Subgroups — C₂²×#376 #33987

Order 256.

2575 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²	C₂	1	3	yes	maximal
2	C₂×#376	C₂	1	24	yes	maximal, direct product factor
3	C₂²×#95	C₂	1	4	yes	maximal
4	C₂⁴×C₄	C₂²	1	6	yes	—
5	C₂⁴×C₄	C₂²	1	1	yes	characteristic
6	C₂²×C₄²	C₄	1	48	yes	complemented
7	C₂²×C₄²	C₂²	1	36	yes	—
8	#376	C₂²	1	64	yes	direct product factor
9	C₂×#95	C₂²	1	48	yes	—
10	C₂⁵	C₂³	1	1	yes	characteristic
11	C₂³×C₄	—	2	48	no	—
12	C₂³×C₄	C₂×C₄	1	48	yes	—
13	C₂³×C₄	C₂×C₄	1	24	yes	—
14	C₂³×C₄	C₂³	1	36	yes	—
15	C₂³×C₄	C₂³	1	6	yes	—
16	C₂×C₄²	C₂×C₄	1	288	yes	complemented
17	C₂×C₄²	C₂³	1	48	yes	—
18	#95	C₂³	1	64	yes	—
19	C₂⁴	C₂²×C₄	1	12	yes	—
20	C₂⁴	#41	1	16	yes	—
21	C₂⁴	C₂⁴	1	3	yes	—
22	C₂²×C₄	—	2	192	no	—
23	C₂²×C₄	—	2	144	no	—
24	C₂²×C₄	C₄²	1	64	yes	—
25	C₂²×C₄	C₂²×C₄	1	144	yes	—
26	C₂²×C₄	C₂²×C₄	1	72	yes	—
27	C₂²×C₄	C₂⁴	1	24	yes	—
28	C₂²×C₄	C₂⁴	1	4	yes	—
29	C₄²	C₂²×C₄	1	192	yes	complemented
30	C₂³	C₂×C₄²	1	16	yes	—
31	C₂³	#117	1	96	yes	—
32	C₂³	C₂³×C₄	1	18	yes	—
33	C₂³	C₂×#41	1	24	yes	—
34	C₂³	C₂⁵	1	1	yes	characteristic
35	C₂×C₄	—	2	288	no	—
36	C₂×C₄	—	2	48	no	—
37	C₂×C₄	C₂×C₄²	1	96	yes	—
38	C₂×C₄	C₂³×C₄	1	48	yes	—
39	C₂×C₄	C₂³×C₄	1	24	yes	—
40	C₂²	#376	1	64	yes	direct product factor
41	C₂²	C₂²×C₄²	1	12	yes	—
42	C₂²	C₂×#117	1	72	yes	—
43	C₂²	C₂⁴×C₄	1	3	yes	—
44	C₂²	C₂²×#41	1	4	yes	—
45	C₄	—	2	48	no	—
46	C₄	C₂²×C₄²	1	16	yes	—
47	C₂	C₂×#376	1	24	yes	direct product factor
48	C₂	C₂³×C₄²	1	1	yes	characteristic
49	C₂	C₂²×#117	1	6	yes	—

	subgroup	G/H
center	C₂⁴×C₄	C₂²
commutator	C₂	C₂³×C₄²
Frattini, cosocle	C₂³	C₂⁵
socle, prime radical	C₂⁵	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂×#376	C₂	direct (N × H)
6. C₂²×C₄²	C₄	semidirect
8. #376	C₂²	direct (N × H)
16. C₂×C₄²	C₂×C₄	semidirect
29. C₄²	C₂²×C₄	semidirect
40. C₂²	#376	direct (N × H)
47. C₂	C₂×#376	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄²	2
C₂×#376	2
C₂²×#95	2

Subgroups — C22×#376 #33987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#376 #33987