Finite Group Databasebeta

← #17992907

Subgroups — #17992907

Order 4736.

264 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 79 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×#11924492C211yesmaximal, characteristic
2#14557583C212yesmaximal, complemented
3#14557258C212yesmaximal, complemented
4#14557257C211yesmaximal, characteristic
5C37×#323C211yesmaximal, characteristic
6C23×Dic37C411yescharacteristic
7#11924492—22no—
8#11924492—22no—
9C2×#10596936C411yescharacteristic
10C2×#10596936C2211yescharacteristic
11C2×C22⋊Dic37C411yescharacteristic
12C2×C4×Dic37C411yescharacteristic
13C2×C4×Dic37C2211yescharacteristic
14#11924465—22no—
15C22⋊#64436C2212yes—
16C8×Dic37—22no—
17C2×C22⋊C4×C37C2211yescharacteristic
18C22⋊C8×C37C2212yes—
19C24×C37C2×C411yescharacteristic
20C22×C4×C37C2×C411yescharacteristic
21C22×C4×C37C2311yescharacteristic
22C22×Dic37—21no—
23C22×Dic37—21no—
24C22×Dic37—22no—
25C22×Dic37C814yescomplemented
26C22×Dic37C2×C411yescharacteristic
27C22×Dic37C2×C411yescharacteristic
28C22×Dic37C2×C411yescharacteristic
29C22×Dic37C2×C411yescharacteristic
30C2×C8×C37—22no—
31C22⋊C4×C37—22no—
32C22⋊Dic37—22no—
33#10596936—22no—
34#10596936—22no—
35C4×Dic37—21no—
36C4×Dic37—21no—
37C4×Dic37D412yes—
38C4×Dic37D412yes—
39C2×#64436—22no—
40C23×C37—21no—
41C23×C37—21no—
42C23×C37—41no—
43C23×C37—41no—
44C23×C37C2×C812yes—
45C23×C37C22×C411yescharacteristic
46C2×C4×C37—21no—
47C2×C4×C37—41no—
48C2×C4×C37—41no—
49C2×C4×C37C2×D412yes—
50C2×Dic37—21no—
51C2×Dic37—21no—
52C2×Dic37—24no—
53C2×Dic37—24no—
54C2×Dic37—21no—
55C2×Dic37—41no—
56C2×Dic37—41no—
57C2×Dic37C22⋊C412yes—
58C2×Dic37C22⋊C411yescharacteristic
59C2×Dic37C22⋊C411yescharacteristic
60C2×Dic37C2×C812yes—
61C2×Dic37C2×C812yes—
62C2×Dic37M1612yes—
63C8×C37—42no—
64#64436—42no—
65C22×C37—21no—
66C22×C37—21no—
67C22×C37—22no—
68C22×C37—42no—
69C22×C37—42no—
70C22×C37—41no—
71C22×C37—41no—
72C22×C37C2×C22⋊C411yescharacteristic
73C22×C37C22×C811yescharacteristic
74C22×C37C2×M1611yescharacteristic
75C4×C37—22no—
76C4×C37—41no—
77Dic37—22no—
78Dic37—22no—
79Dic37—41no—
80Dic37C22⋊C812yes—
81Dic37C22⋊C812yes—
82#1458—371nomaximal, Sylow
83C2×C37—21no—
84C2×C37—21no—
85C2×C37—42no—
86C2×C37C2×C22⋊C811yescharacteristic
87C2×C37#41011yescharacteristic
88C2×C37#41311yescharacteristic
89C2×#117—371no—
90#431—372no—
91#324—372no—
92#323—371no—
93#323D3711yescharacteristic
94C37#145811yescharacteristic, complemented, Sylow
95C23×C4—371no—
96#117—742no—
97#117—742no—
98C2×C4⋊C4—371no—
99C2×C4⋊C4—371no—
100C2×C22⋊C4—371no—
101C2×C22⋊C4C2×D3711yescharacteristic
102C2×C42—371no—
103C2×C42—371no—
104C4⋊C8—742no—
105C22⋊C8—372no—
106C22⋊C8C2×D3712yes—
107C4×C8—742no—
108C24C4×D3711yescharacteristic
109C22×C4—371no—
110C22×C4—374no—
111C22×C4—371no—
112C22×C4—371no—
113C22×C4—371no—
114C22×C4—741no—
115C22×C4—741no—
116C22×C4—742no—
117C22×C4C4×D3711yescharacteristic
118C22×C4C22×D3711yescharacteristic
119C2×C8—22no—
120C2×C8—742no—
121C4⋊C4—742no—
122C4⋊C4—742no—
123C22⋊C4—22no—
124C22⋊C4—742no—
125C42—372no—
126C42—372no—
127C42—741no—
128C42—741no—
129C23—21no—
130C23—21no—
131C23—41no—
132C23—41no—
133C23C8×D3712yes—
134C23C2×C4×D3711yescharacteristic
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—371no—
139C2×C4—371no—
140C2×C4—372no—
141C2×C4—372no—
142C2×C4—372no—
143C2×C4—372no—
144C2×C4—744no—
145C2×C4—744no—
146C2×C4—741no—
147C2×C4—741no—
148C2×C4—741no—
149C2×C4—1481no—
150C2×C4—1481no—
151C2×C4D4×D3712yes—
152C8—42no—
153C8—1482no—
154C22—21no—
155C22—21no—
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—41no—
161C22C22⋊C4×D3711yescharacteristic
162C22C2×C8×D3711yescharacteristic
163C22M16×D3711yescharacteristic
164C4—22no—
165C4—41no—
166C4—372no—
167C4—372no—
168C4—742no—
169C4—742no—
170C4—1481no—
171C2—21no—
172C2—21no—
173C2—42no—
174C2C22⋊C8×D3711yescharacteristic
175C2#1455750511yescharacteristic
176C2#1455751411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC22×C37C22×C8
FrattiniC22×C4C22×D37
FittingC37×#323C2
socleC22×C37C2×C22⋊C4
prime radicalC24×C37C2×C4
cosocleC22×C4×C37C23
hypercenter#323D37
hypocenterC37#1458
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #14557583C2semidirect
3. #14557258C2semidirect
25. C22×Dic37C8semidirect
94. C37#1458semidirect

Maximal subgroups

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

subgroupindex
C2×#119244922
#145575832
#145572582
#145572572
C37×#3232
#145837