Finite Group Databasebeta

← #18003999

Subgroups — #18003999

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#14558102C212yesmaximal, complemented
3#14558097C211yesmaximal, characteristic, complemented
4#14557721C218yesmaximal, complemented
5#14557506C212yesmaximal, complemented
6C37×#410C211yesmaximal, 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—
15C22×D148C2211yescharacteristic, complemented
16#11924533—22no—
17#11924532—21no—
18#11924525—21no—
19#11924524—22no—
20#11924511—24no—
21#11924510—22no—
22#11924506C2218yescomplemented
23#11924504C2214yescomplemented
24#11924495C2211yescharacteristic, complemented
25#11924450C2218yescomplemented
26C2×#41×C37C2211yescharacteristic
27#117×C37C2212yescomplemented
28#99×C37C2214yescomplemented
29C23×D37C2312yes—
30#41×C37—22no—
31#41×C37—22no—
32C2×Q8×C37D411yescharacteristic, complemented
33C2×D4×C37D411yescharacteristic, complemented
34C2×D4×C37C2312yes—
35C22×C4×C37D412yescomplemented
36C22×C4×C37C2311yescharacteristic
37C2×C22⋊D37—24no—
38C2×C22⋊D37—24no—
39C2×C22⋊D37C2314yes—
40#10596966—24no—
41Q8×D37—24no—
42#10596964—24no—
43#10596964—28no—
44D4×D37—24no—
45D4×D37—28no—
46#10596962—24no—
47#10596962—24no—
48#10596962—22no—
49#10596962—22no—
50#10596962—24no—
51#10596962—22no—
52#10596962—22no—
53C2×D148—22no—
54C2×D148—21no—
55C2×D148—22no—
56C2×D148—22no—
57C2×D148—21no—
58C2×D148—28no—
59C2×D148D412yescomplemented
60C2×C4×D37—24no—
61C2×C4×D37D414yescomplemented
62C2×Dic74—22no—
63C2×Dic74D412yescomplemented
64C4⋊C4×C37—22no—
65C22⋊C4×C37C2314yes—
66C42×C37—22no—
67C22⋊Dic37C2312yes—
68#10596938—24no—
69#10596938—28no—
70C4⋊Dic37—21no—
71C4×Dic37—21no—
72C23×C37C2×D412yes—
73C23×C37C2411yescharacteristic
74C22×D37—24no—
75C22×D37—24no—
76C22×D37—22no—
77C22×D37—82no—
78C22×D37C2×D414yes—
79Q8×C37—22no—
80D4×C37—24no—
81D4×C37—22no—
82C2×C4×C37—22no—
83C2×C4×C37—22no—
84C2×C4×C37—24no—
85C2×C4×C37C2×D412yes—
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37C2×D411yescharacteristic
88C2×C4×C37C2×D412yes—
89C2×C4×C37C2×D412yes—
90C22⋊D37—28no—
91C22⋊D37—24no—
92C22⋊D37—24no—
93C22⋊D37—84no—
94C2×Dic37—24no—
95C2×Dic37—22no—
96C2×Dic37C2×D414yes—
97D148—24no—
98D148—22no—
99D148—22no—
100D148—41no—
101D148—42no—
102D148—41no—
103D148—88no—
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×C37C22×D412yes—
114C22×C37C22×D411yescharacteristic
115C2×D37—24no—
116C2×D37—44no—
117C2×D37—48no—
118C2×D37—44no—
119C2×D37—42no—
120C2×D37—84no—
121C4×C37—22no—
122C4×C37—44no—
123C4×C37#12011yescharacteristic
124C4×C37#12012yes—
125C4×C37#12011yescharacteristic
126Dic37—24no—
127Dic37—42no—
128#3027—371nomaximal, Sylow
129C2×C37—21no—
130C2×C37—22no—
131C2×C37—42no—
132C2×C37C2×#12011yescharacteristic
133D37—44no—
134D37—82no—
135#585—371no—
136#535—371no—
137#535—372no—
138B(4,𝔽2)—378no—
139#410—372no—
140#410D3711yescharacteristic, complemented
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×D4—371no—
152#127—742no—
153#127—741no—
154#124—742no—
155#124—741no—
156#121—744no—
157#121—742no—
158#120—374no—
159#120—378no—
160#117—371no—
161#117C2×D3712yescomplemented
162#99—378no—
163#99C2×D3714yescomplemented
164C24—372no—
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—744no—
175#41—742no—
176#41—742no—
177C2×Q8—372no—
178C2×Q8—742no—
179C2×Q8—744no—
180C2×Q8D14811yescharacteristic, complemented
181C2×D4—374no—
182C2×D4—372no—
183C2×D4—748no—
184C2×D4—742no—
185C2×D4—748no—
186C2×D4—744no—
187C2×D4—744no—
188C2×D4—744no—
189C2×D4—741no—
190C2×D4—741no—
191C2×D4—742no—
192C2×D4—742no—
193C2×D4D14811yescharacteristic, complemented
194C2×D4C22×D3712yes—
195C22×C4—374no—
196C22×C4—744no—
197C22×C4D14812yescomplemented
198C22×C4C22×D3711yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—741no—
201C22⋊C4—372no—
202C22⋊C4—748no—
203C22⋊C4—744no—
204C22⋊C4C22×D3714yes—
205C42—22no—
206C42—741no—
207C23—374no—
208C23—2962no—
209C23—744no—
210C23—744no—
211C23—742no—
212C23C2×D14812yes—
213C23C23×D3711yescharacteristic
214Q8—22no—
215Q8—744no—
216Q8—742no—
217Q8—742no—
218D4—24no—
219D4—22no—
220D4—2968no—
221D4—2964no—
222D4—744no—
223D4—748no—
224D4—744no—
225D4—744no—
226D4—742no—
227D4—742no—
228D4—1481no—
229D4—1481no—
230D4—1482no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—374no—
235C2×C4—748no—
236C2×C4—744no—
237C2×C4—744no—
238C2×C4—744no—
239C2×C4—742no—
240C2×C4C2×D14812yes—
241C2×C4C2×D14811yescharacteristic
242C2×C4C2×D14811yescharacteristic
243C2×C4D4×D3712yes—
244C2×C4D4×D3712yes—
245C22—22no—
246C22—41no—
247C22—42no—
248C22—2964no—
249C22—744no—
250C22—1488no—
251C22—1484no—
252C22—1484no—
253C22—1482no—
254C22C2×D4×D3712yes—
255C22C22×D14811yescharacteristic
256C4—22no—
257C4—44no—
258C4—744no—
259C4—1482no—
260C4#1192450611yescharacteristic
261C4#1192450611yescharacteristic
262C4#1192450612yes—
263C2—22no—
264C2—21no—
265C2—42no—
266C2—2962no—
267C2—1484no—
268C2C2×#1192450611yescharacteristic
subgroupG/H
centerC2C2×#11924506
commutator, cosocleC23×C37C24
FrattiniC23C23×D37
FittingC37×#410C2
socleC2×C37C2×#120
hypercenter#410D37
hypocenterC37#3027
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #14558369C2semidirect
2. #14558102C2semidirect
3. #14558097C2semidirect
4. #14557721C2semidirect
5. #14557506C2semidirect
6. C37×#410C2semidirect
15. C22×D148C22semidirect
22. #11924506C22semidirect
23. #11924504C22semidirect
24. #11924495C22semidirect
25. #11924450C22semidirect
27. #117×C37C22semidirect
28. #99×C37C22semidirect
32. C2×Q8×C37D4semidirect
33. C2×D4×C37D4semidirect
35. C22×C4×C37D4semidirect
59. C2×D148D4semidirect
61. C2×C4×D37D4semidirect
63. C2×Dic74D4semidirect
140. #410D37semidirect
141. C37#3027semidirect
161. #117C2×D37semidirect
163. #99C2×D37semidirect
180. C2×Q8D148semidirect
193. C2×D4D148semidirect
197. C22×C4D148semidirect

Maximal subgroups

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

subgroupindex
#145583692
#145581022
#145580972
#145577212
#145575062
C37×#4102
#302737