Subgroups — #17989677

Order 4672.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#10596842	C₂	1	2	yes	maximal
2	C₈×#64408	C₂	1	1	yes	maximal, characteristic
3	C₂×#10596842	—	2	2	no	—
4	#11924036	C₄	1	1	yes	characteristic
5	C₄×#64408	C₂²	1	1	yes	characteristic
6	C₈×D₇₃	C₄	1	1	yes	characteristic
7	C₂×#64408	D₄	1	1	yes	characteristic
8	C₂×#64408	Q₈	1	1	yes	characteristic
9	#10596842	—	4	2	no	—
10	C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
11	#10596833	—	2	1	no	—
12	C₈×C₇₃	C₈	1	1	yes	characteristic, complemented
13	#10596831	C₈	1	1	yes	characteristic, complemented
14	C₂×D₇₃	C₄⋊C₄	1	1	yes	characteristic
15	#64408	—	2	1	no	—
16	#64408	D₈	1	1	yes	characteristic
17	#64408	Q₁₆	1	1	yes	characteristic
18	C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
19	Dic₇₃	M₁₆	1	1	yes	characteristic
20	C₂×C₇₃	C₄⋊C₈	1	1	yes	characteristic
21	D₇₃	#107	1	1	yes	characteristic
22	D₇₃	#108	1	1	yes	characteristic
23	C₇₃	#335	1	1	yes	characteristic, complemented, Sylow
24	#335	—	73	1	no	maximal, Sylow
25	C₄⋊C₈	—	73	2	no	—
26	C₄×C₈	—	73	1	no	—
27	C₂×C₈	—	73	1	no	—
28	C₂×C₈	—	73	1	no	—
29	C₂×C₈	—	146	2	no	—
30	C₄²	—	73	1	no	—
31	C₂×C₄	—	73	1	no	—
32	C₂×C₄	—	73	1	no	—
33	C₂×C₄	—	73	1	no	—
34	C₈	—	292	2	no	—
35	C₈	—	73	1	no	—
36	C₈	—	146	1	no	—
37	C₈	#10596842	1	1	yes	characteristic, complemented
38	C₂²	—	73	1	no	—
39	C₄	—	73	1	no	—
40	C₄	—	73	1	no	—
41	C₄	—	73	1	no	—
42	C₄	—	146	1	no	—
43	C₄	C₂×#10596842	1	1	yes	characteristic
44	C₂	—	73	1	no	—
45	C₂	—	73	1	no	—
46	C₂	C₄⋊#10596842	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.