Subgroups — #322×C₄₈₇ #44528504

Order 31168.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×C₄₈₇	C₂	1	2	yes	maximal
2	C₄×C₈×C₄₈₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₄₈₇	C₄	1	4	yes	—
4	C₂×C₈×C₄₈₇	C₄	1	2	yes	—
5	C₄²×C₄₈₇	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₄₈₇	C₂×C₄	1	1	yes	characteristic
7	C₂×C₄×C₄₈₇	C₂×C₄	1	2	yes	—
8	C₈×C₄₈₇	—	2	4	no	—
9	C₈×C₄₈₇	C₈	1	4	yes	complemented
10	C₂²×C₄₈₇	C₄²	1	1	yes	characteristic
11	C₄×C₄₈₇	C₂×C₈	1	2	yes	—
12	C₄×C₄₈₇	M₁₆	1	4	yes	—
13	C₂×C₄₈₇	C₄×C₈	1	1	yes	characteristic
14	C₂×C₄₈₇	#97	1	2	yes	—
15	C₄₈₇	#322	1	1	yes	characteristic, direct product factor, Sylow
16	#322	C₄₈₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₄×C₈	C₂×C₄₈₇	1	2	yes	—
18	C₄×C₈	C₂×C₄₈₇	1	1	yes	characteristic
19	C₂×C₈	C₄×C₄₈₇	1	4	yes	—
20	C₂×C₈	C₄×C₄₈₇	1	2	yes	—
21	C₄²	C₂²×C₄₈₇	1	1	yes	characteristic
22	C₂×C₄	C₂×C₄×C₄₈₇	1	1	yes	characteristic
23	C₂×C₄	C₂×C₄×C₄₈₇	1	2	yes	—
24	C₈	—	2	4	no	—
25	C₈	C₈×C₄₈₇	1	4	yes	complemented
26	C₂²	C₄²×C₄₈₇	1	1	yes	characteristic
27	C₄	C₂×C₈×C₄₈₇	1	2	yes	—
28	C₄	M₁₆×C₄₈₇	1	4	yes	—
29	C₂	C₄×C₈×C₄₈₇	1	1	yes	characteristic
30	C₂	#97×C₄₈₇	1	2	yes	—

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
C₄×C₈×C₄₈₇	2
#322	487