Subgroups — #20299682

Order 7232.

66 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	C₄	1	4	yes	—
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	C₂×C₄	1	2	yes	—
8	#11744762	—	2	4	no	—
9	C₄×D₁₁₃	C₂×C₄	1	1	yes	characteristic
10	#11744753	C₈	1	2	yes	complemented
11	C₈×C₁₁₃	C₈	1	1	yes	characteristic, complemented
12	#11744751	C₈	1	1	yes	characteristic, complemented
13	C₂×D₁₁₃	C₄²	1	1	yes	characteristic
14	#90673	M₁₆	1	4	yes	—
15	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
16	Dic₁₁₃	C₂×C₈	1	1	yes	characteristic
17	C₂×C₁₁₃	C₄×C₈	1	1	yes	characteristic
18	D₁₁₃	#97	1	2	yes	—
19	C₁₁₃	#322	1	1	yes	characteristic, complemented, Sylow
20	#322	—	113	1	no	maximal, Sylow
21	C₄×C₈	—	113	1	no	—
22	C₄×C₈	—	113	2	no	—
23	C₂×C₈	—	113	1	no	—
24	C₂×C₈	—	113	1	no	—
25	C₂×C₈	—	113	4	no	—
26	C₄²	—	113	1	no	—
27	C₂×C₄	—	113	2	no	—
28	C₂×C₄	—	113	1	no	—
29	C₈	—	113	2	no	—
30	C₈	—	113	1	no	—
31	C₈	—	226	4	no	—
32	C₈	#11744762	1	1	yes	characteristic, complemented
33	C₂²	—	113	1	no	—
34	C₄	—	113	4	no	—
35	C₄	—	113	1	no	—
36	C₄	C₂×#11744762	1	1	yes	characteristic
37	C₂	—	113	2	no	—
38	C₂	C₄×#11744762	1	1	yes	characteristic

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