Finite Group Databasebeta

← C2×#13069782 #14781172

Subgroups — C2×#13069782 #14781172

Order 2816.

1482 conjugacy classes of subgroups; only the 291 normal subgroups are shown.

normal subgroups only

This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 291 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×#10622556C213yesmaximal
2#13069782C218yesmaximal, direct product factor
3C2×#10622164C213yesmaximal
4C2×C11×#543C211yesmaximal, characteristic
5C24×Dic11C2211yescharacteristic
6C11×#543—26no—
7C11×#543C2214yes—
8C2×C11×C22⋊Q8—26no—
9C22×C11×C22⋊C4C2213yes—
10C22×C22⋊Dic11C2213yes—
11C2×C11⋊#95—26no—
12#10622556—26no—
13#10622556C22112yes—
14#10622164C22112yes—
15C25×C11C2311yescharacteristic
16C22×Q8×C11—22no—
17C23×C4×C11D416yes—
18C23×Dic11—23no—
19C23×Dic11—23no—
20C23×Dic11—26no—
21C23×Dic11—23no—
22C23×Dic11Q814yescomplemented
23C23×Dic11C2312yes—
24C11×C22⋊Q8—224no—
25C11×C22⋊Q8—224no—
26C2×C11×C4⋊C4—26no—
27C2×C11×C22⋊C4—26no—
28C2×C11×C22⋊C4—26no—
29C2×C11×C22⋊C4D416yes—
30C2×C11×C22⋊C4C2316yes—
31C2×C22⋊Dic11—212no—
32C2×C22⋊Dic11—23no—
33C2×C22⋊Dic11C2316yes—
34C11⋊#95—224no—
35C2×#2030—111nomaximal, Sylow
36C24×C11—44no—
37C24×C11C2×D413yes—
38C24×C11C2×D413yes—
39C24×C11C2×Q812yes—
40C24×C11#4116yes—
41C24×C11C2411yescharacteristic
42C2×Q8×C11—28no—
43C2×Q8×C11—84no—
44C22×C4×C11—26no—
45C22×C4×C11—26no—
46C22×C4×C11—412no—
47C22×C4×C11C2×D4112yes—
48C22×Dic11—212no—
49C22×Dic11—212no—
50C22×Dic11—26no—
51C22×Dic11—26no—
52C22×Dic11—26no—
53C22×Dic11—412no—
54C22×Dic11—43no—
55C22×Dic11—41no—
56C22×Dic11—46no—
57C22×Dic11—46no—
58C22×Dic11—46no—
59C22×Dic11C2×Q814yescomplemented
60C11×C4⋊C4—224no—
61C11×C22⋊C4—212no—
62C11×C22⋊C4—212no—
63C22⋊Dic11—212no—
64C22⋊Dic11—46no—
65C2×#543D1111yescharacteristic
66C2×#381—113no—
67#2030—118no—
68C2×#342—113no—
69C23×C11—212no—
70C23×C11—46no—
71C23×C11—44no—
72C23×C11—412no—
73C23×C11—42no—
74C23×C11#12013yes—
75C23×C11#12011yescharacteristic
76C23×C11C22⋊Q816yes—
77C23×C11C22⋊Q816yes—
78C23×C11#12416yes—
79C23×C11#12416yes—
80C23×C11C22×D413yes—
81C23×C11C22×Q811yescharacteristic
82C23×C11C2×#4113yes—
83Q8×C11—88no—
84C2×C4×C11—212no—
85C2×C4×C11—412no—
86C2×C4×C11—412no—
87C2×C4×C11—86no—
88C2×Dic11—212no—
89C2×Dic11—42no—
90C2×Dic11—46no—
91C2×Dic11—412no—
92C2×Dic11—44no—
93C2×Dic11—412no—
94C2×Dic11—46no—
95C2×Dic11—812no—
96C24×C4—111no—
97#543—26no—
98#543C2×D1114yes—
99C2×C22⋊Q8—26no—
100C22×C22⋊C4—113no—
101C22×C22⋊C4C2×D1113yes—
102#381—1112no—
103#381—226no—
104C2×#95—226no—
105#342—1112no—
106C22×C11—26no—
107C22×C11—26no—
108C22×C11—212no—
109C22×C11—212no—
110C22×C11—46no—
111C22×C11—46no—
112C22×C11—41no—
113C22×C11—43no—
114C22×C11#39316yes—
115C22×C11#39312yes—
116C22×C11#45814yes—
117C22×C11C2×#12011yescharacteristic
118C22×C11C2×C22⋊Q813yes—
119C22×C11C2×#12413yes—
120C4×C11—412no—
121Dic11—44no—
122Dic11—86no—
123C25C22×D1111yescharacteristic
124C22×Q8—22no—
125C23×C4—114no—
126C23×C4—112no—
127C23×C4—226no—
128C23×C4—223no—
129C23×C4—223no—
130C23×C4—223no—
131C23×C4C22⋊D1116yes—
132C22⋊Q8—224no—
133C22⋊Q8—224no—
134C2×C4⋊C4—26no—
135C2×C22⋊C4—26no—
136C2×C22⋊C4—26no—
137C2×C22⋊C4—116no—
138C2×C22⋊C4—2212no—
139C2×C22⋊C4—223no—
140C2×C22⋊C4C22⋊D1116yes—
141C2×C22⋊C4C22×D1116yes—
142#95—2224no—
143C2×C11—23no—
144C2×C11—23no—
145C2×C11—26no—
146C2×C11#203014yescomplemented
147C2×C11C2×#39311yescharacteristic
148C2×C11C2×#45812yes—
149C24—44no—
150C24Q8×D1112yes—
151C24#434316yes—
152C24C2×C22⋊D1113yes—
153C24C2×C22⋊D1113yes—
154C24C23×D1111yescharacteristic
155C2×Q8—28no—
156C2×Q8—84no—
157C22×C4—26no—
158C22×C4—26no—
159C22×C4—412no—
160C22×C4—114no—
161C22×C4—2212no—
162C22×C4—2212no—
163C22×C4—226no—
164C22×C4—226no—
165C22×C4—226no—
166C22×C4—446no—
167C22×C4—446no—
168C22×C4—443no—
169C22×C4—441no—
170C22×C4—4412no—
171C22×C4—446no—
172C22×C4C2×C22⋊D11112yes—
173C4⋊C4—224no—
174C22⋊C4—212no—
175C22⋊C4—212no—
176C22⋊C4—2212no—
177C22⋊C4—446no—
178C11C2×#203011yescharacteristic, complemented, Sylow
179C23—212no—
180C23—44no—
181C23—412no—
182C23—46no—
183C23—42no—
184C23#6699916yes—
185C23#6699916yes—
186C23#6700016yes—
187C23#6700016yes—
188C23#6700613yes—
189C23#6700611yescharacteristic
190C23C2×Q8×D1111yescharacteristic
191C23C2×#434313yes—
192C23C22×C22⋊D1113yes—
193Q8—88no—
194C2×C4—212no—
195C2×C4—412no—
196C2×C4—412no—
197C2×C4—86no—
198C2×C4—2212no—
199C2×C4—446no—
200C2×C4—4412no—
201C2×C4—444no—
202C2×C4—442no—
203C2×C4—4412no—
204C2×C4—446no—
205C2×C4—8812no—
206C22—212no—
207C22—212no—
208C22—26no—
209C22—26no—
210C22—46no—
211C22—46no—
212C22—41no—
213C22—43no—
214C22#1062284416yes—
215C22#1062284412yes—
216C22#1062285614yes—
217C22C2×#6699913yes—
218C22C2×#6700013yes—
219C22C2×#6700611yescharacteristic
220C4—412no—
221C4—444no—
222C4—886no—
223C2—23no—
224C2—23no—
225C2—26no—
226C2#1306978214yesdirect product factor
227C2C2×#1062284411yescharacteristic
228C2C2×#1062285612yes—
subgroupG/H
centerC23#67006
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC2×C11×#543C2
socleC23×C11#120
prime radicalC25×C11C23
hypercenterC2×#543D11
hypocenterC11C2×#2030
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C25 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
2. #13069782C2direct (N × H)
22. C23×Dic11Q8semidirect
59. C22×Dic11C2×Q8semidirect
146. C2×C11#2030semidirect
178. C11C2×#2030semidirect
226. C2#13069782direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225562
#130697822
C2×#106221642
C2×C11×#5432
C2×#203011