Subgroups — #14563250

Order 2432.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926921	C₂	1	6	yes	maximal, complemented
2	C₈²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₅₂	—	2	12	no	—
4	#10597320	C₂²	1	4	yes	—
5	C₄×C₈×C₁₉	C₂²	1	3	yes	—
6	C₂×D₇₆	—	2	12	no	—
7	C₂×C₈×C₁₉	D₄	1	6	yes	—
8	C₄²×C₁₉	C₂³	1	1	yes	characteristic
9	D₁₅₂	—	4	24	no	—
10	C₂²×D₁₉	—	4	4	no	—
11	C₂×C₄×C₁₉	C₂×D₄	1	3	yes	—
12	D₇₆	—	4	24	no	—
13	C₈×C₁₉	D₈	1	12	yes	complemented
14	#1712	—	19	1	no	maximal, Sylow
15	C₂²×C₁₉	#127	1	1	yes	characteristic
16	C₂×D₁₉	—	8	12	no	—
17	C₄×C₁₉	C₂×D₈	1	6	yes	—
18	#493	—	19	6	no	—
19	C₈²	D₁₉	1	1	yes	characteristic, complemented
20	C₂×C₁₉	#493	1	3	yes	—
21	D₁₉	—	16	4	no	—
22	C₂×D₈	—	38	12	no	—
23	#127	—	19	4	no	—
24	C₄×C₈	C₂×D₁₉	1	3	yes	—
25	C₁₉	#1712	1	1	yes	characteristic, complemented, Sylow
26	C₂×D₄	—	38	12	no	—
27	D₈	—	76	24	no	—
28	C₂×C₈	D₇₆	1	6	yes	—
29	C₄²	C₂²×D₁₉	1	1	yes	characteristic
30	C₂³	—	76	4	no	—
31	D₄	—	76	24	no	—
32	C₂×C₄	C₂×D₇₆	1	3	yes	—
33	C₈	D₁₅₂	1	12	yes	complemented
34	C₂²	—	152	12	no	—
35	C₂²	#10597320	1	1	yes	characteristic
36	C₄	C₂×D₁₅₂	1	6	yes	—
37	C₂	—	304	4	no	—
38	C₂	#11926921	1	3	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.