Finite Group Databasebeta

← #17995728

Subgroups — #17995728

Order 4736.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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#14558095C211yesmaximal, characteristic
2C2×#11924520C212yesmaximal, complemented
3C2×#11924450C212yesmaximal, complemented
4#14557394C211yesmaximal, characteristic, complemented
5C37×#342C211yesmaximal, characteristic, complemented
6C22×C22⋊D37C2212yes—
7C23×Dic37C2211yescharacteristic
8#11924520—22no—
9#11924520—24no—
10#11924520—24no—
11#11924510—22no—
12#11924506—22no—
13C2×C4⋊Dic37—22no—
14C2×C22⋊Dic37C2211yescharacteristic
15C2×#10596938—22no—
16#11924450—24no—
17#11924443—22no—
18C2×C22⋊C4×C37C2211yescharacteristic
19C2×C22⋊C4×C37C2212yes—
20C24×C37C2311yescharacteristic
21C23×D37D412yes—
22C22×C4×C37—22no—
23C22×C4×C37D412yes—
24C2×C22⋊D37—22no—
25C2×C22⋊D37—22no—
26C2×C22⋊D37—22no—
27C2×C22⋊D37—22no—
28C2×C22⋊D37—22no—
29C2×C22⋊D37—22no—
30C22×Dic37—22no—
31C22×Dic37—22no—
32C22×Dic37—21no—
33C22×Dic37—21no—
34C22×Dic37—21no—
35C22×Dic37D412yes—
36C22×Dic37D412yescomplemented
37C2×D148—22no—
38C22⋊C4×C37—22no—
39C22⋊C4×C37—22no—
40C22⋊C4×C37D414yescomplemented
41C22⋊Dic37—22no—
42#10596938—28no—
43#10596938—24no—
44C4⋊Dic37—28no—
45C4⋊Dic37—22no—
46C23×C37—42no—
47C23×C37C2×D411yescharacteristic
48C23×C37C2×D412yes—
49C23×C37C2×D412yes—
50C23×C37C2×D411yescharacteristic
51C23×C37#4111yescharacteristic
52C22×D37—22no—
53C22×D37—22no—
54C22×D37—22no—
55C22×D37—44no—
56C2×C4×C37—24no—
57C2×C4×C37—22no—
58C2×C4×C37—44no—
59C2×C4×C37—42no—
60C22⋊D37—42no—
61C22⋊D37—42no—
62C22⋊D37—42no—
63C22⋊D37—42no—
64C2×Dic37—22no—
65C2×Dic37—24no—
66C2×Dic37—22no—
67C2×Dic37—22no—
68C2×Dic37—22no—
69C2×Dic37—41no—
70C2×Dic37—42no—
71C2×Dic37—41no—
72C2×Dic37—42no—
73C2×Dic37—41no—
74D148—82no—
75C22×C37—22no—
76C22×C37—24no—
77C22×C37—42no—
78C22×C37—41no—
79C22×C37—41no—
80C22×C37#12012yes—
81C22×C37#12011yescharacteristic
82C22×C37#12111yescharacteristic
83C22×C37#12112yes—
84C22×C37#12711yescharacteristic
85C2×D37—44no—
86C2×D37—42no—
87C2×D37—44no—
88C2×D37—82no—
89C4×C37—44no—
90C4×C37—42no—
91Dic37—42no—
92Dic37—42no—
93Dic37—81no—
94#2022—371nomaximal, Sylow
95C2×C37—21no—
96C2×C37—22no—
97C2×C37—22no—
98C2×C37—21no—
99C2×C37#39211yescharacteristic
100C2×C37#45812yes—
101D37—82no—
102#534—371no—
103C2×#123—372no—
104C2×#99—372no—
105#381—371no—
106#342D3711yescharacteristic, complemented
107C37#202211yescharacteristic, complemented, Sylow
108C22×D4—372no—
109C23×C4—371no—
110#123—744no—
111#123—742no—
112#123—744no—
113#121—742no—
114#120—742no—
115C2×C4⋊C4—742no—
116C2×C22⋊C4—371no—
117C2×C22⋊C4—742no—
118C2×C22⋊C4C2×D3711yescharacteristic
119C2×C22⋊C4C2×D3712yes—
120#99—744no—
121#95—742no—
122C24—372no—
123C24C22×D3711yescharacteristic
124C2×D4—742no—
125C2×D4—742no—
126C2×D4—742no—
127C2×D4—742no—
128C2×D4—742no—
129C2×D4—742no—
130C2×D4—742no—
131C22×C4—22no—
132C22×C4—372no—
133C22×C4—372no—
134C22×C4—741no—
135C22×C4—742no—
136C22×C4—742no—
137C22×C4—741no—
138C22×C4—741no—
139C22×C4D14812yes—
140C4⋊C4—748no—
141C4⋊C4—742no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—748no—
145C22⋊C4—744no—
146C22⋊C4—742no—
147C22⋊C4D14814yescomplemented
148C23—42no—
149C23—742no—
150C23—742no—
151C23—742no—
152C23—1484no—
153C23C2×D14811yescharacteristic
154C23C2×D14812yes—
155C23D4×D3712yes—
156C23D4×D3711yescharacteristic
157C23#1059696611yescharacteristic
158D4—2962no—
159D4—1482no—
160D4—1482no—
161D4—1482no—
162D4—1482no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—44no—
166C2×C4—42no—
167C2×C4—744no—
168C2×C4—742no—
169C2×C4—742no—
170C2×C4—742no—
171C2×C4—742no—
172C2×C4—1482no—
173C2×C4—1481no—
174C2×C4—1481no—
175C2×C4—1482no—
176C2×C4—1481no—
177C22—22no—
178C22—24no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—2962no—
183C22—1484no—
184C22—1482no—
185C22—1484no—
186C22#1192450612yes—
187C22#1192450611yescharacteristic
188C22#1192451111yescharacteristic
189C22#1192451112yes—
190C22#1192453311yescharacteristic
191C4—44no—
192C4—42no—
193C4—2961no—
194C4—1482no—
195C4—1482no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—2962no—
201C2#1455744311yescharacteristic
202C2#1455772412yes—
subgroupG/H
centerC22#11924506
commutator, cosocleC24×C37C23
FrattiniC24C22×D37
FittingC37×#342C2
socleC22×C37#120
prime radical#14558095C2
hypercenter#342D37
hypocenterC37#2022
LCSG ▷ C24×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#11924520C2semidirect
3. C2×#11924450C2semidirect
4. #14557394C2semidirect
5. C37×#342C2semidirect
36. C22×Dic37D4semidirect
40. C22⋊C4×C37D4semidirect
106. #342D37semidirect
107. C37#2022semidirect
147. C22⋊C4D148semidirect

Maximal subgroups

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

subgroupindex
#145580952
C2×#119245202
C2×#119244502
#145573942
C37×#3422
#202237