Finite Group Databasebeta

← #18004131

Subgroups — #18004131

Order 4736.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#11924562C211yesmaximal, characteristic, complemented
2C2×#11924556C211yesmaximal, characteristic, complemented
3#14558013C211yesmaximal, characteristic, complemented
4#14557752C212yesmaximal, complemented
5#14557745C212yesmaximal, complemented
6#14557730C212yesmaximal, complemented
7#14557725C212yesmaximal, complemented
8#14557560C211yesmaximal, characteristic, complemented
9#14557534C211yesmaximal, characteristic, complemented
10C2×#11924457C211yesmaximal, characteristic, complemented
11C37×#535C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13#11924562—24no—
14#11924556—24no—
15C2×#10596942C2211yescharacteristic, complemented
16C2×#10596940C2212yes—
17C2×#10596940C2211yescharacteristic, complemented
18C2×#10596941C2211yescharacteristic, complemented
19C2×#10596939C2212yes—
20C2×#10596939C2211yescharacteristic, complemented
21C2×#10596934C2211yescharacteristic
22C22×#64436C2211yescharacteristic
23C4×Dic74C2212yescomplemented
24C4×D148C2212yescomplemented
25#11924496—22no—
26#11924494—21no—
27C2×C4⋊Dic37C2211yescharacteristic
28C4⋊C4×D37—21no—
29C4⋊#64436C2212yescomplemented
30C4⋊#64436C2212yescomplemented
31#11924460C2212yescomplemented
32#11924457C2212yes—
33#11924457C2212yes—
34#11924457C2212yescomplemented
35C2×#41×C37C2211yescharacteristic
36C22×D4×C37C2211yescharacteristic
37#127×C37C2212yes—
38#124×C37C2212yes—
39#121×C37—21no—
40#121×C37—21no—
41#120×C37—22no—
42#117×C37C2211yescharacteristic
43C24×C37—21no—
44#41×C37—22no—
45#41×C37—22no—
46C2×Q8×C37C2311yescharacteristic
47C2×D4×C37—21no—
48C2×D4×C37—22no—
49C2×D4×C37—21no—
50C2×D4×C37—22no—
51C2×D4×C37—22no—
52C2×D4×C37—22no—
53C2×D4×C37C2312yes—
54C2×D4×C37C2311yescharacteristic
55C22×C4×C37—21no—
56C22×C4×C37C2311yescharacteristic
57C2×C22⋊D37—21no—
58C22×Dic37—21no—
59#10596962—22no—
60#10596962D414yescomplemented
61C2×D148C2311yescharacteristic
62C2×C4×D37—21no—
63C2×C4×D37—22no—
64C2×Dic74C2311yescharacteristic
65C4⋊C4×C37D411yescharacteristic
66C4⋊C4×C37D411yescharacteristic
67C22⋊C4×C37—22no—
68C22⋊C4×C37—22no—
69C22⋊C4×C37D412yes—
70C42×C37C2312yes—
71#10596942—22no—
72#10596941—22no—
73#10596940—24no—
74#10596940—22no—
75#10596939—24no—
76#10596939—22no—
77#10596938—22no—
78C4⋊Dic37—21no—
79C4⋊Dic37C2312yes—
80#10596936—22no—
81C4×Dic37—22no—
82#10596934—22no—
83C2×#64436—22no—
84C2×#64436C2311yescharacteristic
85C2×#64436C2311yescharacteristic
86C2×#64436C2312yes—
87C23×C37—22no—
88C23×C37—21no—
89C23×C37—42no—
90C23×C37—81no—
91C23×C37—81no—
92C23×C37C2×D411yescharacteristic
93C22×D37—21no—
94Q8×C37—21no—
95Q8×C37—21no—
96D4×C37—22no—
97D4×C37—21no—
98D4×C37—22no—
99D4×C37—21no—
100D4×C37—42no—
101D4×C37—42no—
102D4×C37—82no—
103D4×C37—82no—
104C2×C4×C37—21no—
105C2×C4×C37—42no—
106C2×C4×C37C2×D412yes—
107C2×C4×C37C2×D412yes—
108C2×C4×C37C2×D412yes—
109C2×C4×C37C2×D411yescharacteristic
110C2×C4×C37#4112yes—
111C2×C4×C37C2411yescharacteristic
112C22⋊D37—24no—
113C2×Dic37—21no—
114C2×Dic37—22no—
115C2×Dic37—81no—
116D148—21no—
117D148C2×D412yes—
118C4×D37—24no—
119C4×D37—82no—
120Dic74—21no—
121Dic74C2×D412yes—
122#64436—21no—
123#64436—21no—
124#64436—22no—
125C22×C37—21no—
126C22×C37—21no—
127C22×C37—41no—
128C22×C37—42no—
129C22×C37—41no—
130C22×C37—42no—
131C22×C37—41no—
132C22×C37—42no—
133C22×C37—84no—
134C22×C37#12112yes—
135C22×C37C22×D411yescharacteristic
136C2×D37—22no—
137C2×D37—41no—
138C2×D37—41no—
139C4×C37—22no—
140C4×C37—22no—
141C4×C37—41no—
142C4×C37#12112yes—
143C4×C37C22×D411yescharacteristic
144C4×C37C2×#4111yescharacteristic
145Dic37—22no—
146Dic37—42no—
147#3045—371nomaximal, Sylow
148C2×C37—22no—
149C2×C37—81no—
150C2×C37—82no—
151C2×C37C2×#12111yescharacteristic
152C2×C37#57611yescharacteristic
153C2×C37#57711yescharacteristic
154D37—42no—
155C2×AGL(1,ℤ/8)—371no—
156C2×#135—371no—
157#535D3711yescharacteristic, complemented
158#520—371no—
159#464—372no—
160#463—372no—
161#460—372no—
162#459—372no—
163#424—371no—
164#417—371no—
165C2×#102—371no—
166C37#304511yescharacteristic, complemented, Sylow
167C2×#41—371no—
168C2×#41C2×D3711yescharacteristic
169C22×D4C2×D3711yescharacteristic
170AGL(1,ℤ/8)—744no—
171#135—744no—
172C2×Q16—371no—
173C2×SD16—371no—
174C2×SD16—371no—
175C2×SD16—372no—
176C2×D8—371no—
177C2×D8—372no—
178C2×M16—371no—
179C22×C8—371no—
180#127C2×D3712yes—
181#124C2×D3712yes—
182#121—21no—
183#121—21no—
184#120—22no—
185C4×Q8—372no—
186C4×D4—372no—
187C4×D4—742no—
188#117—741no—
189#117C2×D3711yescharacteristic
190C2×C4⋊C4—371no—
191C2×C4⋊C4—741no—
192C4⋊C8—372no—
193C4⋊C8—372no—
194#103—372no—
195#102—372no—
196#102—372no—
197#102—372no—
198C24—21no—
199#41—22no—
200#41—22no—
201#41—374no—
202#41—742no—
203C2×Q8—371no—
204C2×Q8C22×D3711yescharacteristic
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—371no—
212C2×D4—741no—
213C2×D4C22×D3712yes—
214C2×D4C22×D3711yescharacteristic
215C22×C4—21no—
216C22×C4—741no—
217C22×C4—742no—
218C22×C4—741no—
219C22×C4C22×D3711yescharacteristic
220Q16—742no—
221SD16—742no—
222SD16—744no—
223SD16—742no—
224D8—742no—
225D8—744no—
226M16—742no—
227C2×C8—371no—
228C2×C8—371no—
229C2×C8—372no—
230C2×C8—742no—
231C4⋊C4—372no—
232C4⋊C4—742no—
233C4⋊C4—741no—
234C4⋊C4C22⋊D3711yescharacteristic
235C4⋊C4C22⋊D3711yescharacteristic
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—742no—
239C22⋊C4C22⋊D3712yes—
240C42—742no—
241C42C22×D3712yes—
242C23—22no—
243C23—21no—
244C23—42no—
245C23—81no—
246C23—81no—
247C23—741no—
248C23C2×C22⋊D3711yescharacteristic
249Q8—21no—
250Q8—21no—
251Q8—372no—
252Q8—741no—
253D4—22no—
254D4—21no—
255D4—22no—
256D4—21no—
257D4—42no—
258D4—42no—
259D4—82no—
260D4—82no—
261D4—372no—
262D4—744no—
263D4—741no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—2962no—
267C2×C4—2961no—
268C2×C4—741no—
269C2×C4—744no—
270C2×C4—742no—
271C2×C4D4×D3712yes—
272C2×C4#1059696412yes—
273C2×C4C2×C22⋊D3712yes—
274C2×C4C2×C22⋊D3712yes—
275C2×C4C2×C22⋊D3711yescharacteristic
276C2×C4C23×D3711yescharacteristic
277C8—741no—
278C8—741no—
279C8—742no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—42no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—42no—
288C22—84no—
289C22—742no—
290C22—1481no—
291C22—1481no—
292C22#1192450712yes—
293C22C22×C22⋊D3711yescharacteristic
294C4—22no—
295C4—22no—
296C4—41no—
297C4—742no—
298C4—1482no—
299C4#1192450712yes—
300C4C2×D4×D3711yescharacteristic
301C4C2×#1059696411yescharacteristic
302C2—22no—
303C2—82no—
304C2—81no—
305C2—1482no—
306C2C2×#1192450711yescharacteristic
307C2#1455833611yescharacteristic
308C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#535C2
socleC22×C37C22×D4
hypercenter#535D37
hypocenterC37#3045
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. C2×#11924556C2semidirect
3. #14558013C2semidirect
4. #14557752C2semidirect
5. #14557745C2semidirect
6. #14557730C2semidirect
7. #14557725C2semidirect
8. #14557560C2semidirect
9. #14557534C2semidirect
10. C2×#11924457C2semidirect
11. C37×#535C2semidirect
15. C2×#10596942C22semidirect
17. C2×#10596940C22semidirect
18. C2×#10596941C22semidirect
20. C2×#10596939C22semidirect
23. C4×Dic74C22semidirect
24. C4×D148C22semidirect
29. C4⋊#64436C22semidirect
30. C4⋊#64436C22semidirect
31. #11924460C22semidirect
34. #11924457C22semidirect
60. #10596962D4semidirect
157. #535D37semidirect
166. C37#3045semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
C2×#119245562
#145580132
#145577522
#145577452
#145577302
#145577252
#145575602
#145575342
C2×#119244572
C37×#5352
#304537