Finite Group Databasebeta

← #17993765

Subgroups — #17993765

Order 4736.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#14558257C211yesmaximal, characteristic
2#14557825C211yesmaximal, characteristic, complemented
3#14557820C211yesmaximal, characteristic
4#14557279C211yesmaximal, characteristic, complemented
5#14557265C211yesmaximal, characteristic, complemented
6#14557262C211yesmaximal, characteristic
7C37×#487C211yesmaximal, characteristic, complemented
8#11924531—22no—
9#11924525—21no—
10#11924516—21no—
11Q8×Dic37—21no—
12C4×Dic74C2211yescharacteristic
13C4×D148C2211yescharacteristic
14#11924494—21no—
15#11924469—21no—
16#11924467—21no—
17C4⋊#64436C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924459—21no—
20#11924456—21no—
21C4⋊Q8×C37C2211yescharacteristic
22C4⋊Q8×C37C2211yescharacteristic
23#103×C37—22no—
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26C2×Q8×C37—21no—
27C2×D148D411yescharacteristic
28C2×C4×D37—21no—
29C2×Dic74D411yescharacteristic
30C2×C8×C37—21no—
31C4⋊C4×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37D412yes—
35C42×C37C2311yescharacteristic
36#10596938—22no—
37#10596938—22no—
38#10596938—21no—
39C4⋊Dic37—22no—
40C4⋊Dic37D411yescharacteristic
41C4⋊Dic37D411yescharacteristic
42#10596936—21no—
43C4×Dic37—22no—
44C4×Dic37—21no—
45C2×#64436—21no—
46C2×#64436—21no—
47C22×D37—21no—
48Q8×C37—42no—
49Q8×C37—41no—
50Q8×C37—41no—
51C2×C4×C37—22no—
52C2×C4×C37—41no—
53C2×C4×C37C2×D411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C2×C4×C37C2×D411yescharacteristic
56C2×Dic37—21no—
57C2×Dic37—21no—
58C2×Dic37—21no—
59D148—21no—
60D148—21no—
61C4×D37—41no—
62C4×D37—41no—
63Dic74—21no—
64Dic74—21no—
65C8×C37—41no—
66#64436—41no—
67#64436—41no—
68C22×C37#12011yescharacteristic
69C2×D37—41no—
70C2×D37—41no—
71C2×D37—41no—
72C4×C37—21no—
73C4×C37—42no—
74C4×C37—81no—
75C4×C37#13511yescharacteristic
76C4×C37#13511yescharacteristic
77C4×C37#13711yescharacteristic
78C4×C37#13711yescharacteristic
79Dic37—41no—
80Dic37—41no—
81Dic37—41no—
82#1638—371nomaximal, Sylow
83C2×C37#45211yescharacteristic
84C2×C37#45211yescharacteristic
85C2×C37#45411yescharacteristic
86D37—81no—
87#556—371no—
88#487D3711yescharacteristic, complemented
89#477—371no—
90#476—371no—
91#332—371no—
92Q8⋊C8—371no—
93D4⋊C8—371no—
94C37#163811yescharacteristic, complemented, Sylow
95C4⋊Q8C2×D3711yescharacteristic
96C4⋊Q8C2×D3711yescharacteristic
97#126—742no—
98#124—741no—
99C22⋊Q8—741no—
100C4×Q8—371no—
101C4×Q8—741no—
102C4×D4—371no—
103#117—741no—
104#107—741no—
105#106—741no—
106C4⋊C8—371no—
107C4⋊C8—371no—
108#103—22no—
109#103—741no—
110#102—741no—
111C4×C8C2×D3711yescharacteristic
112C2×Q8—21no—
113C2×Q8—21no—
114C2×Q8—371no—
115C2×D4—371no—
116C22×C4—741no—
117C2×C8—21no—
118C2×C8—741no—
119C2×C8—741no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—371no—
124C4⋊C4—371no—
125C4⋊C4—742no—
126C4⋊C4—741no—
127C4⋊C4C22⋊D3712yes—
128C22⋊C4—742no—
129C22⋊C4—742no—
130C22⋊C4—741no—
131C42—742no—
132C42—741no—
133C42C22×D3711yescharacteristic
134C23—741no—
135Q8—42no—
136Q8—41no—
137Q8—41no—
138Q8—741no—
139Q8—741no—
140D4—741no—
141D4—741no—
142C2×C4—22no—
143C2×C4—41no—
144C2×C4—741no—
145C2×C4—741no—
146C2×C4—741no—
147C2×C4—1481no—
148C2×C4—1481no—
149C2×C4D4×D3711yescharacteristic
150C2×C4D4×D3711yescharacteristic
151C2×C4C2×C22⋊D3711yescharacteristic
152C8—41no—
153C8—1481no—
154C8—1481no—
155C22—1481no—
156C22—1481no—
157C22—1481no—
158C22#1192450411yescharacteristic
159C4—21no—
160C4—42no—
161C4—81no—
162C4—1481no—
163C4—1481no—
164C4—1481no—
165C4#1192455711yescharacteristic
166C4#1192455911yescharacteristic
167C4#1192456511yescharacteristic
168C4#1192456811yescharacteristic
169C2—2961no—
170C2#1455769211yescharacteristic
171C2#1455769411yescharacteristic
172C2#1455770511yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#487C2
socleC22×C37#120
prime radicalC2×D148D4
hypercenter#487D37
hypocenterC37#1638
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #14557825C2semidirect
4. #14557279C2semidirect
5. #14557265C2semidirect
7. C37×#487C2semidirect
88. #487D37semidirect
94. C37#1638semidirect

Maximal subgroups

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

subgroupindex
#145582572
#145578252
#145578202
#145572792
#145572652
#145572622
C37×#4872
#163837