Finite Group Databasebeta

← #18010281

Subgroups — #18010281

Order 4736.

424 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C22×D37⋊C8C211yesmaximal, characteristic
2C2×#11924615C211yesmaximal, characteristic
3#14558406C214yesmaximal, complemented
4#117×D37C211yesmaximal, characteristic
5C2×D37⋊C8—21no—
6C2×D37⋊C8—22no—
7C2×D37⋊C8C414yescomplemented
8C2×D37⋊C8C2212yes—
9C22×#64438—21no—
10#11924615—22no—
11#11924615C414yescomplemented
12C2×C4⋊#3866C2212yes—
13C2×C22⋊#3866—21no—
14C2×C4×#3866—21no—
15C22×C4×D37C2211yescharacteristic
16#11924495C411yescharacteristic, complemented
17#11924494C412yescomplemented
18#11924493—21no—
19#11924492—21no—
20C4⋊C4×D37C2212yes—
21C22⋊C4×D37—21no—
22C42×D37—21no—
23#117×C37C411yescharacteristic, complemented
24C23×D37D411yescharacteristic
25C22×#3866—22no—
26C22×C4×C37C2×C411yescharacteristic
27C22×Dic37D411yescharacteristic
28C2×C4×D37—22no—
29C2×C4×D37C2×C411yescharacteristic
30C2×C4×D37C2×C412yes—
31C2×C4×D37C2×C412yes—
32C2×C4×D37D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C4×D37D412yes—
35C2×C4×D37Q812yes—
36C2×C4×D37C2311yescharacteristic
37C22⋊#3866—24no—
38C2×#64438—24no—
39C2×#64438—22no—
40C4⋊#3866—22no—
41C4⋊#3866C2×C414yes—
42C4×#3866—24no—
43D37⋊C8—24no—
44D37⋊C8—22no—
45D37⋊C8C2×C414yes—
46C4⋊C4×C37C2×C412yes—
47C22⋊C4×C37—21no—
48C42×C37—21no—
49C22⋊Dic37—21no—
50#10596938—22no—
51C4⋊Dic37C2×C412yes—
52#10596936—22no—
53C4×Dic37—21no—
54C4×Dic37—22no—
55C23×C37C22⋊C411yescharacteristic
56C22×D37—24no—
57C22×D37C22⋊C411yescharacteristic
58C22×D37C22⋊C412yes—
59C22×D37C4⋊C412yes—
60C22×D37C2×D411yescharacteristic
61C2×#3866—24no—
62C2×#3866—44no—
63C2×C4×C37—22no—
64C2×C4×C37C4212yes—
65C2×C4×C37C22⋊C411yescharacteristic
66C2×C4×C37C4⋊C412yes—
67C2×C4×C37C22×C411yescharacteristic
68C2×Dic37—22no—
69C2×Dic37C22⋊C411yescharacteristic
70C2×Dic37C22⋊C412yes—
71C2×Dic37C4⋊C412yes—
72C2×Dic37C2×D411yescharacteristic
73C4×D37—44no—
74C4×D37C4212yes—
75C4×D37C22⋊C412yes—
76C4×D37C22⋊C412yes—
77C4×D37C4⋊C412yes—
78C4×D37C4⋊C412yes—
79C4×D37C4⋊C412yes—
80C4×D37C22×C411yescharacteristic
81C4×D37C22×C411yescharacteristic
82C4×D37C2×D411yescharacteristic
83C4×D37C2×Q811yescharacteristic
84#64438—24no—
85C22×C37—22no—
86C22×C37#9512yes—
87C22×C37C2×C22⋊C411yescharacteristic
88C2×D37—22no—
89C2×D37—24no—
90C2×D37—24no—
91C2×D37#9512yes—
92C2×D37C2×C22⋊C411yescharacteristic
93C2×D37C2×C4⋊C411yescharacteristic
94C2×D37#13514yes—
95#3866—44no—
96C4×C37—42no—
97C4×C37#9512yes—
98C4×C37C2×C4211yescharacteristic
99C4×C37C2×C4⋊C411yescharacteristic
100Dic37—42no—
101Dic37#9512yes—
102Dic37C2×C22⋊C411yescharacteristic
103Dic37C2×C4⋊C411yescharacteristic
104#1735—371nomaximal, Sylow
105C2×C37—22no—
106C2×C37C2×#9511yescharacteristic
107C2×C37#41612yes—
108D37—22no—
109D37#41612yes—
110D37#42712yes—
111C23×C8—371no—
112C2×#117—371no—
113C2×#117—371no—
114#340—374no—
115C37#173511yescharacteristic, complemented, Sylow
116C23×C4—371no—
117C22×C8—372no—
118C22×C8—374no—
119C22×C8—741no—
120C22×C8—742no—
121C22×C8—741no—
122#117—374no—
123#117—371no—
124#117—372no—
125#117—741no—
126#117—741no—
127#117—742no—
128#117#386611yescharacteristic, complemented
129C2×C4⋊C4—372no—
130C2×C4⋊C4—372no—
131C2×C22⋊C4—741no—
132C2×C22⋊C4—741no—
133C2×C42—741no—
134C2×C42—741no—
135C24—371no—
136C22×C4—371no—
137C22×C4—372no—
138C22×C4—372no—
139C22×C4—372no—
140C22×C4—372no—
141C22×C4—371no—
142C22×C4—371no—
143C22×C4—371no—
144C22×C4—371no—
145C22×C4—742no—
146C22×C4—742no—
147C22×C4C2×#386611yescharacteristic
148C2×C8—374no—
149C2×C8—744no—
150C2×C8—742no—
151C2×C8—744no—
152C2×C8—742no—
153C4⋊C4—374no—
154C4⋊C4—372no—
155C4⋊C4—742no—
156C4⋊C4—742no—
157C4⋊C4C2×#386612yes—
158C22⋊C4—21no—
159C22⋊C4—742no—
160C22⋊C4—744no—
161C22⋊C4—741no—
162C42—21no—
163C42—742no—
164C42—744no—
165C42—741no—
166C23—371no—
167C23—372no—
168C23—372no—
169C23—371no—
170C23—744no—
171C23C22⋊#386611yescharacteristic
172C2×C4—22no—
173C2×C4—372no—
174C2×C4—372no—
175C2×C4—371no—
176C2×C4—371no—
177C2×C4—372no—
178C2×C4—372no—
179C2×C4—372no—
180C2×C4—372no—
181C2×C4—371no—
182C2×C4—371no—
183C2×C4—372no—
184C2×C4—371no—
185C2×C4—372no—
186C2×C4—371no—
187C2×C4—744no—
188C2×C4—742no—
189C2×C4—1484no—
190C2×C4—1484no—
191C2×C4C4×#386612yes—
192C2×C4C4⋊#386612yes—
193C2×C4C22⋊#386611yescharacteristic
194C2×C4C22×#386611yescharacteristic
195C8—744no—
196C22—22no—
197C22—371no—
198C22—371no—
199C22—374no—
200C22—372no—
201C22—744no—
202C22—744no—
203C22—742no—
204C22(C2×#3866)⋊C412yes—
205C22C2×C22⋊#386611yescharacteristic
206C4—42no—
207C4—371no—
208C4—372no—
209C4—371no—
210C4—1484no—
211C4—1482no—
212C4(C2×#3866)⋊C412yes—
213C4C2×C4×#386611yescharacteristic
214C4C2×C4⋊#386611yescharacteristic
215C2—22no—
216C2—372no—
217C2—372no—
218C2—742no—
219C2C2×(C2×#3866)⋊C411yescharacteristic
220C2#1455852312yes—
subgroupG/H
centerC2×C4C22⋊#3866
commutatorC4×C37C2×C42
FrattiniC2×C4C22×#3866
Fitting#117×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×D37D4
cosocleC2×C4×D37C23
hypercenter#117#3866
hypocenterC37#1735
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #14558406C2semidirect
7. C2×D37⋊C8C4semidirect
11. #11924615C4semidirect
16. #11924495C4semidirect
17. #11924494C4semidirect
23. #117×C37C4semidirect
115. C37#1735semidirect
128. #117#3866semidirect

Maximal subgroups

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

subgroupindex
C22×D37⋊C82
C2×#119246152
#145584062
#117×D372
#173537