Finite Group Databasebeta

← #13081483

Subgroups — #13081483

Order 1408.

352 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 131 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#10623070C212yesmaximal, complemented
2C4×C11×D8C211yesmaximal, characteristic
3D8×Dic11C211yesmaximal, characteristic
4D8×Dic11C211yesmaximal, characteristic
5#10622622C212yesmaximal, complemented
6#10622491C211yesmaximal, characteristic, complemented
7#10622487C211yesmaximal, characteristic, complemented
8#10622376C212yesmaximal, complemented
9#10622374C212yesmaximal, complemented
10#10622296C211yesmaximal, characteristic, complemented
11C8×Dic22C211yesmaximal, characteristic, complemented
12C2×C11×D8C2211yescharacteristic
13C4×D4×C11C2212yes—
14D4×Dic11C2212yes—
15D4×Dic11C2212yes—
16#66977—22no—
17C2×Dic11⋊C4—22no—
18#66943C2212yes—
19#66941C2212yes—
20#66931—22no—
21#66931—22no—
22#66923C2212yes—
23C4×Dic22C2211yescharacteristic
24C11×#107C2211yescharacteristic
25C11×#102C2212yes—
26C4×C8×C11C2211yescharacteristic
27#66896C2212yes—
28#66896C2212yes—
29#66882C2211yescharacteristic
30#66882C2211yescharacteristic
31#66881C2212yes—
32Dic11⋊C8C2211yescharacteristic
33Dic11⋊C8C2211yescharacteristic
34C8×Dic11C2211yescharacteristic
35C8×Dic11C2211yescharacteristic
36#66872C2212yes—
37#66871C2212yes—
38C4⋊(C11⋊C8)C2211yescharacteristic
39C2×D4×C11C2312yes—
40C22×C4×C11—22no—
41C22×Dic11—22no—
42C22×Dic11—22no—
43C2×Dic22—22no—
44C2×Dic22D411yescharacteristic
45C11×D8Q814yescomplemented
46C2×C8×C11C2311yescharacteristic
47C2×C8×C11C2311yescharacteristic
48C11×C4⋊C4C2312yes—
49C11×C22⋊C4—22no—
50C42×C11C2311yescharacteristic
51C22⋊Dic11—22no—
52C22⋊Dic11—22no—
53C4⋊Dic11—22no—
54C4⋊Dic11D411yescharacteristic
55C4⋊Dic11C2312yes—
56C4⋊Dic11C2312yes—
57Dic11⋊C4—22no—
58Dic11⋊C4—22no—
59Dic11⋊C4—22no—
60Dic11⋊C4—22no—
61Dic11⋊C4D411yescharacteristic
62Dic11⋊C4D411yescharacteristic
63C4×Dic11C2311yescharacteristic
64C4×Dic11C2311yescharacteristic
65C2×C11⋊C8C2311yescharacteristic
66C2×C11⋊C8C2311yescharacteristic
67#3380—111nomaximal, Sylow
68C23×C11—22no—
69D4×C11—22no—
70D4×C11C2×Q814yes—
71C2×C4×C11—22no—
72C2×C4×C11—82no—
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2411yescharacteristic
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—44no—
79C2×Dic11—82no—
80C2×Dic11C2×D411yescharacteristic
81C2×Dic11C2×D411yescharacteristic
82C2×Dic11C2×D411yescharacteristic
83C2×Dic11C2×D411yescharacteristic
84Dic22—22no—
85Dic22—82no—
86C8×C11—21no—
87C8×C11C2×Q812yes—
88C11⋊C8—21no—
89C11⋊C8—21no—
90#554—112no—
91#500—111no—
92#499—111no—
93#499—111no—
94#478—112no—
95#478—112no—
96#476—112no—
97C8×Q8—111no—
98C4×D8—111no—
99C4×D8—111no—
100C4×D8D1111yescharacteristic
101C22×C11—24no—
102C22×C11—42no—
103C22×C11—42no—
104C22×C11C22×D411yescharacteristic
105C4×C11—21no—
106C4×C11—21no—
107C4×C11—42no—
108C4×C11C22×Q811yescharacteristic
109C4×C112−1+411yescharacteristic
110Dic11—21no—
111Dic11—21no—
112Dic11—21no—
113Dic11—42no—
114Dic11—42no—
115Dic11#13512yes—
116C2×D8C2×D1111yescharacteristic
117C4⋊Q8—112no—
118#125—112no—
119#125—112no—
120C22⋊Q8—222no—
121C22⋊Q8—222no—
122C22⋊Q8—222no—
123C4×Q8—111no—
124C4×D4—112no—
125C4×D4—112no—
126C4×D4C2×D1112yes—
127C2×C4⋊C4—222no—
128#107—111no—
129#107—111no—
130#107—112no—
131#107C2×D1111yescharacteristic
132#106—112no—
133#106—112no—
134C4⋊C8—111no—
135C4⋊C8—111no—
136C4⋊C8—111no—
137#102—112no—
138#102—112no—
139#102C2×D1112yes—
140C4×C8—111no—
141C4×C8—111no—
142C4×C8C2×D1111yescharacteristic
143C2×C11—44no—
144C2×C11D4×Q811yescharacteristic
145C2×C11C2×#13511yescharacteristic
146C2×C11#57611yescharacteristic
147C2×Q8—111no—
148C2×Q8—222no—
149C2×D4C22×D1112yes—
150C22×C4—22no—
151C22×C4—222no—
152C22×C4—222no—
153D8Dic2214yescomplemented
154C2×C8—111no—
155C2×C8—111no—
156C2×C8C22×D1111yescharacteristic
157C2×C8C22×D1111yescharacteristic
158C4⋊C4—111no—
159C4⋊C4—111no—
160C4⋊C4—111no—
161C4⋊C4—112no—
162C4⋊C4—112no—
163C4⋊C4—222no—
164C4⋊C4—222no—
165C4⋊C4—222no—
166C4⋊C4—222no—
167C4⋊C4—222no—
168C4⋊C4C22×D1112yes—
169C22⋊C4—22no—
170C22⋊C4—222no—
171C22⋊C4—222no—
172C42—111no—
173C42—111no—
174C42C22×D1111yescharacteristic
175C11#338011yescharacteristic, complemented, Sylow
176C23—22no—
177Q8—222no—
178Q8—882no—
179D4—22no—
180D4C2×Dic2214yes—
181C2×C4—22no—
182C2×C4—82no—
183C2×C4—111no—
184C2×C4—111no—
185C2×C4—111no—
186C2×C4—111no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—444no—
190C2×C4—882no—
191C2×C4D4×D1111yescharacteristic
192C2×C4D4×D1111yescharacteristic
193C2×C4C23×D1111yescharacteristic
194C8—21no—
195C8—221no—
196C8—221no—
197C8C2×Dic2212yes—
198C22—24no—
199C22—42no—
200C22—42no—
201C22C2×D4×D1111yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—112no—
206C4—221no—
207C4—221no—
208C4—221no—
209C4—442no—
210C4—442no—
211C4C22×Dic2211yescharacteristic
212C4#6704311yescharacteristic
213C2—44no—
214C2D4×Dic2211yescharacteristic
215C2#1062328811yescharacteristic
216C2D11×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×D8C2
socleC22×C11C22×D4
prime radicalC2×C11×D8C22
hypercenterC4×D8D11
hypocenterC11#3380
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10623070C2semidirect
5. #10622622C2semidirect
6. #10622491C2semidirect
7. #10622487C2semidirect
8. #10622376C2semidirect
9. #10622374C2semidirect
10. #10622296C2semidirect
11. C8×Dic22C2semidirect
45. C11×D8Q8semidirect
153. D8Dic22semidirect
175. C11#3380semidirect

Maximal subgroups

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

subgroupindex
#106230702
C4×C11×D82
D8×Dic112
#106226222
#106224912
#106224872
#106223762
#106223742
#106222962
C8×Dic222
#338011