Finite Group Databasebeta

← #18006409

Subgroups — #18006409

Order 4736.

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

normal subgroups only

This group has 494 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#14558187C211yesmaximal, characteristic, complemented
2#14557879C211yesmaximal, characteristic, complemented
3#14557844C212yesmaximal, complemented
4#14557813C211yesmaximal, characteristic, complemented
5#14557767C212yesmaximal, complemented
6#14557725C211yesmaximal, characteristic, complemented
7#14557667C212yesmaximal, complemented
8C4×#10596939C211yesmaximal, characteristic, complemented
9D4×#64436C211yesmaximal, characteristic, complemented
10C2×#11924457C212yesmaximal, complemented
11D42×C37C211yesmaximal, characteristic, complemented
12C2×#10596964—21no—
13C2×#10596939C2211yescharacteristic
14C2×#10596939C2212yescomplemented
15C22×#64436C2212yescomplemented
16#11924536C2211yescharacteristic, complemented
17#11924520—22no—
18#11924516—21no—
19#11924510C2212yescomplemented
20C4×D148C2211yescharacteristic, complemented
21C2×C4⋊Dic37C2212yescomplemented
22#11924469C2212yescomplemented
23#11924469C2211yescharacteristic, complemented
24C4⋊#64436C2211yescharacteristic, complemented
25#11924457C2211yescharacteristic
26#11924457C2212yes—
27#11924457C2212yescomplemented
28#11924457C2212yescomplemented
29#11924457C2212yescomplemented
30#11924456C2211yescharacteristic, complemented
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—
54C2×C22⋊D37—22no—
55C22×Dic37—22no—
56#10596964—44no—
57C2×D148C2311yescharacteristic
58C2×C4×D37—21no—
59C2×Dic74—21no—
60C4⋊C4×C37D411yescharacteristic
61C4⋊C4×C37C2311yescharacteristic
62C22⋊C4×C37—21no—
63C22⋊C4×C37—22no—
64C22⋊C4×C37D412yes—
65C42×C37C2311yescharacteristic
66#10596939—22no—
67#10596939—42no—
68#10596938—21no—
69#10596938—22no—
70C4⋊Dic37—22no—
71C4⋊Dic37—21no—
72C4⋊Dic37C2311yescharacteristic
73C4⋊Dic37C2312yes—
74C2×#64436—42no—
75C2×#64436C2311yescharacteristic
76C2×#64436C2312yes—
77C2×#64436C2311yescharacteristic
78C23×C37—21no—
79C23×C37—22no—
80C23×C37—44no—
81C23×C37—44no—
82C23×C37—82no—
83C23×C37C2×D412yes—
84C22×D37—21no—
85D4×C37—22no—
86D4×C37—21no—
87D4×C37—22no—
88D4×C37—44no—
89D4×C37—44no—
90D4×C37—42no—
91D4×C37—81no—
92D4×C37D814yescomplemented
93D4×C37#4112yescomplemented
94C2×C4×C37—22no—
95C2×C4×C37—22no—
96C2×C4×C37—21no—
97C2×C4×C37—42no—
98C2×C4×C37C2×D411yescharacteristic
99C2×C4×C37C2×D412yes—
100C2×C4×C37C2×D411yescharacteristic
101C2×C4×C37C2411yescharacteristic
102C22⋊D37—44no—
103C2×Dic37—22no—
104C2×Dic37—21no—
105C2×Dic37—44no—
106D148—21no—
107D148—21no—
108C4×D37—42no—
109Dic74—42no—
110#64436—21no—
111#64436—21no—
112#64436—22no—
113C22×C37—22no—
114C22×C37—22no—
115C22×C37—22no—
116C22×C37—41no—
117C22×C37—41no—
118C22×C37—42no—
119C22×C37—42no—
120C22×C37—42no—
121C22×C37—88no—
122C22×C37C2×D814yes—
123C22×C37C22×D411yescharacteristic
124C2×D37—41no—
125C2×D37—41no—
126C2×D37—41no—
127C4×C37—22no—
128C4×C37—21no—
129C4×C37—41no—
130C4×C37C2×D812yes—
131C4×C37C2×#4111yescharacteristic
132C4×C37H(5,𝔽2)11yescharacteristic
133Dic37—42no—
134Dic37—41no—
135#3294—371nomaximal, Sylow
136C2×C37—24no—
137C2×C37—42no—
138C2×C37—82no—
139C2×C37#54611yescharacteristic
140C2×C37C22×D811yescharacteristic
141C2×C37#57711yescharacteristic
142D37—81no—
143#547—371no—
144D42D3711yescharacteristic, complemented
145#486—371no—
146#480—372no—
147#474—371no—
148#466—372no—
149#459—371no—
150#447—372no—
151C4×D8—371no—
152C8×D4—371no—
153C2×#102—372no—
154C37#329411yescharacteristic, complemented, Sylow
155C2×#41—741no—
156C22×D4—21no—
157C22×D4C2×D3712yes—
158C2×D8—371no—
159C2×D8—372no—
160C22×C8—372no—
161C4⋊Q8—371no—
162#127C2×D3711yescharacteristic
163#123—742no—
164C22⋊Q8—741no—
165#121—21no—
166#121—372no—
167#121C2×D3712yes—
168#120—22no—
169C4×D4—371no—
170C4×D4C2×D3711yescharacteristic
171C4×D4C2×D3711yescharacteristic
172C2×C4⋊C4—372no—
173#107—371no—
174#107—372no—
175C4⋊C8—371no—
176#102—371no—
177#102—372no—
178#102—372no—
179#102—372no—
180#102—372no—
181#102—371no—
182C22⋊C8—372no—
183C4×C8—371no—
184C24—22no—
185#41—1484no—
186C2×Q8—741no—
187C2×D4—24no—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—21no—
192C2×D4—42no—
193C2×D4—44no—
194C2×D4—371no—
195C2×D4—742no—
196C2×D4C22⋊D3711yescharacteristic
197C2×D4C22×D3712yes—
198C2×D4C22×D3711yescharacteristic
199C22×C4—21no—
200C22×C4—742no—
201C22×C4—741no—
202C22×C4C22×D3712yes—
203D8—742no—
204D8—1482no—
205C2×C8—371no—
206C2×C8—371no—
207C2×C8—372no—
208C2×C8—1482no—
209C4⋊C4—371no—
210C4⋊C4—372no—
211C4⋊C4—742no—
212C4⋊C4—741no—
213C4⋊C4C22⋊D3711yescharacteristic
214C4⋊C4C22×D3711yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—22no—
217C22⋊C4—741no—
218C22⋊C4—742no—
219C22⋊C4C22⋊D3712yes—
220C42C22×D3711yescharacteristic
221C23—21no—
222C23—22no—
223C23—44no—
224C23—44no—
225C23—82no—
226C23—741no—
227C23C2×C22⋊D3712yes—
228Q8—1482no—
229D4—22no—
230D4—21no—
231D4—22no—
232D4—44no—
233D4—44no—
234D4—42no—
235D4—81no—
236D4—741no—
237D4—741no—
238D4—1484no—
239D4#1059693914yescomplemented
240D4#1059696412yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—741no—
246C2×C4—742no—
247C2×C4—1484no—
248C2×C4—1482no—
249C2×C4C2×C22⋊D3711yescharacteristic
250C2×C4C2×C22⋊D3712yes—
251C2×C4C2×C22⋊D3711yescharacteristic
252C2×C4C23×D3711yescharacteristic
253C8—741no—
254C8—741no—
255C8—742no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—41no—
260C22—41no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—88no—
265C22—1481no—
266C22—1481no—
267C22—1481no—
268C22C2×#1059693914yes—
269C22C22×C22⋊D3711yescharacteristic
270C4—21no—
271C4—22no—
272C4—41no—
273C4—1481no—
274C4—1482no—
275C4C2×#1059693912yes—
276C4C2×#1059696411yescharacteristic
277C4#1192458111yescharacteristic
278C2—24no—
279C2—42no—
280C2—82no—
281C2—2961no—
282C2#1455817711yescharacteristic
283C2C22×#1059693911yescharacteristic
284C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingD42×C37C2
socleC22×C37C22×D4
hypercenterD42D37
hypocenterC37#3294
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. #14558187C2semidirect
2. #14557879C2semidirect
3. #14557844C2semidirect
4. #14557813C2semidirect
5. #14557767C2semidirect
6. #14557725C2semidirect
7. #14557667C2semidirect
8. C4×#10596939C2semidirect
9. D4×#64436C2semidirect
10. C2×#11924457C2semidirect
11. D42×C37C2semidirect
14. C2×#10596939C22semidirect
15. C22×#64436C22semidirect
16. #11924536C22semidirect
19. #11924510C22semidirect
20. C4×D148C22semidirect
21. C2×C4⋊Dic37C22semidirect
22. #11924469C22semidirect
23. #11924469C22semidirect
24. C4⋊#64436C22semidirect
27. #11924457C22semidirect
28. #11924457C22semidirect
29. #11924457C22semidirect
30. #11924456C22semidirect
31. C22⋊#64436C22semidirect
32. C4×#64436C22semidirect
92. D4×C37D8semidirect
93. D4×C37#41semidirect
144. D42D37semidirect
154. C37#3294semidirect
239. D4#10596939semidirect
240. D4#10596964semidirect

Maximal subgroups

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

subgroupindex
#145581872
#145578792
#145578442
#145578132
#145577672
#145577252
#145576672
C4×#105969392
D4×#644362
C2×#119244572
D42×C372
#329437