Subgroups — #14582660

Order 2752.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063284	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
5	C₂²×Dic₄₃	—	2	1	no	—
6	M₁₆×C₄₃	—	2	1	no	—
7	M₁₆×C₄₃	C₄	1	2	yes	complemented
8	C₂×C₈×C₄₃	—	2	1	no	—
9	C₂²⋊Dic₄₃	—	2	1	no	—
10	C₄⋊Dic₄₃	C₄	1	2	yes	complemented
11	C₄×Dic₄₃	—	2	1	no	—
12	C₄×Dic₄₃	—	2	1	no	—
13	C₄×Dic₄₃	C₄	1	2	yes	complemented
14	C₂³×C₄₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₃	Q₈	1	1	yes	characteristic
21	C₂×Dic₄₃	—	2	4	no	—
22	C₂×Dic₄₃	—	2	2	no	—
23	C₂×Dic₄₃	—	2	2	no	—
24	C₈×C₄₃	—	2	2	no	—
25	C₂²×C₄₃	—	2	2	no	—
26	C₂²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
29	C₄×C₄₃	C₄²	1	1	yes	characteristic
30	C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
33	Dic₄₃	—	2	4	no	—
34	Dic₄₃	—	4	2	no	—
35	C₂×C₄₃	—	2	1	no	—
36	C₂×C₄₃	—	2	1	no	—
37	C₂×C₄₃	#95	1	1	yes	characteristic
38	C₂×C₄₃	#104	1	2	yes	—
39	#339	—	43	1	no	maximal, Sylow
40	C₄₃	#339	1	1	yes	characteristic, complemented, Sylow
41	C₂×M₁₆	D₄₃	1	1	yes	characteristic
42	#117	—	43	1	no	—
43	C₂×C₄²	—	43	1	no	—
44	C₂²×C₄	—	86	1	no	—
45	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
46	M₁₆	—	2	1	no	—
47	M₁₆	Dic₄₃	1	2	yes	complemented
48	C₂×C₈	—	2	1	no	—
49	C₄⋊C₄	—	43	2	no	—
50	C₂²⋊C₄	—	86	1	no	—
51	C₄²	—	43	2	no	—
52	C₄²	—	86	1	no	—
53	C₄²	—	86	1	no	—
54	C₂³	D₁₇₂	1	1	yes	characteristic
55	C₂×C₄	—	86	4	no	—
56	C₂×C₄	—	86	2	no	—
57	C₂×C₄	—	86	2	no	—
58	C₂×C₄	Dic₈₆	1	1	yes	characteristic
59	C₂×C₄	C₄×D₄₃	1	1	yes	characteristic
60	C₂×C₄	C₄×D₄₃	1	1	yes	characteristic
61	C₂×C₄	C₂×Dic₄₃	1	1	yes	characteristic
62	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
63	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
64	C₈	—	2	2	no	—
65	C₂²	—	2	2	no	—
66	C₂²	C₄⋊Dic₄₃	1	1	yes	characteristic
67	C₂²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
68	C₂²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
69	C₄	—	86	4	no	—
70	C₄	—	172	2	no	—
71	C₄	C₄×Dic₄₃	1	1	yes	characteristic
72	C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
73	C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
74	C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	2	1	no	—
77	C₂	C₄₃⋊#95	1	1	yes	characteristic
78	C₂	#13063251	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₄₃
commutator	C₄×C₄₃	C₄²
Frattini	C₂²×C₄	C₂×D₄₃
Fitting	C₂×M₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂²⋊C₄
prime radical	C₂³×C₄₃	D₄
cosocle	C₂²×C₄×C₄₃	C₂²
hypercenter	C₂×M₁₆	D₄₃
hypocenter	C₄₃	#339
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
7. M₁₆×C₄₃	C₄	semidirect
10. C₄⋊Dic₄₃	C₄	semidirect
13. C₄×Dic₄₃	C₄	semidirect
40. C₄₃	#339	semidirect
47. M₁₆	Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
#13063284	2
C₂×C₄×Dic₄₃	2
C₂×M₁₆×C₄₃	2
#339	43