Finite Group Databasebeta

← #17993818

Subgroups — #17993818

Order 4736.

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

normal subgroups only

This group has 200 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#14558263C211yesmaximal, characteristic
2#14557883C211yesmaximal, characteristic
3#14557819C211yesmaximal, characteristic
4#14557744C211yesmaximal, characteristic
5#14557263C211yesmaximal, characteristic
6#14557263C211yesmaximal, characteristic
7C37×#333C211yesmaximal, characteristic
8C2×Dic148—21no—
9#11924536C2211yescharacteristic
10#11924535—21no—
11#11924535—21no—
12#11924534—22no—
13C4×Dic74C2211yescharacteristic
14C4×Dic74C2211yescharacteristic
15#11924501—21no—
16#11924501—21no—
17#11924468—21no—
18#11924461—21no—
19#11924461—21no—
20#11924460—22no—
21C4×#64436C2211yescharacteristic
22C4⋊Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×Q8×C37D412yes—
26C2×Dic74—21no—
27C2×Dic74—22no—
28C2×Dic74D411yescharacteristic
29C2×Dic74D411yescharacteristic
30C2×C8×C37—21no—
31C2×C8×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C42×C37C2311yescharacteristic
35C4⋊Dic37—21no—
36C4⋊Dic37—21no—
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—
47Dic148—42no—
48Q8×C37—42no—
49C2×C4×C37—22no—
50C2×C4×C37C2×D411yescharacteristic
51C2×C4×C37C2×D411yescharacteristic
52C2×C4×C37C2×D411yescharacteristic
53C2×Dic37—21no—
54C2×Dic37—21no—
55C2×Dic37—21no—
56C2×Dic37—21no—
57C2×Dic37—41no—
58Dic74—21no—
59Dic74—21no—
60Dic74—41no—
61Dic74—41no—
62Dic74—82no—
63Dic74SD1612yes—
64Dic74Q1612yescomplemented
65C8×C37—41no—
66C8×C37—41no—
67#64436—41no—
68C22×C37#12011yescharacteristic
69C4×C37—21no—
70C4×C37—42no—
71C4×C37C2×SD1611yescharacteristic
72C4×C37C2×Q1611yescharacteristic
73C4×C37#13711yescharacteristic
74C4×C37#13711yescharacteristic
75Dic37—22no—
76Dic37—22no—
77Dic37—41no—
78Dic37—41no—
79Dic37—81no—
80#1645—371nomaximal, Sylow
81C2×C37#44811yescharacteristic
82C2×C37#45111yescharacteristic
83C2×C37#45511yescharacteristic
84Q82—371no—
85#487—371no—
86#475—371no—
87#462—371no—
88#333D3711yescharacteristic
89Q8⋊C8—371no—
90Q8⋊C8—371no—
91C37#164511yescharacteristic, complemented, Sylow
92C2×Q16—741no—
93C4⋊Q8—371no—
94C4⋊Q8—741no—
95C4⋊Q8—741no—
96C4⋊Q8—742no—
97C4⋊Q8C2×D3711yescharacteristic
98C4×Q8—371no—
99C4×Q8—371no—
100C4×Q8—741no—
101C4×Q8—741no—
102#106—741no—
103C4⋊C8C2×D3711yescharacteristic
104C4⋊C8C2×D3711yescharacteristic
105#103—741no—
106#103—741no—
107#103—742no—
108C4×C8—371no—
109C2×Q8—371no—
110C2×Q8—371no—
111C2×Q8—742no—
112C2×Q8—741no—
113C2×Q8D14812yes—
114Q16—1482no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—741no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—371no—
121C4⋊C4—371no—
122C4⋊C4—742no—
123C4⋊C4—742no—
124C4⋊C4—741no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C42—742no—
129C42—741no—
130C42—741no—
131C42C22×D3711yescharacteristic
132Q8—42no—
133Q8—372no—
134Q8—372no—
135Q8—2962no—
136Q8—741no—
137Q8—741no—
138Q8—1481no—
139Q8—1481no—
140C2×C4—22no—
141C2×C4—741no—
142C2×C4—741no—
143C2×C4—741no—
144C2×C4—741no—
145C2×C4—1481no—
146C2×C4C2×D14811yescharacteristic
147C2×C4D4×D3711yescharacteristic
148C2×C4D4×D3711yescharacteristic
149C8—41no—
150C8—41no—
151C8—1481no—
152C22#1192450611yescharacteristic
153C4—21no—
154C4—42no—
155C4—2961no—
156C4—742no—
157C4—742no—
158C4—1481no—
159C4—1481no—
160C4SD16×D3711yescharacteristic
161C4Q16×D3711yescharacteristic
162C4#1192456511yescharacteristic
163C4#1192456811yescharacteristic
164C2#1455767311yescharacteristic
165C2#1455769011yescharacteristic
166C2#1455771311yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#333C2
socle, prime radicalC22×C37#120
hypercenter#333D37
hypocenterC37#1645
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
64. Dic74Q16semidirect
91. C37#1645semidirect

Maximal subgroups

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

subgroupindex
#145582632
#145578832
#145578192
#145577442
#145572632
C37×#3332
#164537