Subgroups — C₂×#41×C₃₃₇ #24924861

Order 10784.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₃₃₇	C₂	1	8	yes	maximal, direct product factor
2	C₂×Q₈×C₃₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄×C₃₃₇	C₂	1	3	yes	maximal, complemented
4	C₂²×C₄×C₃₃₇	C₂	1	3	yes	maximal, complemented
5	C₂³×C₃₃₇	C₂²	1	3	yes	—
6	Q₈×C₃₃₇	C₂²	1	4	yes	complemented
7	D₄×C₃₃₇	C₂²	1	12	yes	complemented
8	C₂×C₄×C₃₃₇	C₂²	1	3	yes	—
9	C₂×C₄×C₃₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₃₃₇	C₂²	1	12	yes	complemented
11	C₂²×C₃₃₇	—	2	6	no	—
12	C₂²×C₃₃₇	C₂³	1	6	yes	—
13	C₂²×C₃₃₇	C₂³	1	1	yes	characteristic
14	C₄×C₃₃₇	C₂³	1	6	yes	—
15	C₄×C₃₃₇	C₂³	1	2	yes	—
16	C₂×C₃₃₇	—	2	6	no	—
17	C₂×C₃₃₇	#41	1	2	yes	direct product factor
18	C₂×C₃₃₇	C₂⁴	1	1	yes	characteristic
19	C₃₃₇	C₂×#41	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×#41	C₃₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	#41	C₂×C₃₃₇	1	8	yes	direct product factor
22	C₂×Q₈	C₂×C₃₃₇	1	1	yes	characteristic, complemented
23	C₂×D₄	C₂×C₃₃₇	1	3	yes	complemented
24	C₂²×C₄	C₂×C₃₃₇	1	3	yes	complemented
25	C₂³	C₂²×C₃₃₇	1	3	yes	—
26	Q₈	C₂²×C₃₃₇	1	4	yes	complemented
27	D₄	C₂²×C₃₃₇	1	12	yes	complemented
28	C₂×C₄	C₂²×C₃₃₇	1	1	yes	characteristic
29	C₂×C₄	C₂²×C₃₃₇	1	3	yes	—
30	C₂×C₄	C₂²×C₃₃₇	1	12	yes	complemented
31	C₂²	—	2	6	no	—
32	C₂²	C₂³×C₃₃₇	1	6	yes	—
33	C₂²	C₂³×C₃₃₇	1	1	yes	characteristic
34	C₄	C₂³×C₃₃₇	1	2	yes	—
35	C₄	C₂³×C₃₃₇	1	6	yes	—
36	C₂	—	2	6	no	—
37	C₂	#41×C₃₃₇	1	2	yes	direct product factor
38	C₂	C₂⁴×C₃₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₃₇	C₂²
commutator, Frattini, cosocle	C₂	C₂⁴×C₃₃₇
socle	C₂²×C₃₃₇	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #41×C₃₃₇	C₂	direct (N × H)
2. C₂×Q₈×C₃₃₇	C₂	semidirect
3. C₂×D₄×C₃₃₇	C₂	semidirect
4. C₂²×C₄×C₃₃₇	C₂	semidirect
6. Q₈×C₃₃₇	C₂²	semidirect
7. D₄×C₃₃₇	C₂²	semidirect
10. C₂×C₄×C₃₃₇	C₂²	semidirect
17. C₂×C₃₃₇	#41	direct (N × H)
19. C₃₃₇	C₂×#41	direct (N × H)
20. C₂×#41	C₃₃₇	direct (N × H)
21. #41	C₂×C₃₃₇	direct (N × H)
22. C₂×Q₈	C₂×C₃₃₇	semidirect
23. C₂×D₄	C₂×C₃₃₇	semidirect
24. C₂²×C₄	C₂×C₃₃₇	semidirect
26. Q₈	C₂²×C₃₃₇	semidirect
27. D₄	C₂²×C₃₃₇	semidirect
30. C₂×C₄	C₂²×C₃₃₇	semidirect
37. C₂	#41×C₃₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
#41×C₃₃₇	2
C₂×Q₈×C₃₃₇	2
C₂×D₄×C₃₃₇	2
C₂²×C₄×C₃₃₇	2
C₂×#41	337

Subgroups — C2×#41×C337 #24924861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#41×C₃₃₇ #24924861