Finite Group Databasebeta

← C2×#13066634 #14664022

Subgroups — C2×#13066634 #14664022

Order 2816.

446 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊(C11⋊C16)C211yesmaximal, characteristic
2C2×#10622190C211yesmaximal, characteristic
3#13066634C214yesmaximal, direct product factor
4C2×C11×#467C211yesmaximal, characteristic
5C22×C11×Q16C411yescharacteristic
6C23×C8×C11C2211yescharacteristic
7C2×C11×C22⋊Q8—21no—
8C22×#4318—21no—
9C11×#467—21no—
10C11×#467—21no—
11C11×#467C412yes—
12C11×#467C2212yes—
13C2×C11×#107C411yescharacteristic
14C2×C11×#103—21no—
15C22×C11⋊C16—21no—
16#10622190—21no—
17#10622190C2212yes—
18C22⋊(C11⋊C16)—21no—
19C22⋊(C11⋊C16)C2212yes—
20C22×Q8×C11—21no—
21C23×C4×C11D411yescharacteristic
22C2×C11×Q16—21no—
23C2×C11×Q16—42no—
24C2×C11×Q16C2×C412yes—
25C22×C8×C11—42no—
26C22×C8×C11C2×C411yescharacteristic
27C22×C8×C11C2×C411yescharacteristic
28C22×C8×C11D411yescharacteristic
29C22×C8×C11D411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C22×C8×C11C2311yescharacteristic
32C11×C22⋊Q8—22no—
33C11×C22⋊Q8—22no—
34C11×C22⋊Q8—41no—
35C11×C22⋊Q8—41no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—41no—
38C2×C11×C22⋊C4—41no—
39C2×#4318—24no—
40C2×#4318—22no—
41C2×#4318—42no—
42C2×#4318—41no—
43C22×C11⋊C8—41no—
44C11×#107—21no—
45C11×#107C2×C412yes—
46C11×#103—22no—
47C11×#103—22no—
48C2×C11⋊C16—22no—
49C2×C11⋊C16—42no—
50C2×#1350—111nomaximal, Sylow
51C24×C11SD1611yescharacteristic
52C2×Q8×C11—22no—
53C2×Q8×C11—41no—
54C2×Q8×C11—42no—
55C2×Q8×C11—42no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11D811yescharacteristic
63C22×C4×C11D811yescharacteristic
64C22×C4×C11SD1611yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C11×Q16—42no—
67C11×Q16—42no—
68C2×C8×C11—22no—
69C2×C8×C11—22no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11C22⋊C411yescharacteristic
75C2×C8×C11C22⋊C411yescharacteristic
76C2×C8×C11C22×C411yescharacteristic
77C2×C8×C11C2×D411yescharacteristic
78C11×C4⋊C4—22no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—42no—
81C11×C4⋊C4—42no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—42no—
84#4318—24no—
85#4318—44no—
86#4318—42no—
87C2×C11⋊C8—44no—
88C2×C11⋊C8—42no—
89C11⋊C16—42no—
90C2×#467D1111yescharacteristic
91C2×C22⋊C16—111no—
92C2×#341—111no—
93#1350—114no—
94C23×C11—22no—
95C23×C11—22no—
96C23×C11—22no—
97C23×C11#10211yescharacteristic
98C23×C11#10211yescharacteristic
99C23×C11C2×SD1611yescharacteristic
100Q8×C11—42no—
101Q8×C11—42no—
102Q8×C11—82no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—82no—
113C2×C4×C11—82no—
114C2×C4×C11#9912yes—
115C2×C4×C11#10211yescharacteristic
116C2×C4×C11#10211yescharacteristic
117C2×C4×C11#10412yes—
118C2×C4×C11C2×C22⋊C411yescharacteristic
119C2×C4×C11C2×D811yescharacteristic
120C8×C11—21no—
121C8×C11—21no—
122C8×C11—21no—
123C8×C11—21no—
124C11⋊C8—44no—
125C22×Q16Dic1111yescharacteristic
126C22×M16—221no—
127C23×C8C2×D1111yescharacteristic
128C2×C22⋊Q8—21no—
129C22×C16—221no—
130#467—21no—
131#467—21no—
132#467Dic1112yes—
133#467C2×D1112yes—
134C2×#107Dic1111yescharacteristic
135C2×#103—21no—
136C22⋊C16—112no—
137C22⋊C16—221no—
138#341—112no—
139#341—221no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—44no—
147C22×C11#32712yes—
148C22×C11#35912yes—
149C22×C11#36212yes—
150C22×C11C2×#10211yescharacteristic
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—82no—
154C4×C11—82no—
155C4×C11#32712yes—
156C4×C11C2×#9911yescharacteristic
157C4×C11C2×#10411yescharacteristic
158C22×Q8—21no—
159C23×C4C22⋊D1111yescharacteristic
160C2×Q16—21no—
161C2×Q16—42no—
162C2×Q16C2×Dic1112yes—
163C2×M16—224no—
164C2×M16—222no—
165C2×M16—442no—
166C2×M16—441no—
167C22×C8—42no—
168C22×C8—441no—
169C22×C8C2×Dic1111yescharacteristic
170C22×C8C2×Dic1111yescharacteristic
171C22×C8C22⋊D1111yescharacteristic
172C22×C8C22⋊D1111yescharacteristic
173C22×C8C22⋊D1111yescharacteristic
174C22×C8C22×D1111yescharacteristic
175C22⋊Q8—22no—
176C22⋊Q8—22no—
177C22⋊Q8—41no—
178C22⋊Q8—41no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—41no—
181C2×C22⋊C4—41no—
182C2×C16—222no—
183C2×C16—442no—
184#107—21no—
185#107C2×Dic1112yes—
186#103—22no—
187#103—22no—
188C2×C11—41no—
189C2×C11—41no—
190C2×C11#135014yescomplemented
191C2×C11C2×#32711yescharacteristic
192C2×C11C2×#35911yescharacteristic
193C2×C11C2×#36211yescharacteristic
194C24#432411yescharacteristic
195C2×Q8—22no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—42no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4#432311yescharacteristic
204C22×C4#432311yescharacteristic
205C22×C4#432411yescharacteristic
206C22×C4C22⋊Dic1111yescharacteristic
207C22×C4C22⋊Dic1111yescharacteristic
208C22×C4C2×C22⋊D1111yescharacteristic
209Q16—42no—
210Q16—42no—
211M16—224no—
212M16—442no—
213M16—444no—
214C2×C8—22no—
215C2×C8—22no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—444no—
221C2×C8—442no—
222C2×C8C22⋊Dic1111yescharacteristic
223C2×C8C22⋊Dic1111yescharacteristic
224C2×C8C22×Dic1111yescharacteristic
225C2×C8C2×C22⋊D1111yescharacteristic
226C4⋊C4—22no—
227C4⋊C4—41no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C22⋊C4—42no—
231C22⋊C4—42no—
232C16—442no—
233C11C2×#135011yescharacteristic, complemented, Sylow
234C23—22no—
235C23—22no—
236C23—22no—
237C23#6689611yescharacteristic
238C23#6689611yescharacteristic
239C23C2×#432411yescharacteristic
240Q8—42no—
241Q8—42no—
242Q8—82no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4#6689611yescharacteristic
255C2×C4#6689611yescharacteristic
256C2×C4#6689812yes—
257C2×C4#6690112yes—
258C2×C4C2×#432311yescharacteristic
259C2×C4C2×C22⋊Dic1111yescharacteristic
260C8—21no—
261C8—21no—
262C8—21no—
263C8—21no—
264C8—444no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22#1062217512yes—
273C22#1062220312yes—
274C22#1062220512yes—
275C22C2×#6689611yescharacteristic
276C4—21no—
277C4—21no—
278C4—82no—
279C4—82no—
280C4#1062217512yes—
281C4C2×#6689811yescharacteristic
282C4C2×#6690111yescharacteristic
283C2—41no—
284C2—41no—
285C2#1306663414yesdirect product factor
286C2C2×#1062217511yescharacteristic
287C2C2×#1062220511yescharacteristic
288C2C2×#1062220311yescharacteristic
subgroupG/H
centerC23#66896
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#467C2
socleC23×C11#102
prime radicalC24×C11SD16
cosocleC22×C8×C11C23
hypercenterC2×#467D11
hypocenterC11C2×#1350
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
3. #13066634C2direct (N × H)
190. C2×C11#1350semidirect
233. C11C2×#1350semidirect
285. C2#13066634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊(C11⋊C16)2
C2×#106221902
#130666342
C2×C11×#4672
C2×#135011