Subgroups — #21456343

Order 7808.

348 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840319	C₂	1	2	yes	maximal
2	#16840171	C₂	1	8	yes	maximal, complemented
3	#16839800	C₂	1	4	yes	maximal
4	C₂×#97×C₆₁	C₂	1	1	yes	maximal, characteristic
5	#14519777	C₂²	1	4	yes	—
6	#14519769	C₂²	1	4	yes	—
7	#14519756	—	2	4	no	—
8	C₄×Dic₁₂₂	—	2	4	no	—
9	#14519736	C₂²	1	4	yes	—
10	#14519711	C₂²	1	8	yes	—
11	#14519709	C₂²	1	8	yes	—
12	C₂²×C₈×C₆₁	C₂²	1	2	yes	—
13	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
14	#97×C₆₁	C₂²	1	4	yes	—
15	C₂²×C₄×C₆₁	D₄	1	2	yes	—
16	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
17	C₂×Dic₁₂₂	—	2	4	no	—
18	C₂×C₈×C₆₁	Q₈	1	8	yes	complemented
19	C₂×C₈×C₆₁	C₂³	1	4	yes	—
20	C₄²×C₆₁	D₄	1	2	yes	—
21	C₄²×C₆₁	C₂³	1	2	yes	—
22	C₂²⋊Dic₆₁	—	2	4	no	—
23	C₄⋊Dic₆₁	—	2	4	no	—
24	C₄⋊Dic₆₁	C₂³	1	8	yes	—
25	#11758196	—	2	8	no	—
26	C₄×Dic₆₁	—	2	4	no	—
27	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₆₁	—	4	2	no	—
29	C₂×C₄×C₆₁	C₂×D₄	1	4	yes	—
30	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₂×Q₈	1	4	yes	—
32	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
33	C₂×Dic₆₁	—	2	8	no	—
34	Dic₁₂₂	—	4	8	no	—
35	C₈×C₆₁	C₂×Q₈	1	8	yes	—
36	C₂²×C₆₁	—	2	2	no	—
37	C₂²×C₆₁	C₄⋊Q₈	1	2	yes	—
38	C₂²×C₆₁	C₂²×D₄	1	1	yes	characteristic
39	C₄×C₆₁	—	2	4	no	—
40	C₄×C₆₁	C₄⋊Q₈	1	2	yes	—
41	C₄×C₆₁	C₂²×Q₈	1	2	yes	—
42	Dic₆₁	—	4	8	no	—
43	#3162	—	61	1	no	maximal, Sylow
44	C₂×C₆₁	—	2	2	no	—
45	C₂×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
46	C₂×C₆₁	#575	1	2	yes	—
47	#533	—	61	2	no	—
48	#501	—	61	8	no	—
49	#427	—	61	4	no	—
50	C₂×#97	D₆₁	1	1	yes	characteristic
51	C₆₁	#3162	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₈	C₂×D₆₁	1	2	yes	—
53	C₄⋊Q₈	—	61	4	no	—
54	#125	—	61	4	no	—
55	C₂²⋊Q₈	—	122	4	no	—
56	C₄×Q₈	—	122	4	no	—
57	#117	—	61	4	no	—
58	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
59	#107	—	61	8	no	—
60	#106	—	61	8	no	—
61	#97	C₂×D₆₁	1	4	yes	—
62	C₂×Q₈	—	122	4	no	—
63	C₂²×C₄	D₂₄₄	1	2	yes	—
64	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
65	C₂×C₈	Dic₁₂₂	1	8	yes	complemented
66	C₂×C₈	C₂²×D₆₁	1	4	yes	—
67	C₄⋊C₄	—	61	8	no	—
68	C₄⋊C₄	—	122	8	no	—
69	C₄⋊C₄	—	122	4	no	—
70	C₂²⋊C₄	—	122	4	no	—
71	C₄²	—	122	4	no	—
72	C₄²	D₂₄₄	1	2	yes	—
73	C₄²	C₂²×D₆₁	1	2	yes	—
74	C₂³	C₂×D₂₄₄	1	1	yes	characteristic
75	Q₈	—	244	8	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	—	122	8	no	—
78	C₂×C₄	C₂×Dic₁₂₂	1	4	yes	—
79	C₂×C₄	C₂×D₂₄₄	1	4	yes	—
80	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
81	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
82	C₈	C₂×Dic₁₂₂	1	8	yes	—
83	C₂²	—	2	2	no	—
84	C₂²	#14519777	1	2	yes	—
85	C₂²	C₂²×D₂₄₄	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	—	244	8	no	—
88	C₄	#14519777	1	2	yes	—
89	C₄	C₂²×Dic₁₂₂	1	2	yes	—
90	C₂	—	2	2	no	—
91	C₂	C₂×#14519777	1	1	yes	characteristic
92	C₂	#16840562	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₂₄₄
commutator	C₂×C₄×C₆₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₆₁
Fitting	C₂×#97×C₆₁	C₂
socle	C₂²×C₆₁	C₂²×D₄
hypercenter	C₂×#97	D₆₁
hypocenter	C₆₁	#3162
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
2. #16840171	C₂	semidirect
18. C₂×C₈×C₆₁	Q₈	semidirect
51. C₆₁	#3162	semidirect
65. C₂×C₈	Dic₁₂₂	semidirect