Subgroups — #14583017

Order 2752.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063347	C₂	1	1	yes	maximal, characteristic
2	#13063331	C₂	1	2	yes	maximal, complemented
3	#13063261	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063253	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#10621898	C₂²	1	2	yes	—
7	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₄²×C₄₃	C₂²	1	1	yes	characteristic
10	#10621877	C₂²	1	2	yes	—
11	Dic₁₇₂	C₄	1	1	yes	characteristic, complemented
12	D₃₄₄	C₄	1	1	yes	characteristic, complemented
13	#10621873	C₄	1	2	yes	complemented
14	#10621872	—	2	2	no	—
15	C₈×D₄₃	—	2	2	no	—
16	C₂×C₄×C₄₃	—	2	1	no	—
17	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²⋊D₄₃	—	2	2	no	—
19	D₁₇₂	C₂×C₄	1	2	yes	—
20	C₄×D₄₃	—	2	2	no	—
21	Dic₈₆	C₂×C₄	1	2	yes	—
22	C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
23	C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
24	C₈×C₄₃	D₄	1	1	yes	characteristic
25	C₈×C₄₃	D₄	1	1	yes	characteristic
26	C₄₃⋊C₈	—	2	2	no	—
27	C₂²×C₄₃	#41	1	1	yes	characteristic
28	C₂×D₄₃	—	2	2	no	—
29	C₄×C₄₃	—	2	2	no	—
30	C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
32	Dic₄₃	—	2	2	no	—
33	C₂×C₄₃	—	2	1	no	—
34	C₂×C₄₃	C₄×D₄	1	1	yes	characteristic
35	D₄₃	—	4	2	no	—
36	#443	—	43	1	no	maximal, Sylow
37	C₄₃	#443	1	1	yes	characteristic, complemented, Sylow
38	#135	—	43	1	no	—
39	#131	—	43	2	no	—
40	#108	—	43	1	no	—
41	#104	—	43	2	no	—
42	C₄×C₈	D₄₃	1	1	yes	characteristic, complemented
43	#41	—	43	2	no	—
44	Q₁₆	—	43	1	no	—
45	SD₁₆	—	43	2	no	—
46	D₈	—	43	1	no	—
47	M₁₆	—	43	2	no	—
48	M₁₆	—	86	2	no	—
49	C₂×C₈	—	86	2	no	—
50	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
51	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
52	C₄²	C₂×D₄₃	1	1	yes	characteristic
53	Q₈	—	43	2	no	—
54	D₄	—	43	2	no	—
55	D₄	—	86	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	86	2	no	—
58	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
59	C₈	—	86	2	no	—
60	C₈	C₄×D₄₃	1	1	yes	characteristic
61	C₈	C₄×D₄₃	1	1	yes	characteristic
62	C₈	D₁₇₂	1	1	yes	characteristic
63	C₈	D₁₇₂	1	1	yes	characteristic
64	C₂²	—	86	2	no	—
65	C₂²	#10621898	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	—	86	2	no	—
68	C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
69	C₄	C₂×D₁₇₂	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	172	2	no	—
72	C₂	C₄×D₁₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₁₇₂
commutator	C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	C₄×C₈×C₄₃	C₂
socle	C₂×C₄₃	C₄×D₄
prime radical	#13063347	C₂
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	C₄×C₈	D₄₃
hypocenter	C₄₃	#443
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13063331	C₂	semidirect
3. #13063261	C₂	semidirect
4. #13063253	C₂	semidirect
5. C₄×C₈×C₄₃	C₂	semidirect
11. Dic₁₇₂	C₄	semidirect
12. D₃₄₄	C₄	semidirect
13. #10621873	C₄	semidirect
37. C₄₃	#443	semidirect
42. C₄×C₈	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#13063347	2
#13063331	2
#13063261	2
#13063253	2
C₄×C₈×C₄₃	2
#443	43