Finite Group Databasebeta

← C11×#18411 #14595604

Subgroups — C11×#18411 #14595604

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic
2C11×#3230C212yesmaximal
3C11×#2568C211yesmaximal, characteristic
4C11×#1617C218yesmaximal
5C11×#1503C212yesmaximal
6C11×#1461C211yesmaximal, characteristic
7Q82×C11—22no—
8C11×#557—22no—
9C11×#557—24no—
10C11×#544—21no—
11C11×#544C2214yes—
12C11×#533—22no—
13C11×#533C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C11×#519—21no—
16C2×C4×Q8×C11C2211yescharacteristic
17C11×#500—22no—
18C11×#487—22no—
19C11×#484C2218yes—
20C11×#477—24no—
21C11×#431C2212yes—
22C11×#400C2214yes—
23C11×#391—21no—
24C11×#391—22no—
25C11×#382—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#328C2218yes—
28C11×#324C2214yes—
29C22×Q8×C11—21no—
30C22×Q8×C11D411yescharacteristic
31C11×C4⋊Q8—22no—
32C11×C4⋊Q8—22no—
33C11×C4⋊Q8—24no—
34C11×C4⋊Q8—28no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8—22no—
37C11×C4⋊Q8D412yes—
38C11×C4⋊Q8D412yes—
39C11×#125—24no—
40C11×#125—24no—
41C11×#125—28no—
42C11×#125—22no—
43C11×C22⋊Q8—22no—
44C11×C22⋊Q8—24no—
45C11×C22⋊Q8C2314yes—
46C4×Q8×C11—24no—
47C4×Q8×C11—24no—
48C4×Q8×C11—24no—
49C4×Q8×C11—24no—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C4×Q8×C11D414yes—
54C11×#117—24no—
55C11×#117—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C42×C11—21no—
62C2×C42×C11D412yes—
63C2×C42×C11C2311yescharacteristic
64C11×#107—28no—
65C11×C4⋊C8—22no—
66C11×#103—28no—
67C11×C22⋊C8C2314yes—
68C4×C8×C11—22no—
69C11×#95—24no—
70C11×#95—24no—
71C11×#95C2312yes—
72#18411C1111yesmaximal, characteristic, direct product factor, Sylow
73C2×Q8×C11—24no—
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—44no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11Q1614yes—
81C2×Q8×C11C2×D414yes—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2411yescharacteristic
89C2×C8×C11—24no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—28no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4C2×D414yes—
105C11×C22⋊C4—24no—
106C42×C11—28no—
107C42×C11—22no—
108C42×C11—22no—
109C42×C11—24no—
110C42×C11—42no—
111C42×C11C2×D412yes—
112C42×C11C2×D412yes—
113#3502C2×C1111yescharacteristic
114#3230C2×C1112yes—
115#2568C2×C1111yescharacteristic
116#1617C2×C1118yes—
117#1503C2×C1112yes—
118#1461C2×C1111yescharacteristic
119C23×C11C22×D411yescharacteristic
120Q8×C11—28no—
121Q8×C11—44no—
122Q8×C11—44no—
123Q8×C11—82no—
124Q8×C11—84no—
125Q8×C11—82no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—24no—
130C2×C4×C11—24no—
131C2×C4×C11—22no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—44no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12012yes—
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11C2×Q1614yes—
143C2×C4×C11C2×Q1612yes—
144C2×C4×C11#13712yes—
145C2×C4×C11C22×D412yes—
146C8×C11—44no—
147Q82—22no—
148#557—22no—
149#557—24no—
150#544—21no—
151#544C22×C1114yes—
152#533—22no—
153#533C22×C1112yes—
154C2×C4⋊Q8C22×C1111yescharacteristic
155#519—21no—
156C2×C4×Q8C22×C1111yescharacteristic
157#500—22no—
158#487—22no—
159#484C22×C1118yes—
160#477—24no—
161#431C22×C1112yes—
162#400C22×C1114yes—
163#391—21no—
164#391—22no—
165#382—21no—
166C4×C4⋊C4C22×C1111yescharacteristic
167#328C22×C1118yes—
168#324C22×C1114yes—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11C2×#12011yescharacteristic
172C22×C11C22×Q1611yescharacteristic
173C22×C11C2×#13711yescharacteristic
174C4×C11—24no—
175C4×C11—21no—
176C4×C11—22no—
177C4×C11—44no—
178C4×C11—42no—
179C4×C11—44no—
180C4×C11—82no—
181C4×C11—82no—
182C4×C11#45114yes—
183C4×C11#45412yes—
184C22×Q8—21no—
185C22×Q8D4×C1111yescharacteristic
186C4⋊Q8—22no—
187C4⋊Q8—22no—
188C4⋊Q8—24no—
189C4⋊Q8—28no—
190C4⋊Q8—22no—
191C4⋊Q8—22no—
192C4⋊Q8D4×C1112yes—
193C4⋊Q8D4×C1112yes—
194#125—24no—
195#125—24no—
196#125—28no—
197#125—22no—
198C22⋊Q8—22no—
199C22⋊Q8—24no—
200C22⋊Q8C23×C1114yes—
201C4×Q8—24no—
202C4×Q8—24no—
203C4×Q8—24no—
204C4×Q8—24no—
205C4×Q8—22no—
206C4×Q8—22no—
207C4×Q8—22no—
208C4×Q8D4×C1114yes—
209#117—24no—
210#117—22no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4D4×C1111yescharacteristic
214C2×C4⋊C4C23×C1112yes—
215C2×C4⋊C4C23×C1112yes—
216C2×C42—21no—
217C2×C42D4×C1112yes—
218C2×C42C23×C1111yescharacteristic
219#107—28no—
220C4⋊C8—22no—
221#103—28no—
222C22⋊C8C23×C1114yes—
223C4×C8—22no—
224#95—24no—
225#95—24no—
226#95C23×C1112yes—
227C2×C11—21no—
228C2×C11—21no—
229C2×C11C2×#45111yescharacteristic
230C2×C11C2×#45411yescharacteristic
231C2×C11#302811yescharacteristic
232C2×Q8—24no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—44no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8C11×Q1614yes—
240C2×Q8C2×D4×C1114yes—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4C2×D4×C1111yescharacteristic
244C22×C4C2×D4×C1112yes—
245C22×C4C2×D4×C1112yes—
246C22×C4C2×D4×C1111yescharacteristic
247C22×C4C24×C1111yescharacteristic
248C2×C8—24no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—28no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—24no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4C2×D4×C1114yes—
264C22⋊C4—24no—
265C42—28no—
266C42—22no—
267C42—22no—
268C42—24no—
269C42—42no—
270C42C2×D4×C1112yes—
271C42C2×D4×C1112yes—
272C11#1841111yescharacteristic, direct product factor, Sylow
273C23C22×D4×C1111yescharacteristic
274Q8—28no—
275Q8—44no—
276Q8—44no—
277Q8—82no—
278Q8—84no—
279Q8—82no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4C11×#12011yescharacteristic
294C2×C4C11×#12012yes—
295C2×C4C11×#12011yescharacteristic
296C2×C4C2×C11×Q1614yes—
297C2×C4C2×C11×Q1612yes—
298C2×C4C11×#13712yes—
299C2×C4C22×D4×C1112yes—
300C8—44no—
301C22—21no—
302C22—21no—
303C22C2×C11×#12011yescharacteristic
304C22C22×C11×Q1611yescharacteristic
305C22C2×C11×#13711yescharacteristic
306C4—24no—
307C4—21no—
308C4—22no—
309C4—44no—
310C4—42no—
311C4—44no—
312C4—82no—
313C4—82no—
314C4C11×#45114yes—
315C4C11×#45412yes—
316C2—21no—
317C2—21no—
318C2C2×C11×#45111yescharacteristic
319C2C2×C11×#45411yescharacteristic
320C2C11×#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
72. #18411C11direct (N × H)
272. C11#18411direct (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×#32302
C11×#25682
C11×#16172
C11×#15032
C11×#14612
#1841111