Finite Group Databasebeta

← #18004980

Subgroups — #18004980

Order 4736.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#14558086C211yesmaximal, characteristic, complemented
2C2×#11924523C211yesmaximal, characteristic
3#14557891C214yesmaximal, complemented
4#14557886C214yesmaximal, complemented
5#14557543C211yesmaximal, characteristic, complemented
6#14557541C211yesmaximal, characteristic, complemented
7#14557538C211yesmaximal, characteristic
8M16×Dic37C211yesmaximal, characteristic, complemented
9C37×#418C211yesmaximal, characteristic
10C22×Dic74C2211yescharacteristic
11C2×#10596934C2211yescharacteristic
12#11924535C2212yescomplemented
13#11924527C2212yescomplemented
14#11924523—22no—
15#11924523C2212yes—
16#11924523C2212yes—
17#11924513—22no—
18C4×Dic74—22no—
19#11924495C2211yescharacteristic
20C2×C22⋊Dic37—22no—
21C2×C4×Dic37C2211yescharacteristic
22#11924461C2214yescomplemented
23#11924459C2214yescomplemented
24#11924457C2214yes—
25#11924446C2212yescomplemented
26C8×Dic37C2212yescomplemented
27C22×D4×C37C2211yescharacteristic
28C2×M16×C37C2211yescharacteristic
29#117×C37C2211yescharacteristic
30#102×C37C2214yes—
31C24×C37—21no—
32C2×D4×C37—21no—
33C2×D4×C37—22no—
34C2×D4×C37—22no—
35C2×D4×C37C2312yes—
36C22×C4×C37C2311yescharacteristic
37C22×Dic37—21no—
38C22×Dic37D412yes—
39C2×Dic74—22no—
40C2×Dic74—22no—
41C2×Dic74—21no—
42C2×Dic74—22no—
43C2×Dic74C2312yes—
44M16×C37—22no—
45C2×C8×C37C2312yes—
46C4⋊C4×C37C2312yes—
47C22⋊C4×C37—21no—
48C42×C37—21no—
49C22⋊Dic37—21no—
50C22⋊Dic37—24no—
51C22⋊Dic37—24no—
52C4⋊Dic37—22no—
53C4⋊Dic37C2312yes—
54#10596936—22no—
55#10596936—22no—
56C4×Dic37—21no—
57C4×Dic37D412yes—
58C4×Dic37C2311yescharacteristic
59C4×Dic37C2311yescharacteristic
60#10596934—22no—
61C2×#64436C2312yes—
62C23×C37—22no—
63C23×C37—44no—
64C23×C37—42no—
65C23×C37C2×D411yescharacteristic
66D4×C37—22no—
67D4×C37—22no—
68D4×C37—42no—
69C2×C4×C37—22no—
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37#4112yes—
72C2×C4×C37#4112yes—
73C2×C4×C37C2411yescharacteristic
74C2×Dic37—22no—
75C2×Dic37—22no—
76C2×Dic37—42no—
77C2×Dic37—42no—
78C2×Dic37C2×D412yes—
79C2×Dic37C2×D412yes—
80Dic74—22no—
81Dic74—22no—
82Dic74—44no—
83Dic74—42no—
84C8×C37—22no—
85#64436—22no—
86C22×C37—22no—
87C22×C37—42no—
88C22×C37—44no—
89C22×C37—84no—
90C22×C37#12412yes—
91C22×C37C22×D411yescharacteristic
92C4×C37—42no—
93C4×C37#12412yes—
94C4×C37C2×#4111yescharacteristic
95C4×C37C2×#4111yescharacteristic
96Dic37—22no—
97Dic37—22no—
98Dic37—42no—
99Dic37—42no—
100#3140—371nomaximal, Sylow
101C2×C37—22no—
102C2×C37—82no—
103C2×C37C2×#12411yescharacteristic
104C2×C37#57512yes—
105#533—371no—
106C2×#124—371no—
107#489—374no—
108#488—374no—
109#419—371no—
110#419—371no—
111#418—371no—
112#418D3711yescharacteristic
113C4×M16—371no—
114C37#314011yescharacteristic, complemented, Sylow
115C22×Q8—371no—
116C22×D4C2×D3711yescharacteristic
117C2×M16—371no—
118C2×M16C2×D3711yescharacteristic
119C4⋊Q8—372no—
120#125—372no—
121#124—372no—
122#124—372no—
123#124—742no—
124C22⋊Q8—742no—
125C4×Q8—742no—
126#117—371no—
127#117C2×D3711yescharacteristic
128C2×C22⋊C4—742no—
129C2×C42—371no—
130#103—374no—
131#103—374no—
132#102—374no—
133#102C2×D3714yes—
134#97—372no—
135C4×C8—372no—
136C24—21no—
137C2×Q8—372no—
138C2×Q8—742no—
139C2×Q8—741no—
140C2×Q8—742no—
141C2×Q8—742no—
142C2×D4—22no—
143C2×D4—21no—
144C2×D4—22no—
145C2×D4C22×D3712yes—
146C22×C4—372no—
147C22×C4—741no—
148C22×C4C22×D3711yescharacteristic
149M16—22no—
150M16—742no—
151C2×C8—372no—
152C2×C8C22×D3712yes—
153C4⋊C4—372no—
154C4⋊C4—742no—
155C4⋊C4—742no—
156C4⋊C4—742no—
157C4⋊C4C22×D3712yes—
158C22⋊C4—21no—
159C22⋊C4—744no—
160C22⋊C4—744no—
161C22⋊C4—741no—
162C42—21no—
163C42—372no—
164C42—371no—
165C42—371no—
166C42—741no—
167C23—22no—
168C23—44no—
169C23—42no—
170C23D4×D3711yescharacteristic
171Q8—742no—
172Q8—742no—
173Q8—1484no—
174Q8—1482no—
175D4—22no—
176D4—22no—
177D4—42no—
178C2×C4—22no—
179C2×C4—372no—
180C2×C4—372no—
181C2×C4—742no—
182C2×C4—742no—
183C2×C4—1482no—
184C2×C4—1482no—
185C2×C4#1059696212yes—
186C2×C4D4×D3711yescharacteristic
187C2×C4#1059696412yes—
188C2×C4C23×D3711yescharacteristic
189C8—22no—
190C8—742no—
191C22—22no—
192C22—42no—
193C22—44no—
194C22—84no—
195C22#1192452212yes—
196C22C2×D4×D3711yescharacteristic
197C4—42no—
198C4—742no—
199C4—742no—
200C4—1482no—
201C4—1482no—
202C4#1192452212yes—
203C4C2×#1059696411yescharacteristic
204C4C2×#1059696211yescharacteristic
205C2—22no—
206C2—82no—
207C2C2×#1192452211yescharacteristic
208C2#1455832912yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#418C2
socleC22×C37C22×D4
prime radicalC22×D4×C37C22
hypercenter#418D37
hypocenterC37#3140
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #14558086C2semidirect
3. #14557891C2semidirect
4. #14557886C2semidirect
5. #14557543C2semidirect
6. #14557541C2semidirect
8. M16×Dic37C2semidirect
12. #11924535C22semidirect
13. #11924527C22semidirect
22. #11924461C22semidirect
23. #11924459C22semidirect
25. #11924446C22semidirect
26. C8×Dic37C22semidirect
114. C37#3140semidirect

Maximal subgroups

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

subgroupindex
#145580862
C2×#119245232
#145578912
#145578862
#145575432
#145575412
#145575382
M16×Dic372
C37×#4182
#314037