Finite Group Databasebeta

← #18004242

Subgroups — #18004242

Order 4736.

524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×D8×D37C211yesmaximal, characteristic, complemented
2C2×#11924544C211yesmaximal, characteristic, complemented
3#14558099C212yesmaximal, complemented
4#14557787C211yesmaximal, characteristic, complemented
5#14557786C211yesmaximal, characteristic, complemented
6#14557783C211yesmaximal, characteristic, complemented
7#14557768C212yesmaximal, complemented
8#14557767C212yesmaximal, complemented
9#14557568C211yesmaximal, characteristic, complemented
10#14557536C212yesmaximal, complemented
11C37×#469C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C2×D4×D37C2212yes—
14C2×D296C2211yescharacteristic
15C2×#10596939C2212yes—
16D8×D37—24no—
17#11924544—24no—
18C2×#10596929C2211yescharacteristic
19C2×#10596929C2211yescharacteristic, complemented
20C22×#64436C2211yescharacteristic, complemented
21C2×C8×D37C2211yescharacteristic
22C2×C8×D37C2211yescharacteristic, complemented
23#11924532—22no—
24#11924522—22no—
25#11924511C2212yescomplemented
26#11924510C2212yescomplemented
27#11924507C2212yescomplemented
28#11924506—22no—
29#11924504—22no—
30#11924494C2212yes—
31#11924469C2212yescomplemented
32#11924468C2211yescharacteristic, complemented
33#11924458C2212yescomplemented
34#11924457C2212yescomplemented
35#11924456C2212yescomplemented
36C2×D8×C37C2211yescharacteristic
37C2×M16×C37C2211yescharacteristic, complemented
38#121×C37C2212yescomplemented
39#106×C37C2211yescharacteristic, complemented
40#102×C37C2212yescomplemented
41C23×D37—22no—
42C2×D4×C37—22no—
43C2×D4×C37C2312yes—
44C22×C4×C37C2311yescharacteristic
45C2×C22⋊D37—22no—
46C2×C22⋊D37—22no—
47C2×C22⋊D37—22no—
48C2×C22⋊D37D411yescharacteristic
49C2×C22⋊D37D411yescharacteristic
50D4×D37—24no—
51D4×D37—24no—
52#10596962—22no—
53#10596962—22no—
54C2×D148—22no—
55C2×D148D411yescharacteristic
56C2×D148C2312yes—
57C2×C4×D37C2311yescharacteristic
58C2×C4×D37C2311yescharacteristic
59C2×Dic74D411yescharacteristic
60D8×C37—22no—
61M16×C37—22no—
62C2×C8×C37C2311yescharacteristic
63C2×C8×C37C2311yescharacteristic
64C4⋊C4×C37C2312yes—
65C22⋊C4×C37—22no—
66C22⋊Dic37—22no—
67#10596939—24no—
68#10596938—22no—
69#10596938—22no—
70#10596938—22no—
71C4⋊Dic37C2312yes—
72C4×Dic37—22no—
73C2×#64436—22no—
74C2×#64436C2311yescharacteristic
75C2×#64436C2311yescharacteristic
76D296—22no—
77#10596929—22no—
78#10596929—22no—
79C8×D37—22no—
80C8×D37D414yescomplemented
81C23×C37—22no—
82C23×C37C2×D411yescharacteristic
83C22×D37—22no—
84C22×D37—44no—
85C22×D37—82no—
86C22×D37—82no—
87C22×D37C2×D411yescharacteristic
88C22×D37C2×D411yescharacteristic
89D4×C37—22no—
90D4×C37—22no—
91D4×C37—82no—
92C2×C4×C37—21no—
93C2×C4×C37—21no—
94C2×C4×C37—22no—
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37C2411yescharacteristic
97C22⋊D37—22no—
98C22⋊D37—22no—
99C22⋊D37—44no—
100C22⋊D37—82no—
101C22⋊D37—82no—
102C2×Dic37—22no—
103C2×Dic37C2×D411yescharacteristic
104C2×Dic37C2×D411yescharacteristic
105D148—22no—
106D148—22no—
107D148—22no—
108D148—82no—
109C4×D37—21no—
110C4×D37—21no—
111C4×D37C2×D412yes—
112C4×D37#4112yes—
113Dic74—22no—
114C8×C37—21no—
115C8×C37C2×D412yes—
116#64436—21no—
117#64436C2×D412yes—
118C22×C37—21no—
119C22×C37—22no—
120C22×C37—42no—
121C22×C37—42no—
122C22×C37—42no—
123C22×C37C22×D411yescharacteristic
124C2×D37—22no—
125C2×D37—21no—
126C2×D37—22no—
127C2×D37—42no—
128C2×D37—42no—
129C2×D37—42no—
130C2×D37—88no—
131C2×D37#12112yes—
132C4×C37—21no—
133C4×C37—42no—
134C4×C37C22×D411yescharacteristic
135C4×C37C2×#4111yescharacteristic
136Dic37—21no—
137Dic37—42no—
138Dic37#12112yes—
139#3058—371nomaximal, Sylow
140C2×C37—41no—
141C2×C37—82no—
142C2×C37C2×#12111yescharacteristic
143C2×C37#57612yes—
144D37—22no—
145D37—41no—
146D37—82no—
147C22×D8—371no—
148C2×#131—371no—
149#535—372no—
150#469—371no—
151#469—371no—
152#469—371no—
153#469D3711yescharacteristic, complemented
154#466—372no—
155#466—372no—
156#427—371no—
157#418—372no—
158C37#305811yescharacteristic, complemented, Sylow
159C2×#41—371no—
160C22×D4—372no—
161C2×D8—372no—
162C2×D8—371no—
163C2×D8—744no—
164C2×D8C2×D3711yescharacteristic
165#131—744no—
166C2×M16—371no—
167C2×M16—371no—
168C2×M16C2×D3711yescharacteristic, complemented
169C22×C8—371no—
170C22×C8—371no—
171C22×C8—371no—
172#127—742no—
173#124—742no—
174#121—372no—
175#121—372no—
176#121—372no—
177#121C2×D3712yescomplemented
178#120—742no—
179#120—742no—
180#117—372no—
181#107—372no—
182#106—371no—
183#106C2×D3711yescharacteristic, complemented
184#102—372no—
185#102—372no—
186#102—372no—
187#102C2×D3712yescomplemented
188C24—742no—
189#41—742no—
190#41—742no—
191C2×Q8—371no—
192C2×D4—22no—
193C2×D4—371no—
194C2×D4—371no—
195C2×D4—371no—
196C2×D4—372no—
197C2×D4—742no—
198C2×D4—744no—
199C2×D4—744no—
200C2×D4—742no—
201C2×D4—742no—
202C2×D4—742no—
203C2×D4C22×D3712yes—
204C22×C4—371no—
205C22×C4—371no—
206C22×C4C22×D3711yescharacteristic
207D8—22no—
208D8—744no—
209D8—742no—
210M16—22no—
211M16—742no—
212M16—742no—
213C2×C8—371no—
214C2×C8—374no—
215C2×C8—371no—
216C2×C8—742no—
217C2×C8—742no—
218C2×C8C22×D3711yescharacteristic
219C2×C8C22×D3711yescharacteristic
220C4⋊C4—372no—
221C4⋊C4C22×D3712yes—
222C22⋊C4—22no—
223C22⋊C4—742no—
224C22⋊C4—742no—
225C22⋊C4—742no—
226C22⋊C4—742no—
227C42—742no—
228C23—22no—
229C23—371no—
230C23—371no—
231C23—2962no—
232C23—2962no—
233C23—742no—
234C23—1484no—
235C23D4×D3711yescharacteristic
236Q8—742no—
237D4—22no—
238D4—22no—
239D4—82no—
240D4—2962no—
241D4—2962no—
242D4—2962no—
243D4—742no—
244D4—742no—
245D4—742no—
246D4—742no—
247D4—742no—
248D4—1484no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—371no—
253C2×C4—372no—
254C2×C4—372no—
255C2×C4—371no—
256C2×C4—741no—
257C2×C4—741no—
258C2×C4—742no—
259C2×C4D4×D3711yescharacteristic
260C2×C4C23×D3711yescharacteristic
261C8—21no—
262C8—372no—
263C8—741no—
264C8D4×D3712yes—
265C22—21no—
266C22—22no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—372no—
271C22—2968no—
272C22—742no—
273C22—741no—
274C22—742no—
275C22—1482no—
276C22—1482no—
277C22—1482no—
278C22C2×D4×D3711yescharacteristic
279C4—21no—
280C4—42no—
281C4—372no—
282C4—741no—
283C4—1482no—
284C4C2×D4×D3711yescharacteristic
285C4#41×D3711yescharacteristic
286C2—41no—
287C2—82no—
288C2—2962no—
289C2—742no—
290C2—1481no—
291C2#121×D3711yescharacteristic
292C2#1455833712yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#469C2
socleC22×C37C22×D4
hypercenter#469D37
hypocenterC37#3058
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D37C2semidirect
2. C2×#11924544C2semidirect
3. #14558099C2semidirect
4. #14557787C2semidirect
5. #14557786C2semidirect
6. #14557783C2semidirect
7. #14557768C2semidirect
8. #14557767C2semidirect
9. #14557568C2semidirect
10. #14557536C2semidirect
11. C37×#469C2semidirect
19. C2×#10596929C22semidirect
20. C22×#64436C22semidirect
22. C2×C8×D37C22semidirect
25. #11924511C22semidirect
26. #11924510C22semidirect
27. #11924507C22semidirect
31. #11924469C22semidirect
32. #11924468C22semidirect
33. #11924458C22semidirect
34. #11924457C22semidirect
35. #11924456C22semidirect
37. C2×M16×C37C22semidirect
38. #121×C37C22semidirect
39. #106×C37C22semidirect
40. #102×C37C22semidirect
80. C8×D37D4semidirect
153. #469D37semidirect
158. C37#3058semidirect
168. C2×M16C2×D37semidirect
177. #121C2×D37semidirect
183. #106C2×D37semidirect
187. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D372
C2×#119245442
#145580992
#145577872
#145577862
#145577832
#145577682
#145577672
#145575682
#145575362
C37×#4692
#305837