Subgroups — C₂×#17984020 #22577434

Order 8768.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₁₃₇	C₂	1	2	yes	maximal
2	#17984020	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₃₇	—	2	2	no	—
5	C₄⋊Dic₁₃₇	—	2	2	no	—
6	C₄⋊Dic₁₃₇	C₂²	1	4	yes	—
7	C₂²×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₁₃₇	C₄	1	4	yes	complemented
9	C₂×C₈×C₁₃₇	C₂²	1	2	yes	—
10	C₂×Dic₁₃₇	—	2	4	no	—
11	C₂×Dic₁₃₇	—	4	4	no	—
12	C₂³×C₁₃₇	D₄	1	1	yes	characteristic
13	C₂×C₄×C₁₃₇	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₁₃₇	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₃₇	Q₈	1	2	yes	—
16	C₂×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
17	C₈×C₁₃₇	C₂×C₄	1	4	yes	complemented
18	C₂²×C₁₃₇	C₄⋊C₄	1	2	yes	—
19	C₂²×C₁₃₇	SD₁₆	1	4	yes	—
20	C₂²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
21	C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
22	C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
23	C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
24	Dic₁₃₇	—	4	4	no	—
25	C₂×C₁₃₇	#106	1	4	yes	complemented
26	C₂×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₁₃₇	C₂×SD₁₆	1	2	yes	—
28	C₁₃₇	C₂×#106	1	1	yes	characteristic, complemented, Sylow
29	C₂×#106	—	137	1	no	maximal, Sylow
30	C₂²×C₈	D₁₃₇	1	1	yes	characteristic
31	C₂×C₄⋊C₄	—	137	2	no	—
32	#106	—	137	4	no	—
33	C₂²×C₄	—	274	2	no	—
34	C₂²×C₄	C₂×D₁₃₇	1	1	yes	characteristic
35	C₂×C₈	Dic₁₃₇	1	4	yes	complemented
36	C₂×C₈	C₂×D₁₃₇	1	2	yes	—
37	C₄⋊C₄	—	274	2	no	—
38	C₄⋊C₄	—	137	4	no	—
39	C₂³	D₅₄₈	1	1	yes	characteristic
40	C₂×C₄	—	274	4	no	—
41	C₂×C₄	—	548	4	no	—
42	C₂×C₄	C₂×Dic₁₃₇	1	2	yes	—
43	C₂×C₄	D₅₄₈	1	1	yes	characteristic
44	C₂×C₄	Dic₂₇₄	1	2	yes	—
45	C₂×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
46	C₈	C₂×Dic₁₃₇	1	4	yes	complemented
47	C₂²	C₄⋊Dic₁₃₇	1	2	yes	—
48	C₂²	#14555499	1	4	yes	—
49	C₂²	C₂×D₅₄₈	1	1	yes	characteristic
50	C₄	—	548	4	no	—
51	C₄	C₄⋊Dic₁₃₇	1	2	yes	—
52	C₄	C₂²×Dic₁₃₇	1	1	yes	characteristic
53	C₄	C₂×Dic₂₇₄	1	1	yes	characteristic
54	C₂	#17984020	1	4	yes	direct product factor
55	C₂	C₂×C₄⋊Dic₁₃₇	1	1	yes	characteristic
56	C₂	C₂×#14555499	1	2	yes	—

	subgroup	G/H
center	C₂³	D₅₄₈
commutator	C₄×C₁₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₃₇
Fitting	C₂²×C₈×C₁₃₇	C₂
socle	C₂³×C₁₃₇	D₄
hypercenter	C₂²×C₈	D₁₃₇
hypocenter	C₁₃₇	C₂×#106
LCS	G ▷ C₄×C₁₃₇ ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #17984020	C₂	direct (N × H)
8. C₂×C₈×C₁₃₇	C₄	semidirect
17. C₈×C₁₃₇	C₂×C₄	semidirect
25. C₂×C₁₃₇	#106	semidirect
28. C₁₃₇	C₂×#106	semidirect
35. C₂×C₈	Dic₁₃₇	semidirect
46. C₈	C₂×Dic₁₃₇	semidirect
54. C₂	#17984020	direct (N × H)

Subgroups — C2×#17984020 #22577434

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17984020 #22577434