Finite Group Databasebeta

← #18010878

Subgroups — #18010878

Order 4736.

238 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 54 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#14558512C212yesmaximal
2#14558439C214yesmaximal, complemented
3#14558107C211yesmaximal, characteristic
4#11924615—22no—
5#11924595C2214yes—
6#11924594—22no—
7C2×#10596962C2211yescharacteristic
8#11924534C412yescomplemented
9#11924525C2212yes—
10#11924519—22no—
11#11924512—22no—
12#11924495C411yescharacteristic, complemented
13C22×Q8×C37C411yescharacteristic, complemented
14C2×Q8×C37—21no—
15C2×Q8×C37—42no—
16C2×Q8×C37C2×C412yes—
17C22×C4×C37—21no—
18C22×C4×C37C2×C411yescharacteristic
19C2×C22⋊D37D412yes—
20#10596962—42no—
21C2×D148C2311yescharacteristic
22C2×C4×D37D412yes—
23C2×Dic74C2×C411yescharacteristic
24C22⋊#3866—24no—
25C4⋊#3866—42no—
26C4×#3866—42no—
27C22⋊Dic37—21no—
28#10596938—24no—
29C4⋊Dic37—21no—
30#10596936—24no—
31C4×Dic37C2×C412yes—
32C23×C37C22⋊C411yescharacteristic
33C22×D37C2×D412yes—
34C2×#3866—44no—
35Q8×C37—42no—
36Q8×C37—42no—
37C2×C4×C37—22no—
38C2×C4×C37—22no—
39C2×C4×C37—42no—
40C2×C4×C37C22⋊C411yescharacteristic
41C2×C4×C37C22×C411yescharacteristic
42C22⋊D37—42no—
43C2×Dic37—22no—
44C2×Dic37C22⋊C412yes—
45D148—41no—
46C4×D37—22no—
47C4×D37—22no—
48Dic74—41no—
49C22×C37—21no—
50C22×C37—41no—
51C22×C37C2×C22⋊C411yescharacteristic
52C2×D37—22no—
53C2×D37—42no—
54#3866—84no—
55C4×C37—21no—
56C4×C37—42no—
57C4×C37#9912yes—
58Dic37—22no—
59Dic37—42no—
60#2129—371nomaximal, Sylow
61C2×C37—21no—
62C2×C37—41no—
63C2×C37C2×#9911yescharacteristic
64D37—42no—
65#536—371no—
66#410—372no—
67#354—374no—
68C37#212911yescharacteristic, complemented, Sylow
69C2×#41—371no—
70C22×Q8#386611yescharacteristic, complemented
71C4⋊Q8—372no—
72#124—372no—
73#123—742no—
74C22⋊Q8—742no—
75#117—371no—
76#117—742no—
77#99—374no—
78#99—742no—
79#41—1482no—
80C2×Q8—21no—
81C2×Q8—42no—
82C2×Q8—371no—
83C2×Q8C2×#386612yes—
84C2×D4—372no—
85C2×D4—371no—
86C22×C4—21no—
87C22×C4—372no—
88C22×C4C2×#386611yescharacteristic
89C4⋊C4—744no—
90C4⋊C4—741no—
91C4⋊C4—1482no—
92C22⋊C4—744no—
93C22⋊C4—741no—
94C22⋊C4—744no—
95C42—372no—
96C42—1482no—
97C23—372no—
98C23C22⋊#386611yescharacteristic
99Q8—42no—
100Q8—42no—
101Q8—1481no—
102D4—1481no—
103D4—1482no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—42no—
107C2×C4—372no—
108C2×C4—742no—
109C2×C4—742no—
110C2×C4—742no—
111C2×C4—1484no—
112C2×C4C22⋊#386611yescharacteristic
113C2×C4C22×#386611yescharacteristic
114C22—21no—
115C22—41no—
116C22—742no—
117C22—1482no—
118C22C2×C22⋊#386611yescharacteristic
119C4—21no—
120C4—42no—
121C4—2964no—
122C4—742no—
123C4—1482no—
124C4#1192459412yes—
125C2—21no—
126C2—41no—
127C2—1482no—
128C2C2×#1192459411yescharacteristic
subgroupG/H
centerC2C2×#11924594
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22×Q8×C37C4
socleC2×C37C2×#99
prime radicalC2×#10596962C22
cosocleC2×D148C23
hypercenterC22×Q8#3866
hypocenterC37#2129
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #14558439C2semidirect
8. #11924534C4semidirect
12. #11924495C4semidirect
13. C22×Q8×C37C4semidirect
68. C37#2129semidirect
70. C22×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585122
#145584392
#145581072
#212937