Subgroups — C₄×#338 #10698

Order 256.

429 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×M₁₆	C₂	1	3	yes	maximal
2	C₂×#338	C₂	1	4	yes	maximal
3	C₂²×M₁₆	C₂²	1	6	yes	—
4	C₂²×C₄²	C₂²	1	1	yes	characteristic
5	C₄×M₁₆	—	2	12	no	—
6	C₂×#97	C₄	1	6	yes	—
7	C₂×C₄×C₈	C₄	1	6	yes	—
8	#338	C₄	1	16	yes	direct product factor
9	C₂³×C₄	Q₈	1	2	yes	—
10	C₂³×C₄	C₂³	1	1	yes	characteristic
11	C₂×M₁₆	—	2	12	no	—
12	C₂×M₁₆	—	2	12	no	—
13	C₂×M₁₆	C₂×C₄	1	24	yes	—
14	C₂²×C₈	C₂×C₄	1	12	yes	—
15	C₂×C₄²	C₂×C₄	1	3	yes	—
16	C₂×C₄²	C₂×C₄	1	3	yes	—
17	C₂×C₄²	D₄	1	6	yes	—
18	#97	—	2	12	no	—
19	C₄×C₈	—	2	12	no	—
20	C₂⁴	C₂×Q₈	1	1	yes	characteristic
21	C₂²×C₄	—	4	4	no	—
22	C₂²×C₄	C₄⋊C₄	1	6	yes	—
23	C₂²×C₄	C₄⋊C₄	1	6	yes	—
24	C₂²×C₄	C₂²×C₄	1	3	yes	—
25	C₂²×C₄	C₂²×C₄	1	4	yes	—
26	C₂²×C₄	C₂×D₄	1	3	yes	—
27	C₂²×C₄	#41	1	4	yes	—
28	M₁₆	—	2	48	no	—
29	C₂×C₈	—	2	12	no	—
30	C₂×C₈	—	2	12	no	—
31	C₂×C₈	C₄²	1	24	yes	—
32	C₄²	C₄²	1	3	yes	—
33	C₄²	C₄²	1	1	yes	characteristic
34	C₄²	C₂²⋊C₄	1	6	yes	—
35	C₄²	C₂²⋊C₄	1	6	yes	—
36	C₂³	—	4	2	no	—
37	C₂³	C₂×C₄⋊C₄	1	3	yes	—
38	C₂³	C₄×Q₈	1	4	yes	—
39	C₂×C₄	—	2	12	no	—
40	C₂×C₄	—	4	6	no	—
41	C₂×C₄	#95	1	6	yes	—
42	C₂×C₄	#95	1	2	yes	—
43	C₂×C₄	C₂×C₄²	1	1	yes	characteristic
44	C₂×C₄	C₂×C₄²	1	6	yes	—
45	C₂×C₄	C₂×C₂²⋊C₄	1	3	yes	—
46	C₂×C₄	#117	1	6	yes	—
47	C₂×C₄	C₄×D₄	1	12	yes	—
48	C₈	—	2	24	no	—
49	C₂²	—	2	6	no	—
50	C₂²	—	4	4	no	—
51	C₂²	C₂×#95	1	1	yes	characteristic
52	C₂²	C₄×C₄⋊C₄	1	6	yes	—
53	C₄	—	2	6	no	—
54	C₄	#338	1	4	yes	direct product factor
55	C₄	C₄³	1	1	yes	characteristic
56	C₄	#376	1	1	yes	characteristic
57	C₄	C₄×C₂²⋊C₄	1	6	yes	—
58	C₂	—	2	6	no	—
59	C₂	C₄×#95	1	1	yes	characteristic
60	C₂	C₂×#338	1	2	yes	—

	subgroup	G/H
center	C₄²	C₄²
commutator	C₄	C₄³
Frattini, cosocle	C₂³×C₄	C₂³
socle	C₂²	C₂×#95
prime radical	C₂⁴	C₂×Q₈
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄² ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
8. #338	C₄	direct (N × H)
54. C₄	#338	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×M₁₆	2
C₂×#338	2

Subgroups — C4×#338 #10698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#338 #10698