Finite Group Databasebeta

← #13070310

Subgroups — #13070310

Order 1408.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#10623356C211yesmaximal, characteristic
2C11×#413C211yesmaximal, characteristic
3#10622850C211yesmaximal, characteristic
4#10622116C214yesmaximal, complemented
5C2×C11×#41C2211yescharacteristic
6C22×Dic22C411yescharacteristic
7C2×C11×M16—21no—
8#66997C2212yes—
9#66989C412yes—
10#66988—21no—
11#66988—21no—
12#66979C411yescharacteristic
13#66977—21no—
14#66977—21no—
15C2×#4318—21no—
16C11×#101C2212yes—
17C11×#100—21no—
18#66900C2212yes—
19#66897—21no—
20C11×#41—41no—
21C11×#41—41no—
22C2×Q8×C11C2311yescharacteristic
23C2×D4×C11C2×C411yescharacteristic
24C2×D4×C11D411yescharacteristic
25C2×D4×C11D411yescharacteristic
26C22×C4×C11C2×C411yescharacteristic
27C22×C4×C11D411yescharacteristic
28C22×C4×C11D411yescharacteristic
29C22×Dic11—21no—
30C2×Dic22—21no—
31C2×Dic22—41no—
32C2×Dic22—41no—
33C2×Dic22C2×C412yes—
34C11×M16—22no—
35C11×M16—41no—
36C2×C8×C11—41no—
37C22⋊Dic11—22no—
38C22⋊Dic11—22no—
39C22⋊Dic11—21no—
40C4⋊Dic11—21no—
41Dic11⋊C4—22no—
42Dic11⋊C4—22no—
43C4×Dic11C2×C412yes—
44#4318—22no—
45#4318—41no—
46C2×C11⋊C8—41no—
47#2135—111nomaximal, Sylow
48C23×C11C22⋊C411yescharacteristic
49C23×C11C22⋊C411yescharacteristic
50C23×C11C22⋊C411yescharacteristic
51Q8×C11—41no—
52D4×C11—41no—
53D4×C11—41no—
54D4×C11—41no—
55C2×C4×C11—21no—
56C2×C4×C11—21no—
57C2×C4×C11—21no—
58C2×C4×C11—21no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11C22⋊C411yescharacteristic
62C2×C4×C11C22×C411yescharacteristic
63C2×C4×C11C2×D411yescharacteristic
64C2×C4×C11C2×D411yescharacteristic
65C2×Dic11—22no—
66C2×Dic11—22no—
67C2×Dic11—42no—
68Dic22—41no—
69Dic22—41no—
70Dic22—42no—
71C8×C11—42no—
72C11⋊C8—42no—
73#536—111no—
74#413—111no—
75#413D1111yescharacteristic
76#356—114no—
77C22×C11—21no—
78C22×C11—21no—
79C22×C11—21no—
80C22×C11—41no—
81C22×C11—41no—
82C22×C11—41no—
83C22×C11C2×C22⋊C411yescharacteristic
84C4×C11—21no—
85C4×C11—21no—
86C4×C11—21no—
87C4×C11#9911yescharacteristic
88C4×C11#9911yescharacteristic
89Dic11—42no—
90Dic11—42no—
91C2×#41C2×D1111yescharacteristic
92C22×Q8—111no—
93C2×M16—21no—
94C2×M16—221no—
95C4⋊Q8—112no—
96#124—112no—
97#123—221no—
98#123—221no—
99C22⋊Q8—221no—
100C22⋊Q8—221no—
101#117—111no—
102#101—112no—
103#101C2×D1112yes—
104#100—21no—
105#100—221no—
106C2×C11—21no—
107C2×C11—41no—
108C2×C11—41no—
109C2×C11—41no—
110C2×C11C2×#9911yescharacteristic
111#41—41no—
112#41—41no—
113C2×Q8—112no—
114C2×Q8—221no—
115C2×Q8—441no—
116C2×Q8—441no—
117C2×Q8C22×D1111yescharacteristic
118C2×D4C4×D1111yescharacteristic
119C2×D4D4411yescharacteristic
120C2×D4C22⋊D1111yescharacteristic
121C22×C4—221no—
122C22×C4C4×D1111yescharacteristic
123C22×C4D4411yescharacteristic
124C22×C4C22⋊D1111yescharacteristic
125M16—22no—
126M16—41no—
127M16—222no—
128M16—441no—
129C2×C8—41no—
130C2×C8—441no—
131C4⋊C4—221no—
132C4⋊C4—222no—
133C4⋊C4—222no—
134C22⋊C4—221no—
135C22⋊C4—222no—
136C22⋊C4—222no—
137C42—112no—
138C11#213511yescharacteristic, complemented, Sylow
139C23(C2×D11)⋊C411yescharacteristic
140C23(C2×D11)⋊C411yescharacteristic
141C23(C2×D11)⋊C411yescharacteristic
142Q8—41no—
143Q8—442no—
144Q8—441no—
145Q8—441no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—222no—
156C2×C4—222no—
157C2×C4—442no—
158C2×C4(C2×D11)⋊C411yescharacteristic
159C2×C4C2×C4×D1111yescharacteristic
160C2×C4C2×D4411yescharacteristic
161C2×C4C2×C22⋊D1111yescharacteristic
162C8—42no—
163C8—442no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×(C2×D11)⋊C411yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—442no—
175C4—442no—
176C4#6687011yescharacteristic
177C4#6687011yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#6687011yescharacteristic
subgroupG/H
centerC2C2×#66870
commutatorC2×C4×C11C22×C4
FrattiniC2×Q8C22×D11
FittingC11×#413C2
socleC2×C11C2×#99
prime radicalC2×C11×#41C22
cosocleC2×Q8×C11C23
hypercenter#413D11
hypocenterC11#2135
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
4. #10622116C2semidirect
138. C11#2135semidirect

Maximal subgroups

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

subgroupindex
#106233562
C11×#4132
#106228502
#106221162
#213511