Subgroups — #14583082

Order 2752.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063355	C₂	1	2	yes	maximal, complemented
2	#13063323	C₂	1	1	yes	maximal, characteristic, complemented
3	#13063252	C₂	1	2	yes	maximal, complemented
4	#13063244	C₂	1	1	yes	maximal, characteristic, complemented
5	2₋¹⁺⁴×C₄₃	C₂	1	1	yes	maximal, characteristic
6	#41×C₄₃	—	2	2	no	—
7	#41×C₄₃	—	2	2	no	—
8	#41×C₄₃	C₂²	1	2	yes	—
9	C₂×Q₈×C₄₃	—	2	2	no	—
10	C₂×Q₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₈₆	C₂²	1	1	yes	characteristic
12	#10621885	—	2	2	no	—
13	#10621883	—	2	2	no	—
14	Dic₄₃⋊C₄	—	2	2	no	—
15	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
16	#10621877	C₂²	1	2	yes	—
17	Q₈×C₄₃	—	2	2	no	—
18	Q₈×C₄₃	—	2	2	no	—
19	Q₈×C₄₃	D₄	1	2	yes	—
20	D₄×C₄₃	—	2	2	no	—
21	D₄×C₄₃	—	2	2	no	—
22	D₄×C₄₃	D₄	1	2	yes	—
23	C₂×C₄×C₄₃	—	2	4	no	—
24	C₂×C₄×C₄₃	—	2	2	no	—
25	C₂×C₄×C₄₃	D₄	1	2	yes	—
26	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
27	C₂×Dic₄₃	—	2	1	no	—
28	C₂×Dic₄₃	—	2	1	no	—
29	Dic₈₆	—	2	2	no	—
30	C₄₃⋊C₈	—	2	2	no	—
31	C₂²×C₄₃	—	2	2	no	—
32	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₄₃	—	2	2	no	—
34	C₄×C₄₃	—	2	2	no	—
35	C₄×C₄₃	C₂×D₄	1	2	yes	—
36	Dic₄₃	—	2	2	no	—
37	Dic₄₃	—	4	1	no	—
38	C₂×C₄₃	—	2	1	no	—
39	C₂×C₄₃	—	4	2	no	—
40	C₂×C₄₃	#120	1	1	yes	characteristic
41	#456	—	43	1	no	maximal, Sylow
42	C₄₃	#456	1	1	yes	characteristic, complemented, Sylow
43	2₋¹⁺⁴	D₄₃	1	1	yes	characteristic
44	#137	—	43	2	no	—
45	C₄⋊Q₈	—	43	1	no	—
46	#104	—	43	2	no	—
47	#101	—	43	1	no	—
48	#41	—	2	2	no	—
49	#41	—	2	2	no	—
50	#41	C₂×D₄₃	1	2	yes	—
51	C₂×Q₈	—	2	2	no	—
52	C₂×Q₈	—	43	1	no	—
53	C₂×Q₈	C₂×D₄₃	1	1	yes	characteristic
54	Q₁₆	—	86	2	no	—
55	SD₁₆	—	86	2	no	—
56	M₁₆	—	43	2	no	—
57	C₄⋊C₄	—	86	2	no	—
58	C₄²	—	43	1	no	—
59	Q₈	—	2	2	no	—
60	Q₈	—	2	2	no	—
61	Q₈	—	86	2	no	—
62	Q₈	C₂²⋊D₄₃	1	2	yes	—
63	D₄	—	2	2	no	—
64	D₄	—	2	2	no	—
65	D₄	C₂²⋊D₄₃	1	2	yes	—
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	2	2	no	—
68	C₂×C₄	—	86	1	no	—
69	C₂×C₄	—	86	1	no	—
70	C₂×C₄	C₂²⋊D₄₃	1	2	yes	—
71	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
72	C₈	—	86	2	no	—
73	C₂²	—	2	2	no	—
74	C₂²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	2	2	no	—
77	C₄	—	86	2	no	—
78	C₄	—	172	1	no	—
79	C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
80	C₂	—	2	1	no	—
81	C₂	—	4	2	no	—
82	C₂	#13063294	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13063294
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting, prime radical	2₋¹⁺⁴×C₄₃	C₂
socle	C₂×C₄₃	#120
hypercenter	2₋¹⁺⁴	D₄₃
hypocenter	C₄₃	#456
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ 2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. #13063355	C₂	semidirect
2. #13063323	C₂	semidirect
3. #13063252	C₂	semidirect
4. #13063244	C₂	semidirect
42. C₄₃	#456	semidirect

Maximal subgroups

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

subgroup	index
#13063355	2
#13063323	2
#13063252	2
#13063244	2
2₋¹⁺⁴×C₄₃	2
#456	43