Finite Group Databasebeta

← #18010880

Subgroups — #18010880

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#14558440C214yesmaximal, complemented
3#14558109C211yesmaximal, characteristic
4#11924615—22no—
5#11924595C2214yes—
6#11924594—22no—
7C2×#10596962C2211yescharacteristic
8C22×Dic74C411yescharacteristic, complemented
9#11924536C412yescomplemented
10#11924524C2212yes—
11#11924520—22no—
12#11924516—22no—
13#117×C37C411yescharacteristic, complemented
14C22×C4×C37C2×C411yescharacteristic
15C2×C22⋊D37D412yes—
16C22×Dic37—21no—
17#10596962—42no—
18C2×D148C2311yescharacteristic
19C2×C4×D37D412yes—
20C2×Dic74—21no—
21C2×Dic74—42no—
22C2×Dic74C2×C412yes—
23C2×Dic74C2×C411yescharacteristic
24C22⋊#3866—24no—
25C4⋊#3866—42no—
26C4×#3866—42no—
27C4⋊C4×C37—21no—
28C22⋊C4×C37—21no—
29C42×C37C2×C412yes—
30#10596938—24no—
31C4⋊Dic37—24no—
32C23×C37C22⋊C411yescharacteristic
33C22×D37C2×D412yes—
34C2×#3866—44no—
35C2×C4×C37—22no—
36C2×C4×C37—22no—
37C2×C4×C37C22⋊C411yescharacteristic
38C2×C4×C37C22×C411yescharacteristic
39C22⋊D37—42no—
40C2×Dic37—22no—
41C2×Dic37—42no—
42C2×Dic37C22⋊C412yes—
43D148—41no—
44C4×D37—22no—
45C4×D37—22no—
46Dic74—41no—
47Dic74—42no—
48Dic74—42no—
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—371no—
71C4⋊Q8—372no—
72#124—372no—
73#123—742no—
74C22⋊Q8—742no—
75#117—742no—
76#117#386611yescharacteristic, complemented
77#99—374no—
78#99—742no—
79#41—1482no—
80C2×Q8—371no—
81C2×Q8—372no—
82C2×Q8—741no—
83C2×Q8—1482no—
84C2×D4—372no—
85C2×D4—371no—
86C22×C4—372no—
87C22×C4—741no—
88C22×C4C2×#386611yescharacteristic
89C4⋊C4—21no—
90C4⋊C4—744no—
91C4⋊C4—1482no—
92C22⋊C4—21no—
93C22⋊C4—744no—
94C22⋊C4—744no—
95C42—1482no—
96C42C2×#386612yes—
97C23—372no—
98C23C22⋊#386611yescharacteristic
99Q8—1481no—
100Q8—1482no—
101Q8—1482no—
102D4—1481no—
103D4—1482no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—372no—
107C2×C4—742no—
108C2×C4—742no—
109C2×C4—742no—
110C2×C4—1484no—
111C2×C4—1482no—
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#1192459512yes—
125C2—21no—
126C2—41no—
127C2—1482no—
128C2C2×#1192459511yescharacteristic
subgroupG/H
centerC2C2×#11924595
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#117×C37C4
socleC2×C37C2×#99
prime radicalC2×#10596962C22
cosocleC2×D148C23
hypercenter#117#3866
hypocenterC37#2129
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #14558440C2semidirect
8. C22×Dic74C4semidirect
9. #11924536C4semidirect
13. #117×C37C4semidirect
68. C37#2129semidirect
76. #117#3866semidirect

Maximal subgroups

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

subgroupindex
#145585122
#145584402
#145581092
#212937