Subgroups — C₂×D₆₇₃₆ #41003261

Order 26944.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₃₆₈	C₂	1	2	yes	maximal, complemented
2	D₆₇₃₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₄₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆₈₄	—	2	2	no	—
5	D₃₃₆₈	—	2	2	no	—
6	D₃₃₆₈	C₂²	1	4	yes	complemented
7	C₂×C₈×C₄₂₁	C₂²	1	1	yes	characteristic
8	C₁₆×C₄₂₁	C₂²	1	2	yes	complemented
9	C₂²×D₄₂₁	—	4	2	no	—
10	D₁₆₈₄	—	2	4	no	—
11	D₁₆₈₄	—	4	2	no	—
12	C₂×C₄×C₄₂₁	D₄	1	1	yes	characteristic
13	C₈×C₄₂₁	D₄	1	1	yes	characteristic
14	C₈×C₄₂₁	C₂³	1	1	yes	characteristic
15	C₂²×C₄₂₁	D₈	1	1	yes	characteristic
16	C₂×D₄₂₁	—	4	4	no	—
17	C₂×D₄₂₁	—	8	4	no	—
18	C₄×C₄₂₁	D₈	1	1	yes	characteristic
19	C₄×C₄₂₁	C₂×D₄	1	1	yes	characteristic
20	C₂×C₄₂₁	D₁₆	1	2	yes	complemented
21	C₂×C₄₂₁	C₂×D₈	1	1	yes	characteristic
22	D₄₂₁	—	8	4	no	—
23	C₄₂₁	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₁₆	—	421	1	no	maximal, Sylow
25	C₂×D₈	—	421	2	no	—
26	D₁₆	—	421	4	no	—
27	C₂×C₁₆	D₄₂₁	1	1	yes	characteristic, complemented
28	C₂×D₄	—	842	2	no	—
29	D₈	—	842	2	no	—
30	D₈	—	421	4	no	—
31	C₂×C₈	C₂×D₄₂₁	1	1	yes	characteristic
32	C₁₆	C₂×D₄₂₁	1	2	yes	complemented
33	C₂³	—	1684	2	no	—
34	D₄	—	842	4	no	—
35	D₄	—	1684	2	no	—
36	C₂×C₄	D₁₆₈₄	1	1	yes	characteristic
37	C₈	D₁₆₈₄	1	1	yes	characteristic
38	C₈	C₂²×D₄₂₁	1	1	yes	characteristic
39	C₂²	—	3368	4	no	—
40	C₂²	—	1684	4	no	—
41	C₂²	D₃₃₆₈	1	1	yes	characteristic
42	C₄	D₃₃₆₈	1	1	yes	characteristic
43	C₄	C₂×D₁₆₈₄	1	1	yes	characteristic
44	C₂	—	3368	4	no	—
45	C₂	D₆₇₃₆	1	2	yes	direct product factor
46	C₂	C₂×D₃₃₆₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₃₆₈
commutator, cosocle	C₈×C₄₂₁	C₂³
Frattini	C₈	C₂²×D₄₂₁
Fitting	C₂×C₁₆×C₄₂₁	C₂
socle	C₂²×C₄₂₁	D₈
hypercenter	C₂×C₁₆	D₄₂₁
hypocenter	C₄₂₁	C₂×D₁₆
LCS	G ▷ C₈×C₄₂₁ ▷ C₄×C₄₂₁ ▷ C₂×C₄₂₁ ▷ C₄₂₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₃₃₆₈	C₂	semidirect
2. D₆₇₃₆	C₂	direct (N × H)
3. C₂×C₁₆×C₄₂₁	C₂	semidirect
6. D₃₃₆₈	C₂²	semidirect
8. C₁₆×C₄₂₁	C₂²	semidirect
20. C₂×C₄₂₁	D₁₆	semidirect
23. C₄₂₁	C₂×D₁₆	semidirect
27. C₂×C₁₆	D₄₂₁	semidirect
32. C₁₆	C₂×D₄₂₁	semidirect
45. C₂	D₆₇₃₆	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₃₃₆₈	2
D₆₇₃₆	2
C₂×C₁₆×C₄₂₁	2
C₂×D₁₆	421

Subgroups — C2×D6736 #41003261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₆₇₃₆ #41003261