Subgroups — #21460727

Order 7808.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840765	C₂	1	2	yes	maximal
2	#16839785	C₂	1	1	yes	maximal, characteristic
3	C₂×#11758217	C₄	1	4	yes	—
4	#14519844	—	2	2	no	—
5	C₄⋊#92420	—	2	2	no	—
6	C₂×#11758194	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
8	#14519706	—	2	2	no	—
9	C₂×M₁₆×C₆₁	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂²×Dic₆₁	C₂×C₄	1	2	yes	—
12	#11758217	—	4	4	no	—
13	C₂×#92420	—	2	4	no	—
14	M₁₆×C₆₁	—	4	1	no	—
15	C₂×C₈×C₆₁	—	2	1	no	—
16	C₄×Dic₆₁	D₄	1	1	yes	characteristic
17	C₄×Dic₆₁	D₄	1	2	yes	—
18	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
19	#11758194	—	4	1	no	—
20	C₂×#92418	—	2	1	no	—
21	C₂³×C₆₁	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₆₁	—	2	1	no	—
23	C₂×C₄×C₆₁	—	2	1	no	—
24	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
26	C₂×Dic₆₁	—	2	2	no	—
27	C₂×Dic₆₁	—	2	2	no	—
28	C₂×Dic₆₁	C₂²⋊C₄	1	2	yes	—
29	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
30	#92420	—	4	4	no	—
31	C₈×C₆₁	—	4	1	no	—
32	#92418	—	4	1	no	—
33	C₂²×C₆₁	—	2	2	no	—
34	C₂²×C₆₁	—	2	1	no	—
35	C₂²×C₆₁	#95	1	1	yes	characteristic
36	C₄×C₆₁	—	2	1	no	—
37	C₄×C₆₁	#100	1	1	yes	characteristic
38	C₄×C₆₁	#101	1	1	yes	characteristic
39	Dic₆₁	—	2	2	no	—
40	Dic₆₁	#100	1	2	yes	—
41	Dic₆₁	#101	1	2	yes	—
42	#1309	—	61	1	no	maximal, Sylow
43	C₂×C₆₁	—	4	1	no	—
44	C₂×C₆₁	#343	1	2	yes	—
45	C₂×C₆₁	#343	1	1	yes	characteristic
46	#423	—	61	2	no	—
47	#423	—	61	1	no	—
48	C₆₁	#1309	1	1	yes	characteristic, complemented, Sylow
49	C₂×M₁₆	—	61	4	no	—
50	C₂×M₁₆	—	61	1	no	—
51	C₂×M₁₆	#6923	1	1	yes	characteristic
52	C₂×C₄²	—	61	1	no	—
53	C₄⋊C₈	—	122	2	no	—
54	C₄⋊C₈	—	122	2	no	—
55	C₄⋊C₈	—	122	2	no	—
56	C₂²×C₄	—	61	2	no	—
57	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
58	M₁₆	—	4	1	no	—
59	M₁₆	—	244	1	no	—
60	M₁₆	—	244	4	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	—	122	4	no	—
63	C₂×C₈	—	122	1	no	—
64	C₄²	—	61	1	no	—
65	C₄²	—	61	1	no	—
66	C₄²	—	61	2	no	—
67	C₂³	C₄×#6923	1	1	yes	characteristic
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	61	2	no	—
71	C₂×C₄	—	61	2	no	—
72	C₂×C₄	—	122	2	no	—
73	C₂×C₄	—	122	2	no	—
74	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
75	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
76	C₈	—	4	1	no	—
77	C₈	—	244	4	no	—
78	C₈	—	244	1	no	—
79	C₂²	—	2	2	no	—
80	C₂²	—	2	1	no	—
81	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	61	2	no	—
84	C₄	—	61	2	no	—
85	C₄	—	122	2	no	—
86	C₄	#14519837	1	1	yes	characteristic
87	C₄	#14519838	1	1	yes	characteristic
88	C₂	—	4	1	no	—
89	C₂	#16840641	1	2	yes	—
90	C₂	#16840642	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×#6923)⋊C₄
commutator	C₂³×C₆₁	C₄²
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×M₁₆×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	C₂×M₁₆	#6923
hypocenter	C₆₁	#1309
LCS	G ▷ C₂³×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
48. C₆₁	#1309	semidirect