Finite Group Databasebeta

← #13078547

Subgroups — #13078547

Order 1408.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×C11×#117C211yesmaximal, characteristic, complemented
2#10623322C211yesmaximal, characteristic
3#10622820C211yesmaximal, characteristic, complemented
4#10622616C214yesmaximal, complemented
5#10622609C214yesmaximal, complemented
6#10622579C212yesmaximal, complemented
7#10622577C212yesmaximal, complemented
8C23×C4×C11C2211yescharacteristic
9C2×#4339C2211yescharacteristic
10C11×#117—22no—
11C11×#117C2214yes—
12C2×C11×C4⋊C4C2212yes—
13C2×C11×C22⋊C4—21no—
14C2×C42×C11—21no—
15#67006—21no—
16#66983C2212yes—
17#66982—21no—
18C4×C22⋊D11—22no—
19#66979C2211yescharacteristic
20#66977C2212yes—
21C2×#4318C2212yes—
22C22⋊(C11⋊C8)C2214yes—
23#66874C2214yescomplemented
24#66873C2214yescomplemented
25#66872C2214yescomplemented
26#66871C2214yescomplemented
27C24×C11D411yescharacteristic
28C22×C4×C11—24no—
29C22×C4×C11—22no—
30C22×C4×C11D412yes—
31C22×C4×C11D411yescharacteristic
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C2×C22⋊D11—22no—
35C2×C22⋊D11—21no—
36#4339—24no—
37C2×D44C2311yescharacteristic
38C2×C4×D11—21no—
39C2×Dic22C2311yescharacteristic
40C11×C4⋊C4—22no—
41C11×C4⋊C4C2314yes—
42C11×C22⋊C4—24no—
43C42×C11—24no—
44C22⋊Dic11—22no—
45C22⋊Dic11—21no—
46(C2×D11)⋊C4—22no—
47C4⋊Dic11C2312yes—
48Dic11⋊C4—22no—
49C4×Dic11—21no—
50#4318—24no—
51C2×C11⋊C8C2314yes—
52#3093—111nomaximal, Sylow
53C23×C11—22no—
54C23×C11—42no—
55C23×C11C2×D412yes—
56C23×C11C2×D411yescharacteristic
57C22×D11—21no—
58C2×C4×C11—22no—
59C2×C4×C11—24no—
60C2×C4×C11—24no—
61C2×C4×C11—24no—
62C2×C4×C11—44no—
63C2×C4×C11C2×D412yes—
64C2×C4×C11C2×D411yescharacteristic
65C2×C4×C11#4114yes—
66C2×C4×C11C2411yescharacteristic
67C22⋊D11—44no—
68C22⋊D11—42no—
69C2×Dic11—22no—
70C2×Dic11—21no—
71D44—22no—
72C4×D11—42no—
73Dic22—22no—
74C11⋊C8—24no—
75#525—111no—
76C2×#117D1111yescharacteristic, complemented
77#485—114no—
78#482—114no—
79#428—112no—
80#417—112no—
81#407—111no—
82C22×C11—22no—
83C22×C11—22no—
84C22×C11—22no—
85C22×C11—22no—
86C22×C11—44no—
87C22×C11#12312yes—
88C22×C11C22×D411yescharacteristic
89C2×D11—41no—
90C2×D11—42no—
91C4×C11—22no—
92C4×C11—44no—
93C4×C11#12312yes—
94C4×C11C2×#4112yes—
95Dic11—41no—
96Dic11—42no—
97C2×#41—111no—
98C23×C4C2×D1111yescharacteristic
99C2×M16—112no—
100#123—221no—
101C22⋊Q8—112no—
102#121—112no—
103#120—221no—
104C4×D4—222no—
105#117—22no—
106#117—111no—
107#117C2×D1114yes—
108C2×C4⋊C4C2×D1112yes—
109C2×C22⋊C4—21no—
110C2×C42—21no—
111#107—114no—
112#106—114no—
113#103—114no—
114#102—114no—
115C22⋊C8—114no—
116C2×C11—22no—
117C2×C11—42no—
118C2×C11C2×#12311yescharacteristic
119C2×C11#57512yes—
120D11—81no—
121C24C22⋊D1111yescharacteristic
122#41—224no—
123C2×Q8—111no—
124C2×D4—111no—
125C2×D4—222no—
126C2×D4—221no—
127C22×C4—24no—
128C22×C4—22no—
129C22×C4—221no—
130C22×C4C22⋊D1111yescharacteristic
131C22×C4C22⋊D1112yes—
132C22×C4C22×D1112yes—
133C22×C4C22×D1111yescharacteristic
134M16—224no—
135C2×C8—114no—
136C4⋊C4—22no—
137C4⋊C4—112no—
138C4⋊C4—222no—
139C4⋊C4C22×D1114yes—
140C22⋊C4—24no—
141C22⋊C4—221no—
142C22⋊C4—222no—
143C22⋊C4—222no—
144C42—24no—
145C42—221no—
146C11#309311yescharacteristic, complemented, Sylow
147C23—22no—
148C23—42no—
149C23—221no—
150C23C2×C22⋊D1112yes—
151C23C2×C22⋊D1111yescharacteristic
152Q8—222no—
153D4—222no—
154D4—444no—
155D4—442no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—222no—
162C2×C4—221no—
163C2×C4—442no—
164C2×C4#433914yes—
165C2×C4C2×C22⋊D1112yes—
166C2×C4C2×C22⋊D1111yescharacteristic
167C2×C4C23×D1111yescharacteristic
168C8—224no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—441no—
175C22—442no—
176C22#6698212yes—
177C22C22×C22⋊D1111yescharacteristic
178C4—22no—
179C4—44no—
180C4—441no—
181C4—442no—
182C4#6698212yes—
183C4C2×#433912yes—
184C2—22no—
185C2—42no—
186C2—881no—
187C2C2×#6698211yescharacteristic
188C2#1062335312yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#117C2
socleC22×C11C22×D4
prime radical#10623322C2
hypercenterC2×#117D11
hypocenterC11#3093
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C11×#117C2semidirect
3. #10622820C2semidirect
4. #10622616C2semidirect
5. #10622609C2semidirect
6. #10622579C2semidirect
7. #10622577C2semidirect
23. #66874C22semidirect
24. #66873C22semidirect
25. #66872C22semidirect
26. #66871C22semidirect
76. C2×#117D11semidirect
146. C11#3093semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1172
#106233222
#106228202
#106226162
#106226092
#106225792
#106225772
#309311