Finite Group Databasebeta

← #13080017

Subgroups — #13080017

Order 1408.

354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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#10623010C212yesmaximal, complemented
2C11×#423C211yesmaximal, characteristic, complemented
3#10622750C211yesmaximal, characteristic, complemented
4#10622748C211yesmaximal, characteristic
5#10622747C212yesmaximal, complemented
6#10622460C212yesmaximal, complemented
7#10622458C212yesmaximal, complemented
8#10622457C212yesmaximal, complemented
9#10622442C212yesmaximal, complemented
10C2×C11×M16C2211yescharacteristic
11C2×C11×M16C2211yescharacteristic
12C2×C42×C11C2211yescharacteristic
13#66983C2212yes—
14#66982—22no—
15C4×C22⋊D11—22no—
16#66977C2212yes—
17C2×Dic44C2211yescharacteristic
18C2×D88C2211yescharacteristic
19C2×#4314C2212yes—
20#66929—22no—
21#66928C2212yes—
22C4×D44C2212yes—
23#66925—22no—
24#66923C2212yes—
25C4×Dic22C2212yes—
26C11×C4⋊C8C2212yes—
27C11×C4⋊C8C2212yes—
28#66885C2212yes—
29#66885C2212yes—
30#66882C2212yes—
31#66881C2211yescharacteristic
32#66881C2211yescharacteristic
33#66880C2212yes—
34#66880C2212yes—
35C22×C4×C11D412yes—
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11—22no—
38C2×D44C2312yes—
39C2×C4×D11—22no—
40C2×Dic22C2312yes—
41C11×M16—41no—
42C11×M16—41no—
43C2×C8×C11C2311yescharacteristic
44C2×C8×C11C2312yes—
45C2×C8×C11C2311yescharacteristic
46C42×C11D411yescharacteristic
47C42×C11D411yescharacteristic
48C42×C11C2312yes—
49C22⋊Dic11—22no—
50(C2×D11)⋊C4—22no—
51(C2×D11)⋊C4—22no—
52(C2×D11)⋊C4—22no—
53(C2×D11)⋊C4—22no—
54C4⋊Dic11C2312yes—
55C4⋊Dic11C2312yes—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58Dic11⋊C4—22no—
59Dic11⋊C4—22no—
60C4×Dic11—22no—
61Dic44—41no—
62D88—41no—
63#4314—42no—
64#3256—111nomaximal, Sylow
65C23×C11C2×D411yescharacteristic
66C22×D11—22no—
67C2×C4×C11—21no—
68C2×C4×C11—21no—
69C2×C4×C11—42no—
70C2×C4×C11C2×D412yes—
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2×D412yes—
73C2×C4×C11C2411yescharacteristic
74C22⋊D11—44no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78D44—22no—
79D44—22no—
80C4×D11—44no—
81Dic22—22no—
82Dic22—22no—
83C8×C11—22no—
84C8×C11—21no—
85C8×C11—21no—
86#529—112no—
87#479—112no—
88#478—112no—
89#470—111no—
90#469—111no—
91#468—112no—
92#464—112no—
93#463—112no—
94#423D1111yescharacteristic, complemented
95C22×C11—21no—
96C22×C11—22no—
97C22×C11C22×D411yescharacteristic
98C2×D11—42no—
99C2×D11—42no—
100C2×D11—42no—
101C4×C11—21no—
102C4×C11—22no—
103C4×C11—22no—
104C4×C11H(5,𝔽2)11yescharacteristic
105C4×C112−1+411yescharacteristic
106Dic11—42no—
107Dic11—42no—
108Dic11—42no—
109C2×Q16—111no—
110C2×SD16—112no—
111C2×D8—111no—
112C2×M16C2×D1111yescharacteristic
113C2×M16C2×D1111yescharacteristic
114#126—222no—
115#125—112no—
116#124—112no—
117#123—222no—
118C22⋊Q8—112no—
119#121—112no—
120C4×Q8—112no—
121C4×D4—112no—
122C4×D4—222no—
123#117—222no—
124C2×C42C2×D1111yescharacteristic
125#107—112no—
126#106—111no—
127#106—111no—
128C4⋊C8C2×D1112yes—
129C4⋊C8C2×D1112yes—
130#103—112no—
131#103—112no—
132#102—112no—
133#102—112no—
134C2×C11—41no—
135C2×C11#53711yescharacteristic
136C2×C11#57512yes—
137D11—82no—
138C2×Q8—112no—
139C2×D4—112no—
140C2×D4—222no—
141C22×C4—222no—
142C22×C4D4412yes—
143C22×C4C22×D1111yescharacteristic
144Q16—441no—
145SD16—442no—
146D8—441no—
147M16—41no—
148M16—41no—
149C2×C8C22×D1111yescharacteristic
150C2×C8C22×D1112yes—
151C2×C8C22×D1111yescharacteristic
152C4⋊C4—112no—
153C4⋊C4—112no—
154C4⋊C4—222no—
155C4⋊C4—222no—
156C4⋊C4—222no—
157C4⋊C4—222no—
158C22⋊C4—222no—
159C22⋊C4—222no—
160C22⋊C4—222no—
161C22⋊C4—222no—
162C22⋊C4—222no—
163C42—222no—
164C42D4411yescharacteristic
165C42D4411yescharacteristic
166C42C22×D1112yes—
167C11#325611yescharacteristic, complemented, Sylow
168C23—222no—
169C23C2×D4411yescharacteristic
170Q8—222no—
171Q8—222no—
172D4—222no—
173D4—222no—
174D4—444no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—222no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—444no—
182C2×C4C2×D4412yes—
183C2×C4C2×D4412yes—
184C2×C4C2×D4411yescharacteristic
185C2×C4C23×D1111yescharacteristic
186C8—21no—
187C8—22no—
188C8—21no—
189C22—22no—
190C22—21no—
191C22—442no—
192C22—442no—
193C22—442no—
194C22C22×D4411yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—442no—
199C4—442no—
200C4—442no—
201C4#6703711yescharacteristic
202C4#6704011yescharacteristic
203C2—41no—
204C2—882no—
205C2#1062304111yescharacteristic
206C2#1062327912yes—
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#423C2
socleC22×C11C22×D4
prime radical#10622748C2
hypercenter#423D11
hypocenterC11#3256
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. #10623010C2semidirect
2. C11×#423C2semidirect
3. #10622750C2semidirect
5. #10622747C2semidirect
6. #10622460C2semidirect
7. #10622458C2semidirect
8. #10622457C2semidirect
9. #10622442C2semidirect
94. #423D11semidirect
167. C11#3256semidirect

Maximal subgroups

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

subgroupindex
#106230102
C11×#4232
#106227502
#106227482
#106227472
#106224602
#106224582
#106224572
#106224422
#325611