Finite Group Databasebeta

← #13069607

Subgroups — #13069607

Order 1408.

228 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 83 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×#66943C211yesmaximal, characteristic
2#10622731C211yesmaximal, characteristic
3M16×Dic11C211yesmaximal, characteristic
4C11×#343C211yesmaximal, characteristic
5#10622192C211yesmaximal, characteristic
6#10622192C211yesmaximal, characteristic
7#10622168C211yesmaximal, characteristic
8C2×C11×M16C2211yescharacteristic
9C2×C11×M16C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic11C412yes—
12C2×C4⋊Dic11C2211yescharacteristic
13C2×Dic11⋊C4C412yes—
14C2×C4×Dic11C2211yescharacteristic
15C2×#4318C2211yescharacteristic
16C2×#4318C2211yescharacteristic
17#66943—21no—
18#66943—21no—
19#66943—21no—
20#66943—21no—
21#66879—21no—
22Dic11⋊C8—21no—
23Dic11⋊C8—21no—
24C8×Dic11—21no—
25C22×C4×C11C2×C412yes—
26C22×C4×C11C2311yescharacteristic
27C22×Dic11C2×C412yes—
28C22×Dic11C2×C411yescharacteristic
29C22×Dic11C2×C411yescharacteristic
30C11×M16—21no—
31C11×M16—21no—
32C11×M16—21no—
33C11×M16Q812yes—
34C2×C8×C11—21no—
35C2×C8×C11—21no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4—21no—
38C4⋊Dic11—22no—
39C4⋊Dic11—22no—
40C4⋊Dic11—21no—
41C4⋊Dic11—21no—
42Dic11⋊C4—22no—
43Dic11⋊C4—22no—
44C4×Dic11D411yescharacteristic
45C4×Dic11D411yescharacteristic
46C4×Dic11D411yescharacteristic
47C4×Dic11D411yescharacteristic
48#4318—21no—
49#4318—21no—
50#4318—21no—
51#4318Q812yes—
52C2×C11⋊C8—21no—
53C2×C11⋊C8—21no—
54#1998—111nomaximal, Sylow
55C23×C11C22×C411yescharacteristic
56C2×C4×C11—22no—
57C2×C4×C11—42no—
58C2×C4×C11C2×D411yescharacteristic
59C2×C4×C11C2×D411yescharacteristic
60C2×C4×C11C2×Q811yescharacteristic
61C2×C4×C11C2×Q811yescharacteristic
62C2×C4×C11#4111yescharacteristic
63C2×C4×C11#4111yescharacteristic
64C2×Dic11—22no—
65C2×Dic11—41no—
66C2×Dic11—41no—
67C2×Dic11—42no—
68C2×Dic11C22⋊C411yescharacteristic
69C2×Dic11C22⋊C411yescharacteristic
70C2×Dic11C22⋊C411yescharacteristic
71C2×Dic11C22⋊C411yescharacteristic
72C8×C11—22no—
73C8×C11—41no—
74C11⋊C8—22no—
75C11⋊C8—41no—
76C2×#125—111no—
77#423—111no—
78C4×M16—111no—
79#343—111no—
80#343—111no—
81#343—111no—
82#343D1111yescharacteristic
83C22×C11—21no—
84C22×C11—21no—
85C22×C11C2×C22⋊C411yescharacteristic
86C22×C11C4×Q811yescharacteristic
87C22×C11C4×Q811yescharacteristic
88C4×C11—42no—
89C4×C11C22⋊Q811yescharacteristic
90C4×C11C22⋊Q811yescharacteristic
91C4×C11#12411yescharacteristic
92C4×C11C4⋊Q811yescharacteristic
93Dic11—21no—
94Dic11—21no—
95Dic11—21no—
96Dic11—21no—
97Dic11—42no—
98C2×M16—111no—
99C2×M16—111no—
100C2×M16C2×D1111yescharacteristic
101C2×M16C2×D1111yescharacteristic
102#125—221no—
103#125—221no—
104#125—221no—
105#125—221no—
106C2×C4⋊C4—111no—
107C2×C4⋊C4—112no—
108C2×C4⋊C4—112no—
109C2×C4⋊C4C2×D1111yescharacteristic
110C2×C42—111no—
111C4⋊C8—221no—
112C4⋊C8—221no—
113#97—221no—
114C4×C8—221no—
115C2×C11—21no—
116C2×C11—21no—
117C2×C11#39111yescharacteristic
118C2×C11#41311yescharacteristic
119C2×C11#41311yescharacteristic
120C22×C4—111no—
121C22×C4—111no—
122C22×C4—112no—
123C22×C4C4×D1112yes—
124C22×C4C22×D1111yescharacteristic
125M16—21no—
126M16—21no—
127M16—21no—
128M16—112no—
129M16—221no—
130M16—221no—
131M16—221no—
132M16Dic2212yes—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—221no—
136C2×C8—221no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—222no—
140C4⋊C4—222no—
141C4⋊C4—222no—
142C4⋊C4—222no—
143C4⋊C4—221no—
144C4⋊C4—221no—
145C42—111no—
146C42—111no—
147C42—111no—
148C42—111no—
149C11#199811yescharacteristic, complemented, Sylow
150C23C2×C4×D1111yescharacteristic
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—111no—
154C2×C4—111no—
155C2×C4—111no—
156C2×C4—111no—
157C2×C4—222no—
158C2×C4—441no—
159C2×C4—441no—
160C2×C4—442no—
161C2×C4C2×Dic2211yescharacteristic
162C2×C4#433911yescharacteristic
163C2×C4D4×D1111yescharacteristic
164C2×C4D4×D1111yescharacteristic
165C2×C4#434111yescharacteristic
166C2×C4Q8×D1111yescharacteristic
167C8—22no—
168C8—41no—
169C8—222no—
170C8—441no—
171C22—21no—
172C22—21no—
173C22C4×Dic2211yescharacteristic
174C22C22⋊C4×D1111yescharacteristic
175C22#6694011yescharacteristic
176C4—42no—
177C4—221no—
178C4—221no—
179C4—221no—
180C4—221no—
181C4—442no—
182C4#6693111yescharacteristic
183C4#6693811yescharacteristic
184C4#6694111yescharacteristic
185C4#6694911yescharacteristic
186C2—21no—
187C2—21no—
188C2#1062225911yescharacteristic
189C2#1062235811yescharacteristic
190C2#1062236411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D11
commutator, prime radicalC23×C11C22×C4
FrattiniC22×C4C22×D11
FittingC11×#343C2
socleC22×C11C2×C22⋊C4
cosocleC22×C4×C11C23
hypercenter#343D11
hypocenterC11#1998
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
149. C11#1998semidirect

Maximal subgroups

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

subgroupindex
C2×#669432
#106227312
M16×Dic112
C11×#3432
#106221922
#106221682
#199811