Finite Group Databasebeta

← C11×#2635 #13065473

Subgroups — C11×#2635 #13065473

Order 1408.

620 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#121C211yesmaximal, characteristic, complemented
2C2×C4×D4×C11C211yesmaximal, characteristic, complemented
3C11×#400C211yesmaximal, characteristic, complemented
4C11×#399C211yesmaximal, characteristic, complemented
5C11×#394C211yesmaximal, characteristic, complemented
6C11×#394C212yesmaximal, complemented
7C11×#392C211yesmaximal, characteristic, complemented
8C11×#392C212yesmaximal, complemented
9C11×#388C212yesmaximal, complemented
10C11×#386C212yesmaximal, complemented
11C11×#381C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×D4×C11C2212yes—
14C22×D4×C11C2211yescharacteristic
15C22×D4×C11C2212yes—
16C23×C4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C11×#121—24no—
19C4×D4×C11—24no—
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2212yes—
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2212yes—
26C2×C11×C22⋊C4C2212yes—
27C2×C11×C22⋊C4C2212yes—
28C2×C11×C22⋊C4C2212yes—
29C2×C11×C22⋊C4C2212yes—
30C2×C11×C22⋊C4C2212yes—
31C2×C42×C11C2211yescharacteristic
32C11×#95C2212yes—
33C11×#95C2211yescharacteristic
34C11×#95C2211yescharacteristic
35C11×#95C2212yes—
36C11×#95C2212yes—
37C24×C11C2312yes—
38C24×C11C2311yescharacteristic
39C24×C11C2311yescharacteristic
40C2×D4×C11—22no—
41C2×D4×C11—22no—
42C2×D4×C11—24no—
43C2×D4×C11—24no—
44C2×D4×C11—22no—
45C2×D4×C11—22no—
46C2×D4×C11—42no—
47C2×D4×C11—42no—
48C2×D4×C11—42no—
49C2×D4×C11—42no—
50C2×D4×C11—42no—
51C22×C4×C11—22no—
52C22×C4×C11—42no—
53C22×C4×C11—42no—
54C22×C4×C11D414yescomplemented
55C22×C4×C11C2312yes—
56C22×C4×C11C2312yes—
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2312yes—
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C11×C4⋊C4—22no—
64C11×C4⋊C4—22no—
65C11×C4⋊C4—42no—
66C11×C22⋊C4—22no—
67C11×C22⋊C4—22no—
68C11×C22⋊C4—24no—
69C11×C22⋊C4—24no—
70C11×C22⋊C4—42no—
71C11×C22⋊C4—42no—
72C11×C22⋊C4—42no—
73C11×C22⋊C4—42no—
74C42×C11—22no—
75#2635C1111yesmaximal, characteristic, direct product factor, Sylow
76C23×C11—21no—
77C23×C11—21no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—22no—
89C23×C11—22no—
90C23×C11—22no—
91C23×C11C2×D412yes—
92C23×C11#4112yes—
93C23×C11C2411yescharacteristic
94D4×C11—28no—
95D4×C11—44no—
96D4×C11—48no—
97D4×C11—48no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—44no—
116C2×C4×C11—44no—
117C2×C4×C11C2×D412yes—
118C2×C4×C11C2×D412yes—
119C2×C4×C11#4112yes—
120C2×#121C2×C1111yescharacteristic, complemented
121C2×C4×D4C2×C1111yescharacteristic, complemented
122#400C2×C1111yescharacteristic, complemented
123#399C2×C1111yescharacteristic, complemented
124#394C2×C1111yescharacteristic, complemented
125#394C2×C1112yescomplemented
126#392C2×C1111yescharacteristic, complemented
127#392C2×C1112yescomplemented
128#388C2×C1112yescomplemented
129#386C2×C1112yescomplemented
130#381C2×C1111yescharacteristic, complemented
131C22×C11—22no—
132C22×C11—22no—
133C22×C11—22no—
134C22×C11—22no—
135C22×C11—24no—
136C22×C11—41no—
137C22×C11—41no—
138C22×C11—42no—
139C22×C11—42no—
140C22×C11—42no—
141C22×C11—42no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11—42no—
145C22×C11—42no—
146C22×C11—42no—
147C22×C11—42no—
148C22×C11C22×D411yescharacteristic
149C22×C11C2×#4111yescharacteristic
150C22×C11C2×#4111yescharacteristic
151C22×C11H(5,𝔽2)12yes—
152C22×C11H(5,𝔽2)12yes—
153C4×C11—22no—
154C4×C11—22no—
155C4×C11—22no—
156C4×C11—41no—
157C4×C11—41no—
158C4×C11—42no—
159C4×C11—42no—
160C4×C11—42no—
161C22×D4C22×C1111yescharacteristic
162C22×D4C22×C1112yes—
163C22×D4C22×C1111yescharacteristic
164C22×D4C22×C1112yes—
165C23×C4C22×C1111yescharacteristic
166C23×C4C22×C1111yescharacteristic
167#121—24no—
168C4×D4—24no—
169C2×C4⋊C4C22×C1111yescharacteristic
170C2×C4⋊C4C22×C1111yescharacteristic
171C2×C4⋊C4C22×C1112yes—
172C2×C22⋊C4C22×C1111yescharacteristic
173C2×C22⋊C4C22×C1111yescharacteristic
174C2×C22⋊C4C22×C1112yes—
175C2×C22⋊C4C22×C1112yes—
176C2×C22⋊C4C22×C1112yes—
177C2×C22⋊C4C22×C1112yes—
178C2×C22⋊C4C22×C1112yes—
179C2×C22⋊C4C22×C1112yes—
180C2×C42C22×C1111yescharacteristic
181#95C22×C1112yes—
182#95C22×C1111yescharacteristic
183#95C22×C1111yescharacteristic
184#95C22×C1112yes—
185#95C22×C1112yes—
186C2×C11—42no—
187C2×C11—42no—
188C2×C11—82no—
189C2×C11#52511yescharacteristic
190C2×C11#53411yescharacteristic
191C2×C11#53511yescharacteristic
192C2×C11#53812yes—
193C2×C11#54012yes—
194C24C23×C1112yes—
195C24C23×C1111yescharacteristic
196C24C23×C1111yescharacteristic
197C2×D4—22no—
198C2×D4—22no—
199C2×D4—24no—
200C2×D4—24no—
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—42no—
207C2×D4—42no—
208C22×C4—22no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4D4×C1114yescomplemented
212C22×C4C23×C1112yes—
213C22×C4C23×C1112yes—
214C22×C4C23×C1111yescharacteristic
215C22×C4C23×C1112yes—
216C22×C4C23×C1111yescharacteristic
217C22×C4C23×C1111yescharacteristic
218C22×C4C23×C1111yescharacteristic
219C22×C4C23×C1111yescharacteristic
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—42no—
223C22⋊C4—22no—
224C22⋊C4—22no—
225C22⋊C4—24no—
226C22⋊C4—24no—
227C22⋊C4—42no—
228C22⋊C4—42no—
229C22⋊C4—42no—
230C22⋊C4—42no—
231C42—22no—
232C11#263511yescharacteristic, direct product factor, Sylow
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23C2×D4×C1112yes—
249C23C11×#4112yes—
250C23C24×C1111yescharacteristic
251D4—28no—
252D4—44no—
253D4—48no—
254D4—48no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—44no—
273C2×C4—44no—
274C2×C4C2×D4×C1112yes—
275C2×C4C2×D4×C1112yes—
276C2×C4C11×#4112yes—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—24no—
282C22—41no—
283C22—41no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22C22×D4×C1111yescharacteristic
295C22C2×C11×#4111yescharacteristic
296C22C2×C11×#4111yescharacteristic
297C22C11×H(5,𝔽2)12yes—
298C22C11×H(5,𝔽2)12yes—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—41no—
303C4—42no—
304C4—41no—
305C4—42no—
306C4—42no—
307C2—42no—
308C2—42no—
309C2—82no—
310C2C11×#52511yescharacteristic
311C2C11×#53411yescharacteristic
312C2C11×#53511yescharacteristic
313C2C11×#53812yes—
314C2C11×#54012yes—
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#121C2semidirect
2. C2×C4×D4×C11C2semidirect
3. C11×#400C2semidirect
4. C11×#399C2semidirect
5. C11×#394C2semidirect
6. C11×#394C2semidirect
7. C11×#392C2semidirect
8. C11×#392C2semidirect
9. C11×#388C2semidirect
10. C11×#386C2semidirect
11. C11×#381C2semidirect
54. C22×C4×C11D4semidirect
75. #2635C11direct (N × H)
120. C2×#121C2×C11semidirect
121. C2×C4×D4C2×C11semidirect
122. #400C2×C11semidirect
123. #399C2×C11semidirect
124. #394C2×C11semidirect
125. #394C2×C11semidirect
126. #392C2×C11semidirect
127. #392C2×C11semidirect
128. #388C2×C11semidirect
129. #386C2×C11semidirect
130. #381C2×C11semidirect
211. C22×C4D4×C11semidirect
232. C11#2635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×C4×D4×C112
C11×#4002
C11×#3992
C11×#3942
C11×#3922
C11×#3882
C11×#3862
C11×#3812
#263511