Finite Group Databasebeta

← #13079357

Subgroups — #13079357

Order 1408.

358 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C11×#533C211yesmaximal, characteristic
2#10623001C211yesmaximal, characteristic
3#10622706C211yesmaximal, characteristic, complemented
4#10622705C211yesmaximal, characteristic, complemented
5#10622694C211yesmaximal, characteristic, complemented
6#10622692C211yesmaximal, characteristic, complemented
7#10622665C214yesmaximal
8#10622643C214yesmaximal, complemented
9C4×#4318C211yesmaximal, characteristic
10C11×C4⋊Q8C2211yescharacteristic
11C11×C4⋊Q8C2211yescharacteristic
12C11×#125—21no—
13C11×C22⋊Q8—21no—
14C11×C22⋊Q8C2212yes—
15C4×Q8×C11—21no—
16C4×Q8×C11C2212yes—
17C11×#117—21no—
18C2×C42×C11C2211yescharacteristic
19C2×#4326C2214yes—
20#66979—21no—
21#66977—21no—
22#66977C2212yes—
23C2×#4318C2212yes—
24#66923—21no—
25#66922C2211yescharacteristic
26#66922C2211yescharacteristic
27C4×Dic22—21no—
28C4×Dic22C2212yes—
29#66899C2214yes—
30#66874C2214yes—
31#66872C2214yes—
32#66867C2212yes—
33C4×C11⋊C8C2211yescharacteristic
34C4×C11⋊C8C2211yescharacteristic
35C2×Q8×C11—21no—
36C2×Q8×C11C2312yes—
37C22×C4×C11D411yescharacteristic
38C22×C4×C11D411yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C2×Dic22—21no—
41C2×Dic22C2312yes—
42C11×C4⋊C4—21no—
43C11×C4⋊C4—21no—
44C11×C4⋊C4—21no—
45C11×C4⋊C4—22no—
46C11×C4⋊C4—22no—
47C11×C4⋊C4C2312yes—
48C11×C22⋊C4—22no—
49C42×C11—22no—
50C42×C11D411yescharacteristic
51C42×C11D411yescharacteristic
52C42×C11C2311yescharacteristic
53C42×C11C2311yescharacteristic
54C22⋊Dic11—22no—
55#4326—28no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58C4⋊Dic11—21no—
59C4⋊Dic11C2312yes—
60Dic11⋊C4—22no—
61Dic11⋊C4—22no—
62C4×Dic11—22no—
63#4318—24no—
64C2×C11⋊C8C2312yes—
65C2×C11⋊C8C2312yes—
66#3185—111nomaximal, Sylow
67C23×C11C2×D411yescharacteristic
68Q8×C11—24no—
69Q8×C11—42no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2411yescharacteristic
81C2×Dic11—22no—
82C2×Dic11—22no—
83Dic22—24no—
84Dic22—42no—
85C11⋊C8—22no—
86C11⋊C8#4114yes—
87#533—111no—
88#533D1111yescharacteristic
89#498—111no—
90#494—111no—
91#487—111no—
92#487—111no—
93#470—114no—
94#441—114no—
95C4×M16—111no—
96C22×C11—21no—
97C22×C11—21no—
98C22×C11—21no—
99C22×C11C22×D411yescharacteristic
100C4×C11—21no—
101C4×C11—21no—
102C4×C11—21no—
103C4×C11—42no—
104C4×C11—42no—
105C4×C11#13712yes—
106C4×C11#13712yes—
107C4×C11C2×#4112yes—
108Dic11—42no—
109Dic11—42no—
110C2×Q16—114no—
111C2×M16—112no—
112C4⋊Q8—111no—
113C4⋊Q8—111no—
114C4⋊Q8C2×D1111yescharacteristic
115C4⋊Q8C2×D1111yescharacteristic
116#125—21no—
117#125—221no—
118C22⋊Q8—21no—
119C22⋊Q8—112no—
120C22⋊Q8—221no—
121C22⋊Q8C2×D1112yes—
122C4×Q8—21no—
123C4×Q8—112no—
124C4×Q8—221no—
125C4×Q8C2×D1112yes—
126#117—21no—
127#117—221no—
128C2×C42C2×D1111yescharacteristic
129#106—114no—
130#103—114no—
131#103—114no—
132#97—112no—
133C4×C8—111no—
134C4×C8—111no—
135C2×C11—41no—
136C2×C11#53211yescharacteristic
137C2×C11C2×#13711yescharacteristic
138C2×C11C2×#13711yescharacteristic
139C2×Q8—21no—
140C2×Q8—112no—
141C2×Q8—221no—
142C2×Q8C22×D1112yes—
143C22×C4C22⋊D1111yescharacteristic
144C22×C4C22⋊D1111yescharacteristic
145C22×C4C22×D1111yescharacteristic
146Q16—228no—
147M16—224no—
148C2×C8—112no—
149C2×C8—112no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—112no—
156C4⋊C4—221no—
157C4⋊C4—221no—
158C4⋊C4—222no—
159C4⋊C4—222no—
160C4⋊C4—221no—
161C4⋊C4C22×D1112yes—
162C22⋊C4—22no—
163C22⋊C4—222no—
164C42—22no—
165C42—222no—
166C42C22⋊D1111yescharacteristic
167C42C22⋊D1111yescharacteristic
168C42C22×D1111yescharacteristic
169C42C22×D1111yescharacteristic
170C11#318511yescharacteristic, complemented, Sylow
171C23C2×C22⋊D1111yescharacteristic
172Q8—24no—
173Q8—42no—
174Q8—224no—
175Q8—442no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4C2×C22⋊D1111yescharacteristic
184C2×C4C2×C22⋊D1111yescharacteristic
185C2×C4C2×C22⋊D1111yescharacteristic
186C2×C4C2×C22⋊D1111yescharacteristic
187C2×C4C2×C22⋊D1111yescharacteristic
188C2×C4C23×D1111yescharacteristic
189C8—114no—
190C8—222no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22C22×C22⋊D1111yescharacteristic
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—42no—
200C4—442no—
201C4—442no—
202C4#6699512yes—
203C4#6700412yes—
204C4#41×D1112yes—
205C2—41no—
206C2C2×#6699511yescharacteristic
207C2C2×#6700411yescharacteristic
208C2#1062336311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#533C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#533D11
hypocenterC11#3185
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #10622706C2semidirect
4. #10622705C2semidirect
5. #10622694C2semidirect
6. #10622692C2semidirect
8. #10622643C2semidirect
170. C11#3185semidirect

Maximal subgroups

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

subgroupindex
C11×#5332
#106230012
#106227062
#106227052
#106226942
#106226922
#106226652
#106226432
C4×#43182
#318511