Finite Group Databasebeta

← #18009845

Subgroups — #18009845

Order 4736.

312 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 68 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#14558504C212yesmaximal
2#14558379C212yesmaximal, complemented
3#14558378C212yesmaximal, complemented
4C2×C4⋊C4×D37C211yesmaximal, characteristic
5C2×#10596953—22no—
6#11924593—22no—
7C22⋊#64438C2214yes—
8C22×C4×D37C411yescharacteristic
9C22×C4×D37C411yescharacteristic
10C22×C4×D37C2211yescharacteristic
11C2×C4⋊Dic37C2211yescharacteristic
12C2×#10596936C411yescharacteristic
13C2×#10596936C2211yescharacteristic
14C4⋊C4×D37—22no—
15C4⋊C4×D37—22no—
16C2×C4⋊C4×C37C411yescharacteristic
17C23×D37C2×C411yescharacteristic
18C22×C4×C37C2×C411yescharacteristic
19C22×C4×C37C2×C411yescharacteristic
20C22×C4×C37C2×C411yescharacteristic
21C22×Dic37C2×C411yescharacteristic
22C22×Dic37C2×C411yescharacteristic
23C22×Dic37C2311yescharacteristic
24C2×C4×D37—21no—
25C2×C4×D37—21no—
26C2×C4×D37—22no—
27C2×C4×D37—22no—
28C2×C4×D37—21no—
29C2×C4×D37—21no—
30C2×C4×D37—42no—
31C2×C4×D37—42no—
32C2×C4×D37D412yes—
33C2×C4×D37D412yes—
34C2×#64438—24no—
35#10596953—44no—
36C4⋊C4×C37—22no—
37C4⋊Dic37—22no—
38#10596936—22no—
39#10596936—22no—
40C23×C37C22×C411yescharacteristic
41C22×D37—21no—
42C22×D37—21no—
43C22×D37—22no—
44C22×D37—22no—
45C22×D37C22⋊C411yescharacteristic
46C22×D37C22⋊C411yescharacteristic
47C2×C4×C37—21no—
48C2×C4×C37—21no—
49C2×C4×C37—21no—
50C2×C4×C37—41no—
51C2×C4×C37—41no—
52C2×C4×C37C22⋊C412yes—
53C2×C4×C37M1612yescomplemented
54C2×Dic37—21no—
55C2×Dic37—21no—
56C2×Dic37—21no—
57C2×Dic37—41no—
58C2×Dic37—41no—
59C2×Dic37M1612yescomplemented
60C2×Dic37C2×D412yes—
61C4×D37—24no—
62C4×D37—24no—
63C4×D37—24no—
64C4×D37—42no—
65C4×D37—42no—
66C4×D37—42no—
67#64438—44no—
68C22×C37—21no—
69C22×C37—21no—
70C22×C37C2×C22⋊C411yescharacteristic
71C22×C37C2×M1611yescharacteristic
72C22×C37C2×M1611yescharacteristic
73C2×D37—24no—
74C2×D37—24no—
75C2×D37—21no—
76C2×D37—21no—
77C2×D37—21no—
78C2×D37—21no—
79C2×D37#9912yes—
80C2×D37#10112yes—
81C4×C37—22no—
82C4×C37—22no—
83C4×C37—41no—
84Dic37—22no—
85Dic37—22no—
86Dic37—41no—
87#1463—371nomaximal, Sylow
88C2×C37—21no—
89C2×C37—21no—
90C2×C37#40711yescharacteristic
91C2×C37C2×#9911yescharacteristic
92C2×C37C2×#10111yescharacteristic
93D37—22no—
94D37—22no—
95C22×C4⋊C4—371no—
96#407—372no—
97#324—372no—
98#324—372no—
99C37#146311yescharacteristic, complemented, Sylow
100C23×C4—371no—
101C23×C4—371no—
102C23×C4—371no—
103C2×M16—742no—
104C2×C4⋊C4—371no—
105C2×C4⋊C4—371no—
106C2×C4⋊C4—371no—
107C2×C4⋊C4—742no—
108C2×C4⋊C4—742no—
109C2×C4⋊C4#386611yescharacteristic
110C22⋊C8—374no—
111C22⋊C8—742no—
112C24—371no—
113C22×C4—371no—
114C22×C4—371no—
115C22×C4—372no—
116C22×C4—372no—
117C22×C4—371no—
118C22×C4—742no—
119C22×C4—741no—
120C22×C4—741no—
121C22×C4—741no—
122C22×C4—741no—
123C22×C4—742no—
124C22×C4—1482no—
125C22×C4—1482no—
126C22×C4C2×#386611yescharacteristic
127C22×C4C2×#386611yescharacteristic
128C22×C4C2×#386611yescharacteristic
129M16—1484no—
130C2×C8—744no—
131C4⋊C4—22no—
132C4⋊C4—742no—
133C4⋊C4—742no—
134C4⋊C4—742no—
135C23—371no—
136C23—371no—
137C23—742no—
138C23—742no—
139C23—741no—
140C23—741no—
141C23C22×#386611yescharacteristic
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—372no—
148C2×C4—372no—
149C2×C4—744no—
150C2×C4—744no—
151C2×C4—744no—
152C2×C4—741no—
153C2×C4—741no—
154C2×C4—741no—
155C2×C4—1482no—
156C2×C4—1482no—
157C2×C4—1482no—
158C2×C4—1481no—
159C2×C4—1481no—
160C2×C4#1059695312yescomplemented
161C2×C4C22⋊#386612yes—
162C8—1484no—
163C22—21no—
164C22—21no—
165C22—372no—
166C22—372no—
167C22—744no—
168C22—744no—
169C22—741no—
170C22—741no—
171C22—741no—
172C22—741no—
173C22C2×C22⋊#386611yescharacteristic
174C22D37⋊M1611yescharacteristic
175C22C2×#1059695311yescharacteristic
176C4—22no—
177C4—22no—
178C4—41no—
179C4—742no—
180C4—742no—
181C4—1481no—
182C2—21no—
183C2—21no—
184C2—742no—
185C2—742no—
186C2#1455850411yescharacteristic
187C2D37⋊#9911yescharacteristic
188C2D37⋊#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#1463
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
2. #14558379C2semidirect
3. #14558378C2semidirect
53. C2×C4×C37M16semidirect
59. C2×Dic37M16semidirect
99. C37#1463semidirect
160. C2×C4#10596953semidirect

Maximal subgroups

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

subgroupindex
#145585042
#145583792
#145583782
C2×C4⋊C4×D372
#146337