Finite Group Databasebeta

← #13074988

Subgroups — #13074988

Order 1408.

592 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 157 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×#66931C214yesmaximal, complemented
2C11×#390C211yesmaximal, characteristic
3#10622833C212yesmaximal
4#10622592C212yesmaximal, complemented
5#10622561C214yesmaximal, complemented
6#10622541C212yesmaximal, complemented
7C22×D4×C11C2211yescharacteristic
8C23×Dic11C2212yes—
9C22×Dic22C2212yes—
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C22⋊C4C2214yes—
12C2×C42×C11C2211yescharacteristic
13C2×C22⋊Dic11C2214yes—
14C2×C22⋊Dic11C2212yes—
15C2×C4⋊Dic11C2212yes—
16C2×C4⋊Dic11C2212yes—
17C2×Dic11⋊C4C2214yes—
18C2×Dic11⋊C4C2214yes—
19#66931—216no—
20C11⋊#95C2214yes—
21C11⋊#95C2212yes—
22C24×C11C2312yes—
23C2×D4×C11—41no—
24C2×D4×C11—41no—
25C2×D4×C11Q814yescomplemented
26C22×C4×C11C2312yes—
27C22×C4×C11C2312yes—
28C22×C4×C11C2311yescharacteristic
29C22×Dic11—28no—
30C22×Dic11—42no—
31C22×Dic11C2314yes—
32C22×Dic11C2314yes—
33C2×Dic22—28no—
34C2×Dic22—42no—
35C11×C4⋊C4—41no—
36C11×C22⋊C4—28no—
37C42×C11—41no—
38C22⋊Dic11—28no—
39C22⋊Dic11—42no—
40C4⋊Dic11—42no—
41C4⋊Dic11D418yescomplemented
42Dic11⋊C4—28no—
43Dic11⋊C4—28no—
44#2683—111nomaximal, Sylow
45C23×C11—24no—
46C23×C11—22no—
47C23×C11—22no—
48C23×C11—24no—
49C23×C11C2×Q814yes—
50C23×C11C2411yescharacteristic
51D4×C11—44no—
52C2×C4×C11—22no—
53C2×C4×C11—21no—
54C2×C4×C11—21no—
55C2×C4×C11—22no—
56C2×C4×C11—24no—
57C2×C4×C11—22no—
58C2×C4×C11C2×D414yes—
59C2×C4×C11C2×Q812yes—
60C2×Dic11—24no—
61C2×Dic11—24no—
62C2×Dic11—24no—
63C2×Dic11—24no—
64C2×Dic11—24no—
65C2×Dic11—48no—
66C2×Dic11C2×D418yes—
67Dic22—48no—
68C2×C22⋊Q8—114no—
69#396—114no—
70#395—112no—
71#390D1111yescharacteristic
72#389—112no—
73#386—112no—
74C22×C11—24no—
75C22×C11—28no—
76C22×C11—44no—
77C22×C11—42no—
78C22×C11—42no—
79C22×C11C22×D412yes—
80C22×C11C22×Q811yescharacteristic
81C22×C11H(5,𝔽2)11yescharacteristic
82C22×C11H(5,𝔽2)11yescharacteristic
83C22×C112−1+412yes—
84C4×C11—24no—
85C4×C11—22no—
86C4×C11—42no—
87Dic11—28no—
88Dic11—44no—
89C22×Q8—112no—
90C22×D4C2×D1111yescharacteristic
91C23×C4—112no—
92C22⋊Q8—2216no—
93C2×C4⋊C4—112no—
94C2×C4⋊C4—114no—
95C2×C4⋊C4—114no—
96C2×C4⋊C4—112no—
97C2×C4⋊C4C2×D1111yescharacteristic
98C2×C22⋊C4—114no—
99C2×C22⋊C4—112no—
100C2×C22⋊C4C2×D1114yes—
101C2×C42C2×D1111yescharacteristic
102#95—114no—
103#95—112no—
104C2×C11—44no—
105C2×C11#53712yes—
106C2×C11#54311yescharacteristic
107C2×C11D4211yescharacteristic
108C2×C11D4×Q812yes—
109C2×C11#56311yescharacteristic
110C24C22×D1112yes—
111C2×Q8—228no—
112C2×Q8—442no—
113C2×D4—41no—
114C2×D4—41no—
115C2×D4Dic2214yescomplemented
116C22×C4—114no—
117C22×C4—114no—
118C22×C4—228no—
119C22×C4—442no—
120C22×C4C22×D1112yes—
121C22×C4C22×D1111yescharacteristic
122C22×C4C22×D1112yes—
123C4⋊C4—41no—
124C4⋊C4—118no—
125C4⋊C4—228no—
126C4⋊C4—228no—
127C4⋊C4—442no—
128C22⋊C4—28no—
129C22⋊C4—228no—
130C22⋊C4—442no—
131C42—41no—
132C11#268311yescharacteristic, complemented, Sylow
133C23—24no—
134C23—22no—
135C23—22no—
136C23—24no—
137C23C2×Dic2214yes—
138C23C23×D1111yescharacteristic
139Q8—448no—
140D4—44no—
141C2×C4—22no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—24no—
146C2×C4—22no—
147C2×C4—118no—
148C2×C4—224no—
149C2×C4—224no—
150C2×C4—224no—
151C2×C4—224no—
152C2×C4—224no—
153C2×C4—448no—
154C2×C4C2×Dic2212yes—
155C2×C4D4×D1114yes—
156C22—24no—
157C22—28no—
158C22—42no—
159C22—44no—
160C22—42no—
161C22C22×Dic2211yescharacteristic
162C22C2×D4×D1112yes—
163C22#6703711yescharacteristic
164C22#6703711yescharacteristic
165C22#6704312yes—
166C4—22no—
167C4—24no—
168C4—42no—
169C4—228no—
170C4—444no—
171C2—44no—
172C2#1062301411yescharacteristic
173C2D4×Dic2212yes—
174C2#1062312812yes—
175C2#1062320311yescharacteristic
176C2#1062324811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2683
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#66931C2semidirect
4. #10622592C2semidirect
5. #10622561C2semidirect
6. #10622541C2semidirect
25. C2×D4×C11Q8semidirect
41. C4⋊Dic11D4semidirect
115. C2×D4Dic22semidirect
132. C11#2683semidirect

Maximal subgroups

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

subgroupindex
C2×#669312
C11×#3902
#106228332
#106225922
#106225612
#106225412
#268311