Subgroups — #43252710

Order 28544.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₂₃⋊C₁₆	C₂	1	2	yes	maximal
2	C₈²×C₂₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₂₃⋊C₁₆	C₄	1	4	yes	—
4	C₄×C₈×C₂₂₃	C₄	1	2	yes	—
5	C₄×C₈×C₂₂₃	C₂²	1	1	yes	characteristic
6	C₂₂₃⋊C₁₆	C₈	1	8	yes	complemented
7	C₂×C₈×C₂₂₃	C₈	1	4	yes	—
8	C₂×C₈×C₂₂₃	C₂×C₄	1	2	yes	—
9	C₄²×C₂₂₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₂₂₃	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₂₂₃	C₂×C₈	1	2	yes	—
12	C₈×C₂₂₃	—	2	4	no	—
13	C₈×C₂₂₃	C₂×C₈	1	4	yes	—
14	C₂²×C₂₂₃	C₄×C₈	1	1	yes	characteristic
15	C₄×C₂₂₃	C₄×C₈	1	2	yes	—
16	C₄×C₂₂₃	M₃₂	1	4	yes	—
17	C₂×C₂₂₃	C₈²	1	1	yes	characteristic
18	C₂×C₂₂₃	#346	1	2	yes	—
19	C₂₂₃	#1311	1	1	yes	characteristic, complemented, Sylow
20	#1311	—	223	1	no	maximal, Sylow
21	C₄×C₁₆	—	223	2	no	—
22	C₈²	D₂₂₃	1	1	yes	characteristic
23	C₂×C₁₆	—	223	4	no	—
24	C₄×C₈	Dic₂₂₃	1	2	yes	—
25	C₄×C₈	C₂×D₂₂₃	1	1	yes	characteristic
26	C₂×C₈	C₂₂₃⋊C₈	1	4	yes	—
27	C₂×C₈	C₄×D₂₂₃	1	2	yes	—
28	C₄²	C₂×Dic₂₂₃	1	1	yes	characteristic
29	C₁₆	—	223	8	no	—
30	C₂×C₄	C₄×Dic₂₂₃	1	1	yes	characteristic
31	C₂×C₄	C₂×C₂₂₃⋊C₈	1	2	yes	—
32	C₈	—	2	4	no	—
33	C₈	C₈×D₂₂₃	1	4	yes	—
34	C₂²	C₄×C₂₂₃⋊C₈	1	1	yes	characteristic
35	C₄	C₈×Dic₂₂₃	1	2	yes	—
36	C₄	#20297244	1	4	yes	—
37	C₂	C₈×C₂₂₃⋊C₈	1	1	yes	characteristic
38	C₂	#28383356	1	2	yes	—

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

N	H ≅ G/N	type
6. C₂₂₃⋊C₁₆	C₈	semidirect
19. C₂₂₃	#1311	semidirect

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