Finite Group Databasebeta

← C11×#23566 #14600759

Subgroups — C11×#23566 #14600759

Order 2816.

1118 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 366 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×#3458C211yesmaximal, characteristic
2C11×#2317C213yesmaximal
3C11×#2062C218yesmaximal
4C11×#1740C213yesmaximal
5C11×#544—23no—
6C11×#544—23no—
7C11×#543C2214yes—
8C11×#533—26no—
9C2×C11×#117C2213yes—
10C2×C11×#117C2213yes—
11C22×C11×C4⋊C4C2211yescharacteristic
12C11×#389—26no—
13C11×#385C22112yes—
14C11×#384—23no—
15C11×#382—23no—
16C11×#342C22112yes—
17C23×C4×C11C2312yes—
18C23×C4×C11C2311yescharacteristic
19C11×C4⋊Q8—26no—
20C11×C4⋊Q8—26no—
21C11×#125—212no—
22C11×C22⋊Q8—212no—
23C11×C22⋊Q8—212no—
24C4×Q8×C11—24no—
25C4×Q8×C11—24no—
26C11×#117—26no—
27C11×#117—26no—
28C11×#117—26no—
29C11×#117Q8112yescomplemented
30C2×C11×C4⋊C4—23no—
31C2×C11×C4⋊C4—23no—
32C2×C11×C4⋊C4—23no—
33C2×C11×C4⋊C4—212no—
34C2×C11×C4⋊C4D413yes—
35C2×C11×C4⋊C4D413yes—
36C2×C11×C22⋊C4C2316yes—
37C2×C11×C22⋊C4C2316yes—
38C2×C42×C11—23no—
39C2×C42×C11D416yes—
40C11×#95—212no—
41#23566C1111yesmaximal, characteristic, direct product factor, Sylow
42C24×C11C2411yescharacteristic
43C2×Q8×C11—24no—
44C2×Q8×C11—24no—
45C22×C4×C11—26no—
46C22×C4×C11—26no—
47C22×C4×C11—82no—
48C22×C4×C11C2×D416yes—
49C22×C4×C11C2×D416yes—
50C22×C4×C11C2×D413yes—
51C22×C4×C11C2×D413yes—
52C22×C4×C11C2×Q816yes—
53C22×C4×C11#4112yes—
54C11×C4⋊C4—212no—
55C11×C4⋊C4—212no—
56C11×C4⋊C4—26no—
57C11×C4⋊C4—26no—
58C11×C4⋊C4—212no—
59C11×C4⋊C4—41no—
60C11×C4⋊C4—43no—
61C11×C4⋊C4—812no—
62C11×C22⋊C4—212no—
63C11×C22⋊C4—26no—
64C11×C22⋊C4C2×Q8112yes—
65C42×C11—26no—
66C42×C11—26no—
67C42×C11—212no—
68#3458C2×C1111yescharacteristic
69#2317C2×C1113yes—
70#2062C2×C1118yes—
71#1740C2×C1113yes—
72C23×C11—41no—
73C23×C11—41no—
74C23×C11C22×D413yes—
75C23×C11C22×Q813yes—
76C23×C11C2×#4111yescharacteristic
77Q8×C11—84no—
78Q8×C11—84no—
79C2×C4×C11—26no—
80C2×C4×C11—26no—
81C2×C4×C11—212no—
82C2×C4×C11—46no—
83C2×C4×C11—46no—
84C2×C4×C11—46no—
85C2×C4×C11—46no—
86C2×C4×C11—412no—
87C2×C4×C11—42no—
88C2×C4×C11#12011yescharacteristic
89C2×C4×C11#12013yes—
90C2×C4×C11C22⋊Q816yes—
91C2×C4×C11C22⋊Q816yes—
92C2×C4×C11C4⋊Q816yes—
93C2×C4×C11C4⋊Q816yes—
94#544—23no—
95#544—23no—
96#543C22×C1114yes—
97#533—26no—
98C2×#117C22×C1113yes—
99C2×#117C22×C1113yes—
100C22×C4⋊C4C22×C1111yescharacteristic
101#389—26no—
102#385C22×C11112yes—
103#384—23no—
104#382—23no—
105#342C22×C11112yes—
106C22×C11—23no—
107C22×C11—23no—
108C22×C11—43no—
109C22×C11—41no—
110C22×C11C2×#12011yescharacteristic
111C22×C11C2×C22⋊Q813yes—
112C22×C11C2×C4⋊Q813yes—
113C4×C11—412no—
114C4×C11—46no—
115C4×C11—46no—
116C4×C11—82no—
117C4×C11#39512yes—
118C4×C11#39516yes—
119C23×C4C23×C1112yes—
120C23×C4C23×C1111yescharacteristic
121C4⋊Q8—26no—
122C4⋊Q8—26no—
123#125—212no—
124C22⋊Q8—212no—
125C22⋊Q8—212no—
126C4×Q8—24no—
127C4×Q8—24no—
128#117—26no—
129#117—26no—
130#117—26no—
131#117Q8×C11112yescomplemented
132C2×C4⋊C4—23no—
133C2×C4⋊C4—23no—
134C2×C4⋊C4—23no—
135C2×C4⋊C4—212no—
136C2×C4⋊C4D4×C1113yes—
137C2×C4⋊C4D4×C1113yes—
138C2×C22⋊C4C23×C1116yes—
139C2×C22⋊C4C23×C1116yes—
140C2×C42—23no—
141C2×C42D4×C1116yes—
142#95—212no—
143C2×C11—23no—
144C2×C11—23no—
145C2×C11C2×#39511yescharacteristic
146C2×C11#302711yescharacteristic
147C2×C11#302811yescharacteristic
148C24C24×C1111yescharacteristic
149C2×Q8—24no—
150C2×Q8—24no—
151C22×C4—26no—
152C22×C4—26no—
153C22×C4—82no—
154C22×C4C2×D4×C1116yes—
155C22×C4C2×D4×C1116yes—
156C22×C4C2×D4×C1113yes—
157C22×C4C2×D4×C1113yes—
158C22×C4C2×Q8×C1116yes—
159C22×C4C11×#4112yes—
160C4⋊C4—212no—
161C4⋊C4—212no—
162C4⋊C4—26no—
163C4⋊C4—26no—
164C4⋊C4—212no—
165C4⋊C4—41no—
166C4⋊C4—43no—
167C4⋊C4—812no—
168C22⋊C4—212no—
169C22⋊C4—26no—
170C22⋊C4C2×Q8×C11112yes—
171C42—26no—
172C42—26no—
173C42—212no—
174C11#2356611yescharacteristic, direct product factor, Sylow
175C23—41no—
176C23—41no—
177C23C22×D4×C1113yes—
178C23C22×Q8×C1113yes—
179C23C2×C11×#4111yescharacteristic
180Q8—84no—
181Q8—84no—
182C2×C4—26no—
183C2×C4—26no—
184C2×C4—212no—
185C2×C4—46no—
186C2×C4—46no—
187C2×C4—46no—
188C2×C4—46no—
189C2×C4—412no—
190C2×C4—42no—
191C2×C4C11×#12011yescharacteristic
192C2×C4C11×#12013yes—
193C2×C4C11×C22⋊Q816yes—
194C2×C4C11×C22⋊Q816yes—
195C2×C4C11×C4⋊Q816yes—
196C2×C4C11×C4⋊Q816yes—
197C22—23no—
198C22—23no—
199C22—43no—
200C22—41no—
201C22C2×C11×#12011yescharacteristic
202C22C2×C11×C22⋊Q813yes—
203C22C2×C11×C4⋊Q813yes—
204C4—412no—
205C4—46no—
206C4—46no—
207C4—82no—
208C4C11×#39512yes—
209C4C11×#39516yes—
210C2—23no—
211C2—23no—
212C2C2×C11×#39511yescharacteristic
213C2C11×#302711yescharacteristic
214C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
prime radicalC24×C11C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
29. C11×#117Q8semidirect
41. #23566C11direct (N × H)
131. #117Q8×C11semidirect
174. C11#23566direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34582
C11×#23172
C11×#20622
C11×#17402
#2356611