Finite Group Databasebeta

← #18004520

Subgroups — #18004520

Order 4736.

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

normal subgroups only

This group has 458 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#14558046C211yesmaximal, characteristic
2C2×C4⋊C4×D37C211yesmaximal, characteristic, complemented
3#14557867C212yesmaximal, complemented
4#14557861C211yesmaximal, characteristic, complemented
5#14557853C212yesmaximal, complemented
6#14557847C211yesmaximal, characteristic, complemented
7#14557846C211yesmaximal, characteristic, complemented
8#14557572C212yesmaximal, complemented
9#14557533C212yesmaximal, complemented
10#14557495C211yesmaximal, characteristic, complemented
11C37×#483C211yesmaximal, characteristic, complemented
12C2×#10596966C2211yescharacteristic
13C22×C4×D37—21no—
14C22×C4×D37C2211yescharacteristic
15C2×#10596929C2212yes—
16#11924521—21no—
17#11924512C2211yescharacteristic
18#11924511C2211yescharacteristic
19#11924510C2211yescharacteristic
20#11924506—21no—
21#11924498—21no—
22#11924496—21no—
23#11924494C2211yescharacteristic
24C2×C4⋊Dic37C2211yescharacteristic
25C2×#10596936—21no—
26C4⋊C4×D37—21no—
27C4⋊C4×D37—21no—
28C4⋊C4×D37C2212yes—
29C4⋊C4×D37C2212yes—
30#11924470C2212yescomplemented
31#11924469C2212yescomplemented
32#11924467C2212yescomplemented
33#11924460C2212yescomplemented
34#11924458C2212yescomplemented
35#11924456C2212yescomplemented
36C22⋊#64436C2211yescharacteristic
37#11924448C2212yes—
38C22⋊Q8×C37C2211yescharacteristic
39C2×C4⋊C4×C37C2211yescharacteristic
40#106×C37C2212yescomplemented
41#103×C37C2212yescomplemented
42C22⋊C8×C37C2211yescharacteristic
43C23×D37D411yescharacteristic
44C2×Q8×C37C2311yescharacteristic
45C22×C4×C37—21no—
46C22×C4×C37C2311yescharacteristic
47C2×C22⋊D37—21no—
48C22×Dic37—21no—
49C22×Dic37D411yescharacteristic
50#10596966—24no—
51C2×D148—21no—
52C2×D148—21no—
53C2×D148C2311yescharacteristic
54C2×C4×D37—24no—
55C2×C4×D37—22no—
56C2×C4×D37—22no—
57C2×C4×D37—21no—
58C2×C4×D37—44no—
59C2×C4×D37D411yescharacteristic
60C2×C4×D37D411yescharacteristic
61C2×C4×D37C2311yescharacteristic
62C2×C4×D37C2311yescharacteristic
63C2×C8×C37C2312yes—
64C4⋊C4×C37—21no—
65C4⋊C4×C37—21no—
66C4⋊C4×C37C2312yes—
67C4⋊C4×C37C2311yescharacteristic
68C22⋊C4×C37—21no—
69#10596938—21no—
70#10596938—21no—
71#10596938—21no—
72#10596938—21no—
73C4⋊Dic37—21no—
74C4⋊Dic37C2312yes—
75C4⋊Dic37C2311yescharacteristic
76#10596936—22no—
77#10596936—22no—
78#10596936—21no—
79C4×Dic37—21no—
80C2×#64436C2312yes—
81#10596929—24no—
82C23×C37C2×D411yescharacteristic
83C22×D37—22no—
84C22×D37—22no—
85C22×D37—22no—
86C22×D37—21no—
87C22×D37C2×D411yescharacteristic
88C22×D37C2×D411yescharacteristic
89Q8×C37—22no—
90C2×C4×C37—22no—
91C2×C4×C37—21no—
92C2×C4×C37—22no—
93C2×C4×C37—21no—
94C2×C4×C37—42no—
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37C2411yescharacteristic
97C22⋊D37—42no—
98C2×Dic37—22no—
99C2×Dic37—21no—
100C2×Dic37—22no—
101C2×Dic37—42no—
102C2×Dic37C2×D411yescharacteristic
103C2×Dic37C2×D411yescharacteristic
104D148—22no—
105D148—42no—
106D148—42no—
107C4×D37—22no—
108C4×D37—22no—
109C4×D37—22no—
110C4×D37—44no—
111C4×D37—44no—
112C4×D37—42no—
113C4×D37#4114yes—
114C8×C37—22no—
115#64436—22no—
116C22×C37—21no—
117C22×C37—21no—
118C22×C37AGL(1,ℤ/8)12yes—
119C22×C37C22×D411yescharacteristic
120C2×D37—28no—
121C2×D37—21no—
122C2×D37—21no—
123C2×D37—21no—
124C2×D37—21no—
125C2×D37—41no—
126C2×D37—41no—
127C2×D37—41no—
128C2×D37#12312yes—
129C2×D37#13712yes—
130C4×C37—21no—
131C4×C37—41no—
132C4×C37—42no—
133C4×C37—41no—
134C4×C37C2×#4112yes—
135Dic37—21no—
136Dic37—42no—
137Dic37—41no—
138Dic37#12312yes—
139#3092—371nomaximal, Sylow
140C2×C37—22no—
141C2×C37C2×#12311yescharacteristic
142C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
143C2×C37C2×#13711yescharacteristic
144D37—22no—
145D37—22no—
146D37—81no—
147#525—371no—
148C22×C4⋊C4—371no—
149#484—372no—
150#483—371no—
151#483D3711yescharacteristic, complemented
152#481—372no—
153#480—371no—
154#480—371no—
155#428—372no—
156#417—372no—
157#407—371no—
158C37#309211yescharacteristic, complemented, Sylow
159C2×#41—371no—
160C23×C4—371no—
161C23×C4—741no—
162C2×M16—372no—
163#123—741no—
164C22⋊Q8—371no—
165C22⋊Q8C2×D3711yescharacteristic
166#121—371no—
167#121—371no—
168#120—741no—
169C4×D4—741no—
170C4×D4—741no—
171#117—371no—
172C2×C4⋊C4—371no—
173C2×C4⋊C4—372no—
174C2×C4⋊C4—372no—
175C2×C4⋊C4—741no—
176C2×C4⋊C4—741no—
177C2×C4⋊C4—741no—
178C2×C4⋊C4C2×D3711yescharacteristic
179#107—372no—
180#107—372no—
181#106—372no—
182#106C2×D3712yescomplemented
183#103—372no—
184#103C2×D3712yescomplemented
185#102—372no—
186#102—372no—
187C22⋊C8—371no—
188C22⋊C8—372no—
189C22⋊C8C2×D3711yescharacteristic
190C24—371no—
191#41—744no—
192C2×Q8C22×D3711yescharacteristic
193C2×D4—371no—
194C2×D4—741no—
195C2×D4—741no—
196C2×D4—741no—
197C22×C4—21no—
198C22×C4—371no—
199C22×C4—371no—
200C22×C4—371no—
201C22×C4—371no—
202C22×C4—371no—
203C22×C4—744no—
204C22×C4—741no—
205C22×C4—742no—
206C22×C4—742no—
207C22×C4—741no—
208C22×C4—1484no—
209C22×C4C22×D3711yescharacteristic
210M16—744no—
211C2×C8—372no—
212C2×C8C22×D3712yes—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—372no—
216C4⋊C4—371no—
217C4⋊C4—742no—
218C4⋊C4—742no—
219C4⋊C4—741no—
220C4⋊C4—741no—
221C4⋊C4C22×D3712yes—
222C4⋊C4C22×D3711yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—741no—
225C22⋊C4—741no—
226C22⋊C4—741no—
227C22⋊C4—741no—
228C42—741no—
229C23—371no—
230C23—371no—
231C23—742no—
232C23—742no—
233C23—742no—
234C23—741no—
235C23D4×D3711yescharacteristic
236Q8—22no—
237D4—742no—
238D4—1482no—
239D4—1482no—
240D4—1482no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—42no—
246C2×C4—371no—
247C2×C4—374no—
248C2×C4—371no—
249C2×C4—742no—
250C2×C4—742no—
251C2×C4—742no—
252C2×C4—742no—
253C2×C4—741no—
254C2×C4—742no—
255C2×C4—1482no—
256C2×C4—1484no—
257C2×C4—1484no—
258C2×C4—1482no—
259C2×C4D4×D3711yescharacteristic
260C2×C4C23×D3711yescharacteristic
261C8—22no—
262C8—742no—
263C22—21no—
264C22—21no—
265C22—372no—
266C22—372no—
267C22—748no—
268C22—741no—
269C22—741no—
270C22—741no—
271C22—741no—
272C22—1481no—
273C22—1481no—
274C22—1481no—
275C22#1192456312yes—
276C22C2×D4×D3711yescharacteristic
277C4—21no—
278C4—41no—
279C4—42no—
280C4—41no—
281C4—372no—
282C4—741no—
283C4—1482no—
284C4—1481no—
285C4#41×D3712yes—
286C2—22no—
287C2—2961no—
288C2—742no—
289C2—742no—
290C2#123×D3711yescharacteristic
291C2C2×#1192456311yescharacteristic
292C2#137×D3711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#483C2
socleC22×C37C22×D4
prime radical#14558046C2
hypercenter#483D37
hypocenterC37#3092
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D37C2semidirect
3. #14557867C2semidirect
4. #14557861C2semidirect
5. #14557853C2semidirect
6. #14557847C2semidirect
7. #14557846C2semidirect
8. #14557572C2semidirect
9. #14557533C2semidirect
10. #14557495C2semidirect
11. C37×#483C2semidirect
30. #11924470C22semidirect
31. #11924469C22semidirect
32. #11924467C22semidirect
33. #11924460C22semidirect
34. #11924458C22semidirect
35. #11924456C22semidirect
40. #106×C37C22semidirect
41. #103×C37C22semidirect
151. #483D37semidirect
158. C37#3092semidirect
182. #106C2×D37semidirect
184. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580462
C2×C4⋊C4×D372
#145578672
#145578612
#145578532
#145578472
#145578462
#145575722
#145575332
#145574952
C37×#4832
#309237