Subgroups — C₂×#11758414 #14521469

Order 1984.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₂₄₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758414	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×C₃₁	—	2	1	no	—
6	C₂×D₁₂₄	—	2	1	no	—
7	D₈×C₃₁	—	2	1	no	—
8	D₈×C₃₁	C₂²	1	2	yes	complemented
9	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
10	D₂₄₈	—	2	1	no	—
11	D₂₄₈	C₂²	1	2	yes	complemented
12	C₃₁⋊C₁₆	C₂²	1	2	yes	complemented
13	C₂³×C₃₁	—	4	1	no	—
14	C₂²×D₃₁	—	4	1	no	—
15	D₄×C₃₁	—	2	2	no	—
16	D₄×C₃₁	—	4	1	no	—
17	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
18	D₁₂₄	—	2	2	no	—
19	D₁₂₄	—	4	1	no	—
20	C₈×C₃₁	D₄	1	1	yes	characteristic
21	C₈×C₃₁	C₂³	1	1	yes	characteristic
22	C₂²×C₃₁	—	4	2	no	—
23	C₂²×C₃₁	—	8	2	no	—
24	C₂²×C₃₁	D₈	1	1	yes	characteristic
25	C₂×D₃₁	—	4	2	no	—
26	C₂×D₃₁	—	8	2	no	—
27	C₄×C₃₁	D₈	1	1	yes	characteristic
28	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
29	C₂×D₁₆	—	31	1	no	maximal, Sylow
30	C₂×C₃₁	—	8	2	no	—
31	C₂×C₃₁	D₁₆	1	2	yes	complemented
32	C₂×C₃₁	C₂×D₈	1	1	yes	characteristic
33	D₃₁	—	8	2	no	—
34	C₂×D₈	—	31	1	no	—
35	C₂×D₈	D₃₁	1	1	yes	characteristic, complemented
36	D₁₆	—	31	4	no	—
37	C₂×C₁₆	—	31	1	no	—
38	C₃₁	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₄	—	2	1	no	—
40	C₂×D₄	—	62	1	no	—
41	D₈	—	2	1	no	—
42	D₈	—	31	2	no	—
43	D₈	—	62	1	no	—
44	D₈	C₂×D₃₁	1	2	yes	complemented
45	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
46	C₁₆	—	31	2	no	—
47	C₂³	—	4	1	no	—
48	C₂³	—	124	1	no	—
49	D₄	—	2	2	no	—
50	D₄	—	4	1	no	—
51	D₄	—	62	2	no	—
52	D₄	—	124	1	no	—
53	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
54	C₈	C₂²⋊D₃₁	1	1	yes	characteristic
55	C₈	C₂²×D₃₁	1	1	yes	characteristic
56	C₂²	—	4	2	no	—
57	C₂²	—	8	2	no	—
58	C₂²	—	124	2	no	—
59	C₂²	—	248	2	no	—
60	C₂²	#92479	1	1	yes	characteristic
61	C₄	#92479	1	1	yes	characteristic
62	C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
63	C₂	—	8	2	no	—
64	C₂	—	248	2	no	—
65	C₂	#11758414	1	2	yes	direct product factor
66	C₂	C₂×#92479	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#92479
commutator, cosocle	C₈×C₃₁	C₂³
Frattini	C₈	C₂²×D₃₁
Fitting	C₂×D₈×C₃₁	C₂
socle	C₂²×C₃₁	D₈
hypercenter	C₂×D₈	D₃₁
hypocenter	C₃₁	C₂×D₁₆
LCS	G ▷ C₈×C₃₁ ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₈×C₃₁	C₂	semidirect
2. C₂×D₂₄₈	C₂	semidirect
3. #11758414	C₂	direct (N × H)
4. C₂×C₃₁⋊C₁₆	C₂	semidirect
8. D₈×C₃₁	C₂²	semidirect
11. D₂₄₈	C₂²	semidirect
12. C₃₁⋊C₁₆	C₂²	semidirect
31. C₂×C₃₁	D₁₆	semidirect
35. C₂×D₈	D₃₁	semidirect
38. C₃₁	C₂×D₁₆	semidirect
44. D₈	C₂×D₃₁	semidirect
65. C₂	#11758414	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×D₈×C₃₁	2
C₂×D₂₄₈	2
#11758414	2
C₂×C₃₁⋊C₁₆	2
C₂×D₁₆	31

Subgroups — C2×#11758414 #14521469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11758414 #14521469