Finite Group Databasebeta

← #17993003

Subgroups — #17993003

Order 4736.

212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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#14558070C211yesmaximal, characteristic
2#14557585C211yesmaximal, characteristic, complemented
3#14557584C211yesmaximal, characteristic, complemented
4Q8⋊#64436C211yesmaximal, characteristic, complemented
5#14557262C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8#11924531—21no—
9#11924527C411yescharacteristic
10#11924525C411yescharacteristic
11#11924521—21no—
12#11924512C411yescharacteristic
13#11924511C411yescharacteristic
14C4×D148—21no—
15C4×D148C2211yescharacteristic
16#11924493—21no—
17C42×D37C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924465—21no—
20#11924448—21no—
21#11924448—21no—
22C4×#64436C2211yescharacteristic
23C8×Dic37—21no—
24C4×Q8×C37C2211yescharacteristic
25C4⋊C8×C37C2211yescharacteristic
26C4×C8×C37C2211yescharacteristic
27C2×Q8×C37C2×C411yescharacteristic
28C2×D148—21no—
29C2×D148C2×C411yescharacteristic
30C2×C4×D37—21no—
31C2×C4×D37C2×C411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C8×C37—21no—
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37C2×C411yescharacteristic
38C42×C37—21no—
39C42×C37C2311yescharacteristic
40#10596938—21no—
41#10596938—21no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45C4⋊Dic37—21no—
46C4⋊Dic37C2×C411yescharacteristic
47#10596936—21no—
48#10596936—21no—
49C4×Dic37C2×C411yescharacteristic
50C4×Dic37D411yescharacteristic
51C4×Dic37D411yescharacteristic
52C2×#64436—21no—
53C2×#64436—21no—
54C22×D37—21no—
55C22×D37C22⋊C411yescharacteristic
56Q8×C37—21no—
57Q8×C37—21no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37C22×C411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37C2×D411yescharacteristic
63C2×Dic37—21no—
64C2×Dic37C22⋊C411yescharacteristic
65C2×Dic37C22⋊C411yescharacteristic
66C2×Dic37C22⋊C411yescharacteristic
67D148—21no—
68D148—21no—
69D148—42no—
70C4×D37—21no—
71C4×D37—21no—
72C4×D37—21no—
73C4×D37—21no—
74C4×D37—41no—
75C4×D37—41no—
76C4×D37—41no—
77C8×C37—41no—
78C8×C37—41no—
79#64436—41no—
80#64436—41no—
81C22×C37C2×C22⋊C411yescharacteristic
82C2×D37—21no—
83C2×D37—21no—
84C2×D37—21no—
85C2×D37—41no—
86C2×D37—41no—
87C2×D37—41no—
88C4×C37—21no—
89C4×C37—41no—
90C4×C37—41no—
91C4×C37#13111yescharacteristic
92C4×C37#13111yescharacteristic
93C4×C37#13511yescharacteristic
94C4×C37#13511yescharacteristic
95Dic37—21no—
96Dic37—21no—
97Dic37—21no—
98Dic37—41no—
99#1482—371nomaximal, Sylow
100C2×C37#40811yescharacteristic
101C2×C37#41611yescharacteristic
102C2×C37#42111yescharacteristic
103D37—41no—
104D37—81no—
105#529—371no—
106#431—371no—
107#431—371no—
108Q8⋊C8—371no—
109Q8⋊C8D3711yescharacteristic, complemented
110D4⋊C8—371no—
111D4⋊C8—371no—
112C37#148211yescharacteristic, complemented, Sylow
113#126—741no—
114#125—371no—
115#124—371no—
116#123—741no—
117C22⋊Q8—371no—
118#121—371no—
119C4×Q8C2×D3711yescharacteristic
120C4×D4—371no—
121C4×D4—741no—
122#117—741no—
123C2×C42—371no—
124C4⋊C8—371no—
125C4⋊C8—741no—
126C4⋊C8C2×D3711yescharacteristic
127C22⋊C8—741no—
128C22⋊C8—741no—
129C4×C8—371no—
130C4×C8—741no—
131C4×C8C2×D3711yescharacteristic
132C2×Q8C4×D3711yescharacteristic
133C2×D4—371no—
134C2×D4—741no—
135C22×C4—371no—
136C22×C4—371no—
137C22×C4—371no—
138C22×C4—741no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—741no—
142C2×C8—741no—
143C4⋊C4—21no—
144C4⋊C4—371no—
145C4⋊C4—741no—
146C4⋊C4—741no—
147C4⋊C4—741no—
148C4⋊C4C4×D3711yescharacteristic
149C22⋊C4—741no—
150C22⋊C4—741no—
151C22⋊C4—741no—
152C22⋊C4—741no—
153C22⋊C4—741no—
154C42—21no—
155C42—371no—
156C42—371no—
157C42—371no—
158C42C22×D3711yescharacteristic
159C23—371no—
160C23—741no—
161Q8—21no—
162Q8—21no—
163D4—741no—
164D4—741no—
165D4—1482no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—371no—
169C2×C4—371no—
170C2×C4—371no—
171C2×C4—741no—
172C2×C4—741no—
173C2×C4—741no—
174C2×C4—741no—
175C2×C4—741no—
176C2×C4—1481no—
177C2×C4—1481no—
178C2×C4—1481no—
179C2×C4C2×C4×D3711yescharacteristic
180C2×C4D4×D3711yescharacteristic
181C2×C4D4×D3711yescharacteristic
182C8—41no—
183C8—41no—
184C8—1481no—
185C8—1481no—
186C22—741no—
187C22—741no—
188C22—741no—
189C22—1481no—
190C22—1481no—
191C22—1481no—
192C22C22⋊C4×D3711yescharacteristic
193C4—21no—
194C4—41no—
195C4—41no—
196C4—741no—
197C4—741no—
198C4—741no—
199C4—1481no—
200C4#1192454211yescharacteristic
201C4#1192454411yescharacteristic
202C4#1192455711yescharacteristic
203C4#1192455911yescharacteristic
204C2—2961no—
205C2—1481no—
206C2#1455749811yescharacteristic
207C2#1455752811yescharacteristic
208C2#1455754811yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37C2×C22⋊C4
prime radical#11924511C4
cosocleC42×C37C23
hypercenterQ8⋊C8D37
hypocenterC37#1482
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #14557585C2semidirect
3. #14557584C2semidirect
4. Q8⋊#64436C2semidirect
5. #14557262C2semidirect
6. #14557260C2semidirect
7. C37×Q8⋊C8C2semidirect
109. Q8⋊C8D37semidirect
112. C37#1482semidirect

Maximal subgroups

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

subgroupindex
#145580702
#145575852
#145575842
Q8⋊#644362
#145572622
#145572602
C37×Q8⋊C82
#148237