Finite Group Databasebeta

← #17993640

Subgroups — #17993640

Order 4736.

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

normal subgroups only

This group has 202 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#14558164C211yesmaximal, characteristic
2#14557869C212yesmaximal
3#14557472C211yesmaximal, characteristic
4#14557271C212yesmaximal
5C37×#324C211yesmaximal, characteristic
6#11924535—22no—
7#11924527—22no—
8#11924515—21no—
9#11924515C2212yes—
10#11924495—21no—
11C2×C4⋊Dic37C2211yescharacteristic
12#11924470—22no—
13#11924461—22no—
14#11924443—21no—
15#11924443—21no—
16#11924443C2211yescharacteristic
17C2×C4⋊C4×C37C2211yescharacteristic
18C22⋊C8×C37C2212yes—
19C22×C4×C37D411yescharacteristic
20C22×C4×C37D411yescharacteristic
21C22×C4×C37C2311yescharacteristic
22C22×Dic37—21no—
23C22×Dic37—21no—
24C2×Dic74—21no—
25C2×Dic74D412yes—
26C2×C8×C37—22no—
27C4⋊C4×C37—22no—
28C22⋊Dic37—22no—
29C4⋊Dic37—21no—
30C4⋊Dic37—21no—
31C4⋊Dic37—21no—
32C4⋊Dic37—22no—
33C4⋊Dic37D412yes—
34#10596936—22no—
35#10596936—22no—
36C4×Dic37—22no—
37C23×C37C2×D411yescharacteristic
38C2×C4×C37—21no—
39C2×C4×C37—21no—
40C2×C4×C37—21no—
41C2×C4×C37—41no—
42C2×C4×C37—41no—
43C2×C4×C37Q1612yes—
44C2×C4×C37C2×D412yes—
45C2×Dic37—22no—
46C2×Dic37—22no—
47C2×Dic37—41no—
48C2×Dic37—41no—
49C2×Dic37—42no—
50C2×Dic37—41no—
51C2×Dic37—41no—
52Dic74—42no—
53Dic74—81no—
54C8×C37—42no—
55C22×C37—21no—
56C22×C37—21no—
57C22×C37#12011yescharacteristic
58C22×C37C2×Q1611yescharacteristic
59C22×C37#13711yescharacteristic
60C4×C37—22no—
61C4×C37—22no—
62C4×C37—41no—
63Dic37—42no—
64Dic37—42no—
65Dic37—81no—
66Dic37—81no—
67#1617—371nomaximal, Sylow
68C2×C37—21no—
69C2×C37—21no—
70C2×C37#45111yescharacteristic
71C2×C37#45411yescharacteristic
72C2×C37#45811yescharacteristic
73#544—371no—
74#484—372no—
75#400—371no—
76#328—372no—
77#324D3711yescharacteristic
78C37#161711yescharacteristic, complemented, Sylow
79C4⋊Q8—742no—
80#125—742no—
81C22⋊Q8—372no—
82C22⋊Q8—741no—
83#117—741no—
84C2×C4⋊C4—371no—
85C2×C4⋊C4C2×D3711yescharacteristic
86#107—742no—
87#103—742no—
88C22⋊C8C2×D3712yes—
89#95—371no—
90#95—741no—
91#95—741no—
92C2×Q8—372no—
93C2×Q8—741no—
94C22×C4—741no—
95C22×C4—741no—
96C22×C4D14811yescharacteristic
97C22×C4D14811yescharacteristic
98C22×C4C22×D3711yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—372no—
102C4⋊C4—742no—
103C4⋊C4—741no—
104C4⋊C4—741no—
105C4⋊C4—741no—
106C4⋊C4—742no—
107C4⋊C4—742no—
108C22⋊C4—742no—
109C42—742no—
110C23C2×D14811yescharacteristic
111Q8—2961no—
112Q8—1482no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—742no—
119C2×C4—742no—
120C2×C4—1481no—
121C2×C4—1481no—
122C2×C4—1482no—
123C2×C4—1481no—
124C2×C4—1481no—
125C2×C4Dic14812yes—
126C2×C4D4×D3712yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#1192450611yescharacteristic
131C22C2×Dic14811yescharacteristic
132C22#1192456911yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—2961no—
137C4—2961no—
138C4—1482no—
139C4—1482no—
140C2—21no—
141C2—21no—
142C2#1455769111yescharacteristic
143C2#1455770811yescharacteristic
144C2#1455772411yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#324C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#324D37
hypocenterC37#1617
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
78. C37#1617semidirect

Maximal subgroups

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

subgroupindex
#145581642
#145578692
#145574722
#145572712
C37×#3242
#161737