Finite Group Databasebeta

← C11×#11803 #14588996

Subgroups — C11×#11803 #14588996

Order 2816.

478 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C2×C11×#398C211yesmaximal, characteristic
2C11×#1821C211yesmaximal, characteristic
3C11×#1463C211yesmaximal, characteristic
4C11×#1346C214yesmaximal, complemented
5C22×C11×C4⋊C4—21no—
6C22×C11×C4⋊C4C411yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C11×#407—21no—
9C11×#407—21no—
10C11×#398—21no—
11C11×#398—21no—
12C11×#398C412yes—
13C11×#398C2212yes—
14C2×C11×#95—21no—
15C2×C11×#95C411yescharacteristic
16C11×#343—21no—
17C11×#343C2212yes—
18C11×#324—21no—
19C11×#324C2212yes—
20C23×C4×C11—21no—
21C23×C4×C11—21no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C2×C11×M16—22no—
26C2×C11×M16—41no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4—41no—
33C2×C11×C4⋊C4—41no—
34C2×C11×C4⋊C4—44no—
35C2×C11×C4⋊C4C2×C412yes—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4C2311yescharacteristic
40C11×C22⋊C8—22no—
41C11×C22⋊C8—41no—
42C11×C22⋊C8—41no—
43C11×C22⋊C8—41no—
44C11×#95—22no—
45C11×#95—21no—
46C11×#95—22no—
47C11×#95C2×C412yes—
48#11803C1111yesmaximal, characteristic, direct product factor, Sylow
49C24×C11C22⋊C411yescharacteristic
50C22×C4×C11—24no—
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—22no—
57C22×C4×C11—21no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—41no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C11×M16—42no—
76C11×M16—42no—
77C11×M16—82no—
78C2×C8×C11—42no—
79C2×C8×C11—42no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—44no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—44no—
88C2×#398C2×C1111yescharacteristic
89#1821C2×C1111yescharacteristic
90#1463C2×C1111yescharacteristic
91#1346C2×C1114yescomplemented
92C23×C11—22no—
93C23×C11—22no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11#9911yescharacteristic
97C23×C11#9911yescharacteristic
98C23×C11C2×C22⋊C411yescharacteristic
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—24no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—48no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—81no—
125C2×C4×C11—82no—
126C2×C4×C11—82no—
127C2×C4×C11AGL(1,ℤ/8)12yes—
128C8×C11—82no—
129C8×C11—82no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4C4×C1111yescharacteristic
132C22×C4⋊C4C22×C1111yescharacteristic
133#407—21no—
134#407—21no—
135#398—21no—
136#398—21no—
137#398C4×C1112yes—
138#398C22×C1112yes—
139C2×#95—21no—
140C2×#95C4×C1111yescharacteristic
141#343—21no—
142#343C22×C1112yes—
143#324—21no—
144#324C22×C1112yes—
145C22×C11—24no—
146C22×C11—24no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11#35212yes—
154C22×C11#35612yes—
155C22×C11C2×#9911yescharacteristic
156C22×C11#41811yescharacteristic
157C22×C11#42111yescharacteristic
158C4×C11—22no—
159C4×C11—44no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—82no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4C2×C4×C1111yescharacteristic
169C23×C4D4×C1111yescharacteristic
170C23×C4D4×C1111yescharacteristic
171C2×M16—22no—
172C2×M16—41no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4C2×C4×C1112yes—
182C2×C4⋊C4C2×C4×C1111yescharacteristic
183C2×C4⋊C4D4×C1111yescharacteristic
184C2×C4⋊C4D4×C1111yescharacteristic
185C2×C4⋊C4C23×C1111yescharacteristic
186C22⋊C8—22no—
187C22⋊C8—41no—
188C22⋊C8—41no—
189C22⋊C8—41no—
190#95—22no—
191#95—21no—
192#95—22no—
193#95C2×C4×C1112yes—
194C2×C11—21no—
195C2×C11—22no—
196C2×C11—22no—
197C2×C11—21no—
198C2×C11#151011yescharacteristic
199C2×C11C2×#35211yescharacteristic
200C2×C11C2×#35611yescharacteristic
201C24C11×C22⋊C411yescharacteristic
202C22×C4—24no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—41no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4C11×C22⋊C411yescharacteristic
222C22×C4C11×C22⋊C411yescharacteristic
223C22×C4C11×C22⋊C411yescharacteristic
224C22×C4C22×C4×C1111yescharacteristic
225C22×C4C2×D4×C1111yescharacteristic
226C22×C4C2×D4×C1111yescharacteristic
227M16—42no—
228M16—42no—
229M16—82no—
230C2×C8—42no—
231C2×C8—42no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—44no—
239C4⋊C4—44no—
240C11#1180311yescharacteristic, direct product factor, Sylow
241C23—22no—
242C23—22no—
243C23—21no—
244C23—21no—
245C23C11×#9911yescharacteristic
246C23C11×#9911yescharacteristic
247C23C2×C11×C22⋊C411yescharacteristic
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—24no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—48no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4C11×AGL(1,ℤ/8)12yes—
277C8—82no—
278C8—82no—
279C22—24no—
280C22—24no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C11×#35212yes—
288C22C11×#35612yes—
289C22C2×C11×#9911yescharacteristic
290C22C11×#41811yescharacteristic
291C22C11×#42111yescharacteristic
292C4—22no—
293C4—44no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—82no—
300C2—21no—
301C2—22no—
302C2—22no—
303C2—21no—
304C2C11×#151011yescharacteristic
305C2C2×C11×#35211yescharacteristic
306C2C2×C11×#35611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC24×C11C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C22×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1346C2semidirect
48. #11803C11direct (N × H)
91. #1346C2×C11semidirect
240. C11#11803direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3982
C11×#18212
C11×#14632
C11×#13462
#1180311