Finite Group Databasebeta

← #13076971

Subgroups — #13076971

Order 1408.

752 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 181 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×#124C211yesmaximal, characteristic, complemented
2C2×#67000C211yesmaximal, characteristic, complemented
3C2×#66997C211yesmaximal, characteristic, complemented
4C2×#66993C211yesmaximal, characteristic
5C2×#66989C211yesmaximal, characteristic, complemented
6C2×#66928C211yesmaximal, characteristic, complemented
7#10622570C218yesmaximal, complemented
8C42×Dic11C211yesmaximal, characteristic, complemented
9C22×Q8×C11C2211yescharacteristic
10C22×D4×C11C2211yescharacteristic
11C22×C22⋊D11C2214yes—
12C22×D44C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C11×#124—24no—
15C2×C11×C22⋊C4C2214yes—
16C2×C42×C11C2211yescharacteristic
17C2×C22⋊Dic11C2214yes—
18#67000—24no—
19#66997—24no—
20#66993—24no—
21#66989—24no—
22C2×(C2×D11)⋊C4C2214yes—
23C2×(C2×D11)⋊C4C2214yes—
24C2×Dic11⋊C4C2214yes—
25C2×C4×Dic11C2214yes—
26C2×C4×Dic11C2211yescharacteristic
27C2×C4×Dic11C2211yescharacteristic
28#66928—24no—
29C24×C11C2312yes—
30C23×D11C2312yes—
31C2×Q8×C11—22no—
32C2×Q8×C11—22no—
33C2×Q8×C11—22no—
34C2×D4×C11—22no—
35C2×D4×C11—22no—
36C2×D4×C11—22no—
37C22×C4×C11C2312yes—
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—28no—
41C2×C22⋊D11—216no—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C2×D44—22no—
46C2×D44—22no—
47C2×D44—22no—
48C2×Dic22—22no—
49C2×Dic22—22no—
50C2×Dic22—22no—
51C11×C22⋊C4—28no—
52C42×C11D414yescomplemented
53C22⋊Dic11—28no—
54(C2×D11)⋊C4—28no—
55(C2×D11)⋊C4—28no—
56Dic11⋊C4—28no—
57C4×Dic11—28no—
58C4×Dic11D414yes—
59C4×Dic11D414yescomplemented
60#2858—111nomaximal, Sylow
61C23×C11—22no—
62C23×C11—22no—
63C23×C11—22no—
64C23×C11—28no—
65C23×C11C2411yescharacteristic
66C22×D11—22no—
67C22×D11—22no—
68C22×D11—22no—
69C22×D11—28no—
70Q8×C11—44no—
71D4×C11—44no—
72C2×C4×C11—24no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11C2×D412yes—
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2×D414yes—
79C2×C4×C11C2×D412yes—
80C22⋊D11—416no—
81C2×Dic11—24no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11C2×D414yes—
86C2×Dic11C2×D414yes—
87C2×Dic11#4118yes—
88D44—44no—
89Dic22—44no—
90C2×C4⋊Q8—111no—
91C2×#127—111no—
92C2×#124—111no—
93C2×#124—111no—
94C2×#124—111no—
95C2×#124D1111yescharacteristic, complemented
96#390—118no—
97C43—111no—
98C22×C11—44no—
99C22×C11—42no—
100C22×C11—44no—
101C22×C11—44no—
102C22×C11C22×D411yescharacteristic
103C22×C11C22×D411yescharacteristic
104C22×C11C22×D411yescharacteristic
105C22×C11C2×#4114yes—
106C2×D11—44no—
107C2×D11—42no—
108C2×D11—44no—
109C2×D11—44no—
110C4×C11—24no—
111C4×C11—42no—
112C4×C11#12714yes—
113Dic11—24no—
114Dic11—42no—
115Dic11#12418yescomplemented
116C22×Q8—111no—
117C22×Q8C2×D1111yescharacteristic
118C22×D4—114no—
119C22×D4—111no—
120C22×D4C2×D1111yescharacteristic
121C4⋊Q8—224no—
122#127—224no—
123#124—24no—
124#124—224no—
125#124—224no—
126#124—224no—
127C2×C4⋊C4—114no—
128C2×C22⋊C4—114no—
129C2×C22⋊C4—114no—
130C2×C22⋊C4—114no—
131C2×C22⋊C4C2×D1114yes—
132C2×C42—111no—
133C2×C42—111no—
134C2×C42—114no—
135C2×C42C2×D1111yescharacteristic
136C2×C11—82no—
137C2×C11C2×#12412yes—
138C2×C11C2×#12711yescharacteristic
139C2×C11#53212yes—
140C2×C11#53212yes—
141D11—82no—
142C24—112no—
143C24C22×D1112yes—
144C2×Q8—22no—
145C2×Q8—22no—
146C2×Q8—22no—
147C2×Q8—222no—
148C2×Q8—222no—
149C2×Q8—222no—
150C2×D4—22no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—228no—
154C2×D4—2216no—
155C2×D4—222no—
156C2×D4—222no—
157C2×D4—222no—
158C22×C4—112no—
159C22×C4—112no—
160C22×C4—112no—
161C22×C4C22×D1112yes—
162C22×C4C22×D1112yes—
163C22×C4C22×D1111yescharacteristic
164C4⋊C4—228no—
165C22⋊C4—28no—
166C22⋊C4—228no—
167C22⋊C4—228no—
168C22⋊C4—228no—
169C42—114no—
170C42—114no—
171C42—228no—
172C42C22⋊D1114yescomplemented
173C11#285811yescharacteristic, complemented, Sylow
174C23—22no—
175C23—22no—
176C23—28no—
177C23—22no—
178C23—222no—
179C23—222no—
180C23—228no—
181C23—222no—
182C23C23×D1111yescharacteristic
183Q8—44no—
184Q8—444no—
185D4—44no—
186D4—4416no—
187D4—444no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—114no—
193C2×C4—118no—
194C2×C4—114no—
195C2×C4—224no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4D4×D1112yes—
200C2×C4D4×D1112yes—
201C2×C4C2×C22⋊D1114yes—
202C2×C4C2×C22⋊D1112yes—
203C22—42no—
204C22—44no—
205C22—44no—
206C22—44no—
207C22—442no—
208C22—444no—
209C22—444no—
210C22—444no—
211C22C2×D4×D1111yescharacteristic
212C22C2×D4×D1111yescharacteristic
213C22#41×D1114yes—
214C22C22×C22⋊D1111yescharacteristic
215C4—24no—
216C4—42no—
217C4—118no—
218C4—224no—
219C4—442no—
220C4#6699314yes—
221C2—82no—
222C2—882no—
223C2#1062319912yes—
224C2D11×#12412yes—
225C2C2×#6699311yescharacteristic
226C2#1062336312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#124C2
prime radicalC2×#66993C2
hypercenterC2×#124D11
hypocenterC11#2858
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C11×#124C2semidirect
2. C2×#67000C2semidirect
3. C2×#66997C2semidirect
5. C2×#66989C2semidirect
6. C2×#66928C2semidirect
7. #10622570C2semidirect
8. C42×Dic11C2semidirect
52. C42×C11D4semidirect
59. C4×Dic11D4semidirect
95. C2×#124D11semidirect
115. Dic11#124semidirect
172. C42C22⋊D11semidirect
173. C11#2858semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×#670002
C2×#669972
C2×#669932
C2×#669892
C2×#669282
#106225702
C42×Dic112
#285811