Finite Group Databasebeta

← C2×#13076613 #14959891

Subgroups — C2×#13076613 #14959891

Order 2816.

4438 conjugacy classes of subgroups; only the 667 normal subgroups are shown.

normal subgroups only

This group has 4438 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
1C22×#67006C212yesmaximal, complemented
2#13076613C2116yesmaximal, direct product factor
3C2×#10622566C213yesmaximal, complemented
4C2×#10622574C216yesmaximal, complemented
5C2×#10622573C213yesmaximal, complemented
6C2×C11×#379C211yesmaximal, characteristic, complemented
7C26×C11C2211yescharacteristic
8C23×C22⋊D11C2216yes—
9C23×D44C2211yescharacteristic, complemented
10C22×C11×C22⋊C4C2213yes—
11C22×C11×C22⋊C4C2213yes—
12C2×#67006—216no—
13C2×#67006C22116yescomplemented
14C22×C22⋊Dic11C2216yes—
15C22×(C2×D11)⋊C4C2216yescomplemented
16C22×C4⋊Dic11C2213yescomplemented
17C11×#379C2218yescomplemented
18C2×C11⋊#95C2213yescomplemented
19C2×C11⋊#95C2213yescomplemented
20#10622574C22148yescomplemented
21#10622573C22124yescomplemented
22#10622566C22124yescomplemented
23C25×C11—46no—
24C25×C11—46no—
25C25×C11D418yescomplemented
26C25×C11C2313yes—
27C25×C11C2314yes—
28C24×D11C2312yes—
29C23×C4×C11C2313yes—
30C23×C4×C11C2311yescharacteristic
31C22×C22⋊D11—224no—
32C22×C22⋊D11—412no—
33C22×C22⋊D11—412no—
34C22×C22⋊D11C23124yes—
35C23×Dic11C2316yes—
36C22×D44—46no—
37C22×D44C2314yescomplemented
38C2×C11×C22⋊C4—46no—
39C2×C11×C22⋊C4—46no—
40C2×C11×C22⋊C4C23112yes—
41C2×C11×C22⋊C4C23112yes—
42#67006—264no—
43C2×C22⋊Dic11—224no—
44C2×C22⋊Dic11C23124yes—
45C2×(C2×D11)⋊C4—412no—
46C2×(C2×D11)⋊C4C23124yescomplemented
47C2×C4⋊Dic11—46no—
48C2×C4⋊Dic11C23112yescomplemented
49C11⋊#95C23112yescomplemented
50C11⋊#95C23112yescomplemented
51C2×#2812—111nomaximal, Sylow
52C24×C11—26no—
53C24×C11—26no—
54C24×C11—212no—
55C24×C11—212no—
56C24×C11—448no—
57C24×C11—412no—
58C24×C11—412no—
59C24×C11—448no—
60C24×C11—416no—
61C24×C11C2×D4112yes—
62C24×C11C2×D4116yescomplemented
63C24×C11C2416yes—
64C24×C11C2411yescharacteristic
65C23×D11—24no—
66C23×D11—212no—
67C23×D11—212no—
68C23×D11C2414yes—
69C22×C4×C11—26no—
70C22×C4×C11—212no—
71C22×C4×C11—26no—
72C22×C4×C11C2412yes—
73C22×C4×C11C2416yes—
74C2×C22⋊D11—248no—
75C2×C22⋊D11—424no—
76C2×C22⋊D11—424no—
77C2×C22⋊D11—496no—
78C22×Dic11—212no—
79C22×Dic11—212no—
80C22×Dic11—212no—
81C22×Dic11C24112yes—
82C2×D44—412no—
83C2×D44—416no—
84C11×C22⋊C4—412no—
85C11×C22⋊C4—412no—
86C22⋊Dic11—248no—
87(C2×D11)⋊C4—424no—
88C4⋊Dic11—412no—
89C22×#120—112no—
90#2812—1116no—
91C2×#397—113no—
92C2×#394—116no—
93C2×#392—113no—
94C2×#379D1111yescharacteristic, complemented
95C23×C11—248no—
96C23×C11—224no—
97C23×C11—26no—
98C23×C11—26no—
99C23×C11—212no—
100C23×C11—212no—
101C23×C11—448no—
102C23×C11—448no—
103C23×C11—416no—
104C23×C11—4128no—
105C23×C11—424no—
106C23×C11—412no—
107C23×C11—412no—
108C23×C11C22×D4112yes—
109C23×C11C22×D412yes—
110C23×C11H(5,𝔽2)16yes—
111C23×C11H(5,𝔽2)16yes—
112C23×C11C2511yescharacteristic
113C22×D11—24no—
114C22×D11—212no—
115C22×D11—212no—
116C22×D11—424no—
117C22×D11—424no—
118C22×D11—48no—
119C2×C4×C11—26no—
120C2×C4×C11—212no—
121C2×C4×C11—26no—
122C2×C4×C11—412no—
123C2×C4×C11—44no—
124C22⋊D11—496no—
125C2×Dic11—212no—
126C2×Dic11—212no—
127C2×Dic11—212no—
128C2×Dic11—424no—
129D44—416no—
130C26C2×D1111yescharacteristic
131C23×D4—116no—
132C23×D4—111no—
133C2×#120—1116no—
134C2×#120—2216no—
135C22×C4⋊C4—113no—
136C22×C22⋊C4—116no—
137C22×C22⋊C4—116no—
138C22×C22⋊C4C2×D1113yes—
139C22×C22⋊C4C2×D1113yes—
140#397—1124no—
141#394—1148no—
142#392—1124no—
143#379C2×D1118yescomplemented
144C2×#95—113no—
145C2×#95—113no—
146C22×C11—212no—
147C22×C11—224no—
148C22×C11—464no—
149C22×C11—412no—
150C22×C11—46no—
151C22×C11—46no—
152C22×C11—448no—
153C22×C11#534112yes—
154C22×C11#560112yes—
155C22×C11H(3,𝔽4)14yes—
156C22×C11C23×D411yescharacteristic
157C22×C11C2×H(5,𝔽2)13yes—
158C22×C11C2×H(5,𝔽2)13yes—
159C2×D11—412no—
160C2×D11—412no—
161C2×D11—44no—
162C2×D11—816no—
163C4×C11—46no—
164C4×C11—42no—
165Dic11—412no—
166C25—46no—
167C25—46no—
168C25—112no—
169C25D4418yescomplemented
170C25C22×D1113yes—
171C25C22×D1114yes—
172C22×D4—1124no—
173C22×D4—114no—
174C22×D4—2224no—
175C22×D4—446no—
176C22×D4—4412no—
177C22×D4—4412no—
178C23×C4—116no—
179C23×C4C22×D1113yes—
180C23×C4C22×D1111yescharacteristic
181#120—2264no—
182C2×C4⋊C4—1112no—
183C2×C4⋊C4—446no—
184C2×C22⋊C4—46no—
185C2×C22⋊C4—46no—
186C2×C22⋊C4—1124no—
187C2×C22⋊C4—1124no—
188C2×C22⋊C4—2224no—
189C2×C22⋊C4—4412no—
190C2×C22⋊C4C22×D11112yes—
191C2×C22⋊C4C22×D11112yes—
192#95—1112no—
193#95—1112no—
194C2×C11—412no—
195C2×C11#281218yescomplemented
196C2×C11C2×#53413yes—
197C2×C11C2×#56013yes—
198C2×C11C2×H(3,𝔽4)11yescharacteristic
199D11—84no—
200C24—26no—
201C24—26no—
202C24—212no—
203C24—212no—
204C24—412no—
205C24—412no—
206C24—448no—
207C24—416no—
208C24—448no—
209C24—114no—
210C24—224no—
211C24—2212no—
212C24—2212no—
213C24C2×D44112yes—
214C24C2×D44116yescomplemented
215C24C23×D1116yes—
216C24C23×D1111yescharacteristic
217C2×D4—2248no—
218C2×D4—4412no—
219C2×D4—4416no—
220C2×D4—4424no—
221C2×D4—4424no—
222C2×D4—4496no—
223C22×C4—212no—
224C22×C4—26no—
225C22×C4—26no—
226C22×C4—1112no—
227C22×C4—2212no—
228C22×C4—2212no—
229C22×C4—2212no—
230C22×C4C23×D1112yes—
231C22×C4C23×D1116yes—
232C4⋊C4—4412no—
233C22⋊C4—412no—
234C22⋊C4—412no—
235C22⋊C4—2248no—
236C22⋊C4—4424no—
237C11C2×#281211yescharacteristic, complemented, Sylow
238C23—248no—
239C23—224no—
240C23—26no—
241C23—26no—
242C23—212no—
243C23—212no—
244C23—448no—
245C23—448no—
246C23—416no—
247C23—4128no—
248C23—412no—
249C23—412no—
250C23—424no—
251C23—224no—
252C23—2212no—
253C23—2212no—
254C23—4424no—
255C23—448no—
256C23—4424no—
257C23C22×D44112yes—
258C23C22×D4412yes—
259C23#6703716yes—
260C23#6703716yes—
261C23C24×D1111yescharacteristic
262D4—4416no—
263D4—4496no—
264C2×C4—212no—
265C2×C4—26no—
266C2×C4—26no—
267C2×C4—44no—
268C2×C4—412no—
269C2×C4—2212no—
270C2×C4—2212no—
271C2×C4—2212no—
272C2×C4—4424no—
273C22—224no—
274C22—212no—
275C22—464no—
276C22—412no—
277C22—46no—
278C22—46no—
279C22—448no—
280C22—4412no—
281C22—4412no—
282C22—444no—
283C22—8816no—
284C22#10623024112yes—
285C22#1062312514yes—
286C22#10623126112yes—
287C22C23×D4411yescharacteristic
288C22C2×#6703713yes—
289C22C2×#6703713yes—
290C4—46no—
291C4—42no—
292C4—4412no—
293C2—412no—
294C2—884no—
295C2#1307661318yesdirect product factor
296C2C2×#1062302413yes—
297C2C2×#1062312613yes—
298C2C2×#1062312511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#379C2
socleC24×C11C24
hypercenterC2×#379D11
hypocenterC11C2×#2812
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#67006C2semidirect
2. #13076613C2direct (N × H)
3. C2×#10622566C2semidirect
4. C2×#10622574C2semidirect
5. C2×#10622573C2semidirect
6. C2×C11×#379C2semidirect
9. C23×D44C22semidirect
13. C2×#67006C22semidirect
15. C22×(C2×D11)⋊C4C22semidirect
16. C22×C4⋊Dic11C22semidirect
17. C11×#379C22semidirect
18. C2×C11⋊#95C22semidirect
19. C2×C11⋊#95C22semidirect
20. #10622574C22semidirect
21. #10622573C22semidirect
22. #10622566C22semidirect
25. C25×C11D4semidirect
37. C22×D44C23semidirect
46. C2×(C2×D11)⋊C4C23semidirect
48. C2×C4⋊Dic11C23semidirect
49. C11⋊#95C23semidirect
50. C11⋊#95C23semidirect
62. C24×C11C2×D4semidirect
94. C2×#379D11semidirect
143. #379C2×D11semidirect
169. C25D44semidirect
195. C2×C11#2812semidirect
214. C24C2×D44semidirect
237. C11C2×#2812semidirect
295. C2#13076613direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670062
#130766132
C2×#106225662
C2×#106225742
C2×#106225732
C2×C11×#3792
C2×#281211