Subgroups — #22578272

Order 8768.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃₇⋊M₁₆	C₂	1	2	yes	maximal
2	C₂×#14555493	C₂	1	1	yes	maximal, characteristic
3	#14555520	—	2	2	no	—
4	#14555519	—	2	2	no	—
5	#14555518	C₄	1	4	yes	—
6	C₂×C₄×D₁₃₇	C₂²	1	1	yes	characteristic
7	#14555493	—	2	2	no	—
8	C₂×#11764040	C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₃₇	C₄	1	1	yes	characteristic
10	#11764047	—	2	4	no	—
11	C₂²×D₁₃₇	Q₈	1	1	yes	characteristic
12	C₂×Dic₁₃₇	D₄	1	1	yes	characteristic
13	C₄×D₁₃₇	C₂×C₄	1	2	yes	—
14	C₄×D₁₃₇	D₄	1	2	yes	—
15	#11764040	—	2	1	no	—
16	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
17	C₈×C₁₃₇	—	2	1	no	—
18	C₂²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₁₃₇	—	4	1	no	—
20	C₂×D₁₃₇	C₄⋊C₄	1	2	yes	—
21	C₄×C₁₃₇	C₄²	1	1	yes	characteristic
22	C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₁₃₇	C₂²⋊C₄	1	2	yes	—
24	C₂×C₁₃₇	—	2	1	no	—
25	C₂×C₁₃₇	#95	1	1	yes	characteristic
26	D₁₃₇	—	2	2	no	—
27	C₁₃₇	#338	1	1	yes	characteristic, complemented, Sylow
28	#338	—	137	1	no	maximal, Sylow
29	C₂×M₁₆	—	137	2	no	—
30	C₂×M₁₆	—	137	1	no	—
31	C₂²×C₄	—	137	1	no	—
32	M₁₆	—	274	2	no	—
33	M₁₆	—	274	2	no	—
34	M₁₆	—	274	2	no	—
35	C₂×C₈	—	137	4	no	—
36	C₂×C₈	—	137	1	no	—
37	C₂×C₈	#10587739	1	1	yes	characteristic
38	C₂³	—	137	1	no	—
39	C₂×C₄	—	137	1	no	—
40	C₂×C₄	—	137	2	no	—
41	C₂×C₄	—	137	2	no	—
42	C₂×C₄	C₂×#10587739	1	1	yes	characteristic
43	C₈	—	2	1	no	—
44	C₈	—	274	4	no	—
45	C₈	—	274	1	no	—
46	C₂²	—	548	1	no	—
47	C₂²	—	137	2	no	—
48	C₂²	C₄⋊#10587739	1	1	yes	characteristic
49	C₄	—	137	2	no	—
50	C₄	C₄×#10587739	1	1	yes	characteristic
51	C₄	C₂²⋊#10587739	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	274	2	no	—
54	C₂	(C₂×#10587739)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×#10587739
commutator	C₄×C₁₃₇	C₄²
Frattini	C₂×C₄	C₂×#10587739
Fitting	C₂×C₈×C₁₃₇	C₄
socle	C₂×C₁₃₇	#95
hypercenter	C₂×C₈	#10587739
hypocenter	C₁₃₇	#338
LCS	G ▷ C₄×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
27. C₁₃₇	#338	semidirect