Finite Group Databasebeta

← #18010503

Subgroups — #18010503

Order 4736.

306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 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#14558504C211yesmaximal, characteristic
2C4×C22⋊#3866C211yesmaximal, characteristic
3#14558403C214yesmaximal, complemented
4C2×#11924494C211yesmaximal, characteristic
5C2×#10596953C2212yes—
6C2×C22⋊#3866—21no—
7C2×C4×#3866C2212yes—
8#11924593—21no—
9C22⋊#64438—21no—
10(C2×#3866)⋊C4—21no—
11C22×C4×D37C2211yescharacteristic
12#11924494—21no—
13#11924494—21no—
14#11924494C412yescomplemented
15#11924494C2212yes—
16C2×C4⋊Dic37C411yescharacteristic, complemented
17C2×#10596938—21no—
18C2×C4×Dic37—21no—
19C2×C4⋊C4×C37C411yescharacteristic, complemented
20C23×D37D411yescharacteristic
21C22×#3866—22no—
22C22×C4×C37—21no—
23C22×C4×C37C2×C411yescharacteristic
24C22×Dic37—21no—
25C22×Dic37D411yescharacteristic
26C2×C4×D37—24no—
27C2×C4×D37C2×C411yescharacteristic
28C2×C4×D37D411yescharacteristic
29C2×C4×D37D411yescharacteristic
30C2×C4×D37C2311yescharacteristic
31C22⋊#3866—24no—
32C2×#64438—22no—
33C4×#3866—24no—
34#10596953—24no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37C2×C412yes—
37#10596938—22no—
38#10596938—22no—
39C4⋊Dic37—21no—
40C4⋊Dic37C2×C412yes—
41C4×Dic37—22no—
42C4×Dic37—22no—
43C23×C37C22⋊C411yescharacteristic
44C22×D37—22no—
45C22×D37—22no—
46C22×D37—41no—
47C22×D37C22⋊C411yescharacteristic
48C22×D37C2×D411yescharacteristic
49C2×#3866—24no—
50C2×#3866—42no—
51C2×#3866—42no—
52C2×C4×C37—22no—
53C2×C4×C37—22no—
54C2×C4×C37—42no—
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22×C411yescharacteristic
57C2×Dic37—22no—
58C2×Dic37—22no—
59C2×Dic37—42no—
60C2×Dic37C22⋊C411yescharacteristic
61C2×Dic37C2×D411yescharacteristic
62C4×D37—22no—
63C4×D37—22no—
64C4×D37—22no—
65C4×D37#4114yes—
66#64438—42no—
67C22×C37—21no—
68C22×C37—21no—
69C22×C37#10412yes—
70C22×C37C2×C22⋊C411yescharacteristic
71C2×D37—21no—
72C2×D37—21no—
73C2×D37—21no—
74C2×D37—21no—
75C2×D37—21no—
76C2×D37—44no—
77C2×D37#12312yes—
78#3866—44no—
79C4×C37—21no—
80C4×C37—42no—
81C4×C37#11712yes—
82Dic37—21no—
83Dic37—42no—
84Dic37#12312yes—
85#1826—371nomaximal, Sylow
86C2×C37—22no—
87C2×C37#38111yescharacteristic
88C2×C37C2×#10411yescharacteristic
89C2×C37#42111yescharacteristic
90D37—22no—
91D37—41no—
92C2×#117—371no—
93#407—371no—
94C4×C22⋊C4—371no—
95#339—374no—
96C37#182611yescharacteristic, complemented, Sylow
97C23×C4—371no—
98C2×M16—372no—
99#117—372no—
100#117—372no—
101#117—741no—
102#117—741no—
103C2×C4⋊C4—371no—
104C2×C4⋊C4#386611yescharacteristic, complemented
105C2×C22⋊C4—741no—
106C2×C22⋊C4—741no—
107C2×C42—372no—
108C2×C42—741no—
109C22⋊C8—741no—
110C22⋊C8—741no—
111#95—741no—
112C24—371no—
113C22×C4—21no—
114C22×C4—371no—
115C22×C4—371no—
116C22×C4—371no—
117C22×C4—371no—
118C22×C4—371no—
119C22×C4—744no—
120C22×C4—742no—
121C22×C4—741no—
122C22×C4C2×#386611yescharacteristic
123M16—744no—
124C2×C8—742no—
125C4⋊C4—21no—
126C4⋊C4—372no—
127C4⋊C4—741no—
128C4⋊C4C2×#386612yes—
129C22⋊C4—742no—
130C22⋊C4—742no—
131C22⋊C4—744no—
132C42—742no—
133C42—742no—
134C42—744no—
135C23—371no—
136C23—371no—
137C23—742no—
138C23—742no—
139C23—1481no—
140C23C22⋊#386611yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—371no—
145C2×C4—374no—
146C2×C4—371no—
147C2×C4—742no—
148C2×C4—742no—
149C2×C4—742no—
150C2×C4—742no—
151C2×C4—744no—
152C2×C4—742no—
153C2×C4—1482no—
154C2×C4—1482no—
155C2×C4—1482no—
156C2×C4C22⋊#386611yescharacteristic
157C2×C4C22×#386611yescharacteristic
158C8—1482no—
159C22—21no—
160C22—21no—
161C22—372no—
162C22—741no—
163C22—741no—
164C22—741no—
165C22—741no—
166C22—741no—
167C22—1484no—
168C22#1192460112yes—
169C22C2×C22⋊#386611yescharacteristic
170C4—21no—
171C4—42no—
172C4—372no—
173C4—741no—
174C4—1484no—
175C4—1482no—
176C4#1192461512yes—
177C2—22no—
178C2—742no—
179C2—1481no—
180C2#1455847611yescharacteristic
181C2C2×#1192460111yescharacteristic
182C2#1455853111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×D37D4
cosocleC2×C4×D37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1826
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14558403C2semidirect
14. #11924494C4semidirect
16. C2×C4⋊Dic37C4semidirect
19. C2×C4⋊C4×C37C4semidirect
96. C37#1826semidirect
104. C2×C4⋊C4#3866semidirect

Maximal subgroups

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

subgroupindex
#145585042
C4×C22⋊#38662
#145584032
C2×#119244942
#182637