Subgroups — C₈×#16864520 #46831015

Order 34624.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#16864520	C₂	1	2	yes	maximal
2	C₈×Dic₅₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#16864520	C₄	1	4	yes	—
4	C₂×#16864513	C₄	1	1	yes	characteristic
5	C₄×Dic₅₄₁	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₅₄₁	C₄	1	1	yes	characteristic
7	#16864520	C₈	1	8	yes	direct product factor
8	C₂×Dic₅₄₁	C₂×C₄	1	2	yes	—
9	#16864513	C₈	1	2	yes	complemented
10	C₂×C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
11	C₈×C₅₄₁	C₈	1	2	yes	complemented
12	C₂²×C₅₄₁	C₄²	1	1	yes	characteristic
13	C₄×C₅₄₁	C₂×C₈	1	1	yes	characteristic
14	C₄×C₅₄₁	C₂×C₈	1	1	yes	characteristic
15	Dic₅₄₁	C₂×C₈	1	4	yes	—
16	C₂×C₅₄₁	C₄×C₈	1	2	yes	—
17	C₂×C₅₄₁	C₄×C₈	1	1	yes	characteristic
18	C₅₄₁	C₈²	1	1	yes	characteristic, complemented, Sylow
19	C₈²	—	541	1	no	maximal, Sylow
20	C₄×C₈	—	541	2	no	—
21	C₄×C₈	—	541	1	no	—
22	C₂×C₈	—	541	4	no	—
23	C₂×C₈	—	541	1	no	—
24	C₂×C₈	#14524194	1	1	yes	characteristic
25	C₄²	—	541	1	no	—
26	C₂×C₄	—	541	2	no	—
27	C₂×C₄	C₂×#14524194	1	1	yes	characteristic
28	C₈	—	541	8	no	—
29	C₈	—	541	2	no	—
30	C₈	#16864520	1	2	yes	direct product factor
31	C₂²	C₄×#14524194	1	1	yes	characteristic
32	C₄	—	541	4	no	—
33	C₄	C₂×#16864520	1	1	yes	characteristic
34	C₄	D₅₄₁⋊C₈	1	1	yes	characteristic
35	C₂	C₈×#14524194	1	2	yes	—
36	C₂	C₄×#16864520	1	1	yes	characteristic

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

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