Finite Group Databasebeta

← #13073999

Subgroups — #13073999

Order 1408.

468 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 185 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×#66923C211yesmaximal, characteristic
2C2×C4×Dic22C211yesmaximal, characteristic
3C4×C11×C4⋊C4C211yesmaximal, characteristic
4#10622598C212yesmaximal
5#10622598C212yesmaximal
6#10622541C214yesmaximal
7#10622274C212yesmaximal
8#10622269C212yesmaximal
9C22×Dic22C2211yescharacteristic
10C2×C11×C4⋊C4C2212yes—
11C2×C42×C11C2212yes—
12C2×C42×C11C2211yescharacteristic
13C2×C4⋊Dic11C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2214yes—
17C2×C4⋊Dic11C2214yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×C4×Dic11C2212yes—
22#66923—24no—
23C4×Dic22—24no—
24C11×#95C2212yes—
25C11⋊#95C2214yes—
26C11⋊#95C2214yes—
27C22×C4×C11C2311yescharacteristic
28C22×C4×C11C2311yescharacteristic
29C22×C4×C11C2314yes—
30C22×C4×C11C2311yescharacteristic
31C22×Dic11C2312yes—
32C22×Dic11C2312yes—
33C22×Dic11C2312yes—
34C22×Dic11C2312yes—
35C2×Dic22—24no—
36C2×Dic22—22no—
37C11×C4⋊C4Q818yescomplemented
38C42×C11—42no—
39C42×C11D414yes—
40C4⋊Dic11—28no—
41C4⋊Dic11—22no—
42C4⋊Dic11—22no—
43C4⋊Dic11—22no—
44C4⋊Dic11—44no—
45Dic11⋊C4—24no—
46Dic11⋊C4—24no—
47Dic11⋊C4—24no—
48C4×Dic11—24no—
49#2584—111nomaximal, Sylow
50C23×C11C2411yescharacteristic
51C2×C4×C11—24no—
52C2×C4×C11—22no—
53C2×C4×C11—24no—
54C2×C4×C11—21no—
55C2×C4×C11—21no—
56C2×C4×C11C2×D412yes—
57C2×C4×C11C2×D412yes—
58C2×C4×C11C2×D412yes—
59C2×C4×C11C2×Q818yes—
60C2×C4×C11C2×Q814yes—
61C2×Dic11—22no—
62C2×Dic11—22no—
63C2×Dic11—22no—
64C2×Dic11—22no—
65C2×Dic11—22no—
66C2×Dic11—24no—
67C2×Dic11—22no—
68C2×Dic11—22no—
69C2×Dic11—22no—
70C2×Dic11—22no—
71C2×Dic11#4114yes—
72Dic22—28no—
73C2×#125—111no—
74C2×C4×Q8—111no—
75#398—112no—
76#395—112no—
77#389—112no—
78#389—112no—
79#389—114no—
80C4×C4⋊C4D1111yescharacteristic
81C22×C11C22×D411yescharacteristic
82C22×C11C22×Q812yes—
83C22×C11C2×#4112yes—
84C22×C11H(5,𝔽2)11yescharacteristic
85C22×C112−1+411yescharacteristic
86C4×C11—22no—
87C4×C11—22no—
88C4×C11—28no—
89C4×C11C4⋊Q814yes—
90Dic11—24no—
91Dic11—42no—
92Dic11—42no—
93Dic11—42no—
94C22×Q8—111no—
95#125—224no—
96C4×Q8—224no—
97C2×C4⋊C4—112no—
98C2×C4⋊C4—111no—
99C2×C4⋊C4—112no—
100C2×C4⋊C4—111no—
101C2×C4⋊C4—111no—
102C2×C4⋊C4—112no—
103C2×C4⋊C4—114no—
104C2×C4⋊C4—114no—
105C2×C4⋊C4C2×D1112yes—
106C2×C42—112no—
107C2×C42C2×D1112yes—
108C2×C42C2×D1111yescharacteristic
109#95—114no—
110#95—114no—
111#95C2×D1112yes—
112C2×C11#52511yescharacteristic
113C2×C11C2×C4⋊Q811yescharacteristic
114C2×C11#53711yescharacteristic
115C2×C11#55412yes—
116C2×C11#55712yes—
117C2×Q8—224no—
118C2×Q8—222no—
119C22×C4—112no—
120C22×C4—112no—
121C22×C4—112no—
122C22×C4—112no—
123C22×C4C22×D1114yes—
124C22×C4C22×D1111yescharacteristic
125C22×C4C22×D1111yescharacteristic
126C22×C4C22×D1111yescharacteristic
127C4⋊C4—228no—
128C4⋊C4—224no—
129C4⋊C4—222no—
130C4⋊C4—224no—
131C4⋊C4—224no—
132C4⋊C4—222no—
133C4⋊C4—222no—
134C4⋊C4—444no—
135C4⋊C4Dic2218yescomplemented
136C42—42no—
137C42—224no—
138C42D4414yes—
139C11#258411yescharacteristic, complemented, Sylow
140C23C23×D1111yescharacteristic
141Q8—228no—
142C2×C4—21no—
143C2×C4—24no—
144C2×C4—21no—
145C2×C4—24no—
146C2×C4—22no—
147C2×C4—114no—
148C2×C4—222no—
149C2×C4—222no—
150C2×C4—222no—
151C2×C4—222no—
152C2×C4—222no—
153C2×C4—222no—
154C2×C4—222no—
155C2×C4—222no—
156C2×C4—222no—
157C2×C4—224no—
158C2×C4C2×Dic2218yes—
159C2×C4C2×Dic2214yes—
160C2×C4C2×D4412yes—
161C2×C4C2×D4412yes—
162C2×C4C2×D4412yes—
163C22C22×Dic2212yes—
164C22C22×D4411yescharacteristic
165C22#6703711yescharacteristic
166C22#6704011yescharacteristic
167C22#41×D1112yes—
168C4—22no—
169C4—22no—
170C4—28no—
171C4—224no—
172C4—442no—
173C4—442no—
174C4—442no—
175C4#6692214yes—
176C2C2×#6692211yescharacteristic
177C2#1062304111yescharacteristic
178C2#1062305511yescharacteristic
179C2#1062307012yes—
180C2#1062310012yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC4×C11×C4⋊C4C2
hypercenterC4×C4⋊C4D11
hypocenterC11#2584
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
37. C11×C4⋊C4Q8semidirect
135. C4⋊C4Dic22semidirect
139. C11#2584semidirect

Maximal subgroups

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

subgroupindex
C2×#669232
C2×C4×Dic222
C4×C11×C4⋊C42
#106225982
#106225412
#106222742
#106222692
#258411