Subgroups — C₂×#2104 #23846

Order 256.

411 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2104	C₂	1	8	yes	maximal, direct product factor
2	C₂×#342	C₂	1	7	yes	maximal
3	C₂²×C₂²⋊C₄	C₂²	1	7	yes	—
4	#342	C₂²	1	28	yes	—
5	C₂⁵	C₂³	1	1	yes	characteristic
6	C₂³×C₄	—	2	7	no	—
7	C₂×C₂²⋊C₄	—	2	14	no	—
8	C₂×C₂²⋊C₄	—	2	14	no	—
9	C₂×C₂²⋊C₄	—	2	7	no	—
10	C₂×C₂²⋊C₄	C₂³	1	14	yes	—
11	C₂⁴	—	8	2	no	—
12	C₂⁴	#41	1	7	yes	—
13	C₂⁴	#41	1	7	yes	—
14	C₂⁴	C₂⁴	1	1	yes	characteristic
15	C₂²×C₄	—	2	14	no	—
16	C₂²×C₄	—	4	7	no	—
17	C₂²×C₄	—	4	7	no	—
18	C₂²×C₄	—	8	14	no	—
19	C₂²⋊C₄	—	2	28	no	—
20	C₂²⋊C₄	—	4	14	no	—
21	C₂³	—	4	14	no	—
22	C₂³	—	8	7	no	—
23	C₂³	—	8	1	no	—
24	C₂³	#126	1	7	yes	—
25	C₂³	#126	1	14	yes	—
26	C₂³	#126	1	7	yes	—
27	C₂³	C₂×#41	1	7	yes	—
28	C₂×C₄	—	4	14	no	—
29	C₂×C₄	—	8	14	no	—
30	C₂×C₄	—	8	14	no	—
31	C₂×C₄	—	8	14	no	—
32	C₂²	—	2	14	no	—
33	C₂²	—	4	7	no	—
34	C₂²	—	4	7	no	—
35	C₂²	—	4	14	no	—
36	C₂²	#401	1	7	yes	—
37	C₂²	#401	1	1	yes	characteristic
38	C₂²	C₂×#126	1	7	yes	—
39	C₄	—	8	14	no	—
40	C₂	—	2	7	no	—
41	C₂	—	2	7	no	—
42	C₂	#2104	1	2	yes	direct product factor
43	C₂	C₂×#401	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#401
commutator, Frattini, cosocle	C₂⁴	C₂⁴
prime radical	C₂⁵	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ G
LECS	G ▷ C₂⁴ ▷ C₂ ▷ C₁

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

N	H ≅ G/N	type
1. #2104	C₂	direct (N × H)
42. C₂	#2104	direct (N × H)

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

subgroup	index
#2104	2
C₂×#342	2