Subgroups — #24984513

Order 11008.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₇₅₂	C₂	1	1	yes	maximal, characteristic
3	C₄₃×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₆₈₈	—	2	1	no	—
5	D₁₃₇₆	—	2	1	no	—
6	C₄₃×C₆₄	C₂²	1	1	yes	characteristic
7	Dic₃₄₄	—	4	1	no	—
8	D₆₈₈	—	4	1	no	—
9	C₃₂×C₄₃	D₄	1	1	yes	characteristic
10	Dic₁₇₂	—	8	1	no	—
11	D₃₄₄	—	8	1	no	—
12	C₁₆×C₄₃	D₈	1	1	yes	characteristic
13	D₁₇₂	—	16	1	no	—
14	Dic₈₆	—	16	1	no	—
15	C₈×C₄₃	D₁₆	1	1	yes	characteristic
16	SD₂₅₆	—	43	1	no	maximal, Sylow
17	C₂×D₄₃	—	32	1	no	—
18	C₄×C₄₃	D₃₂	1	1	yes	characteristic
19	Dic₄₃	—	32	1	no	—
20	Q₁₂₈	—	43	1	no	—
21	D₆₄	—	43	1	no	—
22	C₁₂₈	D₄₃	1	1	yes	characteristic, complemented
23	C₂×C₄₃	D₆₄	1	1	yes	characteristic
24	D₄₃	—	64	1	no	—
25	Q₆₄	—	86	1	no	—
26	D₃₂	—	86	1	no	—
27	C₆₄	C₂×D₄₃	1	1	yes	characteristic
28	C₄₃	SD₂₅₆	1	1	yes	characteristic, complemented, Sylow
29	Q₃₂	—	172	1	no	—
30	D₁₆	—	172	1	no	—
31	C₃₂	D₁₇₂	1	1	yes	characteristic
32	Q₁₆	—	344	1	no	—
33	D₈	—	344	1	no	—
34	C₁₆	D₃₄₄	1	1	yes	characteristic
35	Q₈	—	688	1	no	—
36	D₄	—	688	1	no	—
37	C₈	D₆₈₈	1	1	yes	characteristic
38	C₂²	—	1376	1	no	—
39	C₄	—	1376	1	no	—
40	C₄	D₁₃₇₆	1	1	yes	characteristic
41	C₂	—	2752	1	no	—
42	C₂	D₂₇₅₂	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.