Subgroups — C₂×#14270996 #16821783

Order 3712.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
2	#14270996	C₂	1	4	yes	maximal, direct product factor
3	C₂×#11745142	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×D₂₉	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×#90768	C₄	1	1	yes	characteristic
8	C₁₆×D₂₉	C₄	1	2	yes	—
9	C₁₆×D₂₉	C₂²	1	2	yes	—
10	C₂₉×C₃₂	C₂²	1	2	yes	complemented
11	#11745142	C₂²	1	2	yes	complemented
12	C₂×C₄×D₂₉	C₈	1	1	yes	characteristic
13	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
14	C₂×#6597	C₈	1	1	yes	characteristic
15	C₈×D₂₉	C₈	1	2	yes	—
16	C₈×D₂₉	C₂×C₄	1	2	yes	—
17	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₂₉	C₂³	1	1	yes	characteristic
19	#90768	C₂×C₄	1	2	yes	—
20	C₂²×D₂₉	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
22	C₂×Dic₂₉	C₁₆	1	1	yes	characteristic
23	C₄×D₂₉	C₁₆	1	2	yes	—
24	C₄×D₂₉	C₂×C₈	1	2	yes	—
25	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
26	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
27	#6597	C₂×C₈	1	2	yes	—
28	C₂×M₆₄	—	29	1	no	maximal, Sylow
29	C₂²×C₂₉	C₂×C₁₆	1	1	yes	characteristic
30	C₂×D₂₉	—	2	2	no	—
31	C₂×D₂₉	C₂×C₁₆	1	2	yes	—
32	C₄×C₂₉	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
34	Dic₂₉	C₂×C₁₆	1	2	yes	—
35	C₂²×C₁₆	—	29	1	no	—
36	M₆₄	—	29	4	no	—
37	C₂×C₃₂	—	29	1	no	—
38	C₂×C₃₂	D₂₉	1	1	yes	characteristic, complemented
39	C₂×C₂₉	M₆₄	1	2	yes	complemented
40	C₂×C₂₉	C₂²×C₁₆	1	1	yes	characteristic
41	D₂₉	—	2	2	no	—
42	C₂²×C₈	—	29	1	no	—
43	C₂×C₁₆	—	29	1	no	—
44	C₂×C₁₆	—	29	2	no	—
45	C₂×C₁₆	—	29	2	no	—
46	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
47	C₃₂	—	29	2	no	—
48	C₃₂	C₂×D₂₉	1	2	yes	complemented
49	C₂₉	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	29	1	no	—
51	C₂×C₈	—	29	1	no	—
52	C₂×C₈	—	29	2	no	—
53	C₂×C₈	—	29	2	no	—
54	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
55	C₁₆	—	29	2	no	—
56	C₁₆	C₄×D₂₉	1	1	yes	characteristic
57	C₁₆	C₂²×D₂₉	1	1	yes	characteristic
58	C₂³	—	29	1	no	—
59	C₂×C₄	—	29	1	no	—
60	C₂×C₄	—	29	2	no	—
61	C₂×C₄	—	29	2	no	—
62	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
63	C₈	—	29	2	no	—
64	C₈	C₈×D₂₉	1	1	yes	characteristic
65	C₈	C₂×C₄×D₂₉	1	1	yes	characteristic
66	C₂²	—	29	2	no	—
67	C₂²	—	58	2	no	—
68	C₂²	C₁₆×D₂₉	1	1	yes	characteristic
69	C₄	—	29	2	no	—
70	C₄	C₁₆×D₂₉	1	1	yes	characteristic
71	C₄	C₂×C₈×D₂₉	1	1	yes	characteristic
72	C₂	—	58	2	no	—
73	C₂	#14270996	1	2	yes	direct product factor
74	C₂	C₂×C₁₆×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×D₂₉
commutator	C₂×C₂₉	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₂₉
Fitting	C₂×C₂₉×C₃₂	C₂
socle	C₂²×C₂₉	C₂×C₁₆
prime radical	C₂²×D₂₉	C₁₆
cosocle	C₁₆×C₂₉	C₂³
hypercenter	C₂×C₃₂	D₂₉
hypocenter	C₂₉	C₂×M₆₄
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #14270996	C₂	direct (N × H)
3. C₂×#11745142	C₂	semidirect
4. C₂×C₂₉×C₃₂	C₂	semidirect
10. C₂₉×C₃₂	C₂²	semidirect
11. #11745142	C₂²	semidirect
38. C₂×C₃₂	D₂₉	semidirect
39. C₂×C₂₉	M₆₄	semidirect
48. C₃₂	C₂×D₂₉	semidirect
49. C₂₉	C₂×M₆₄	semidirect
73. C₂	#14270996	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×C₁₆×D₂₉	2
#14270996	2
C₂×#11745142	2
C₂×C₂₉×C₃₂	2
C₂×M₆₄	29

Subgroups — C2×#14270996 #16821783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14270996 #16821783