Subgroups — #20299688

Order 7232.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11744762	C₂	1	2	yes	maximal
2	C₈×#90673	C₂	1	1	yes	maximal, characteristic
3	C₂×#11744762	—	2	2	no	—
4	#14268655	C₄	1	1	yes	characteristic
5	C₄×#90673	C₂²	1	1	yes	characteristic
6	C₈×D₁₁₃	C₄	1	1	yes	characteristic
7	C₂×#90673	D₄	1	1	yes	characteristic
8	C₂×#90673	Q₈	1	1	yes	characteristic
9	#11744762	—	4	2	no	—
10	C₄×D₁₁₃	C₂×C₄	1	1	yes	characteristic
11	#11744753	—	2	1	no	—
12	C₈×C₁₁₃	C₈	1	1	yes	characteristic, complemented
13	#11744751	C₈	1	1	yes	characteristic, complemented
14	C₂×D₁₁₃	C₄⋊C₄	1	1	yes	characteristic
15	#90673	—	2	1	no	—
16	#90673	D₈	1	1	yes	characteristic
17	#90673	Q₁₆	1	1	yes	characteristic
18	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
19	Dic₁₁₃	M₁₆	1	1	yes	characteristic
20	C₂×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
21	D₁₁₃	#107	1	1	yes	characteristic
22	D₁₁₃	#108	1	1	yes	characteristic
23	C₁₁₃	#335	1	1	yes	characteristic, complemented, Sylow
24	#335	—	113	1	no	maximal, Sylow
25	C₄⋊C₈	—	113	2	no	—
26	C₄×C₈	—	113	1	no	—
27	C₂×C₈	—	113	1	no	—
28	C₂×C₈	—	113	1	no	—
29	C₂×C₈	—	226	2	no	—
30	C₄²	—	113	1	no	—
31	C₂×C₄	—	113	1	no	—
32	C₂×C₄	—	113	1	no	—
33	C₂×C₄	—	113	1	no	—
34	C₈	—	113	1	no	—
35	C₈	—	452	2	no	—
36	C₈	—	226	1	no	—
37	C₈	#11744762	1	1	yes	characteristic, complemented
38	C₂²	—	113	1	no	—
39	C₄	—	113	1	no	—
40	C₄	—	113	1	no	—
41	C₄	—	113	1	no	—
42	C₄	—	226	1	no	—
43	C₄	C₂×#11744762	1	1	yes	characteristic
44	C₂	—	113	1	no	—
45	C₂	—	113	1	no	—
46	C₂	C₄⋊#11744762	1	1	yes	characteristic

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