Subgroups — C₂×#16813157 #20297317

Order 7136.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₉₂	C₂	1	1	yes	maximal, characteristic
2	#16813157	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₂₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₂₂₃	—	2	1	no	—
6	D₈₉₂	—	2	1	no	—
7	D₈₉₂	C₂²	1	2	yes	—
8	C₂₂₃⋊C₈	C₂²	1	2	yes	complemented
9	Q₈×C₂₂₃	—	2	1	no	—
10	Q₈×C₂₂₃	C₂²	1	2	yes	complemented
11	C₂×C₄×C₂₂₃	—	2	1	no	—
12	C₂×C₄×C₂₂₃	C₂²	1	1	yes	characteristic
13	C₂²×C₂₂₃	D₄	1	1	yes	characteristic
14	C₂×D₂₂₃	—	2	2	no	—
15	C₂×D₂₂₃	—	4	2	no	—
16	C₄×C₂₂₃	—	2	2	no	—
17	C₄×C₂₂₃	D₄	1	1	yes	characteristic
18	C₄×C₂₂₃	C₂³	1	1	yes	characteristic
19	C₂×C₂₂₃	SD₁₆	1	2	yes	complemented
20	C₂×C₂₂₃	C₂×D₄	1	1	yes	characteristic
21	D₂₂₃	—	4	2	no	—
22	C₂₂₃	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₂×SD₁₆	—	223	1	no	maximal, Sylow
24	C₂×Q₈	D₂₂₃	1	1	yes	characteristic, complemented
25	C₂×D₄	—	223	1	no	—
26	SD₁₆	—	223	4	no	—
27	C₂×C₈	—	223	1	no	—
28	C₂³	—	446	1	no	—
29	Q₈	—	2	1	no	—
30	Q₈	C₂×D₂₂₃	1	2	yes	complemented
31	D₄	—	446	1	no	—
32	D₄	—	223	2	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	C₂×D₂₂₃	1	1	yes	characteristic
35	C₈	—	223	2	no	—
36	C₂²	—	892	2	no	—
37	C₂²	—	446	2	no	—
38	C₂²	C₂²⋊D₂₂₃	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	C₂²⋊D₂₂₃	1	1	yes	characteristic
41	C₄	C₂²×D₂₂₃	1	1	yes	characteristic
42	C₂	—	892	2	no	—
43	C₂	#16813157	1	2	yes	direct product factor
44	C₂	C₂×C₂²⋊D₂₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₂₂₃
commutator	C₄×C₂₂₃	C₂³
Frattini	C₄	C₂²×D₂₂₃
Fitting	C₂×Q₈×C₂₂₃	C₂
socle	C₂²×C₂₂₃	D₄
hypercenter	C₂×Q₈	D₂₂₃
hypocenter	C₂₂₃	C₂×SD₁₆
LCS	G ▷ C₄×C₂₂₃ ▷ C₂×C₂₂₃ ▷ C₂₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #16813157	C₂	direct (N × H)
3. C₂×C₂₂₃⋊C₈	C₂	semidirect
4. C₂×Q₈×C₂₂₃	C₂	semidirect
8. C₂₂₃⋊C₈	C₂²	semidirect
10. Q₈×C₂₂₃	C₂²	semidirect
19. C₂×C₂₂₃	SD₁₆	semidirect
22. C₂₂₃	C₂×SD₁₆	semidirect
24. C₂×Q₈	D₂₂₃	semidirect
30. Q₈	C₂×D₂₂₃	semidirect
43. C₂	#16813157	direct (N × H)

Subgroups — C2×#16813157 #20297317

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16813157 #20297317