Subgroups — #21443694

Order 7808.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839786	C₂	1	2	yes	maximal
2	C₂×C₄⋊C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#11758194	—	2	2	no	—
4	C₄⋊#92418	—	2	2	no	—
5	C₄⋊#92418	C₄	1	4	yes	—
6	C₂²×C₈×C₆₁	C₄	1	2	yes	—
7	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
8	C₄⋊C₈×C₆₁	—	2	2	no	—
9	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₆₁	Q₈	1	1	yes	characteristic
12	C₂×C₈×C₆₁	—	2	2	no	—
13	C₂×C₈×C₆₁	—	4	2	no	—
14	C₄²×C₆₁	C₂×C₄	1	2	yes	—
15	C₄²×C₆₁	D₄	1	2	yes	—
16	#11758194	—	4	2	no	—
17	#11758194	—	4	2	no	—
18	C₂×#92418	—	2	4	no	—
19	C₂³×C₆₁	C₄⋊C₄	1	1	yes	characteristic
20	C₂×C₄×C₆₁	—	2	1	no	—
21	C₂×C₄×C₆₁	—	2	1	no	—
22	C₂×C₄×C₆₁	—	4	1	no	—
23	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
26	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
28	C₂×C₄×C₆₁	SD₁₆	1	2	yes	—
29	C₂×C₄×C₆₁	Q₁₆	1	1	yes	characteristic
30	C₈×C₆₁	—	4	2	no	—
31	#92418	—	4	4	no	—
32	C₂²×C₆₁	—	2	1	no	—
33	C₂²×C₆₁	—	2	1	no	—
34	C₂²×C₆₁	#95	1	1	yes	characteristic
35	C₂²×C₆₁	#106	1	1	yes	characteristic
36	C₂²×C₆₁	#107	1	1	yes	characteristic
37	C₄×C₆₁	—	2	2	no	—
38	C₄×C₆₁	—	2	1	no	—
39	C₄×C₆₁	#100	1	1	yes	characteristic
40	C₄×C₆₁	#101	1	1	yes	characteristic
41	C₄×C₆₁	#102	1	2	yes	—
42	C₄×C₆₁	#103	1	2	yes	—
43	#1292	—	61	1	no	maximal, Sylow
44	C₂×C₆₁	—	2	1	no	—
45	C₂×C₆₁	—	2	1	no	—
46	C₂×C₆₁	#338	1	1	yes	characteristic
47	C₂×C₆₁	#340	1	1	yes	characteristic
48	C₂×C₆₁	#343	1	1	yes	characteristic
49	#423	—	61	2	no	—
50	C₂×C₄⋊C₈	D₆₁	1	1	yes	characteristic
51	C₆₁	#1292	1	1	yes	characteristic, complemented, Sylow
52	C₂×M₁₆	—	122	2	no	—
53	C₂²×C₈	Dic₆₁	1	2	yes	—
54	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
55	C₄⋊C₈	—	2	2	no	—
56	C₄⋊C₈	—	61	4	no	—
57	C₄⋊C₈	—	122	2	no	—
58	C₂²×C₄	Dic₁₂₂	1	1	yes	characteristic
59	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
60	C₂²×C₄	C₂×Dic₆₁	1	1	yes	characteristic
61	M₁₆	—	244	2	no	—
62	M₁₆	—	244	2	no	—
63	C₂×C₈	—	2	2	no	—
64	C₂×C₈	—	4	2	no	—
65	C₂×C₈	—	122	4	no	—
66	C₄²	C₄×D₆₁	1	2	yes	—
67	C₄²	C₂²⋊D₆₁	1	2	yes	—
68	C₂³	C₄⋊Dic₆₁	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	#11758190	1	2	yes	—
73	C₂×C₄	D₄₈₈	1	1	yes	characteristic
74	C₂×C₄	Dic₂₄₄	1	1	yes	characteristic
75	C₂×C₄	C₄×Dic₆₁	1	1	yes	characteristic
76	C₂×C₄	#11758196	1	2	yes	—
77	C₂×C₄	#11758198	1	2	yes	—
78	C₂×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
79	C₈	—	4	2	no	—
80	C₈	—	244	4	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	#14519684	1	1	yes	characteristic
84	C₂²	#14519709	1	1	yes	characteristic
85	C₂²	#14519711	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	1	no	—
88	C₄	#14519694	1	1	yes	characteristic
89	C₄	#14519696	1	1	yes	characteristic
90	C₄	#14519699	1	2	yes	—
91	C₄	#14519702	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	1	no	—
94	C₂	#16839520	1	1	yes	characteristic
95	C₂	#16839525	1	1	yes	characteristic
96	C₂	#16839531	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14519684
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₂×C₄²	C₂×D₆₁
Fitting	C₂×C₄⋊C₈×C₆₁	C₂
socle	C₂²×C₆₁	#95
hypercenter	C₂×C₄⋊C₈	D₆₁
hypocenter	C₆₁	#1292
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
51. C₆₁	#1292	semidirect