Subgroups — C₂×#13063270 #14583324

Order 2752.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃₄₄	C₂	1	1	yes	maximal, characteristic
3	#13063270	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₇₂	—	2	1	no	—
6	C₂×Dic₈₆	—	2	1	no	—
7	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
8	Dic₁₇₂	—	2	1	no	—
9	Dic₁₇₂	C₂²	1	2	yes	complemented
10	D₃₄₄	—	2	1	no	—
11	D₃₄₄	C₂²	1	2	yes	—
12	C₁₆×C₄₃	C₂²	1	2	yes	complemented
13	C₂²×D₄₃	—	4	1	no	—
14	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
15	C₂×Dic₄₃	—	4	1	no	—
16	D₁₇₂	—	2	2	no	—
17	D₁₇₂	—	4	1	no	—
18	Dic₈₆	—	2	2	no	—
19	Dic₈₆	—	4	1	no	—
20	C₈×C₄₃	D₄	1	1	yes	characteristic
21	C₈×C₄₃	C₂³	1	1	yes	characteristic
22	C₂²×C₄₃	D₈	1	1	yes	characteristic
23	C₂×D₄₃	—	4	2	no	—
24	C₂×D₄₃	—	8	2	no	—
25	C₄×C₄₃	D₈	1	1	yes	characteristic
26	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
27	Dic₄₃	—	4	2	no	—
28	C₂×C₄₃	SD₃₂	1	2	yes	complemented
29	C₂×C₄₃	C₂×D₈	1	1	yes	characteristic
30	D₄₃	—	8	2	no	—
31	C₂×SD₃₂	—	43	1	no	maximal, Sylow
32	C₄₃	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
33	C₂×Q₁₆	—	43	1	no	—
34	C₂×D₈	—	43	1	no	—
35	SD₃₂	—	43	4	no	—
36	C₂×C₁₆	D₄₃	1	1	yes	characteristic, complemented
37	C₂×Q₈	—	86	1	no	—
38	C₂×D₄	—	86	1	no	—
39	Q₁₆	—	43	2	no	—
40	Q₁₆	—	86	1	no	—
41	D₈	—	43	2	no	—
42	D₈	—	86	1	no	—
43	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
44	C₁₆	C₂×D₄₃	1	2	yes	complemented
45	C₂³	—	172	1	no	—
46	Q₈	—	86	2	no	—
47	Q₈	—	172	1	no	—
48	D₄	—	86	2	no	—
49	D₄	—	172	1	no	—
50	C₂×C₄	—	172	1	no	—
51	C₂×C₄	D₁₇₂	1	1	yes	characteristic
52	C₈	D₁₇₂	1	1	yes	characteristic
53	C₈	C₂²×D₄₃	1	1	yes	characteristic
54	C₂²	—	344	2	no	—
55	C₂²	—	172	2	no	—
56	C₂²	D₃₄₄	1	1	yes	characteristic
57	C₄	—	172	2	no	—
58	C₄	D₃₄₄	1	1	yes	characteristic
59	C₄	C₂×D₁₇₂	1	1	yes	characteristic
60	C₂	—	344	2	no	—
61	C₂	#13063270	1	2	yes	direct product factor
62	C₂	C₂×D₃₄₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₄₄
commutator, cosocle	C₈×C₄₃	C₂³
Frattini	C₈	C₂²×D₄₃
Fitting	C₂×C₁₆×C₄₃	C₂
socle	C₂²×C₄₃	D₈
prime radical	C₂×D₃₄₄	C₂
hypercenter	C₂×C₁₆	D₄₃
hypocenter	C₄₃	C₂×SD₃₂
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₇₂	C₂	semidirect
3. #13063270	C₂	direct (N × H)
4. C₂×C₁₆×C₄₃	C₂	semidirect
9. Dic₁₇₂	C₂²	semidirect
12. C₁₆×C₄₃	C₂²	semidirect
28. C₂×C₄₃	SD₃₂	semidirect
32. C₄₃	C₂×SD₃₂	semidirect
36. C₂×C₁₆	D₄₃	semidirect
44. C₁₆	C₂×D₄₃	semidirect
61. C₂	#13063270	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₁₇₂	2
C₂×D₃₄₄	2
#13063270	2
C₂×C₁₆×C₄₃	2
C₂×SD₃₂	43

Subgroups — C2×#13063270 #14583324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13063270 #14583324