Finite Group Databasebeta

← C2×#13066540 #14662832

Subgroups — C2×#13066540 #14662832

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊(C11⋊C16)C212yesmaximal, complemented
2#13066540C214yesmaximal, direct product factor
3C22×C11×C22⋊C8C211yesmaximal, characteristic
4C24×C4×C11C411yescharacteristic
5C23×C8×C11C411yescharacteristic
6C23×C8×C11C2211yescharacteristic
7C2×C11×C22⋊C8—22no—
8C2×C11×C22⋊C8—22no—
9C2×C11×C22⋊C8C412yes—
10C2×C11×C22⋊C8C2212yes—
11C22×C11⋊C16—22no—
12C22⋊(C11⋊C16)—22no—
13C22⋊(C11⋊C16)C2214yescomplemented
14C25×C11C811yescharacteristic
15C23×C4×C11—21no—
16C23×C4×C11—21no—
17C23×C4×C11—21no—
18C23×C4×C11—21no—
19C23×C4×C11—42no—
20C23×C4×C11—42no—
21C23×C4×C11C811yescharacteristic
22C23×C4×C11C812yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11C2×C412yes—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C22×C8×C11—42no—
28C22×C8×C11—42no—
29C22×C8×C11C2×C412yes—
30C22×C8×C11C2×C411yescharacteristic
31C22×C8×C11D412yes—
32C22×C8×C11D412yes—
33C22×C8×C11C2311yescharacteristic
34C11×C22⋊C8—24no—
35C11×C22⋊C8—24no—
36C2×C11⋊C16—24no—
37C2×C11⋊C16—44no—
38C2×#1314—111nomaximal, Sylow
39C24×C11—21no—
40C24×C11—21no—
41C24×C11—22no—
42C24×C11—42no—
43C24×C11—42no—
44C24×C11C1614yescomplemented
45C24×C11C2×C811yescharacteristic
46C24×C11C2×C812yes—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—44no—
56C22×C4×C11—44no—
57C22×C4×C11—42no—
58C22×C4×C11—42no—
59C22×C4×C11—44no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C2×C811yescharacteristic
68C22×C4×C11C2×C812yes—
69C22×C4×C11M1611yescharacteristic
70C22×C4×C11M1611yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C2×C8×C11—24no—
73C2×C8×C11—22no—
74C2×C8×C11—41no—
75C2×C8×C11—42no—
76C2×C8×C11—41no—
77C2×C8×C11—42no—
78C2×C8×C11—42no—
79C2×C8×C11—42no—
80C2×C8×C11C22⋊C412yes—
81C2×C8×C11C2×D412yes—
82C11⋊C16—44no—
83C22×C22⋊C8D1111yescharacteristic
84C2×C22⋊C16—112no—
85#1314—114no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—24no—
89C23×C11—24no—
90C23×C11—22no—
91C23×C11—22no—
92C23×C11—42no—
93C23×C11—48no—
94C23×C11—42no—
95C23×C11—42no—
96C23×C11—48no—
97C23×C11—42no—
98C23×C11—42no—
99C23×C11—42no—
100C23×C11C22⋊C811yescharacteristic
101C23×C11C22⋊C811yescharacteristic
102C23×C11C2×C1612yes—
103C23×C11C2×C1614yescomplemented
104C23×C11M3212yes—
105C23×C11C22×C811yescharacteristic
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—44no—
115C2×C4×C11—44no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—44no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11C22⋊C811yescharacteristic
123C2×C4×C11C22⋊C811yescharacteristic
124C2×C4×C11#9912yes—
125C2×C4×C11#10012yes—
126C2×C4×C11C2×C22⋊C411yescharacteristic
127C2×C4×C11C2×M1611yescharacteristic
128C8×C11—22no—
129C8×C11—22no—
130C8×C11—42no—
131C24×C4Dic1111yescharacteristic
132C23×C8Dic1111yescharacteristic
133C23×C8C2×D1111yescharacteristic
134C22×C16—222no—
135C2×C22⋊C8—22no—
136C2×C22⋊C8—22no—
137C2×C22⋊C8Dic1112yes—
138C2×C22⋊C8C2×D1112yes—
139C22⋊C16—114no—
140C22⋊C16—222no—
141C22×C11—24no—
142C22×C11—24no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—24no—
148C22×C11—44no—
149C22×C11—48no—
150C22×C11—44no—
151C22×C11—48no—
152C22×C11—42no—
153C22×C11—42no—
154C22×C11#32312yes—
155C22×C11C22⋊C1612yes—
156C22×C11C22⋊C1612yes—
157C22×C11#34912yes—
158C22×C11C2×C22⋊C811yescharacteristic
159C22×C11C22×C1611yescharacteristic
160C22×C11C2×M3211yescharacteristic
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—42no—
164C4×C11#32312yes—
165C4×C11C2×#9911yescharacteristic
166C4×C11C2×#10011yescharacteristic
167C25C11⋊C811yescharacteristic
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—42no—
173C23×C4—42no—
174C23×C4C11⋊C811yescharacteristic
175C23×C4C11⋊C812yes—
176C23×C4C2×Dic1111yescharacteristic
177C23×C4C2×Dic1112yes—
178C22×C8—21no—
179C22×C8—21no—
180C22×C8—42no—
181C22×C8—42no—
182C22×C8C2×Dic1112yes—
183C22×C8C2×Dic1111yescharacteristic
184C22×C8C22⋊D1112yes—
185C22×C8C22⋊D1112yes—
186C22×C8C22×D1111yescharacteristic
187C2×C16—224no—
188C2×C16—444no—
189C22⋊C8—24no—
190C22⋊C8—24no—
191C2×C11—22no—
192C2×C11—21no—
193C2×C11—21no—
194C2×C11—44no—
195C2×C11#131414yescomplemented
196C2×C11C2×#32311yescharacteristic
197C2×C11C2×C22⋊C1611yescharacteristic
198C2×C11C2×#34911yescharacteristic
199C24—22no—
200C24—21no—
201C24—21no—
202C24—42no—
203C24—42no—
204C24C11⋊C1614yescomplemented
205C24C2×C11⋊C811yescharacteristic
206C24C2×C11⋊C812yes—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—44no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—44no—
219C22×C4—44no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4C2×C11⋊C811yescharacteristic
226C22×C4C2×C11⋊C812yes—
227C22×C4#431811yescharacteristic
228C22×C4#431811yescharacteristic
229C22×C4C22⋊Dic1111yescharacteristic
230C22×C4C22⋊Dic1111yescharacteristic
231C22×C4C22×Dic1111yescharacteristic
232C2×C8—24no—
233C2×C8—22no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8C22⋊Dic1112yes—
241C2×C8C2×C22⋊D1112yes—
242C16—444no—
243C11C2×#131411yescharacteristic, complemented, Sylow
244C23—22no—
245C23—22no—
246C23—22no—
247C23—24no—
248C23—24no—
249C23—22no—
250C23—42no—
251C23—48no—
252C23—42no—
253C23—42no—
254C23—48no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23C2×C11⋊C1612yes—
259C23C2×C11⋊C1614yescomplemented
260C23#6687612yes—
261C23C22⋊(C11⋊C8)11yescharacteristic
262C23C22⋊(C11⋊C8)11yescharacteristic
263C23C22×C11⋊C811yescharacteristic
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—44no—
273C2×C4—44no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—44no—
279C2×C4—42no—
280C2×C4C22⋊(C11⋊C8)11yescharacteristic
281C2×C4C22⋊(C11⋊C8)11yescharacteristic
282C2×C4#6689712yes—
283C2×C4#6689812yes—
284C2×C4C2×#431811yescharacteristic
285C2×C4C2×C22⋊Dic1111yescharacteristic
286C8—22no—
287C8—22no—
288C8—42no—
289C22—24no—
290C22—24no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—24no—
296C22—44no—
297C22—48no—
298C22—44no—
299C22—48no—
300C22—42no—
301C22—42no—
302C22#1062216312yes—
303C22C22⋊(C11⋊C16)12yes—
304C22C22⋊(C11⋊C16)12yes—
305C22#1062219112yes—
306C22C22×C11⋊C1611yescharacteristic
307C22C2×#6687611yescharacteristic
308C22C2×C22⋊(C11⋊C8)11yescharacteristic
309C4—21no—
310C4—21no—
311C4—42no—
312C4#1062216312yes—
313C4C2×#6689711yescharacteristic
314C4C2×#6689811yescharacteristic
315C2—22no—
316C2—21no—
317C2—21no—
318C2—44no—
319C2#1306654014yesdirect product factor
320C2C2×#1062216311yescharacteristic
321C2C2×C22⋊(C11⋊C16)11yescharacteristic
322C2C2×#1062219111yescharacteristic
subgroupG/H
centerC22×C4C22⋊Dic11
commutatorC22×C11C22×C16
FrattiniC22×C8C22×D11
FittingC22×C11×C22⋊C8C2
socleC23×C11C22⋊C8
prime radicalC25×C11C8
cosocleC22×C8×C11C23
hypercenterC22×C22⋊C8D11
hypocenterC11C2×#1314
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊(C11⋊C16)C2semidirect
2. #13066540C2direct (N × H)
13. C22⋊(C11⋊C16)C22semidirect
44. C24×C11C16semidirect
103. C23×C11C2×C16semidirect
195. C2×C11#1314semidirect
204. C24C11⋊C16semidirect
243. C11C2×#1314semidirect
259. C23C2×C11⋊C16semidirect
319. C2#13066540direct (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
#130665402
C22×C11×C22⋊C82
C2×#131411