Finite Group Databasebeta

← #14775849

Subgroups — #14775849

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078404C211yesmaximal, characteristic
2#13077563C211yesmaximal, characteristic, complemented
3#13077184C211yesmaximal, characteristic
4#13069593C211yesmaximal, characteristic, complemented
5#13069391C211yesmaximal, characteristic, complemented
6#13069368C212yesmaximal, complemented
7#13069218C212yesmaximal, complemented
8#13068889C212yesmaximal
9#13068469C211yesmaximal, characteristic, complemented
10#13068461C212yesmaximal
11C4×C11×#104C211yesmaximal, characteristic
12C4×C11×#41C2211yescharacteristic
13C2×#67001C2212yes—
14#10623001C2211yescharacteristic
15C2×C11×#104C2211yescharacteristic
16C2×C11×#104C2211yescharacteristic
17C4×C11×M16C2211yescharacteristic
18C43×C11C2211yescharacteristic
19#10622846C2212yes—
20C2×#66886C2212yes—
21#10622735C2212yes—
22#10622732C2212yes—
23#10622635C412yescomplemented
24#10622634C411yescharacteristic, complemented
25#10622633C411yescharacteristic, complemented
26#10622622C412yescomplemented
27#10622621C411yescharacteristic, complemented
28#10622620C411yescharacteristic, complemented
29#10622612—22no—
30#10622612C2212yes—
31#10622611C2212yes—
32#10622537—21no—
33#10622537C2211yescharacteristic
34C2×C4⋊(C11⋊C8)—21no—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×#66867C2212yes—
38#10622314—22no—
39#10622292—21no—
40C8×Dic22—21no—
41C11×#339C2211yescharacteristic
42C11×#339C2211yescharacteristic
43#10622196C2212yes—
44#10622162C2212yes—
45#10622161C2212yes—
46#10622161C2212yes—
47C2×C11×#41C2311yescharacteristic
48C2×C11×M16C2311yescharacteristic
49C2×C11×M16C2311yescharacteristic
50C4×Q8×C11C2×C411yescharacteristic
51C4×Q8×C11C2×C411yescharacteristic
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11C2×C411yescharacteristic
55C4×D4×C11C2×C411yescharacteristic
56C11×#117—21no—
57C11×#117C2311yescharacteristic
58C2×C42×C11—21no—
59C2×C42×C11—21no—
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C42×C11C2311yescharacteristic
64#67001—24no—
65#67001—42no—
66#66979C2312yes—
67#66977—21no—
68#66977—21no—
69C2×#4318—22no—
70C2×#4318C2312yes—
71C22×C11⋊C8—22no—
72C22×C11⋊C8C2312yes—
73C22×C11⋊C8C2312yes—
74#66923C2×C412yes—
75#66922C2×C411yescharacteristic
76#66922C2×C411yescharacteristic
77C4×Dic22—21no—
78C4×Dic22—21no—
79C11×#104—22no—
80C11×#104Q814yescomplemented
81C11×#97—21no—
82C4×C8×C11—21no—
83#66899C2×C412yes—
84#66899C2×C412yes—
85#66896C2×C412yes—
86#66896C2×C412yes—
87#66886—42no—
88#66879—22no—
89Dic11⋊C8—22no—
90Dic11⋊C8—22no—
91C8×Dic11—22no—
92#66872C2×C412yes—
93#66872C2×C412yes—
94#66871C2×C412yes—
95#66871C2×C412yes—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—22no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)C2×C411yescharacteristic
101C4⋊(C11⋊C8)C2×C411yescharacteristic
102C4⋊(C11⋊C8)C2×C412yes—
103C4⋊(C11⋊C8)D411yescharacteristic
104C4⋊(C11⋊C8)D411yescharacteristic
105C4⋊(C11⋊C8)D412yes—
106#66867—42no—
107#22983—111nomaximal, Sylow
108C11×#41—21no—
109C11×#41—21no—
110C11×#41C2×Q812yes—
111C11×#41#4112yes—
112C2×Q8×C11C22×C411yescharacteristic
113C2×D4×C11—21no—
114C2×D4×C11C22×C411yescharacteristic
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C2×Dic22—21no—
124C2×Dic22—21no—
125C11×M16—21no—
126C11×M16—21no—
127C11×M16—21no—
128C11×M16C2×Q812yes—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4C22×C411yescharacteristic
134C11×C4⋊C4C22×C411yescharacteristic
135C11×C22⋊C4—21no—
136C11×C22⋊C4—21no—
137C11×C22⋊C4—21no—
138C42×C11—21no—
139C42×C11—21no—
140C42×C11—21no—
141C42×C11—21no—
142C42×C11—21no—
143C42×C11—21no—
144C42×C11—42no—
145C42×C11—42no—
146C42×C11C22×C411yescharacteristic
147C42×C11C22×C411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11C2×Q812yes—
151C22⋊Dic11—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11C22×C412yes—
155C4⋊Dic11C22×C412yes—
156Dic11⋊C4—22no—
157Dic11⋊C4—22no—
158C4×Dic11—22no—
159#4318—22no—
160#4318—22no—
161#4318—44no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—44no—
168C2×C11⋊C8C22×C412yes—
169C2×C11⋊C8C22×C412yes—
170C2×C11⋊C8C2×D412yes—
171C2×C11⋊C8C2×D412yes—
172#3076—111no—
173#2962—111no—
174#2906—111no—
175#1994—111no—
176#1950—111no—
177#1946—112no—
178#1922—112no—
179#1866—112no—
180#1767—111no—
181#1765—112no—
182C4×#104D1111yescharacteristic
183C23×C11—21no—
184C23×C11C2×#4111yescharacteristic
185Q8×C11—21no—
186Q8×C11C4×Q812yes—
187D4×C11—22no—
188D4×C11—22no—
189D4×C11—21no—
190D4×C11C4×Q812yes—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—81no—
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11C4×D411yescharacteristic
208C2×C4×C11C4×D411yescharacteristic
209C2×C4×C11C4×D411yescharacteristic
210C2×C4×C11C23×C411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×Q811yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C2×C4×C112−1+411yescharacteristic
216C2×Dic11—22no—
217C2×Dic11—22no—
218Dic22—42no—
219Dic22—81no—
220C8×C11—22no—
221C8×C11—41no—
222C11⋊C8—22no—
223C11⋊C8—22no—
224C11⋊C8—22no—
225C11⋊C8—22no—
226C11⋊C8—42no—
227C2×#131—112no—
228#533—111no—
229C4×#41C2×D1111yescharacteristic
230#479—112no—
231#478—112no—
232#477—111no—
233#476—111no—
234#475—111no—
235#474—111no—
236#446—221no—
237#446—222no—
238C8×Q8—221no—
239C2×#108—112no—
240#427—112no—
241#424—112no—
242#424—112no—
243#424—222no—
244#423—111no—
245#423—221no—
246C2×C4⋊C8—111no—
247C2×C4⋊C8—111no—
248C2×C4⋊C8—221no—
249C2×#104C2×D1111yescharacteristic
250C2×#104C2×D1111yescharacteristic
251#416—112no—
252#405—112no—
253C4×M16C2×D1111yescharacteristic
254C2×#97—112no—
255C43C2×D1111yescharacteristic
256#341—112no—
257#339—112no—
258#339—112no—
259#339C2×D1111yescharacteristic
260#339C2×D1111yescharacteristic
261#336—112no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—22no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11C2×C4×D411yescharacteristic
268C22×C11#55211yescharacteristic
269C22×C11#55411yescharacteristic
270C4×C11—22no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—41no—
277C4×C11—41no—
278C4×C11#44412yes—
279C4×C11C2×C4×Q811yescharacteristic
280C4×C11#52011yescharacteristic
281C4×C11#54611yescharacteristic
282C4×C11D4×Q811yescharacteristic
283Dic11—42no—
284Dic11—42no—
285C2×#41C22×D1111yescharacteristic
286#131—224no—
287#131—442no—
288C2×M16—112no—
289C2×M16—222no—
290C2×M16C22×D1111yescharacteristic
291C2×M16C22×D1111yescharacteristic
292C22×C8—112no—
293C22×C8—112no—
294C22×C8—222no—
295C4⋊Q8—111no—
296C4⋊Q8—111no—
297#125—112no—
298C22⋊Q8—221no—
299C22⋊Q8—221no—
300C4×Q8—221no—
301C4×Q8—221no—
302C4×Q8C4×D1111yescharacteristic
303C4×Q8C4×D1111yescharacteristic
304C4×D4—21no—
305C4×D4—21no—
306C4×D4C4×D1111yescharacteristic
307C4×D4C4×D1111yescharacteristic
308#117—21no—
309#117—112no—
310#117C22×D1111yescharacteristic
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42C22×D1111yescharacteristic
315C2×C42C22×D1111yescharacteristic
316C2×C42C22×D1111yescharacteristic
317#108—442no—
318#107—112no—
319#107—112no—
320#106—112no—
321#106—112no—
322C4⋊C8—111no—
323C4⋊C8—111no—
324C4⋊C8—112no—
325C4⋊C8—111no—
326C4⋊C8—111no—
327C4⋊C8—112no—
328C4⋊C8—222no—
329C4⋊C8—222no—
330C4⋊C8—222no—
331C4⋊C8—222no—
332C4⋊C8—221no—
333C4⋊C8—221no—
334#104—22no—
335#104Dic2214yescomplemented
336#103—112no—
337#103—112no—
338#102—112no—
339#102—112no—
340#97—21no—
341#97—222no—
342#97—442no—
343C4×C8—21no—
344C4×C8—222no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11—42no—
348C2×C11#236011yescharacteristic
349C2×C11C2×#44411yescharacteristic
350C2×C11#295611yescharacteristic
351#41—21no—
352#41—21no—
353#41C2×Dic2212yes—
354#41#433912yes—
355C2×Q8—221no—
356C2×Q8—221no—
357C2×Q8C2×C4×D1111yescharacteristic
358C2×D4—21no—
359C2×D4C2×C4×D1111yescharacteristic
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4#434111yescharacteristic
366C22×C4#434111yescharacteristic
367C22×C4C23×D1111yescharacteristic
368M16—21no—
369M16—21no—
370M16—21no—
371M16—222no—
372M16—222no—
373M16—444no—
374M16C2×Dic2212yes—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—112no—
378C2×C8—112no—
379C2×C8—112no—
380C2×C8—112no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—444no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—112no—
390C4⋊C4—112no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4C2×C4×D1111yescharacteristic
396C4⋊C4C2×C4×D1111yescharacteristic
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—222no—
401C42—21no—
402C42—21no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42—21no—
407C42—42no—
408C42—42no—
409C42—222no—
410C42C2×Dic2212yes—
411C42C2×C4×D1111yescharacteristic
412C42C2×C4×D1111yescharacteristic
413C42D4×D1111yescharacteristic
414C42D4×D1111yescharacteristic
415C11#2298311yescharacteristic, complemented, Sylow
416C23—21no—
417C23C2×#434111yescharacteristic
418Q8—21no—
419Q8—442no—
420Q8—881no—
421Q8C4×Dic2212yes—
422D4—22no—
423D4—22no—
424D4—21no—
425D4C4×Dic2212yes—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—81no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4(C22⋊D11)⋊C411yescharacteristic
444C2×C4(C22⋊D11)⋊C411yescharacteristic
445C2×C4(C22⋊D11)⋊C411yescharacteristic
446C2×C4(C22⋊D11)⋊C411yescharacteristic
447C2×C4C22×Dic2211yescharacteristic
448C2×C4C22×C4×D1111yescharacteristic
449C2×C4C2×#433911yescharacteristic
450C2×C4C2×D4×D1111yescharacteristic
451C2×C4#6704211yescharacteristic
452C2×C4#6704311yescharacteristic
453C8—22no—
454C8—41no—
455C8—222no—
456C8—222no—
457C8—222no—
458C8—222no—
459C8—442no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22C2×(C22⋊D11)⋊C411yescharacteristic
466C22#1062307211yescharacteristic
467C22#1062307411yescharacteristic
468C4—22no—
469C4—21no—
470C4—21no—
471C4—21no—
472C4—42no—
473C4—42no—
474C4—41no—
475C4—41no—
476C4—442no—
477C4—442no—
478C4#1062243612yes—
479C4C2×C4×Dic2211yescharacteristic
480C4#1062305411yescharacteristic
481C4D4×Dic2211yescharacteristic
482C4#1062308111yescharacteristic
483C2—21no—
484C2—21no—
485C2—42no—
486C2#1307161911yescharacteristic
487C2C2×#1062243611yescharacteristic
488C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#104C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenterC4×#104D11
hypocenterC11#22983
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
2. #13077563C2semidirect
4. #13069593C2semidirect
5. #13069391C2semidirect
6. #13069368C2semidirect
7. #13069218C2semidirect
9. #13068469C2semidirect
23. #10622635C4semidirect
24. #10622634C4semidirect
25. #10622633C4semidirect
26. #10622622C4semidirect
27. #10622621C4semidirect
28. #10622620C4semidirect
80. C11×#104Q8semidirect
335. #104Dic22semidirect
415. C11#22983semidirect

Maximal subgroups

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

subgroupindex
#130784042
#130775632
#130771842
#130695932
#130693912
#130693682
#130692182
#130688892
#130684692
#130684612
C4×C11×#1042
#2298311