Subgroups — #14582976

Order 2752.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10621872	C₂	1	2	yes	maximal, complemented
2	C₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic
3	(C₂×D₄₃)⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₇₂	C₄	1	1	yes	characteristic
7	C₂×C₄×D₄₃	C₂²	1	2	yes	—
8	C₂×C₈×C₄₃	C₂²	1	2	yes	—
9	C₄²×C₄₃	C₂²	1	1	yes	characteristic
10	(C₂×D₄₃)⋊C₄	C₄	1	2	yes	—
11	C₄⋊Dic₄₃	C₄	1	1	yes	characteristic
12	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	#10621872	—	2	4	no	—
15	C₂²×D₄₃	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₃	C₂×C₄	1	2	yes	—
20	D₁₇₂	—	2	2	no	—
21	C₄×D₄₃	—	2	2	no	—
22	C₄×D₄₃	—	2	2	no	—
23	C₈×C₄₃	—	2	2	no	—
24	C₄₃⋊C₈	—	2	1	no	—
25	C₄₃⋊C₈	D₄	1	2	yes	complemented
26	C₂²×C₄₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₄₃	—	2	2	no	—
28	C₂×D₄₃	—	2	2	no	—
29	C₂×D₄₃	—	2	2	no	—
30	C₄×C₄₃	—	2	1	no	—
31	C₄×C₄₃	M₁₆	1	2	yes	complemented
32	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₄₃	#41	1	1	yes	characteristic
34	Dic₄₃	—	2	2	no	—
35	C₂×C₄₃	C₄×D₄	1	1	yes	characteristic
36	C₂×C₄₃	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₄₃	#131	1	1	yes	characteristic
38	D₄₃	—	4	2	no	—
39	#436	—	43	1	no	maximal, Sylow
40	C₄₃	#436	1	1	yes	characteristic, complemented, Sylow
41	C₂×M₁₆	—	43	2	no	—
42	C₄×D₄	—	43	1	no	—
43	C₄⋊C₈	D₄₃	1	1	yes	characteristic, complemented
44	C₂²⋊C₈	—	43	2	no	—
45	C₄×C₈	—	43	1	no	—
46	C₂×D₄	—	43	1	no	—
47	C₂²×C₄	—	43	2	no	—
48	M₁₆	—	86	4	no	—
49	C₂×C₈	—	43	1	no	—
50	C₂×C₈	—	43	1	no	—
51	C₂×C₈	C₂×D₄₃	1	2	yes	—
52	C₄⋊C₄	—	43	1	no	—
53	C₂²⋊C₄	—	43	2	no	—
54	C₄²	C₂×D₄₃	1	1	yes	characteristic
55	C₂³	—	43	2	no	—
56	D₄	—	86	2	no	—
57	C₂×C₄	—	43	2	no	—
58	C₂×C₄	—	86	2	no	—
59	C₂×C₄	—	86	2	no	—
60	C₂×C₄	C₄×D₄₃	1	1	yes	characteristic
61	C₂×C₄	C₄×D₄₃	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
63	C₈	—	2	2	no	—
64	C₈	—	43	2	no	—
65	C₈	—	86	1	no	—
66	C₂²	—	86	2	no	—
67	C₂²	—	86	2	no	—
68	C₂²	—	86	2	no	—
69	C₂²	C₂×C₄×D₄₃	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	86	2	no	—
72	C₄	#10621872	1	2	yes	complemented
73	C₄	D₄×D₄₃	1	1	yes	characteristic
74	C₄	#10621902	1	1	yes	characteristic
75	C₂	—	172	2	no	—
76	C₂	#13063287	1	1	yes	characteristic
77	C₂	C₂×#10621872	1	1	yes	characteristic
78	C₂	#13063333	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₃
commutator, socle	C₂²×C₄₃	C₂²×C₄
Fitting	C₄⋊C₈×C₄₃	C₂
prime radical	C₂×D₁₇₂	C₄
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	C₄⋊C₈	D₄₃
hypocenter	C₄₃	#436
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#10621872	C₂	semidirect
3. (C₂×D₄₃)⋊C₈	C₂	semidirect
4. C₄×C₄₃⋊C₈	C₂	semidirect
5. C₄⋊C₈×C₄₃	C₂	semidirect
25. C₄₃⋊C₈	D₄	semidirect
31. C₄×C₄₃	M₁₆	semidirect
40. C₄₃	#436	semidirect
43. C₄⋊C₈	D₄₃	semidirect
72. C₄	#10621872	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
C₄×D₁₇₂	2
(C₂×D₄₃)⋊C₈	2
C₄×C₄₃⋊C₈	2
C₄⋊C₈×C₄₃	2
#436	43