Finite Group Databasebeta

← C2×#13076688 #14960305

Subgroups — C2×#13076688 #14960305

Order 2816.

2502 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66929C211yesmaximal, characteristic, complemented
2#13076688C2116yesmaximal, direct product factor
3C2×#10622597C213yesmaximal, complemented
4C2×#10622561C213yesmaximal, complemented
5C2×#10622607C213yesmaximal, complemented
6C2×#10622574C213yesmaximal
7C2×#10622548C211yesmaximal, characteristic, complemented
8C22×C11×#126C211yesmaximal, characteristic, complemented
9C23×C22⋊D11C2211yescharacteristic
10C2×C11×#126—28no—
11C2×C11×#126C2218yescomplemented
12C22×C11×C4⋊C4C2213yes—
13C22×C11×C22⋊C4C2213yes—
14C22×C42×C11C2211yescharacteristic
15C22×C22⋊Dic11C2213yes—
16C22×(C2×D11)⋊C4C2213yes—
17C22×(C2×D11)⋊C4C2213yes—
18C22×C4⋊Dic11C2213yes—
19C22×C4⋊Dic11C2213yes—
20C22×Dic11⋊C4C2213yes—
21C22×Dic11⋊C4C2213yes—
22C2×#66929—28no—
23C2×#66929C2218yescomplemented
24C2×C11⋊#95C2213yes—
25C2×C11⋊#95C2213yes—
26#10622607C22124yescomplemented
27#10622597C22124yescomplemented
28#10622574C22124yes—
29#10622561C22124yescomplemented
30#10622548C2218yescomplemented
31C25×C11C2311yescharacteristic
32C24×D11C2311yescharacteristic
33C23×C4×C11C2313yes—
34C23×C4×C11C2313yes—
35C22×C22⋊D11—46no—
36C22×C22⋊D11C2314yes—
37C23×Dic11C2313yes—
38C23×Dic11C2313yes—
39C23×Dic11C2311yescharacteristic
40C11×#126—232no—
41C2×C11×C4⋊C4—212no—
42C2×C11×C4⋊C4C23112yes—
43C2×C11×C22⋊C4—212no—
44C2×C11×C22⋊C4C23112yes—
45C2×C42×C11D418yescomplemented
46C2×C42×C11C2314yes—
47C2×C22⋊Dic11—46no—
48C2×C22⋊Dic11C23112yes—
49C2×(C2×D11)⋊C4—212no—
50C2×(C2×D11)⋊C4—46no—
51C2×(C2×D11)⋊C4C23112yes—
52C2×(C2×D11)⋊C4C23112yes—
53C2×C4⋊Dic11—46no—
54C2×C4⋊Dic11—46no—
55C2×C4⋊Dic11C23112yes—
56C2×C4⋊Dic11C23112yes—
57C2×Dic11⋊C4—212no—
58C2×Dic11⋊C4—46no—
59C2×Dic11⋊C4C23112yes—
60C2×Dic11⋊C4C23112yes—
61#66929—232no—
62C11⋊#95C23112yes—
63C11⋊#95C23112yes—
64C2×#2823—111nomaximal, Sylow
65C24×C11—22no—
66C24×C11—26no—
67C24×C11—26no—
68C24×C11C2412yes—
69C24×C11C2411yescharacteristic
70C23×D11—22no—
71C23×D11—26no—
72C23×D11—26no—
73C23×D11C2412yes—
74C22×C4×C11—26no—
75C22×C4×C11—26no—
76C22×C4×C11—26no—
77C22×C4×C11—26no—
78C22×C4×C11—26no—
79C22×C4×C11C2×D4112yes—
80C22×C4×C11C2416yes—
81C22×C4×C11C2416yes—
82C2×C22⋊D11—412no—
83C2×C22⋊D11—416no—
84C22×Dic11—26no—
85C22×Dic11—26no—
86C22×Dic11—26no—
87C22×Dic11—26no—
88C22×Dic11—26no—
89C22×Dic11—26no—
90C22×Dic11—26no—
91C22×Dic11C2412yes—
92C22×Dic11C2416yes—
93C22×Dic11C2416yes—
94C11×C4⋊C4—224no—
95C11×C22⋊C4—224no—
96C42×C11C2×D4116yescomplemented
97C22⋊Dic11—412no—
98(C2×D11)⋊C4—224no—
99(C2×D11)⋊C4—412no—
100C4⋊Dic11—412no—
101C4⋊Dic11—412no—
102Dic11⋊C4—224no—
103Dic11⋊C4—412no—
104C22×#126—111no—
105C22×#126D1111yescharacteristic, complemented
106#2823—1116no—
107C2×#398—113no—
108C2×#396—113no—
109C2×#396—113no—
110C2×#394—113no—
111C2×#384—111no—
112C23×C11—22no—
113C23×C11—26no—
114C23×C11—26no—
115C23×C11—412no—
116C23×C11—44no—
117C23×C11—412no—
118C23×C11C22×D412yes—
119C23×C11H(5,𝔽2)16yes—
120C23×C112−1+416yes—
121C23×C11C2511yescharacteristic
122C22×D11—22no—
123C22×D11—26no—
124C22×D11—26no—
125C22×D11—412no—
126C22×D11—44no—
127C22×D11—412no—
128C2×C4×C11—224no—
129C2×C4×C11—26no—
130C2×C4×C11—26no—
131C2×C4×C11—26no—
132C2×C4×C11—26no—
133C2×C4×C11—26no—
134C2×C4×C11—412no—
135C2×C4×C11C22×D4112yes—
136C22⋊D11—416no—
137C2×Dic11—26no—
138C2×Dic11—26no—
139C2×Dic11—26no—
140C2×Dic11—26no—
141C2×Dic11—26no—
142C2×Dic11—26no—
143C2×Dic11—26no—
144C2×Dic11—412no—
145C2×Dic11—412no—
146C2×Dic11—44no—
147C23×D4—111no—
148C2×#126—28no—
149C2×#126—118no—
150C2×#126—228no—
151C2×#126C2×D1118yescomplemented
152C22×C4⋊C4—113no—
153C22×C4⋊C4—113no—
154C22×C4⋊C4—113no—
155C22×C4⋊C4—113no—
156C22×C4⋊C4C2×D1113yes—
157C22×C22⋊C4—113no—
158C22×C22⋊C4—113no—
159C22×C22⋊C4—113no—
160C22×C22⋊C4C2×D1113yes—
161C22×C42C2×D1111yescharacteristic
162#398—1124no—
163#396—1124no—
164#396—1124no—
165#394—1124no—
166#384—118no—
167C2×#95—113no—
168C2×#95—113no—
169C22×C11—46no—
170C22×C11—42no—
171C22×C11—46no—
172C22×C11—88no—
173C22×C11#537112yes—
174C22×C11#56014yes—
175C22×C11#563112yes—
176C22×C11C23×D411yescharacteristic
177C22×C11C2×H(5,𝔽2)13yes—
178C22×C11C2×2−1+413yes—
179C2×D11—46no—
180C2×D11—42no—
181C2×D11—46no—
182C2×D11—88no—
183C4×C11—212no—
184C4×C11—46no—
185Dic11—46no—
186Dic11—46no—
187Dic11—42no—
188C25—111no—
189C25C22×D1111yescharacteristic
190C22×D4—114no—
191C22×D4—446no—
192C23×C4—113no—
193C23×C4—113no—
194C23×C4—111no—
195C23×C4C22×D1113yes—
196C23×C4C22×D1113yes—
197#126—232no—
198#126—2232no—
199C2×C4⋊C4—212no—
200C2×C4⋊C4—1112no—
201C2×C4⋊C4—1112no—
202C2×C4⋊C4—1112no—
203C2×C4⋊C4—1112no—
204C2×C4⋊C4—2212no—
205C2×C4⋊C4—446no—
206C2×C4⋊C4—446no—
207C2×C4⋊C4—446no—
208C2×C4⋊C4C22×D11112yes—
209C2×C22⋊C4—212no—
210C2×C22⋊C4—1112no—
211C2×C22⋊C4—1112no—
212C2×C22⋊C4—1112no—
213C2×C22⋊C4—2212no—
214C2×C22⋊C4—446no—
215C2×C22⋊C4—446no—
216C2×C22⋊C4C22×D11112yes—
217C2×C42C22⋊D1118yescomplemented
218C2×C42C22×D1114yes—
219#95—1112no—
220#95—1112no—
221C2×C11—82no—
222C2×C11#282318yescomplemented
223C2×C11C2×#53713yes—
224C2×C11C2×#56011yescharacteristic
225C2×C11C2×#56313yes—
226D11—82no—
227C24—26no—
228C24—26no—
229C24—22no—
230C24—112no—
231C24—226no—
232C24—226no—
233C24—222no—
234C24C23×D1112yes—
235C24C23×D1111yescharacteristic
236C2×D4—4412no—
237C2×D4—4416no—
238C22×C4—26no—
239C22×C4—26no—
240C22×C4—26no—
241C22×C4—26no—
242C22×C4—26no—
243C22×C4—112no—
244C22×C4—116no—
245C22×C4—116no—
246C22×C4—226no—
247C22×C4—226no—
248C22×C4—226no—
249C22×C4—226no—
250C22×C4—226no—
251C22×C4—226no—
252C22×C4—226no—
253C22×C4C2×C22⋊D11112yes—
254C22×C4C23×D1116yes—
255C22×C4C23×D1116yes—
256C4⋊C4—224no—
257C4⋊C4—2224no—
258C4⋊C4—4412no—
259C4⋊C4—4412no—
260C4⋊C4—4412no—
261C22⋊C4—224no—
262C22⋊C4—2224no—
263C22⋊C4—4412no—
264C22⋊C4—4412no—
265C42C2×C22⋊D11116yescomplemented
266C11C2×#282311yescharacteristic, complemented, Sylow
267C23—26no—
268C23—26no—
269C23—22no—
270C23—44no—
271C23—412no—
272C23—412no—
273C23—226no—
274C23—226no—
275C23—222no—
276C23—444no—
277C23—4412no—
278C23—4412no—
279C23#6704216yes—
280C23#6704316yes—
281C23C22×C22⋊D1112yes—
282C23C24×D1111yescharacteristic
283D4—4416no—
284C2×C4—224no—
285C2×C4—26no—
286C2×C4—26no—
287C2×C4—26no—
288C2×C4—26no—
289C2×C4—26no—
290C2×C4—412no—
291C2×C4—226no—
292C2×C4—226no—
293C2×C4—226no—
294C2×C4—226no—
295C2×C4—226no—
296C2×C4—226no—
297C2×C4—226no—
298C2×C4—444no—
299C2×C4—4412no—
300C2×C4—4412no—
301C2×C4C22×C22⋊D11112yes—
302C22—46no—
303C22—42no—
304C22—46no—
305C22—88no—
306C22—446no—
307C22—442no—
308C22—446no—
309C22—888no—
310C22#1062324214yes—
311C22#10623243112yes—
312C22#10623364112yes—
313C22C2×#6704213yes—
314C22C2×#6704313yes—
315C22C23×C22⋊D1111yescharacteristic
316C4—212no—
317C4—46no—
318C4—446no—
319C4—442no—
320C4—446no—
321C2—82no—
322C2—882no—
323C2#1307668818yesdirect product factor
324C2C2×#1062336413yes—
325C2C2×#1062324211yescharacteristic
326C2C2×#1062324313yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#126C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22×#126D11
hypocenterC11C2×#2823
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×#66929C2semidirect
2. #13076688C2direct (N × H)
3. C2×#10622597C2semidirect
4. C2×#10622561C2semidirect
5. C2×#10622607C2semidirect
7. C2×#10622548C2semidirect
8. C22×C11×#126C2semidirect
11. C2×C11×#126C22semidirect
23. C2×#66929C22semidirect
26. #10622607C22semidirect
27. #10622597C22semidirect
29. #10622561C22semidirect
30. #10622548C22semidirect
45. C2×C42×C11D4semidirect
96. C42×C11C2×D4semidirect
105. C22×#126D11semidirect
151. C2×#126C2×D11semidirect
217. C2×C42C22⋊D11semidirect
222. C2×C11#2823semidirect
265. C42C2×C22⋊D11semidirect
266. C11C2×#2823semidirect
323. C2#13076688direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669292
#130766882
C2×#106225972
C2×#106225612
C2×#106226072
C2×#106225742
C2×#106225482
C22×C11×#1262
C2×#282311