Finite Group Databasebeta

← #13074446

Subgroups — #13074446

Order 1408.

472 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 165 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×#117C211yesmaximal, characteristic
2C2×#66923C211yesmaximal, characteristic, complemented
3#10622825C212yesmaximal
4#10622597C214yesmaximal, complemented
5#10622561C214yesmaximal
6#10622548C211yesmaximal, characteristic, complemented
7#10622541C212yesmaximal, complemented
8C23×C4×C11C2211yescharacteristic
9C11×#117—24no—
10C2×C11×C4⋊C4C2212yes—
11C2×C11×C22⋊C4C2212yes—
12C2×C42×C11C2211yescharacteristic
13C2×C42×C11C2211yescharacteristic
14C2×C22⋊Dic11C2214yes—
15C2×C4⋊Dic11C2212yes—
16C2×C4⋊Dic11C2212yes—
17C2×C4⋊Dic11C2214yes—
18C2×Dic11⋊C4C2214yes—
19C2×Dic11⋊C4C2214yes—
20#66923—24no—
21C11⋊#95C2214yes—
22C11⋊#95C2214yes—
23C24×C11C2311yescharacteristic
24C22×C4×C11—22no—
25C22×C4×C11—22no—
26C22×C4×C11Q814yes—
27C22×C4×C11C2312yes—
28C22×C4×C11C2312yes—
29C22×C4×C11C2311yescharacteristic
30C22×C4×C11C2311yescharacteristic
31C22×Dic11C2314yes—
32C22×Dic11C2314yes—
33C11×C4⋊C4—24no—
34C11×C22⋊C4—24no—
35C42×C11—22no—
36C42×C11D414yes—
37C22⋊Dic11—44no—
38C4⋊Dic11—24no—
39C4⋊Dic11—24no—
40C4⋊Dic11—44no—
41Dic11⋊C4—28no—
42Dic11⋊C4—44no—
43#2629—111nomaximal, Sylow
44C23×C11—21no—
45C23×C11—21no—
46C23×C11—22no—
47C23×C11—22no—
48C23×C11C2×Q812yes—
49C23×C11C2411yescharacteristic
50C2×C4×C11—21no—
51C2×C4×C11—21no—
52C2×C4×C11—22no—
53C2×C4×C11—22no—
54C2×C4×C11—28no—
55C2×C4×C11—22no—
56C2×C4×C11—22no—
57C2×C4×C11—22no—
58C2×C4×C11C2×D414yes—
59C2×C4×C11C2×D412yes—
60C2×C4×C11C2×Q812yes—
61C2×C4×C11C2×Q812yes—
62C2×C4×C11#4112yes—
63C2×Dic11—24no—
64C2×Dic11—24no—
65C2×Dic11—24no—
66C2×Dic11—24no—
67C2×Dic11—24no—
68C2×Dic11—24no—
69C2×#125—111no—
70C2×#117D1111yescharacteristic
71#398—114no—
72#396—114no—
73#389—112no—
74#384—111no—
75#380—112no—
76C22×C11—22no—
77C22×C11—24no—
78C22×C11—42no—
79C22×C11—41no—
80C22×C11—41no—
81C22×C11C22×D411yescharacteristic
82C22×C11C22×Q811yescharacteristic
83C22×C11C2×#4111yescharacteristic
84C22×C11H(5,𝔽2)12yes—
85C22×C112−1+412yes—
86C4×C11—22no—
87C4×C11—24no—
88C4×C11—42no—
89C4×C11C22⋊Q814yes—
90Dic11—44no—
91Dic11—44no—
92C23×C4C2×D1111yescharacteristic
93#125—224no—
94#117—24no—
95C2×C4⋊C4—112no—
96C2×C4⋊C4—114no—
97C2×C4⋊C4—112no—
98C2×C4⋊C4—114no—
99C2×C4⋊C4—114no—
100C2×C4⋊C4C2×D1112yes—
101C2×C22⋊C4—114no—
102C2×C22⋊C4C2×D1112yes—
103C2×C42C2×D1111yescharacteristic
104C2×C42C2×D1111yescharacteristic
105#95—114no—
106#95—114no—
107C2×C11—42no—
108C2×C11C2×C22⋊Q811yescharacteristic
109C2×C11#53712yes—
110C2×C11#54011yescharacteristic
111C2×C11#54111yescharacteristic
112C2×C11#54412yes—
113C24C22×D1111yescharacteristic
114C22×C4—22no—
115C22×C4—22no—
116C22×C4—114no—
117C22×C4—114no—
118C22×C4Dic2214yes—
119C22×C4C22×D1112yes—
120C22×C4C22×D1111yescharacteristic
121C22×C4C22×D1112yes—
122C22×C4C22×D1111yescharacteristic
123C4⋊C4—24no—
124C4⋊C4—224no—
125C4⋊C4—228no—
126C4⋊C4—224no—
127C4⋊C4—444no—
128C4⋊C4—444no—
129C22⋊C4—24no—
130C22⋊C4—444no—
131C42—22no—
132C42C22⋊D1114yes—
133C11#262911yescharacteristic, complemented, Sylow
134C23—21no—
135C23—22no—
136C23—22no—
137C23—21no—
138C23C2×Dic2212yes—
139C23C23×D1111yescharacteristic
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—21no—
144C2×C4—28no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—224no—
149C2×C4—224no—
150C2×C4—224no—
151C2×C4—224no—
152C2×C4—224no—
153C2×C4—224no—
154C2×C4C2×Dic2212yes—
155C2×C4C2×Dic2212yes—
156C2×C4#433912yes—
157C2×C4C2×C22⋊D1114yes—
158C2×C4C2×C22⋊D1112yes—
159C22—24no—
160C22—22no—
161C22—41no—
162C22—41no—
163C22—42no—
164C22C22×Dic2211yescharacteristic
165C22C2×#433911yescharacteristic
166C22#6704212yes—
167C22#6704312yes—
168C22C22×C22⋊D1111yescharacteristic
169C4—22no—
170C4—24no—
171C4—42no—
172C4—444no—
173C4—444no—
174C4#6697714yes—
175C2—42no—
176C2#1062304911yescharacteristic
177C2#1062305012yes—
178C2#1062306611yescharacteristic
179C2C2×#6697711yescharacteristic
180C2#1062336412yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#117C2
prime radicalC24×C11C23
hypercenterC2×#117D11
hypocenterC11#2629
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#66923C2semidirect
4. #10622597C2semidirect
6. #10622548C2semidirect
7. #10622541C2semidirect
133. C11#2629semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1172
C2×#669232
#106228252
#106225972
#106225612
#106225482
#106225412
#262911