Finite Group Databasebeta

← C11×#11782 #14588975

Subgroups — C11×#11782 #14588975

Order 2816.

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

normal subgroups only

This group has 414 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×#2546C211yesmaximal, characteristic
2C4×C11×#101C211yesmaximal, characteristic
3C11×#1467C211yesmaximal, characteristic
4C11×#1346C214yesmaximal
5C2×C11×C4⋊Q8—21no—
6C2×C11×C4⋊Q8C411yescharacteristic
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#432—21no—
9C2×C11×#101—21no—
10C4×C11×M16—21no—
11C11×#398C412yes—
12C11×#398C2212yes—
13C11×#391—21no—
14C11×#389—21no—
15C11×#389—21no—
16C4×C11×C4⋊C4C411yescharacteristic
17C11×#343C2212yes—
18C11×#324—21no—
19C11×#324C2212yes—
20C22×Q8×C11—21no—
21C22×Q8×C11D411yescharacteristic
22C2×C11×M16—22no—
23C11×C4⋊Q8—41no—
24C11×C4⋊Q8—41no—
25C11×C4⋊Q8—44no—
26C4×Q8×C11—41no—
27C4×Q8×C11—41no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C42×C11—21no—
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C11×C4⋊C8—41no—
41C11×#101—24no—
42C11×C22⋊C8—22no—
43C11×#97—41no—
44C11×#97—41no—
45C4×C8×C11—41no—
46C11×#95—22no—
47C11×#95—22no—
48C11×#95C2×C412yes—
49#11782C1111yesmaximal, characteristic, direct product factor, Sylow
50C2×Q8×C11—22no—
51C2×Q8×C11—22no—
52C2×Q8×C11—41no—
53C2×Q8×C11—42no—
54C2×Q8×C11—42no—
55C2×Q8×C11—42no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C11×M16—24no—
66C11×M16—42no—
67C2×C8×C11—42no—
68C2×C8×C11—42no—
69C11×C4⋊C4—24no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—44no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—44no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—42no—
85#2546C2×C1111yescharacteristic
86C4×#101C2×C1111yescharacteristic
87#1467C2×C1111yescharacteristic
88#1346C2×C1114yes—
89C23×C11C2×C22⋊C411yescharacteristic
90Q8×C11—44no—
91Q8×C11—84no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—24no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
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#9911yescharacteristic
113C2×C4×C11#9911yescharacteristic
114C2×C4×C11#10412yes—
115C2×C4×C11AGL(1,ℤ/8)12yes—
116C8×C11—44no—
117C8×C11—82no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8C4×C1111yescharacteristic
120C2×C4×Q8C22×C1111yescharacteristic
121#432—21no—
122C2×#101—21no—
123C4×M16—21no—
124#398C4×C1112yes—
125#398C22×C1112yes—
126#391—21no—
127#389—21no—
128#389—21no—
129C4×C4⋊C4C4×C1111yescharacteristic
130#343C22×C1112yes—
131#324—21no—
132#324C22×C1112yes—
133C22×C11—21no—
134C22×C11—21no—
135C22×C11C2×#9911yescharacteristic
136C22×C11#41811yescharacteristic
137C22×C11C2×#10411yescharacteristic
138C4×C11—21no—
139C4×C11—22no—
140C4×C11—22no—
141C4×C11—44no—
142C4×C11—41no—
143C4×C11—41no—
144C4×C11—41no—
145C4×C11—41no—
146C4×C11—82no—
147C4×C11#35612yes—
148C22×Q8—21no—
149C22×Q8D4×C1111yescharacteristic
150C2×M16—22no—
151C4⋊Q8—41no—
152C4⋊Q8—41no—
153C4⋊Q8—44no—
154C4×Q8—41no—
155C4×Q8—41no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4C2×C4×C1112yes—
161C2×C4⋊C4C2×C4×C1111yescharacteristic
162C2×C4⋊C4D4×C1111yescharacteristic
163C2×C4⋊C4C23×C1111yescharacteristic
164C2×C42—21no—
165C2×C42C2×C4×C1111yescharacteristic
166C2×C42D4×C1111yescharacteristic
167C2×C42D4×C1111yescharacteristic
168C4⋊C8—41no—
169#101—24no—
170C22⋊C8—22no—
171#97—41no—
172#97—41no—
173C4×C8—41no—
174#95—22no—
175#95—22no—
176#95C2×C4×C1112yes—
177C2×C11—21no—
178C2×C11—21no—
179C2×C11#150711yescharacteristic
180C2×C11#212311yescharacteristic
181C2×C11C2×#35611yescharacteristic
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—41no—
185C2×Q8—42no—
186C2×Q8—42no—
187C2×Q8—42no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4C11×C22⋊C411yescharacteristic
191C22×C4C11×C22⋊C411yescharacteristic
192C22×C4C11×C22⋊C411yescharacteristic
193C22×C4C11×C22⋊C411yescharacteristic
194C22×C4C22×C4×C1111yescharacteristic
195C22×C4C2×D4×C1111yescharacteristic
196C22×C4C2×D4×C1111yescharacteristic
197M16—24no—
198M16—42no—
199C2×C8—42no—
200C2×C8—42no—
201C4⋊C4—24no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—42no—
206C4⋊C4—44no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—44no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—42no—
217C11#1178211yescharacteristic, direct product factor, Sylow
218C23C2×C11×C22⋊C411yescharacteristic
219Q8—44no—
220Q8—84no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4C11×#9911yescharacteristic
242C2×C4C11×#9911yescharacteristic
243C2×C4C11×#10412yes—
244C2×C4C11×AGL(1,ℤ/8)12yes—
245C8—44no—
246C8—82no—
247C22—21no—
248C22—21no—
249C22C2×C11×#9911yescharacteristic
250C22C11×#41811yescharacteristic
251C22C2×C11×#10411yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—44no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—41no—
260C4—82no—
261C4C11×#35612yes—
262C2—21no—
263C2—21no—
264C2C11×#150711yescharacteristic
265C2C11×#212311yescharacteristic
266C2C2×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
49. #11782C11direct (N × H)
217. C11#11782direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25462
C4×C11×#1012
C11×#14672
C11×#13462
#1178211