Finite Group Databasebeta

← #17993893

Subgroups — #17993893

Order 4736.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#14558287C211yesmaximal, characteristic, complemented
2#14557920C211yesmaximal, characteristic
3#14557897C211yesmaximal, characteristic, complemented
4#14557275C211yesmaximal, characteristic, complemented
5#14557274C211yesmaximal, characteristic, complemented
6#14557272C211yesmaximal, characteristic, complemented
7C37×#490C211yesmaximal, characteristic, complemented
8C2×#10596940—21no—
9C2×#10596939—21no—
10#11924535—21no—
11#11924531—21no—
12#11924531—21no—
13#11924528C2211yescharacteristic
14#11924524C2211yescharacteristic
15#11924521—21no—
16#11924516—21no—
17#11924514—21no—
18#11924457—21no—
19#11924457—21no—
20#11924447C2211yescharacteristic
21#11924447C2211yescharacteristic
22#127×C37C2211yescharacteristic
23#125×C37C2211yescharacteristic
24#102×C37—21no—
25#102×C37—21no—
26#97×C37C2211yescharacteristic
27C2×D4×C37—21no—
28C2×D4×C37—21no—
29C2×D4×C37—21no—
30C2×D148D411yescharacteristic
31C2×C4×D37—21no—
32C2×Dic74—21no—
33C2×Dic74D411yescharacteristic
34C2×C8×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37D411yescharacteristic
38C4⋊C4×C37D411yescharacteristic
39C42×C37C2311yescharacteristic
40#10596940—42no—
41#10596939—42no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45#10596938—21no—
46#10596938—21no—
47C4⋊Dic37—21no—
48C4⋊Dic37D411yescharacteristic
49C4⋊Dic37D411yescharacteristic
50#10596936—21no—
51#10596936—21no—
52#10596936—21no—
53C4×Dic37—21no—
54C2×#64436—21no—
55C2×#64436—21no—
56C23×C37—41no—
57C22×D37—21no—
58D4×C37—41no—
59D4×C37—41no—
60D4×C37—42no—
61D4×C37—42no—
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37—21no—
70D148—41no—
71C4×D37—81no—
72Dic74—41no—
73Dic74—81no—
74C8×C37—41no—
75#64436—22no—
76#64436—41no—
77C22×C37—81no—
78C22×C37—81no—
79C22×C37—81no—
80C22×C37#12011yescharacteristic
81C2×D37—41no—
82C2×D37—41no—
83C2×D37—41no—
84C4×C37—21no—
85C4×C37—21no—
86C4×C37—21no—
87C4×C37—41no—
88C4×C37—41no—
89Dic37—41no—
90Dic37—41no—
91Dic37—41no—
92#1657—371nomaximal, Sylow
93C2×C37—161no—
94C2×C37#45311yescharacteristic
95C2×C37#45411yescharacteristic
96C2×C37#45411yescharacteristic
97D37—81no—
98#563—371no—
99#496—371no—
100#490—371no—
101#490D3711yescharacteristic, complemented
102#330—371no—
103#330—371no—
104#329—371no—
105C37#165711yescharacteristic, complemented, Sylow
106C2×SD16—741no—
107C2×D8—741no—
108C4⋊Q8—741no—
109#127C2×D3711yescharacteristic
110#126—741no—
111#126—741no—
112#125—371no—
113#125C2×D3711yescharacteristic
114#124—371no—
115#123—741no—
116C22⋊Q8—741no—
117C22⋊Q8—741no—
118#102—21no—
119#102—21no—
120#102—741no—
121#102—741no—
122#97—371no—
123#97—371no—
124#97C2×D3711yescharacteristic
125C2×Q8—371no—
126C2×Q8—741no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—371no—
131C22×C4—741no—
132SD16—1482no—
133D8—1482no—
134C2×C8—21no—
135C2×C8—741no—
136C2×C8—741no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—371no—
140C4⋊C4—371no—
141C4⋊C4—741no—
142C4⋊C4—741no—
143C4⋊C4—741no—
144C4⋊C4—741no—
145C4⋊C4C22⋊D3711yescharacteristic
146C4⋊C4C22⋊D3711yescharacteristic
147C22⋊C4—741no—
148C22⋊C4—741no—
149C22⋊C4—741no—
150C22⋊C4—741no—
151C22⋊C4—741no—
152C42—741no—
153C42C22×D3711yescharacteristic
154C23—41no—
155C23—741no—
156Q8—2961no—
157Q8—1481no—
158D4—41no—
159D4—41no—
160D4—42no—
161D4—42no—
162D4—1481no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—2961no—
166C2×C4—741no—
167C2×C4—741no—
168C2×C4—741no—
169C2×C4D4×D3711yescharacteristic
170C2×C4D4×D3711yescharacteristic
171C2×C4C2×C22⋊D3711yescharacteristic
172C8—41no—
173C8—742no—
174C8—1481no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—1481no—
179C22—1481no—
180C22—1481no—
181C22#1192450411yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—1481no—
188C4—1481no—
189C4—1481no—
190C2—161no—
191C2—2961no—
192C2#1455769911yescharacteristic
193C2#1455770411yescharacteristic
194C2#1455770511yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#490C2
socleC22×C37#120
prime radical#14557920C2
hypercenter#490D37
hypocenterC37#1657
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #14558287C2semidirect
3. #14557897C2semidirect
4. #14557275C2semidirect
5. #14557274C2semidirect
6. #14557272C2semidirect
7. C37×#490C2semidirect
101. #490D37semidirect
105. C37#1657semidirect

Maximal subgroups

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

subgroupindex
#145582872
#145579202
#145578972
#145572752
#145572742
#145572722
C37×#4902
#165737