Subgroups — #15671611

Order 2944.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₃₆	C₂	1	1	yes	maximal, characteristic
2	C₂₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×Q₃₂	—	2	1	no	—
5	D₃₆₈	—	2	1	no	—
6	C₂₃×C₃₂	C₂²	1	1	yes	characteristic
7	Q₁₆×C₂₃	—	4	1	no	—
8	D₁₈₄	—	4	1	no	—
9	C₁₆×C₂₃	D₄	1	1	yes	characteristic
10	Q₈×C₂₃	—	8	1	no	—
11	D₉₂	—	8	1	no	—
12	C₈×C₂₃	D₈	1	1	yes	characteristic
13	SD₁₂₈	—	23	1	no	maximal, Sylow
14	C₂×D₂₃	—	16	1	no	—
15	C₄×C₂₃	—	16	1	no	—
16	C₄×C₂₃	D₁₆	1	1	yes	characteristic
17	Q₆₄	D₂₃	1	1	yes	characteristic, complemented
18	D₃₂	—	23	1	no	—
19	C₆₄	—	23	1	no	—
20	C₂×C₂₃	D₃₂	1	1	yes	characteristic
21	D₂₃	—	32	1	no	—
22	Q₃₂	—	2	1	no	—
23	D₁₆	—	46	1	no	—
24	C₃₂	C₂×D₂₃	1	1	yes	characteristic
25	C₂₃	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
26	Q₁₆	—	4	1	no	—
27	D₈	—	92	1	no	—
28	C₁₆	C₂²⋊D₂₃	1	1	yes	characteristic
29	Q₈	—	8	1	no	—
30	D₄	—	184	1	no	—
31	C₈	#67272	1	1	yes	characteristic
32	C₂²	—	368	1	no	—
33	C₄	—	16	1	no	—
34	C₄	#10625008	1	1	yes	characteristic
35	C₂	—	736	1	no	—
36	C₂	#13092252	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.