Finite Group Databasebeta

← #14640939

Subgroups — #14640939

Order 2816.

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

normal subgroups only

This group has 314 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#13068654C211yesmaximal, characteristic
2C2×#10622190C211yesmaximal, characteristic
3C11×#2112C211yesmaximal, characteristic
4C23×C8×C11C2211yescharacteristic
5C22×#4318—21no—
6C2×C11×M32—21no—
7#10622820—21no—
8C2×#66883C412yes—
9C11×C22⋊C16—21no—
10C11×C22⋊C16C412yes—
11#10622190—21no—
12#10622190—21no—
13#10622190C412yes—
14C23×C4×C11D411yescharacteristic
15C22×C8×C11—42no—
16C22×C8×C11C2×C411yescharacteristic
17C22×C8×C11C2×C411yescharacteristic
18C22×C8×C11C2×C411yescharacteristic
19C22×C8×C11D411yescharacteristic
20C22×C8×C11D411yescharacteristic
21C22×C8×C11Q811yescharacteristic
22C2×#4318—24no—
23C2×#4318—22no—
24C2×#4318—22no—
25C2×#4318—42no—
26C2×#4318—41no—
27C22×C11⋊C8—41no—
28C11×M32—42no—
29C2×C11×C16—22no—
30C22⋊(C11⋊C8)—41no—
31C22⋊(C11⋊C8)—41no—
32#66883—42no—
33#7265—111nomaximal, Sylow
34C24×C11Q1611yescharacteristic
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×C11SD1611yescharacteristic
43C2×C8×C11—22no—
44C2×C8×C11—22no—
45C2×C8×C11—41no—
46C2×C8×C11—41no—
47C2×C8×C11—41no—
48C2×C8×C11—41no—
49C2×C8×C11C4211yescharacteristic
50C2×C8×C11C22⋊C411yescharacteristic
51C2×C8×C11C4⋊C411yescharacteristic
52C2×C8×C11C4⋊C411yescharacteristic
53#4318—24no—
54#4318—44no—
55#4318—42no—
56#4318—42no—
57#4318—42no—
58C2×C11⋊C8—44no—
59C2×C11⋊C8—42no—
60C2×C11⋊C8—42no—
61C11×C16—42no—
62#2112D1111yescharacteristic
63#1810—111no—
64C2×#341—111no—
65C23×C11—22no—
66C23×C11—41no—
67C23×C11—41no—
68C23×C11#10311yescharacteristic
69C23×C11#10311yescharacteristic
70C23×C11#10711yescharacteristic
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11#9511yescharacteristic
79C2×C4×C11#9912yes—
80C2×C4×C11#10211yescharacteristic
81C2×C4×C11#10211yescharacteristic
82C2×C4×C11#10412yes—
83C2×C4×C11#10611yescharacteristic
84C8×C11—21no—
85C8×C11—21no—
86C8×C11—21no—
87C8×C11—21no—
88C11⋊C8—44no—
89C11⋊C8—82no—
90C22×M16—221no—
91C23×C8C2×D1111yescharacteristic
92C2×M32—21no—
93C2×#108—112no—
94#407—221no—
95C22⋊C16—21no—
96C22⋊C16Dic1112yes—
97#341—112no—
98#341—221no—
99#341—221no—
100C22×C11—21no—
101C22×C11—21no—
102C22×C11—21no—
103C22×C11—21no—
104C22×C11—21no—
105C22×C11—21no—
106C22×C11—21no—
107C22×C11—21no—
108C22×C11—44no—
109C22×C11#32812yes—
110C22×C11#34011yescharacteristic
111C4×C11—21no—
112C4×C11—21no—
113C4×C11#32712yes—
114C4×C11#33911yescharacteristic
115C4×C11#34211yescharacteristic
116C23×C4D4411yescharacteristic
117C2×M16—224no—
118C2×M16—222no—
119C2×M16—222no—
120C2×M16—442no—
121C2×M16—441no—
122C22×C8—42no—
123C22×C8—441no—
124C22×C8Dic2211yescharacteristic
125C22×C8C4×D1111yescharacteristic
126C22×C8C4×D1111yescharacteristic
127C22×C8C2×Dic1111yescharacteristic
128C22×C8C22⋊D1111yescharacteristic
129C22×C8C22⋊D1111yescharacteristic
130M32—42no—
131C2×C16—22no—
132#108—442no—
133C22⋊C8—441no—
134C22⋊C8—441no—
135C2×C11—22no—
136C2×C11—41no—
137C2×C11—41no—
138C2×C11#129411yescharacteristic
139C2×C11#138511yescharacteristic
140C2×C11#138811yescharacteristic
141C24Dic4411yescharacteristic
142C22×C4—22no—
143C22×C4—22no—
144C22×C4#431411yescharacteristic
145C22×C4#431411yescharacteristic
146C22×C4D8811yescharacteristic
147C22×C4C4⋊Dic1111yescharacteristic
148C22×C4(C2×D11)⋊C411yescharacteristic
149C22×C4(C2×D11)⋊C411yescharacteristic
150M16—224no—
151M16—444no—
152M16—442no—
153M16—442no—
154M16—442no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—41no—
161C2×C8—444no—
162C2×C8—442no—
163C2×C8—442no—
164C2×C8C4×Dic1111yescharacteristic
165C2×C8Dic11⋊C411yescharacteristic
166C2×C8Dic11⋊C411yescharacteristic
167C2×C8C22⋊Dic1111yescharacteristic
168C16—42no—
169C11#726511yescharacteristic, complemented, Sylow
170C23—22no—
171C23—41no—
172C23—41no—
173C23#6688011yescharacteristic
174C23#6688011yescharacteristic
175C23#6688211yescharacteristic
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4#6687012yes—
184C2×C4#6688111yescharacteristic
185C2×C4#6688511yescharacteristic
186C2×C4#6688511yescharacteristic
187C2×C4#6688912yes—
188C2×C4C11⋊#9511yescharacteristic
189C8—21no—
190C8—21no—
191C8—21no—
192C8—21no—
193C8—444no—
194C8—882no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—44no—
204C22#1062210512yes—
205C22#1062218911yescharacteristic
206C4—21no—
207C4—21no—
208C4#1062210812yes—
209C4#1062216511yescharacteristic
210C4#1062219311yescharacteristic
211C2—22no—
212C2—41no—
213C2—41no—
214C2#1306649611yescharacteristic
215C2#1306672011yescharacteristic
216C2#1306672811yescharacteristic
subgroupG/H
centerC22#10622189
commutatorC2×C8×C11C42
FrattiniC23×C8C2×D11
FittingC11×#2112C2
socleC22×C11#340
prime radicalC24×C11Q16
cosocleC23×C8×C11C22
hypercenter#2112D11
hypocenterC11#7265
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
169. C11#7265semidirect

Maximal subgroups

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

subgroupindex
#130686542
C2×#106221902
C11×#21122
#726511