Subgroups — C₂²×#13093963 #20256483

Order 6016.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093963	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₄×D₄₇	C₄	1	1	yes	characteristic
6	C₂²×C₄₇⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₈×D₄₇	C₄	1	6	yes	—
8	C₂×C₈×D₄₇	C₂²	1	6	yes	—
9	#13093963	C₂²	1	16	yes	direct product factor
10	C₂×C₄₇⋊C₁₆	C₂²	1	6	yes	complemented
11	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₄₇	C₂²	1	6	yes	complemented
13	C₂³×D₄₇	C₈	1	1	yes	characteristic
14	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₄₇	C₈	1	1	yes	characteristic
16	C₂×C₄×D₄₇	C₈	1	6	yes	—
17	C₂×C₄×D₄₇	C₂×C₄	1	6	yes	—
18	C₂×C₈×C₄₇	C₂×C₄	1	3	yes	—
19	C₂×C₈×C₄₇	C₂³	1	3	yes	—
20	C₂×C₄₇⋊C₈	C₂×C₄	1	6	yes	—
21	C₈×D₄₇	C₂×C₄	1	12	yes	—
22	C₈×D₄₇	C₂³	1	4	yes	—
23	C₁₆×C₄₇	C₂³	1	4	yes	complemented
24	C₄₇⋊C₁₆	C₂³	1	4	yes	complemented
25	C₂³×C₄₇	C₂×C₈	1	1	yes	characteristic
26	C₂²×D₄₇	—	2	4	no	—
27	C₂²×D₄₇	C₂×C₈	1	6	yes	—
28	C₂×C₄×C₄₇	C₂×C₈	1	3	yes	—
29	C₂×C₄×C₄₇	C₂²×C₄	1	3	yes	—
30	C₂×Dic₄₇	C₂×C₈	1	6	yes	—
31	C₄×D₄₇	C₂×C₈	1	12	yes	—
32	C₄×D₄₇	C₂²×C₄	1	4	yes	—
33	C₈×C₄₇	C₂²×C₄	1	3	yes	—
34	C₈×C₄₇	C₂⁴	1	1	yes	characteristic
35	C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
36	C₂²×C₄₇	M₃₂	1	4	yes	complemented
37	C₂²×C₄₇	C₂²×C₈	1	3	yes	—
38	C₂×D₄₇	—	2	12	no	—
39	C₂×D₄₇	C₂²×C₈	1	4	yes	—
40	C₄×C₄₇	C₂²×C₈	1	3	yes	—
41	C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
42	Dic₄₇	C₂²×C₈	1	4	yes	—
43	C₂²×M₃₂	—	47	1	no	maximal, Sylow
44	C₂×C₄₇	C₂×M₃₂	1	6	yes	complemented
45	C₂×C₄₇	C₂³×C₈	1	1	yes	characteristic
46	D₄₇	—	2	4	no	—
47	C₂³×C₈	—	47	1	no	—
48	C₂×M₃₂	—	47	12	no	—
49	C₂²×C₁₆	—	47	1	no	—
50	C₂²×C₁₆	D₄₇	1	1	yes	characteristic, complemented
51	C₄₇	C₂²×M₃₂	1	1	yes	characteristic, complemented, Sylow
52	C₂³×C₄	—	47	1	no	—
53	C₂²×C₈	—	47	1	no	—
54	C₂²×C₈	—	47	6	no	—
55	C₂²×C₈	—	47	6	no	—
56	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
57	M₃₂	—	47	16	no	—
58	C₂×C₁₆	—	47	6	no	—
59	C₂×C₁₆	C₂×D₄₇	1	6	yes	complemented
60	C₂⁴	—	47	1	no	—
61	C₂²×C₄	—	47	1	no	—
62	C₂²×C₄	—	47	6	no	—
63	C₂²×C₄	—	47	6	no	—
64	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
65	C₂×C₈	—	47	6	no	—
66	C₂×C₈	—	47	12	no	—
67	C₂×C₈	—	47	4	no	—
68	C₂×C₈	C₄×D₄₇	1	3	yes	—
69	C₂×C₈	C₂²×D₄₇	1	3	yes	—
70	C₁₆	—	47	4	no	—
71	C₁₆	C₂²×D₄₇	1	4	yes	complemented
72	C₂³	—	47	6	no	—
73	C₂³	—	94	4	no	—
74	C₂³	C₈×D₄₇	1	1	yes	characteristic
75	C₂×C₄	—	47	6	no	—
76	C₂×C₄	—	47	12	no	—
77	C₂×C₄	—	47	4	no	—
78	C₂×C₄	C₈×D₄₇	1	3	yes	—
79	C₂×C₄	C₂×C₄×D₄₇	1	3	yes	—
80	C₈	—	47	4	no	—
81	C₈	C₂×C₄×D₄₇	1	3	yes	—
82	C₈	C₂³×D₄₇	1	1	yes	characteristic
83	C₂²	—	47	4	no	—
84	C₂²	—	94	12	no	—
85	C₂²	#13093963	1	4	yes	direct product factor
86	C₂²	C₂×C₈×D₄₇	1	3	yes	—
87	C₄	—	47	4	no	—
88	C₄	C₂×C₈×D₄₇	1	3	yes	—
89	C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
90	C₂	—	94	4	no	—
91	C₂	C₂×#13093963	1	6	yes	direct product factor
92	C₂	C₂²×C₈×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂×D₄₇
commutator	C₂×C₄₇	C₂³×C₈
Frattini	C₈	C₂³×D₄₇
Fitting	C₂²×C₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₈
hypercenter	C₂²×C₁₆	D₄₇
hypocenter	C₄₇	C₂²×M₃₂
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#13093963	C₂	direct (N × H)
3. C₂²×C₄₇⋊C₁₆	C₂	semidirect
4. C₂²×C₁₆×C₄₇	C₂	semidirect
9. #13093963	C₂²	direct (N × H)
10. C₂×C₄₇⋊C₁₆	C₂²	semidirect
12. C₂×C₁₆×C₄₇	C₂²	semidirect
23. C₁₆×C₄₇	C₂³	semidirect
24. C₄₇⋊C₁₆	C₂³	semidirect
36. C₂²×C₄₇	M₃₂	semidirect
44. C₂×C₄₇	C₂×M₃₂	semidirect
50. C₂²×C₁₆	D₄₇	semidirect
51. C₄₇	C₂²×M₃₂	semidirect
59. C₂×C₁₆	C₂×D₄₇	semidirect
71. C₁₆	C₂²×D₄₇	semidirect
85. C₂²	#13093963	direct (N × H)
91. C₂	C₂×#13093963	direct (N × H)

Subgroups — C22×#13093963 #20256483

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#13093963 #20256483