Subgroups — C₂×#17984142 #22578360

Order 8768.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14555518	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10587739	C₂	1	1	yes	maximal, characteristic
3	#17984142	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×D₁₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10587739	C₄	1	2	yes	—
6	#14555518	C₄	1	2	yes	complemented
7	#14555518	C₂²	1	2	yes	—
8	C₂×#11764047	C₄	1	2	yes	complemented
9	C₄×#10587739	C₄	1	2	yes	—
10	C₄×#10587739	C₂²	1	2	yes	—
11	C₂×C₄×D₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×#11764040	C₄	1	1	yes	characteristic, complemented
13	C₈×D₁₃₇	C₄	1	2	yes	complemented
14	C₈×D₁₃₇	C₂²	1	2	yes	—
15	C₂×C₈×C₁₃₇	C₄	1	1	yes	characteristic, complemented
16	C₂×#10587739	—	2	4	no	—
17	C₂×#10587739	C₂×C₄	1	4	yes	—
18	#11764047	C₂×C₄	1	4	yes	complemented
19	C₂²×D₁₃₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
21	C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
22	C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
23	C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
24	C₄×D₁₃₇	C₂³	1	1	yes	characteristic
25	#11764040	C₂×C₄	1	2	yes	complemented
26	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
27	C₈×C₁₃₇	C₂×C₄	1	2	yes	complemented
28	C₂²×C₁₃₇	C₄²	1	1	yes	characteristic
29	C₂×D₁₃₇	C₄²	1	1	yes	characteristic
30	C₂×D₁₃₇	M₁₆	1	4	yes	—
31	C₂×D₁₃₇	C₂²×C₄	1	1	yes	characteristic
32	#10587739	—	2	4	no	—
33	C₄×C₁₃₇	C₄²	1	1	yes	characteristic
34	C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
35	Dic₁₃₇	C₄²	1	1	yes	characteristic
36	Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₁₃₇	#97	1	2	yes	complemented
38	C₂×C₁₃₇	C₂×C₄²	1	1	yes	characteristic
39	D₁₃₇	#97	1	2	yes	complemented
40	D₁₃₇	C₂×M₁₆	1	2	yes	—
41	C₁₃₇	C₂×#97	1	1	yes	characteristic, complemented, Sylow
42	C₂×#97	—	137	1	no	maximal, Sylow
43	C₂²×C₈	—	137	1	no	—
44	C₂²×C₈	—	137	1	no	—
45	C₂×C₄²	—	137	1	no	—
46	#97	—	137	4	no	—
47	C₂²×C₄	—	137	2	no	—
48	C₂²×C₄	—	137	1	no	—
49	C₂×C₈	—	137	2	no	—
50	C₂×C₈	—	137	2	no	—
51	C₂×C₈	—	137	2	no	—
52	C₂×C₈	—	137	1	no	—
53	C₂×C₈	—	137	2	no	—
54	C₂×C₈	—	137	2	no	—
55	C₂×C₈	#10587739	1	1	yes	characteristic, complemented
56	C₄²	—	137	2	no	—
57	C₄²	—	137	2	no	—
58	C₂³	—	137	1	no	—
59	C₂×C₄	—	274	4	no	—
60	C₂×C₄	—	137	4	no	—
61	C₂×C₄	—	137	1	no	—
62	C₂×C₄	—	137	1	no	—
63	C₂×C₄	—	137	1	no	—
64	C₂×C₄	—	137	1	no	—
65	C₂×C₄	—	137	1	no	—
66	C₂×C₄	C₂×#10587739	1	1	yes	characteristic
67	C₈	—	137	4	no	—
68	C₈	—	137	2	no	—
69	C₈	C₂×#10587739	1	2	yes	complemented
70	C₂²	—	137	4	no	—
71	C₂²	—	137	1	no	—
72	C₂²	—	137	1	no	—
73	C₂²	C₄×#10587739	1	1	yes	characteristic
74	C₄	—	274	4	no	—
75	C₄	—	137	1	no	—
76	C₄	—	137	1	no	—
77	C₄	C₄×#10587739	1	1	yes	characteristic
78	C₄	C₂²×#10587739	1	1	yes	characteristic
79	C₂	—	137	2	no	—
80	C₂	—	137	2	no	—
81	C₂	#17984142	1	2	yes	direct product factor
82	C₂	C₂×C₄×#10587739	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#10587739
commutator	C₂×C₁₃₇	C₂×C₄²
Frattini	C₄	C₂²×#10587739
Fitting	C₂×C₈×C₁₃₇	C₄
socle	C₂²×C₁₃₇	C₄²
hypercenter	C₂×C₈	#10587739
hypocenter	C₁₃₇	C₂×#97
LCS	G ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. #17984142	C₂	direct (N × H)
6. #14555518	C₄	semidirect
8. C₂×#11764047	C₄	semidirect
12. C₂×#11764040	C₄	semidirect
13. C₈×D₁₃₇	C₄	semidirect
15. C₂×C₈×C₁₃₇	C₄	semidirect
18. #11764047	C₂×C₄	semidirect
25. #11764040	C₂×C₄	semidirect
27. C₈×C₁₃₇	C₂×C₄	semidirect
37. C₂×C₁₃₇	#97	semidirect
39. D₁₃₇	#97	semidirect
41. C₁₃₇	C₂×#97	semidirect
55. C₂×C₈	#10587739	semidirect
69. C₈	C₂×#10587739	semidirect
81. C₂	#17984142	direct (N × H)

Subgroups — C2×#17984142 #22578360

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17984142 #22578360