Subgroups — C₂×#17984176 #22578480

Order 8768.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984176	C₂	1	8	yes	maximal, direct product factor
2	C₂×#14555520	C₂	1	3	yes	maximal, complemented
3	C₂×#14555518	C₂	1	3	yes	maximal, complemented
4	C₂×#14555511	C₂	1	1	yes	maximal, characteristic
5	#14555520	C₂²	1	12	yes	complemented
6	#14555518	C₂²	1	12	yes	complemented
7	C₂×#11764047	C₂²	1	1	yes	characteristic
8	C₂×#11764047	C₂²	1	3	yes	—
9	#14555511	C₄	1	4	yes	—
10	#14555511	C₂²	1	4	yes	—
11	C₂×D₅₄₈	C₄	1	3	yes	—
12	C₂×C₄×D₁₃₇	C₂²	1	3	yes	—
13	C₂×Q₈×C₁₃₇	C₄	1	1	yes	characteristic
14	#11764047	C₂³	1	2	yes	—
15	#11764047	C₂³	1	6	yes	—
16	C₂²×D₁₃₇	C₂×C₄	1	3	yes	—
17	D₅₄₈	C₂×C₄	1	12	yes	—
18	C₂×Dic₁₃₇	C₂³	1	1	yes	characteristic
19	C₄×D₁₃₇	C₂×C₄	1	6	yes	—
20	C₄×D₁₃₇	C₂³	1	6	yes	—
21	Q₈×C₁₃₇	C₂×C₄	1	4	yes	—
22	C₂×C₄×C₁₃₇	C₂×C₄	1	3	yes	—
23	C₂²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
24	C₂×D₁₃₇	—	2	6	no	—
25	C₂×D₁₃₇	C₂²×C₄	1	6	yes	—
26	C₄×C₁₃₇	C₂²×C₄	1	6	yes	—
27	Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
28	Dic₁₃₇	C₂⁴	1	1	yes	characteristic
29	C₂×C₁₃₇	#131	1	2	yes	complemented
30	C₂×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
31	D₁₃₇	—	2	6	no	—
32	C₁₃₇	C₂×#131	1	1	yes	characteristic, complemented, Sylow
33	C₂×#131	—	137	1	no	maximal, Sylow
34	C₂×#41	—	137	1	no	—
35	#131	—	137	8	no	—
36	C₂×M₁₆	—	137	3	no	—
37	C₂²×C₈	—	137	3	no	—
38	#41	—	137	4	no	—
39	#41	—	137	4	no	—
40	C₂×Q₈	#10587739	1	1	yes	characteristic
41	C₂×D₄	—	137	3	no	—
42	C₂²×C₄	—	137	3	no	—
43	M₁₆	—	137	12	no	—
44	C₂×C₈	—	137	1	no	—
45	C₂×C₈	—	137	3	no	—
46	C₂×C₈	—	137	12	no	—
47	C₂³	—	137	3	no	—
48	Q₈	C₂×#10587739	1	4	yes	—
49	D₄	—	137	12	no	—
50	C₂×C₄	—	137	1	no	—
51	C₂×C₄	—	137	6	no	—
52	C₂×C₄	—	137	6	no	—
53	C₂×C₄	C₂×#10587739	1	3	yes	—
54	C₈	—	137	2	no	—
55	C₈	—	137	6	no	—
56	C₂²	—	274	6	no	—
57	C₂²	—	137	6	no	—
58	C₂²	C₂²×#10587739	1	1	yes	characteristic
59	C₄	—	137	1	no	—
60	C₄	—	137	1	no	—
61	C₄	C₂²×#10587739	1	6	yes	—
62	C₂	—	274	6	no	—
63	C₂	#17984176	1	2	yes	direct product factor
64	C₂	C₂³×#10587739	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#10587739
commutator	C₂×C₁₃₇	C₂³×C₄
Frattini	C₂	C₂³×#10587739
Fitting	C₂×Q₈×C₁₃₇	C₄
socle	C₂²×C₁₃₇	C₂²×C₄
hypercenter	C₂×Q₈	#10587739
hypocenter	C₁₃₇	C₂×#131
LCS	G ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. #17984176	C₂	direct (N × H)
2. C₂×#14555520	C₂	semidirect
3. C₂×#14555518	C₂	semidirect
5. #14555520	C₂²	semidirect
6. #14555518	C₂²	semidirect
29. C₂×C₁₃₇	#131	semidirect
32. C₁₃₇	C₂×#131	semidirect
63. C₂	#17984176	direct (N × H)

Subgroups — C2×#17984176 #22578480

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17984176 #22578480