Finite Group Databasebeta

← #18009683

Subgroups — #18009683

Order 4736.

166 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 38 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#14558513C211yesmaximal, characteristic
2#14558506C211yesmaximal, characteristic
3#14557505C211yesmaximal, characteristic
4C2×#10596957C411yescharacteristic, complemented
5C22×#64438C411yescharacteristic, complemented
6#11924615—21no—
7#11924594—21no—
8#11924594C412yescomplemented
9#11924593—21no—
10C22⋊#64438—21no—
11C2×#10596964C2211yescharacteristic
12#11924492—21no—
13#11924451C411yescharacteristic, complemented
14#11924450—21no—
15#99×C37C411yescharacteristic, complemented
16C2×D4×C37C2×C411yescharacteristic
17C2×C22⋊D37C2×C411yescharacteristic
18C2×C22⋊D37D411yescharacteristic
19C22×Dic37C2×C411yescharacteristic
20C22×Dic37D411yescharacteristic
21#10596964—41no—
22#10596964—41no—
23C2×C4×D37D411yescharacteristic
24C2×Dic74Q811yescharacteristic
25C22⋊#3866—22no—
26#10596957—41no—
27C2×#64438—21no—
28C2×#64438—21no—
29C2×#64438—41no—
30C4⋊#3866—41no—
31C4×#3866—41no—
32C22⋊C4×C37—21no—
33C22⋊Dic37—21no—
34#10596936—41no—
35C4×Dic37—41no—
36C23×C37C4211yescharacteristic
37C23×C37C22⋊C411yescharacteristic
38C22×D37C22⋊C411yescharacteristic
39C2×#3866—42no—
40D4×C37—41no—
41C2×C4×C37—41no—
42C2×C4×C37C4⋊C411yescharacteristic
43C22⋊D37—41no—
44C22⋊D37—41no—
45C2×Dic37—21no—
46C2×Dic37—21no—
47C2×Dic37—21no—
48C2×Dic37—21no—
49C2×Dic37—41no—
50C2×Dic37C22⋊C411yescharacteristic
51C2×Dic37C4⋊C411yescharacteristic
52C2×Dic37C4⋊C411yescharacteristic
53C4×D37—21no—
54C4×D37—21no—
55Dic74—41no—
56#64438—41no—
57#64438—41no—
58C22×C37—21no—
59C22×C37—21no—
60C22×C37—41no—
61C22×C37—41no—
62C22×C37#9511yescharacteristic
63C2×D37—21no—
64C2×D37—41no—
65#3866—82no—
66C4×C37—21no—
67C4×C37—81no—
68Dic37—21no—
69Dic37—21no—
70Dic37—81no—
71Dic37#9911yescharacteristic
72Dic37#9911yescharacteristic
73#1391—371nomaximal, Sylow
74C2×C37—21no—
75C2×C37—41no—
76C2×C37—41no—
77C2×C37#34211yescharacteristic
78D37—41no—
79#410—371no—
80#410—371no—
81#408—371no—
82C37#139111yescharacteristic, complemented, Sylow
83C2×#41—371no—
84C2×M16—371no—
85C22×C8—371no—
86#117—741no—
87#117—741no—
88#99—372no—
89#99—371no—
90#99—741no—
91#99—741no—
92#99#386611yescharacteristic, complemented
93C22⋊C8—741no—
94C22⋊C8—741no—
95#41—1481no—
96#41—1481no—
97C2×Q8—371no—
98C2×D4—371no—
99C2×D4—371no—
100C2×D4C2×#386611yescharacteristic
101C22×C4—371no—
102C22×C4—371no—
103C22×C4—371no—
104M16—1481no—
105C2×C8—741no—
106C2×C8—741no—
107C2×C8—1481no—
108C4⋊C4—1481no—
109C4⋊C4—1481no—
110C22⋊C4—21no—
111C22⋊C4—742no—
112C22⋊C4—741no—
113C42—1481no—
114C42—1481no—
115C23—371no—
116C23C4×#386611yescharacteristic
117C23C22⋊#386611yescharacteristic
118Q8—1481no—
119D4—41no—
120D4—1481no—
121D4—1481no—
122C2×C4—41no—
123C2×C4—371no—
124C2×C4—371no—
125C2×C4—371no—
126C2×C4—741no—
127C2×C4—741no—
128C2×C4—741no—
129C2×C4—741no—
130C2×C4—741no—
131C2×C4—741no—
132C2×C4—1481no—
133C2×C4—1482no—
134C2×C4C4⋊#386611yescharacteristic
135C8—1481no—
136C8—1481no—
137C22—21no—
138C22—21no—
139C22—41no—
140C22—41no—
141C22—741no—
142C22—1481no—
143C22(C2×#3866)⋊C411yescharacteristic
144C4—21no—
145C4—81no—
146C4—371no—
147C4—371no—
148C4—2961no—
149C4—2962no—
150C4—741no—
151C4—741no—
152C2—21no—
153C2—41no—
154C2—41no—
155C2—1481no—
156C2#1455841011yescharacteristic
subgroupG/H
centerC2#14558410
commutatorC23×C37C42
FrattiniC2×D4C2×#3866
Fitting#99×C37C4
socleC2×C37#342
prime radical, cosocleC2×#10596964C22
hypercenter#99#3866
hypocenterC37#1391
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C2×#10596957C4semidirect
5. C22×#64438C4semidirect
8. #11924594C4semidirect
13. #11924451C4semidirect
15. #99×C37C4semidirect
82. C37#1391semidirect
92. #99#3866semidirect

Maximal subgroups

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

subgroupindex
#145585132
#145585062
#145575052
#139137