Finite Group Databasebeta

← #18004388

Subgroups — #18004388

Order 4736.

440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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#14558088C211yesmaximal, characteristic, complemented
2C4×D4×D37C211yesmaximal, characteristic
3#14557836C212yesmaximal, complemented
4#14557835C212yesmaximal, complemented
5#14557824C211yesmaximal, characteristic, complemented
6#14557823C211yesmaximal, characteristic, complemented
7#14557810C211yesmaximal, characteristic, complemented
8#14557574C212yesmaximal, complemented
9#14557555C211yesmaximal, characteristic, complemented
10#14557536C212yesmaximal
11C37×#474C211yesmaximal, characteristic, complemented
12C2×D4×D37C2211yescharacteristic
13C22×C4×D37—21no—
14C2×#10596929C2212yes—
15#11924536C2211yescharacteristic, complemented
16#11924527C2212yescomplemented
17#11924516—21no—
18#11924512—21no—
19Q8×Dic37—21no—
20#11924501—21no—
21C4×D148C2211yescharacteristic
22D4×Dic37C2211yescharacteristic
23#11924498C2211yescharacteristic
24C4×C22⋊D37—21no—
25#11924496—21no—
26#11924494C2212yes—
27C4⋊C4×D37C2211yescharacteristic
28C22⋊C4×D37—21no—
29C42×D37C2211yescharacteristic
30#11924469C2212yescomplemented
31#11924468C2212yescomplemented
32#11924467C2212yescomplemented
33C4⋊#64436C2211yescharacteristic, complemented
34#11924465C2212yescomplemented
35#11924458C2212yes—
36#11924457C2212yes—
37#11924456C2212yes—
38C4⋊Q8×C37C2211yescharacteristic, complemented
39C4×D4×C37C2211yescharacteristic
40#107×C37C2212yescomplemented
41C4⋊C8×C37C2211yescharacteristic, complemented
42#102×C37C2212yes—
43C23×D37—21no—
44C2×Q8×C37—21no—
45C2×D4×C37C2311yescharacteristic
46C22×C4×C37—21no—
47C2×C22⋊D37—21no—
48C22×Dic37—21no—
49D4×D37—22no—
50D4×D37Q814yescomplemented
51C2×D148C2311yescharacteristic
52C2×C4×D37—21no—
53C2×C4×D37—21no—
54C2×C4×D37—21no—
55C2×C4×D37—44no—
56C2×C4×D37D411yescharacteristic
57C2×C4×D37D411yescharacteristic
58C2×C4×D37C2311yescharacteristic
59C2×Dic74—21no—
60C2×C8×C37C2312yes—
61C4⋊C4×C37—21no—
62C4⋊C4×C37C2311yescharacteristic
63C4⋊C4×C37C2312yes—
64C22⋊C4×C37—21no—
65C42×C37C2311yescharacteristic
66C22⋊Dic37—21no—
67#10596938—22no—
68#10596938—21no—
69#10596938—21no—
70C4⋊Dic37—21no—
71C4⋊Dic37—22no—
72C4⋊Dic37C2311yescharacteristic
73C4⋊Dic37C2312yes—
74#10596936—21no—
75#10596936—22no—
76C4×Dic37—22no—
77C4×Dic37D411yescharacteristic
78C4×Dic37D411yescharacteristic
79C4×Dic37C2311yescharacteristic
80C2×#64436C2312yes—
81#10596929—24no—
82C23×C37—21no—
83C22×D37—21no—
84C22×D37—24no—
85C22×D37—42no—
86C22×D37—42no—
87C22×D37C2×D411yescharacteristic
88Q8×C37—42no—
89D4×C37—21no—
90D4×C37C2×Q812yes—
91C2×C4×C37—22no—
92C2×C4×C37—21no—
93C2×C4×C37—42no—
94C2×C4×C37C2×D411yescharacteristic
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37C2411yescharacteristic
97C22⋊D37—24no—
98C2×Dic37—22no—
99C2×Dic37—21no—
100C2×Dic37—42no—
101C2×Dic37C2×D411yescharacteristic
102C2×Dic37C2×D411yescharacteristic
103C2×Dic37C2×D411yescharacteristic
104D148—21no—
105D148C2×Q812yes—
106C4×D37—22no—
107C4×D37—41no—
108C4×D37—42no—
109C4×D37—42no—
110C4×D37—42no—
111C4×D37C2×Q812yes—
112C4×D37#4112yes—
113Dic74—42no—
114C8×C37—22no—
115#64436—22no—
116C22×C37—22no—
117C22×C37—41no—
118C22×C37—41no—
119C22×C37C22×D411yescharacteristic
120C2×D37—21no—
121C2×D37—21no—
122C2×D37—22no—
123C2×D37—48no—
124C2×D37—41no—
125C2×D37—41no—
126C2×D37C22⋊Q812yes—
127C4×C37—21no—
128C4×C37—41no—
129C4×C37—42no—
130C4×C37AGL(1,ℤ/8)12yes—
131C4×C37C22×Q811yescharacteristic
132C4×C37C2×#4111yescharacteristic
133Dic37—21no—
134Dic37—21no—
135Dic37—41no—
136Dic37—42no—
137Dic37C22⋊Q812yes—
138#3077—371nomaximal, Sylow
139C2×C37—42no—
140C2×C37C2×C22⋊Q811yescharacteristic
141C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
142C2×C37#57511yescharacteristic
143D37—22no—
144D37—42no—
145#533—371no—
146C2×C4×D4—371no—
147#478—372no—
148#478—372no—
149#476—371no—
150#476—371no—
151#474—371no—
152#474D3711yescharacteristic, complemented
153#428—372no—
154#423—371no—
155#418—372no—
156C37#307711yescharacteristic, complemented, Sylow
157C22×D4—371no—
158C23×C4—741no—
159C2×M16—372no—
160C4⋊Q8—371no—
161C4⋊Q8C2×D3711yescharacteristic, complemented
162#125—372no—
163C22⋊Q8—741no—
164C22⋊Q8—741no—
165C4×Q8—741no—
166C4×Q8—741no—
167C4×D4—371no—
168C4×D4—371no—
169C4×D4—371no—
170C4×D4—741no—
171C4×D4—741no—
172C4×D4C2×D3711yescharacteristic
173#117—372no—
174C2×C4⋊C4—371no—
175C2×C22⋊C4—741no—
176C2×C42—371no—
177#107—372no—
178#107C2×D3712yescomplemented
179#106—372no—
180#106—372no—
181C4⋊C8—372no—
182C4⋊C8—371no—
183C4⋊C8C2×D3711yescharacteristic, complemented
184#102—372no—
185#102—372no—
186#102—372no—
187#102C2×D3712yes—
188C24—741no—
189C2×Q8—21no—
190C2×Q8—741no—
191C2×D4—374no—
192C2×D4—371no—
193C2×D4—742no—
194C2×D4—741no—
195C2×D4C22×D3711yescharacteristic
196C22×C4—21no—
197C22×C4—371no—
198C22×C4—371no—
199C22×C4—371no—
200C22×C4—741no—
201C22×C4—741no—
202C22×C4—741no—
203C22×C4—741no—
204C22×C4—1484no—
205M16—744no—
206C2×C8—372no—
207C2×C8C22×D3712yes—
208C4⋊C4—21no—
209C4⋊C4—372no—
210C4⋊C4—371no—
211C4⋊C4—741no—
212C4⋊C4—742no—
213C4⋊C4—742no—
214C4⋊C4—741no—
215C4⋊C4C22×D3712yes—
216C4⋊C4C22×D3711yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—741no—
219C22⋊C4—742no—
220C22⋊C4—741no—
221C22⋊C4—741no—
222C42—371no—
223C42—371no—
224C42—371no—
225C42—742no—
226C42C22×D3711yescharacteristic
227C23—21no—
228C23—371no—
229C23—744no—
230C23—741no—
231C23—1482no—
232C23—1482no—
233Q8—42no—
234Q8—1482no—
235D4—21no—
236D4—372no—
237D4—744no—
238D4—741no—
239D4Q8×D3712yes—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—371no—
244C2×C4—372no—
245C2×C4—372no—
246C2×C4—371no—
247C2×C4—371no—
248C2×C4—742no—
249C2×C4—742no—
250C2×C4—741no—
251C2×C4—1481no—
252C2×C4—1482no—
253C2×C4—1482no—
254C2×C4—1482no—
255C2×C4—1482no—
256C2×C4D4×D3711yescharacteristic
257C2×C4D4×D3711yescharacteristic
258C2×C4C23×D3711yescharacteristic
259C8—22no—
260C8—742no—
261C22—22no—
262C22—41no—
263C22—41no—
264C22—372no—
265C22—741no—
266C22—741no—
267C22—742no—
268C22—1488no—
269C22—1481no—
270C22—1481no—
271C22C2×D4×D3711yescharacteristic
272C4—21no—
273C4—41no—
274C4—42no—
275C4—372no—
276C4—741no—
277C4—741no—
278C4—1481no—
279C4—1482no—
280C4#1192456012yes—
281C4C2×Q8×D3711yescharacteristic
282C4#41×D3711yescharacteristic
283C2—42no—
284C2—742no—
285C2—1482no—
286C2C22⋊Q8×D3711yescharacteristic
287C2C2×#1192456011yescharacteristic
288C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#474C2
socleC22×C37C22×D4
prime radicalC2×D4×D37C22
hypercenter#474D37
hypocenterC37#3077
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #14558088C2semidirect
3. #14557836C2semidirect
4. #14557835C2semidirect
5. #14557824C2semidirect
6. #14557823C2semidirect
7. #14557810C2semidirect
8. #14557574C2semidirect
9. #14557555C2semidirect
11. C37×#474C2semidirect
15. #11924536C22semidirect
16. #11924527C22semidirect
30. #11924469C22semidirect
31. #11924468C22semidirect
32. #11924467C22semidirect
33. C4⋊#64436C22semidirect
34. #11924465C22semidirect
38. C4⋊Q8×C37C22semidirect
40. #107×C37C22semidirect
41. C4⋊C8×C37C22semidirect
50. D4×D37Q8semidirect
152. #474D37semidirect
156. C37#3077semidirect
161. C4⋊Q8C2×D37semidirect
178. #107C2×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
#145580882
C4×D4×D372
#145578362
#145578352
#145578242
#145578232
#145578102
#145575742
#145575552
#145575362
C37×#4742
#307737