Subgroups — C₂×#10621884 #13063338

Order 1376.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₇₂	C₂	1	1	yes	maximal, characteristic
3	#10621884	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₄₃	—	2	1	no	—
6	Q₈×C₄₃	—	2	1	no	—
7	Q₈×C₄₃	C₂²	1	2	yes	complemented
8	C₂×C₄×C₄₃	—	2	1	no	—
9	C₂×C₄×C₄₃	C₂²	1	1	yes	characteristic
10	D₁₇₂	—	2	1	no	—
11	D₁₇₂	C₂²	1	2	yes	—
12	C₄₃⋊C₈	C₂²	1	2	yes	complemented
13	C₂²×C₄₃	D₄	1	1	yes	characteristic
14	C₂×D₄₃	—	2	2	no	—
15	C₂×D₄₃	—	4	2	no	—
16	C₄×C₄₃	—	2	2	no	—
17	C₄×C₄₃	D₄	1	1	yes	characteristic
18	C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂×C₄₃	SD₁₆	1	2	yes	complemented
20	C₂×C₄₃	C₂×D₄	1	1	yes	characteristic
21	D₄₃	—	4	2	no	—
22	C₄₃	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₂×SD₁₆	—	43	1	no	maximal, Sylow
24	C₂×Q₈	D₄₃	1	1	yes	characteristic, complemented
25	C₂×D₄	—	43	1	no	—
26	SD₁₆	—	43	4	no	—
27	C₂×C₈	—	43	1	no	—
28	C₂³	—	86	1	no	—
29	Q₈	—	2	1	no	—
30	Q₈	C₂×D₄₃	1	2	yes	complemented
31	D₄	—	43	2	no	—
32	D₄	—	86	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	C₂×D₄₃	1	1	yes	characteristic
35	C₈	—	43	2	no	—
36	C₂²	—	86	2	no	—
37	C₂²	—	172	2	no	—
38	C₂²	C₂²⋊D₄₃	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	C₂²⋊D₄₃	1	1	yes	characteristic
41	C₄	C₂²×D₄₃	1	1	yes	characteristic
42	C₂	—	172	2	no	—
43	C₂	#10621884	1	2	yes	direct product factor
44	C₂	C₂×C₂²⋊D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₄₃
commutator, cosocle	C₄×C₄₃	C₂³
Frattini	C₄	C₂²×D₄₃
Fitting	C₂×Q₈×C₄₃	C₂
socle	C₂²×C₄₃	D₄
prime radical	C₂×D₁₇₂	C₂
hypercenter	C₂×Q₈	D₄₃
hypocenter	C₄₃	C₂×SD₁₆
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₄₃	C₂	semidirect
3. #10621884	C₂	direct (N × H)
4. C₂×C₄₃⋊C₈	C₂	semidirect
7. Q₈×C₄₃	C₂²	semidirect
12. C₄₃⋊C₈	C₂²	semidirect
19. C₂×C₄₃	SD₁₆	semidirect
22. C₄₃	C₂×SD₁₆	semidirect
24. C₂×Q₈	D₄₃	semidirect
30. Q₈	C₂×D₄₃	semidirect
43. C₂	#10621884	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×Q₈×C₄₃	2
C₂×D₁₇₂	2
#10621884	2
C₂×C₄₃⋊C₈	2
C₂×SD₁₆	43

Subgroups — C2×#10621884 #13063338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10621884 #13063338