Finite Group Databasebeta

← #18006411

Subgroups — #18006411

Order 4736.

494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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#14558188C211yesmaximal, characteristic, complemented
2D4×D148C211yesmaximal, characteristic, complemented
3#14557880C211yesmaximal, characteristic, complemented
4#14557848C212yesmaximal, complemented
5#14557813C211yesmaximal, characteristic, complemented
6#14557768C212yesmaximal, complemented
7#14557728C211yesmaximal, characteristic, complemented
8#14557665C212yesmaximal, complemented
9C8×D148C211yesmaximal, characteristic, complemented
10#102×D37C212yesmaximal, complemented
11C4×D8×C37C211yesmaximal, characteristic, complemented
12C2×#10596962—21no—
13C22×D148—21no—
14C2×D4×D37C2212yes—
15C2×#10596939C2212yescomplemented
16C2×C8×D37C2212yescomplemented
17#11924536C2211yescharacteristic, complemented
18#11924533C2211yescharacteristic
19#11924518—22no—
20#11924515—21no—
21#11924511C2212yes—
22#11924510—21no—
23#11924507C2212yescomplemented
24#11924506—22no—
25C4×D148C2211yescharacteristic
26C4⋊C4×D37C2212yescomplemented
27#11924469C2212yescomplemented
28C4⋊#64436C2211yescharacteristic, complemented
29#11924458C2212yescomplemented
30#11924458C2212yescomplemented
31#11924457C2212yes—
32#11924456C2212yescomplemented
33#11924448C2212yescomplemented
34C2×D8×C37C2211yescharacteristic
35C4×D4×C37C2211yescharacteristic
36C4×D4×C37C2211yescharacteristic, complemented
37#107×C37C2211yescharacteristic, complemented
38#102×C37C2211yescharacteristic
39#102×C37C2211yescharacteristic, complemented
40C4×C8×C37C2211yescharacteristic, complemented
41C23×D37—22no—
42C2×D4×C37C2311yescharacteristic
43C2×D4×C37C2311yescharacteristic
44C22×C4×C37—21no—
45C22×C4×C37—21no—
46C2×C22⋊D37—22no—
47C2×C22⋊D37—22no—
48D4×D37—24no—
49D4×D37—42no—
50#10596962—44no—
51C2×D148—22no—
52C2×D148—21no—
53C2×D148—21no—
54C2×D148—44no—
55C2×D148D411yescharacteristic
56C2×D148C2312yes—
57C2×C4×D37—22no—
58C2×C4×D37C2312yes—
59C2×Dic74—21no—
60D8×C37—22no—
61C2×C8×C37C2311yescharacteristic
62C2×C8×C37C2311yescharacteristic
63C4⋊C4×C37C2311yescharacteristic
64C4⋊C4×C37C2311yescharacteristic
65C22⋊C4×C37—21no—
66C22⋊C4×C37—21no—
67C42×C37C2311yescharacteristic
68C22⋊Dic37—22no—
69#10596939—42no—
70#10596938—22no—
71#10596938D412yes—
72C4⋊Dic37—21no—
73C4⋊Dic37D411yescharacteristic
74C4⋊Dic37C2312yes—
75#10596936—22no—
76C2×#64436C2312yes—
77C8×D37—42no—
78C23×C37—21no—
79C23×C37—21no—
80C22×D37—22no—
81C22×D37—44no—
82C22×D37—44no—
83C22×D37—82no—
84C22×D37C2×D412yes—
85D4×C37—21no—
86D4×C37—21no—
87D4×C37—21no—
88D4×C37#4112yescomplemented
89C2×C4×C37—21no—
90C2×C4×C37—21no—
91C2×C4×C37—42no—
92C2×C4×C37—42no—
93C2×C4×C37C2×D411yescharacteristic
94C2×C4×C37C2×D411yescharacteristic
95C2×C4×C37C2411yescharacteristic
96C22⋊D37—44no—
97C22⋊D37—44no—
98C2×Dic37—22no—
99C2×Dic37C2×D412yes—
100D148—22no—
101D148—22no—
102D148—44no—
103D148—42no—
104D148—81no—
105D148D814yescomplemented
106C4×D37—22no—
107C4×D37—22no—
108C4×D37—44no—
109Dic74—42no—
110C8×C37—21no—
111C8×C37—21no—
112#64436—22no—
113C22×C37—22no—
114C22×C37—41no—
115C22×C37—41no—
116C22×C37—41no—
117C22×C37—41no—
118C22×C37—41no—
119C22×C37C22×D411yescharacteristic
120C2×D37—22no—
121C2×D37—22no—
122C2×D37—42no—
123C2×D37—42no—
124C2×D37—42no—
125C2×D37—88no—
126C2×D37C2×D814yes—
127C4×C37—21no—
128C4×C37—41no—
129C4×C37—41no—
130C4×C37C2×D812yes—
131C4×C37C2×#4111yescharacteristic
132C4×C37H(5,𝔽2)11yescharacteristic
133Dic37—22no—
134Dic37—42no—
135#3294—371nomaximal, Sylow
136C2×C37—42no—
137C2×C37—81no—
138C2×C37#54611yescharacteristic
139C2×C37C22×D811yescharacteristic
140C2×C37#57711yescharacteristic
141D37—24no—
142D37—82no—
143#547—371no—
144D42—371no—
145#486—371no—
146#480—372no—
147#474—371no—
148#466—372no—
149#459—371no—
150#447—372no—
151C4×D8D3711yescharacteristic, complemented
152C8×D4—371no—
153C2×#102—372no—
154C37#329411yescharacteristic, complemented, Sylow
155C2×#41—741no—
156C22×D4—372no—
157C22×D4—741no—
158C2×D8—372no—
159C2×D8C2×D3711yescharacteristic
160C22×C8—372no—
161C4⋊Q8—371no—
162#127—371no—
163#123—742no—
164C22⋊Q8—741no—
165#121—372no—
166#121—372no—
167#121—741no—
168#120—742no—
169C4×D4—371no—
170C4×D4C2×D3711yescharacteristic
171C4×D4C2×D3711yescharacteristic, complemented
172C2×C4⋊C4—372no—
173#107—372no—
174#107C2×D3711yescharacteristic, complemented
175C4⋊C8—371no—
176#102—372no—
177#102—372no—
178#102—372no—
179#102—372no—
180#102C2×D3711yescharacteristic
181#102C2×D3711yescharacteristic, complemented
182C22⋊C8—372no—
183C4×C8C2×D3711yescharacteristic, complemented
184C24—742no—
185#41—1484no—
186C2×Q8—741no—
187C2×D4—371no—
188C2×D4—372no—
189C2×D4—742no—
190C2×D4—742no—
191C2×D4—744no—
192C2×D4—742no—
193C2×D4—741no—
194C2×D4—741no—
195C2×D4—1484no—
196C2×D4—1482no—
197C2×D4C22×D3711yescharacteristic
198C2×D4C22×D3711yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—372no—
202C22×C4—742no—
203D8—22no—
204D8—1482no—
205C2×C8—372no—
206C2×C8—1482no—
207C2×C8C22×D3711yescharacteristic
208C2×C8C22×D3711yescharacteristic
209C4⋊C4—371no—
210C4⋊C4—372no—
211C4⋊C4—742no—
212C4⋊C4—741no—
213C4⋊C4C22×D3711yescharacteristic
214C4⋊C4C22×D3711yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—372no—
218C22⋊C4—742no—
219C22⋊C4—742no—
220C42C22×D3711yescharacteristic
221C23—21no—
222C23—21no—
223C23—372no—
224C23—2962no—
225C23—742no—
226C23—1484no—
227C23—1484no—
228Q8—1482no—
229D4—21no—
230D4—21no—
231D4—21no—
232D4—374no—
233D4—2961no—
234D4—742no—
235D4—742no—
236D4—1484no—
237D4—1484no—
238D4—1484no—
239D4—1482no—
240D4#1059696212yescomplemented
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—372no—
246C2×C4—742no—
247C2×C4—742no—
248C2×C4—742no—
249C2×C4—1484no—
250C2×C4D4×D3711yescharacteristic
251C2×C4D4×D3711yescharacteristic
252C2×C4C23×D3711yescharacteristic
253C8—21no—
254C8—21no—
255C8—742no—
256C22—22no—
257C22—41no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—374no—
263C22—2968no—
264C22—742no—
265C22—742no—
266C22—1482no—
267C22—1482no—
268C22—1482no—
269C22C2×D4×D3711yescharacteristic
270C4—21no—
271C4—41no—
272C4—41no—
273C4—742no—
274C4—1482no—
275C4D8×D3712yes—
276C4C2×#1059696211yescharacteristic
277C4#1192458211yescharacteristic
278C2—42no—
279C2—81no—
280C2—2962no—
281C2—744no—
282C2#1455817911yescharacteristic
283C2C2×D8×D3711yescharacteristic
284C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC4×D8×C37C2
socleC22×C37C22×D4
hypercenterC4×D8D37
hypocenterC37#3294
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #14558188C2semidirect
2. D4×D148C2semidirect
3. #14557880C2semidirect
4. #14557848C2semidirect
5. #14557813C2semidirect
6. #14557768C2semidirect
7. #14557728C2semidirect
8. #14557665C2semidirect
9. C8×D148C2semidirect
10. #102×D37C2semidirect
11. C4×D8×C37C2semidirect
15. C2×#10596939C22semidirect
16. C2×C8×D37C22semidirect
17. #11924536C22semidirect
23. #11924507C22semidirect
26. C4⋊C4×D37C22semidirect
27. #11924469C22semidirect
28. C4⋊#64436C22semidirect
29. #11924458C22semidirect
30. #11924458C22semidirect
32. #11924456C22semidirect
33. #11924448C22semidirect
36. C4×D4×C37C22semidirect
37. #107×C37C22semidirect
39. #102×C37C22semidirect
40. C4×C8×C37C22semidirect
88. D4×C37#41semidirect
105. D148D8semidirect
151. C4×D8D37semidirect
154. C37#3294semidirect
171. C4×D4C2×D37semidirect
174. #107C2×D37semidirect
181. #102C2×D37semidirect
183. C4×C8C2×D37semidirect
240. D4#10596962semidirect

Maximal subgroups

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

subgroupindex
#145581882
D4×D1482
#145578802
#145578482
#145578132
#145577682
#145577282
#145576652
C8×D1482
#102×D372
C4×D8×C372
#329437