Subgroups — C₂²×#13093964 #20256484

Order 6016.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13093964	C₂	1	12	yes	maximal, direct product factor
2	C₂²×C₄₇⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	C₂³×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	#13093964	C₂²	1	16	yes	direct product factor
5	C₂×C₄₇⋊C₁₆	C₂²	1	12	yes	complemented
6	C₂³×C₄×C₄₇	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₄₇	C₄	1	1	yes	characteristic
8	C₂²×C₈×C₄₇	C₄	1	6	yes	—
9	C₂²×C₈×C₄₇	C₂²	1	6	yes	—
10	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄₇	C₈	1	1	yes	characteristic
12	C₂²×C₄×C₄₇	C₈	1	6	yes	—
13	C₂²×C₄×C₄₇	C₈	1	1	yes	characteristic
14	C₂²×C₄×C₄₇	C₂×C₄	1	6	yes	—
15	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₇	C₂×C₄	1	12	yes	—
17	C₂×C₈×C₄₇	C₂×C₄	1	6	yes	—
18	C₂×C₈×C₄₇	C₂×C₄	1	3	yes	—
19	C₂×C₈×C₄₇	C₂³	1	3	yes	—
20	C₂×C₈×C₄₇	C₂³	1	4	yes	—
21	C₄₇⋊C₁₆	C₂³	1	8	yes	complemented
22	C₂³×C₄₇	—	2	4	no	—
23	C₂³×C₄₇	C₂×C₈	1	6	yes	—
24	C₂³×C₄₇	C₂×C₈	1	1	yes	characteristic
25	C₂×C₄×C₄₇	C₂×C₈	1	12	yes	—
26	C₂×C₄×C₄₇	C₂×C₈	1	6	yes	—
27	C₂×C₄×C₄₇	C₂×C₈	1	3	yes	—
28	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
29	C₂×C₄×C₄₇	C₂²×C₄	1	3	yes	—
30	C₈×C₄₇	C₂²×C₄	1	3	yes	—
31	C₈×C₄₇	C₂²×C₄	1	4	yes	—
32	C₈×C₄₇	C₂⁴	1	1	yes	characteristic
33	C₂²×C₄₇	—	2	12	no	—
34	C₂²×C₄₇	M₃₂	1	4	yes	complemented
35	C₂²×C₄₇	C₂²×C₈	1	4	yes	—
36	C₂²×C₄₇	C₂²×C₈	1	3	yes	—
37	C₄×C₄₇	C₂²×C₈	1	3	yes	—
38	C₄×C₄₇	C₂²×C₈	1	4	yes	—
39	C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
40	C₂²×M₃₂	—	47	1	no	maximal, Sylow
41	C₂×C₄₇	—	2	4	no	—
42	C₂×C₄₇	C₂×M₃₂	1	6	yes	complemented
43	C₂×C₄₇	C₂³×C₈	1	1	yes	characteristic
44	C₂³×C₈	D₄₇	1	1	yes	characteristic
45	C₂×M₃₂	—	47	12	no	—
46	C₂²×C₁₆	—	47	2	no	—
47	C₄₇	C₂²×M₃₂	1	1	yes	characteristic, complemented, Sylow
48	C₂³×C₄	Dic₄₇	1	1	yes	characteristic
49	C₂²×C₈	Dic₄₇	1	1	yes	characteristic
50	C₂²×C₈	Dic₄₇	1	6	yes	—
51	C₂²×C₈	C₂×D₄₇	1	6	yes	—
52	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
53	M₃₂	—	47	16	no	—
54	C₂×C₁₆	—	47	12	no	—
55	C₂⁴	C₄₇⋊C₈	1	1	yes	characteristic
56	C₂²×C₄	C₄₇⋊C₈	1	6	yes	—
57	C₂²×C₄	C₄₇⋊C₈	1	1	yes	characteristic
58	C₂²×C₄	C₂×Dic₄₇	1	6	yes	—
59	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
60	C₂×C₈	C₂×Dic₄₇	1	6	yes	—
61	C₂×C₈	C₂×Dic₄₇	1	12	yes	—
62	C₂×C₈	C₂×Dic₄₇	1	3	yes	—
63	C₂×C₈	C₂²×D₄₇	1	3	yes	—
64	C₂×C₈	C₂²×D₄₇	1	4	yes	—
65	C₁₆	—	47	8	no	—
66	C₂³	—	2	4	no	—
67	C₂³	C₂×C₄₇⋊C₈	1	6	yes	—
68	C₂³	C₂×C₄₇⋊C₈	1	1	yes	characteristic
69	C₂×C₄	C₂×C₄₇⋊C₈	1	12	yes	—
70	C₂×C₄	C₂×C₄₇⋊C₈	1	6	yes	—
71	C₂×C₄	C₂×C₄₇⋊C₈	1	3	yes	—
72	C₂×C₄	C₂²×Dic₄₇	1	4	yes	—
73	C₂×C₄	C₂²×Dic₄₇	1	3	yes	—
74	C₈	C₂²×Dic₄₇	1	4	yes	—
75	C₈	C₂²×Dic₄₇	1	3	yes	—
76	C₈	C₂³×D₄₇	1	1	yes	characteristic
77	C₂²	—	2	12	no	—
78	C₂²	#13093964	1	4	yes	direct product factor
79	C₂²	C₂²×C₄₇⋊C₈	1	4	yes	—
80	C₂²	C₂²×C₄₇⋊C₈	1	3	yes	—
81	C₄	C₂²×C₄₇⋊C₈	1	3	yes	—
82	C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
83	C₄	C₂³×Dic₄₇	1	1	yes	characteristic
84	C₂	—	2	4	no	—
85	C₂	C₂×#13093964	1	6	yes	direct product factor
86	C₂	C₂³×C₄₇⋊C₈	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#13093964	C₂	direct (N × H)
2. C₂²×C₄₇⋊C₁₆	C₂	semidirect
4. #13093964	C₂²	direct (N × H)
5. C₂×C₄₇⋊C₁₆	C₂²	semidirect
21. C₄₇⋊C₁₆	C₂³	semidirect
34. C₂²×C₄₇	M₃₂	semidirect
42. C₂×C₄₇	C₂×M₃₂	semidirect
47. C₄₇	C₂²×M₃₂	semidirect
78. C₂²	#13093964	direct (N × H)
85. C₂	C₂×#13093964	direct (N × H)

Subgroups — C22×#13093964 #20256484

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#13093964 #20256484