Subgroups — #30636647

Order 16256.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₂₇⋊C₁₆	C₂	1	2	yes	maximal
2	C₈²×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₂₇⋊C₁₆	C₄	1	4	yes	—
4	C₄×C₈×C₁₂₇	C₄	1	2	yes	—
5	C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
6	C₁₂₇⋊C₁₆	C₈	1	8	yes	complemented
7	C₂×C₈×C₁₂₇	C₈	1	4	yes	—
8	C₂×C₈×C₁₂₇	C₂×C₄	1	2	yes	—
9	C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₁₂₇	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₁₂₇	C₂×C₈	1	2	yes	—
12	C₈×C₁₂₇	—	2	4	no	—
13	C₈×C₁₂₇	C₂×C₈	1	4	yes	—
14	C₂²×C₁₂₇	C₄×C₈	1	1	yes	characteristic
15	C₄×C₁₂₇	C₄×C₈	1	2	yes	—
16	C₄×C₁₂₇	M₃₂	1	4	yes	—
17	C₂×C₁₂₇	C₈²	1	1	yes	characteristic
18	C₂×C₁₂₇	#346	1	2	yes	—
19	#1311	—	127	1	no	maximal, Sylow
20	C₁₂₇	#1311	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₁₆	—	127	2	no	—
22	C₈²	D₁₂₇	1	1	yes	characteristic
23	C₂×C₁₆	—	127	4	no	—
24	C₄×C₈	Dic₁₂₇	1	2	yes	—
25	C₄×C₈	C₂×D₁₂₇	1	1	yes	characteristic
26	C₂×C₈	C₁₂₇⋊C₈	1	4	yes	—
27	C₂×C₈	C₄×D₁₂₇	1	2	yes	—
28	C₄²	C₂×Dic₁₂₇	1	1	yes	characteristic
29	C₁₆	—	127	8	no	—
30	C₂×C₄	C₄×Dic₁₂₇	1	1	yes	characteristic
31	C₂×C₄	C₂×C₁₂₇⋊C₈	1	2	yes	—
32	C₈	—	2	4	no	—
33	C₈	C₈×D₁₂₇	1	4	yes	—
34	C₂²	C₄×C₁₂₇⋊C₈	1	1	yes	characteristic
35	C₄	C₈×Dic₁₂₇	1	2	yes	—
36	C₄	#16861149	1	4	yes	—
37	C₂	C₈×C₁₂₇⋊C₈	1	1	yes	characteristic
38	C₂	#22549652	1	2	yes	—

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

N	H ≅ G/N	type
6. C₁₂₇⋊C₁₆	C₈	semidirect
20. C₁₂₇	#1311	semidirect

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