Finite Group Databasebeta

← #13081487

Subgroups — #13081487

Order 1408.

338 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 133 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×#557C211yesmaximal, characteristic, complemented
2#10623110C211yesmaximal, characteristic
3#10622700C211yesmaximal, characteristic
4#10622692C211yesmaximal, characteristic, complemented
5#10622679C212yesmaximal
6#10622677C212yesmaximal, complemented
7C4×#4325C212yesmaximal
8C4×#4325C211yesmaximal, characteristic
9Q8×C11⋊C8C211yesmaximal, characteristic, complemented
10#10622635C212yesmaximal, complemented
11#10622634C211yesmaximal, characteristic, complemented
12C11×C4⋊Q8—21no—
13C11×C4⋊Q8C2211yescharacteristic
14C11×#125—22no—
15C11×#125C2212yes—
16C4×Q8×C11—21no—
17C4×Q8×C11C2211yescharacteristic
18C4×Q8×C11C2212yes—
19C4×Q8×C11C2211yescharacteristic
20#66999—21no—
21C2×#4325C2211yescharacteristic
22#66949—22no—
23C4⋊C4×D11—21no—
24C4×D44C2212yes—
25C4×D44C2211yescharacteristic
26#66923C2212yes—
27#66922C2211yescharacteristic
28#66899C2212yes—
29#66899C2211yescharacteristic
30#66873C2211yescharacteristic
31#66873C2212yes—
32#66872C2212yes—
33#66872C2211yescharacteristic
34#66872C2212yes—
35#66871C2212yes—
36#66871C2212yes—
37C4⋊(C11⋊C8)C2211yescharacteristic
38C4⋊(C11⋊C8)C2212yes—
39C4×C11⋊C8C2212yes—
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11D411yescharacteristic
43C2×Q8×C11C2311yescharacteristic
44C2×D44C2311yescharacteristic
45C2×C4×D11—21no—
46C2×C4×D11—22no—
47C2×Dic22—21no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—21no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4D411yescharacteristic
54C11×C4⋊C4D412yes—
55C11×C4⋊C4C2311yescharacteristic
56C11×C4⋊C4C2312yes—
57C42×C11—22no—
58C42×C11—21no—
59C42×C11C2311yescharacteristic
60C42×C11C2312yes—
61#4325Q814yescomplemented
62(C2×D11)⋊C4—21no—
63(C2×D11)⋊C4—22no—
64C4⋊Dic11—21no—
65C4⋊Dic11C2311yescharacteristic
66C4⋊Dic11C2312yes—
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69C2×C11⋊C8C2312yes—
70C2×C11⋊C8C2311yescharacteristic
71C2×C11⋊C8C2311yescharacteristic
72#3381—111nomaximal, Sylow
73C22×D11—21no—
74Q8×C11—22no—
75Q8×C11—21no—
76Q8×C11—42no—
77Q8×C11C2×Q812yes—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11C2×D412yes—
82C2×C4×C11C2×D412yes—
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2411yescharacteristic
86C2×Dic11—21no—
87C2×Dic11—22no—
88D44—21no—
89D44C2×Q812yes—
90C4×D11—42no—
91C4×D11—82no—
92Dic22—81no—
93C11⋊C8—22no—
94C11⋊C8—21no—
95C11⋊C8C2×Q812yes—
96#557D1111yescharacteristic, complemented
97#554—111no—
98#499—112no—
99#498—111no—
100#479—112no—
101#478—112no—
102#477—111no—
103#474—111no—
104C8×Q8—111no—
105C4×SD16—111no—
106C4×SD16—112no—
107C22×C11C22×D411yescharacteristic
108C2×D11—22no—
109C2×D11—41no—
110C2×D11—41no—
111C4×C11—22no—
112C4×C11—22no—
113C4×C11—21no—
114C4×C11—22no—
115C4×C11—42no—
116C4×C11—41no—
117C4×C11#13512yes—
118C4×C11C22×Q811yescharacteristic
119C4×C112−1+411yescharacteristic
120Dic11—41no—
121Dic11—42no—
122C2×SD16—111no—
123C4⋊Q8—21no—
124C4⋊Q8—111no—
125C4⋊Q8C2×D1111yescharacteristic
126#125—22no—
127#125—112no—
128#125C2×D1112yes—
129C22⋊Q8—221no—
130C22⋊Q8—222no—
131C4×Q8—21no—
132C4×Q8C2×D1111yescharacteristic
133C4×Q8C2×D1112yes—
134C4×Q8C2×D1111yescharacteristic
135C4×D4—111no—
136C4×D4—112no—
137C2×C4⋊C4—221no—
138#107—112no—
139#107—112no—
140#106—112no—
141#106—111no—
142#106—112no—
143C4⋊C8—111no—
144C4⋊C8—112no—
145#103—112no—
146#103—111no—
147#102—112no—
148#102—111no—
149C4×C8—111no—
150C4×C8—112no—
151C2×C11D4×Q811yescharacteristic
152C2×C11C2×#13511yescharacteristic
153C2×C11#57711yescharacteristic
154D11—42no—
155C2×Q8—21no—
156C2×Q8—221no—
157C2×Q8C22⋊D1111yescharacteristic
158C2×Q8C22×D1111yescharacteristic
159C2×D4—111no—
160C22×C4—221no—
161C22×C4—222no—
162SD16—114no—
163C2×C8—111no—
164C2×C8—111no—
165C2×C8—112no—
166C4⋊C4—22no—
167C4⋊C4—21no—
168C4⋊C4—22no—
169C4⋊C4—21no—
170C4⋊C4—22no—
171C4⋊C4—112no—
172C4⋊C4—111no—
173C4⋊C4—222no—
174C4⋊C4—221no—
175C4⋊C4—222no—
176C4⋊C4C22⋊D1111yescharacteristic
177C4⋊C4C22⋊D1112yes—
178C4⋊C4C22×D1112yes—
179C4⋊C4C22×D1111yescharacteristic
180C22⋊C4—221no—
181C22⋊C4—222no—
182C42—22no—
183C42—21no—
184C42C22×D1112yes—
185C42C22×D1111yescharacteristic
186C11#338111yescharacteristic, complemented, Sylow
187C23—221no—
188Q8—22no—
189Q8—21no—
190Q8—42no—
191Q8—881no—
192Q8Q8×D1112yes—
193D4—112no—
194D4—221no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—221no—
199C2×C4—222no—
200C2×C4—442no—
201C2×C4—882no—
202C2×C4C2×C22⋊D1112yes—
203C2×C4C2×C22⋊D1112yes—
204C2×C4C2×C22⋊D1111yescharacteristic
205C2×C4C2×C22⋊D1111yescharacteristic
206C2×C4C23×D1111yescharacteristic
207C8—112no—
208C8—221no—
209C8—222no—
210C22—222no—
211C22—441no—
212C22—441no—
213C22C22×C22⋊D1111yescharacteristic
214C4—22no—
215C4—22no—
216C4—22no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—441no—
221C4—442no—
222C4#6700312yes—
223C4C2×Q8×D1111yescharacteristic
224C4#6704011yescharacteristic
225C2—442no—
226C2Q8×C22⋊D1111yescharacteristic
227C2C2×#6700311yescharacteristic
228C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#557C2
socleC22×C11C22×D4
prime radicalC2×D44C23
hypercenter#557D11
hypocenterC11#3381
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C11×#557C2semidirect
4. #10622692C2semidirect
6. #10622677C2semidirect
9. Q8×C11⋊C8C2semidirect
10. #10622635C2semidirect
11. #10622634C2semidirect
61. #4325Q8semidirect
96. #557D11semidirect
186. C11#3381semidirect

Maximal subgroups

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

subgroupindex
C11×#5572
#106231102
#106227002
#106226922
#106226792
#106226772
C4×#43252
Q8×C11⋊C82
#106226352
#106226342
#338111