Subgroups — C₄₇×#1409 #20239019

Order 6016.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#492	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#353	C₂	1	2	yes	maximal
3	C₂×SD₁₆×C₄₇	—	2	2	no	—
4	C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
5	#127×C₄₇	C₂²	1	1	yes	characteristic
6	#99×C₄₇	—	2	2	no	—
7	C₄×C₈×C₄₇	C₄	1	1	yes	characteristic, complemented
8	C₂×Q₈×C₄₇	—	2	1	no	—
9	C₂×D₄×C₄₇	—	4	1	no	—
10	C₂×D₄×C₄₇	D₄	1	2	yes	—
11	SD₁₆×C₄₇	—	4	4	no	—
12	C₂×C₈×C₄₇	—	2	1	no	—
13	C₄⋊C₄×C₄₇	—	4	1	no	—
14	C₂²⋊C₄×C₄₇	—	4	2	no	—
15	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄₇	—	2	2	no	—
17	Q₈×C₄₇	—	4	2	no	—
18	D₄×C₄₇	—	4	2	no	—
19	D₄×C₄₇	—	8	2	no	—
20	C₂×C₄×C₄₇	—	2	1	no	—
21	C₂×C₄×C₄₇	—	4	1	no	—
22	C₂×C₄×C₄₇	—	8	2	no	—
23	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
24	C₈×C₄₇	—	2	2	no	—
25	C₂²×C₄₇	—	4	2	no	—
26	C₂²×C₄₇	—	8	2	no	—
27	C₂²×C₄₇	#99	1	1	yes	characteristic
28	C₄×C₄₇	—	2	2	no	—
29	C₄×C₄₇	—	2	1	no	—
30	C₄×C₄₇	—	8	1	no	—
31	C₄×C₄₇	—	16	2	no	—
32	#1409	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×C₄₇	—	2	1	no	—
34	C₂×C₄₇	—	8	2	no	—
35	C₂×C₄₇	#353	1	1	yes	characteristic
36	#492	C₂×C₄₇	1	1	yes	characteristic
37	#353	C₂×C₄₇	1	2	yes	—
38	C₄₇	#1409	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×SD₁₆	—	2	2	no	—
40	C₄⋊Q₈	C₄×C₄₇	1	1	yes	characteristic, complemented
41	#127	C₂²×C₄₇	1	1	yes	characteristic
42	#99	—	2	2	no	—
43	C₄×C₈	C₄×C₄₇	1	1	yes	characteristic, complemented
44	C₂×Q₈	—	2	1	no	—
45	C₂×D₄	—	4	1	no	—
46	C₂×D₄	D₄×C₄₇	1	2	yes	—
47	SD₁₆	—	4	4	no	—
48	C₂×C₈	—	2	1	no	—
49	C₄⋊C₄	—	4	1	no	—
50	C₂²⋊C₄	—	4	2	no	—
51	C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
52	C₂³	—	2	2	no	—
53	Q₈	—	4	2	no	—
54	D₄	—	4	2	no	—
55	D₄	—	8	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	4	1	no	—
58	C₂×C₄	—	8	2	no	—
59	C₂×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₂²	—	4	2	no	—
62	C₂²	—	8	2	no	—
63	C₂²	#99×C₄₇	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	2	1	no	—
66	C₄	—	8	1	no	—
67	C₄	—	16	2	no	—
68	C₂	—	2	1	no	—
69	C₂	—	8	2	no	—
70	C₂	C₄₇×#353	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₇	#353
commutator	C₄²	C₂×C₄×C₄₇
Frattini, cosocle	#127	C₂²×C₄₇
prime radical	#127×C₄₇	C₂²
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₇ ◁ C₂²×C₄₇ ◁ C₂×C₄×C₄₇ ◁ #127×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄⋊Q₈×C₄₇	C₄	semidirect
7. C₄×C₈×C₄₇	C₄	semidirect
32. #1409	C₄₇	direct (N × H)
38. C₄₇	#1409	direct (N × H)
40. C₄⋊Q₈	C₄×C₄₇	semidirect
43. C₄×C₈	C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#492	2
C₄₇×#353	2
#1409	47

Subgroups — C47×#1409 #20239019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#1409 #20239019