Finite Group Databasebeta

← C11×#23164 #14600357

Subgroups — C11×#23164 #14600357

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#499C211yesmaximal, characteristic
2C11×#2370C212yesmaximal
3C11×#1989C212yesmaximal
4C11×#1943C211yesmaximal, characteristic
5C11×#1943C211yesmaximal, characteristic
6C11×#1920C212yesmaximal
7C11×#1919C212yesmaximal
8C11×#1776C211yesmaximal, characteristic
9C11×#1776C211yesmaximal, characteristic
10C4×C11×#106C211yesmaximal, characteristic
11C11×#1770C211yesmaximal, characteristic
12C2×C11×#125C2212yes—
13C11×#499C418yescomplemented
14C2×C11×#107C2211yescharacteristic
15C2×C11×#107C2211yescharacteristic
16C2×C11×#106C2211yescharacteristic
17C2×C11×#106C2212yes—
18C2×C11×#106C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C11×#389—22no—
24C11×#389C2212yes—
25C11×#389C2212yes—
26C11×#387—22no—
27C11×#387—22no—
28C4×C11×C4⋊C4—22no—
29C4×C11×C4⋊C4C2212yes—
30C4×C11×C4⋊C4C2212yes—
31C4×C11×C4⋊C4C2212yes—
32C4×C11×C4⋊C4C2211yescharacteristic
33C11×#340C2212yes—
34C11×#340C2212yes—
35C11×#340C2212yes—
36C11×#340C2212yes—
37C11×#340C2212yes—
38C11×#336C2211yescharacteristic
39C11×#336C2211yescharacteristic
40C22×C8×C11C2311yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C11×#125—24no—
45C11×#125C2×C418yes—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4D412yes—
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C42×C11—22no—
56C2×C42×C11—22no—
57C2×C42×C11—22no—
58C2×C42×C11C2311yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C11×#107C2×C414yes—
62C11×#107C2×C414yes—
63C11×#106—22no—
64C11×#106C2×C418yes—
65C11×#106Q814yes—
66C11×C4⋊C8—22no—
67C11×#97—22no—
68C11×#97—22no—
69C4×C8×C11C2×C414yes—
70C11×#95—22no—
71C11×#95—22no—
72C11×#95—22no—
73C11×#95—22no—
74C11×#95—22no—
75C11×#95D412yes—
76#23164C1111yesmaximal, characteristic, direct product factor, Sylow
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2411yescharacteristic
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—21no—
94C2×C8×C11C22×C412yes—
95C2×C8×C11C22×C412yes—
96C2×C8×C11C2×Q812yes—
97C2×C8×C11#4112yes—
98C11×C4⋊C4—28no—
99C11×C4⋊C4—28no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—42no—
106C11×C4⋊C4—44no—
107C11×C4⋊C4—82no—
108C11×C4⋊C4C22×C414yes—
109C11×C4⋊C4C22×C414yes—
110C11×C4⋊C4C2×Q814yes—
111C42×C11—21no—
112C42×C11—21no—
113C42×C11—21no—
114C42×C11—21no—
115C42×C11—44no—
116C42×C11—82no—
117C42×C11—82no—
118C42×C11C22×C412yes—
119C42×C11#4112yes—
120C2×#499C2×C1111yescharacteristic
121#2370C2×C1112yes—
122#1989C2×C1112yes—
123#1943C2×C1111yescharacteristic
124#1943C2×C1111yescharacteristic
125#1920C2×C1112yes—
126#1919C2×C1112yes—
127#1776C2×C1111yescharacteristic
128#1776C2×C1111yescharacteristic
129C4×#106C2×C1111yescharacteristic
130#1770C2×C1111yescharacteristic
131C23×C11C22×D411yescharacteristic
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—24no—
135C2×C4×C11—24no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—24no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11C4×D412yes—
153C2×C4×C11C4×D412yes—
154C2×C4×C11C23×C411yescharacteristic
155C2×C4×C11C22×Q811yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C2×C4×C112−1+411yescharacteristic
159C2×C4×C112−1+411yescharacteristic
160C8×C11—22no—
161C8×C11—41no—
162C8×C11—41no—
163C8×C11C4×Q814yes—
164C2×#125C22×C1112yes—
165#499C4×C1118yescomplemented
166C2×#107C22×C1111yescharacteristic
167C2×#107C22×C1111yescharacteristic
168C2×#106C22×C1111yescharacteristic
169C2×#106C22×C1112yes—
170C2×#106C22×C1111yescharacteristic
171C2×C4⋊C8C22×C1111yescharacteristic
172C2×#97C22×C1111yescharacteristic
173C2×#97C22×C1111yescharacteristic
174C2×C4×C8C22×C1111yescharacteristic
175#389—22no—
176#389C22×C1112yes—
177#389C22×C1112yes—
178#387—22no—
179#387—22no—
180C4×C4⋊C4—22no—
181C4×C4⋊C4C22×C1112yes—
182C4×C4⋊C4C22×C1112yes—
183C4×C4⋊C4C22×C1112yes—
184C4×C4⋊C4C22×C1111yescharacteristic
185#340C22×C1112yes—
186#340C22×C1112yes—
187#340C22×C1112yes—
188#340C22×C1112yes—
189#340C22×C1112yes—
190#336C22×C1111yescharacteristic
191#336C22×C1111yescharacteristic
192C22×C11C2×C4×D411yescharacteristic
193C22×C11#54711yescharacteristic
194C22×C11D4×Q811yescharacteristic
195C22×C11#57512yes—
196C22×C11#57712yes—
197C4×C11—22no—
198C4×C11—22no—
199C4×C11—42no—
200C4×C11—42no—
201C4×C11—44no—
202C4×C11—44no—
203C4×C11—44no—
204C4×C11—82no—
205C4×C11C2×C4×Q811yescharacteristic
206C4×C11#51911yescharacteristic
207C4×C11#55611yescharacteristic
208C4×C11#55711yescharacteristic
209C22×C8C23×C1111yescharacteristic
210C22×C8C23×C1111yescharacteristic
211C22×C8C23×C1111yescharacteristic
212C22×C8C23×C1111yescharacteristic
213#125—24no—
214#125C2×C4×C1118yes—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4D4×C1112yes—
220C2×C4⋊C4C23×C1112yes—
221C2×C4⋊C4C23×C1112yes—
222C2×C4⋊C4C23×C1112yes—
223C2×C4⋊C4C23×C1112yes—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42—22no—
227C2×C42C23×C1111yescharacteristic
228C2×C42C23×C1111yescharacteristic
229C2×C42C23×C1111yescharacteristic
230#107C2×C4×C1114yes—
231#107C2×C4×C1114yes—
232#106—22no—
233#106C2×C4×C1118yes—
234#106Q8×C1114yes—
235C4⋊C8—22no—
236#97—22no—
237#97—22no—
238C4×C8C2×C4×C1114yes—
239#95—22no—
240#95—22no—
241#95—22no—
242#95—22no—
243#95—22no—
244#95D4×C1112yes—
245C2×C11#236511yescharacteristic
246C2×C11#294311yescharacteristic
247C2×C11#295211yescharacteristic
248C2×C11#335112yes—
249C2×C11#338812yes—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4C2×D4×C1112yes—
255C22×C4C2×D4×C1112yes—
256C22×C4C2×D4×C1111yescharacteristic
257C22×C4C2×D4×C1111yescharacteristic
258C22×C4C24×C1111yescharacteristic
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8C22×C4×C1112yes—
268C2×C8C22×C4×C1112yes—
269C2×C8C2×Q8×C1112yes—
270C2×C8C11×#4112yes—
271C4⋊C4—28no—
272C4⋊C4—28no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—42no—
279C4⋊C4—44no—
280C4⋊C4—82no—
281C4⋊C4C22×C4×C1114yes—
282C4⋊C4C22×C4×C1114yes—
283C4⋊C4C2×Q8×C1114yes—
284C42—21no—
285C42—21no—
286C42—21no—
287C42—21no—
288C42—44no—
289C42—82no—
290C42—82no—
291C42C22×C4×C1112yes—
292C42C11×#4112yes—
293C11#2316411yescharacteristic, direct product factor, Sylow
294C23C22×D4×C1111yescharacteristic
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4C4×D4×C1112yes—
316C2×C4C4×D4×C1112yes—
317C2×C4C23×C4×C1111yescharacteristic
318C2×C4C22×Q8×C1111yescharacteristic
319C2×C4C2×C11×#4111yescharacteristic
320C2×C4C2×C11×#4111yescharacteristic
321C2×C4C11×2−1+411yescharacteristic
322C2×C4C11×2−1+411yescharacteristic
323C8—22no—
324C8—41no—
325C8—41no—
326C8C4×Q8×C1114yes—
327C22C2×C4×D4×C1111yescharacteristic
328C22C11×#54711yescharacteristic
329C22D4×Q8×C1111yescharacteristic
330C22C11×#57512yes—
331C22C11×#57712yes—
332C4—22no—
333C4—22no—
334C4—44no—
335C4—44no—
336C4—42no—
337C4—42no—
338C4—44no—
339C4—82no—
340C4C2×C4×Q8×C1111yescharacteristic
341C4C11×#51911yescharacteristic
342C4C11×#55611yescharacteristic
343C4C11×#55711yescharacteristic
344C2C11×#236511yescharacteristic
345C2C11×#294311yescharacteristic
346C2C11×#295211yescharacteristic
347C2C11×#335112yes—
348C2C11×#338812yes—
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
13. C11×#499C4semidirect
76. #23164C11direct (N × H)
165. #499C4×C11semidirect
293. C11#23164direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4992
C11×#23702
C11×#19892
C11×#19432
C11×#19202
C11×#19192
C11×#17762
C4×C11×#1062
C11×#17702
#2316411