Finite Group Databasebeta

← #18005291

Subgroups — #18005291

Order 4736.

410 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 119 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#14558081C211yesmaximal, characteristic, complemented
2#14558062C211yesmaximal, characteristic, complemented
3#14557942C211yesmaximal, characteristic, complemented
4#14557897C211yesmaximal, characteristic, complemented
5#14557892C211yesmaximal, characteristic, complemented
6#14557766C212yesmaximal, complemented
7#14557759C212yesmaximal, complemented
8#14557645C212yesmaximal, complemented
9#14557634C212yesmaximal, complemented
10#97×D37C211yesmaximal, characteristic, complemented
11C37×#496C211yesmaximal, characteristic, complemented
12C2×#10596964—21no—
13C2×C8×D37C2212yes—
14#11924536C2211yescharacteristic
15#11924529—21no—
16#11924528C2211yescharacteristic
17#11924523—21no—
18#11924518—21no—
19#11924512C2211yescharacteristic
20#11924507—21no—
21#11924507C2212yes—
22#11924507C2211yescharacteristic
23Q8×Dic37C2211yescharacteristic
24D4×Dic37—21no—
25D4×Dic37C2211yescharacteristic
26D4×Dic37C2212yes—
27#11924496—21no—
28#11924492—21no—
29C42×D37C2211yescharacteristic
30#11924470C2212yes—
31#11924468C2212yes—
32#11924460C2212yes—
33#11924457C2212yes—
34#11924457C2212yes—
35#11924457C2212yes—
36#11924447C2211yescharacteristic
37#11924446C2212yes—
38C2×SD16×C37C2212yes—
39C2×D8×C37C2212yes—
40#127×C37C2211yescharacteristic
41#124×C37C2211yescharacteristic
42#97×C37C2211yescharacteristic
43C2×Q8×C37C2311yescharacteristic
44C2×D4×C37—21no—
45C2×D4×C37—21no—
46C2×D4×C37C2311yescharacteristic
47C2×D4×C37C2312yes—
48C2×C22⋊D37—21no—
49C2×C22⋊D37—22no—
50C22×Dic37—21no—
51C22×Dic37—22no—
52#10596964—44no—
53C2×C4×D37D411yescharacteristic
54C2×C4×D37D411yescharacteristic
55C2×C4×D37C2311yescharacteristic
56C2×Dic74—21no—
57SD16×C37—24no—
58D8×C37—24no—
59C2×C8×C37C2312yes—
60C22⋊C4×C37—21no—
61C22⋊C4×C37—21no—
62C42×C37C2311yescharacteristic
63C22⋊Dic37—21no—
64C22⋊Dic37—22no—
65C22⋊Dic37—22no—
66C22⋊Dic37—21no—
67#10596938—21no—
68C4⋊Dic37—21no—
69C4⋊Dic37—21no—
70C4⋊Dic37C2312yes—
71C4⋊Dic37C2311yescharacteristic
72C4⋊Dic37C2311yescharacteristic
73#10596936—21no—
74#10596936—21no—
75#10596936—21no—
76C4×Dic37—21no—
77C4×Dic37D411yescharacteristic
78C4×Dic37D411yescharacteristic
79C4×Dic37C2311yescharacteristic
80C2×#64436C2312yes—
81C8×D37—24no—
82C23×C37—21no—
83C23×C37—22no—
84C22×D37C2×D411yescharacteristic
85Q8×C37—22no—
86D4×C37—22no—
87D4×C37—22no—
88D4×C37—22no—
89D4×C37—42no—
90D4×C37—42no—
91C2×C4×C37—21no—
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37C2×D411yescharacteristic
94C2×C4×C37C2411yescharacteristic
95C22⋊D37—44no—
96C22⋊D37—42no—
97C2×Dic37—21no—
98C2×Dic37—21no—
99C2×Dic37—22no—
100C2×Dic37—44no—
101C2×Dic37—42no—
102C2×Dic37C2×D411yescharacteristic
103C2×Dic37C2×D411yescharacteristic
104C2×Dic37C2×D411yescharacteristic
105C4×D37—22no—
106C4×D37—22no—
107C4×D37—41no—
108Dic74—42no—
109C8×C37#4114yescomplemented
110#64436—22no—
111C22×C37—41no—
112C22×C37—42no—
113C22×C37—42no—
114C22×C37—41no—
115C22×C37—41no—
116C22×C37—42no—
117C22×C37C22×D411yescharacteristic
118C2×D37—21no—
119C2×D37—21no—
120C2×D37AGL(1,ℤ/8)12yes—
121C4×C37—21no—
122C4×C37—21no—
123C4×C37—41no—
124C4×C37C2×#4112yes—
125Dic37—21no—
126Dic37—21no—
127Dic37—21no—
128Dic37—42no—
129Dic37—41no—
130Dic37—41no—
131#3180—371nomaximal, Sylow
132C2×C37—82no—
133C2×C37—81no—
134C2×C37#53211yescharacteristic
135C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C37#57511yescharacteristic
137D37—22no—
138#532—371no—
139#529—371no—
140#501—371no—
141#496D3711yescharacteristic, complemented
142#490—371no—
143#489—371no—
144#466—372no—
145#465—372no—
146#442—372no—
147#440—372no—
148C2×#97—371no—
149C37#318011yescharacteristic, complemented, Sylow
150C2×#41—741no—
151C2×SD16C2×D3712yes—
152C2×D8C2×D3712yes—
153C22×C8—372no—
154C4⋊Q8—371no—
155#127C2×D3711yescharacteristic
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#103—372no—
175#102—372no—
176#102—372no—
177#102—372no—
178#97—372no—
179#97—371no—
180#97C2×D3711yescharacteristic
181#41—1484no—
182C2×Q8—741no—
183C2×Q8C22×D3711yescharacteristic
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—741no—
187C2×D4—742no—
188C2×D4C22×D3711yescharacteristic
189C2×D4C22×D3712yes—
190C22×C4—371no—
191C22×C4—371no—
192C22×C4—371no—
193C22×C4—741no—
194C22×C4—742no—
195SD16—24no—
196D8—24no—
197C2×C8—372no—
198C2×C8—744no—
199C2×C8C22×D3712yes—
200C4⋊C4—371no—
201C4⋊C4—371no—
202C4⋊C4—372no—
203C4⋊C4—741no—
204C4⋊C4—741no—
205C4⋊C4—741no—
206C4⋊C4—741no—
207C4⋊C4—741no—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—741no—
211C22⋊C4—741no—
212C22⋊C4—742no—
213C22⋊C4—741no—
214C22⋊C4—742no—
215C42—371no—
216C42—371no—
217C42—371no—
218C42—741no—
219C42C22×D3711yescharacteristic
220C23—21no—
221C23—22no—
222C23—371no—
223Q8—22no—
224Q8—1482no—
225D4—22no—
226D4—22no—
227D4—22no—
228D4—42no—
229D4—42no—
230D4—1484no—
231D4—1482no—
232C2×C4—21no—
233C2×C4—371no—
234C2×C4—371no—
235C2×C4—371no—
236C2×C4—742no—
237C2×C4—742no—
238C2×C4—741no—
239C2×C4—741no—
240C2×C4—742no—
241C2×C4—1481no—
242C2×C4—1484no—
243C2×C4—1482no—
244C2×C4D4×D3711yescharacteristic
245C2×C4D4×D3711yescharacteristic
246C2×C4C23×D3711yescharacteristic
247C8—742no—
248C8#1059696414yescomplemented
249C22—42no—
250C22—41no—
251C22—41no—
252C22—42no—
253C22—41no—
254C22—42no—
255C22—372no—
256C22—741no—
257C22—741no—
258C22C2×D4×D3711yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—741no—
263C4—741no—
264C4—741no—
265C4—1482no—
266C4—1481no—
267C4—1481no—
268C4C2×#1059696412yes—
269C2—82no—
270C2—81no—
271C2—742no—
272C2#1455808111yescharacteristic
273C2AGL(1,ℤ/8)×D3711yescharacteristic
274C2#1455832911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#496C2
socleC22×C37C22×D4
hypercenter#496D37
hypocenterC37#3180
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14558081C2semidirect
2. #14558062C2semidirect
3. #14557942C2semidirect
4. #14557897C2semidirect
5. #14557892C2semidirect
6. #14557766C2semidirect
7. #14557759C2semidirect
8. #14557645C2semidirect
9. #14557634C2semidirect
10. #97×D37C2semidirect
11. C37×#496C2semidirect
109. C8×C37#41semidirect
141. #496D37semidirect
149. C37#3180semidirect
248. C8#10596964semidirect

Maximal subgroups

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

subgroupindex
#145580812
#145580622
#145579422
#145578972
#145578922
#145577662
#145577592
#145576452
#145576342
#97×D372
C37×#4962
#318037