Finite Group Databasebeta

← #14640924

Subgroups — #14640924

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#13068654C211yesmaximal, characteristic
2#13068333C211yesmaximal, characteristic
3C2×C11×C22⋊C16C211yesmaximal, characteristic
4C23×C8×C11C2211yescharacteristic
5C2×#66979—21no—
6C22×C11×C16—21no—
7#10622820—21no—
8C2×#66883C412yescomplemented
9C11×C22⋊C16—21no—
10C11×C22⋊C16C412yescomplemented
11#10622190—21no—
12#10622189—21no—
13#10622189C412yes—
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×C22⋊Dic11—41no—
23#66979—24no—
24#66979—42no—
25C2×C4⋊Dic11—22no—
26C2×C4×Dic11—41no—
27C2×#4318—22no—
28C2×C11×C16—22no—
29C2×C11×C16—42no—
30C22⋊(C11⋊C8)—41no—
31C22⋊(C11⋊C8)—41no—
32#66883—42no—
33#7260—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—
44C2×C8×C11—22no—
45C2×C8×C11—22no—
46C2×C8×C11—41no—
47C2×C8×C11—41no—
48C2×C8×C11—41no—
49C2×C8×C11—41no—
50C2×C8×C11C4211yescharacteristic
51C2×C8×C11C22⋊C411yescharacteristic
52C2×C8×C11C4⋊C411yescharacteristic
53C2×C8×C11C4⋊C411yescharacteristic
54C22⋊Dic11—44no—
55C4⋊Dic11—24no—
56C4⋊Dic11—42no—
57C4×Dic11—44no—
58#4318—42no—
59#4318—42no—
60C2×C11⋊C8—42no—
61C11×C16—42no—
62C2×C22⋊C16D1111yescharacteristic
63#1810—111no—
64#1735—111no—
65C23×C11—22no—
66C23×C11—22no—
67C23×C11—41no—
68C23×C11#10211yescharacteristic
69C23×C11#10311yescharacteristic
70C23×C11#10611yescharacteristic
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#10311yescharacteristic
82C2×C4×C11#10412yes—
83C2×C4×C11#10711yescharacteristic
84C2×Dic11—44no—
85C2×Dic11—82no—
86C2×Dic11—82no—
87C8×C11—21no—
88C8×C11—21no—
89C8×C11—21no—
90C8×C11—21no—
91C11⋊C8—82no—
92C23×C8C2×D1111yescharacteristic
93C2×#117—221no—
94C22×C16—21no—
95C2×#108—112no—
96#407—221no—
97C22⋊C16—21no—
98C22⋊C16Dic1112yescomplemented
99#341—221no—
100#340—112no—
101#340—221no—
102C22×C11—21no—
103C22×C11—21no—
104C22×C11—21no—
105C22×C11—21no—
106C22×C11—21no—
107C22×C11—21no—
108C22×C11—21no—
109C22×C11—44no—
110C22×C11#32812yes—
111C22×C11#34011yescharacteristic
112C22×C11#35912yes—
113C4×C11—21no—
114C4×C11—21no—
115C4×C11#32712yes—
116C4×C11#33911yescharacteristic
117C4×C11#34211yescharacteristic
118Dic11—84no—
119C23×C4D4411yescharacteristic
120C2×M16—222no—
121C22×C8—42no—
122C22×C8Dic2211yescharacteristic
123C22×C8C4×D1111yescharacteristic
124C22×C8C4×D1111yescharacteristic
125C22×C8C2×Dic1111yescharacteristic
126C22×C8C22⋊D1111yescharacteristic
127C22×C8C22⋊D1111yescharacteristic
128#117—224no—
129#117—442no—
130C2×C4⋊C4—222no—
131C2×C22⋊C4—441no—
132C2×C42—441no—
133C2×C16—22no—
134C2×C16—42no—
135#108—442no—
136C22⋊C8—441no—
137C22⋊C8—441no—
138C2×C11—22no—
139C2×C11—22no—
140C2×C11—41no—
141C2×C11#129411yescharacteristic
142C2×C11#138211yescharacteristic
143C2×C11#138911yescharacteristic
144C24#431411yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—442no—
148C22×C4#431411yescharacteristic
149C22×C4D8811yescharacteristic
150C22×C4Dic4411yescharacteristic
151C22×C4C4⋊Dic1111yescharacteristic
152C22×C4(C2×D11)⋊C411yescharacteristic
153C22×C4(C2×D11)⋊C411yescharacteristic
154M16—442no—
155M16—442no—
156C2×C8—22no—
157C2×C8—22no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—442no—
163C2×C8C4×Dic1111yescharacteristic
164C2×C8Dic11⋊C411yescharacteristic
165C2×C8Dic11⋊C411yescharacteristic
166C2×C8C22⋊Dic1111yescharacteristic
167C4⋊C4—224no—
168C4⋊C4—442no—
169C22⋊C4—444no—
170C42—444no—
171C16—42no—
172C11#726011yescharacteristic, complemented, Sylow
173C23—22no—
174C23—22no—
175C23—41no—
176C23#6688011yescharacteristic
177C23#6688111yescharacteristic
178C23#6688511yescharacteristic
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—444no—
187C2×C4—882no—
188C2×C4—882no—
189C2×C4#6687012yes—
190C2×C4#6688011yescharacteristic
191C2×C4#6688211yescharacteristic
192C2×C4#6688511yescharacteristic
193C2×C4#6688912yes—
194C2×C4C11⋊#9511yescharacteristic
195C8—21no—
196C8—21no—
197C8—21no—
198C8—21no—
199C8—882no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—44no—
208C22#1062210512yes—
209C22#1062214812yes—
210C22#1062218911yescharacteristic
211C4—21no—
212C4—21no—
213C4—884no—
214C4#1062210812yes—
215C4#1062216511yescharacteristic
216C4#1062219311yescharacteristic
217C2—22no—
218C2—22no—
219C2—41no—
220C2#1306649611yescharacteristic
221C2#1306671211yescharacteristic
222C2#1306673111yescharacteristic
subgroupG/H
centerC2×C4#66885
commutatorC2×C8×C11C42
FrattiniC23×C8C2×D11
FittingC2×C11×C22⋊C16C2
socleC22×C11#340
prime radicalC24×C11SD16
cosocleC23×C8×C11C22
hypercenterC2×C22⋊C16D11
hypocenterC11#7260
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
8. C2×#66883C4semidirect
10. C11×C22⋊C16C4semidirect
98. C22⋊C16Dic11semidirect
172. C11#7260semidirect

Maximal subgroups

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

subgroupindex
#130686542
#130683332
C2×C11×C22⋊C162
#726011