Finite Group Databasebeta

← #14640739

Subgroups — #14640739

Order 2816.

342 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#10622191C211yesmaximal, characteristic
2#13068309C211yesmaximal, characteristic
3C2×C11×#349C211yesmaximal, characteristic
4C22×C11×M16C2211yescharacteristic
5C22×C4×Dic11C411yescharacteristic
6C22×#4318C411yescharacteristic
7C2×C11×M32—21no—
8C2×#66876—21no—
9C11×#349—21no—
10C11×#349C412yescomplemented
11#10622191—21no—
12#10622191C412yescomplemented
13#10622188—21no—
14#10622188—21no—
15C23×C4×C11C2×C411yescharacteristic
16C23×Dic11C812yes—
17C2×C11×M16—41no—
18C2×C11×M16—41no—
19C2×C11×M16C2×C411yescharacteristic
20C2×C11×M16C2×C411yescharacteristic
21C2×C11×M16D411yescharacteristic
22C2×C11×M16Q811yescharacteristic
23C22×C8×C11D411yescharacteristic
24C22×C8×C11D411yescharacteristic
25C2×C4×Dic11—21no—
26C2×C4×Dic11—21no—
27C2×C4×Dic11—41no—
28C2×C4×Dic11—41no—
29C2×#4318—21no—
30C2×#4318—41no—
31C2×#4318—41no—
32C2×#4318C812yes—
33C22×C11⋊C8—21no—
34C11×M32—22no—
35C11×M32—41no—
36C2×C11×C16—41no—
37#66876—22no—
38#66876—41no—
39C2×C11⋊C16—41no—
40#7191—111nomaximal, Sylow
41C24×C11C2×C811yescharacteristic
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×C11C4⋊C411yescharacteristic
49C22×C4×C11C2×C811yescharacteristic
50C22×C4×C11M1611yescharacteristic
51C22×C4×C11M1611yescharacteristic
52C22×Dic11—22no—
53C22×Dic11—42no—
54C22×Dic11—44no—
55C11×M16—41no—
56C11×M16—41no—
57C11×M16—41no—
58C11×M16—41no—
59C2×C8×C11—21no—
60C2×C8×C11—21no—
61C2×C8×C11—21no—
62C2×C8×C11—21no—
63C2×C8×C11C22⋊C411yescharacteristic
64C2×C8×C11C22⋊C411yescharacteristic
65C2×C8×C11C4⋊C411yescharacteristic
66C2×C8×C11C4⋊C411yescharacteristic
67C4×Dic11—42no—
68C4×Dic11—41no—
69C4×Dic11—41no—
70#4318—42no—
71#4318—42no—
72C2×C11⋊C8—22no—
73C2×C11⋊C8—41no—
74C2×C11⋊C8—41no—
75C11×C16—42no—
76C11⋊C16—42no—
77C2×#349—111no—
78C2×#349D1111yescharacteristic
79#1728—111no—
80C23×C11—21no—
81C23×C11—21no—
82C23×C11—42no—
83C23×C11C4×C811yescharacteristic
84C23×C11C22⋊C811yescharacteristic
85C23×C11C4⋊C811yescharacteristic
86C2×C4×C11—21no—
87C2×C4×C11—21no—
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#9511yescharacteristic
97C2×C4×C11#9711yescharacteristic
98C2×C4×C11C22⋊C811yescharacteristic
99C2×C4×C11#9911yescharacteristic
100C2×C4×C11#9911yescharacteristic
101C2×C4×C11#10011yescharacteristic
102C2×C4×C11#10111yescharacteristic
103C2×C4×C11C4⋊C811yescharacteristic
104C2×Dic11—24no—
105C2×Dic11—42no—
106C2×Dic11—44no—
107C2×Dic11—42no—
108C2×Dic11—44no—
109C8×C11—21no—
110C8×C11—21no—
111C8×C11—21no—
112C8×C11—21no—
113C11⋊C8—42no—
114C22×M16—111no—
115C22×M16C2×D1111yescharacteristic
116C22×C42—111no—
117C2×M32—21no—
118C2×M32—221no—
119#349—21no—
120#349—112no—
121#349—221no—
122#349Dic1112yescomplemented
123#336—221no—
124#336—221no—
125C22×C11—22no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11—41no—
129C22×C11—41no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11#32311yescharacteristic
133C22×C11#32411yescharacteristic
134C22×C11#33611yescharacteristic
135C4×C11—21no—
136C4×C11—21no—
137C4×C11#32311yescharacteristic
138C4×C11#32411yescharacteristic
139C4×C11#34211yescharacteristic
140C4×C11#34311yescharacteristic
141Dic11—44no—
142C23×C4—112no—
143C23×C4C4×D1111yescharacteristic
144C2×M16—41no—
145C2×M16—41no—
146C2×M16—112no—
147C2×M16—221no—
148C2×M16—441no—
149C2×M16—441no—
150C2×M16Dic2211yescharacteristic
151C2×M16C4×D1111yescharacteristic
152C2×M16C2×Dic1111yescharacteristic
153C2×M16C22⋊D1111yescharacteristic
154C22×C8—221no—
155C22×C8D4411yescharacteristic
156C22×C8C22⋊D1111yescharacteristic
157C2×C42—221no—
158C2×C42—221no—
159C2×C42—441no—
160C2×C42—441no—
161M32—22no—
162M32—41no—
163M32—222no—
164M32—441no—
165C2×C16—41no—
166C2×C16—441no—
167C2×C11—21no—
168C2×C11—21no—
169C2×C11—41no—
170C2×C11—41no—
171C2×C11#128011yescharacteristic
172C2×C11#132012yes—
173C24C8×D1111yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—222no—
179C22×C4—444no—
180C22×C4—442no—
181C22×C4C8×D1111yescharacteristic
182C22×C4#431311yescharacteristic
183C22×C4#431311yescharacteristic
184C22×C4C4×Dic1111yescharacteristic
185C22×C4Dic11⋊C411yescharacteristic
186C22×C4(C2×D11)⋊C411yescharacteristic
187M16—41no—
188M16—41no—
189M16—41no—
190M16—41no—
191M16—442no—
192M16—442no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—222no—
198C2×C8—441no—
199C2×C8—441no—
200C2×C8Dic11⋊C411yescharacteristic
201C2×C8C4⋊Dic1111yescharacteristic
202C2×C8(C2×D11)⋊C411yescharacteristic
203C2×C8C22⋊Dic1111yescharacteristic
204C42—442no—
205C42—441no—
206C42—441no—
207C16—42no—
208C16—442no—
209C11#719111yescharacteristic, complemented, Sylow
210C23—21no—
211C23—21no—
212C23—42no—
213C23C8×Dic1111yescharacteristic
214C23Dic11⋊C811yescharacteristic
215C23(C2×D11)⋊C811yescharacteristic
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—224no—
227C2×C4—442no—
228C2×C4—444no—
229C2×C4—442no—
230C2×C4—444no—
231C2×C4#6687011yescharacteristic
232C2×C4#6687011yescharacteristic
233C2×C4Dic11⋊C811yescharacteristic
234C2×C4#6687911yescharacteristic
235C2×C4(C2×D11)⋊C811yescharacteristic
236C2×C4#6688711yescharacteristic
237C2×C4#6688811yescharacteristic
238C2×C4C11⋊#9511yescharacteristic
239C8—21no—
240C8—21no—
241C8—21no—
242C8—21no—
243C8—442no—
244C22—22no—
245C22—21no—
246C22—21no—
247C22—41no—
248C22—41no—
249C22—42no—
250C22—42no—
251C22#1062210611yescharacteristic
252C22#1062210711yescharacteristic
253C22#1062218811yescharacteristic
254C4—21no—
255C4—21no—
256C4—444no—
257C4#1062210611yescharacteristic
258C4#1062210711yescharacteristic
259C4#1062216511yescharacteristic
260C4#1062219211yescharacteristic
261C2—21no—
262C2—21no—
263C2—41no—
264C2—41no—
265C2#1306645811yescharacteristic
266C2#1306655112yes—
subgroupG/H
centerC2×C4#66870
commutatorC23×C11C4×C8
FrattiniC22×M16C2×D11
FittingC2×C11×#349C2
socleC22×C11#323
prime radicalC24×C11C2×C8
cosocleC22×C11×M16C22
hypercenterC2×#349D11
hypocenterC11#7191
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×M16 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
10. C11×#349C4semidirect
12. #10622191C4semidirect
122. #349Dic11semidirect
209. C11#7191semidirect

Maximal subgroups

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

subgroupindex
C2×#106221912
#130683092
C2×C11×#3492
#719111