Subgroups — C₂×C₄×#6599 #14272118

Order 1856.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6599	C₂	1	2	yes	maximal
2	C₂×C₄×Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	C₄×#6599	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₂₉	C₄	1	1	yes	characteristic
5	C₂²×Dic₂₉	C₄	1	1	yes	characteristic
6	C₂²×Dic₂₉	C₂²	1	1	yes	characteristic
7	C₂×#6599	C₄	1	8	yes	direct product factor
8	C₂×#6599	C₂²	1	4	yes	—
9	C₄×Dic₂₉	C₄	1	2	yes	—
10	C₄×Dic₂₉	C₂²	1	2	yes	—
11	C₂³×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₂₉	C₈	1	4	yes	complemented
13	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
14	C₂×Dic₂₉	C₈	1	4	yes	complemented
15	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₂₉	C₂×C₄	1	4	yes	—
17	C₂×Dic₂₉	C₂×C₄	1	2	yes	—
18	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
19	#6599	C₂×C₄	1	8	yes	direct product factor
20	C₂²×C₂₉	C₄²	1	2	yes	—
21	C₂²×C₂₉	C₂×C₈	1	2	yes	—
22	C₂²×C₂₉	C₂×C₈	1	2	yes	—
23	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₂₉	C₂×C₈	1	4	yes	complemented
25	Dic₂₉	C₄²	1	2	yes	—
26	Dic₂₉	C₂×C₈	1	4	yes	complemented
27	Dic₂₉	C₂²×C₄	1	2	yes	—
28	C₂×C₄×C₈	—	29	1	no	maximal, Sylow
29	C₂×C₂₉	C₄×C₈	1	4	yes	complemented
30	C₂×C₂₉	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₂₉	C₂²×C₈	1	1	yes	characteristic
32	C₂×C₂₉	C₂²×C₈	1	1	yes	characteristic
33	C₂²×C₈	—	29	2	no	—
34	C₂×C₄²	—	29	1	no	—
35	C₄×C₈	—	29	4	no	—
36	C₂₉	C₂×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₄	—	29	1	no	—
38	C₂²×C₄	—	29	1	no	—
39	C₂²×C₄	#1181	1	1	yes	characteristic
40	C₂×C₈	—	29	4	no	—
41	C₂×C₈	—	29	8	no	—
42	C₄²	—	29	2	no	—
43	C₄²	—	29	2	no	—
44	C₂³	C₂×#1181	1	1	yes	characteristic
45	C₂×C₄	—	29	4	no	—
46	C₂×C₄	—	29	4	no	—
47	C₂×C₄	—	29	1	no	—
48	C₂×C₄	—	29	2	no	—
49	C₂×C₄	—	29	1	no	—
50	C₂×C₄	#6599	1	4	yes	direct product factor
51	C₂×C₄	C₂×#1181	1	2	yes	—
52	C₈	—	29	8	no	—
53	C₂²	D₂₉⋊C₈	1	2	yes	—
54	C₂²	C₄×#1181	1	2	yes	—
55	C₂²	C₂×#6599	1	2	yes	—
56	C₂²	C₂²×#1181	1	1	yes	characteristic
57	C₄	—	29	4	no	—
58	C₄	—	29	2	no	—
59	C₄	—	29	2	no	—
60	C₄	C₂×#6599	1	4	yes	direct product factor
61	C₂	C₄×#6599	1	4	yes	direct product factor
62	C₂	C₂×D₂₉⋊C₈	1	1	yes	characteristic
63	C₂	C₂×C₄×#1181	1	1	yes	characteristic
64	C₂	C₂²×#6599	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	#1181
commutator, hypocenter	C₂₉	C₂×C₄×C₈
Frattini	C₂²	C₂²×#1181
Fitting	C₂²×C₄×C₂₉	C₄
socle, prime radical	C₂³×C₂₉	C₂×C₄
cosocle	C₂×Dic₂₉	C₂³
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. C₄×#6599	C₂	direct (N × H)
7. C₂×#6599	C₄	direct (N × H)
12. C₂×C₄×C₂₉	C₈	semidirect
14. C₂×Dic₂₉	C₈	semidirect
19. #6599	C₂×C₄	direct (N × H)
24. C₄×C₂₉	C₂×C₈	semidirect
26. Dic₂₉	C₂×C₈	semidirect
29. C₂×C₂₉	C₄×C₈	semidirect
36. C₂₉	C₂×C₄×C₈	semidirect
50. C₂×C₄	#6599	direct (N × H)
60. C₄	C₂×#6599	direct (N × H)
61. C₂	C₄×#6599	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#6599	2
C₂×C₄×Dic₂₉	2
C₄×#6599	2
C₂×C₄×C₈	29

Subgroups — C2×C4×#6599 #14272118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#6599 #14272118