Finite Group Databasebeta

← #18009985

Subgroups — #18009985

Order 4736.

272 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 60 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#14558555C211yesmaximal, characteristic, complemented
2#14558469C211yesmaximal, characteristic, complemented
3#14558384C214yesmaximal, complemented
4#14558081C211yesmaximal, characteristic
5C2×C4×#3866—21no—
6C4⋊#64438—21no—
7#11924593C2212yes—
8#11924591—21no—
9(C2×#3866)⋊C4—21no—
10(C2×#3866)⋊C4C2212yes—
11C2×#10596964—21no—
12#11924536C411yescharacteristic, complemented
13#11924523—21no—
14#11924507—21no—
15#11924507C2212yes—
16D4×Dic37—21no—
17D4×Dic37C412yescomplemented
18C42×D37C2211yescharacteristic
19#127×C37C411yescharacteristic, complemented
20C22×#3866—22no—
21C2×D4×C37—21no—
22C2×D4×C37—21no—
23C2×D4×C37C2×C412yes—
24C2×C22⋊D37—22no—
25C22×Dic37—22no—
26#10596964—44no—
27C2×C4×D37D411yescharacteristic
28C2×C4×D37D411yescharacteristic
29C2×C4×D37C2311yescharacteristic
30C2×Dic74—21no—
31C2×#64438—22no—
32C4×#3866—24no—
33C42×C37C2×C411yescharacteristic
34C22⋊Dic37—22no—
35C22⋊Dic37—22no—
36C4⋊Dic37—21no—
37C4⋊Dic37C2×C412yes—
38C4×Dic37C2×C411yescharacteristic
39C4×Dic37D411yescharacteristic
40C4×Dic37D411yescharacteristic
41C23×C37—22no—
42C22×D37C2×D411yescharacteristic
43C2×#3866—24no—
44C2×#3866—42no—
45C2×#3866—42no—
46D4×C37—42no—
47D4×C37—42no—
48D4×C37—42no—
49C2×C4×C37C22⋊C411yescharacteristic
50C2×C4×C37C22⋊C411yescharacteristic
51C2×C4×C37C22×C411yescharacteristic
52C22⋊D37—44no—
53C2×Dic37—22no—
54C2×Dic37—44no—
55C2×Dic37C22⋊C411yescharacteristic
56C2×Dic37C22⋊C411yescharacteristic
57C2×Dic37C2×D411yescharacteristic
58C4×D37—22no—
59C4×D37—22no—
60C4×D37—41no—
61Dic74—42no—
62#64438—42no—
63C22×C37—42no—
64C22×C37—42no—
65C22×C37—42no—
66C22×C37C2×C22⋊C411yescharacteristic
67C2×D37—21no—
68C2×D37—21no—
69C2×D37AGL(1,ℤ/8)12yes—
70#3866—44no—
71C4×C37—21no—
72C4×C37—21no—
73C4×C37#10412yes—
74Dic37—21no—
75Dic37—21no—
76Dic37—21no—
77Dic37—42no—
78#1505—371nomaximal, Sylow
79C2×C37—82no—
80C2×C37#41011yescharacteristic
81C2×C37#41811yescharacteristic
82C2×C37C2×#10411yescharacteristic
83D37—22no—
84#532—371no—
85#432—371no—
86#376—371no—
87#327—374no—
88C37#150511yescharacteristic, complemented, Sylow
89C2×#41—741no—
90C4⋊Q8—371no—
91#127#386611yescharacteristic, complemented
92#124—741no—
93#121—372no—
94#121—741no—
95C4×D4—372no—
96C4×D4—741no—
97C2×C42—371no—
98C2×C42—741no—
99C4⋊C8—741no—
100C22⋊C8—372no—
101#97—741no—
102#95—372no—
103#95—741no—
104#41—1484no—
105C2×Q8—741no—
106C2×D4—21no—
107C2×D4—21no—
108C2×D4—742no—
109C2×D4C2×#386612yes—
110C22×C4—371no—
111C22×C4—371no—
112C22×C4—371no—
113C22×C4—742no—
114C22×C4—742no—
115C2×C8—742no—
116C4⋊C4—372no—
117C4⋊C4—741no—
118C22⋊C4—742no—
119C22⋊C4—742no—
120C42—371no—
121C42—371no—
122C42—371no—
123C42—744no—
124C42C2×#386611yescharacteristic
125C23—22no—
126C23—371no—
127Q8—1482no—
128D4—42no—
129D4—42no—
130D4—42no—
131D4—1484no—
132C2×C4—371no—
133C2×C4—371no—
134C2×C4—371no—
135C2×C4—742no—
136C2×C4—742no—
137C2×C4—744no—
138C2×C4—742no—
139C2×C4—1481no—
140C2×C4—1484no—
141C2×C4—1482no—
142C2×C4—1482no—
143C2×C4C22⋊#386611yescharacteristic
144C2×C4C22⋊#386611yescharacteristic
145C2×C4C22×#386611yescharacteristic
146C8—1482no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22—372no—
151C22—741no—
152C22—741no—
153C22C2×C22⋊#386611yescharacteristic
154C4—21no—
155C4—21no—
156C4—741no—
157C4—741no—
158C4—741no—
159C4—1484no—
160C4—1482no—
161C4#1192460012yes—
162C2—82no—
163C2—742no—
164C2#1455851311yescharacteristic
165C2#1455852511yescharacteristic
166C2C2×#1192460011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#127×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558081C2
cosocleC2×C4×D37C23
hypercenter#127#3866
hypocenterC37#1505
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #14558555C2semidirect
2. #14558469C2semidirect
3. #14558384C2semidirect
12. #11924536C4semidirect
17. D4×Dic37C4semidirect
19. #127×C37C4semidirect
88. C37#1505semidirect
91. #127#3866semidirect

Maximal subgroups

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

subgroupindex
#145585552
#145584692
#145583842
#145580812
#150537