Subgroups — #1842

Order 128.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈	C₂	1	6	yes	maximal
2	C₄³	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈	C₂²	1	4	yes	—
4	C₂×C₄²	C₄	1	3	yes	—
5	C₂×C₄²	C₄	1	1	yes	characteristic
6	C₂×C₄²	C₂²	1	3	yes	—
7	C₄⋊C₈	—	2	12	no	—
8	C₂²×C₄	C₂×C₄	1	3	yes	—
9	C₂²×C₄	C₂×C₄	1	3	yes	—
10	C₂²×C₄	C₂³	1	1	yes	characteristic
11	C₂×C₈	—	2	12	no	—
12	C₄²	—	2	6	no	—
13	C₄²	C₈	1	4	yes	complemented
14	C₄²	D₄	1	6	yes	—
15	C₄²	Q₈	1	6	yes	—
16	C₂³	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₄	—	2	6	no	—
18	C₂×C₄	C₄⋊C₄	1	6	yes	—
19	C₂×C₄	C₄⋊C₄	1	6	yes	—
20	C₂×C₄	C₂×C₈	1	6	yes	—
21	C₂×C₄	M₁₆	1	6	yes	—
22	C₂×C₄	C₂×D₄	1	3	yes	—
23	C₂×C₄	C₂×Q₈	1	3	yes	—
24	C₈	—	4	4	no	—
25	C₂²	C₂×C₄⋊C₄	1	3	yes	—
26	C₂²	C₂²×C₈	1	1	yes	characteristic
27	C₂²	C₂×M₁₆	1	3	yes	—
28	C₄	—	2	6	no	—
29	C₄	C₄⋊C₈	1	12	yes	complemented
30	C₄	#127	1	1	yes	characteristic
31	C₄	C₄⋊Q₈	1	3	yes	—
32	C₂	#384	1	1	yes	characteristic
33	C₂	C₂×C₄⋊C₈	1	3	yes	—
34	C₂	#423	1	3	yes	—

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

N	H ≅ G/N	type
13. C₄²	C₈	semidirect
29. C₄	C₄⋊C₈	semidirect

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

subgroup	index
C₂×C₄⋊C₈	2
C₄³	2