Finite Group Databasebeta

← #13079756

Subgroups — #13079756

Order 1408.

360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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#10623259C211yesmaximal, characteristic
2D11×C4⋊Q8C211yesmaximal, characteristic
3C11×#487C211yesmaximal, characteristic, complemented
4#10622694C211yesmaximal, characteristic, complemented
5#10622692C211yesmaximal, characteristic, complemented
6#10622418C214yesmaximal
7#10622404C214yesmaximal, complemented
8#10622298C211yesmaximal, characteristic
9#10622293C211yesmaximal, characteristic, complemented
10C2×Q8×D11—21no—
11C11×C4⋊Q8C2211yescharacteristic
12C11×C4⋊Q8C2211yescharacteristic
13#66999C2212yes—
14Q8×Dic11C2212yes—
15#66997—21no—
16#66950—21no—
17#66945—21no—
18C4⋊C4×D11—21no—
19C4⋊C4×D11C2212yes—
20#66943—21no—
21#66941—21no—
22#66941C2212yes—
23#66940—21no—
24C42×D11C2211yescharacteristic
25#66922C2211yescharacteristic
26#66922C2211yescharacteristic
27C11×#103C2214yes—
28C4×C8×C11C2211yescharacteristic
29#66899C2214yes—
30(C2×D11)⋊C8C2212yes—
31#66881C2214yes—
32Dic11⋊C8C2212yes—
33#66872C2214yes—
34C4×C11⋊C8C2211yescharacteristic
35C2×Q8×C11—21no—
36C2×Q8×C11C2312yes—
37Q8×D11—44no—
38C2×C4×D11—22no—
39C2×C4×D11D411yescharacteristic
40C2×C4×D11D411yescharacteristic
41C2×C4×D11C2311yescharacteristic
42C2×Dic22—22no—
43C2×Dic22—21no—
44C2×Dic22—21no—
45C2×C8×C11C2312yes—
46C11×C4⋊C4—21no—
47C11×C4⋊C4—21no—
48C11×C4⋊C4—21no—
49C11×C4⋊C4C2312yes—
50C42×C11C2311yescharacteristic
51(C2×D11)⋊C4—22no—
52C4⋊Dic11—22no—
53C4⋊Dic11—21no—
54C4⋊Dic11—21no—
55C4⋊Dic11C2312yes—
56C4⋊Dic11C2312yes—
57Dic11⋊C4—22no—
58Dic11⋊C4—22no—
59Dic11⋊C4—22no—
60C4×Dic11—22no—
61C4×Dic11D411yescharacteristic
62C4×Dic11D411yescharacteristic
63C4×Dic11C2311yescharacteristic
64C2×C11⋊C8C2312yes—
65#3229—111nomaximal, Sylow
66C22×D11C2×D411yescharacteristic
67Q8×C11—24no—
68Q8×C11—42no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2411yescharacteristic
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11C2×D411yescharacteristic
77C2×Dic11C2×D411yescharacteristic
78C2×Dic11C2×D411yescharacteristic
79C4×D11—22no—
80C4×D11—22no—
81C4×D11—44no—
82C4×D11SD1614yes—
83Dic22—42no—
84Dic22—42no—
85Dic22—44no—
86C8×C11—22no—
87C11⋊C8—22no—
88#533—111no—
89C2×C4⋊Q8—111no—
90#498—111no—
91#498—111no—
92#487—111no—
93#487D1111yescharacteristic, complemented
94#483—114no—
95#475—114no—
96#431—111no—
97C22×C11C22×D411yescharacteristic
98C2×D11—21no—
99C2×D11—21no—
100C2×D11C2×SD1612yes—
101C4×C11—42no—
102C4×C11—42no—
103C4×C11C2×SD1612yes—
104C4×C11#13712yes—
105C4×C112−1+412yes—
106Dic11—21no—
107Dic11—21no—
108Dic11—42no—
109Dic11—42no—
110Dic11C2×SD1612yes—
111C22×Q8—221no—
112C4⋊Q8—112no—
113C4⋊Q8—111no—
114C4⋊Q8—111no—
115C4⋊Q8—221no—
116C4⋊Q8—221no—
117C4⋊Q8C2×D1111yescharacteristic
118C4⋊Q8C2×D1111yescharacteristic
119#125—221no—
120C22⋊Q8—112no—
121C22⋊Q8—221no—
122C4×Q8—112no—
123C4×Q8—221no—
124#117—221no—
125C2×C4⋊C4—112no—
126C2×C4⋊C4—221no—
127C2×C42—111no—
128#106—114no—
129#106—114no—
130C4⋊C8—112no—
131#103—114no—
132#103C2×D1114yes—
133C22⋊C8—112no—
134C4×C8—111no—
135C4×C8C2×D1111yescharacteristic
136C2×C11#53611yescharacteristic
137C2×C11C22×SD1611yescharacteristic
138C2×C11C2×#13711yescharacteristic
139D11—22no—
140C2×Q8—21no—
141C2×Q8—222no—
142C2×Q8—221no—
143C2×Q8—221no—
144C2×Q8—444no—
145C2×Q8C22×D1112yes—
146C22×C4—111no—
147C22×C4—111no—
148C22×C4—111no—
149C22×C4—222no—
150C2×C8—112no—
151C2×C8C22×D1112yes—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—112no—
156C4⋊C4—112no—
157C4⋊C4—222no—
158C4⋊C4—222no—
159C4⋊C4—222no—
160C4⋊C4—222no—
161C4⋊C4—221no—
162C4⋊C4—221no—
163C4⋊C4C22×D1112yes—
164C22⋊C4—222no—
165C42—111no—
166C42—111no—
167C42—111no—
168C42—222no—
169C42C22×D1111yescharacteristic
170C11#322911yescharacteristic, complemented, Sylow
171C23—111no—
172Q8—24no—
173Q8—42no—
174Q8—444no—
175Q8—442no—
176Q8—442no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—111no—
180C2×C4—114no—
181C2×C4—111no—
182C2×C4—111no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—444no—
188C2×C4D4×D1111yescharacteristic
189C2×C4D4×D1111yescharacteristic
190C2×C4C23×D1111yescharacteristic
191C8—22no—
192C8—222no—
193C22—112no—
194C22—221no—
195C22—221no—
196C22C2×D4×D1111yescharacteristic
197C4—42no—
198C4—42no—
199C4—112no—
200C4—221no—
201C4—221no—
202C4—442no—
203C4—442no—
204C4SD16×D1112yes—
205C4#6697112yes—
206C4#6704312yes—
207C2—222no—
208C2#1062320611yescharacteristic
209C2C2×SD16×D1111yescharacteristic
210C2C2×#6697111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#487C2
socleC22×C11C22×D4
prime radicalC22×D11C2×D4
hypercenter#487D11
hypocenterC11#3229
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. C11×#487C2semidirect
4. #10622694C2semidirect
5. #10622692C2semidirect
7. #10622404C2semidirect
9. #10622293C2semidirect
93. #487D11semidirect
170. C11#3229semidirect

Maximal subgroups

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

subgroupindex
#106232592
D11×C4⋊Q82
C11×#4872
#106226942
#106226922
#106224182
#106224042
#106222982
#106222932
#322911