Subgroups — #14271540

Order 1856.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₃₂	C₂	1	4	yes	maximal, complemented
2	#11745236	C₂	1	2	yes	maximal, complemented
3	C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₁₆	—	2	4	no	—
5	C₂×D₁₁₆	C₂²	1	4	yes	—
6	C₂×C₈×C₂₉	C₂²	1	2	yes	—
7	C₄²×C₂₉	C₂²	1	1	yes	characteristic
8	D₂₃₂	—	2	8	no	—
9	C₂²×D₂₉	—	2	4	no	—
10	C₂×C₄×C₂₉	D₄	1	2	yes	—
11	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
12	D₁₁₆	—	2	8	no	—
13	D₁₁₆	—	4	8	no	—
14	C₈×C₂₉	D₄	1	4	yes	complemented
15	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
16	C₂×D₂₉	—	4	4	no	—
17	C₂×D₂₉	—	4	8	no	—
18	C₄×C₂₉	D₈	1	4	yes	complemented
19	C₄×C₂₉	C₂×D₄	1	2	yes	—
20	#493	—	29	1	no	maximal, Sylow
21	C₂×C₂₉	#127	1	1	yes	characteristic
22	C₂×C₂₉	C₂×D₈	1	2	yes	—
23	D₂₉	—	8	4	no	—
24	C₂×D₈	—	29	4	no	—
25	#127	—	29	2	no	—
26	C₄×C₈	D₂₉	1	1	yes	characteristic, complemented
27	C₂₉	#493	1	1	yes	characteristic, complemented, Sylow
28	C₂×D₄	—	29	4	no	—
29	C₂×D₄	—	58	4	no	—
30	D₈	—	58	8	no	—
31	C₂×C₈	C₂×D₂₉	1	2	yes	—
32	C₄²	C₂×D₂₉	1	1	yes	characteristic
33	C₂³	—	58	4	no	—
34	D₄	—	58	8	no	—
35	D₄	—	116	8	no	—
36	C₂×C₄	D₁₁₆	1	2	yes	—
37	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
38	C₈	D₁₁₆	1	4	yes	complemented
39	C₂²	—	116	4	no	—
40	C₂²	—	116	8	no	—
41	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
42	C₄	D₂₃₂	1	4	yes	complemented
43	C₄	C₂×D₁₁₆	1	2	yes	—
44	C₂	—	232	4	no	—
45	C₂	#11745236	1	1	yes	characteristic
46	C₂	C₂×D₂₃₂	1	2	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.