Subgroups — #20298319

Order 7232.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11744751	C₂	1	2	yes	maximal
2	C₄×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11744751	C₄	1	4	yes	—
4	C₂×C₈×C₁₁₃	C₄	1	2	yes	—
5	C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
7	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
8	C₈×C₁₁₃	C₈	1	4	yes	complemented
9	#11744751	—	2	4	no	—
10	C₂²×C₁₁₃	C₄²	1	1	yes	characteristic
11	C₄×C₁₁₃	C₂×C₈	1	2	yes	—
12	C₄×C₁₁₃	M₁₆	1	4	yes	—
13	C₂×C₁₁₃	C₄×C₈	1	1	yes	characteristic
14	C₂×C₁₁₃	#97	1	2	yes	—
15	C₁₁₃	#322	1	1	yes	characteristic, complemented, Sylow
16	#322	—	113	1	no	maximal, Sylow
17	C₄×C₈	—	113	2	no	—
18	C₄×C₈	D₁₁₃	1	1	yes	characteristic
19	C₂×C₈	—	113	4	no	—
20	C₂×C₈	Dic₁₁₃	1	2	yes	—
21	C₄²	C₂×D₁₁₃	1	1	yes	characteristic
22	C₂×C₄	C₄×D₁₁₃	1	2	yes	—
23	C₂×C₄	C₂×Dic₁₁₃	1	1	yes	characteristic
24	C₈	—	226	4	no	—
25	C₈	#11744751	1	4	yes	complemented
26	C₂²	C₄×Dic₁₁₃	1	1	yes	characteristic
27	C₄	C₂×#11744751	1	2	yes	—
28	C₄	#14268630	1	4	yes	—
29	C₂	C₄×#11744751	1	1	yes	characteristic
30	C₂	#16813532	1	2	yes	—

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