Subgroups — C₄×C₇²×C₄₉ #72188331

Order 9604.

666 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₇²×C₄₉	C₄	1	1	yes	characteristic, direct product factor, Sylow
3	C₄×C₇³	C₇	1	1	yes	maximal, characteristic
4	C₄×C₇×C₄₉	C₇	1	56	yes	maximal, direct product factor
5	C₂×C₇³	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₄₉	C₂×C₇	1	56	yes	—
7	C₇³	C₄×C₇	1	1	yes	characteristic
8	C₇×C₄₉	C₄×C₇	1	56	yes	direct product factor
9	C₄×C₇²	C₄₉	1	49	yes	direct product factor
10	C₄×C₇²	C₇²	1	8	yes	—
11	C₄×C₄₉	C₇²	1	49	yes	direct product factor
12	C₂×C₇²	C₂×C₄₉	1	49	yes	—
13	C₂×C₇²	C₂×C₇²	1	8	yes	—
14	C₂×C₄₉	C₂×C₇²	1	49	yes	—
15	C₇²	C₄×C₄₉	1	49	yes	direct product factor
16	C₇²	C₄×C₇²	1	8	yes	—
17	C₄₉	C₄×C₇²	1	49	yes	direct product factor
18	C₄×C₇	C₇×C₄₉	1	56	yes	direct product factor
19	C₄×C₇	C₇³	1	1	yes	characteristic
20	C₂×C₇	C₂×C₇×C₄₉	1	56	yes	—
21	C₂×C₇	C₂×C₇³	1	1	yes	characteristic
22	C₇	C₄×C₇×C₄₉	1	56	yes	direct product factor
23	C₇	C₄×C₇³	1	1	yes	characteristic
24	C₄	C₇²×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂	C₂×C₇²×C₄₉	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.