Subgroups — C₂×#14521527 #16858902

Order 3968.

1488 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521527	C₂	1	16	yes	maximal, direct product factor
2	C₂×Q₈×Dic₃₁	C₂	1	8	yes	maximal, complemented
3	C₂×#11758503	C₂	1	6	yes	maximal
4	C₂³×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₃₁	C₄	1	16	yes	complemented
6	C₂²×Q₈×C₃₁	C₂²	1	4	yes	—
7	C₂²×Q₈×C₃₁	C₂²	1	8	yes	—
8	C₂³×C₄×C₃₁	C₂²	1	3	yes	—
9	C₂×C₂²⋊Dic₃₁	C₂²	1	4	yes	—
10	Q₈×Dic₃₁	C₂²	1	64	yes	complemented
11	#11758503	C₂²	1	48	yes	—
12	C₂×C₄⋊Dic₃₁	C₂²	1	12	yes	—
13	C₂×C₄×Dic₃₁	C₂²	1	12	yes	—
14	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
15	C₂×Q₈×C₃₁	C₂×C₄	1	32	yes	—
16	C₂×Q₈×C₃₁	C₂×C₄	1	64	yes	complemented
17	C₂×Q₈×C₃₁	C₂³	1	16	yes	—
18	C₂²×C₄×C₃₁	C₂×C₄	1	24	yes	—
19	C₂²×C₄×C₃₁	C₂³	1	6	yes	—
20	C₂²×C₄×C₃₁	C₂³	1	12	yes	—
21	C₂²×Dic₃₁	C₂³	1	8	yes	—
22	C₂²⋊Dic₃₁	C₂³	1	16	yes	—
23	C₄⋊Dic₃₁	C₂³	1	48	yes	—
24	C₄×Dic₃₁	C₂³	1	48	yes	—
25	C₂³×C₃₁	—	2	4	no	—
26	C₂³×C₃₁	C₂²×C₄	1	4	yes	—
27	C₂³×C₃₁	C₂⁴	1	2	yes	—
28	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
29	Q₈×C₃₁	C₂²×C₄	1	64	yes	—
30	C₂×C₄×C₃₁	C₂²×C₄	1	24	yes	—
31	C₂×C₄×C₃₁	C₂²×C₄	1	48	yes	—
32	C₂×C₄×C₃₁	C₂⁴	1	12	yes	—
33	C₂×Dic₃₁	—	2	16	no	—
34	C₂×Dic₃₁	C₂⁴	1	16	yes	—
35	C₂×#519	—	31	1	no	maximal, Sylow
36	C₂²×C₃₁	—	2	8	no	—
37	C₂²×C₃₁	—	2	4	no	—
38	C₂²×C₃₁	C₂³×C₄	1	4	yes	—
39	C₂²×C₃₁	C₂³×C₄	1	2	yes	—
40	C₂²×C₃₁	2₋¹⁺⁴	1	4	yes	—
41	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
42	C₄×C₃₁	C₂³×C₄	1	24	yes	—
43	Dic₃₁	—	2	16	no	—
44	C₂³×Q₈	D₃₁	1	1	yes	characteristic
45	#519	—	31	16	no	—
46	C₂×C₄×Q₈	—	31	8	no	—
47	C₂×#117	—	31	6	no	—
48	C₂×C₃₁	—	2	4	no	—
49	C₂×C₃₁	#519	1	4	yes	complemented
50	C₂×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
51	C₂×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
52	C₂²×Q₈	Dic₃₁	1	16	yes	complemented
53	C₂²×Q₈	C₂×D₃₁	1	4	yes	—
54	C₂²×Q₈	C₂×D₃₁	1	8	yes	—
55	C₂³×C₄	C₂×D₃₁	1	3	yes	—
56	C₄×Q₈	—	31	64	no	—
57	#117	—	31	48	no	—
58	C₂×C₄⋊C₄	—	31	12	no	—
59	C₂×C₂²⋊C₄	—	31	4	no	—
60	C₂×C₄²	—	31	12	no	—
61	C₃₁	C₂×#519	1	1	yes	characteristic, complemented, Sylow
62	C₂⁴	C₂²×D₃₁	1	1	yes	characteristic
63	C₂×Q₈	C₂×Dic₃₁	1	32	yes	—
64	C₂×Q₈	C₂×Dic₃₁	1	64	yes	complemented
65	C₂×Q₈	C₂²×D₃₁	1	16	yes	—
66	C₂²×C₄	—	31	8	no	—
67	C₂²×C₄	C₂×Dic₃₁	1	24	yes	—
68	C₂²×C₄	C₂²×D₃₁	1	12	yes	—
69	C₂²×C₄	C₂²×D₃₁	1	6	yes	—
70	C₄⋊C₄	—	31	48	no	—
71	C₂²⋊C₄	—	31	16	no	—
72	C₄²	—	31	48	no	—
73	C₂³	—	2	4	no	—
74	C₂³	C₂²×Dic₃₁	1	4	yes	—
75	C₂³	C₂³×D₃₁	1	2	yes	—
76	C₂³	C₂³×D₃₁	1	1	yes	characteristic
77	Q₈	C₂²×Dic₃₁	1	64	yes	—
78	C₂×C₄	—	31	16	no	—
79	C₂×C₄	—	62	16	no	—
80	C₂×C₄	C₂²×Dic₃₁	1	24	yes	—
81	C₂×C₄	C₂²×Dic₃₁	1	48	yes	—
82	C₂×C₄	C₂³×D₃₁	1	12	yes	—
83	C₂²	—	2	4	no	—
84	C₂²	—	2	8	no	—
85	C₂²	#11758564	1	4	yes	—
86	C₂²	C₂³×Dic₃₁	1	4	yes	—
87	C₂²	C₂³×Dic₃₁	1	2	yes	—
88	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
89	C₄	—	62	16	no	—
90	C₄	C₂³×Dic₃₁	1	24	yes	—
91	C₂	—	2	4	no	—
92	C₂	#14521527	1	4	yes	direct product factor
93	C₂	C₂⁴×Dic₃₁	1	1	yes	characteristic
94	C₂	C₂×#11758564	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂³×D₃₁
commutator	C₂×C₃₁	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₂³×Q₈×C₃₁	C₂
socle	C₂³×C₃₁	C₂⁴
prime radical	C₂⁴×C₃₁	C₂³
cosocle	C₂²×C₃₁	C₂⁵
hypercenter	C₂³×Q₈	D₃₁
hypocenter	C₃₁	C₂×#519
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
1. #14521527	C₂	direct (N × H)
2. C₂×Q₈×Dic₃₁	C₂	semidirect
5. C₂²×Q₈×C₃₁	C₄	semidirect
10. Q₈×Dic₃₁	C₂²	semidirect
16. C₂×Q₈×C₃₁	C₂×C₄	semidirect
49. C₂×C₃₁	#519	semidirect
52. C₂²×Q₈	Dic₃₁	semidirect
61. C₃₁	C₂×#519	semidirect
64. C₂×Q₈	C₂×Dic₃₁	semidirect
92. C₂	#14521527	direct (N × H)

Maximal subgroups

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

subgroup	index
#14521527	2
C₂×Q₈×Dic₃₁	2
C₂×#11758503	2
C₂³×Q₈×C₃₁	2
C₂×#519	31

Subgroups — C2×#14521527 #16858902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14521527 #16858902