Subgroups — C₇²×C₂₅₆ #72190881

Order 12544.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₂₈	C₂	1	1	yes	maximal, characteristic
2	C₇²×C₆₄	C₄	1	1	yes	characteristic
3	C₇×C₂₅₆	C₇	1	8	yes	maximal, direct product factor
4	C₇²×C₃₂	C₈	1	1	yes	characteristic
5	C₇×C₁₂₈	C₂×C₇	1	8	yes	—
6	C₇²×C₁₆	C₁₆	1	1	yes	characteristic
7	C₇×C₆₄	C₄×C₇	1	8	yes	—
8	C₇²×C₈	C₃₂	1	1	yes	characteristic
9	C₂₅₆	C₇²	1	1	yes	characteristic, direct product factor, Sylow
10	C₇×C₃₂	C₇×C₈	1	8	yes	—
11	C₄×C₇²	C₆₄	1	1	yes	characteristic
12	C₁₂₈	C₂×C₇²	1	1	yes	characteristic
13	C₇×C₁₆	C₇×C₁₆	1	8	yes	—
14	C₂×C₇²	C₁₂₈	1	1	yes	characteristic
15	C₆₄	C₄×C₇²	1	1	yes	characteristic
16	C₇×C₈	C₇×C₃₂	1	8	yes	—
17	C₇²	C₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
18	C₃₂	C₇²×C₈	1	1	yes	characteristic
19	C₄×C₇	C₇×C₆₄	1	8	yes	—
20	C₁₆	C₇²×C₁₆	1	1	yes	characteristic
21	C₂×C₇	C₇×C₁₂₈	1	8	yes	—
22	C₈	C₇²×C₃₂	1	1	yes	characteristic
23	C₇	C₇×C₂₅₆	1	8	yes	direct product factor
24	C₄	C₇²×C₆₄	1	1	yes	characteristic
25	C₂	C₇²×C₁₂₈	1	1	yes	characteristic

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.

subgroup	index
C₇²×C₁₂₈	2
C₇×C₂₅₆	7