Subgroups — C₂³×#95 #33986

Order 256.

7167 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄	C₂	1	3	yes	maximal
2	C₂²×#95	C₂	1	28	yes	maximal, direct product factor
3	C₂⁶	C₂²	1	1	yes	characteristic
4	C₂⁴×C₄	—	2	48	no	—
5	C₂⁴×C₄	C₄	1	48	yes	complemented
6	C₂⁴×C₄	C₂²	1	42	yes	—
7	C₂×#95	C₂²	1	112	yes	direct product factor
8	C₂⁵	C₂×C₄	1	24	yes	—
9	C₂⁵	D₄	1	24	yes	—
10	C₂⁵	Q₈	1	8	yes	—
11	C₂⁵	C₂³	1	7	yes	—
12	C₂³×C₄	—	2	384	no	—
13	C₂³×C₄	—	2	336	no	—
14	C₂³×C₄	C₂×C₄	1	336	yes	complemented
15	C₂³×C₄	C₂³	1	84	yes	—
16	#95	C₂³	1	64	yes	direct product factor
17	C₂⁴	C₄²	1	64	yes	—
18	C₂⁴	C₂²⋊C₄	1	192	yes	—
19	C₂⁴	C₄⋊C₄	1	192	yes	—
20	C₂⁴	C₂²×C₄	1	84	yes	—
21	C₂⁴	C₂×D₄	1	84	yes	—
22	C₂⁴	C₂×Q₈	1	28	yes	—
23	C₂⁴	C₂⁴	1	7	yes	—
24	C₂²×C₄	—	2	1344	no	—
25	C₂²×C₄	—	2	336	no	—
26	C₂²×C₄	C₂²×C₄	1	336	yes	complemented
27	C₂²×C₄	C₂⁴	1	24	yes	—
28	C₂³	#95	1	512	yes	direct product factor
29	C₂³	C₂×C₄²	1	112	yes	—
30	C₂³	C₂×C₂²⋊C₄	1	336	yes	—
31	C₂³	C₂×C₄⋊C₄	1	336	yes	—
32	C₂³	C₂³×C₄	1	42	yes	—
33	C₂³	C₂²×D₄	1	42	yes	—
34	C₂³	C₂²×Q₈	1	14	yes	—
35	C₂³	C₂⁵	1	1	yes	characteristic
36	C₂×C₄	—	2	672	no	—
37	C₂×C₄	—	2	48	no	—
38	C₂×C₄	C₂³×C₄	1	48	yes	complemented
39	C₂²	C₂×#95	1	448	yes	direct product factor
40	C₂²	C₂²×C₄²	1	28	yes	—
41	C₂²	C₂²×C₂²⋊C₄	1	84	yes	—
42	C₂²	C₂²×C₄⋊C₄	1	84	yes	—
43	C₂²	C₂⁴×C₄	1	3	yes	—
44	C₂²	C₂³×D₄	1	3	yes	—
45	C₂²	C₂³×Q₈	1	1	yes	characteristic
46	C₄	—	2	48	no	—
47	C₂	C₂²×#95	1	56	yes	direct product factor
48	C₂	C₂³×C₄²	1	1	yes	characteristic
49	C₂	C₂³×C₂²⋊C₄	1	3	yes	—
50	C₂	C₂³×C₄⋊C₄	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁶	C₂²
commutator	C₂	C₂³×C₄²
Frattini, cosocle	C₂³	C₂⁵
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁶ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂²×#95	C₂	direct (N × H)
5. C₂⁴×C₄	C₄	semidirect
7. C₂×#95	C₂²	direct (N × H)
14. C₂³×C₄	C₂×C₄	semidirect
16. #95	C₂³	direct (N × H)
26. C₂²×C₄	C₂²×C₄	semidirect
28. C₂³	#95	direct (N × H)
38. C₂×C₄	C₂³×C₄	semidirect
39. C₂²	C₂×#95	direct (N × H)
47. C₂	C₂²×#95	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₄	2
C₂²×#95	2

Subgroups — C23×#95 #33986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#95 #33986