Subgroups — C₄×#20297750 #43273132

Order 28736.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20297750	C₂	1	2	yes	maximal
2	C₄×#16813320	C₂	1	1	yes	maximal, characteristic
3	#20297750	C₄	1	4	yes	direct product factor
4	C₂×#16813320	C₄	1	1	yes	characteristic
5	C₂×#16813320	C₂²	1	1	yes	characteristic
6	C₄×#14267798	C₄	1	1	yes	characteristic
7	#16813320	C₈	1	2	yes	—
8	#16813320	C₂×C₄	1	2	yes	—
9	C₂×#14267798	C₈	1	1	yes	characteristic
10	C₂×#14267798	C₂×C₄	1	1	yes	characteristic
11	C₄×D₄₄₉	C₈	1	1	yes	characteristic
12	C₂×D₄₄₉	C₂×C₈	1	1	yes	characteristic
13	#14267798	C₁₆	1	2	yes	complemented
14	#14267798	C₄²	1	1	yes	characteristic
15	#14267798	C₂×C₈	1	1	yes	characteristic
16	C₄×C₄₄₉	C₁₆	1	1	yes	characteristic, complemented
17	Dic₄₄₉	C₁₆	1	1	yes	characteristic, complemented
18	C₂×C₄₄₉	C₂×C₁₆	1	1	yes	characteristic
19	D₄₄₉	C₄×C₈	1	1	yes	characteristic
20	D₄₄₉	C₂×C₁₆	1	1	yes	characteristic
21	C₄₄₉	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₆	—	449	1	no	maximal, Sylow
23	C₂×C₁₆	—	449	2	no	—
24	C₄×C₈	—	449	1	no	—
25	C₂×C₈	—	449	1	no	—
26	C₂×C₈	—	449	1	no	—
27	C₄²	—	449	1	no	—
28	C₁₆	—	449	4	no	—
29	C₂×C₄	—	449	1	no	—
30	C₂×C₄	—	449	1	no	—
31	C₂×C₄	—	449	1	no	—
32	C₈	—	449	2	no	—
33	C₈	—	449	2	no	—
34	C₂²	—	449	1	no	—
35	C₄	—	449	1	no	—
36	C₄	—	449	1	no	—
37	C₄	—	449	2	no	—
38	C₄	—	449	1	no	—
39	C₄	#20297750	1	1	yes	characteristic, direct product factor
40	C₂	—	449	1	no	—
41	C₂	—	449	1	no	—
42	C₂	C₂×#20297750	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.