Subgroups — #43245575

Order 28192.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28381199	C₂	1	2	yes	maximal
2	C₈×D₈₈₁	C₂	1	1	yes	maximal, characteristic
3	#20296498	—	2	2	no	—
4	C₄×D₈₈₁	C₂²	1	1	yes	characteristic
5	#20296491	C₄	1	1	yes	characteristic
6	C₈×C₈₈₁	C₄	1	1	yes	characteristic
7	C₂×D₈₈₁	Q₈	1	1	yes	characteristic
8	C₄×C₈₈₁	C₂×C₄	1	1	yes	characteristic
9	Dic₈₈₁	D₄	1	1	yes	characteristic
10	C₂×C₈₈₁	C₄⋊C₄	1	1	yes	characteristic
11	D₈₈₁	—	2	1	no	—
12	C₈₈₁	#108	1	1	yes	characteristic, complemented, Sylow
13	#108	—	881	1	no	maximal, Sylow
14	M₁₆	—	881	2	no	—
15	C₂×C₈	—	881	1	no	—
16	C₂×C₄	—	881	1	no	—
17	C₈	—	881	1	no	—
18	C₈	—	1762	2	no	—
19	C₈	#16812931	1	1	yes	characteristic
20	C₂²	—	881	1	no	—
21	C₄	—	881	1	no	—
22	C₄	C₂×#16812931	1	1	yes	characteristic
23	C₂	—	1762	1	no	—
24	C₂	C₄⋊#16812931	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
12. C₈₈₁	#108	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.