Finite Group Databasebeta

← #18010078

Subgroups — #18010078

Order 4736.

196 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 58 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#14558553C211yesmaximal, characteristic
2#14558553C211yesmaximal, characteristic
3#14558390C214yesmaximal, complemented
4C2×#11924527C211yesmaximal, characteristic
5#11924603—21no—
6#11924603—21no—
7C22⋊#64438—21no—
8C22⋊#64438—21no—
9#11924591C2212yes—
10#11924591C2212yes—
11#11924527—21no—
12#11924527—21no—
13#11924527C412yes—
14#11924527C2212yes—
15C2×C4⋊Dic37—21no—
16C2×C4⋊Dic37C411yescharacteristic
17C2×#10596936—21no—
18C2×C4×Dic37C2211yescharacteristic
19C2×C4⋊C4×C37C411yescharacteristic
20C22×C4×C37—21no—
21C22×C4×C37C2×C411yescharacteristic
22C22×Dic37—21no—
23C22×Dic37D411yescharacteristic
24C22×Dic37D411yescharacteristic
25C2×#64438—22no—
26C2×#64438—22no—
27C4⋊C4×C37—21no—
28C4⋊C4×C37C2×C412yes—
29C4⋊Dic37—21no—
30C4⋊Dic37—22no—
31C4⋊Dic37—22no—
32C4⋊Dic37C2×C412yes—
33#10596936—22no—
34#10596936—22no—
35C4×Dic37C2×C411yescharacteristic
36C4×Dic37D411yescharacteristic
37C4×Dic37D411yescharacteristic
38C4×Dic37C2311yescharacteristic
39C23×C37C22⋊C411yescharacteristic
40C2×C4×C37—22no—
41C2×C4×C37—22no—
42C2×C4×C37—42no—
43C2×C4×C37C22⋊C411yescharacteristic
44C2×C4×C37C22×C411yescharacteristic
45C2×Dic37—22no—
46C2×Dic37—41no—
47C2×Dic37—41no—
48C2×Dic37—42no—
49C2×Dic37C22⋊C411yescharacteristic
50C2×Dic37C22⋊C411yescharacteristic
51C2×Dic37C2×D411yescharacteristic
52C2×Dic37C2×D411yescharacteristic
53#64438—42no—
54#64438—42no—
55C22×C37—21no—
56C22×C37—21no—
57C22×C37#10112yes—
58C22×C37C2×C22⋊C411yescharacteristic
59C4×C37—21no—
60C4×C37—21no—
61C4×C37—42no—
62Dic37—21no—
63Dic37—21no—
64Dic37—21no—
65Dic37—21no—
66Dic37—42no—
67#1534—371nomaximal, Sylow
68C2×C37—22no—
69C2×C37C2×#10111yescharacteristic
70C2×C37#42111yescharacteristic
71C2×C37#42111yescharacteristic
72C2×#125—371no—
73#432—371no—
74#432—371no—
75#330—374no—
76C37#153411yescharacteristic, complemented, Sylow
77#125—372no—
78#125—372no—
79#125—741no—
80#125—741no—
81C2×C4⋊C4—371no—
82C2×C4⋊C4—741no—
83C2×C4⋊C4—741no—
84C2×C4⋊C4#386611yescharacteristic
85C2×C42—371no—
86C4⋊C8—741no—
87C4⋊C8—741no—
88C22⋊C8—741no—
89C22⋊C8—741no—
90#97—372no—
91#97—372no—
92C22×C4—21no—
93C22×C4—371no—
94C22×C4—371no—
95C22×C4—741no—
96C22×C4C2×#386611yescharacteristic
97C2×C8—742no—
98C2×C8—742no—
99C4⋊C4—21no—
100C4⋊C4—372no—
101C4⋊C4—742no—
102C4⋊C4—742no—
103C4⋊C4—742no—
104C4⋊C4—742no—
105C4⋊C4—741no—
106C4⋊C4C2×#386612yes—
107C42—371no—
108C42—371no—
109C42—371no—
110C42—371no—
111C23C22⋊#386611yescharacteristic
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—42no—
115C2×C4—371no—
116C2×C4—371no—
117C2×C4—371no—
118C2×C4—371no—
119C2×C4—742no—
120C2×C4—1481no—
121C2×C4—1481no—
122C2×C4—1482no—
123C2×C4C22⋊#386611yescharacteristic
124C2×C4C22×#386611yescharacteristic
125C8—1482no—
126C8—1482no—
127C22—21no—
128C22—21no—
129C22#1192459712yes—
130C22C2×C22⋊#386611yescharacteristic
131C4—21no—
132C4—21no—
133C4—42no—
134C4—741no—
135C4—741no—
136C4—741no—
137C4—741no—
138C4—1482no—
139C2—22no—
140C2C2×#1192459711yescharacteristic
141C2#1455853111yescharacteristic
142C2#1455853211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×C37C22⋊C4
cosocleC4×Dic37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1534
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14558390C2semidirect
76. C37#1534semidirect

Maximal subgroups

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

subgroupindex
#145585532
#145583902
C2×#119245272
#153437