Subgroups — #21461760

Order 7808.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519848	C₂	1	4	yes	maximal
2	#16840766	C₂	1	2	yes	maximal
3	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758213	C₂²	1	4	yes	—
5	#14519848	—	2	8	no	—
6	C₄⋊#92420	—	2	4	no	—
7	C₂×C₈×D₆₁	C₂²	1	2	yes	—
8	C₄²×D₆₁	C₂²	1	1	yes	characteristic
9	C₄×#92418	C₄	1	1	yes	characteristic
10	C₈×Dic₆₁	C₄	1	2	yes	—
11	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
12	C₂×C₄×D₆₁	Q₈	1	2	yes	—
13	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
14	C₂×#92420	—	2	4	no	—
15	#11758213	—	2	8	no	—
16	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
17	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₆₁	D₄	1	2	yes	—
20	C₂×#92418	C₂×C₄	1	2	yes	—
21	C₈×D₆₁	D₄	1	4	yes	—
22	C₈×D₆₁	Q₈	1	4	yes	—
23	C₂²×D₆₁	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
26	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
27	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
28	C₄×D₆₁	—	2	4	no	—
29	C₄×D₆₁	C₂×D₄	1	2	yes	—
30	C₄×D₆₁	C₂×Q₈	1	2	yes	—
31	#92420	—	4	4	no	—
32	C₈×C₆₁	C₄⋊C₄	1	4	yes	—
33	#92418	C₄⋊C₄	1	4	yes	—
34	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×D₆₁	—	2	2	no	—
36	C₂×D₆₁	C₄⋊Q₈	1	2	yes	—
37	C₄×C₆₁	#108	1	4	yes	complemented
38	C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
39	Dic₆₁	—	2	2	no	—
40	Dic₆₁	#127	1	1	yes	characteristic
41	Dic₆₁	C₄⋊Q₈	1	1	yes	characteristic
42	#1848	—	61	1	no	maximal, Sylow
43	C₂×C₆₁	#384	1	1	yes	characteristic
44	C₂×C₆₁	C₂×#108	1	2	yes	—
45	D₆₁	—	2	2	no	—
46	C₂×#108	—	61	4	no	—
47	#423	—	61	2	no	—
48	C₂×C₄×C₈	—	61	1	no	—
49	C₆₁	#1848	1	1	yes	characteristic, complemented, Sylow
50	C₂×M₁₆	—	61	4	no	—
51	C₂²×C₈	—	61	2	no	—
52	C₂×C₄²	—	61	1	no	—
53	#108	—	122	8	no	—
54	C₄⋊C₈	—	122	4	no	—
55	C₄×C₈	—	61	2	no	—
56	C₄×C₈	—	61	1	no	—
57	C₄×C₈	#6923	1	1	yes	characteristic
58	C₂²×C₄	—	61	1	no	—
59	C₂²×C₄	—	61	2	no	—
60	M₁₆	—	122	8	no	—
61	C₂×C₈	—	61	2	no	—
62	C₂×C₈	—	61	4	no	—
63	C₂×C₈	—	61	4	no	—
64	C₂×C₈	—	122	4	no	—
65	C₂×C₈	C₂×#6923	1	2	yes	—
66	C₄²	—	61	2	no	—
67	C₄²	—	61	1	no	—
68	C₄²	C₂×#6923	1	1	yes	characteristic
69	C₂³	—	61	1	no	—
70	C₂×C₄	—	61	1	no	—
71	C₂×C₄	—	61	2	no	—
72	C₂×C₄	—	61	2	no	—
73	C₂×C₄	—	61	2	no	—
74	C₂×C₄	—	122	4	no	—
75	C₂×C₄	C₄⋊#6923	1	2	yes	—
76	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
77	C₈	—	61	4	no	—
78	C₈	—	244	4	no	—
79	C₈	C₄⋊#6923	1	4	yes	—
80	C₂²	—	61	2	no	—
81	C₂²	—	122	2	no	—
82	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
83	C₄	—	61	1	no	—
84	C₄	—	61	1	no	—
85	C₄	—	122	2	no	—
86	C₄	#14519848	1	4	yes	complemented
87	C₄	C₂×C₄⋊#6923	1	2	yes	—
88	C₂	—	122	2	no	—
89	C₂	#16840708	1	1	yes	characteristic
90	C₂	C₂×#14519848	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1848
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
37. C₄×C₆₁	#108	semidirect
49. C₆₁	#1848	semidirect
86. C₄	#14519848	semidirect