Subgroups — C₂³×#11758202 #21460541

Order 7808.

1464 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₁₂₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×#11758202	C₂	1	28	yes	maximal, direct product factor
3	C₂³×#92418	C₂	1	1	yes	maximal, characteristic
4	C₂³×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₂₂	—	2	7	no	—
6	C₂²×Dic₁₂₂	C₂²	1	14	yes	—
7	C₂³×Dic₆₁	—	2	1	no	—
8	C₂×#11758202	C₂²	1	112	yes	direct product factor
9	C₂²×#92418	C₂²	1	14	yes	—
10	C₂²×Q₈×C₆₁	—	2	7	no	—
11	C₂²×Q₈×C₆₁	C₂²	1	14	yes	—
12	C₂³×C₄×C₆₁	—	2	1	no	—
13	C₂³×C₄×C₆₁	C₂²	1	1	yes	characteristic
14	C₂⁴×C₆₁	D₄	1	1	yes	characteristic
15	C₂×Q₈×C₆₁	—	2	42	no	—
16	C₂×Q₈×C₆₁	C₂³	1	28	yes	—
17	C₂²×C₄×C₆₁	—	2	14	no	—
18	C₂²×C₄×C₆₁	D₄	1	7	yes	—
19	C₂²×C₄×C₆₁	C₂³	1	7	yes	—
20	C₂²×Dic₆₁	—	2	14	no	—
21	C₂×Dic₁₂₂	—	2	42	no	—
22	C₂×Dic₁₂₂	C₂³	1	28	yes	—
23	#11758202	C₂³	1	64	yes	direct product factor
24	C₂×#92418	C₂³	1	28	yes	—
25	C₂³×C₆₁	Q₁₆	1	8	yes	complemented
26	C₂³×C₆₁	C₂×D₄	1	7	yes	—
27	Q₈×C₆₁	—	2	28	no	—
28	Q₈×C₆₁	C₂⁴	1	8	yes	—
29	C₂×C₄×C₆₁	—	2	28	no	—
30	C₂×C₄×C₆₁	C₂×D₄	1	21	yes	—
31	C₂×C₄×C₆₁	C₂⁴	1	7	yes	—
32	C₂×Dic₆₁	—	2	28	no	—
33	Dic₁₂₂	—	2	28	no	—
34	Dic₁₂₂	C₂⁴	1	8	yes	—
35	#92418	C₂⁴	1	8	yes	—
36	C₂²×C₆₁	C₂×Q₁₆	1	28	yes	complemented
37	C₂²×C₆₁	C₂²×D₄	1	7	yes	—
38	C₄×C₆₁	—	2	8	no	—
39	C₄×C₆₁	C₂²×D₄	1	7	yes	—
40	C₄×C₆₁	C₂⁵	1	1	yes	characteristic
41	Dic₆₁	—	2	8	no	—
42	C₂³×Q₁₆	—	61	1	no	maximal, Sylow
43	C₂×C₆₁	C₂²×Q₁₆	1	14	yes	complemented
44	C₂×C₆₁	C₂³×D₄	1	1	yes	characteristic
45	C₂³×Q₈	—	61	1	no	—
46	C₂³×Q₈	D₆₁	1	1	yes	characteristic
47	C₂²×Q₁₆	—	61	28	no	—
48	C₂³×C₈	—	61	1	no	—
49	C₆₁	C₂³×Q₁₆	1	1	yes	characteristic, complemented, Sylow
50	C₂²×Q₈	—	2	7	no	—
51	C₂²×Q₈	—	61	14	no	—
52	C₂²×Q₈	—	122	7	no	—
53	C₂²×Q₈	C₂×D₆₁	1	14	yes	—
54	C₂³×C₄	—	2	1	no	—
55	C₂³×C₄	—	122	1	no	—
56	C₂³×C₄	C₂×D₆₁	1	1	yes	characteristic
57	C₂×Q₁₆	—	61	112	no	—
58	C₂²×C₈	—	61	14	no	—
59	C₂⁴	C₂²⋊D₆₁	1	1	yes	characteristic
60	C₂×Q₈	—	2	42	no	—
61	C₂×Q₈	—	61	28	no	—
62	C₂×Q₈	—	122	42	no	—
63	C₂×Q₈	C₂²×D₆₁	1	28	yes	—
64	C₂²×C₄	—	2	14	no	—
65	C₂²×C₄	—	122	14	no	—
66	C₂²×C₄	C₂²⋊D₆₁	1	7	yes	—
67	C₂²×C₄	C₂²×D₆₁	1	7	yes	—
68	Q₁₆	—	61	64	no	—
69	C₂×C₈	—	61	28	no	—
70	C₂³	#11758202	1	8	yes	direct product factor
71	C₂³	C₂×C₂²⋊D₆₁	1	7	yes	—
72	Q₈	—	2	28	no	—
73	Q₈	—	61	8	no	—
74	Q₈	—	122	28	no	—
75	Q₈	C₂³×D₆₁	1	8	yes	—
76	C₂×C₄	—	2	28	no	—
77	C₂×C₄	—	122	28	no	—
78	C₂×C₄	C₂×C₂²⋊D₆₁	1	21	yes	—
79	C₂×C₄	C₂³×D₆₁	1	7	yes	—
80	C₈	—	61	8	no	—
81	C₂²	C₂×#11758202	1	28	yes	direct product factor
82	C₂²	C₂²×C₂²⋊D₆₁	1	7	yes	—
83	C₄	—	2	8	no	—
84	C₄	—	122	8	no	—
85	C₄	C₂²×C₂²⋊D₆₁	1	7	yes	—
86	C₄	C₂⁴×D₆₁	1	1	yes	characteristic
87	C₂	C₂²×#11758202	1	14	yes	direct product factor
88	C₂	C₂³×C₂²⋊D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²⋊D₆₁
commutator	C₄×C₆₁	C₂⁵
Frattini	C₄	C₂⁴×D₆₁
Fitting	C₂³×Q₈×C₆₁	C₂
socle	C₂⁴×C₆₁	D₄
hypercenter	C₂³×Q₈	D₆₁
hypocenter	C₆₁	C₂³×Q₁₆
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂²×#11758202	C₂	direct (N × H)
8. C₂×#11758202	C₂²	direct (N × H)
23. #11758202	C₂³	direct (N × H)
25. C₂³×C₆₁	Q₁₆	semidirect
36. C₂²×C₆₁	C₂×Q₁₆	semidirect
43. C₂×C₆₁	C₂²×Q₁₆	semidirect
49. C₆₁	C₂³×Q₁₆	semidirect
70. C₂³	#11758202	direct (N × H)
81. C₂²	C₂×#11758202	direct (N × H)
87. C₂	C₂²×#11758202	direct (N × H)

Subgroups — C23×#11758202 #21460541

Conjugacy classes of subgroups

Complements

Subgroups — C₂³×#11758202 #21460541