Finite Group Databasebeta

← #17993638

Subgroups — #17993638

Order 4736.

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

normal subgroups only

This group has 202 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#14557866C212yesmaximal
2#14557472C211yesmaximal, characteristic
3#14557270C212yesmaximal
4#14557259C211yesmaximal, characteristic
5C37×#544C211yesmaximal, characteristic
6C2×C4⋊Dic37C2211yescharacteristic
7#11924469—22no—
8#11924460—22no—
9C22⋊#64436C2212yes—
10#11924443—21no—
11#11924443—21no—
12#11924443C2211yescharacteristic
13C4⋊Q8×C37—22no—
14#125×C37—22no—
15C22⋊Q8×C37—21no—
16C22⋊Q8×C37C2212yes—
17#117×C37—21no—
18C2×C4⋊C4×C37C2211yescharacteristic
19C2×Q8×C37—21no—
20C2×Q8×C37D412yes—
21C22×C4×C37D411yescharacteristic
22C22×C4×C37D411yescharacteristic
23C22×C4×C37C2311yescharacteristic
24C22×Dic37—21no—
25C22×Dic37—21no—
26C4⋊C4×C37—21no—
27C4⋊C4×C37—21no—
28C4⋊C4×C37—21no—
29C4⋊C4×C37—22no—
30C4⋊C4×C37—22no—
31C4⋊C4×C37—22no—
32C4⋊C4×C37D412yes—
33C22⋊C4×C37—22no—
34C42×C37—22no—
35C4⋊Dic37—22no—
36C2×#64436—22no—
37C23×C37C2×D411yescharacteristic
38Q8×C37—42no—
39Q8×C37—81no—
40C2×C4×C37—21no—
41C2×C4×C37—21no—
42C2×C4×C37—22no—
43C2×C4×C37—22no—
44C2×C4×C37—21no—
45C2×C4×C37—41no—
46C2×C4×C37—41no—
47C2×C4×C37Q1612yes—
48C2×C4×C37C2×D412yes—
49C2×Dic37—41no—
50C2×Dic37—41no—
51C2×Dic37—42no—
52C2×Dic37—41no—
53C2×Dic37—41no—
54#64436—42no—
55C22×C37—21no—
56C22×C37—21no—
57C22×C37#12011yescharacteristic
58C22×C37C2×Q1611yescharacteristic
59C22×C37#13711yescharacteristic
60C4×C37—22no—
61C4×C37—22no—
62C4×C37—42no—
63C4×C37—41no—
64C4×C37—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#544D3711yescharacteristic
74#484—372no—
75#400—371no—
76#328—372no—
77#324—371no—
78C37#161711yescharacteristic, complemented, Sylow
79C4⋊Q8—22no—
80#125—22no—
81C22⋊Q8—21no—
82C22⋊Q8C2×D3712yes—
83#117—21no—
84C2×C4⋊C4—371no—
85C2×C4⋊C4C2×D3711yescharacteristic
86#107—742no—
87#103—742no—
88C22⋊C8—372no—
89#95—371no—
90#95—741no—
91#95—741no—
92C2×Q8—21no—
93C2×Q8C22⋊D3712yes—
94C22×C4—741no—
95C22×C4—741no—
96C22×C4C22⋊D3711yescharacteristic
97C22×C4C22⋊D3711yescharacteristic
98C22×C4C22×D3711yescharacteristic
99C2×C8—742no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—742no—
107C4⋊C4C22⋊D3712yes—
108C22⋊C4—22no—
109C42—22no—
110C23C2×C22⋊D3711yescharacteristic
111Q8—42no—
112Q8—81no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—21no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—1481no—
121C2×C4—1481no—
122C2×C4—1482no—
123C2×C4—1481no—
124C2×C4—1481no—
125C2×C4#1059694212yes—
126C2×C4C2×C22⋊D3712yes—
127C8—1482no—
128C22—21no—
129C22—21no—
130C22#1192450511yescharacteristic
131C22C2×#1059694211yescharacteristic
132C22#1192456711yescharacteristic
133C4—22no—
134C4—22no—
135C4—42no—
136C4—41no—
137C4—42no—
138C4—2961no—
139C4—2961no—
140C2—21no—
141C2—21no—
142C2#1455768911yescharacteristic
143C2#1455770611yescharacteristic
144C2#1455772311yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#544C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#544D37
hypocenterC37#1617
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

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
#145578662
#145574722
#145572702
#145572592
C37×#5442
#161737