Finite Group Databasebeta

← #18010016

Subgroups — #18010016

Order 4736.

252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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#14558556C211yesmaximal, characteristic, complemented
2#14558478C211yesmaximal, characteristic, complemented
3#14558384C214yesmaximal, complemented
4#14558081C211yesmaximal, characteristic
5#11924603—21no—
6#11924593C2212yes—
7#11924591—21no—
8(C2×#3866)⋊C4—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—
32C42×C37C2×C411yescharacteristic
33C22⋊Dic37—22no—
34C22⋊Dic37—22no—
35C4⋊Dic37—21no—
36C4⋊Dic37C2×C412yes—
37C4×Dic37C2×C411yescharacteristic
38C4×Dic37D411yescharacteristic
39C4×Dic37D411yescharacteristic
40C23×C37—22no—
41C22×D37C2×D411yescharacteristic
42C2×#3866—42no—
43C2×#3866—42no—
44C2×#3866—42no—
45D4×C37—42no—
46D4×C37—42no—
47D4×C37—42no—
48C2×C4×C37C22⋊C411yescharacteristic
49C2×C4×C37C22⋊C411yescharacteristic
50C2×C4×C37C22×C411yescharacteristic
51C22⋊D37—44no—
52C2×Dic37—22no—
53C2×Dic37—44no—
54C2×Dic37C22⋊C411yescharacteristic
55C2×Dic37C22⋊C411yescharacteristic
56C2×Dic37C2×D411yescharacteristic
57C4×D37—22no—
58C4×D37—41no—
59C4×D37—41no—
60Dic74—42no—
61#64438—42no—
62C22×C37—42no—
63C22×C37—42no—
64C22×C37—42no—
65C22×C37C2×C22⋊C411yescharacteristic
66C2×D37—21no—
67C2×D37—21no—
68C2×D37AGL(1,ℤ/8)12yes—
69#3866—82no—
70C4×C37—21no—
71C4×C37—21no—
72C4×C37—21no—
73Dic37—21no—
74Dic37—21no—
75Dic37—21no—
76Dic37—42no—
77#1514—371nomaximal, Sylow
78C2×C37—82no—
79C2×C37#41011yescharacteristic
80C2×C37#41811yescharacteristic
81C2×C37#42111yescharacteristic
82D37—22no—
83#532—371no—
84#432—371no—
85#383—371no—
86#327—374no—
87C37#151411yescharacteristic, complemented, Sylow
88C2×#41—741no—
89C4⋊Q8—371no—
90#127#386611yescharacteristic, complemented
91#124—741no—
92#121—372no—
93#121—741no—
94C4×D4—372no—
95C4×D4—741no—
96C2×C42—371no—
97C4⋊C8—741no—
98C22⋊C8—372no—
99#97—741no—
100#95—372no—
101#95—741no—
102#95—741no—
103#41—1484no—
104C2×Q8—741no—
105C2×D4—21no—
106C2×D4—21no—
107C2×D4—742no—
108C2×D4C2×#386612yes—
109C22×C4—371no—
110C22×C4—371no—
111C22×C4—371no—
112C22×C4—742no—
113C22×C4—742no—
114C2×C8—742no—
115C4⋊C4—372no—
116C4⋊C4—741no—
117C22⋊C4—742no—
118C22⋊C4—742no—
119C42—371no—
120C42—371no—
121C42—371no—
122C42C2×#386611yescharacteristic
123C23—22no—
124C23—371no—
125Q8—1482no—
126D4—42no—
127D4—42no—
128D4—42no—
129D4—1484no—
130C2×C4—371no—
131C2×C4—371no—
132C2×C4—371no—
133C2×C4—742no—
134C2×C4—742no—
135C2×C4—1481no—
136C2×C4—1481no—
137C2×C4—1482no—
138C2×C4—1482no—
139C2×C4—1482no—
140C2×C4—1484no—
141C2×C4C22⋊#386611yescharacteristic
142C2×C4C22⋊#386611yescharacteristic
143C2×C4C22×#386611yescharacteristic
144C8—1482no—
145C22—42no—
146C22—42no—
147C22—42no—
148C22—372no—
149C22—741no—
150C22—741no—
151C22C2×C22⋊#386611yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—2962no—
156C4—741no—
157C4—741no—
158C4—741no—
159C4—1482no—
160C2—82no—
161C2—742no—
162C2#1455851311yescharacteristic
163C2#1455852511yescharacteristic
164C2#1455853111yescharacteristic
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#1514
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. #14558556C2semidirect
2. #14558478C2semidirect
3. #14558384C2semidirect
12. #11924536C4semidirect
17. D4×Dic37C4semidirect
19. #127×C37C4semidirect
87. C37#1514semidirect
90. #127#3866semidirect

Maximal subgroups

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

subgroupindex
#145585562
#145584782
#145583842
#145580812
#151437