×C22⋊D6111yescharacteristic
581C22×C4C2×C22⋊D6111yescharacteristic
582M16—4881no—
583M16—4881no—
584M16—2442no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—4881no—
594C2×C8—2442no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4C22⋊Dic6111yescharacteristic
605C4⋊C4C22⋊Dic6111yescharacteristic
606C4⋊C4C22⋊Dic6111yescharacteristic
607C4⋊C4C22⋊Dic6111yescharacteristic
608C4⋊C4C22⋊Dic6111yescharacteristic
609C4⋊C4C22⋊Dic6111yescharacteristic
610C4⋊C4C22×Dic6112yes—
611C4⋊C4C22×Dic6112yes—
612C4⋊C4C22×Dic6112yes—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4C22⋊Dic6111yescharacteristic
622C22⋊C4C22⋊Dic6111yescharacteristic
623C22⋊C4C22⋊Dic6111yescharacteristic
624C22⋊C4C22⋊Dic6111yescharacteristic
625C22⋊C4C22⋊Dic6111yescharacteristic
626C22⋊C4C22⋊Dic6111yescharacteristic
627C42—22no—
628C42—22no—
629C42C22×Dic6111yescharacteristic
630C42C22×Dic6111yescharacteristic
631C42C22×Dic6111yescharacteristic
632C42C2×C22⋊D6111yescharacteristic
633C42C2×C22⋊D6111yescharacteristic
634C42C2×C22⋊D6111yescharacteristic
635C42C2×C22⋊D6111yescharacteristic
636C42C2×C22⋊D6111yescharacteristic
637C42C2×C22⋊D6111yescharacteristic
638C42C23×D6111yescharacteristic
639C23—22no—
640C23C2×C22⋊Dic6111yescharacteristic
641C23C2×C22⋊Dic6111yescharacteristic
642C23C2×C22⋊Dic6111yescharacteristic
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—82no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—42no—
655D4—44no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—82no—
661D4—82no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—44no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4—82no—
684C2×C4C2×C22⋊Dic6111yescharacteristic
685C2×C4C2×C22⋊Dic6111yescharacteristic
686C2×C4C2×C22⋊Dic6111yescharacteristic
687C2×C4C2×C22⋊Dic6111yescharacteristic
688C2×C4C2×C22⋊Dic6111yescharacteristic
689C2×C4C2×C22⋊Dic6111yescharacteristic
690C2×C4C2×C22⋊Dic6111yescharacteristic
691C2×C4C2×C22⋊Dic6111yescharacteristic
692C2×C4C2×C22⋊Dic6111yescharacteristic
693C2×C4C23×Dic6111yescharacteristic
694C2×C4C22×C22⋊D6111yescharacteristic
695C2×C4C22×C22⋊D6111yescharacteristic
696C8—2441no—
697C8—2441no—
698C8—2441no—
699C8—2441no—
700C8—2441no—
701C8—2441no—
702C8—2441no—
703C8—2441no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22C22×C22⋊Dic6111yescharacteristic
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—21no—
724C4—21no—
725C4—21no—
726C4—21no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4#1684056011yescharacteristic
731C4#1684056011yescharacteristic
732C4#1684056511yescharacteristic
733C4#1684057311yescharacteristic
734C2—41no—
735C2—41no—
736C2—41no—
737C2—82no—
738C2#2145430211yescharacteristic
739C2#2145433811yescharacteristic
740C2#2145434511yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
Fitting, prime radicalC61×#3511C2
socleC22×C61C22×C22⋊C4
cosocleC42×C61C24
hypercenter#3511D61
hypocenterC61#17769
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #21454936C2semidirect
2. #21454485C2semidirect
3. #21444557C2semidirect
4. #21444541C2semidirect
5. #21444541C2semidirect
6. #21444536C2semidirect
7. #21444524C2semidirect
8. #21444524C2semidirect
9. #21444519C2semidirect
10. #21444519C2semidirect
11. #21444496C2semidirect
12. #21444491C2semidirect
13. #21444484C2semidirect
14. #21444468C2semidirect
441. C61#17769semidirect

Maximal subgroups

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

subgroupindex
#214549362
#214544852
#214445572
#214445412
#214445362
#214445242
#214445192
#214444962
#214444912
#214444842
#214444682
C61×#35112
#1776961