Finite Group Databasebeta

← #18010025

Subgroups — #18010025

Order 4736.

264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 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#14558551C211yesmaximal, characteristic, complemented
2#14558477C211yesmaximal, characteristic, complemented
3#14558384C214yesmaximal, complemented
4#14558081C211yesmaximal, characteristic
5C2×C4⋊#3866—21no—
6#11924603—21no—
7#11924593C2212yes—
8C4×#64438—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—42no—
27#10596964—42no—
28C2×C4×D37D411yescharacteristic
29C2×C4×D37D411yescharacteristic
30C2×C4×D37C2311yescharacteristic
31C2×Dic74—21no—
32C2×#64438—22no—
33C4⋊#3866—42no—
34C42×C37C2×C411yescharacteristic
35C22⋊Dic37—22no—
36C22⋊Dic37—22no—
37C4⋊Dic37—21no—
38C4⋊Dic37C2×C412yes—
39C4×Dic37C2×C411yescharacteristic
40C4×Dic37D411yescharacteristic
41C4×Dic37D411yescharacteristic
42C23×C37—22no—
43C22×D37C2×D411yescharacteristic
44C2×#3866—42no—
45C2×#3866—42no—
46C2×#3866—42no—
47D4×C37—42no—
48D4×C37—42no—
49D4×C37—42no—
50C2×C4×C37C22⋊C411yescharacteristic
51C2×C4×C37C22⋊C411yescharacteristic
52C2×C4×C37C22×C411yescharacteristic
53C22⋊D37—42no—
54C22⋊D37—42no—
55C2×Dic37—22no—
56C2×Dic37—44no—
57C2×Dic37C22⋊C411yescharacteristic
58C2×Dic37C22⋊C411yescharacteristic
59C2×Dic37C2×D411yescharacteristic
60C4×D37—41no—
61C4×D37—41no—
62C4×D37D812yes—
63C4×D37SD1612yes—
64Dic74—42no—
65#64438—42no—
66C22×C37—42no—
67C22×C37—42no—
68C22×C37—42no—
69C22×C37C2×C22⋊C411yescharacteristic
70C2×D37—21no—
71C2×D37—21no—
72C2×D37C2×D811yescharacteristic
73C2×D37C2×SD1611yescharacteristic
74#3866—82no—
75C4×C37—21no—
76C4×C37—21no—
77C4×C37#10212yes—
78Dic37—21no—
79Dic37—21no—
80Dic37—42no—
81Dic37#10212yes—
82#1517—371nomaximal, Sylow
83C2×C37—82no—
84C2×C37#41011yescharacteristic
85C2×C37C2×#10211yescharacteristic
86C2×C37#42111yescharacteristic
87D37—21no—
88D37—21no—
89#532—371no—
90#431—371no—
91#382—371no—
92#327—374no—
93C37#151711yescharacteristic, complemented, Sylow
94C2×#41—741no—
95C4⋊Q8—371no—
96#127#386611yescharacteristic, complemented
97#124—741no—
98#121—372no—
99#121—741no—
100C4×D4—372no—
101C4×D4—741no—
102C2×C4⋊C4—741no—
103C2×C42—371no—
104C4⋊C8—741no—
105C22⋊C8—372no—
106C4×C8—741no—
107#95—372no—
108#95—741no—
109#41—1482no—
110#41—1482no—
111C2×Q8—741no—
112C2×D4—21no—
113C2×D4—21no—
114C2×D4—742no—
115C2×D4C2×#386612yes—
116C22×C4—371no—
117C22×C4—371no—
118C22×C4—371no—
119C22×C4—742no—
120C22×C4—742no—
121C2×C8—742no—
122C4⋊C4—372no—
123C4⋊C4—741no—
124C4⋊C4—1482no—
125C22⋊C4—742no—
126C22⋊C4—742no—
127C42—371no—
128C42—371no—
129C42—371no—
130C42C2×#386611yescharacteristic
131C23—22no—
132C23—371no—
133Q8—1482no—
134D4—42no—
135D4—42no—
136D4—42no—
137D4—1482no—
138D4—1482no—
139C2×C4—371no—
140C2×C4—372no—
141C2×C4—372no—
142C2×C4—371no—
143C2×C4—371no—
144C2×C4—742no—
145C2×C4—1481no—
146C2×C4—1481no—
147C2×C4—1484no—
148C2×C4—1482no—
149C2×C4—1482no—
150C2×C4—1482no—
151C2×C4C22⋊#386611yescharacteristic
152C2×C4C22⋊#386611yescharacteristic
153C2×C4C22×#386611yescharacteristic
154C8—1482no—
155C22—42no—
156C22—42no—
157C22—42no—
158C22—371no—
159C22—371no—
160C22—741no—
161C22—741no—
162C22C2×C22⋊#386611yescharacteristic
163C4—21no—
164C4—21no—
165C4—372no—
166C4—2962no—
167C4—741no—
168C4—741no—
169C4—1482no—
170C4#1192459812yes—
171C2—82no—
172C2—741no—
173C2—741no—
174C2#1455851311yescharacteristic
175C2C2×#1192459811yescharacteristic
176C2#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#1517
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. #14558551C2semidirect
2. #14558477C2semidirect
3. #14558384C2semidirect
12. #11924536C4semidirect
17. D4×Dic37C4semidirect
19. #127×C37C4semidirect
93. C37#1517semidirect
96. #127#3866semidirect

Maximal subgroups

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

subgroupindex
#145585512
#145584772
#145583842
#145580812
#151737