Subgroups — C₂²×#14519709 #21454391

Order 7808.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Dic₆₁	C₂	1	2	yes	maximal
2	C₂×#14519709	C₂	1	12	yes	maximal, direct product factor
3	C₂³×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₆₁	—	2	2	no	—
5	C₂×C₄⋊Dic₆₁	—	2	6	no	—
6	C₂×C₄⋊Dic₆₁	C₂²	1	12	yes	—
7	#14519709	C₂²	1	16	yes	direct product factor
8	C₂³×C₄×C₆₁	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₆₁	C₄	1	8	yes	complemented
10	C₂²×C₈×C₆₁	C₂²	1	6	yes	—
11	C₂⁴×C₆₁	D₄	1	1	yes	characteristic
12	C₂²×C₄×C₆₁	C₂×C₄	1	4	yes	—
13	C₂²×C₄×C₆₁	D₄	1	3	yes	—
14	C₂²×C₄×C₆₁	Q₈	1	4	yes	—
15	C₂²×C₄×C₆₁	C₂³	1	3	yes	—
16	C₂²×Dic₆₁	—	2	12	no	—
17	C₂²×Dic₆₁	—	4	8	no	—
18	C₂×C₈×C₆₁	C₂×C₄	1	24	yes	complemented
19	C₂×C₈×C₆₁	C₂³	1	4	yes	—
20	C₄⋊Dic₆₁	—	2	12	no	—
21	C₄⋊Dic₆₁	C₂³	1	8	yes	—
22	C₂³×C₆₁	C₄⋊C₄	1	4	yes	—
23	C₂³×C₆₁	SD₁₆	1	8	yes	—
24	C₂³×C₆₁	C₂×D₄	1	3	yes	—
25	C₂×C₄×C₆₁	C₄⋊C₄	1	12	yes	—
26	C₂×C₄×C₆₁	C₂²×C₄	1	6	yes	—
27	C₂×C₄×C₆₁	C₂×D₄	1	3	yes	—
28	C₂×C₄×C₆₁	C₂×Q₈	1	6	yes	—
29	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
30	C₂×Dic₆₁	—	2	8	no	—
31	C₂×Dic₆₁	—	4	24	no	—
32	C₈×C₆₁	C₂²×C₄	1	8	yes	complemented
33	C₂²×C₆₁	#106	1	16	yes	complemented
34	C₂²×C₆₁	C₂×C₄⋊C₄	1	6	yes	—
35	C₂²×C₆₁	C₂×SD₁₆	1	12	yes	—
36	C₂²×C₆₁	C₂²×D₄	1	1	yes	characteristic
37	C₄×C₆₁	C₂×C₄⋊C₄	1	6	yes	—
38	C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
39	C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
40	Dic₆₁	—	4	8	no	—
41	C₂²×#106	—	61	1	no	maximal, Sylow
42	C₂×C₆₁	C₂×#106	1	12	yes	complemented
43	C₂×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₆₁	C₂²×SD₁₆	1	2	yes	—
45	C₂³×C₈	D₆₁	1	1	yes	characteristic
46	C₂²×C₄⋊C₄	—	61	2	no	—
47	C₂×#106	—	61	12	no	—
48	C₆₁	C₂²×#106	1	1	yes	characteristic, complemented, Sylow
49	C₂³×C₄	—	122	2	no	—
50	C₂³×C₄	C₂×D₆₁	1	1	yes	characteristic
51	C₂²×C₈	Dic₆₁	1	8	yes	complemented
52	C₂²×C₈	C₂×D₆₁	1	6	yes	—
53	C₂×C₄⋊C₄	—	61	12	no	—
54	C₂×C₄⋊C₄	—	122	6	no	—
55	#106	—	61	16	no	—
56	C₂⁴	D₂₄₄	1	1	yes	characteristic
57	C₂²×C₄	—	122	12	no	—
58	C₂²×C₄	—	244	8	no	—
59	C₂²×C₄	Dic₁₂₂	1	4	yes	—
60	C₂²×C₄	D₂₄₄	1	3	yes	—
61	C₂²×C₄	C₂×Dic₆₁	1	4	yes	—
62	C₂²×C₄	C₂²×D₆₁	1	3	yes	—
63	C₂×C₈	C₂×Dic₆₁	1	24	yes	complemented
64	C₂×C₈	C₂²×D₆₁	1	4	yes	—
65	C₄⋊C₄	—	61	8	no	—
66	C₄⋊C₄	—	122	12	no	—
67	C₂³	#11758190	1	8	yes	—
68	C₂³	C₄⋊Dic₆₁	1	4	yes	—
69	C₂³	C₂×D₂₄₄	1	3	yes	—
70	C₂×C₄	—	122	8	no	—
71	C₂×C₄	—	244	24	no	—
72	C₂×C₄	C₄⋊Dic₆₁	1	12	yes	—
73	C₂×C₄	C₂×Dic₁₂₂	1	6	yes	—
74	C₂×C₄	C₂×D₂₄₄	1	3	yes	—
75	C₂×C₄	C₂²×Dic₆₁	1	6	yes	—
76	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
77	C₈	C₂²×Dic₆₁	1	8	yes	complemented
78	C₂²	#14519709	1	16	yes	direct product factor
79	C₂²	C₂×C₄⋊Dic₆₁	1	6	yes	—
80	C₂²	C₂×#11758190	1	12	yes	—
81	C₂²	C₂²×D₂₄₄	1	1	yes	characteristic
82	C₄	—	244	8	no	—
83	C₄	C₂×C₄⋊Dic₆₁	1	6	yes	—
84	C₄	C₂³×Dic₆₁	1	1	yes	characteristic
85	C₄	C₂²×Dic₁₂₂	1	1	yes	characteristic
86	C₂	C₂×#14519709	1	12	yes	direct product factor
87	C₂	C₂²×C₄⋊Dic₆₁	1	1	yes	characteristic
88	C₂	C₂²×#11758190	1	2	yes	—

	subgroup	G/H
center	C₂⁴	D₂₄₄
commutator	C₄×C₆₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₆₁
Fitting	C₂³×C₈×C₆₁	C₂
socle	C₂⁴×C₆₁	D₄
hypercenter	C₂³×C₈	D₆₁
hypocenter	C₆₁	C₂²×#106
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#14519709	C₂	direct (N × H)
7. #14519709	C₂²	direct (N × H)
9. C₂²×C₈×C₆₁	C₄	semidirect
18. C₂×C₈×C₆₁	C₂×C₄	semidirect
32. C₈×C₆₁	C₂²×C₄	semidirect
33. C₂²×C₆₁	#106	semidirect
42. C₂×C₆₁	C₂×#106	semidirect
48. C₆₁	C₂²×#106	semidirect
51. C₂²×C₈	Dic₆₁	semidirect
63. C₂×C₈	C₂×Dic₆₁	semidirect
77. C₈	C₂²×Dic₆₁	semidirect
78. C₂²	#14519709	direct (N × H)
86. C₂	C₂×#14519709	direct (N × H)

Subgroups — C22×#14519709 #21454391

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#14519709 #21454391