Subgroups — #22578266

Order 8768.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11764047	C₂	1	2	yes	maximal
2	C₈×Dic₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#11764047	—	2	2	no	—
4	C₂×#11764040	C₄	1	1	yes	characteristic
5	C₄×Dic₁₃₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₃₇	C₄	1	1	yes	characteristic
7	#11764047	—	4	2	no	—
8	C₂×Dic₁₃₇	D₄	1	1	yes	characteristic
9	C₂×Dic₁₃₇	Q₈	1	1	yes	characteristic
10	#11764040	—	2	1	no	—
11	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₃₇	C₈	1	2	yes	complemented
13	C₂²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₃₇	M₁₆	1	1	yes	characteristic
16	Dic₁₃₇	—	2	1	no	—
17	Dic₁₃₇	D₈	1	1	yes	characteristic
18	Dic₁₃₇	Q₁₆	1	1	yes	characteristic
19	C₂×C₁₃₇	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₁₃₇	#107	1	1	yes	characteristic
21	C₂×C₁₃₇	#108	1	1	yes	characteristic
22	C₁₃₇	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	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	#10587739	1	1	yes	characteristic
29	C₄²	—	137	1	no	—
30	C₂×C₄	—	137	1	no	—
31	C₂×C₄	—	137	1	no	—
32	C₂×C₄	C₂×#10587739	1	1	yes	characteristic
33	C₈	—	274	1	no	—
34	C₈	—	548	2	no	—
35	C₈	#11764047	1	2	yes	complemented
36	C₂²	C₄⋊#10587739	1	1	yes	characteristic
37	C₄	—	274	1	no	—
38	C₄	—	137	1	no	—
39	C₄	—	137	1	no	—
40	C₄	C₂×#11764047	1	1	yes	characteristic
41	C₄	#14555520	1	1	yes	characteristic
42	C₂	C₄⋊#11764047	1	1	yes	characteristic
43	C₂	#17984157	1	1	yes	characteristic
44	C₂	#17984159	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#10587739
commutator	C₄×C₁₃₇	C₂×C₈
Frattini	C₂×C₄	C₂×#10587739
Fitting	C₂×C₈×C₁₃₇	C₄
socle	C₂²×C₁₃₇	C₄⋊C₄
hypercenter	C₂×C₈	#10587739
hypocenter	C₁₃₇	#335
LCS	G ▷ C₄×C₁₃₇ ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
12. C₈×C₁₃₇	C₈	semidirect
22. C₁₃₇	#335	semidirect
35. C₈	#11764047	semidirect