Finite Group Databasebeta

← #14909611

Subgroups — #14909611

Order 2816.

616 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 127 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
1#13078259C212yesmaximal, complemented
2#13070810C212yesmaximal, complemented
3#13070805C212yesmaximal, complemented
4#13070717C212yesmaximal, complemented
5#13070702C211yesmaximal, characteristic, complemented
6#13070529C212yesmaximal, complemented
7#13070526C212yesmaximal, complemented
8#13070229C211yesmaximal, characteristic, complemented
9C11×#2215C211yesmaximal, characteristic, complemented
10C2×D8×D11C2212yescomplemented
11C2×#66954C2211yescharacteristic
12#10623138—22no—
13C2×C11×D16C2211yescharacteristic
14C22×C11×C16C2211yescharacteristic, complemented
15C11×#466C2212yescomplemented
16#10622770C2212yes—
17C2×#66890C2212yes—
18#10622728C2212yescomplemented
19C2×#66876C2211yescharacteristic, complemented
20#10622652—22no—
21C2×D176C2211yescharacteristic
22#10622496C2212yes—
23#10622493C2212yescomplemented
24#10622395—22no—
25#10622383—22no—
26C11×#366C2211yescharacteristic, complemented
27C11×#357C2212yescomplemented
28#10622200C2212yescomplemented
29#10622147C2212yescomplemented
30(C2×D11)⋊C16C2212yescomplemented
31(C2×D11)⋊C16C2212yescomplemented
32#10622142C2211yescharacteristic, complemented
33#10622129C2212yescomplemented
34#10622128C2212yescomplemented
35C2×D4×D11—22no—
36C2×#4339D411yescharacteristic
37C2×C11×D8C2312yes—
38C22×C8×C11C2311yescharacteristic
39C11×#121—22no—
40#66993—42no—
41#66991—22no—
42#66990—42no—
43C2×#4323—22no—
44#66983—22no—
45C2×#4318D411yescharacteristic
46D8×D11—42no—
47D8×D11—42no—
48C2×D88C2312yes—
49#66954—41no—
50#66954—41no—
51C2×#4313D412yes—
52C2×C8×D11C2312yes—
53#66948—22no—
54#66945—22no—
55#66938—42no—
56#66935—42no—
57C11×D16—41no—
58C2×C11×C16—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#66872—22no—
71D176—41no—
72#33765—111nomaximal, Sylow
73C23×D11—42no—
74C2×D4×C11—22no—
75C2×D4×C11—42no—
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11D812yes—
81D4×D11—44no—
82D4×D11—44no—
83#4339—41no—
84#4339—41no—
85C2×D44—22no—
86C2×D44—42no—
87C2×D44D811yescharacteristic
88C2×C4×D11C2×D412yes—
89C2×Dic22D811yescharacteristic
90C11×D8—22no—
91C11×D8—22no—
92C2×C8×C11—21no—
93C2×C8×C11—21no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4—22no—
97C11×C22⋊C4—42no—
98C22⋊Dic11—42no—
99#4323—44no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103C4⋊Dic11—22no—
104C4×Dic11—42no—
105#4318—41no—
106C2×C11⋊C8C2×D412yes—
107D88—22no—
108D88—22no—
109#4313—42no—
110C8×D11—22no—
111C8×D11—22no—
112C11×C16—21no—
113C11×C16—21no—
114C11⋊C16—22no—
115#3058—112no—
116#2234—112no—
117#2234—112no—
118#2218—112no—
119#2215—111no—
120#2215D1111yescharacteristic, complemented
121#2184—112no—
122#2184—112no—
123#2113—111no—
124C23×C11—42no—
125C23×C11C2×D811yescharacteristic
126C22×D11—42no—
127C22×D11—84no—
128C22×D11—162no—
129C22×D11—162no—
130C22×D11C2×D812yes—
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—162no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—42no—
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C22⋊D11—42no—
140C22⋊D11—84no—
141C22⋊D11—162no—
142C22⋊D11—162no—
143C2×Dic11—42no—
144C2×Dic11C2×D812yes—
145D44—41no—
146D44—42no—
147D44—42no—
148D44—162no—
149C4×D11—22no—
150C4×D11—22no—
151Dic22—41no—
152C8×C11—21no—
153C8×C11H(5,𝔽2)11yescharacteristic
154C8×C11H(5,𝔽2)11yescharacteristic
155C11⋊C8—22no—
156C22×D8—112no—
157C2×#131—111no—
158#535—222no—
159C2×D16—112no—
160C2×D16—111no—
161C2×D16C2×D1111yescharacteristic
162C2×M32—111no—
163C22×C16C2×D1111yescharacteristic, complemented
164#469—222no—
165#469—222no—
166#466—112no—
167#466—112no—
168#466—112no—
169#466C2×D1112yescomplemented
170#427—112no—
171#418—222no—
172#367—112no—
173#366—111no—
174#366C2×D1111yescharacteristic, complemented
175#357—112no—
176#357—112no—
177#357—112no—
178#357C2×D1112yescomplemented
179C22⋊C16—112no—
180C22⋊C16—112no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—82no—
185C22×C11—82no—
186C22×C11—82no—
187C22×C11C22×D811yescharacteristic
188C2×D11—22no—
189C2×D11—22no—
190C2×D11—22no—
191C2×D11—82no—
192C2×D11—82no—
193C2×D11—82no—
194C2×D11—168no—
195C4×C11—21no—
196C4×C11—82no—
197C4×C11#53411yescharacteristic
198C4×C11#57511yescharacteristic
199Dic11—22no—
200Dic11—82no—
201C2×#41—111no—
202C22×D4—222no—
203C2×D8—112no—
204C2×D8—222no—
205C2×D8—442no—
206C2×D8—442no—
207C2×D8C22×D1112yes—
208#131—441no—
209#131—441no—
210C2×M16—111no—
211C2×M16—112no—
212C22×C8—112no—
213C22×C8C22×D1111yescharacteristic
214#127—442no—
215#124—442no—
216#121—22no—
217#121—222no—
218#121—222no—
219#121—222no—
220#120—442no—
221#120—442no—
222#117—222no—
223D16—41no—
224D16—441no—
225D16—442no—
226M32—441no—
227C2×C16—41no—
228C2×C16—112no—
229C2×C16C22×D1111yescharacteristic
230C2×C16C22×D1111yescharacteristic
231#107—112no—
232#107C22×D1112yes—
233#106—222no—
234#102—22no—
235#102—222no—
236#102—222no—
237#102—222no—
238C2×C11—41no—
239C2×C11—162no—
240C2×C11#318611yescharacteristic
241C2×C11#341511yescharacteristic
242C2×C11#341511yescharacteristic
243D11—42no—
244D11—162no—
245C24—442no—
246#41—441no—
247#41—441no—
248C2×Q8—111no—
249C2×D4—22no—
250C2×D4—42no—
251C2×D4—112no—
252C2×D4—111no—
253C2×D4—222no—
254C2×D4—442no—
255C2×D4—442no—
256C2×D4—444no—
257C2×D4—444no—
258C2×D4—442no—
259C2×D4—442no—
260C22×C4—112no—
261C22×C4D4×D1111yescharacteristic
262D8—22no—
263D8—22no—
264D8—222no—
265D8—222no—
266D8—444no—
267M16—442no—
268M16—441no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—112no—
272C2×C8—222no—
273C2×C8—222no—
274C2×C8D4×D1111yescharacteristic
275C2×C8C23×D1111yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—222no—
278C22⋊C4—42no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C22⋊C4—442no—
283C42—442no—
284C16—21no—
285C16—21no—
286C16—222no—
287C11#3376511yescharacteristic, complemented, Sylow
288C23—42no—
289C23—112no—
290C23—442no—
291C23—884no—
292C23—1762no—
293C23—1762no—
294C23D8×D1111yescharacteristic
295Q8—441no—
296D4—42no—
297D4—42no—
298D4—162no—
299D4—441no—
300D4—442no—
301D4—442no—
302D4—442no—
303D4—884no—
304D4—1762no—
305D4—1762no—
306D4—1762no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—112no—
311C2×C4—222no—
312C2×C4—222no—
313C2×C4—442no—
314C2×C4D8×D1111yescharacteristic
315C2×C4C2×D4×D1111yescharacteristic
316C8—21no—
317C8—222no—
318C8#6703711yescharacteristic
319C8#6704211yescharacteristic
320C22—21no—
321C22—21no—
322C22—21no—
323C22—82no—
324C22—82no—
325C22—82no—
326C22—222no—
327C22—222no—
328C22—222no—
329C22—882no—
330C22—882no—
331C22—882no—
332C22—1768no—
333C22C2×D8×D1111yescharacteristic
334C4—21no—
335C4—82no—
336C4—222no—
337C4—882no—
338C4#1062313611yescharacteristic
339C4#1062329911yescharacteristic
340C2—41no—
341C2—162no—
342C2—442no—
343C2—1762no—
344C2#1307936311yescharacteristic
345C2#1308175311yescharacteristic
346C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2215C2
socleC22×C11C22×D8
hypercenter#2215D11
hypocenterC11#33765
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. #13078259C2semidirect
2. #13070810C2semidirect
3. #13070805C2semidirect
4. #13070717C2semidirect
5. #13070702C2semidirect
6. #13070529C2semidirect
7. #13070526C2semidirect
8. #13070229C2semidirect
9. C11×#2215C2semidirect
10. C2×D8×D11C22semidirect
14. C22×C11×C16C22semidirect
15. C11×#466C22semidirect
18. #10622728C22semidirect
19. C2×#66876C22semidirect
23. #10622493C22semidirect
26. C11×#366C22semidirect
27. C11×#357C22semidirect
28. #10622200C22semidirect
29. #10622147C22semidirect
30. (C2×D11)⋊C16C22semidirect
31. (C2×D11)⋊C16C22semidirect
32. #10622142C22semidirect
33. #10622129C22semidirect
34. #10622128C22semidirect
120. #2215D11semidirect
163. C22×C16C2×D11semidirect
169. #466C2×D11semidirect
174. #366C2×D11semidirect
178. #357C2×D11semidirect
287. C11#33765semidirect

Maximal subgroups

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

subgroupindex
#130782592
#130708102
#130708052
#130707172
#130707022
#130705292
#130705262
#130702292
C11×#22152
#3376511