Finite Group Databasebeta

← #17995055

Subgroups — #17995055

Order 4736.

378 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11924495C211yesmaximal, characteristic, complemented
2C2×#11924451C212yesmaximal
3#14557396C211yesmaximal, characteristic, complemented
4#14557300C212yesmaximal, complemented
5C2×#123×C37C211yesmaximal, characteristic
6#11924495—24no—
7C2×C4⋊Dic37—21no—
8C2×C22⋊Dic37C2212yes—
9C2×C22⋊Dic37C2212yes—
10C2×C4×Dic37—21no—
11#11924451—24no—
12#11924443—22no—
13C22×D4×C37C2211yescharacteristic
14C23×C4×C37C2211yescharacteristic
15#123×C37—21no—
16#123×C37—21no—
17#123×C37—22no—
18C2×C4⋊C4×C37C412yescomplemented
19C2×C22⋊C4×C37C412yescomplemented
20C2×C22⋊C4×C37C2211yescharacteristic
21C24×C37C2×C411yescharacteristic
22C24×C37C2311yescharacteristic
23C2×D4×C37—21no—
24C2×D4×C37—21no—
25C2×D4×C37—22no—
26C2×D4×C37—22no—
27C22×C4×C37—22no—
28C22×C4×C37—22no—
29C22×C4×C37C2×C411yescharacteristic
30C22×C4×C37C2×C412yes—
31C22×C4×C37C2×C412yes—
32C22×C4×C37D411yescharacteristic
33C22×C4×C37D411yescharacteristic
34C22×C4×C37D412yes—
35C22×Dic37—22no—
36C22×Dic37—22no—
37C4⋊C4×C37—22no—
38C4⋊C4×C37—22no—
39C22⋊C4×C37—21no—
40C22⋊C4×C37—21no—
41C22⋊C4×C37—22no—
42C22⋊C4×C37—22no—
43C22⋊Dic37—22no—
44C22⋊Dic37—22no—
45C22⋊Dic37—22no—
46C22⋊Dic37D414yes—
47C4⋊Dic37—24no—
48C4×Dic37—24no—
49C23×C37—21no—
50C23×C37—22no—
51C23×C37—42no—
52C23×C37—42no—
53C23×C37C22×C411yescharacteristic
54C23×C37C2×D412yes—
55C23×C37C2×D411yescharacteristic
56C23×C37C2×D411yescharacteristic
57C23×C37#4112yes—
58D4×C37—41no—
59D4×C37—42no—
60D4×C37—41no—
61C2×C4×C37—24no—
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37—24no—
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37—22no—
68C2×C4×C37—21no—
69C2×C4×C37—22no—
70C2×C4×C37—42no—
71C2×C4×C37C22⋊C412yes—
72C2×C4×C37C22⋊C412yes—
73C2×Dic37—24no—
74C2×Dic37—44no—
75C2×Dic37—44no—
76C2×Dic37—42no—
77C22×C37—22no—
78C22×C37—22no—
79C22×C37—22no—
80C22×C37—42no—
81C22×C37—42no—
82C22×C37—41no—
83C22×C37—42no—
84C22×C37—82no—
85C22×C37C2×C22⋊C411yescharacteristic
86C22×C37C4×D412yes—
87C22×C37#12011yescharacteristic
88C22×C37#12112yes—
89C22×C37#12311yescharacteristic
90C4×C37—22no—
91C4×C37—22no—
92C4×C37—41no—
93C4×C37—42no—
94Dic37—44no—
95Dic37—82no—
96#1899—371nomaximal, Sylow
97C2×C37—21no—
98C2×C37—22no—
99C2×C37—22no—
100C2×C37—21no—
101C2×C37—81no—
102C2×C37#38611yescharacteristic
103C2×C37#41012yes—
104C2×#123D3711yescharacteristic
105C2×#117—371no—
106C2×#99—372no—
107#381—371no—
108#342—372no—
109C37#189911yescharacteristic, complemented, Sylow
110C22×D4C2×D3711yescharacteristic
111C23×C4C2×D3711yescharacteristic
112#123—22no—
113#123—21no—
114#123—21no—
115#117—744no—
116C2×C4⋊C4—741no—
117C2×C4⋊C4Dic3712yescomplemented
118C2×C22⋊C4—372no—
119C2×C22⋊C4—372no—
120C2×C22⋊C4Dic3712yescomplemented
121C2×C22⋊C4C2×D3711yescharacteristic
122C2×C42—741no—
123#99—744no—
124#95—742no—
125C24C2×Dic3711yescharacteristic
126C24C22×D3711yescharacteristic
127C2×D4—22no—
128C2×D4—22no—
129C2×D4—21no—
130C2×D4—21no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—742no—
134C22×C4—742no—
135C22×C4C2×Dic3711yescharacteristic
136C22×C4C2×Dic3712yes—
137C22×C4C2×Dic3712yes—
138C22×C4C22⋊D3712yes—
139C22×C4C22⋊D3711yescharacteristic
140C22×C4C22⋊D3711yescharacteristic
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—744no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—22no—
147C22⋊C4—22no—
148C22⋊C4—374no—
149C22⋊C4—742no—
150C22⋊C4—742no—
151C22⋊C4—742no—
152C42—744no—
153C23—21no—
154C23—22no—
155C23—42no—
156C23—42no—
157C23D4×D3712yes—
158C23#1059696412yes—
159C23C22×Dic3711yescharacteristic
160C23C2×C22⋊D3711yescharacteristic
161C23C2×C22⋊D3711yescharacteristic
162D4—41no—
163D4—42no—
164D4—41no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—744no—
176C2×C4—1484no—
177C2×C4—1482no—
178C2×C4—1484no—
179C2×C4C22⋊Dic3712yes—
180C2×C4C22⋊Dic3712yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—42no—
187C22—41no—
188C22—82no—
189C22C2×C22⋊Dic3711yescharacteristic
190C22D4×Dic3712yes—
191C22#1192450411yescharacteristic
192C22#1192450812yes—
193C22#1192451711yescharacteristic
194C4—22no—
195C4—22no—
196C4—42no—
197C4—41no—
198C4—2962no—
199C4—1484no—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2—81no—
205C2#1455741311yescharacteristic
206C2#1455750712yes—
subgroupG/H
centerC22C2×C22⋊Dic37
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC2×#123×C37C2
socleC22×C37C2×C22⋊C4
prime radicalC22×D4×C37C22
cosocleC24×C37C23
hypercenterC2×#123D37
hypocenterC37#1899
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#11924495C2semidirect
3. #14557396C2semidirect
4. #14557300C2semidirect
18. C2×C4⋊C4×C37C4semidirect
19. C2×C22⋊C4×C37C4semidirect
109. C37#1899semidirect
117. C2×C4⋊C4Dic37semidirect
120. C2×C22⋊C4Dic37semidirect

Maximal subgroups

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

subgroupindex
C2×#119244952
C2×#119244512
#145573962
#145573002
C2×#123×C372
#189937