Finite Group Databasebeta

← #19142858

Subgroups — #19142858

Order 5504.

548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#14582836C211yesmaximal, characteristic, complemented
2#14582834C213yesmaximal, complemented
3#14582823C211yesmaximal, characteristic, complemented
4#14582822C213yesmaximal, complemented
5#14582821C213yesmaximal, complemented
6#14582754C213yesmaximal
7C43×#396C211yesmaximal, characteristic, complemented
8C24×D43C2211yescharacteristic
9C2×C4⋊Dic43C2213yescomplemented
10C2×Dic43⋊C4C2213yescomplemented
11C2×Dic43⋊C4C2213yescomplemented
12C2×C22⋊Dic43C2213yes—
13C2×(C2×D43)⋊C4C2213yes—
14C2×(C2×D43)⋊C4C2213yes—
15C2×(C2×D43)⋊C4C2213yes—
16C2×(C2×D43)⋊C4C2213yes—
17C43⋊#95C2213yescomplemented
18C2×C4⋊C4×C43C2213yescomplemented
19C2×C22⋊C4×C43C2213yes—
20#95×C43C2211yescharacteristic, complemented
21C24×C43C2311yescharacteristic
22C23×D43—43no—
23C23×D43—43no—
24C23×D43Q814yes—
25C23×D43C2311yescharacteristic
26C23×D43C2311yescharacteristic
27C22×C4×C43C2313yes—
28C22×C4×C43C2313yes—
29C22×Dic43C2313yes—
30C22×Dic43C2313yes—
31C4⋊C4×C43—43no—
32C22⋊C4×C43—43no—
33C22⋊Dic43—43no—
34(C2×D43)⋊C4—43no—
35(C2×D43)⋊C4—43no—
36(C2×D43)⋊C4—43no—
37(C2×D43)⋊C4—43no—
38C4⋊Dic43—43no—
39Dic43⋊C4—43no—
40Dic43⋊C4—43no—
41C23×C43—23no—
42C23×C43—23no—
43C23×C43C2×Q812yes—
44C23×C43C2411yescharacteristic
45C22×D43—23no—
46C22×D43—23no—
47C22×D43—23no—
48C22×D43—23no—
49C22×D43—412no—
50C22×D43—412no—
51C22×D43—44no—
52C22×D43C2×Q812yes—
53C22×D43C2×Q812yes—
54C2×C4×C43—23no—
55C2×C4×C43—23no—
56C2×C4×C43—23no—
57C2×C4×C43—23no—
58C2×C4×C43—23no—
59C2×C4×C43—23no—
60C2×Dic43—23no—
61C2×Dic43—23no—
62C2×Dic43—23no—
63C2×Dic43—23no—
64C2×Dic43—23no—
65C2×Dic43—23no—
66C22×C43—26no—
67C22×C43—43no—
68C22×C43—41no—
69C22×C43C22×Q811yescharacteristic
70C22×C43H(5,𝔽2)13yes—
71C22×C43H(5,𝔽2)13yes—
72C2×D43—26no—
73C2×D43—26no—
74C2×D43—416no—
75C2×D43—43no—
76C2×D43—43no—
77C2×D43—41no—
78C2×D43—41no—
79C4×C43—43no—
80C4×C43—43no—
81Dic43—43no—
82Dic43—43no—
83#2842—431nomaximal, Sylow
84C2×C43—42no—
85C2×C43#54313yes—
86C2×C43#56013yes—
87C2×C43#56011yescharacteristic
88D43—42no—
89D43—42no—
90#399—433no—
91#399—431no—
92#396—433no—
93#396—433no—
94#396—431no—
95#396D4311yescharacteristic, complemented
96#379—433no—
97C43#284211yescharacteristic, complemented, Sylow
98C25—431no—
99C2×C4⋊C4—433no—
100C2×C4⋊C4—433no—
101C2×C4⋊C4—433no—
102C2×C4⋊C4C2×D4313yescomplemented
103C2×C22⋊C4—433no—
104C2×C22⋊C4—433no—
105C2×C22⋊C4—433no—
106C2×C22⋊C4—433no—
107C2×C22⋊C4—433no—
108C2×C22⋊C4C2×D4313yes—
109#95—433no—
110#95C2×D4311yescharacteristic, complemented
111C24—431no—
112C24—431no—
113C24—434no—
114C24—1723no—
115C24—1723no—
116C24C22×D4311yescharacteristic
117C22×C4—433no—
118C22×C4—433no—
119C22×C4C22×D4313yes—
120C22×C4C22×D4313yes—
121C4⋊C4—43no—
122C4⋊C4—1723no—
123C4⋊C4—1723no—
124C4⋊C4—1723no—
125C22⋊C4—43no—
126C22⋊C4—1723no—
127C22⋊C4—1723no—
128C22⋊C4—1723no—
129C22⋊C4—1723no—
130C22⋊C4—1723no—
131C23—23no—
132C23—23no—
133C23—432no—
134C23—432no—
135C23—863no—
136C23—863no—
137C23—863no—
138C23—863no—
139C23—17212no—
140C23—17212no—
141C23—1724no—
142C23Q8×D4312yes—
143C23C23×D4311yescharacteristic
144C2×C4—23no—
145C2×C4—23no—
146C2×C4—23no—
147C2×C4—23no—
148C2×C4—23no—
149C2×C4—23no—
150C2×C4—863no—
151C2×C4—863no—
152C2×C4—863no—
153C2×C4—863no—
154C2×C4—863no—
155C2×C4—863no—
156C22—26no—
157C22—43no—
158C22—41no—
159C22—866no—
160C22—866no—
161C22—17216no—
162C22—1723no—
163C22—1723no—
164C22—1721no—
165C22—1721no—
166C22C2×Q8×D4311yescharacteristic
167C22#1306337013yes—
168C22#1306337113yes—
169C4—43no—
170C4—43no—
171C4—1723no—
172C4—1723no—
173C2—42no—
174C2—1722no—
175C2—1722no—
176C2#1458352413yes—
177C2#1458363713yes—
178C2#1458364011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#396C2
hypercenter#396D43
hypocenterC43#2842
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #14582836C2semidirect
2. #14582834C2semidirect
3. #14582823C2semidirect
4. #14582822C2semidirect
5. #14582821C2semidirect
7. C43×#396C2semidirect
9. C2×C4⋊Dic43C22semidirect
10. C2×Dic43⋊C4C22semidirect
11. C2×Dic43⋊C4C22semidirect
17. C43⋊#95C22semidirect
18. C2×C4⋊C4×C43C22semidirect
20. #95×C43C22semidirect
95. #396D43semidirect
97. C43#2842semidirect
102. C2×C4⋊C4C2×D43semidirect
110. #95C2×D43semidirect