Finite Group Databasebeta

← #17993895

Subgroups — #17993895

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#14557923C211yesmaximal, characteristic
3#14557898C212yesmaximal, complemented
4#14557274C212yesmaximal, complemented
5C37×#329C211yesmaximal, characteristic, complemented
6C2×#10596941—21no—
7C2×#10596939—21no—
8#11924534—21no—
9#11924533C2211yescharacteristic
10#11924529—22no—
11#11924528C2212yes—
12#11924517—21no—
13#11924513—22no—
14#11924458—22no—
15#11924458—22no—
16#11924447C2211yescharacteristic
17#124×C37C2211yescharacteristic
18#97×C37C2212yes—
19C2×Q8×C37D411yescharacteristic
20C2×D4×C37D411yescharacteristic
21C22×Dic37—21no—
22C2×D148—21no—
23C2×D148—22no—
24C2×Dic74—21no—
25C2×C8×C37—22no—
26C22⋊C4×C37—22no—
27C42×C37C2311yescharacteristic
28C22⋊Dic37—22no—
29C22⋊Dic37—21no—
30#10596941—42no—
31#10596939—42no—
32C4⋊Dic37D412yes—
33C4⋊Dic37D412yes—
34#10596936—22no—
35#10596936—22no—
36#10596936—22no—
37C4×Dic37—21no—
38C2×#64436—21no—
39C23×C37—21no—
40C22×D37—41no—
41Q8×C37—41no—
42D4×C37—41no—
43C2×C4×C37—21no—
44C2×C4×C37C2×D411yescharacteristic
45C2×C4×C37C2×D412yes—
46C2×Dic37—22no—
47C2×Dic37—22no—
48C2×Dic37—81no—
49D148—41no—
50D148—41no—
51D148—44no—
52Dic74—81no—
53C8×C37—42no—
54#64436—22no—
55C22×C37—41no—
56C22×C37—42no—
57C22×C37#12011yescharacteristic
58C2×D37—81no—
59C2×D37—82no—
60C4×C37—21no—
61C4×C37—22no—
62C4×C37—41no—
63Dic37—42no—
64Dic37—42no—
65#1657—371nomaximal, Sylow
66C2×C37—81no—
67C2×C37#45311yescharacteristic
68C2×C37#45412yes—
69D37—161no—
70#563—371no—
71#496—371no—
72#490—372no—
73#330—372no—
74#329D3711yescharacteristic, complemented
75C37#165711yescharacteristic, complemented, Sylow
76C2×SD16—741no—
77C2×D8—741no—
78C4⋊Q8—741no—
79#127—371no—
80#126—742no—
81#125—372no—
82#124C2×D3711yescharacteristic
83#123—741no—
84C22⋊Q8—742no—
85#102—742no—
86#102—742no—
87#97—371no—
88#97C2×D3712yes—
89C2×Q8—741no—
90C2×Q8D14811yescharacteristic
91C2×D4—741no—
92C2×D4—742no—
93C2×D4D14811yescharacteristic
94C22×C4—741no—
95SD16—1482no—
96D8—1482no—
97C2×C8—22no—
98C2×C8—741no—
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—1481no—
111Q8—41no—
112Q8—2961no—
113D4—41no—
114D4—1481no—
115D4—1481no—
116D4—1484no—
117C2×C4—21no—
118C2×C4—2961no—
119C2×C4—742no—
120C2×C4—742no—
121C2×C4C2×D14811yescharacteristic
122C2×C4D4×D3712yes—
123C8—42no—
124C8—742no—
125C22—41no—
126C22—42no—
127C22—2961no—
128C22—2962no—
129C22#1192450611yescharacteristic
130C4—21no—
131C4—22no—
132C4—41no—
133C4—1482no—
134C4—1482no—
135C2—81no—
136C2—5921no—
137C2#1455770311yescharacteristic
138C2#1455770712yes—
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#329C2
socleC22×C37#120
prime radical#14557923C2
hypercenter#329D37
hypocenterC37#1657
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #14558283C2semidirect
3. #14557898C2semidirect
4. #14557274C2semidirect
5. C37×#329C2semidirect
74. #329D37semidirect
75. C37#1657semidirect

Maximal subgroups

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

subgroupindex
#145582832
#145579232
#145578982
#145572742
C37×#3292
#165737