Finite Group Databasebeta

← #18003949

Subgroups — #18003949

Order 4736.

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

normal subgroups only

This group has 724 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#14558333C212yesmaximal, complemented
3#14558079C211yesmaximal, characteristic, complemented
4#14557718C212yesmaximal, complemented
5#14557713C212yesmaximal, complemented
6#14557708C212yesmaximal, complemented
7#14557703C212yesmaximal, complemented
8C2×#11924462C212yesmaximal, complemented
9C37×#413C211yesmaximal, characteristic, complemented
10#11924584C2212yes—
11#11924583—22no—
12#11924582—22no—
13#11924581—22no—
14#11924581C2212yes—
15C2×#10596962—22no—
16C2×#10596962C2212yes—
17C2×#10596962C2211yescharacteristic, complemented
18#41×D37—24no—
19#11924569—22no—
20#11924569C2214yescomplemented
21#11924564—22no—
22#11924564C2214yescomplemented
23#11924558—24no—
24#11924534C2211yescharacteristic, complemented
25#11924532C2211yescharacteristic, complemented
26#11924525C2211yescharacteristic, complemented
27#11924523C2211yescharacteristic, complemented
28#11924508—22no—
29C4×C22⋊D37—22no—
30C2×C4×Dic37C2211yescharacteristic, complemented
31#11924462C2214yescomplemented
32#11924462C2214yescomplemented
33C2×#41×C37C2211yescharacteristic
34C2×M16×C37C2212yescomplemented
35#101×C37C2212yescomplemented
36#100×C37C2212yescomplemented
37#41×C37—22no—
38#41×C37—22no—
39C2×Q8×C37C2311yescharacteristic
40C2×D4×C37D412yes—
41C2×D4×C37C2311yescharacteristic
42C22×C4×C37D412yes—
43C22×C4×C37C2311yescharacteristic
44C2×C22⋊D37—24no—
45C2×C22⋊D37—22no—
46C2×C22⋊D37—22no—
47C2×C22⋊D37—21no—
48C22×Dic37—21no—
49#10596966—24no—
50Q8×D37—24no—
51#10596964—28no—
52#10596964—24no—
53D4×D37—28no—
54D4×D37—24no—
55#10596962—24no—
56#10596962—24no—
57#10596962—22no—
58#10596962—24no—
59#10596962—22no—
60#10596962—22no—
61#10596962—22no—
62#10596962D414yescomplemented
63#10596962C2314yes—
64C2×D148—22no—
65C2×D148D412yescomplemented
66C2×D148C2311yescharacteristic
67C2×C4×D37—24no—
68C2×C4×D37—22no—
69C2×C4×D37—21no—
70C2×Dic74—22no—
71C2×Dic74D412yescomplemented
72C2×Dic74C2311yescharacteristic
73M16×C37—22no—
74M16×C37C2314yes—
75C2×C8×C37—22no—
76C22⋊Dic37—22no—
77#10596938—22no—
78#10596936—22no—
79C4×Dic37—21no—
80C4×Dic37C2311yescharacteristic
81C4×Dic37C2311yescharacteristic
82Dic148—24no—
83D296—24no—
84#10596930—24no—
85#10596930—24no—
86C23×C37C2×D412yes—
87C23×C37C2×D411yescharacteristic
88C22×D37—24no—
89C22×D37—22no—
90C22×D37—21no—
91Q8×C37—22no—
92D4×C37—24no—
93D4×C37—22no—
94C2×C4×C37—22no—
95C2×C4×C37—22no—
96C2×C4×C37C2×D412yes—
97C2×C4×C37C2×D411yescharacteristic
98C2×C4×C37C2×D412yes—
99C2×C4×C37C2×D412yes—
100C2×C4×C37C2411yescharacteristic
101C22⋊D37—28no—
102C22⋊D37—24no—
103C22⋊D37—24no—
104C22⋊D37—44no—
105C22⋊D37—42no—
106C2×Dic37—24no—
107C2×Dic37—22no—
108C2×Dic37—21no—
109C2×Dic37—21no—
110C2×Dic37—21no—
111C2×Dic37—42no—
112D148—24no—
113D148—22no—
114D148—22no—
115D148C2×D414yes—
116C4×D37—28no—
117C4×D37—24no—
118C4×D37—24no—
119C4×D37—41no—
120C4×D37—41no—
121Dic74—24no—
122Dic74—22no—
123Dic74—22no—
124Dic74C2×D414yes—
125C8×C37—24no—
126C22×C37—22no—
127C22×C37—41no—
128C22×C37—42no—
129C22×C37#12012yes—
130C22×C37C22×D411yescharacteristic
131C2×D37—24no—
132C2×D37—42no—
133C2×D37—41no—
134C2×D37—82no—
135C2×D37—84no—
136C4×C37—22no—
137C4×C37#12011yescharacteristic
138C4×C37#12011yescharacteristic
139C4×C37C22×D412yes—
140Dic37—22no—
141Dic37—24no—
142Dic37—41no—
143Dic37—41no—
144#3018—371nomaximal, Sylow
145C2×C37—21no—
146C2×C37—22no—
147C2×C37—42no—
148C2×C37C2×#12011yescharacteristic
149D37—44no—
150D37—81no—
151#585—371no—
152#575—372no—
153#532—371no—
154#456—372no—
155#455—372no—
156#454—372no—
157#453—372no—
158C2×#104—372no—
159#413D3711yescharacteristic, complemented
160C37#301811yescharacteristic, complemented, Sylow
1612−1+4—372no—
1622−1+4—742no—
163H(5,𝔽2)—372no—
164H(5,𝔽2)—742no—
165H(5,𝔽2)—742no—
166C2×#41—372no—
167C2×#41—371no—
168C2×#41—744no—
169C2×#41—742no—
170C2×#41C2×D3711yescharacteristic
171#137—374no—
172#137—742no—
173AGL(1,ℤ/8)—374no—
174AGL(1,ℤ/8)—742no—
175#135—744no—
176C2×M16C2×D3712yescomplemented
177C4⋊Q8—371no—
178#127—371no—
179#124—371no—
180#124—371no—
181#121—742no—
182C4×D4—742no—
183C2×C42—371no—
184#104—374no—
185#104—374no—
186#101C2×D3712yescomplemented
187#100C2×D3712yescomplemented
188#41—22no—
189#41—22no—
190#41—374no—
191#41—374no—
192#41—744no—
193#41—744no—
194#41—744no—
195#41—748no—
196#41—744no—
197#41—742no—
198#41—744no—
199#41—742no—
200#41—742no—
201#41—742no—
202C2×Q8—372no—
203C2×Q8—371no—
204C2×Q8—742no—
205C2×Q8—744no—
206C2×Q8C22×D3711yescharacteristic
207C2×D4—372no—
208C2×D4—371no—
209C2×D4—742no—
210C2×D4—744no—
211C2×D4—748no—
212C2×D4—742no—
213C2×D4—744no—
214C2×D4—742no—
215C2×D4—741no—
216C2×D4D14812yes—
217C2×D4C22×D3711yescharacteristic
218C22×C4—744no—
219C22×C4—742no—
220C22×C4—741no—
221C22×C4—741no—
222C22×C4D14812yes—
223C22×C4C22×D3711yescharacteristic
224Q16—744no—
225SD16—744no—
226SD16—744no—
227D8—744no—
228M16—22no—
229M16C22×D3714yes—
230C2×C8—22no—
231C4⋊C4—742no—
232C22⋊C4—742no—
233C22⋊C4—742no—
234C42—371no—
235C42—371no—
236C42—741no—
237C23—744no—
238C23—742no—
239C23—741no—
240C23C2×D14812yes—
241C23C2×D14811yescharacteristic
242Q8—22no—
243Q8—374no—
244Q8—744no—
245Q8—742no—
246Q8—742no—
247D4—24no—
248D4—22no—
249D4—374no—
250D4—744no—
251D4—748no—
252D4—744no—
253D4—744no—
254D4—742no—
255D4—742no—
256D4—1484no—
257D4—1482no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—748no—
261C2×C4—744no—
262C2×C4—742no—
263C2×C4—741no—
264C2×C4—744no—
265C2×C4—744no—
266C2×C4—741no—
267C2×C4—741no—
268C2×C4—1482no—
269C2×C4—1481no—
270C2×C4—1481no—
271C2×C4C2×D14812yes—
272C2×C4C2×D14811yescharacteristic
273C2×C4D4×D3712yes—
274C2×C4D4×D3712yes—
275C2×C4C23×D3711yescharacteristic
276C8—24no—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—2962no—
281C22—2964no—
282C22—744no—
283C22—1482no—
284C22—1481no—
285C22#1192450612yes—
286C22C22×D14811yescharacteristic
287C4—22no—
288C4—742no—
289C4—744no—
290C4—1481no—
291C4—1481no—
292C4#1192450611yescharacteristic
293C4#1192450611yescharacteristic
294C4C2×D4×D3712yes—
295C2—21no—
296C2—22no—
297C2—42no—
298C2—2961no—
299C2—1484no—
300C2C2×#1192450611yescharacteristic
subgroupG/H
centerC4#11924506
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#413C2
socleC2×C37C2×#120
hypercenter#413D37
hypocenterC37#3018
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #14558369C2semidirect
2. #14558333C2semidirect
3. #14558079C2semidirect
4. #14557718C2semidirect
5. #14557713C2semidirect
6. #14557708C2semidirect
7. #14557703C2semidirect
8. C2×#11924462C2semidirect
9. C37×#413C2semidirect
17. C2×#10596962C22semidirect
20. #11924569C22semidirect
22. #11924564C22semidirect
24. #11924534C22semidirect
25. #11924532C22semidirect
26. #11924525C22semidirect
27. #11924523C22semidirect
30. C2×C4×Dic37C22semidirect
31. #11924462C22semidirect
32. #11924462C22semidirect
34. C2×M16×C37C22semidirect
35. #101×C37C22semidirect
36. #100×C37C22semidirect
62. #10596962D4semidirect
65. C2×D148D4semidirect
71. C2×Dic74D4semidirect
159. #413D37semidirect
160. C37#3018semidirect
176. C2×M16C2×D37semidirect
186. #101C2×D37semidirect
187. #100C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583692
#145583332
#145580792
#145577182
#145577132
#145577082
#145577032
C2×#119244622
C37×#4132
#301837