Finite Group Databasebeta

← C11×#34346 #14611539

Subgroups — C11×#34346 #14611539

Order 2816.

2442 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic
2C11×#2381C212yesmaximal, complemented
3C11×#2380C212yesmaximal, complemented
4C11×#2379C214yesmaximal, complemented
5C11×#2377C218yesmaximal, complemented
6C11×#2297C214yesmaximal, complemented
7C11×#2290C218yesmaximal, complemented
8C11×#2283C212yesmaximal, complemented
9C22×C11×#41C2212yes—
10C11×#532C4116yescomplemented
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#127C2211yescharacteristic
13C2×C11×#124C2212yes—
14C2×C11×#121C2214yes—
15C2×C4×D4×C11C2214yes—
16C2×C11×#117C2214yes—
17C22×C42×C11C2214yes—
18C22×C42×C11C2211yescharacteristic
19C11×#391C2218yes—
20C11×#390C2218yes—
21C11×#388C22116yes—
22C11×#387C22116yes—
23C11×#386C2218yes—
24C11×#386C22116yes—
25C11×#386C2218yes—
26C11×#385C22116yes—
27C11×#383C2214yes—
28C11×#382C2214yes—
29C11×#381C2214yes—
30C11×#380C2214yes—
31C4×C11×C4⋊C4C2214yes—
32C4×C11×C22⋊C4C2214yes—
33C4×C11×C22⋊C4C2218yes—
34C11×#376C2214yes—
35C2×C11×#41—44no—
36C2×C11×#41—44no—
37C2×C11×#41C2×C4116yescomplemented
38C22×Q8×C11C2312yes—
39C22×D4×C11C2314yes—
40C22×D4×C11C2314yes—
41C22×D4×C11C2312yes—
42C23×C4×C11C2314yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2318yes—
45C23×C4×C11C2312yes—
46C11×C4⋊Q8C2×C418yescomplemented
47C11×#127C2×C418yes—
48C11×#124C2×C4116yescomplemented
49C11×#121C2×C4132yescomplemented
50C4×D4×C11C2×C4132yescomplemented
51C11×#117—48no—
52C2×C11×C4⋊C4C2318yes—
53C2×C11×C4⋊C4C2318yes—
54C2×C11×C4⋊C4C2314yes—
55C2×C11×C22⋊C4C2318yes—
56C2×C11×C22⋊C4C2318yes—
57C2×C11×C22⋊C4C23116yes—
58C2×C11×C22⋊C4C2318yes—
59C2×C42×C11—48no—
60C2×C42×C11C2×C418yescomplemented
61C2×C42×C11C2318yes—
62C2×C42×C11C2318yes—
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2312yes—
66C11×#95C2318yes—
67C11×#95C2318yes—
68C11×#95C2318yes—
69C11×#95C23116yes—
70C11×#95C2318yes—
71#34346C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11C2414yes—
73C24×C11C2411yescharacteristic
74C11×#41—432no—
75C2×Q8×C11—42no—
76C2×Q8×C11—42no—
77C2×Q8×C11C22×C418yes—
78C2×D4×C11—48no—
79C2×D4×C11—44no—
80C2×D4×C11—44no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11C22×C4116yes—
84C2×D4×C11C22×C4116yes—
85C2×D4×C11C22×C418yes—
86C22×C4×C11—28no—
87C22×C4×C11—28no—
88C22×C4×C11—24no—
89C22×C4×C11—48no—
90C22×C4×C11—44no—
91C22×C4×C11—416no—
92C22×C4×C11C22×C414yes—
93C22×C4×C11C22×C4116yes—
94C22×C4×C11C22×C418yes—
95C22×C4×C11C24116yes—
96C22×C4×C11C2412yes—
97C22×C4×C11C2411yescharacteristic
98C22×C4×C11C2412yes—
99C22×C4×C11C2414yes—
100C22×C4×C11C2411yescharacteristic
101C11×C4⋊C4—48no—
102C11×C4⋊C4—48no—
103C11×C4⋊C4C22×C4116yes—
104C11×C22⋊C4—48no—
105C11×C22⋊C4—416no—
106C11×C22⋊C4—48no—
107C11×C22⋊C4C22×C4132yes—
108C42×C11—216no—
109C42×C11—48no—
110C42×C11C22×C418yes—
111C42×C11C22×C414yes—
112C42×C11C22×C414yes—
113C2×#532C2×C1111yescharacteristic
114#2381C2×C1112yescomplemented
115#2380C2×C1112yescomplemented
116#2379C2×C1114yescomplemented
117#2377C2×C1118yescomplemented
118#2297C2×C1114yescomplemented
119#2290C2×C1118yescomplemented
120#2283C2×C1112yescomplemented
121C23×C11—24no—
122C23×C11—24no—
123C23×C11—22no—
124C23×C11—24no—
125C23×C11—216no—
126C23×C11C23×C418yes—
127C23×C11C23×C412yes—
128C23×C11C2511yescharacteristic
129Q8×C11—48no—
130D4×C11—416no—
131D4×C11—48no—
132D4×C11—416no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—22no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—232no—
139C2×C4×C11—28no—
140C2×C4×C11—216no—
141C2×C4×C11—216no—
142C2×C4×C11—216no—
143C2×C4×C11—48no—
144C2×C4×C11—432no—
145C2×C4×C11C23×C414yes—
146C2×C4×C11C23×C414yes—
147C2×C4×C11C23×C412yes—
148C2×C4×C11C23×C418yes—
149C2×C4×C11C23×C412yes—
150C2×C4×C11H(5,𝔽2)14yes—
151C22×#41C22×C1112yes—
152#532C4×C11116yescomplemented
153C2×C4⋊Q8C22×C1111yescharacteristic
154C2×#127C22×C1111yescharacteristic
155C2×#124C22×C1112yes—
156C2×#121C22×C1114yes—
157C2×C4×D4C22×C1114yes—
158C2×#117C22×C1114yes—
159C22×C42C22×C1114yes—
160C22×C42C22×C1111yescharacteristic
161#391C22×C1118yes—
162#390C22×C1118yes—
163#388C22×C11116yes—
164#387C22×C11116yes—
165#386C22×C1118yes—
166#386C22×C11116yes—
167#386C22×C1118yes—
168#385C22×C11116yes—
169#383C22×C1114yes—
170#382C22×C1114yes—
171#381C22×C1114yes—
172#380C22×C1114yes—
173C4×C4⋊C4C22×C1114yes—
174C4×C22⋊C4C22×C1114yes—
175C4×C22⋊C4C22×C1118yes—
176#376C22×C1114yes—
177C22×C11—22no—
178C22×C11—28no—
179C22×C11—24no—
180C22×C11—216no—
181C22×C11—48no—
182C22×C11—48no—
183C22×C11—44no—
184C22×C11C24×C411yescharacteristic
185C22×C11C2×H(5,𝔽2)12yes—
186C22×C11#58514yes—
187C4×C11—22no—
188C4×C11—28no—
189C4×C11—24no—
190C4×C11—24no—
191C4×C11—416no—
192C4×C11#51814yes—
193C2×#41—44no—
194C2×#41—44no—
195C2×#41C2×C4×C11116yescomplemented
196C22×Q8C23×C1112yes—
197C22×D4C23×C1114yes—
198C22×D4C23×C1114yes—
199C22×D4C23×C1112yes—
200C23×C4C23×C1114yes—
201C23×C4C23×C1111yescharacteristic
202C23×C4C23×C1118yes—
203C23×C4C23×C1112yes—
204C4⋊Q8C2×C4×C1118yescomplemented
205#127C2×C4×C1118yes—
206#124C2×C4×C11116yescomplemented
207#121C2×C4×C11132yescomplemented
208C4×D4C2×C4×C11132yescomplemented
209#117—48no—
210C2×C4⋊C4C23×C1118yes—
211C2×C4⋊C4C23×C1118yes—
212C2×C4⋊C4C23×C1114yes—
213C2×C22⋊C4C23×C1118yes—
214C2×C22⋊C4C23×C1118yes—
215C2×C22⋊C4C23×C11116yes—
216C2×C22⋊C4C23×C1118yes—
217C2×C42—48no—
218C2×C42C2×C4×C1118yescomplemented
219C2×C42C23×C1118yes—
220C2×C42C23×C1118yes—
221C2×C42C23×C1112yes—
222C2×C42C23×C1111yescharacteristic
223C2×C42C23×C1111yescharacteristic
224#95C23×C1118yes—
225#95C23×C1118yes—
226#95C23×C1118yes—
227#95C23×C11116yes—
228#95C23×C1118yes—
229C2×C11—42no—
230C2×C11—48no—
231C2×C11C2×#51811yescharacteristic
232C2×C11#342812yes—
233C2×C11#352914yes—
234C24C24×C1114yes—
235C24C24×C1111yescharacteristic
236#41—432no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8C22×C4×C1118yes—
240C2×D4—44no—
241C2×D4—44no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—48no—
245C2×D4C22×C4×C11116yes—
246C2×D4C22×C4×C11116yes—
247C2×D4C22×C4×C1118yes—
248C22×C4—28no—
249C22×C4—28no—
250C22×C4—24no—
251C22×C4—48no—
252C22×C4—44no—
253C22×C4—416no—
254C22×C4C22×C4×C1114yes—
255C22×C4C22×C4×C11116yes—
256C22×C4C22×C4×C1118yes—
257C22×C4C24×C11116yes—
258C22×C4C24×C1112yes—
259C22×C4C24×C1111yescharacteristic
260C22×C4C24×C1112yes—
261C22×C4C24×C1114yes—
262C22×C4C24×C1111yescharacteristic
263C4⋊C4—48no—
264C4⋊C4—48no—
265C4⋊C4C22×C4×C11116yes—
266C22⋊C4—48no—
267C22⋊C4—48no—
268C22⋊C4—416no—
269C22⋊C4C22×C4×C11132yes—
270C42—216no—
271C42—48no—
272C42C22×C4×C1118yes—
273C42C22×C4×C1114yes—
274C42C22×C4×C1114yes—
275C11#3434611yescharacteristic, direct product factor, Sylow
276C23—24no—
277C23—24no—
278C23—22no—
279C23—24no—
280C23—216no—
281C23C23×C4×C1118yes—
282C23C23×C4×C1112yes—
283C23C25×C1111yescharacteristic
284Q8—48no—
285D4—416no—
286D4—48no—
287D4—416no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—232no—
294C2×C4—28no—
295C2×C4—216no—
296C2×C4—216no—
297C2×C4—216no—
298C2×C4—48no—
299C2×C4—432no—
300C2×C4C23×C4×C1114yes—
301C2×C4C23×C4×C1114yes—
302C2×C4C23×C4×C1112yes—
303C2×C4C23×C4×C1118yes—
304C2×C4C23×C4×C1112yes—
305C2×C4C11×H(5,𝔽2)14yes—
306C22—22no—
307C22—28no—
308C22—24no—
309C22—216no—
310C22—48no—
311C22—48no—
312C22—44no—
313C22C24×C4×C1111yescharacteristic
314C22C2×C11×H(5,𝔽2)12yes—
315C22C11×#58514yes—
316C4—22no—
317C4—28no—
318C4—24no—
319C4—24no—
320C4—416no—
321C4C11×#51814yes—
322C2—42no—
323C2—48no—
324C2C2×C11×#51811yescharacteristic
325C2C11×#342812yes—
326C2C11×#352914yes—
subgroupG/H
centerC22×C4×C11C24
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC2×C11×#532C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2381C2semidirect
3. C11×#2380C2semidirect
4. C11×#2379C2semidirect
5. C11×#2377C2semidirect
6. C11×#2297C2semidirect
7. C11×#2290C2semidirect
8. C11×#2283C2semidirect
10. C11×#532C4semidirect
37. C2×C11×#41C2×C4semidirect
46. C11×C4⋊Q8C2×C4semidirect
48. C11×#124C2×C4semidirect
49. C11×#121C2×C4semidirect
50. C4×D4×C11C2×C4semidirect
60. C2×C42×C11C2×C4semidirect
71. #34346C11direct (N × H)
114. #2381C2×C11semidirect
115. #2380C2×C11semidirect
116. #2379C2×C11semidirect
117. #2377C2×C11semidirect
118. #2297C2×C11semidirect
119. #2290C2×C11semidirect
120. #2283C2×C11semidirect
152. #532C4×C11semidirect
195. C2×#41C2×C4×C11semidirect
204. C4⋊Q8C2×C4×C11semidirect
206. #124C2×C4×C11semidirect
207. #121C2×C4×C11semidirect
208. C4×D4C2×C4×C11semidirect
218. C2×C42C2×C4×C11semidirect
275. C11#34346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5322
C11×#23812
C11×#23802
C11×#23792
C11×#23772
C11×#22972
C11×#22902
C11×#22832
#3434611