Finite Group Databasebeta

← #18004968

Subgroups — #18004968

Order 4736.

484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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×#11924532C211yesmaximal, characteristic
3#14557896C214yesmaximal, complemented
4#14557878C214yesmaximal, complemented
5#14557539C211yesmaximal, characteristic, complemented
6#14557538C211yesmaximal, characteristic, complemented
7#14557537C211yesmaximal, characteristic, complemented
8M16×Dic37C211yesmaximal, characteristic, complemented
9C37×#418C211yesmaximal, characteristic, complemented
10C22×D148C2211yescharacteristic
11C22×C22⋊D37—22no—
12C2×#10596934C2211yescharacteristic
13#11924535C2212yescomplemented
14#11924532—22no—
15#11924532C2212yes—
16#11924532C2212yes—
17#11924527C2212yescomplemented
18#11924513—22no—
19C4×Dic74—22no—
20#11924495C2211yescharacteristic
21C2×C4×Dic37C2211yescharacteristic
22#11924458C2214yescomplemented
23#11924457C2214yescomplemented
24#11924456C2214yescomplemented
25#11924446C2212yescomplemented
26C8×Dic37C2212yescomplemented
27C22×D4×C37C2211yescharacteristic
28C2×M16×C37C2211yescharacteristic
29#117×C37C2211yescharacteristic
30#102×C37C2214yescomplemented
31C24×C37—21no—
32C23×D37—21no—
33C2×D4×C37—21no—
34C2×D4×C37—22no—
35C2×D4×C37—22no—
36C2×D4×C37C2312yes—
37C22×C4×C37C2311yescharacteristic
38C2×C22⋊D37—24no—
39C2×C22⋊D37—24no—
40C2×C22⋊D37—48no—
41C22×Dic37D412yes—
42C2×D148—22no—
43C2×D148—22no—
44C2×D148—21no—
45C2×D148C2312yes—
46C2×Dic74—22no—
47M16×C37—22no—
48C2×C8×C37C2312yes—
49C4⋊C4×C37C2312yes—
50C22⋊C4×C37—21no—
51C42×C37—21no—
52C22⋊Dic37—21no—
53C4⋊Dic37—22no—
54C4⋊Dic37C2312yes—
55#10596936—22no—
56#10596936—22no—
57C4×Dic37—21no—
58C4×Dic37D412yes—
59C4×Dic37C2311yescharacteristic
60C4×Dic37C2311yescharacteristic
61#10596934—22no—
62C2×#64436C2312yes—
63C23×C37—22no—
64C23×C37—44no—
65C23×C37—42no—
66C23×C37C2×D411yescharacteristic
67C22×D37—22no—
68C22×D37—44no—
69C22×D37—42no—
70D4×C37—22no—
71D4×C37—22no—
72D4×C37—42no—
73C2×C4×C37—22no—
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37#4112yes—
76C2×C4×C37#4112yes—
77C2×C4×C37C2411yescharacteristic
78C22⋊D37—48no—
79C22⋊D37—48no—
80C2×Dic37—24no—
81C2×Dic37—22no—
82C2×Dic37C2×D412yes—
83C2×Dic37C2×D412yes—
84D148—22no—
85D148—22no—
86D148—42no—
87Dic74—44no—
88C8×C37—22no—
89#64436—22no—
90C22×C37—22no—
91C22×C37—42no—
92C22×C37—44no—
93C22×C37—84no—
94C22×C37#12412yes—
95C22×C37C22×D411yescharacteristic
96C2×D37—42no—
97C2×D37—44no—
98C2×D37—84no—
99C4×C37—42no—
100C4×C37#12412yes—
101C4×C37C2×#4111yescharacteristic
102C4×C37C2×#4111yescharacteristic
103Dic37—22no—
104Dic37—42no—
105Dic37AGL(1,ℤ/8)14yes—
106#3138—371nomaximal, Sylow
107C2×C37—22no—
108C2×C37—82no—
109C2×C37C2×#12411yescharacteristic
110C2×C37C2×AGL(1,ℤ/8)12yes—
111D37—82no—
112#533—371no—
113C2×#127—371no—
114#490—374no—
115#486—374no—
116#418—371no—
117#418—371no—
118#418—371no—
119#418D3711yescharacteristic, complemented
120C4×M16—371no—
121C37#313811yescharacteristic, complemented, Sylow
122C22×D4—371no—
123C22×D4—742no—
124C22×D4C2×D3711yescharacteristic
125C2×M16—371no—
126C2×M16C2×D3711yescharacteristic
127C4⋊Q8—372no—
128#127—372no—
129#127—372no—
130#127—742no—
131#125—372no—
132C22⋊Q8—742no—
133C4×Q8—742no—
134#117—371no—
135#117C2×D3711yescharacteristic
136C2×C42—371no—
137#102—374no—
138#102—374no—
139#102—374no—
140#102C2×D3714yescomplemented
141#97—372no—
142C4×C8—372no—
143C24—21no—
144C24—741no—
145C2×Q8—742no—
146C2×D4—22no—
147C2×D4—21no—
148C2×D4—22no—
149C2×D4—372no—
150C2×D4—744no—
151C2×D4—744no—
152C2×D4—742no—
153C2×D4—741no—
154C2×D4—742no—
155C2×D4—1488no—
156C2×D4C22×D3712yes—
157C22×C4—372no—
158C22×C4C22×D3711yescharacteristic
159M16—22no—
160M16—742no—
161C2×C8—372no—
162C2×C8C22×D3712yes—
163C4⋊C4—372no—
164C4⋊C4—742no—
165C4⋊C4—742no—
166C4⋊C4—742no—
167C4⋊C4C22×D3712yes—
168C22⋊C4—21no—
169C22⋊C4—741no—
170C42—21no—
171C42—372no—
172C42—371no—
173C42—371no—
174C42—741no—
175C23—22no—
176C23—44no—
177C23—42no—
178C23—742no—
179C23—1484no—
180C23—1482no—
181C23D4×D3711yescharacteristic
182Q8—1484no—
183D4—22no—
184D4—22no—
185D4—42no—
186D4—742no—
187D4—742no—
188D4—1488no—
189D4—1488no—
190D4—1482no—
191C2×C4—22no—
192C2×C4—372no—
193C2×C4—372no—
194C2×C4—744no—
195C2×C4—742no—
196C2×C4#1059696212yes—
197C2×C4D4×D3711yescharacteristic
198C2×C4#1059696412yes—
199C2×C4C23×D3711yescharacteristic
200C8—22no—
201C8—742no—
202C22—22no—
203C22—42no—
204C22—44no—
205C22—84no—
206C22—2964no—
207C22—1482no—
208C22—1484no—
209C22#1192452212yes—
210C22C2×D4×D3711yescharacteristic
211C4—42no—
212C4—374no—
213C4—742no—
214C4—1482no—
215C4#1192452212yes—
216C4C2×#1059696411yescharacteristic
217C4C2×#1059696211yescharacteristic
218C2—22no—
219C2—82no—
220C2—2962no—
221C2C2×#1192452211yescharacteristic
222C2AGL(1,ℤ/8)×D3712yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#418C2
socleC22×C37C22×D4
prime radicalC2×#11924532C2
hypercenter#418D37
hypocenterC37#3138
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. #14557896C2semidirect
4. #14557878C2semidirect
5. #14557539C2semidirect
6. #14557538C2semidirect
7. #14557537C2semidirect
8. M16×Dic37C2semidirect
9. C37×#418C2semidirect
13. #11924535C22semidirect
17. #11924527C22semidirect
22. #11924458C22semidirect
23. #11924457C22semidirect
24. #11924456C22semidirect
25. #11924446C22semidirect
26. C8×Dic37C22semidirect
30. #102×C37C22semidirect
119. #418D37semidirect
121. C37#3138semidirect
140. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580862
C2×#119245322
#145578962
#145578782
#145575392
#145575382
#145575372
M16×Dic372
C37×#4182
#313837