Subgroups — #22578492

Order 8768.

54 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	—	2	2	no	—
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	—	4	2	no	—
8	C₂×#10587739	D₄	1	1	yes	characteristic
9	C₂×#10587739	Q₈	1	1	yes	characteristic
10	#11764047	—	2	1	no	—
11	C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
12	#11764040	C₈	1	1	yes	characteristic, complemented
13	C₈×C₁₃₇	C₈	1	1	yes	characteristic, complemented
14	C₂×D₁₃₇	C₄⋊C₄	1	1	yes	characteristic
15	#10587739	—	2	1	no	—
16	#10587739	SD₁₆	1	2	yes	—
17	C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
18	Dic₁₃₇	M₁₆	1	1	yes	characteristic
19	C₂×C₁₃₇	C₄⋊C₈	1	1	yes	characteristic
20	D₁₃₇	#106	1	1	yes	characteristic
21	D₁₃₇	#108	1	1	yes	characteristic
22	C₁₃₇	#334	1	1	yes	characteristic, complemented, Sylow
23	#334	—	137	1	no	maximal, Sylow
24	C₄⋊C₈	—	137	2	no	—
25	C₄×C₈	—	137	1	no	—
26	C₂×C₈	—	274	2	no	—
27	C₂×C₈	—	137	1	no	—
28	C₂×C₈	—	137	1	no	—
29	C₄²	—	137	1	no	—
30	C₂×C₄	—	137	1	no	—
31	C₂×C₄	—	137	1	no	—
32	C₂×C₄	—	137	1	no	—
33	C₈	—	274	1	no	—
34	C₈	—	548	2	no	—
35	C₈	—	137	1	no	—
36	C₈	#11764049	1	1	yes	characteristic, complemented
37	C₂²	—	137	1	no	—
38	C₄	—	274	1	no	—
39	C₄	—	137	2	no	—
40	C₄	—	137	1	no	—
41	C₄	C₂×#11764049	1	1	yes	characteristic
42	C₂	—	137	1	no	—
43	C₂	—	137	1	no	—
44	C₂	C₄⋊#11764049	1	1	yes	characteristic

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