Subgroups — #16819079

Order 3712.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271561	C₂	1	3	yes	maximal, complemented
2	#14271536	C₂	1	3	yes	maximal
3	C₈²×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90773	—	2	6	no	—
5	#11745236	C₂²	1	1	yes	characteristic
6	#11745231	C₂²	1	3	yes	—
7	C₄×C₈×C₂₉	C₂²	1	3	yes	—
8	#11745165	—	2	6	no	—
9	C₂×D₁₁₆	—	2	3	no	—
10	C₂×Dic₅₈	—	2	3	no	—
11	C₂×C₈×C₂₉	D₄	1	6	yes	—
12	C₄²×C₂₉	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₂₉	—	2	6	no	—
14	#90773	—	4	12	no	—
15	C₂²×D₂₉	—	4	1	no	—
16	C₂×C₄×C₂₉	C₂×D₄	1	3	yes	—
17	C₂×Dic₂₉	—	4	3	no	—
18	D₁₁₆	—	4	6	no	—
19	Dic₅₈	—	4	6	no	—
20	C₈×C₂₉	SD₁₆	1	12	yes	complemented
21	#1705	—	29	1	no	maximal, Sylow
22	C₂²×C₂₉	#127	1	1	yes	characteristic
23	C₂×D₂₉	—	8	3	no	—
24	C₄×C₂₉	C₂×SD₁₆	1	6	yes	—
25	Dic₂₉	—	8	3	no	—
26	#498	—	29	3	no	—
27	#492	—	29	3	no	—
28	C₈²	D₂₉	1	1	yes	characteristic, complemented
29	C₂×C₂₉	#492	1	3	yes	—
30	D₂₉	—	16	1	no	—
31	C₂×SD₁₆	—	58	6	no	—
32	C₄⋊Q₈	—	29	3	no	—
33	#127	—	29	1	no	—
34	#106	—	58	6	no	—
35	C₄×C₈	C₂×D₂₉	1	3	yes	—
36	C₂₉	#1705	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	58	3	no	—
38	C₂×D₄	—	58	3	no	—
39	SD₁₆	—	116	12	no	—
40	C₂×C₈	D₁₁₆	1	6	yes	—
41	C₄⋊C₄	—	58	6	no	—
42	C₄²	C₂²×D₂₉	1	1	yes	characteristic
43	C₂³	—	116	1	no	—
44	Q₈	—	116	6	no	—
45	D₄	—	116	6	no	—
46	C₂×C₄	—	116	3	no	—
47	C₂×C₄	C₂×D₁₁₆	1	3	yes	—
48	C₈	#90773	1	12	yes	complemented
49	C₂²	—	232	3	no	—
50	C₂²	#11745236	1	1	yes	characteristic
51	C₄	—	232	3	no	—
52	C₄	C₂×#90773	1	6	yes	—
53	C₂	—	464	1	no	—
54	C₂	#14271536	1	3	yes	—

	subgroup	G/H
center	C₂²	#11745236
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₈²×C₂₉	C₂
socle	C₂²×C₂₉	#127
prime radical	#11745236	C₂²
hypercenter	C₈²	D₂₉
hypocenter	C₂₉	#1705
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #14271561	C₂	semidirect
3. C₈²×C₂₉	C₂	semidirect
20. C₈×C₂₉	SD₁₆	semidirect
28. C₈²	D₂₉	semidirect
36. C₂₉	#1705	semidirect
48. C₈	#90773	semidirect

Maximal subgroups

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

subgroup	index
#14271561	2
#14271536	2
C₈²×C₂₉	2
#1705	29