Finite Group Databasebeta

← C11×#11795 #14588988

Subgroups — C11×#11795 #14588988

Order 2816.

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

normal subgroups only

This group has 394 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
1C11×#2567C211yesmaximal, characteristic
2C4×C11×#101C211yesmaximal, characteristic
3C11×#1467C211yesmaximal, characteristic
4C11×#1354C214yesmaximal
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C11×#432—21no—
8C2×C11×#101—21no—
9C4×C11×M16—21no—
10C11×#395C412yes—
11C11×#395C2212yes—
12C11×#391—21no—
13C11×#389—21no—
14C11×#389—21no—
15C11×#384—21no—
16C4×C11×C4⋊C4C411yescharacteristic
17C11×#343C2212yes—
18C11×#324—21no—
19C11×#324C2212yes—
20C22×Q8×C11C2×C412yes—
21C22×Q8×C11D411yescharacteristic
22C2×C11×M16—22no—
23C11×C4⋊Q8—41no—
24C11×C4⋊Q8—41no—
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C42×C11—21no—
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C11×C4⋊C8—41no—
40C11×#101—24no—
41C11×C22⋊C8—22no—
42C11×#97—41no—
43C11×#97—41no—
44C4×C8×C11—41no—
45C11×#95—22no—
46C11×#95—22no—
47C11×#95C2×C412yes—
48#11795C1111yesmaximal, characteristic, direct product factor, Sylow
49C2×Q8×C11—22no—
50C2×Q8×C11—22no—
51C2×Q8×C11—41no—
52C2×Q8×C11—42no—
53C2×Q8×C11—82no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C11×M16—24no—
64C11×M16—42no—
65C2×C8×C11—42no—
66C2×C8×C11—42no—
67C11×C4⋊C4—24no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—82no—
75C11×C4⋊C4—82no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—42no—
83#2567C2×C1111yescharacteristic
84C4×#101C2×C1111yescharacteristic
85#1467C2×C1111yescharacteristic
86#1354C2×C1114yes—
87C23×C11C2×C22⋊C411yescharacteristic
88Q8×C11—44no—
89Q8×C11—84no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—22no—
95C2×C4×C11—24no—
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—42no—
103C2×C4×C11—42no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11#9911yescharacteristic
111C2×C4×C11#9911yescharacteristic
112C2×C4×C11#10412yes—
113C2×C4×C11#13712yes—
114C8×C11—44no—
115C8×C11—82no—
116C2×C4⋊Q8C4×C1111yescharacteristic
117C2×C4×Q8C22×C1111yescharacteristic
118#432—21no—
119C2×#101—21no—
120C4×M16—21no—
121#395C4×C1112yes—
122#395C22×C1112yes—
123#391—21no—
124#389—21no—
125#389—21no—
126#384—21no—
127C4×C4⋊C4C4×C1111yescharacteristic
128#343C22×C1112yes—
129#324—21no—
130#324C22×C1112yes—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11C2×#9911yescharacteristic
134C22×C11#41911yescharacteristic
135C22×C11C2×#10411yescharacteristic
136C4×C11—21no—
137C4×C11—22no—
138C4×C11—22no—
139C4×C11—44no—
140C4×C11—41no—
141C4×C11—41no—
142C4×C11—41no—
143C4×C11—41no—
144C4×C11—82no—
145C4×C11#35612yes—
146C22×Q8C2×C4×C1112yes—
147C22×Q8D4×C1111yescharacteristic
148C2×M16—22no—
149C4⋊Q8—41no—
150C4⋊Q8—41no—
151C4×Q8—41no—
152C4×Q8—41no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4C2×C4×C1111yescharacteristic
159C2×C4⋊C4D4×C1111yescharacteristic
160C2×C4⋊C4C23×C1111yescharacteristic
161C2×C42—21no—
162C2×C42C2×C4×C1111yescharacteristic
163C2×C42D4×C1111yescharacteristic
164C2×C42D4×C1111yescharacteristic
165C4⋊C8—41no—
166#101—24no—
167C22⋊C8—22no—
168#97—41no—
169#97—41no—
170C4×C8—41no—
171#95—22no—
172#95—22no—
173#95C2×C4×C1112yes—
174C2×C11—21no—
175C2×C11—21no—
176C2×C11#150811yescharacteristic
177C2×C11#212211yescharacteristic
178C2×C11C2×#35611yescharacteristic
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—41no—
182C2×Q8—42no—
183C2×Q8—82no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4C11×C22⋊C411yescharacteristic
187C22×C4C11×C22⋊C411yescharacteristic
188C22×C4C11×C22⋊C411yescharacteristic
189C22×C4C11×C22⋊C411yescharacteristic
190C22×C4C22×C4×C1111yescharacteristic
191C22×C4C2×D4×C1111yescharacteristic
192C22×C4C2×D4×C1111yescharacteristic
193M16—24no—
194M16—42no—
195C2×C8—42no—
196C2×C8—42no—
197C4⋊C4—24no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—82no—
205C4⋊C4—82no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—42no—
213C11#1179511yescharacteristic, direct product factor, Sylow
214C23C2×C11×C22⋊C411yescharacteristic
215Q8—44no—
216Q8—84no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—24no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4C11×#9911yescharacteristic
238C2×C4C11×#9911yescharacteristic
239C2×C4C11×#10412yes—
240C2×C4C11×#13712yes—
241C8—44no—
242C8—82no—
243C22—21no—
244C22—21no—
245C22C2×C11×#9911yescharacteristic
246C22C11×#41911yescharacteristic
247C22C2×C11×#10411yescharacteristic
248C4—21no—
249C4—22no—
250C4—22no—
251C4—44no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—41no—
256C4—82no—
257C4C11×#35612yes—
258C2—21no—
259C2—21no—
260C2C11×#150811yescharacteristic
261C2C11×#212211yescharacteristic
262C2C2×C11×#35611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC23×C11C2×C22⋊C4
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
48. #11795C11direct (N × H)
213. C11#11795direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25672
C4×C11×#1012
C11×#14672
C11×#13542
#1179511