Subgroups — #30636947

Order 16256.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₀₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₂₇⋊C₆₄	C₂	1	1	yes	maximal, characteristic
3	Q₆₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	Dic₁₀₁₆	—	2	1	no	—
5	Q₃₂×C₁₂₇	—	2	1	no	—
6	C₃₂×C₁₂₇	C₂²	1	1	yes	characteristic
7	Dic₅₀₈	—	4	1	no	—
8	Q₁₆×C₁₂₇	—	4	1	no	—
9	C₁₆×C₁₂₇	D₄	1	1	yes	characteristic
10	Dic₂₅₄	—	8	1	no	—
11	Q₈×C₁₂₇	—	8	1	no	—
12	C₈×C₁₂₇	D₈	1	1	yes	characteristic
13	C₄×C₁₂₇	—	16	1	no	—
14	C₄×C₁₂₇	D₁₆	1	1	yes	characteristic
15	Dic₁₂₇	—	16	1	no	—
16	C₂×C₁₂₇	D₃₂	1	1	yes	characteristic
17	Q₁₂₈	—	127	1	no	maximal, Sylow
18	C₁₂₇	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	Q₆₄	—	127	1	no	—
20	Q₆₄	D₁₂₇	1	1	yes	characteristic
21	C₆₄	—	127	1	no	—
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	254	1	no	—
24	C₃₂	C₂×D₁₂₇	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	508	1	no	—
27	C₁₆	C₂²⋊D₁₂₇	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	1016	1	no	—
30	C₈	#14523233	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	2032	1	no	—
33	C₄	#16861150	1	1	yes	characteristic
34	C₂	#22549711	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₂₇	Q₁₂₈	semidirect

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