Subgroups — D₄×C₄₉ #87629

Order 392.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄₉	C₂	1	2	yes	maximal, complemented
2	C₄×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₉	—	2	2	no	—
4	C₂×C₄₉	C₂²	1	1	yes	characteristic
5	C₇×D₄	C₇	1	1	yes	maximal, characteristic
6	C₄₉	D₄	1	1	yes	characteristic, direct product factor, Sylow
7	C₂²×C₇	C₂×C₇	1	2	yes	—
8	C₄×C₇	C₂×C₇	1	1	yes	characteristic
9	C₂×C₇	—	2	2	no	—
10	C₂×C₇	C₂²×C₇	1	1	yes	characteristic
11	D₄	C₄₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₇	C₇×D₄	1	1	yes	characteristic
13	C₂²	C₂×C₄₉	1	2	yes	complemented
14	C₄	C₂×C₄₉	1	1	yes	characteristic, complemented
15	C₂	—	2	2	no	—
16	C₂	C₂²×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.