Finite Group Databasebeta

← C11×#36691 #14613884

Subgroups — C11×#36691 #14613884

Order 2816.

1474 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2845C212yesmaximal, complemented
2C11×#2844C212yesmaximal, complemented
3C11×#2843C214yesmaximal, complemented
4C11×#2841C218yesmaximal
5C11×#2402C214yesmaximal, complemented
6C11×#2399C214yesmaximal, complemented
7C11×#2396C214yesmaximal
8C11×#2285C211yesmaximal, characteristic
9C11×#2283C212yesmaximal
10C2×C4×Q8×C11C2214yes—
11C2×C11×#117C2212yes—
12C22×C42×C11C2211yescharacteristic
13C11×#400C2214yes—
14C11×#400C2218yes—
15C11×#400C2218yes—
16C11×#399C2214yes—
17C11×#398C2218yes—
18C11×#398C2218yes—
19C11×#398C2218yes—
20C11×#398C2218yes—
21C11×#398C2218yes—
22C11×#396C2218yes—
23C11×#395C2214yes—
24C11×#395C2218yes—
25C11×#395C2218yes—
26C11×#393C2214yes—
27C11×#384C2212yes—
28C11×#383C2214yes—
29C11×#382C2214yes—
30C11×#382C2211yescharacteristic
31C11×#382C2211yescharacteristic
32C11×#381C2214yes—
33C11×#380C2214yes—
34C11×#380C2214yes—
35C4×C11×C4⋊C4C2218yes—
36C4×C11×C4⋊C4C2214yes—
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C4⋊C4C2214yes—
39C4×C11×C4⋊C4C2212yes—
40C4×C11×C22⋊C4C2214yes—
41C11×#376C2214yes—
42C22×Q8×C11C2314yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C4×Q8×C11—48no—
46C11×#117—44no—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2314yes—
50C2×C11×C4⋊C4C2314yes—
51C2×C11×C4⋊C4C2318yes—
52C2×C11×C4⋊C4C2318yes—
53C2×C11×C4⋊C4C2318yes—
54C2×C11×C4⋊C4C2318yes—
55C2×C11×C4⋊C4C2314yes—
56C2×C11×C4⋊C4C2318yes—
57C2×C11×C22⋊C4C2314yes—
58C2×C11×C22⋊C4C2318yes—
59C2×C42×C11Q818yescomplemented
60C2×C42×C11C2314yes—
61C2×C42×C11C2314yes—
62C2×C42×C11C2314yes—
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2312yes—
66C11×#95C2318yes—
67C11×#95C2318yes—
68C11×#95C2318yes—
69C11×#95C2314yes—
70C11×#95C2314yes—
71C11×#95C2314yes—
72C11×#95C2314yes—
73C11×#95C2318yes—
74C11×#95C2314yes—
75C11×#95C2318yes—
76C11×#95C2314yes—
77#36691C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11C2411yescharacteristic
79C2×Q8×C11—44no—
80C2×Q8×C11—48no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—44no—
84C22×C4×C11C2×Q814yes—
85C22×C4×C11C2×Q818yes—
86C22×C4×C11C2418yes—
87C22×C4×C11C2414yes—
88C22×C4×C11C2418yes—
89C22×C4×C11C2414yes—
90C22×C4×C11C2411yescharacteristic
91C22×C4×C11C2412yes—
92C22×C4×C11C2412yes—
93C22×C4×C11C2411yescharacteristic
94C11×C4⋊C4—44no—
95C11×C4⋊C4—48no—
96C11×C4⋊C4—44no—
97C11×C4⋊C4—48no—
98C11×C4⋊C4—48no—
99C11×C4⋊C4—48no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4—48no—
103C11×C4⋊C4—44no—
104C11×C22⋊C4—48no—
105C11×C22⋊C4—44no—
106C42×C11—28no—
107C42×C11—28no—
108C42×C11—28no—
109C42×C11C2×Q814yes—
110C42×C11C2×Q814yes—
111C42×C11C2×Q818yes—
112#2845C2×C1112yescomplemented
113#2844C2×C1112yescomplemented
114#2843C2×C1114yescomplemented
115#2841C2×C1118yes—
116#2402C2×C1114yescomplemented
117#2399C2×C1114yescomplemented
118#2396C2×C1114yes—
119#2285C2×C1111yescharacteristic
120#2283C2×C1112yes—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—24no—
124C23×C11C22×Q812yes—
125C23×C11C2511yescharacteristic
126Q8×C11—416no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—24no—
130C2×C4×C11—24no—
131C2×C4×C11—28no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—28no—
135C2×C4×C11—28no—
136C2×C4×C11—28no—
137C2×C4×C11—28no—
138C2×C4×C11—28no—
139C2×C4×C11—28no—
140C2×C4×C11—28no—
141C2×C4×C11—28no—
142C2×C4×C11—48no—
143C2×C4×C11C22×Q812yes—
144C2×C4×C11C22×Q814yes—
145C2×C4×C11C22×Q814yes—
146C2×C4×C11C22×Q812yes—
147C2×C4×C11H(5,𝔽2)12yes—
148C2×C4×C112−1+412yes—
149C2×C4×Q8C22×C1114yes—
150C2×#117C22×C1112yes—
151C22×C42C22×C1111yescharacteristic
152#400C22×C1118yes—
153#400C22×C1118yes—
154#400C22×C1114yes—
155#399C22×C1114yes—
156#398C22×C1118yes—
157#398C22×C1118yes—
158#398C22×C1118yes—
159#398C22×C1118yes—
160#398C22×C1118yes—
161#396C22×C1118yes—
162#395C22×C1118yes—
163#395C22×C1118yes—
164#395C22×C1114yes—
165#393C22×C1114yes—
166#384C22×C1112yes—
167#383C22×C1114yes—
168#382C22×C1111yescharacteristic
169#382C22×C1114yes—
170#382C22×C1111yescharacteristic
171#381C22×C1114yes—
172#380C22×C1114yes—
173#380C22×C1114yes—
174C4×C4⋊C4C22×C1118yes—
175C4×C4⋊C4C22×C1114yes—
176C4×C4⋊C4C22×C1112yes—
177C4×C4⋊C4C22×C1114yes—
178C4×C4⋊C4C22×C1112yes—
179C4×C22⋊C4C22×C1114yes—
180#376C22×C1114yes—
181C22×C11—22no—
182C22×C11—24no—
183C22×C11—42no—
184C22×C11—42no—
185C22×C11C23×Q811yescharacteristic
186C22×C11C2×H(5,𝔽2)11yescharacteristic
187C22×C11C2×2−1+411yescharacteristic
188C22×C11#58514yes—
189C4×C11—22no—
190C4×C11—24no—
191C4×C11—24no—
192C4×C11—44no—
193C4×C11—44no—
194C4×C11—48no—
195C4×C11—48no—
196C4×C11#54414yes—
197C22×Q8C23×C1114yes—
198C23×C4C23×C1111yescharacteristic
199C23×C4C23×C1112yes—
200C4×Q8—48no—
201#117—44no—
202C2×C4⋊C4C23×C1112yes—
203C2×C4⋊C4C23×C1112yes—
204C2×C4⋊C4C23×C1114yes—
205C2×C4⋊C4C23×C1118yes—
206C2×C4⋊C4C23×C1114yes—
207C2×C4⋊C4C23×C1114yes—
208C2×C4⋊C4C23×C1118yes—
209C2×C4⋊C4C23×C1118yes—
210C2×C4⋊C4C23×C1118yes—
211C2×C4⋊C4C23×C1118yes—
212C2×C22⋊C4C23×C1114yes—
213C2×C22⋊C4C23×C1118yes—
214C2×C42Q8×C1118yescomplemented
215C2×C42C23×C1114yes—
216C2×C42C23×C1114yes—
217C2×C42C23×C1114yes—
218C2×C42C23×C1112yes—
219C2×C42C23×C1111yescharacteristic
220C2×C42C23×C1111yescharacteristic
221#95C23×C1118yes—
222#95C23×C1118yes—
223#95C23×C1118yes—
224#95C23×C1114yes—
225#95C23×C1114yes—
226#95C23×C1114yes—
227#95C23×C1114yes—
228#95C23×C1118yes—
229#95C23×C1114yes—
230#95C23×C1118yes—
231#95C23×C1114yes—
232C2×C11—42no—
233C2×C11C2×#54411yescharacteristic
234C2×C11#345812yes—
235C2×C11#352912yes—
236C2×C11#353112yes—
237C24C24×C1111yescharacteristic
238C2×Q8—44no—
239C2×Q8—48no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—44no—
243C22×C4C2×Q8×C1114yes—
244C22×C4C2×Q8×C1118yes—
245C22×C4C24×C1118yes—
246C22×C4C24×C1114yes—
247C22×C4C24×C1118yes—
248C22×C4C24×C1114yes—
249C22×C4C24×C1111yescharacteristic
250C22×C4C24×C1112yes—
251C22×C4C24×C1112yes—
252C22×C4C24×C1111yescharacteristic
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—48no—
256C4⋊C4—44no—
257C4⋊C4—44no—
258C4⋊C4—48no—
259C4⋊C4—44no—
260C4⋊C4—48no—
261C4⋊C4—48no—
262C4⋊C4—48no—
263C22⋊C4—44no—
264C22⋊C4—48no—
265C42—28no—
266C42—28no—
267C42—28no—
268C42C2×Q8×C1114yes—
269C42C2×Q8×C1114yes—
270C42C2×Q8×C1118yes—
271C11#3669111yescharacteristic, direct product factor, Sylow
272C23—21no—
273C23—21no—
274C23—24no—
275C23C22×Q8×C1112yes—
276C23C25×C1111yescharacteristic
277Q8—416no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—24no—
281C2×C4—24no—
282C2×C4—28no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—28no—
286C2×C4—28no—
287C2×C4—28no—
288C2×C4—28no—
289C2×C4—28no—
290C2×C4—28no—
291C2×C4—28no—
292C2×C4—28no—
293C2×C4—48no—
294C2×C4C22×Q8×C1112yes—
295C2×C4C22×Q8×C1114yes—
296C2×C4C22×Q8×C1114yes—
297C2×C4C22×Q8×C1112yes—
298C2×C4C11×H(5,𝔽2)12yes—
299C2×C4C11×2−1+412yes—
300C22—22no—
301C22—24no—
302C22—42no—
303C22—42no—
304C22C23×Q8×C1111yescharacteristic
305C22C2×C11×H(5,𝔽2)11yescharacteristic
306C22C2×C11×2−1+411yescharacteristic
307C22C11×#58514yes—
308C4—22no—
309C4—24no—
310C4—24no—
311C4—44no—
312C4—48no—
313C4—44no—
314C4—48no—
315C4C11×#54414yes—
316C2—42no—
317C2C2×C11×#54411yescharacteristic
318C2C11×#345812yes—
319C2C11×#352912yes—
320C2C11×#353112yes—
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC24×C11C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2845C2semidirect
2. C11×#2844C2semidirect
3. C11×#2843C2semidirect
5. C11×#2402C2semidirect
6. C11×#2399C2semidirect
59. C2×C42×C11Q8semidirect
77. #36691C11direct (N × H)
112. #2845C2×C11semidirect
113. #2844C2×C11semidirect
114. #2843C2×C11semidirect
116. #2402C2×C11semidirect
117. #2399C2×C11semidirect
214. C2×C42Q8×C11semidirect
271. C11#36691direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28452
C11×#28442
C11×#28432
C11×#28412
C11×#24022
C11×#23992
C11×#23962
C11×#22852
C11×#22832
#3669111