Finite Group Databasebeta

← #17996710

Subgroups — #17996710

Order 4736.

160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 160 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
1C2×#11924481C211yesmaximal, characteristic, complemented
2C2×#11924475C211yesmaximal, characteristic, complemented
3#14557775C211yesmaximal, characteristic, complemented
4#14557770C211yesmaximal, characteristic
5#14557336C211yesmaximal, characteristic, complemented
6#14557333C211yesmaximal, characteristic, complemented
7C37×#366C211yesmaximal, characteristic, complemented
8C2×Dic148C2211yescharacteristic
9C2×D296C2211yescharacteristic
10C2×C8×D37C2211yescharacteristic
11#11924516—21no—
12#11924511—21no—
13#11924481—22no—
14#11924475—22no—
15C2×#10596925C2211yescharacteristic
16#11924459—21no—
17#11924456—21no—
18C2×C16×C37C2211yescharacteristic
19#107×C37C2211yescharacteristic
20#107×C37C2211yescharacteristic
21C2×D148—21no—
22C2×D148—41no—
23C2×C4×D37D411yescharacteristic
24C2×Dic74—21no—
25C2×C8×C37C2311yescharacteristic
26C4⋊C4×C37—21no—
27C4⋊C4×C37—21no—
28#10596938—41no—
29#10596938—41no—
30C4⋊Dic37—41no—
31C2×#64436D411yescharacteristic
32Dic148—21no—
33Dic148—21no—
34D296—21no—
35D296—21no—
36C8×D37—21no—
37C8×D37—21no—
38C16×C37D412yescomplemented
39#10596925—21no—
40C22×D37—41no—
41C22×D37D811yescharacteristic
42C2×C4×C37—41no—
43C2×C4×C37—41no—
44C2×C4×C37C2×D411yescharacteristic
45C2×Dic37—41no—
46C2×Dic37D811yescharacteristic
47D148—41no—
48D148—41no—
49D148—82no—
50C4×D37—21no—
51C4×D37—21no—
52Dic74—41no—
53Dic74—41no—
54C8×C37C2×D411yescharacteristic
55C8×C37#4111yescharacteristic
56#64436—21no—
57C22×C37C2×D811yescharacteristic
58C2×D37—21no—
59C2×D37—21no—
60C2×D37—21no—
61C2×D37—81no—
62C2×D37—81no—
63C2×D37—81no—
64C4×C37—81no—
65C4×C37—81no—
66C4×C37#12111yescharacteristic
67C4×C37#13511yescharacteristic
68Dic37—21no—
69Dic37—81no—
70#2220—371nomaximal, Sylow
71C2×C37#46611yescharacteristic
72C2×C37#50911yescharacteristic
73C2×C37#51011yescharacteristic
74D37—41no—
75D37—161no—
76C2×SD32—371no—
77C2×M32—371no—
78#467—371no—
79#466—371no—
80#366D3711yescharacteristic, complemented
81#358—371no—
82#357—371no—
83C37#222011yescharacteristic, complemented, Sylow
84C2×Q16—371no—
85C2×D8—371no—
86C22×C8—371no—
87C22⋊Q8—741no—
88#121—741no—
89SD32—742no—
90M32—742no—
91C2×C16—371no—
92C2×C16C2×D3711yescharacteristic
93#107C2×D3711yescharacteristic
94#107C2×D3711yescharacteristic
95#103—741no—
96#102—741no—
97C2×Q8—741no—
98C2×D4—741no—
99C2×D4—1481no—
100C22×C4—371no—
101Q16—741no—
102Q16—741no—
103D8—741no—
104D8—741no—
105C2×C8—371no—
106C2×C8—741no—
107C2×C8—741no—
108C2×C8C22×D3711yescharacteristic
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—1481no—
112C22⋊C4—1481no—
113C22⋊C4—1481no—
114C16—741no—
115C16D14812yescomplemented
116C23—371no—
117C23—1481no—
118Q8—1481no—
119Q8—1481no—
120D4—2962no—
121D4—1481no—
122D4—1481no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—371no—
126C2×C4—741no—
127C2×C4—741no—
128C2×C4—1481no—
129C2×C4D4×D3711yescharacteristic
130C8—741no—
131C8C2×D14811yescharacteristic
132C8#1059696611yescharacteristic
133C22—2961no—
134C22—2961no—
135C22—2961no—
136C22—741no—
137C22—741no—
138C22—741no—
139C22D8×D3711yescharacteristic
140C4—81no—
141C4—81no—
142C4—2961no—
143C4—741no—
144C4#1192451111yescharacteristic
145C4#1192455911yescharacteristic
146C2—5921no—
147C2—1481no—
148C2#1455777011yescharacteristic
149C2#1455796711yescharacteristic
150C2#1455797511yescharacteristic
subgroupG/H
centerC22D8×D37
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#366C2
socleC22×C37C2×D8
prime radical#14557770C2
hypercenter#366D37
hypocenterC37#2220
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
1. C2×#11924481C2semidirect
2. C2×#11924475C2semidirect
3. #14557775C2semidirect
5. #14557336C2semidirect
6. #14557333C2semidirect
7. C37×#366C2semidirect
38. C16×C37D4semidirect
80. #366D37semidirect
83. C37#2220semidirect
115. C16D148semidirect

Maximal subgroups

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

subgroupindex
C2×#119244812
C2×#119244752
#145577752
#145577702
#145573362
#145573332
C37×#3662
#222037