Subgroups — #1579

Order 128.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Q₈	C₂	1	2	yes	maximal
2	C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic
3	#334	C₂	1	1	yes	maximal, characteristic
4	Q₈⋊C₈	C₂	1	2	yes	maximal
5	#322	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆	C₄	1	1	yes	characteristic
7	C₄×Q₈	C₂²	1	2	yes	—
8	#107	C₄	1	1	yes	characteristic
9	C₄⋊C₈	—	2	2	no	—
10	C₄⋊C₈	C₂²	1	2	yes	—
11	#103	C₄	1	2	yes	—
12	C₄×C₈	—	2	2	no	—
13	C₄×C₈	C₂²	1	1	yes	characteristic
14	C₄×C₈	C₂²	1	1	yes	characteristic
15	C₄×C₈	C₂²	1	1	yes	characteristic
16	C₂×Q₈	C₂×C₄	1	2	yes	—
17	Q₁₆	C₈	1	4	yes	complemented
18	C₂×C₈	—	2	2	no	—
19	C₂×C₈	—	2	1	no	—
20	C₂×C₈	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈	D₄	1	2	yes	—
23	C₄⋊C₄	—	2	2	no	—
24	C₄⋊C₄	C₂×C₄	1	2	yes	—
25	C₄²	—	2	2	no	—
26	C₄²	C₂³	1	1	yes	characteristic
27	Q₈	—	2	2	no	—
28	Q₈	C₂×C₈	1	4	yes	—
29	C₂×C₄	—	2	2	no	—
30	C₂×C₄	—	2	2	no	—
31	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄	#41	1	1	yes	characteristic
34	C₈	—	2	1	no	—
35	C₈	—	2	2	no	—
36	C₈	—	4	1	no	—
37	C₈	—	4	2	no	—
38	C₈	C₂×C₈	1	2	yes	—
39	C₂²	C₄×D₄	1	1	yes	characteristic
40	C₄	—	2	4	no	—
41	C₄	—	2	1	no	—
42	C₄	—	4	2	no	—
43	C₄	C₂²×C₈	1	1	yes	characteristic
44	C₄	#131	1	1	yes	characteristic
45	C₄	#137	1	2	yes	—
46	C₂	C₈×D₄	1	1	yes	characteristic
47	C₂	#441	1	1	yes	characteristic
48	C₂	#444	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. Q₁₆	C₈	semidirect

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