Finite Group Databasebeta

← #18003997

Subgroups — #18003997

Order 4736.

772 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 145 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#14558369C211yesmaximal, characteristic, complemented
2#14558100C212yesmaximal, complemented
3#14557719C218yesmaximal, complemented
4#14557507C211yesmaximal, characteristic, complemented
5#14557506C212yesmaximal, complemented
6C37×#535C211yesmaximal, characteristic, complemented
7#11924584—21no—
8#11924583—22no—
9#11924582—22no—
10#11924581—21no—
11#11924581C2214yes—
12C2×#10596962—22no—
13C2×#10596962C2212yes—
14#41×D37—24no—
15#11924532—22no—
16#11924523—22no—
17#11924507—24no—
18#11924505C2218yescomplemented
19#11924495C2212yescomplemented
20#11924451C2214yescomplemented
21#11924450C2218yescomplemented
22C2×#41×C37C2211yescharacteristic
23C22×D4×C37C2211yescharacteristic, complemented
24#127×C37—21no—
25#124×C37—21no—
26#121×C37—22no—
27#120×C37C2214yescomplemented
28#117×C37C2211yescharacteristic, complemented
29C24×C37C2312yes—
30#41×C37—22no—
31#41×C37—22no—
32C2×Q8×C37D411yescharacteristic, complemented
33C2×D4×C37—24no—
34C2×D4×C37—22no—
35C2×D4×C37—22no—
36C2×D4×C37—21no—
37C2×D4×C37—21no—
38C2×D4×C37D411yescharacteristic, complemented
39C2×D4×C37C2312yes—
40C22×C4×C37D412yescomplemented
41C22×C4×C37C2311yescharacteristic
42C2×C22⋊D37—24no—
43C2×C22⋊D37—28no—
44C2×C22⋊D37C2314yes—
45#10596966—24no—
46Q8×D37—24no—
47#10596964—24no—
48#10596964—28no—
49D4×D37—24no—
50D4×D37—28no—
51#10596962—24no—
52#10596962—24no—
53#10596962—22no—
54#10596962—22no—
55#10596962—24no—
56#10596962—22no—
57#10596962—22no—
58C2×D148—22no—
59C2×D148D412yescomplemented
60C2×C4×D37—24no—
61C2×C4×D37D414yescomplemented
62C2×Dic74—22no—
63C2×Dic74D412yescomplemented
64C4⋊C4×C37—21no—
65C22⋊C4×C37—24no—
66C22⋊C4×C37C2312yes—
67C42×C37—21no—
68C22⋊Dic37—28no—
69C22⋊Dic37C2314yes—
70C4⋊Dic37—22no—
71C4×Dic37—22no—
72C23×C37—24no—
73C23×C37—22no—
74C23×C37—82no—
75C23×C37C2×D412yes—
76C23×C37C2411yescharacteristic
77C22×D37—24no—
78C22×D37C2×D414yes—
79Q8×C37—22no—
80D4×C37—24no—
81D4×C37—22no—
82D4×C37—41no—
83D4×C37—42no—
84D4×C37—41no—
85D4×C37—84no—
86C2×C4×C37—22no—
87C2×C4×C37—22no—
88C2×C4×C37—22no—
89C2×C4×C37C2×D412yes—
90C2×C4×C37C2×D412yes—
91C2×C4×C37C2×D412yes—
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37C2×D411yescharacteristic
94C22⋊D37—28no—
95C22⋊D37—24no—
96C22⋊D37—24no—
97C22⋊D37—88no—
98C2×Dic37—24no—
99C2×Dic37—24no—
100C2×Dic37C2×D414yes—
101D148—24no—
102D148—22no—
103D148—22no—
104C4×D37—28no—
105C4×D37—24no—
106C4×D37—24no—
107Dic74—24no—
108Dic74—22no—
109Dic74—22no—
110C22×C37—22no—
111C22×C37—41no—
112C22×C37—42no—
113C22×C37—48no—
114C22×C37—44no—
115C22×C37—42no—
116C22×C37C22×D412yes—
117C22×C37C22×D411yescharacteristic
118C2×D37—24no—
119C2×D37—44no—
120C2×D37—84no—
121C4×C37—22no—
122C4×C37—42no—
123C4×C37#12011yescharacteristic
124C4×C37#12012yes—
125C4×C37#12011yescharacteristic
126Dic37—24no—
127Dic37—44no—
128#3027—371nomaximal, Sylow
129C2×C37—22no—
130C2×C37—21no—
131C2×C37—42no—
132C2×C37—82no—
133C2×C37C2×#12011yescharacteristic
134D37—44no—
135#585—371no—
136#535—372no—
137#535D3711yescharacteristic, complemented
138B(4,𝔽2)—378no—
139#410—371no—
140#410—372no—
141C37#302711yescharacteristic, complemented, Sylow
1422−1+4—742no—
1432−1+4—741no—
144H(5,𝔽2)—374no—
145H(5,𝔽2)—742no—
146H(5,𝔽2)—741no—
147C2×#41—372no—
148C2×#41—744no—
149C2×#41—742no—
150C2×#41C2×D3711yescharacteristic
151C22×D4C2×D3711yescharacteristic, complemented
152#127—21no—
153#127—742no—
154#124—21no—
155#124—742no—
156#121—22no—
157#121—744no—
158#120—378no—
159#120C2×D3714yescomplemented
160#117—372no—
161#117C2×D3711yescharacteristic, complemented
162#99—374no—
163#99—378no—
164C24C22×D3712yes—
165#41—22no—
166#41—22no—
167#41—744no—
168#41—744no—
169#41—748no—
170#41—744no—
171#41—744no—
172#41—742no—
173#41—742no—
174#41—742no—
175#41—742no—
176#41—744no—
177C2×Q8—372no—
178C2×Q8—742no—
179C2×Q8—744no—
180C2×Q8C22⋊D3711yescharacteristic, complemented
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—374no—
187C2×D4—372no—
188C2×D4—742no—
189C2×D4—748no—
190C2×D4—744no—
191C2×D4—748no—
192C2×D4—744no—
193C2×D4C22⋊D3711yescharacteristic, complemented
194C2×D4C22×D3712yes—
195C22×C4—374no—
196C22×C4—744no—
197C22×C4C22⋊D3712yescomplemented
198C22×C4C22×D3711yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—742no—
201C22⋊C4—24no—
202C22⋊C4—374no—
203C22⋊C4—748no—
204C22⋊C4C22×D3712yes—
205C42—21no—
206C42—742no—
207C23—24no—
208C23—22no—
209C23—82no—
210C23—374no—
211C23—744no—
212C23C2×C22⋊D3712yes—
213C23C23×D3711yescharacteristic
214Q8—22no—
215Q8—744no—
216Q8—742no—
217Q8—742no—
218D4—24no—
219D4—22no—
220D4—41no—
221D4—41no—
222D4—42no—
223D4—84no—
224D4—2968no—
225D4—744no—
226D4—748no—
227D4—744no—
228D4—744no—
229D4—742no—
230D4—742no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—374no—
235C2×C4—748no—
236C2×C4—744no—
237C2×C4—744no—
238C2×C4—744no—
239C2×C4—744no—
240C2×C4D4×D3712yes—
241C2×C4D4×D3712yes—
242C2×C4C2×C22⋊D3712yes—
243C2×C4C2×C22⋊D3711yescharacteristic
244C2×C4C2×C22⋊D3711yescharacteristic
245C22—22no—
246C22—41no—
247C22—42no—
248C22—44no—
249C22—48no—
250C22—42no—
251C22—2964no—
252C22—744no—
253C22—1484no—
254C22C2×D4×D3712yes—
255C22C22×C22⋊D3711yescharacteristic
256C4—22no—
257C4—42no—
258C4—744no—
259C4—1484no—
260C4#1192450411yescharacteristic
261C4#1192450411yescharacteristic
262C4#1192450412yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—82no—
267C2—1484no—
268C2C2×#1192450411yescharacteristic
subgroupG/H
centerC2C2×#11924504
commutator, cosocleC23×C37C24
FrattiniC23C23×D37
FittingC37×#535C2
socleC2×C37C2×#120
hypercenter#535D37
hypocenterC37#3027
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #14558369C2semidirect
2. #14558100C2semidirect
3. #14557719C2semidirect
4. #14557507C2semidirect
5. #14557506C2semidirect
6. C37×#535C2semidirect
18. #11924505C22semidirect
19. #11924495C22semidirect
20. #11924451C22semidirect
21. #11924450C22semidirect
23. C22×D4×C37C22semidirect
27. #120×C37C22semidirect
28. #117×C37C22semidirect
32. C2×Q8×C37D4semidirect
38. C2×D4×C37D4semidirect
40. C22×C4×C37D4semidirect
59. C2×D148D4semidirect
61. C2×C4×D37D4semidirect
63. C2×Dic74D4semidirect
137. #535D37semidirect
141. C37#3027semidirect
151. C22×D4C2×D37semidirect
159. #120C2×D37semidirect
161. #117C2×D37semidirect
180. C2×Q8C22⋊D37semidirect
193. C2×D4C22⋊D37semidirect
197. C22×C4C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145583692
#145581002
#145577192
#145575072
#145575062
C37×#5352
#302737