Subgroups — #49149042

Order 36928.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32914759	C₂	1	2	yes	maximal
2	C₈×#14556313	C₂	1	1	yes	maximal, characteristic
3	#22604430	C₄	1	4	yes	complemented
4	#22604426	C₂²	1	1	yes	characteristic
5	C₄×#14556313	C₄	1	1	yes	characteristic
6	C₈×D₅₇₇	C₄	1	1	yes	characteristic
7	C₂×#14556313	C₈	1	2	yes	—
8	#17987237	C₂×C₄	1	2	yes	—
9	C₄×D₅₇₇	C₂×C₄	1	1	yes	characteristic
10	#17987230	C₈	1	1	yes	characteristic
11	C₈×C₅₇₇	C₈	1	1	yes	characteristic
12	C₂×D₅₇₇	C₂×C₈	1	1	yes	characteristic
13	#14556313	C₁₆	1	4	yes	complemented
14	C₄×C₅₇₇	C₂×C₈	1	1	yes	characteristic
15	Dic₅₇₇	C₄²	1	1	yes	characteristic
16	C₂×C₅₇₇	C₄×C₈	1	1	yes	characteristic
17	D₅₇₇	C₂×C₁₆	1	2	yes	—
18	C₅₇₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₄×C₁₆	—	577	1	no	maximal, Sylow
20	C₂×C₁₆	—	577	2	no	—
21	C₄×C₈	—	577	1	no	—
22	C₂×C₈	—	577	1	no	—
23	C₂×C₈	—	577	1	no	—
24	C₄²	—	577	1	no	—
25	C₁₆	—	577	4	no	—
26	C₂×C₄	—	577	2	no	—
27	C₂×C₄	—	577	1	no	—
28	C₈	—	577	2	no	—
29	C₈	—	577	1	no	—
30	C₈	#17987239	1	1	yes	characteristic
31	C₂²	—	577	1	no	—
32	C₄	—	577	4	no	—
33	C₄	—	577	1	no	—
34	C₄	C₂×#17987239	1	1	yes	characteristic
35	C₂	—	577	2	no	—
36	C₂	C₄×#17987239	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.