Finite Group Databasebeta

← #17993892

Subgroups — #17993892

Order 4736.

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

normal subgroups only

This group has 206 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, complemented
2#14557897C212yesmaximal, complemented
3#14557274C212yesmaximal, complemented
4#14557273C211yesmaximal, characteristic, complemented
5C37×#496C211yesmaximal, characteristic
6#11924534—21no—
7#11924529—22no—
8#11924528C2212yes—
9#11924517—21no—
10#11924513—22no—
11#11924457—22no—
12#11924457—22no—
13#11924447C2212yes—
14C2×SD16×C37—21no—
15C2×D8×C37—21no—
16#127×C37C2211yescharacteristic
17#124×C37C2211yescharacteristic
18#97×C37C2211yescharacteristic
19C2×Q8×C37D411yescharacteristic
20C2×D4×C37—21no—
21C2×D4×C37—22no—
22C2×D4×C37D411yescharacteristic
23C22×Dic37—21no—
24C2×Dic74—21no—
25SD16×C37—42no—
26D8×C37—42no—
27C2×C8×C37—21no—
28C22⋊C4×C37—22no—
29C42×C37C2311yescharacteristic
30C22⋊Dic37—22no—
31C22⋊Dic37—21no—
32C4⋊Dic37D412yes—
33C4⋊Dic37D412yes—
34#10596936—22no—
35#10596936—22no—
36#10596936—22no—
37C4×Dic37—21no—
38C2×#64436—22no—
39C23×C37—21no—
40C23×C37—41no—
41Q8×C37—41no—
42D4×C37—41no—
43D4×C37—41no—
44D4×C37—41no—
45D4×C37—44no—
46C2×C4×C37—21no—
47C2×C4×C37C2×D412yes—
48C2×C4×C37C2×D411yescharacteristic
49C2×Dic37—22no—
50C2×Dic37—22no—
51C2×Dic37—81no—
52Dic74—81no—
53C8×C37—22no—
54#64436—42no—
55C22×C37—41no—
56C22×C37—42no—
57C22×C37—81no—
58C22×C37—82no—
59C22×C37#12011yescharacteristic
60C4×C37—21no—
61C4×C37—22no—
62C4×C37—41no—
63Dic37—42no—
64Dic37—42no—
65#1657—371nomaximal, Sylow
66C2×C37—81no—
67C2×C37—161no—
68C2×C37#45311yescharacteristic
69C2×C37#45412yes—
70#563—371no—
71#496D3711yescharacteristic
72#490—372no—
73#330—372no—
74#329—371no—
75C37#165711yescharacteristic, complemented, Sylow
76C2×SD16—21no—
77C2×D8—21no—
78C4⋊Q8—741no—
79#127C2×D3711yescharacteristic
80#126—742no—
81#125—372no—
82#124C2×D3711yescharacteristic
83#123—741no—
84C22⋊Q8—742no—
85#102—742no—
86#102—742no—
87#97—372no—
88#97C2×D3711yescharacteristic
89C2×Q8—741no—
90C2×Q8C22⋊D3711yescharacteristic
91C2×D4—22no—
92C2×D4—21no—
93C2×D4C22⋊D3711yescharacteristic
94C22×C4—741no—
95SD16—42no—
96D8—42no—
97C2×C8—21no—
98C2×C8—742no—
99C4⋊C4—372no—
100C4⋊C4—372no—
101C4⋊C4—742no—
102C4⋊C4—742no—
103C4⋊C4—742no—
104C22⋊C4—22no—
105C22⋊C4—742no—
106C22⋊C4—741no—
107C42—741no—
108C42C22×D3711yescharacteristic
109C23—21no—
110C23—41no—
111Q8—41no—
112Q8—2961no—
113D4—41no—
114D4—41no—
115D4—41no—
116D4—44no—
117C2×C4—21no—
118C2×C4—2961no—
119C2×C4—742no—
120C2×C4—742no—
121C2×C4D4×D3712yes—
122C2×C4C2×C22⋊D3711yescharacteristic
123C8—22no—
124C8—1482no—
125C22—41no—
126C22—42no—
127C22—81no—
128C22—82no—
129C22#1192450411yescharacteristic
130C4—21no—
131C4—22no—
132C4—41no—
133C4—1482no—
134C4—1482no—
135C2—81no—
136C2—161no—
137C2#1455770011yescharacteristic
138C2#1455770412yes—
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
Fitting, prime radicalC37×#496C2
socleC22×C37#120
hypercenter#496D37
hypocenterC37#1657
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14558283C2semidirect
2. #14557897C2semidirect
3. #14557274C2semidirect
4. #14557273C2semidirect
75. C37#1657semidirect

Maximal subgroups

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

subgroupindex
#145582832
#145578972
#145572742
#145572732
C37×#4962
#165737