Subgroups — #16817794

Order 3712.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#90772	C₂	1	3	yes	maximal
2	#14270884	C₂	1	3	yes	maximal, complemented
3	C₈²×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90772	C₄	1	6	yes	—
5	C₄²×D₂₉	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₂₉	C₂²	1	3	yes	—
7	#11745163	C₄	1	6	yes	—
8	C₄×#6597	C₂²	1	3	yes	—
9	C₂×C₄×D₂₉	C₂×C₄	1	3	yes	—
10	C₂×C₈×C₂₉	C₂×C₄	1	6	yes	—
11	C₄²×C₂₉	C₂³	1	1	yes	characteristic
12	C₄×Dic₂₉	C₂×C₄	1	3	yes	—
13	C₂×#6597	C₂×C₄	1	6	yes	—
14	#90772	—	2	12	no	—
15	C₂²×D₂₉	C₄²	1	1	yes	characteristic
16	C₂×C₄×C₂₉	C₂²×C₄	1	3	yes	—
17	C₂×Dic₂₉	C₄²	1	3	yes	—
18	C₄×D₂₉	—	2	6	no	—
19	C₈×C₂₉	M₁₆	1	12	yes	complemented
20	#6597	—	2	6	no	—
21	#1455	—	29	1	no	maximal, Sylow
22	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
23	C₂×D₂₉	—	2	3	no	—
24	C₄×C₂₉	C₂×M₁₆	1	6	yes	—
25	Dic₂₉	—	2	3	no	—
26	C₄×M₁₆	—	29	3	no	—
27	#322	—	29	3	no	—
28	C₈²	D₂₉	1	1	yes	characteristic, complemented
29	C₂×C₂₉	C₄×M₁₆	1	3	yes	—
30	D₂₉	—	4	1	no	—
31	C₂×M₁₆	—	29	6	no	—
32	C₂×C₄²	—	29	1	no	—
33	#97	—	29	6	no	—
34	C₄×C₈	—	29	3	no	—
35	C₄×C₈	C₂×D₂₉	1	3	yes	—
36	C₂₉	#1455	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₄	—	29	3	no	—
38	M₁₆	—	58	12	no	—
39	C₂×C₈	—	29	6	no	—
40	C₂×C₈	C₄×D₂₉	1	6	yes	—
41	C₄²	—	29	3	no	—
42	C₄²	C₂²×D₂₉	1	1	yes	characteristic
43	C₂³	—	29	1	no	—
44	C₂×C₄	—	29	3	no	—
45	C₂×C₄	—	58	6	no	—
46	C₂×C₄	C₂×C₄×D₂₉	1	3	yes	—
47	C₈	—	58	6	no	—
48	C₈	#90772	1	12	yes	complemented
49	C₂²	—	58	3	no	—
50	C₂²	C₄²×D₂₉	1	1	yes	characteristic
51	C₄	—	58	3	no	—
52	C₄	C₂×#90772	1	6	yes	—
53	C₂	—	116	1	no	—
54	C₂	C₄×#90772	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂×C₄²
Fitting	C₈²×C₂₉	C₂
prime radical	C₂²×D₂₉	C₄²
cosocle	C₄²×C₂₉	C₂³
hypercenter	C₈²	D₂₉
hypocenter	C₂₉	#1455
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #14270884	C₂	semidirect
3. C₈²×C₂₉	C₂	semidirect
19. C₈×C₂₉	M₁₆	semidirect
28. C₈²	D₂₉	semidirect
36. C₂₉	#1455	semidirect
48. C₈	#90772	semidirect

Maximal subgroups

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

subgroup	index
C₄×#90772	2
#14270884	2
C₈²×C₂₉	2
#1455	29