Subgroups — #14270932

Order 1856.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#90777	C₂	1	2	yes	maximal
3	C₂²×C₄×C₂₉	C₄	1	2	yes	—
4	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
5	C₄⋊C₄×C₂₉	—	2	2	no	—
6	#90777	—	2	2	no	—
7	#90777	C₄	1	4	yes	complemented
8	C₂×#6597	—	2	2	no	—
9	C₂³×C₂₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₂₉	—	2	2	no	—
11	C₂×C₄×C₂₉	—	4	2	no	—
12	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
13	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
14	C₂×C₄×C₂₉	D₄	1	2	yes	—
15	C₂×C₄×C₂₉	Q₈	1	1	yes	characteristic
16	#6597	—	2	4	no	—
17	C₂²×C₂₉	—	2	1	no	—
18	C₂²×C₂₉	—	2	1	no	—
19	C₂²×C₂₉	C₄²	1	1	yes	characteristic
20	C₂²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₂²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
22	C₄×C₂₉	—	4	2	no	—
23	C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
24	C₄×C₂₉	C₄⋊C₄	1	2	yes	—
25	#343	—	29	1	no	maximal, Sylow
26	C₂×C₂₉	—	2	1	no	—
27	C₂×C₂₉	—	2	1	no	—
28	C₂×C₂₉	#95	1	1	yes	characteristic
29	C₂×C₂₉	#100	1	1	yes	characteristic
30	C₂×C₂₉	#101	1	1	yes	characteristic
31	C₂×M₁₆	—	29	2	no	—
32	C₂×C₄⋊C₄	D₂₉	1	1	yes	characteristic
33	C₂₉	#343	1	1	yes	characteristic, complemented, Sylow
34	C₂²×C₄	Dic₂₉	1	2	yes	—
35	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
36	M₁₆	—	29	4	no	—
37	M₁₆	—	58	2	no	—
38	C₂×C₈	—	58	2	no	—
39	C₄⋊C₄	—	2	2	no	—
40	C₂³	C₂×Dic₂₉	1	1	yes	characteristic
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	—	4	2	no	—
43	C₂×C₄	Dic₅₈	1	1	yes	characteristic
44	C₂×C₄	C₄×D₂₉	1	2	yes	—
45	C₂×C₄	D₁₁₆	1	1	yes	characteristic
46	C₂×C₄	C₂²⋊D₂₉	1	2	yes	—
47	C₈	—	58	4	no	—
48	C₂²	—	2	1	no	—
49	C₂²	—	2	1	no	—
50	C₂²	C₄×Dic₂₉	1	1	yes	characteristic
51	C₂²	C₄⋊Dic₂₉	1	1	yes	characteristic
52	C₂²	C₂²⋊Dic₂₉	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	#90779	1	2	yes	—
55	C₄	#90781	1	2	yes	—
56	C₂	—	2	1	no	—
57	C₂	—	2	1	no	—
58	C₂	#11745179	1	1	yes	characteristic
59	C₂	#11745181	1	1	yes	characteristic
60	C₂	#11745184	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊Dic₂₉
commutator	C₂²×C₂₉	C₄²
Frattini	C₂²×C₄	C₂×D₂₉
Fitting	C₂×C₄⋊C₄×C₂₉	C₂
socle	C₂²×C₂₉	C₂²⋊C₄
prime radical	C₂³×C₂₉	C₂×C₄
cosocle	C₂²×C₄×C₂₉	C₂²
hypercenter	C₂×C₄⋊C₄	D₂₉
hypocenter	C₂₉	#343
LCS	G ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
7. #90777	C₄	semidirect
33. C₂₉	#343	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×C₂₉	2
C₂×#90777	2
#343	29