Finite Group Databasebeta

← #13079822

Subgroups — #13079822

Order 1408.

324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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×C11×#125C211yesmaximal, characteristic
2#10623001C211yesmaximal, characteristic
3#10622682C212yesmaximal, complemented
4#10622678C212yesmaximal, complemented
5#10622676C214yesmaximal, complemented
6#10622584C212yesmaximal
7#10622583C212yesmaximal
8#10622539C211yesmaximal, characteristic
9C11×#125—21no—
10C11×#125—21no—
11C11×#125C2212yes—
12C11×#125C2212yes—
13C2×C11×C4⋊C4—21no—
14C2×C11×C4⋊C4—21no—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C42×C11C2211yescharacteristic
18#66979—21no—
19#66977—21no—
20#66977C2212yes—
21#66923—21no—
22#66922C2211yescharacteristic
23#66922C2211yescharacteristic
24C4×Dic22—21no—
25C4×Dic22C2212yes—
26C22⋊(C11⋊C8)C2212yes—
27#66874C2214yes—
28#66874C2214yes—
29#66872C2214yes—
30#66871C2214yes—
31C4⋊(C11⋊C8)C2212yes—
32#66867C2212yes—
33C22×C4×C11—21no—
34C22×C4×C11—21no—
35C22×C4×C11D411yescharacteristic
36C22×C4×C11D411yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C2×Dic22—21no—
39C2×Dic22C2312yes—
40C11×C4⋊C4—22no—
41C11×C4⋊C4—22no—
42C11×C4⋊C4—22no—
43C11×C4⋊C4—22no—
44C11×C4⋊C4—21no—
45C11×C4⋊C4—21no—
46C11×C4⋊C4C2312yes—
47C11×C4⋊C4C2312yes—
48C42×C11D411yescharacteristic
49C42×C11D411yescharacteristic
50C42×C11C2311yescharacteristic
51C42×C11C2311yescharacteristic
52C22⋊Dic11—22no—
53C4⋊Dic11—21no—
54C4⋊Dic11—21no—
55C4⋊Dic11—21no—
56C4⋊Dic11C2312yes—
57Dic11⋊C4—22no—
58Dic11⋊C4—22no—
59C4×Dic11—22no—
60C2×C11⋊C8C2314yes—
61#3236—111nomaximal, Sylow
62C23×C11C2×D411yescharacteristic
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—41no—
68C2×C4×C11—42no—
69C2×C4×C11—42no—
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2411yescharacteristic
76C2×Dic11—22no—
77C2×Dic11—22no—
78Dic22—24no—
79Dic22—42no—
80C11⋊C8—24no—
81#533—111no—
82C2×#125D1111yescharacteristic
83#501—112no—
84#491—112no—
85#484—112no—
86#483—112no—
87#479—114no—
88#432—111no—
89C22×C11—21no—
90C22×C11—21no—
91C22×C11#13712yes—
92C22×C11C22×D411yescharacteristic
93C4×C11—21no—
94C4×C11—21no—
95C4×C11—21no—
96C4×C11—21no—
97C4×C11—21no—
98C4×C11—42no—
99C4×C11—42no—
100C4×C112−1+412yes—
101Dic11—42no—
102Dic11—42no—
103C4⋊Q8—111no—
104C4⋊Q8—111no—
105#125—21no—
106#125—21no—
107#125—221no—
108#125C2×D1112yes—
109#125C2×D1112yes—
110C22⋊Q8—112no—
111C22⋊Q8—221no—
112C4×Q8—112no—
113C4×Q8—221no—
114#117—221no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4C2×D1111yescharacteristic
118C2×C4⋊C4C2×D1111yescharacteristic
119C2×C42C2×D1111yescharacteristic
120#107—114no—
121#106—114no—
122C4⋊C8—112no—
123#103—114no—
124#103—114no—
125C22⋊C8—112no—
126#97—112no—
127C2×C11—22no—
128C2×C11#53611yescharacteristic
129C2×C11C2×#13711yescharacteristic
130C2×C11#57511yescharacteristic
131C2×Q8—112no—
132C2×Q8—221no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4C22⋊D1111yescharacteristic
136C22×C4C22⋊D1111yescharacteristic
137C22×C4C22×D1111yescharacteristic
138C2×C8—114no—
139C4⋊C4—22no—
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—112no—
146C4⋊C4—221no—
147C4⋊C4—221no—
148C4⋊C4—222no—
149C4⋊C4—222no—
150C4⋊C4—221no—
151C4⋊C4C22×D1112yes—
152C4⋊C4C22×D1112yes—
153C22⋊C4—222no—
154C42—222no—
155C42C22⋊D1111yescharacteristic
156C42C22⋊D1111yescharacteristic
157C42C22×D1111yescharacteristic
158C42C22×D1111yescharacteristic
159C11#323611yescharacteristic, complemented, Sylow
160C23C2×C22⋊D1111yescharacteristic
161Q8—224no—
162Q8—442no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—222no—
171C2×C4—222no—
172C2×C4C2×C22⋊D1111yescharacteristic
173C2×C4C2×C22⋊D1111yescharacteristic
174C2×C4C2×C22⋊D1111yescharacteristic
175C2×C4C2×C22⋊D1111yescharacteristic
176C2×C4C2×C22⋊D1111yescharacteristic
177C2×C4C23×D1111yescharacteristic
178C8—224no—
179C22—21no—
180C22—21no—
181C22#6700412yes—
182C22C22×C22⋊D1111yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—42no—
189C4—42no—
190C4—442no—
191C4—442no—
192C4#6704012yes—
193C2—22no—
194C2#1062334711yescharacteristic
195C2#1062335311yescharacteristic
196C2C2×#6700411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#125C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenterC2×#125D11
hypocenterC11#3236
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #10622682C2semidirect
4. #10622678C2semidirect
5. #10622676C2semidirect
159. C11#3236semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1252
#106230012
#106226822
#106226782
#106226762
#106225842
#106225832
#106225392
#323611