Finite Group Databasebeta

← #17993172

Subgroups — #17993172

Order 4736.

218 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 61 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#14558069C211yesmaximal, characteristic
2#14557583C211yesmaximal, characteristic, complemented
3#14557400C211yesmaximal, characteristic, complemented
4#14557270C211yesmaximal, characteristic, complemented
5#14557268C211yesmaximal, characteristic
6#14557266C211yesmaximal, characteristic
7C37×#328C211yesmaximal, characteristic, complemented
8#11924531—21no—
9#11924527C411yescharacteristic, complemented
10#11924525C411yescharacteristic, complemented
11#11924520—21no—
12#11924510C2211yescharacteristic
13Q8×Dic37C411yescharacteristic, complemented
14#11924498C411yescharacteristic, complemented
15#11924496—21no—
16#11924494—21no—
17C2×C4×Dic37C2211yescharacteristic
18#11924465—21no—
19C22⋊#64436C2211yescharacteristic
20C8×Dic37—21no—
21#11924443—21no—
22#11924443—21no—
23#11924443C2211yescharacteristic
24C22⋊Q8×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26#95×C37C2211yescharacteristic
27C2×Q8×C37C2×C411yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37C2311yescharacteristic
30C2×C22⋊D37—21no—
31C22×Dic37—21no—
32C22×Dic37D411yescharacteristic
33C22×Dic37D411yescharacteristic
34C2×D148C2×C411yescharacteristic
35C2×C4×D37—21no—
36C2×C8×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37C2×C411yescharacteristic
39C22⋊C4×C37—21no—
40#10596938—21no—
41#10596938—21no—
42#10596938—21no—
43#10596938—21no—
44C4⋊Dic37—21no—
45C4⋊Dic37—21no—
46C4⋊Dic37C2×C411yescharacteristic
47#10596936—21no—
48C4×Dic37—21no—
49C4×Dic37C2×C411yescharacteristic
50C4×Dic37C2×C411yescharacteristic
51C4×Dic37D411yescharacteristic
52C4×Dic37D411yescharacteristic
53C2×#64436—21no—
54C23×C37C2×D411yescharacteristic
55C22×D37—21no—
56Q8×C37—41no—
57C2×C4×C37—21no—
58C2×C4×C37—21no—
59C2×C4×C37—41no—
60C2×C4×C37—41no—
61C2×C4×C37—41no—
62C2×C4×C37—41no—
63C2×C4×C37C22×C411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C22⋊D37—41no—
66C22⋊D37—41no—
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37—21no—
70C2×Dic37—41no—
71C2×Dic37—41no—
72C2×Dic37—41no—
73C2×Dic37—41no—
74C2×Dic37C22⋊C411yescharacteristic
75C2×Dic37C22⋊C411yescharacteristic
76C2×Dic37C22⋊C411yescharacteristic
77C2×Dic37C22⋊C411yescharacteristic
78D148—41no—
79C4×D37—42no—
80C8×C37—41no—
81#64436—41no—
82C22×C37—21no—
83C22×C37—21no—
84C22×C37C2×C22⋊C411yescharacteristic
85C22×C37#13511yescharacteristic
86C22×C37#13511yescharacteristic
87C2×D37—41no—
88C2×D37—41no—
89C2×D37—41no—
90C4×C37—21no—
91C4×C37—21no—
92C4×C37—41no—
93C4×C37—41no—
94C4×C37—81no—
95Dic37—21no—
96Dic37—21no—
97Dic37—21no—
98Dic37—21no—
99Dic37—41no—
100Dic37—81no—
101#1521—371nomaximal, Sylow
102C2×C37—21no—
103C2×C37—21no—
104C2×C37#41011yescharacteristic
105C2×C37#41611yescharacteristic
106C2×C37#42111yescharacteristic
107D37—81no—
108#529—371no—
109#431—371no—
110#383—371no—
111#328—371no—
112#328D3711yescharacteristic, complemented
113#327—371no—
114#327—371no—
115C37#152111yescharacteristic, complemented, Sylow
116#126—741no—
117#125—371no—
118#124—371no—
119#123—741no—
120C22⋊Q8C2×D3711yescharacteristic
121#121—371no—
122C4×Q8—371no—
123C4×D4—371no—
124C4×D4—741no—
125#117—741no—
126C2×C42—371no—
127C4⋊C8—741no—
128C22⋊C8—371no—
129C22⋊C8C2×D3711yescharacteristic
130C4×C8—741no—
131#95—371no—
132#95—741no—
133#95—741no—
134#95C2×D3711yescharacteristic
135C2×Q8C4×D3711yescharacteristic
136C2×D4—371no—
137C2×D4—741no—
138C22×C4—21no—
139C22×C4—371no—
140C22×C4—371no—
141C22×C4—741no—
142C22×C4—741no—
143C22×C4C22×D3711yescharacteristic
144C2×C8—21no—
145C2×C8—741no—
146C4⋊C4—21no—
147C4⋊C4—371no—
148C4⋊C4—741no—
149C4⋊C4—741no—
150C4⋊C4—741no—
151C4⋊C4C4×D3711yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—741no—
154C22⋊C4—741no—
155C22⋊C4—741no—
156C22⋊C4—741no—
157C42—371no—
158C42—371no—
159C42—371no—
160C42—371no—
161C42—741no—
162C23—741no—
163C23D4×D3711yescharacteristic
164Q8—41no—
165D4—1481no—
166D4—1481no—
167D4—1481no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—371no—
175C2×C4—371no—
176C2×C4—371no—
177C2×C4—371no—
178C2×C4—741no—
179C2×C4—741no—
180C2×C4—741no—
181C2×C4—1482no—
182C2×C4—1481no—
183C2×C4—1481no—
184C2×C4—1481no—
185C2×C4—1481no—
186C2×C4C2×C4×D3711yescharacteristic
187C2×C4D4×D3711yescharacteristic
188C8—41no—
189C8—1481no—
190C22—21no—
191C22—21no—
192C22—1481no—
193C22—1481no—
194C22—1481no—
195C22C22⋊C4×D3711yescharacteristic
196C22#1192455711yescharacteristic
197C22#1192455911yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—2961no—
204C4—741no—
205C4—741no—
206C4—741no—
207C4—741no—
208C4—1481no—
209C2—21no—
210C2—21no—
211C2—2961no—
212C2#1455750511yescharacteristic
213C2#1455752811yescharacteristic
214C2#1455754811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#328C2
socleC22×C37C2×C22⋊C4
prime radical#11924510C22
cosocleC22×C4×C37C23
hypercenter#328D37
hypocenterC37#1521
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #14557583C2semidirect
3. #14557400C2semidirect
4. #14557270C2semidirect
7. C37×#328C2semidirect
9. #11924527C4semidirect
10. #11924525C4semidirect
13. Q8×Dic37C4semidirect
14. #11924498C4semidirect
112. #328D37semidirect
115. C37#1521semidirect

Maximal subgroups

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

subgroupindex
#145580692
#145575832
#145574002
#145572702
#145572682
#145572662
C37×#3282
#152137