Finite Group Databasebeta

← C11×#10390 #14587583

Subgroups — C11×#10390 #14587583

Order 2816.

762 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2840C211yesmaximal, characteristic, complemented
2C11×#1781C213yesmaximal
3C11×#1304C213yesmaximal, complemented
4C23×D4×C11C2211yescharacteristic
5C2×C11×#99—26no—
6C11×#393—26no—
7C11×#379C2213yes—
8C11×#379C2213yes—
9C25×C11Q811yescharacteristic, complemented
10C25×C11C2311yescharacteristic
11C22×Q8×C11—22no—
12C22×D4×C11—23no—
13C22×D4×C11—23no—
14C22×D4×C11—44no—
15C23×C4×C11Q811yescharacteristic, complemented
16C2×C11×C22⋊C4—23no—
17C2×C11×C22⋊C4—26no—
18C2×C11×C22⋊C4—26no—
19C2×C11×C22⋊C4D416yes—
20C11×#99—412no—
21C11×#95—26no—
22#10390C1111yesmaximal, characteristic, direct product factor, Sylow
23C24×C11—23no—
24C24×C11—42no—
25C24×C11—42no—
26C24×C11—82no—
27C24×C11—82no—
28C24×C11C2×D413yes—
29C24×C11C2×Q811yescharacteristic
30C24×C11#4113yes—
31C2×Q8×C11—84no—
32C2×Q8×C11—82no—
33C2×D4×C11—212no—
34C2×D4×C11—46no—
35C2×D4×C11—46no—
36C2×D4×C11—46no—
37C2×D4×C11—41no—
38C2×D4×C11—43no—
39C22×C4×C11—23no—
40C22×C4×C11—26no—
41C22×C4×C11—42no—
42C22×C4×C11—43no—
43C11×C22⋊C4—46no—
44C11×C22⋊C4—46no—
45C11×C22⋊C4—86no—
46C11×C22⋊C4—86no—
47#2840C2×C1111yescharacteristic, complemented
48#1781C2×C1113yes—
49#1304C2×C1113yescomplemented
50C23×C11—26no—
51C23×C11—26no—
52C23×C11—41no—
53C23×C11—42no—
54C23×C11—46no—
55C23×C11—46no—
56C23×C11—43no—
57C23×C11—43no—
58C23×C11—41no—
59C23×C11—86no—
60C23×C11—88no—
61C23×C11—88no—
62C23×C11#12011yescharacteristic
63C23×C11C22⋊Q813yes—
64C23×C11#12413yes—
65Q8×C11—88no—
66D4×C11—412no—
67D4×C11—44no—
68C2×C4×C11—26no—
69C2×C4×C11—43no—
70C2×C4×C11—41no—
71C2×C4×C11—412no—
72C2×C4×C11—46no—
73C2×C4×C11—83no—
74C2×C4×C11—86no—
75C23×D4C22×C1111yescharacteristic
76C2×#99—26no—
77#393—26no—
78#379C22×C1113yes—
79#379C22×C1113yes—
80C22×C11—22no—
81C22×C11—23no—
82C22×C11—23no—
83C22×C11—26no—
84C22×C11—26no—
85C22×C11—44no—
86C22×C11—42no—
87C22×C11—86no—
88C22×C11—86no—
89C22×C11—86no—
90C22×C11—86no—
91C22×C11—82no—
92C22×C11#39311yescharacteristic
93C22×C11B(4,𝔽2)12yes—
94C4×C11—42no—
95C4×C11—86no—
96C4×C11—163no—
97C25Q8×C1111yescharacteristic, complemented
98C25C23×C1111yescharacteristic
99C22×Q8—22no—
100C22×D4—23no—
101C22×D4—23no—
102C22×D4—44no—
103C23×C4Q8×C1111yescharacteristic, complemented
104C2×C22⋊C4—23no—
105C2×C22⋊C4—26no—
106C2×C22⋊C4—26no—
107C2×C22⋊C4D4×C1116yes—
108#99—412no—
109#95—26no—
110C2×C11—22no—
111C2×C11—43no—
112C2×C11—43no—
113C2×C11—82no—
114C2×C11#202911yescharacteristic
115C2×C11#203212yes—
116C24—23no—
117C24—42no—
118C24—42no—
119C24—82no—
120C24—82no—
121C24C2×D4×C1113yes—
122C24C2×Q8×C1111yescharacteristic
123C24C11×#4113yes—
124C2×Q8—84no—
125C2×Q8—82no—
126C2×D4—212no—
127C2×D4—46no—
128C2×D4—46no—
129C2×D4—46no—
130C2×D4—41no—
131C2×D4—43no—
132C22×C4—23no—
133C22×C4—26no—
134C22×C4—42no—
135C22×C4—43no—
136C22⋊C4—46no—
137C22⋊C4—46no—
138C22⋊C4—86no—
139C22⋊C4—86no—
140C11#1039011yescharacteristic, direct product factor, Sylow
141C23—26no—
142C23—26no—
143C23—41no—
144C23—42no—
145C23—46no—
146C23—46no—
147C23—43no—
148C23—43no—
149C23—41no—
150C23—86no—
151C23—88no—
152C23—88no—
153C23C11×#12011yescharacteristic
154C23C11×C22⋊Q813yes—
155C23C11×#12413yes—
156Q8—88no—
157D4—412no—
158D4—44no—
159C2×C4—26no—
160C2×C4—43no—
161C2×C4—41no—
162C2×C4—412no—
163C2×C4—46no—
164C2×C4—83no—
165C2×C4—86no—
166C22—22no—
167C22—23no—
168C22—23no—
169C22—26no—
170C22—26no—
171C22—44no—
172C22—42no—
173C22—86no—
174C22—86no—
175C22—86no—
176C22—86no—
177C22—82no—
178C22C11×#39311yescharacteristic
179C22C11×B(4,𝔽2)12yes—
180C4—42no—
181C4—86no—
182C4—163no—
183C2—22no—
184C2—43no—
185C2—43no—
186C2—82no—
187C2C11×#202911yescharacteristic
188C2C11×#203212yes—
subgroupG/H
center, socleC22×C11#393
commutator, Frattini, cosocleC25C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2840C2semidirect
3. C11×#1304C2semidirect
9. C25×C11Q8semidirect
15. C23×C4×C11Q8semidirect
22. #10390C11direct (N × H)
47. #2840C2×C11semidirect
49. #1304C2×C11semidirect
97. C25Q8×C11semidirect
103. C23×C4Q8×C11semidirect
140. C11#10390direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28402
C11×#17812
C11×#13042
#1039011