Subgroups — C₂³×Dic₁₂₂ #16840586

Order 3904.

850 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₂₂	C₂	1	28	yes	maximal, direct product factor
2	C₂³×Dic₆₁	C₂	1	2	yes	maximal
3	C₂³×C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂⁴×C₆₁	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₆₁	C₂²	1	14	yes	—
6	C₂²×Dic₆₁	C₂²	1	28	yes	—
7	C₂×Dic₁₂₂	C₂²	1	112	yes	direct product factor
8	C₂³×C₆₁	Q₈	1	8	yes	complemented
9	C₂³×C₆₁	C₂³	1	7	yes	—
10	C₂×C₄×C₆₁	C₂³	1	28	yes	—
11	C₂×Dic₆₁	C₂³	1	56	yes	—
12	Dic₁₂₂	C₂³	1	64	yes	direct product factor
13	C₂²×C₆₁	C₂×Q₈	1	28	yes	complemented
14	C₂²×C₆₁	C₂⁴	1	7	yes	—
15	C₄×C₆₁	C₂⁴	1	8	yes	—
16	Dic₆₁	C₂⁴	1	16	yes	—
17	C₂×C₆₁	C₂²×Q₈	1	14	yes	complemented
18	C₂×C₆₁	C₂⁵	1	1	yes	characteristic
19	C₂³×Q₈	—	61	1	no	maximal, Sylow
20	C₆₁	C₂³×Q₈	1	1	yes	characteristic, complemented, Sylow
21	C₂²×Q₈	—	61	28	no	—
22	C₂³×C₄	—	61	2	no	—
23	C₂³×C₄	D₆₁	1	1	yes	characteristic
24	C₂⁴	C₂×D₆₁	1	1	yes	characteristic
25	C₂×Q₈	—	61	112	no	—
26	C₂²×C₄	—	61	28	no	—
27	C₂²×C₄	C₂×D₆₁	1	14	yes	—
28	C₂³	Dic₁₂₂	1	8	yes	direct product factor
29	C₂³	C₂²×D₆₁	1	7	yes	—
30	Q₈	—	61	64	no	—
31	C₂×C₄	—	61	56	no	—
32	C₂×C₄	C₂²×D₆₁	1	28	yes	—
33	C₂²	C₂×Dic₁₂₂	1	28	yes	direct product factor
34	C₂²	C₂³×D₆₁	1	7	yes	—
35	C₄	—	61	16	no	—
36	C₄	C₂³×D₆₁	1	8	yes	—
37	C₂	C₂²×Dic₁₂₂	1	14	yes	direct product factor
38	C₂	C₂⁴×D₆₁	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.