Subgroups — #24905755

Order 10624.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19127754	C₂	1	2	yes	maximal
2	#19127423	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×C₈×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₈₃⋊C₈)	C₄	1	4	yes	—
5	C₂²⋊(C₈₃⋊C₈)	C₄	1	4	yes	—
6	C₄×C₈₃⋊C₈	C₂²	1	4	yes	—
7	C₂²×C₈×C₈₃	C₄	1	2	yes	—
8	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₈₃	C₄	1	2	yes	—
10	C₄×C₈×C₈₃	C₂²	1	2	yes	—
11	C₂×C₈₃⋊C₈	C₂×C₄	1	8	yes	—
12	C₂²×C₄×C₈₃	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₈₃	—	2	4	no	—
15	C₂×C₈×C₈₃	C₂×C₄	1	4	yes	—
16	C₄²×C₈₃	C₂×C₄	1	2	yes	—
17	C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₈₃	C₂³	1	1	yes	characteristic
19	C₂³×C₈₃	C₄²	1	1	yes	characteristic
20	C₂×C₄×C₈₃	—	2	4	no	—
21	C₂×C₄×C₈₃	C₄²	1	2	yes	—
22	C₂×C₄×C₈₃	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₈₃	M₁₆	1	4	yes	—
24	C₂×C₄×C₈₃	C₂²×C₄	1	2	yes	—
25	C₂×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
26	C₈×C₈₃	—	2	4	no	—
27	C₈₃⋊C₈	—	2	8	no	—
28	C₂²×C₈₃	—	2	2	no	—
29	C₂²×C₈₃	#97	1	2	yes	—
30	C₂²×C₈₃	C₂×C₄²	1	1	yes	characteristic
31	C₄×C₈₃	—	2	2	no	—
32	C₄×C₈₃	#97	1	2	yes	—
33	C₄×C₈₃	C₂×M₁₆	1	2	yes	—
34	C₄×C₈₃	#131	1	4	yes	—
35	C₂×C₈₃	—	2	2	no	—
36	C₂×C₈₃	C₂×#97	1	1	yes	characteristic
37	C₂×C₈₃	#405	1	2	yes	—
38	#1452	—	83	1	no	maximal, Sylow
39	C₈₃	#1452	1	1	yes	characteristic, complemented, Sylow
40	#431	—	83	2	no	—
41	C₂×C₄×C₈	D₈₃	1	1	yes	characteristic
42	#322	—	83	4	no	—
43	C₂²×C₈	Dic₈₃	1	2	yes	—
44	C₂×C₄²	C₂×D₈₃	1	1	yes	characteristic
45	C₄⋊C₈	—	83	4	no	—
46	C₂²⋊C₈	—	83	4	no	—
47	C₄×C₈	—	83	4	no	—
48	C₄×C₈	Dic₈₃	1	2	yes	—
49	C₄×C₈	C₂×D₈₃	1	2	yes	—
50	C₂²×C₄	C₄×D₈₃	1	2	yes	—
51	C₂²×C₄	C₂×Dic₈₃	1	1	yes	characteristic
52	C₂×C₈	—	2	4	no	—
53	C₂×C₈	—	83	8	no	—
54	C₂×C₈	C₂×Dic₈₃	1	4	yes	—
55	C₄²	C₄×D₈₃	1	2	yes	—
56	C₄²	C₂×Dic₈₃	1	1	yes	characteristic
57	C₄²	C₂²×D₈₃	1	1	yes	characteristic
58	C₂³	C₄×Dic₈₃	1	1	yes	characteristic
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	C₄×Dic₈₃	1	2	yes	—
61	C₂×C₄	C₄×Dic₈₃	1	1	yes	characteristic
62	C₂×C₄	#13050574	1	4	yes	—
63	C₂×C₄	C₂×C₄×D₈₃	1	2	yes	—
64	C₂×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
65	C₈	—	2	4	no	—
66	C₈	—	166	8	no	—
67	C₂²	—	2	2	no	—
68	C₂²	#14581703	1	2	yes	—
69	C₂²	C₂×C₄×Dic₈₃	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	#14581703	1	2	yes	—
72	C₄	C₂×#13050574	1	2	yes	—
73	C₄	#14581798	1	4	yes	—
74	C₂	—	2	2	no	—
75	C₂	C₂×#14581703	1	1	yes	characteristic
76	C₂	#19127656	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₈₃
commutator, socle	C₂²×C₈₃	C₂×C₄²
Fitting	C₂×C₄×C₈×C₈₃	C₂
prime radical	C₂³×C₈₃	C₄²
cosocle	C₄²×C₈₃	C₂³
hypercenter	C₂×C₄×C₈	D₈₃
hypocenter	C₈₃	#1452
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #19127423	C₂	semidirect
39. C₈₃	#1452	semidirect