Subgroups — C₂×#20297745 #28385424

Order 14368.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20297745	C₂	1	4	yes	maximal, direct product factor
2	C₂×#16813318	C₂	1	2	yes	maximal, complemented
3	C₂²×Dic₄₄₉	C₂	1	1	yes	maximal, characteristic
4	#16813318	C₂²	1	4	yes	complemented
5	C₂×Dic₄₄₉	C₄	1	2	yes	—
6	C₂×Dic₄₄₉	C₄	1	1	yes	characteristic
7	C₂×Dic₄₄₉	C₂²	1	1	yes	characteristic
8	C₂×Dic₄₄₉	C₂²	1	2	yes	—
9	C₂³×C₄₄₉	C₄	1	1	yes	characteristic
10	C₂²×C₄₄₉	—	2	2	no	—
11	C₂²×C₄₄₉	C₂×C₄	1	2	yes	—
12	C₂²×C₄₄₉	C₂×C₄	1	1	yes	characteristic
13	Dic₄₄₉	C₂×C₄	1	1	yes	characteristic
14	Dic₄₄₉	C₂×C₄	1	2	yes	—
15	Dic₄₄₉	C₂³	1	1	yes	characteristic
16	C₂×C₄₄₉	—	2	2	no	—
17	C₂×C₄₄₉	M₁₆	1	2	yes	complemented
18	C₂×C₄₄₉	C₂²×C₄	1	1	yes	characteristic
19	C₄₄₉	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
20	C₂×M₁₆	—	449	1	no	maximal, Sylow
21	C₂²×C₄	—	449	1	no	—
22	M₁₆	—	449	4	no	—
23	C₂×C₈	—	449	2	no	—
24	C₂³	#14267798	1	1	yes	characteristic
25	C₂×C₄	—	449	2	no	—
26	C₂×C₄	—	449	2	no	—
27	C₂×C₄	—	449	1	no	—
28	C₂×C₄	—	449	1	no	—
29	C₈	—	449	4	no	—
30	C₂²	—	2	2	no	—
31	C₂²	C₂×#14267798	1	2	yes	—
32	C₂²	C₂×#14267798	1	1	yes	characteristic
33	C₄	—	449	1	no	—
34	C₄	—	449	1	no	—
35	C₄	—	449	2	no	—
36	C₂	—	2	2	no	—
37	C₂	#20297745	1	2	yes	direct product factor
38	C₂	C₂²×#14267798	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.