Finite Group Databasebeta

← #18006420

Subgroups — #18006420

Order 4736.

462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 141 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#14558240C211yesmaximal, characteristic, complemented
2#14557879C211yesmaximal, characteristic, complemented
3#14557849C212yesmaximal, complemented
4#14557823C211yesmaximal, characteristic, complemented
5#14557760C212yesmaximal, complemented
6#14557730C211yesmaximal, characteristic, complemented
7#14557684C212yesmaximal, complemented
8C4×#10596940C211yesmaximal, characteristic, complemented
9D4×#64436C211yesmaximal, characteristic, complemented
10C2×#11924457C212yesmaximal, complemented
11D42×C37C211yesmaximal, characteristic
12C2×#10596940C2211yescharacteristic
13C2×#10596940C2212yescomplemented
14C22×#64436C2212yescomplemented
15#11924536C2211yescharacteristic, complemented
16#11924527—21no—
17#11924515C2212yescomplemented
18#11924513—22no—
19C4×Dic74C2211yescharacteristic, complemented
20D4×Dic37—21no—
21C2×C4⋊Dic37C2212yescomplemented
22#11924467C2212yescomplemented
23#11924467C2211yescharacteristic, complemented
24C4⋊#64436C2211yescharacteristic, complemented
25#11924459C2211yescharacteristic, complemented
26#11924457C2211yescharacteristic
27#11924457C2212yes—
28#11924457C2212yescomplemented
29#11924457C2212yescomplemented
30#11924457C2212yescomplemented
31C22⋊#64436C2212yescomplemented
32C4×#64436C2211yescharacteristic, complemented
33C22×D4×C37—21no—
34C22×D4×C37C2212yes—
35#127×C37C2211yescharacteristic
36#121×C37—21no—
37#121×C37C2212yes—
38#120×C37—22no—
39C4×D4×C37C2211yescharacteristic
40C4×D4×C37C2211yescharacteristic
41C24×C37—22no—
42C2×D4×C37—24no—
43C2×D4×C37—22no—
44C2×D4×C37—22no—
45C2×D4×C37—21no—
46C2×D4×C37—21no—
47C2×D4×C37—42no—
48C2×D4×C37—44no—
49C2×D4×C37D411yescharacteristic
50C2×D4×C37C2312yes—
51C2×D4×C37C2311yescharacteristic
52C22×C4×C37—21no—
53C22×C4×C37C2312yes—
54C22×Dic37—22no—
55C2×Dic74—21no—
56C2×Dic74C2311yescharacteristic
57C4⋊C4×C37D411yescharacteristic
58C4⋊C4×C37C2311yescharacteristic
59C22⋊C4×C37—21no—
60C22⋊C4×C37—22no—
61C22⋊C4×C37D412yes—
62C42×C37C2311yescharacteristic
63C22⋊Dic37—22no—
64#10596940—22no—
65#10596940—42no—
66C4⋊Dic37—22no—
67C4⋊Dic37—21no—
68C4⋊Dic37C2311yescharacteristic
69C4⋊Dic37C2312yes—
70#10596936—21no—
71#10596936—22no—
72C4×Dic37—21no—
73C2×#64436—42no—
74C2×#64436C2311yescharacteristic
75C2×#64436C2312yes—
76C2×#64436C2311yescharacteristic
77C23×C37—21no—
78C23×C37—22no—
79C23×C37—44no—
80C23×C37—44no—
81C23×C37—82no—
82C23×C37C2×D412yes—
83D4×C37—22no—
84D4×C37—21no—
85D4×C37—22no—
86D4×C37—44no—
87D4×C37—44no—
88D4×C37—42no—
89D4×C37—81no—
90D4×C37SD1614yescomplemented
91D4×C37#4112yes—
92C2×C4×C37—22no—
93C2×C4×C37—22no—
94C2×C4×C37—21no—
95C2×C4×C37—42no—
96C2×C4×C37C2×D412yes—
97C2×C4×C37C2×D411yescharacteristic
98C2×C4×C37C2×D411yescharacteristic
99C2×C4×C37C2411yescharacteristic
100C2×Dic37—21no—
101C2×Dic37—21no—
102C2×Dic37—22no—
103C2×Dic37—82no—
104Dic74—21no—
105Dic74—21no—
106Dic74—81no—
107#64436—21no—
108#64436—21no—
109#64436—22no—
110C22×C37—22no—
111C22×C37—22no—
112C22×C37—22no—
113C22×C37—41no—
114C22×C37—41no—
115C22×C37—42no—
116C22×C37—42no—
117C22×C37—42no—
118C22×C37—88no—
119C22×C37C2×SD1614yes—
120C22×C37C22×D411yescharacteristic
121C4×C37—22no—
122C4×C37—21no—
123C4×C37—41no—
124C4×C37C2×SD1612yes—
125C4×C37C2×#4111yescharacteristic
126C4×C37H(5,𝔽2)11yescharacteristic
127Dic37—41no—
128Dic37—42no—
129Dic37—41no—
130#3295—371nomaximal, Sylow
131C2×C37—24no—
132C2×C37—42no—
133C2×C37—82no—
134C2×C37#54611yescharacteristic
135C2×C37C22×SD1611yescharacteristic
136C2×C37#57611yescharacteristic
137#554—371no—
138D42D3711yescharacteristic
139#486—371no—
140#481—372no—
141#476—371no—
142#465—372no—
143#460—371no—
144#450—372no—
145C4×SD16—371no—
146C8×D4—371no—
147C2×#102—372no—
148C37#329511yescharacteristic, complemented, Sylow
149C22×D4—21no—
150C22×D4C2×D3712yes—
151C2×SD16—371no—
152C2×SD16—372no—
153C22×C8—372no—
154C4⋊Q8—371no—
155#127C2×D3711yescharacteristic
156#125—741no—
157C22⋊Q8—372no—
158C22⋊Q8—742no—
159#121—21no—
160#121C2×D3712yes—
161#120—22no—
162C4×Q8—371no—
163C4×D4—741no—
164C4×D4C2×D3711yescharacteristic
165C4×D4C2×D3711yescharacteristic
166C2×C4⋊C4—372no—
167#106—371no—
168#106—372no—
169C4⋊C8—371no—
170#103—371no—
171#102—371no—
172#102—372no—
173#102—372no—
174#102—372no—
175#102—372no—
176C22⋊C8—372no—
177C4×C8—371no—
178C24—22no—
179C2×Q8—371no—
180C2×Q8—741no—
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—42no—
187C2×D4—44no—
188C2×D4C22⋊D3711yescharacteristic
189C2×D4C22×D3712yes—
190C2×D4C22×D3711yescharacteristic
191C22×C4—21no—
192C22×C4—742no—
193C22×C4C22×D3712yes—
194SD16—742no—
195SD16—1482no—
196C2×C8—371no—
197C2×C8—371no—
198C2×C8—372no—
199C2×C8—1482no—
200C4⋊C4—371no—
201C4⋊C4—372no—
202C4⋊C4—741no—
203C4⋊C4—742no—
204C4⋊C4—742no—
205C4⋊C4—741no—
206C4⋊C4C22⋊D3711yescharacteristic
207C4⋊C4C22×D3711yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—22no—
210C22⋊C4—742no—
211C22⋊C4C22⋊D3712yes—
212C42—741no—
213C42C22×D3711yescharacteristic
214C23—21no—
215C23—22no—
216C23—44no—
217C23—44no—
218C23—82no—
219C23C2×C22⋊D3712yes—
220Q8—2961no—
221Q8—741no—
222Q8—741no—
223D4—22no—
224D4—21no—
225D4—22no—
226D4—44no—
227D4—44no—
228D4—42no—
229D4—81no—
230D4#1059694014yescomplemented
231D4#1059696412yes—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—2962no—
237C2×C4—741no—
238C2×C4—741no—
239C2×C4—742no—
240C2×C4C2×C22⋊D3711yescharacteristic
241C2×C4C2×C22⋊D3712yes—
242C2×C4C2×C22⋊D3711yescharacteristic
243C2×C4C23×D3711yescharacteristic
244C8—741no—
245C8—741no—
246C8—742no—
247C22—22no—
248C22—22no—
249C22—22no—
250C22—41no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—88no—
256C22C2×#1059694014yes—
257C22C22×C22⋊D3711yescharacteristic
258C4—21no—
259C4—22no—
260C4—41no—
261C4—1481no—
262C4—1482no—
263C4—1481no—
264C4C2×#1059694012yes—
265C4C2×#1059696411yescharacteristic
266C4#1192458111yescharacteristic
267C2—24no—
268C2—42no—
269C2—82no—
270C2#1455817711yescharacteristic
271C2C22×#1059694011yescharacteristic
272C2#1455833611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
Fitting, prime radicalD42×C37C2
socleC22×C37C22×D4
hypercenterD42D37
hypocenterC37#3295
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #14558240C2semidirect
2. #14557879C2semidirect
3. #14557849C2semidirect
4. #14557823C2semidirect
5. #14557760C2semidirect
6. #14557730C2semidirect
7. #14557684C2semidirect
8. C4×#10596940C2semidirect
9. D4×#64436C2semidirect
10. C2×#11924457C2semidirect
13. C2×#10596940C22semidirect
14. C22×#64436C22semidirect
15. #11924536C22semidirect
17. #11924515C22semidirect
19. C4×Dic74C22semidirect
21. C2×C4⋊Dic37C22semidirect
22. #11924467C22semidirect
23. #11924467C22semidirect
24. C4⋊#64436C22semidirect
25. #11924459C22semidirect
28. #11924457C22semidirect
29. #11924457C22semidirect
30. #11924457C22semidirect
31. C22⋊#64436C22semidirect
32. C4×#64436C22semidirect
90. D4×C37SD16semidirect
148. C37#3295semidirect
230. D4#10596940semidirect

Maximal subgroups

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

subgroupindex
#145582402
#145578792
#145578492
#145578232
#145577602
#145577302
#145576842
C4×#105969402
D4×#644362
C2×#119244572
D42×C372
#329537