Finite Group Databasebeta

← #18010343

Subgroups — #18010343

Order 4736.

412 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 94 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×#11924594C212yesmaximal
2C4×C22⋊#3866C212yesmaximal, complemented
3#14558411C212yesmaximal, complemented
4C2×#11924496C211yesmaximal, characteristic
5C2×C22⋊#3866C2214yes—
6C2×C4×#3866—22no—
7#11924594C418yescomplemented
8(C2×#3866)⋊C4—22no—
9C22×C22⋊D37C2211yescharacteristic
10C23×Dic37C411yescharacteristic, complemented
11C22×C4×D37C2211yescharacteristic
12#11924496—22no—
13#11924496—22no—
14C2×#10596936C411yescharacteristic, complemented
15C2×#10596938C2211yescharacteristic
16C2×C4×Dic37C411yescharacteristic, complemented
17C2×C22⋊C4×C37C411yescharacteristic, complemented
18C24×C37C2×C411yescharacteristic
19C23×D37C2311yescharacteristic
20C22×#3866—24no—
21C22×C4×C37C2×C411yescharacteristic
22C22×C4×C37C2×C411yescharacteristic
23C2×C22⋊D37—22no—
24C2×C22⋊D37—22no—
25C2×C22⋊D37C2×C414yes—
26C22×Dic37—21no—
27C22×Dic37—21no—
28C22×Dic37—42no—
29C22×Dic37C2×C411yescharacteristic
30C22×Dic37C2×C411yescharacteristic
31C22×Dic37C2×C411yescharacteristic
32C2×C4×D37—42no—
33C2×C4×D37D412yes—
34C2×C4×D37D412yes—
35C22⋊#3866—24no—
36C22⋊#3866C2×C418yescomplemented
37C4×#3866—44no—
38C22⋊C4×C37—22no—
39#10596938—22no—
40#10596936—22no—
41C4×Dic37—21no—
42C4×Dic37—21no—
43C23×C37—21no—
44C23×C37—21no—
45C23×C37—41no—
46C23×C37—41no—
47C23×C37C4212yescomplemented
48C23×C37C22×C411yescharacteristic
49C22×D37—41no—
50C22×D37—41no—
51C22×D37C22×C412yes—
52C22×D37C2×D412yes—
53C22×D37#4112yes—
54C2×#3866—28no—
55C2×#3866—44no—
56C2×#3866—44no—
57C2×C4×C37—21no—
58C2×C4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37C22⋊C412yes—
61C22⋊D37—28no—
62C2×Dic37—21no—
63C2×Dic37—21no—
64C2×Dic37—22no—
65C2×Dic37—21no—
66C2×Dic37—42no—
67C2×Dic37—42no—
68C2×Dic37—41no—
69C2×Dic37C4212yescomplemented
70C2×Dic37C22⋊C411yescharacteristic
71C2×Dic37C22⋊C411yescharacteristic
72C4×D37—24no—
73C4×D37—42no—
74C22×C37—21no—
75C22×C37—21no—
76C22×C37—22no—
77C22×C37—42no—
78C22×C37—42no—
79C22×C37—41no—
80C22×C37—41no—
81C22×C37C2×C4211yescharacteristic
82C22×C37C2×C22⋊C411yescharacteristic
83C22×C37#11711yescharacteristic
84C2×D37—22no—
85C2×D37—22no—
86C2×D37—42no—
87C2×D37—42no—
88C2×D37C4×D414yes—
89#3866—48no—
90C4×C37—22no—
91C4×C37—41no—
92Dic37—22no—
93Dic37—21no—
94Dic37—41no—
95Dic37#9912yescomplemented
96C4×#99—371nomaximal, Sylow
97C2×C37—21no—
98C2×C37—21no—
99C2×C37—42no—
100C2×C37C4×C22⋊C411yescharacteristic
101C2×C37C2×#9911yescharacteristic
102C2×C37#41011yescharacteristic
103D37—24no—
104C2×C4×D4—371no—
105C2×#99—372no—
106C4×C22⋊C4—372no—
107#342—372no—
108C37C4×#9911yescharacteristic, complemented, Sylow
109C22×D4—371no—
110C23×C4—371no—
111C23×C4—371no—
112C4×D4—742no—
113C4×D4—742no—
114C2×C4⋊C4—371no—
115C2×C22⋊C4—374no—
116C2×C22⋊C4—371no—
117C2×C22⋊C4#386611yescharacteristic, complemented
118C2×C42—371no—
119C2×C42—742no—
120#99—378no—
121#95—742no—
122C24—371no—
123C24C2×#386611yescharacteristic
124C2×D4—374no—
125C2×D4—742no—
126C2×D4—742no—
127C22×C4—371no—
128C22×C4—371no—
129C22×C4—372no—
130C22×C4—372no—
131C22×C4—371no—
132C22×C4—741no—
133C22×C4—741no—
134C22×C4—744no—
135C22×C4—1482no—
136C22×C4—1482no—
137C22×C4C2×#386611yescharacteristic
138C22×C4C2×#386611yescharacteristic
139C4⋊C4—742no—
140C22⋊C4—22no—
141C22⋊C4—378no—
142C22⋊C4—742no—
143C22⋊C4—744no—
144C42—741no—
145C42—741no—
146C42—1484no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—372no—
152C23—372no—
153C23—372no—
154C23—1481no—
155C23—1481no—
156C23C4×#386612yescomplemented
157C23C22×#386611yescharacteristic
158D4—748no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—371no—
163C2×C4—372no—
164C2×C4—371no—
165C2×C4—744no—
166C2×C4—742no—
167C2×C4—741no—
168C2×C4—741no—
169C2×C4—748no—
170C2×C4—741no—
171C2×C4—1482no—
172C2×C4—1482no—
173C2×C4—1482no—
174C2×C4—1484no—
175C2×C4—1484no—
176C2×C4—1481no—
177C2×C4C22⋊#386612yes—
178C22—21no—
179C22—21no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—374no—
186C22—742no—
187C22—742no—
188C22—1482no—
189C22—1482no—
190C22C2×C4×#386611yescharacteristic
191C22C2×C22⋊#386611yescharacteristic
192C22#1192461511yescharacteristic
193C4—22no—
194C4—41no—
195C4—372no—
196C4—742no—
197C4—741no—
198C4—1488no—
199C4—1481no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2—744no—
204C2C4×C22⋊#386611yescharacteristic
205C2D37⋊#9911yescharacteristic
206C2#1455851311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC22×C37C2×C42
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×C22⋊D37C22
cosocleC23×D37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37C4×#99
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#3866C2semidirect
3. #14558411C2semidirect
7. #11924594C4semidirect
10. C23×Dic37C4semidirect
14. C2×#10596936C4semidirect
16. C2×C4×Dic37C4semidirect
17. C2×C22⋊C4×C37C4semidirect
36. C22⋊#3866C2×C4semidirect
47. C23×C37C42semidirect
69. C2×Dic37C42semidirect
95. Dic37#99semidirect
108. C37C4×#99semidirect
117. C2×C22⋊C4#3866semidirect
156. C23C4×#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119245942
C4×C22⋊#38662
#145584112
C2×#119244962
C4×#9937