Finite Group Databasebeta

← #14910205

Subgroups — #14910205

Order 2816.

464 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 143 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#13079275C212yesmaximal
2#13070781C214yesmaximal, complemented
3#13070724C212yesmaximal
4#13070707C212yesmaximal
5#13070667C214yesmaximal, complemented
6C11×#2151C211yesmaximal, characteristic
7#10623049—22no—
8C2×C11×M32C2211yescharacteristic
9C22×C11×C16C2211yescharacteristic
10C11×#405C2211yescharacteristic
11#10622750—22no—
12#10622729C2214yes—
13C2×Dic88C2212yes—
14C2×Dic88C2212yes—
15#10622329—22no—
16#10622316—22no—
17#10622312C2212yes—
18C4×Dic44C2214yes—
19#10622296C2212yes—
20C11×C4⋊C16C2214yes—
21#10622143C2212yes—
22#10622142C2212yes—
23#10622141C2214yes—
24#10622141C2214yes—
25C2×C11×M16D411yescharacteristic
26C22×C8×C11C2311yescharacteristic
27C11×#117D411yescharacteristic
28#66977—24no—
29C2×Dic44—22no—
30C2×Dic44C2314yes—
31#66942—44no—
32#66932—44no—
33#66923—22no—
34#66922—22no—
35C4×Dic22—24no—
36C11×M32—41no—
37C2×C11×C16—41no—
38C2×C11×C16C2312yes—
39C2×C11×C16C2312yes—
40C11×#97D412yes—
41C4×C8×C11C2312yes—
42#66882C2314yes—
43#66881—22no—
44#66880—24no—
45#66880—24no—
46Dic88—42no—
47Dic88—42no—
48#33827—111nomaximal, Sylow
49C22×C4×C11C2×D411yescharacteristic
50C2×Dic22—24no—
51C11×M16—41no—
52C2×C8×C11—21no—
53C2×C8×C11—21no—
54C2×C8×C11C2×D411yescharacteristic
55C2×C8×C11C2×D412yes—
56C2×C8×C11C2411yescharacteristic
57C11×C4⋊C4D812yes—
58C11×C22⋊C4D812yes—
59C42×C11C2×D412yes—
60C22⋊Dic11—44no—
61C4⋊Dic11—24no—
62C4⋊Dic11—44no—
63Dic11⋊C4—44no—
64Dic11⋊C4—44no—
65Dic11⋊C4—44no—
66C4×Dic11—44no—
67Dic44—24no—
68Dic44—24no—
69Dic44—44no—
70C11×C16—22no—
71C11×C16—22no—
72#3177—112no—
73#2229—114no—
74#2219—112no—
75#2216—112no—
76#2209—114no—
77#2151D1111yescharacteristic
78C23×C11C2×D811yescharacteristic
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11C2×D814yes—
82C2×C4×C11C2×D811yescharacteristic
83C2×C4×C11C22×D411yescharacteristic
84C2×Dic11—44no—
85C2×Dic11—44no—
86Dic22—44no—
87Dic22—44no—
88C8×C11—21no—
89C8×C11—22no—
90C8×C11H(5,𝔽2)11yescharacteristic
91C8×C112−1+411yescharacteristic
92#541—222no—
93C2×Q32—112no—
94C2×Q32—112no—
95C2×M32C2×D1111yescharacteristic
96C22×C16C2×D1111yescharacteristic
97#499—112no—
98#494—112no—
99#491—222no—
100#470—222no—
101#467—114no—
102#441—222no—
103C4×Q16—114no—
104#405C2×D1111yescharacteristic
105#367—112no—
106#366—112no—
107C4⋊C16C2×D1114yes—
108#358—114no—
109#358—114no—
110C22×C11—22no—
111C22×C11—21no—
112C22×C11C22×D811yescharacteristic
113C4×C11—24no—
114C4×C11—21no—
115C4×C11#53711yescharacteristic
116C4×C11#57511yescharacteristic
117Dic11—84no—
118Dic11—84no—
119C2×Q16—114no—
120C2×Q16—222no—
121C2×M16D4411yescharacteristic
122C22×C8C22×D1111yescharacteristic
123C4⋊Q8—222no—
124#126—444no—
125#125—222no—
126#125—444no—
127C22⋊Q8—224no—
128C4×Q8—224no—
129#117D4411yescharacteristic
130Q32—442no—
131Q32—442no—
132M32—41no—
133C2×C16—41no—
134C2×C16C22×D1112yes—
135C2×C16C22×D1112yes—
136#107—114no—
137#106—222no—
138#103—224no—
139#103—224no—
140#97D4412yes—
141C4×C8C22×D1112yes—
142C2×C11—41no—
143C2×C11#324511yescharacteristic
144C2×C11#341712yes—
145C2×Q8—224no—
146C22×C4C2×D4411yescharacteristic
147Q16—224no—
148Q16—224no—
149Q16—444no—
150M16—41no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8C2×D4412yes—
154C2×C8C2×D4411yescharacteristic
155C2×C8C23×D1111yescharacteristic
156C4⋊C4—224no—
157C4⋊C4—444no—
158C4⋊C4—444no—
159C4⋊C4—444no—
160C4⋊C4—444no—
161C4⋊C4D8812yes—
162C22⋊C4—444no—
163C22⋊C4D8812yes—
164C42—444no—
165C42C2×D4412yes—
166C16—22no—
167C16—22no—
168C11#3382711yescharacteristic, complemented, Sylow
169C23C2×D8811yescharacteristic
170Q8—444no—
171Q8—444no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—444no—
175C2×C4—444no—
176C2×C4C2×D8814yes—
177C2×C4C2×D8811yescharacteristic
178C2×C4C22×D4411yescharacteristic
179C8—22no—
180C8—21no—
181C8#6703711yescharacteristic
182C8#6704011yescharacteristic
183C22—21no—
184C22—22no—
185C22C22×D8811yescharacteristic
186C4—21no—
187C4—24no—
188C4—884no—
189C4—884no—
190C4#1062304111yescharacteristic
191C4#1062327911yescharacteristic
192C2—41no—
193C2#1307992611yescharacteristic
194C2#1308176912yes—
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2151C2
socleC22×C11C22×D8
prime radicalC23×C11C2×D8
hypercenter#2151D11
hypocenterC11#33827
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2151

Complements

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

NH ≅ G/Ntype
2. #13070781C2semidirect
5. #13070667C2semidirect
168. C11#33827semidirect

Maximal subgroups

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

subgroupindex
#130792752
#130707812
#130707242
#130707072
#130706672
C11×#21512
#3382711