Finite Group Databasebeta

← #18005194

Subgroups — #18005194

Order 4736.

408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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#14558084C211yesmaximal, characteristic, complemented
2#14558062C211yesmaximal, characteristic, complemented
3#14557939C211yesmaximal, characteristic, complemented
4#14557923C211yesmaximal, characteristic, complemented
5#14557898C211yesmaximal, characteristic, complemented
6#14557785C212yesmaximal, complemented
7#14557782C212yesmaximal, complemented
8#14557618C212yesmaximal, complemented
9#14557613C212yesmaximal, complemented
10#14557485C211yesmaximal, characteristic, complemented
11C37×#489C211yesmaximal, characteristic, complemented
12C2×#10596966—21no—
13C2×#10596941C2212yes—
14C2×#10596939C2212yes—
15C2×#10596929C2212yes—
16#11924533C2211yescharacteristic
17#11924529—21no—
18#11924528C2211yescharacteristic
19#11924525—21no—
20#11924518—21no—
21#11924512C2211yescharacteristic
22#11924511—21no—
23#11924511C2212yes—
24#11924507C2211yescharacteristic
25Q8×Dic37C2211yescharacteristic
26D4×Dic37C2211yescharacteristic
27#11924498—21no—
28#11924498C2212yes—
29#11924496—21no—
30#11924492—21no—
31C42×D37C2211yescharacteristic
32#11924469C2212yes—
33#11924467C2212yes—
34#11924458C2212yes—
35#11924458C2212yes—
36#11924447C2211yescharacteristic
37C8×Dic37C2212yes—
38C4⋊Q8×C37C2211yescharacteristic
39#124×C37C2211yescharacteristic
40#103×C37C2212yes—
41#102×C37C2212yes—
42#97×C37C2211yescharacteristic
43C2×Q8×C37—21no—
44C2×Q8×C37C2311yescharacteristic
45C2×D4×C37C2311yescharacteristic
46C2×C22⋊D37—21no—
47C22×Dic37—21no—
48#10596966—44no—
49C2×D148—22no—
50C2×D148—21no—
51C2×D148—21no—
52C2×D148C2312yes—
53C2×C4×D37—22no—
54C2×C4×D37D411yescharacteristic
55C2×C4×D37D411yescharacteristic
56C2×C4×D37C2311yescharacteristic
57C2×C8×C37C2312yes—
58C4⋊C4×C37—21no—
59C4⋊C4×C37C2312yes—
60C22⋊C4×C37—21no—
61C22⋊C4×C37—21no—
62C42×C37C2311yescharacteristic
63C22⋊Dic37—21no—
64C22⋊Dic37—21no—
65#10596941—24no—
66#10596939—24no—
67#10596938—21no—
68#10596938—22no—
69#10596938—22no—
70C4⋊Dic37—21no—
71C4⋊Dic37C2311yescharacteristic
72C4⋊Dic37C2311yescharacteristic
73#10596936—21no—
74#10596936—21no—
75#10596936—21no—
76C4×Dic37—21no—
77C4×Dic37D411yescharacteristic
78C4×Dic37D411yescharacteristic
79C4×Dic37C2311yescharacteristic
80C2×#64436C2312yes—
81#10596929—24no—
82C23×C37—21no—
83C22×D37—22no—
84C22×D37C2×D411yescharacteristic
85Q8×C37—22no—
86Q8×C37—42no—
87D4×C37—22no—
88C2×C4×C37—21no—
89C2×C4×C37—22no—
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37C2×D411yescharacteristic
92C2×C4×C37C2411yescharacteristic
93C22⋊D37—42no—
94C2×Dic37—21no—
95C2×Dic37—21no—
96C2×Dic37—42no—
97C2×Dic37C2×D411yescharacteristic
98C2×Dic37C2×D411yescharacteristic
99C2×Dic37C2×D411yescharacteristic
100D148—22no—
101D148—22no—
102D148—42no—
103D148—42no—
104D148—44no—
105C4×D37—22no—
106C4×D37—22no—
107C4×D37—41no—
108C4×D37—44no—
109C8×C37—22no—
110#64436#4114yescomplemented
111C22×C37—41no—
112C22×C37—41no—
113C22×C37—41no—
114C22×C37C22×D411yescharacteristic
115C2×D37—21no—
116C2×D37—21no—
117C2×D37—21no—
118C2×D37—42no—
119C2×D37—42no—
120C2×D37—42no—
121C4×C37—21no—
122C4×C37—21no—
123C4×C37—41no—
124C4×C37—42no—
125C4×C37C2×#4112yes—
126Dic37—21no—
127Dic37—21no—
128Dic37—41no—
129Dic37—41no—
130Dic37AGL(1,ℤ/8)12yes—
131#3171—371nomaximal, Sylow
132C2×C37—81no—
133C2×C37#53211yescharacteristic
134C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
135C2×C37#57511yescharacteristic
136D37—41no—
137D37—82no—
138#532—371no—
139#529—371no—
140#501—371no—
141#496—371no—
142#490—371no—
143#489D3711yescharacteristic, complemented
144#469—372no—
145#468—372no—
146C4×SD16—372no—
147C4×D8—372no—
148C4×M16—371no—
149C37#317111yescharacteristic, complemented, Sylow
150C2×#41—741no—
151C2×SD16—372no—
152C2×D8—372no—
153C2×M16—372no—
154C4⋊Q8C2×D3711yescharacteristic
155#127—371no—
156#126—741no—
157#125—371no—
158#124—741no—
159#124C2×D3711yescharacteristic
160#123—741no—
161C22⋊Q8—371no—
162#121—371no—
163#121—372no—
164#121—741no—
165C4×Q8—371no—
166C4×D4—371no—
167C4×D4—372no—
168C4×D4—741no—
169C4×D4—741no—
170#117—741no—
171C2×C42—371no—
172#107—372no—
173#106—372no—
174#103C2×D3712yes—
175#102—372no—
176#102—372no—
177#102C2×D3712yes—
178#97—371no—
179#97C2×D3711yescharacteristic
180C4×C8—372no—
181#41—1484no—
182C2×Q8—21no—
183C2×Q8C22×D3711yescharacteristic
184C2×D4—372no—
185C2×D4—742no—
186C2×D4—741no—
187C2×D4—741no—
188C2×D4—741no—
189C2×D4C22×D3711yescharacteristic
190C22×C4—371no—
191C22×C4—371no—
192C22×C4—371no—
193C22×C4—742no—
194C22×C4—741no—
195SD16—744no—
196D8—744no—
197M16—744no—
198C2×C8—372no—
199C2×C8C22×D3712yes—
200C4⋊C4—21no—
201C4⋊C4—371no—
202C4⋊C4—371no—
203C4⋊C4—741no—
204C4⋊C4—741no—
205C4⋊C4—741no—
206C4⋊C4—741no—
207C4⋊C4C22×D3712yes—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—742no—
211C22⋊C4—742no—
212C22⋊C4—741no—
213C22⋊C4—741no—
214C22⋊C4—741no—
215C42—371no—
216C42—371no—
217C42—371no—
218C42—741no—
219C42C22×D3711yescharacteristic
220C23—21no—
221C23—371no—
222C23—742no—
223Q8—22no—
224Q8—42no—
225D4—22no—
226D4—742no—
227D4—742no—
228D4—1482no—
229D4—1482no—
230D4—1484no—
231D4—1482no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—371no—
235C2×C4—371no—
236C2×C4—371no—
237C2×C4—742no—
238C2×C4—742no—
239C2×C4—741no—
240C2×C4—741no—
241C2×C4—1481no—
242C2×C4—1484no—
243C2×C4—1482no—
244C2×C4D4×D3711yescharacteristic
245C2×C4D4×D3711yescharacteristic
246C2×C4C23×D3711yescharacteristic
247C8—22no—
248C8—374no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—741no—
253C22—741no—
254C22—741no—
255C22—1482no—
256C22—1482no—
257C22—1482no—
258C22C2×D4×D3711yescharacteristic
259C4—21no—
260C4—21no—
261C4—42no—
262C4—41no—
263C4—372no—
264C4—741no—
265C4—741no—
266C4—1481no—
267C4—1481no—
268C4#41×D3712yes—
269C2—81no—
270C2—2962no—
271C2—1481no—
272C2#1455808211yescharacteristic
273C2AGL(1,ℤ/8)×D3711yescharacteristic
274C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#489C2
socleC22×C37C22×D4
hypercenter#489D37
hypocenterC37#3171
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #14558084C2semidirect
2. #14558062C2semidirect
3. #14557939C2semidirect
4. #14557923C2semidirect
5. #14557898C2semidirect
6. #14557785C2semidirect
7. #14557782C2semidirect
8. #14557618C2semidirect
9. #14557613C2semidirect
10. #14557485C2semidirect
11. C37×#489C2semidirect
110. #64436#41semidirect
143. #489D37semidirect
149. C37#3171semidirect

Maximal subgroups

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

subgroupindex
#145580842
#145580622
#145579392
#145579232
#145578982
#145577852
#145577822
#145576182
#145576132
#145574852
C37×#4892
#317137