Finite Group Databasebeta

← #14672320

Subgroups — #14672320

Order 2816.

316 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 111 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#13077548C211yesmaximal, characteristic
2#13070221C211yesmaximal, characteristic
3#13066701C212yesmaximal
4#13066697C212yesmaximal
5C11×#2153C211yesmaximal, characteristic
6#10623048C411yescharacteristic
7C2×C11×M32C2212yes—
8C11×#405C2211yescharacteristic
9#10622732C411yescharacteristic
10#10622731C411yescharacteristic
11#10622714C2211yescharacteristic
12C2×C8×Dic11C2211yescharacteristic
13C2×#66876C2212yes—
14#10622612C411yescharacteristic
15#10622314—22no—
16C8×Dic22—22no—
17C11×#364—22no—
18#10622104—22no—
19C2×C11×M16C2×C411yescharacteristic
20C22×C8×C11C2311yescharacteristic
21C11×#117C2×C411yescharacteristic
22#66979C2×C411yescharacteristic
23C2×C4×Dic11C2×C411yescharacteristic
24C2×#4318C2×C411yescharacteristic
25C22×C11⋊C8C2×C411yescharacteristic
26#66943—21no—
27#66941—21no—
28#66931—22no—
29C4×Dic22—22no—
30C11×M32—22no—
31C11×M32—22no—
32C2×C11×C16—22no—
33C11×#97D412yes—
34C4×C8×C11D412yes—
35#66879—21no—
36Dic11⋊C8—22no—
37Dic11⋊C8—22no—
38C8×Dic11—21no—
39C8×Dic11—21no—
40C8×Dic11—21no—
41#66876—22no—
42#66876Q814yescomplemented
43C2×C11⋊C16—22no—
44C4⋊(C11⋊C8)—22no—
45#13270—111nomaximal, Sylow
46C22×C4×C11C22×C411yescharacteristic
47C22×Dic11—21no—
48C2×Dic22—22no—
49C11×M16—22no—
50C2×C8×C11C22⋊C412yes—
51C2×C8×C11C2×D411yescharacteristic
52C2×C8×C11C2×D411yescharacteristic
53C2×C8×C11C2×Q812yes—
54C2×C8×C11#4112yes—
55C11×C4⋊C4—21no—
56C11×C22⋊C4—21no—
57C42×C11C22⋊C412yes—
58C22⋊Dic11M1612yes—
59C4⋊Dic11—22no—
60C4⋊Dic11—21no—
61Dic11⋊C4—22no—
62Dic11⋊C4—22no—
63C4×Dic11—21no—
64C4×Dic11—21no—
65C4×Dic11M1611yescharacteristic
66C4×Dic11M1611yescharacteristic
67#4318—22no—
68C2×C11⋊C8—21no—
69C2×C11⋊C8—21no—
70C2×C11⋊C8—22no—
71C11×C16—42no—
72C11⋊C16—24no—
73#2960—111no—
74#2153D1111yescharacteristic
75#2110—111no—
76#1378—112no—
77#1376—112no—
78C23×C11C2×M1611yescharacteristic
79C2×C4×C11—22no—
80C2×C4×C11C2×C22⋊C411yescharacteristic
81C2×C4×C11C4×Q812yes—
82C2×C4×C11C2×M1611yescharacteristic
83C2×C4×C11#13112yes—
84C2×Dic11—21no—
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11—42no—
88Dic22—44no—
89C8×C11—22no—
90C8×C11C22⋊Q812yes—
91C8×C11#12411yescharacteristic
92C8×C11C4⋊Q811yescharacteristic
93C11⋊C8—41no—
94C11⋊C8—41no—
95#533—111no—
96C2×M32—112no—
97C2×M32C2×D1112yes—
98#446—222no—
99C8×Q8—222no—
100#424—111no—
101#424—111no—
102#423—111no—
103#405—111no—
104#405C2×D1111yescharacteristic
105C2×C4×C8—111no—
106#364—22no—
107#347—222no—
108C22×C11—41no—
109C22×C11#40711yescharacteristic
110C22×C11#44612yes—
111C4×C11—42no—
112C4×C11#39111yescharacteristic
113C4×C11#40811yescharacteristic
114C4×C11#44612yes—
115Dic11—22no—
116Dic11—42no—
117Dic11—41no—
118C2×M16—111no—
119C2×M16C4×D1111yescharacteristic
120C22×C8—111no—
121C22×C8C22×D1111yescharacteristic
122C4⋊Q8—221no—
123#125—221no—
124C22⋊Q8—222no—
125C4×Q8—222no—
126#117—111no—
127#117C4×D1111yescharacteristic
128C2×C42—111no—
129M32—22no—
130M32—22no—
131M32—114no—
132M32—222no—
133C2×C16—22no—
134C2×C16—222no—
135C4⋊C8—222no—
136C4⋊C8—222no—
137C4⋊C8—222no—
138#97—221no—
139#97D4412yes—
140C4×C8—221no—
141C4×C8—221no—
142C4×C8—221no—
143C4×C8C22⋊D1112yes—
144C2×C11—21no—
145C2×C11—22no—
146C2×C11#198511yescharacteristic
147C2×Q8—222no—
148C22×C4—221no—
149C22×C4C2×C4×D1111yescharacteristic
150M16—22no—
151M16—222no—
152C2×C8—222no—
153C2×C8—221no—
154C2×C8—221no—
155C2×C8(C2×D11)⋊C412yes—
156C2×C8C2×D4411yescharacteristic
157C2×C8#434112yes—
158C2×C8Q8×D1112yes—
159C2×C8C2×C22⋊D1111yescharacteristic
160C4⋊C4—21no—
161C4⋊C4—222no—
162C4⋊C4—222no—
163C4⋊C4—222no—
164C4⋊C4—221no—
165C22⋊C4—21no—
166C22⋊C4—112no—
167C42—111no—
168C42—111no—
169C42—221no—
170C42—221no—
171C42(C2×D11)⋊C412yes—
172C16—42no—
173C16—224no—
174C11#1327011yescharacteristic, complemented, Sylow
175C23M16×D1111yescharacteristic
176Q8—444no—
177C2×C4—22no—
178C2×C4—221no—
179C2×C4—221no—
180C2×C4—222no—
181C2×C4—442no—
182C2×C4#6694012yes—
183C2×C4#6695412yes—
184C2×C4M16×D1111yescharacteristic
185C2×C4C2×(C2×D11)⋊C411yescharacteristic
186C8—22no—
187C8—441no—
188C8—441no—
189C8#6695012yes—
190C8#6698911yescharacteristic
191C8#6699711yescharacteristic
192C22—41no—
193C22#1062244112yes—
194C22#1062273911yescharacteristic
195C4—42no—
196C4—222no—
197C4—441no—
198C4—442no—
199C4#1062244112yes—
200C4#1062258711yescharacteristic
201C4#1062272311yescharacteristic
202C2—21no—
203C2—22no—
204C2#1306955511yescharacteristic
subgroupG/H
centerC8#66989
commutatorC22×C4×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#2153C2
socleC2×C11#1985
prime radicalC23×C11C2×M16
cosocleC22×C8×C11C23
hypercenter#2153D11
hypocenterC11#13270
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2153

Complements

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

NH ≅ G/Ntype
42. #66876Q8semidirect
174. C11#13270semidirect

Maximal subgroups

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

subgroupindex
#130775482
#130702212
#130667012
#130666972
C11×#21532
#1327011