Subgroups — #13094031

Order 1504.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₄₇	C₂	1	1	yes	maximal, characteristic
2	#10625329	C₂	1	3	yes	maximal, complemented
3	C₂×C₄₇⋊C₈	C₂	1	3	yes	maximal, complemented
4	Q₈×C₄₇	C₄	1	1	yes	characteristic
5	D₄×C₄₇	C₄	1	3	yes	—
6	C₂×C₄×C₄₇	C₂²	1	3	yes	—
7	C₄₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₄₇⋊C₈	C₂²	1	3	yes	—
9	C₂²×C₄₇	C₂×C₄	1	3	yes	—
10	C₄×C₄₇	C₂×C₄	1	3	yes	—
11	C₄×C₄₇	C₂³	1	1	yes	characteristic
12	C₂×C₄₇	—	2	3	no	—
13	C₂×C₄₇	C₂²×C₄	1	1	yes	characteristic
14	C₄₇	#131	1	1	yes	characteristic, complemented, Sylow
15	#131	—	47	1	no	maximal, Sylow
16	#41	D₄₇	1	1	yes	characteristic
17	M₁₆	—	47	3	no	—
18	C₂×C₈	—	47	3	no	—
19	Q₈	Dic₄₇	1	1	yes	characteristic
20	D₄	Dic₄₇	1	3	yes	—
21	C₂×C₄	C₂×D₄₇	1	3	yes	—
22	C₈	—	47	1	no	—
23	C₈	—	47	3	no	—
24	C₂²	C₂×Dic₄₇	1	3	yes	—
25	C₄	C₂×Dic₄₇	1	3	yes	—
26	C₄	C₂²×D₄₇	1	1	yes	characteristic
27	C₂	—	2	3	no	—
28	C₂	C₂²×Dic₄₇	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.