Finite Group Databasebeta

← #17992930

Subgroups — #17992930

Order 4736.

252 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 85 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#14557590C212yesmaximal, complemented
2#14557259C212yesmaximal, complemented
3#14557257C212yesmaximal
4C2×#117×C37C211yesmaximal, characteristic
5C4⋊#64436—22no—
6C22⋊#64436C2214yes—
7#11924447—22no—
8C23×C4×C37C411yescharacteristic
9#117×C37—22no—
10#117×C37—22no—
11C2×C4⋊C4×C37C411yescharacteristic
12C2×C4⋊C4×C37C2211yescharacteristic
13C2×C22⋊C4×C37C411yescharacteristic
14C2×C22⋊C4×C37C2211yescharacteristic
15C2×C42×C37C411yescharacteristic
16C2×C42×C37C2211yescharacteristic
17C24×C37C2×C411yescharacteristic
18C22×C4×C37—22no—
19C22×C4×C37—21no—
20C22×C4×C37—21no—
21C22×C4×C37—22no—
22C22×C4×C37C2×C411yescharacteristic
23C22×C4×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C22×C4×C37C2×C411yescharacteristic
27C22×C4×C37C2311yescharacteristic
28C4⋊C4×C37—22no—
29C4⋊C4×C37—22no—
30C22⋊C4×C37—22no—
31C22⋊C4×C37—22no—
32C42×C37—21no—
33C42×C37—21no—
34C42×C37D412yes—
35C42×C37D412yes—
36C2×#64436—24no—
37C23×C37—21no—
38C23×C37—21no—
39C23×C37—41no—
40C23×C37—41no—
41C23×C37M1612yes—
42C23×C37C22×C411yescharacteristic
43C2×C4×C37—24no—
44C2×C4×C37—24no—
45C2×C4×C37—21no—
46C2×C4×C37—21no—
47C2×C4×C37—21no—
48C2×C4×C37—21no—
49C2×C4×C37—21no—
50C2×C4×C37—21no—
51C2×C4×C37—41no—
52C2×C4×C37—41no—
53C2×C4×C37—41no—
54C2×C4×C37—41no—
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22⋊C412yes—
58C2×C4×C37M1612yes—
59C2×C4×C37C2×D412yes—
60#64436—44no—
61C22×C37—21no—
62C22×C37—21no—
63C22×C37—22no—
64C22×C37—42no—
65C22×C37—42no—
66C22×C37—41no—
67C22×C37—41no—
68C22×C37C2×C22⋊C411yescharacteristic
69C22×C37C2×M1611yescharacteristic
70C22×C37C2×M1611yescharacteristic
71C4×C37—21no—
72C4×C37—21no—
73C4×C37—22no—
74C4×C37—22no—
75C4×C37—22no—
76C4×C37—41no—
77C4×C37—41no—
78#1464—371nomaximal, Sylow
79C2×C37—21no—
80C2×C37—21no—
81C2×C37—42no—
82C2×C37#40711yescharacteristic
83C2×C37#41011yescharacteristic
84C2×C37#41311yescharacteristic
85C2×#117D3711yescharacteristic
86#432—372no—
87#324—372no—
88#323—372no—
89C37#146411yescharacteristic, complemented, Sylow
90C23×C4Dic3711yescharacteristic
91#117—22no—
92#117—22no—
93C2×C4⋊C4Dic3711yescharacteristic
94C2×C4⋊C4C2×D3711yescharacteristic
95C2×C22⋊C4Dic3711yescharacteristic
96C2×C22⋊C4C2×D3711yescharacteristic
97C2×C42Dic3711yescharacteristic
98C2×C42C2×D3711yescharacteristic
99C4⋊C8—742no—
100C22⋊C8—374no—
101#97—742no—
102C24C2×Dic3711yescharacteristic
103C22×C4—22no—
104C22×C4—22no—
105C22×C4—21no—
106C22×C4—21no—
107C22×C4C2×Dic3711yescharacteristic
108C22×C4C2×Dic3711yescharacteristic
109C22×C4C2×Dic3711yescharacteristic
110C22×C4C2×Dic3711yescharacteristic
111C22×C4C2×Dic3711yescharacteristic
112C22×C4C22×D3711yescharacteristic
113C2×C8—744no—
114C4⋊C4—22no—
115C4⋊C4—22no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C42—21no—
119C42—21no—
120C42C22⋊D3712yes—
121C42C22⋊D3712yes—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1059693412yes—
127C23C22×Dic3711yescharacteristic
128C2×C4—24no—
129C2×C4—24no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4#1059693412yes—
141C2×C4C22⋊Dic3711yescharacteristic
142C2×C4C22⋊Dic3711yescharacteristic
143C2×C4C22⋊Dic3712yes—
144C2×C4C2×C22⋊D3712yes—
145C8—1484no—
146C22—21no—
147C22—21no—
148C22—22no—
149C22—42no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22C2×C22⋊Dic3711yescharacteristic
154C22C2×#1059693411yescharacteristic
155C22C2×#1059693411yescharacteristic
156C4—22no—
157C4—21no—
158C4—21no—
159C4—22no—
160C4—22no—
161C4—41no—
162C4—41no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1455749711yescharacteristic
167C2#1455750711yescharacteristic
168C2#1455751711yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic37
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#117×C37C2
socleC22×C37C2×C22⋊C4
prime radicalC24×C37C2×C4
cosocleC22×C4×C37C23
hypercenterC2×#117D37
hypocenterC37#1464
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #14557590C2semidirect
2. #14557259C2semidirect
89. C37#1464semidirect

Maximal subgroups

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

subgroupindex
#145575902
#145572592
#145572572
C2×#117×C372
#146437