Finite Group Databasebeta

← #17993665

Subgroups — #17993665

Order 4736.

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

normal subgroups only

This group has 236 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#14558244C211yesmaximal, characteristic, complemented
2#14557730C211yesmaximal, characteristic, complemented
3#14557725C211yesmaximal, characteristic
4#14557282C211yesmaximal, characteristic, complemented
5#14557265C211yesmaximal, characteristic, complemented
6#14557262C211yesmaximal, characteristic, complemented
7C37×#492C211yesmaximal, characteristic, complemented
8C2×#10596940—21no—
9C2×#10596939—21no—
10#11924527—21no—
11#11924516—21no—
12#11924512—22no—
13C4×Dic74C2211yescharacteristic
14C4×D148C2211yescharacteristic
15#11924498—21no—
16C4⋊C4×D37—21no—
17C4⋊#64436C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924457—21no—
20#11924457—21no—
21C2×SD16×C37—22no—
22C4⋊Q8×C37C2211yescharacteristic
23#127×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37D412yes—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—21no—
29C2×D148D411yescharacteristic
30C2×C4×D37—21no—
31C2×C4×D37—22no—
32C2×Dic74D411yescharacteristic
33SD16×C37—44no—
34C2×C8×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37—21no—
37C42×C37C2311yescharacteristic
38#10596940—42no—
39#10596939—42no—
40#10596938—22no—
41#10596938—21no—
42C4⋊Dic37—22no—
43C4⋊Dic37D411yescharacteristic
44C4⋊Dic37D411yescharacteristic
45#10596936—22no—
46#10596936—21no—
47C4×Dic37—21no—
48C2×#64436—21no—
49C2×#64436—21no—
50C23×C37—41no—
51C22×D37—21no—
52Q8×C37—42no—
53D4×C37—42no—
54D4×C37—41no—
55D4×C37—41no—
56D4×C37—41no—
57D4×C37—41no—
58C2×C4×C37—22no—
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×Dic37—21no—
63C2×Dic37—21no—
64C2×Dic37—21no—
65D148—21no—
66D148SD1612yescomplemented
67C4×D37—41no—
68C4×D37—41no—
69C4×D37—82no—
70Dic74—21no—
71Dic74—21no—
72C8×C37—22no—
73#64436—41no—
74#64436—41no—
75C22×C37—81no—
76C22×C37—81no—
77C22×C37—81no—
78C22×C37#12011yescharacteristic
79C2×D37—22no—
80C2×D37—41no—
81C2×D37—41no—
82C4×C37—21no—
83C4×C37—42no—
84C4×C37C2×SD1611yescharacteristic
85C4×C37#13511yescharacteristic
86C4×C37AGL(1,ℤ/8)11yescharacteristic
87C4×C37#13711yescharacteristic
88Dic37—41no—
89Dic37—41no—
90Dic37—41no—
91#1622—371nomaximal, Sylow
92C2×C37—161no—
93C2×C37#44811yescharacteristic
94C2×C37#44911yescharacteristic
95C2×C37#45311yescharacteristic
96D37—42no—
97#554—371no—
98#492D3711yescharacteristic, complemented
99#460—371no—
100#459—371no—
101#333—371no—
102Q8⋊C8—371no—
103D4⋊C8—371no—
104C37#162211yescharacteristic, complemented, Sylow
105C2×SD16—22no—
106C2×SD16—741no—
107C2×D8—741no—
108C4⋊Q8C2×D3711yescharacteristic
109#127C2×D3711yescharacteristic
110#125—741no—
111C22⋊Q8—741no—
112C22⋊Q8—742no—
113C4×Q8—371no—
114C4×D4—371no—
115C4×D4—741no—
116C2×C4⋊C4—741no—
117C4⋊C8—371no—
118C4⋊C8—371no—
119#102—741no—
120#102—741no—
121C4×C8C2×D3711yescharacteristic
122C2×Q8—371no—
123C2×Q8C22⋊D3712yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—371no—
128C22×C4—742no—
129C22×C4—741no—
130SD16—44no—
131SD16—1482no—
132D8—1482no—
133C2×C8—21no—
134C2×C8—741no—
135C2×C8—741no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—371no—
139C4⋊C4—371no—
140C4⋊C4—742no—
141C4⋊C4—742no—
142C4⋊C4—741no—
143C22⋊C4—742no—
144C22⋊C4—741no—
145C42—741no—
146C42C22×D3711yescharacteristic
147C23—41no—
148C23—741no—
149Q8—42no—
150Q8—741no—
151Q8—741no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—372no—
158D4—741no—
159C2×C4—22no—
160C2×C4—2962no—
161C2×C4—741no—
162C2×C4—741no—
163C2×C4—741no—
164C2×C4—1481no—
165C2×C4—1481no—
166C2×C4D4×D3711yescharacteristic
167C2×C4D4×D3711yescharacteristic
168C2×C4C2×C22⋊D3711yescharacteristic
169C8—22no—
170C8—1481no—
171C8—1481no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—742no—
176C22—1481no—
177C22—1481no—
178C22#1192450411yescharacteristic
179C4—21no—
180C4—42no—
181C4—1481no—
182C4—1481no—
183C4—1481no—
184C4SD16×D3711yescharacteristic
185C4#1192455711yescharacteristic
186C4#1192456311yescharacteristic
187C4#1192456511yescharacteristic
188C2—161no—
189C2—1482no—
190C2#1455767011yescharacteristic
191C2#1455767711yescharacteristic
192C2#1455770011yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#492C2
socleC22×C37#120
prime radical#14557725C2
hypercenter#492D37
hypocenterC37#1622
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #14558244C2semidirect
2. #14557730C2semidirect
4. #14557282C2semidirect
5. #14557265C2semidirect
6. #14557262C2semidirect
7. C37×#492C2semidirect
66. D148SD16semidirect
98. #492D37semidirect
104. C37#1622semidirect

Maximal subgroups

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

subgroupindex
#145582442
#145577302
#145577252
#145572822
#145572652
#145572622
C37×#4922
#162237