Finite Group Databasebeta

← #18009874

Subgroups — #18009874

Order 4736.

270 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 64 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
2D37⋊(C22⋊C8)C211yesmaximal, characteristic
3#14558378C214yesmaximal, complemented
4C2×#11924516C211yesmaximal, characteristic
5C2×#10596953—21no—
6C2×D37⋊C8—21no—
7#11924593—21no—
8#11924593—21no—
9C22⋊#64438C2212yes—
10C22⋊#64438C2212yes—
11C22×Dic74C411yescharacteristic
12C22×C4×D37C2211yescharacteristic
13#11924516—21no—
14#11924516—21no—
15#11924516—21no—
16#11924516—21no—
17C2×C4⋊Dic37C2212yes—
18C2×#10596938C412yes—
19C2×C4⋊C4×C37C411yescharacteristic
20C23×D37C2×C411yescharacteristic
21C22×C4×C37C2×C412yes—
22C22×C4×C37C2×C411yescharacteristic
23C22×Dic37C2×C412yes—
24C22×Dic37C2311yescharacteristic
25C2×C4×D37—42no—
26C2×C4×D37D411yescharacteristic
27C2×C4×D37D411yescharacteristic
28C2×C4×D37D411yescharacteristic
29C2×C4×D37D411yescharacteristic
30C2×Dic74—21no—
31C2×Dic74—21no—
32C2×Dic74—42no—
33C2×#64438—22no—
34C2×#64438—22no—
35#10596953—42no—
36D37⋊C8—42no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37—21no—
39#10596938—22no—
40#10596938—22no—
41C4⋊Dic37—22no—
42C4⋊Dic37—22no—
43C23×C37C22×C411yescharacteristic
44C22×D37—22no—
45C22×D37—22no—
46C22×D37—41no—
47C22×D37C22⋊C411yescharacteristic
48C22×D37C22⋊C411yescharacteristic
49C2×C4×C37—22no—
50C2×C4×C37—22no—
51C2×C4×C37—24no—
52C2×C4×C37C22⋊C411yescharacteristic
53C2×C4×C37C22⋊C411yescharacteristic
54C2×Dic37—22no—
55C2×Dic37—41no—
56C2×Dic37—42no—
57C2×Dic37C2×D411yescharacteristic
58C2×Dic37C2×D411yescharacteristic
59C4×D37—22no—
60C4×D37—22no—
61C4×D37—41no—
62C4×D37—41no—
63Dic74—42no—
64Dic74—42no—
65#64438—42no—
66#64438—42no—
67C22×C37—21no—
68C22×C37—21no—
69C22×C37C2×C22⋊C411yescharacteristic
70C22×C37#13112yes—
71C2×D37—21no—
72C2×D37—21no—
73C2×D37—21no—
74C2×D37—21no—
75C2×D37—21no—
76C2×D37—44no—
77C2×D37#10112yes—
78C4×C37—21no—
79C4×C37—42no—
80C4×C37#9912yes—
81Dic37—21no—
82Dic37—21no—
83Dic37—42no—
84#1472—371nomaximal, Sylow
85C2×C37—22no—
86C2×C37#40811yescharacteristic
87C2×C37C2×#9911yescharacteristic
88C2×C37C2×#10111yescharacteristic
89D37—22no—
90D37—41no—
91C2×C22⋊Q8—371no—
92#407—371no—
93C2×C22⋊C8—371no—
94#324—374no—
95C37#147211yescharacteristic, complemented, Sylow
96C22×Q8—371no—
97C23×C4—371no—
98C2×M16—741no—
99C22×C8—741no—
100C22⋊Q8—741no—
101C22⋊Q8—741no—
102C22⋊Q8—741no—
103C22⋊Q8—741no—
104C2×C4⋊C4—372no—
105C2×C4⋊C4#386611yescharacteristic
106C2×C22⋊C4—372no—
107C22⋊C8—372no—
108C22⋊C8—372no—
109C22⋊C8—741no—
110C22⋊C8—741no—
111C24—371no—
112C2×Q8—741no—
113C2×Q8—741no—
114C2×Q8—1482no—
115C22×C4—371no—
116C22×C4—371no—
117C22×C4—371no—
118C22×C4—371no—
119C22×C4—371no—
120C22×C4—372no—
121C22×C4—1482no—
122C22×C4C2×#386612yes—
123C22×C4C2×#386611yescharacteristic
124M16—1482no—
125C2×C8—742no—
126C2×C8—742no—
127C2×C8—1482no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—742no—
131C4⋊C4—742no—
132C22⋊C4—742no—
133C22⋊C4—742no—
134C23—371no—
135C23—371no—
136C23—742no—
137C23—742no—
138C23—1481no—
139C23C22×#386611yescharacteristic
140Q8—1482no—
141Q8—1482no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—371no—
146C2×C4—371no—
147C2×C4—742no—
148C2×C4—742no—
149C2×C4—742no—
150C2×C4—1481no—
151C2×C4—1481no—
152C2×C4—1481no—
153C2×C4—1482no—
154C2×C4C22⋊#386611yescharacteristic
155C2×C4C22⋊#386611yescharacteristic
156C8—1482no—
157C8—1482no—
158C22—21no—
159C22—21no—
160C22—372no—
161C22—741no—
162C22—741no—
163C22—741no—
164C22—741no—
165C22—741no—
166C22—1484no—
167C22C2×C22⋊#386611yescharacteristic
168C22#1192462312yes—
169C4—21no—
170C4—42no—
171C4—741no—
172C4—741no—
173C4—1482no—
174C4#1192459512yes—
175C2—22no—
176C2—742no—
177C2—1481no—
178C2#1455850711yescharacteristic
179C2C2×#1192459511yescharacteristic
180C2D37⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×D37C2×C4
cosocleC22×Dic37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1472
LCSG ▷ C23×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. #14558378C2semidirect
95. C37#1472semidirect

Maximal subgroups

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

subgroupindex
#145585042
D37⋊(C22⋊C8)2
#145583782
C2×#119245162
#147237