Finite Group Databasebeta

← C2×#13076880 #14960184

Subgroups — C2×#13076880 #14960184

Order 2816.

3294 conjugacy classes of subgroups; only the 667 normal subgroups are shown.

normal subgroups only

This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 667 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
1#13076880C2116yesmaximal, direct product factor
2C2×#10622562C214yesmaximal, complemented
3C2×#10622561C218yesmaximal, complemented
4C2×#10622860C212yesmaximal
5C2×C11×#379C211yesmaximal, characteristic
6C26×C11C2211yescharacteristic
7C22×C11×C22⋊C4C2214yes—
8C22×C11×C22⋊C4C2212yes—
9C22×C22⋊Dic11C2214yes—
10C22×C22⋊Dic11C2214yes—
11C22×C22⋊Dic11C2214yes—
12C22×C4⋊Dic11C2214yescomplemented
13C22×Dic11⋊C4C2218yescomplemented
14C11×#379C2218yes—
15#10622860C22116yes—
16C2×C11⋊#95C2214yescomplemented
17#10622562C22132yescomplemented
18#10622561C22164yescomplemented
19C25×C11—48no—
20C25×C11—44no—
21C25×C11Q818yes—
22C25×C11C2312yes—
23C25×C11C2311yescharacteristic
24C25×C11C2314yes—
25C23×C4×C11C2314yes—
26C23×Dic11C2318yes—
27C2×C11×C22⋊C4—48no—
28C2×C11×C22⋊C4—44no—
29C2×C11×C22⋊C4C23116yes—
30C2×C11×C22⋊C4C2318yes—
31C2×C22⋊Dic11—48no—
32C2×C22⋊Dic11—48no—
33C2×C22⋊Dic11—48no—
34C2×C22⋊Dic11C23116yes—
35C2×C22⋊Dic11C23116yes—
36C2×C22⋊Dic11C23116yes—
37C2×C4⋊Dic11—48no—
38C2×C4⋊Dic11C23116yescomplemented
39C2×Dic11⋊C4—416no—
40C2×Dic11⋊C4C23132yescomplemented
41C11⋊#95C23116yescomplemented
42C2×#2842—111nomaximal, Sylow
43C24×C11—28no—
44C24×C11—28no—
45C24×C11—28no—
46C24×C11—28no—
47C24×C11—24no—
48C24×C11—432no—
49C24×C11—416no—
50C24×C11—416no—
51C24×C11—48no—
52C24×C11—464no—
53C24×C11C2×Q818yes—
54C24×C11C2×Q814yes—
55C24×C11C2×Q8116yes—
56C24×C11C2414yes—
57C24×C11C2412yes—
58C24×C11C2411yescharacteristic
59C22×C4×C11—216no—
60C22×C4×C11—28no—
61C22×C4×C11C2418yes—
62C22×Dic11—216no—
63C22×Dic11—216no—
64C22×Dic11—216no—
65C22×Dic11C24116yes—
66C11×C22⋊C4—416no—
67C11×C22⋊C4—48no—
68C22⋊Dic11—416no—
69C22⋊Dic11—416no—
70C22⋊Dic11—416no—
71C4⋊Dic11—416no—
72Dic11⋊C4—432no—
73#2842—1116no—
74C2×#399—114no—
75C2×#396—118no—
76C2×#379—112no—
77C2×#379D1111yescharacteristic
78C23×C11—216no—
79C23×C11—216no—
80C23×C11—216no—
81C23×C11—216no—
82C23×C11—28no—
83C23×C11—28no—
84C23×C11—28no—
85C23×C11—28no—
86C23×C11—28no—
87C23×C11—24no—
88C23×C11—432no—
89C23×C11—416no—
90C23×C11—4128no—
91C23×C11—464no—
92C23×C11—432no—
93C23×C11—416no—
94C23×C11C22×Q818yes—
95C23×C11C22×Q814yes—
96C23×C11C22×Q812yes—
97C23×C11H(5,𝔽2)18yes—
98C23×C11H(5,𝔽2)14yes—
99C23×C11C2511yescharacteristic
100C2×C4×C11—216no—
101C2×C4×C11—28no—
102C2×C4×C11—416no—
103C2×Dic11—216no—
104C2×Dic11—216no—
105C2×Dic11—216no—
106C2×Dic11—432no—
107C26C2×D1111yescharacteristic
108C22×C4⋊C4—118no—
109C22×C4⋊C4—114no—
110C22×C22⋊C4—114no—
111C22×C22⋊C4—114no—
112C22×C22⋊C4—114no—
113C22×C22⋊C4C2×D1114yes—
114C22×C22⋊C4C2×D1112yes—
115#399—1132no—
116#396—1164no—
117#379—1116no—
118#379C2×D1118yes—
119C2×#95—114no—
120C22×C11—28no—
121C22×C11—28no—
122C22×C11—28no—
123C22×C11—28no—
124C22×C11—24no—
125C22×C11—464no—
126C22×C11—432no—
127C22×C11—416no—
128C22×C11—416no—
129C22×C11—48no—
130C22×C11#54318yes—
131C22×C11#54314yes—
132C22×C11#560116yes—
133C22×C11C23×Q811yescharacteristic
134C22×C11C2×H(5,𝔽2)14yes—
135C22×C11C2×H(5,𝔽2)12yes—
136C4×C11—48no—
137Dic11—416no—
138C25—48no—
139C25—44no—
140C25Dic2218yes—
141C25C22×D1112yes—
142C25C22×D1111yescharacteristic
143C25C22×D1114yes—
144C23×C4—118no—
145C23×C4C22×D1114yes—
146C2×C4⋊C4—1132no—
147C2×C4⋊C4—1116no—
148C2×C4⋊C4—4416no—
149C2×C4⋊C4—448no—
150C2×C22⋊C4—48no—
151C2×C22⋊C4—44no—
152C2×C22⋊C4—1116no—
153C2×C22⋊C4—1116no—
154C2×C22⋊C4—1116no—
155C2×C22⋊C4—448no—
156C2×C22⋊C4—448no—
157C2×C22⋊C4—448no—
158C2×C22⋊C4C22×D11116yes—
159C2×C22⋊C4C22×D1118yes—
160#95—1116no—
161C2×C11—48no—
162C2×C11—44no—
163C2×C11#284218yescomplemented
164C2×C11C2×#54312yes—
165C2×C11C2×#54311yescharacteristic
166C2×C11C2×#56014yes—
167C24—28no—
168C24—24no—
169C24—28no—
170C24—28no—
171C24—28no—
172C24—416no—
173C24—48no—
174C24—432no—
175C24—416no—
176C24—464no—
177C24C2×Dic2218yes—
178C24C2×Dic2214yes—
179C24C2×Dic22116yes—
180C24C23×D1114yes—
181C24C23×D1112yes—
182C24C23×D1111yescharacteristic
183C22×C4—216no—
184C22×C4—28no—
185C22×C4—1116no—
186C22×C4—2216no—
187C22×C4—2216no—
188C22×C4—2216no—
189C22×C4C23×D1118yes—
190C4⋊C4—4432no—
191C4⋊C4—4416no—
192C22⋊C4—416no—
193C22⋊C4—48no—
194C22⋊C4—4416no—
195C22⋊C4—4416no—
196C22⋊C4—4416no—
197C11C2×#284211yescharacteristic, complemented, Sylow
198C23—216no—
199C23—28no—
200C23—216no—
201C23—216no—
202C23—216no—
203C23—28no—
204C23—24no—
205C23—28no—
206C23—28no—
207C23—28no—
208C23—432no—
209C23—416no—
210C23—464no—
211C23—4128no—
212C23—432no—
213C23—416no—
214C23C22×Dic2218yes—
215C23C22×Dic2214yes—
216C23C22×Dic2212yes—
217C23#6703718yes—
218C23#6703714yes—
219C23C24×D1111yescharacteristic
220C2×C4—216no—
221C2×C4—28no—
222C2×C4—416no—
223C2×C4—2216no—
224C2×C4—2216no—
225C2×C4—2216no—
226C2×C4—4432no—
227C22—28no—
228C22—24no—
229C22—28no—
230C22—28no—
231C22—28no—
232C22—464no—
233C22—416no—
234C22—48no—
235C22—432no—
236C22—416no—
237C22#1062301418yes—
238C22#1062301414yes—
239C22#10623126116yes—
240C22C23×Dic2211yescharacteristic
241C22C2×#6703714yes—
242C22C2×#6703712yes—
243C4—48no—
244C4—4416no—
245C2—48no—
246C2—44no—
247C2#1307688018yesdirect product factor
248C2C2×#1062301412yes—
249C2C2×#1062301411yescharacteristic
250C2C2×#1062312614yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#379C2
socleC24×C11C24
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11C2×#2842
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. #13076880C2direct (N × H)
2. C2×#10622562C2semidirect
3. C2×#10622561C2semidirect
12. C22×C4⋊Dic11C22semidirect
13. C22×Dic11⋊C4C22semidirect
16. C2×C11⋊#95C22semidirect
17. #10622562C22semidirect
18. #10622561C22semidirect
38. C2×C4⋊Dic11C23semidirect
40. C2×Dic11⋊C4C23semidirect
41. C11⋊#95C23semidirect
163. C2×C11#2842semidirect
197. C11C2×#2842semidirect
247. C2#13076880direct (N × H)

Maximal subgroups

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

subgroupindex
#130768802
C2×#106225622
C2×#106225612
C2×#106228602
C2×C11×#3792
C2×#284211