Finite Group Databasebeta

← #17993224

Subgroups — #17993224

Order 4736.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#14558062C211yesmaximal, characteristic
2#14557588C211yesmaximal, characteristic, complemented
3#14557588C211yesmaximal, characteristic, complemented
4#14557274C211yesmaximal, characteristic, complemented
5#14557274C211yesmaximal, characteristic, complemented
6#14557273C211yesmaximal, characteristic, complemented
7C37×#329C211yesmaximal, characteristic, complemented
8#11924529—21no—
9#11924528C2211yescharacteristic
10#11924518—21no—
11#11924512C411yescharacteristic
12#11924507C411yescharacteristic
13Q8×Dic37C411yescharacteristic
14D4×Dic37C411yescharacteristic
15#11924496—21no—
16#11924492—21no—
17C42×D37C2211yescharacteristic
18#11924465—21no—
19#11924465—21no—
20#11924448—21no—
21#11924448—21no—
22#11924447C2211yescharacteristic
23#11924447C2211yescharacteristic
24#124×C37C2211yescharacteristic
25#97×C37C2211yescharacteristic
26#97×C37C2211yescharacteristic
27C2×Q8×C37C2×C411yescharacteristic
28C2×D4×C37C2×C411yescharacteristic
29C2×C22⋊D37—21no—
30C22×Dic37—21no—
31C2×C4×D37C2×C411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C8×C37—21no—
35C2×C8×C37—21no—
36C22⋊C4×C37—21no—
37C22⋊C4×C37—21no—
38C42×C37C2311yescharacteristic
39C22⋊Dic37—21no—
40C22⋊Dic37—21no—
41#10596938—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37C2×C411yescharacteristic
44C4⋊Dic37C2×C411yescharacteristic
45#10596936—21no—
46#10596936—21no—
47#10596936—21no—
48C4×Dic37—21no—
49C4×Dic37C2×C411yescharacteristic
50C4×Dic37D411yescharacteristic
51C4×Dic37D411yescharacteristic
52C2×#64436—21no—
53C2×#64436—21no—
54C23×C37—21no—
55C22×D37C22⋊C411yescharacteristic
56Q8×C37—41no—
57D4×C37—41no—
58C2×C4×C37—21no—
59C2×C4×C37C22×C411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C22⋊D37—42no—
63C2×Dic37—21no—
64C2×Dic37—21no—
65C2×Dic37—42no—
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C22⋊C411yescharacteristic
68C2×Dic37C22⋊C411yescharacteristic
69C4×D37—41no—
70C4×D37—41no—
71C4×D37—41no—
72C8×C37—41no—
73C8×C37—41no—
74#64436—41no—
75#64436—41no—
76C22×C37—41no—
77C22×C37—41no—
78C22×C37—41no—
79C22×C37C2×C22⋊C411yescharacteristic
80C2×D37—21no—
81C2×D37—21no—
82C2×D37—21no—
83C4×C37—21no—
84C4×C37—21no—
85C4×C37—21no—
86C4×C37—41no—
87Dic37—21no—
88Dic37—21no—
89Dic37—21no—
90Dic37—41no—
91Dic37—41no—
92#1535—371nomaximal, Sylow
93C2×C37—81no—
94C2×C37#41311yescharacteristic
95C2×C37#42111yescharacteristic
96C2×C37#42111yescharacteristic
97D37—41no—
98#529—371no—
99#432—371no—
100#432—371no—
101#330—371no—
102#330—371no—
103#329—371no—
104#329D3711yescharacteristic, complemented
105C37#153511yescharacteristic, complemented, Sylow
106#126—741no—
107#125—371no—
108#124C2×D3711yescharacteristic
109#123—741no—
110C22⋊Q8—371no—
111#121—371no—
112C4×Q8—371no—
113C4×D4—371no—
114C4×D4—741no—
115#117—741no—
116C2×C42—371no—
117C4⋊C8—741no—
118C4⋊C8—741no—
119C22⋊C8—741no—
120C22⋊C8—741no—
121#97—371no—
122#97—371no—
123#97C2×D3711yescharacteristic
124#97C2×D3711yescharacteristic
125C2×Q8C4×D3711yescharacteristic
126C2×D4—741no—
127C2×D4C4×D3711yescharacteristic
128C22×C4—371no—
129C22×C4—371no—
130C22×C4—371no—
131C22×C4—741no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—741no—
135C2×C8—741no—
136C4⋊C4—371no—
137C4⋊C4—371no—
138C4⋊C4—741no—
139C4⋊C4—741no—
140C4⋊C4—741no—
141C4⋊C4—741no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C22⋊C4—741no—
145C22⋊C4—741no—
146C22⋊C4—741no—
147C42—371no—
148C42—371no—
149C42—371no—
150C42—741no—
151C42C22×D3711yescharacteristic
152C23—21no—
153C23—371no—
154Q8—41no—
155D4—41no—
156D4—1482no—
157C2×C4—21no—
158C2×C4—371no—
159C2×C4—371no—
160C2×C4—371no—
161C2×C4—741no—
162C2×C4—741no—
163C2×C4—1481no—
164C2×C4—1481no—
165C2×C4—1481no—
166C2×C4—1482no—
167C2×C4C2×C4×D3711yescharacteristic
168C2×C4D4×D3711yescharacteristic
169C2×C4D4×D3711yescharacteristic
170C8—41no—
171C8—41no—
172C8—1481no—
173C8—1481no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22—741no—
178C22—741no—
179C22—741no—
180C22C22⋊C4×D3711yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—741no—
186C4—741no—
187C4—741no—
188C4—1481no—
189C4—1481no—
190C2—81no—
191C2—1481no—
192C2#1455751411yescharacteristic
193C2#1455754811yescharacteristic
194C2#1455754811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#329C2
socleC22×C37C2×C22⋊C4
prime radical#11924507C4
cosocleC42×C37C23
hypercenter#329D37
hypocenterC37#1535
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14557588C2semidirect
3. #14557588C2semidirect
4. #14557274C2semidirect
5. #14557274C2semidirect
6. #14557273C2semidirect
7. C37×#329C2semidirect
104. #329D37semidirect
105. C37#1535semidirect

Maximal subgroups

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

subgroupindex
#145580622
#145575882
#145572742
#145572732
C37×#3292
#153537