Finite Group Databasebeta

← C11×#18374 #14595567

Subgroups — C11×#18374 #14595567

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic
2C11×#3236C212yesmaximal
3C11×#2634C211yesmaximal, characteristic
4C11×#1617C214yesmaximal
5C11×#1611C214yesmaximal
6C11×#1515C212yesmaximal
7C11×#1467C211yesmaximal, characteristic
8Q82×C11—22no—
9C11×#557—22no—
10C11×#557—24no—
11C11×#544—21no—
12C11×#544C2214yes—
13C11×#533—22no—
14C11×#533C2212yes—
15C2×C11×#125C2211yescharacteristic
16C11×#519—21no—
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#501—22no—
19C11×#491—22no—
20C11×#484C2214yes—
21C11×#483C2214yes—
22C11×#479—24no—
23C11×#432C2212yes—
24C11×#400—21no—
25C11×#400C2212yes—
26C11×#398C2212yes—
27C11×#395—21no—
28C11×#387—22no—
29C11×#383C2211yescharacteristic
30C11×#328C2218yes—
31C11×#324C2214yes—
32C22×Q8×C11D411yescharacteristic
33C11×C4⋊Q8—22no—
34C11×C4⋊Q8—22no—
35C11×C4⋊Q8—24no—
36C11×C4⋊Q8—28no—
37C11×C4⋊Q8D412yes—
38C11×C4⋊Q8D412yes—
39C11×#125—24no—
40C11×#125—24no—
41C11×#125—28no—
42C11×#125—22no—
43C11×#125—22no—
44C11×#125—22no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8C2314yes—
48C4×Q8×C11—24no—
49C4×Q8×C11—24no—
50C4×Q8×C11—24no—
51C4×Q8×C11—24no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11D414yes—
56C11×#117—24no—
57C11×#117—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C42×C11D412yes—
66C2×C42×C11C2311yescharacteristic
67C11×#107—24no—
68C11×#106—24no—
69C11×C4⋊C8—22no—
70C11×#103—24no—
71C11×#103—24no—
72C11×C22⋊C8C2314yes—
73C11×#97—22no—
74C11×#95—21no—
75C11×#95—21no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95C2312yes—
80#18374C1111yesmaximal, characteristic, direct product factor, Sylow
81C2×Q8×C11—24no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—24no—
85C2×Q8×C11C2×D414yes—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2411yescharacteristic
94C2×C8×C11—24no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4—28no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—44no—
112C11×C4⋊C4C2×D414yes—
113C11×C22⋊C4—24no—
114C42×C11—28no—
115C42×C11—22no—
116C42×C11—22no—
117C42×C11—24no—
118C42×C11C2×D412yes—
119C42×C11C2×D412yes—
120#3502C2×C1111yescharacteristic
121#3236C2×C1112yes—
122#2634C2×C1111yescharacteristic
123#1617C2×C1114yes—
124#1611C2×C1114yes—
125#1515C2×C1112yes—
126#1467C2×C1111yescharacteristic
127C23×C11C22×D411yescharacteristic
128Q8×C11—28no—
129Q8×C11—44no—
130Q8×C11—44no—
131Q8×C11—84no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12012yes—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#13714yes—
152C2×C4×C11C22×D412yes—
153C8×C11—44no—
154Q82—22no—
155#557—22no—
156#557—24no—
157#544—21no—
158#544C22×C1114yes—
159#533—22no—
160#533C22×C1112yes—
161C2×#125C22×C1111yescharacteristic
162#519—21no—
163C2×C4×Q8C22×C1111yescharacteristic
164#501—22no—
165#491—22no—
166#484C22×C1114yes—
167#483C22×C1114yes—
168#479—24no—
169#432C22×C1112yes—
170#400—21no—
171#400C22×C1112yes—
172#398C22×C1112yes—
173#395—21no—
174#387—22no—
175#383C22×C1111yescharacteristic
176#328C22×C1118yes—
177#324C22×C1114yes—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11C2×#12011yescharacteristic
181C22×C11C2×#13712yes—
182C4×C11—22no—
183C4×C11—24no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—22no—
187C4×C11—44no—
188C4×C11—42no—
189C4×C11—44no—
190C4×C11—82no—
191C4×C11—81no—
192C4×C11—81no—
193C22×Q8D4×C1111yescharacteristic
194C4⋊Q8—22no—
195C4⋊Q8—22no—
196C4⋊Q8—24no—
197C4⋊Q8—28no—
198C4⋊Q8D4×C1112yes—
199C4⋊Q8D4×C1112yes—
200#125—24no—
201#125—24no—
202#125—28no—
203#125—22no—
204#125—22no—
205#125—22no—
206C22⋊Q8—22no—
207C22⋊Q8—24no—
208C22⋊Q8C23×C1114yes—
209C4×Q8—24no—
210C4×Q8—24no—
211C4×Q8—24no—
212C4×Q8—24no—
213C4×Q8—22no—
214C4×Q8—22no—
215C4×Q8—22no—
216C4×Q8D4×C1114yes—
217#117—24no—
218#117—22no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4D4×C1111yescharacteristic
223C2×C4⋊C4C23×C1111yescharacteristic
224C2×C4⋊C4C23×C1111yescharacteristic
225C2×C4⋊C4C23×C1112yes—
226C2×C42D4×C1112yes—
227C2×C42C23×C1111yescharacteristic
228#107—24no—
229#106—24no—
230C4⋊C8—22no—
231#103—24no—
232#103—24no—
233C22⋊C8C23×C1114yes—
234#97—22no—
235#95—21no—
236#95—21no—
237#95—22no—
238#95—22no—
239#95—22no—
240#95C23×C1112yes—
241C2×C11—22no—
242C2×C11#300411yescharacteristic
243C2×C11#302011yescharacteristic
244C2×C11#302811yescharacteristic
245C2×Q8—24no—
246C2×Q8—22no—
247C2×Q8—22no—
248C2×Q8—24no—
249C2×Q8C2×D4×C1114yes—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C2×D4×C1111yescharacteristic
254C22×C4C2×D4×C1112yes—
255C22×C4C2×D4×C1112yes—
256C22×C4C2×D4×C1111yescharacteristic
257C22×C4C24×C1111yescharacteristic
258C2×C8—24no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—28no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—24no—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C4⋊C4—41no—
275C4⋊C4—44no—
276C4⋊C4C2×D4×C1114yes—
277C22⋊C4—24no—
278C42—28no—
279C42—22no—
280C42—22no—
281C42—24no—
282C42C2×D4×C1112yes—
283C42C2×D4×C1112yes—
284C11#1837411yescharacteristic, direct product factor, Sylow
285C23C22×D4×C1111yescharacteristic
286Q8—28no—
287Q8—44no—
288Q8—44no—
289Q8—84no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4C11×#12011yescharacteristic
307C2×C4C11×#12012yes—
308C2×C4C11×#12011yescharacteristic
309C2×C4C11×#13714yes—
310C2×C4C22×D4×C1112yes—
311C8—44no—
312C22—21no—
313C22—21no—
314C22C2×C11×#12011yescharacteristic
315C22C2×C11×#13712yes—
316C4—22no—
317C4—24no—
318C4—21no—
319C4—21no—
320C4—22no—
321C4—44no—
322C4—42no—
323C4—44no—
324C4—82no—
325C4—81no—
326C4—81no—
327C2—22no—
328C2C11×#300411yescharacteristic
329C2C11×#302011yescharacteristic
330C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×C11C22×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
80. #18374C11direct (N × H)
284. C11#18374direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35022
C11×#32362
C11×#26342
C11×#16172
C11×#16112
C11×#15152
C11×#14672
#1837411