Subgroups — #41⋊C₂₇ #88395

Order 432.

35 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈⋊C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#41	C₃	1	1	yes	maximal, characteristic
3	C₄×C₂₇	—	4	1	no	maximal
4	Q₈×C₉	C₂×C₃	1	1	yes	characteristic
5	D₄×C₉	—	3	1	no	—
6	C₂×C₄×C₉	—	3	1	no	—
7	C₂×C₂₇	—	4	1	no	—
8	C₃×#41	C₉	1	1	yes	characteristic
9	C₂²×C₉	—	3	1	no	—
10	C₄×C₉	—	3	1	no	—
11	C₄×C₉	A₄	1	1	yes	characteristic
12	C₂₇	—	4	1	no	Sylow
13	C₃×Q₈	C₂×C₉	1	1	yes	characteristic
14	C₃×D₄	—	3	1	no	—
15	C₂×C₃×C₄	—	3	1	no	—
16	C₂×C₉	—	6	1	no	—
17	C₂×C₉	C₂×A₄	1	1	yes	characteristic
18	#41	C₂₇	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₃	—	3	1	no	—
20	C₃×C₄	—	3	1	no	—
21	C₃×C₄	C₂²⋊C₉	1	1	yes	characteristic
22	C₉	#41⋊C₃	1	1	yes	characteristic
23	Q₈	C₂×C₂₇	1	1	yes	characteristic
24	D₄	—	3	1	no	—
25	C₂×C₄	—	3	1	no	—
26	C₂×C₃	—	6	1	no	—
27	C₂×C₃	C₂×C₂²⋊C₉	1	1	yes	characteristic
28	C₂²	—	3	1	no	—
29	C₄	—	3	1	no	—
30	C₄	C₂²⋊C₂₇	1	1	yes	characteristic
31	C₃	#41⋊C₉	1	1	yes	characteristic
32	C₂	—	6	1	no	—
33	C₂	C₂×C₂²⋊C₂₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. Q₈⋊C₂₇	C₂	semidirect
18. #41	C₂₇	semidirect

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