Finite Group Databasebeta

← #18005315

Subgroups — #18005315

Order 4736.

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

normal subgroups only

This group has 402 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#14558083C211yesmaximal, characteristic
2#14557936C211yesmaximal, characteristic, complemented
3#14557907C211yesmaximal, characteristic, complemented
4#14557883C211yesmaximal, characteristic, complemented
5#14557881C211yesmaximal, characteristic, complemented
6#14557781C214yesmaximal, complemented
7#14557631C214yesmaximal, complemented
8C4×#10596934C211yesmaximal, characteristic, complemented
9C37×#533C211yesmaximal, characteristic, complemented
10C2×#10596962—21no—
11C2×#10596941C2214yes—
12C2×#10596934C2212yes—
13#11924536C2211yescharacteristic
14#11924533C2211yescharacteristic
15#11924524—21no—
16#11924510—21no—
17#11924510C2212yes—
18C4×D148—21no—
19C4×D148C2212yes—
20#11924469C2214yes—
21#11924460C2214yes—
22#11924456C2214yes—
23#11924447C2212yes—
24C4×#64436C2211yescharacteristic
25C4×#64436C2211yescharacteristic
26C4⋊Q8×C37C2211yescharacteristic
27C4⋊Q8×C37C2211yescharacteristic
28#125×C37—21no—
29C22⋊Q8×C37—21no—
30C22⋊Q8×C37C2212yes—
31C4×Q8×C37—21no—
32C4×Q8×C37C2212yes—
33#117×C37—21no—
34C2×C42×C37C2211yescharacteristic
35C2×Q8×C37—21no—
36C2×Q8×C37C2312yes—
37C22×C4×C37D411yescharacteristic
38C22×C4×C37D411yescharacteristic
39C22×C4×C37C2311yescharacteristic
40C2×C22⋊D37—22no—
41#10596962—44no—
42C2×D148—21no—
43C2×D148—21no—
44C2×D148C2312yes—
45C2×C4×D37—22no—
46C2×Dic74—21no—
47C4⋊C4×C37—21no—
48C4⋊C4×C37—21no—
49C4⋊C4×C37—21no—
50C4⋊C4×C37—22no—
51C4⋊C4×C37—22no—
52C4⋊C4×C37C2312yes—
53C22⋊C4×C37—22no—
54C42×C37—22no—
55C42×C37D411yescharacteristic
56C42×C37D411yescharacteristic
57C42×C37C2311yescharacteristic
58C42×C37C2311yescharacteristic
59#10596941—28no—
60#10596938—22no—
61#10596938—22no—
62C4⋊Dic37—21no—
63C4⋊Dic37C2312yes—
64#10596934—24no—
65C2×#64436C2312yes—
66C2×#64436C2312yes—
67C23×C37C2×D411yescharacteristic
68C22×D37—22no—
69Q8×C37—24no—
70Q8×C37—42no—
71C2×C4×C37—22no—
72C2×C4×C37—22no—
73C2×C4×C37—22no—
74C2×C4×C37—22no—
75C2×C4×C37—22no—
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2411yescharacteristic
82C22⋊D37—44no—
83C2×Dic37—22no—
84D148—24no—
85D148—42no—
86D148—42no—
87C4×D37—44no—
88Dic74—42no—
89#64436—22no—
90#64436#4114yescomplemented
91C22×C37—21no—
92C22×C37—21no—
93C22×C37—21no—
94C22×C37C22×D411yescharacteristic
95C2×D37—42no—
96C2×D37—42no—
97C2×D37—42no—
98C4×C37—21no—
99C4×C37—21no—
100C4×C37—21no—
101C4×C37—42no—
102C4×C37—42no—
103C4×C37AGL(1,ℤ/8)12yes—
104C4×C37#13712yes—
105C4×C37C2×#4112yes—
106Dic37—42no—
107#3182—371nomaximal, Sylow
108C2×C37—41no—
109C2×C37#53211yescharacteristic
110C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C37C2×#13711yescharacteristic
112D37—82no—
113#533D3711yescharacteristic, complemented
114#532—371no—
115#500—371no—
116#492—371no—
117#487—371no—
118#486—371no—
119#468—374no—
120#440—374no—
121C4×M16—371no—
122C37#318211yescharacteristic, complemented, Sylow
123C2×#41—741no—
124C2×SD16—374no—
125C2×M16—372no—
126C4⋊Q8—371no—
127C4⋊Q8C2×D3711yescharacteristic
128C4⋊Q8C2×D3711yescharacteristic
129#127—371no—
130#125—21no—
131#124—741no—
132C22⋊Q8—21no—
133C22⋊Q8C2×D3712yes—
134#121—372no—
135#121—741no—
136C4×Q8—21no—
137C4×Q8C2×D3712yes—
138C4×D4—372no—
139C4×D4—741no—
140#117—21no—
141C2×C42C2×D3711yescharacteristic
142#107—374no—
143#103—374no—
144#102—374no—
145#97—372no—
146C4×C8—371no—
147C4×C8—371no—
148#41—1484no—
149C2×Q8—21no—
150C2×Q8—741no—
151C2×Q8C22×D3712yes—
152C2×D4—372no—
153C2×D4—742no—
154C2×D4—741no—
155C2×D4—741no—
156C22×C4—742no—
157C22×C4C22⋊D3711yescharacteristic
158C22×C4C22⋊D3711yescharacteristic
159C22×C4C22×D3711yescharacteristic
160SD16—748no—
161M16—744no—
162C2×C8—372no—
163C2×C8—372no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—372no—
170C4⋊C4—741no—
171C4⋊C4C22×D3712yes—
172C22⋊C4—22no—
173C22⋊C4—742no—
174C22⋊C4—742no—
175C42—22no—
176C42C22⋊D3711yescharacteristic
177C42C22⋊D3711yescharacteristic
178C42C22×D3711yescharacteristic
179C42C22×D3711yescharacteristic
180C23—742no—
181C23C2×C22⋊D3711yescharacteristic
182Q8—24no—
183Q8—42no—
184Q8—1482no—
185D4—744no—
186D4—1484no—
187D4—1482no—
188D4—1482no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—742no—
195C2×C4—1484no—
196C2×C4C2×C22⋊D3711yescharacteristic
197C2×C4C2×C22⋊D3711yescharacteristic
198C2×C4C2×C22⋊D3711yescharacteristic
199C2×C4C2×C22⋊D3711yescharacteristic
200C2×C4C2×C22⋊D3711yescharacteristic
201C2×C4C23×D3711yescharacteristic
202C8—374no—
203C8—742no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—1482no—
208C22—1482no—
209C22—1482no—
210C22C22×C22⋊D3711yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—42no—
216C4—1482no—
217C4#1192456112yes—
218C4#1192456712yes—
219C4#41×D3712yes—
220C2—41no—
221C2—2962no—
222C2#1455807911yescharacteristic
223C2C2×#1192456111yescharacteristic
224C2C2×#1192456711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#533C2
socleC22×C37C22×D4
prime radical#14558083C2
hypercenter#533D37
hypocenterC37#3182
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #14557936C2semidirect
3. #14557907C2semidirect
4. #14557883C2semidirect
5. #14557881C2semidirect
6. #14557781C2semidirect
7. #14557631C2semidirect
8. C4×#10596934C2semidirect
9. C37×#533C2semidirect
90. #64436#41semidirect
113. #533D37semidirect
122. C37#3182semidirect

Maximal subgroups

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

subgroupindex
#145580832
#145579362
#145579072
#145578832
#145578812
#145577812
#145576312
C4×#105969342
C37×#5332
#318237