Finite Group Databasebeta

← #17993323

Subgroups — #17993323

Order 4736.

202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 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#14558088C211yesmaximal, characteristic
2#14557589C211yesmaximal, characteristic
3#14557555C211yesmaximal, characteristic
4#14557282C211yesmaximal, characteristic, complemented
5#14557280C211yesmaximal, characteristic, complemented
6#14557278C211yesmaximal, characteristic, complemented
7C37×#333C211yesmaximal, characteristic, complemented
8C2×#10596929—21no—
9#11924536C2211yescharacteristic
10#11924527—21no—
11#11924516—21no—
12#11924512C412yes—
13Q8×Dic37C412yes—
14#11924501—21no—
15#11924494—21no—
16C42×D37C2211yescharacteristic
17C4⋊#64436C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924465—21no—
20#11924448—21no—
21#11924446—21no—
22C4⋊Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×Q8×C37C2×C412yes—
26C2×C4×D37C2×C411yescharacteristic
27C2×C4×D37D411yescharacteristic
28C2×C4×D37D411yescharacteristic
29C2×Dic74—21no—
30C2×C8×C37—21no—
31C2×C8×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C42×C37C2311yescharacteristic
35#10596938—22no—
36C4⋊Dic37—21no—
37C4⋊Dic37—22no—
38C4⋊Dic37C2×C412yes—
39#10596936—22no—
40C4×Dic37—22no—
41C4×Dic37C2×C411yescharacteristic
42C4×Dic37D411yescharacteristic
43C4×Dic37D411yescharacteristic
44C2×#64436—21no—
45C2×#64436—21no—
46#10596929—42no—
47C22×D37C22⋊C411yescharacteristic
48Q8×C37—42no—
49C2×C4×C37—22no—
50C2×C4×C37C22×C411yescharacteristic
51C2×C4×C37C2×D411yescharacteristic
52C2×C4×C37C2×D411yescharacteristic
53C2×Dic37—22no—
54C2×Dic37C22⋊C411yescharacteristic
55C2×Dic37C22⋊C411yescharacteristic
56C2×Dic37C22⋊C411yescharacteristic
57C4×D37—21no—
58C4×D37—21no—
59C4×D37—21no—
60C4×D37—21no—
61C4×D37—41no—
62Dic74—41no—
63Dic74—41no—
64C8×C37—41no—
65C8×C37—41no—
66#64436—41no—
67#64436—41no—
68C22×C37C2×C22⋊C411yescharacteristic
69C2×D37—21no—
70C2×D37—21no—
71C2×D37—21no—
72C4×C37—21no—
73C4×C37—42no—
74C4×C37AGL(1,ℤ/8)11yescharacteristic
75C4×C37#13711yescharacteristic
76C4×C37#13711yescharacteristic
77C4×C37#13711yescharacteristic
78Dic37—21no—
79Dic37—21no—
80Dic37—21no—
81Dic37—42no—
82#1559—371nomaximal, Sylow
83C2×C37#41311yescharacteristic
84C2×C37#41711yescharacteristic
85C2×C37#41911yescharacteristic
86D37—41no—
87#533—371no—
88#432—371no—
89#423—371no—
90#333—371no—
91#333D3711yescharacteristic, complemented
92#332—371no—
93#332—371no—
94C37#155911yescharacteristic, complemented, Sylow
95C2×M16—741no—
96C4⋊Q8—371no—
97C4⋊Q8C2×D3711yescharacteristic
98#125—741no—
99C22⋊Q8—372no—
100C22⋊Q8—741no—
101C4×Q8—372no—
102C4×Q8—741no—
103#117—741no—
104C2×C42—371no—
105C4⋊C8—371no—
106C4⋊C8—371no—
107C4⋊C8—741no—
108C4⋊C8C2×D3711yescharacteristic
109C4⋊C8C2×D3711yescharacteristic
110C22⋊C8—741no—
111#97—741no—
112C2×Q8—741no—
113C2×Q8C4×D3712yes—
114C22×C4—371no—
115C22×C4—371no—
116C22×C4—371no—
117M16—1482no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—741no—
121C2×C8—741no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—372no—
125C4⋊C4—742no—
126C4⋊C4—742no—
127C4⋊C4—741no—
128C22⋊C4—742no—
129C42—371no—
130C42—371no—
131C42—371no—
132C42—742no—
133C42C22×D3711yescharacteristic
134C23—371no—
135Q8—42no—
136Q8—1481no—
137Q8—1481no—
138C2×C4—22no—
139C2×C4—371no—
140C2×C4—371no—
141C2×C4—371no—
142C2×C4—741no—
143C2×C4—741no—
144C2×C4—741no—
145C2×C4—741no—
146C2×C4—742no—
147C2×C4—1481no—
148C2×C4C2×C4×D3711yescharacteristic
149C2×C4D4×D3711yescharacteristic
150C2×C4D4×D3711yescharacteristic
151C8—41no—
152C8—41no—
153C8—1481no—
154C8—1481no—
155C22—741no—
156C22—741no—
157C22—741no—
158C22C22⋊C4×D3711yescharacteristic
159C4—21no—
160C4—42no—
161C4—741no—
162C4—741no—
163C4—741no—
164C4—1482no—
165C4#1192456311yescharacteristic
166C4#1192456511yescharacteristic
167C4#1192456811yescharacteristic
168C4#1192456811yescharacteristic
169C2—1481no—
170C2#1455751411yescharacteristic
171C2#1455753311yescharacteristic
172C2#1455754011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#333C2
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C22⋊C4
cosocleC42×C37C23
hypercenter#333D37
hypocenterC37#1559
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #14557282C2semidirect
5. #14557280C2semidirect
6. #14557278C2semidirect
7. C37×#333C2semidirect
91. #333D37semidirect
94. C37#1559semidirect

Maximal subgroups

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

subgroupindex
#145580882
#145575892
#145575552
#145572822
#145572802
#145572782
C37×#3332
#155937