Subgroups — #8815

Order 256.

211 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1844	C₂	1	2	yes	maximal
2	#1834	C₂	1	4	yes	maximal
3	C₂×C₈²	C₂	1	1	yes	maximal, characteristic
4	C₂×#106	—	2	4	no	—
5	C₂×C₄×C₈	C₂²	1	2	yes	—
6	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
7	#384	C₂²	1	4	yes	—
8	#340	—	2	8	no	—
9	C₈²	C₄	1	4	yes	complemented
10	C₂²×C₈	D₄	1	4	yes	—
11	C₂²×C₈	D₄	1	2	yes	—
12	C₂×C₄⋊C₄	—	2	8	no	—
13	C₂×C₄⋊C₄	—	2	4	no	—
14	C₂×C₄²	C₂³	1	1	yes	characteristic
15	#106	—	4	8	no	—
16	C₄×C₈	C₂×C₄	1	4	yes	—
17	C₄×C₈	C₂×C₄	1	2	yes	—
18	C₄×C₈	Q₈	1	4	yes	—
19	C₄×C₈	Q₈	1	2	yes	—
20	C₂²×C₄	—	4	4	no	—
21	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
22	C₂²×C₄	C₂×D₄	1	2	yes	—
23	C₂×C₈	—	2	8	no	—
24	C₂×C₈	C₄⋊C₄	1	8	yes	—
25	C₂×C₈	C₄⋊C₄	1	4	yes	—
26	C₂×C₈	SD₁₆	1	8	yes	—
27	C₄⋊C₄	—	4	8	no	—
28	C₄⋊C₄	—	4	16	no	—
29	C₄²	C₂²×C₄	1	1	yes	characteristic
30	C₄²	C₂×Q₈	1	1	yes	characteristic
31	C₄²	C₂×Q₈	1	2	yes	—
32	C₂³	#127	1	1	yes	characteristic
33	C₂×C₄	—	8	4	no	—
34	C₂×C₄	—	8	8	no	—
35	C₂×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄	C₂×C₄⋊C₄	1	2	yes	—
37	C₂×C₄	C₄⋊Q₈	1	1	yes	characteristic
38	C₂×C₄	C₄⋊Q₈	1	2	yes	—
39	C₂×C₄	C₂×SD₁₆	1	4	yes	—
40	C₂×C₄	#135	1	8	yes	—
41	C₈	—	2	8	no	—
42	C₈	#106	1	8	yes	—
43	C₂²	#384	1	1	yes	characteristic
44	C₂²	#492	1	2	yes	—
45	C₂²	#495	1	4	yes	—
46	C₄	—	16	4	no	—
47	C₄	C₂×#106	1	2	yes	—
48	C₄	#427	1	4	yes	—
49	C₄	#498	1	2	yes	—
50	C₄	#499	1	4	yes	—
51	C₂	#1708	1	4	yes	—
52	C₂	#1844	1	1	yes	characteristic
53	C₂	#1846	1	2	yes	—

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

N	H ≅ G/N	type
9. C₈²	C₄	semidirect

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