Finite Group Databasebeta

← #18004887

Subgroups — #18004887

Order 4736.

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

normal subgroups only

This group has 382 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#14558138C211yesmaximal, characteristic
2#14557857C212yesmaximal, complemented
3#14557840C212yesmaximal, complemented
4#14557733C212yesmaximal, complemented
5#14557672C212yesmaximal, complemented
6#14557631C212yesmaximal, complemented
7C4×#10596941C212yesmaximal, complemented
8#14557594C211yesmaximal, characteristic, complemented
9C37×#519C211yesmaximal, characteristic, complemented
10C2×#10596941C2212yes—
11C2×#10596941C2212yes—
12#11924533C2211yescharacteristic
13#11924528C2211yescharacteristic
14#11924521—22no—
15#11924510C2212yes—
16#11924509—22no—
17C4×D148C2212yes—
18#11924469C2212yes—
19#11924467C2212yes—
20C4⋊#64436C2212yes—
21#11924460C2212yes—
22#11924460C2212yes—
23#11924456C2212yes—
24#11924456C2212yes—
25C22⋊#64436C2212yes—
26#11924447C2211yescharacteristic
27C4×#64436C2211yescharacteristic
28C22×Q8×C37C2211yescharacteristic
29C4×Q8×C37—22no—
30C4×Q8×C37C2212yes—
31C4×Q8×C37C2212yes—
32#117×C37—22no—
33#117×C37C2211yescharacteristic
34#117×C37C2211yescharacteristic
35C2×Q8×C37—24no—
36C2×Q8×C37—21no—
37C2×Q8×C37C2312yes—
38C22×C4×C37—21no—
39C22×C4×C37C2311yescharacteristic
40C2×C22⋊D37—22no—
41C2×D148—22no—
42C2×D148C2312yes—
43C2×C4×D37—22no—
44C4⋊C4×C37—22no—
45C4⋊C4×C37—22no—
46C4⋊C4×C37D412yes—
47C4⋊C4×C37C2312yes—
48C22⋊C4×C37—21no—
49C22⋊C4×C37D412yes—
50C42×C37—22no—
51C42×C37—22no—
52C42×C37—21no—
53C42×C37C2311yescharacteristic
54C42×C37C2311yescharacteristic
55#10596941—24no—
56#10596941—24no—
57#10596938—22no—
58#10596938—22no—
59C4⋊Dic37C2312yes—
60#10596936—22no—
61C2×#64436C2312yes—
62C2×#64436C2312yes—
63C23×C37C2×D411yescharacteristic
64C22×D37—22no—
65Q8×C37—24no—
66Q8×C37—22no—
67Q8×C37#4114yes—
68C2×C4×C37—24no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37C2×D412yes—
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37C2×D412yes—
75C2×C4×C37C2411yescharacteristic
76C22⋊D37—82no—
77C2×Dic37—22no—
78D148—22no—
79D148—22no—
80D148—82no—
81C4×D37—82no—
82#64436—22no—
83#64436—22no—
84C22×C37—21no—
85C22×C37—22no—
86C22×C37C22×D411yescharacteristic
87C2×D37—42no—
88C2×D37—42no—
89C2×D37—42no—
90C4×C37—24no—
91C4×C37—21no—
92C4×C37—22no—
93C4×C37—22no—
94C4×C37—42no—
95C4×C37C2×#4112yes—
96Dic37—42no—
97#3126—371nomaximal, Sylow
98C2×C37—41no—
99C2×C37#52511yescharacteristic
100C2×C37#57712yes—
101D37—82no—
102#540—371no—
103#519D3711yescharacteristic, complemented
104#482—372no—
105#479—372no—
106#460—372no—
107#448—372no—
108#440—372no—
109C4×SD16—372no—
110#433—371no—
111C37#312611yescharacteristic, complemented, Sylow
112C22×Q8C2×D3711yescharacteristic
113C2×SD16—372no—
114C2×SD16—372no—
115#127—371no—
116#125—371no—
117#123—742no—
118#121—372no—
119#121—742no—
120C4×Q8—22no—
121C4×Q8C2×D3712yes—
122C4×Q8C2×D3712yes—
123C4×D4—372no—
124#117—22no—
125#117C2×D3711yescharacteristic
126#117C2×D3711yescharacteristic
127#107—372no—
128#106—372no—
129C4⋊C8—372no—
130#103—372no—
131#103—372no—
132#102—372no—
133#102—372no—
134C22⋊C8—372no—
135#97—371no—
136C4×C8—371no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8C22×D3712yes—
140C2×D4—372no—
141C2×D4—742no—
142C2×D4—742no—
143C22×C4—21no—
144C22×C4—742no—
145C22×C4C22×D3711yescharacteristic
146SD16—744no—
147SD16—744no—
148C2×C8—372no—
149C2×C8—372no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—372no—
153C4⋊C4—742no—
154C4⋊C4C22⋊D3712yes—
155C4⋊C4C22×D3712yes—
156C22⋊C4—21no—
157C22⋊C4—742no—
158C22⋊C4—742no—
159C22⋊C4C22⋊D3712yes—
160C42—22no—
161C42—22no—
162C42—21no—
163C42C22×D3711yescharacteristic
164C42C22×D3711yescharacteristic
165C23—742no—
166C23C2×C22⋊D3711yescharacteristic
167Q8—24no—
168Q8—22no—
169Q8#1059696214yes—
170D4—2962no—
171D4—2962no—
172D4—742no—
173D4—742no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—2962no—
179C2×C4—742no—
180C2×C4C2×C22⋊D3712yes—
181C2×C4C2×C22⋊D3712yes—
182C2×C4C2×C22⋊D3711yescharacteristic
183C2×C4C23×D3711yescharacteristic
184C8—742no—
185C8—742no—
186C22—21no—
187C22—22no—
188C22—1482no—
189C22—1482no—
190C22—1482no—
191C22C22×C22⋊D3711yescharacteristic
192C4—24no—
193C4—21no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—1482no—
198C4C2×#1059696212yes—
199C2—41no—
200C2—2962no—
201C2#1455804411yescharacteristic
202C2#1455834112yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#519C2
socleC22×C37C22×D4
prime radical#14558138C2
hypercenter#519D37
hypocenterC37#3126
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #14557857C2semidirect
3. #14557840C2semidirect
4. #14557733C2semidirect
5. #14557672C2semidirect
6. #14557631C2semidirect
7. C4×#10596941C2semidirect
8. #14557594C2semidirect
9. C37×#519C2semidirect
103. #519D37semidirect
111. C37#3126semidirect

Maximal subgroups

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

subgroupindex
#145581382
#145578572
#145578402
#145577332
#145576722
#145576312
C4×#105969412
#145575942
C37×#5192
#312637