Subgroups — C₄×#14519687 #21445503

Order 7808.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519687	C₂	1	4	yes	maximal
2	C₂×C₄×#92418	C₂	1	1	yes	maximal, characteristic
3	C₄²×Dic₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92418	C₂²	1	2	yes	—
6	C₂×C₄×Dic₆₁	C₄	1	4	yes	—
7	C₂×C₄×Dic₆₁	C₂²	1	2	yes	—
8	#14519687	C₄	1	16	yes	direct product factor
9	C₄×#92418	C₄	1	4	yes	complemented
10	C₂²×C₈×C₆₁	C₂²	1	2	yes	—
11	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₆₁	C₄	1	4	yes	complemented
13	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
15	C₂²×Dic₆₁	C₂×C₄	1	4	yes	—
16	C₂×C₈×C₆₁	C₂×C₄	1	8	yes	—
17	C₂×C₈×C₆₁	C₂×C₄	1	4	yes	—
18	C₄²×C₆₁	C₂×C₄	1	2	yes	—
19	C₄²×C₆₁	C₂×C₄	1	2	yes	—
20	C₄×Dic₆₁	—	2	8	no	—
21	C₄×Dic₆₁	C₂×C₄	1	8	yes	—
22	C₂×#92418	C₂×C₄	1	4	yes	—
23	C₂×#92418	C₂×C₄	1	8	yes	—
24	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₄²	1	4	yes	—
26	C₂×C₄×C₆₁	M₁₆	1	8	yes	—
27	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₂²×C₄	1	4	yes	—
29	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₆₁	—	2	8	no	—
31	C₂×Dic₆₁	C₄²	1	8	yes	—
32	C₈×C₆₁	C₄²	1	8	yes	complemented
33	#92418	C₄²	1	8	yes	complemented
34	C₂²×C₆₁	C₂×C₄²	1	2	yes	—
35	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
36	C₂²×C₆₁	C₂×M₁₆	1	4	yes	—
37	C₄×C₆₁	#97	1	8	yes	complemented
38	C₄×C₆₁	C₂×C₄²	1	2	yes	—
39	C₄×C₆₁	C₂×C₄²	1	2	yes	—
40	Dic₆₁	—	2	8	no	—
41	C₄×#97	—	61	1	no	maximal, Sylow
42	C₂×C₆₁	C₄³	1	1	yes	characteristic
43	C₂×C₆₁	C₂×#97	1	2	yes	—
44	C₂×C₆₁	C₄×M₁₆	1	4	yes	—
45	C₂×#97	—	61	4	no	—
46	C₂×C₄×C₈	—	61	1	no	—
47	C₂×C₄×C₈	D₆₁	1	1	yes	characteristic
48	C₄³	—	61	1	no	—
49	C₆₁	C₄×#97	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₈	—	61	2	no	—
51	C₂²×C₈	C₂×D₆₁	1	2	yes	—
52	C₂×C₄²	—	61	2	no	—
53	C₂×C₄²	—	61	4	no	—
54	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
55	#97	—	61	16	no	—
56	C₄×C₈	—	61	4	no	—
57	C₄×C₈	Dic₆₁	1	4	yes	complemented
58	C₂²×C₄	—	61	4	no	—
59	C₂²×C₄	C₄×D₆₁	1	2	yes	—
60	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
61	C₂×C₈	—	61	4	no	—
62	C₂×C₈	—	61	8	no	—
63	C₂×C₈	C₄×D₆₁	1	8	yes	—
64	C₂×C₈	C₂×Dic₆₁	1	4	yes	—
65	C₄²	—	61	8	no	—
66	C₄²	—	122	8	no	—
67	C₄²	C₄×D₆₁	1	2	yes	—
68	C₄²	C₂×Dic₆₁	1	2	yes	—
69	C₂³	C₂×C₄×D₆₁	1	1	yes	characteristic
70	C₂×C₄	—	61	8	no	—
71	C₂×C₄	—	122	8	no	—
72	C₂×C₄	#11758189	1	8	yes	—
73	C₂×C₄	C₄×Dic₆₁	1	4	yes	—
74	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
75	C₂×C₄	C₂×C₄×D₆₁	1	4	yes	—
76	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
77	C₈	—	61	8	no	—
78	C₈	C₄×Dic₆₁	1	8	yes	complemented
79	C₂²	C₄²×D₆₁	1	2	yes	—
80	C₂²	C₂×C₄×Dic₆₁	1	1	yes	characteristic
81	C₂²	C₂×#11758189	1	4	yes	—
82	C₄	—	122	8	no	—
83	C₄	#14519687	1	8	yes	direct product factor
84	C₄	C₄²×D₆₁	1	2	yes	—
85	C₄	C₂×C₄×Dic₆₁	1	2	yes	—
86	C₂	C₄²×Dic₆₁	1	1	yes	characteristic
87	C₂	C₂×#14519687	1	2	yes	—
88	C₂	C₄×#11758189	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂×D₆₁
commutator	C₂×C₆₁	C₄³
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×C₄×C₈×C₆₁	C₂
socle	C₂³×C₆₁	C₂²×C₄
hypercenter	C₂×C₄×C₈	D₆₁
hypocenter	C₆₁	C₄×#97
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
8. #14519687	C₄	direct (N × H)
9. C₄×#92418	C₄	semidirect
12. C₄×C₈×C₆₁	C₄	semidirect
32. C₈×C₆₁	C₄²	semidirect
33. #92418	C₄²	semidirect
37. C₄×C₆₁	#97	semidirect
49. C₆₁	C₄×#97	semidirect
57. C₄×C₈	Dic₆₁	semidirect
78. C₈	C₄×Dic₆₁	semidirect
83. C₄	#14519687	direct (N × H)

Subgroups — C4×#14519687 #21445503

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14519687 #21445503