Finite Group Databasebeta

← #17993771

Subgroups — #17993771

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#14558256C211yesmaximal, characteristic
2#14557884C211yesmaximal, characteristic, complemented
3#14557828C211yesmaximal, characteristic, complemented
4#14557824C211yesmaximal, characteristic
5#14557280C211yesmaximal, characteristic, complemented
6#14557262C211yesmaximal, characteristic
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8#11924536C2211yescharacteristic
9#11924536C2211yescharacteristic
10#11924531—22no—
11#11924524—21no—
12#11924512—21no—
13C4×Dic74—21no—
14C4×D148C2211yescharacteristic
15#11924494—21no—
16#11924469—21no—
17#11924468—21no—
18C4⋊#64436C2211yescharacteristic
19#11924461—22no—
20#11924460—21no—
21#11924458—21no—
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37D411yescharacteristic
26C2×D148D411yescharacteristic
27C2×C4×D37—21no—
28C2×Dic74—21no—
29C2×Dic74—21no—
30C2×C8×C37—21no—
31C2×C8×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37D411yescharacteristic
34C42×C37—21no—
35C42×C37C2311yescharacteristic
36#10596938—22no—
37#10596938—22no—
38#10596938—21no—
39C4⋊Dic37—21no—
40C4⋊Dic37—21no—
41C4⋊Dic37—21no—
42C4⋊Dic37D411yescharacteristic
43C4⋊Dic37D412yes—
44#10596936—22no—
45C4×Dic37—22no—
46C2×#64436—21no—
47C22×D37—21no—
48Q8×C37—21no—
49Q8×C37—21no—
50C2×C4×C37—21no—
51C2×C4×C37—21no—
52C2×C4×C37C2×D411yescharacteristic
53C2×C4×C37C2×D411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C2×Dic37—21no—
56C2×Dic37—22no—
57C2×Dic37—41no—
58D148—21no—
59D148—21no—
60C4×D37—41no—
61C4×D37—41no—
62Dic74—41no—
63Dic74—41no—
64Dic74—42no—
65C8×C37—41no—
66C8×C37—41no—
67#64436—41no—
68C22×C37#12011yescharacteristic
69C2×D37—41no—
70C2×D37—41no—
71C2×D37—41no—
72C4×C37—21no—
73C4×C37—41no—
74C4×C37—41no—
75C4×C37#13511yescharacteristic
76C4×C37#13511yescharacteristic
77C4×C37#13711yescharacteristic
78C4×C37#13711yescharacteristic
79Dic37—42no—
80Dic37—41no—
81Dic37—81no—
82#1638—371nomaximal, Sylow
83C2×C37#45211yescharacteristic
84C2×C37#45211yescharacteristic
85C2×C37#45411yescharacteristic
86D37—81no—
87#556—371no—
88#487—371no—
89#477—371no—
90#476—371no—
91#332—371no—
92Q8⋊C8D3711yescharacteristic, complemented
93D4⋊C8—371no—
94C37#163811yescharacteristic, complemented, Sylow
95C4⋊Q8—371no—
96C4⋊Q8—371no—
97#126—742no—
98#124—741no—
99C22⋊Q8—741no—
100C4×Q8—741no—
101C4×Q8C2×D3711yescharacteristic
102C4×D4—371no—
103#117—741no—
104#107—741no—
105#106—741no—
106C4⋊C8—371no—
107C4⋊C8C2×D3711yescharacteristic
108#103—742no—
109#103—741no—
110#102—741no—
111C4×C8C2×D3711yescharacteristic
112C2×Q8—741no—
113C2×Q8—741no—
114C2×Q8D14811yescharacteristic
115C2×D4—371no—
116C22×C4—741no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—741no—
120C4⋊C4—21no—
121C4⋊C4—372no—
122C4⋊C4—371no—
123C4⋊C4—742no—
124C4⋊C4—741no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4D14811yescharacteristic
128C22⋊C4—742no—
129C22⋊C4—742no—
130C22⋊C4—741no—
131C42—21no—
132C42—742no—
133C42C22×D3711yescharacteristic
134C23—741no—
135Q8—21no—
136Q8—21no—
137Q8—1482no—
138Q8—1481no—
139Q8—1481no—
140D4—741no—
141D4—741no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—741no—
145C2×C4—742no—
146C2×C4—1481no—
147C2×C4—1481no—
148C2×C4—1481no—
149C2×C4C2×D14811yescharacteristic
150C2×C4D4×D3711yescharacteristic
151C2×C4D4×D3711yescharacteristic
152C8—41no—
153C8—41no—
154C8—1481no—
155C22—1481no—
156C22—1481no—
157C22—1481no—
158C22#1192450611yescharacteristic
159C4—21no—
160C4—41no—
161C4—41no—
162C4—2961no—
163C4—1481no—
164C4—1482no—
165C4#1192455711yescharacteristic
166C4#1192455811yescharacteristic
167C4#1192456811yescharacteristic
168C4#1192456911yescharacteristic
169C2—2961no—
170C2#1455769711yescharacteristic
171C2#1455769811yescharacteristic
172C2#1455770711yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37#120
prime radicalC2×D148D4
hypercenterQ8⋊C8D37
hypocenterC37#1638
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
2. #14557884C2semidirect
3. #14557828C2semidirect
5. #14557280C2semidirect
7. C37×Q8⋊C8C2semidirect
92. Q8⋊C8D37semidirect
94. C37#1638semidirect

Maximal subgroups

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

subgroupindex
#145582562
#145578842
#145578282
#145578242
#145572802
#145572622
C37×Q8⋊C82
#163837