Finite Group Databasebeta

← #17996712

Subgroups — #17996712

Order 4736.

160 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 47 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×#11924479C211yesmaximal, characteristic, complemented
2C2×#11924475C211yesmaximal, characteristic, complemented
3#14557771C211yesmaximal, characteristic, complemented
4#14557770C211yesmaximal, characteristic
5#14557358C211yesmaximal, characteristic, complemented
6#14557335C211yesmaximal, characteristic, complemented
7C37×#358C211yesmaximal, characteristic, complemented
8C2×D296C2211yescharacteristic
9C2×C8×D37C2211yescharacteristic
10#11924512—21no—
11#11924511—21no—
12#11924479—22no—
13#11924475—22no—
14C2×#10596925C2211yescharacteristic
15#11924470C2211yescharacteristic
16#11924460—21no—
17#11924456—21no—
18C2×Q16×C37C2211yescharacteristic
19C2×C16×C37C2211yescharacteristic
20#107×C37C2211yescharacteristic
21C2×Q8×C37—21no—
22C2×D148—21no—
23C2×D148—41no—
24C2×C4×D37D411yescharacteristic
25Q16×C37—21no—
26Q16×C37—21no—
27C2×C8×C37C2311yescharacteristic
28C4⋊C4×C37—21no—
29#10596938—41no—
30#10596938—41no—
31C4⋊Dic37—21no—
32#10596936—41no—
33C2×#64436D411yescharacteristic
34D296—21no—
35D296—21no—
36C8×D37—21no—
37C8×D37—21no—
38C16×C37—21no—
39#10596925D412yescomplemented
40C22×D37—41no—
41C22×D37D811yescharacteristic
42Q8×C37—41no—
43Q8×C37—41no—
44C2×C4×C37—41no—
45C2×C4×C37—41no—
46C2×C4×C37C2×D411yescharacteristic
47C2×Dic37—41no—
48C2×Dic37D811yescharacteristic
49D148—41no—
50D148—41no—
51D148—82no—
52C4×D37—21no—
53C4×D37—21no—
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#366—371no—
81#358D3711yescharacteristic, complemented
82#357—371no—
83C37#222011yescharacteristic, complemented, Sylow
84C2×Q16C2×D3711yescharacteristic
85C2×D8—371no—
86C22×C8—371no—
87C22⋊Q8—741no—
88#121—741no—
89SD32—742no—
90M32—742no—
91C2×C16—371no—
92C2×C16C2×D3711yescharacteristic
93#107—371no—
94#107C2×D3711yescharacteristic
95#103—741no—
96#102—741no—
97C2×Q8—21no—
98C2×D4—741no—
99C2×D4—1481no—
100C22×C4—371no—
101Q16—21no—
102Q16—21no—
103D8—741no—
104D8—741no—
105C2×C8—371no—
106C2×C8—741no—
107C2×C8—741no—
108C2×C8C22×D3711yescharacteristic
109C4⋊C4—21no—
110C4⋊C4—741no—
111C4⋊C4—1481no—
112C22⋊C4—1481no—
113C22⋊C4—1481no—
114C16—21no—
115C16—372no—
116C23—371no—
117C23—1481no—
118Q8—41no—
119Q8—41no—
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—
131C8#1059696211yescharacteristic
132C8D4×D3711yescharacteristic
133C22—2961no—
134C22—2961no—
135C22—2961no—
136C22—741no—
137C22—741no—
138C22—741no—
139C22D8×D3711yescharacteristic
140C4—81no—
141C4—81no—
142C4—2961no—
143C4—741no—
144C4#1192450911yescharacteristic
145C4#1192455711yescharacteristic
146C2—5921no—
147C2—1481no—
148C2#1455776811yescharacteristic
149C2#1455797011yescharacteristic
150C2#1455797511yescharacteristic
subgroupG/H
centerC22D8×D37
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#358C2
socleC22×C37C2×D8
prime radical#14557770C2
hypercenter#358D37
hypocenterC37#2220
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. C2×#11924479C2semidirect
2. C2×#11924475C2semidirect
3. #14557771C2semidirect
5. #14557358C2semidirect
6. #14557335C2semidirect
7. C37×#358C2semidirect
39. #10596925D4semidirect
81. #358D37semidirect
83. C37#2220semidirect

Maximal subgroups

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

subgroupindex
C2×#119244792
C2×#119244752
#145577712
#145577702
#145573582
#145573352
C37×#3582
#222037