Finite Group Databasebeta

← C11×#11807 #14589000

Subgroups — C11×#11807 #14589000

Order 2816.

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

normal subgroups only

This group has 388 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×#2621C211yesmaximal, characteristic
2C11×#1822C211yesmaximal, characteristic
3C11×#1464C211yesmaximal, characteristic
4C11×#1346C214yesmaximal, complemented
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C11×C22⋊Q8—21no—
7C2×C11×#117C2211yescharacteristic
8C11×#432—21no—
9C11×#407—21no—
10C11×#398—21no—
11C11×#398C2212yes—
12C11×#397—21no—
13C11×#397C412yes—
14C11×#391—21no—
15C11×#382C411yescharacteristic
16C11×#343—21no—
17C11×#343C2212yes—
18C11×#324C2212yes—
19C11×#323—21no—
20C22×Q8×C11—21no—
21C23×C4×C11D411yescharacteristic
22C2×C11×M16—22no—
23C11×C4⋊Q8—41no—
24C11×C4⋊Q8—41no—
25C11×C22⋊Q8—44no—
26C11×#117—41no—
27C11×#117—41no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C11×C4⋊C8—41no—
40C11×C22⋊C8—22no—
41C11×C22⋊C8—41no—
42C11×C22⋊C8—41no—
43C11×#97—41no—
44C11×#95—21no—
45C11×#95—22no—
46C11×#95—22no—
47C11×#95C2×C412yes—
48#11807C1111yesmaximal, characteristic, direct product factor, Sylow
49C24×C11C22⋊C411yescharacteristic
50C2×Q8×C11—42no—
51C2×Q8×C11—42no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—41no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C11×M16—42no—
67C11×M16—42no—
68C2×C8×C11—42no—
69C2×C8×C11—42no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—44no—
76C11×C22⋊C4—41no—
77C11×C22⋊C4—41no—
78C11×C22⋊C4—44no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83#2621C2×C1111yescharacteristic
84#1822C2×C1111yescharacteristic
85#1464C2×C1111yescharacteristic
86#1346C2×C1114yescomplemented
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—41no—
91C23×C11—41no—
92C23×C11C2×C22⋊C411yescharacteristic
93Q8×C11—82no—
94Q8×C11—82no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11#9911yescharacteristic
116C2×C4×C11#9911yescharacteristic
117C2×C4×C11AGL(1,ℤ/8)12yes—
118C8×C11—82no—
119C8×C11—82no—
120C2×C4⋊Q8C4×C1111yescharacteristic
121C2×C22⋊Q8—21no—
122C2×#117C22×C1111yescharacteristic
123#432—21no—
124#407—21no—
125#398—21no—
126#398C22×C1112yes—
127#397—21no—
128#397C4×C1112yes—
129#391—21no—
130#382C4×C1111yescharacteristic
131#343—21no—
132#343C22×C1112yes—
133#324C22×C1112yes—
134#323—21no—
135C22×C11—21no—
136C22×C11—21no—
137C22×C11—42no—
138C22×C11—41no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11—81no—
142C22×C11C2×#9911yescharacteristic
143C22×C11#41811yescharacteristic
144C22×C11#42111yescharacteristic
145C4×C11—21no—
146C4×C11—21no—
147C4×C11—22no—
148C4×C11—41no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11—41no—
152C4×C11—82no—
153C4×C11—82no—
154C22×Q8—21no—
155C23×C4D4×C1111yescharacteristic
156C2×M16—22no—
157C4⋊Q8—41no—
158C4⋊Q8—41no—
159C22⋊Q8—44no—
160#117—41no—
161#117—41no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4C2×C4×C1112yes—
166C2×C4⋊C4D4×C1111yescharacteristic
167C2×C4⋊C4C23×C1111yescharacteristic
168C2×C22⋊C4—22no—
169C2×C22⋊C4C2×C4×C1111yescharacteristic
170C2×C22⋊C4D4×C1111yescharacteristic
171C2×C42C2×C4×C1111yescharacteristic
172C2×C42D4×C1111yescharacteristic
173C4⋊C8—41no—
174C22⋊C8—22no—
175C22⋊C8—41no—
176C22⋊C8—41no—
177#97—41no—
178#95—21no—
179#95—22no—
180#95—22no—
181#95C2×C4×C1112yes—
182C2×C11—21no—
183C2×C11—21no—
184C2×C11—81no—
185C2×C11#151011yescharacteristic
186C2×C11#212311yescharacteristic
187C2×C11#213511yescharacteristic
188C24C11×C22⋊C411yescharacteristic
189C2×Q8—42no—
190C2×Q8—42no—
191C2×Q8—41no—
192C2×Q8—41no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—41no—
199C22×C4C11×C22⋊C411yescharacteristic
200C22×C4C11×C22⋊C411yescharacteristic
201C22×C4C11×C22⋊C411yescharacteristic
202C22×C4C22×C4×C1111yescharacteristic
203C22×C4C2×D4×C1111yescharacteristic
204C22×C4C2×D4×C1111yescharacteristic
205M16—42no—
206M16—42no—
207C2×C8—42no—
208C2×C8—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—44no—
215C22⋊C4—41no—
216C22⋊C4—41no—
217C22⋊C4—44no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C11#1180711yescharacteristic, direct product factor, Sylow
223C23—21no—
224C23—21no—
225C23—21no—
226C23—41no—
227C23—41no—
228C23C2×C11×C22⋊C411yescharacteristic
229Q8—82no—
230Q8—82no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4C11×#9911yescharacteristic
252C2×C4C11×#9911yescharacteristic
253C2×C4C11×AGL(1,ℤ/8)12yes—
254C8—82no—
255C8—82no—
256C22—21no—
257C22—21no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—81no—
263C22C2×C11×#9911yescharacteristic
264C22C11×#41811yescharacteristic
265C22C11×#42111yescharacteristic
266C4—22no—
267C4—21no—
268C4—21no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—41no—
273C4—82no—
274C4—82no—
275C2—21no—
276C2—21no—
277C2—81no—
278C2C11×#151011yescharacteristic
279C2C11×#212311yescharacteristic
280C2C11×#213511yescharacteristic
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 ◁ C22×C4×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1346C2semidirect
48. #11807C11direct (N × H)
86. #1346C2×C11semidirect
222. C11#11807direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26212
C11×#18222
C11×#14642
C11×#13462
#1180711