Finite Group Databasebeta

← #18010461

Subgroups — #18010461

Order 4736.

336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 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#14558536C212yesmaximal, complemented
2C2×#11924596C212yesmaximal
3#14558413C212yesmaximal, complemented
4C2×#11924496C211yesmaximal, characteristic
5C2×#10596957C2214yes—
6#11924603—22no—
7C4⋊#64438—22no—
8#11924596—24no—
9C22×C22⋊D37C2211yescharacteristic
10C23×Dic37C411yescharacteristic
11C22×C4×D37C411yescharacteristic
12#11924496—22no—
13#11924496—22no—
14C2×#10596936C2211yescharacteristic
15C2×#10596938C411yescharacteristic
16C2×C4×Dic37C2211yescharacteristic
17C2×C22⋊C4×C37C411yescharacteristic
18C24×C37C2×C411yescharacteristic
19C23×D37C2×C411yescharacteristic
20C22×C4×C37C2×C411yescharacteristic
21C22×C4×C37C2×C411yescharacteristic
22C2×C22⋊D37—22no—
23C2×C22⋊D37—22no—
24C2×C22⋊D37D412yes—
25C2×C22⋊D37Q812yes—
26C22×Dic37—21no—
27C22×Dic37—21no—
28C22×Dic37—42no—
29C22×Dic37C2×C411yescharacteristic
30C22×Dic37C2×C411yescharacteristic
31C22×Dic37C2311yescharacteristic
32C2×C4×D37—21no—
33C2×C4×D37—21no—
34C2×C4×D37—42no—
35#10596957—24no—
36#10596957—24no—
37C2×#64438—24no—
38C22⋊C4×C37—22no—
39#10596938—22no—
40#10596936—22no—
41C4×Dic37D412yes—
42C4×Dic37D412yes—
43C23×C37—21no—
44C23×C37—21no—
45C23×C37—41no—
46C23×C37—41no—
47C23×C37C4⋊C412yes—
48C23×C37C22×C411yescharacteristic
49C22×D37—21no—
50C22×D37—21no—
51C22×D37—41no—
52C22×D37—41no—
53C22×D37C4⋊C412yes—
54C2×C4×C37—21no—
55C2×C4×C37—41no—
56C2×C4×C37—41no—
57C2×C4×C37C22⋊C412yes—
58C22⋊D37—24no—
59C22⋊D37—24no—
60C2×Dic37—22no—
61C2×Dic37—21no—
62C2×Dic37—42no—
63C2×Dic37—42no—
64C2×Dic37—41no—
65C2×Dic37C22⋊C411yescharacteristic
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C2×D411yescharacteristic
68C2×Dic37C2×D412yes—
69C2×Dic37C2×Q811yescharacteristic
70C2×Dic37#4112yes—
71C4×D37—42no—
72C4×D37—42no—
73#64438—44no—
74C22×C37—21no—
75C22×C37—21no—
76C22×C37—22no—
77C22×C37—42no—
78C22×C37—42no—
79C22×C37—41no—
80C22×C37—41no—
81C22×C37C2×C22⋊C411yescharacteristic
82C22×C37C2×C4⋊C411yescharacteristic
83C22×C37#11711yescharacteristic
84C2×D37—22no—
85C2×D37—42no—
86C2×D37—41no—
87C2×D37—41no—
88C2×D37—42no—
89C4×C37—22no—
90C4×C37—41no—
91Dic37—21no—
92Dic37—41no—
93Dic37#10012yescomplemented
94Dic37#12112yes—
95Dic37C22⋊Q812yes—
96#1800—371nomaximal, Sylow
97C2×C37—21no—
98C2×C37—21no—
99C2×C37—42no—
100C2×C37#38011yescharacteristic
101C2×C37C2×#10011yescharacteristic
102C2×C37#41311yescharacteristic
103D37—42no—
104C2×C4×D4—371no—
105#423—372no—
106C2×#100—372no—
107#343—372no—
108C37#180011yescharacteristic, complemented, Sylow
109C22×D4—371no—
110C23×C4—371no—
111C23×C4—371no—
112C2×M16—374no—
113C4×D4—742no—
114C4×D4—742no—
115C2×C4⋊C4—371no—
116C2×C22⋊C4—371no—
117C2×C22⋊C4#386611yescharacteristic
118C2×C42—371no—
119C4⋊C8—742no—
120C4⋊C8—742no—
121#100—744no—
122C24—371no—
123C24C2×#386611yescharacteristic
124C2×D4—372no—
125C2×D4—372no—
126C2×D4—742no—
127C2×D4—742no—
128C22×C4—371no—
129C22×C4—371no—
130C22×C4—371no—
131C22×C4—741no—
132C22×C4—741no—
133C22×C4—741no—
134C22×C4—741no—
135C22×C4—1482no—
136C22×C4—1482no—
137C22×C4C2×#386611yescharacteristic
138C22×C4C2×#386611yescharacteristic
139M16—744no—
140M16—744no—
141C2×C8—744no—
142C4⋊C4—742no—
143C22⋊C4—22no—
144C22⋊C4—742no—
145C42—372no—
146C42—372no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—372no—
152C23—741no—
153C23—741no—
154C23—1481no—
155C23—1481no—
156C23C4⋊#386612yes—
157C23C22×#386611yescharacteristic
158D4—744no—
159D4—744no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—372no—
164C2×C4—371no—
165C2×C4—371no—
166C2×C4—371no—
167C2×C4—372no—
168C2×C4—371no—
169C2×C4—742no—
170C2×C4—741no—
171C2×C4—1482no—
172C2×C4—1482no—
173C2×C4—1482no—
174C2×C4—1482no—
175C2×C4—1481no—
176C2×C4C22⋊#386612yes—
177C8—1484no—
178C22—21no—
179C22—21no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—742no—
186C22—1482no—
187C22—1482no—
188C22—1481no—
189C22—1481no—
190C22C2×C22⋊#386611yescharacteristic
191C22C2×C4⋊#386611yescharacteristic
192C22#1192461511yescharacteristic
193C4—22no—
194C4—41no—
195C4—372no—
196C4—372no—
197C4—372no—
198C4—741no—
199C4—1481no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2—1482no—
204C2#1455847511yescharacteristic
205C2D37⋊#10011yescharacteristic
206C2#1455852011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×C22⋊D37C22
cosocleC22×Dic37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37#1800
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #14558536C2semidirect
3. #14558413C2semidirect
93. Dic37#100semidirect
108. C37#1800semidirect

Maximal subgroups

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

subgroupindex
#145585362
C2×#119245962
#145584132
C2×#119244962
#180037