Finite Group Databasebeta

← #18011073

Subgroups — #18011073

Order 4736.

512 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 162 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#14558482C218yesmaximal, complemented
2#14558476C212yesmaximal
3#14558475C212yesmaximal
4C4×C22⋊#3866C212yesmaximal
5C2×C4⋊C4×D37C211yesmaximal, characteristic
6C2×C4⋊#3866C2214yes—
7C2×C22⋊#3866C2214yes—
8C2×C4×#3866C2214yes—
9(C2×#3866)⋊C4C2214yes—
10(C2×#3866)⋊C4C2214yes—
11(C2×#3866)⋊C4C2218yes—
12C22×C4×D37C2211yescharacteristic
13C22×C4×D37C2211yescharacteristic
14C22×C4×D37C2211yescharacteristic
15C2×C4⋊Dic37C411yescharacteristic, complemented
16C2×#10596936C411yescharacteristic, complemented
17C2×#10596936C411yescharacteristic, complemented
18C4⋊C4×D37C414yescomplemented
19C4⋊C4×D37C2214yes—
20C2×C4⋊C4×C37C411yescharacteristic, complemented
21C23×D37C2311yescharacteristic
22C22×#3866C2318yes—
23C22×C4×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C22×Dic37C2×C411yescharacteristic
27C22×Dic37C2×C411yescharacteristic
28C22×Dic37C2×C411yescharacteristic
29C2×C4×D37—24no—
30C2×C4×D37—42no—
31C2×C4×D37—42no—
32C2×C4×D37C2×C412yes—
33C2×C4×D37C2×C412yes—
34C2×C4×D37C2×C412yes—
35C2×C4×D37C2312yes—
36C2×C4×D37C2312yes—
37C2×C4×D37C2312yes—
38C22⋊#3866—28no—
39C4⋊#3866—44no—
40C4×#3866—44no—
41C4⋊C4×C37C2×C414yes—
42C4⋊Dic37C2×C414yes—
43#10596936C2×C414yes—
44#10596936C2×C414yes—
45C23×C37C22×C411yescharacteristic
46C22×D37—22no—
47C22×D37—22no—
48C22×D37C22×C411yescharacteristic
49C22×D37#4114yes—
50C22×D37C2411yescharacteristic
51C2×#3866—28no—
52C2×#3866—28no—
53C2×#3866—28no—
54C2×C4×C37—22no—
55C2×C4×C37—41no—
56C2×C4×C37—41no—
57C2×C4×C37C22×C412yes—
58C2×C4×C37C22×C412yes—
59C2×C4×C37C22×C412yes—
60C2×Dic37—22no—
61C2×Dic37—41no—
62C2×Dic37—41no—
63C2×Dic37C22×C412yes—
64C2×Dic37C22×C412yes—
65C2×Dic37C22×C412yes—
66C4×D37—24no—
67C4×D37—24no—
68C4×D37—24no—
69C4×D37—24no—
70C4×D37—42no—
71C4×D37—42no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37#11712yes—
75C22×C37C23×C411yescharacteristic
76C2×D37—21no—
77C2×D37—21no—
78C2×D37—28no—
79C2×D37#11712yes—
80C2×D37C2×#4112yes—
81C2×D37H(5,𝔽2)12yes—
82C2×D372−1+412yes—
83#3866—48no—
84C4×C37—22no—
85C4×C37—22no—
86C4×C37—22no—
87Dic37—22no—
88Dic37—22no—
89Dic37—22no—
90#2313—371nomaximal, Sylow
91C2×C37—22no—
92C2×C37C2×#11711yescharacteristic
93C2×C37#51811yescharacteristic
94C2×C37#51911yescharacteristic
95D37—22no—
96D37#53914yes—
97C22×C4⋊C4—371no—
98#387—378no—
99#381—372no—
100#380—372no—
101C4×C22⋊C4—372no—
102C37#231311yescharacteristic, complemented, Sylow
103C23×C4—371no—
104C23×C4—371no—
105C23×C4—371no—
106C2×C4⋊C4—371no—
107C2×C4⋊C4—371no—
108C2×C4⋊C4—371no—
109C2×C4⋊C4—374no—
110C2×C4⋊C4—374no—
111C2×C4⋊C4—374no—
112C2×C4⋊C4#386611yescharacteristic, complemented
113C2×C22⋊C4—374no—
114C2×C42—374no—
115#95—374no—
116#95—374no—
117#95—378no—
118C24—371no—
119C22×C4—371no—
120C22×C4—371no—
121C22×C4—371no—
122C22×C4—372no—
123C22×C4—372no—
124C22×C4—372no—
125C22×C4—372no—
126C22×C4—372no—
127C22×C4—372no—
128C22×C4—378no—
129C22×C4—744no—
130C22×C4—1482no—
131C22×C4—1482no—
132C22×C4C2×#386611yescharacteristic
133C22×C4C2×#386611yescharacteristic
134C22×C4C2×#386611yescharacteristic
135C4⋊C4—374no—
136C4⋊C4—374no—
137C4⋊C4—374no—
138C4⋊C4—1484no—
139C4⋊C4C2×#386614yes—
140C22⋊C4—748no—
141C42—1484no—
142C23—371no—
143C23—374no—
144C23—371no—
145C23—742no—
146C23—742no—
147C23C22×#386611yescharacteristic
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—372no—
152C2×C4—372no—
153C2×C4—372no—
154C2×C4—744no—
155C2×C4—744no—
156C2×C4—744no—
157C2×C4—744no—
158C2×C4—742no—
159C2×C4—748no—
160C2×C4—748no—
161C2×C4—748no—
162C2×C4—1482no—
163C2×C4—1482no—
164C2×C4—1481no—
165C2×C4—1481no—
166C2×C4C22×#386612yes—
167C2×C4C22×#386612yes—
168C2×C4C22×#386612yes—
169C22—21no—
170C22—21no—
171C22—372no—
172C22—372no—
173C22—372no—
174C22—372no—
175C22—748no—
176C22—741no—
177C22—741no—
178C22#1192461512yes—
179C22C23×#386611yescharacteristic
180C4—22no—
181C4—22no—
182C4—22no—
183C4—742no—
184C4—742no—
185C4—742no—
186C4—1488no—
187C2—22no—
188C2—374no—
189C2—742no—
190C2C2×#1192461511yescharacteristic
191C2#1455860011yescharacteristic
192C2#1455860111yescharacteristic
subgroupG/H
center, FrattiniC22C23×#3866
commutator, socleC22×C37C23×C4
FittingC2×C4⋊C4×C37C4
prime radicalC23×D37C23
cosocleC22×D37C24
hypercenterC2×C4⋊C4#3866
hypocenterC37#2313
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14558482C2semidirect
15. C2×C4⋊Dic37C4semidirect
16. C2×#10596936C4semidirect
17. C2×#10596936C4semidirect
18. C4⋊C4×D37C4semidirect
20. C2×C4⋊C4×C37C4semidirect
102. C37#2313semidirect
112. C2×C4⋊C4#3866semidirect

Maximal subgroups

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

subgroupindex
#145584822
#145584762
#145584752
C4×C22⋊#38662
C2×C4⋊C4×D372
#231337