Finite Group Databasebeta

← #14720731

Subgroups — #14720731

Order 2816.

948 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077583C211yesmaximal, characteristic, complemented
2#13077282C211yesmaximal, characteristic, complemented
3#13067085C211yesmaximal, characteristic, complemented
4#13067081C211yesmaximal, characteristic, complemented
5#13067076C211yesmaximal, characteristic, complemented
6#13067063C211yesmaximal, characteristic, complemented
7#13067055C211yesmaximal, characteristic, complemented
8#13067050C211yesmaximal, characteristic, complemented
9#13067033C211yesmaximal, characteristic, complemented
10#13067029C211yesmaximal, characteristic, complemented
11#13067024C211yesmaximal, characteristic, complemented
12#13067011C211yesmaximal, characteristic, complemented
13#13067003C211yesmaximal, characteristic, complemented
14#13066998C211yesmaximal, characteristic, complemented
15C11×#3480C211yesmaximal, characteristic
16C11×#559—21no—
17C11×#559C411yescharacteristic
18C11×#557C411yescharacteristic
19C11×#556—21no—
20C11×#556C411yescharacteristic
21C11×#553—21no—
22C11×#553—21no—
23C11×#553C411yescharacteristic
24C11×#553C411yescharacteristic
25C11×#550C411yescharacteristic
26C11×#548C411yescharacteristic
27C11×#548C411yescharacteristic
28C11×#532—21no—
29C11×#532C2211yescharacteristic
30C11×#529—21no—
31C11×#529—21no—
32C11×#529C2211yescharacteristic
33C11×#529C2211yescharacteristic
34C4×C11×#41—21no—
35C4×C11×#41C2211yescharacteristic
36C4×C11×#41C2211yescharacteristic
37C4×C11×#41C2211yescharacteristic
38C2×C4×Q8×C11C2211yescharacteristic
39#10622847—21no—
40#10622637—21no—
41#10622625—21no—
42#10622624—21no—
43#10622624—21no—
44#10622613—21no—
45#10622613—21no—
46#10622610—21no—
47#10622539C2211yescharacteristic
48#10622539C2211yescharacteristic
49#10622538C2211yescharacteristic
50#10622538C2211yescharacteristic
51#10622538C2211yescharacteristic
52#10622538C2211yescharacteristic
53#10622538C2211yescharacteristic
54#10622537C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C4×#4318C2211yescharacteristic
57C4×#4318C2211yescharacteristic
58C2×C4×C11⋊C8C2211yescharacteristic
59Q8⋊(C11⋊C8)C2211yescharacteristic
60Q8⋊(C11⋊C8)C2211yescharacteristic
61Q8⋊(C11⋊C8)C2211yescharacteristic
62Q8⋊(C11⋊C8)C2211yescharacteristic
63Q8⋊(C11⋊C8)C2211yescharacteristic
64Q8⋊(C11⋊C8)C2211yescharacteristic
65Q8⋊(C11⋊C8)C2211yescharacteristic
66Q8⋊(C11⋊C8)C2211yescharacteristic
67D4⋊(C11⋊C8)C2211yescharacteristic
68D4⋊(C11⋊C8)C2211yescharacteristic
69D4⋊(C11⋊C8)C2211yescharacteristic
70D4⋊(C11⋊C8)C2211yescharacteristic
71D4⋊(C11⋊C8)C2211yescharacteristic
72D4⋊(C11⋊C8)C2211yescharacteristic
73D4⋊(C11⋊C8)C2211yescharacteristic
74D4⋊(C11⋊C8)C2211yescharacteristic
75C2×C11×#41—21no—
76C2×C11×#41C2×C411yescharacteristic
77C2×C11×#41C2×C411yescharacteristic
78C2×C11×#41D411yescharacteristic
79C22×Q8×C11C2×C411yescharacteristic
80C11×C4⋊Q8—21no—
81C11×C4⋊Q8C2×C411yescharacteristic
82C11×#127—21no—
83C11×#127C2×C411yescharacteristic
84C11×#126—21no—
85C11×#126—21no—
86C11×#126—21no—
87C11×#126—21no—
88C11×#126—21no—
89C11×#126—21no—
90C11×#125—21no—
91C11×#125—21no—
92C11×#125C2×C411yescharacteristic
93C11×#125C2×C411yescharacteristic
94C11×#124—21no—
95C11×#124—21no—
96C11×#124—21no—
97C11×#124—21no—
98C11×#124—21no—
99C11×#124C2×C411yescharacteristic
100C11×#124C2×C411yescharacteristic
101C11×#123—21no—
102C11×#123—21no—
103C11×#123—21no—
104C11×#123—21no—
105C11×#123—21no—
106C11×#123—21no—
107C11×C22⋊Q8—21no—
108C11×C22⋊Q8—21no—
109C11×C22⋊Q8C2×C411yescharacteristic
110C11×C22⋊Q8C2×C411yescharacteristic
111C11×#121—21no—
112C11×#121—21no—
113C11×#121—21no—
114C11×#121—21no—
115C11×#121—21no—
116C11×#121—21no—
117C11×#121—21no—
118C11×#121C2×C411yescharacteristic
119C11×#121C2×C411yescharacteristic
120C11×#121C2×C411yescharacteristic
121C11×#121C2×C411yescharacteristic
122C4×Q8×C11—21no—
123C4×Q8×C11—21no—
124C4×Q8×C11—21no—
125C4×Q8×C11—21no—
126C4×Q8×C11C2×C411yescharacteristic
127C4×Q8×C11C2×C411yescharacteristic
128C4×Q8×C11C2×C411yescharacteristic
129C4×Q8×C11C2×C411yescharacteristic
130C4×Q8×C11C2×C411yescharacteristic
131C4×Q8×C11D411yescharacteristic
132C4×Q8×C11C2311yescharacteristic
133C4×Q8×C11C2311yescharacteristic
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11—21no—
138C4×D4×C11—21no—
139C4×D4×C11—21no—
140C4×D4×C11—21no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—21no—
144C4×D4×C11—21no—
145C4×D4×C11—21no—
146C4×D4×C11—21no—
147C4×D4×C11C2×C411yescharacteristic
148C4×D4×C11C2×C411yescharacteristic
149C4×D4×C11C2×C411yescharacteristic
150C4×D4×C11C2×C411yescharacteristic
151C4×D4×C11C2×C411yescharacteristic
152C4×D4×C11D411yescharacteristic
153C4×D4×C11D411yescharacteristic
154C4×D4×C11D411yescharacteristic
155C4×D4×C11C2311yescharacteristic
156C4×D4×C11C2311yescharacteristic
157C11×#117—21no—
158C11×#117—21no—
159C11×#117—21no—
160C11×#117—21no—
161C11×#117C2×C411yescharacteristic
162C11×#117C2×C411yescharacteristic
163C11×#117D411yescharacteristic
164C11×#117D411yescharacteristic
165C11×#117D411yescharacteristic
166C2×C11×C4⋊C4—21no—
167C2×C11×C4⋊C4C2×C411yescharacteristic
168C2×C42×C11—21no—
169C2×C42×C11—21no—
170C2×C42×C11—21no—
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2311yescharacteristic
174C2×#4318—21no—
175C2×#4318—21no—
176C2×#4318—21no—
177C22×C11⋊C8—21no—
178C22×C11⋊C8—21no—
179C22⋊(C11⋊C8)—21no—
180C22⋊(C11⋊C8)—21no—
181C22⋊(C11⋊C8)—21no—
182C22⋊(C11⋊C8)—21no—
183C22⋊(C11⋊C8)—21no—
184C22⋊(C11⋊C8)—21no—
185C22⋊(C11⋊C8)—21no—
186C4⋊(C11⋊C8)—21no—
187C4⋊(C11⋊C8)—21no—
188C4⋊(C11⋊C8)—21no—
189C4⋊(C11⋊C8)—21no—
190C4⋊(C11⋊C8)—21no—
191C4⋊(C11⋊C8)C2311yescharacteristic
192C4⋊(C11⋊C8)C2311yescharacteristic
193C4⋊(C11⋊C8)C2311yescharacteristic
194C4⋊(C11⋊C8)C2311yescharacteristic
195#66867—21no—
196#66867—21no—
197#66867—21no—
198#66867—21no—
199C4×C11⋊C8—21no—
200C4×C11⋊C8—21no—
201C4×C11⋊C8—21no—
202C4×C11⋊C8C2311yescharacteristic
203C4×C11⋊C8C2311yescharacteristic
204C4×C11⋊C8C2311yescharacteristic
205C4×C11⋊C8C2311yescharacteristic
206#17516—111nomaximal, Sylow
207C11×#41—22no—
208C11×#41—22no—
209C11×#41—41no—
210C11×#41—41no—
211C11×#41—41no—
212C11×#41—41no—
213C11×#41—42no—
214C11×#41—42no—
215C2×Q8×C11—21no—
216C2×Q8×C11—21no—
217C2×Q8×C11—22no—
218C2×Q8×C11—41no—
219C2×Q8×C11C22⋊C411yescharacteristic
220C2×Q8×C11C22×C411yescharacteristic
221C2×Q8×C11C22×C411yescharacteristic
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11C22⋊C411yescharacteristic
231C2×D4×C11C22⋊C411yescharacteristic
232C2×D4×C11C22⋊C411yescharacteristic
233C2×D4×C11C22×C411yescharacteristic
234C2×D4×C11C22×C411yescharacteristic
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11C22×C411yescharacteristic
244C22×C4×C11C22×C411yescharacteristic
245C22×C4×C11C22×C411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4C22⋊C411yescharacteristic
267C11×C4⋊C4C22⋊C411yescharacteristic
268C11×C4⋊C4C22⋊C411yescharacteristic
269C11×C4⋊C4C22⋊C411yescharacteristic
270C11×C4⋊C4C22⋊C411yescharacteristic
271C11×C4⋊C4C22⋊C411yescharacteristic
272C11×C4⋊C4C22×C411yescharacteristic
273C11×C4⋊C4C22×C411yescharacteristic
274C11×C4⋊C4C22×C411yescharacteristic
275C11×C4⋊C4C22×C411yescharacteristic
276C11×C22⋊C4—21no—
277C11×C22⋊C4—21no—
278C11×C22⋊C4—21no—
279C11×C22⋊C4—21no—
280C11×C22⋊C4—21no—
281C11×C22⋊C4—21no—
282C11×C22⋊C4—21no—
283C11×C22⋊C4—21no—
284C11×C22⋊C4—21no—
285C11×C22⋊C4—21no—
286C11×C22⋊C4—21no—
287C11×C22⋊C4—21no—
288C11×C22⋊C4—21no—
289C11×C22⋊C4—21no—
290C11×C22⋊C4—21no—
291C11×C22⋊C4—21no—
292C11×C22⋊C4C22⋊C411yescharacteristic
293C11×C22⋊C4C22⋊C411yescharacteristic
294C11×C22⋊C4C22⋊C411yescharacteristic
295C11×C22⋊C4C22⋊C411yescharacteristic
296C11×C22⋊C4C22⋊C411yescharacteristic
297C11×C22⋊C4C22⋊C411yescharacteristic
298C42×C11—21no—
299C42×C11—21no—
300C42×C11—21no—
301C42×C11—21no—
302C42×C11—21no—
303C42×C11—21no—
304C42×C11—21no—
305C42×C11—21no—
306C42×C11C22×C411yescharacteristic
307C42×C11C22×C411yescharacteristic
308C42×C11C22×C411yescharacteristic
309C42×C11C2×D411yescharacteristic
310C42×C11C2×D411yescharacteristic
311C42×C11C2×D411yescharacteristic
312C42×C11C2×D411yescharacteristic
313C42×C11C2×D411yescharacteristic
314C42×C11C2×D411yescharacteristic
315C42×C11C2411yescharacteristic
316#4318—42no—
317#4318—42no—
318#4318—42no—
319C2×C11⋊C8—21no—
320C2×C11⋊C8—21no—
321C2×C11⋊C8—21no—
322C2×C11⋊C8—21no—
323C2×C11⋊C8—21no—
324C2×C11⋊C8—21no—
325C2×C11⋊C8—21no—
326C2×C11⋊C8—21no—
327C2×C11⋊C8—42no—
328C2×C11⋊C8—42no—
329#3480D1111yescharacteristic
330#2965—111no—
331#2925—111no—
332#1496—111no—
333#1495—111no—
334#1494—111no—
335#1491—111no—
336#1489—111no—
337#1488—111no—
338#1484—111no—
339#1483—111no—
340#1482—111no—
341#1479—111no—
342#1477—111no—
343#1476—111no—
344C23×C11—21no—
345C23×C11—21no—
346C23×C11C2×C22⋊C411yescharacteristic
347C23×C11C2×C22⋊C411yescharacteristic
348C23×C11C2×C22⋊C411yescharacteristic
349Q8×C11—21no—
350Q8×C11—21no—
351Q8×C11—21no—
352Q8×C11—41no—
353Q8×C11—42no—
354Q8×C11—42no—
355Q8×C11#13112yes—
356D4×C11—21no—
357D4×C11—21no—
358D4×C11—21no—
359D4×C11—21no—
360D4×C11—41no—
361D4×C11—41no—
362D4×C11—41no—
363D4×C11—42no—
364D4×C11—42no—
365D4×C11—42no—
366D4×C11—42no—
367D4×C11—42no—
368D4×C11—81no—
369D4×C11—81no—
370D4×C11—81no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—42no—
393C2×C4×C11—42no—
394C2×C4×C11—42no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—81no—
400C2×C4×C11—81no—
401C2×C4×C11—81no—
402C2×C4×C11C2×C22⋊C411yescharacteristic
403C2×C4×C11C2×C22⋊C411yescharacteristic
404C2×C4×C11C2×C22⋊C411yescharacteristic
405C2×C4×C11C2×C22⋊C411yescharacteristic
406C2×C4×C11C2×C22⋊C411yescharacteristic
407C2×C4×C11C2×C22⋊C411yescharacteristic
408C2×C4×C11C2×C22⋊C411yescharacteristic
409C2×C4×C11C2×C22⋊C411yescharacteristic
410C2×C4×C11C2×C22⋊C411yescharacteristic
411C2×C4×C11C23×C411yescharacteristic
412C2×C4×C11C22×D411yescharacteristic
413C2×C4×C11C22×D411yescharacteristic
414C11⋊C8—22no—
415C11⋊C8—41no—
416C11⋊C8—41no—
417C11⋊C8—41no—
418C11⋊C8—41no—
419C11⋊C8—41no—
420C11⋊C8—41no—
421C11⋊C8—41no—
422#559—21no—
423#559Dic1111yescharacteristic
424#557Dic1111yescharacteristic
425#556—21no—
426#556Dic1111yescharacteristic
427#553—21no—
428#553—21no—
429#553Dic1111yescharacteristic
430#553Dic1111yescharacteristic
431#550Dic1111yescharacteristic
432#548Dic1111yescharacteristic
433#548Dic1111yescharacteristic
434#532—21no—
435#532C2×D1111yescharacteristic
436#529—21no—
437#529—21no—
438#529C2×D1111yescharacteristic
439#529C2×D1111yescharacteristic
440C4×#41—21no—
441C4×#41C2×D1111yescharacteristic
442C4×#41C2×D1111yescharacteristic
443C4×#41C2×D1111yescharacteristic
444C2×C4×Q8C2×D1111yescharacteristic
445#446—221no—
446#436—221no—
447#435—221no—
448#435—221no—
449#433—221no—
450#433—221no—
451#432—111no—
452#432—111no—
453#431—111no—
454#431—111no—
455#431—111no—
456#431—111no—
457#431—111no—
458#423—111no—
459C2×C4⋊C8—111no—
460#408—221no—
461#405—221no—
462C4×M16—111no—
463C4×M16—111no—
464C2×C4×C8—111no—
465Q8⋊C8—111no—
466Q8⋊C8—111no—
467Q8⋊C8—111no—
468Q8⋊C8—111no—
469Q8⋊C8—111no—
470Q8⋊C8—111no—
471Q8⋊C8—111no—
472Q8⋊C8—111no—
473D4⋊C8—111no—
474D4⋊C8—111no—
475D4⋊C8—111no—
476D4⋊C8—111no—
477D4⋊C8—111no—
478D4⋊C8—111no—
479D4⋊C8—111no—
480D4⋊C8—111no—
481C22×C11—21no—
482C22×C11—21no—
483C22×C11—21no—
484C22×C11—21no—
485C22×C11—21no—
486C22×C11—21no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—41no—
491C22×C11—41no—
492C22×C11—41no—
493C22×C11—41no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11C22×C22⋊C411yescharacteristic
497C4×C11—21no—
498C4×C11—21no—
499C4×C11—21no—
500C4×C11—22no—
501C4×C11—21no—
502C4×C11—21no—
503C4×C11—21no—
504C4×C11—21no—
505C4×C11—21no—
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—41no—
509C4×C11—41no—
510C4×C11—41no—
511C4×C11—41no—
512C4×C11—41no—
513C4×C11C2×#13111yescharacteristic
514C4×C11#56811yescharacteristic
515C4×C11#57511yescharacteristic
516C4×C11#57511yescharacteristic
517C2×#41—21no—
518C2×#41C2×Dic1111yescharacteristic
519C2×#41C2×Dic1111yescharacteristic
520C2×#41C22⋊D1111yescharacteristic
521C22×Q8C2×Dic1111yescharacteristic
522C2×M16—221no—
523C2×M16—221no—
524C2×M16—221no—
525C22×C8—221no—
526C22×C8—221no—
527C4⋊Q8—21no—
528C4⋊Q8C2×Dic1111yescharacteristic
529#127—21no—
530#127C2×Dic1111yescharacteristic
531#126—21no—
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#125—21no—
538#125—21no—
539#125C2×Dic1111yescharacteristic
540#125C2×Dic1111yescharacteristic
541#124—21no—
542#124—21no—
543#124—21no—
544#124—21no—
545#124—21no—
546#124C2×Dic1111yescharacteristic
547#124C2×Dic1111yescharacteristic
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552#123—21no—
553#123—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8C2×Dic1111yescharacteristic
557C22⋊Q8C2×Dic1111yescharacteristic
558#121—21no—
559#121—21no—
560#121—21no—
561#121—21no—
562#121—21no—
563#121—21no—
564#121—21no—
565#121C2×Dic1111yescharacteristic
566#121C2×Dic1111yescharacteristic
567#121C2×Dic1111yescharacteristic
568#121C2×Dic1111yescharacteristic
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8C2×Dic1111yescharacteristic
574C4×Q8C2×Dic1111yescharacteristic
575C4×Q8C2×Dic1111yescharacteristic
576C4×Q8C2×Dic1111yescharacteristic
577C4×Q8C2×Dic1111yescharacteristic
578C4×Q8C22⋊D1111yescharacteristic
579C4×Q8C22×D1111yescharacteristic
580C4×Q8C22×D1111yescharacteristic
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4C2×Dic1111yescharacteristic
595C4×D4C2×Dic1111yescharacteristic
596C4×D4C2×Dic1111yescharacteristic
597C4×D4C2×Dic1111yescharacteristic
598C4×D4C2×Dic1111yescharacteristic
599C4×D4C22⋊D1111yescharacteristic
600C4×D4C22⋊D1111yescharacteristic
601C4×D4C22⋊D1111yescharacteristic
602C4×D4C22×D1111yescharacteristic
603C4×D4C22×D1111yescharacteristic
604#117—21no—
605#117—21no—
606#117—21no—
607#117—21no—
608#117C2×Dic1111yescharacteristic
609#117C2×Dic1111yescharacteristic
610#117C22⋊D1111yescharacteristic
611#117C22⋊D1111yescharacteristic
612#117C22⋊D1111yescharacteristic
613C2×C4⋊C4—21no—
614C2×C4⋊C4C2×Dic1111yescharacteristic
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42C22×D1111yescharacteristic
619C2×C42C22×D1111yescharacteristic
620C2×C42C22×D1111yescharacteristic
621C4⋊C8—111no—
622C4⋊C8—111no—
623C4⋊C8—111no—
624C4⋊C8—111no—
625C4⋊C8—221no—
626C4⋊C8—221no—
627C4⋊C8—221no—
628C4⋊C8—221no—
629C4⋊C8—221no—
630C22⋊C8—221no—
631C22⋊C8—221no—
632C22⋊C8—221no—
633C22⋊C8—221no—
634C22⋊C8—221no—
635C22⋊C8—221no—
636C22⋊C8—221no—
637#97—221no—
638#97—221no—
639#97—221no—
640#97—221no—
641C4×C8—111no—
642C4×C8—111no—
643C4×C8—111no—
644C4×C8—111no—
645C4×C8—221no—
646C4×C8—221no—
647C4×C8—221no—
648C2×C11—41no—
649C2×C11—41no—
650C2×C11—41no—
651C2×C11—81no—
652C2×C11—81no—
653C2×C11#288011yescharacteristic
654C2×C11#289611yescharacteristic
655C2×C11#290111yescharacteristic
656#41—22no—
657#41—22no—
658#41—41no—
659#41—41no—
660#41—41no—
661#41—41no—
662#41—42no—
663#41—42no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—22no—
667C2×Q8—41no—
668C2×Q8C22⋊Dic1111yescharacteristic
669C2×Q8C22×Dic1111yescharacteristic
670C2×Q8C22×Dic1111yescharacteristic
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4C22⋊Dic1111yescharacteristic
680C2×D4C22⋊Dic1111yescharacteristic
681C2×D4C22⋊Dic1111yescharacteristic
682C2×D4C22×Dic1111yescharacteristic
683C2×D4C22×Dic1111yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4C22×Dic1111yescharacteristic
693C22×C4C22×Dic1111yescharacteristic
694C22×C4C22×Dic1111yescharacteristic
695C22×C4C2×C22⋊D1111yescharacteristic
696C22×C4C2×C22⋊D1111yescharacteristic
697C22×C4C2×C22⋊D1111yescharacteristic
698C22×C4C2×C22⋊D1111yescharacteristic
699C22×C4C2×C22⋊D1111yescharacteristic
700C22×C4C2×C22⋊D1111yescharacteristic
701M16—442no—
702M16—442no—
703M16—442no—
704C2×C8—221no—
705C2×C8—221no—
706C2×C8—221no—
707C2×C8—221no—
708C2×C8—221no—
709C2×C8—221no—
710C2×C8—221no—
711C2×C8—221no—
712C2×C8—442no—
713C2×C8—442no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4C22⋊Dic1111yescharacteristic
729C4⋊C4C22⋊Dic1111yescharacteristic
730C4⋊C4C22⋊Dic1111yescharacteristic
731C4⋊C4C22⋊Dic1111yescharacteristic
732C4⋊C4C22⋊Dic1111yescharacteristic
733C4⋊C4C22⋊Dic1111yescharacteristic
734C4⋊C4C22×Dic1111yescharacteristic
735C4⋊C4C22×Dic1111yescharacteristic
736C4⋊C4C22×Dic1111yescharacteristic
737C4⋊C4C22×Dic1111yescharacteristic
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4C22⋊Dic1111yescharacteristic
755C22⋊C4C22⋊Dic1111yescharacteristic
756C22⋊C4C22⋊Dic1111yescharacteristic
757C22⋊C4C22⋊Dic1111yescharacteristic
758C22⋊C4C22⋊Dic1111yescharacteristic
759C22⋊C4C22⋊Dic1111yescharacteristic
760C42—21no—
761C42—21no—
762C42—21no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42C22×Dic1111yescharacteristic
769C42C22×Dic1111yescharacteristic
770C42C22×Dic1111yescharacteristic
771C42C2×C22⋊D1111yescharacteristic
772C42C2×C22⋊D1111yescharacteristic
773C42C2×C22⋊D1111yescharacteristic
774C42C2×C22⋊D1111yescharacteristic
775C42C2×C22⋊D1111yescharacteristic
776C42C2×C22⋊D1111yescharacteristic
777C42C23×D1111yescharacteristic
778C11#1751611yescharacteristic, complemented, Sylow
779C23—21no—
780C23—21no—
781C23C2×C22⋊Dic1111yescharacteristic
782C23C2×C22⋊Dic1111yescharacteristic
783C23C2×C22⋊Dic1111yescharacteristic
784Q8—21no—
785Q8—21no—
786Q8—21no—
787Q8—41no—
788Q8—42no—
789Q8—42no—
790Q8#6700112yes—
791D4—21no—
792D4—21no—
793D4—21no—
794D4—21no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—42no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—81no—
804D4—81no—
805D4—81no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4C2×C22⋊Dic1111yescharacteristic
838C2×C4C2×C22⋊Dic1111yescharacteristic
839C2×C4C2×C22⋊Dic1111yescharacteristic
840C2×C4C2×C22⋊Dic1111yescharacteristic
841C2×C4C2×C22⋊Dic1111yescharacteristic
842C2×C4C2×C22⋊Dic1111yescharacteristic
843C2×C4C2×C22⋊Dic1111yescharacteristic
844C2×C4C2×C22⋊Dic1111yescharacteristic
845C2×C4C2×C22⋊Dic1111yescharacteristic
846C2×C4C23×Dic1111yescharacteristic
847C2×C4C22×C22⋊D1111yescharacteristic
848C2×C4C22×C22⋊D1111yescharacteristic
849C8—222no—
850C8—441no—
851C8—441no—
852C8—441no—
853C8—441no—
854C8—441no—
855C8—441no—
856C8—441no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22C22×C22⋊Dic1111yescharacteristic
873C4—21no—
874C4—21no—
875C4—21no—
876C4—22no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4C2×#6700111yescharacteristic
890C4#1062335011yescharacteristic
891C4#1062335311yescharacteristic
892C4#1062335311yescharacteristic
893C2—41no—
894C2—41no—
895C2—41no—
896C2—81no—
897C2—81no—
898C2#1307706511yescharacteristic
899C2#1307713511yescharacteristic
900C2#1307716311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3480C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3480D11
hypocenterC11#17516
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3480

Complements

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

NH ≅ G/Ntype
1. #13077583C2semidirect
2. #13077282C2semidirect
3. #13067085C2semidirect
4. #13067081C2semidirect
5. #13067076C2semidirect
6. #13067063C2semidirect
7. #13067055C2semidirect
8. #13067050C2semidirect
9. #13067033C2semidirect
10. #13067029C2semidirect
11. #13067024C2semidirect
12. #13067011C2semidirect
13. #13067003C2semidirect
14. #13066998C2semidirect
778. C11#17516semidirect

Maximal subgroups

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

subgroupindex
#130775832
#130772822
#130670852
#130670812
#130670762
#130670632
#130670552
#130670502
#130670332
#130670292
#130670242
#130670112
#130670032
#130669982
C11×#34802
#1751611