Subgroups — #43273097

Order 28736.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#16813320	C₂	1	2	yes	maximal
2	C₈×#14267798	C₂	1	1	yes	maximal, characteristic
3	C₂×#16813320	—	2	2	no	—
4	#20297744	C₄	1	1	yes	characteristic
5	C₄×#14267798	C₂²	1	1	yes	characteristic
6	C₈×D₄₄₉	C₄	1	1	yes	characteristic
7	#16813320	—	4	2	no	—
8	C₂×#14267798	D₄	1	1	yes	characteristic
9	C₂×#14267798	Q₈	1	1	yes	characteristic
10	#16813318	—	2	1	no	—
11	C₄×D₄₄₉	C₂×C₄	1	1	yes	characteristic
12	#16813311	C₈	1	1	yes	characteristic, complemented
13	C₈×C₄₄₉	C₈	1	1	yes	characteristic, complemented
14	C₂×D₄₄₉	C₄⋊C₄	1	1	yes	characteristic
15	#14267798	—	2	1	no	—
16	#14267798	D₈	1	1	yes	characteristic
17	#14267798	Q₁₆	1	1	yes	characteristic
18	C₄×C₄₄₉	C₂×C₈	1	1	yes	characteristic
19	Dic₄₄₉	M₁₆	1	1	yes	characteristic
20	C₂×C₄₄₉	C₄⋊C₈	1	1	yes	characteristic
21	D₄₄₉	#107	1	1	yes	characteristic
22	D₄₄₉	#108	1	1	yes	characteristic
23	C₄₄₉	#335	1	1	yes	characteristic, complemented, Sylow
24	#335	—	449	1	no	maximal, Sylow
25	C₄⋊C₈	—	449	2	no	—
26	C₄×C₈	—	449	1	no	—
27	C₂×C₈	—	898	2	no	—
28	C₂×C₈	—	449	1	no	—
29	C₂×C₈	—	449	1	no	—
30	C₄²	—	449	1	no	—
31	C₂×C₄	—	449	1	no	—
32	C₂×C₄	—	449	1	no	—
33	C₂×C₄	—	449	1	no	—
34	C₈	—	1796	2	no	—
35	C₈	—	898	1	no	—
36	C₈	—	449	1	no	—
37	C₈	#16813320	1	1	yes	characteristic, complemented
38	C₂²	—	449	1	no	—
39	C₄	—	898	1	no	—
40	C₄	—	449	1	no	—
41	C₄	—	449	1	no	—
42	C₄	—	449	1	no	—
43	C₄	C₂×#16813320	1	1	yes	characteristic
44	C₂	—	449	1	no	—
45	C₂	—	449	1	no	—
46	C₂	C₄⋊#16813320	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.