Subgroups — C₈×#11764049 #22578486

Order 8768.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11764049	C₂	1	2	yes	maximal
2	C₈×#10587739	C₂	1	1	yes	maximal, characteristic
3	C₂×#11764049	C₄	1	4	yes	—
4	#14555518	C₄	1	1	yes	characteristic
5	C₄×#10587739	C₂²	1	1	yes	characteristic
6	C₈×D₁₃₇	C₄	1	1	yes	characteristic
7	#11764049	C₈	1	8	yes	direct product factor
8	C₂×#10587739	C₂×C₄	1	2	yes	—
9	#11764047	C₈	1	2	yes	complemented
10	C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
11	#11764040	C₈	1	1	yes	characteristic, complemented
12	C₈×C₁₃₇	C₈	1	1	yes	characteristic, complemented
13	C₂×D₁₃₇	C₄²	1	1	yes	characteristic
14	#10587739	C₂×C₈	1	4	yes	—
15	C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
16	Dic₁₃₇	C₂×C₈	1	1	yes	characteristic
17	C₂×C₁₃₇	C₄×C₈	1	1	yes	characteristic
18	D₁₃₇	C₄×C₈	1	2	yes	—
19	C₁₃₇	C₈²	1	1	yes	characteristic, complemented, Sylow
20	C₈²	—	137	1	no	maximal, Sylow
21	C₄×C₈	—	137	1	no	—
22	C₄×C₈	—	137	2	no	—
23	C₂×C₈	—	137	1	no	—
24	C₂×C₈	—	137	4	no	—
25	C₂×C₈	—	137	1	no	—
26	C₄²	—	137	1	no	—
27	C₂×C₄	—	137	2	no	—
28	C₂×C₄	—	137	1	no	—
29	C₈	—	137	2	no	—
30	C₈	—	137	8	no	—
31	C₈	—	137	1	no	—
32	C₈	#11764049	1	1	yes	characteristic, direct product factor
33	C₂²	—	137	1	no	—
34	C₄	—	137	4	no	—
35	C₄	—	137	1	no	—
36	C₄	C₂×#11764049	1	1	yes	characteristic
37	C₂	—	137	2	no	—
38	C₂	C₄×#11764049	1	1	yes	characteristic

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