Subgroups — #14583331

Order 2752.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063347	C₂	1	2	yes	maximal, complemented
2	Dic₃₄₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#13063270	C₂	1	2	yes	maximal, complemented
4	D₆₈₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#10621898	—	2	2	no	—
7	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
8	Dic₁₇₂	C₂²	1	2	yes	—
9	D₃₄₄	C₂²	1	2	yes	—
10	#10621873	—	2	2	no	—
11	C₁₆×C₄₃	C₂²	1	1	yes	characteristic
12	C₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
14	C₂²⋊D₄₃	—	4	2	no	—
15	D₁₇₂	—	2	2	no	—
16	C₄×D₄₃	—	4	2	no	—
17	Dic₈₆	—	2	2	no	—
18	C₈×C₄₃	D₄	1	1	yes	characteristic
19	C₈×C₄₃	C₂³	1	1	yes	characteristic
20	C₂²×C₄₃	D₈	1	1	yes	characteristic
21	C₂×D₄₃	—	4	2	no	—
22	C₄×C₄₃	D₈	1	1	yes	characteristic
23	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
24	Dic₄₃	—	4	2	no	—
25	C₂×C₄₃	—	2	1	no	—
26	C₂×C₄₃	C₂×D₈	1	1	yes	characteristic
27	D₄₃	—	8	2	no	—
28	#508	—	43	1	no	maximal, Sylow
29	C₄₃	#508	1	1	yes	characteristic, complemented, Sylow
30	#135	—	43	2	no	—
31	Q₃₂	—	43	1	no	—
32	SD₃₂	—	43	2	no	—
33	D₁₆	—	43	1	no	—
34	C₂×C₁₆	D₄₃	1	1	yes	characteristic, complemented
35	#41	—	86	2	no	—
36	Q₁₆	—	43	2	no	—
37	SD₁₆	—	86	2	no	—
38	D₈	—	43	2	no	—
39	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
40	C₁₆	C₂×D₄₃	1	1	yes	characteristic
41	C₁₆	C₂×D₄₃	1	1	yes	characteristic
42	Q₈	—	86	2	no	—
43	D₄	—	86	2	no	—
44	D₄	—	172	2	no	—
45	C₂×C₄	—	172	2	no	—
46	C₂×C₄	D₁₇₂	1	1	yes	characteristic
47	C₈	D₁₇₂	1	1	yes	characteristic
48	C₈	C₂²×D₄₃	1	1	yes	characteristic
49	C₂²	—	172	2	no	—
50	C₂²	D₃₄₄	1	1	yes	characteristic
51	C₄	—	172	2	no	—
52	C₄	D₃₄₄	1	1	yes	characteristic
53	C₄	C₂×D₁₇₂	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	344	2	no	—
56	C₂	C₂×D₃₄₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₃₄₄
commutator, cosocle	C₈×C₄₃	C₂³
Frattini	C₈	C₂²×D₄₃
Fitting	C₂×C₁₆×C₄₃	C₂
socle	C₂×C₄₃	C₂×D₈
hypercenter	C₂×C₁₆	D₄₃
hypocenter	C₄₃	#508
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #13063347	C₂	semidirect
2. Dic₃₄₄	C₂	semidirect
3. #13063270	C₂	semidirect
4. D₆₈₈	C₂	semidirect
5. C₂×C₁₆×C₄₃	C₂	semidirect
29. C₄₃	#508	semidirect
34. C₂×C₁₆	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
Dic₃₄₄	2
#13063270	2
D₆₈₈	2
C₂×C₁₆×C₄₃	2
#508	43