Finite Group Databasebeta

← #17993907

Subgroups — #17993907

Order 4736.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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#14557943C212yesmaximal, complemented
2#14557928C211yesmaximal, characteristic
3#14557275C212yesmaximal, complemented
4#14557273C211yesmaximal, characteristic
5C37×#563C211yesmaximal, characteristic
6C2×#10596942—21no—
7C2×#10596940—21no—
8#11924536C2211yescharacteristic
9#11924469—22no—
10#11924467—22no—
11#11924447C2212yes—
12#11924447C2211yescharacteristic
13C4⋊Q8×C37—21no—
14#126×C37—22no—
15#125×C37C2212yes—
16#124×C37C2211yescharacteristic
17#123×C37—21no—
18C22⋊Q8×C37—22no—
19C2×Q8×C37—21no—
20C2×Q8×C37D411yescharacteristic
21C2×D4×C37D411yescharacteristic
22C22×C4×C37—21no—
23C2×Dic74—21no—
24C4⋊C4×C37—22no—
25C4⋊C4×C37—22no—
26C4⋊C4×C37—22no—
27C4⋊C4×C37D412yes—
28C4⋊C4×C37D412yes—
29C22⋊C4×C37—22no—
30C22⋊C4×C37—21no—
31C22⋊C4×C37—22no—
32C42×C37—21no—
33C42×C37C2311yescharacteristic
34#10596942—42no—
35#10596940—42no—
36C4⋊Dic37—22no—
37C2×#64436—21no—
38C2×#64436—22no—
39C23×C37—21no—
40Q8×C37—41no—
41Q8×C37—81no—
42D4×C37—41no—
43C2×C4×C37—22no—
44C2×C4×C37—21no—
45C2×C4×C37—22no—
46C2×C4×C37—81no—
47C2×C4×C37C2×D412yes—
48C2×C4×C37C2×D411yescharacteristic
49C2×Dic37—41no—
50Dic74—41no—
51Dic74—41no—
52#64436—24no—
53#64436—22no—
54C22×C37—41no—
55C22×C37—42no—
56C22×C37#12011yescharacteristic
57C4×C37—21no—
58C4×C37—22no—
59C4×C37—42no—
60C4×C37—41no—
61C4×C37—42no—
62Dic37—81no—
63#1660—371nomaximal, Sylow
64C2×C37—81no—
65C2×C37#45311yescharacteristic
66C2×C37#45612yes—
67#563D3711yescharacteristic
68#501—372no—
69#497—371no—
70#330—372no—
71#329—371no—
72C37#166011yescharacteristic, complemented, Sylow
73C2×Q16—741no—
74C2×SD16—741no—
75C4⋊Q8—21no—
76C4⋊Q8—371no—
77#126—22no—
78#125C2×D3712yes—
79#124C2×D3711yescharacteristic
80#123—21no—
81C22⋊Q8—22no—
82#107—742no—
83#106—742no—
84#97—372no—
85#97—371no—
86C2×Q8—21no—
87C2×Q8—741no—
88C2×Q8C22⋊D3711yescharacteristic
89C2×D4C22⋊D3711yescharacteristic
90C22×C4—21no—
91Q16—1482no—
92SD16—1482no—
93C2×C8—742no—
94C2×C8—741no—
95C4⋊C4—22no—
96C4⋊C4—22no—
97C4⋊C4—22no—
98C4⋊C4—742no—
99C4⋊C4C22⋊D3712yes—
100C4⋊C4C22⋊D3712yes—
101C22⋊C4—22no—
102C22⋊C4—21no—
103C22⋊C4—22no—
104C42—21no—
105C42C22×D3711yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—81no—
109Q8—1481no—
110Q8—1481no—
111D4—41no—
112C2×C4—22no—
113C2×C4—21no—
114C2×C4—22no—
115C2×C4—81no—
116C2×C4—1481no—
117C2×C4C2×C22⋊D3712yes—
118C2×C4C2×C22⋊D3711yescharacteristic
119C8—742no—
120C8—744no—
121C22—41no—
122C22—42no—
123C22#1192450511yescharacteristic
124C4—21no—
125C4—22no—
126C4—42no—
127C4—41no—
128C4—42no—
129C4—2961no—
130C2—81no—
131C2#1455770111yescharacteristic
132C2#1455771612yes—
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#563C2
socleC22×C37#120
prime radicalC2×D4×C37D4
hypercenter#563D37
hypocenterC37#1660
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #14557943C2semidirect
3. #14557275C2semidirect
72. C37#1660semidirect

Maximal subgroups

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

subgroupindex
#145579432
#145579282
#145572752
#145572732
C37×#5632
#166037