Subgroups — #22578506

Order 8768.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14555522	C₂	1	2	yes	maximal
2	C₄×#11764047	C₂	1	1	yes	maximal, characteristic
3	#14555522	—	2	2	no	—
4	C₂×#11764047	C₄	1	1	yes	characteristic
5	C₂×#11764047	C₂²	1	1	yes	characteristic
6	C₄×Dic₁₃₇	C₄	1	1	yes	characteristic
7	#11764047	—	2	1	no	—
8	#11764047	D₄	1	1	yes	characteristic
9	#11764047	Q₈	1	1	yes	characteristic
10	C₂×Dic₁₃₇	C₈	1	1	yes	characteristic
11	C₂×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₃₇	C₈	1	1	yes	characteristic
13	C₂²×C₁₃₇	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₃₇	—	2	1	no	—
15	Dic₁₃₇	C₁₆	1	2	yes	complemented
16	Dic₁₃₇	C₄⋊C₄	1	1	yes	characteristic
17	Dic₁₃₇	M₁₆	1	1	yes	characteristic
18	C₂×C₁₃₇	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₁₃₇	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₁₃₇	M₃₂	1	1	yes	characteristic
21	C₁₃₇	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	137	1	no	maximal, Sylow
23	C₂×C₁₆	—	137	2	no	—
24	C₄×C₈	—	137	1	no	—
25	C₂×C₈	—	137	1	no	—
26	C₂×C₈	—	137	1	no	—
27	C₄²	—	137	1	no	—
28	C₁₆	—	274	2	no	—
29	C₂×C₄	—	137	1	no	—
30	C₂×C₄	—	137	1	no	—
31	C₂×C₄	#11764049	1	1	yes	characteristic
32	C₈	—	274	1	no	—
33	C₈	—	137	1	no	—
34	C₈	—	137	1	no	—
35	C₂²	C₂×#11764049	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	—	137	1	no	—
38	C₄	—	137	1	no	—
39	C₄	—	137	2	no	—
40	C₂	C₄⋊#11764049	1	1	yes	characteristic
41	C₂	#17984183	1	1	yes	characteristic
42	C₂	#17984184	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. Dic₁₃₇	C₁₆	semidirect
21. C₁₃₇	C₄⋊C₁₆	semidirect