Finite Group Databasebeta

← #17993705

Subgroups — #17993705

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#14557879C211yesmaximal, characteristic, complemented
3#14557725C211yesmaximal, characteristic
4#14557278C211yesmaximal, characteristic, complemented
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#460C211yesmaximal, characteristic, complemented
8C2×#10596939—21no—
9#11924536C2211yescharacteristic
10#11924531—22no—
11#11924524—21no—
12#11924512—21no—
13C4×Dic74—21no—
14C4×D148C2211yescharacteristic
15#11924494—21no—
16C4⋊#64436C2211yescharacteristic
17#11924457—21no—
18#11924457—22no—
19C4×#64436C2211yescharacteristic
20C2×SD16×C37—21no—
21#127×C37C2211yescharacteristic
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24#102×C37—21no—
25C2×Q8×C37D411yescharacteristic
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—21no—
29C2×D148D411yescharacteristic
30C2×C4×D37—21no—
31C2×Dic74—21no—
32SD16×C37—42no—
33C2×C8×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37D411yescharacteristic
36C42×C37—21no—
37C42×C37C2311yescharacteristic
38#10596939—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—
48C2×#64436—21no—
49C23×C37—41no—
50C22×D37—21no—
51Q8×C37—21no—
52Q8×C37—21no—
53D4×C37—42no—
54D4×C37—41no—
55D4×C37—41no—
56D4×C37—41no—
57D4×C37—41no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37C2×D411yescharacteristic
63C2×Dic37—21no—
64C2×Dic37—22no—
65D148—21no—
66D148—21no—
67C4×D37—41no—
68C4×D37—41no—
69Dic74—41no—
70Dic74—41no—
71C8×C37—41no—
72#64436—41no—
73#64436—41no—
74C22×C37—81no—
75C22×C37—81no—
76C22×C37—81no—
77C22×C37#12011yescharacteristic
78C2×D37—41no—
79C2×D37—41no—
80C2×D37—41no—
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—161no—
92C2×C37#44911yescharacteristic
93C2×C37#44911yescharacteristic
94C2×C37#45411yescharacteristic
95D37—81no—
96#556—371no—
97#486—371no—
98#460D3711yescharacteristic, complemented
99#459—371no—
100#332—371no—
101Q8⋊C8—371no—
102D4⋊C8—371no—
103C37#162811yescharacteristic, complemented, Sylow
104C2×SD16—21no—
105C2×D8—741no—
106C4⋊Q8—371no—
107#127C2×D3711yescharacteristic
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—21no—
118#102—741no—
119#102—742no—
120C4×C8—371no—
121C2×Q8—741no—
122C2×Q8C22⋊D3711yescharacteristic
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—371no—
127C22×C4—741no—
128SD16—42no—
129D8—1482no—
130C2×C8—21no—
131C2×C8—741no—
132C2×C8—741no—
133C4⋊C4—21no—
134C4⋊C4—371no—
135C4⋊C4—372no—
136C4⋊C4—742no—
137C4⋊C4—741no—
138C4⋊C4C22⋊D3711yescharacteristic
139C22⋊C4—742no—
140C22⋊C4—742no—
141C22⋊C4—741no—
142C42—21no—
143C42—742no—
144C42C22×D3711yescharacteristic
145C23—41no—
146C23—741no—
147Q8—21no—
148Q8—21no—
149Q8—1481no—
150Q8—1481no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—741no—
157D4—741no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—741no—
161C2×C4—742no—
162C2×C4—1481no—
163C2×C4—1481no—
164C2×C4D4×D3711yescharacteristic
165C2×C4D4×D3711yescharacteristic
166C2×C4C2×C22⋊D3711yescharacteristic
167C8—41no—
168C8—1481no—
169C8—1481no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—1481no—
174C22—1481no—
175C22—1481no—
176C22#1192450411yescharacteristic
177C4—21no—
178C4—41no—
179C4—41no—
180C4—1481no—
181C4—1482no—
182C4#1192455611yescharacteristic
183C4#1192455711yescharacteristic
184C4#1192456211yescharacteristic
185C4#1192456311yescharacteristic
186C2—161no—
187C2—2961no—
188C2#1455767611yescharacteristic
189C2#1455767711yescharacteristic
190C2#1455770411yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#460C2
socleC22×C37#120
prime radical#14557725C2
hypercenter#460D37
hypocenterC37#1628
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #14558256C2semidirect
2. #14557879C2semidirect
4. #14557278C2semidirect
5. Q8⋊#64436C2semidirect
6. #14557260C2semidirect
7. C37×#460C2semidirect
98. #460D37semidirect
103. C37#1628semidirect

Maximal subgroups

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

subgroupindex
#145582562
#145578792
#145577252
#145572782
Q8⋊#644362
#145572602
C37×#4602
#162837