Finite Group Databasebeta

← C11×#13301 #14590494

Subgroups — C11×#13301 #14590494

Order 2816.

404 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2568C211yesmaximal, characteristic
2C11×#1801C211yesmaximal, characteristic
3C4×C11×#101C211yesmaximal, characteristic
4C11×#1394C214yesmaximal
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C11×#423—21no—
8C2×C11×#101C2212yes—
9C2×C11×#101C2212yes—
10C4×C11×M16—21no—
11C11×#400—21no—
12C11×#400—21no—
13C11×#391—21no—
14C11×#391—21no—
15C11×#391C2212yes—
16C11×#382C412yes—
17C4×C11×C4⋊C4C411yescharacteristic
18C11×#343—21no—
19C11×#343—21no—
20C22×Q8×C11—21no—
21C22×Q8×C11C2311yescharacteristic
22C2×C11×M16—22no—
23C2×C11×M16—22no—
24C11×C4⋊Q8—41no—
25C11×C4⋊Q8—41no—
26C4×Q8×C11—41no—
27C4×Q8×C11—41no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4C2×C412yes—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2×C412yes—
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C11×C4⋊C8—41no—
39C11×C4⋊C8—41no—
40C11×#101—22no—
41C11×#101—24no—
42C11×#101Q814yescomplemented
43C11×#97—41no—
44C4×C8×C11—41no—
45C11×#95—21no—
46C11×#95—22no—
47C11×#95—22no—
48C11×#95—22no—
49C11×#95—22no—
50#13301C1111yesmaximal, characteristic, direct product factor, Sylow
51C2×Q8×C11—41no—
52C2×Q8×C11—41no—
53C2×Q8×C11—44no—
54C2×Q8×C11—41no—
55C2×Q8×C11—41no—
56C2×Q8×C11C2×Q812yes—
57C2×Q8×C11#4112yes—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C11×M16—24no—
68C11×M16—42no—
69C11×M16—42no—
70C11×M16—42no—
71C2×C8×C11—42no—
72C2×C8×C11—42no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—42no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—42no—
86#2568C2×C1111yescharacteristic
87#1801C2×C1111yescharacteristic
88C4×#101C2×C1111yescharacteristic
89#1394C2×C1114yes—
90C23×C11C2×C22⋊C411yescharacteristic
91Q8×C11—42no—
92Q8×C11—42no—
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—22no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—44no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11#9911yescharacteristic
114C2×C4×C11#9911yescharacteristic
115C2×C4×C11C4×Q812yes—
116C2×C4×C11C22⋊Q812yes—
117C2×C4×C11#12411yescharacteristic
118C2×C4×C11C4⋊Q811yescharacteristic
119C8×C11—44no—
120C8×C11—82no—
121C2×C4⋊Q8C4×C1111yescharacteristic
122C2×C4×Q8C22×C1111yescharacteristic
123#423—21no—
124C2×#101C22×C1112yes—
125C2×#101C22×C1112yes—
126C4×M16—21no—
127#400—21no—
128#400—21no—
129#391—21no—
130#391—21no—
131#391C22×C1112yes—
132#382C4×C1112yes—
133C4×C4⋊C4C4×C1111yescharacteristic
134#343—21no—
135#343—21no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11#39111yescharacteristic
139C22×C11C2×#9911yescharacteristic
140C22×C11#41011yescharacteristic
141C4×C11—21no—
142C4×C11—22no—
143C4×C11—22no—
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—41no—
147C4×C11—41no—
148C4×C11—41no—
149C4×C11—82no—
150C4×C11—82no—
151C4×C11#35512yes—
152C22×Q8—21no—
153C22×Q8C23×C1111yescharacteristic
154C2×M16—22no—
155C2×M16—22no—
156C4⋊Q8—41no—
157C4⋊Q8—41no—
158C4×Q8—41no—
159C4×Q8—41no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C2×C4×C1112yes—
163C2×C4⋊C4C2×C4×C1111yescharacteristic
164C2×C4⋊C4D4×C1111yescharacteristic
165C2×C4⋊C4D4×C1111yescharacteristic
166C2×C42C2×C4×C1111yescharacteristic
167C2×C42C2×C4×C1112yes—
168C2×C42D4×C1111yescharacteristic
169C2×C42D4×C1111yescharacteristic
170C4⋊C8—41no—
171C4⋊C8—41no—
172#101—22no—
173#101—24no—
174#101Q8×C1114yescomplemented
175#97—41no—
176C4×C8—41no—
177#95—21no—
178#95—22no—
179#95—22no—
180#95—22no—
181#95—22no—
182C2×C11—21no—
183C2×C11—21no—
184C2×C11#199611yescharacteristic
185C2×C11C2×#35511yescharacteristic
186C2×C11#213511yescharacteristic
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8—44no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8C2×Q8×C1112yes—
193C2×Q8C11×#4112yes—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4C11×C22⋊C411yescharacteristic
197C22×C4C11×C22⋊C411yescharacteristic
198C22×C4C11×C22⋊C411yescharacteristic
199C22×C4C11×C22⋊C411yescharacteristic
200C22×C4C22×C4×C1111yescharacteristic
201C22×C4C2×D4×C1111yescharacteristic
202C22×C4C2×D4×C1111yescharacteristic
203M16—24no—
204M16—42no—
205M16—42no—
206M16—42no—
207C2×C8—42no—
208C2×C8—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—42no—
222C11#1330111yescharacteristic, direct product factor, Sylow
223C23C2×C11×C22⋊C411yescharacteristic
224Q8—42no—
225Q8—42no—
226Q8—82no—
227Q8—82no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4C11×#9911yescharacteristic
247C2×C4C11×#9911yescharacteristic
248C2×C4C4×Q8×C1112yes—
249C2×C4C11×C22⋊Q812yes—
250C2×C4C11×#12411yescharacteristic
251C2×C4C11×C4⋊Q811yescharacteristic
252C8—44no—
253C8—82no—
254C22—21no—
255C22—21no—
256C22C11×#39111yescharacteristic
257C22C2×C11×#9911yescharacteristic
258C22C11×#41011yescharacteristic
259C4—21no—
260C4—22no—
261C4—21no—
262C4—22no—
263C4—21no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—82no—
268C4—82no—
269C4C11×#35512yes—
270C2—21no—
271C2—21no—
272C2C11×#199611yescharacteristic
273C2C2×C11×#35511yescharacteristic
274C2C11×#213511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC22×Q8C23×C11
prime radicalC23×C11C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ 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
42. C11×#101Q8semidirect
50. #13301C11direct (N × H)
174. #101Q8×C11semidirect
222. C11#13301direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25682
C11×#18012
C4×C11×#1012
C11×#13942
#1330111