Subgroups — C₂×#14270989 #16821269

Order 3712.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745166	C₂	1	2	yes	maximal
2	#14270989	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
5	C₂×C₄⋊Dic₂₉	—	2	2	no	—
6	C₂×C₁₆×C₂₉	C₄	1	4	yes	complemented
7	C₂×C₁₆×C₂₉	C₂²	1	2	yes	—
8	#11745166	—	2	2	no	—
9	#11745166	C₂²	1	4	yes	—
10	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
11	C₂²×Dic₂₉	—	4	2	no	—
12	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
14	C₂×C₈×C₂₉	Q₈	1	2	yes	—
15	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
16	C₄⋊Dic₂₉	—	2	4	no	—
17	C₄⋊Dic₂₉	—	4	2	no	—
18	C₁₆×C₂₉	C₂×C₄	1	4	yes	complemented
19	C₂³×C₂₉	D₈	1	1	yes	characteristic
20	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
21	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
22	C₂×C₄×C₂₉	Q₁₆	1	2	yes	—
23	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₂₉	—	4	4	no	—
25	C₂×Dic₂₉	—	8	4	no	—
26	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
27	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₂₉	C₂×Q₈	1	1	yes	characteristic
29	C₂×#366	—	29	1	no	maximal, Sylow
30	C₂²×C₂₉	#107	1	2	yes	—
31	C₂²×C₂₉	D₁₆	1	2	yes	—
32	C₂²×C₂₉	Q₃₂	1	2	yes	—
33	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
34	C₄×C₂₉	#107	1	2	yes	—
35	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₄×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
37	Dic₂₉	—	8	4	no	—
38	C₂²×C₁₆	D₂₉	1	1	yes	characteristic
39	C₂×#107	—	29	2	no	—
40	#366	—	29	4	no	—
41	C₂×C₂₉	#366	1	4	yes	complemented
42	C₂×C₂₉	C₂×#107	1	1	yes	characteristic
43	C₂×C₂₉	C₂×D₁₆	1	1	yes	characteristic
44	C₂×C₂₉	C₂×Q₃₂	1	1	yes	characteristic
45	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
46	C₂×C₄⋊C₄	—	58	2	no	—
47	C₂×C₁₆	Dic₂₉	1	4	yes	complemented
48	C₂×C₁₆	C₂×D₂₉	1	2	yes	—
49	#107	—	29	4	no	—
50	#107	—	58	2	no	—
51	C₂₉	C₂×#366	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₄	—	116	2	no	—
53	C₂²×C₄	D₁₁₆	1	1	yes	characteristic
54	C₂×C₈	Dic₅₈	1	2	yes	—
55	C₂×C₈	D₁₁₆	1	1	yes	characteristic
56	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
57	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
58	C₄⋊C₄	—	58	4	no	—
59	C₄⋊C₄	—	116	2	no	—
60	C₁₆	C₂×Dic₂₉	1	4	yes	complemented
61	C₂³	D₂₃₂	1	1	yes	characteristic
62	C₂×C₄	—	116	4	no	—
63	C₂×C₄	—	232	4	no	—
64	C₂×C₄	D₂₃₂	1	1	yes	characteristic
65	C₂×C₄	Dic₁₁₆	1	2	yes	—
66	C₂×C₄	C₄⋊Dic₂₉	1	2	yes	—
67	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
68	C₈	C₄⋊Dic₂₉	1	2	yes	—
69	C₈	C₂×Dic₅₈	1	1	yes	characteristic
70	C₈	C₂²×Dic₂₉	1	1	yes	characteristic
71	C₂²	D₄₆₄	1	2	yes	—
72	C₂²	Dic₂₃₂	1	2	yes	—
73	C₂²	#11745166	1	2	yes	—
74	C₂²	C₂×D₂₃₂	1	1	yes	characteristic
75	C₄	—	232	4	no	—
76	C₄	#11745166	1	2	yes	—
77	C₄	C₂×Dic₁₁₆	1	1	yes	characteristic
78	C₄	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
79	C₂	#14270989	1	4	yes	direct product factor
80	C₂	C₂×#11745166	1	1	yes	characteristic
81	C₂	C₂×D₄₆₄	1	1	yes	characteristic
82	C₂	C₂×Dic₂₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₃₂
commutator	C₈×C₂₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₂²×C₁₆×C₂₉	C₂
socle, prime radical	C₂³×C₂₉	D₈
cosocle	C₂×C₈×C₂₉	C₂³
hypercenter	C₂²×C₁₆	D₂₉
hypocenter	C₂₉	C₂×#366
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #14270989	C₂	direct (N × H)
6. C₂×C₁₆×C₂₉	C₄	semidirect
18. C₁₆×C₂₉	C₂×C₄	semidirect
41. C₂×C₂₉	#366	semidirect
47. C₂×C₁₆	Dic₂₉	semidirect
51. C₂₉	C₂×#366	semidirect
60. C₁₆	C₂×Dic₂₉	semidirect
79. C₂	#14270989	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×#11745166	2
#14270989	2
C₂²×C₁₆×C₂₉	2
C₂×#366	29

Subgroups — C2×#14270989 #16821269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14270989 #16821269