Finite Group Databasebeta

← #14910217

Subgroups — #14910217

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#13070762C212yesmaximal, complemented
3#13070756C212yesmaximal, complemented
4#13070719C211yesmaximal, characteristic
5#13070714C212yesmaximal, complemented
6#13070680C212yesmaximal, complemented
7#13070674C212yesmaximal, complemented
8#13070376C211yesmaximal, characteristic, complemented
9C11×#2219C211yesmaximal, characteristic, complemented
10#10623174—22no—
11C2×C11×Q32C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C11×#467C2212yes—
14#10622804C2212yes—
15Q16×Dic11C2212yes—
16C2×#66892C2212yes—
17#10622728C2212yes—
18#10622714C2211yescharacteristic
19C22×C11⋊C16C2211yescharacteristic
20#10622662—22no—
21C2×D176C2211yescharacteristic
22#10622487C2212yes—
23#10622485C2212yes—
24#10622430—22no—
25#10622408—22no—
26C11×#367C2211yescharacteristic
27C11×#358C2212yes—
28#10622202C2212yes—
29#10622147C2212yes—
30#10622143C2211yescharacteristic
31Dic11⋊C16C2212yes—
32Dic11⋊C16C2212yes—
33#10622129C2212yes—
34#10622128C2212yes—
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—
52C11×M32—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—
63C2×C11⋊C16—41no—
64C2×C11⋊C16C2312yes—
65#66873—22no—
66#66871—22no—
67D176—41no—
68#33829—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⋊Dic11D811yescharacteristic
85C22⋊Dic11D811yescharacteristic
86#4325—44no—
87(C2×D11)⋊C4—42no—
88(C2×D11)⋊C4—42no—
89(C2×D11)⋊C4—42no—
90(C2×D11)⋊C4—42no—
91C4⋊Dic11—22no—
92C4⋊Dic11—42no—
93C4⋊Dic11D812yes—
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#2226—112no—
106#2225—112no—
107#2219D1111yescharacteristic, complemented
108#2218—111no—
109#2217—112no—
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×M32C2×D1111yescharacteristic
140C22×C16—111no—
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#367—111no—
152#367—112no—
153#367C2×D1111yescharacteristic
154C4⋊C16—112no—
155C4⋊C16—112no—
156#358—112no—
157#358C2×D1112yes—
158#357—112no—
159#357—112no—
160C22×C11—22no—
161C22×C11—21no—
162C22×C11C22×D811yescharacteristic
163C2×D11—82no—
164C2×D11—82no—
165C2×D11—82no—
166C4×C11—21no—
167C4×C11—82no—
168C4×C11—82no—
169C4×C11#53711yescharacteristic
170C4×C11#57511yescharacteristic
171Dic11—22no—
172Dic11—22no—
173Dic11—82no—
174C2×Q16C22×D1112yes—
175C2×SD16—222no—
176C2×D8—112no—
177C2×M16—111no—
178C22×C8C22×D1111yescharacteristic
179C4⋊Q8—222no—
180#126—442no—
181#124—222no—
182#124—442no—
183#123—442no—
184C22⋊Q8—22no—
185C22⋊Q8—442no—
186#121—222no—
187C4×Q8—222no—
188C4×D4—222no—
189#117—111no—
190Q32—41no—
191SD32—442no—
192D16—441no—
193M32—41no—
194C2×C16—112no—
195C2×C16—441no—
196C2×C16C22×D1111yescharacteristic
197C2×C16C22×D1111yescharacteristic
198#107—112no—
199#107—222no—
200#107C22×D1112yes—
201#103—22no—
202#103—222no—
203#102—222no—
204#102—222no—
205#97—112no—
206C4×C8—112no—
207C2×C11—41no—
208C2×C11#324511yescharacteristic
209C2×C11#341612yes—
210D11—162no—
211C2×Q8—22no—
212C2×Q8—442no—
213C2×D4—222no—
214C2×D4—442no—
215C22×C4—442no—
216C22×C4D4×D1111yescharacteristic
217Q16—22no—
218Q16—22no—
219SD16—444no—
220D8—222no—
221D8—222no—
222M16—441no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—112no—
226C2×C8D4×D1111yescharacteristic
227C2×C8C23×D1111yescharacteristic
228C4⋊C4—22no—
229C4⋊C4—42no—
230C4⋊C4—112no—
231C4⋊C4—222no—
232C4⋊C4—442no—
233C4⋊C4—442no—
234C22⋊C4—42no—
235C22⋊C4—111no—
236C22⋊C4—111no—
237C22⋊C4—442no—
238C22⋊C4—442no—
239C22⋊C4—442no—
240C22⋊C4—442no—
241C42—112no—
242C42—442no—
243C16—21no—
244C16—21no—
245C16—222no—
246C11#3382911yescharacteristic, complemented, Sylow
247C23—442no—
248C23D8×D1111yescharacteristic
249Q8—42no—
250Q8—42no—
251Q8—1762no—
252D4—442no—
253D4—442no—
254D4—1762no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—112no—
260C2×C4—112no—
261C2×C4—442no—
262C2×C4—1762no—
263C2×C4D8×D1111yescharacteristic
264C2×C4C2×D4×D1111yescharacteristic
265C8—21no—
266C8—222no—
267C8#6703711yescharacteristic
268C8#6704311yescharacteristic
269C22—21no—
270C22—22no—
271C22—882no—
272C22—882no—
273C22—882no—
274C22C2×D8×D1111yescharacteristic
275C4—21no—
276C4—82no—
277C4—82no—
278C4—222no—
279C4—222no—
280C4—882no—
281C4#1062312811yescharacteristic
282C4#1062329911yescharacteristic
283C2—41no—
284C2—1762no—
285C2#1307992211yescharacteristic
286C2#1308176112yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2219C2
socleC22×C11C22×D8
prime radical#13070719C2
hypercenter#2219D11
hypocenterC11#33829
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2219

Complements

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

NH ≅ G/Ntype
1. #13079256C2semidirect
2. #13070762C2semidirect
3. #13070756C2semidirect
5. #13070714C2semidirect
6. #13070680C2semidirect
7. #13070674C2semidirect
8. #13070376C2semidirect
9. C11×#2219C2semidirect
107. #2219D11semidirect
246. C11#33829semidirect

Maximal subgroups

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

subgroupindex
#130792562
#130707622
#130707562
#130707192
#130707142
#130706802
#130706742
#130703762
C11×#22192
#3382911