Subgroups — C₂×#11758524 #14521567

Order 1984.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₁₂₄	C₂	1	1	yes	maximal, characteristic
3	#11758524	C₂	1	8	yes	maximal, direct product factor
4	C₂×(C₂×D₃₁)⋊C₄	C₂	1	4	yes	maximal, complemented
5	C₂×C₄×Dic₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₃₁	C₂²	1	2	yes	—
7	C₂×Q₈×C₃₁	—	2	4	no	—
8	C₂×Q₈×C₃₁	C₂²	1	4	yes	complemented
9	C₂²×C₄×C₃₁	C₂²	1	2	yes	—
10	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃₁	C₂²	1	2	yes	—
12	C₂×D₁₂₄	—	2	4	no	—
13	C₂×D₁₂₄	C₂²	1	4	yes	—
14	(C₂×D₃₁)⋊C₄	C₂²	1	16	yes	complemented
15	C₄×Dic₃₁	C₂²	1	4	yes	complemented
16	C₂³×C₃₁	C₂³	1	1	yes	characteristic
17	C₂²×D₃₁	—	2	4	no	—
18	C₂²×D₃₁	—	2	8	no	—
19	C₂²×D₃₁	C₂³	1	4	yes	—
20	Q₈×C₃₁	—	2	8	no	—
21	C₂×C₄×C₃₁	—	2	4	no	—
22	C₂×C₄×C₃₁	D₄	1	4	yes	—
23	C₂×C₄×C₃₁	C₂³	1	4	yes	—
24	C₂×C₄×C₃₁	C₂³	1	2	yes	—
25	C₂×Dic₃₁	—	2	4	no	—
26	C₂×Dic₃₁	C₂³	1	4	yes	—
27	D₁₂₄	—	2	8	no	—
28	C₂²×C₃₁	C₂×D₄	1	2	yes	—
29	C₂²×C₃₁	#41	1	4	yes	—
30	C₂²×C₃₁	C₂⁴	1	1	yes	characteristic
31	C₂×D₃₁	—	2	4	no	—
32	C₂×D₃₁	—	2	8	no	—
33	C₂×D₃₁	—	4	8	no	—
34	C₄×C₃₁	—	2	4	no	—
35	C₄×C₃₁	C₂×D₄	1	4	yes	—
36	Dic₃₁	—	2	4	no	—
37	C₂×#124	—	31	1	no	maximal, Sylow
38	C₂×C₃₁	#124	1	4	yes	complemented
39	C₂×C₃₁	C₂²×D₄	1	1	yes	characteristic
40	C₂×C₃₁	C₂×#41	1	2	yes	—
41	D₃₁	—	4	4	no	—
42	C₂²×Q₈	D₃₁	1	1	yes	characteristic, complemented
43	C₂²×D₄	—	31	1	no	—
44	#124	—	31	8	no	—
45	C₂×C₂²⋊C₄	—	31	4	no	—
46	C₂×C₄²	—	31	1	no	—
47	C₃₁	C₂×#124	1	1	yes	characteristic, complemented, Sylow
48	C₂⁴	—	31	2	no	—
49	C₂×Q₈	—	2	4	no	—
50	C₂×Q₈	C₂×D₃₁	1	4	yes	complemented
51	C₂×D₄	—	31	4	no	—
52	C₂×D₄	—	62	4	no	—
53	C₂²×C₄	—	31	2	no	—
54	C₂²×C₄	C₂×D₃₁	1	2	yes	—
55	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
56	C₂²⋊C₄	—	31	16	no	—
57	C₄²	—	31	4	no	—
58	C₂³	—	31	4	no	—
59	C₂³	—	62	8	no	—
60	C₂³	—	62	4	no	—
61	C₂³	C₂²×D₃₁	1	1	yes	characteristic
62	Q₈	—	2	8	no	—
63	D₄	—	62	8	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	31	4	no	—
66	C₂×C₄	—	62	4	no	—
67	C₂×C₄	C₂²⋊D₃₁	1	4	yes	—
68	C₂×C₄	C₂²×D₃₁	1	4	yes	—
69	C₂×C₄	C₂²×D₃₁	1	2	yes	—
70	C₂²	—	62	8	no	—
71	C₂²	—	62	4	no	—
72	C₂²	—	124	8	no	—
73	C₂²	#92499	1	4	yes	—
74	C₂²	C₂×C₂²⋊D₃₁	1	2	yes	—
75	C₂²	C₂³×D₃₁	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	62	4	no	—
78	C₄	C₂×C₂²⋊D₃₁	1	4	yes	—
79	C₂	—	124	4	no	—
80	C₂	#11758524	1	4	yes	direct product factor
81	C₂	C₂×#92499	1	2	yes	—
82	C₂	C₂²×C₂²⋊D₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃₁
commutator, cosocle	C₂²×C₃₁	C₂⁴
Frattini	C₂²	C₂³×D₃₁
Fitting	C₂²×Q₈×C₃₁	C₂
socle	C₂³×C₃₁	C₂³
prime radical	C₂²×D₁₂₄	C₂
hypercenter	C₂²×Q₈	D₃₁
hypocenter	C₃₁	C₂×#124
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Q₈×C₃₁	C₂	semidirect
3. #11758524	C₂	direct (N × H)
4. C₂×(C₂×D₃₁)⋊C₄	C₂	semidirect
5. C₂×C₄×Dic₃₁	C₂	semidirect
8. C₂×Q₈×C₃₁	C₂²	semidirect
14. (C₂×D₃₁)⋊C₄	C₂²	semidirect
15. C₄×Dic₃₁	C₂²	semidirect
38. C₂×C₃₁	#124	semidirect
42. C₂²×Q₈	D₃₁	semidirect
47. C₃₁	C₂×#124	semidirect
50. C₂×Q₈	C₂×D₃₁	semidirect
80. C₂	#11758524	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Q₈×C₃₁	2
C₂²×D₁₂₄	2
#11758524	2
C₂×(C₂×D₃₁)⋊C₄	2
C₂×C₄×Dic₃₁	2
C₂×#124	31

Subgroups — C2×#11758524 #14521567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11758524 #14521567