Subgroups — C₂×#14521429 #16856127

Order 3968.

552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₂₄	C₂	1	4	yes	maximal
2	C₂×#11758446	C₂	1	2	yes	maximal
3	#14521429	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₆₂	C₂²	1	4	yes	—
6	C₂²×C₈×C₃₁	C₂²	1	2	yes	—
7	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₃₁	—	2	4	no	—
9	C₂×Dic₁₂₄	—	2	16	no	—
10	C₂×Dic₁₂₄	C₂²	1	16	yes	—
11	#11758446	—	2	4	no	—
12	#11758446	C₂²	1	8	yes	—
13	C₄×C₈×C₃₁	C₂²	1	4	yes	—
14	C₂²×C₄×C₃₁	D₄	1	2	yes	—
15	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
16	C₂²×Dic₃₁	—	2	4	no	—
17	C₂×Dic₆₂	—	2	16	no	—
18	C₂×Dic₆₂	—	2	4	no	—
19	C₂×Dic₆₂	C₂³	1	8	yes	—
20	C₂×C₈×C₃₁	D₄	1	8	yes	—
21	C₂×C₈×C₃₁	C₂³	1	4	yes	—
22	C₄²×C₃₁	D₄	1	2	yes	—
23	C₄²×C₃₁	C₂³	1	2	yes	—
24	C₄⋊Dic₃₁	—	2	16	no	—
25	Dic₁₂₄	—	2	32	no	—
26	C₂³×C₃₁	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₃₁	Q₁₆	1	8	yes	complemented
28	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₃₁	C₂×D₄	1	4	yes	—
30	C₂×C₄×C₃₁	C₂×D₄	1	4	yes	—
31	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
32	C₂×Dic₃₁	—	2	8	no	—
33	C₂×Dic₃₁	—	4	8	no	—
34	Dic₆₂	—	2	16	no	—
35	Dic₆₂	—	4	8	no	—
36	C₈×C₃₁	C₂×D₄	1	8	yes	—
37	C₂×#494	—	31	1	no	maximal, Sylow
38	C₂²×C₃₁	#127	1	2	yes	—
39	C₂²×C₃₁	C₂×Q₁₆	1	4	yes	—
40	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
41	C₄×C₃₁	#127	1	2	yes	—
42	C₄×C₃₁	C₂×Q₁₆	1	8	yes	complemented
43	C₄×C₃₁	C₂²×D₄	1	2	yes	—
44	Dic₃₁	—	4	8	no	—
45	C₂²×Q₁₆	—	31	4	no	—
46	C₂×C₄⋊Q₈	—	31	2	no	—
47	#494	—	31	8	no	—
48	C₂×C₄×C₈	D₃₁	1	1	yes	characteristic
49	C₂×C₃₁	#494	1	4	yes	complemented
50	C₂×C₃₁	C₂×#127	1	1	yes	characteristic
51	C₂×C₃₁	C₂²×Q₁₆	1	2	yes	—
52	C₂²×Q₈	—	31	4	no	—
53	C₂×Q₁₆	—	31	16	no	—
54	C₂×Q₁₆	—	62	16	no	—
55	C₂²×C₈	C₂×D₃₁	1	2	yes	—
56	C₄⋊Q₈	—	31	8	no	—
57	C₄⋊Q₈	—	62	4	no	—
58	C₂×C₄⋊C₄	—	62	4	no	—
59	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
60	C₄×C₈	C₂×D₃₁	1	4	yes	—
61	C₃₁	C₂×#494	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	31	8	no	—
63	C₂×Q₈	—	62	4	no	—
64	C₂×Q₈	—	62	16	no	—
65	C₂²×C₄	—	62	4	no	—
66	C₂²×C₄	D₁₂₄	1	2	yes	—
67	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
68	Q₁₆	—	62	32	no	—
69	C₂×C₈	D₁₂₄	1	8	yes	—
70	C₂×C₈	C₂²×D₃₁	1	4	yes	—
71	C₄⋊C₄	—	62	16	no	—
72	C₄²	D₁₂₄	1	2	yes	—
73	C₄²	C₂²×D₃₁	1	2	yes	—
74	C₂³	C₂×D₁₂₄	1	1	yes	characteristic
75	Q₈	—	62	16	no	—
76	Q₈	—	124	8	no	—
77	C₂×C₄	—	62	8	no	—
78	C₂×C₄	—	124	8	no	—
79	C₂×C₄	Dic₁₂₄	1	8	yes	complemented
80	C₂×C₄	C₂×D₁₂₄	1	1	yes	characteristic
81	C₂×C₄	C₂×D₁₂₄	1	4	yes	—
82	C₂×C₄	C₂×D₁₂₄	1	4	yes	—
83	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
84	C₈	C₂×D₁₂₄	1	8	yes	—
85	C₂²	#11758451	1	2	yes	—
86	C₂²	C₂×Dic₁₂₄	1	4	yes	—
87	C₂²	C₂²×D₁₂₄	1	1	yes	characteristic
88	C₄	—	124	8	no	—
89	C₄	#11758451	1	2	yes	—
90	C₄	C₂×Dic₁₂₄	1	8	yes	complemented
91	C₄	C₂²×D₁₂₄	1	2	yes	—
92	C₂	#14521429	1	4	yes	direct product factor
93	C₂	C₂×#11758451	1	1	yes	characteristic
94	C₂	C₂²×Dic₁₂₄	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₁₂₄
commutator, cosocle	C₂×C₄×C₃₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₃₁
Fitting	C₂×C₄×C₈×C₃₁	C₂
socle, prime radical	C₂³×C₃₁	C₂×D₄
hypercenter	C₂×C₄×C₈	D₃₁
hypocenter	C₃₁	C₂×#494
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #14521429	C₂	direct (N × H)
27. C₂×C₄×C₃₁	Q₁₆	semidirect
42. C₄×C₃₁	C₂×Q₁₆	semidirect
49. C₂×C₃₁	#494	semidirect
61. C₃₁	C₂×#494	semidirect
79. C₂×C₄	Dic₁₂₄	semidirect
90. C₄	C₂×Dic₁₂₄	semidirect
92. C₂	#14521429	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×Dic₁₂₄	2
C₂×#11758446	2
#14521429	2
C₂×C₄×C₈×C₃₁	2
C₂×#494	31

Subgroups — C2×#14521429 #16856127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14521429 #16856127