Subgroups — C₂³×#376 #7625199

Order 512.

20898 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄²	C₂	1	3	yes	maximal
2	C₂²×#376	C₂	1	56	yes	maximal, direct product factor
3	C₂³×#95	C₂	1	4	yes	maximal
4	C₂⁵×C₄	C₂²	1	6	yes	—
5	C₂⁵×C₄	C₂²	1	1	yes	characteristic
6	C₂³×C₄²	C₄	1	96	yes	complemented
7	C₂³×C₄²	C₂²	1	84	yes	—
8	C₂×#376	C₂²	1	448	yes	direct product factor
9	C₂²×#95	C₂²	1	112	yes	—
10	C₂⁶	C₂³	1	1	yes	characteristic
11	C₂⁴×C₄	—	2	96	no	—
12	C₂⁴×C₄	C₂×C₄	1	96	yes	—
13	C₂⁴×C₄	C₂×C₄	1	48	yes	—
14	C₂⁴×C₄	C₂³	1	84	yes	—
15	C₂⁴×C₄	C₂³	1	14	yes	—
16	C₂²×C₄²	C₂×C₄	1	1344	yes	complemented
17	C₂²×C₄²	C₂³	1	336	yes	—
18	#376	C₂³	1	512	yes	direct product factor
19	C₂×#95	C₂³	1	448	yes	—
20	C₂⁵	C₂²×C₄	1	24	yes	—
21	C₂⁵	#41	1	32	yes	—
22	C₂⁵	C₂⁴	1	7	yes	—
23	C₂³×C₄	—	2	768	no	—
24	C₂³×C₄	—	2	672	no	—
25	C₂³×C₄	C₄²	1	256	yes	—
26	C₂³×C₄	C₂²×C₄	1	672	yes	—
27	C₂³×C₄	C₂²×C₄	1	336	yes	—
28	C₂³×C₄	C₂⁴	1	168	yes	—
29	C₂³×C₄	C₂⁴	1	28	yes	—
30	C₂×C₄²	C₂²×C₄	1	2688	yes	complemented
31	C₂×C₄²	C₂⁴	1	192	yes	—
32	#95	C₂⁴	1	256	yes	—
33	C₂⁴	C₂×C₄²	1	64	yes	—
34	C₂⁴	#117	1	384	yes	—
35	C₂⁴	C₂³×C₄	1	84	yes	—
36	C₂⁴	C₂×#41	1	112	yes	—
37	C₂⁴	C₂⁵	1	7	yes	—
38	C₂²×C₄	—	2	2688	no	—
39	C₂²×C₄	—	2	672	no	—
40	C₂²×C₄	C₂×C₄²	1	896	yes	—
41	C₂²×C₄	C₂³×C₄	1	672	yes	—
42	C₂²×C₄	C₂³×C₄	1	336	yes	—
43	C₂²×C₄	C₂⁵	1	48	yes	—
44	C₂²×C₄	C₂⁵	1	8	yes	—
45	C₄²	C₂³×C₄	1	768	yes	complemented
46	C₂³	#376	1	512	yes	direct product factor
47	C₂³	C₂²×C₄²	1	112	yes	—
48	C₂³	C₂×#117	1	672	yes	—
49	C₂³	C₂⁴×C₄	1	42	yes	—
50	C₂³	C₂²×#41	1	56	yes	—
51	C₂³	C₂⁶	1	1	yes	characteristic
52	C₂×C₄	—	2	96	no	—
53	C₂×C₄	—	2	1344	no	—
54	C₂×C₄	C₂²×C₄²	1	448	yes	—
55	C₂×C₄	C₂⁴×C₄	1	96	yes	—
56	C₂×C₄	C₂⁴×C₄	1	48	yes	—
57	C₂²	C₂×#376	1	448	yes	direct product factor
58	C₂²	C₂³×C₄²	1	28	yes	—
59	C₂²	C₂²×#117	1	168	yes	—
60	C₂²	C₂⁵×C₄	1	3	yes	—
61	C₂²	C₂³×#41	1	4	yes	—
62	C₄	—	2	96	no	—
63	C₄	C₂³×C₄²	1	32	yes	—
64	C₂	C₂²×#376	1	56	yes	direct product factor
65	C₂	C₂⁴×C₄²	1	1	yes	characteristic
66	C₂	C₂³×#117	1	6	yes	—

	subgroup	G/H
center	C₂⁵×C₄	C₂²
commutator	C₂	C₂⁴×C₄²
Frattini, cosocle	C₂³	C₂⁶
socle, prime radical	C₂⁶	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂²×#376	C₂	direct (N × H)
6. C₂³×C₄²	C₄	semidirect
8. C₂×#376	C₂²	direct (N × H)
16. C₂²×C₄²	C₂×C₄	semidirect
18. #376	C₂³	direct (N × H)
30. C₂×C₄²	C₂²×C₄	semidirect
45. C₄²	C₂³×C₄	semidirect
46. C₂³	#376	direct (N × H)
57. C₂²	C₂×#376	direct (N × H)
64. C₂	C₂²×#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
C₂⁴×C₄²	2
C₂²×#376	2
C₂³×#95	2

Subgroups — C23×#376 #7625199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#376 #7625199