Subgroups — #43272932

Order 28736.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28385410	C₂	1	1	yes	maximal, characteristic
2	#28385408	C₂	1	1	yes	maximal, characteristic
3	#28385279	C₂	1	1	yes	maximal, characteristic
4	#20297746	—	2	1	no	—
5	C₄⋊#14267798	—	2	1	no	—
6	C₈×D₄₄₉	C₂²	1	1	yes	characteristic
7	#20297711	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₄₄₉	C₄	1	1	yes	characteristic, complemented
9	C₂×#14267798	—	4	1	no	—
10	#16813318	—	4	1	no	—
11	C₄×D₄₄₉	D₄	1	1	yes	characteristic
12	#16813311	Q₈	1	1	yes	characteristic
13	C₈×C₄₄₉	C₂×C₄	1	1	yes	characteristic
14	C₂×D₄₄₉	SD₁₆	1	1	yes	characteristic
15	#14267798	—	8	1	no	—
16	C₄×C₄₄₉	C₄⋊C₄	1	1	yes	characteristic
17	Dic₄₄₉	SD₁₆	1	1	yes	characteristic
18	C₂×C₄₄₉	#106	1	1	yes	characteristic
19	D₄₄₉	—	2	1	no	—
20	C₄₄₉	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	449	1	no	maximal, Sylow
22	M₃₂	—	449	1	no	—
23	#108	—	449	1	no	—
24	#106	—	449	1	no	—
25	M₁₆	—	898	1	no	—
26	C₂×C₈	—	449	1	no	—
27	C₄⋊C₄	—	898	1	no	—
28	C₁₆	—	449	1	no	—
29	C₁₆	#14267798	1	1	yes	characteristic, complemented
30	C₂×C₄	—	1796	1	no	—
31	C₂×C₄	—	449	1	no	—
32	C₈	—	1796	1	no	—
33	C₈	—	449	1	no	—
34	C₈	C₂×#14267798	1	1	yes	characteristic
35	C₂²	—	449	1	no	—
36	C₄	—	3592	1	no	—
37	C₄	—	449	1	no	—
38	C₄	C₄⋊#14267798	1	1	yes	characteristic
39	C₂	—	898	1	no	—
40	C₂	#28385408	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.