Finite Group Databasebeta

← #18005312

Subgroups — #18005312

Order 4736.

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

normal subgroups only

This group has 402 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#14558088C211yesmaximal, characteristic, complemented
2#14558081C211yesmaximal, characteristic
3#14557938C211yesmaximal, characteristic, complemented
4#14557883C211yesmaximal, characteristic, complemented
5#14557879C211yesmaximal, characteristic, complemented
6#14557776C214yesmaximal, complemented
7#14557634C214yesmaximal, complemented
8C4×#10596929C211yesmaximal, characteristic, complemented
9C37×#492C211yesmaximal, characteristic, complemented
10C2×#10596964—21no—
11C2×#10596929C2212yes—
12#11924536C2211yescharacteristic
13#11924536C2211yescharacteristic
14#11924527—21no—
15#11924523—21no—
16#11924516—21no—
17#11924512C2212yes—
18#11924507—21no—
19#11924507C2212yes—
20Q8×Dic37C2212yes—
21#11924501—21no—
22D4×Dic37—21no—
23D4×Dic37C2212yes—
24#11924494—21no—
25C42×D37C2211yescharacteristic
26#11924470C2214yes—
27#11924460C2214yes—
28#11924457C2214yes—
29#11924446C2212yes—
30C4×#64436C2211yescharacteristic
31C2×SD16×C37C2214yes—
32C4⋊Q8×C37C2211yescharacteristic
33#127×C37C2211yescharacteristic
34C4×C8×C37C2211yescharacteristic
35C2×Q8×C37C2312yes—
36C2×D4×C37—21no—
37C2×D4×C37—21no—
38C2×D4×C37C2312yes—
39C2×C22⋊D37—22no—
40C22×Dic37—22no—
41#10596964—44no—
42C2×C4×D37D411yescharacteristic
43C2×C4×D37D411yescharacteristic
44C2×C4×D37C2311yescharacteristic
45C2×Dic74—21no—
46C2×Dic74—21no—
47SD16×C37—28no—
48C2×C8×C37C2312yes—
49C4⋊C4×C37—21no—
50C4⋊C4×C37—21no—
51C42×C37C2311yescharacteristic
52C22⋊Dic37—22no—
53C22⋊Dic37—22no—
54#10596938—22no—
55C4⋊Dic37—21no—
56C4⋊Dic37—21no—
57C4⋊Dic37—22no—
58C4⋊Dic37C2312yes—
59C4⋊Dic37C2312yes—
60#10596936—22no—
61C4×Dic37—22no—
62C4×Dic37D411yescharacteristic
63C4×Dic37D411yescharacteristic
64C4×Dic37C2311yescharacteristic
65C2×#64436C2312yes—
66#10596929—24no—
67C23×C37—22no—
68C22×D37C2×D411yescharacteristic
69Q8×C37—24no—
70D4×C37—24no—
71D4×C37—42no—
72D4×C37—42no—
73C2×C4×C37—22no—
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37C2411yescharacteristic
77C22⋊D37—44no—
78C2×Dic37—22no—
79C2×Dic37—22no—
80C2×Dic37—44no—
81C2×Dic37C2×D411yescharacteristic
82C2×Dic37C2×D411yescharacteristic
83C2×Dic37C2×D411yescharacteristic
84C4×D37—22no—
85C4×D37—22no—
86C4×D37—22no—
87Dic74—42no—
88Dic74—42no—
89C8×C37#4114yescomplemented
90#64436—22no—
91C22×C37—42no—
92C22×C37—42no—
93C22×C37—42no—
94C22×C37C22×D411yescharacteristic
95C2×D37—21no—
96C2×D37—21no—
97C2×D37—21no—
98C4×C37—42no—
99C4×C37AGL(1,ℤ/8)12yes—
100C4×C37#13712yes—
101C4×C37C2×#4112yes—
102Dic37—21no—
103Dic37—21no—
104Dic37—21no—
105Dic37—42no—
106Dic37—42no—
107#3182—371nomaximal, Sylow
108C2×C37—82no—
109C2×C37#53211yescharacteristic
110C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C37C2×#13711yescharacteristic
112D37—41no—
113#533—371no—
114#532—371no—
115#500—371no—
116#492D3711yescharacteristic, complemented
117#487—371no—
118#486—371no—
119#468—374no—
120#440—374no—
121C4×M16—371no—
122C37#318211yescharacteristic, complemented, Sylow
123C2×#41—741no—
124C2×SD16C2×D3714yes—
125C2×M16—372no—
126C4⋊Q8—371no—
127C4⋊Q8—371no—
128C4⋊Q8C2×D3711yescharacteristic
129#127C2×D3711yescharacteristic
130#125—741no—
131#124—741no—
132C22⋊Q8—372no—
133C22⋊Q8—741no—
134#121—372no—
135#121—741no—
136C4×Q8—372no—
137C4×Q8—741no—
138C4×D4—372no—
139C4×D4—741no—
140#117—741no—
141C2×C42—371no—
142#107—374no—
143#103—374no—
144#102—374no—
145#97—372no—
146C4×C8—371no—
147C4×C8C2×D3711yescharacteristic
148#41—1484no—
149C2×Q8—741no—
150C2×Q8—741no—
151C2×Q8C22×D3712yes—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4—742no—
155C2×D4C22×D3712yes—
156C22×C4—371no—
157C22×C4—371no—
158C22×C4—371no—
159C22×C4—742no—
160SD16—28no—
161M16—744no—
162C2×C8—372no—
163C2×C8C22×D3712yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—372no—
167C4⋊C4—372no—
168C4⋊C4—742no—
169C4⋊C4—742no—
170C4⋊C4—741no—
171C4⋊C4—741no—
172C22⋊C4—742no—
173C22⋊C4—742no—
174C22⋊C4—742no—
175C42—371no—
176C42—371no—
177C42—371no—
178C42—742no—
179C42C22×D3711yescharacteristic
180C23—22no—
181C23—371no—
182Q8—24no—
183Q8—1482no—
184Q8—1482no—
185D4—24no—
186D4—42no—
187D4—42no—
188D4—1484no—
189C2×C4—22no—
190C2×C4—371no—
191C2×C4—371no—
192C2×C4—371no—
193C2×C4—742no—
194C2×C4—742no—
195C2×C4—742no—
196C2×C4—742no—
197C2×C4—742no—
198C2×C4—1484no—
199C2×C4D4×D3711yescharacteristic
200C2×C4D4×D3711yescharacteristic
201C2×C4C23×D3711yescharacteristic
202C8—742no—
203C8#1059696414yescomplemented
204C22—42no—
205C22—42no—
206C22—42no—
207C22—741no—
208C22—741no—
209C22—741no—
210C22C2×D4×D3711yescharacteristic
211C4—42no—
212C4—741no—
213C4—741no—
214C4—741no—
215C4—1482no—
216C4—1482no—
217C4#1192456312yes—
218C4#1192456512yes—
219C4C2×#1059696412yes—
220C2—82no—
221C2—1481no—
222C2#1455808111yescharacteristic
223C2C2×#1192456311yescharacteristic
224C2C2×#1192456511yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#492C2
socleC22×C37C22×D4
prime radical#14558081C2
hypercenter#492D37
hypocenterC37#3182
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #14558088C2semidirect
3. #14557938C2semidirect
4. #14557883C2semidirect
5. #14557879C2semidirect
6. #14557776C2semidirect
7. #14557634C2semidirect
8. C4×#10596929C2semidirect
9. C37×#492C2semidirect
89. C8×C37#41semidirect
116. #492D37semidirect
122. C37#3182semidirect
203. C8#10596964semidirect

Maximal subgroups

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

subgroupindex
#145580882
#145580812
#145579382
#145578832
#145578792
#145577762
#145576342
C4×#105969292
C37×#4922
#318237