Finite Group Databasebeta

← C11×#13306 #14590499

Subgroups — C11×#13306 #14590499

Order 2816.

566 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C22×C11×Q32C211yesmaximal, characteristic, complemented
2C2×C11×#467C212yesmaximal
3C2×C11×#358C212yesmaximal, complemented
4C2×C11×C22⋊C16C211yesmaximal, characteristic
5C11×#1380C211yesmaximal, characteristic, complemented
6C22×C11×Q16C2212yes—
7C23×C8×C11C2211yescharacteristic
8C2×C11×C22⋊Q8—22no—
9C2×C11×Q32—24no—
10C2×C11×Q32—22no—
11C22×C11×C16C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C11×#467—24no—
14C11×#467—24no—
15C2×C11×#107C2212yes—
16C2×C11×#103—22no—
17C11×#358—24no—
18C11×C22⋊C16—22no—
19C22×Q8×C11—22no—
20C23×C4×C11D411yescharacteristic
21C2×C11×Q16—22no—
22C2×C11×Q16—22no—
23C2×C11×Q16—22no—
24C2×C11×Q16—22no—
25C2×C11×Q16—22no—
26C2×C11×Q16D414yes—
27C22×C8×C11—21no—
28C22×C8×C11—22no—
29C22×C8×C11—22no—
30C22×C8×C11—21no—
31C22×C8×C11D411yescharacteristic
32C22×C8×C11C2311yescharacteristic
33C11×C22⋊Q8—28no—
34C11×C22⋊Q8—44no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—42no—
37C2×C11×C22⋊C4—42no—
38C11×Q32—28no—
39C2×C11×C16—22no—
40C2×C11×C16—21no—
41C2×C11×C16—22no—
42C2×C11×C16D412yes—
43C11×#107—22no—
44C11×#107D414yes—
45C11×#103—28no—
46#13306C1111yesmaximal, characteristic, direct product factor, Sylow
47C24×C11D811yescharacteristic
48C2×Q8×C11—24no—
49C2×Q8×C11—42no—
50C2×Q8×C11—42no—
51C2×Q8×C11—42no—
52C2×Q8×C11—42no—
53C2×Q8×C11—42no—
54C22×C4×C11—22no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11D811yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C11×Q16—24no—
63C11×Q16—24no—
64C11×Q16—42no—
65C11×Q16—42no—
66C2×C8×C11—22no—
67C2×C8×C11—21no—
68C2×C8×C11—41no—
69C2×C8×C11—42no—
70C2×C8×C11—41no—
71C2×C8×C11C2×D412yes—
72C2×C8×C11C2×D412yes—
73C2×C8×C11C2×D411yescharacteristic
74C2×C8×C11#4111yescharacteristic
75C11×C4⋊C4—24no—
76C11×C4⋊C4—48no—
77C11×C4⋊C4—42no—
78C11×C22⋊C4—48no—
79C11×C16—22no—
80C11×C16—41no—
81C22×Q32C2×C1111yescharacteristic, complemented
82C2×#467C2×C1112yes—
83C2×#358C2×C1112yescomplemented
84C2×C22⋊C16C2×C1111yescharacteristic
85#1380C2×C1111yescharacteristic, complemented
86C23×C11—22no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—22no—
90C23×C11Q3212yescomplemented
91C23×C11C2×D811yescharacteristic
92Q8×C11—44no—
93Q8×C11—44no—
94Q8×C11—82no—
95Q8×C11—82no—
96C2×C4×C11—22no—
97C2×C4×C11—21no—
98C2×C4×C11—41no—
99C2×C4×C11—42no—
100C2×C4×C11—41no—
101C2×C4×C11—44no—
102C2×C4×C11—44no—
103C2×C4×C11—82no—
104C2×C4×C11—82no—
105C2×C4×C11—82no—
106C2×C4×C11—82no—
107C2×C4×C11#12012yes—
108C2×C4×C11#12111yescharacteristic
109C2×C4×C11#13511yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)12yes—
111C8×C11—41no—
112C8×C11#12011yescharacteristic
113C8×C11#12112yes—
114C8×C11#12711yescharacteristic
115C22×Q16C22×C1112yes—
116C23×C8C22×C1111yescharacteristic
117C2×C22⋊Q8—22no—
118C2×Q32—24no—
119C2×Q32—22no—
120C22×C16C22×C1111yescharacteristic
121C22×C16C22×C1111yescharacteristic
122#467—24no—
123#467—24no—
124C2×#107C22×C1112yes—
125C2×#103—22no—
126#358—24no—
127C22⋊C16—22no—
128C22×C11—24no—
129C22×C11—22no—
130C22×C11—42no—
131C22×C11—41no—
132C22×C11—41no—
133C22×C11#44712yes—
134C22×C11#46611yescharacteristic
135C22×C11C2×Q3211yescharacteristic
136C22×C11#50811yescharacteristic
137C22×C11#51012yes—
138C4×C11—41no—
139C4×C11—84no—
140C4×C11—84no—
141C4×C11#39211yescharacteristic
142C4×C11#44912yes—
143C4×C11#46911yescharacteristic
144C22×Q8—22no—
145C23×C4D4×C1111yescharacteristic
146C2×Q16—22no—
147C2×Q16—22no—
148C2×Q16—22no—
149C2×Q16—22no—
150C2×Q16—22no—
151C2×Q16D4×C1114yes—
152C22×C8—21no—
153C22×C8—22no—
154C22×C8—22no—
155C22×C8—21no—
156C22×C8D4×C1111yescharacteristic
157C22×C8C23×C1111yescharacteristic
158C22⋊Q8—28no—
159C22⋊Q8—44no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—42no—
162C2×C22⋊C4—42no—
163Q32—28no—
164C2×C16—22no—
165C2×C16—21no—
166C2×C16—22no—
167C2×C16D4×C1112yes—
168#107—22no—
169#107D4×C1114yes—
170#103—28no—
171C2×C11—42no—
172C2×C11#199911yescharacteristic
173C2×C11#218812yes—
174C2×C11#218912yes—
175C2×C11#221611yescharacteristic
176C2×C11#221911yescharacteristic
177C24C11×D811yescharacteristic
178C2×Q8—24no—
179C2×Q8—42no—
180C2×Q8—42no—
181C2×Q8—42no—
182C2×Q8—42no—
183C2×Q8—42no—
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4C11×D811yescharacteristic
191C22×C4C2×D4×C1111yescharacteristic
192Q16—24no—
193Q16—24no—
194Q16—42no—
195Q16—42no—
196C2×C8—22no—
197C2×C8—21no—
198C2×C8—41no—
199C2×C8—42no—
200C2×C8—41no—
201C2×C8C2×D4×C1112yes—
202C2×C8C2×D4×C1111yescharacteristic
203C2×C8C2×D4×C1112yes—
204C2×C8C11×#4111yescharacteristic
205C4⋊C4—24no—
206C4⋊C4—48no—
207C4⋊C4—42no—
208C22⋊C4—48no—
209C16—22no—
210C16—41no—
211C11#1330611yescharacteristic, direct product factor, Sylow
212C23—21no—
213C23—22no—
214C23—22no—
215C23—21no—
216C23C11×Q3212yescomplemented
217C23C2×C11×D811yescharacteristic
218Q8—44no—
219Q8—44no—
220Q8—82no—
221Q8—82no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—44no—
228C2×C4—44no—
229C2×C4—82no—
230C2×C4—82no—
231C2×C4—82no—
232C2×C4—82no—
233C2×C4C11×#12012yes—
234C2×C4C11×#12111yescharacteristic
235C2×C4C11×#13511yescharacteristic
236C2×C4C11×AGL(1,ℤ/8)12yes—
237C8—41no—
238C8C11×#12011yescharacteristic
239C8C11×#12112yes—
240C8C11×#12711yescharacteristic
241C22—24no—
242C22—22no—
243C22—42no—
244C22—41no—
245C22—41no—
246C22C11×#44712yes—
247C22C11×#46611yescharacteristic
248C22C2×C11×Q3211yescharacteristic
249C22C11×#50811yescharacteristic
250C22C11×#51012yes—
251C4—41no—
252C4—84no—
253C4—84no—
254C4C11×#39211yescharacteristic
255C4C11×#44912yes—
256C4C11×#46911yescharacteristic
257C2—42no—
258C2C11×#199911yescharacteristic
259C2C11×#218812yes—
260C2C11×#218912yes—
261C2C11×#221611yescharacteristic
262C2C11×#221911yescharacteristic
subgroupG/H
center, socleC23×C11C2×D8
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC24×C11D8
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×Q32C2semidirect
3. C2×C11×#358C2semidirect
5. C11×#1380C2semidirect
46. #13306C11direct (N × H)
81. C22×Q32C2×C11semidirect
83. C2×#358C2×C11semidirect
85. #1380C2×C11semidirect
90. C23×C11Q32semidirect
211. C11#13306direct (N × H)
216. C23C11×Q32semidirect

Maximal subgroups

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

subgroupindex
C22×C11×Q322
C2×C11×#4672
C2×C11×#3582
C2×C11×C22⋊C162
C11×#13802
#1330611