Subgroups — C₂³×#107 #60102

Order 256.

1807 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₂²×#107	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₄	—	2	2	no	—
5	C₂⁴×C₄	C₂²	1	1	yes	characteristic
6	C₂³×C₈	C₄	1	16	yes	complemented
7	C₂³×C₈	C₂²	1	14	yes	—
8	C₂²×C₄⋊C₄	—	2	14	no	—
9	C₂²×C₄⋊C₄	C₂²	1	28	yes	—
10	C₂×#107	C₂²	1	112	yes	direct product factor
11	C₂⁵	D₄	1	1	yes	characteristic
12	C₂³×C₄	—	2	28	no	—
13	C₂³×C₄	—	4	16	no	—
14	C₂³×C₄	C₂×C₄	1	8	yes	—
15	C₂³×C₄	D₄	1	7	yes	—
16	C₂³×C₄	Q₈	1	8	yes	—
17	C₂³×C₄	C₂³	1	7	yes	—
18	C₂²×C₈	C₂×C₄	1	112	yes	complemented
19	C₂²×C₈	C₂³	1	28	yes	—
20	C₂×C₄⋊C₄	—	2	84	no	—
21	C₂×C₄⋊C₄	C₂³	1	56	yes	—
22	#107	C₂³	1	64	yes	direct product factor
23	C₂⁴	C₄⋊C₄	1	8	yes	—
24	C₂⁴	D₈	1	8	yes	—
25	C₂⁴	Q₁₆	1	8	yes	—
26	C₂⁴	C₂×D₄	1	7	yes	—
27	C₂²×C₄	—	2	56	no	—
28	C₂²×C₄	—	4	112	no	—
29	C₂²×C₄	C₄⋊C₄	1	56	yes	—
30	C₂²×C₄	C₂²×C₄	1	28	yes	—
31	C₂²×C₄	C₂×D₄	1	21	yes	—
32	C₂²×C₄	C₂×Q₈	1	28	yes	—
33	C₂²×C₄	C₂⁴	1	7	yes	—
34	C₂×C₈	C₂²×C₄	1	112	yes	complemented
35	C₂×C₈	C₂⁴	1	8	yes	—
36	C₄⋊C₄	—	2	56	no	—
37	C₄⋊C₄	C₂⁴	1	16	yes	—
38	C₂³	#107	1	64	yes	direct product factor
39	C₂³	C₂×C₄⋊C₄	1	28	yes	—
40	C₂³	C₂×D₈	1	28	yes	—
41	C₂³	C₂×Q₁₆	1	28	yes	—
42	C₂³	C₂²×D₄	1	7	yes	—
43	C₂×C₄	—	2	16	no	—
44	C₂×C₄	—	4	112	no	—
45	C₂×C₄	C₂×C₄⋊C₄	1	84	yes	—
46	C₂×C₄	C₂³×C₄	1	14	yes	—
47	C₂×C₄	C₂²×D₄	1	7	yes	—
48	C₂×C₄	C₂²×Q₈	1	14	yes	—
49	C₂×C₄	C₂⁵	1	1	yes	characteristic
50	C₈	C₂³×C₄	1	16	yes	complemented
51	C₂²	C₂×#107	1	112	yes	direct product factor
52	C₂²	C₂²×C₄⋊C₄	1	14	yes	—
53	C₂²	C₂²×D₈	1	14	yes	—
54	C₂²	C₂²×Q₁₆	1	14	yes	—
55	C₂²	C₂³×D₄	1	1	yes	characteristic
56	C₄	—	4	16	no	—
57	C₄	C₂²×C₄⋊C₄	1	14	yes	—
58	C₄	C₂⁴×C₄	1	1	yes	characteristic
59	C₄	C₂³×Q₈	1	1	yes	characteristic
60	C₂	C₂²×#107	1	28	yes	direct product factor
61	C₂	C₂³×C₄⋊C₄	1	1	yes	characteristic
62	C₂	C₂³×D₈	1	1	yes	characteristic
63	C₂	C₂³×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁵	D₄
commutator	C₄	C₂⁴×C₄
Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. C₂²×#107	C₂	direct (N × H)
6. C₂³×C₈	C₄	semidirect
10. C₂×#107	C₂²	direct (N × H)
18. C₂²×C₈	C₂×C₄	semidirect
22. #107	C₂³	direct (N × H)
34. C₂×C₈	C₂²×C₄	semidirect
38. C₂³	#107	direct (N × H)
50. C₈	C₂³×C₄	semidirect
51. C₂²	C₂×#107	direct (N × H)
60. C₂	C₂²×#107	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁴×C₈	2
C₂³×C₄⋊C₄	2
C₂²×#107	2

Subgroups — C23×#107 #60102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#107 #60102