Subgroups — #32914733

Order 18464.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14556313	C₂	1	2	yes	maximal
2	C₈×D₅₇₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#14556313	—	2	2	no	—
4	C₄×D₅₇₇	C₂²	1	1	yes	characteristic
5	#17987230	C₄	1	1	yes	characteristic, complemented
6	C₈×C₅₇₇	C₄	1	1	yes	characteristic, complemented
7	C₂×D₅₇₇	D₄	1	1	yes	characteristic
8	#14556313	—	4	2	no	—
9	C₄×C₅₇₇	C₂×C₄	1	1	yes	characteristic
10	Dic₅₇₇	Q₈	1	1	yes	characteristic
11	C₂×C₅₇₇	C₄⋊C₄	1	1	yes	characteristic
12	D₅₇₇	D₈	1	1	yes	characteristic
13	D₅₇₇	Q₁₆	1	1	yes	characteristic
14	C₅₇₇	#107	1	1	yes	characteristic, complemented, Sylow
15	#107	—	577	1	no	maximal, Sylow
16	C₂×C₈	—	577	1	no	—
17	C₄⋊C₄	—	577	2	no	—
18	C₂×C₄	—	577	1	no	—
19	C₂×C₄	—	1154	2	no	—
20	C₈	—	577	1	no	—
21	C₈	#14556313	1	1	yes	characteristic, complemented
22	C₂²	—	577	1	no	—
23	C₄	—	2308	2	no	—
24	C₄	—	577	1	no	—
25	C₄	C₂×#14556313	1	1	yes	characteristic
26	C₂	—	577	1	no	—
27	C₂	—	577	1	no	—
28	C₂	C₄⋊#14556313	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.