Subgroups — #16818794

Order 3712.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271529	C₂	1	3	yes	maximal
2	#14270905	C₂	1	3	yes	maximal, complemented
3	C₂₉×#564	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#125	—	2	6	no	—
5	C₂₉×#125	C₂²	1	3	yes	—
6	#11745236	C₂²	1	1	yes	characteristic
7	#11745157	—	2	6	no	—
8	#11745151	C₂²	1	3	yes	—
9	C₂×D₁₁₆	—	2	3	no	—
10	C₄⋊C₄×C₂₉	—	2	6	no	—
11	C₄⋊C₄×C₂₉	—	2	6	no	—
12	C₄⋊C₄×C₂₉	D₄	1	6	yes	—
13	C₄²×C₂₉	—	2	2	no	—
14	C₄²×C₂₉	C₂³	1	1	yes	characteristic
15	C₂×#6597	—	2	3	no	—
16	C₂²×D₂₉	—	4	1	no	—
17	C₂×C₄×C₂₉	—	2	6	no	—
18	C₂×C₄×C₂₉	C₂×D₄	1	3	yes	—
19	D₁₁₆	—	4	6	no	—
20	#6597	—	4	3	no	—
21	#1658	—	29	1	no	maximal, Sylow
22	C₂²×C₂₉	#120	1	1	yes	characteristic
23	C₂×D₂₉	—	8	3	no	—
24	C₄×C₂₉	—	2	3	no	—
25	C₄×C₂₉	—	4	6	no	—
26	#564	D₂₉	1	1	yes	characteristic, complemented
27	#490	—	29	3	no	—
28	#330	—	29	3	no	—
29	C₂×C₂₉	#454	1	3	yes	—
30	D₂₉	—	16	1	no	—
31	#127	—	29	1	no	—
32	#125	—	2	6	no	—
33	#125	C₂×D₂₉	1	3	yes	—
34	#102	—	58	6	no	—
35	#97	—	29	3	no	—
36	C₂₉	#1658	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₄	—	58	3	no	—
38	C₂×C₈	—	58	3	no	—
39	C₄⋊C₄	—	2	6	no	—
40	C₄⋊C₄	—	2	6	no	—
41	C₄⋊C₄	C₂²⋊D₂₉	1	6	yes	—
42	C₄²	—	2	2	no	—
43	C₄²	C₂²×D₂₉	1	1	yes	characteristic
44	C₂³	—	116	1	no	—
45	D₄	—	116	6	no	—
46	C₂×C₄	—	2	6	no	—
47	C₂×C₄	C₂×C₂²⋊D₂₉	1	3	yes	—
48	C₈	—	116	3	no	—
49	C₂²	—	232	3	no	—
50	C₂²	#11745315	1	1	yes	characteristic
51	C₄	—	2	3	no	—
52	C₄	—	4	6	no	—
53	C₂	—	464	1	no	—
54	C₂	#14271336	1	3	yes	—

	subgroup	G/H
center	C₂²	#11745315
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#564	C₂
socle	C₂²×C₂₉	#120
prime radical	#11745236	C₂²
hypercenter	#564	D₂₉
hypocenter	C₂₉	#1658
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #564

Complements

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

N	H ≅ G/N	type
2. #14270905	C₂	semidirect
3. C₂₉×#564	C₂	semidirect
26. #564	D₂₉	semidirect
36. C₂₉	#1658	semidirect

Maximal subgroups

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

subgroup	index
#14271529	2
#14270905	2
C₂₉×#564	2
#1658	29