Subgroups — C₂×#13063313 #14583416

Order 2752.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₁₇₂	C₂	1	1	yes	maximal, characteristic
3	#13063313	C₂	1	8	yes	maximal, direct product factor
4	C₂×(C₂×D₄₃)⋊C₄	C₂	1	4	yes	maximal, complemented
5	C₂×C₄²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄₃	C₂²	1	2	yes	—
7	C₂²×C₄×C₄₃	C₂²	1	2	yes	—
8	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂²×Dic₄₃	C₂²	1	2	yes	—
10	C₂×D₁₇₂	—	2	4	no	—
11	C₂×D₁₇₂	C₂²	1	4	yes	—
12	C₂×Dic₈₆	—	2	4	no	—
13	C₂×Dic₈₆	C₂²	1	4	yes	complemented
14	C₄²×C₄₃	C₂²	1	4	yes	complemented
15	(C₂×D₄₃)⋊C₄	C₂²	1	16	yes	complemented
16	C₂³×C₄₃	C₂³	1	1	yes	characteristic
17	C₂²×D₄₃	—	2	4	no	—
18	C₂²×D₄₃	—	2	8	no	—
19	C₂²×D₄₃	C₂³	1	4	yes	—
20	C₂×C₄×C₄₃	—	2	4	no	—
21	C₂×C₄×C₄₃	D₄	1	4	yes	—
22	C₂×C₄×C₄₃	C₂³	1	4	yes	—
23	C₂×C₄×C₄₃	C₂³	1	2	yes	—
24	C₂×Dic₄₃	—	2	4	no	—
25	C₂×Dic₄₃	C₂³	1	4	yes	—
26	D₁₇₂	—	2	8	no	—
27	Dic₈₆	—	2	8	no	—
28	C₂²×C₄₃	C₂×D₄	1	2	yes	—
29	C₂²×C₄₃	#41	1	4	yes	—
30	C₂²×C₄₃	C₂⁴	1	1	yes	characteristic
31	C₂×D₄₃	—	2	4	no	—
32	C₂×D₄₃	—	2	8	no	—
33	C₂×D₄₃	—	4	8	no	—
34	C₄×C₄₃	—	2	4	no	—
35	C₄×C₄₃	C₂×D₄	1	4	yes	—
36	Dic₄₃	—	2	4	no	—
37	C₂×C₄₃	#124	1	4	yes	complemented
38	C₂×C₄₃	C₂²×D₄	1	1	yes	characteristic
39	C₂×C₄₃	C₂×#41	1	2	yes	—
40	D₄₃	—	4	4	no	—
41	C₂×#124	—	43	1	no	maximal, Sylow
42	C₄₃	C₂×#124	1	1	yes	characteristic, complemented, Sylow
43	C₂²×Q₈	—	43	1	no	—
44	C₂²×D₄	—	43	1	no	—
45	#124	—	43	8	no	—
46	C₂×C₂²⋊C₄	—	43	4	no	—
47	C₂×C₄²	D₄₃	1	1	yes	characteristic, complemented
48	C₂⁴	—	43	2	no	—
49	C₂×Q₈	—	43	4	no	—
50	C₂×Q₈	—	86	4	no	—
51	C₂×D₄	—	43	4	no	—
52	C₂×D₄	—	86	4	no	—
53	C₂²×C₄	—	43	2	no	—
54	C₂²×C₄	C₂×D₄₃	1	2	yes	—
55	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
56	C₂²⋊C₄	—	43	16	no	—
57	C₄²	C₂×D₄₃	1	4	yes	complemented
58	C₂³	—	43	4	no	—
59	C₂³	—	86	4	no	—
60	C₂³	—	86	8	no	—
61	C₂³	C₂²×D₄₃	1	1	yes	characteristic
62	Q₈	—	86	8	no	—
63	D₄	—	86	8	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	43	4	no	—
66	C₂×C₄	—	86	4	no	—
67	C₂×C₄	D₁₇₂	1	4	yes	—
68	C₂×C₄	C₂²×D₄₃	1	4	yes	—
69	C₂×C₄	C₂²×D₄₃	1	2	yes	—
70	C₂²	—	86	4	no	—
71	C₂²	—	86	8	no	—
72	C₂²	—	172	8	no	—
73	C₂²	C₂×D₁₇₂	1	2	yes	—
74	C₂²	#10621898	1	4	yes	—
75	C₂²	C₂³×D₄₃	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	86	4	no	—
78	C₄	C₂×D₁₇₂	1	4	yes	—
79	C₂	—	172	4	no	—
80	C₂	#13063313	1	4	yes	direct product factor
81	C₂	C₂²×D₁₇₂	1	1	yes	characteristic
82	C₂	C₂×#10621898	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁴
Frattini	C₂²	C₂³×D₄₃
Fitting	C₂×C₄²×C₄₃	C₂
socle	C₂³×C₄₃	C₂³
prime radical	C₂²×D₁₇₂	C₂
hypercenter	C₂×C₄²	D₄₃
hypocenter	C₄₃	C₂×#124
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂²×Dic₈₆	C₂	semidirect
3. #13063313	C₂	direct (N × H)
4. C₂×(C₂×D₄₃)⋊C₄	C₂	semidirect
5. C₂×C₄²×C₄₃	C₂	semidirect
13. C₂×Dic₈₆	C₂²	semidirect
14. C₄²×C₄₃	C₂²	semidirect
15. (C₂×D₄₃)⋊C₄	C₂²	semidirect
37. C₂×C₄₃	#124	semidirect
42. C₄₃	C₂×#124	semidirect
47. C₂×C₄²	D₄₃	semidirect
57. C₄²	C₂×D₄₃	semidirect
80. C₂	#13063313	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₈₆	2
C₂²×D₁₇₂	2
#13063313	2
C₂×(C₂×D₄₃)⋊C₄	2
C₂×C₄²×C₄₃	2
C₂×#124	43

Subgroups — C2×#13063313 #14583416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13063313 #14583416