Subgroups — #21460760

Order 7808.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840607	C₂	1	2	yes	maximal
2	#16839627	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#92420	—	2	2	no	—
4	C₂×C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
5	C₂×C₄×Dic₆₁	C₄	1	1	yes	characteristic
6	#14519684	—	2	2	no	—
7	C₂×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₆₁	—	2	1	no	—
9	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
10	C₂²×Dic₆₁	—	2	1	no	—
11	C₂²×Dic₆₁	D₄	1	2	yes	—
12	C₂×#92420	—	4	2	no	—
13	C₄⋊C₄×C₆₁	—	4	1	no	—
14	C₄⋊Dic₆₁	—	4	1	no	—
15	C₄×Dic₆₁	—	2	1	no	—
16	C₄×Dic₆₁	C₈	1	2	yes	complemented
17	C₂³×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₆₁	—	2	1	no	—
19	C₂×C₄×C₆₁	—	2	1	no	—
20	C₂×C₄×C₆₁	—	4	2	no	—
21	C₂×C₄×C₆₁	—	4	1	no	—
22	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
24	C₂×Dic₆₁	—	2	2	no	—
25	C₂×Dic₆₁	—	2	2	no	—
26	C₂×Dic₆₁	—	4	1	no	—
27	C₂×Dic₆₁	—	4	1	no	—
28	C₂×Dic₆₁	—	4	2	no	—
29	#92420	—	8	2	no	—
30	C₂²×C₆₁	—	2	1	no	—
31	C₂²×C₆₁	—	2	1	no	—
32	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
33	C₂²×C₆₁	#99	1	1	yes	characteristic
34	C₂²×C₆₁	#101	1	1	yes	characteristic
35	C₄×C₆₁	—	2	1	no	—
36	C₄×C₆₁	—	2	1	no	—
37	C₄×C₆₁	—	8	1	no	—
38	Dic₆₁	—	4	2	no	—
39	Dic₆₁	—	4	2	no	—
40	#1324	—	61	1	no	maximal, Sylow
41	C₂×C₆₁	—	2	1	no	—
42	C₂×C₆₁	—	2	1	no	—
43	C₂×C₆₁	#324	1	1	yes	characteristic
44	C₂×C₆₁	#354	1	1	yes	characteristic
45	C₂×C₆₁	#355	1	1	yes	characteristic
46	#382	—	61	1	no	—
47	#324	—	61	2	no	—
48	C₆₁	#1324	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₄⋊C₄	—	61	1	no	—
50	C₂×C₄⋊C₄	#6923	1	1	yes	characteristic
51	C₂×C₄²	—	61	1	no	—
52	C₂²⋊C₈	—	122	2	no	—
53	#95	—	122	2	no	—
54	C₂²×C₄	—	2	1	no	—
55	C₂²×C₄	—	61	2	no	—
56	C₂²×C₄	—	122	1	no	—
57	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
58	C₂×C₈	—	244	2	no	—
59	C₄⋊C₄	—	4	1	no	—
60	C₄⋊C₄	—	244	1	no	—
61	C₄²	—	61	2	no	—
62	C₄²	—	122	1	no	—
63	C₂³	C₂²⋊#6923	1	1	yes	characteristic
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	4	2	no	—
67	C₂×C₄	—	4	1	no	—
68	C₂×C₄	—	122	2	no	—
69	C₂×C₄	—	122	2	no	—
70	C₂×C₄	—	244	1	no	—
71	C₂×C₄	—	244	1	no	—
72	C₂×C₄	—	244	2	no	—
73	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
74	C₂×C₄	#11758213	1	1	yes	characteristic
75	C₈	—	488	2	no	—
76	C₂²	—	2	1	no	—
77	C₂²	—	2	1	no	—
78	C₂²	#14519834	1	1	yes	characteristic
79	C₂²	#14519835	1	1	yes	characteristic
80	C₂²	#14519838	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	—	2	1	no	—
83	C₄	—	8	1	no	—
84	C₄	—	244	2	no	—
85	C₄	—	244	2	no	—
86	C₂	—	2	1	no	—
87	C₂	—	2	1	no	—
88	C₂	#16840608	1	1	yes	characteristic
89	C₂	#16840668	1	1	yes	characteristic
90	C₂	#16840670	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14519835
commutator	C₂×C₄×C₆₁	C₂×C₈
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×C₄⋊C₄×C₆₁	C₄
socle	C₂²×C₆₁	#99
hypercenter	C₂×C₄⋊C₄	#6923
hypocenter	C₆₁	#1324
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
16. C₄×Dic₆₁	C₈	semidirect
48. C₆₁	#1324	semidirect