Finite Group Databasebeta

← C11×#11806 #14588999

Subgroups — C11×#11806 #14588999

Order 2816.

488 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2619C211yesmaximal, characteristic
2C11×#1822C211yesmaximal, characteristic, complemented
3C11×#1464C211yesmaximal, characteristic, complemented
4C11×#1345C214yesmaximal, complemented
5C2×C11×#127C411yescharacteristic
6C2×C11×#121—21no—
7C2×C11×#117C2211yescharacteristic
8C11×#432—21no—
9C11×#407—21no—
10C11×#394—21no—
11C11×#394C2212yes—
12C11×#392—21no—
13C11×#392C412yes—
14C11×#390—21no—
15C11×#382C411yescharacteristic
16C11×#343—21no—
17C11×#343C2212yes—
18C11×#324C2212yes—
19C11×#323—21no—
20C22×D4×C11—22no—
21C22×D4×C11—21no—
22C22×D4×C11—21no—
23C22×D4×C11C2×C412yes—
24C23×C4×C11D411yescharacteristic
25C2×C11×M16—22no—
26C11×#127—41no—
27C11×#127—41no—
28C11×#121—44no—
29C11×#117—41no—
30C11×#117—41no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C11×C4⋊C8—41no—
42C11×C22⋊C8—22no—
43C11×C22⋊C8—41no—
44C11×C22⋊C8—41no—
45C11×#97—41no—
46C11×#95—21no—
47C11×#95C2×C412yes—
48#11806C1111yesmaximal, characteristic, direct product factor, Sylow
49C24×C11—22no—
50C24×C11C22⋊C411yescharacteristic
51C2×D4×C11—42no—
52C2×D4×C11—42no—
53C2×D4×C11—42no—
54C2×D4×C11—42no—
55C2×D4×C11—44no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—82no—
59C2×D4×C11—82no—
60C2×D4×C11—82no—
61C2×D4×C11—82no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—41no—
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—42no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—44no—
83C11×C22⋊C4—82no—
84C11×C22⋊C4—82no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89#2619C2×C1111yescharacteristic
90#1822C2×C1111yescharacteristic, complemented
91#1464C2×C1111yescharacteristic, complemented
92#1345C2×C1114yescomplemented
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11—42no—
99C23×C11—42no—
100C23×C11—42no—
101C23×C11—42no—
102C23×C11—42no—
103C23×C11—42no—
104C23×C11—42no—
105C23×C11C2×C22⋊C411yescharacteristic
106D4×C11—82no—
107D4×C11—82no—
108D4×C11—84no—
109D4×C11—84no—
110D4×C11—88no—
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—21no—
118C2×C4×C11—21no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11#9911yescharacteristic
129C2×C4×C11#9911yescharacteristic
130C2×C4×C11AGL(1,ℤ/8)12yes—
131C8×C11—82no—
132C8×C11—82no—
133C2×#127C4×C1111yescharacteristic
134C2×#121—21no—
135C2×#117C22×C1111yescharacteristic
136#432—21no—
137#407—21no—
138#394—21no—
139#394C22×C1112yes—
140#392—21no—
141#392C4×C1112yes—
142#390—21no—
143#382C4×C1111yescharacteristic
144#343—21no—
145#343C22×C1112yes—
146#324C22×C1112yes—
147#323—21no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—42no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—81no—
155C22×C11—82no—
156C22×C11—82no—
157C22×C11—82no—
158C22×C11—82no—
159C22×C11—82no—
160C22×C11—82no—
161C22×C11—82no—
162C22×C11C2×#9911yescharacteristic
163C22×C11#41811yescharacteristic
164C22×C11#42111yescharacteristic
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—22no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—82no—
173C22×D4—22no—
174C22×D4—21no—
175C22×D4—21no—
176C22×D4C2×C4×C1112yes—
177C23×C4D4×C1111yescharacteristic
178C2×M16—22no—
179#127—41no—
180#127—41no—
181#121—44no—
182#117—41no—
183#117—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4D4×C1111yescharacteristic
186C2×C4⋊C4C23×C1111yescharacteristic
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4C2×C4×C1111yescharacteristic
191C2×C22⋊C4D4×C1111yescharacteristic
192C2×C42C2×C4×C1111yescharacteristic
193C2×C42D4×C1111yescharacteristic
194C4⋊C8—41no—
195C22⋊C8—22no—
196C22⋊C8—41no—
197C22⋊C8—41no—
198#97—41no—
199#95—21no—
200#95C2×C4×C1112yes—
201C2×C11—21no—
202C2×C11—21no—
203C2×C11—81no—
204C2×C11—162no—
205C2×C11#151011yescharacteristic
206C2×C11#212211yescharacteristic
207C2×C11#213411yescharacteristic
208C24—22no—
209C24C11×C22⋊C411yescharacteristic
210C2×D4—42no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—44no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—82no—
218C2×D4—82no—
219C2×D4—82no—
220C2×D4—82no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—41no—
226C22×C4C11×C22⋊C411yescharacteristic
227C22×C4C11×C22⋊C411yescharacteristic
228C22×C4C11×C22⋊C411yescharacteristic
229C22×C4C22×C4×C1111yescharacteristic
230C22×C4C2×D4×C1111yescharacteristic
231C22×C4C2×D4×C1111yescharacteristic
232M16—42no—
233M16—42no—
234C2×C8—42no—
235C2×C8—42no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—44no—
242C22⋊C4—82no—
243C22⋊C4—82no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C11#1180611yescharacteristic, direct product factor, Sylow
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23C2×C11×C22⋊C411yescharacteristic
262D4—82no—
263D4—82no—
264D4—84no—
265D4—84no—
266D4—88no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4C11×#9911yescharacteristic
285C2×C4C11×#9911yescharacteristic
286C2×C4C11×AGL(1,ℤ/8)12yes—
287C8—82no—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—82no—
297C22—82no—
298C22—82no—
299C22—82no—
300C22—82no—
301C22—82no—
302C22—82no—
303C22C2×C11×#9911yescharacteristic
304C22C11×#41811yescharacteristic
305C22C11×#42111yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—82no—
314C2—21no—
315C2—21no—
316C2—81no—
317C2—162no—
318C2C11×#151011yescharacteristic
319C2C11×#212211yescharacteristic
320C2C11×#213411yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC11×#2619C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1822C2semidirect
3. C11×#1464C2semidirect
4. C11×#1345C2semidirect
48. #11806C11direct (N × H)
90. #1822C2×C11semidirect
91. #1464C2×C11semidirect
92. #1345C2×C11semidirect
248. C11#11806direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26192
C11×#18222
C11×#14642
C11×#13452
#1180611