Finite Group Databasebeta

← C11×#19073 #14596266

Subgroups — C11×#19073 #14596266

Order 2816.

1252 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3549C211yesmaximal, characteristic, complemented
2C11×#3151C213yesmaximal, complemented
3C11×#1655C218yesmaximal, complemented
4C11×#1525C213yesmaximal, complemented
5C2×C11×AGL(1,ℤ/8)—26no—
6C11×H(3,𝔽4)C2214yescomplemented
7C11×#555—23no—
8D42×C11—23no—
9C11×#535—26no—
10C11×#532C2213yes—
11C2×C11×#127C2211yescharacteristic, complemented
12C11×#496C22112yescomplemented
13C11×#493—23no—
14C11×#492—23no—
15C4×C11×M16C2213yescomplemented
16C11×#329C22112yescomplemented
17C2×C11×#41D416yes—
18C22×D4×C11—26no—
19C22×D4×C11—23no—
20C11×AGL(1,ℤ/8)—424no—
21C2×C11×SD16—212no—
22C2×C11×D8—212no—
23C2×C11×M16—23no—
24C11×C4⋊Q8D413yes—
25C11×#127—24no—
26C11×#127—23no—
27C11×#127D413yes—
28C11×#127C2312yes—
29C11×#124—212no—
30C11×#124C2316yes—
31C11×#121—212no—
32C11×#121—26no—
33C11×#120—24no—
34C11×#120—212no—
35C4×D4×C11—26no—
36C11×#117—26no—
37C2×C42×C11C2311yescharacteristic
38C11×#97C2316yes—
39C4×C8×C11—23no—
40#19073C1111yesmaximal, characteristic, direct product factor, Sylow
41C24×C11—24no—
42C24×C11—41no—
43C11×#41—412no—
44C2×Q8×C11C2×D416yes—
45C2×D4×C11—212no—
46C2×D4×C11—26no—
47C2×D4×C11—26no—
48C2×D4×C11—26no—
49C2×D4×C11—412no—
50C2×D4×C11—43no—
51C2×D4×C11—812no—
52C2×D4×C11C2×D416yes—
53C22×C4×C11—26no—
54C22×C4×C11C2×D413yes—
55C11×SD16—424no—
56C11×D8—424no—
57C11×M16—212no—
58C2×C8×C11—26no—
59C11×C4⋊C4—26no—
60C11×C22⋊C4—212no—
61C11×C22⋊C4—212no—
62C42×C11—24no—
63C42×C11C2×D413yes—
64C42×C11C2411yescharacteristic
65#3549C2×C1111yescharacteristic, complemented
66#3151C2×C1113yescomplemented
67#1655C2×C1118yescomplemented
68#1525C2×C1113yescomplemented
69C23×C11—26no—
70C23×C11—42no—
71C23×C11—86no—
72C23×C11—812no—
73C23×C11#12011yescharacteristic
74Q8×C11—46no—
75D4×C11—46no—
76D4×C11—412no—
77D4×C11—412no—
78D4×C11—86no—
79D4×C11—812no—
80D4×C11—86no—
81C2×C4×C11—26no—
82C2×C4×C11—26no—
83C2×C4×C11—412no—
84C2×C4×C11#12013yes—
85C2×C4×C11C22×D413yes—
86C8×C11—212no—
87C2×AGL(1,ℤ/8)—26no—
88H(3,𝔽4)C22×C1114yescomplemented
89#555—23no—
90D42—23no—
91#535—26no—
92#532C22×C1113yes—
93C2×#127C22×C1111yescharacteristic, complemented
94#496C22×C11112yescomplemented
95#493—23no—
96#492—23no—
97C4×M16C22×C1113yescomplemented
98#329C22×C11112yescomplemented
99C22×C11—23no—
100C22×C11—46no—
101C22×C11—412no—
102C22×C11—86no—
103C22×C11—164no—
104C22×C11—168no—
105C22×C11C2×#12011yescharacteristic
106C4×C11—23no—
107C4×C11—46no—
108C4×C11#45316yes—
109C2×#41D4×C1116yes—
110C22×D4—26no—
111C22×D4—23no—
112AGL(1,ℤ/8)—424no—
113C2×SD16—212no—
114C2×D8—212no—
115C2×M16—23no—
116C4⋊Q8D4×C1113yes—
117#127—24no—
118#127—23no—
119#127D4×C1113yes—
120#127C23×C1112yes—
121#124—212no—
122#124C23×C1116yes—
123#121—212no—
124#121—26no—
125#120—24no—
126#120—212no—
127C4×D4—26no—
128#117—26no—
129C2×C42C23×C1111yescharacteristic
130#97C23×C1116yes—
131C4×C8—23no—
132C2×C11—41no—
133C2×C11—86no—
134C2×C11—162no—
135C2×C11C2×#45313yes—
136C24—24no—
137C24—41no—
138#41—412no—
139C2×Q8C2×D4×C1116yes—
140C2×D4—212no—
141C2×D4—26no—
142C2×D4—26no—
143C2×D4—26no—
144C2×D4—412no—
145C2×D4—43no—
146C2×D4—812no—
147C2×D4C2×D4×C1116yes—
148C22×C4—26no—
149C22×C4C2×D4×C1113yes—
150SD16—424no—
151D8—424no—
152M16—212no—
153C2×C8—26no—
154C4⋊C4—26no—
155C22⋊C4—212no—
156C22⋊C4—212no—
157C42—24no—
158C42C2×D4×C1113yes—
159C42C24×C1111yescharacteristic
160C11#1907311yescharacteristic, direct product factor, Sylow
161C23—26no—
162C23—42no—
163C23—86no—
164C23—812no—
165C23C11×#12011yescharacteristic
166Q8—46no—
167D4—46no—
168D4—412no—
169D4—412no—
170D4—86no—
171D4—812no—
172D4—86no—
173C2×C4—26no—
174C2×C4—26no—
175C2×C4—412no—
176C2×C4C11×#12013yes—
177C2×C4C22×D4×C1113yes—
178C8—212no—
179C22—23no—
180C22—46no—
181C22—412no—
182C22—86no—
183C22—164no—
184C22—168no—
185C22C2×C11×#12011yescharacteristic
186C4—23no—
187C4—46no—
188C4C11×#45316yes—
189C2—41no—
190C2—86no—
191C2—162no—
192C2C2×C11×#45313yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ 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×#3549C2semidirect
2. C11×#3151C2semidirect
3. C11×#1655C2semidirect
4. C11×#1525C2semidirect
6. C11×H(3,𝔽4)C22semidirect
11. C2×C11×#127C22semidirect
12. C11×#496C22semidirect
15. C4×C11×M16C22semidirect
16. C11×#329C22semidirect
40. #19073C11direct (N × H)
65. #3549C2×C11semidirect
66. #3151C2×C11semidirect
67. #1655C2×C11semidirect
68. #1525C2×C11semidirect
88. H(3,𝔽4)C22×C11semidirect
93. C2×#127C22×C11semidirect
94. #496C22×C11semidirect
97. C4×M16C22×C11semidirect
98. #329C22×C11semidirect
160. C11#19073direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35492
C11×#31512
C11×#16552
C11×#15252
#1907311