Subgroups — C₁₆×#10587739 #22578287

Order 8768.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984161	C₂	1	1	yes	maximal, characteristic
2	C₈×#10587739	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#14555518	C₄	1	1	yes	characteristic
5	C₄×#10587739	C₄	1	1	yes	characteristic
6	#14555513	C₄	1	2	yes	complemented
7	C₈×D₁₃₇	C₂²	1	1	yes	characteristic
8	#14555485	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₁₃₇	C₄	1	1	yes	characteristic, complemented
10	C₂×#10587739	C₈	1	2	yes	—
11	#11764047	C₈	1	2	yes	—
12	C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
13	#11764040	C₂×C₄	1	1	yes	characteristic
14	C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×D₁₃₇	C₂×C₈	1	1	yes	characteristic
16	#10587739	C₁₆	1	4	yes	direct product factor
17	C₄×C₁₃₇	C₄²	1	1	yes	characteristic
18	Dic₁₃₇	C₂×C₈	1	1	yes	characteristic
19	C₂×C₁₃₇	C₄×C₈	1	1	yes	characteristic
20	D₁₃₇	C₂×C₁₆	1	2	yes	—
21	C₁₃₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₆	—	137	1	no	maximal, Sylow
23	C₂×C₁₆	—	137	1	no	—
24	C₂×C₁₆	—	137	1	no	—
25	C₄×C₈	—	137	1	no	—
26	C₂×C₈	—	137	1	no	—
27	C₂×C₈	—	137	1	no	—
28	C₄²	—	137	1	no	—
29	C₁₆	—	137	2	no	—
30	C₁₆	—	137	1	no	—
31	C₁₆	#10587739	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	137	2	no	—
33	C₂×C₄	—	137	1	no	—
34	C₈	—	137	2	no	—
35	C₈	—	137	1	no	—
36	C₈	C₂×#10587739	1	1	yes	characteristic
37	C₂²	—	137	1	no	—
38	C₄	—	137	4	no	—
39	C₄	—	137	1	no	—
40	C₄	C₄×#10587739	1	1	yes	characteristic
41	C₂	—	137	2	no	—
42	C₂	C₈×#10587739	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₆	#10587739
commutator, hypocenter	C₁₃₇	C₄×C₁₆
Frattini	C₈	C₂×#10587739
Fitting	C₁₆×C₁₃₇	C₄
socle	C₂×C₁₃₇	C₄×C₈
LCS	G ▷ C₁₃₇
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
6. #14555513	C₄	semidirect
8. #14555485	C₄	semidirect
9. C₁₆×C₁₃₇	C₄	semidirect
16. #10587739	C₁₆	direct (N × H)
21. C₁₃₇	C₄×C₁₆	semidirect
31. C₁₆	#10587739	direct (N × H)

Subgroups — C16×#10587739 #22578287

Conjugacy classes of subgroups

Complements

Subgroups — C₁₆×#10587739 #22578287