Finite Group Databasebeta

← C2×#13077556 #15618145

Subgroups — C2×#13077556 #15618145

Order 2816.

1894 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic
2#13077556C2116yesmaximal, direct product factor
3C2×#10622314C218yesmaximal, complemented
4C2×#10622715C212yesmaximal
5C2×#10622537C211yesmaximal, characteristic
6C2×#10622714C212yesmaximal
7C22×C11×#97C211yesmaximal, characteristic
8C23×C8×C11C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C22×C42×C11C2211yescharacteristic
11C2×#66979C2212yes—
12C2×#66977C414yes—
13C22×#4318C2212yes—
14#10623001C418yes—
15#10623001C2218yes—
16C2×#66923C412yes—
17C2×#66922C412yes—
18C2×C4×Dic22C2214yes—
19C2×C11×#97C2214yes—
20C2×C11×#97C2218yes—
21#10622715C22116yes—
22#10622714C22116yes—
23C2×#66879C2214yes—
24C2×Dic11⋊C8C2218yes—
25C2×C8×Dic11C2214yes—
26#10622537C2218yes—
27C2×C4⋊(C11⋊C8)C2214yes—
28#10622314C22164yescomplemented
29C23×C4×C11C2×C412yes—
30C23×C4×C11C2311yescharacteristic
31C22×Dic22C2×C414yes—
32C22×C8×C11—24no—
33C22×C8×C11Q818yescomplemented
34C22×C8×C11C2312yes—
35C22×C8×C11C2314yes—
36C22×C8×C11C2312yes—
37C22×C8×C11C2314yes—
38C2×C42×C11C2×C411yescharacteristic
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11C2×C414yes—
41C2×C42×C11C2312yes—
42C2×C42×C11C2314yes—
43C2×C22⋊Dic11C2×C414yes—
44#66979C2×C418yes—
45#66979C2318yes—
46C2×C4⋊Dic11C2×C414yes—
47C2×C4⋊Dic11C2×C414yes—
48#66977C2×C4132yes—
49C2×Dic11⋊C4C2×C418yes—
50C2×C4×Dic11C2314yes—
51C2×#4318—28no—
52C2×#4318C2318yes—
53C22×C11⋊C8C2314yes—
54#66923C2×C4116yes—
55#66922C2×C4116yes—
56C4×Dic22C2×C4116yes—
57C4×Dic22C23116yes—
58C11×#97C23116yes—
59#66879C23116yes—
60Dic11⋊C8C23132yes—
61C8×Dic11C23116yes—
62C4⋊(C11⋊C8)C23116yes—
63C2×#2961—111nomaximal, Sylow
64C24×C11C22×C411yescharacteristic
65C22×C4×C11—44no—
66C22×C4×C11C22×C412yes—
67C22×C4×C11C22×C412yes—
68C22×C4×C11C22×C418yes—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C22×C412yes—
71C22×C4×C11C2×Q814yes—
72C22×C4×C11#4114yes—
73C22×C4×C11C2412yes—
74C22×C4×C11C2411yescharacteristic
75C22×Dic11C22×C418yes—
76C2×Dic22—48no—
77C2×Dic22C22×C4116yes—
78C2×C8×C11—24no—
79C2×C8×C11—28no—
80C2×C8×C11C2×Q818yes—
81C2×C8×C11C2×Q8116yescomplemented
82C2×C8×C11C2414yes—
83C2×C8×C11C2414yes—
84C42×C11C22×C414yes—
85C42×C11C22×C414yes—
86C42×C11C22×C414yes—
87C42×C11C2414yes—
88C22⋊Dic11C22×C4116yes—
89C4⋊Dic11C22×C4116yes—
90C4⋊Dic11C22×C4116yes—
91Dic11⋊C4C22×C4132yes—
92C4×Dic11C22×C418yes—
93C4×Dic11C2418yes—
94#4318—216no—
95C2×C11⋊C8—28no—
96C2×C11⋊C8C2418yes—
97C2×#533—111no—
98#2961—1116no—
99C2×#446—118no—
100C2×#424—112no—
101C2×#423—111no—
102C2×#405—112no—
103C22×#97D1111yescharacteristic
104C23×C11—24no—
105C23×C11C4×Q814yes—
106C23×C11C23×C412yes—
107C23×C11C23×C411yescharacteristic
108C2×C4×C11—24no—
109C2×C4×C11—24no—
110C2×C4×C11—48no—
111C2×C4×C11C4×Q818yes—
112C2×C4×C11C4×Q814yes—
113C2×C4×C11C23×C414yes—
114C2×C4×C11C23×C414yes—
115C2×C4×C11C23×C411yescharacteristic
116C2×C4×C11C23×C412yes—
117C2×C4×C11C22×Q812yes—
118C2×C4×C11C22×Q814yes—
119C2×C4×C11C2×#4112yes—
120C2×C4×C11C2×#4114yes—
121C2×C4×C11C2511yescharacteristic
122C2×Dic11—216no—
123C2×Dic11C23×C4116yes—
124Dic22—416no—
125C8×C11—24no—
126C8×C11C22×Q818yes—
127C11⋊C8—28no—
128C22×M16—112no—
129C23×C8C2×D1111yescharacteristic
130C23×C8C2×D1111yescharacteristic
131#533—118no—
132#533—118no—
133C2×C4⋊Q8—112no—
134C2×#125—112no—
135C2×C22⋊Q8—114no—
136C2×C4×Q8—114no—
137C2×#117—112no—
138C22×C42C2×D1111yescharacteristic
139#446—1164no—
140#424—1116no—
141#423—118no—
142C2×C4⋊C8—118no—
143C2×C4⋊C8—114no—
144#405—1116no—
145C2×#97—114no—
146C2×#97C2×D1114yes—
147C2×#97C2×D1118yes—
148C2×C4×C8—114no—
149C22×C11—28no—
150C22×C11—24no—
151C22×C11C2×C4×Q814yes—
152C22×C11C2×C4×Q812yes—
153C22×C11#56814yes—
154C22×C11C24×C411yescharacteristic
155C4×C11—24no—
156C4×C11—24no—
157C4×C11C2×C4×Q812yes—
158C4×C11C2×C4×Q814yes—
159C4×C11C23×Q811yescharacteristic
160C4×C11C22×#4111yescharacteristic
161Dic11—216no—
162C22×Q8—114no—
163C23×C4C4×D1112yes—
164C23×C4C22×D1111yescharacteristic
165C2×M16—118no—
166C2×M16—228no—
167C22×C8—24no—
168C22×C8—114no—
169C22×C8Dic2218yescomplemented
170C22×C8C22×D1114yes—
171C22×C8C22×D1112yes—
172C22×C8C22×D1112yes—
173C22×C8C22×D1114yes—
174C4⋊Q8—1116no—
175#125—1116no—
176C22⋊Q8—1132no—
177C4×Q8—1116no—
178C4×Q8—1116no—
179#117—118no—
180#117—118no—
181C2×C4⋊C4—114no—
182C2×C4⋊C4—118no—
183C2×C4⋊C4—114no—
184C2×C22⋊C4—114no—
185C2×C42—114no—
186C2×C42C4×D1111yescharacteristic
187C2×C42C4×D1111yescharacteristic
188C2×C42C4×D1114yes—
189C2×C42C22×D1114yes—
190C2×C42C22×D1112yes—
191C4⋊C8—1132no—
192C4⋊C8—1116no—
193#97—1116no—
194#97C22×D11116yes—
195C4×C8—1116no—
196C2×C11—24no—
197C2×C11#296114yescomplemented
198C2×C11C22×C4×Q811yescharacteristic
199C2×C11C2×#56812yes—
200C24C2×C4×D1111yescharacteristic
201C2×Q8—1116no—
202C2×Q8—448no—
203C22×C4—44no—
204C22×C4—118no—
205C22×C4C2×Dic2214yes—
206C22×C4C2×C4×D1112yes—
207C22×C4C2×C4×D1112yes—
208C22×C4C2×C4×D1118yes—
209C22×C4C2×C4×D1111yescharacteristic
210C22×C4C2×C4×D1112yes—
211C22×C4#433914yes—
212C22×C4C23×D1112yes—
213C22×C4C23×D1111yescharacteristic
214M16—2216no—
215C2×C8—24no—
216C2×C8—28no—
217C2×C8—118no—
218C2×C8—228no—
219C2×C8C2×Dic2218yes—
220C2×C8C2×Dic22116yescomplemented
221C2×C8C23×D1114yes—
222C2×C8C23×D1114yes—
223C4⋊C4—1116no—
224C4⋊C4—1132no—
225C4⋊C4—1116no—
226C22⋊C4—1116no—
227C42—118no—
228C42—118no—
229C42C2×C4×D1114yes—
230C42C2×C4×D1114yes—
231C42C2×C4×D1114yes—
232C42C23×D1114yes—
233C11C2×#296111yescharacteristic, complemented, Sylow
234C23—24no—
235C23C4×Dic2214yes—
236C23C22×C4×D1112yes—
237C23C22×C4×D1111yescharacteristic
238Q8—4416no—
239C2×C4—24no—
240C2×C4—24no—
241C2×C4—48no—
242C2×C4—1116no—
243C2×C4—2216no—
244C2×C4C4×Dic2218yes—
245C2×C4C4×Dic2214yes—
246C2×C4C22×Dic2212yes—
247C2×C4C22×Dic2214yes—
248C2×C4C22×C4×D1114yes—
249C2×C4C22×C4×D1114yes—
250C2×C4C22×C4×D1111yescharacteristic
251C2×C4C22×C4×D1112yes—
252C2×C4C2×#433912yes—
253C2×C4C2×#433914yes—
254C2×C4C24×D1111yescharacteristic
255C8—24no—
256C8—228no—
257C8C22×Dic2218yes—
258C22—28no—
259C22—24no—
260C22C2×C4×Dic2214yes—
261C22C2×C4×Dic2212yes—
262C22#1062327614yes—
263C22C23×C4×D1111yescharacteristic
264C4—24no—
265C4—24no—
266C4—2216no—
267C4C2×C4×Dic2212yes—
268C4C2×C4×Dic2214yes—
269C4C23×Dic2211yescharacteristic
270C4C22×#433911yescharacteristic
271C2—24no—
272C2#1307755614yesdirect product factor
273C2C22×C4×Dic2211yescharacteristic
274C2C2×#1062327612yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC22×C11×#97C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC2×C4×C11C25
hypercenterC22×#97D11
hypocenterC11C2×#2961
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×#97

Complements

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

NH ≅ G/Ntype
2. #13077556C2direct (N × H)
3. C2×#10622314C2semidirect
28. #10622314C22semidirect
33. C22×C8×C11Q8semidirect
81. C2×C8×C11C2×Q8semidirect
169. C22×C8Dic22semidirect
197. C2×C11#2961semidirect
220. C2×C8C2×Dic22semidirect
233. C11C2×#2961semidirect
272. C2#13077556direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230012
#130775562
C2×#106223142
C2×#106227152
C2×#106225372
C2×#106227142
C22×C11×#972
C2×#296111