Finite Group Databasebeta

← #17993693

Subgroups — #17993693

Order 4736.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#14558258C211yesmaximal, characteristic, complemented
2#14557881C211yesmaximal, characteristic
3#14557734C211yesmaximal, characteristic
4#14557734C211yesmaximal, characteristic
5#14557263C211yesmaximal, characteristic, complemented
6#14557263C211yesmaximal, characteristic, complemented
7C37×#332C211yesmaximal, characteristic, complemented
8C2×#10596930—21no—
9C2×#10596930—21no—
10#11924534—21no—
11#11924533C2211yescharacteristic
12#11924527—21no—
13#11924526—22no—
14Q8×Dic37—21no—
15C4×Dic74C2211yescharacteristic
16C4×Dic74C2211yescharacteristic
17#11924501—21no—
18#11924458—21no—
19#11924458—21no—
20#11924456—22no—
21C4×#64436C2211yescharacteristic
22C4⋊Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26C2×D148—21no—
27C2×D148—21no—
28C2×D148—21no—
29C2×Dic74D411yescharacteristic
30C2×Dic74D411yescharacteristic
31C2×C8×C37—21no—
32C2×C8×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37D412yes—
35C42×C37C2311yescharacteristic
36C4⋊Dic37—22no—
37C4⋊Dic37D411yescharacteristic
38C4⋊Dic37D411yescharacteristic
39#10596936—22no—
40#10596936—22no—
41#10596936—21no—
42#10596936—21no—
43C4×Dic37—22no—
44C4×Dic37—21no—
45C4×Dic37—21no—
46C2×#64436—21no—
47#10596930—42no—
48#10596930—42no—
49C22×D37—41no—
50Q8×C37—41no—
51Q8×C37—41no—
52C2×C4×C37—22no—
53C2×C4×C37C2×D411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C2×C4×C37C2×D411yescharacteristic
56C2×Dic37—21no—
57C2×Dic37—21no—
58C2×Dic37—21no—
59C2×Dic37—21no—
60D148—42no—
61D148—41no—
62D148—41no—
63D148—41no—
64D148—41no—
65Dic74—21no—
66Dic74—21no—
67Dic74—21no—
68Dic74SD1612yescomplemented
69C8×C37—41no—
70C8×C37—41no—
71#64436—41no—
72C22×C37#12011yescharacteristic
73C2×D37—81no—
74C2×D37—81no—
75C2×D37—81no—
76C4×C37—21no—
77C4×C37—42no—
78C4×C37C2×SD1611yescharacteristic
79C4×C37#13511yescharacteristic
80C4×C37AGL(1,ℤ/8)11yescharacteristic
81C4×C37#13711yescharacteristic
82Dic37—22no—
83Dic37—41no—
84Dic37—41no—
85Dic37—41no—
86#1626—371nomaximal, Sylow
87C2×C37#44811yescharacteristic
88C2×C37#44911yescharacteristic
89C2×C37#45411yescharacteristic
90D37—161no—
91#557—371no—
92#486—371no—
93#460—371no—
94#460—371no—
95#332D3711yescharacteristic, complemented
96Q8⋊C8—371no—
97Q8⋊C8—371no—
98C37#162611yescharacteristic, complemented, Sylow
99C2×SD16—741no—
100C2×SD16—741no—
101C4⋊Q8—741no—
102C4⋊Q8C2×D3711yescharacteristic
103#127—371no—
104#125—741no—
105#125—742no—
106C4×Q8—371no—
107C4×Q8—371no—
108C4×Q8—741no—
109C4×Q8—741no—
110C4⋊C8C2×D3711yescharacteristic
111C4⋊C8C2×D3711yescharacteristic
112#102—741no—
113#102—741no—
114#102—742no—
115C4×C8—371no—
116C2×Q8—21no—
117C2×Q8—371no—
118C2×Q8—371no—
119C2×D4—741no—
120C2×D4—741no—
121C2×D4—741no—
122SD16—1482no—
123SD16—1482no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—741no—
127C4⋊C4—21no—
128C4⋊C4—371no—
129C4⋊C4—371no—
130C4⋊C4—742no—
131C4⋊C4—742no—
132C4⋊C4—742no—
133C4⋊C4—741no—
134C4⋊C4—741no—
135C4⋊C4D14812yes—
136C42—742no—
137C42—741no—
138C42—741no—
139C42C22×D3711yescharacteristic
140C23—1481no—
141Q8—41no—
142Q8—41no—
143Q8—372no—
144Q8—741no—
145Q8—741no—
146Q8—741no—
147D4—1482no—
148D4—1481no—
149D4—1481no—
150D4—1481no—
151D4—1481no—
152C2×C4—22no—
153C2×C4—741no—
154C2×C4—741no—
155C2×C4—741no—
156C2×C4—741no—
157C2×C4C2×D14811yescharacteristic
158C2×C4D4×D3711yescharacteristic
159C2×C4D4×D3711yescharacteristic
160C8—41no—
161C8—41no—
162C8—1481no—
163C22—2961no—
164C22—2961no—
165C22—2961no—
166C22#1192450611yescharacteristic
167C4—21no—
168C4—42no—
169C4—742no—
170C4—1481no—
171C4—1481no—
172C4—1481no—
173C4SD16×D3711yescharacteristic
174C4#1192455711yescharacteristic
175C4#1192456011yescharacteristic
176C4#1192456811yescharacteristic
177C2—5921no—
178C2#1455767311yescharacteristic
179C2#1455767911yescharacteristic
180C2#1455770811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#332C2
socleC22×C37#120
prime radical#11924533C22
hypercenter#332D37
hypocenterC37#1626
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #14558258C2semidirect
5. #14557263C2semidirect
6. #14557263C2semidirect
7. C37×#332C2semidirect
68. Dic74SD16semidirect
95. #332D37semidirect
98. C37#1626semidirect

Maximal subgroups

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

subgroupindex
#145582582
#145578812
#145577342
#145572632
C37×#3322
#162637