Finite Group Databasebeta

← #13073088

Subgroups — #13073088

Order 1408.

708 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 181 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×#121C211yesmaximal, characteristic
2C2×#66988C214yesmaximal, complemented
3C22×C4⋊Dic11C211yesmaximal, characteristic, complemented
4#10622834C212yesmaximal, complemented
5C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
6#10622589C212yesmaximal, complemented
7#10622562C214yesmaximal, complemented
8C22×D4×C11C2212yes—
9C22×D4×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C23×Dic11C2212yes—
12C11×#121—24no—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4C2212yes—
15C2×C22⋊Dic11C2218yes—
16C2×C22⋊Dic11C2212yes—
17#66988—216no—
18C2×C4⋊Dic11—24no—
19C2×C4⋊Dic11C2212yes—
20C2×C4⋊Dic11C2212yes—
21C2×Dic11⋊C4C2218yes—
22C2×C4×Dic11C2212yes—
23C11⋊#95C2212yes—
24C24×C11C2312yes—
25C24×C11C2311yescharacteristic
26C2×D4×C11—28no—
27C2×D4×C11—24no—
28C2×D4×C11—22no—
29C2×D4×C11—24no—
30C22×C4×C11—24no—
31C22×C4×C11D414yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C22×Dic11—24no—
36C22×Dic11—28no—
37C22×Dic11C2314yes—
38C22×Dic11C2314yes—
39C11×C4⋊C4—22no—
40C11×C22⋊C4—24no—
41C22⋊Dic11—216no—
42C22⋊Dic11D418yescomplemented
43C4⋊Dic11—24no—
44C4⋊Dic11—24no—
45Dic11⋊C4—216no—
46C4×Dic11—24no—
47#2501—111nomaximal, Sylow
48C23×C11—22no—
49C23×C11—22no—
50C23×C11—24no—
51C23×C11—22no—
52C23×C11—24no—
53C23×C11—24no—
54C23×C11C2×D414yes—
55C23×C11C2×D412yes—
56C23×C11C2411yescharacteristic
57D4×C11—48no—
58D4×C11—44no—
59C2×C4×C11—22no—
60C2×C4×C11—28no—
61C2×C4×C11—24no—
62C2×C4×C11—22no—
63C2×C4×C11C2×D412yes—
64C2×C4×C11C2×D412yes—
65C2×C4×C11#4114yes—
66C2×Dic11—24no—
67C2×Dic11—24no—
68C2×Dic11—28no—
69C2×Dic11—24no—
70C2×Dic11—48no—
71C2×Dic11C2×D418yes—
72C2×#123—114no—
73C2×#121D1111yescharacteristic
74C22×C4⋊C4—111no—
75#399—114no—
76#390—112no—
77#384—112no—
78C4×C22⋊C4—111no—
79C22×C11—22no—
80C22×C11—22no—
81C22×C11—28no—
82C22×C11—42no—
83C22×C11—42no—
84C22×C11—42no—
85C22×C11—48no—
86C22×C11#12714yes—
87C22×C11C22×D412yes—
88C22×C11C22×D411yescharacteristic
89C22×C11C2×#4112yes—
90C22×C112−1+412yes—
91C4×C11—22no—
92C4×C11—42no—
93C4×C11#12314yescomplemented
94Dic11—28no—
95Dic11—44no—
96C22×D4C2×D1112yes—
97C22×D4C2×D1111yescharacteristic
98C23×C4—112no—
99C23×C4C2×D1111yescharacteristic
100#123—2216no—
101#121—24no—
102C2×C4⋊C4—112no—
103C2×C4⋊C4—112no—
104C2×C4⋊C4—118no—
105C2×C4⋊C4—224no—
106C2×C4⋊C4C2×D1111yescharacteristic
107C2×C22⋊C4—112no—
108C2×C22⋊C4—118no—
109C2×C22⋊C4C2×D1112yes—
110C2×C42—112no—
111#95—112no—
112C2×C11—24no—
113C2×C11—82no—
114C2×C11C2×#12311yescharacteristic
115C2×C11C2×#12711yescharacteristic
116C2×C11#53611yescharacteristic
117C2×C11#54714yes—
118C24C22×D1112yes—
119C24C22×D1111yescharacteristic
120C2×D4—28no—
121C2×D4—24no—
122C2×D4—24no—
123C2×D4—22no—
124C22×C4—24no—
125C22×C4—114no—
126C22×C4—114no—
127C22×C4—228no—
128C22×C4—224no—
129C22×C4C22⋊D1114yes—
130C22×C4C22×D1112yes—
131C22×C4C22×D1111yescharacteristic
132C22×C4C22×D1111yescharacteristic
133C4⋊C4—22no—
134C4⋊C4—2216no—
135C4⋊C4—224no—
136C4⋊C4—224no—
137C22⋊C4—24no—
138C22⋊C4—118no—
139C22⋊C4—2216no—
140C42—224no—
141C11#250111yescharacteristic, complemented, Sylow
142C23—22no—
143C23—22no—
144C23—24no—
145C23—24no—
146C23—24no—
147C23—22no—
148C23D4×D1114yes—
149C23C2×C22⋊D1112yes—
150C23C23×D1111yescharacteristic
151D4—48no—
152D4—44no—
153C2×C4—22no—
154C2×C4—28no—
155C2×C4—24no—
156C2×C4—22no—
157C2×C4—118no—
158C2×C4—224no—
159C2×C4—224no—
160C2×C4—228no—
161C2×C4—224no—
162C2×C4—448no—
163C2×C4#434114yes—
164C2×C4C2×C22⋊D1112yes—
165C2×C4C2×C22⋊D1112yes—
166C22—22no—
167C22—22no—
168C22—28no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—48no—
173C22#6699314yes—
174C22C2×D4×D1112yes—
175C22C2×#434112yes—
176C22#6704312yes—
177C22C22×C22⋊D1111yescharacteristic
178C4—22no—
179C4—42no—
180C4—228no—
181C4—444no—
182C4#6698814yescomplemented
183C2—24no—
184C2—82no—
185C2#1062314214yes—
186C2C2×#6698811yescharacteristic
187C2C2×#6699311yescharacteristic
188C2#1062335611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2501
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#66988C2semidirect
3. C22×C4⋊Dic11C2semidirect
4. #10622834C2semidirect
5. C4×C22⋊Dic11C2semidirect
6. #10622589C2semidirect
7. #10622562C2semidirect
42. C22⋊Dic11D4semidirect
93. C4×C11#123semidirect
141. C11#2501semidirect
182. C4#66988semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669882
C22×C4⋊Dic112
#106228342
C4×C22⋊Dic112
#106225892
#106225622
#250111