Finite Group Databasebeta

← #17995538

Subgroups — #17995538

Order 4736.

260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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
2M16×Dic37C211yesmaximal, characteristic
3C4×#10596936C211yesmaximal, characteristic
4#14557294C211yesmaximal, characteristic
5#14557293C211yesmaximal, characteristic
6#14557292C211yesmaximal, characteristic
7C37×#339C211yesmaximal, characteristic
8C2×#10596934C2211yescharacteristic
9#11924535C411yescharacteristic, complemented
10#11924535C411yescharacteristic, complemented
11#11924527C411yescharacteristic, complemented
12#11924527C411yescharacteristic, complemented
13#11924513—21no—
14#11924513—21no—
15C4×Dic74—21no—
16C4×Dic74—21no—
17#11924495C2211yescharacteristic
18C2×#10596936—21no—
19C2×C4×Dic37C2211yescharacteristic
20C2×C4×Dic37C2211yescharacteristic
21#11924446—21no—
22C8×Dic37—21no—
23#11924443—21no—
24C2×M16×C37C2211yescharacteristic
25#117×C37C2211yescharacteristic
26C2×C42×C37C2211yescharacteristic
27C22×C4×C37—21no—
28C22×C4×C37C2311yescharacteristic
29C22×Dic37—21no—
30C22×Dic37D411yescharacteristic
31C22×Dic37D411yescharacteristic
32C2×Dic74—21no—
33C2×Dic74—21no—
34M16×C37—21no—
35M16×C37Q812yescomplemented
36C2×C8×C37—21no—
37C4⋊C4×C37C2×C411yescharacteristic
38C4⋊C4×C37C2×C411yescharacteristic
39C22⋊C4×C37—21no—
40C42×C37—21no—
41C42×C37—21no—
42C42×C37—21no—
43C22⋊Dic37—21no—
44C4⋊Dic37—21no—
45C4⋊Dic37—21no—
46C4⋊Dic37C2×C411yescharacteristic
47C4⋊Dic37C2×C411yescharacteristic
48#10596936—24no—
49#10596936—21no—
50#10596936—21no—
51#10596936—21no—
52#10596936—21no—
53C4×Dic37—21no—
54C4×Dic37—21no—
55C4×Dic37—21no—
56C4×Dic37C2×C411yescharacteristic
57C4×Dic37C2×C411yescharacteristic
58C4×Dic37D411yescharacteristic
59C4×Dic37D411yescharacteristic
60#10596934—21no—
61#10596934Q812yescomplemented
62C2×#64436—21no—
63C23×C37C2×D411yescharacteristic
64C2×C4×C37—22no—
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37—41no—
68C2×C4×C37—41no—
69C2×C4×C37C22×C411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×Q811yescharacteristic
72C2×C4×C37C2×Q811yescharacteristic
73C2×C4×C37#4111yescharacteristic
74C2×C4×C37#4111yescharacteristic
75C2×Dic37—22no—
76C2×Dic37—22no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37—41no—
80C2×Dic37—41no—
81C2×Dic37—41no—
82C2×Dic37C22⋊C411yescharacteristic
83C2×Dic37C22⋊C411yescharacteristic
84C2×Dic37C22⋊C411yescharacteristic
85C2×Dic37C22⋊C411yescharacteristic
86Dic74—42no—
87Dic74—42no—
88C8×C37—22no—
89#64436—22no—
90C22×C37—21no—
91C22×C37—21no—
92C22×C37C2×C22⋊C411yescharacteristic
93C22×C37#12411yescharacteristic
94C22×C37C4⋊Q811yescharacteristic
95C4×C37—42no—
96C4×C37—41no—
97C4×C37—41no—
98C4×C37C4×Q811yescharacteristic
99C4×C37C4×Q811yescharacteristic
100C4×C37C22⋊Q811yescharacteristic
101C4×C37C22⋊Q811yescharacteristic
102Dic37—21no—
103Dic37—21no—
104Dic37—21no—
105Dic37—42no—
106Dic37—41no—
107Dic37—41no—
108Dic37#10412yes—
109#1986—371nomaximal, Sylow
110C2×C37—21no—
111C2×C37—21no—
112C2×C37#39111yescharacteristic
113C2×C37C2×#10411yescharacteristic
114C2×C37#42111yescharacteristic
115#533—371no—
116C4×M16—371no—
117C4×C4⋊C4—371no—
118#339—371no—
119#339—371no—
120#339—371no—
121#339D3711yescharacteristic
122C37#198611yescharacteristic, complemented, Sylow
123C2×M16—371no—
124C2×M16C2×D3711yescharacteristic
125C4⋊Q8—371no—
126C4⋊Q8—371no—
127#125—371no—
128#125—371no—
129C22⋊Q8—741no—
130C22⋊Q8—741no—
131C4×Q8—741no—
132C4×Q8—741no—
133#117—371no—
134#117C2×D3711yescharacteristic
135C2×C4⋊C4—741no—
136C2×C42—371no—
137C2×C42—371no—
138C2×C42C2×D3711yescharacteristic
139#97—741no—
140C4×C8—741no—
141#95—741no—
142C2×Q8—741no—
143C2×Q8—741no—
144C22×C4—21no—
145C22×C4—371no—
146C22×C4—371no—
147C22×C4—741no—
148C22×C4C22×D3711yescharacteristic
149M16—21no—
150M16—372no—
151M16—741no—
152M16Dic7412yescomplemented
153C2×C8—21no—
154C2×C8—741no—
155C4⋊C4—371no—
156C4⋊C4—371no—
157C4⋊C4—741no—
158C4⋊C4—741no—
159C4⋊C4—741no—
160C4⋊C4—741no—
161C4⋊C4—741no—
162C4⋊C4—741no—
163C4⋊C4—744no—
164C4⋊C4C4×D3711yescharacteristic
165C4⋊C4C4×D3711yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—741no—
168C42—21no—
169C42—21no—
170C42—21no—
171C42—371no—
172C42—371no—
173C42—371no—
174C42—371no—
175C42—741no—
176C42—741no—
177C42—741no—
178C23D4×D3711yescharacteristic
179Q8—1482no—
180Q8—1482no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—371no—
187C2×C4—371no—
188C2×C4—371no—
189C2×C4—371no—
190C2×C4—742no—
191C2×C4—742no—
192C2×C4—741no—
193C2×C4—741no—
194C2×C4—1481no—
195C2×C4—1481no—
196C2×C4—1481no—
197C2×C4C2×Dic7411yescharacteristic
198C2×C4C2×C4×D3711yescharacteristic
199C2×C4#1059696211yescharacteristic
200C2×C4D4×D3711yescharacteristic
201C2×C4#1059696411yescharacteristic
202C2×C4Q8×D3711yescharacteristic
203C8—22no—
204C8—742no—
205C22—21no—
206C22—21no—
207C22C22⋊C4×D3711yescharacteristic
208C22#1192452211yescharacteristic
209C22#1192453511yescharacteristic
210C4—42no—
211C4—41no—
212C4—41no—
213C4—372no—
214C4—741no—
215C4—741no—
216C4—741no—
217C4—1482no—
218C4—1481no—
219C4—1481no—
220C4#1192450111yescharacteristic
221C4C4×Dic7411yescharacteristic
222C4#1192451311yescharacteristic
223C4#1192451411yescharacteristic
224C2—21no—
225C2—21no—
226C2#1455743711yescharacteristic
227C2#104×D3711yescharacteristic
228C2#1455754811yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37C2×C22⋊C4
prime radicalC23×C37C2×D4
cosocleC22×C4×C37C23
hypercenter#339D37
hypocenterC37#1986
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
9. #11924535C4semidirect
10. #11924535C4semidirect
11. #11924527C4semidirect
12. #11924527C4semidirect
35. M16×C37Q8semidirect
61. #10596934Q8semidirect
122. C37#1986semidirect
152. M16Dic74semidirect

Maximal subgroups

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

subgroupindex
#145580862
M16×Dic372
C4×#105969362
#145572942
#145572932
#145572922
C37×#3392
#198637