Subgroups — SD₁₆×C₄₉ #11716005

Order 784.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₄₉	C₂	1	1	yes	maximal, characteristic
3	C₈×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄₉	—	2	1	no	—
5	C₄×C₄₉	—	2	1	no	—
6	C₄×C₄₉	C₂²	1	1	yes	characteristic
7	C₇×SD₁₆	C₇	1	1	yes	maximal, characteristic
8	C₂×C₄₉	—	4	1	no	—
9	C₂×C₄₉	D₄	1	1	yes	characteristic
10	C₇×Q₈	C₂×C₇	1	1	yes	characteristic
11	C₇×D₄	C₂×C₇	1	1	yes	characteristic
12	C₇×C₈	C₂×C₇	1	1	yes	characteristic
13	C₄₉	SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
14	C₂²×C₇	—	2	1	no	—
15	C₄×C₇	—	2	1	no	—
16	C₄×C₇	C₂²×C₇	1	1	yes	characteristic
17	SD₁₆	C₄₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₇	—	4	1	no	—
19	C₂×C₇	C₇×D₄	1	1	yes	characteristic
20	Q₈	C₂×C₄₉	1	1	yes	characteristic, complemented
21	D₄	C₂×C₄₉	1	1	yes	characteristic
22	C₈	C₂×C₄₉	1	1	yes	characteristic, complemented
23	C₇	C₇×SD₁₆	1	1	yes	characteristic
24	C₂²	—	2	1	no	—
25	C₄	—	2	1	no	—
26	C₄	C₂²×C₄₉	1	1	yes	characteristic
27	C₂	—	4	1	no	—
28	C₂	D₄×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.