Finite Group Databasebeta

← C11×#10302 #14587495

Subgroups — C11×#10302 #14587495

Order 2816.

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

normal subgroups only

This group has 516 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×#3255C211yesmaximal, characteristic, complemented
2C11×#3254C212yesmaximal
3C11×#1994C212yesmaximal, complemented
4C11×#1962C211yesmaximal, characteristic
5C11×#1309C211yesmaximal, characteristic, complemented
6C11×#533C2212yes—
7C11×#532C2211yescharacteristic
8C11×#477—22no—
9C11×#475—22no—
10C11×#474—22no—
11C11×#470—22no—
12C11×#468—24no—
13C11×#462—22no—
14C11×#461—22no—
15C11×#460—22no—
16C11×#423C2211yescharacteristic
17C11×#423C2212yes—
18C2×C11×#104—22no—
19C43×C11C2211yescharacteristic
20C11×#339—24no—
21C2×C11×#41—21no—
22C2×C11×Q16—22no—
23C2×C11×SD16—24no—
24C2×C11×M16D414yes—
25C2×C11×M16D412yes—
26C11×C4⋊Q8D411yescharacteristic
27C11×C4⋊Q8D412yes—
28C11×C4⋊Q8D412yes—
29C11×#127D411yescharacteristic
30C11×#125—22no—
31C11×#124—21no—
32C11×C22⋊Q8—22no—
33C11×C22⋊Q8—22no—
34C11×#121—22no—
35C4×Q8×C11—22no—
36C4×Q8×C11—22no—
37C4×D4×C11—22no—
38C11×#117—22no—
39C2×C42×C11—22no—
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C11×#107—24no—
43C11×#106—22no—
44C11×C4⋊C8—22no—
45C11×C4⋊C8—22no—
46C11×C4⋊C8—22no—
47C11×#104—44no—
48C11×#103—24no—
49C11×#103—24no—
50C11×#102—24no—
51#10302C1111yesmaximal, characteristic, direct product factor, Sylow
52C11×#41—42no—
53C11×#41—42no—
54C2×Q8×C11—22no—
55C2×Q8×C11—22no—
56C2×Q8×C11—21no—
57C2×D4×C11—22no—
58C2×D4×C11—21no—
59C2×D4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D412yes—
63C22×C4×C11C2×D411yescharacteristic
64C11×Q16—82no—
65C11×SD16—84no—
66C11×M16—42no—
67C11×M16—44no—
68C2×C8×C11—24no—
69C2×C8×C11—22no—
70C11×C4⋊C4—22no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C22⋊C4—42no—
78C11×C22⋊C4—42no—
79C42×C11—22no—
80C42×C11—24no—
81C42×C11—41no—
82C42×C11—42no—
83C42×C11—42no—
84C42×C11C2×D412yes—
85C42×C11C2×D411yescharacteristic
86C42×C11#4111yescharacteristic
87#3255C2×C1111yescharacteristic, complemented
88#3254C2×C1112yes—
89#1994C2×C1112yescomplemented
90#1962C2×C1111yescharacteristic
91#1309C2×C1111yescharacteristic, complemented
92C23×C11—41no—
93C23×C11#12711yescharacteristic
94Q8×C11—42no—
95Q8×C11—42no—
96Q8×C11—42no—
97Q8×C11—42no—
98Q8×C11—42no—
99D4×C11—42no—
100D4×C11—42no—
101D4×C11—42no—
102D4×C11—82no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—42no—
108C2×C4×C11—44no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—41no—
112C2×C4×C11—81no—
113C2×C4×C11—81no—
114C2×C4×C11#12011yescharacteristic
115C2×C4×C11#12012yes—
116C2×C4×C11#12112yes—
117C2×C4×C11#12111yescharacteristic
118C8×C11—42no—
119C8×C11—44no—
120#533C22×C1112yes—
121#532C22×C1111yescharacteristic
122#477—22no—
123#475—22no—
124#474—22no—
125#470—22no—
126#468—24no—
127#462—22no—
128#461—22no—
129#460—22no—
130#423C22×C1111yescharacteristic
131#423C22×C1112yes—
132C2×#104—22no—
133C43C22×C1111yescharacteristic
134#339—24no—
135C22×C11—21no—
136C22×C11—22no—
137C22×C11—81no—
138C22×C11—82no—
139C22×C11#39211yescharacteristic
140C4×C11—21no—
141C4×C11—22no—
142C4×C11—44no—
143C4×C11—81no—
144C4×C11—82no—
145C4×C11—82no—
146C4×C11#45311yescharacteristic
147C4×C11#45411yescharacteristic
148C4×C11#45512yes—
149C4×C11#45612yes—
150C2×#41—21no—
151C2×Q16—22no—
152C2×SD16—24no—
153C2×M16D4×C1114yes—
154C2×M16D4×C1112yes—
155C4⋊Q8D4×C1111yescharacteristic
156C4⋊Q8D4×C1112yes—
157C4⋊Q8D4×C1112yes—
158#127D4×C1111yescharacteristic
159#125—22no—
160#124—21no—
161C22⋊Q8—22no—
162C22⋊Q8—22no—
163#121—22no—
164C4×Q8—22no—
165C4×Q8—22no—
166C4×D4—22no—
167#117—22no—
168C2×C42—22no—
169C2×C42—21no—
170C2×C42C23×C1111yescharacteristic
171#107—24no—
172#106—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176#104—44no—
177#103—24no—
178#103—24no—
179#102—24no—
180C2×C11—41no—
181C2×C11—161no—
182C2×C11#200611yescharacteristic
183C2×C11#200712yes—
184#41—42no—
185#41—42no—
186C2×Q8—22no—
187C2×Q8—22no—
188C2×Q8—21no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4C2×D4×C1112yes—
195C22×C4C2×D4×C1111yescharacteristic
196Q16—82no—
197SD16—84no—
198M16—42no—
199M16—44no—
200C2×C8—24no—
201C2×C8—22no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C22⋊C4—42no—
210C22⋊C4—42no—
211C42—22no—
212C42—24no—
213C42—41no—
214C42—42no—
215C42—42no—
216C42C2×D4×C1112yes—
217C42C2×D4×C1111yescharacteristic
218C42C11×#4111yescharacteristic
219C11#1030211yescharacteristic, direct product factor, Sylow
220C23—41no—
221C23C11×#12711yescharacteristic
222Q8—42no—
223Q8—42no—
224Q8—42no—
225Q8—42no—
226Q8—42no—
227D4—42no—
228D4—42no—
229D4—42no—
230D4—82no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—42no—
236C2×C4—44no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4C11×#12011yescharacteristic
243C2×C4C11×#12012yes—
244C2×C4C11×#12112yes—
245C2×C4C11×#12111yescharacteristic
246C8—42no—
247C8—44no—
248C22—21no—
249C22—22no—
250C22—81no—
251C22—82no—
252C22C11×#39211yescharacteristic
253C4—21no—
254C4—22no—
255C4—44no—
256C4—81no—
257C4—82no—
258C4—82no—
259C4C11×#45311yescharacteristic
260C4C11×#45411yescharacteristic
261C4C11×#45512yes—
262C4C11×#45612yes—
263C2—41no—
264C2—161no—
265C2C11×#200611yescharacteristic
266C2C11×#200712yes—
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3255C2semidirect
3. C11×#1994C2semidirect
5. C11×#1309C2semidirect
51. #10302C11direct (N × H)
87. #3255C2×C11semidirect
89. #1994C2×C11semidirect
91. #1309C2×C11semidirect
219. C11#10302direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32552
C11×#32542
C11×#19942
C11×#19622
C11×#13092
#1030211