Finite Group Databasebeta

← #17993820

Subgroups — #17993820

Order 4736.

200 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×Dic74C211yesmaximal, characteristic
2#14557884C211yesmaximal, characteristic
3#14557818C211yesmaximal, characteristic
4#14557744C211yesmaximal, characteristic
5#14557281C211yesmaximal, characteristic
6#14557265C211yesmaximal, characteristic
7C37×Q8⋊C8C211yesmaximal, characteristic
8C2×Dic148—21no—
9#11924536—21no—
10#11924536C2211yescharacteristic
11#11924536C2211yescharacteristic
12#11924535—22no—
13#11924535—21no—
14Q8×Dic37—21no—
15C4×Dic74—21no—
16C4×Dic74C2211yescharacteristic
17#11924467—21no—
18C4⋊#64436C2211yescharacteristic
19#11924461—22no—
20#11924461—21no—
21#11924460—21no—
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37D411yescharacteristic
26C2×Dic74—21no—
27C2×Dic74—22no—
28C2×Dic74D411yescharacteristic
29C2×Dic74D412yes—
30C2×C8×C37—21no—
31C2×C8×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37D411yescharacteristic
34C42×C37—21no—
35C42×C37C2311yescharacteristic
36C4⋊Dic37—22no—
37C4⋊Dic37—21no—
38C4⋊Dic37—21no—
39C4⋊Dic37—21no—
40C4⋊Dic37—21no—
41C4⋊Dic37D411yescharacteristic
42#10596936—22no—
43#10596936—21no—
44C4×Dic37—22no—
45C4×Dic37—21no—
46C2×#64436—21no—
47Dic148—42no—
48Q8×C37—21no—
49Q8×C37Q1612yescomplemented
50C2×C4×C37—21no—
51C2×C4×C37—21no—
52C2×C4×C37C2×D411yescharacteristic
53C2×C4×C37C2×D411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C2×Dic37—21no—
56C2×Dic37—22no—
57C2×Dic37—21no—
58C2×Dic37—41no—
59Dic74—21no—
60Dic74—42no—
61Dic74—41no—
62Dic74—41no—
63Dic74—82no—
64Dic74SD1612yes—
65C8×C37—41no—
66C8×C37—41no—
67#64436—41no—
68C22×C37#12011yescharacteristic
69C4×C37—22no—
70C4×C37—21no—
71C4×C37—41no—
72C4×C37C2×SD1611yescharacteristic
73C4×C37C2×Q1611yescharacteristic
74C4×C37#13711yescharacteristic
75C4×C37#13711yescharacteristic
76Dic37—22no—
77Dic37—42no—
78Dic37—41no—
79Dic37—81no—
80#1645—371nomaximal, Sylow
81C2×C37#44811yescharacteristic
82C2×C37#45111yescharacteristic
83C2×C37#45511yescharacteristic
84Q82—371no—
85#487—371no—
86#475—371no—
87#462—371no—
88#333—371no—
89Q8⋊C8—371no—
90Q8⋊C8D3711yescharacteristic
91C37#164511yescharacteristic, complemented, Sylow
92C2×Q16—741no—
93C4⋊Q8—371no—
94C4⋊Q8—371no—
95C4⋊Q8—741no—
96C4⋊Q8—742no—
97C4⋊Q8—741no—
98C4×Q8—371no—
99C4×Q8—741no—
100C4×Q8—741no—
101C4×Q8C2×D3711yescharacteristic
102#106—741no—
103C4⋊C8—371no—
104C4⋊C8C2×D3711yescharacteristic
105#103—741no—
106#103—742no—
107#103—741no—
108C4×C8C2×D3711yescharacteristic
109C2×Q8—371no—
110C2×Q8—372no—
111C2×Q8—742no—
112C2×Q8—741no—
113C2×Q8D14811yescharacteristic
114Q16—1482no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—741no—
118C4⋊C4—21no—
119C4⋊C4—371no—
120C4⋊C4—742no—
121C4⋊C4—742no—
122C4⋊C4—741no—
123C4⋊C4—741no—
124C4⋊C4—741no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4D14811yescharacteristic
128C42—21no—
129C42—742no—
130C42—741no—
131C42C22×D3711yescharacteristic
132Q8—21no—
133Q8—372no—
134Q8—2962no—
135Q8—741no—
136Q8—1482no—
137Q8—1481no—
138Q8—1481no—
139Q8Dic14812yescomplemented
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—741no—
143C2×C4—741no—
144C2×C4—742no—
145C2×C4—1481no—
146C2×C4C2×D14811yescharacteristic
147C2×C4D4×D3711yescharacteristic
148C2×C4D4×D3711yescharacteristic
149C8—41no—
150C8—41no—
151C8—1481no—
152C22#1192450611yescharacteristic
153C4—21no—
154C4—22no—
155C4—41no—
156C4—2961no—
157C4—742no—
158C4—1481no—
159C4—1482no—
160C4SD16×D3711yescharacteristic
161C4C2×Dic14811yescharacteristic
162C4#1192456811yescharacteristic
163C4#1192456911yescharacteristic
164C2#1455767311yescharacteristic
165C2#1455769111yescharacteristic
166C2#1455771211yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socle, prime radicalC22×C37#120
hypercenterQ8⋊C8D37
hypocenterC37#1645
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
49. Q8×C37Q16semidirect
91. C37#1645semidirect
139. Q8Dic148semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic742
#145578842
#145578182
#145577442
#145572812
#145572652
C37×Q8⋊C82
#164537