Finite Group Databasebeta

← #14640923

Subgroups — #14640923

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
1C2×C22⋊(C11⋊C16)C211yesmaximal, characteristic
2#13068654C211yesmaximal, characteristic
3C11×#1735C211yesmaximal, characteristic
4C23×C8×C11C2211yescharacteristic
5C2×C11×#117—21no—
6#10622820—21no—
7C2×#66883C412yescomplemented
8C22×C11⋊C16—21no—
9C11×#340—21no—
10C11×#340C412yes—
11#10622190—21no—
12C22⋊(C11⋊C16)—21no—
13C22⋊(C11⋊C16)C412yescomplemented
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
22C11×#117—24no—
23C11×#117—42no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C22⋊C4—41no—
26C2×C42×C11—41no—
27C2×#4318—22no—
28C22⋊(C11⋊C8)—41no—
29C22⋊(C11⋊C8)—41no—
30#66883—42no—
31C2×C11⋊C16—22no—
32C2×C11⋊C16—42no—
33#7260—111nomaximal, Sylow
34C24×C11SD1611yescharacteristic
35C22×C4×C11—22no—
36C22×C4×C11—22no—
37C22×C4×C11—42no—
38C22×C4×C11C22⋊C411yescharacteristic
39C22×C4×C11C22⋊C411yescharacteristic
40C22×C4×C11C4⋊C411yescharacteristic
41C22×C4×C11D811yescharacteristic
42C22×C4×C11SD1611yescharacteristic
43C22×C4×C11Q1611yescharacteristic
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
54C11×C4⋊C4—24no—
55C11×C4⋊C4—42no—
56C11×C22⋊C4—44no—
57C42×C11—44no—
58#4318—42no—
59#4318—42no—
60C2×C11⋊C8—42no—
61C11⋊C16—42no—
62C2×C22⋊C16—111no—
63#1810—111no—
64#1735D1111yescharacteristic
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—44no—
79C2×C4×C11—82no—
80C2×C4×C11—82no—
81C2×C4×C11#9511yescharacteristic
82C2×C4×C11#9912yes—
83C2×C4×C11#10211yescharacteristic
84C2×C4×C11#10311yescharacteristic
85C2×C4×C11#10412yes—
86C2×C4×C11#10711yescharacteristic
87C8×C11—21no—
88C8×C11—21no—
89C8×C11—21no—
90C8×C11—21no—
91C11⋊C8—82no—
92C23×C8C2×D1111yescharacteristic
93C2×#117—21no—
94C22×C16—221no—
95C2×#108—112no—
96#407—221no—
97C22⋊C16—112no—
98C22⋊C16—221no—
99#341—221no—
100#340—21no—
101#340Dic1112yes—
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—84no—
116C4×C11#32712yes—
117C4×C11#33911yescharacteristic
118C4×C11#34211yescharacteristic
119C23×C4C22⋊D1111yescharacteristic
120C2×M16—222no—
121C22×C8—42no—
122C22×C8Dic2211yescharacteristic
123C22×C8C4×D1111yescharacteristic
124C22×C8C4×D1111yescharacteristic
125C22×C8D4411yescharacteristic
126C22×C8C2×Dic1111yescharacteristic
127C22×C8C22⋊D1111yescharacteristic
128#117—24no—
129#117—42no—
130C2×C4⋊C4—22no—
131C2×C22⋊C4—41no—
132C2×C42—41no—
133C2×C16—222no—
134C2×C16—442no—
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#432411yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—42no—
148C22×C4Dic11⋊C411yescharacteristic
149C22×C4(C2×D11)⋊C411yescharacteristic
150C22×C4#432311yescharacteristic
151C22×C4#432511yescharacteristic
152C22×C4#432611yescharacteristic
153C22×C4C22⋊Dic1111yescharacteristic
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×C8C4⋊Dic1111yescharacteristic
166C2×C8(C2×D11)⋊C411yescharacteristic
167C4⋊C4—24no—
168C4⋊C4—42no—
169C22⋊C4—44no—
170C42—44no—
171C16—442no—
172C11#726011yescharacteristic, complemented, Sylow
173C23—22no—
174C23—22no—
175C23—41no—
176C23#6687211yescharacteristic
177C23#6687411yescharacteristic
178C23#6689611yescharacteristic
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—44no—
187C2×C4—82no—
188C2×C4—82no—
189C2×C4#6686912yes—
190C2×C4#6687012yes—
191C2×C4#6687111yescharacteristic
192C2×C4#6687311yescharacteristic
193C2×C4C11⋊#9511yescharacteristic
194C2×C4#6689911yescharacteristic
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#1062209012yes—
209C22#1062216711yescharacteristic
210C22#1062220512yes—
211C4—21no—
212C4—21no—
213C4—84no—
214C4#1062208912yes—
215C4#1062216111yescharacteristic
216C4#1062216511yescharacteristic
217C2—22no—
218C2—22no—
219C2—41no—
220C2#1306649511yescharacteristic
221C2#1306671111yescharacteristic
222C2#1306673211yescharacteristic
subgroupG/H
centerC2×C4#66873
commutatorC2×C8×C11C42
FrattiniC23×C8C2×D11
FittingC11×#1735C2
socleC22×C11#340
prime radicalC24×C11SD16
cosocleC23×C8×C11C22
hypercenter#1735D11
hypocenterC11#7260
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ #1735

Complements

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

NH ≅ G/Ntype
7. C2×#66883C4semidirect
13. C22⋊(C11⋊C16)C4semidirect
172. C11#7260semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊(C11⋊C16)2
#130686542
C11×#17352
#726011