Subgroups — C₈²×#64408 #34001920

Order 18688.

750 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×#64408	C₂	1	3	yes	maximal
2	C₈×#11924036	C₂	1	3	yes	maximal
3	C₈²×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₄×#11924036	C₂²	1	3	yes	—
5	C₂×C₈×#64408	C₄	1	12	yes	—
6	C₄²×#64408	C₂²	1	1	yes	characteristic
7	C₈×#10596833	C₄	1	12	yes	complemented
8	C₄×C₈×D₇₃	C₂²	1	3	yes	—
9	C₈×#10596831	C₄	1	3	yes	complemented
10	C₈²×C₇₃	C₄	1	1	yes	characteristic, complemented
11	C₂×#11924036	C₂×C₄	1	6	yes	—
12	C₂×C₄×#64408	C₂×C₄	1	6	yes	—
13	C₄×#10596833	C₂×C₄	1	12	yes	—
14	C₈×#64408	C₈	1	48	yes	direct product factor
15	C₂×C₈×D₇₃	C₂×C₄	1	6	yes	—
16	C₄²×D₇₃	C₂³	1	1	yes	characteristic
17	C₄×#10596831	C₂×C₄	1	3	yes	—
18	C₈×Dic₇₃	C₂×C₄	1	6	yes	—
19	C₄×C₈×C₇₃	C₂×C₄	1	3	yes	—
20	C₂²×#64408	C₄²	1	4	yes	—
21	#11924036	C₂×C₈	1	24	yes	—
22	C₂×#10596833	C₄²	1	12	yes	—
23	C₄×#64408	C₂×C₈	1	24	yes	—
24	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
25	C₂×#10596831	C₄²	1	6	yes	—
26	C₈×D₇₃	C₂×C₈	1	24	yes	—
27	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
28	C₂×C₈×C₇₃	C₄²	1	6	yes	—
29	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
30	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
31	C₂×#64408	C₄×C₈	1	24	yes	—
32	C₂×C₄×C₇₃	C₂×C₄²	1	3	yes	—
33	C₂×Dic₇₃	C₂×C₄²	1	3	yes	—
34	C₄×D₇₃	C₂²×C₈	1	12	yes	—
35	#10596833	C₄×C₈	1	24	yes	complemented
36	C₈×C₇₃	C₄×C₈	1	12	yes	complemented
37	#10596831	C₄×C₈	1	12	yes	complemented
38	C₂²×C₇₃	C₄³	1	1	yes	characteristic
39	C₂×D₇₃	C₂×C₄×C₈	1	6	yes	—
40	#64408	C₈²	1	16	yes	direct product factor
41	C₄×C₇₃	C₂×C₄×C₈	1	6	yes	—
42	Dic₇₃	C₂×C₄×C₈	1	6	yes	—
43	C₄×C₈²	—	73	1	no	maximal, Sylow
44	C₂×C₇₃	C₄²×C₈	1	3	yes	—
45	D₇₃	C₂×C₈²	1	4	yes	—
46	C₄²×C₈	—	73	3	no	—
47	C₂×C₈²	—	73	3	no	—
48	C₂×C₈²	—	73	1	no	—
49	C₇₃	C₄×C₈²	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₄×C₈	—	73	12	no	—
51	C₂×C₄×C₈	—	73	3	no	—
52	C₂×C₄×C₈	—	73	3	no	—
53	C₄³	—	73	1	no	—
54	C₈²	—	73	12	no	—
55	C₈²	—	73	3	no	—
56	C₈²	#64408	1	1	yes	characteristic, direct product factor
57	C₂²×C₈	—	73	6	no	—
58	C₂²×C₈	—	73	6	no	—
59	C₂×C₄²	—	73	6	no	—
60	C₂×C₄²	—	73	1	no	—
61	C₄×C₈	—	73	12	no	—
62	C₄×C₈	—	73	48	no	—
63	C₄×C₈	—	73	6	no	—
64	C₄×C₈	—	73	3	no	—
65	C₄×C₈	C₂×#64408	1	3	yes	—
66	C₂²×C₄	—	73	4	no	—
67	C₂²×C₄	—	73	3	no	—
68	C₂×C₈	—	73	12	no	—
69	C₂×C₈	—	73	24	no	—
70	C₂×C₈	—	73	6	no	—
71	C₂×C₈	—	73	24	no	—
72	C₂×C₈	C₄×#64408	1	6	yes	—
73	C₄²	—	73	24	no	—
74	C₄²	—	73	3	no	—
75	C₄²	C₂²×#64408	1	1	yes	characteristic
76	C₂³	—	73	1	no	—
77	C₂×C₄	—	73	24	no	—
78	C₂×C₄	—	73	3	no	—
79	C₂×C₄	—	73	12	no	—
80	C₂×C₄	C₂×C₄×#64408	1	3	yes	—
81	C₈	—	73	24	no	—
82	C₈	—	73	12	no	—
83	C₈	C₈×#64408	1	12	yes	direct product factor
84	C₂²	—	73	6	no	—
85	C₂²	C₄²×#64408	1	1	yes	characteristic
86	C₄	—	73	16	no	—
87	C₄	—	73	6	no	—
88	C₄	C₂×C₈×#64408	1	6	yes	—
89	C₂	—	73	4	no	—
90	C₂	C₄×C₈×#64408	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₈²	#64408
commutator, hypocenter	C₇₃	C₄×C₈²
Frattini	C₄²	C₂²×#64408
Fitting	C₈²×C₇₃	C₄
socle	C₂²×C₇₃	C₄³
prime radical	C₂²×D₇₃	C₂×C₄²
cosocle	C₄²×D₇₃	C₂³
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₈²

Complements

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

N	H ≅ G/N	type
7. C₈×#10596833	C₄	semidirect
9. C₈×#10596831	C₄	semidirect
10. C₈²×C₇₃	C₄	semidirect
14. C₈×#64408	C₈	direct (N × H)
35. #10596833	C₄×C₈	semidirect
36. C₈×C₇₃	C₄×C₈	semidirect
37. #10596831	C₄×C₈	semidirect
40. #64408	C₈²	direct (N × H)
49. C₇₃	C₄×C₈²	semidirect
56. C₈²	#64408	direct (N × H)
83. C₈	C₈×#64408	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₈×#64408	2
C₈×#11924036	2
C₈²×D₇₃	2
C₄×C₈²	73

Subgroups — C82×#64408 #34001920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈²×#64408 #34001920