Finite Group Databasebeta

← #18004938

Subgroups — #18004938

Order 4736.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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
2#14558082C211yesmaximal, characteristic
3#14557900C212yesmaximal, complemented
4#14557896C212yesmaximal, complemented
5#14557895C211yesmaximal, characteristic, complemented
6#14557893C211yesmaximal, characteristic, complemented
7#14557892C211yesmaximal, characteristic, complemented
8#14557528C212yesmaximal, complemented
9#14557526C212yesmaximal, complemented
10#97×D37C211yesmaximal, characteristic, complemented
11C37×#489C211yesmaximal, characteristic, complemented
12C2×#10596966C2211yescharacteristic
13C2×#10596964C2211yescharacteristic
14C2×C8×D37C2212yes—
15#11924536C2211yescharacteristic
16#11924534C2211yescharacteristic
17#11924532C2211yescharacteristic
18#11924527C2212yes—
19#11924524C2211yescharacteristic
20#11924516—21no—
21#11924512—21no—
22#11924509—21no—
23#11924509—21no—
24Q8×Dic37—21no—
25#11924501—21no—
26#11924496—21no—
27#11924496—21no—
28#11924494C2212yes—
29C42×D37C2211yescharacteristic
30#11924461C2212yes—
31#11924460C2212yes—
32#11924459C2212yes—
33#11924458C2212yes—
34#11924457C2212yes—
35#11924456C2212yes—
36#11924447C2211yescharacteristic
37#11924446C2212yes—
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—
47C2×C22⋊D37—21no—
48C2×C22⋊D37—21no—
49C22×Dic37—21no—
50#10596966—24no—
51#10596964—24no—
52C2×D148—21no—
53C2×D148C2311yescharacteristic
54C2×C4×D37—21no—
55C2×C4×D37D411yescharacteristic
56C2×C4×D37D411yescharacteristic
57C2×C4×D37C2311yescharacteristic
58C2×Dic74—21no—
59C2×Dic74C2311yescharacteristic
60C2×C8×C37C2312yes—
61C4⋊C4×C37—21no—
62C4⋊C4×C37C2312yes—
63C22⋊C4×C37—21no—
64C22⋊C4×C37—21no—
65C42×C37C2311yescharacteristic
66#10596938—22no—
67#10596938—21no—
68#10596938—21no—
69C4⋊Dic37—21no—
70C4⋊Dic37—22no—
71C4⋊Dic37C2312yes—
72#10596936—21no—
73#10596936—21no—
74#10596936—22no—
75C4×Dic37—22no—
76C4×Dic37D411yescharacteristic
77C4×Dic37D411yescharacteristic
78C4×Dic37C2311yescharacteristic
79C2×#64436C2312yes—
80C8×D37—24no—
81C23×C37—21no—
82C22×D37—21no—
83C22×D37C2×D411yescharacteristic
84Q8×C37—22no—
85Q8×C37—42no—
86D4×C37—22no—
87C2×C4×C37—22no—
88C2×C4×C37—21no—
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37C2411yescharacteristic
92C22⋊D37—42no—
93C22⋊D37—42no—
94C22⋊D37—42no—
95C2×Dic37—22no—
96C2×Dic37—21no—
97C2×Dic37—42no—
98C2×Dic37C2×D411yescharacteristic
99C2×Dic37C2×D411yescharacteristic
100C2×Dic37C2×D411yescharacteristic
101D148—22no—
102D148—42no—
103C4×D37—41no—
104C4×D37—41no—
105C4×D37—42no—
106C4×D37#4114yes—
107Dic74—22no—
108Dic74—42no—
109C8×C37—22no—
110#64436—22no—
111C22×C37—41no—
112C22×C37—41no—
113C22×C37—41no—
114C22×C37C22×D411yescharacteristic
115C2×D37—21no—
116C2×D37—21no—
117C2×D37—41no—
118C2×D37—41no—
119C2×D37—41no—
120C2×D37#12412yes—
121C4×C37—21no—
122C4×C37—21no—
123C4×C37—41no—
124C4×C37—42no—
125C4×C37C2×#4112yes—
126Dic37—21no—
127Dic37—21no—
128Dic37—41no—
129Dic37—42no—
130Dic37#12412yes—
131#3135—371nomaximal, Sylow
132C2×C37—81no—
133C2×C37C2×#12411yescharacteristic
134C2×C37#57511yescharacteristic
135C2×C37#57511yescharacteristic
136D37—22no—
137D37—81no—
138#533—371no—
139#532—371no—
140#491—372no—
141#490—372no—
142#489—371no—
143#489—371no—
144#489—371no—
145#489D3711yescharacteristic, complemented
146#416—372no—
147#416—372no—
148C2×#97—371no—
149C37#313511yescharacteristic, complemented, Sylow
150C2×#41—371no—
151C2×#41—371no—
152C22×C8—372no—
153C4⋊Q8—371no—
154C4⋊Q8—371no—
155C4⋊Q8C2×D3711yescharacteristic
156#127—371no—
157#125—372no—
158#124—371no—
159#124C2×D3711yescharacteristic
160C22⋊Q8—741no—
161C22⋊Q8—741no—
162#121—741no—
163#121—741no—
164C4×Q8—741no—
165C4×Q8—741no—
166C4×D4—741no—
167C4×D4—741no—
168#117—372no—
169C2×C42—371no—
170#103—372no—
171#103—372no—
172#103—372no—
173#103C2×D3712yes—
174#102—372no—
175#102—372no—
176#102—372no—
177#102C2×D3712yes—
178#97—372no—
179#97—371no—
180#97C2×D3711yescharacteristic
181#41—744no—
182#41—744no—
183C2×Q8—21no—
184C2×Q8—371no—
185C2×Q8—741no—
186C2×Q8C22×D3711yescharacteristic
187C2×D4—371no—
188C2×D4—741no—
189C2×D4—741no—
190C2×D4—741no—
191C2×D4—741no—
192C2×D4C22×D3711yescharacteristic
193C22×C4—371no—
194C22×C4—371no—
195C22×C4—371no—
196C22×C4—741no—
197C22×C4—741no—
198C2×C8—372no—
199C2×C8—744no—
200C2×C8C22×D3712yes—
201C4⋊C4—21no—
202C4⋊C4—372no—
203C4⋊C4—741no—
204C4⋊C4—741no—
205C4⋊C4—742no—
206C4⋊C4—742no—
207C4⋊C4—741no—
208C4⋊C4C22×D3712yes—
209C22⋊C4—21no—
210C22⋊C4—21no—
211C22⋊C4—742no—
212C22⋊C4—741no—
213C22⋊C4—741no—
214C42—371no—
215C42—371no—
216C42—371no—
217C42—742no—
218C42C22×D3711yescharacteristic
219C23—21no—
220C23—371no—
221C23—741no—
222Q8—22no—
223Q8—42no—
224Q8—742no—
225Q8—1482no—
226D4—22no—
227D4—742no—
228D4—1482no—
229D4—1482no—
230D4—1482no—
231D4—1482no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—371no—
235C2×C4—374no—
236C2×C4—371no—
237C2×C4—371no—
238C2×C4—742no—
239C2×C4—741no—
240C2×C4—1481no—
241C2×C4—1481no—
242C2×C4—1482no—
243C2×C4—1482no—
244C2×C4D4×D3711yescharacteristic
245C2×C4D4×D3711yescharacteristic
246C2×C4C23×D3711yescharacteristic
247C8—22no—
248C8—742no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—372no—
253C22—741no—
254C22—741no—
255C22—1481no—
256C22—1481no—
257C22—1481no—
258C22C2×D4×D3711yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—42no—
263C4—372no—
264C4—741no—
265C4—741no—
266C4—1481no—
267C4—1482no—
268C4#41×D3712yes—
269C2—81no—
270C2—2961no—
271C2—742no—
272C2#124×D3711yescharacteristic
273C2#1455832911yescharacteristic
274C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#489C2
socleC22×C37C22×D4
prime radical#14558082C2
hypercenter#489D37
hypocenterC37#3135
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. #14558088C2semidirect
3. #14557900C2semidirect
4. #14557896C2semidirect
5. #14557895C2semidirect
6. #14557893C2semidirect
7. #14557892C2semidirect
8. #14557528C2semidirect
9. #14557526C2semidirect
10. #97×D37C2semidirect
11. C37×#489C2semidirect
145. #489D37semidirect
149. C37#3135semidirect

Maximal subgroups

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

subgroupindex
#145580882
#145580822
#145579002
#145578962
#145578952
#145578932
#145578922
#145575282
#145575262
#97×D372
C37×#4892
#313537