Finite Group Databasebeta

← #14663090

Subgroups — #14663090

Order 2816.

430 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 155 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#13070415C212yesmaximal, complemented
2#13066540C214yesmaximal, complemented
3C2×C8×D4×C11C211yesmaximal, characteristic
4C23×C8×C11C412yes—
5C2×C4×D4×C11C411yescharacteristic
6C8×D4×C11—22no—
7C8×D4×C11—22no—
8C2×C11×C4⋊C8C411yescharacteristic
9C2×C11×C22⋊C8C2212yes—
10C2×C4×C8×C11C2211yescharacteristic
11C22⋊(C11⋊C16)C2214yes—
12C4⋊(C11⋊C16)—22no—
13C4×C11⋊C16—22no—
14C22×D4×C11C811yescharacteristic
15C23×C4×C11C2×C412yes—
16C22×C8×C11—22no—
17C22×C8×C11—22no—
18C22×C8×C11—44no—
19C22×C8×C11C2×C411yescharacteristic
20C22×C8×C11C2×C412yes—
21C22×C8×C11C2311yescharacteristic
22C4×D4×C11—22no—
23C4×D4×C11—22no—
24C2×C11×C4⋊C4C811yescharacteristic
25C2×C11×C22⋊C4C812yes—
26C2×C42×C11C2×C411yescharacteristic
27C11×C4⋊C8—22no—
28C11×C22⋊C8—24no—
29C4×C8×C11D412yes—
30C4×C8×C11D412yes—
31C2×C11⋊C16—24no—
32#11487—111nomaximal, Sylow
33C24×C11C2×C812yes—
34C2×D4×C11—22no—
35C2×D4×C11—22no—
36C2×D4×C11C1614yescomplemented
37C22×C4×C11—22no—
38C22×C4×C11—22no—
39C22×C4×C11—42no—
40C22×C4×C11—42no—
41C22×C4×C11C2×C812yes—
42C22×C4×C11C2×C811yescharacteristic
43C22×C4×C11C2×C811yescharacteristic
44C22×C4×C11C22×C411yescharacteristic
45C2×C8×C11—22no—
46C2×C8×C11—22no—
47C2×C8×C11—41no—
48C2×C8×C11—42no—
49C2×C8×C11—44no—
50C2×C8×C11—44no—
51C2×C8×C11C22⋊C411yescharacteristic
52C2×C8×C11C22⋊C411yescharacteristic
53C2×C8×C11C2×D412yes—
54C11×C4⋊C4—22no—
55C11×C22⋊C4—24no—
56C42×C11C22⋊C412yes—
57C42×C11M1612yes—
58C11⋊C16—44no—
59C2×C8×D4D1111yescharacteristic
60#2162—112no—
61#1314—114no—
62C23×C11—22no—
63C23×C11—22no—
64C23×C11—42no—
65C23×C11—42no—
66C23×C11C2×C1614yes—
67C23×C11C22×C811yescharacteristic
68D4×C11—28no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—22no—
72C2×C4×C11—41no—
73C2×C4×C11—44no—
74C2×C4×C11—42no—
75C2×C4×C11—42no—
76C2×C4×C11—42no—
77C2×C4×C11C22⋊C812yes—
78C2×C4×C11C22⋊C812yes—
79C2×C4×C11C2×C1612yes—
80C2×C4×C11M3212yes—
81C2×C4×C11C2×C22⋊C411yescharacteristic
82C2×C4×C11C2×M1611yescharacteristic
83C8×C11—22no—
84C8×C11—21no—
85C8×C11—42no—
86C8×C11#10012yes—
87C23×C8Dic1112yes—
88C2×C4×D4Dic1111yescharacteristic
89C8×D4—22no—
90C8×D4—22no—
91C2×C4⋊C8Dic1111yescharacteristic
92C2×C22⋊C8C2×D1112yes—
93C2×C4×C8C2×D1111yescharacteristic
94C4⋊C16—222no—
95C22⋊C16—114no—
96C4×C16—222no—
97C22×C11—21no—
98C22×C11—21no—
99C22×C11—24no—
100C22×C11—44no—
101C22×C11—44no—
102C22×C11—42no—
103C22×C11—42no—
104C22×C11C2×C22⋊C811yescharacteristic
105C22×C11C22×C1611yescharacteristic
106C22×C11C2×M3211yescharacteristic
107C4×C11—22no—
108C4×C11—21no—
109C4×C11—42no—
110C4×C11C22⋊C1614yes—
111C4×C11#41011yescharacteristic
112C4×C11C2×#10011yescharacteristic
113C22×D4C11⋊C811yescharacteristic
114C23×C4C2×Dic1112yes—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—44no—
118C22×C8C2×Dic1111yescharacteristic
119C22×C8C2×Dic1112yes—
120C22×C8C22×D1111yescharacteristic
121C4×D4—22no—
122C4×D4—22no—
123C2×C4⋊C4C11⋊C811yescharacteristic
124C2×C22⋊C4C11⋊C812yes—
125C2×C42C2×Dic1111yescharacteristic
126C2×C16—224no—
127C4⋊C8—22no—
128C22⋊C8—24no—
129C4×C8C22⋊D1112yes—
130C4×C8C22⋊D1112yes—
131C2×C11—21no—
132C2×C11—21no—
133C2×C11—44no—
134C2×C11#146011yescharacteristic
135C2×C11C2×C22⋊C1611yescharacteristic
136C2×C11#211511yescharacteristic
137C24C2×C11⋊C812yes—
138C2×D4—22no—
139C2×D4—22no—
140C2×D4C11⋊C1614yescomplemented
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4C2×C11⋊C812yes—
146C22×C4C2×C11⋊C811yescharacteristic
147C22×C4C2×C11⋊C811yescharacteristic
148C22×C4C22×Dic1111yescharacteristic
149C2×C8—22no—
150C2×C8—22no—
151C2×C8—41no—
152C2×C8—44no—
153C2×C8—44no—
154C2×C8—42no—
155C2×C8C22⋊Dic1111yescharacteristic
156C2×C8C22⋊Dic1111yescharacteristic
157C2×C8C2×C22⋊D1112yes—
158C4⋊C4—22no—
159C22⋊C4—24no—
160C42#431812yes—
161C42C22⋊Dic1112yes—
162C16—444no—
163C11#1148711yescharacteristic, complemented, Sylow
164C23—22no—
165C23—22no—
166C23—42no—
167C23—42no—
168C23C2×C11⋊C1614yes—
169C23C22×C11⋊C811yescharacteristic
170D4—28no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—41no—
175C2×C4—44no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4C2×C11⋊C1612yes—
180C2×C4#6687612yes—
181C2×C4C22⋊(C11⋊C8)12yes—
182C2×C4C22⋊(C11⋊C8)12yes—
183C2×C4C2×#431811yescharacteristic
184C2×C4C2×C22⋊Dic1111yescharacteristic
185C8—21no—
186C8—22no—
187C8—42no—
188C8#6689712yes—
189C22—21no—
190C22—21no—
191C22—24no—
192C22—44no—
193C22—44no—
194C22—42no—
195C22—42no—
196C22C22×C11⋊C1611yescharacteristic
197C22C2×#6687611yescharacteristic
198C22C2×C22⋊(C11⋊C8)11yescharacteristic
199C4—22no—
200C4—21no—
201C4—42no—
202C4C22⋊(C11⋊C16)14yes—
203C4C2×#6689711yescharacteristic
204C4#1062285311yescharacteristic
205C2—21no—
206C2—21no—
207C2—44no—
208C2#1306693711yescharacteristic
209C2C2×C22⋊(C11⋊C16)11yescharacteristic
210C2#1307023711yescharacteristic
subgroupG/H
centerC2×C8C22⋊Dic11
commutatorC22×C11C22×C16
FrattiniC22×C8C22×D11
FittingC2×C8×D4×C11C2
socleC22×C11C2×C22⋊C8
prime radicalC22×D4×C11C8
cosocleC22×C8×C11C23
hypercenterC2×C8×D4D11
hypocenterC11#11487
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. #13070415C2semidirect
2. #13066540C2semidirect
36. C2×D4×C11C16semidirect
140. C2×D4C11⋊C16semidirect
163. C11#11487semidirect

Maximal subgroups

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

subgroupindex
#130704152
#130665402
C2×C8×D4×C112
#1148711