Finite Group Databasebeta

← #17995663

Subgroups — #17995663

Order 4736.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#14558333C211yesmaximal, characteristic, complemented
2#14558044C212yesmaximal, complemented
3#14557549C212yesmaximal, complemented
4#14557290C211yesmaximal, characteristic, complemented
5C37×#407C211yesmaximal, characteristic, complemented
6C2×#10596962C2212yes—
7#11924569—22no—
8#11924564—22no—
9#11924558—22no—
10#11924519—22no—
11#11924515—22no—
12#11924510—22no—
13#11924505—22no—
14C4×C22⋊D37—24no—
15#11924495C2212yes—
16#11924462—24no—
17C23×C4×C37C2211yescharacteristic
18C2×M16×C37C2211yescharacteristic
19C2×M16×C37C2211yescharacteristic
20C22⋊C8×C37—22no—
21C24×C37D411yescharacteristic
22C22×C4×C37—22no—
23C22×C4×C37—22no—
24C22×C4×C37—21no—
25C22×C4×C37—21no—
26C22×C4×C37D411yescharacteristic
27C22×C4×C37C2311yescharacteristic
28C2×C22⋊D37—24no—
29C2×C22⋊D37—22no—
30#10596962—22no—
31#10596962—22no—
32#10596962—22no—
33#10596962—22no—
34C2×D148D412yescomplemented
35C2×C4×D37—22no—
36C2×Dic74D412yescomplemented
37M16×C37—22no—
38M16×C37—22no—
39C2×C8×C37—21no—
40C2×C8×C37D412yescomplemented
41C22⋊Dic37—24no—
42C22⋊Dic37—22no—
43#10596938—24no—
44C4⋊Dic37—22no—
45#10596936—24no—
46C4×Dic37D414yescomplemented
47Dic148—22no—
48D296—22no—
49#10596930—24no—
50C23×C37—22no—
51C23×C37—21no—
52C23×C37—42no—
53C23×C37C2×D411yescharacteristic
54C22×D37—22no—
55C2×C4×C37—22no—
56C2×C4×C37—21no—
57C2×C4×C37—41no—
58C2×C4×C37—42no—
59C2×C4×C37—41no—
60C2×C4×C37C2×D412yes—
61C2×C4×C37C2×D412yes—
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37#4111yescharacteristic
64C22⋊D37—48no—
65C22⋊D37—42no—
66C22⋊D37—42no—
67C2×Dic37—24no—
68C2×Dic37—22no—
69D148—22no—
70D148—22no—
71C4×D37—42no—
72C4×D37—42no—
73Dic74—22no—
74Dic74—22no—
75C8×C37—22no—
76C8×C37—41no—
77C22×C37—24no—
78C22×C37—22no—
79C22×C37—41no—
80C22×C37—42no—
81C22×C37—41no—
82C22×C37—41no—
83C22×C37#12012yes—
84C22×C37#12111yescharacteristic
85C2×D37—44no—
86C2×D37—42no—
87C4×C37—41no—
88C4×C37#12011yescharacteristic
89C4×C37#12112yes—
90C4×C37#12711yescharacteristic
91Dic37—44no—
92Dic37—42no—
93#2010—371nomaximal, Sylow
94C2×C37—22no—
95C2×C37—21no—
96C2×C37—42no—
97C2×C37#39211yescharacteristic
98D37—82no—
99#575—371no—
100#525—372no—
101#421—372no—
102#407D3711yescharacteristic, complemented
103H(3,ℤ/4)—371no—
104C37#201011yescharacteristic, complemented, Sylow
105C2×#41—372no—
106C23×C4C2×D3711yescharacteristic
107#137—742no—
108AGL(1,ℤ/8)—742no—
109#135—742no—
110C2×M16C2×D3711yescharacteristic
111C2×M16C2×D3711yescharacteristic
112#123—742no—
113C22⋊Q8—742no—
114#121—742no—
115#120—742no—
116C4×D4—744no—
117#117—372no—
118#104—744no—
119C22⋊C8—22no—
120C24D14811yescharacteristic
121#41—742no—
122#41—742no—
123#41—742no—
124#41—742no—
125C2×Q8—372no—
126C2×D4—372no—
127C2×D4—744no—
128C2×D4—742no—
129C22×C4—21no—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—21no—
133C22×C4—742no—
134C22×C4D14811yescharacteristic
135C22×C4C22×D3711yescharacteristic
136Q16—742no—
137SD16—744no—
138D8—742no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D3712yescomplemented
143C4⋊C4—744no—
144C4⋊C4—742no—
145C22⋊C4—744no—
146C22⋊C4—744no—
147C22⋊C4—742no—
148C42—374no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—742no—
153C23C2×D14811yescharacteristic
154Q8—742no—
155Q8—742no—
156D4—742no—
157D4—742no—
158D4—1488no—
159D4—1482no—
160D4—1482no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—744no—
167C2×C4—742no—
168C2×C4—1482no—
169C2×C4—1482no—
170C2×C4#1059696211yescharacteristic
171C2×C4D4×D3712yes—
172C2×C4D4×D3712yes—
173C2×C4C2×C22⋊D3711yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—1484no—
183C22—1482no—
184C22#1192450612yes—
185C22#1192451011yescharacteristic
186C4—41no—
187C4—1484no—
188C4—1482no—
189C4#1192450411yescharacteristic
190C4#1192450912yes—
191C4#1192453211yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—2962no—
196C2#1455744211yescharacteristic
subgroupG/H
centerC4#11924532
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#407C2
socleC2×C37#392
hypercenter#407D37
hypocenterC37#2010
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #14558333C2semidirect
2. #14558044C2semidirect
3. #14557549C2semidirect
4. #14557290C2semidirect
5. C37×#407C2semidirect
34. C2×D148D4semidirect
36. C2×Dic74D4semidirect
40. C2×C8×C37D4semidirect
46. C4×Dic37D4semidirect
102. #407D37semidirect
104. C37#2010semidirect
142. C2×C8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145583332
#145580442
#145575492
#145572902
C37×#4072
#201037