Finite Group Databasebeta

← #17993695

Subgroups — #17993695

Order 4736.

210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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#14558262C211yesmaximal, characteristic, complemented
2#14557880C211yesmaximal, characteristic
3#14557734C211yesmaximal, characteristic
4#14557733C211yesmaximal, characteristic
5#14557280C211yesmaximal, characteristic, complemented
6#14557265C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596930—21no—
9C2×#10596941—21no—
10#11924536—21no—
11#11924536C2211yescharacteristic
12#11924533C2211yescharacteristic
13#11924527—21no—
14#11924527—22no—
15Q8×Dic37—21no—
16C4×Dic74—21no—
17C4×Dic74C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924458—21no—
20#11924458—22no—
21#11924456—21no—
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37D411yescharacteristic
26C2×D148—21no—
27C2×D148—21no—
28C2×D148—21no—
29C2×Dic74—21no—
30C2×Dic74D411yescharacteristic
31C2×C8×C37—21no—
32C2×C8×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37D411yescharacteristic
35C42×C37—21no—
36C42×C37C2311yescharacteristic
37#10596941—42no—
38C4⋊Dic37—22no—
39C4⋊Dic37—22no—
40C4⋊Dic37—21no—
41C4⋊Dic37D411yescharacteristic
42C4⋊Dic37D412yes—
43#10596936—22no—
44#10596936—21no—
45C4×Dic37—22no—
46C4×Dic37—21no—
47C2×#64436—21no—
48#10596930—42no—
49C22×D37—41no—
50Q8×C37—21no—
51Q8×C37SD1612yescomplemented
52C2×C4×C37—21no—
53C2×C4×C37—21no—
54C2×C4×C37C2×D411yescharacteristic
55C2×C4×C37C2×D411yescharacteristic
56C2×C4×C37C2×D411yescharacteristic
57C2×Dic37—21no—
58C2×Dic37—21no—
59C2×Dic37—22no—
60D148—42no—
61D148—41no—
62D148—41no—
63D148—41no—
64D148—41no—
65Dic74—21no—
66Dic74—21no—
67Dic74—41no—
68Dic74—41no—
69C8×C37—41no—
70C8×C37—41no—
71#64436—41no—
72C22×C37#12011yescharacteristic
73C2×D37—81no—
74C2×D37—81no—
75C2×D37—81no—
76C4×C37—22no—
77C4×C37—21no—
78C4×C37—41no—
79C4×C37C2×SD1611yescharacteristic
80C4×C37#13511yescharacteristic
81C4×C37AGL(1,ℤ/8)11yescharacteristic
82C4×C37#13711yescharacteristic
83Dic37—41no—
84Dic37—42no—
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#332—371no—
96Q8⋊C8—371no—
97Q8⋊C8D3711yescharacteristic, complemented
98C37#162611yescharacteristic, complemented, Sylow
99C2×SD16—741no—
100C2×SD16—741no—
101C4⋊Q8—371no—
102C4⋊Q8—741no—
103#127—371no—
104#125—742no—
105#125—741no—
106C4×Q8—371no—
107C4×Q8—741no—
108C4×Q8—741no—
109C4×Q8C2×D3711yescharacteristic
110C4⋊C8—371no—
111C4⋊C8C2×D3711yescharacteristic
112#102—741no—
113#102—742no—
114#102—741no—
115C4×C8C2×D3711yescharacteristic
116C2×Q8—371no—
117C2×Q8—741no—
118C2×Q8D14811yescharacteristic
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—372no—
130C4⋊C4—742no—
131C4⋊C4—742no—
132C4⋊C4—742no—
133C4⋊C4—741no—
134C4⋊C4—741no—
135C4⋊C4D14811yescharacteristic
136C42—21no—
137C42—742no—
138C42—741no—
139C42C22×D3711yescharacteristic
140C23—1481no—
141Q8—21no—
142Q8—741no—
143Q8—741no—
144Q8—1481no—
145Q8—1481no—
146Q8#1059693012yescomplemented
147D4—1482no—
148D4—1481no—
149D4—1481no—
150D4—1481no—
151D4—1481no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—741no—
155C2×C4—742no—
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—22no—
169C4—41no—
170C4—1481no—
171C4—1481no—
172C4—1482no—
173C4C2×#1059693011yescharacteristic
174C4#1192455911yescharacteristic
175C4#1192456311yescharacteristic
176C4#1192456911yescharacteristic
177C2—5921no—
178C2#1455767411yescharacteristic
179C2#1455768111yescharacteristic
180C2#1455770711yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37#120
prime radical#11924533C22
hypercenterQ8⋊C8D37
hypocenterC37#1626
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #14558262C2semidirect
5. #14557280C2semidirect
6. #14557265C2semidirect
7. C37×Q8⋊C8C2semidirect
51. Q8×C37SD16semidirect
97. Q8⋊C8D37semidirect
98. C37#1626semidirect
146. Q8#10596930semidirect

Maximal subgroups

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

subgroupindex
#145582622
#145578802
#145577342
#145577332
#145572802
#145572652
C37×Q8⋊C82
#162637