Finite Group Databasebeta

← #14640936

Subgroups — #14640936

Order 2816.

374 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 103 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×#10622189C211yesmaximal, characteristic
3C11×#2112C211yesmaximal, characteristic
4C23×C8×C11C2211yescharacteristic
5C22×C4⋊Dic11—21no—
6C2×C11×M32—21no—
7#10622820—21no—
8C2×#66883C412yescomplemented
9C11×C22⋊C16—21no—
10C11×C22⋊C16C412yescomplemented
11#10622190—21no—
12#10622189—21no—
13#10622189C412yes—
14C23×C4×C11D411yescharacteristic
15C23×Dic11—41no—
16C22×C8×C11—42no—
17C22×C8×C11C2×C411yescharacteristic
18C22×C8×C11C2×C411yescharacteristic
19C22×C8×C11C2×C411yescharacteristic
20C22×C8×C11D411yescharacteristic
21C22×C8×C11D411yescharacteristic
22C22×C8×C11Q811yescharacteristic
23C2×C4⋊Dic11—24no—
24C2×C4⋊Dic11—22no—
25C2×C4⋊Dic11—42no—
26C2×C4⋊Dic11—41no—
27C2×#4318—22no—
28C11×M32—42no—
29C2×C11×C16—22no—
30C22⋊(C11⋊C8)—41no—
31C22⋊(C11⋊C8)—41no—
32#66883—42no—
33#7264—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—44no—
44C22×Dic11—42no—
45C22×Dic11—82no—
46C22×Dic11—82no—
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×C11C4211yescharacteristic
54C2×C8×C11C22⋊C411yescharacteristic
55C2×C8×C11C4⋊C411yescharacteristic
56C2×C8×C11C4⋊C411yescharacteristic
57C4⋊Dic11—24no—
58C4⋊Dic11—44no—
59C4⋊Dic11—42no—
60#4318—42no—
61#4318—42no—
62C2×C11⋊C8—42no—
63C11×C16—42no—
64#2112D1111yescharacteristic
65#1810—111no—
66C2×#340—111no—
67C23×C11—22no—
68C23×C11—21no—
69C23×C11—21no—
70C23×C11—22no—
71C23×C11#10211yescharacteristic
72C23×C11#10311yescharacteristic
73C23×C11#10611yescharacteristic
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11#9511yescharacteristic
82C2×C4×C11#9912yes—
83C2×C4×C11#10211yescharacteristic
84C2×C4×C11#10311yescharacteristic
85C2×C4×C11#10412yes—
86C2×C4×C11#10711yescharacteristic
87C2×Dic11—44no—
88C2×Dic11—88no—
89C2×Dic11—82no—
90C2×Dic11—82no—
91C8×C11—21no—
92C8×C11—21no—
93C8×C11—21no—
94C8×C11—21no—
95C11⋊C8—82no—
96C23×C8C2×D1111yescharacteristic
97C22×C4⋊C4—221no—
98C2×M32—21no—
99C2×#108—112no—
100#407—221no—
101C22⋊C16—21no—
102C22⋊C16Dic1112yescomplemented
103#341—221no—
104#340—112no—
105#340—221no—
106C22×C11—24no—
107C22×C11—24no—
108C22×C11—21no—
109C22×C11—21no—
110C22×C11—21no—
111C22×C11—21no—
112C22×C11—21no—
113C22×C11—21no—
114C22×C11#32812yes—
115C22×C11#34011yescharacteristic
116C22×C11#36111yescharacteristic
117C22×C11#36211yescharacteristic
118C22×C11#36512yes—
119C4×C11—21no—
120C4×C11—21no—
121C4×C11#32712yes—
122C4×C11#33911yescharacteristic
123C4×C11#34211yescharacteristic
124Dic11—84no—
125C23×C4—441no—
126C23×C4D4411yescharacteristic
127C2×M16—222no—
128C22×C8—42no—
129C22×C8Dic2211yescharacteristic
130C22×C8C4×D1111yescharacteristic
131C22×C8C4×D1111yescharacteristic
132C22×C8C2×Dic1111yescharacteristic
133C22×C8C22⋊D1111yescharacteristic
134C22×C8C22⋊D1111yescharacteristic
135C2×C4⋊C4—224no—
136C2×C4⋊C4—222no—
137C2×C4⋊C4—442no—
138C2×C4⋊C4—441no—
139M32—42no—
140C2×C16—22no—
141#108—442no—
142C22⋊C8—441no—
143C22⋊C8—441no—
144C2×C11—21no—
145C2×C11—22no—
146C2×C11—21no—
147C2×C11—22no—
148C2×C11#129411yescharacteristic
149C2×C11#138311yescharacteristic
150C2×C11#138711yescharacteristic
151C24#431411yescharacteristic
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—444no—
155C22×C4—442no—
156C22×C4—882no—
157C22×C4—882no—
158C22×C4#431411yescharacteristic
159C22×C4D8811yescharacteristic
160C22×C4Dic4411yescharacteristic
161C22×C4C4⋊Dic1111yescharacteristic
162C22×C4(C2×D11)⋊C411yescharacteristic
163C22×C4(C2×D11)⋊C411yescharacteristic
164M16—442no—
165M16—442no—
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—442no—
173C2×C8C4×Dic1111yescharacteristic
174C2×C8Dic11⋊C411yescharacteristic
175C2×C8Dic11⋊C411yescharacteristic
176C2×C8C22⋊Dic1111yescharacteristic
177C4⋊C4—224no—
178C4⋊C4—444no—
179C4⋊C4—442no—
180C16—42no—
181C11#726411yescharacteristic, complemented, Sylow
182C23—22no—
183C23—22no—
184C23—21no—
185C23—21no—
186C23#6688011yescharacteristic
187C23#6688111yescharacteristic
188C23#6688511yescharacteristic
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—444no—
197C2×C4—888no—
198C2×C4—882no—
199C2×C4—882no—
200C2×C4#6687012yes—
201C2×C4#6688011yescharacteristic
202C2×C4#6688211yescharacteristic
203C2×C4#6688511yescharacteristic
204C2×C4#6688912yes—
205C2×C4C11⋊#9511yescharacteristic
206C8—21no—
207C8—21no—
208C8—21no—
209C8—21no—
210C8—882no—
211C22—24no—
212C22—24no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22#1062210512yes—
220C22#1062215112yes—
221C22#1062215411yescharacteristic
222C22#1062215511yescharacteristic
223C22#1062218911yescharacteristic
224C4—21no—
225C4—21no—
226C4—884no—
227C4#1062210812yes—
228C4#1062216511yescharacteristic
229C4#1062219311yescharacteristic
230C2—21no—
231C2—22no—
232C2—22no—
233C2—21no—
234C2#1306649611yescharacteristic
235C2#1306671511yescharacteristic
236C2#1306672511yescharacteristic
subgroupG/H
centerC22#10622189
commutatorC2×C8×C11C42
FrattiniC23×C8C2×D11
FittingC11×#2112C2
socleC22×C11#340
prime radicalC24×C11SD16
cosocleC23×C8×C11C22
hypercenter#2112D11
hypocenterC11#7264
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
8. C2×#66883C4semidirect
10. C11×C22⋊C16C4semidirect
102. C22⋊C16Dic11semidirect
181. C11#7264semidirect

Maximal subgroups

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

subgroupindex
#130686542
C2×#106221892
C11×#21122
#726411