Finite Group Databasebeta

← #17995628

Subgroups — #17995628

Order 4736.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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×#11924569C211yesmaximal, characteristic, complemented
2#14558102C211yesmaximal, characteristic
3C2×#11924524C211yesmaximal, characteristic, complemented
4C2×#11924464C211yesmaximal, characteristic, complemented
5#14557541C211yesmaximal, characteristic, complemented
6C2×#11924452C211yesmaximal, characteristic, complemented
7C37×#339C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10C22×D148C2211yescharacteristic
11#11924569—22no—
12#11924569—22no—
13C2×Dic148—21no—
14C2×#10596930—21no—
15C2×#10596934C2211yescharacteristic
16#11924533—21no—
17#11924524—21no—
18#11924524—22no—
19#11924524—22no—
20#11924511—22no—
21#11924506—22no—
22C2×#10596938—22no—
23#11924464—22no—
24#11924459—22no—
25#11924452—22no—
26C2×M16×C37C2211yescharacteristic
27#117×C37C2211yescharacteristic
28C2×C42×C37C2211yescharacteristic
29C23×D37D412yes—
30C22×C4×C37—21no—
31C22×C4×C37C2311yescharacteristic
32C2×C22⋊D37—21no—
33C22×Dic37—21no—
34#10596962—21no—
35#10596962—21no—
36#10596962—21no—
37#10596962—21no—
38C2×D148—21no—
39C2×D148—21no—
40C2×D148—21no—
41C2×D148—21no—
42C2×D148—21no—
43C2×D148—21no—
44C2×D148—24no—
45C2×D148D411yescharacteristic
46C2×C4×D37—21no—
47C2×Dic74—21no—
48C2×Dic74—21no—
49C2×Dic74—21no—
50C2×Dic74—21no—
51C2×Dic74—21no—
52C2×Dic74D411yescharacteristic
53C2×Dic74D412yescomplemented
54M16×C37—21no—
55M16×C37D412yescomplemented
56C2×C8×C37—21no—
57C4⋊C4×C37D412yes—
58C22⋊C4×C37—21no—
59C42×C37—21no—
60C42×C37—21no—
61C42×C37D412yescomplemented
62#10596938—28no—
63#10596938—24no—
64#10596934—21no—
65#10596934—21no—
66C2×#64436—21no—
67Dic148—24no—
68#10596930—24no—
69C23×C37C2×D411yescharacteristic
70C22×D37—22no—
71C22×D37—22no—
72C22×D37—21no—
73C22×D37—22no—
74C22×D37—44no—
75C2×C4×C37—22no—
76C2×C4×C37—22no—
77C2×C4×C37—42no—
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37#4111yescharacteristic
84C22⋊D37—41no—
85C22⋊D37—41no—
86C2×Dic37—22no—
87C2×Dic37—21no—
88C2×Dic37—41no—
89C2×Dic37—41no—
90D148—21no—
91D148—21no—
92D148—41no—
93D148—41no—
94D148—41no—
95D148—41no—
96D148—84no—
97C4×D37—41no—
98C4×D37—41no—
99Dic74—22no—
100Dic74—21no—
101Dic74—22no—
102Dic74—21no—
103Dic74—41no—
104Dic74—41no—
105C8×C37—22no—
106#64436—41no—
107C22×C37—22no—
108C22×C37#12011yescharacteristic
109C22×C37#12011yescharacteristic
110C22×C37#12111yescharacteristic
111C2×D37—44no—
112C2×D37—41no—
113C2×D37—42no—
114C2×D37—42no—
115C2×D37—44no—
116C2×D37—82no—
117C4×C37—42no—
118C4×C37—42no—
119C4×C37#12011yescharacteristic
120C4×C37#12111yescharacteristic
121C4×C37#12111yescharacteristic
122C4×C37#12711yescharacteristic
123Dic37—42no—
124Dic37—41no—
125#2004—371nomaximal, Sylow
126C2×C37—21no—
127C2×C37—21no—
128C2×C37#39211yescharacteristic
129C2×C37#45512yes—
130D37—81no—
131D37—82no—
132C2×#137—371no—
133#535—371no—
134C2×#124—371no—
135C2×#104—371no—
136#419—371no—
137C2×#100—371no—
138#339D3711yescharacteristic, complemented
139C37#200411yescharacteristic, complemented, Sylow
140C2×#41—371no—
141C22×Q8—371no—
142C22×D4—371no—
143#137—742no—
144#137—742no—
145C2×Q16—741no—
146C2×SD16—741no—
147C2×M16—371no—
148C2×M16C2×D3711yescharacteristic
149#127—741no—
150#124—742no—
151#124—741no—
152#124—742no—
153#121—742no—
154#120—742no—
155#117C2×D3711yescharacteristic
156C2×C22⋊C4—742no—
157C2×C42C2×D3711yescharacteristic
158#104—742no—
159#103—742no—
160#100—742no—
161C24—372no—
162#41—741no—
163#41—741no—
164#41—741no—
165#41—741no—
166C2×Q8—371no—
167C2×Q8—372no—
168C2×Q8—741no—
169C2×Q8—741no—
170C2×Q8—741no—
171C2×Q8—741no—
172C2×Q8—741no—
173C2×D4—371no—
174C2×D4—744no—
175C2×D4—741no—
176C2×D4—741no—
177C2×D4—741no—
178C2×D4—741no—
179C2×D4—741no—
180C2×D4—741no—
181C2×D4—741no—
182C22×C4—21no—
183C22×C4—741no—
184C22×C4—741no—
185C22×C4C22×D3711yescharacteristic
186Q16—744no—
187SD16—744no—
188M16—21no—
189M16—741no—
190M16—741no—
191M16D14812yescomplemented
192C2×C8—21no—
193C2×C8—741no—
194C4⋊C4D14812yes—
195C22⋊C4—21no—
196C22⋊C4—748no—
197C22⋊C4—744no—
198C42—21no—
199C42—21no—
200C42D14812yescomplemented
201C23—742no—
202C23—742no—
203C23—742no—
204C23—741no—
205C23—1484no—
206C23D4×D3711yescharacteristic
207Q8—742no—
208Q8—741no—
209Q8—742no—
210Q8—741no—
211Q8—1481no—
212Q8—1481no—
213D4—2964no—
214D4—741no—
215D4—741no—
216D4—1481no—
217D4—1481no—
218D4—1481no—
219D4—1481no—
220D4—1481no—
221D4—1481no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—742no—
226C2×C4—741no—
227C2×C4—1481no—
228C2×C4—1481no—
229C2×C4—1481no—
230C2×C4—1481no—
231C2×C4C2×D14811yescharacteristic
232C2×C4C2×D14811yescharacteristic
233C2×C4C2×D14811yescharacteristic
234C2×C4D4×D3711yescharacteristic
235C2×C4D4×D3711yescharacteristic
236C2×C4#1059696611yescharacteristic
237C8—22no—
238C8—1481no—
239C22—22no—
240C22—2962no—
241C22—1484no—
242C22—1481no—
243C22—1482no—
244C22—1482no—
245C22—1484no—
246C22#1192450611yescharacteristic
247C22#1192450611yescharacteristic
248C22#1192451111yescharacteristic
249C4—42no—
250C4—42no—
251C4—1481no—
252C4—1482no—
253C4#1192450611yescharacteristic
254C4#1192451111yescharacteristic
255C4#1192451111yescharacteristic
256C4#1192453311yescharacteristic
257C2—21no—
258C2—21no—
259C2—2962no—
260C2—2961no—
261C2#1455744311yescharacteristic
262C2#1455771212yes—
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37#120
prime radical#14558102C2
hypercenter#339D37
hypocenterC37#2004
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#11924569C2semidirect
3. C2×#11924524C2semidirect
4. C2×#11924464C2semidirect
5. #14557541C2semidirect
6. C2×#11924452C2semidirect
7. C37×#339C2semidirect
53. C2×Dic74D4semidirect
55. M16×C37D4semidirect
61. C42×C37D4semidirect
138. #339D37semidirect
139. C37#2004semidirect
191. M16D148semidirect
200. C42D148semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
#145581022
C2×#119245242
C2×#119244642
#145575412
C2×#119244522
C37×#3392
#200437