Finite Group Databasebeta

← #18010456

Subgroups — #18010456

Order 4736.

380 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 80 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
2#14558475C212yesmaximal, complemented
3#14558411C212yesmaximal, complemented
4C2×C4×C22⋊D37C211yesmaximal, characteristic
5C2×C4⋊#3866—22no—
6C2×C22⋊#3866C2214yes—
7#11924594—24no—
8(C2×#3866)⋊C4—22no—
9C22×C22⋊D37C2211yescharacteristic
10C22×C4×D37C2211yescharacteristic
11C4×C22⋊D37—22no—
12C4×C22⋊D37—22no—
13C2×#10596936C411yescharacteristic, complemented
14C2×C22⋊Dic37C411yescharacteristic, complemented
15C2×#10596938C2211yescharacteristic
16C2×C4×Dic37C411yescharacteristic, complemented
17C23×C4×C37C411yescharacteristic, complemented
18C24×C37C2×C411yescharacteristic
19C23×D37C2311yescharacteristic
20C22×#3866—24no—
21C22×C4×C37—21no—
22C22×C4×C37—21no—
23C22×C4×C37—42no—
24C22×C4×C37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C2×C22⋊D37—22no—
27C2×C22⋊D37—22no—
28C2×C22⋊D37D412yes—
29C2×C22⋊D37Q812yes—
30C22×Dic37C2×C411yescharacteristic
31C22×Dic37C2×C411yescharacteristic
32C22×Dic37C2×C411yescharacteristic
33C2×C4×D37—42no—
34C2×C4×D37D412yes—
35C2×C4×D37D412yes—
36C22⋊#3866—24no—
37C22⋊#3866—24no—
38C4⋊#3866—44no—
39C22⋊Dic37—22no—
40#10596938—22no—
41#10596936—22no—
42C4×Dic37—21no—
43C4×Dic37—21no—
44C23×C37—21no—
45C23×C37—21no—
46C23×C37—41no—
47C23×C37—41no—
48C23×C37C4⋊C412yescomplemented
49C23×C37C22×C411yescharacteristic
50C22×D37—41no—
51C22×D37—41no—
52C22×D37C2×D412yes—
53C22×D37C2×D411yescharacteristic
54C22×D37C2×Q811yescharacteristic
55C22×D37#4112yes—
56C2×#3866—44no—
57C2×#3866—44no—
58C2×#3866—44no—
59C2×C4×C37—22no—
60C2×C4×C37—21no—
61C2×C4×C37—42no—
62C2×C4×C37—42no—
63C2×C4×C37—41no—
64C2×C4×C37C22⋊C411yescharacteristic
65C2×C4×C37C22⋊C411yescharacteristic
66C22⋊D37—24no—
67C22⋊D37—24no—
68C2×Dic37—21no—
69C2×Dic37—21no—
70C2×Dic37—21no—
71C2×Dic37—41no—
72C2×Dic37—41no—
73C2×Dic37C22⋊C412yes—
74C2×Dic37C4⋊C412yescomplemented
75C4×D37—24no—
76C4×D37—42no—
77C22×C37—21no—
78C22×C37—21no—
79C22×C37—22no—
80C22×C37—42no—
81C22×C37—42no—
82C22×C37—41no—
83C22×C37—41no—
84C22×C37C2×C22⋊C411yescharacteristic
85C22×C37C2×C4⋊C411yescharacteristic
86C22×C37#11711yescharacteristic
87C2×D37—22no—
88C2×D37—22no—
89C2×D37—41no—
90C2×D37—41no—
91C2×D37—42no—
92C2×D37#12112yes—
93C2×D37C22⋊Q812yes—
94#3866—84no—
95C4×C37—21no—
96C4×C37—41no—
97C4×C37#9912yescomplemented
98Dic37—22no—
99Dic37—22no—
100Dic37—41no—
101#1799—371nomaximal, Sylow
102C2×C37—21no—
103C2×C37—21no—
104C2×C37—42no—
105C2×C37#38011yescharacteristic
106C2×C37C2×#9911yescharacteristic
107C2×C37#41011yescharacteristic
108D37—22no—
109D37—22no—
110C2×C4×D4—371no—
111C2×#99—372no—
112#380—372no—
113#342—372no—
114C37#179911yescharacteristic, complemented, Sylow
115C22×D4—371no—
116C23×C4—371no—
117C23×C4#386611yescharacteristic, complemented
118C4×D4—742no—
119C4×D4—742no—
120C2×C4⋊C4—371no—
121C2×C4⋊C4—742no—
122C2×C22⋊C4—371no—
123C2×C22⋊C4—371no—
124C2×C22⋊C4—374no—
125C2×C42—371no—
126#99—744no—
127#95—742no—
128C24—371no—
129C24C2×#386611yescharacteristic
130C2×D4—372no—
131C2×D4—372no—
132C2×D4—742no—
133C2×D4—742no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—42no—
137C22×C4—371no—
138C22×C4—371no—
139C22×C4—372no—
140C22×C4—372no—
141C22×C4—371no—
142C22×C4—744no—
143C22×C4—1482no—
144C22×C4C2×#386611yescharacteristic
145C22×C4C2×#386611yescharacteristic
146C4⋊C4—742no—
147C4⋊C4—1484no—
148C22⋊C4—742no—
149C22⋊C4—742no—
150C22⋊C4—744no—
151C22⋊C4—744no—
152C42—741no—
153C42—741no—
154C23—21no—
155C23—21no—
156C23—41no—
157C23—41no—
158C23—372no—
159C23—371no—
160C23—371no—
161C23—372no—
162C23—1481no—
163C23—1481no—
164C23C4⋊#386612yescomplemented
165C23C22×#386611yescharacteristic
166D4—744no—
167D4—744no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—372no—
174C2×C4—372no—
175C2×C4—741no—
176C2×C4—741no—
177C2×C4—744no—
178C2×C4—741no—
179C2×C4—1482no—
180C2×C4—1484no—
181C2×C4—1484no—
182C2×C4—1484no—
183C2×C4—1481no—
184C2×C4—1481no—
185C2×C4C22⋊#386611yescharacteristic
186C2×C4C22⋊#386611yescharacteristic
187C22—21no—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22—372no—
195C22—372no—
196C22—742no—
197C22—742no—
198C22—1481no—
199C22—1481no—
200C22—1482no—
201C22C2×C22⋊#386611yescharacteristic
202C22C2×C4⋊#386611yescharacteristic
203C22#1192461511yescharacteristic
204C4—21no—
205C4—41no—
206C4—2964no—
207C4—742no—
208C4—742no—
209C4—1481no—
210C4#1192459412yescomplemented
211C2—21no—
212C2—21no—
213C2—42no—
214C2—742no—
215C2—742no—
216C2#1455847511yescharacteristic
217C2C2×#1192459411yescharacteristic
218C2#1455851211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC23×C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×C22⋊D37C22
cosocleC23×D37C23
hypercenterC23×C4#3866
hypocenterC37#1799
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #14558475C2semidirect
3. #14558411C2semidirect
13. C2×#10596936C4semidirect
14. C2×C22⋊Dic37C4semidirect
16. C2×C4×Dic37C4semidirect
17. C23×C4×C37C4semidirect
48. C23×C37C4⋊C4semidirect
74. C2×Dic37C4⋊C4semidirect
97. C4×C37#99semidirect
114. C37#1799semidirect
117. C23×C4#3866semidirect
164. C23C4⋊#3866semidirect
210. C4#11924594semidirect

Maximal subgroups

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

subgroupindex
C2×#119245942
#145584752
#145584112
C2×C4×C22⋊D372
#179937