Finite Group Databasebeta

← #14640934

Subgroups — #14640934

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#13070227C211yesmaximal, characteristic
2C2×#10622189C211yesmaximal, characteristic
3C11×#1810C211yesmaximal, characteristic
4C23×C8×C11C2211yescharacteristic
5C22×C4⋊Dic11—21no—
6C2×C11×#108C412yescomplemented
7C11×#407—21no—
8C2×#66876—21no—
9C11×#341—21no—
10#10622189—21no—
11#10622189C412yes—
12C22⋊(C11⋊C16)—21no—
13C22⋊(C11⋊C16)C412yescomplemented
14C23×C4×C11D411yescharacteristic
15C23×Dic11—41no—
16C2×C11×M16—22no—
17C22×C8×C11—42no—
18C22×C8×C11C2×C411yescharacteristic
19C22×C8×C11C2×C411yescharacteristic
20C22×C8×C11C2×C411yescharacteristic
21C22×C8×C11D411yescharacteristic
22C22×C8×C11D411yescharacteristic
23C22×C8×C11Q811yescharacteristic
24C2×C4⋊Dic11—24no—
25C2×C4⋊Dic11—22no—
26C2×C4⋊Dic11—42no—
27C2×C4⋊Dic11—41no—
28C11×#108—42no—
29C11×C22⋊C8—41no—
30C11×C22⋊C8—41no—
31#66876—42no—
32C2×C11⋊C16—22no—
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—
47C11×M16—42no—
48C11×M16—42no—
49C2×C8×C11—22no—
50C2×C8×C11—22no—
51C2×C8×C11—41no—
52C2×C8×C11—41no—
53C2×C8×C11—41no—
54C2×C8×C11—41no—
55C2×C8×C11—42no—
56C2×C8×C11C4211yescharacteristic
57C2×C8×C11C22⋊C411yescharacteristic
58C2×C8×C11C4⋊C411yescharacteristic
59C2×C8×C11C4⋊C411yescharacteristic
60C4⋊Dic11—24no—
61C4⋊Dic11—44no—
62C4⋊Dic11—42no—
63C11⋊C16—42no—
64#2112—111no—
65#1810D1111yescharacteristic
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—
95C8×C11—82no—
96C23×C8C2×D1111yescharacteristic
97C22×C4⋊C4—221no—
98C2×M32—221no—
99C2×#108Dic1112yescomplemented
100#407—21no—
101C22⋊C16—112no—
102C22⋊C16—221no—
103#341—21no—
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×C4C22⋊D1111yescharacteristic
127C2×M16—22no—
128C22×C8—42no—
129C22×C8Dic2211yescharacteristic
130C22×C8C4×D1111yescharacteristic
131C22×C8C4×D1111yescharacteristic
132C22×C8D4411yescharacteristic
133C22×C8C2×Dic1111yescharacteristic
134C22×C8C22⋊D1111yescharacteristic
135C2×C4⋊C4—224no—
136C2×C4⋊C4—222no—
137C2×C4⋊C4—442no—
138C2×C4⋊C4—441no—
139M32—442no—
140C2×C16—222no—
141#108—42no—
142C22⋊C8—41no—
143C22⋊C8—41no—
144C2×C11—21no—
145C2×C11—22no—
146C2×C11—21no—
147C2×C11—22no—
148C2×C11#129411yescharacteristic
149C2×C11#138311yescharacteristic
150C2×C11#138711yescharacteristic
151C24#432511yescharacteristic
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—444no—
155C22×C4—442no—
156C22×C4—882no—
157C22×C4—882no—
158C22×C4Dic11⋊C411yescharacteristic
159C22×C4(C2×D11)⋊C411yescharacteristic
160C22×C4#432311yescharacteristic
161C22×C4#432411yescharacteristic
162C22×C4#432611yescharacteristic
163C22×C4C22⋊Dic1111yescharacteristic
164M16—42no—
165M16—42no—
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—42no—
173C2×C8C4×Dic1111yescharacteristic
174C2×C8Dic11⋊C411yescharacteristic
175C2×C8C4⋊Dic1111yescharacteristic
176C2×C8(C2×D11)⋊C411yescharacteristic
177C4⋊C4—224no—
178C4⋊C4—442no—
179C4⋊C4—444no—
180C16—442no—
181C11#726411yescharacteristic, complemented, Sylow
182C23—22no—
183C23—21no—
184C23—21no—
185C23—22no—
186C23#6687211yescharacteristic
187C23#6687311yescharacteristic
188C23#6689911yescharacteristic
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—444no—
197C2×C4—888no—
198C2×C4—882no—
199C2×C4—882no—
200C2×C4#6687111yescharacteristic
201C2×C4#6687411yescharacteristic
202C2×C4C11⋊#9511yescharacteristic
203C2×C4#6689611yescharacteristic
204C2×C4#6689812yes—
205C2×C4#6690112yes—
206C8—21no—
207C8—21no—
208C8—21no—
209C8—21no—
210C8—82no—
211C22—24no—
212C22—24no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22#1062213212yes—
220C22#1062213311yescharacteristic
221C22#1062213411yescharacteristic
222C22#1062216711yescharacteristic
223C22#1062217612yes—
224C4—21no—
225C4—21no—
226C4—884no—
227C4#1062216411yescharacteristic
228C4#1062217011yescharacteristic
229C4#1062217512yes—
230C2—21no—
231C2—22no—
232C2—21no—
233C2—22no—
234C2#1306649411yescharacteristic
235C2#1306671611yescharacteristic
236C2#1306672611yescharacteristic
subgroupG/H
centerC22#10622167
commutatorC2×C8×C11C42
FrattiniC23×C8C2×D11
FittingC11×#1810C2
socleC22×C11#340
prime radicalC24×C11SD16
cosocleC23×C8×C11C22
hypercenter#1810D11
hypocenterC11#7264
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #1810

Complements

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

NH ≅ G/Ntype
6. C2×C11×#108C4semidirect
13. C22⋊(C11⋊C16)C4semidirect
99. C2×#108Dic11semidirect
181. C11#7264semidirect

Maximal subgroups

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

subgroupindex
#130702272
C2×#106221892
C11×#18102
#726411