Subgroups — #14583022

Order 2752.

104 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	#97×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	2	yes	—
25	C₄₃⋊C₈	—	2	2	no	—
26	C₂²×C₄₃	#41	1	1	yes	characteristic
27	C₂×D₄₃	—	2	2	no	—
28	C₄×C₄₃	—	4	1	no	—
29	C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	Dic₄₃	—	2	2	no	—
32	C₂×C₄₃	—	2	1	no	—
33	C₂×C₄₃	C₄×D₄	1	1	yes	characteristic
34	D₄₃	—	4	2	no	—
35	#444	—	43	1	no	maximal, Sylow
36	C₄₃	#444	1	1	yes	characteristic, complemented, Sylow
37	#135	—	43	1	no	—
38	#131	—	43	2	no	—
39	#108	—	43	1	no	—
40	#104	—	43	2	no	—
41	#97	D₄₃	1	1	yes	characteristic, complemented
42	#41	—	43	2	no	—
43	Q₁₆	—	43	1	no	—
44	SD₁₆	—	43	2	no	—
45	D₈	—	43	1	no	—
46	M₁₆	—	43	2	no	—
47	M₁₆	—	86	2	no	—
48	C₂×C₈	—	86	2	no	—
49	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
50	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
51	C₄²	C₂×D₄₃	1	1	yes	characteristic
52	Q₈	—	43	2	no	—
53	D₄	—	43	2	no	—
54	D₄	—	86	2	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	86	2	no	—
57	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
58	C₈	—	86	2	no	—
59	C₈	C₄×D₄₃	1	1	yes	characteristic
60	C₈	C₄×D₄₃	1	1	yes	characteristic
61	C₈	D₁₇₂	1	2	yes	—
62	C₂²	—	86	2	no	—
63	C₂²	#10621898	1	1	yes	characteristic
64	C₄	—	4	1	no	—
65	C₄	—	86	2	no	—
66	C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
67	C₄	C₂×D₁₇₂	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	172	2	no	—
70	C₂	C₄×D₁₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₁₇₂
commutator	C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	#97×C₄₃	C₂
socle	C₂×C₄₃	C₄×D₄
prime radical	#13063347	C₂
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	#97	D₄₃
hypocenter	C₄₃	#444
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

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. #97×C₄₃	C₂	semidirect
11. Dic₁₇₂	C₄	semidirect
12. D₃₄₄	C₄	semidirect
13. #10621873	C₄	semidirect
36. C₄₃	#444	semidirect
41. #97	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
#97×C₄₃	2
#444	43