Finite Group Databasebeta

← #14640932

Subgroups — #14640932

Order 2816.

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

normal subgroups only

This group has 336 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
1#13070227C211yesmaximal, characteristic
2#13068641C211yesmaximal, characteristic
3C2×C11×#341C211yesmaximal, characteristic
4C22×C11×M16—21no—
5C23×C8×C11C2211yescharacteristic
6#10622825—21no—
7C2×#66881C412yes—
8C2×#66876—21no—
9C11×#341—21no—
10C11×#341C412yescomplemented
11#10622189—21no—
12C22⋊(C11⋊C16)—21no—
13C22⋊(C11⋊C16)C412yescomplemented
14C23×C4×C11D411yescharacteristic
15C2×C11×M16—24no—
16C2×C11×M16—22no—
17C2×C11×M16—42no—
18C2×C11×M16—41no—
19C22×C8×C11—42no—
20C22×C8×C11—41no—
21C22×C8×C11C2×C411yescharacteristic
22C22×C8×C11C2×C411yescharacteristic
23C22×C8×C11C2×C411yescharacteristic
24C22×C8×C11D411yescharacteristic
25C22×C8×C11D411yescharacteristic
26C22×C8×C11Q811yescharacteristic
27C2×C22⋊Dic11—41no—
28C2×C4⋊Dic11—22no—
29C11⋊#95—41no—
30#66881—42no—
31#66876—42no—
32C2×C11⋊C16—22no—
33#7263—111nomaximal, Sylow
34C24×C11SD1611yescharacteristic
35C22×C4×C11—22no—
36C22×C4×C11—22no—
37C22×C4×C11C22⋊C411yescharacteristic
38C22×C4×C11C22⋊C411yescharacteristic
39C22×C4×C11C4⋊C411yescharacteristic
40C22×C4×C11D811yescharacteristic
41C22×C4×C11SD1611yescharacteristic
42C22×C4×C11Q1611yescharacteristic
43C22×Dic11—42no—
44C11×M16—24no—
45C11×M16—44no—
46C11×M16—42no—
47C2×C8×C11—22no—
48C2×C8×C11—22no—
49C2×C8×C11—41no—
50C2×C8×C11—41no—
51C2×C8×C11—41no—
52C2×C8×C11—41no—
53C2×C8×C11—44no—
54C2×C8×C11—42no—
55C2×C8×C11C4211yescharacteristic
56C2×C8×C11C22⋊C411yescharacteristic
57C2×C8×C11C4⋊C411yescharacteristic
58C2×C8×C11C4⋊C411yescharacteristic
59C22⋊Dic11—82no—
60C4⋊Dic11—42no—
61C4⋊Dic11—42no—
62C11⋊C16—42no—
63#2112—111no—
64#1807—111no—
65C2×#341D1111yescharacteristic
66C23×C11—22no—
67C23×C11—22no—
68C23×C11—41no—
69C23×C11#10211yescharacteristic
70C23×C11#10311yescharacteristic
71C23×C11#10611yescharacteristic
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11#9511yescharacteristic
80C2×C4×C11#9912yes—
81C2×C4×C11#10211yescharacteristic
82C2×C4×C11#10311yescharacteristic
83C2×C4×C11#10412yes—
84C2×C4×C11#10711yescharacteristic
85C2×Dic11—82no—
86C2×Dic11—82no—
87C2×Dic11—82no—
88C8×C11—21no—
89C8×C11—21no—
90C8×C11—21no—
91C8×C11—21no—
92C8×C11—44no—
93C22×M16—21no—
94C23×C8C2×D1111yescharacteristic
95C2×M32—221no—
96C2×#106—112no—
97#380—221no—
98C22⋊C16—112no—
99C22⋊C16—221no—
100#341—21no—
101#341Dic1112yescomplemented
102#340—221no—
103C22×C11—21no—
104C22×C11—21no—
105C22×C11—21no—
106C22×C11—21no—
107C22×C11—21no—
108C22×C11—21no—
109C22×C11—21no—
110C22×C11—44no—
111C22×C11#32712yes—
112C22×C11#34011yescharacteristic
113C22×C11#36512yes—
114C4×C11—21no—
115C4×C11—21no—
116C4×C11#32812yes—
117C4×C11#33911yescharacteristic
118C4×C11#34211yescharacteristic
119Dic11—162no—
120C23×C4C22⋊D1111yescharacteristic
121C2×M16—24no—
122C2×M16—22no—
123C2×M16—42no—
124C2×M16—41no—
125C22×C8—42no—
126C22×C8—41no—
127C22×C8Dic2211yescharacteristic
128C22×C8C4×D1111yescharacteristic
129C22×C8C4×D1111yescharacteristic
130C22×C8D4411yescharacteristic
131C22×C8C2×Dic1111yescharacteristic
132C22×C8C22⋊D1111yescharacteristic
133C2×C4⋊C4—222no—
134C2×C22⋊C4—441no—
135M32—442no—
136C2×C16—222no—
137#106—442no—
138#95—441no—
139C2×C11—22no—
140C2×C11—22no—
141C2×C11—41no—
142C2×C11#129411yescharacteristic
143C2×C11#138311yescharacteristic
144C2×C11#138911yescharacteristic
145C24#432511yescharacteristic
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—442no—
149C22×C4Dic11⋊C411yescharacteristic
150C22×C4(C2×D11)⋊C411yescharacteristic
151C22×C4#432311yescharacteristic
152C22×C4#432411yescharacteristic
153C22×C4#432611yescharacteristic
154C22×C4C22⋊Dic1111yescharacteristic
155M16—24no—
156M16—44no—
157M16—42no—
158C2×C8—22no—
159C2×C8—22no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—44no—
165C2×C8—42no—
166C2×C8C4×Dic1111yescharacteristic
167C2×C8Dic11⋊C411yescharacteristic
168C2×C8C4⋊Dic1111yescharacteristic
169C2×C8(C2×D11)⋊C411yescharacteristic
170C4⋊C4—442no—
171C4⋊C4—442no—
172C22⋊C4—882no—
173C16—442no—
174C11#726311yescharacteristic, complemented, Sylow
175C23—22no—
176C23—22no—
177C23—41no—
178C23#6687211yescharacteristic
179C23#6687311yescharacteristic
180C23#6689911yescharacteristic
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—882no—
189C2×C4—882no—
190C2×C4—882no—
191C2×C4#6686912yes—
192C2×C4#6687012yes—
193C2×C4#6687111yescharacteristic
194C2×C4#6687411yescharacteristic
195C2×C4C11⋊#9511yescharacteristic
196C2×C4#6689611yescharacteristic
197C8—21no—
198C8—21no—
199C8—21no—
200C8—21no—
201C8—44no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—44no—
210C22#1062208912yes—
211C22#1062213212yes—
212C22#1062216711yescharacteristic
213C4—21no—
214C4—21no—
215C4—1762no—
216C4#1062209012yes—
217C4#1062216111yescharacteristic
218C4#1062216511yescharacteristic
219C2—22no—
220C2—22no—
221C2—41no—
222C2#1306649511yescharacteristic
223C2#1306671611yescharacteristic
224C2#1306673011yescharacteristic
subgroupG/H
centerC22#10622167
commutatorC2×C8×C11C42
FrattiniC23×C8C2×D11
FittingC2×C11×#341C2
socleC22×C11#340
prime radicalC24×C11SD16
cosocleC23×C8×C11C22
hypercenterC2×#341D11
hypocenterC11#7263
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
10. C11×#341C4semidirect
13. C22⋊(C11⋊C16)C4semidirect
101. #341Dic11semidirect
174. C11#7263semidirect

Maximal subgroups

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

subgroupindex
#130702272
#130686412
C2×C11×#3412
#726311