Finite Group Databasebeta

← #17993908

Subgroups — #17993908

Order 4736.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#14558283C211yesmaximal, characteristic
2#14557942C212yesmaximal, complemented
3#14557928C211yesmaximal, characteristic
4#14557274C212yesmaximal, complemented
5C37×#329C211yesmaximal, characteristic
6C2×#10596942—21no—
7C2×#10596940—21no—
8#11924536C2211yescharacteristic
9#11924534—21no—
10#11924529—22no—
11#11924528C2212yes—
12#11924517—21no—
13#11924513—22no—
14#11924470—22no—
15#11924468—22no—
16#11924447C2211yescharacteristic
17#124×C37C2211yescharacteristic
18#97×C37C2212yes—
19C2×Q8×C37D411yescharacteristic
20C2×D4×C37D411yescharacteristic
21C22×Dic37—21no—
22C2×Dic74—21no—
23C2×Dic74—21no—
24C2×C8×C37—22no—
25C22⋊C4×C37—22no—
26C42×C37C2311yescharacteristic
27C22⋊Dic37—22no—
28C22⋊Dic37—21no—
29#10596942—42no—
30#10596940—42no—
31C4⋊Dic37—22no—
32C4⋊Dic37D412yes—
33C4⋊Dic37D412yes—
34#10596936—22no—
35#10596936—22no—
36#10596936—22no—
37C4×Dic37—21no—
38C2×#64436—21no—
39C23×C37—21no—
40Q8×C37—41no—
41D4×C37—41no—
42C2×C4×C37—21no—
43C2×C4×C37C2×D411yescharacteristic
44C2×C4×C37C2×D412yes—
45C2×Dic37—22no—
46C2×Dic37—22no—
47C2×Dic37—41no—
48C2×Dic37—81no—
49Dic74—41no—
50Dic74—41no—
51Dic74—81no—
52C8×C37—24no—
53#64436—22no—
54C22×C37—41no—
55C22×C37—42no—
56C22×C37#12011yescharacteristic
57C4×C37—21no—
58C4×C37—22no—
59C4×C37—41no—
60Dic37—42no—
61Dic37—42no—
62Dic37—81no—
63#1660—371nomaximal, Sylow
64C2×C37—81no—
65C2×C37#45311yescharacteristic
66C2×C37#45612yes—
67#563—371no—
68#501—372no—
69#497—371no—
70#330—372no—
71#329D3711yescharacteristic
72C37#166011yescharacteristic, complemented, Sylow
73C2×Q16—741no—
74C2×SD16—741no—
75C4⋊Q8—371no—
76C4⋊Q8—741no—
77#126—742no—
78#125—372no—
79#124C2×D3711yescharacteristic
80#123—741no—
81C22⋊Q8—742no—
82#107—742no—
83#106—742no—
84#97—371no—
85#97C2×D3712yes—
86C2×Q8—741no—
87C2×Q8—741no—
88C2×Q8D14811yescharacteristic
89C2×D4D14811yescharacteristic
90C22×C4—741no—
91Q16—1482no—
92SD16—1482no—
93C2×C8—22no—
94C2×C8—741no—
95C4⋊C4—372no—
96C4⋊C4—372no—
97C4⋊C4—742no—
98C4⋊C4—742no—
99C4⋊C4—742no—
100C4⋊C4—742no—
101C22⋊C4—22no—
102C22⋊C4—742no—
103C22⋊C4—741no—
104C42—741no—
105C42C22×D3711yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—2961no—
109Q8—1481no—
110Q8—1481no—
111D4—41no—
112C2×C4—21no—
113C2×C4—2961no—
114C2×C4—742no—
115C2×C4—742no—
116C2×C4—1481no—
117C2×C4C2×D14811yescharacteristic
118C2×C4D4×D3712yes—
119C8—24no—
120C8—742no—
121C22—41no—
122C22—42no—
123C22#1192450611yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—2961no—
128C4—1482no—
129C4—1482no—
130C2—81no—
131C2#1455770311yescharacteristic
132C2#1455771712yes—
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#329C2
socleC22×C37#120
prime radicalC2×D4×C37D4
hypercenter#329D37
hypocenterC37#1660
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14557942C2semidirect
4. #14557274C2semidirect
72. C37#1660semidirect

Maximal subgroups

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

subgroupindex
#145582832
#145579422
#145579282
#145572742
C37×#3292
#166037