Finite Group Databasebeta

← #13074493

Subgroups — #13074493

Order 1408.

416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#125C211yesmaximal, characteristic
2C2×C4×Dic22C211yesmaximal, characteristic
3#10622599C212yesmaximal
4#10622595C212yesmaximal
5#10622593C212yesmaximal
6#10622592C212yesmaximal
7#10622591C214yesmaximal
8#10622550C211yesmaximal, characteristic
9C22×Dic22C2211yescharacteristic
10C11×#125—24no—
11C2×C11×C4⋊C4C2212yes—
12C2×C11×C4⋊C4C2212yes—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C42×C11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2214yes—
19C2×C4×Dic11C2212yes—
20C4×Dic22—24no—
21C11⋊#95C2212yes—
22C11⋊#95C2212yes—
23C11⋊#95C2212yes—
24C11⋊#95C2214yes—
25C11⋊#95C2214yes—
26C11⋊#95C2214yes—
27C22×C4×C11C2312yes—
28C22×C4×C11C2312yes—
29C22×C4×C11C2311yescharacteristic
30C22×C4×C11C2311yescharacteristic
31C22×C4×C11C2311yescharacteristic
32C22×Dic11C2314yes—
33C22×Dic11C2312yes—
34C22×Dic11C2312yes—
35C2×Dic22—24no—
36C2×Dic22—22no—
37C11×C4⋊C4—24no—
38C11×C4⋊C4—22no—
39C11×C4⋊C4—22no—
40C11×C4⋊C4—24no—
41C42×C11D414yes—
42C4⋊Dic11—22no—
43Dic11⋊C4—28no—
44Dic11⋊C4—24no—
45C4×Dic11—24no—
46#2634—111nomaximal, Sylow
47C23×C11C2411yescharacteristic
48C2×C4×C11—22no—
49C2×C4×C11—22no—
50C2×C4×C11—22no—
51C2×C4×C11—22no—
52C2×C4×C11—22no—
53C2×C4×C11—24no—
54C2×C4×C11—24no—
55C2×C4×C11C2×D412yes—
56C2×C4×C11C2×D412yes—
57C2×C4×C11C2×D412yes—
58C2×Dic11—22no—
59C2×Dic11—22no—
60C2×Dic11—22no—
61C2×Dic11—24no—
62C2×Dic11—24no—
63C2×Dic11—24no—
64C2×Dic11—24no—
65C2×Dic11#4114yes—
66Dic22—28no—
67C2×#125D1111yescharacteristic
68C2×C4×Q8—111no—
69#400—112no—
70#400—112no—
71#398—112no—
72#395—112no—
73#387—114no—
74#383—111no—
75C22×C11C22×D411yescharacteristic
76C22×C11C2×#4112yes—
77C22×C112−1+412yes—
78C22×C112−1+412yes—
79C4×C11—22no—
80C4×C11—22no—
81C4×C11—22no—
82C4×C11—42no—
83C4×C11—42no—
84Dic11—24no—
85Dic11—42no—
86Dic11—44no—
87C22×Q8—111no—
88#125—24no—
89C4×Q8—224no—
90C2×C4⋊C4—112no—
91C2×C4⋊C4—111no—
92C2×C4⋊C4—114no—
93C2×C4⋊C4C2×D1112yes—
94C2×C4⋊C4C2×D1112yes—
95C2×C4⋊C4C2×D1111yescharacteristic
96C2×C4⋊C4C2×D1111yescharacteristic
97C2×C42—112no—
98C2×C42C2×D1111yescharacteristic
99#95—112no—
100#95—112no—
101#95—112no—
102#95—114no—
103#95—114no—
104#95—114no—
105C2×C11#52511yescharacteristic
106C2×C11#53611yescharacteristic
107C2×C11#53611yescharacteristic
108C2×C11#54114yes—
109C2×Q8—224no—
110C2×Q8—222no—
111C22×C4—112no—
112C22×C4—114no—
113C22×C4—112no—
114C22×C4C22×D1112yes—
115C22×C4C22×D1112yes—
116C22×C4C22×D1111yescharacteristic
117C22×C4C22×D1111yescharacteristic
118C22×C4C22×D1111yescharacteristic
119C4⋊C4—24no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—24no—
123C4⋊C4—228no—
124C4⋊C4—224no—
125C4⋊C4—222no—
126C42—224no—
127C42C22⋊D1114yes—
128C11#263411yescharacteristic, complemented, Sylow
129C23C23×D1111yescharacteristic
130Q8—228no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—24no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—114no—
139C2×C4—222no—
140C2×C4—222no—
141C2×C4—224no—
142C2×C4—224no—
143C2×C4—224no—
144C2×C4—224no—
145C2×C4—222no—
146C2×C4C2×C22⋊D1112yes—
147C2×C4C2×C22⋊D1112yes—
148C2×C4C2×C22⋊D1112yes—
149C22#6704012yes—
150C22#41×D1112yes—
151C22#6704312yes—
152C22C22×C22⋊D1111yescharacteristic
153C4—22no—
154C4—22no—
155C4—22no—
156C4—42no—
157C4—42no—
158C4—224no—
159C4—442no—
160C4—444no—
161C2#1062322714yes—
162C2#1062334711yescharacteristic
163C2#1062335611yescharacteristic
164C2#1062335911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC2×C11×#125C2
hypercenterC2×#125D11
hypocenterC11#2634
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
128. C11#2634semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1252
C2×C4×Dic222
#106225992
#106225952
#106225932
#106225922
#106225912
#106225502
#263411