Finite Group Databasebeta

← #14720819

Subgroups — #14720819

Order 2816.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077741C211yesmaximal, characteristic, complemented
2#13077260C211yesmaximal, characteristic, complemented
3#13067089C211yesmaximal, characteristic, complemented
4#13067081C211yesmaximal, characteristic, complemented
5#13067076C211yesmaximal, characteristic, complemented
6#13067063C211yesmaximal, characteristic, complemented
7#13067050C211yesmaximal, characteristic, complemented
8#13067045C211yesmaximal, characteristic, complemented
9#13067029C211yesmaximal, characteristic, complemented
10#13067024C211yesmaximal, characteristic, complemented
11#13067019C211yesmaximal, characteristic, complemented
12#13067011C211yesmaximal, characteristic, complemented
13#13067003C211yesmaximal, characteristic, complemented
14C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
15C11×#3482C211yesmaximal, characteristic
16C11×#557C411yescharacteristic
17C11×#556—21no—
18C11×#556C411yescharacteristic
19C11×#552—21no—
20C11×#552—21no—
21C11×#552C411yescharacteristic
22C11×#552C411yescharacteristic
23D4×Q8×C11C411yescharacteristic
24C11×#548C411yescharacteristic
25C11×#548C411yescharacteristic
26C11×#547—21no—
27C11×#547C411yescharacteristic
28C11×#533—21no—
29C11×#533C2211yescharacteristic
30C11×#529—21no—
31C11×#529—21no—
32C11×#529C2211yescharacteristic
33C11×#529C2211yescharacteristic
34C4×C11×#41—21no—
35C4×C11×#41C2211yescharacteristic
36C4×C11×#41C2211yescharacteristic
37C2×C4×Q8×C11C2211yescharacteristic
38C2×C4×Q8×C11C2211yescharacteristic
39#10622847—21no—
40#10622637—21no—
41#10622624—21no—
42#10622624—21no—
43D4×C11⋊C8—21no—
44#10622613—21no—
45#10622613—21no—
46#10622612—21no—
47#10622539C2211yescharacteristic
48#10622539C2211yescharacteristic
49#10622538C2211yescharacteristic
50#10622538C2211yescharacteristic
51#10622538C2211yescharacteristic
52#10622538C2211yescharacteristic
53#10622538C2211yescharacteristic
54#10622537C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4⋊(C11⋊C8)C2211yescharacteristic
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
67Q8⋊(C11⋊C8)C2211yescharacteristic
68Q8⋊(C11⋊C8)C2211yescharacteristic
69Q8⋊(C11⋊C8)C2211yescharacteristic
70Q8⋊(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×#41D411yescharacteristic
78C22×Q8×C11C2×C411yescharacteristic
79C22×Q8×C11C2×C411yescharacteristic
80C11×C4⋊Q8—21no—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8C2×C411yescharacteristic
83C11×C4⋊Q8C2×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×#125—21no—
93C11×#125—21no—
94C11×#125—21no—
95C11×#125C2×C411yescharacteristic
96C11×#125C2×C411yescharacteristic
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⋊Q8—21no—
110C11×C22⋊Q8—21no—
111C11×C22⋊Q8—21no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8C2×C411yescharacteristic
115C11×C22⋊Q8C2×C411yescharacteristic
116C11×C22⋊Q8C2×C411yescharacteristic
117C11×C22⋊Q8C2×C411yescharacteristic
118C11×#121—21no—
119C11×#121—21no—
120C11×#121C2×C411yescharacteristic
121C11×#121C2×C411yescharacteristic
122C4×Q8×C11—21no—
123C4×Q8×C11—21no—
124C4×Q8×C11—21no—
125C4×Q8×C11—21no—
126C4×Q8×C11—21no—
127C4×Q8×C11—21no—
128C4×Q8×C11C2×C411yescharacteristic
129C4×Q8×C11C2×C411yescharacteristic
130C4×Q8×C11C2×C411yescharacteristic
131C4×Q8×C11C2×C411yescharacteristic
132C4×Q8×C11C2×C411yescharacteristic
133C4×Q8×C11C2×C411yescharacteristic
134C4×Q8×C11D411yescharacteristic
135C4×Q8×C11C2311yescharacteristic
136C4×Q8×C11C2311yescharacteristic
137C4×Q8×C11C2311yescharacteristic
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×C11C2×C411yescharacteristic
146C4×D4×C11C2×C411yescharacteristic
147C4×D4×C11C2×C411yescharacteristic
148C4×D4×C11C2×C411yescharacteristic
149C4×D4×C11D411yescharacteristic
150C4×D4×C11D411yescharacteristic
151C4×D4×C11D411yescharacteristic
152C4×D4×C11C2311yescharacteristic
153C11×#117—21no—
154C11×#117—21no—
155C11×#117—21no—
156C11×#117—21no—
157C11×#117—21no—
158C11×#117—21no—
159C11×#117—21no—
160C11×#117C2×C411yescharacteristic
161C11×#117D411yescharacteristic
162C11×#117D411yescharacteristic
163C11×#117D411yescharacteristic
164C2×C11×C4⋊C4—21no—
165C2×C11×C4⋊C4—21no—
166C2×C11×C4⋊C4C2×C411yescharacteristic
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—
176C22×C11⋊C8—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)—21no—
192C4⋊(C11⋊C8)—21no—
193C4⋊(C11⋊C8)C2311yescharacteristic
194C4⋊(C11⋊C8)C2311yescharacteristic
195C4⋊(C11⋊C8)C2311yescharacteristic
196C4⋊(C11⋊C8)C2311yescharacteristic
197#66867—21no—
198#66867—21no—
199#66867—21no—
200C4×C11⋊C8—21no—
201C4×C11⋊C8—21no—
202C4×C11⋊C8C2311yescharacteristic
203C4×C11⋊C8C2311yescharacteristic
204C4×C11⋊C8C2311yescharacteristic
205C4×C11⋊C8C2311yescharacteristic
206#17524—111nomaximal, Sylow
207C11×#41—22no—
208C11×#41—42no—
209C11×#41—41no—
210C11×#41—44no—
211C2×Q8×C11—21no—
212C2×Q8×C11—21no—
213C2×Q8×C11—21no—
214C2×Q8×C11—22no—
215C2×Q8×C11—22no—
216C2×Q8×C11—41no—
217C2×Q8×C11—41no—
218C2×Q8×C11C22⋊C411yescharacteristic
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×C11C22⋊C411yescharacteristic
226C2×D4×C11C22⋊C411yescharacteristic
227C2×D4×C11C22⋊C411yescharacteristic
228C2×D4×C11C22×C411yescharacteristic
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11C22×C411yescharacteristic
237C22×C4×C11C22×C411yescharacteristic
238C22×C4×C11C22×C411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
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⋊C4C22⋊C411yescharacteristic
290C11×C22⋊C4C22⋊C411yescharacteristic
291C11×C22⋊C4C22⋊C411yescharacteristic
292C11×C22⋊C4C22⋊C411yescharacteristic
293C11×C22⋊C4C22⋊C411yescharacteristic
294C11×C22⋊C4C22⋊C411yescharacteristic
295C42×C11—21no—
296C42×C11—21no—
297C42×C11—21no—
298C42×C11—21no—
299C42×C11—21no—
300C42×C11—21no—
301C42×C11—21no—
302C42×C11—21no—
303C42×C11—21no—
304C42×C11C22×C411yescharacteristic
305C42×C11C22×C411yescharacteristic
306C42×C11C22×C411yescharacteristic
307C42×C11C2×D411yescharacteristic
308C42×C11C2×D411yescharacteristic
309C42×C11C2×D411yescharacteristic
310C42×C11C2×D411yescharacteristic
311C42×C11C2×D411yescharacteristic
312C42×C11C2×D411yescharacteristic
313C42×C11C2411yescharacteristic
314#4318—42no—
315#4318—81no—
316C2×C11⋊C8—21no—
317C2×C11⋊C8—21no—
318C2×C11⋊C8—21no—
319C2×C11⋊C8—21no—
320C2×C11⋊C8—21no—
321C2×C11⋊C8—21no—
322C2×C11⋊C8—21no—
323C2×C11⋊C8—21no—
324C2×C11⋊C8—42no—
325C2×C11⋊C8—81no—
326C2×C11⋊C8—81no—
327#3482D1111yescharacteristic
328#2990—111no—
329#2922—111no—
330#1497—111no—
331#1495—111no—
332#1494—111no—
333#1491—111no—
334#1488—111no—
335#1487—111no—
336#1483—111no—
337#1482—111no—
338#1481—111no—
339#1479—111no—
340#1477—111no—
341C2×Q8⋊C8—111no—
342C23×C11—21no—
343C23×C11C2×C22⋊C411yescharacteristic
344C23×C11C2×C22⋊C411yescharacteristic
345C23×C11C2×C22⋊C411yescharacteristic
346Q8×C11—21no—
347Q8×C11—21no—
348Q8×C11—21no—
349Q8×C11—21no—
350Q8×C11—21no—
351Q8×C11—41no—
352Q8×C11—42no—
353Q8×C11—42no—
354Q8×C11—42no—
355Q8×C11#13112yes—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—21no—
359D4×C11—21no—
360D4×C11—41no—
361D4×C11—42no—
362D4×C11—42no—
363D4×C11—42no—
364C2×C4×C11—21no—
365C2×C4×C11—22no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—21no—
370C2×C4×C11—21no—
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—41no—
385C2×C4×C11—41no—
386C2×C4×C11—42no—
387C2×C4×C11—42no—
388C2×C4×C11—42no—
389C2×C4×C11—42no—
390C2×C4×C11—42no—
391C2×C4×C11—42no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11C2×C22⋊C411yescharacteristic
395C2×C4×C11C2×C22⋊C411yescharacteristic
396C2×C4×C11C2×C22⋊C411yescharacteristic
397C2×C4×C11C2×C22⋊C411yescharacteristic
398C2×C4×C11C2×C22⋊C411yescharacteristic
399C2×C4×C11C2×C22⋊C411yescharacteristic
400C2×C4×C11C2×C22⋊C411yescharacteristic
401C2×C4×C11C2×C22⋊C411yescharacteristic
402C2×C4×C11C2×C22⋊C411yescharacteristic
403C2×C4×C11C23×C411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C11⋊C8—41no—
407C11⋊C8—41no—
408C11⋊C8—41no—
409C11⋊C8—41no—
410C11⋊C8—41no—
411C11⋊C8—41no—
412C11⋊C8—41no—
413C11⋊C8—41no—
414#557Dic1111yescharacteristic
415#556—21no—
416#556Dic1111yescharacteristic
417#552—21no—
418#552—21no—
419#552Dic1111yescharacteristic
420#552Dic1111yescharacteristic
421D4×Q8Dic1111yescharacteristic
422#548Dic1111yescharacteristic
423#548Dic1111yescharacteristic
424#547—21no—
425#547Dic1111yescharacteristic
426#533—21no—
427#533C2×D1111yescharacteristic
428#529—21no—
429#529—21no—
430#529C2×D1111yescharacteristic
431#529C2×D1111yescharacteristic
432C4×#41—21no—
433C4×#41C2×D1111yescharacteristic
434C4×#41C2×D1111yescharacteristic
435C2×C4×Q8C2×D1111yescharacteristic
436C2×C4×Q8C2×D1111yescharacteristic
437#446—221no—
438#435—221no—
439#435—221no—
440C8×D4—221no—
441#433—221no—
442#433—221no—
443#432—111no—
444#432—111no—
445#431—111no—
446#431—111no—
447#431—111no—
448#431—111no—
449#431—111no—
450#424—221no—
451#423—111no—
452C2×C4⋊C8—111no—
453C2×C4⋊C8—111no—
454#408—221no—
455C4×M16—111no—
456C2×C4×C8—111no—
457Q8⋊C8—111no—
458Q8⋊C8—111no—
459Q8⋊C8—111no—
460Q8⋊C8—111no—
461Q8⋊C8—111no—
462Q8⋊C8—111no—
463Q8⋊C8—111no—
464Q8⋊C8—111no—
465Q8⋊C8—111no—
466Q8⋊C8—111no—
467Q8⋊C8—111no—
468Q8⋊C8—111no—
469D4⋊C8—111no—
470D4⋊C8—111no—
471D4⋊C8—111no—
472D4⋊C8—111no—
473C22×C11—21no—
474C22×C11—21no—
475C22×C11—21no—
476C22×C11—21no—
477C22×C11—21no—
478C22×C11—21no—
479C22×C11—21no—
480C22×C11—21no—
481C22×C11—41no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11#42112yes—
485C22×C11C22×C22⋊C411yescharacteristic
486C4×C11—21no—
487C4×C11—21no—
488C4×C11—21no—
489C4×C11—22no—
490C4×C11—21no—
491C4×C11—21no—
492C4×C11—21no—
493C4×C11—21no—
494C4×C11—21no—
495C4×C11—21no—
496C4×C11—21no—
497C4×C11—41no—
498C4×C11—41no—
499C4×C11—41no—
500C4×C11—41no—
501C4×C11—41no—
502C4×C11—41no—
503C4×C11C2×#13111yescharacteristic
504C4×C11#56811yescharacteristic
505C4×C11#57711yescharacteristic
506C4×C11#57811yescharacteristic
507C2×#41—21no—
508C2×#41C2×Dic1111yescharacteristic
509C2×#41C22⋊D1111yescharacteristic
510C22×Q8C2×Dic1111yescharacteristic
511C22×Q8C2×Dic1111yescharacteristic
512C2×M16—221no—
513C2×M16—221no—
514C22×C8—221no—
515C22×C8—221no—
516C22×C8—221no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519C4⋊Q8C2×Dic1111yescharacteristic
520C4⋊Q8C2×Dic1111yescharacteristic
521#126—21no—
522#126—21no—
523#126—21no—
524#126—21no—
525#126—21no—
526#126—21no—
527#125—21no—
528#125—21no—
529#125—21no—
530#125—21no—
531#125—21no—
532#125C2×Dic1111yescharacteristic
533#125C2×Dic1111yescharacteristic
534#124—21no—
535#124—21no—
536#124C2×Dic1111yescharacteristic
537#124C2×Dic1111yescharacteristic
538#123—21no—
539#123—21no—
540#123—21no—
541#123—21no—
542#123—21no—
543#123—21no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8C2×Dic1111yescharacteristic
552C22⋊Q8C2×Dic1111yescharacteristic
553C22⋊Q8C2×Dic1111yescharacteristic
554C22⋊Q8C2×Dic1111yescharacteristic
555#121—21no—
556#121—21no—
557#121C2×Dic1111yescharacteristic
558#121C2×Dic1111yescharacteristic
559C4×Q8—21no—
560C4×Q8—21no—
561C4×Q8—21no—
562C4×Q8—21no—
563C4×Q8—21no—
564C4×Q8—21no—
565C4×Q8C2×Dic1111yescharacteristic
566C4×Q8C2×Dic1111yescharacteristic
567C4×Q8C2×Dic1111yescharacteristic
568C4×Q8C2×Dic1111yescharacteristic
569C4×Q8C2×Dic1111yescharacteristic
570C4×Q8C2×Dic1111yescharacteristic
571C4×Q8C22⋊D1111yescharacteristic
572C4×Q8C22×D1111yescharacteristic
573C4×Q8C22×D1111yescharacteristic
574C4×Q8C22×D1111yescharacteristic
575C4×D4—21no—
576C4×D4—21no—
577C4×D4—21no—
578C4×D4—21no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4C2×Dic1111yescharacteristic
583C4×D4C2×Dic1111yescharacteristic
584C4×D4C2×Dic1111yescharacteristic
585C4×D4C2×Dic1111yescharacteristic
586C4×D4C22⋊D1111yescharacteristic
587C4×D4C22⋊D1111yescharacteristic
588C4×D4C22⋊D1111yescharacteristic
589C4×D4C22×D1111yescharacteristic
590#117—21no—
591#117—21no—
592#117—21no—
593#117—21no—
594#117—21no—
595#117—21no—
596#117—21no—
597#117C2×Dic1111yescharacteristic
598#117C22⋊D1111yescharacteristic
599#117C22⋊D1111yescharacteristic
600#117C22⋊D1111yescharacteristic
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4C2×Dic1111yescharacteristic
604C2×C4⋊C4C2×Dic1111yescharacteristic
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42C22×D1111yescharacteristic
609C2×C42C22×D1111yescharacteristic
610C2×C42C22×D1111yescharacteristic
611C4⋊C8—111no—
612C4⋊C8—111no—
613C4⋊C8—111no—
614C4⋊C8—111no—
615C4⋊C8—221no—
616C4⋊C8—221no—
617C4⋊C8—221no—
618C4⋊C8—221no—
619C4⋊C8—221no—
620C4⋊C8—221no—
621C4⋊C8—221no—
622C22⋊C8—221no—
623C22⋊C8—221no—
624C22⋊C8—221no—
625C22⋊C8—221no—
626C22⋊C8—221no—
627C22⋊C8—221no—
628C22⋊C8—221no—
629#97—221no—
630#97—221no—
631#97—221no—
632C4×C8—111no—
633C4×C8—111no—
634C4×C8—111no—
635C4×C8—111no—
636C4×C8—221no—
637C4×C8—221no—
638C2×C11—22no—
639C2×C11—41no—
640C2×C11—41no—
641C2×C11—81no—
642C2×C11#288011yescharacteristic
643C2×C11#289811yescharacteristic
644C2×C11C2×#42111yescharacteristic
645#41—22no—
646#41—42no—
647#41—41no—
648#41—44no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—22no—
653C2×Q8—22no—
654C2×Q8—41no—
655C2×Q8—41no—
656C2×Q8C22⋊Dic1111yescharacteristic
657C2×Q8C22×Dic1111yescharacteristic
658C2×Q8C22×Dic1111yescharacteristic
659C2×Q8C22×Dic1111yescharacteristic
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4C22⋊Dic1111yescharacteristic
664C2×D4C22⋊Dic1111yescharacteristic
665C2×D4C22⋊Dic1111yescharacteristic
666C2×D4C22×Dic1111yescharacteristic
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4C22×Dic1111yescharacteristic
675C22×C4C22×Dic1111yescharacteristic
676C22×C4C22×Dic1111yescharacteristic
677C22×C4C2×C22⋊D1111yescharacteristic
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C2×C22⋊D1111yescharacteristic
683M16—442no—
684M16—881no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—442no—
694C2×C8—881no—
695C2×C8—881no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4C22⋊Dic1111yescharacteristic
718C4⋊C4C22⋊Dic1111yescharacteristic
719C4⋊C4C22⋊Dic1111yescharacteristic
720C4⋊C4C22⋊Dic1111yescharacteristic
721C4⋊C4C22⋊Dic1111yescharacteristic
722C4⋊C4C22⋊Dic1111yescharacteristic
723C4⋊C4C22×Dic1111yescharacteristic
724C4⋊C4C22×Dic1111yescharacteristic
725C4⋊C4C22×Dic1111yescharacteristic
726C4⋊C4C22×Dic1111yescharacteristic
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4C22⋊Dic1111yescharacteristic
741C22⋊C4C22⋊Dic1111yescharacteristic
742C22⋊C4C22⋊Dic1111yescharacteristic
743C22⋊C4C22⋊Dic1111yescharacteristic
744C22⋊C4C22⋊Dic1111yescharacteristic
745C22⋊C4C22⋊Dic1111yescharacteristic
746C42—21no—
747C42—21no—
748C42—21no—
749C42—21no—
750C42—21no—
751C42—21no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42C22×Dic1111yescharacteristic
756C42C22×Dic1111yescharacteristic
757C42C22×Dic1111yescharacteristic
758C42C2×C22⋊D1111yescharacteristic
759C42C2×C22⋊D1111yescharacteristic
760C42C2×C22⋊D1111yescharacteristic
761C42C2×C22⋊D1111yescharacteristic
762C42C2×C22⋊D1111yescharacteristic
763C42C2×C22⋊D1111yescharacteristic
764C42C23×D1111yescharacteristic
765C11#1752411yescharacteristic, complemented, Sylow
766C23—21no—
767C23C2×C22⋊Dic1111yescharacteristic
768C23C2×C22⋊Dic1111yescharacteristic
769C23C2×C22⋊Dic1111yescharacteristic
770Q8—21no—
771Q8—21no—
772Q8—21no—
773Q8—21no—
774Q8—21no—
775Q8—41no—
776Q8—42no—
777Q8—42no—
778Q8—42no—
779Q8#6700112yes—
780D4—22no—
781D4—22no—
782D4—21no—
783D4—21no—
784D4—41no—
785D4—42no—
786D4—42no—
787D4—42no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4C2×C22⋊Dic1111yescharacteristic
819C2×C4C2×C22⋊Dic1111yescharacteristic
820C2×C4C2×C22⋊Dic1111yescharacteristic
821C2×C4C2×C22⋊Dic1111yescharacteristic
822C2×C4C2×C22⋊Dic1111yescharacteristic
823C2×C4C2×C22⋊Dic1111yescharacteristic
824C2×C4C2×C22⋊Dic1111yescharacteristic
825C2×C4C2×C22⋊Dic1111yescharacteristic
826C2×C4C2×C22⋊Dic1111yescharacteristic
827C2×C4C23×Dic1111yescharacteristic
828C2×C4C22×C22⋊D1111yescharacteristic
829C2×C4C22×C22⋊D1111yescharacteristic
830C8—441no—
831C8—441no—
832C8—441no—
833C8—441no—
834C8—441no—
835C8—441no—
836C8—441no—
837C8—441no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22#1062284912yes—
850C22C22×C22⋊Dic1111yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—22no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4C2×#6700111yescharacteristic
869C4#1062335011yescharacteristic
870C4#1062336811yescharacteristic
871C4#1062336911yescharacteristic
872C2—22no—
873C2—41no—
874C2—41no—
875C2—81no—
876C2#1307706511yescharacteristic
877C2#1307714911yescharacteristic
878C2C2×#1062284911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3482C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3482D11
hypocenterC11#17524
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #13077741C2semidirect
2. #13077260C2semidirect
3. #13067089C2semidirect
4. #13067081C2semidirect
5. #13067076C2semidirect
6. #13067063C2semidirect
7. #13067050C2semidirect
8. #13067045C2semidirect
9. #13067029C2semidirect
10. #13067024C2semidirect
11. #13067019C2semidirect
12. #13067011C2semidirect
13. #13067003C2semidirect
14. C2×Q8⋊(C11⋊C8)C2semidirect
765. C11#17524semidirect

Maximal subgroups

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

subgroupindex
#130777412
#130772602
#130670892
#130670812
#130670762
#130670632
#130670502
#130670452
#130670292
#130670242
#130670192
#130670112
#130670032
C2×Q8⋊(C11⋊C8)2
C11×#34822
#1752411