Subgroups — #14582938

Order 2752.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10621872	C₂	1	1	yes	maximal, characteristic
2	#13063283	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#13063259	C₂	1	1	yes	maximal, characteristic, complemented
5	#13063258	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063256	C₂	1	1	yes	maximal, characteristic, complemented
7	#106×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄₃	—	2	1	no	—
9	C₂×C₄×D₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
13	(C₂×D₄₃)⋊C₄	—	2	1	no	—
14	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
16	Dic₄₃⋊C₄	—	2	1	no	—
17	C₄×Dic₄₃	—	2	1	no	—
18	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	#10621872	C₄	1	4	yes	complemented
20	C₂²×D₄₃	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₃	—	2	1	no	—
22	C₂×C₄×C₄₃	—	2	1	no	—
23	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
24	C₂×Dic₄₃	—	2	1	no	—
25	C₂×Dic₄₃	—	2	1	no	—
26	C₂×Dic₄₃	D₄	1	1	yes	characteristic
27	C₄×D₄₃	—	4	2	no	—
28	C₄×D₄₃	C₂×C₄	1	2	yes	—
29	C₄×D₄₃	Q₈	1	2	yes	—
30	C₈×C₄₃	C₂×C₄	1	2	yes	complemented
31	C₄₃⋊C₈	C₂×C₄	1	2	yes	complemented
32	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×D₄₃	—	2	1	no	—
34	C₂×D₄₃	—	2	1	no	—
35	C₂×D₄₃	C₄⋊C₄	1	2	yes	—
36	C₄×C₄₃	—	4	1	no	—
37	C₄×C₄₃	—	4	1	no	—
38	C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
39	C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
40	Dic₄₃	—	4	1	no	—
41	Dic₄₃	—	4	1	no	—
42	Dic₄₃	C₄⋊C₄	1	2	yes	—
43	C₂×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
45	C₂×C₄₃	#137	1	1	yes	characteristic
46	D₄₃	—	2	2	no	—
47	#428	—	43	1	no	maximal, Sylow
48	C₄₃	#428	1	1	yes	characteristic, complemented, Sylow
49	C₂×M₁₆	—	43	1	no	—
50	#117	—	43	1	no	—
51	C₂×C₄⋊C₄	—	43	1	no	—
52	#107	—	43	1	no	—
53	#107	—	43	1	no	—
54	#106	—	43	1	no	—
55	#106	D₄₃	1	1	yes	characteristic, complemented
56	C₂²×C₄	—	43	1	no	—
57	C₂²×C₄	—	86	1	no	—
58	M₁₆	—	43	4	no	—
59	C₂×C₈	—	43	1	no	—
60	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
61	C₄⋊C₄	—	43	1	no	—
62	C₄⋊C₄	—	43	1	no	—
63	C₄⋊C₄	—	86	1	no	—
64	C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
65	C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
66	C₂²⋊C₄	—	86	1	no	—
67	C₄²	—	86	1	no	—
68	C₂³	—	43	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	43	1	no	—
72	C₂×C₄	—	43	2	no	—
73	C₂×C₄	—	43	2	no	—
74	C₂×C₄	—	86	1	no	—
75	C₂×C₄	—	86	1	no	—
76	C₂×C₄	—	172	2	no	—
77	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
78	C₈	—	43	2	no	—
79	C₈	C₄×D₄₃	1	2	yes	complemented
80	C₂²	—	43	2	no	—
81	C₂²	—	86	1	no	—
82	C₂²	—	86	1	no	—
83	C₂²	D₄×D₄₃	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	43	2	no	—
87	C₄	—	172	1	no	—
88	C₄	—	172	1	no	—
89	C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
90	C₄	Q₈×D₄₃	1	1	yes	characteristic
91	C₂	—	86	2	no	—
92	C₂	C₄⋊C₄×D₄₃	1	1	yes	characteristic
93	C₂	#13063352	1	1	yes	characteristic
94	C₂	#13063354	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	#106×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
prime radical	C₂²×D₄₃	D₄
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	#106	D₄₃
hypocenter	C₄₃	#428
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
4. #13063259	C₂	semidirect
5. #13063258	C₂	semidirect
6. #13063256	C₂	semidirect
7. #106×C₄₃	C₂	semidirect
19. #10621872	C₄	semidirect
30. C₈×C₄₃	C₂×C₄	semidirect
31. C₄₃⋊C₈	C₂×C₄	semidirect
48. C₄₃	#428	semidirect
55. #106	D₄₃	semidirect
79. C₈	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10621872	2
#13063283	2
C₄⋊C₄×D₄₃	2
#13063259	2
#13063258	2
#13063256	2
#106×C₄₃	2
#428	43