Finite Group Databasebeta

← C2×#13071358 #14912605

Subgroups — C2×#13071358 #14912605

Order 2816.

2398 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071358C2116yesmaximal, direct product factor
2C2×#10622598C212yesmaximal
3C2×#10622598C214yesmaximal
4C2×#10622594C214yesmaximal
5C2×#10622548C211yesmaximal, characteristic
6C2×C4⋊C4×Dic11C212yesmaximal
7C2×#10622545C211yesmaximal, characteristic
8C22×C11×#125C211yesmaximal, characteristic
9C2×C11×#125C4116yescomplemented
10C2×C11×#125C2218yes—
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C4⋊C4C2214yes—
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2212yes—
15C22×C4⋊Dic11C2214yes—
16C22×C4⋊Dic11C2214yes—
17C22×C4×Dic11C2211yescharacteristic
18C22×C4×Dic11C2214yes—
19C22×C4×Dic11C2211yescharacteristic
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2214yes—
23C2×C11⋊#95C2214yes—
24#10622598C22132yes—
25#10622598C22116yes—
26#10622594C22132yes—
27C4⋊C4×Dic11C22116yes—
28#10622548C2218yes—
29#10622545C2218yes—
30C23×C4×C11C2314yes—
31C23×C4×C11C2312yes—
32C23×C4×C11C2311yescharacteristic
33C23×Dic11C2311yescharacteristic
34C23×Dic11C2314yes—
35C23×Dic11C2311yescharacteristic
36C23×Dic11C2312yes—
37C11×#125C2×C4164yescomplemented
38C2×C11×C4⋊C4C2×C4132yes—
39C2×C11×C4⋊C4C2×C4116yes—
40C2×C11×C4⋊C4C2318yes—
41C2×C11×C4⋊C4C23116yes—
42C2×C42×C11C2×C418yes—
43C2×C42×C11C2314yes—
44C2×C4⋊Dic11—28no—
45C2×C4⋊Dic11—48no—
46C2×C4⋊Dic11—48no—
47C2×C4⋊Dic11C2318yes—
48C2×C4⋊Dic11C23116yes—
49C2×C4⋊Dic11C23116yes—
50C2×C4×Dic11—24no—
51C2×C4×Dic11—48no—
52C2×C4×Dic11Q818yes—
53C2×C4×Dic11C2314yes—
54C2×C4×Dic11C23116yes—
55C2×C4×Dic11C2314yes—
56C11⋊#95C2318yes—
57C11⋊#95C2318yes—
58C11⋊#95C23116yes—
59C11⋊#95C23116yes—
60C2×#2330—111nomaximal, Sylow
61C24×C11C2411yescharacteristic
62C22×C4×C11—28no—
63C22×C4×C11—24no—
64C22×C4×C11—28no—
65C22×C4×C11—24no—
66C22×C4×C11C22×C418yes—
67C22×C4×C11C22×C4116yes—
68C22×C4×C11C22×C414yes—
69C22×C4×C11C2×Q814yes—
70C22×C4×C11#4114yes—
71C22×C4×C11C2418yes—
72C22×C4×C11C2414yes—
73C22×C4×C11C2412yes—
74C22×Dic11—22no—
75C22×Dic11—22no—
76C22×Dic11—28no—
77C22×Dic11—24no—
78C22×Dic11—28no—
79C22×Dic11—24no—
80C22×Dic11—28no—
81C22×Dic11—24no—
82C22×Dic11—24no—
83C22×Dic11C2×Q818yes—
84C22×Dic11C2412yes—
85C22×Dic11C2412yes—
86C22×Dic11C2418yes—
87C22×Dic11C2414yes—
88C11×C4⋊C4C22×C4164yes—
89C11×C4⋊C4C22×C4132yes—
90C42×C11C22×C4116yes—
91C4⋊Dic11—216no—
92C4⋊Dic11—416no—
93C4⋊Dic11—416no—
94C4×Dic11—28no—
95C4×Dic11—416no—
96C4×Dic11C2×Q8116yes—
97C22×#125D1111yescharacteristic
98#2330—1116no—
99C2×#389—112no—
100C2×#389—114no—
101C2×#387—114no—
102C2×#384—111no—
103C2×C4×C4⋊C4—112no—
104C2×#376—111no—
105C23×C11C23×C412yes—
106C23×C11C22×Q812yes—
107C23×C11C2×#4112yes—
108C23×C11H(5,𝔽2)14yes—
109C23×C112−1+414yes—
110C23×C11C2511yescharacteristic
111C2×C4×C11—232no—
112C2×C4×C11—216no—
113C2×C4×C11—28no—
114C2×C4×C11—24no—
115C2×C4×C11—28no—
116C2×C4×C11—24no—
117C2×C4×C11C4×Q8116yes—
118C2×C4×C11C23×C418yes—
119C2×C4×C11C23×C4116yes—
120C2×C4×C11C23×C414yes—
121C2×C4×C11C22×Q814yes—
122C2×C4×C11C2×#4114yes—
123C2×Dic11—216no—
124C2×Dic11—24no—
125C2×Dic11—24no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—28no—
129C2×Dic11—28no—
130C2×Dic11—24no—
131C2×Dic11—28no—
132C2×Dic11—24no—
133C2×Dic11—44no—
134C2×Dic11—416no—
135C2×Dic11—44no—
136C2×Dic11C22×Q818yes—
137C2×#125Dic11116yescomplemented
138C2×#125C2×D1118yes—
139C22×C4⋊C4—112no—
140C22×C4⋊C4—114no—
141C22×C4⋊C4—114no—
142C22×C4⋊C4C2×D1112yes—
143C22×C4⋊C4C2×D1114yes—
144C22×C42—111no—
145C22×C42—111no—
146C22×C42—114no—
147C22×C42C2×D1111yescharacteristic
148#389—1132no—
149#389—1116no—
150#387—1132no—
151#384—118no—
152C4×C4⋊C4—1116no—
153#376—118no—
154C2×#95—112no—
155C2×#95—112no—
156C2×#95—114no—
157C2×#95—114no—
158C22×C11C2×C4×Q814yes—
159C22×C11#52018yes—
160C22×C11#54014yes—
161C22×C11#54114yes—
162C22×C11#54418yes—
163C22×C11C24×C411yescharacteristic
164C22×C11C23×Q811yescharacteristic
165C22×C11C22×#4111yescharacteristic
166C22×C11C2×H(5,𝔽2)12yes—
167C22×C11C2×2−1+412yes—
168C4×C11—216no—
169C4×C11—28no—
170C4×C11C2×C4×Q818yes—
171Dic11—28no—
172Dic11—42no—
173Dic11—48no—
174Dic11—42no—
175C23×C4—112no—
176C23×C4—111no—
177C23×C4—114no—
178C23×C4—111no—
179C23×C4C22×D1112yes—
180C23×C4C22×D1114yes—
181C23×C4C22×D1111yescharacteristic
182#125C2×Dic11164yescomplemented
183C2×C4⋊C4—118no—
184C2×C4⋊C4—1116no—
185C2×C4⋊C4—1116no—
186C2×C4⋊C4—228no—
187C2×C4⋊C4—448no—
188C2×C4⋊C4—448no—
189C2×C4⋊C4C2×Dic11132yes—
190C2×C4⋊C4C2×Dic11116yes—
191C2×C4⋊C4C22×D1118yes—
192C2×C4⋊C4C22×D11116yes—
193C2×C42—118no—
194C2×C42—114no—
195C2×C42—114no—
196C2×C42—1116no—
197C2×C42—224no—
198C2×C42—448no—
199C2×C42C2×Dic1118yes—
200C2×C42C22×D1114yes—
201#95—118no—
202#95—118no—
203#95—1116no—
204#95—1116no—
205C2×C11#233018yescomplemented
206C2×C11C22×C4×Q811yescharacteristic
207C2×C11C2×#52012yes—
208C2×C11C2×#54011yescharacteristic
209C2×C11C2×#54111yescharacteristic
210C2×C11C2×#54412yes—
211C24C23×D1111yescharacteristic
212C22×C4—28no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—28no—
216C22×C4—118no—
217C22×C4—114no—
218C22×C4—112no—
219C22×C4—112no—
220C22×C4—118no—
221C22×C4—224no—
222C22×C4—224no—
223C22×C4—222no—
224C22×C4—222no—
225C22×C4—228no—
226C22×C4—228no—
227C22×C4—224no—
228C22×C4—228no—
229C22×C4—224no—
230C22×C4Q8×D1114yes—
231C22×C4#434314yes—
232C22×C4C22×Dic1118yes—
233C22×C4C22×Dic11116yes—
234C22×C4C22×Dic1114yes—
235C22×C4C23×D1118yes—
236C22×C4C23×D1114yes—
237C22×C4C23×D1112yes—
238C4⋊C4—2216no—
239C4⋊C4—4416no—
240C4⋊C4—4416no—
241C4⋊C4C22×Dic11164yes—
242C4⋊C4C22×Dic11132yes—
243C42—1116no—
244C42—228no—
245C42—4416no—
246C42C22×Dic11116yes—
247C11C2×#233011yescharacteristic, complemented, Sylow
248C23C2×Q8×D1112yes—
249C23C2×#434312yes—
250C23#6704214yes—
251C23#6704314yes—
252C23C23×Dic1112yes—
253C23C24×D1111yescharacteristic
254C2×C4—232no—
255C2×C4—216no—
256C2×C4—28no—
257C2×C4—24no—
258C2×C4—28no—
259C2×C4—24no—
260C2×C4—118no—
261C2×C4—224no—
262C2×C4—224no—
263C2×C4—2216no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—228no—
267C2×C4—228no—
268C2×C4—224no—
269C2×C4—228no—
270C2×C4—224no—
271C2×C4—444no—
272C2×C4—444no—
273C2×C4—4416no—
274C2×C4Q8×Dic11116yes—
275C2×C4C2×Q8×D1114yes—
276C2×C4C2×#434314yes—
277C2×C4C23×Dic1118yes—
278C2×C4C23×Dic11116yes—
279C2×C4C23×Dic1114yes—
280C22#1062322018yes—
281C22#1062322814yes—
282C22#1062322914yes—
283C22C2×Q8×Dic1114yes—
284C22#1062335818yes—
285C22C22×Q8×D1111yescharacteristic
286C22C22×#434311yescharacteristic
287C22C2×#6704212yes—
288C22C2×#6704312yes—
289C22C24×Dic1111yescharacteristic
290C4—216no—
291C4—28no—
292C4—228no—
293C4—442no—
294C4—448no—
295C4—442no—
296C4C2×Q8×Dic1118yes—
297C2#1307135818yesdirect product factor
298C2C22×Q8×Dic1111yescharacteristic
299C2C2×#1062335812yes—
300C2C2×#1062322911yescharacteristic
301C2C2×#1062322811yescharacteristic
302C2C2×#1062322012yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC22×C11×#125C2
socle, prime radicalC24×C11C24
cosocleC23×C11C25
hypercenterC22×#125D11
hypocenterC11C2×#2330
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #13071358C2direct (N × H)
9. C2×C11×#125C4semidirect
37. C11×#125C2×C4semidirect
137. C2×#125Dic11semidirect
182. #125C2×Dic11semidirect
205. C2×C11#2330semidirect
247. C11C2×#2330semidirect
297. C2#13071358direct (N × H)

Maximal subgroups

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

subgroupindex
#130713582
C2×#106225982
C2×#106225942
C2×#106225482
C2×C4⋊C4×Dic112
C2×#106225452
C22×C11×#1252
C2×#233011