Finite Group Databasebeta

← #13071192

Subgroups — #13071192

Order 1408.

1160 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C23×C22⋊D11C211yesmaximal, characteristic
2C2×C22⋊C4×D11C212yesmaximal, complemented
3C11×#379C211yesmaximal, characteristic, complemented
4#10622860C211yesmaximal, characteristic, complemented
5#10622569C218yesmaximal, complemented
6#10622556C212yesmaximal, complemented
7C25×C11C2211yescharacteristic
8C24×D11C2211yescharacteristic
9C22×C22⋊D11—28no—
10C22×C22⋊D11C418yescomplemented
11C22×C22⋊D11C2214yes—
12C23×Dic11C2211yescharacteristic
13C22×C4×D11C2214yescomplemented
14C2×C11×C22⋊C4C2212yes—
15C2×C11×C22⋊C4C2214yescomplemented
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2214yescomplemented
18C2×(C2×D11)⋊C4C2214yescomplemented
19C22⋊C4×D11—28no—
20C11⋊#95C2218yescomplemented
21C24×C11—24no—
22C24×C11—44no—
23C24×C11C2×C414yescomplemented
24C24×C11C2312yes—
25C24×C11C2311yescharacteristic
26C23×D11—44no—
27C23×D11C2×C414yes—
28C23×D11D418yes—
29C23×D11C2312yes—
30C22×C4×C11C2314yes—
31C2×C22⋊D11—232no—
32C2×C22⋊D11—28no—
33C2×C22⋊D11—28no—
34C2×C22⋊D11C2×C4116yescomplemented
35C22×Dic11—24no—
36C22×Dic11C2×C414yescomplemented
37C22×Dic11C2314yes—
38C22×Dic11C2312yes—
39C2×C4×D11—28no—
40C2×C4×D11—48no—
41C11×C22⋊C4—24no—
42C11×C22⋊C4—44no—
43C22⋊Dic11—24no—
44C22⋊Dic11—44no—
45(C2×D11)⋊C4—28no—
46#2308—111nomaximal, Sylow
47C23×C11—24no—
48C23×C11—28no—
49C23×C11—24no—
50C23×C11—24no—
51C23×C11—24no—
52C23×C11—48no—
53C23×C11—416no—
54C23×C11C22×C414yes—
55C23×C11C22×C412yes—
56C23×C11C2×D414yes—
57C23×C11C2411yescharacteristic
58C22×D11—28no—
59C22×D11—48no—
60C22×D11—416no—
61C22×D11C22⋊C4116yescomplemented
62C22×D11C22×C414yes—
63C22×D11C2×D414yes—
64C22×D11C2×D414yes—
65C2×C4×C11—24no—
66C2×C4×C11—28no—
67C22⋊D11—232no—
68C2×Dic11—28no—
69C2×Dic11—24no—
70C2×Dic11—24no—
71C2×Dic11—28no—
72C2×Dic11C22×C414yes—
73C4×D11—416no—
74C23×D4—111no—
75C22×C22⋊C4—112no—
76#386—118no—
77#381—112no—
78#379—111no—
79#379D1111yescharacteristic, complemented
80C22×C11—24no—
81C22×C11—28no—
82C22×C11—24no—
83C22×C11—24no—
84C22×C11—24no—
85C22×C11—416no—
86C22×C11—48no—
87C22×C11C2×C22⋊C414yes—
88C22×C11C23×C411yescharacteristic
89C22×C11C22×D412yes—
90C22×C11H(5,𝔽2)14yes—
91C2×D11—28no—
92C2×D11—28no—
93C2×D11—28no—
94C2×D11—416no—
95C2×D11C2×C22⋊C418yes—
96C4×C11—44no—
97Dic11—24no—
98Dic11—44no—
99C25—111no—
100C25C2×D1111yescharacteristic
101C22×D4—114no—
102C22×D4—118no—
103C22×D4—228no—
104C23×C4—111no—
105C23×C4—114no—
106C2×C22⋊C4—112no—
107C2×C22⋊C4—114no—
108C2×C22⋊C4—114no—
109C2×C22⋊C4—228no—
110C2×C22⋊C4C2×D1112yes—
111C2×C22⋊C4C2×D1114yescomplemented
112#95—118no—
113C2×C11—24no—
114C2×C11—44no—
115C2×C11C22×C22⋊C411yescharacteristic
116C2×C11#51812yes—
117C2×C11#53414yes—
118D11—28no—
119C24—24no—
120C24—44no—
121C24—112no—
122C24—114no—
123C24—118no—
124C24—444no—
125C24C4×D1114yescomplemented
126C24C22×D1112yes—
127C24C22×D1111yescharacteristic
128C2×D4—1116no—
129C2×D4—2232no—
130C2×D4—228no—
131C2×D4—228no—
132C22×C4—114no—
133C22×C4—112no—
134C22×C4—114no—
135C22×C4—228no—
136C22×C4—224no—
137C22×C4—448no—
138C22×C4C22×D1114yes—
139C22⋊C4—24no—
140C22⋊C4—44no—
141C22⋊C4—228no—
142C22⋊C4—224no—
143C22⋊C4—444no—
144C11#230811yescharacteristic, complemented, Sylow
145C23—24no—
146C23—28no—
147C23—24no—
148C23—24no—
149C23—24no—
150C23—48no—
151C23—416no—
152C23—114no—
153C23—114no—
154C23—114no—
155C23—1116no—
156C23—228no—
157C23—448no—
158C23—4416no—
159C23C2×C4×D1114yes—
160C23C2×C4×D1112yes—
161C23D4×D1114yes—
162C23C23×D1111yescharacteristic
163D4—2232no—
164C2×C4—24no—
165C2×C4—28no—
166C2×C4—114no—
167C2×C4—228no—
168C2×C4—224no—
169C2×C4—224no—
170C2×C4—228no—
171C2×C4—4416no—
172C22—24no—
173C22—28no—
174C22—24no—
175C22—24no—
176C22—24no—
177C22—416no—
178C22—48no—
179C22—118no—
180C22—228no—
181C22—228no—
182C22—228no—
183C22—4416no—
184C22C22⋊C4×D1114yes—
185C22C22×C4×D1111yescharacteristic
186C22C2×D4×D1112yes—
187C22#6703714yes—
188C4—44no—
189C4—224no—
190C4—444no—
191C2—24no—
192C2—44no—
193C2—228no—
194C2C2×C22⋊C4×D1111yescharacteristic
195C2#1062301712yes—
196C2#1062312014yes—
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC11×#379C2
socle, cosocleC23×C11C24
prime radicalC23×C22⋊D11C2
hypercenter#379D11
hypocenterC11#2308
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D11C2semidirect
3. C11×#379C2semidirect
4. #10622860C2semidirect
5. #10622569C2semidirect
6. #10622556C2semidirect
10. C22×C22⋊D11C4semidirect
13. C22×C4×D11C22semidirect
15. C2×C11×C22⋊C4C22semidirect
17. C2×C22⋊Dic11C22semidirect
18. C2×(C2×D11)⋊C4C22semidirect
20. C11⋊#95C22semidirect
23. C24×C11C2×C4semidirect
34. C2×C22⋊D11C2×C4semidirect
36. C22×Dic11C2×C4semidirect
61. C22×D11C22⋊C4semidirect
79. #379D11semidirect
111. C2×C22⋊C4C2×D11semidirect
125. C24C4×D11semidirect
144. C11#2308semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D112
C2×C22⋊C4×D112
C11×#3792
#106228602
#106225692
#106225562
#230811