Subgroups — #49148873

Order 36928.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32914734	C₂	1	1	yes	maximal, characteristic
2	#32914732	C₂	1	1	yes	maximal, characteristic
3	#32914603	C₂	1	1	yes	maximal, characteristic
4	#22604428	—	2	1	no	—
5	C₄⋊#14556313	—	2	1	no	—
6	C₈×D₅₇₇	C₂²	1	1	yes	characteristic
7	#22604393	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₅₇₇	C₄	1	1	yes	characteristic, complemented
9	C₂×#14556313	—	4	1	no	—
10	#17987237	—	4	1	no	—
11	C₄×D₅₇₇	D₄	1	1	yes	characteristic
12	#17987230	Q₈	1	1	yes	characteristic
13	C₈×C₅₇₇	C₂×C₄	1	1	yes	characteristic
14	C₂×D₅₇₇	SD₁₆	1	1	yes	characteristic
15	#14556313	—	8	1	no	—
16	C₄×C₅₇₇	C₄⋊C₄	1	1	yes	characteristic
17	Dic₅₇₇	SD₁₆	1	1	yes	characteristic
18	C₂×C₅₇₇	#106	1	1	yes	characteristic
19	D₅₇₇	—	2	1	no	—
20	C₅₇₇	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	577	1	no	maximal, Sylow
22	M₃₂	—	577	1	no	—
23	#108	—	577	1	no	—
24	#106	—	577	1	no	—
25	M₁₆	—	1154	1	no	—
26	C₂×C₈	—	577	1	no	—
27	C₄⋊C₄	—	1154	1	no	—
28	C₁₆	—	577	1	no	—
29	C₁₆	#14556313	1	1	yes	characteristic, complemented
30	C₂×C₄	—	2308	1	no	—
31	C₂×C₄	—	577	1	no	—
32	C₈	—	2308	1	no	—
33	C₈	—	577	1	no	—
34	C₈	C₂×#14556313	1	1	yes	characteristic
35	C₂²	—	577	1	no	—
36	C₄	—	4616	1	no	—
37	C₄	—	577	1	no	—
38	C₄	C₄⋊#14556313	1	1	yes	characteristic
39	C₂	—	1154	1	no	—
40	C₂	#32914732	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.