Finite Group Databasebeta

← #14910213

Subgroups — #14910213

Order 2816.

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

normal subgroups only

This group has 488 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#13079256C212yesmaximal, complemented
2#13070766C212yesmaximal, complemented
3#13070752C212yesmaximal, complemented
4#13070731C212yesmaximal, complemented
5#13070702C211yesmaximal, characteristic
6#13070680C212yesmaximal, complemented
7#13070674C212yesmaximal, complemented
8#13070374C211yesmaximal, characteristic, complemented
9C11×#2216C211yesmaximal, characteristic, complemented
10#10623174—22no—
11C2×C11×Q32C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C11×#467C2212yes—
14#10622804C2212yes—
15Q16×Dic11C2212yes—
16C2×#66892C2212yes—
17#10622728C2212yes—
18#10622714C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20#10622662—22no—
21C2×D176C2211yescharacteristic
22#10622487C2212yes—
23#10622485C2212yes—
24#10622430—22no—
25#10622408—22no—
26C11×#366C2211yescharacteristic
27C11×#358C2212yes—
28#10622202C2212yes—
29#10622147C2212yes—
30#10622142C2211yescharacteristic
31Dic11⋊C16C2212yes—
32Dic11⋊C16C2212yes—
33#10622129C2212yes—
34#10622127C2212yes—
35C2×C11×Q16C2312yes—
36C22×C8×C11C2311yescharacteristic
37C11×C22⋊Q8—22no—
38#67000—22no—
39Q8×Dic11—22no—
40C2×#4325—22no—
41#66983—22no—
42#66979D411yescharacteristic
43C2×#4318D411yescharacteristic
44C2×D88C2312yes—
45#66951—42no—
46#66950—42no—
47#66946—22no—
48#66941—22no—
49#66938—42no—
50#66936—42no—
51C11×Q32—41no—
52C2×C11×C16—41no—
53C2×C11×C16C2311yescharacteristic
54C2×C11×C16C2311yescharacteristic
55C11×#107C2312yes—
56C11×#103—22no—
57#66899—22no—
58#66892—42no—
59#66885—22no—
60#66882C2312yes—
61#66879D412yes—
62C8×Dic11C2312yes—
63#66876—41no—
64C2×C11⋊C16C2312yes—
65#66873—22no—
66#66871—22no—
67D176—41no—
68#33828—111nomaximal, Sylow
69C2×Q8×C11—22no—
70C22×C4×C11C2×D411yescharacteristic
71C2×C22⋊D11—42no—
72C2×D44—22no—
73C2×C4×D11—42no—
74C2×Dic22—42no—
75C11×Q16—22no—
76C11×Q16—22no—
77C2×C8×C11—21no—
78C2×C8×C11—21no—
79C2×C8×C11C2×D411yescharacteristic
80C2×C8×C11C2411yescharacteristic
81C11×C4⋊C4—22no—
82C11×C4⋊C4—42no—
83C11×C22⋊C4—42no—
84C22⋊Dic11D812yes—
85#4325—44no—
86(C2×D11)⋊C4—42no—
87(C2×D11)⋊C4—42no—
88(C2×D11)⋊C4—42no—
89(C2×D11)⋊C4—42no—
90C4⋊Dic11—22no—
91C4⋊Dic11—42no—
92C4⋊Dic11D811yescharacteristic
93C4⋊Dic11D811yescharacteristic
94Dic11⋊C4—42no—
95C4×Dic11—42no—
96C4×Dic11C2×D412yes—
97#4318—41no—
98C2×C11⋊C8C2×D412yes—
99D88—22no—
100D88—22no—
101C11×C16—21no—
102C11×C16—21no—
103C11⋊C16—22no—
104#3175—112no—
105#2227—112no—
106#2224—112no—
107#2220—112no—
108#2216D1111yescharacteristic, complemented
109#2215—111no—
110#2211—112no—
111#2210—112no—
112#2151—111no—
113C23×C11C2×D811yescharacteristic
114C22×D11—42no—
115Q8×C11—42no—
116Q8×C11—42no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11C2×D811yescharacteristic
122C2×C4×C11C22×D411yescharacteristic
123C22⋊D11—162no—
124C2×Dic11—42no—
125C2×Dic11C2×D812yes—
126C2×Dic11C2×D812yes—
127D44—42no—
128D44—42no—
129C4×D11—162no—
130Dic22—162no—
131C8×C11—21no—
132C8×C11H(5,𝔽2)11yescharacteristic
133C8×C112−1+411yescharacteristic
134C11⋊C8—22no—
135#542—222no—
136C2×Q32C2×D1111yescharacteristic
137C2×SD32—112no—
138C2×D16—111no—
139C2×M32—111no—
140C22×C16C2×D1111yescharacteristic
141#500—112no—
142#495—112no—
143#489—222no—
144#468—222no—
145#467C2×D1112yes—
146#466—112no—
147#440—222no—
148C4×Q16—112no—
149C4×D8—112no—
150#405—111no—
151#366—111no—
152#366—112no—
153#366C2×D1111yescharacteristic
154C4⋊C16—112no—
155C4⋊C16—112no—
156#358—112no—
157#358C2×D1112yes—
158#357—112no—
159#357—112no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11C22×D811yescharacteristic
164C2×D11—82no—
165C2×D11—82no—
166C2×D11—82no—
167C4×C11—21no—
168C4×C11—82no—
169C4×C11—82no—
170C4×C11#53711yescharacteristic
171C4×C11#57511yescharacteristic
172Dic11—22no—
173Dic11—22no—
174Dic11—82no—
175C2×Q16C22×D1112yes—
176C2×SD16—222no—
177C2×D8—112no—
178C2×M16—111no—
179C22×C8C22×D1111yescharacteristic
180C4⋊Q8—222no—
181#126—442no—
182#124—222no—
183#124—442no—
184#123—442no—
185C22⋊Q8—22no—
186C22⋊Q8—442no—
187#121—222no—
188C4×Q8—222no—
189C4×D4—222no—
190#117—111no—
191Q32—41no—
192SD32—442no—
193D16—441no—
194M32—441no—
195C2×C16—41no—
196C2×C16—112no—
197C2×C16C22×D1111yescharacteristic
198C2×C16C22×D1111yescharacteristic
199#107—112no—
200#107—222no—
201#107C22×D1112yes—
202#103—22no—
203#103—222no—
204#102—222no—
205#102—222no—
206#97—112no—
207C4×C8—112no—
208C2×C11—41no—
209C2×C11#324511yescharacteristic
210C2×C11#341511yescharacteristic
211C2×C11#341711yescharacteristic
212D11—162no—
213C2×Q8—22no—
214C2×Q8—442no—
215C2×D4—222no—
216C2×D4—442no—
217C22×C4—442no—
218C22×C4D4×D1111yescharacteristic
219Q16—22no—
220Q16—22no—
221SD16—444no—
222D8—222no—
223D8—222no—
224M16—441no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—112no—
228C2×C8D4×D1111yescharacteristic
229C2×C8C23×D1111yescharacteristic
230C4⋊C4—22no—
231C4⋊C4—42no—
232C4⋊C4—111no—
233C4⋊C4—111no—
234C4⋊C4—222no—
235C4⋊C4—442no—
236C4⋊C4—442no—
237C22⋊C4—42no—
238C22⋊C4—112no—
239C22⋊C4—442no—
240C22⋊C4—442no—
241C22⋊C4—442no—
242C22⋊C4—442no—
243C42—112no—
244C42—442no—
245C16—21no—
246C16—21no—
247C16—222no—
248C11#3382811yescharacteristic, complemented, Sylow
249C23—442no—
250C23D8×D1111yescharacteristic
251Q8—42no—
252Q8—42no—
253Q8—1762no—
254D4—442no—
255D4—442no—
256D4—1762no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—112no—
262C2×C4—112no—
263C2×C4—442no—
264C2×C4—1762no—
265C2×C4D8×D1111yescharacteristic
266C2×C4C2×D4×D1111yescharacteristic
267C8—21no—
268C8—222no—
269C8#6703711yescharacteristic
270C8#6704311yescharacteristic
271C22—21no—
272C22—21no—
273C22—21no—
274C22—882no—
275C22—882no—
276C22—882no—
277C22C2×D8×D1111yescharacteristic
278C4—21no—
279C4—82no—
280C4—82no—
281C4—222no—
282C4—222no—
283C4—882no—
284C4#1062312811yescharacteristic
285C4#1062329911yescharacteristic
286C2—41no—
287C2—1762no—
288C2#1307992211yescharacteristic
289C2#1308175411yescharacteristic
290C2#1308176511yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2216C2
socleC22×C11C22×D8
prime radical#13070702C2
hypercenter#2216D11
hypocenterC11#33828
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2216

Complements

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

NH ≅ G/Ntype
1. #13079256C2semidirect
2. #13070766C2semidirect
3. #13070752C2semidirect
4. #13070731C2semidirect
6. #13070680C2semidirect
7. #13070674C2semidirect
8. #13070374C2semidirect
9. C11×#2216C2semidirect
108. #2216D11semidirect
248. C11#33828semidirect

Maximal subgroups

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

subgroupindex
#130792562
#130707662
#130707522
#130707312
#130707022
#130706802
#130706742
#130703742
C11×#22162
#3382811