Subgroups — #43272895

Order 28736.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20297739	C₂	1	2	yes	maximal
2	C₄×#16813311	C₂	1	1	yes	maximal, characteristic
3	#20297739	C₄	1	4	yes	complemented
4	C₂×#16813311	C₄	1	1	yes	characteristic
5	C₂×#16813311	C₂²	1	1	yes	characteristic
6	C₄²×C₄₄₉	C₄	1	1	yes	characteristic
7	#16813311	C₈	1	2	yes	—
8	#16813311	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₄₄₉	C₈	1	2	yes	—
10	C₂×C₄×C₄₄₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄₄₉	C₂×C₈	1	1	yes	characteristic
12	C₄×C₄₄₉	—	2	2	no	—
13	C₄×C₄₄₉	C₄²	1	1	yes	characteristic
14	C₄×C₄₄₉	C₂×C₈	1	1	yes	characteristic
15	C₂×C₄₄₉	C₄×C₈	1	1	yes	characteristic
16	C₂×C₄₄₉	M₃₂	1	2	yes	—
17	C₄₄₉	#346	1	1	yes	characteristic, complemented, Sylow
18	#346	—	449	1	no	maximal, Sylow
19	C₂×C₁₆	—	449	2	no	—
20	C₄×C₈	—	449	1	no	—
21	C₂×C₈	—	449	1	no	—
22	C₂×C₈	—	449	1	no	—
23	C₄²	#14267798	1	1	yes	characteristic
24	C₁₆	—	449	4	no	—
25	C₂×C₄	#16813318	1	2	yes	—
26	C₂×C₄	C₂×#14267798	1	1	yes	characteristic
27	C₈	—	449	2	no	—
28	C₈	—	449	2	no	—
29	C₂²	C₂×#16813318	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	C₄×#14267798	1	1	yes	characteristic
32	C₄	#20297744	1	1	yes	characteristic
33	C₂	C₄×#16813318	1	1	yes	characteristic
34	C₂	#28385414	1	2	yes	—

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

N	H ≅ G/N	type
3. #20297739	C₄	semidirect
17. C₄₄₉	#346	semidirect

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