Subgroups — #13063354

Order 1376.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#10621900	C₂	1	1	yes	maximal, characteristic
3	SD₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#10621885	C₂	1	1	yes	maximal, characteristic, complemented
5	#10621883	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
7	#10621872	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₄₃	C₂²	1	1	yes	characteristic
9	D₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²⋊D₄₃	—	2	1	no	—
11	C₂×Dic₄₃	—	2	1	no	—
12	C₄×D₄₃	—	2	1	no	—
13	C₄×D₄₃	C₂²	1	1	yes	characteristic
14	Dic₈₆	—	2	1	no	—
15	Dic₈₆	C₂²	1	1	yes	characteristic
16	Dic₈₆	C₂²	1	1	yes	characteristic
17	C₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₄₃	—	2	1	no	—
20	C₂×D₄₃	D₄	1	1	yes	characteristic
21	C₄×C₄₃	—	2	1	no	—
22	C₄×C₄₃	C₂³	1	1	yes	characteristic
23	Dic₄₃	—	2	1	no	—
24	Dic₄₃	—	2	1	no	—
25	Dic₄₃	D₄	1	1	yes	characteristic
26	C₂×C₄₃	—	4	1	no	—
27	C₂×C₄₃	C₂×D₄	1	1	yes	characteristic
28	D₄₃	—	2	1	no	—
29	C₄₃	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	43	1	no	maximal, Sylow
31	#41	—	43	1	no	—
32	C₂×Q₈	—	43	1	no	—
33	Q₁₆	—	43	1	no	—
34	Q₁₆	—	43	1	no	—
35	SD₁₆	—	43	1	no	—
36	SD₁₆	D₄₃	1	1	yes	characteristic, complemented
37	M₁₆	—	43	1	no	—
38	Q₈	—	43	1	no	—
39	Q₈	—	43	1	no	—
40	Q₈	—	86	1	no	—
41	Q₈	C₂×D₄₃	1	1	yes	characteristic
42	D₄	—	86	1	no	—
43	D₄	C₂×D₄₃	1	1	yes	characteristic
44	C₂×C₄	—	43	1	no	—
45	C₂×C₄	—	86	1	no	—
46	C₂×C₄	—	86	1	no	—
47	C₈	—	43	1	no	—
48	C₈	C₂×D₄₃	1	1	yes	characteristic
49	C₂²	—	2	1	no	—
50	C₂²	—	43	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	43	1	no	—
53	C₄	—	86	1	no	—
54	C₄	—	86	1	no	—
55	C₄	C₂²×D₄₃	1	1	yes	characteristic
56	C₂	—	4	1	no	—
57	C₂	—	86	1	no	—
58	C₂	D₄×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₄₃
commutator, cosocle	C₄×C₄₃	C₂³
Frattini	C₄	C₂²×D₄₃
Fitting	SD₁₆×C₄₃	C₂
socle	C₂×C₄₃	C₂×D₄
prime radical	#10621900	C₂
hypercenter	SD₁₆	D₄₃
hypocenter	C₄₃	#137
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×D₄₃	C₂	semidirect
3. SD₁₆×C₄₃	C₂	semidirect
4. #10621885	C₂	semidirect
5. #10621883	C₂	semidirect
6. Dic₁₇₂	C₂	semidirect
7. #10621872	C₂	semidirect
29. C₄₃	#137	semidirect
36. SD₁₆	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₄₃	2
#10621900	2
SD₁₆×C₄₃	2
#10621885	2
#10621883	2
Dic₁₇₂	2
#10621872	2
#137	43