Subgroups — C₂×#14270997 #16821784

Order 3712.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270997	C₂	1	4	yes	maximal, direct product factor
2	C₂×#11745142	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₉	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₂₉	C₄	1	2	yes	—
7	C₂×C₁₆×C₂₉	C₂²	1	2	yes	—
8	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
9	#11745142	C₂²	1	4	yes	complemented
10	C₂²×C₄×C₂₉	C₈	1	1	yes	characteristic
11	C₂×C₈×C₂₉	C₈	1	2	yes	—
12	C₂×C₈×C₂₉	C₈	1	1	yes	characteristic
13	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₁₆×C₂₉	C₂×C₄	1	2	yes	—
16	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₂₉	C₂³	1	1	yes	characteristic
18	C₂³×C₂₉	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₂₉	C₁₆	1	2	yes	—
20	C₂×C₄×C₂₉	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
22	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
23	C₈×C₂₉	C₂×C₈	1	2	yes	—
24	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
25	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
26	C₂×M₆₄	—	29	1	no	maximal, Sylow
27	C₂²×C₂₉	—	2	2	no	—
28	C₂²×C₂₉	C₂×C₁₆	1	2	yes	—
29	C₂²×C₂₉	C₂×C₁₆	1	1	yes	characteristic
30	C₄×C₂₉	C₂×C₁₆	1	1	yes	characteristic
31	C₄×C₂₉	C₂×C₁₆	1	2	yes	—
32	C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
33	C₂²×C₁₆	D₂₉	1	1	yes	characteristic
34	M₆₄	—	29	4	no	—
35	C₂×C₃₂	—	29	2	no	—
36	C₂×C₂₉	—	2	2	no	—
37	C₂×C₂₉	M₆₄	1	2	yes	complemented
38	C₂×C₂₉	C₂²×C₁₆	1	1	yes	characteristic
39	C₂²×C₈	Dic₂₉	1	1	yes	characteristic
40	C₂×C₁₆	Dic₂₉	1	1	yes	characteristic
41	C₂×C₁₆	Dic₂₉	1	2	yes	—
42	C₂×C₁₆	C₂×D₂₉	1	2	yes	—
43	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
44	C₃₂	—	29	4	no	—
45	C₂₉	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₄	#6597	1	1	yes	characteristic
47	C₂×C₈	#6597	1	1	yes	characteristic
48	C₂×C₈	#6597	1	2	yes	—
49	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
50	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
51	C₁₆	C₂×Dic₂₉	1	2	yes	—
52	C₁₆	C₂×Dic₂₉	1	1	yes	characteristic
53	C₁₆	C₂²×D₂₉	1	1	yes	characteristic
54	C₂³	#90768	1	1	yes	characteristic
55	C₂×C₄	#90768	1	2	yes	—
56	C₂×C₄	#90768	1	1	yes	characteristic
57	C₂×C₄	C₂×#6597	1	2	yes	—
58	C₂×C₄	C₂×#6597	1	1	yes	characteristic
59	C₈	C₂×#6597	1	2	yes	—
60	C₈	C₂×#6597	1	1	yes	characteristic
61	C₈	C₂²×Dic₂₉	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	C₂×#90768	1	2	yes	—
64	C₂²	C₂×#90768	1	1	yes	characteristic
65	C₄	C₂×#90768	1	1	yes	characteristic
66	C₄	C₂×#90768	1	2	yes	—
67	C₄	C₂²×#6597	1	1	yes	characteristic
68	C₂	—	2	2	no	—
69	C₂	#14270997	1	2	yes	direct product factor
70	C₂	C₂²×#90768	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #14270997	C₂	direct (N × H)
2. C₂×#11745142	C₂	semidirect
9. #11745142	C₂²	semidirect
37. C₂×C₂₉	M₆₄	semidirect
45. C₂₉	C₂×M₆₄	semidirect
69. C₂	#14270997	direct (N × H)

Maximal subgroups

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

subgroup	index
#14270997	2
C₂×#11745142	2
C₂²×C₁₆×C₂₉	2
C₂×M₆₄	29

Subgroups — C2×#14270997 #16821784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14270997 #16821784