Subgroups — #22549705

Order 8128.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₂₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#16861145	C₂	1	1	yes	maximal, characteristic
3	#108×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	#14523232	—	2	1	no	—
5	C₁₂₇⋊C₁₆	C₄	1	2	yes	—
6	M₁₆×C₁₂₇	—	2	1	no	—
7	C₂×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
8	C₁₂₇⋊C₈	—	4	1	no	—
9	C₂×C₄×C₁₂₇	D₄	1	1	yes	characteristic
10	C₈×C₁₂₇	—	4	1	no	—
11	C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₂₇	Q₈	1	1	yes	characteristic
13	C₂²×C₁₂₇	Q₁₆	1	1	yes	characteristic
14	C₄×C₁₂₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₂₇	D₈	1	1	yes	characteristic
16	C₂×C₁₂₇	—	2	1	no	—
17	C₂×C₁₂₇	#107	1	1	yes	characteristic
18	C₁₂₇	#368	1	1	yes	characteristic, complemented, Sylow
19	#368	—	127	1	no	maximal, Sylow
20	C₂×C₁₆	—	127	1	no	—
21	#108	—	127	1	no	—
22	#108	D₁₂₇	1	1	yes	characteristic
23	M₁₆	—	2	1	no	—
24	M₁₆	—	254	1	no	—
25	C₂×C₈	C₂×D₁₂₇	1	1	yes	characteristic
26	C₁₆	—	127	2	no	—
27	C₂×C₄	C₂²⋊D₁₂₇	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	508	1	no	—
30	C₈	C₄×D₁₂₇	1	1	yes	characteristic
31	C₈	Dic₂₅₄	1	1	yes	characteristic
32	C₂²	#14523238	1	1	yes	characteristic
33	C₄	Dic₁₂₇⋊C₄	1	1	yes	characteristic
34	C₄	#14523233	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#16861142	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₂₇	#368	semidirect