Finite Group Databasebeta

← #17993755

Subgroups — #17993755

Order 4736.

188 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 55 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#14558258C211yesmaximal, characteristic
2#14557885C211yesmaximal, characteristic
3#14557829C211yesmaximal, characteristic
4#14557829C211yesmaximal, characteristic
5#14557263C211yesmaximal, characteristic
6#14557263C211yesmaximal, characteristic
7C37×#332C211yesmaximal, characteristic
8#11924536C2211yescharacteristic
9#11924534—21no—
10#11924527—21no—
11#11924526—22no—
12Q8×Dic37—21no—
13C4×Dic74C2211yescharacteristic
14C4×Dic74C2211yescharacteristic
15#11924501—21no—
16#11924470—21no—
17#11924470—21no—
18#11924461—21no—
19#11924461—21no—
20#11924459—22no—
21C4×#64436C2211yescharacteristic
22C4⋊Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26C2×Dic74—21no—
27C2×Dic74D411yescharacteristic
28C2×Dic74D411yescharacteristic
29C2×C8×C37—21no—
30C2×C8×C37—21no—
31C4⋊C4×C37—21no—
32C4⋊C4×C37D412yes—
33C42×C37C2311yescharacteristic
34C4⋊Dic37—22no—
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—
47Q8×C37—41no—
48Q8×C37—41no—
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—21no—
61Dic74—42no—
62Dic74Q1612yes—
63C8×C37—41no—
64C8×C37—41no—
65#64436—41no—
66C22×C37#12011yescharacteristic
67C4×C37—21no—
68C4×C37—42no—
69C4×C37C2×Q1611yescharacteristic
70C4×C37#13511yescharacteristic
71C4×C37#13711yescharacteristic
72C4×C37#13711yescharacteristic
73Dic37—22no—
74Dic37—41no—
75Dic37—41no—
76Dic37—41no—
77Dic37—81no—
78#1636—371nomaximal, Sylow
79C2×C37#45111yescharacteristic
80C2×C37#45211yescharacteristic
81C2×C37#45411yescharacteristic
82#557—371no—
83#487—371no—
84#477—371no—
85#477—371no—
86#332D3711yescharacteristic
87Q8⋊C8—371no—
88Q8⋊C8—371no—
89C37#163611yescharacteristic, complemented, Sylow
90C4⋊Q8—371no—
91C4⋊Q8—741no—
92C4⋊Q8C2×D3711yescharacteristic
93#125—741no—
94#125—742no—
95C4×Q8—371no—
96C4×Q8—371no—
97C4×Q8—741no—
98C4×Q8—741no—
99#107—741no—
100#107—741no—
101C4⋊C8C2×D3711yescharacteristic
102C4⋊C8C2×D3711yescharacteristic
103#103—741no—
104#103—741no—
105#103—742no—
106C4×C8—371no—
107C2×Q8—21no—
108C2×Q8—371no—
109C2×Q8—371no—
110C2×Q8—741no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—741no—
114C4⋊C4—21no—
115C4⋊C4—371no—
116C4⋊C4—371no—
117C4⋊C4—742no—
118C4⋊C4—742no—
119C4⋊C4—742no—
120C4⋊C4—741no—
121C4⋊C4—741no—
122C4⋊C4—741no—
123C4⋊C4—741no—
124C4⋊C4D14812yes—
125C42—742no—
126C42—741no—
127C42—741no—
128C42C22×D3711yescharacteristic
129Q8—41no—
130Q8—41no—
131Q8—372no—
132Q8—741no—
133Q8—741no—
134Q8—741no—
135Q8—1482no—
136C2×C4—22no—
137C2×C4—741no—
138C2×C4—741no—
139C2×C4—741no—
140C2×C4—741no—
141C2×C4—1481no—
142C2×C4C2×D14811yescharacteristic
143C2×C4D4×D3711yescharacteristic
144C2×C4D4×D3711yescharacteristic
145C8—41no—
146C8—41no—
147C8—1481no—
148C22#1192450611yescharacteristic
149C4—21no—
150C4—42no—
151C4—2961no—
152C4—742no—
153C4—1481no—
154C4—1481no—
155C4—1481no—
156C4Q16×D3711yescharacteristic
157C4#1192455511yescharacteristic
158C4#1192456511yescharacteristic
159C4#1192456511yescharacteristic
160C2#1455769011yescharacteristic
161C2#1455769611yescharacteristic
162C2#1455770811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#332C2
socle, prime radicalC22×C37#120
hypercenter#332D37
hypocenterC37#1636
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
89. C37#1636semidirect

Maximal subgroups

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

subgroupindex
#145582582
#145578852
#145578292
#145572632
C37×#3322
#163637