Finite Group Databasebeta

← #17993158

Subgroups — #17993158

Order 4736.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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#14558085C211yesmaximal, characteristic
2#14557583C211yesmaximal, characteristic
3#14557397C211yesmaximal, characteristic
4#14557271C211yesmaximal, characteristic
5#14557270C211yesmaximal, characteristic
6#14557269C211yesmaximal, characteristic
7C37×#328C211yesmaximal, characteristic
8#11924535C411yescharacteristic, complemented
9#11924534C411yescharacteristic, complemented
10#11924526—21no—
11#11924515C2211yescharacteristic
12#11924513—21no—
13Q8×Dic37C411yescharacteristic, complemented
14#11924501—21no—
15#11924501C411yescharacteristic, complemented
16#11924492—21no—
17C2×#10596936—21no—
18C2×C4×Dic37C2211yescharacteristic
19#11924465—21no—
20C22⋊#64436C2211yescharacteristic
21C8×Dic37—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
30C22×Dic37—21no—
31C22×Dic37D411yescharacteristic
32C22×Dic37D411yescharacteristic
33C2×Dic74—21no—
34C2×Dic74C2×C411yescharacteristic
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37C2×C411yescharacteristic
38C22⋊C4×C37—21no—
39C22⋊Dic37—21no—
40C4⋊Dic37—21no—
41C4⋊Dic37C2×C411yescharacteristic
42#10596936—21no—
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46#10596936—21no—
47#10596936—42no—
48C4×Dic37—21no—
49C4×Dic37—21no—
50C4×Dic37C2×C411yescharacteristic
51C4×Dic37C2×C411yescharacteristic
52C4×Dic37D411yescharacteristic
53C4×Dic37D411yescharacteristic
54C2×#64436—21no—
55C23×C37C2×D411yescharacteristic
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
65C2×Dic37—21no—
66C2×Dic37—21no—
67C2×Dic37—41no—
68C2×Dic37—41no—
69C2×Dic37—41no—
70C2×Dic37—41no—
71C2×Dic37C22⋊C411yescharacteristic
72C2×Dic37C22⋊C411yescharacteristic
73C2×Dic37C22⋊C411yescharacteristic
74C2×Dic37C22⋊C411yescharacteristic
75C2×Dic37SD1612yes—
76C2×Dic37Q1612yes—
77Dic74—42no—
78Dic74—41no—
79C8×C37—41no—
80#64436—41no—
81C22×C37—21no—
82C22×C37—21no—
83C22×C37C2×C22⋊C411yescharacteristic
84C22×C37C2×SD1611yescharacteristic
85C22×C37C2×Q1611yescharacteristic
86C4×C37—21no—
87C4×C37—21no—
88C4×C37—41no—
89C4×C37—41no—
90C4×C37—81no—
91Dic37—21no—
92Dic37—21no—
93Dic37—41no—
94Dic37—41no—
95Dic37—81no—
96Dic37#10312yes—
97Dic37#10312yes—
98#1518—371nomaximal, Sylow
99C2×C37—21no—
100C2×C37—21no—
101C2×C37#41011yescharacteristic
102C2×C37C2×#10311yescharacteristic
103C2×C37#42111yescharacteristic
104#533—371no—
105#431—371no—
106#382—371no—
107#328—371no—
108#328—371no—
109#328—371no—
110#328D3711yescharacteristic
111C37#151811yescharacteristic, complemented, Sylow
112C4⋊Q8—371no—
113C4⋊Q8—371no—
114#125—741no—
115C22⋊Q8—371no—
116C22⋊Q8—741no—
117C22⋊Q8C2×D3711yescharacteristic
118C4×Q8—371no—
119C4×Q8—371no—
120C4×Q8—741no—
121#117—741no—
122C2×C4⋊C4—741no—
123C2×C42—371no—
124C4⋊C8—741no—
125C22⋊C8—371no—
126C22⋊C8C2×D3711yescharacteristic
127C4×C8—741no—
128#95—371no—
129#95—741no—
130#95C2×D3711yescharacteristic
131C2×Q8—371no—
132C2×Q8—741no—
133C2×Q8C4×D3711yescharacteristic
134C22×C4—21no—
135C22×C4—371no—
136C22×C4—371no—
137C22×C4—741no—
138C22×C4C22×D3711yescharacteristic
139C2×C8—21no—
140C2×C8—741no—
141C4⋊C4—21no—
142C4⋊C4—371no—
143C4⋊C4—741no—
144C4⋊C4—741no—
145C4⋊C4—741no—
146C4⋊C4—741no—
147C4⋊C4—741no—
148C4⋊C4—741no—
149C4⋊C4—1482no—
150C4⋊C4C4×D3711yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—741no—
153C42—371no—
154C42—371no—
155C42—371no—
156C42—371no—
157C42—741no—
158C42—741no—
159C23D4×D3711yescharacteristic
160Q8—41no—
161Q8—1481no—
162Q8—1482no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—371no—
170C2×C4—371no—
171C2×C4—372no—
172C2×C4—372no—
173C2×C4—371no—
174C2×C4—371no—
175C2×C4—741no—
176C2×C4—741no—
177C2×C4—1481no—
178C2×C4—1481no—
179C2×C4—1481no—
180C2×C4—1481no—
181C2×C4C2×C4×D3711yescharacteristic
182C2×C4D4×D3711yescharacteristic
183C8—41no—
184C8—1481no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D3711yescharacteristic
188C22SD16×D3711yescharacteristic
189C22Q16×D3711yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—372no—
196C4—372no—
197C4—2961no—
198C4—741no—
199C4—741no—
200C4—1481no—
201C4—1481no—
202C2—21no—
203C2—21no—
204C2#1455750511yescharacteristic
205C2#103×D3711yescharacteristic
206C2#1455754811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#328C2
socleC22×C37C2×C22⋊C4
prime radicalC23×C37C2×D4
cosocleC22×C4×C37C23
hypercenter#328D37
hypocenterC37#1518
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
8. #11924535C4semidirect
9. #11924534C4semidirect
13. Q8×Dic37C4semidirect
15. #11924501C4semidirect
111. C37#1518semidirect

Maximal subgroups

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

subgroupindex
#145580852
#145575832
#145573972
#145572712
#145572702
#145572692
C37×#3282
#151837