Finite Group Databasebeta

← #18009681

Subgroups — #18009681

Order 4736.

234 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 44 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×#11924596C211yesmaximal, characteristic
2C2×#11924594C211yesmaximal, characteristic
3#14557410C211yesmaximal, characteristic
4C2×#10596957—21no—
5C2×C22⋊#3866—21no—
6#11924596—21no—
7#11924596C412yescomplemented
8#11924594—21no—
9#11924594C412yescomplemented
10C22×C22⋊D37C2211yescharacteristic
11C23×Dic37C411yescharacteristic, complemented
12C2×#10596938—21no—
13#11924443—21no—
14C2×C22⋊C4×C37C411yescharacteristic, complemented
15C24×C37C2×C411yescharacteristic
16C23×D37D411yescharacteristic
17C22×#3866—41no—
18C22×C4×C37—21no—
19C2×C22⋊D37—41no—
20C2×C22⋊D37—41no—
21C2×C22⋊D37C2×C411yescharacteristic
22C2×C22⋊D37C2×C411yescharacteristic
23C2×C22⋊D37D411yescharacteristic
24C2×C22⋊D37Q811yescharacteristic
25C22×Dic37—21no—
26C22×Dic37—42no—
27C22×Dic37—41no—
28C22×Dic37D411yescharacteristic
29C22⋊#3866—22no—
30C22⋊#3866—41no—
31#10596957—22no—
32#10596957—41no—
33C2×#64438—41no—
34C22⋊C4×C37—41no—
35#10596938—42no—
36C23×C37—21no—
37C23×C37—21no—
38C23×C37—41no—
39C23×C37—41no—
40C23×C37C4211yescharacteristic
41C23×C37C22⋊C411yescharacteristic
42C23×C37C4⋊C411yescharacteristic
43C22×D37—21no—
44C22×D37—21no—
45C22×D37—41no—
46C22×D37—41no—
47C22×D37C22⋊C411yescharacteristic
48C22×D37C4⋊C411yescharacteristic
49C2×#3866—42no—
50C2×#3866—81no—
51C2×#3866—81no—
52C2×C4×C37—41no—
53C2×C4×C37—41no—
54C2×C4×C37—41no—
55C22⋊D37—41no—
56C22⋊D37—41no—
57C22⋊D37—41no—
58C22⋊D37—41no—
59C2×Dic37—21no—
60C2×Dic37—21no—
61C2×Dic37—22no—
62C2×Dic37—41no—
63C2×Dic37—42no—
64C2×Dic37—41no—
65C2×Dic37—42no—
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C4⋊C411yescharacteristic
68#64438—42no—
69C22×C37—21no—
70C22×C37—21no—
71C22×C37—21no—
72C22×C37—21no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37—42no—
76C22×C37—41no—
77C22×C37—41no—
78C22×C37#9511yescharacteristic
79C22×C37#9911yescharacteristic
80C22×C37#9911yescharacteristic
81C2×D37—21no—
82C2×D37—21no—
83C2×D37—41no—
84C2×D37—41no—
85C2×D37—41no—
86C2×D37—41no—
87C2×D37—81no—
88#3866—82no—
89C4×C37—81no—
90Dic37—21no—
91Dic37—21no—
92Dic37—42no—
93#1390—371nomaximal, Sylow
94C2×C37—21no—
95C2×C37—21no—
96C2×C37—41no—
97C2×C37—41no—
98C2×C37#34211yescharacteristic
99C2×C37AΣL(1,𝔽16)11yescharacteristic
100C2×C37#35211yescharacteristic
101D37—41no—
102D37—41no—
103C2×#100—371no—
104C2×#99—371no—
105#386—371no—
106C37#139011yescharacteristic, complemented, Sylow
107C22×D4—371no—
108C23×C4—371no—
109C2×M16—741no—
110C2×C22⋊C4—741no—
111C2×C22⋊C4—741no—
112C2×C22⋊C4#386611yescharacteristic, complemented
113#100—372no—
114#100—741no—
115#99—372no—
116#99—741no—
117#95—741no—
118C24—371no—
119C24C2×#386611yescharacteristic
120C2×D4—371no—
121C2×D4—371no—
122C2×D4—371no—
123C2×D4—371no—
124C2×D4—1481no—
125C2×D4—1481no—
126C22×C4—21no—
127C22×C4—371no—
128C22×C4—741no—
129C22×C4—1481no—
130C22×C4—1482no—
131C22×C4—1481no—
132M16—742no—
133M16—1481no—
134C2×C8—1481no—
135C22⋊C4—41no—
136C22⋊C4—742no—
137C22⋊C4—1482no—
138C22⋊C4—1481no—
139C23—21no—
140C23—21no—
141C23—41no—
142C23—41no—
143C23—371no—
144C23—371no—
145C23—741no—
146C23—741no—
147C23—1481no—
148C23—1481no—
149C23C4×#386611yescharacteristic
150C23C4⋊#386611yescharacteristic
151C23C22⋊#386611yescharacteristic
152D4—1481no—
153D4—1481no—
154D4—1481no—
155D4—1481no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—371no—
160C2×C4—371no—
161C2×C4—2961no—
162C2×C4—2961no—
163C2×C4—741no—
164C2×C4—741no—
165C2×C4—742no—
166C2×C4—1482no—
167C2×C4—1481no—
168C2×C4—1482no—
169C2×C4—1481no—
170C2×C4—1482no—
171C8—1482no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—42no—
179C22—41no—
180C22—41no—
181C22—2961no—
182C22—741no—
183C22—741no—
184C22—1481no—
185C22—1481no—
186C22—1481no—
187C22—1481no—
188C22(C2×#3866)⋊C411yescharacteristic
189C22#1192459411yescharacteristic
190C22#1192459511yescharacteristic
191C4—81no—
192C4—2962no—
193C4—741no—
194C4—741no—
195C4—1482no—
196C2—21no—
197C2—21no—
198C2—41no—
199C2—41no—
200C2—1481no—
201C2—1481no—
202C2#1455841111yescharacteristic
203C2#1455843411yescharacteristic
204C2#1455843611yescharacteristic
subgroupG/H
centerC22#11924595
commutatorC23×C37C42
FrattiniC24C2×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37#99
prime radical, cosocleC22×C22⋊D37C22
hypercenterC2×C22⋊C4#3866
hypocenterC37#1390
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
7. #11924596C4semidirect
9. #11924594C4semidirect
11. C23×Dic37C4semidirect
14. C2×C22⋊C4×C37C4semidirect
106. C37#1390semidirect
112. C2×C22⋊C4#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119245962
C2×#119245942
#145574102
#139037