Subgroups — C₂×#17984161 #22578457

Order 8768.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984161	C₂	1	4	yes	maximal, direct product factor
2	C₂×#14555513	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#14555513	C₂²	1	4	yes	complemented
5	C₂×C₄×D₁₃₇	C₄	1	1	yes	characteristic
6	C₂×#11764040	C₂²	1	1	yes	characteristic
7	C₈×D₁₃₇	C₄	1	2	yes	—
8	C₈×D₁₃₇	C₂²	1	2	yes	—
9	C₂×C₈×C₁₃₇	C₄	1	1	yes	characteristic
10	C₂²×D₁₃₇	C₈	1	1	yes	characteristic
11	C₂×Dic₁₃₇	C₈	1	1	yes	characteristic
12	C₄×D₁₃₇	C₈	1	2	yes	—
13	C₄×D₁₃₇	C₂×C₄	1	2	yes	—
14	#11764040	C₂×C₄	1	1	yes	characteristic
15	#11764040	C₂³	1	1	yes	characteristic
16	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
17	C₈×C₁₃₇	C₂×C₄	1	2	yes	—
18	C₂²×C₁₃₇	C₂×C₈	1	1	yes	characteristic
19	C₂×D₁₃₇	C₁₆	1	4	yes	complemented
20	C₂×D₁₃₇	C₂×C₈	1	2	yes	—
21	C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
22	C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
23	Dic₁₃₇	C₂×C₈	1	2	yes	—
24	C₂×C₁₃₇	C₂×C₁₆	1	2	yes	complemented
25	C₂×C₁₃₇	C₂²×C₈	1	1	yes	characteristic
26	D₁₃₇	C₂×C₁₆	1	4	yes	complemented
27	C₁₃₇	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₁₆	—	137	1	no	maximal, Sylow
29	C₂²×C₈	—	137	1	no	—
30	C₂×C₁₆	—	137	2	no	—
31	C₂×C₁₆	—	137	4	no	—
32	C₂²×C₄	—	137	1	no	—
33	C₂×C₈	—	137	1	no	—
34	C₂×C₈	—	137	2	no	—
35	C₂×C₈	—	137	2	no	—
36	C₂×C₈	#10587739	1	1	yes	characteristic
37	C₁₆	—	137	4	no	—
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	—	137	1	no	—
44	C₈	—	137	1	no	—
45	C₈	C₂×#10587739	1	2	yes	—
46	C₂²	—	137	4	no	—
47	C₂²	—	137	2	no	—
48	C₂²	#14555518	1	1	yes	characteristic
49	C₄	—	137	2	no	—
50	C₄	#14555518	1	1	yes	characteristic
51	C₄	C₂²×#10587739	1	1	yes	characteristic
52	C₂	—	137	4	no	—
53	C₂	#17984161	1	2	yes	direct product factor
54	C₂	C₂×#14555518	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	#10587739
commutator, hypocenter	C₁₃₇	C₂²×C₁₆
Frattini	C₄	C₂²×#10587739
Fitting	C₂×C₈×C₁₃₇	C₄
socle	C₂²×C₁₃₇	C₂×C₈
LCS	G ▷ C₁₃₇
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. #17984161	C₂	direct (N × H)
2. C₂×#14555513	C₂	semidirect
4. #14555513	C₂²	semidirect
19. C₂×D₁₃₇	C₁₆	semidirect
24. C₂×C₁₃₇	C₂×C₁₆	semidirect
26. D₁₃₇	C₂×C₁₆	semidirect
27. C₁₃₇	C₂²×C₁₆	semidirect
53. C₂	#17984161	direct (N × H)

Subgroups — C2×#17984161 #22578457

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17984161 #22578457