Subgroups — #14583340

Order 2752.

82 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	#13063271	C₂	1	2	yes	maximal, complemented
3	#13063268	C₂	1	2	yes	maximal, complemented
4	#13063265	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₄₃	—	2	1	no	—
7	#10621898	—	2	1	no	—
8	Q₁₆×C₄₃	—	2	1	no	—
9	Q₁₆×C₄₃	C₂²	1	2	yes	—
10	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	Dic₁₇₂	C₂²	1	1	yes	characteristic
12	D₃₄₄	C₂²	1	1	yes	characteristic
13	#10621873	—	2	1	no	—
14	C₄₃⋊C₁₆	C₂²	1	2	yes	—
15	Q₈×C₄₃	—	2	2	no	—
16	Q₈×C₄₃	—	4	1	no	—
17	C₂×C₄×C₄₃	—	4	1	no	—
18	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
19	C₂²⋊D₄₃	—	4	1	no	—
20	D₁₇₂	—	2	1	no	—
21	C₄×D₄₃	—	4	1	no	—
22	Dic₈₆	—	2	1	no	—
23	C₈×C₄₃	D₄	1	1	yes	characteristic
24	C₈×C₄₃	C₂³	1	1	yes	characteristic
25	C₂²×C₄₃	D₈	1	1	yes	characteristic
26	C₂×D₄₃	—	4	1	no	—
27	C₄×C₄₃	—	4	2	no	—
28	C₄×C₄₃	D₈	1	1	yes	characteristic
29	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
30	Dic₄₃	—	4	1	no	—
31	C₂×C₄₃	—	2	1	no	—
32	C₂×C₄₃	C₂×D₈	1	1	yes	characteristic
33	D₄₃	—	8	1	no	—
34	#510	—	43	1	no	maximal, Sylow
35	C₄₃	#510	1	1	yes	characteristic, complemented, Sylow
36	#135	—	43	1	no	—
37	C₂×Q₁₆	D₄₃	1	1	yes	characteristic, complemented
38	Q₃₂	—	43	2	no	—
39	SD₃₂	—	43	2	no	—
40	M₃₂	—	43	1	no	—
41	#41	—	86	1	no	—
42	C₂×Q₈	—	2	1	no	—
43	Q₁₆	—	2	1	no	—
44	Q₁₆	—	43	1	no	—
45	Q₁₆	C₂×D₄₃	1	2	yes	—
46	SD₁₆	—	86	1	no	—
47	D₈	—	43	1	no	—
48	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
49	C₁₆	—	43	2	no	—
50	Q₈	—	2	2	no	—
51	Q₈	—	4	1	no	—
52	Q₈	—	86	1	no	—
53	D₄	—	86	1	no	—
54	D₄	—	172	1	no	—
55	C₂×C₄	—	4	1	no	—
56	C₂×C₄	—	172	1	no	—
57	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
58	C₈	C₂²⋊D₄₃	1	1	yes	characteristic
59	C₈	C₂²×D₄₃	1	1	yes	characteristic
60	C₂²	—	172	1	no	—
61	C₂²	#10621882	1	1	yes	characteristic
62	C₄	—	4	2	no	—
63	C₄	—	172	1	no	—
64	C₄	#10621882	1	1	yes	characteristic
65	C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
66	C₂	—	2	1	no	—
67	C₂	—	344	1	no	—
68	C₂	C₂×#10621882	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#10621882
commutator, cosocle	C₈×C₄₃	C₂³
Frattini	C₈	C₂²×D₄₃
Fitting	C₂×Q₁₆×C₄₃	C₂
socle	C₂×C₄₃	C₂×D₈
prime radical	#13063347	C₂
hypercenter	C₂×Q₁₆	D₄₃
hypocenter	C₄₃	#510
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #13063271	C₂	semidirect
3. #13063268	C₂	semidirect
4. #13063265	C₂	semidirect
5. C₂×Q₁₆×C₄₃	C₂	semidirect
35. C₄₃	#510	semidirect
37. C₂×Q₁₆	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
#13063271	2
#13063268	2
#13063265	2
C₂×Q₁₆×C₄₃	2
#510	43