Finite Group Databasebeta

← #17993704

Subgroups — #17993704

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#14558253C211yesmaximal, characteristic, complemented
2#14557879C211yesmaximal, characteristic, complemented
3#14557730C211yesmaximal, characteristic, complemented
4#14557280C211yesmaximal, characteristic, complemented
5#14557263C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic, complemented
7C37×#459C211yesmaximal, characteristic
8C2×#10596940—21no—
9#11924536C2211yescharacteristic
10#11924529—22no—
11#11924523—21no—
12#11924515—21no—
13C4×Dic74C2211yescharacteristic
14#11924501—21no—
15#11924495—21no—
16C4⋊#64436C2211yescharacteristic
17#11924457—21no—
18#11924457—22no—
19C4×#64436C2211yescharacteristic
20C2×D8×C37—21no—
21#127×C37C2211yescharacteristic
22C4×D4×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24#102×C37—21no—
25C2×D4×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37D411yescharacteristic
29C22×C4×C37—21no—
30C2×Dic74—21no—
31C2×Dic74D411yescharacteristic
32D8×C37—42no—
33C2×C8×C37—21no—
34C4⋊C4×C37D411yescharacteristic
35C22⋊C4×C37—21no—
36C42×C37C2311yescharacteristic
37C22⋊Dic37—22no—
38C22⋊Dic37—22no—
39#10596940—42no—
40C4⋊Dic37—21no—
41C4⋊Dic37D411yescharacteristic
42C4⋊Dic37D412yes—
43#10596936—22no—
44#10596936—21no—
45C4×Dic37—22no—
46C4×Dic37—21no—
47C2×#64436—21no—
48C2×#64436—21no—
49C23×C37—21no—
50C23×C37—41no—
51D4×C37—21no—
52D4×C37—21no—
53D4×C37—42no—
54D4×C37—41no—
55D4×C37—41no—
56D4×C37—41no—
57D4×C37—41no—
58C2×C4×C37—21no—
59C2×C4×C37—41no—
60C2×C4×C37—41no—
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37C2×D411yescharacteristic
64C2×Dic37—21no—
65C2×Dic37—21no—
66C2×Dic37—22no—
67Dic74—21no—
68Dic74—21no—
69Dic74—41no—
70Dic74—41no—
71C8×C37—41no—
72#64436—41no—
73#64436—41no—
74C22×C37—41no—
75C22×C37—41no—
76C22×C37—41no—
77C22×C37—81no—
78C22×C37—81no—
79C22×C37—81no—
80C22×C37#12011yescharacteristic
81C4×C37—21no—
82C4×C37—41no—
83C4×C37#13511yescharacteristic
84C4×C37#13511yescharacteristic
85C4×C37AGL(1,ℤ/8)11yescharacteristic
86C4×C37AGL(1,ℤ/8)11yescharacteristic
87Dic37—41no—
88Dic37—42no—
89Dic37—41no—
90#1628—371nomaximal, Sylow
91C2×C37—81no—
92C2×C37—161no—
93C2×C37#44911yescharacteristic
94C2×C37#44911yescharacteristic
95C2×C37#45411yescharacteristic
96#556—371no—
97#486—371no—
98#460—371no—
99#459D3711yescharacteristic
100#332—371no—
101Q8⋊C8—371no—
102D4⋊C8—371no—
103C37#162811yescharacteristic, complemented, Sylow
104C2×SD16—741no—
105C2×D8—21no—
106C4⋊Q8—371no—
107#127C2×D3711yescharacteristic
108#126—742no—
109#124—741no—
110C22⋊Q8—741no—
111C4×Q8—371no—
112C4×Q8—741no—
113C4×D4C2×D3711yescharacteristic
114#117—741no—
115C4⋊C8—371no—
116C4⋊C8C2×D3711yescharacteristic
117#102—21no—
118#102—741no—
119#102—742no—
120C4×C8—371no—
121C2×Q8—371no—
122C2×Q8—741no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4C22⋊D3711yescharacteristic
127C22×C4—21no—
128SD16—1482no—
129D8—42no—
130C2×C8—21no—
131C2×C8—741no—
132C2×C8—741no—
133C4⋊C4—371no—
134C4⋊C4—372no—
135C4⋊C4—742no—
136C4⋊C4—741no—
137C4⋊C4—741no—
138C4⋊C4C22⋊D3711yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—742no—
141C22⋊C4—742no—
142C42—742no—
143C42—741no—
144C42C22×D3711yescharacteristic
145C23—21no—
146C23—41no—
147Q8—741no—
148Q8—741no—
149Q8—1481no—
150Q8—1481no—
151D4—21no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—741no—
162C2×C4—742no—
163C2×C4—741no—
164C2×C4D4×D3711yescharacteristic
165C2×C4D4×D3711yescharacteristic
166C2×C4C2×C22⋊D3711yescharacteristic
167C8—41no—
168C8—1481no—
169C8—1481no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22#1192450411yescharacteristic
177C4—21no—
178C4—41no—
179C4—1481no—
180C4—1481no—
181C4—1482no—
182C4#1192455511yescharacteristic
183C4#1192455611yescharacteristic
184C4#1192456011yescharacteristic
185C4#1192456211yescharacteristic
186C2—81no—
187C2—161no—
188C2#1455767511yescharacteristic
189C2#1455767611yescharacteristic
190C2#1455770411yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
Fitting, prime radicalC37×#459C2
socleC22×C37#120
hypercenter#459D37
hypocenterC37#1628
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14558253C2semidirect
2. #14557879C2semidirect
3. #14557730C2semidirect
4. #14557280C2semidirect
5. #14557263C2semidirect
6. D4⋊#64436C2semidirect
103. C37#1628semidirect

Maximal subgroups

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

subgroupindex
#145582532
#145578792
#145577302
#145572802
#145572632
D4⋊#644362
C37×#4592
#162837