Finite Group Databasebeta

← #17993709

Subgroups — #17993709

Order 4736.

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

normal subgroups only

This group has 216 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#14558256C211yesmaximal, characteristic, complemented
2#14557880C211yesmaximal, characteristic, complemented
3#14557733C211yesmaximal, characteristic, complemented
4#14557729C211yesmaximal, characteristic
5#14557280C211yesmaximal, characteristic, complemented
6#14557262C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596941—21no—
9C2×D296—21no—
10#11924536C2211yescharacteristic
11#11924533C2211yescharacteristic
12#11924531—22no—
13#11924524—21no—
14#11924512—21no—
15C4×Dic74—21no—
16C4×D148C2211yescharacteristic
17#11924494—21no—
18C4⋊#64436C2211yescharacteristic
19#11924458—21no—
20#11924458—22no—
21#11924456—21no—
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37D411yescharacteristic
26C2×D148—21no—
27C2×D148—21no—
28C2×D148—21no—
29C2×D148D411yescharacteristic
30C2×C4×D37—21no—
31C2×Dic74—21no—
32C2×C8×C37—21no—
33C2×C8×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37D411yescharacteristic
36C42×C37—21no—
37C42×C37C2311yescharacteristic
38#10596941—42no—
39#10596938—22no—
40#10596938—22no—
41#10596938—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37D411yescharacteristic
44C4⋊Dic37D412yes—
45#10596936—22no—
46C4×Dic37—22no—
47C2×#64436—21no—
48D296—42no—
49C22×D37—21no—
50C22×D37—41no—
51Q8×C37—21no—
52Q8×C37—21no—
53C2×C4×C37—21no—
54C2×C4×C37—21no—
55C2×C4×C37C2×D411yescharacteristic
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×Dic37—21no—
59C2×Dic37—22no—
60D148—21no—
61D148—21no—
62D148—42no—
63D148—41no—
64D148—41no—
65D148—41no—
66D148—41no—
67C4×D37—41no—
68C4×D37—41no—
69Dic74—41no—
70Dic74—41no—
71C8×C37—41no—
72C8×C37—41no—
73#64436—41no—
74C22×C37#12011yescharacteristic
75C2×D37—41no—
76C2×D37—41no—
77C2×D37—41no—
78C2×D37—81no—
79C2×D37—81no—
80C2×D37—81no—
81C4×C37—21no—
82C4×C37—41no—
83C4×C37—41no—
84C4×C37#13511yescharacteristic
85C4×C37#13511yescharacteristic
86C4×C37AGL(1,ℤ/8)11yescharacteristic
87C4×C37AGL(1,ℤ/8)11yescharacteristic
88Dic37—42no—
89Dic37—41no—
90#1628—371nomaximal, Sylow
91C2×C37#44911yescharacteristic
92C2×C37#44911yescharacteristic
93C2×C37#45411yescharacteristic
94D37—81no—
95D37—161no—
96#556—371no—
97#486—371no—
98#460—371no—
99#459—371no—
100#332—371no—
101Q8⋊C8D3711yescharacteristic, complemented
102D4⋊C8—371no—
103C37#162811yescharacteristic, complemented, Sylow
104C2×SD16—741no—
105C2×D8—741no—
106C4⋊Q8—371no—
107#127—371no—
108#126—742no—
109#124—741no—
110C22⋊Q8—741no—
111C4×Q8—741no—
112C4×Q8C2×D3711yescharacteristic
113C4×D4—371no—
114#117—741no—
115C4⋊C8—371no—
116C4⋊C8C2×D3711yescharacteristic
117#102—741no—
118#102—742no—
119#102—741no—
120C4×C8C2×D3711yescharacteristic
121C2×Q8—741no—
122C2×Q8D14811yescharacteristic
123C2×D4—371no—
124C2×D4—741no—
125C2×D4—741no—
126C2×D4—741no—
127C22×C4—741no—
128SD16—1482no—
129D8—1482no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—741no—
133C4⋊C4—21no—
134C4⋊C4—371no—
135C4⋊C4—372no—
136C4⋊C4—742no—
137C4⋊C4—741no—
138C4⋊C4D14811yescharacteristic
139C22⋊C4—742no—
140C22⋊C4—742no—
141C22⋊C4—741no—
142C42—21no—
143C42—742no—
144C42C22×D3711yescharacteristic
145C23—741no—
146C23—1481no—
147Q8—21no—
148Q8—21no—
149Q8—1481no—
150Q8—1481no—
151D4—741no—
152D4—741no—
153D4—1482no—
154D4—1481no—
155D4—1481no—
156D4—1481no—
157D4—1481no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—741no—
161C2×C4—742no—
162C2×C4—1481no—
163C2×C4—1481no—
164C2×C4C2×D14811yescharacteristic
165C2×C4D4×D3711yescharacteristic
166C2×C4D4×D3711yescharacteristic
167C8—41no—
168C8—41no—
169C8—1481no—
170C22—2961no—
171C22—2961no—
172C22—2961no—
173C22—1481no—
174C22—1481no—
175C22—1481no—
176C22#1192450611yescharacteristic
177C4—21no—
178C4—41no—
179C4—41no—
180C4—1481no—
181C4—1482no—
182C4#1192455811yescharacteristic
183C4#1192455911yescharacteristic
184C4#1192456311yescharacteristic
185C4#1192456411yescharacteristic
186C2—2961no—
187C2—5921no—
188C2#1455768011yescharacteristic
189C2#1455768111yescharacteristic
190C2#1455770711yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37#120
prime radical#14557729C2
hypercenterQ8⋊C8D37
hypocenterC37#1628
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
1. #14558256C2semidirect
2. #14557880C2semidirect
3. #14557733C2semidirect
5. #14557280C2semidirect
6. #14557262C2semidirect
7. C37×Q8⋊C8C2semidirect
101. Q8⋊C8D37semidirect
103. C37#1628semidirect

Maximal subgroups

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

subgroupindex
#145582562
#145578802
#145577332
#145577292
#145572802
#145572622
C37×Q8⋊C82
#162837