Finite Group Databasebeta

← C11×#11882 #14589075

Subgroups — C11×#11882 #14589075

Order 2816.

476 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2548C211yesmaximal, characteristic
2C11×#1801C211yesmaximal, characteristic, complemented
3C11×#1461C211yesmaximal, characteristic, complemented
4C11×#1345C214yesmaximal, complemented
5C2×C11×#127C411yescharacteristic
6C2×C11×#124—21no—
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#431—21no—
9C11×#423—21no—
10C2×C11×#101—21no—
11C11×#394C412yes—
12C11×#394C2212yes—
13C11×#390—21no—
14C11×#390—21no—
15C11×#390—21no—
16C4×C11×C4⋊C4C411yescharacteristic
17C11×#343C2212yes—
18C11×#324—21no—
19C11×#324C2212yes—
20C22×Q8×C11D411yescharacteristic
21C22×D4×C11—21no—
22C22×D4×C11—21no—
23C22×D4×C11C2×C412yes—
24C2×C11×M16—22no—
25C11×#127—41no—
26C11×#127—41no—
27C11×#124—42no—
28C11×#124—42no—
29C4×Q8×C11—41no—
30C4×Q8×C11—41no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4—22no—
39C2×C42×C11—21no—
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C11×C4⋊C8—41no—
44C11×C4⋊C8—41no—
45C11×C4⋊C8—41no—
46C11×#101—42no—
47C11×C22⋊C8—22no—
48C4×C8×C11—41no—
49C11×#95C2×C412yes—
50#11882C1111yesmaximal, characteristic, direct product factor, Sylow
51C24×C11—22no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C2×Q8×C11D812yes—
55C2×Q8×C11SD1612yes—
56C2×D4×C11—42no—
57C2×D4×C11—42no—
58C2×D4×C11—42no—
59C2×D4×C11—42no—
60C2×D4×C11—42no—
61C2×D4×C11—41no—
62C2×D4×C11—41no—
63C2×D4×C11—42no—
64C2×D4×C11—82no—
65C22×C4×C11—22no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C11×M16—42no—
74C11×M16—42no—
75C2×C8×C11—42no—
76C2×C8×C11—42no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—42no—
81C11×C22⋊C4—44no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—42no—
84C11×C22⋊C4—82no—
85C11×C22⋊C4—82no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—42no—
93#2548C2×C1111yescharacteristic
94#1801C2×C1111yescharacteristic, complemented
95#1461C2×C1111yescharacteristic, complemented
96#1345C2×C1114yescomplemented
97C23×C11—42no—
98C23×C11—42no—
99C23×C11—42no—
100C23×C11—42no—
101C23×C11—42no—
102C23×C11—42no—
103C23×C11—42no—
104C23×C11C2×C22⋊C411yescharacteristic
105Q8×C11—42no—
106Q8×C11—42no—
107D4×C11—82no—
108D4×C11—84no—
109D4×C11—84no—
110D4×C11—82no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11#9911yescharacteristic
128C2×C4×C11#9911yescharacteristic
129C2×C4×C11#10212yes—
130C2×C4×C11#10212yes—
131C2×C4×C11C2×D811yescharacteristic
132C2×C4×C11C2×SD1611yescharacteristic
133C8×C11—82no—
134C8×C11—82no—
135C2×#127C4×C1111yescharacteristic
136C2×#124—21no—
137C2×C4×Q8C22×C1111yescharacteristic
138#431—21no—
139#423—21no—
140C2×#101—21no—
141#394C4×C1112yes—
142#394C22×C1112yes—
143#390—21no—
144#390—21no—
145#390—21no—
146C4×C4⋊C4C4×C1111yescharacteristic
147#343C22×C1112yes—
148#324—21no—
149#324C22×C1112yes—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—82no—
153C22×C11—82no—
154C22×C11—82no—
155C22×C11—82no—
156C22×C11—82no—
157C22×C11—82no—
158C22×C11—82no—
159C22×C11C2×#9911yescharacteristic
160C22×C11C2×#10211yescharacteristic
161C22×C11#42111yescharacteristic
162C4×C11—21no—
163C4×C11—22no—
164C4×C11—22no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—82no—
171C4×C11#35512yes—
172C22×Q8D4×C1111yescharacteristic
173C22×D4—21no—
174C22×D4—21no—
175C22×D4C2×C4×C1112yes—
176C2×M16—22no—
177#127—41no—
178#127—41no—
179#124—42no—
180#124—42no—
181C4×Q8—41no—
182C4×Q8—41no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4C2×C4×C1111yescharacteristic
185C2×C4⋊C4D4×C1111yescharacteristic
186C2×C4⋊C4C23×C1111yescharacteristic
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C42—21no—
192C2×C42C2×C4×C1111yescharacteristic
193C2×C42D4×C1111yescharacteristic
194C2×C42D4×C1111yescharacteristic
195C4⋊C8—41no—
196C4⋊C8—41no—
197C4⋊C8—41no—
198#101—42no—
199C22⋊C8—22no—
200C4×C8—41no—
201#95C2×C4×C1112yes—
202C2×C11—21no—
203C2×C11—21no—
204C2×C11—162no—
205C2×C11#151911yescharacteristic
206C2×C11#212211yescharacteristic
207C2×C11C2×#35511yescharacteristic
208C24—22no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8C11×D812yes—
212C2×Q8C11×SD1612yes—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—41no—
219C2×D4—41no—
220C2×D4—42no—
221C2×D4—82no—
222C22×C4—22no—
223C22×C4C11×C22⋊C411yescharacteristic
224C22×C4C11×C22⋊C411yescharacteristic
225C22×C4C11×C22⋊C411yescharacteristic
226C22×C4C11×C22⋊C411yescharacteristic
227C22×C4C22×C4×C1111yescharacteristic
228C22×C4C2×D4×C1111yescharacteristic
229C22×C4C2×D4×C1111yescharacteristic
230M16—42no—
231M16—42no—
232C2×C8—42no—
233C2×C8—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C22⋊C4—44no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—82no—
242C22⋊C4—82no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—42no—
250C11#1188211yescharacteristic, direct product factor, Sylow
251C23—42no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23C2×C11×C22⋊C411yescharacteristic
259Q8—42no—
260Q8—42no—
261D4—82no—
262D4—84no—
263D4—84no—
264D4—82no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4C11×#9911yescharacteristic
282C2×C4C11×#9911yescharacteristic
283C2×C4C11×#10212yes—
284C2×C4C11×#10212yes—
285C2×C4C2×C11×D811yescharacteristic
286C2×C4C2×C11×SD1611yescharacteristic
287C8—82no—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—82no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22—82no—
297C22—82no—
298C22C2×C11×#9911yescharacteristic
299C22C2×C11×#10211yescharacteristic
300C22C11×#42111yescharacteristic
301C4—21no—
302C4—21no—
303C4—22no—
304C4—22no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—82no—
310C4C11×#35512yes—
311C2—21no—
312C2—21no—
313C2—162no—
314C2C11×#151911yescharacteristic
315C2C11×#212211yescharacteristic
316C2C2×C11×#35511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC2×C11×#127C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1801C2semidirect
3. C11×#1461C2semidirect
4. C11×#1345C2semidirect
50. #11882C11direct (N × H)
94. #1801C2×C11semidirect
95. #1461C2×C11semidirect
96. #1345C2×C11semidirect
250. C11#11882direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25482
C11×#18012
C11×#14612
C11×#13452
#1188211