Subgroups — C₄₇×#1707 #20239317

Order 6016.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#500	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#498	C₂	1	2	yes	maximal
3	C₄₇×#494	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#487	C₂	1	2	yes	maximal
5	C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₄₇	—	2	2	no	—
7	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
8	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
9	#107×C₄₇	—	2	2	no	—
10	#106×C₄₇	—	2	4	no	—
11	#103×C₄₇	—	2	4	no	—
12	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₄₇	—	2	2	no	—
16	C₂×Q₈×C₄₇	—	2	2	no	—
17	Q₁₆×C₄₇	—	4	4	no	—
18	C₂×C₈×C₄₇	D₄	1	2	yes	—
19	C₂×C₈×C₄₇	D₄	1	2	yes	—
20	C₂×C₈×C₄₇	D₄	1	2	yes	—
21	C₄⋊C₄×C₄₇	—	2	2	no	—
22	C₄⋊C₄×C₄₇	—	2	2	no	—
23	C₄⋊C₄×C₄₇	—	2	2	no	—
24	C₄⋊C₄×C₄₇	—	2	2	no	—
25	C₄²×C₄₇	C₂³	1	1	yes	characteristic
26	Q₈×C₄₇	—	4	4	no	—
27	Q₈×C₄₇	—	4	4	no	—
28	C₂×C₄×C₄₇	—	4	2	no	—
29	C₂×C₄×C₄₇	—	4	2	no	—
30	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₈×C₄₇	—	2	2	no	—
34	C₈×C₄₇	SD₁₆	1	4	yes	—
35	C₈×C₄₇	Q₁₆	1	4	yes	complemented
36	C₂²×C₄₇	#127	1	1	yes	characteristic
37	C₄×C₄₇	—	8	2	no	—
38	C₄×C₄₇	—	8	2	no	—
39	C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
40	C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
41	C₄×C₄₇	#135	1	2	yes	—
42	#1707	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₄₇	#492	1	1	yes	characteristic
44	C₂×C₄₇	#494	1	1	yes	characteristic
45	C₂×C₄₇	#495	1	1	yes	characteristic
46	#500	C₂×C₄₇	1	1	yes	characteristic
47	#498	C₂×C₄₇	1	2	yes	—
48	#494	C₂×C₄₇	1	1	yes	characteristic
49	#487	C₂×C₄₇	1	2	yes	—
50	C₈²	C₂×C₄₇	1	1	yes	characteristic
51	C₄₇	#1707	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×Q₁₆	—	2	2	no	—
53	C₄⋊Q₈	C₂²×C₄₇	1	2	yes	—
54	C₄⋊Q₈	C₂²×C₄₇	1	2	yes	—
55	#107	—	2	2	no	—
56	#106	—	2	4	no	—
57	#103	—	2	4	no	—
58	C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
59	C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
60	C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
61	C₂×Q₈	—	2	2	no	—
62	C₂×Q₈	—	2	2	no	—
63	Q₁₆	—	4	4	no	—
64	C₂×C₈	D₄×C₄₇	1	2	yes	—
65	C₂×C₈	D₄×C₄₇	1	2	yes	—
66	C₂×C₈	D₄×C₄₇	1	2	yes	—
67	C₄⋊C₄	—	2	2	no	—
68	C₄⋊C₄	—	2	2	no	—
69	C₄⋊C₄	—	2	2	no	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄²	C₂³×C₄₇	1	1	yes	characteristic
72	Q₈	—	4	4	no	—
73	Q₈	—	4	4	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	4	2	no	—
76	C₂×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
77	C₂×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
78	C₂×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	SD₁₆×C₄₇	1	4	yes	—
81	C₈	Q₁₆×C₄₇	1	4	yes	complemented
82	C₂²	#127×C₄₇	1	1	yes	characteristic
83	C₄	—	8	2	no	—
84	C₄	—	8	2	no	—
85	C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
86	C₄	C₂×Q₁₆×C₄₇	1	2	yes	—
87	C₄	#135×C₄₇	1	2	yes	—
88	C₂	C₄₇×#492	1	1	yes	characteristic
89	C₂	C₄₇×#494	1	1	yes	characteristic
90	C₂	C₄₇×#495	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₄₇	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₄₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
35. C₈×C₄₇	Q₁₆	semidirect
42. #1707	C₄₇	direct (N × H)
51. C₄₇	#1707	direct (N × H)
81. C₈	Q₁₆×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#500	2
C₄₇×#498	2
C₄₇×#494	2
C₄₇×#487	2
C₈²×C₄₇	2
#1707	47

Subgroups — C47×#1707 #20239317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#1707 #20239317