Finite Group Databasebeta

← C2×#13076881 #14960185

Subgroups — C2×#13076881 #14960185

Order 2816.

3294 conjugacy classes of subgroups; only the 627 normal subgroups are shown.

normal subgroups only

This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 627 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#13076881C2116yesmaximal, direct product factor
2C2×#10622562C213yesmaximal, complemented
3C2×#10622289C212yesmaximal, complemented
4C2×#10622607C216yesmaximal, complemented
5C2×#10622568C213yesmaximal
6C2×C11×#399C211yesmaximal, characteristic, complemented
7C25×D11C2211yescharacteristic
8C22×C11×C4⋊C4C2213yescomplemented
9C22×C11×C22⋊C4C2213yes—
10C22×C22⋊Dic11C2213yes—
11C22×(C2×D11)⋊C4C2216yes—
12C22×(C2×D11)⋊C4C2216yes—
13C22×C4⋊Dic11C2213yescomplemented
14C22×Dic11⋊C4C2216yescomplemented
15C11×#399C2218yescomplemented
16C2×C11×#95C2211yescharacteristic, complemented
17C2×C11⋊#95C2213yescomplemented
18#10622607C22148yescomplemented
19#10622568C22124yes—
20#10622562C22124yescomplemented
21#10622289C22116yescomplemented
22C25×C11C2311yescharacteristic
23C24×D11—46no—
24C24×D11—46no—
25C24×D11Q818yes—
26C24×D11C2312yes—
27C24×D11C2314yes—
28C23×C4×C11C2313yes—
29C23×C4×C11C2313yes—
30C23×Dic11C2316yes—
31C2×C11×C4⋊C4—46no—
32C2×C11×C4⋊C4C23112yescomplemented
33C2×C11×C22⋊C4—46no—
34C2×C11×C22⋊C4C23112yes—
35C2×C22⋊Dic11—46no—
36C2×C22⋊Dic11C23112yes—
37C2×(C2×D11)⋊C4—412no—
38C2×(C2×D11)⋊C4—412no—
39C2×(C2×D11)⋊C4C23124yes—
40C2×(C2×D11)⋊C4C23124yes—
41C2×C4⋊Dic11—46no—
42C2×C4⋊Dic11C23112yescomplemented
43C2×Dic11⋊C4—412no—
44C2×Dic11⋊C4C23124yescomplemented
45C11×#95C2314yescomplemented
46C11⋊#95C23112yescomplemented
47C2×#2842—111nomaximal, Sylow
48C24×C11—26no—
49C24×C11—26no—
50C24×C11C2×Q814yes—
51C24×C11C2412yes—
52C24×C11C2411yescharacteristic
53C23×D11—212no—
54C23×D11—212no—
55C23×D11—448no—
56C23×D11—412no—
57C23×D11—412no—
58C23×D11—416no—
59C23×D11—448no—
60C23×D11C2×Q818yes—
61C23×D11C2×Q8116yes—
62C23×D11C2414yes—
63C22×C4×C11—212no—
64C22×C4×C11—26no—
65C22×C4×C11—212no—
66C22×C4×C11—26no—
67C22×C4×C11C2416yes—
68C22×C4×C11C2416yes—
69C22×Dic11—212no—
70C22×Dic11—212no—
71C22×Dic11—212no—
72C22×Dic11C24112yes—
73C11×C4⋊C4—412no—
74C11×C22⋊C4—412no—
75C22⋊Dic11—412no—
76(C2×D11)⋊C4—424no—
77(C2×D11)⋊C4—424no—
78C4⋊Dic11—412no—
79Dic11⋊C4—424no—
80#2842—1116no—
81C2×#399—113no—
82C2×#399D1111yescharacteristic, complemented
83C2×#396—112no—
84C2×#396—116no—
85C2×#379—113no—
86C23×C11—224no—
87C23×C11—26no—
88C23×C11—26no—
89C23×C11—44no—
90C23×C11—412no—
91C23×C11C22×Q814yes—
92C23×C11C22×Q812yes—
93C23×C11H(5,𝔽2)16yes—
94C23×C11H(5,𝔽2)16yes—
95C23×C11C2511yescharacteristic
96C22×D11—248no—
97C22×D11—212no—
98C22×D11—212no—
99C22×D11—448no—
100C22×D11—4128no—
101C22×D11—416no—
102C22×D11—448no—
103C22×D11—48no—
104C22×D11—424no—
105C22×D11C22×Q818yes—
106C2×C4×C11—212no—
107C2×C4×C11—26no—
108C2×C4×C11—212no—
109C2×C4×C11—26no—
110C2×C4×C11—412no—
111C2×C4×C11—412no—
112C2×Dic11—212no—
113C2×Dic11—212no—
114C2×Dic11—212no—
115C2×Dic11—424no—
116C26—111no—
117C22×C4⋊C4—116no—
118C22×C4⋊C4—113no—
119C22×C4⋊C4C2×D1113yescomplemented
120C22×C22⋊C4—113no—
121C22×C22⋊C4—116no—
122C22×C22⋊C4—116no—
123C22×C22⋊C4C2×D1113yes—
124#399—1124no—
125#399C2×D1118yescomplemented
126#396—1148no—
127#396—1116no—
128#379—1124no—
129C2×#95—113no—
130C2×#95C2×D1111yescharacteristic, complemented
131C22×C11—212no—
132C22×C11—416no—
133C22×C11—42no—
134C22×C11—46no—
135C22×C11#543112yes—
136C22×C11#56014yes—
137C22×C11#560112yes—
138C22×C11C23×Q811yescharacteristic
139C22×C11C2×H(5,𝔽2)13yes—
140C22×C11C2×H(5,𝔽2)13yes—
141C2×D11—224no—
142C2×D11—464no—
143C2×D11—432no—
144C2×D11—44no—
145C2×D11—412no—
146C4×C11—46no—
147C4×C11—46no—
148Dic11—412no—
149C25—112no—
150C25—118no—
151C25—114no—
152C25—446no—
153C25—446no—
154C25C22×D1111yescharacteristic
155C23×C4—116no—
156C23×C4C22×D1113yes—
157C23×C4C22×D1113yes—
158C2×C4⋊C4—46no—
159C2×C4⋊C4—1124no—
160C2×C4⋊C4—1112no—
161C2×C4⋊C4—4412no—
162C2×C4⋊C4—446no—
163C2×C4⋊C4C22×D11112yescomplemented
164C2×C22⋊C4—46no—
165C2×C22⋊C4—1112no—
166C2×C22⋊C4—1124no—
167C2×C22⋊C4—1124no—
168C2×C22⋊C4—4412no—
169C2×C22⋊C4—4412no—
170C2×C22⋊C4—446no—
171C2×C22⋊C4C22×D11112yes—
172#95—1112no—
173#95C22×D1114yescomplemented
174C2×C11—44no—
175C2×C11#284218yescomplemented
176C2×C11C2×#54313yes—
177C2×C11C2×#56011yescharacteristic
178C2×C11C2×#56013yes—
179D11—48no—
180C24—26no—
181C24—26no—
182C24—118no—
183C24—114no—
184C24—1116no—
185C24—2212no—
186C24—2212no—
187C24—4448no—
188C24—4412no—
189C24—4412no—
190C24—4416no—
191C24—4448no—
192C24Q8×D1114yes—
193C24C23×D1112yes—
194C24C23×D1111yescharacteristic
195C22×C4—26no—
196C22×C4—26no—
197C22×C4—212no—
198C22×C4—212no—
199C22×C4—1112no—
200C22×C4—2212no—
201C22×C4—2212no—
202C22×C4—2212no—
203C22×C4C23×D1116yes—
204C22×C4C23×D1116yes—
205C4⋊C4—412no—
206C4⋊C4—4424no—
207C4⋊C4—4412no—
208C22⋊C4—412no—
209C22⋊C4—4424no—
210C22⋊C4—4424no—
211C22⋊C4—4412no—
212C11C2×#284211yescharacteristic, complemented, Sylow
213C23—224no—
214C23—26no—
215C23—26no—
216C23—44no—
217C23—412no—
218C23—118no—
219C23—2248no—
220C23—2212no—
221C23—2212no—
222C23—4448no—
223C23—4416no—
224C23—4448no—
225C23—44128no—
226C23—448no—
227C23—4424no—
228C23#6703716yes—
229C23C2×Q8×D1114yes—
230C23C2×Q8×D1112yes—
231C23#6704216yes—
232C23C24×D1111yescharacteristic
233C2×C4—26no—
234C2×C4—26no—
235C2×C4—212no—
236C2×C4—212no—
237C2×C4—412no—
238C2×C4—412no—
239C2×C4—2212no—
240C2×C4—2212no—
241C2×C4—2212no—
242C2×C4—4424no—
243C22—212no—
244C22—42no—
245C22—46no—
246C22—416no—
247C22—2224no—
248C22—4464no—
249C22—444no—
250C22—4412no—
251C22—4432no—
252C22#10623165112yes—
253C22#10623197112yes—
254C22#1062325114yes—
255C22C2×#6703713yes—
256C22C22×Q8×D1111yescharacteristic
257C22C2×#6704213yes—
258C4—46no—
259C4—46no—
260C4—4412no—
261C2—44no—
262C2—448no—
263C2#1307688118yesdirect product factor
264C2C2×#1062316513yes—
265C2C2×#1062325111yescharacteristic
266C2C2×#1062319713yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#399C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#399D11
hypocenterC11C2×#2842
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. #13076881C2direct (N × H)
2. C2×#10622562C2semidirect
3. C2×#10622289C2semidirect
4. C2×#10622607C2semidirect
6. C2×C11×#399C2semidirect
8. C22×C11×C4⋊C4C22semidirect
13. C22×C4⋊Dic11C22semidirect
14. C22×Dic11⋊C4C22semidirect
15. C11×#399C22semidirect
16. C2×C11×#95C22semidirect
17. C2×C11⋊#95C22semidirect
18. #10622607C22semidirect
20. #10622562C22semidirect
21. #10622289C22semidirect
32. C2×C11×C4⋊C4C23semidirect
42. C2×C4⋊Dic11C23semidirect
44. C2×Dic11⋊C4C23semidirect
45. C11×#95C23semidirect
46. C11⋊#95C23semidirect
82. C2×#399D11semidirect
119. C22×C4⋊C4C2×D11semidirect
125. #399C2×D11semidirect
130. C2×#95C2×D11semidirect
163. C2×C4⋊C4C22×D11semidirect
173. #95C22×D11semidirect
175. C2×C11#2842semidirect
212. C11C2×#2842semidirect
263. C2#13076881direct (N × H)

Maximal subgroups

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

subgroupindex
#130768812
C2×#106225622
C2×#106222892
C2×#106226072
C2×#106225682
C2×C11×#3992
C2×#284211