Finite Group Databasebeta

← #18006408

Subgroups — #18006408

Order 4736.

494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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#14558186C211yesmaximal, characteristic, complemented
2#14558168C211yesmaximal, characteristic, complemented
3#14557845C212yesmaximal, complemented
4#14557810C211yesmaximal, characteristic, complemented
5#14557768C212yesmaximal, complemented
6#14557725C211yesmaximal, characteristic, complemented
7#14557668C212yesmaximal, complemented
8C4×D296C211yesmaximal, characteristic, complemented
9C8×D148C211yesmaximal, characteristic, complemented
10#102×D37C212yesmaximal, complemented
11C37×#486C211yesmaximal, characteristic, complemented
12C2×#10596966—21no—
13C2×D4×D37—21no—
14C2×D4×D37C2212yes—
15C2×D296C2211yescharacteristic
16C2×#10596939C2212yescomplemented
17C2×C8×D37C2212yescomplemented
18#11924521—22no—
19#11924512—21no—
20#11924511C2212yescomplemented
21#11924507—21no—
22#11924507C2212yes—
23#11924504—22no—
24C4×D148C2211yescharacteristic
25C4×D148C2211yescharacteristic
26C4×D148C2211yescharacteristic, complemented
27C4⋊C4×D37C2212yescomplemented
28#11924470C2211yescharacteristic, complemented
29#11924469C2212yescomplemented
30C4⋊#64436C2211yescharacteristic, complemented
31#11924458C2211yescharacteristic
32#11924458C2211yescharacteristic, complemented
33#11924457C2212yescomplemented
34#11924456C2212yes—
35#11924448C2212yescomplemented
36C4⋊Q8×C37C2211yescharacteristic, complemented
37#127×C37C2211yescharacteristic
38#102×C37C2212yescomplemented
39#102×C37C2212yescomplemented
40C4×C8×C37C2211yescharacteristic, complemented
41C23×D37—22no—
42C2×Q8×C37—21no—
43C2×D4×C37—21no—
44C2×D4×C37—21no—
45C2×D4×C37C2312yes—
46C2×C22⋊D37—22no—
47C2×C22⋊D37—22no—
48#10596966—44no—
49D4×D37—24no—
50D4×D37—42no—
51D4×D37—44no—
52C2×D148—22no—
53C2×D148D411yescharacteristic
54C2×D148C2311yescharacteristic
55C2×D148C2311yescharacteristic
56C2×C4×D37—22no—
57C2×C4×D37—21no—
58C2×C4×D37—21no—
59C2×C4×D37C2312yes—
60C2×C8×C37C2311yescharacteristic
61C2×C8×C37C2311yescharacteristic
62C4⋊C4×C37—21no—
63C4⋊C4×C37C2312yes—
64C42×C37C2311yescharacteristic
65C22⋊Dic37—22no—
66#10596939—42no—
67#10596938—21no—
68#10596938—21no—
69#10596938—22no—
70#10596938D412yes—
71C4⋊Dic37D411yescharacteristic
72C4⋊Dic37C2311yescharacteristic
73C4⋊Dic37C2311yescharacteristic
74#10596936—22no—
75C2×#64436C2312yes—
76D296—22no—
77C8×D37—42no—
78C23×C37—22no—
79C22×D37—21no—
80C22×D37—21no—
81C22×D37—44no—
82C22×D37—44no—
83C22×D37—82no—
84C22×D37C2×D412yes—
85Q8×C37—42no—
86D4×C37—22no—
87D4×C37—22no—
88D4×C37—42no—
89D4×C37—81no—
90C2×C4×C37—22no—
91C2×C4×C37C2×D411yescharacteristic
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37C2411yescharacteristic
94C22⋊D37—44no—
95C22⋊D37—44no—
96C2×Dic37—21no—
97C2×Dic37—21no—
98C2×Dic37C2×D412yes—
99D148—21no—
100D148—21no—
101D148—21no—
102D148—44no—
103D148D814yescomplemented
104D148#4112yescomplemented
105C4×D37—22no—
106C4×D37—22no—
107C4×D37—44no—
108C4×D37—42no—
109C4×D37—42no—
110C8×C37—21no—
111C8×C37—21no—
112#64436—22no—
113C22×C37—42no—
114C22×C37—42no—
115C22×C37—42no—
116C22×C37C22×D411yescharacteristic
117C2×D37—22no—
118C2×D37—22no—
119C2×D37—22no—
120C2×D37—41no—
121C2×D37—41no—
122C2×D37—41no—
123C2×D37—41no—
124C2×D37—41no—
125C2×D37—88no—
126C2×D37C2×D814yes—
127C4×C37—21no—
128C4×C37—42no—
129C4×C37C2×D812yes—
130C4×C37C2×#4111yescharacteristic
131C4×C37H(5,𝔽2)11yescharacteristic
132Dic37—22no—
133Dic37—41no—
134Dic37—41no—
135#3294—371nomaximal, Sylow
136C2×C37—82no—
137C2×C37#54611yescharacteristic
138C2×C37C22×D811yescharacteristic
139C2×C37#57711yescharacteristic
140D37—24no—
141D37—42no—
142D37—81no—
143#547—371no—
144D42—371no—
145#486D3711yescharacteristic, complemented
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—372no—
157C22×D4—741no—
158C2×D8—372no—
159C2×D8—371no—
160C22×C8—372no—
161C4⋊Q8C2×D3711yescharacteristic, complemented
162#127C2×D3711yescharacteristic
163#123—742no—
164C22⋊Q8—741no—
165#121—372no—
166#121—372no—
167#121—741no—
168#120—742no—
169C4×D4—371no—
170C4×D4—371no—
171C4×D4—371no—
172C2×C4⋊C4—372no—
173#107—371no—
174#107—372no—
175C4⋊C8—371no—
176#102—372no—
177#102—371no—
178#102—371no—
179#102—372no—
180#102C2×D3712yescomplemented
181#102C2×D3712yescomplemented
182C22⋊C8—372no—
183C4×C8C2×D3711yescharacteristic, complemented
184C24—742no—
185#41—1484no—
186C2×Q8—21no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—371no—
190C2×D4—371no—
191C2×D4—371no—
192C2×D4—742no—
193C2×D4—742no—
194C2×D4—744no—
195C2×D4—742no—
196C2×D4—1482no—
197C2×D4—1484no—
198C2×D4C22×D3712yes—
199C22×C4—372no—
200C22×C4—742no—
201C22×C4—741no—
202C22×C4—741no—
203D8—742no—
204D8—1482no—
205C2×C8—372no—
206C2×C8—1482no—
207C2×C8C22×D3711yescharacteristic
208C2×C8C22×D3711yescharacteristic
209C4⋊C4—21no—
210C4⋊C4—371no—
211C4⋊C4—371no—
212C4⋊C4—371no—
213C4⋊C4—742no—
214C4⋊C4C22×D3712yes—
215C22⋊C4—372no—
216C22⋊C4—742no—
217C22⋊C4—742no—
218C22⋊C4—741no—
219C22⋊C4—741no—
220C42C22×D3711yescharacteristic
221C23—22no—
222C23—372no—
223C23—2962no—
224C23—741no—
225C23—741no—
226C23—1484no—
227C23—1484no—
228Q8—42no—
229D4—22no—
230D4—22no—
231D4—42no—
232D4—81no—
233D4—374no—
234D4—372no—
235D4—741no—
236D4—741no—
237D4—741no—
238D4—1484no—
239D4—1484no—
240D4—1484no—
241C2×C4—22no—
242C2×C4—372no—
243C2×C4—742no—
244C2×C4—742no—
245C2×C4—741no—
246C2×C4—741no—
247C2×C4—1484no—
248C2×C4—1482no—
249C2×C4—1482no—
250C2×C4D4×D3711yescharacteristic
251C2×C4D4×D3711yescharacteristic
252C2×C4C23×D3711yescharacteristic
253C8—21no—
254C8—21no—
255C8—742no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—374no—
260C22—2968no—
261C22—742no—
262C22—742no—
263C22—742no—
264C22—1481no—
265C22—1481no—
266C22—1481no—
267C22—1481no—
268C22—1481no—
269C22C2×D4×D3711yescharacteristic
270C4—21no—
271C4—42no—
272C4—742no—
273C4—1481no—
274C4—1481no—
275C4D8×D3712yes—
276C4#41×D3711yescharacteristic
277C4#1192458211yescharacteristic
278C2—82no—
279C2—2961no—
280C2—744no—
281C2—1482no—
282C2#1455817611yescharacteristic
283C2C2×D8×D3711yescharacteristic
284C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#486C2
socleC22×C37C22×D4
hypercenter#486D37
hypocenterC37#3294
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14558186C2semidirect
2. #14558168C2semidirect
3. #14557845C2semidirect
4. #14557810C2semidirect
5. #14557768C2semidirect
6. #14557725C2semidirect
7. #14557668C2semidirect
8. C4×D296C2semidirect
9. C8×D148C2semidirect
10. #102×D37C2semidirect
11. C37×#486C2semidirect
16. C2×#10596939C22semidirect
17. C2×C8×D37C22semidirect
20. #11924511C22semidirect
26. C4×D148C22semidirect
27. C4⋊C4×D37C22semidirect
28. #11924470C22semidirect
29. #11924469C22semidirect
30. C4⋊#64436C22semidirect
32. #11924458C22semidirect
33. #11924457C22semidirect
35. #11924448C22semidirect
36. C4⋊Q8×C37C22semidirect
38. #102×C37C22semidirect
39. #102×C37C22semidirect
40. C4×C8×C37C22semidirect
103. D148D8semidirect
104. D148#41semidirect
145. #486D37semidirect
154. C37#3294semidirect
161. C4⋊Q8C2×D37semidirect
180. #102C2×D37semidirect
181. #102C2×D37semidirect
183. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581862
#145581682
#145578452
#145578102
#145577682
#145577252
#145576682
C4×D2962
C8×D1482
#102×D372
C37×#4862
#329437