Finite Group Databasebeta

← #17993606

Subgroups — #17993606

Order 4736.

210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 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#14557864C212yesmaximal
3#14557463C211yesmaximal, characteristic
4#14557271C212yesmaximal
5C37×#324C211yesmaximal, characteristic
6#11924535—22no—
7#11924527—22no—
8#11924515—21no—
9#11924515C2212yes—
10#11924495—21no—
11C2×C4⋊Dic37C2211yescharacteristic
12C2×#10596936—21no—
13#11924468—22no—
14#11924461—22no—
15#11924443—21no—
16#11924443C2211yescharacteristic
17C2×C4⋊C4×C37C2211yescharacteristic
18C22⋊C8×C37C2212yes—
19C22×C4×C37D411yescharacteristic
20C22×C4×C37D411yescharacteristic
21C22×C4×C37C2311yescharacteristic
22C22×Dic37—21no—
23C22×Dic37—21no—
24C2×Dic74—21no—
25C2×Dic74D412yes—
26C2×C8×C37—22no—
27C4⋊C4×C37—22no—
28C22⋊Dic37—22no—
29C4⋊Dic37—21no—
30C4⋊Dic37—21no—
31C4⋊Dic37—21no—
32C4⋊Dic37—22no—
33C4⋊Dic37D412yes—
34#10596936—22no—
35#10596936—22no—
36#10596936—42no—
37C4×Dic37—22no—
38C23×C37C2×D411yescharacteristic
39C2×C4×C37—21no—
40C2×C4×C37—21no—
41C2×C4×C37—21no—
42C2×C4×C37—41no—
43C2×C4×C37—41no—
44C2×C4×C37SD1612yes—
45C2×C4×C37C2×D412yes—
46C2×Dic37—22no—
47C2×Dic37—22no—
48C2×Dic37—22no—
49C2×Dic37—41no—
50C2×Dic37—41no—
51C2×Dic37—41no—
52C2×Dic37—41no—
53C2×Dic37—41no—
54Dic74—42no—
55Dic74—81no—
56C8×C37—42no—
57C22×C37—21no—
58C22×C37—21no—
59C22×C37#12011yescharacteristic
60C22×C37C2×SD1611yescharacteristic
61C22×C37#13711yescharacteristic
62C4×C37—22no—
63C4×C37—22no—
64C4×C37—41no—
65Dic37—42no—
66Dic37—42no—
67Dic37—42no—
68Dic37—81no—
69#1611—371nomaximal, Sylow
70C2×C37—21no—
71C2×C37—21no—
72C2×C37#44811yescharacteristic
73C2×C37#45611yescharacteristic
74C2×C37#45811yescharacteristic
75#544—371no—
76#483—372no—
77#398—371no—
78#328—372no—
79#324D3711yescharacteristic
80C37#161111yescharacteristic, complemented, Sylow
81C4⋊Q8—742no—
82#125—742no—
83C22⋊Q8—372no—
84C22⋊Q8—741no—
85#117—741no—
86C2×C4⋊C4—371no—
87C2×C4⋊C4—741no—
88C2×C4⋊C4C2×D3711yescharacteristic
89#106—742no—
90#103—742no—
91C22⋊C8C2×D3712yes—
92#95—371no—
93#95—741no—
94C2×Q8—372no—
95C2×Q8—741no—
96C22×C4—741no—
97C22×C4—741no—
98C22×C4D14811yescharacteristic
99C22×C4D14811yescharacteristic
100C22×C4C22×D3711yescharacteristic
101C2×C8—22no—
102C4⋊C4—22no—
103C4⋊C4—372no—
104C4⋊C4—742no—
105C4⋊C4—741no—
106C4⋊C4—741no—
107C4⋊C4—741no—
108C4⋊C4—742no—
109C4⋊C4—742no—
110C4⋊C4—1482no—
111C22⋊C4—742no—
112C42—742no—
113C23C2×D14811yescharacteristic
114Q8—2961no—
115Q8—1482no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—742no—
122C2×C4—742no—
123C2×C4—742no—
124C2×C4—1481no—
125C2×C4—1481no—
126C2×C4—1481no—
127C2×C4—1481no—
128C2×C4—1481no—
129C2×C4#1059693012yes—
130C2×C4D4×D3712yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22#1192450611yescharacteristic
135C22C2×#1059693011yescharacteristic
136C22#1192456911yescharacteristic
137C4—22no—
138C4—22no—
139C4—41no—
140C4—2961no—
141C4—1482no—
142C4—1482no—
143C4—1482no—
144C2—21no—
145C2—21no—
146C2#1455767411yescharacteristic
147C2#1455771811yescharacteristic
148C2#1455772411yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#324C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#324D37
hypocenterC37#1611
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
80. C37#1611semidirect

Maximal subgroups

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

subgroupindex
#145581642
#145578642
#145574632
#145572712
C37×#3242
#161137