Finite Group Databasebeta

← #17993202

Subgroups — #17993202

Order 4736.

216 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 59 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#14558068C211yesmaximal, characteristic
2#14557588C211yesmaximal, characteristic, complemented
3#14557485C211yesmaximal, characteristic, complemented
4#14557275C211yesmaximal, characteristic, complemented
5#14557272C211yesmaximal, characteristic, complemented
6#14557272C211yesmaximal, characteristic, complemented
7C37×#330C211yesmaximal, characteristic, complemented
8C2×#10596929—21no—
9#11924531—21no—
10#11924524C2211yescharacteristic
11#11924521—21no—
12#11924516C411yescharacteristic
13#11924511C411yescharacteristic
14#11924501C411yescharacteristic
15#11924498—21no—
16#11924498C411yescharacteristic
17#11924494—21no—
18C42×D37C2211yescharacteristic
19#11924465—21no—
20#11924448—21no—
21#11924447C2211yescharacteristic
22#11924447C2211yescharacteristic
23C8×Dic37—21no—
24#125×C37C2211yescharacteristic
25#97×C37C2211yescharacteristic
26#97×C37C2211yescharacteristic
27C2×D148—21no—
28C2×D148C2×C411yescharacteristic
29C2×C4×D37—21no—
30C2×C4×D37C2×C411yescharacteristic
31C2×C4×D37D411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×Dic74C2×C411yescharacteristic
34C2×C8×C37—21no—
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37C2×C411yescharacteristic
39C4⋊C4×C37C2×C411yescharacteristic
40C42×C37C2311yescharacteristic
41#10596938—21no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45#10596938—21no—
46C4⋊Dic37—21no—
47#10596936—21no—
48C4×Dic37—21no—
49C4×Dic37C2×C411yescharacteristic
50C4×Dic37D411yescharacteristic
51C4×Dic37D411yescharacteristic
52C2×#64436—21no—
53C2×#64436—21no—
54#10596929—24no—
55C22×D37—21no—
56C22×D37C22⋊C411yescharacteristic
57C2×C4×C37—21no—
58C2×C4×C37—21no—
59C2×C4×C37C22×C411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×Dic37—21no—
63C2×Dic37C22⋊C411yescharacteristic
64C2×Dic37C22⋊C411yescharacteristic
65C2×Dic37C22⋊C411yescharacteristic
66D148—41no—
67D148—42no—
68C4×D37—22no—
69C4×D37—41no—
70C4×D37—41no—
71C4×D37—42no—
72Dic74—41no—
73C8×C37—22no—
74C8×C37—41no—
75#64436—22no—
76#64436—41no—
77C22×C37C2×C22⋊C411yescharacteristic
78C2×D37—21no—
79C2×D37—21no—
80C2×D37—21no—
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—21no—
90Dic37—21no—
91Dic37—41no—
92Dic37#10412yes—
93#1529—371nomaximal, Sylow
94C2×C37#41311yescharacteristic
95C2×C37C2×#10411yescharacteristic
96C2×C37#42111yescharacteristic
97D37—41no—
98D37—81no—
99#529—371no—
100#432—371no—
101C4×M16—371no—
102#330—371no—
103#330D3711yescharacteristic, complemented
104#329—371no—
105#329—371no—
106C37#152911yescharacteristic, complemented, Sylow
107C2×M16—741no—
108#126—741no—
109#125C2×D3711yescharacteristic
110#124—371no—
111#123—741no—
112C22⋊Q8—371no—
113#121—371no—
114C4×Q8—371no—
115C4×D4—371no—
116C4×D4—741no—
117#117—741no—
118C2×C42—371no—
119C4⋊C8—741no—
120C22⋊C8—741no—
121#97—371no—
122#97—371no—
123#97C2×D3711yescharacteristic
124#97C2×D3711yescharacteristic
125C4×C8—741no—
126C2×Q8—371no—
127C2×D4—371no—
128C2×D4—741no—
129C22×C4—371no—
130C22×C4—371no—
131C22×C4—371no—
132C22×C4—741no—
133M16—744no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—741no—
137C2×C8—741no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—741no—
141C4⋊C4—741no—
142C4⋊C4C4×D3711yescharacteristic
143C4⋊C4C4×D3711yescharacteristic
144C22⋊C4—741no—
145C22⋊C4—741no—
146C22⋊C4—741no—
147C22⋊C4—741no—
148C22⋊C4—741no—
149C42—371no—
150C42—371no—
151C42—371no—
152C42—741no—
153C42C22×D3711yescharacteristic
154C23—371no—
155C23—741no—
156Q8—1481no—
157D4—1481no—
158D4—1482no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—371no—
162C2×C4—371no—
163C2×C4—371no—
164C2×C4—742no—
165C2×C4—741no—
166C2×C4—1481no—
167C2×C4—1481no—
168C2×C4—1482no—
169C2×C4C2×C4×D3711yescharacteristic
170C2×C4D4×D3711yescharacteristic
171C2×C4D4×D3711yescharacteristic
172C8—22no—
173C8—41no—
174C8—742no—
175C8—1481no—
176C22—741no—
177C22—741no—
178C22—741no—
179C22—1481no—
180C22—1481no—
181C22—1481no—
182C22C22⋊C4×D3711yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—372no—
189C4—741no—
190C4—741no—
191C4—1481no—
192C2—2961no—
193C2—1481no—
194C2#1455751611yescharacteristic
195C2#104×D3711yescharacteristic
196C2#1455754811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#330C2
socleC22×C37C2×C22⋊C4
prime radical#11924511C4
cosocleC42×C37C23
hypercenter#330D37
hypocenterC37#1529
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #14557588C2semidirect
3. #14557485C2semidirect
4. #14557275C2semidirect
5. #14557272C2semidirect
6. #14557272C2semidirect
7. C37×#330C2semidirect
103. #330D37semidirect
106. C37#1529semidirect

Maximal subgroups

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

subgroupindex
#145580682
#145575882
#145574852
#145572752
#145572722
C37×#3302
#152937