Subgroups — #37557998

Order 23776.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26045269	C₂	1	2	yes	maximal, complemented
2	Dic₂₉₇₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#26045258	C₂	1	2	yes	maximal, complemented
4	C₈×D₇₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×C₇₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₁₄₈₆	C₂²	1	2	yes	—
7	C₂²⋊D₇₄₃	—	2	2	no	—
8	C₂×Dic₇₄₃	—	2	2	no	—
9	C₄×D₇₄₃	C₂²	1	1	yes	characteristic
10	C₇₄₃⋊C₈	C₂²	1	1	yes	characteristic
11	D₄×C₇₄₃	C₂²	1	2	yes	—
12	C₈×C₇₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₇₄₃	—	2	2	no	—
14	C₂×D₇₄₃	D₄	1	1	yes	characteristic
15	C₄×C₇₄₃	C₂³	1	1	yes	characteristic
16	Dic₇₄₃	—	2	2	no	—
17	Dic₇₄₃	D₄	1	1	yes	characteristic
18	C₂×C₇₄₃	—	4	2	no	—
19	C₂×C₇₄₃	C₂×D₄	1	1	yes	characteristic
20	D₇₄₃	—	2	1	no	—
21	C₇₄₃	#135	1	1	yes	characteristic, complemented, Sylow
22	#135	—	743	1	no	maximal, Sylow
23	#41	—	743	2	no	—
24	Q₁₆	—	743	1	no	—
25	SD₁₆	—	743	2	no	—
26	D₈	D₇₄₃	1	1	yes	characteristic, complemented
27	C₂×C₈	—	743	1	no	—
28	Q₈	—	743	2	no	—
29	D₄	—	1486	2	no	—
30	D₄	C₂×D₇₄₃	1	2	yes	—
31	C₂×C₄	—	1486	2	no	—
32	C₂×C₄	—	743	1	no	—
33	C₈	—	743	1	no	—
34	C₈	C₂×D₇₄₃	1	1	yes	characteristic
35	C₂²	—	2	2	no	—
36	C₂²	—	743	1	no	—
37	C₄	—	1486	2	no	—
38	C₄	—	743	1	no	—
39	C₄	C₂²×D₇₄₃	1	1	yes	characteristic
40	C₂	—	4	2	no	—
41	C₂	—	1486	1	no	—
42	C₂	D₄×D₇₄₃	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.