Subgroups — #7366

Order 256.

79 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1835	C₂	1	1	yes	maximal, characteristic
2	#1324	C₂	1	2	yes	maximal
3	C₂×C₄×C₈	C₄	1	1	yes	characteristic
4	#382	C₄	1	1	yes	characteristic
5	#382	C₂²	1	1	yes	characteristic
6	#340	—	2	2	no	—
7	#324	—	2	2	no	—
8	C₂²×C₈	—	2	1	no	—
9	C₂×C₄⋊C₄	—	2	1	no	—
10	C₂×C₄⋊C₄	D₄	1	2	yes	—
11	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
12	C₂²⋊C₈	—	4	2	no	—
13	C₄×C₈	—	2	1	no	—
14	C₄×C₈	C₈	1	2	yes	complemented
15	#95	—	4	1	no	—
16	#95	—	4	1	no	—
17	C₂²×C₄	—	2	1	no	—
18	C₂²×C₄	—	2	2	no	—
19	C₂²×C₄	—	4	1	no	—
20	C₂²×C₄	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₈	—	2	2	no	—
22	C₂×C₈	—	4	1	no	—
23	C₂×C₈	—	4	1	no	—
24	C₂×C₈	—	8	2	no	—
25	C₄⋊C₄	—	4	2	no	—
26	C₄⋊C₄	—	4	2	no	—
27	C₄²	—	2	1	no	—
28	C₄²	C₂×C₈	1	1	yes	characteristic
29	C₄²	M₁₆	1	1	yes	characteristic
30	C₂³	#99	1	1	yes	characteristic
31	C₂×C₄	—	2	1	no	—
32	C₂×C₄	—	2	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	4	2	no	—
36	C₂×C₄	—	4	2	no	—
37	C₂×C₄	—	8	2	no	—
38	C₂×C₄	—	8	2	no	—
39	C₂×C₄	—	8	1	no	—
40	C₂×C₄	C₂²⋊C₈	1	1	yes	characteristic
41	C₂×C₄	#101	1	1	yes	characteristic
42	C₈	—	4	2	no	—
43	C₈	—	16	2	no	—
44	C₂²	—	2	2	no	—
45	C₂²	#324	1	1	yes	characteristic
46	C₂²	#354	1	1	yes	characteristic
47	C₂²	#355	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	—	2	1	no	—
50	C₄	—	4	1	no	—
51	C₄	—	4	1	no	—
52	C₄	—	8	2	no	—
53	C₄	—	16	1	no	—
54	C₂	—	2	1	no	—
55	C₂	—	2	1	no	—
56	C₂	#1324	1	1	yes	characteristic
57	C₂	#1414	1	2	yes	—

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

N	H ≅ G/N	type
14. C₄×C₈	C₈	semidirect

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

subgroup	index
#1835	2
#1324	2