Finite Group Databasebeta

← C2×#13066960 #14719638

Subgroups — C2×#13066960 #14719638

Order 2816.

1218 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
1C2×#10622539C212yesmaximal
2#13066960C218yesmaximal, direct product factor
3C2×#10622166C214yesmaximal
4C22×C4×Q8×C11C211yesmaximal, characteristic
5C23×Q8×C11C411yescharacteristic
6C2×C4×Q8×C11—22no—
7C2×C4×Q8×C11—22no—
8C2×C4×Q8×C11—24no—
9C2×C4×Q8×C11C414yes—
10C2×C4×Q8×C11C2214yes—
11C22×C11×C4⋊C4C411yescharacteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C42×C11C412yes—
14C22×C42×C11C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2214yes—
16#10622539—24no—
17#10622539C2218yes—
18C2×C4⋊(C11⋊C8)—22no—
19C2×#66867—22no—
20#10622166C22116yes—
21C22×Q8×C11—22no—
22C22×Q8×C11—22no—
23C22×Q8×C11—28no—
24C22×Q8×C11C2×C414yes—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11C2×C412yes—
28C23×C4×C11C2×C412yes—
29C23×C4×C11C2311yescharacteristic
30C4×Q8×C11—28no—
31C4×Q8×C11—28no—
32C4×Q8×C11—28no—
33C4×Q8×C11—28no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4—24no—
38C2×C11×C4⋊C4C2×C414yes—
39C2×C11×C4⋊C4C2×C414yes—
40C2×C11×C4⋊C4C2314yes—
41C2×C42×C11—24no—
42C2×C42×C11—22no—
43C2×C42×C11—22no—
44C2×C42×C11C2×C418yes—
45C2×C42×C11C2×C412yes—
46C2×C42×C11D412yes—
47C2×C42×C11D412yes—
48C2×C42×C11D414yes—
49C2×C42×C11C2312yes—
50C22×C11⋊C8—24no—
51C22⋊(C11⋊C8)—24no—
52C22⋊(C11⋊C8)C2318yes—
53C4⋊(C11⋊C8)—28no—
54#66867—28no—
55C2×#1467—111nomaximal, Sylow
56C24×C11C22×C411yescharacteristic
57C2×Q8×C11—216no—
58C2×Q8×C11—216no—
59C2×Q8×C11—28no—
60C2×Q8×C11—216no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—24no—
64C22×C4×C11—24no—
65C22×C4×C11—24no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—42no—
69C22×C4×C11—44no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C412yes—
72C22×C4×C11C22⋊C412yes—
73C22×C4×C11C22⋊C412yes—
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11M1618yes—
76C22×C4×C11C22×C412yes—
77C22×C4×C11C22×C412yes—
78C22×C4×C11C22×C414yes—
79C22×C4×C11C22×C414yes—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2411yescharacteristic
84C11×C4⋊C4—28no—
85C11×C4⋊C4—28no—
86C11×C4⋊C4—28no—
87C42×C11—28no—
88C42×C11—28no—
89C42×C11C22⋊C414yes—
90C42×C11C22⋊C414yes—
91C42×C11C2×D414yes—
92C42×C11C2×D414yes—
93C2×C11⋊C8—28no—
94C2×C11⋊C8—48no—
95C22×C4×Q8D1111yescharacteristic
96C2×#432—112no—
97#1467—118no—
98C2×#324—114no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11C2×C22⋊C411yescharacteristic
102C23×C11C2×C22⋊C411yescharacteristic
103C23×C11C2×M1614yes—
104C23×C11C23×C411yescharacteristic
105Q8×C11—232no—
106C2×C4×C11—24no—
107C2×C4×C11—24no—
108C2×C4×C11—24no—
109C2×C4×C11—24no—
110C2×C4×C11—24no—
111C2×C4×C11—28no—
112C2×C4×C11—28no—
113C2×C4×C11—24no—
114C2×C4×C11—22no—
115C2×C4×C11—24no—
116C2×C4×C11—24no—
117C2×C4×C11—24no—
118C2×C4×C11—41no—
119C2×C4×C11—42no—
120C2×C4×C11—41no—
121C2×C4×C11—44no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11#10114yes—
125C2×C4×C11C2×C22⋊C412yes—
126C2×C4×C11C2×C22⋊C412yes—
127C2×C4×C11C2×C22⋊C414yes—
128C2×C4×C11C2×C22⋊C412yes—
129C2×C4×C11C2×M1618yes—
130C2×C4×C11C22×D412yes—
131C11⋊C8—48no—
132C23×Q8Dic1111yescharacteristic
133C2×C4×Q8—22no—
134C2×C4×Q8—22no—
135C2×C4×Q8—24no—
136C2×C4×Q8Dic1114yes—
137C2×C4×Q8C2×D1114yes—
138C22×C4⋊C4Dic1111yescharacteristic
139C22×C4⋊C4C2×D1112yes—
140C22×C42Dic1112yes—
141C22×C42C2×D1111yescharacteristic
142#432—118no—
143#432—224no—
144C2×C4⋊C8—222no—
145C2×C22⋊C8—114no—
146C2×#97—222no—
147#324—1116no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—28no—
153C22×C11#40712yes—
154C22×C11#40712yes—
155C22×C11#41012yes—
156C22×C11C2×#10112yes—
157C22×C11C22×C22⋊C411yescharacteristic
158C22×C11C22×M1612yes—
159C4×C11—24no—
160C4×C11—28no—
161C4×C11—22no—
162C4×C11—22no—
163C4×C11—22no—
164C4×C11—44no—
165C4×C11C2×#10114yes—
166C22×Q8—28no—
167C22×Q8—22no—
168C22×Q8—22no—
169C22×Q8C2×Dic1114yes—
170C23×C4C2×Dic1112yes—
171C23×C4C2×Dic1111yescharacteristic
172C23×C4C2×Dic1111yescharacteristic
173C23×C4C2×Dic1112yes—
174C23×C4C22×D1111yescharacteristic
175C22×C8—224no—
176C4×Q8—28no—
177C4×Q8—28no—
178C4×Q8—28no—
179C4×Q8—28no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—24no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4C2×Dic1114yes—
185C2×C4⋊C4C2×Dic1114yes—
186C2×C4⋊C4C22×D1114yes—
187C2×C42—24no—
188C2×C42—22no—
189C2×C42—22no—
190C2×C42C2×Dic1118yes—
191C2×C42C2×Dic1112yes—
192C2×C42C22⋊D1112yes—
193C2×C42C22⋊D1112yes—
194C2×C42C22⋊D1114yes—
195C2×C42C22×D1112yes—
196C4⋊C8—228no—
197C22⋊C8—118no—
198C22⋊C8—224no—
199#97—228no—
200C2×C11—22no—
201C2×C11—22no—
202C2×C11#146714yescomplemented
203C2×C11C2×#40711yescharacteristic
204C2×C11C2×#41011yescharacteristic
205C2×C11C22×#10111yescharacteristic
206C24C22×Dic1111yescharacteristic
207C2×Q8—216no—
208C2×Q8—216no—
209C2×Q8—216no—
210C2×Q8—28no—
211C22×C4—24no—
212C22×C4—24no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—24no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—42no—
219C22×C4—44no—
220C22×C4#431818yes—
221C22×C4C22⋊Dic1112yes—
222C22×C4C22⋊Dic1112yes—
223C22×C4C22⋊Dic1111yescharacteristic
224C22×C4C22⋊Dic1112yes—
225C22×C4C22⋊Dic1111yescharacteristic
226C22×C4C22×Dic1114yes—
227C22×C4C22×Dic1112yes—
228C22×C4C22×Dic1112yes—
229C22×C4C22×Dic1114yes—
230C22×C4C22×Dic1111yescharacteristic
231C22×C4C2×C22⋊D1112yes—
232C22×C4C2×C22⋊D1112yes—
233C22×C4C23×D1111yescharacteristic
234C2×C8—228no—
235C2×C8—448no—
236C4⋊C4—28no—
237C4⋊C4—28no—
238C4⋊C4—28no—
239C42—28no—
240C42—28no—
241C42C22⋊Dic1114yes—
242C42C22⋊Dic1114yes—
243C42C2×C22⋊D1114yes—
244C42C2×C22⋊D1114yes—
245C11C2×#146711yescharacteristic, complemented, Sylow
246C23—22no—
247C23—22no—
248C23C2×#431814yes—
249C23C2×C22⋊Dic1111yescharacteristic
250C23C2×C22⋊Dic1111yescharacteristic
251C23C23×Dic1111yescharacteristic
252Q8—232no—
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—28no—
256C2×C4—28no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—22no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—44no—
269C2×C4—44no—
270C2×C4—44no—
271C2×C4#6690014yes—
272C2×C4C2×#431818yes—
273C2×C4C2×C22⋊Dic1112yes—
274C2×C4C2×C22⋊Dic1112yes—
275C2×C4C2×C22⋊Dic1114yes—
276C2×C4C2×C22⋊Dic1112yes—
277C2×C4C22×C22⋊D1112yes—
278C8—448no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—28no—
284C22#1062282012yes—
285C22#1062282012yes—
286C22C2×#6690012yes—
287C22#1062285312yes—
288C22C22×#431812yes—
289C22C22×C22⋊Dic1111yescharacteristic
290C4—28no—
291C4—24no—
292C4—22no—
293C4—22no—
294C4—22no—
295C4—44no—
296C4C2×#6690014yes—
297C2—22no—
298C2—22no—
299C2#1306696014yesdirect product factor
300C2C2×#1062282011yescharacteristic
301C2C2×#1062285311yescharacteristic
302C2C22×#6690011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C4×Q8×C11C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC22×C4×Q8D11
hypocenterC11C2×#1467
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #13066960C2direct (N × H)
202. C2×C11#1467semidirect
245. C11C2×#1467semidirect
299. C2#13066960direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225392
#130669602
C2×#106221662
C22×C4×Q8×C112
C2×#146711