Subgroups — #22549698

Order 8128.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16861149	C₂	1	1	yes	maximal, characteristic
2	#16861145	C₂	1	1	yes	maximal, characteristic
3	#106×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	#14523232	—	2	1	no	—
5	C₁₂₇⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₂₇	—	2	1	no	—
8	C₁₂₇⋊C₈	—	4	1	no	—
9	C₂×C₄×C₁₂₇	—	4	1	no	—
10	C₂×C₄×C₁₂₇	D₄	1	1	yes	characteristic
11	C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₂₇	Q₈	1	1	yes	characteristic
13	C₂²×C₁₂₇	SD₁₆	1	1	yes	characteristic
14	C₄×C₁₂₇	—	8	1	no	—
15	C₄×C₁₂₇	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₂₇	SD₁₆	1	1	yes	characteristic
17	C₂×C₁₂₇	—	2	1	no	—
18	C₂×C₁₂₇	#106	1	1	yes	characteristic
19	C₁₂₇	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	127	1	no	maximal, Sylow
21	M₃₂	—	127	1	no	—
22	#108	—	127	1	no	—
23	#106	D₁₂₇	1	1	yes	characteristic
24	M₁₆	—	254	1	no	—
25	C₂×C₈	C₂×D₁₂₇	1	1	yes	characteristic
26	C₄⋊C₄	—	2	1	no	—
27	C₁₆	—	127	2	no	—
28	C₂×C₄	—	4	1	no	—
29	C₂×C₄	C₂²⋊D₁₂₇	1	1	yes	characteristic
30	C₈	—	508	1	no	—
31	C₈	C₄×D₁₂₇	1	1	yes	characteristic
32	C₈	Dic₂₅₄	1	1	yes	characteristic
33	C₂²	#14523236	1	1	yes	characteristic
34	C₄	—	8	1	no	—
35	C₄	Dic₁₂₇⋊C₄	1	1	yes	characteristic
36	C₄	#14523235	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#16861140	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₁₂₇⋊C₁₆	C₄	semidirect
19. C₁₂₇	#365	semidirect