Finite Group Databasebeta

← #17995758

Subgroups — #17995758

Order 4736.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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#14558164C211yesmaximal, characteristic
2#14557543C212yesmaximal
3#14557438C211yesmaximal, characteristic
4#14557294C212yesmaximal
5C37×#343C211yesmaximal, characteristic
6C22×Dic74C2211yescharacteristic
7#11924535—22no—
8#11924527—22no—
9#11924515—22no—
10#11924495C2212yes—
11C2×C4×Dic37C2211yescharacteristic
12#11924461—22no—
13#11924461—22no—
14#11924443—22no—
15C2×M16×C37C2212yes—
16C2×C4⋊C4×C37C2211yescharacteristic
17C22×C4×C37D412yes—
18C22×C4×C37C2311yescharacteristic
19C22×Dic37—21no—
20C22×Dic37—21no—
21C2×Dic74—22no—
22C2×Dic74—22no—
23C2×Dic74—21no—
24C2×Dic74—22no—
25C2×Dic74Q812yescomplemented
26M16×C37—22no—
27M16×C37—22no—
28C2×C8×C37—22no—
29C4⋊C4×C37—22no—
30C22⋊Dic37—22no—
31C4⋊Dic37—22no—
32C4⋊Dic37D412yes—
33C4⋊Dic37D412yes—
34#10596936—24no—
35C4×Dic37—22no—
36C4×Dic37—22no—
37C23×C37C2×D411yescharacteristic
38C2×C4×C37—22no—
39C2×C4×C37—42no—
40C2×C4×C37C2×D412yes—
41C2×C4×C37C2×Q811yescharacteristic
42C2×C4×C37#4112yes—
43C2×C4×C37#4111yescharacteristic
44C2×Dic37—22no—
45C2×Dic37—22no—
46C2×Dic37—22no—
47C2×Dic37—22no—
48C2×Dic37—41no—
49C2×Dic37—41no—
50C2×Dic37—41no—
51C2×Dic37—41no—
52Dic74—24no—
53Dic74—42no—
54Dic74—82no—
55C8×C37—42no—
56C22×C37—21no—
57C22×C37—21no—
58C22×C37#12011yescharacteristic
59C22×C37C22⋊Q811yescharacteristic
60C22×C37#12411yescharacteristic
61C4×C37—42no—
62C4×C37C22⋊Q812yes—
63C4×C37#12412yes—
64Dic37—42no—
65Dic37—42no—
66Dic37—42no—
67Dic37—42no—
68#2028—371nomaximal, Sylow
69C2×C37—21no—
70C2×C37—21no—
71C2×C37#39311yescharacteristic
72C2×C37#45511yescharacteristic
73C2×C37#45611yescharacteristic
74#544—371no—
75#419—372no—
76#391—371no—
77#343D3711yescharacteristic
78#339—372no—
79C37#202811yescharacteristic, complemented, Sylow
80C22×Q8—371no—
81C2×M16C2×D3712yes—
82C4⋊Q8—742no—
83#125—742no—
84C22⋊Q8—742no—
85#117—372no—
86C2×C4⋊C4C2×D3711yescharacteristic
87C2×C42—371no—
88#103—742no—
89#103—742no—
90#95—742no—
91C2×Q8—372no—
92C2×Q8—742no—
93C2×Q8—741no—
94C2×Q8—742no—
95C2×Q8—742no—
96C22×C4—741no—
97C22×C4—741no—
98C22×C4D14812yes—
99C22×C4C22×D3711yescharacteristic
100M16—22no—
101M16—22no—
102C2×C8—22no—
103C4⋊C4—22no—
104C4⋊C4—372no—
105C4⋊C4—372no—
106C4⋊C4—744no—
107C4⋊C4—742no—
108C22⋊C4—742no—
109C42—742no—
110C42—742no—
111C23C2×D14811yescharacteristic
112Q8—2962no—
113Q8—744no—
114Q8—1482no—
115C2×C4—22no—
116C2×C4—42no—
117C2×C4—742no—
118C2×C4—742no—
119C2×C4—742no—
120C2×C4—742no—
121C2×C4—1481no—
122C2×C4—1481no—
123C2×C4—1481no—
124C2×C4—1481no—
125C2×C4#1059696212yes—
126C2×C4D4×D3712yes—
127C2×C4#1059696411yescharacteristic
128C2×C4Q8×D3711yescharacteristic
129C8—42no—
130C22—21no—
131C22—21no—
132C22#1192450611yescharacteristic
133C22#1192451611yescharacteristic
134C22#1192452411yescharacteristic
135C4—42no—
136C4—1482no—
137C4—1482no—
138C4—1482no—
139C4—1482no—
140C4#1192451412yes—
141C4#1192452212yes—
142C2—21no—
143C2—21no—
144C2#1455744611yescharacteristic
145C2#1455771311yescharacteristic
146C2#1455771811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#343C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#343D37
hypocenterC37#2028
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
25. C2×Dic74Q8semidirect
79. C37#2028semidirect

Maximal subgroups

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

subgroupindex
#145581642
#145575432
#145574382
#145572942
C37×#3432
#202837