Finite Group Databasebeta

← #14909547

Subgroups — #14909547

Order 2816.

688 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#466C212yesmaximal, complemented
2#13070803C212yesmaximal, complemented
3#13070800C212yesmaximal, complemented
4#13070719C211yesmaximal, characteristic, complemented
5#13070717C212yesmaximal, complemented
6#13070529C212yesmaximal, complemented
7#13070526C212yesmaximal, complemented
8#13070226C211yesmaximal, characteristic, complemented
9C11×#2218C211yesmaximal, characteristic, complemented
10C2×D8×D11C2212yescomplemented
11C22×C8×D11C2211yescharacteristic
12D11×#121—22no—
13C2×C11×D16C2211yescharacteristic, complemented
14C2×C11×M32C2211yescharacteristic, complemented
15C11×#466C2212yescomplemented
16#10622770C2212yes—
17C2×#66890C2212yescomplemented
18#10622728C2212yescomplemented
19C2×#66876C2211yescharacteristic, complemented
20#10622651—22no—
21C2×D176C2211yescharacteristic, complemented
22#10622496C2212yes—
23D11×#107C2212yescomplemented
24#10622388—22no—
25D11×#102—22no—
26C11×#367C2211yescharacteristic, complemented
27C11×#357C2212yescomplemented
28#10622200C2212yescomplemented
29#10622147C2212yescomplemented
30(C2×D11)⋊C16C2212yescomplemented
31(C2×D11)⋊C16C2212yescomplemented
32#10622143C2211yescharacteristic, complemented
33#10622129C2212yescomplemented
34#10622128C2212yescomplemented
35C2×D4×D11—22no—
36C2×D4×D11—42no—
37C22×C4×D11D411yescharacteristic
38C2×C11×D8C2312yes—
39C22×C8×C11C2311yescharacteristic
40C11×#121—22no—
41#66992—42no—
42#66991—22no—
43C2×#4323—22no—
44#66983—22no—
45C22×C11⋊C8D411yescharacteristic
46D8×D11—42no—
47D8×D11—42no—
48C2×D88C2312yes—
49C2×C8×D11—41no—
50C2×C8×D11—41no—
51C2×C8×D11D412yes—
52C2×C8×D11C2312yes—
53#66948—22no—
54C4⋊C4×D11—22no—
55#66937—42no—
56C22⋊C4×D11—42no—
57C11×D16—41no—
58C11×M32—41no—
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2311yescharacteristic
61C11×#107C2312yes—
62C11×#102—22no—
63#66896—22no—
64#66890—42no—
65#66885—22no—
66#66882C2312yes—
67#66876—41no—
68C2×C11⋊C16C2312yes—
69#66873—22no—
70#66871—22no—
71D176—41no—
72#33758—111nomaximal, Sylow
73C23×D11—42no—
74C23×D11D811yescharacteristic
75C2×D4×C11—22no—
76C2×D4×C11—42no—
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—42no—
81C22×Dic11D811yescharacteristic
82D4×D11—44no—
83D4×D11—44no—
84D4×D11—88no—
85C2×D44—22no—
86C2×D44—42no—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×C4×D11—42no—
90C2×C4×D11D812yes—
91C2×C4×D11C2×D412yes—
92C11×D8—22no—
93C11×D8—22no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2411yescharacteristic
98C11×C4⋊C4—22no—
99C11×C22⋊C4—42no—
100C22⋊Dic11—42no—
101#4323—44no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104C4⋊Dic11—22no—
105Dic11⋊C4—42no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8C2×D412yes—
108D88—22no—
109D88—22no—
110C8×D11—22no—
111C8×D11—22no—
112C8×D11—42no—
113C11×C16—21no—
114C11×C16—21no—
115C11⋊C16—22no—
116C2×#466—112no—
117#2233—112no—
118#2233—112no—
119#2218—111no—
120#2218—112no—
121#2218D1111yescharacteristic, complemented
122#2184—112no—
123#2184—112no—
124#2112—111no—
125C23×C11—42no—
126C23×C11C2×D811yescharacteristic
127C22×D11—24no—
128C22×D11—41no—
129C22×D11—42no—
130C22×D11—84no—
131C22×D11—84no—
132C22×D11—84no—
133C22×D11C2×D812yes—
134D4×C11—42no—
135D4×C11—42no—
136D4×C11—84no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—42no—
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C22⋊D11—84no—
143C22⋊D11—84no—
144C22⋊D11—84no—
145C2×Dic11—41no—
146C2×Dic11—42no—
147C2×Dic11C2×D812yes—
148D44—42no—
149D44—42no—
150D44—84no—
151C4×D11—22no—
152C4×D11—22no—
153C4×D11—42no—
154C4×D11—84no—
155C8×C11—21no—
156C8×C11H(5,𝔽2)11yescharacteristic
157C8×C11H(5,𝔽2)11yescharacteristic
158C11⋊C8—22no—
159C22×D8—112no—
160C23×C8—111no—
161C2×#121—222no—
162C2×D16—112no—
163C2×D16—111no—
164C2×D16C2×D1111yescharacteristic, complemented
165C2×M32—111no—
166C2×M32C2×D1111yescharacteristic, complemented
167#466—112no—
168#466—112no—
169#466—112no—
170#466—222no—
171#466—222no—
172#466C2×D1112yescomplemented
173C2×#107—112no—
174C2×#102—222no—
175#367—111no—
176#367—112no—
177#367C2×D1111yescharacteristic, complemented
178#357—112no—
179#357—112no—
180#357—112no—
181#357C2×D1112yescomplemented
182C22⋊C16—112no—
183C22⋊C16—112no—
184C22×C11—22no—
185C22×C11—21no—
186C22×C11—82no—
187C22×C11—82no—
188C22×C11—82no—
189C22×C11C22×D811yescharacteristic
190C2×D11—22no—
191C2×D11—22no—
192C2×D11—44no—
193C2×D11—82no—
194C2×D11—82no—
195C2×D11—82no—
196C2×D11—168no—
197C2×D11#50914yes—
198C4×C11—21no—
199C4×C11—82no—
200C4×C11#53411yescharacteristic
201C4×C11#57511yescharacteristic
202Dic11—22no—
203Dic11—82no—
204C22×D4—222no—
205C22×D4—442no—
206C23×C4—111no—
207C2×D8—112no—
208C2×D8—222no—
209C2×D8—442no—
210C2×D8—442no—
211C2×D8C22×D1112yes—
212C22×C8—111no—
213C22×C8—112no—
214C22×C8—112no—
215C22×C8—441no—
216C22×C8—441no—
217C22×C8C22×D1111yescharacteristic
218#121—22no—
219#121—222no—
220#121—222no—
221#121—222no—
222#121—442no—
223#121—442no—
224C2×C4⋊C4—222no—
225C2×C22⋊C4—442no—
226D16—41no—
227D16—441no—
228D16—442no—
229M32—41no—
230M32—441no—
231C2×C16—112no—
232C2×C16C22×D1111yescharacteristic
233C2×C16C22×D1111yescharacteristic
234#107—112no—
235#107—222no—
236#107C22×D1112yes—
237#102—22no—
238#102—222no—
239#102—222no—
240#102—222no—
241C2×C11—41no—
242C2×C11—162no—
243C2×C11#318611yescharacteristic
244C2×C11C2×#50912yes—
245D11—24no—
246D11—162no—
247C24—111no—
248C24—442no—
249C2×D4—22no—
250C2×D4—42no—
251C2×D4—222no—
252C2×D4—442no—
253C2×D4—442no—
254C2×D4—444no—
255C2×D4—444no—
256C2×D4—442no—
257C2×D4—442no—
258C2×D4—888no—
259C22×C4—111no—
260C22×C4—112no—
261C22×C4—112no—
262C22×C4—441no—
263C22×C4—441no—
264C22×C4—442no—
265C22×C4D4×D1111yescharacteristic
266D8—22no—
267D8—22no—
268D8—222no—
269D8—222no—
270D8—444no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—112no—
274C2×C8—222no—
275C2×C8—222no—
276C2×C8—442no—
277C2×C8—441no—
278C2×C8D4×D1111yescharacteristic
279C2×C8C23×D1111yescharacteristic
280C4⋊C4—22no—
281C4⋊C4—222no—
282C4⋊C4—442no—
283C22⋊C4—42no—
284C22⋊C4—442no—
285C22⋊C4—442no—
286C22⋊C4—442no—
287C16—21no—
288C16—21no—
289C16—222no—
290C11#3375811yescharacteristic, complemented, Sylow
291C23—42no—
292C23—112no—
293C23—224no—
294C23—441no—
295C23—442no—
296C23—884no—
297C23—884no—
298C23—884no—
299C23D8×D1111yescharacteristic
300D4—42no—
301D4—42no—
302D4—84no—
303D4—442no—
304D4—442no—
305D4—884no—
306D4—884no—
307D4—884no—
308D4—884no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—112no—
313C2×C4—222no—
314C2×C4—222no—
315C2×C4—442no—
316C2×C4—441no—
317C2×C4—442no—
318C2×C4—884no—
319C2×C4D8×D1111yescharacteristic
320C2×C4C2×D4×D1111yescharacteristic
321C8—21no—
322C8—222no—
323C8#6703711yescharacteristic
324C8#6704211yescharacteristic
325C22—21no—
326C22—22no—
327C22—82no—
328C22—82no—
329C22—82no—
330C22—114no—
331C22—222no—
332C22—222no—
333C22—444no—
334C22—882no—
335C22—882no—
336C22—882no—
337C22—1768no—
338C22C2×D8×D1111yescharacteristic
339C4—21no—
340C4—82no—
341C4—222no—
342C4—882no—
343C4#1062313611yescharacteristic
344C4#1062329911yescharacteristic
345C2—41no—
346C2—162no—
347C2—224no—
348C2—1762no—
349C2#1307936311yescharacteristic
350C2D11×#50912yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2218C2
socleC22×C11C22×D8
hypercenter#2218D11
hypocenterC11#33758
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2218

Complements

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

NH ≅ G/Ntype
1. D11×#466C2semidirect
2. #13070803C2semidirect
3. #13070800C2semidirect
4. #13070719C2semidirect
5. #13070717C2semidirect
6. #13070529C2semidirect
7. #13070526C2semidirect
8. #13070226C2semidirect
9. C11×#2218C2semidirect
10. C2×D8×D11C22semidirect
13. C2×C11×D16C22semidirect
14. C2×C11×M32C22semidirect
15. C11×#466C22semidirect
17. C2×#66890C22semidirect
18. #10622728C22semidirect
19. C2×#66876C22semidirect
21. C2×D176C22semidirect
23. D11×#107C22semidirect
26. C11×#367C22semidirect
27. C11×#357C22semidirect
28. #10622200C22semidirect
29. #10622147C22semidirect
30. (C2×D11)⋊C16C22semidirect
31. (C2×D11)⋊C16C22semidirect
32. #10622143C22semidirect
33. #10622129C22semidirect
34. #10622128C22semidirect
121. #2218D11semidirect
164. C2×D16C2×D11semidirect
166. C2×M32C2×D11semidirect
172. #466C2×D11semidirect
177. #367C2×D11semidirect
181. #357C2×D11semidirect
290. C11#33758semidirect

Maximal subgroups

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

subgroupindex
D11×#4662
#130708032
#130708002
#130707192
#130707172
#130705292
#130705262
#130702262
C11×#22182
#3375811