Subgroups — C₈×#11924003 #22607846

Order 9344.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11924003	C₂	1	2	yes	maximal
2	C₈²×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924003	C₄	1	4	yes	—
4	C₄×C₈×C₇₃	C₄	1	2	yes	—
5	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
6	#11924003	C₈	1	8	yes	direct product factor
7	C₂×C₈×C₇₃	C₈	1	4	yes	—
8	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
9	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
12	C₈×C₇₃	C₁₆	1	8	yes	complemented
13	C₈×C₇₃	C₂×C₈	1	4	yes	—
14	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
15	C₄×C₇₃	C₄×C₈	1	2	yes	—
16	C₄×C₇₃	C₂×C₁₆	1	4	yes	—
17	C₂×C₇₃	C₈²	1	1	yes	characteristic
18	C₂×C₇₃	C₄×C₁₆	1	2	yes	—
19	C₈×C₁₆	—	73	1	no	maximal, Sylow
20	C₇₃	C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₁₆	—	73	2	no	—
22	C₈²	D₇₃	1	1	yes	characteristic
23	C₂×C₁₆	—	73	4	no	—
24	C₄×C₈	Dic₇₃	1	2	yes	—
25	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
26	C₂×C₈	#10596831	1	4	yes	—
27	C₂×C₈	C₄×D₇₃	1	2	yes	—
28	C₄²	C₂×Dic₇₃	1	1	yes	characteristic
29	C₁₆	—	73	8	no	—
30	C₂×C₄	C₄×Dic₇₃	1	1	yes	characteristic
31	C₂×C₄	C₂×#10596831	1	2	yes	—
32	C₈	#11924003	1	8	yes	direct product factor
33	C₈	C₈×D₇₃	1	4	yes	—
34	C₂²	C₄×#10596831	1	1	yes	characteristic
35	C₄	C₈×Dic₇₃	1	2	yes	—
36	C₄	C₂×#11924003	1	4	yes	—
37	C₂	C₈×#10596831	1	1	yes	characteristic
38	C₂	C₄×#11924003	1	2	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.