Subgroups — #30636934

Order 16256.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22549706	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	#16861145	—	2	2	no	—
4	C₂×C₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
5	C₃₂×C₁₂₇	C₄	1	2	yes	—
6	#14523232	—	4	2	no	—
7	C₂×C₈×C₁₂₇	D₄	1	1	yes	characteristic
8	C₁₆×C₁₂₇	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₁₂₇	Q₈	1	1	yes	characteristic
10	C₁₂₇⋊C₈	—	8	2	no	—
11	C₂×C₄×C₁₂₇	D₈	1	1	yes	characteristic
12	C₈×C₁₂₇	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₁₂₇	Q₁₆	1	1	yes	characteristic
14	C₂²×C₁₂₇	Q₃₂	1	1	yes	characteristic
15	C₄×C₁₂₇	#107	1	1	yes	characteristic
16	C₄×C₁₂₇	D₁₆	1	1	yes	characteristic
17	C₂×C₁₂₇	—	2	1	no	—
18	C₂×C₁₂₇	#366	1	1	yes	characteristic
19	#1425	—	127	1	no	maximal, Sylow
20	C₁₂₇	#1425	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃₂	D₁₂₇	1	1	yes	characteristic
22	#368	—	127	2	no	—
23	C₂×C₁₆	C₂×D₁₂₇	1	1	yes	characteristic
24	#108	—	254	2	no	—
25	C₃₂	Dic₁₂₇	1	2	yes	—
26	M₁₆	—	508	2	no	—
27	C₂×C₈	D₅₀₈	1	1	yes	characteristic
28	C₁₆	C₂×Dic₁₂₇	1	1	yes	characteristic
29	C₁₆	Dic₂₅₄	1	1	yes	characteristic
30	C₂×C₄	D₁₀₁₆	1	1	yes	characteristic
31	C₈	—	1016	2	no	—
32	C₈	C₄⋊Dic₁₂₇	1	1	yes	characteristic
33	C₈	Dic₅₀₈	1	1	yes	characteristic
34	C₂²	Dic₁₀₁₆	1	1	yes	characteristic
35	C₄	#16861143	1	1	yes	characteristic
36	C₄	D₂₀₃₂	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#22549702	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. C₁₂₇	#1425	semidirect

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