Finite Group Databasebeta

← #17992964

Subgroups — #17992964

Order 4736.

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

normal subgroups only

This group has 214 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
1C2×#11924531C211yesmaximal, characteristic
2#14557587C211yesmaximal, characteristic, complemented
3#14557583C211yesmaximal, characteristic, complemented
4#14557259C211yesmaximal, characteristic, complemented
5#14557256C211yesmaximal, characteristic
6#14557256C211yesmaximal, characteristic
7C37×#324C211yesmaximal, characteristic, complemented
8#11924531—21no—
9#11924531—21no—
10#11924531—21no—
11#11924531—21no—
12C2×C4⋊Dic37C411yescharacteristic
13C2×#10596936C411yescharacteristic
14C2×#10596938C411yescharacteristic
15C2×#10596938C411yescharacteristic
16C2×#10596938C2211yescharacteristic
17C2×C4×Dic37C2211yescharacteristic
18#11924465—21no—
19#11924465—21no—
20C22⋊#64436C2211yescharacteristic
21C22⋊#64436C2211yescharacteristic
22#11924446—21no—
23C8×Dic37—21no—
24C2×C4⋊C4×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26C22⋊C8×C37C2211yescharacteristic
27C23×D37C2×C411yescharacteristic
28C22×C4×C37C2×C411yescharacteristic
29C22×C4×C37C2×C411yescharacteristic
30C22×C4×C37C2311yescharacteristic
31C22×Dic37C2×C411yescharacteristic
32C22×Dic37C2×C411yescharacteristic
33C22×Dic37C2×C411yescharacteristic
34C2×C8×C37—21no—
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37—21no—
38#10596938—21no—
39#10596938—21no—
40#10596938—21no—
41#10596938—21no—
42#10596938—21no—
43#10596938—21no—
44C4⋊Dic37—21no—
45C4⋊Dic37—21no—
46#10596936—21no—
47#10596936—21no—
48C4×Dic37D411yescharacteristic
49C4×Dic37D411yescharacteristic
50C4×Dic37D411yescharacteristic
51C4×Dic37D411yescharacteristic
52C2×#64436—21no—
53C2×#64436—21no—
54C23×C37C22×C411yescharacteristic
55C22×D37—21no—
56C22×D37—21no—
57C22×D37—21no—
58C22×D37—41no—
59C22×D37—41no—
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37C2×D411yescharacteristic
68C2×Dic37—21no—
69C2×Dic37—21no—
70C2×Dic37—21no—
71C2×Dic37—41no—
72C2×Dic37—41no—
73C2×Dic37C22⋊C411yescharacteristic
74C2×Dic37C22⋊C411yescharacteristic
75C2×Dic37C22⋊C411yescharacteristic
76C2×Dic37C22⋊C411yescharacteristic
77C8×C37—41no—
78C8×C37—41no—
79#64436—41no—
80#64436—41no—
81C22×C37—21no—
82C22×C37—21no—
83C22×C37C2×C22⋊C411yescharacteristic
84C22×C37#13111yescharacteristic
85C22×C37#13111yescharacteristic
86C2×D37—41no—
87C2×D37—41no—
88C2×D37—41no—
89C2×D37—81no—
90C2×D37—81no—
91C4×C37—21no—
92C4×C37—21no—
93C4×C37—41no—
94C4×C37—41no—
95Dic37—21no—
96Dic37—21no—
97Dic37—21no—
98Dic37—21no—
99Dic37—41no—
100#1473—371nomaximal, Sylow
101C2×C37—21no—
102C2×C37—21no—
103C2×C37#40811yescharacteristic
104C2×C37#41011yescharacteristic
105C2×C37#41311yescharacteristic
106D37—81no—
107C2×#126—371no—
108#432—371no—
109#431—371no—
110#324—371no—
111#324D3711yescharacteristic, complemented
112#323—371no—
113#323—371no—
114C37#147311yescharacteristic, complemented, Sylow
115#126—741no—
116#126—741no—
117#126—741no—
118#126—741no—
119C2×C4⋊C4—371no—
120C2×C4⋊C4—371no—
121C2×C4⋊C4C2×D3711yescharacteristic
122C2×C22⋊C4—371no—
123C2×C22⋊C4—371no—
124C2×C22⋊C4—371no—
125C2×C42—371no—
126C4⋊C8—741no—
127C4⋊C8—741no—
128C22⋊C8—371no—
129C22⋊C8—371no—
130C22⋊C8C2×D3711yescharacteristic
131C22⋊C8C2×D3711yescharacteristic
132#97—741no—
133C4×C8—741no—
134C24—371no—
135C22×C4—371no—
136C22×C4—371no—
137C22×C4—371no—
138C22×C4C4×D3711yescharacteristic
139C22×C4C4×D3711yescharacteristic
140C22×C4C22×D3711yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—741no—
144C2×C8—741no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—741no—
148C4⋊C4—741no—
149C4⋊C4—741no—
150C4⋊C4—741no—
151C22⋊C4—741no—
152C22⋊C4—741no—
153C22⋊C4—741no—
154C22⋊C4—741no—
155C22⋊C4—741no—
156C22⋊C4—741no—
157C42—371no—
158C42—371no—
159C42—371no—
160C42—371no—
161C23—741no—
162C23—741no—
163C23—741no—
164C23—1481no—
165C23—1481no—
166C23C2×C4×D3711yescharacteristic
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—371no—
174C2×C4—371no—
175C2×C4—371no—
176C2×C4—371no—
177C2×C4—741no—
178C2×C4—741no—
179C2×C4—741no—
180C2×C4—1481no—
181C2×C4—1481no—
182C2×C4D4×D3711yescharacteristic
183C2×C4D4×D3711yescharacteristic
184C8—41no—
185C8—41no—
186C8—1481no—
187C8—1481no—
188C22—21no—
189C22—21no—
190C22—2961no—
191C22—2961no—
192C22—1481no—
193C22—1481no—
194C22—1481no—
195C22C22⋊C4×D3711yescharacteristic
196C22#1192454211yescharacteristic
197C22#1192454411yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—741no—
203C4—741no—
204C4—741no—
205C4—741no—
206C4—1481no—
207C2—21no—
208C2—21no—
209C2—2961no—
210C2#1455749811yescharacteristic
211C2#1455750511yescharacteristic
212C2#1455751611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#324C2
socleC22×C37C2×C22⋊C4
prime radicalC23×D37C2×C4
cosocleC22×C4×C37C23
hypercenter#324D37
hypocenterC37#1473
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #14557587C2semidirect
3. #14557583C2semidirect
4. #14557259C2semidirect
7. C37×#324C2semidirect
111. #324D37semidirect
114. C37#1473semidirect

Maximal subgroups

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

subgroupindex
C2×#119245312
#145575872
#145575832
#145572592
#145572562
C37×#3242
#147337