Subgroups — C₂×#13063268 #14583322

Order 2752.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₄₄	C₂	1	1	yes	maximal, characteristic
2	#13063268	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₄₃	—	2	1	no	—
6	C₂×D₁₇₂	—	2	1	no	—
7	Q₁₆×C₄₃	—	2	1	no	—
8	Q₁₆×C₄₃	C₂²	1	2	yes	complemented
9	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	D₃₄₄	—	2	1	no	—
11	D₃₄₄	C₂²	1	2	yes	—
12	C₄₃⋊C₁₆	C₂²	1	2	yes	complemented
13	C₂²×D₄₃	—	4	1	no	—
14	Q₈×C₄₃	—	2	2	no	—
15	Q₈×C₄₃	—	4	1	no	—
16	C₂×C₄×C₄₃	—	4	1	no	—
17	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
18	D₁₇₂	—	2	2	no	—
19	D₁₇₂	—	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	—	4	2	no	—
26	C₄×C₄₃	D₈	1	1	yes	characteristic
27	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
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	D₄₃	1	1	yes	characteristic, complemented
34	C₂×D₈	—	43	1	no	—
35	SD₃₂	—	43	4	no	—
36	C₂×C₁₆	—	43	1	no	—
37	C₂×Q₈	—	2	1	no	—
38	C₂×D₄	—	86	1	no	—
39	Q₁₆	—	2	1	no	—
40	Q₁₆	C₂×D₄₃	1	2	yes	complemented
41	D₈	—	43	2	no	—
42	D₈	—	86	1	no	—
43	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
44	C₁₆	—	43	2	no	—
45	C₂³	—	172	1	no	—
46	Q₈	—	2	2	no	—
47	Q₈	—	4	1	no	—
48	D₄	—	86	2	no	—
49	D₄	—	172	1	no	—
50	C₂×C₄	—	4	1	no	—
51	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
52	C₈	C₂²⋊D₄₃	1	1	yes	characteristic
53	C₈	C₂²×D₄₃	1	1	yes	characteristic
54	C₂²	—	344	2	no	—
55	C₂²	—	172	2	no	—
56	C₂²	#10621882	1	1	yes	characteristic
57	C₄	—	4	2	no	—
58	C₄	#10621882	1	1	yes	characteristic
59	C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
60	C₂	—	344	2	no	—
61	C₂	#13063268	1	2	yes	direct product factor
62	C₂	C₂×#10621882	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10621882
commutator, cosocle	C₈×C₄₃	C₂³
Frattini	C₈	C₂²×D₄₃
Fitting	C₂×Q₁₆×C₄₃	C₂
socle	C₂²×C₄₃	D₈
prime radical	C₂×D₃₄₄	C₂
hypercenter	C₂×Q₁₆	D₄₃
hypocenter	C₄₃	C₂×SD₃₂
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #13063268	C₂	direct (N × H)
3. C₂×C₄₃⋊C₁₆	C₂	semidirect
4. C₂×Q₁₆×C₄₃	C₂	semidirect
8. Q₁₆×C₄₃	C₂²	semidirect
12. C₄₃⋊C₁₆	C₂²	semidirect
28. C₂×C₄₃	SD₃₂	semidirect
32. C₄₃	C₂×SD₃₂	semidirect
33. C₂×Q₁₆	D₄₃	semidirect
40. Q₁₆	C₂×D₄₃	semidirect
61. C₂	#13063268	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×D₃₄₄	2
#13063268	2
C₂×C₄₃⋊C₁₆	2
C₂×Q₁₆×C₄₃	2
C₂×SD₃₂	43

Subgroups — C2×#13063268 #14583322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13063268 #14583322