Finite Group Databasebeta

← #17993836

Subgroups — #17993836

Order 4736.

194 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 55 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#14558261C211yesmaximal, characteristic
2#14557936C211yesmaximal, characteristic
3#14557815C211yesmaximal, characteristic
4#14557280C211yesmaximal, characteristic
5Q8⋊#64436C211yesmaximal, characteristic
6#14557263C211yesmaximal, characteristic
7C37×#462C211yesmaximal, characteristic
8#11924536C2211yescharacteristic
9#11924534—21no—
10#11924528—21no—
11#11924526—22no—
12C4×Dic74—21no—
13C4×Dic74C2211yescharacteristic
14#11924501—21no—
15#11924469—22no—
16#11924467—21no—
17C4⋊#64436C2211yescharacteristic
18#11924459—21no—
19C4×#64436C2211yescharacteristic
20C2×Q16×C37—21no—
21C4⋊Q8×C37C2211yescharacteristic
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24#103×C37—21no—
25C2×Q8×C37—21no—
26C2×Q8×C37D411yescharacteristic
27C2×Dic74—21no—
28C2×Dic74D411yescharacteristic
29Q16×C37—42no—
30C2×C8×C37—21no—
31C4⋊C4×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37D411yescharacteristic
35C42×C37—21no—
36C42×C37C2311yescharacteristic
37C4⋊Dic37—21no—
38C4⋊Dic37D411yescharacteristic
39C4⋊Dic37D412yes—
40#10596936—22no—
41#10596936—22no—
42#10596936—22no—
43#10596936—21no—
44C4×Dic37—22no—
45C4×Dic37—21no—
46C2×#64436—21no—
47C2×#64436—21no—
48Q8×C37—21no—
49Q8×C37—21no—
50Q8×C37—41no—
51Q8×C37—41no—
52C2×C4×C37—21no—
53C2×C4×C37—21no—
54C2×C4×C37—41no—
55C2×C4×C37C2×D411yescharacteristic
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×Dic37—21no—
59C2×Dic37—21no—
60C2×Dic37—22no—
61Dic74—21no—
62Dic74—41no—
63Dic74—41no—
64Dic74Q1612yescomplemented
65C8×C37—41no—
66#64436—22no—
67#64436—41no—
68C22×C37#12011yescharacteristic
69C4×C37—21no—
70C4×C37—41no—
71C4×C37—41no—
72C4×C37—81no—
73C4×C37C2×Q1611yescharacteristic
74C4×C37#13511yescharacteristic
75C4×C37AGL(1,ℤ/8)11yescharacteristic
76C4×C37#13711yescharacteristic
77Dic37—22no—
78Dic37—42no—
79Dic37—41no—
80#1648—371nomaximal, Sylow
81C2×C37#44911yescharacteristic
82C2×C37#45111yescharacteristic
83C2×C37#45611yescharacteristic
84#557—371no—
85#500—371no—
86#475—371no—
87#462D3711yescharacteristic
88#332—371no—
89Q8⋊C8—371no—
90Q8⋊C8—371no—
91C37#164811yescharacteristic, complemented, Sylow
92C2×Q16—21no—
93C4⋊Q8—371no—
94C4⋊Q8—741no—
95C4⋊Q8C2×D3711yescharacteristic
96#125—741no—
97#125—742no—
98C4×Q8—371no—
99C4×Q8—741no—
100C4×Q8—741no—
101C4×Q8C2×D3711yescharacteristic
102#107—742no—
103#106—741no—
104C4⋊C8—371no—
105C4⋊C8C2×D3711yescharacteristic
106#103—21no—
107#103—741no—
108C4×C8—371no—
109C2×Q8—21no—
110C2×Q8—371no—
111C2×Q8—741no—
112C2×Q8C22⋊D3711yescharacteristic
113Q16—42no—
114C2×C8—21no—
115C2×C8—741no—
116C2×C8—741no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—371no—
121C4⋊C4—372no—
122C4⋊C4—742no—
123C4⋊C4—742no—
124C4⋊C4—742no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4C22⋊D3711yescharacteristic
128C42—21no—
129C42—742no—
130C42—741no—
131C42C22×D3711yescharacteristic
132Q8—21no—
133Q8—21no—
134Q8—41no—
135Q8—41no—
136Q8—372no—
137Q8—741no—
138Q8—1481no—
139Q8—1481no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—741no—
144C2×C4—741no—
145C2×C4—742no—
146C2×C4D4×D3711yescharacteristic
147C2×C4D4×D3711yescharacteristic
148C2×C4C2×C22⋊D3711yescharacteristic
149C8—41no—
150C8—742no—
151C8—1481no—
152C22#1192450411yescharacteristic
153C4—21no—
154C4—41no—
155C4—41no—
156C4—81no—
157C4—742no—
158C4—1481no—
159C4—1482no—
160C4Q16×D3711yescharacteristic
161C4#1192455611yescharacteristic
162C4#1192456211yescharacteristic
163C4#1192456811yescharacteristic
164C2#1455767611yescharacteristic
165C2#1455768711yescharacteristic
166C2#1455771411yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#462C2
socle, prime radicalC22×C37#120
hypercenter#462D37
hypocenterC37#1648
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
64. Dic74Q16semidirect
91. C37#1648semidirect

Maximal subgroups

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

subgroupindex
#145582612
#145579362
#145578152
#145572802
Q8⋊#644362
#145572632
C37×#4622
#164837