Finite Group Databasebeta

← #13068926

Subgroups — #13068926

Order 1408.

360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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×#66979C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic
3C2×C11×C22⋊C8C211yesmaximal, characteristic
4C2×#66880C212yesmaximal, complemented
5#10622189C212yesmaximal, complemented
6C23×C4×C11C2211yescharacteristic
7C22×Dic22C2211yescharacteristic
8C22×C8×C11C2212yes—
9C2×C22⋊Dic11—21no—
10C2×C22⋊Dic11—21no—
11#66979—24no—
12C2×C4⋊Dic11C2211yescharacteristic
13C2×C4⋊Dic11C2212yes—
14#66977—22no—
15#66977C414yescomplemented
16C2×Dic11⋊C4—21no—
17C2×C4×Dic11—21no—
18C11×C22⋊C8—22no—
19#66880—24no—
20C24×C11D411yescharacteristic
21C22×C4×C11—22no—
22C22×C4×C11—22no—
23C22×C4×C11C2×C412yes—
24C22×C4×C11D411yescharacteristic
25C22×C4×C11D412yes—
26C22×C4×C11C2311yescharacteristic
27C22×Dic11—22no—
28C22×Dic11—21no—
29C22×Dic11—21no—
30C2×Dic22—22no—
31C2×Dic22—21no—
32C2×Dic22—22no—
33C2×Dic22C2×C412yes—
34C2×C8×C11—22no—
35C2×C8×C11—22no—
36C2×C8×C11—22no—
37C22⋊Dic11—24no—
38C22⋊Dic11—24no—
39C4⋊Dic11—21no—
40C4⋊Dic11—22no—
41C4⋊Dic11C2×C412yes—
42C4⋊Dic11D414yes—
43Dic11⋊C4—24no—
44C4×Dic11—24no—
45#1873—111nomaximal, Sylow
46C23×C11—21no—
47C23×C11—21no—
48C23×C11—22no—
49C23×C11—22no—
50C23×C11C22⋊C412yes—
51C23×C11C2×D411yescharacteristic
52C2×C4×C11—21no—
53C2×C4×C11—21no—
54C2×C4×C11—24no—
55C2×C4×C11—24no—
56C2×C4×C11C22⋊C412yes—
57C2×C4×C11C22×C411yescharacteristic
58C2×C4×C11C2×D412yes—
59C2×C4×C11C2×D411yescharacteristic
60C2×C4×C11#4112yes—
61C2×Dic11—22no—
62C2×Dic11—22no—
63C2×Dic11—24no—
64C2×Dic11—41no—
65C2×Dic11—41no—
66C2×Dic11—42no—
67C2×Dic11—42no—
68C2×Dic11—42no—
69Dic22—24no—
70Dic22—42no—
71C8×C11—42no—
72C2×C22⋊Q8—111no—
73C2×#117—111no—
74C2×#103—112no—
75C2×C22⋊C8D1111yescharacteristic
76#340—112no—
77C22×C11—22no—
78C22×C11—22no—
79C22×C11—22no—
80C22×C11—42no—
81C22×C11—42no—
82C22×C11C2×C22⋊C411yescharacteristic
83C22×C11#12011yescharacteristic
84C22×C11#12311yescharacteristic
85C22×C11#13512yes—
86C22×C11#13712yes—
87C4×C11—22no—
88C4×C11C4×D412yes—
89C4×C11#12112yes—
90Dic11—42no—
91Dic11—42no—
92Dic11—44no—
93C22×Q8—111no—
94C23×C4C2×D1111yescharacteristic
95C22×C8C2×D1112yes—
96C22⋊Q8—114no—
97C22⋊Q8—222no—
98#117—224no—
99C2×C4⋊C4—112no—
100C2×C4⋊C4—111no—
101C2×C4⋊C4—221no—
102C2×C22⋊C4—221no—
103C2×C22⋊C4—221no—
104C2×C42—221no—
105#103—224no—
106C22⋊C8—22no—
107C2×C11—42no—
108C2×C11#38611yescharacteristic
109C2×C11#41611yescharacteristic
110C2×C11#41911yescharacteristic
111C2×C11#45212yes—
112C2×C11#48512yes—
113C24D4411yescharacteristic
114C2×Q8—112no—
115C2×Q8—221no—
116C2×Q8—222no—
117C2×Q8—222no—
118C22×C4—22no—
119C22×C4—22no—
120C22×C4—222no—
121C22×C4—221no—
122C22×C4—221no—
123C22×C4C4×D1112yes—
124C22×C4D4411yescharacteristic
125C22×C4C22⋊D1112yes—
126C22×C4C22×D1111yescharacteristic
127C2×C8—22no—
128C2×C8—22no—
129C2×C8—22no—
130C4⋊C4—112no—
131C4⋊C4—114no—
132C4⋊C4—224no—
133C4⋊C4—222no—
134C4⋊C4—221no—
135C22⋊C4—224no—
136C22⋊C4—224no—
137C42—224no—
138C11#187311yescharacteristic, complemented, Sylow
139C23—21no—
140C23—21no—
141C23—22no—
142C23—22no—
143C23(C2×D11)⋊C412yes—
144C23C2×D4411yescharacteristic
145Q8—224no—
146Q8—442no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—24no—
150C2×C4—24no—
151C2×C4—224no—
152C2×C4—222no—
153C2×C4—222no—
154C2×C4—441no—
155C2×C4—441no—
156C2×C4—442no—
157C2×C4—442no—
158C2×C4—442no—
159C2×C4(C2×D11)⋊C412yes—
160C2×C4C2×C4×D1111yescharacteristic
161C2×C4D4×D1112yes—
162C2×C4#434112yes—
163C2×C4C2×C22⋊D1111yescharacteristic
164C8—42no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22#6693511yescharacteristic
171C22#6693911yescharacteristic
172C22#6695712yes—
173C22#6696212yes—
174C22C2×(C2×D11)⋊C411yescharacteristic
175C4—22no—
176C4—442no—
177C4—442no—
178C4—444no—
179C4(C22⋊D11)⋊C412yes—
180C4#6699212yes—
181C2—42no—
182C2#1062233612yes—
183C2#1062234612yes—
184C2#1062257111yescharacteristic
185C2#1062272611yescharacteristic
186C2#1062273311yescharacteristic
subgroupG/H
centerC23C2×D44
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC2×C11×C22⋊C8C2
socleC23×C11C2×D4
prime radicalC24×C11D4
cosocleC22×C4×C11C23
hypercenterC2×C22⋊C8D11
hypocenterC11#1873
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#66880C2semidirect
5. #10622189C2semidirect
15. #66977C4semidirect
138. C11#1873semidirect

Maximal subgroups

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

subgroupindex
C2×#669792
C2×#669772
C2×C11×C22⋊C82
C2×#668802
#106221892
#187311