Subgroups — #8818

Order 256.

243 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1845	C₂	1	6	yes	maximal
2	C₂×C₈²	C₂	1	1	yes	maximal, characteristic
3	C₂×#107	—	2	12	no	—
4	C₂×C₄×C₈	C₂²	1	3	yes	—
5	#384	C₂²	1	4	yes	—
6	C₈²	C₄	1	4	yes	complemented
7	C₂²×C₈	D₄	1	6	yes	—
8	C₂×C₄⋊C₄	—	2	12	no	—
9	C₂×C₄²	C₂³	1	1	yes	characteristic
10	#107	—	4	24	no	—
11	C₄×C₈	C₂×C₄	1	6	yes	—
12	C₄×C₈	Q₈	1	6	yes	—
13	C₂²×C₄	—	4	4	no	—
14	C₂²×C₄	C₂×D₄	1	3	yes	—
15	C₂×C₈	C₄⋊C₄	1	12	yes	—
16	C₂×C₈	D₈	1	12	yes	—
17	C₂×C₈	Q₁₆	1	12	yes	—
18	C₄⋊C₄	—	4	24	no	—
19	C₄²	C₂²×C₄	1	1	yes	characteristic
20	C₄²	C₂×Q₈	1	3	yes	—
21	C₂³	#127	1	1	yes	characteristic
22	C₂×C₄	—	8	12	no	—
23	C₂×C₄	C₂×C₄⋊C₄	1	3	yes	—
24	C₂×C₄	C₄⋊Q₈	1	3	yes	—
25	C₂×C₄	C₂×D₈	1	6	yes	—
26	C₂×C₄	C₂×Q₁₆	1	6	yes	—
27	C₈	#107	1	24	yes	complemented
28	C₂²	#384	1	1	yes	characteristic
29	C₂²	#493	1	3	yes	—
30	C₂²	#494	1	3	yes	—
31	C₄	—	16	4	no	—
32	C₄	C₂×#107	1	6	yes	—
33	C₄	#500	1	6	yes	—
34	C₂	#1712	1	1	yes	characteristic
35	C₂	#1713	1	3	yes	—
36	C₂	#1845	1	3	yes	—

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

N	H ≅ G/N	type
6. C₈²	C₄	semidirect
27. C₈	#107	semidirect

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

subgroup	index
#1845	2
C₂×C₈²	2