Finite Group Databasebeta

← #18003945

Subgroups — #18003945

Order 4736.

724 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 161 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#14558331C212yesmaximal, complemented
2#14558079C211yesmaximal, characteristic, complemented
3#14557716C212yesmaximal, complemented
4#14557711C212yesmaximal, complemented
5#14557706C212yesmaximal, complemented
6#14557701C212yesmaximal, complemented
7C2×#11924463C212yesmaximal, complemented
8#14557517C211yesmaximal, characteristic, complemented
9C37×#585C211yesmaximal, characteristic, complemented
10C2×#10596962C2211yescharacteristic, complemented
11#11924567—22no—
12#11924566C2214yescomplemented
13#11924562—22no—
14#11924561C2214yescomplemented
15#11924556—24no—
16C2×#10596934C2212yescomplemented
17#11924534C2211yescharacteristic, complemented
18#11924532C2211yescharacteristic, complemented
19#11924525C2211yescharacteristic, complemented
20#11924523C2211yescharacteristic, complemented
21#11924508—22no—
22C4×C22⋊D37—22no—
23C2×C4×Dic37C2211yescharacteristic, complemented
24#11924463C2214yescomplemented
25#11924463C2214yescomplemented
26#11924455C2212yescomplemented
27#11924453C2212yescomplemented
282−1+4×C37—22no—
292−1+4×C37C2212yes—
30H(5,𝔽2)×C37—22no—
31H(5,𝔽2)×C37—22no—
32H(5,𝔽2)×C37C2212yes—
33C2×#41×C37—24no—
34C2×#41×C37—22no—
35C2×#41×C37C2212yes—
36C2×#41×C37C2211yescharacteristic
37#41×C37—24no—
38#41×C37—28no—
39#41×C37—24no—
40#41×C37—24no—
41#41×C37—24no—
42#41×C37—22no—
43#41×C37—22no—
44#41×C37—24no—
45#41×C37—22no—
46#41×C37—22no—
47#41×C37D414yescomplemented
48#41×C37C2314yes—
49C2×Q8×C37—22no—
50C2×Q8×C37—24no—
51C2×Q8×C37D412yescomplemented
52C2×Q8×C37C2311yescharacteristic
53C2×D4×C37—28no—
54C2×D4×C37—22no—
55C2×D4×C37—24no—
56C2×D4×C37—22no—
57C2×D4×C37—24no—
58C2×D4×C37D412yes—
59C2×D4×C37D412yescomplemented
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—24no—
62C22×C4×C37—22no—
63C22×C4×C37D412yes—
64C22×C4×C37C2311yescharacteristic
65C2×C22⋊D37—22no—
66C2×C22⋊D37—21no—
67C22×Dic37—21no—
68#10596962—22no—
69#10596962—22no—
70C2×D148C2311yescharacteristic
71C2×C4×D37—21no—
72C2×Dic74C2311yescharacteristic
73C22⋊Dic37—22no—
74#10596942—24no—
75#10596941—24no—
76#10596940—24no—
77#10596939—24no—
78#10596938—22no—
79#10596936—22no—
80C4×Dic37—21no—
81C4×Dic37C2311yescharacteristic
82C4×Dic37C2311yescharacteristic
83#10596934—22no—
84#10596934C2314yes—
85C2×#64436—22no—
86C23×C37—24no—
87C23×C37—22no—
88C23×C37C2×D412yes—
89C23×C37C2×D411yescharacteristic
90C22×D37—21no—
91Q8×C37—24no—
92Q8×C37—22no—
93Q8×C37—22no—
94Q8×C37C2×D414yes—
95D4×C37—28no—
96D4×C37—24no—
97D4×C37—24no—
98D4×C37—24no—
99D4×C37—24no—
100D4×C37—22no—
101D4×C37—22no—
102D4×C37C2×D414yes—
103C2×C4×C37—24no—
104C2×C4×C37—28no—
105C2×C4×C37—22no—
106C2×C4×C37—24no—
107C2×C4×C37—22no—
108C2×C4×C37—22no—
109C2×C4×C37—24no—
110C2×C4×C37C2×D412yes—
111C2×C4×C37C2×D411yescharacteristic
112C2×C4×C37C2×D412yes—
113C2×C4×C37C2×D412yes—
114C2×C4×C37C2411yescharacteristic
115C22⋊D37—44no—
116C22⋊D37—42no—
117C2×Dic37—21no—
118C2×Dic37—21no—
119C2×Dic37—21no—
120C2×Dic37—42no—
121D148—22no—
122C4×D37—41no—
123C4×D37—41no—
124Dic74—22no—
125#64436—24no—
126C22×C37—22no—
127C22×C37—24no—
128C22×C37—41no—
129C22×C37—42no—
130C22×C37—82no—
131C22×C37—84no—
132C22×C37#12012yes—
133C22×C37C22×D411yescharacteristic
134C2×D37—42no—
135C2×D37—41no—
136C4×C37—24no—
137C4×C37—22no—
138C4×C37#12011yescharacteristic
139C4×C37#12011yescharacteristic
140C4×C37C22×D412yes—
141Dic37—22no—
142Dic37—41no—
143Dic37—41no—
144#3018—371nomaximal, Sylow
145C2×C37—21no—
146C2×C37—22no—
147C2×C37—42no—
148C2×C37—44no—
149C2×C37C2×#12011yescharacteristic
150D37—81no—
151#585D3711yescharacteristic, complemented
152#575—372no—
153#532—371no—
154#456—372no—
155#455—372no—
156#454—372no—
157#453—372no—
158C2×#104—372no—
159#413—371no—
160C37#301811yescharacteristic, complemented, Sylow
1612−1+4—22no—
1622−1+4C2×D3712yes—
163H(5,𝔽2)—22no—
164H(5,𝔽2)—22no—
165H(5,𝔽2)C2×D3712yes—
166C2×#41—24no—
167C2×#41—22no—
168C2×#41—371no—
169C2×#41C2×D3712yes—
170C2×#41C2×D3711yescharacteristic
171#137—374no—
172#137—742no—
173AGL(1,ℤ/8)—374no—
174AGL(1,ℤ/8)—742no—
175#135—744no—
176C2×M16—372no—
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#101—372no—
187#100—372no—
188#41—24no—
189#41—28no—
190#41—24no—
191#41—24no—
192#41—24no—
193#41—22no—
194#41—22no—
195#41—24no—
196#41—22no—
197#41—22no—
198#41—742no—
199#41—742no—
200#41C22⋊D3714yescomplemented
201#41C22×D3714yes—
202C2×Q8—22no—
203C2×Q8—24no—
204C2×Q8—371no—
205C2×Q8C22⋊D3712yescomplemented
206C2×Q8C22×D3711yescharacteristic
207C2×D4—28no—
208C2×D4—22no—
209C2×D4—24no—
210C2×D4—22no—
211C2×D4—24no—
212C2×D4—371no—
213C2×D4—742no—
214C2×D4—741no—
215C2×D4C22⋊D3712yes—
216C2×D4C22⋊D3712yescomplemented
217C2×D4C22×D3711yescharacteristic
218C22×C4—24no—
219C22×C4—22no—
220C22×C4—741no—
221C22×C4—741no—
222C22×C4C22⋊D3712yes—
223C22×C4C22×D3711yescharacteristic
224Q16—744no—
225SD16—744no—
226SD16—744no—
227D8—744no—
228M16—374no—
229M16—742no—
230C2×C8—742no—
231C4⋊C4—742no—
232C22⋊C4—742no—
233C22⋊C4—742no—
234C42—371no—
235C42—371no—
236C42—741no—
237C23—24no—
238C23—22no—
239C23—741no—
240C23C2×C22⋊D3712yes—
241C23C2×C22⋊D3711yescharacteristic
242Q8—24no—
243Q8—22no—
244Q8—22no—
245Q8—742no—
246Q8C2×C22⋊D3714yes—
247D4—28no—
248D4—24no—
249D4—24no—
250D4—24no—
251D4—24no—
252D4—22no—
253D4—22no—
254D4—742no—
255D4—1484no—
256D4—1482no—
257D4C2×C22⋊D3714yes—
258C2×C4—24no—
259C2×C4—28no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—22no—
264C2×C4—24no—
265C2×C4—741no—
266C2×C4—741no—
267C2×C4—741no—
268C2×C4—1482no—
269C2×C4—1481no—
270C2×C4—1481no—
271C2×C4C2×C22⋊D3712yes—
272C2×C4C2×C22⋊D3711yescharacteristic
273C2×C4C2×C22⋊D3712yes—
274C2×C4C2×C22⋊D3712yes—
275C2×C4C23×D3711yescharacteristic
276C8—744no—
277C22—22no—
278C22—24no—
279C22—41no—
280C22—42no—
281C22—82no—
282C22—84no—
283C22—1482no—
284C22—1481no—
285C22#1192450512yes—
286C22C22×C22⋊D3711yescharacteristic
287C4—24no—
288C4—22no—
289C4—742no—
290C4—1481no—
291C4—1481no—
292C4#1192450511yescharacteristic
293C4#1192450511yescharacteristic
294C4C22×C22⋊D3712yes—
295C2—21no—
296C2—22no—
297C2—42no—
298C2—44no—
299C2—2961no—
300C2C2×#1192450511yescharacteristic
subgroupG/H
centerC4#11924505
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#585C2
socleC2×C37C2×#120
hypercenter#585D37
hypocenterC37#3018
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #14558331C2semidirect
2. #14558079C2semidirect
3. #14557716C2semidirect
4. #14557711C2semidirect
5. #14557706C2semidirect
6. #14557701C2semidirect
7. C2×#11924463C2semidirect
8. #14557517C2semidirect
9. C37×#585C2semidirect
10. C2×#10596962C22semidirect
12. #11924566C22semidirect
14. #11924561C22semidirect
16. C2×#10596934C22semidirect
17. #11924534C22semidirect
18. #11924532C22semidirect
19. #11924525C22semidirect
20. #11924523C22semidirect
23. C2×C4×Dic37C22semidirect
24. #11924463C22semidirect
25. #11924463C22semidirect
26. #11924455C22semidirect
27. #11924453C22semidirect
47. #41×C37D4semidirect
51. C2×Q8×C37D4semidirect
59. C2×D4×C37D4semidirect
151. #585D37semidirect
160. C37#3018semidirect
200. #41C22⋊D37semidirect
205. C2×Q8C22⋊D37semidirect
216. C2×D4C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145583312
#145580792
#145577162
#145577112
#145577062
#145577012
C2×#119244632
#145575172
C37×#5852
#301837