Subgroups — C₂×#20296329 #28380786

Order 14048.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20296329	C₂	1	8	yes	maximal, direct product factor
2	C₂×Dic₈₇₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₇₅₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂²⋊D₄₃₉	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₄₃₉	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₄₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₄₃₉	C₂²	1	2	yes	—
8	Dic₈₇₈	C₂²	1	4	yes	complemented
9	D₁₇₅₆	C₂²	1	4	yes	complemented
10	C₂²⋊D₄₃₉	C₂²	1	8	yes	complemented
11	C₂×Dic₄₃₉	C₂²	1	2	yes	—
12	C₄×D₄₃₉	C₂²	1	8	yes	complemented
13	C₂³×C₄₃₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₄₃₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₄₃₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₄₃₉	C₂²	1	4	yes	complemented
17	C₂²×C₄₃₉	—	2	2	no	—
18	C₂²×C₄₃₉	C₂³	1	2	yes	—
19	C₂²×C₄₃₉	C₂³	1	1	yes	characteristic
20	C₂×D₄₃₉	—	2	4	no	—
21	C₂×D₄₃₉	C₂³	1	4	yes	—
22	C₄×C₄₃₉	C₂³	1	2	yes	—
23	C₄×C₄₃₉	C₂³	1	2	yes	—
24	Dic₄₃₉	C₂³	1	4	yes	—
25	C₂×C₄₃₉	—	2	2	no	—
26	C₂×C₄₃₉	#41	1	2	yes	complemented
27	C₂×C₄₃₉	C₂⁴	1	1	yes	characteristic
28	D₄₃₉	—	2	4	no	—
29	C₄₃₉	C₂×#41	1	1	yes	characteristic, complemented, Sylow
30	C₂×#41	—	439	1	no	maximal, Sylow
31	#41	—	439	8	no	—
32	C₂×Q₈	—	439	1	no	—
33	C₂×D₄	—	439	2	no	—
34	C₂×D₄	—	439	1	no	—
35	C₂²×C₄	—	439	2	no	—
36	C₂²×C₄	D₄₃₉	1	1	yes	characteristic, complemented
37	C₂³	—	439	2	no	—
38	C₂³	C₂×D₄₃₉	1	1	yes	characteristic
39	Q₈	—	439	4	no	—
40	D₄	—	439	8	no	—
41	D₄	—	439	4	no	—
42	C₂×C₄	—	439	2	no	—
43	C₂×C₄	—	439	8	no	—
44	C₂×C₄	C₂×D₄₃₉	1	1	yes	characteristic
45	C₂×C₄	C₂×D₄₃₉	1	1	yes	characteristic
46	C₂×C₄	C₂×D₄₃₉	1	4	yes	complemented
47	C₂²	—	2	2	no	—
48	C₂²	—	878	4	no	—
49	C₂²	—	439	4	no	—
50	C₂²	C₂²×D₄₃₉	1	2	yes	—
51	C₂²	C₂²×D₄₃₉	1	1	yes	characteristic
52	C₄	—	439	4	no	—
53	C₄	C₂²×D₄₃₉	1	2	yes	—
54	C₄	C₂²×D₄₃₉	1	2	yes	—
55	C₂	—	2	2	no	—
56	C₂	—	878	4	no	—
57	C₂	#20296329	1	2	yes	direct product factor
58	C₂	C₂³×D₄₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄₃₉
commutator, cosocle	C₂×C₄₃₉	C₂⁴
Frattini	C₂	C₂³×D₄₃₉
Fitting	C₂²×C₄×C₄₃₉	C₂
socle	C₂²×C₄₃₉	C₂³
hypercenter	C₂²×C₄	D₄₃₉
hypocenter	C₄₃₉	C₂×#41
LCS	G ▷ C₂×C₄₃₉ ▷ C₄₃₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. #20296329	C₂	direct (N × H)
2. C₂×Dic₈₇₈	C₂	semidirect
3. C₂×D₁₇₅₆	C₂	semidirect
4. C₂×C₂²⋊D₄₃₉	C₂	semidirect
5. C₂×C₄×D₄₃₉	C₂	semidirect
6. C₂²×C₄×C₄₃₉	C₂	semidirect
8. Dic₈₇₈	C₂²	semidirect
9. D₁₇₅₆	C₂²	semidirect
10. C₂²⋊D₄₃₉	C₂²	semidirect
12. C₄×D₄₃₉	C₂²	semidirect
16. C₂×C₄×C₄₃₉	C₂²	semidirect
26. C₂×C₄₃₉	#41	semidirect
29. C₄₃₉	C₂×#41	semidirect
36. C₂²×C₄	D₄₃₉	semidirect
46. C₂×C₄	C₂×D₄₃₉	semidirect
57. C₂	#20296329	direct (N × H)

Maximal subgroups

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

subgroup	index
#20296329	2
C₂×Dic₈₇₈	2
C₂×D₁₇₅₆	2
C₂×C₂²⋊D₄₃₉	2
C₂×C₄×D₄₃₉	2
C₂²×C₄×C₄₃₉	2
C₂×#41	439

Subgroups — C2×#20296329 #28380786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20296329 #28380786