Subgroups — C₂³×#11758185 #21458912

Order 7808.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11758185	C₂	1	14	yes	maximal, direct product factor
2	C₂³×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#11758185	C₂²	1	28	yes	direct product factor
4	C₂³×C₄×C₆₁	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₆₁	C₄	1	7	yes	—
6	C₂²×C₈×C₆₁	C₂²	1	7	yes	—
7	C₂⁴×C₆₁	C₈	1	1	yes	characteristic
8	C₂²×C₄×C₆₁	C₈	1	7	yes	—
9	C₂²×C₄×C₆₁	C₂×C₄	1	7	yes	—
10	C₂×C₈×C₆₁	C₂×C₄	1	21	yes	—
11	C₂×C₈×C₆₁	C₂³	1	7	yes	—
12	#11758185	C₂³	1	8	yes	direct product factor
13	C₂³×C₆₁	C₁₆	1	8	yes	complemented
14	C₂³×C₆₁	C₂×C₈	1	7	yes	—
15	C₂×C₄×C₆₁	C₂×C₈	1	21	yes	—
16	C₂×C₄×C₆₁	C₂²×C₄	1	7	yes	—
17	C₈×C₆₁	C₂²×C₄	1	7	yes	—
18	C₈×C₆₁	C₂⁴	1	1	yes	characteristic
19	C₂²×C₆₁	C₂×C₁₆	1	28	yes	complemented
20	C₂²×C₆₁	C₂²×C₈	1	7	yes	—
21	C₄×C₆₁	C₂²×C₈	1	7	yes	—
22	C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
23	C₂³×C₁₆	—	61	1	no	maximal, Sylow
24	C₂×C₆₁	C₂²×C₁₆	1	14	yes	complemented
25	C₂×C₆₁	C₂³×C₈	1	1	yes	characteristic
26	C₂³×C₈	D₆₁	1	1	yes	characteristic
27	C₂²×C₁₆	—	61	14	no	—
28	C₆₁	C₂³×C₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₂³×C₄	Dic₆₁	1	1	yes	characteristic
30	C₂²×C₈	Dic₆₁	1	7	yes	—
31	C₂²×C₈	C₂×D₆₁	1	7	yes	—
32	C₂×C₁₆	—	61	28	no	—
33	C₂⁴	#92418	1	1	yes	characteristic
34	C₂²×C₄	#92418	1	7	yes	—
35	C₂²×C₄	C₂×Dic₆₁	1	7	yes	—
36	C₂×C₈	C₂×Dic₆₁	1	21	yes	—
37	C₂×C₈	C₂²×D₆₁	1	7	yes	—
38	C₁₆	—	61	8	no	—
39	C₂³	#11758185	1	8	yes	direct product factor
40	C₂³	C₂×#92418	1	7	yes	—
41	C₂×C₄	C₂×#92418	1	21	yes	—
42	C₂×C₄	C₂²×Dic₆₁	1	7	yes	—
43	C₈	C₂²×Dic₆₁	1	7	yes	—
44	C₈	C₂³×D₆₁	1	1	yes	characteristic
45	C₂²	C₂×#11758185	1	28	yes	direct product factor
46	C₂²	C₂²×#92418	1	7	yes	—
47	C₄	C₂²×#92418	1	7	yes	—
48	C₄	C₂³×Dic₆₁	1	1	yes	characteristic
49	C₂	C₂²×#11758185	1	14	yes	direct product factor
50	C₂	C₂³×#92418	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₈	D₆₁
commutator, hypocenter	C₆₁	C₂³×C₁₆
Frattini	C₈	C₂³×D₆₁
Fitting	C₂³×C₈×C₆₁	C₂
socle	C₂⁴×C₆₁	C₈
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#11758185	C₂	direct (N × H)
3. C₂×#11758185	C₂²	direct (N × H)
12. #11758185	C₂³	direct (N × H)
13. C₂³×C₆₁	C₁₆	semidirect
19. C₂²×C₆₁	C₂×C₁₆	semidirect
24. C₂×C₆₁	C₂²×C₁₆	semidirect
28. C₆₁	C₂³×C₁₆	semidirect
39. C₂³	#11758185	direct (N × H)
45. C₂²	C₂×#11758185	direct (N × H)
49. C₂	C₂²×#11758185	direct (N × H)

Subgroups — C23×#11758185 #21458912

Conjugacy classes of subgroups

Complements

Subgroups — C₂³×#11758185 #21458912