Finite Group Databasebeta

← #14640902

Subgroups — #14640902

Order 2816.

328 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 95 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#13068600C211yesmaximal, characteristic
2#13066930C211yesmaximal, characteristic
3C11×#1742C211yesmaximal, characteristic
4C22×C11×M16—21no—
5C2×C11×#117C2211yescharacteristic
6C2×C22⋊(C11⋊C8)—21no—
7#10622538—21no—
8C2×C4⋊(C11⋊C8)C411yescharacteristic
9C2×C4⋊(C11⋊C8)C411yescharacteristic
10C11×#343—21no—
11C11×#343C412yes—
12#10622166—21no—
13#10622163C412yes—
14#10622162—21no—
15C23×C4×C11D411yescharacteristic
16C2×C11×M16—22no—
17C2×C11×M16—22no—
18C2×C11×M16—22no—
19C2×C11×M16—41no—
20C2×C11×M16—41no—
21C2×C11×M16—41no—
22C22×C8×C11—41no—
23C11×#117—41no—
24C11×#117—41no—
25C2×C11×C4⋊C4C2×C411yescharacteristic
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C22⋊C4C2×C411yescharacteristic
28C2×C11×C22⋊C4Q811yescharacteristic
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C22×C11⋊C8—21no—
32C22×C11⋊C8—21no—
33C22⋊(C11⋊C8)—22no—
34C22⋊(C11⋊C8)—41no—
35C22⋊(C11⋊C8)—41no—
36C4⋊(C11⋊C8)—41no—
37C4⋊(C11⋊C8)—41no—
38C4⋊(C11⋊C8)—41no—
39C4×C11⋊C8—41no—
40#7253—111nomaximal, Sylow
41C24×C11C4⋊C411yescharacteristic
42C22×C4×C11—21no—
43C22×C4×C11—21no—
44C22×C4×C11—21no—
45C22×C4×C11—21no—
46C22×C4×C11C4211yescharacteristic
47C22×C4×C11C22⋊C411yescharacteristic
48C22×C4×C11C22⋊C411yescharacteristic
49C22×C4×C11C22⋊C411yescharacteristic
50C22×C4×C11C4⋊C411yescharacteristic
51C22×C4×C11C4⋊C411yescharacteristic
52C22×C4×C11D811yescharacteristic
53C22×C4×C11SD1611yescharacteristic
54C22×C4×C11SD1611yescharacteristic
55C22×C4×C11Q1611yescharacteristic
56C11×M16—24no—
57C11×M16—42no—
58C11×M16—42no—
59C11×M16—42no—
60C2×C8×C11—42no—
61C2×C8×C11—42no—
62C2×C8×C11—42no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C22⋊C4—41no—
66C11×C22⋊C4—41no—
67C42×C11—21no—
68C42×C11—21no—
69C42×C11—21no—
70C42×C11—21no—
71C2×C11⋊C8—42no—
72C2×C11⋊C8—41no—
73C2×C11⋊C8—41no—
74C2×C11⋊C8—41no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8—41no—
77C2×C11⋊C8—41no—
78#1798—111no—
79#1742D1111yescharacteristic
80#1458—111no—
81C23×C11—21no—
82C23×C11—21no—
83C23×C11—41no—
84C23×C11—41no—
85C23×C11#9511yescharacteristic
86C23×C11#10611yescharacteristic
87C23×C11#10711yescharacteristic
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11#9911yescharacteristic
107C2×C4×C11#9911yescharacteristic
108C2×C4×C11#10211yescharacteristic
109C2×C4×C11#10211yescharacteristic
110C2×C4×C11#10311yescharacteristic
111C2×C4×C11#10311yescharacteristic
112C2×C4×C11#10411yescharacteristic
113C2×C4×C11#10411yescharacteristic
114C8×C11—44no—
115C11⋊C8—82no—
116C11⋊C8—81no—
117C11⋊C8—81no—
118C22×M16—21no—
119C2×#117C2×D1111yescharacteristic
120#431—221no—
121C2×C4⋊C8—111no—
122C2×C4⋊C8—111no—
123C2×C22⋊C8—221no—
124#343—21no—
125#343Dic1112yes—
126#336—221no—
127#324—221no—
128#323—112no—
129C22×C11—21no—
130C22×C11—21no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—41no—
134C22×C11—41no—
135C22×C11—41no—
136C22×C11—41no—
137C22×C11—81no—
138C22×C11#33911yescharacteristic
139C22×C11#34011yescharacteristic
140C22×C11#34211yescharacteristic
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—41no—
144C4×C11—41no—
145C4×C11—41no—
146C4×C11—41no—
147C4×C11#32711yescharacteristic
148C4×C11#32711yescharacteristic
149C4×C11#32811yescharacteristic
150C4×C11#32811yescharacteristic
151C23×C4C22⋊D1111yescharacteristic
152C2×M16—22no—
153C2×M16—22no—
154C2×M16—22no—
155C2×M16—41no—
156C2×M16—41no—
157C2×M16—41no—
158C22×C8—41no—
159C22×C8—221no—
160C22×C8—221no—
161#117—41no—
162#117—41no—
163C2×C4⋊C4C2×Dic1111yescharacteristic
164C2×C4⋊C4C22⋊D1111yescharacteristic
165C2×C22⋊C4Dic2211yescharacteristic
166C2×C22⋊C4C4×D1111yescharacteristic
167C2×C42C4×D1111yescharacteristic
168C2×C42D4411yescharacteristic
169C4⋊C8—441no—
170C4⋊C8—441no—
171C4⋊C8—441no—
172C22⋊C8—222no—
173C22⋊C8—441no—
174C22⋊C8—441no—
175C4×C8—441no—
176C2×C11—21no—
177C2×C11—21no—
178C2×C11—41no—
179C2×C11—41no—
180C2×C11#129411yescharacteristic
181C2×C11#139211yescharacteristic
182C2×C11#139511yescharacteristic
183C24Dic11⋊C411yescharacteristic
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4C4×Dic1111yescharacteristic
189C22×C4Dic11⋊C411yescharacteristic
190C22×C4C4⋊Dic1111yescharacteristic
191C22×C4(C2×D11)⋊C411yescharacteristic
192C22×C4(C2×D11)⋊C411yescharacteristic
193C22×C4#432311yescharacteristic
194C22×C4#432411yescharacteristic
195C22×C4#432511yescharacteristic
196C22×C4#432611yescharacteristic
197C22×C4C22⋊Dic1111yescharacteristic
198M16—24no—
199M16—42no—
200M16—42no—
201M16—42no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—442no—
206C2×C8—441no—
207C2×C8—441no—
208C2×C8—441no—
209C2×C8—441no—
210C2×C8—441no—
211C2×C8—441no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C22⋊C4—41no—
215C22⋊C4—41no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C11#725311yescharacteristic, complemented, Sylow
221C23—21no—
222C23—21no—
223C23—41no—
224C23—41no—
225C23#6687111yescharacteristic
226C23#6687211yescharacteristic
227C23C11⋊#9511yescharacteristic
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4#6686911yescharacteristic
247C2×C4#6686911yescharacteristic
248C2×C4#6687011yescharacteristic
249C2×C4#6687011yescharacteristic
250C2×C4#6687311yescharacteristic
251C2×C4#6687411yescharacteristic
252C2×C4#6689611yescharacteristic
253C2×C4#6689911yescharacteristic
254C8—44no—
255C8—882no—
256C8—881no—
257C8—881no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—41no—
266C22—81no—
267C22#1062216111yescharacteristic
268C22#1062216511yescharacteristic
269C22#1062216711yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4#1062208911yescharacteristic
277C4#1062208911yescharacteristic
278C4#1062209011yescharacteristic
279C4#1062209011yescharacteristic
280C2—21no—
281C2—21no—
282C2—41no—
283C2—41no—
284C2#1306649511yescharacteristic
285C2#1306673811yescharacteristic
286C2#1306674611yescharacteristic
subgroupG/H
centerC2×C4#66870
commutatorC22×C4×C11C42
FrattiniC2×#117C2×D11
FittingC11×#1742C2
socleC22×C11#342
prime radicalC24×C11C4⋊C4
cosocleC2×C11×#117C22
hypercenter#1742D11
hypocenterC11#7253
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#117 ◁ #1742

Complements

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

NH ≅ G/Ntype
220. C11#7253semidirect

Maximal subgroups

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

subgroupindex
#130686002
#130669302
C11×#17422
#725311