Subgroups — #16819110

Order 3712.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271568	C₂	1	4	yes	maximal
2	#14271543	C₂	1	2	yes	maximal
3	C₈²×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₁₆	—	2	4	no	—
5	#11745231	C₂²	1	4	yes	—
6	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₄×C₈×C₂₉	C₂²	1	2	yes	—
8	#11745166	—	2	8	no	—
9	C₂×Dic₅₈	—	2	4	no	—
10	C₂×C₈×C₂₉	D₄	1	2	yes	—
11	C₂×C₈×C₂₉	D₄	1	4	yes	—
12	C₄²×C₂₉	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₂₉	—	2	8	no	—
14	Dic₁₁₆	—	4	8	no	—
15	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
17	C₂×Dic₂₉	—	4	4	no	—
18	Dic₅₈	—	4	8	no	—
19	C₈×C₂₉	D₈	1	4	yes	—
20	C₈×C₂₉	Q₁₆	1	8	yes	complemented
21	#1713	—	29	1	no	maximal, Sylow
22	C₂²×C₂₉	#127	1	1	yes	characteristic
23	C₄×C₂₉	C₂×D₈	1	2	yes	—
24	C₄×C₂₉	C₂×Q₁₆	1	4	yes	—
25	Dic₂₉	—	8	4	no	—
26	#500	—	29	4	no	—
27	#494	—	29	2	no	—
28	C₈²	D₂₉	1	1	yes	characteristic
29	C₂×C₂₉	#493	1	1	yes	characteristic
30	C₂×C₂₉	#494	1	2	yes	—
31	C₂×Q₁₆	—	58	4	no	—
32	C₄⋊Q₈	—	29	4	no	—
33	#107	—	58	8	no	—
34	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
35	C₄×C₈	C₂×D₂₉	1	2	yes	—
36	C₂₉	#1713	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	58	4	no	—
38	Q₁₆	—	116	8	no	—
39	C₂×C₈	D₁₁₆	1	2	yes	—
40	C₂×C₈	D₁₁₆	1	4	yes	—
41	C₄⋊C₄	—	58	8	no	—
42	C₄²	C₂²×D₂₉	1	1	yes	characteristic
43	Q₈	—	116	8	no	—
44	C₂×C₄	—	116	4	no	—
45	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
46	C₂×C₄	C₂×D₁₁₆	1	2	yes	—
47	C₈	D₂₃₂	1	4	yes	—
48	C₈	Dic₁₁₆	1	8	yes	complemented
49	C₂²	#11745236	1	1	yes	characteristic
50	C₄	—	232	4	no	—
51	C₄	C₂×D₂₃₂	1	2	yes	—
52	C₄	C₂×Dic₁₁₆	1	4	yes	—
53	C₂	#14271540	1	1	yes	characteristic
54	C₂	#14271543	1	2	yes	—

	subgroup	G/H
center	C₂²	#11745236
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₈²×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	#127
hypercenter	C₈²	D₂₉
hypocenter	C₂₉	#1713
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
20. C₈×C₂₉	Q₁₆	semidirect
36. C₂₉	#1713	semidirect
48. C₈	Dic₁₁₆	semidirect

Maximal subgroups

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

subgroup	index
#14271568	2
#14271543	2
C₈²×C₂₉	2
#1713	29