Subgroups — #21443913

Order 7808.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519713	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#11758194	—	2	2	no	—
4	#14519713	—	2	2	no	—
5	#14519713	C₄	1	4	yes	—
6	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₆₁	—	2	2	no	—
8	C₂×C₁₆×C₆₁	C₄	1	2	yes	—
9	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
10	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₆₁	D₄	1	2	yes	—
13	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
14	#11758194	—	2	4	no	—
15	#11758194	—	4	2	no	—
16	C₂×#92418	—	4	2	no	—
17	C₁₆×C₆₁	—	2	2	no	—
18	C₂³×C₆₁	Q₁₆	1	1	yes	characteristic
19	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
22	C₂×C₄×C₆₁	SD₁₆	1	2	yes	—
23	C₈×C₆₁	C₄²	1	1	yes	characteristic
24	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
26	#92418	—	4	4	no	—
27	C₂²×C₆₁	—	2	2	no	—
28	C₂²×C₆₁	#103	1	2	yes	—
29	C₂²×C₆₁	#107	1	1	yes	characteristic
30	C₄×C₆₁	#95	1	1	yes	characteristic
31	C₄×C₆₁	#102	1	2	yes	—
32	C₄×C₆₁	#106	1	1	yes	characteristic
33	#1381	—	61	1	no	maximal, Sylow
34	C₂×C₆₁	—	2	2	no	—
35	C₂×C₆₁	#340	1	1	yes	characteristic
36	C₂×C₆₁	#368	1	2	yes	—
37	C₂²×C₁₆	D₆₁	1	1	yes	characteristic
38	C₂×#108	—	61	2	no	—
39	C₆₁	#1381	1	1	yes	characteristic, complemented, Sylow
40	C₂×M₁₆	—	122	2	no	—
41	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
42	C₂×C₁₆	—	2	2	no	—
43	C₂×C₁₆	Dic₆₁	1	2	yes	—
44	#108	—	61	4	no	—
45	#108	—	122	2	no	—
46	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
47	M₁₆	—	122	4	no	—
48	M₁₆	—	244	2	no	—
49	C₂×C₈	—	244	2	no	—
50	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
51	C₂×C₈	C₄×D₆₁	1	2	yes	—
52	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
53	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
54	C₁₆	—	2	2	no	—
55	C₂³	Dic₂₄₄	1	1	yes	characteristic
56	C₂×C₄	#11758190	1	2	yes	—
57	C₂×C₄	D₄₈₈	1	1	yes	characteristic
58	C₂×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
59	C₂×C₄	#11758198	1	2	yes	—
60	C₈	—	244	4	no	—
61	C₈	C₄×Dic₆₁	1	1	yes	characteristic
62	C₈	#11758196	1	2	yes	—
63	C₈	C₂²⋊Dic₆₁	1	1	yes	characteristic
64	C₂²	—	2	2	no	—
65	C₂²	#14519702	1	2	yes	—
66	C₂²	#14519711	1	1	yes	characteristic
67	C₄	#14519684	1	1	yes	characteristic
68	C₄	#14519699	1	2	yes	—
69	C₄	#14519709	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	#16839525	1	1	yes	characteristic
72	C₂	#16839592	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₄₈₈
commutator	C₈×C₆₁	C₄²
Frattini	C₂²×C₈	C₂×D₆₁
Fitting	C₂²×C₁₆×C₆₁	C₂
socle	C₂²×C₆₁	#107
hypercenter	C₂²×C₁₆	D₆₁
hypocenter	C₆₁	#1381
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
39. C₆₁	#1381	semidirect