Finite Group Databasebeta

← C11×#23165 #14600358

Subgroups — C11×#23165 #14600358

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 340 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×#1944C212yesmaximal
5C11×#1921C212yesmaximal
6C11×#1918C212yesmaximal
7C11×#1776C212yesmaximal
8C4×C11×#107C211yesmaximal, characteristic
9C11×#1770C211yesmaximal, characteristic
10C2×C11×#125C2212yes—
11C11×#499C418yescomplemented
12C2×C11×#107C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14C2×C11×#107C2211yescharacteristic
15C2×C11×#107C2211yescharacteristic
16C2×C11×#106C2212yes—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#97C2212yes—
19C2×C4×C8×C11C2211yescharacteristic
20C11×#389—22no—
21C11×#389C2212yes—
22C11×#389C2212yes—
23C11×#387—22no—
24C11×#387—22no—
25C4×C11×C4⋊C4—22no—
26C4×C11×C4⋊C4C2212yes—
27C4×C11×C4⋊C4C2212yes—
28C4×C11×C4⋊C4C2212yes—
29C4×C11×C4⋊C4C2211yescharacteristic
30C11×#340C2212yes—
31C11×#340C2212yes—
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#340C2212yes—
35C11×#336C2212yes—
36C22×C8×C11C2312yes—
37C22×C8×C11C2311yescharacteristic
38C22×C8×C11C2311yescharacteristic
39C11×#125—24no—
40C11×#125C2×C418yes—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C42×C11—22no—
52C2×C42×C11—22no—
53C2×C42×C11—22no—
54C2×C42×C11C2312yes—
55C2×C42×C11C2311yescharacteristic
56C11×#107—22no—
57C11×#107C2×C414yes—
58C11×#107C2×C414yes—
59C11×#107Q814yes—
60C11×#106C2×C418yes—
61C11×C4⋊C8—22no—
62C11×#97—24no—
63C4×C8×C11C2×C414yes—
64C11×#95—22no—
65C11×#95—22no—
66C11×#95—22no—
67C11×#95—22no—
68C11×#95—22no—
69C11×#95D412yes—
70#23165C1111yesmaximal, characteristic, direct product factor, Sylow
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11C2×D412yes—
76C22×C4×C11C2×D412yes—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2411yescharacteristic
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C2×C8×C11—22no—
85C2×C8×C11C22×C412yes—
86C2×C8×C11C22×C412yes—
87C2×C8×C11C2×Q812yes—
88C2×C8×C11#4112yes—
89C11×C4⋊C4—28no—
90C11×C4⋊C4—28no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—44no—
99C11×C4⋊C4—82no—
100C11×C4⋊C4C22×C414yes—
101C11×C4⋊C4C22×C414yes—
102C11×C4⋊C4C2×Q814yes—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11—44no—
106C42×C11—82no—
107C42×C11—82no—
108C42×C11C22×C412yes—
109C42×C11#4112yes—
110C2×#499C2×C1111yescharacteristic
111#2370C2×C1112yes—
112#1989C2×C1112yes—
113#1944C2×C1112yes—
114#1921C2×C1112yes—
115#1918C2×C1112yes—
116#1776C2×C1112yes—
117C4×#107C2×C1111yescharacteristic
118#1770C2×C1111yescharacteristic
119C23×C11C22×D411yescharacteristic
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—24no—
125C2×C4×C11—24no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—24no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11C4×D412yes—
143C2×C4×C11C4×D412yes—
144C2×C4×C11C23×C411yescharacteristic
145C2×C4×C11C22×Q811yescharacteristic
146C2×C4×C11C2×#4111yescharacteristic
147C2×C4×C11C2×#4111yescharacteristic
148C2×C4×C112−1+411yescharacteristic
149C2×C4×C112−1+411yescharacteristic
150C8×C11—22no—
151C8×C11—42no—
152C8×C11C4×Q814yes—
153C2×#125C22×C1112yes—
154#499C4×C1118yescomplemented
155C2×#107C22×C1111yescharacteristic
156C2×#107C22×C1111yescharacteristic
157C2×#107C22×C1111yescharacteristic
158C2×#107C22×C1111yescharacteristic
159C2×#106C22×C1112yes—
160C2×C4⋊C8C22×C1111yescharacteristic
161C2×#97C22×C1112yes—
162C2×C4×C8C22×C1111yescharacteristic
163#389—22no—
164#389C22×C1112yes—
165#389C22×C1112yes—
166#387—22no—
167#387—22no—
168C4×C4⋊C4—22no—
169C4×C4⋊C4C22×C1112yes—
170C4×C4⋊C4C22×C1112yes—
171C4×C4⋊C4C22×C1112yes—
172C4×C4⋊C4C22×C1111yescharacteristic
173#340C22×C1112yes—
174#340C22×C1112yes—
175#340C22×C1112yes—
176#340C22×C1112yes—
177#340C22×C1112yes—
178#336C22×C1112yes—
179C22×C11C2×C4×D411yescharacteristic
180C22×C11#54711yescharacteristic
181C22×C11D4×Q811yescharacteristic
182C22×C11#57511yescharacteristic
183C22×C11#57511yescharacteristic
184C22×C11#57611yescharacteristic
185C22×C11#57811yescharacteristic
186C4×C11—22no—
187C4×C11—22no—
188C4×C11—42no—
189C4×C11—42no—
190C4×C11—44no—
191C4×C11—44no—
192C4×C11—44no—
193C4×C11—82no—
194C4×C11C2×C4×Q811yescharacteristic
195C4×C11#51911yescharacteristic
196C4×C11#55611yescharacteristic
197C4×C11#55711yescharacteristic
198C22×C8C23×C1112yes—
199C22×C8C23×C1111yescharacteristic
200C22×C8C23×C1111yescharacteristic
201#125—24no—
202#125C2×C4×C1118yes—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4D4×C1111yescharacteristic
208C2×C4⋊C4D4×C1111yescharacteristic
209C2×C4⋊C4C23×C1112yes—
210C2×C4⋊C4C23×C1112yes—
211C2×C4⋊C4C23×C1112yes—
212C2×C4⋊C4C23×C1112yes—
213C2×C42—22no—
214C2×C42—22no—
215C2×C42—22no—
216C2×C42C23×C1112yes—
217C2×C42C23×C1111yescharacteristic
218#107—22no—
219#107C2×C4×C1114yes—
220#107C2×C4×C1114yes—
221#107Q8×C1114yes—
222#106C2×C4×C1118yes—
223C4⋊C8—22no—
224#97—24no—
225C4×C8C2×C4×C1114yes—
226#95—22no—
227#95—22no—
228#95—22no—
229#95—22no—
230#95—22no—
231#95D4×C1112yes—
232C2×C11#236511yescharacteristic
233C2×C11#294311yescharacteristic
234C2×C11#295111yescharacteristic
235C2×C11#335211yescharacteristic
236C2×C11#335511yescharacteristic
237C2×C11#338911yescharacteristic
238C2×C11#339011yescharacteristic
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4C2×D4×C1112yes—
244C22×C4C2×D4×C1112yes—
245C22×C4C2×D4×C1111yescharacteristic
246C22×C4C2×D4×C1111yescharacteristic
247C22×C4C24×C1111yescharacteristic
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—22no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8C22×C4×C1112yes—
254C2×C8C22×C4×C1112yes—
255C2×C8C2×Q8×C1112yes—
256C2×C8C11×#4112yes—
257C4⋊C4—28no—
258C4⋊C4—28no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—44no—
267C4⋊C4—82no—
268C4⋊C4C22×C4×C1114yes—
269C4⋊C4C22×C4×C1114yes—
270C4⋊C4C2×Q8×C1114yes—
271C42—22no—
272C42—22no—
273C42—44no—
274C42—82no—
275C42—82no—
276C42C22×C4×C1112yes—
277C42C11×#4112yes—
278C11#2316511yescharacteristic, direct product factor, Sylow
279C23C22×D4×C1111yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4C4×D4×C1112yes—
303C2×C4C4×D4×C1112yes—
304C2×C4C23×C4×C1111yescharacteristic
305C2×C4C22×Q8×C1111yescharacteristic
306C2×C4C2×C11×#4111yescharacteristic
307C2×C4C2×C11×#4111yescharacteristic
308C2×C4C11×2−1+411yescharacteristic
309C2×C4C11×2−1+411yescharacteristic
310C8—22no—
311C8—42no—
312C8C4×Q8×C1114yes—
313C22C2×C4×D4×C1111yescharacteristic
314C22C11×#54711yescharacteristic
315C22D4×Q8×C1111yescharacteristic
316C22C11×#57511yescharacteristic
317C22C11×#57511yescharacteristic
318C22C11×#57611yescharacteristic
319C22C11×#57811yescharacteristic
320C4—22no—
321C4—22no—
322C4—44no—
323C4—44no—
324C4—42no—
325C4—42no—
326C4—44no—
327C4—82no—
328C4C2×C4×Q8×C1111yescharacteristic
329C4C11×#51911yescharacteristic
330C4C11×#55611yescharacteristic
331C4C11×#55711yescharacteristic
332C2C11×#236511yescharacteristic
333C2C11×#294311yescharacteristic
334C2C11×#295111yescharacteristic
335C2C11×#335211yescharacteristic
336C2C11×#335511yescharacteristic
337C2C11×#338911yescharacteristic
338C2C11×#339011yescharacteristic
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
11. C11×#499C4semidirect
70. #23165C11direct (N × H)
154. #499C4×C11semidirect
278. C11#23165direct (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×#19442
C11×#19212
C11×#19182
C11×#17762
C4×C11×#1072
C11×#17702
#2316511