Finite Group Databasebeta

← #17993604

Subgroups — #17993604

Order 4736.

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

normal subgroups only

This group has 210 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#14557861C212yesmaximal
2#14557463C211yesmaximal, characteristic
3#14557270C212yesmaximal
4#14557259C211yesmaximal, characteristic
5C37×#544C211yesmaximal, characteristic
6C2×C4⋊Dic37C2211yescharacteristic
7C2×#10596936—21no—
8#11924467—22no—
9#11924460—22no—
10C22⋊#64436C2212yes—
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—
36#10596936—42no—
37C2×#64436—22no—
38C23×C37C2×D411yescharacteristic
39Q8×C37—42no—
40Q8×C37—81no—
41C2×C4×C37—21no—
42C2×C4×C37—21no—
43C2×C4×C37—22no—
44C2×C4×C37—22no—
45C2×C4×C37—21no—
46C2×C4×C37—41no—
47C2×C4×C37—41no—
48C2×C4×C37SD1612yes—
49C2×C4×C37C2×D412yes—
50C2×Dic37—22no—
51C2×Dic37—41no—
52C2×Dic37—41no—
53C2×Dic37—41no—
54C2×Dic37—41no—
55C2×Dic37—41no—
56#64436—42no—
57C22×C37—21no—
58C22×C37—21no—
59C22×C37#12011yescharacteristic
60C22×C37C2×SD1611yescharacteristic
61C22×C37#13711yescharacteristic
62C4×C37—22no—
63C4×C37—22no—
64C4×C37—42no—
65C4×C37—41no—
66C4×C37—42no—
67Dic37—42no—
68Dic37—81no—
69#1611—371nomaximal, Sylow
70C2×C37—21no—
71C2×C37—21no—
72C2×C37#44811yescharacteristic
73C2×C37#45611yescharacteristic
74C2×C37#45811yescharacteristic
75#544D3711yescharacteristic
76#483—372no—
77#398—371no—
78#328—372no—
79#324—371no—
80C37#161111yescharacteristic, complemented, Sylow
81C4⋊Q8—22no—
82#125—22no—
83C22⋊Q8—21no—
84C22⋊Q8C2×D3712yes—
85#117—21no—
86C2×C4⋊C4—371no—
87C2×C4⋊C4—741no—
88C2×C4⋊C4C2×D3711yescharacteristic
89#106—742no—
90#103—742no—
91C22⋊C8—372no—
92#95—371no—
93#95—741no—
94C2×Q8—21no—
95C2×Q8C22⋊D3712yes—
96C22×C4—741no—
97C22×C4—741no—
98C22×C4C22⋊D3711yescharacteristic
99C22×C4C22⋊D3711yescharacteristic
100C22×C4C22×D3711yescharacteristic
101C2×C8—742no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—742no—
109C4⋊C4—1482no—
110C4⋊C4C22⋊D3712yes—
111C22⋊C4—22no—
112C42—22no—
113C23C2×C22⋊D3711yescharacteristic
114Q8—42no—
115Q8—81no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—742no—
124C2×C4—1481no—
125C2×C4—1481no—
126C2×C4—1481no—
127C2×C4—1481no—
128C2×C4—1481no—
129C2×C4#1059694112yes—
130C2×C4C2×C22⋊D3712yes—
131C8—1482no—
132C22—21no—
133C22—21no—
134C22#1192450511yescharacteristic
135C22C2×#1059694111yescharacteristic
136C22#1192456711yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—42no—
142C4—2961no—
143C4—1482no—
144C2—21no—
145C2—21no—
146C2#1455767211yescharacteristic
147C2#1455771611yescharacteristic
148C2#1455772311yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#544C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#544D37
hypocenterC37#1611
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
80. C37#1611semidirect

Maximal subgroups

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

subgroupindex
#145578612
#145574632
#145572702
#145572592
C37×#5442
#161137