Subgroups — #20298996

Order 7232.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813622	C₂	1	2	yes	maximal
2	#16813554	C₂	1	4	yes	maximal
3	C₄×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₂₆	—	2	2	no	—
5	C₄⋊Dic₁₁₃	—	2	2	no	—
6	C₄⋊Dic₁₁₃	C₂²	1	4	yes	—
7	C₂×C₈×C₁₁₃	C₂²	1	2	yes	—
8	C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₁₃	D₄	1	2	yes	—
10	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
11	C₂×Dic₁₁₃	—	2	4	no	—
12	Dic₂₂₆	—	4	4	no	—
13	C₈×C₁₁₃	Q₈	1	4	yes	complemented
14	C₂²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
15	C₄×C₁₁₃	SD₁₆	1	4	yes	—
16	C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
17	Dic₁₁₃	—	4	4	no	—
18	C₂×C₁₁₃	C₄⋊Q₈	1	1	yes	characteristic
19	C₂×C₁₁₃	C₂×SD₁₆	1	2	yes	—
20	C₁₁₃	#498	1	1	yes	characteristic, complemented, Sylow
21	#498	—	113	1	no	maximal, Sylow
22	C₄⋊Q₈	—	113	2	no	—
23	#106	—	113	4	no	—
24	C₄×C₈	D₁₁₃	1	1	yes	characteristic
25	C₂×Q₈	—	226	2	no	—
26	C₂×C₈	C₂×D₁₁₃	1	2	yes	—
27	C₄⋊C₄	—	113	4	no	—
28	C₄⋊C₄	—	226	2	no	—
29	C₄²	C₂×D₁₁₃	1	1	yes	characteristic
30	Q₈	—	452	4	no	—
31	C₂×C₄	—	226	4	no	—
32	C₂×C₄	D₄₅₂	1	2	yes	—
33	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
34	C₈	Dic₂₂₆	1	4	yes	complemented
35	C₂²	C₂×D₄₅₂	1	1	yes	characteristic
36	C₄	—	452	4	no	—
37	C₄	#14268636	1	4	yes	—
38	C₄	C₂×Dic₂₂₆	1	2	yes	—
39	C₂	#16813622	1	1	yes	characteristic
40	C₂	C₂×#14268636	1	2	yes	—

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