Subgroups — C₄×Q₃₂ #2174

Order 128.

75 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₁₆	C₂	1	2	yes	maximal
3	#366	C₂	1	1	yes	maximal, characteristic
4	#358	C₂	1	2	yes	maximal
5	C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆	C₂²	1	2	yes	—
7	C₄×Q₈	—	2	2	no	—
8	Q₃₂	C₄	1	4	yes	direct product factor
9	C₂×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₁₆	C₂²	1	1	yes	characteristic
11	#107	C₂²	1	2	yes	—
12	#103	—	2	2	no	—
13	C₄×C₈	C₂²	1	1	yes	characteristic
14	C₂×Q₈	—	2	2	no	—
15	Q₁₆	—	2	2	no	—
16	Q₁₆	C₂×C₄	1	4	yes	—
17	C₂×C₈	D₄	1	1	yes	characteristic
18	C₂×C₈	C₂³	1	1	yes	characteristic
19	C₄⋊C₄	—	2	2	no	—
20	C₄⋊C₄	—	4	2	no	—
21	C₄²	—	4	2	no	—
22	C₄²	D₄	1	1	yes	characteristic
23	C₁₆	—	2	1	no	—
24	C₁₆	C₂×C₄	1	2	yes	—
25	Q₈	—	2	4	no	—
26	Q₈	—	4	2	no	—
27	C₂×C₄	—	4	2	no	—
28	C₂×C₄	—	4	2	no	—
29	C₂×C₄	D₈	1	1	yes	characteristic
30	C₂×C₄	D₈	1	1	yes	characteristic
31	C₂×C₄	C₂×D₄	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	C₂²×C₄	1	1	yes	characteristic
34	C₈	#41	1	1	yes	characteristic
35	C₂²	C₂×D₈	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	—	4	4	no	—
38	C₄	—	8	2	no	—
39	C₄	Q₃₂	1	2	yes	direct product factor
40	C₄	C₄×D₄	1	1	yes	characteristic
41	C₄	#135	1	1	yes	characteristic
42	C₂	C₄×D₈	1	1	yes	characteristic
43	C₂	C₂×Q₃₂	1	1	yes	characteristic
44	C₂	#508	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. Q₃₂	C₄	direct (N × H)
39. C₄	Q₃₂	direct (N × H)

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