Subgroups — #14572030

Order 2432.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597320	C₂	1	14	yes	maximal, complemented
2	C₄³×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₇₆	C₂²	1	28	yes	—
4	C₂×C₄²×C₁₉	C₂²	1	7	yes	—
5	#10597320	—	2	56	no	—
6	C₂³×D₁₉	C₂³	1	8	yes	—
7	C₂²×C₄×C₁₉	C₂³	1	7	yes	—
8	C₂×D₇₆	—	2	168	no	—
9	C₄²×C₁₉	D₄	1	28	yes	complemented
10	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
11	C₂²×D₁₉	—	2	56	no	—
12	C₂×C₄×C₁₉	C₂×D₄	1	42	yes	—
13	D₇₆	—	4	112	no	—
14	#2867	—	19	1	no	maximal, Sylow
15	C₂²×C₁₉	C₂²×D₄	1	7	yes	—
16	C₂×D₁₉	—	4	56	no	—
17	C₄×C₁₉	#127	1	28	yes	complemented
18	C₂×#127	—	19	14	no	—
19	C₄³	D₁₉	1	1	yes	characteristic, complemented
20	C₂×C₁₉	C₂×#127	1	7	yes	—
21	D₁₉	—	8	8	no	—
22	C₂²×D₄	—	19	28	no	—
23	#127	—	38	56	no	—
24	C₂×C₄²	C₂×D₁₉	1	7	yes	—
25	C₁₉	#2867	1	1	yes	characteristic, complemented, Sylow
26	C₂⁴	—	19	8	no	—
27	C₂×D₄	—	38	168	no	—
28	C₂²×C₄	C₂²×D₁₉	1	7	yes	—
29	C₄²	D₇₆	1	28	yes	complemented
30	C₂³	—	38	56	no	—
31	C₂³	C₂³×D₁₉	1	1	yes	characteristic
32	D₄	—	76	112	no	—
33	C₂×C₄	C₂×D₇₆	1	42	yes	—
34	C₂²	—	76	56	no	—
35	C₂²	C₂²×D₇₆	1	7	yes	—
36	C₄	#10597320	1	28	yes	complemented
37	C₂	—	152	8	no	—
38	C₂	C₂×#10597320	1	7	yes	—

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.