Subgroups — #30638345

Order 16256.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550253	C₂	1	6	yes	maximal, complemented
2	C₈²×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₀₁₆	—	2	12	no	—
4	#16861206	C₂²	1	4	yes	—
5	C₄×C₈×C₁₂₇	C₂²	1	3	yes	—
6	C₂×D₅₀₈	—	2	12	no	—
7	D₁₀₁₆	—	4	24	no	—
8	C₂×C₈×C₁₂₇	D₄	1	6	yes	—
9	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
10	C₂²×D₁₂₇	—	4	4	no	—
11	D₅₀₈	—	4	24	no	—
12	C₂×C₄×C₁₂₇	C₂×D₄	1	3	yes	—
13	C₈×C₁₂₇	D₈	1	12	yes	complemented
14	C₂²×C₁₂₇	#127	1	1	yes	characteristic
15	C₂×D₁₂₇	—	8	12	no	—
16	C₄×C₁₂₇	C₂×D₈	1	6	yes	—
17	C₂×C₁₂₇	#493	1	3	yes	—
18	D₁₂₇	—	16	4	no	—
19	#1712	—	127	1	no	maximal, Sylow
20	C₁₂₇	#1712	1	1	yes	characteristic, complemented, Sylow
21	#493	—	127	6	no	—
22	C₈²	D₁₂₇	1	1	yes	characteristic, complemented
23	C₂×D₈	—	254	12	no	—
24	#127	—	127	4	no	—
25	C₄×C₈	C₂×D₁₂₇	1	3	yes	—
26	C₂×D₄	—	254	12	no	—
27	D₈	—	508	24	no	—
28	C₂×C₈	D₅₀₈	1	6	yes	—
29	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
30	C₂³	—	508	4	no	—
31	D₄	—	508	24	no	—
32	C₂×C₄	C₂×D₅₀₈	1	3	yes	—
33	C₈	D₁₀₁₆	1	12	yes	complemented
34	C₂²	—	1016	12	no	—
35	C₂²	#16861206	1	1	yes	characteristic
36	C₄	C₂×D₁₀₁₆	1	6	yes	—
37	C₂	—	2032	4	no	—
38	C₂	#22550253	1	3	yes	—

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

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