Subgroups — C₂³×#11744762 #20299721

Order 7232.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11744762	C₂	1	14	yes	maximal, direct product factor
2	C₂³×#90673	C₂	1	1	yes	maximal, characteristic
3	C₂×#11744762	C₂²	1	28	yes	direct product factor
4	C₂²×#90673	C₄	1	7	yes	—
5	C₂²×#90673	C₂²	1	7	yes	—
6	C₂³×D₁₁₃	C₄	1	1	yes	characteristic
7	C₂³×C₁₁₃	C₈	1	1	yes	characteristic, complemented
8	C₂²×D₁₁₃	C₈	1	7	yes	complemented
9	C₂²×D₁₁₃	C₂×C₄	1	7	yes	—
10	C₂×#90673	C₂×C₄	1	21	yes	—
11	C₂×#90673	C₂³	1	7	yes	—
12	#11744762	C₂³	1	8	yes	direct product factor
13	C₂²×C₁₁₃	C₂×C₈	1	7	yes	complemented
14	C₂×D₁₁₃	C₂×C₈	1	21	yes	complemented
15	C₂×D₁₁₃	C₂²×C₄	1	7	yes	—
16	#90673	C₂²×C₄	1	7	yes	—
17	#90673	C₂⁴	1	1	yes	characteristic
18	C₂×C₁₁₃	C₂²×C₈	1	7	yes	complemented
19	D₁₁₃	C₂²×C₈	1	7	yes	complemented
20	D₁₁₃	C₂³×C₄	1	1	yes	characteristic
21	C₁₁₃	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
22	C₂³×C₈	—	113	1	no	maximal, Sylow
23	C₂³×C₄	—	113	1	no	—
24	C₂²×C₈	—	113	14	no	—
25	C₂⁴	—	113	1	no	—
26	C₂²×C₄	—	113	7	no	—
27	C₂²×C₄	—	113	7	no	—
28	C₂×C₈	—	113	28	no	—
29	C₂³	—	113	7	no	—
30	C₂³	—	113	7	no	—
31	C₂³	#11744762	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	113	7	no	—
33	C₂×C₄	—	113	21	no	—
34	C₈	—	113	8	no	—
35	C₂²	—	113	7	no	—
36	C₂²	—	113	21	no	—
37	C₂²	C₂×#11744762	1	7	yes	direct product factor
38	C₄	—	113	1	no	—
39	C₄	—	113	7	no	—
40	C₂	—	113	1	no	—
41	C₂	—	113	7	no	—
42	C₂	C₂²×#11744762	1	7	yes	direct product factor

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