Finite Group Databasebeta

← #18010508

Subgroups — #18010508

Order 4736.

296 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C2×#11924595C212yesmaximal
2#14558410C214yesmaximal, complemented
3#14558007C211yesmaximal, characteristic
4C2×C22⋊#3866C2214yes—
5#11924595—22no—
6#11924595—22no—
7C22×D148C2211yescharacteristic
8C4×D148—22no—
9#11924498—22no—
10#11924495C411yescharacteristic, complemented
11C22⋊C4×D37C412yescomplemented
12C22⋊C4×D37C2212yes—
13#117×C37C411yescharacteristic, complemented
14C23×D37C2×C411yescharacteristic
15C23×D37C2311yescharacteristic
16C22×#3866—24no—
17C22×C4×C37C2×C411yescharacteristic
18C2×D148—24no—
19C2×D148D412yes—
20C2×D148D412yes—
21C2×C4×D37—22no—
22C2×C4×D37—22no—
23C22⋊#3866—24no—
24C22⋊#3866—24no—
25C4⋊C4×C37—21no—
26C22⋊C4×C37C2×C412yes—
27C42×C37—21no—
28C22⋊Dic37C2×C412yes—
29#10596938—22no—
30#10596938—22no—
31C4⋊Dic37—21no—
32C4×Dic37—21no—
33C23×C37C22×C411yescharacteristic
34C22×D37—22no—
35C22×D37—81no—
36C22×D37—81no—
37C22×D37C22⋊C412yes—
38C22×D37C2×D412yes—
39C22×D37#4114yes—
40C2×#3866—44no—
41C2×#3866—84no—
42C2×C4×C37—22no—
43C2×C4×C37—22no—
44C2×C4×C37C22⋊C411yescharacteristic
45C2×C4×C37C22⋊C411yescharacteristic
46C2×Dic37—22no—
47D148—24no—
48D148—24no—
49C4×D37—82no—
50C4×D37—82no—
51C22×C37—41no—
52C22×C37C2×C22⋊C411yescharacteristic
53C22×C37#11712yes—
54C2×D37—22no—
55C2×D37—42no—
56C2×D37—44no—
57C2×D37—42no—
58C2×D37—82no—
59C2×D37#12314yes—
60#3866—84no—
61C4×C37—21no—
62C4×C37—21no—
63C4×C37—42no—
64Dic37—42no—
65#1828—371nomaximal, Sylow
66C2×C37—21no—
67C2×C37—22no—
68C2×C37#38111yescharacteristic
69D37—24no—
70D37—42no—
71#518—371no—
72C2×#99—372no—
73#342—374no—
74C37#182811yescharacteristic, complemented, Sylow
75C22×D4—371no—
76C4×D4—742no—
77C4×D4—742no—
78#117—371no—
79#117#386611yescharacteristic, complemented
80C2×C22⋊C4—372no—
81C2×C22⋊C4—372no—
82C2×C22⋊C4—374no—
83#99—742no—
84#99—742no—
85C24—371no—
86C24—371no—
87C2×D4—372no—
88C2×D4—372no—
89C2×D4—744no—
90C22×C4—742no—
91C22×C4—742no—
92C22×C4—744no—
93C22×C4C2×#386611yescharacteristic
94C4⋊C4—21no—
95C4⋊C4—741no—
96C22⋊C4—372no—
97C22⋊C4—742no—
98C22⋊C4—742no—
99C22⋊C4—744no—
100C22⋊C4—744no—
101C22⋊C4C2×#386612yes—
102C42—21no—
103C42—741no—
104C23—372no—
105C23—374no—
106C23—372no—
107C23—2961no—
108C23—2961no—
109C23—742no—
110C23C22×#386611yescharacteristic
111D4—744no—
112D4—744no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—2962no—
116C2×C4—2962no—
117C2×C4—2964no—
118C2×C4—742no—
119C2×C4—1484no—
120C2×C4C22⋊#386611yescharacteristic
121C2×C4C22⋊#386611yescharacteristic
122C22—41no—
123C22—374no—
124C22—2962no—
125C22—742no—
126C22—1482no—
127C22—1484no—
128C22—1482no—
129C22C2×C22⋊#386611yescharacteristic
130C22#1192461512yes—
131C4—21no—
132C4—21no—
133C4—42no—
134C4—2964no—
135C4—1482no—
136C2—21no—
137C2—22no—
138C2—744no—
139C2—1482no—
140C2#1455847611yescharacteristic
subgroupG/H
centerC2#14558476
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
Fitting#117×C37C4
socleC2×C37#381
prime radicalC22×D148C22
cosocleC23×D37C23
hypercenter#117#3866
hypocenterC37#1828
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C23 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #14558410C2semidirect
10. #11924495C4semidirect
11. C22⋊C4×D37C4semidirect
13. #117×C37C4semidirect
74. C37#1828semidirect
79. #117#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119245952
#145584102
#145580072
#182837