Subgroups — C₂×#14271031 #16821882

Order 3712.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271031	C₂	1	8	yes	maximal, direct product factor
2	C₂×#11745179	C₂	1	6	yes	maximal
3	C₂²×C₄²×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₂₉	C₂²	1	3	yes	—
5	C₂³×Dic₂₉	C₂²	1	4	yes	—
6	C₂×C₄²×C₂₉	C₄	1	8	yes	complemented
7	C₂×C₄²×C₂₉	C₂²	1	4	yes	—
8	#11745179	C₂²	1	24	yes	—
9	C₂⁴×C₂₉	C₂³	1	1	yes	characteristic
10	C₂²×C₄×C₂₉	—	2	12	no	—
11	C₂²×C₄×C₂₉	C₂×C₄	1	12	yes	—
12	C₂²×C₄×C₂₉	C₂³	1	6	yes	—
13	C₂²×Dic₂₉	—	2	24	no	—
14	C₂²×Dic₂₉	C₂³	1	8	yes	—
15	C₄²×C₂₉	C₂×C₄	1	16	yes	complemented
16	C₂³×C₂₉	C₂²×C₄	1	2	yes	—
17	C₂³×C₂₉	#41	1	12	yes	—
18	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
19	C₂×C₄×C₂₉	—	2	24	no	—
20	C₂×C₄×C₂₉	—	2	12	no	—
21	C₂×C₄×C₂₉	C₂²×C₄	1	12	yes	—
22	C₂×Dic₂₉	—	2	24	no	—
23	C₂×Dic₂₉	—	4	16	no	—
24	C₂×#383	—	29	1	no	maximal, Sylow
25	C₂²×C₂₉	#117	1	12	yes	—
26	C₂²×C₂₉	#126	1	16	yes	—
27	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
28	C₂²×C₂₉	C₂×#41	1	6	yes	—
29	C₄×C₂₉	—	2	12	no	—
30	Dic₂₉	—	4	8	no	—
31	C₂²×C₄²	D₂₉	1	1	yes	characteristic
32	#383	—	29	8	no	—
33	C₂×#95	—	29	6	no	—
34	C₂×C₂₉	#383	1	8	yes	complemented
35	C₂×C₂₉	C₂×#117	1	3	yes	—
36	C₂×C₂₉	C₂×#126	1	4	yes	—
37	C₂³×C₄	—	29	4	no	—
38	C₂³×C₄	C₂×D₂₉	1	3	yes	—
39	C₂×C₄²	Dic₂₉	1	8	yes	complemented
40	C₂×C₄²	C₂×D₂₉	1	4	yes	—
41	#95	—	29	24	no	—
42	C₂₉	C₂×#383	1	1	yes	characteristic, complemented, Sylow
43	C₂⁴	C₂²×D₂₉	1	1	yes	characteristic
44	C₂²×C₄	—	2	12	no	—
45	C₂²×C₄	—	29	8	no	—
46	C₂²×C₄	—	58	24	no	—
47	C₂²×C₄	C₂×Dic₂₉	1	12	yes	—
48	C₂²×C₄	C₂²×D₂₉	1	6	yes	—
49	C₄²	C₂×Dic₂₉	1	16	yes	complemented
50	C₂³	#90805	1	12	yes	—
51	C₂³	C₂²×Dic₂₉	1	2	yes	—
52	C₂³	C₂³×D₂₉	1	1	yes	characteristic
53	C₂×C₄	—	2	24	no	—
54	C₂×C₄	—	2	12	no	—
55	C₂×C₄	—	58	24	no	—
56	C₂×C₄	—	116	16	no	—
57	C₂×C₄	C₂²×Dic₂₉	1	12	yes	—
58	C₂²	#11745238	1	16	yes	—
59	C₂²	#11745288	1	12	yes	—
60	C₂²	C₂×#90805	1	6	yes	—
61	C₂²	C₂³×Dic₂₉	1	1	yes	characteristic
62	C₄	—	2	12	no	—
63	C₄	—	116	8	no	—
64	C₂	#14271031	1	8	yes	direct product factor
65	C₂	C₂×#11745288	1	3	yes	—
66	C₂	C₂×#11745238	1	4	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₂₉
commutator	C₂²×C₂₉	C₂³×C₄
Frattini	C₂³	C₂³×D₂₉
Fitting	C₂²×C₄²×C₂₉	C₂
socle, prime radical	C₂⁴×C₂₉	C₂³
cosocle	C₂³×C₂₉	C₂⁴
hypercenter	C₂²×C₄²	D₂₉
hypocenter	C₂₉	C₂×#383
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
1. #14271031	C₂	direct (N × H)
6. C₂×C₄²×C₂₉	C₄	semidirect
15. C₄²×C₂₉	C₂×C₄	semidirect
34. C₂×C₂₉	#383	semidirect
39. C₂×C₄²	Dic₂₉	semidirect
42. C₂₉	C₂×#383	semidirect
49. C₄²	C₂×Dic₂₉	semidirect
64. C₂	#14271031	direct (N × H)

Maximal subgroups

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

subgroup	index
#14271031	2
C₂×#11745179	2
C₂²×C₄²×C₂₉	2
C₂×#383	29

Subgroups — C2×#14271031 #16821882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14271031 #16821882