Finite Group Databasebeta

← #17993919

Subgroups — #17993919

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#14557903C211yesmaximal, characteristic, complemented
2#14557892C212yesmaximal, complemented
3#14557275C211yesmaximal, characteristic, complemented
4#14557273C212yesmaximal, complemented
5C37×#562C211yesmaximal, characteristic
6#11924536C2211yescharacteristic
7#11924460—22no—
8#11924459—22no—
9#11924457—22no—
10#11924447C2211yescharacteristic
11#11924447C2212yes—
12#125×C37C2211yescharacteristic
13#124×C37C2212yes—
14#123×C37—22no—
15C22⋊Q8×C37—22no—
16#121×C37—22no—
17C2×Q8×C37D412yes—
18C2×D4×C37—22no—
19C2×D4×C37D412yes—
20C22×C4×C37—22no—
21C2×Dic74—21no—
22C4⋊C4×C37—22no—
23C4⋊C4×C37—22no—
24C4⋊C4×C37D412yes—
25C22⋊C4×C37—22no—
26C22⋊C4×C37—22no—
27C22⋊C4×C37—22no—
28C42×C37C2311yescharacteristic
29C4⋊Dic37—22no—
30C2×#64436—22no—
31C2×#64436—21no—
32C23×C37—22no—
33Q8×C37—42no—
34D4×C37—42no—
35D4×C37—82no—
36C2×C4×C37—22no—
37C2×C4×C37—22no—
38C2×C4×C37—82no—
39C2×C4×C37C2×D412yes—
40C2×C4×C37C2×D411yescharacteristic
41C2×Dic37—41no—
42Dic74—42no—
43#64436—41no—
44#64436—42no—
45C22×C37—42no—
46C22×C37—42no—
47C22×C37—42no—
48C22×C37#12011yescharacteristic
49C4×C37—21no—
50C4×C37—22no—
51C4×C37—42no—
52C4×C37—42no—
53Dic37—81no—
54#1662—371nomaximal, Sylow
55C2×C37—82no—
56C2×C37#45411yescharacteristic
57C2×C37#45512yes—
58#562D3711yescharacteristic
59#491—371no—
60#489—372no—
61#330—371no—
62#329—372no—
63C37#166211yescharacteristic, complemented, Sylow
64C4⋊Q8—371no—
65#125C2×D3711yescharacteristic
66#124C2×D3712yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—742no—
71#103—742no—
72#102—742no—
73#97—371no—
74#97—372no—
75C2×Q8—741no—
76C2×Q8C22⋊D3712yes—
77C2×D4—22no—
78C2×D4C22⋊D3712yes—
79C22×C4—22no—
80C2×C8—742no—
81C2×C8—741no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—742no—
85C4⋊C4C22⋊D3712yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D3711yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—1482no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—1481no—
99C2×C4C2×C22⋊D3711yescharacteristic
100C2×C4C2×C22⋊D3712yes—
101C8—1481no—
102C8—1482no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#1192450511yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—2961no—
112C2—82no—
113C2#1455770611yescharacteristic
114C2#1455771112yes—
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
Fitting, prime radicalC37×#562C2
socleC22×C37#120
hypercenter#562D37
hypocenterC37#1662
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #14557903C2semidirect
2. #14557892C2semidirect
3. #14557275C2semidirect
4. #14557273C2semidirect
63. C37#1662semidirect

Maximal subgroups

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

subgroupindex
#145579032
#145578922
#145572752
#145572732
C37×#5622
#166237