Finite Group Databasebeta

← #17994983

Subgroups — #17994983

Order 4736.

360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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×#11924524C211yesmaximal, characteristic
2#14558007C211yesmaximal, characteristic
3#14557543C211yesmaximal, characteristic, complemented
4#14557541C211yesmaximal, characteristic, complemented
5C2×#11924452C211yesmaximal, characteristic
6#14557293C211yesmaximal, characteristic, complemented
7C37×#339C211yesmaximal, characteristic, complemented
8C22×Dic74C2211yescharacteristic
9C22×D148C2211yescharacteristic
10C2×#10596934C2211yescharacteristic
11#11924524—22no—
12#11924524C414yescomplemented
13C4×D148—22no—
14#11924498—22no—
15#11924495C2211yescharacteristic
16C2×#10596938—22no—
17C22⋊C4×D37—22no—
18#11924461—22no—
19#11924459—22no—
20#11924452—22no—
21C2×M16×C37C2211yescharacteristic
22#117×C37C2211yescharacteristic
23C2×C42×C37C2211yescharacteristic
24C23×D37D412yes—
25C22×C4×C37—21no—
26C22×C4×C37C2311yescharacteristic
27C22×Dic37—21no—
28C2×D148—21no—
29C2×D148—21no—
30C2×D148—21no—
31C2×D148—21no—
32C2×D148C2×C412yes—
33C2×D148D412yes—
34C2×C4×D37—24no—
35C2×Dic74—21no—
36C2×Dic74—21no—
37C2×Dic74—21no—
38C2×Dic74—21no—
39C2×Dic74—21no—
40C2×Dic74C2×C412yescomplemented
41M16×C37—21no—
42M16×C37—21no—
43C2×C8×C37—21no—
44C4⋊C4×C37D412yes—
45C22⋊C4×C37—21no—
46C42×C37—21no—
47C42×C37—21no—
48C42×C37C2×C412yescomplemented
49C22⋊Dic37—21no—
50#10596938—24no—
51#10596938—28no—
52C4⋊Dic37D412yes—
53C4×Dic37—21no—
54#10596934—21no—
55#10596934—21no—
56C2×#64436—21no—
57C23×C37C2×D411yescharacteristic
58C22×D37—22no—
59C22×D37—22no—
60C22×D37—44no—
61C22×D37C22⋊C414yes—
62C2×C4×C37—22no—
63C2×C4×C37—22no—
64C2×C4×C37—42no—
65C2×C4×C37C22×C411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37C2×D411yescharacteristic
68C2×C4×C37C2×D411yescharacteristic
69C2×C4×C37#4111yescharacteristic
70C2×C4×C37#4111yescharacteristic
71C2×Dic37—22no—
72C2×Dic37—22no—
73C2×Dic37—41no—
74C2×Dic37—41no—
75D148—22no—
76D148—22no—
77D148—22no—
78D148—22no—
79C4×D37—84no—
80Dic74—22no—
81Dic74—22no—
82Dic74—41no—
83Dic74—41no—
84C8×C37—41no—
85#64436—41no—
86C22×C37—22no—
87C22×C37C2×C22⋊C411yescharacteristic
88C22×C37#12011yescharacteristic
89C22×C37#12311yescharacteristic
90C2×D37—24no—
91C2×D37—44no—
92C2×D37—44no—
93C2×D37—82no—
94C4×C37—42no—
95C4×C37—42no—
96C4×C37C4×D411yescharacteristic
97C4×C37C4×D411yescharacteristic
98C4×C37#12111yescharacteristic
99C4×C37#12111yescharacteristic
100Dic37—42no—
101Dic37—42no—
102#1885—371nomaximal, Sylow
103C2×C37—21no—
104C2×C37—21no—
105C2×C37#38611yescharacteristic
106C2×C37#45512yes—
107D37—44no—
108C2×#124—371no—
109#518—371no—
110#419—371no—
111#419—371no—
112C2×#100—371no—
113#339—371no—
114#339D3711yescharacteristic, complemented
115C37#188511yescharacteristic, complemented, Sylow
116C22×Q8—371no—
117C22×D4—371no—
118C2×M16—371no—
119C2×M16C2×D3711yescharacteristic
120#124—374no—
121#124—742no—
122C4×D4—742no—
123C4×D4—742no—
124#117—371no—
125#117C2×D3711yescharacteristic
126C2×C22⋊C4—742no—
127C2×C22⋊C4—742no—
128C2×C42C2×D3711yescharacteristic
129#103—742no—
130#103—742no—
131#100—742no—
132C24—372no—
133C2×Q8—372no—
134C2×Q8—741no—
135C2×Q8—741no—
136C2×Q8—741no—
137C2×Q8—741no—
138C2×Q8—741no—
139C2×D4—372no—
140C2×D4—372no—
141C2×D4—741no—
142C2×D4—741no—
143C2×D4—741no—
144C2×D4—741no—
145C22×C4—21no—
146C22×C4—744no—
147C22×C4—741no—
148C22×C4C22×D3711yescharacteristic
149M16—21no—
150M16—21no—
151M16—741no—
152M16—741no—
153C2×C8—21no—
154C2×C8—741no—
155C4⋊C4—372no—
156C4⋊C4D14812yes—
157C22⋊C4—21no—
158C22⋊C4—748no—
159C22⋊C4—744no—
160C22⋊C4—741no—
161C42—21no—
162C42—21no—
163C42—741no—
164C42C4×D3712yescomplemented
165C23—374no—
166C23—742no—
167C23—742no—
168C23—1484no—
169C23D4×D3711yescharacteristic
170Q8—742no—
171Q8—742no—
172Q8—1481no—
173Q8—1481no—
174D4—742no—
175D4—742no—
176D4—742no—
177D4—742no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—2964no—
182C2×C4—742no—
183C2×C4—742no—
184C2×C4—1481no—
185C2×C4—1481no—
186C2×C4C2×C4×D3711yescharacteristic
187C2×C4C2×D14811yescharacteristic
188C2×C4#1059696211yescharacteristic
189C2×C4D4×D3711yescharacteristic
190C2×C4D4×D3711yescharacteristic
191C2×C4#1059696611yescharacteristic
192C8—41no—
193C8—1481no—
194C22—22no—
195C22—2962no—
196C22—744no—
197C22—1484no—
198C22—1484no—
199C22C22⋊C4×D3711yescharacteristic
200C22#1192450611yescharacteristic
201C22#1192452111yescharacteristic
202C4—42no—
203C4—42no—
204C4—1482no—
205C4—1482no—
206C4#1192449811yescharacteristic
207C4C4×D14811yescharacteristic
208C4#1192450911yescharacteristic
209C4#1192451111yescharacteristic
210C2—21no—
211C2—21no—
212C2—1484no—
213C2#1455741111yescharacteristic
214C2#1455771212yes—
subgroupG/H
centerC22#11924506
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37#120
prime radicalC22×D148C22
cosocleC22×C4×C37C23
hypercenter#339D37
hypocenterC37#1885
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
3. #14557543C2semidirect
4. #14557541C2semidirect
6. #14557293C2semidirect
7. C37×#339C2semidirect
12. #11924524C4semidirect
40. C2×Dic74C2×C4semidirect
48. C42×C37C2×C4semidirect
114. #339D37semidirect
115. C37#1885semidirect
164. C42C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245242
#145580072
#145575432
#145575412
C2×#119244522
#145572932
C37×#3392
#188537