Finite Group Databasebeta

← #18006412

Subgroups — #18006412

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#14558188C211yesmaximal, characteristic, complemented
2#14558168C211yesmaximal, characteristic, complemented
3#14557879C211yesmaximal, characteristic, complemented
4#14557845C212yesmaximal, complemented
5#14557814C211yesmaximal, characteristic, complemented
6#14557766C212yesmaximal, complemented
7#14557665C212yesmaximal, complemented
8C4×#10596939C211yesmaximal, characteristic, complemented
9#14557598C211yesmaximal, characteristic, complemented
10#102×D37C212yesmaximal, complemented
11C37×#459C211yesmaximal, characteristic, complemented
12C2×#10596962—21no—
13C2×D4×D37—21no—
14C2×D4×D37C2212yes—
15C2×#10596939C2211yescharacteristic
16C2×C8×D37C2212yescomplemented
17#11924536C2211yescharacteristic, complemented
18#11924518—22no—
19#11924515—21no—
20#11924507—21no—
21#11924507C2212yes—
22#11924507C2212yescomplemented
23#11924504—22no—
24C4×D148C2211yescharacteristic
25C4×D148C2211yescharacteristic
26C4⋊C4×D37C2212yescomplemented
27#11924470C2212yescomplemented
28#11924469C2211yescharacteristic, complemented
29#11924458C2212yes—
30#11924457C2211yescharacteristic, complemented
31#11924457C2212yescomplemented
32#11924457C2212yescomplemented
33#11924456C2211yescharacteristic
34#11924448C2212yescomplemented
35C4×#64436C2211yescharacteristic, complemented
36C2×D8×C37C2212yescomplemented
37#127×C37C2211yescharacteristic
38C4×D4×C37C2211yescharacteristic, complemented
39C4⋊C8×C37C2211yescharacteristic, complemented
40#102×C37C2212yescomplemented
41C23×D37—22no—
42C2×D4×C37—21no—
43C2×D4×C37—21no—
44C2×D4×C37C2312yes—
45C2×D4×C37C2311yescharacteristic
46C22×C4×C37—21no—
47C2×C22⋊D37—22no—
48C2×C22⋊D37—22no—
49C2×C22⋊D37—22no—
50D4×D37—24no—
51D4×D37—42no—
52D4×D37—44no—
53#10596962—44no—
54C2×D148D411yescharacteristic
55C2×D148C2311yescharacteristic
56C2×C4×D37—22no—
57C2×C4×D37—21no—
58C2×C4×D37C2312yes—
59C2×Dic74—21no—
60D8×C37—42no—
61C2×C8×C37C2312yes—
62C4⋊C4×C37C2311yescharacteristic
63C22⋊C4×C37—21no—
64C42×C37C2311yescharacteristic
65C22⋊Dic37—22no—
66C22⋊Dic37—22no—
67#10596939—22no—
68#10596938—21no—
69#10596938D412yes—
70C4⋊Dic37—21no—
71C4⋊Dic37D411yescharacteristic
72C4⋊Dic37C2312yes—
73C4⋊Dic37C2311yescharacteristic
74#10596936—22no—
75C2×#64436C2311yescharacteristic
76C2×#64436C2311yescharacteristic
77C8×D37—42no—
78C23×C37—21no—
79C23×C37—22no—
80C22×D37—21no—
81C22×D37—44no—
82C22×D37—44no—
83C22×D37—82no—
84C22×D37C2×D412yes—
85D4×C37—21no—
86D4×C37—22no—
87D4×C37—21no—
88D4×C37—22no—
89D4×C37—42no—
90D4×C37—81no—
91C2×C4×C37—21no—
92C2×C4×C37—42no—
93C2×C4×C37C2×D411yescharacteristic
94C2×C4×C37C2×D411yescharacteristic
95C2×C4×C37C2411yescharacteristic
96C22⋊D37—44no—
97C22⋊D37—44no—
98C22⋊D37—44no—
99C2×Dic37—22no—
100C2×Dic37—21no—
101C2×Dic37C2×D412yes—
102D148—21no—
103D148D814yescomplemented
104D148#4112yescomplemented
105C4×D37—22no—
106C4×D37—22no—
107C4×D37—44no—
108C4×D37—42no—
109Dic74—42no—
110C8×C37—22no—
111#64436—21no—
112#64436—21no—
113C22×C37—42no—
114C22×C37—41no—
115C22×C37—41no—
116C22×C37—42no—
117C22×C37—42no—
118C22×C37—41no—
119C22×C37C22×D411yescharacteristic
120C2×D37—22no—
121C2×D37—22no—
122C2×D37—22no—
123C2×D37—41no—
124C2×D37—41no—
125C2×D37—88no—
126C2×D37C2×D814yes—
127C4×C37—21no—
128C4×C37—41no—
129C4×C37C2×D812yes—
130C4×C37C2×#4111yescharacteristic
131C4×C37H(5,𝔽2)11yescharacteristic
132Dic37—22no—
133Dic37—42no—
134Dic37—41no—
135#3294—371nomaximal, Sylow
136C2×C37—82no—
137C2×C37—81no—
138C2×C37#54611yescharacteristic
139C2×C37C22×D811yescharacteristic
140C2×C37#57711yescharacteristic
141D37—24no—
142D37—42no—
143#547—371no—
144D42—371no—
145#486—371no—
146#480—372no—
147#474—371no—
148#466—372no—
149#459D3711yescharacteristic, complemented
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—371no—
159C2×D8C2×D3712yescomplemented
160C22×C8—372no—
161C4⋊Q8—371no—
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×D4C2×D3711yescharacteristic, complemented
172C2×C4⋊C4—372no—
173#107—372no—
174#107—371no—
175C4⋊C8C2×D3711yescharacteristic, complemented
176#102—372no—
177#102—371no—
178#102—372no—
179#102—372no—
180#102—371no—
181#102C2×D3712yescomplemented
182C22⋊C8—372no—
183C4×C8—371no—
184C24—742no—
185#41—1484no—
186C2×Q8—741no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—371no—
190C2×D4—371no—
191C2×D4—742no—
192C2×D4—744no—
193C2×D4—742no—
194C2×D4—742no—
195C2×D4—1482no—
196C2×D4—1484no—
197C2×D4C22×D3712yes—
198C2×D4C22×D3711yescharacteristic
199C22×C4—21no—
200C22×C4—372no—
201C22×C4—742no—
202C22×C4—741no—
203D8—42no—
204D8—742no—
205C2×C8—371no—
206C2×C8—371no—
207C2×C8—1482no—
208C2×C8C22×D3712yes—
209C4⋊C4—371no—
210C4⋊C4—372no—
211C4⋊C4—371no—
212C4⋊C4—742no—
213C4⋊C4—741no—
214C4⋊C4C22×D3711yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—372no—
217C22⋊C4—742no—
218C22⋊C4—742no—
219C22⋊C4—741no—
220C42C22×D3711yescharacteristic
221C23—21no—
222C23—22no—
223C23—372no—
224C23—2962no—
225C23—741no—
226C23—1484no—
227C23—1484no—
228Q8—1482no—
229D4—21no—
230D4—22no—
231D4—21no—
232D4—22no—
233D4—42no—
234D4—81no—
235D4—374no—
236D4—372no—
237D4—741no—
238D4—1484no—
239D4—1484no—
240D4—1484no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—372no—
244C2×C4—742no—
245C2×C4—742no—
246C2×C4—741no—
247C2×C4—742no—
248C2×C4—1484no—
249C2×C4—1482no—
250C2×C4D4×D3711yescharacteristic
251C2×C4D4×D3711yescharacteristic
252C2×C4C23×D3711yescharacteristic
253C8—22no—
254C8—741no—
255C8—741no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—41no—
262C22—374no—
263C22—2968no—
264C22—742no—
265C22—742no—
266C22—742no—
267C22—1481no—
268C22—1481no—
269C22C2×D4×D3711yescharacteristic
270C4—21no—
271C4—41no—
272C4—742no—
273C4—1481no—
274C4—1482no—
275C4D8×D3712yes—
276C4#41×D3711yescharacteristic
277C4#1192458111yescharacteristic
278C2—82no—
279C2—81no—
280C2—744no—
281C2—1482no—
282C2#1455818011yescharacteristic
283C2C2×D8×D3711yescharacteristic
284C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#459C2
socleC22×C37C22×D4
hypercenter#459D37
hypocenterC37#3294
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14558188C2semidirect
2. #14558168C2semidirect
3. #14557879C2semidirect
4. #14557845C2semidirect
5. #14557814C2semidirect
6. #14557766C2semidirect
7. #14557665C2semidirect
8. C4×#10596939C2semidirect
9. #14557598C2semidirect
10. #102×D37C2semidirect
11. C37×#459C2semidirect
16. C2×C8×D37C22semidirect
17. #11924536C22semidirect
22. #11924507C22semidirect
26. C4⋊C4×D37C22semidirect
27. #11924470C22semidirect
28. #11924469C22semidirect
30. #11924457C22semidirect
31. #11924457C22semidirect
32. #11924457C22semidirect
34. #11924448C22semidirect
35. C4×#64436C22semidirect
36. C2×D8×C37C22semidirect
38. C4×D4×C37C22semidirect
39. C4⋊C8×C37C22semidirect
40. #102×C37C22semidirect
103. D148D8semidirect
104. D148#41semidirect
149. #459D37semidirect
154. C37#3294semidirect
159. C2×D8C2×D37semidirect
171. C4×D4C2×D37semidirect
175. C4⋊C8C2×D37semidirect
181. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581882
#145581682
#145578792
#145578452
#145578142
#145577662
#145576652
C4×#105969392
#145575982
#102×D372
C37×#4592
#329437