Subgroups — #14271482

Order 1856.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745292	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745169	C₂	1	2	yes	maximal, complemented
5	#11745165	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊D₂₉	—	2	1	no	—
8	C₂²×Dic₂₉	—	2	1	no	—
9	C₂×D₁₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₂₉	C₂²	1	2	yes	—
11	#90781	—	2	1	no	—
12	C₄⋊Dic₂₉	—	2	1	no	—
13	C₄⋊Dic₂₉	C₂²	1	2	yes	—
14	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
15	C₂³×C₂₉	D₄	1	1	yes	characteristic
16	C₂²×D₂₉	—	2	1	no	—
17	C₂×C₄×C₂₉	—	2	2	no	—
18	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
19	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
20	C₂²⋊D₂₉	—	4	2	no	—
21	C₂×Dic₂₉	—	2	2	no	—
22	C₂×Dic₂₉	—	2	1	no	—
23	C₂×Dic₂₉	—	4	2	no	—
24	D₁₁₆	—	2	2	no	—
25	C₈×C₂₉	—	2	2	no	—
26	C₂²×C₂₉	—	2	1	no	—
27	C₂²×C₂₉	—	2	1	no	—
28	C₂²×C₂₉	SD₁₆	1	2	yes	—
29	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
30	C₂×D₂₉	—	4	1	no	—
31	C₂×D₂₉	—	4	1	no	—
32	C₂×D₂₉	—	4	1	no	—
33	C₄×C₂₉	—	2	1	no	—
34	C₄×C₂₉	#41	1	2	yes	—
35	Dic₂₉	—	4	1	no	—
36	Dic₂₉	—	4	2	no	—
37	#481	—	29	1	no	maximal, Sylow
38	C₂×C₂₉	—	2	2	no	—
39	C₂×C₂₉	#123	1	1	yes	characteristic
40	C₂×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
41	C₂×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
42	D₂₉	—	8	1	no	—
43	#121	—	29	1	no	—
44	C₂×C₄⋊C₄	—	29	1	no	—
45	#106	—	29	2	no	—
46	#102	—	29	2	no	—
47	C₂²⋊C₈	D₂₉	1	1	yes	characteristic, complemented
48	C₂₉	#481	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₄	—	29	1	no	—
50	C₂×D₄	—	58	1	no	—
51	C₂²×C₄	—	58	1	no	—
52	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
53	C₂×C₈	C₂×D₂₉	1	2	yes	—
54	C₄⋊C₄	—	29	2	no	—
55	C₄⋊C₄	—	29	1	no	—
56	C₄⋊C₄	—	58	1	no	—
57	C₂²⋊C₄	—	58	1	no	—
58	C₂³	—	58	1	no	—
59	C₂³	D₁₁₆	1	1	yes	characteristic
60	D₄	—	58	2	no	—
61	D₄	—	116	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	58	1	no	—
64	C₂×C₄	—	58	2	no	—
65	C₂×C₄	—	116	2	no	—
66	C₂×C₄	D₁₁₆	1	1	yes	characteristic
67	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
68	C₈	—	2	2	no	—
69	C₂²	—	2	1	no	—
70	C₂²	—	2	1	no	—
71	C₂²	—	116	1	no	—
72	C₂²	—	116	1	no	—
73	C₂²	—	116	1	no	—
74	C₂²	#90773	1	2	yes	—
75	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	116	1	no	—
78	C₄	—	116	2	no	—
79	C₄	#90807	1	2	yes	—
80	C₂	—	2	2	no	—
81	C₂	—	232	1	no	—
82	C₂	#11745248	1	1	yes	characteristic
83	C₂	C₂×#90773	1	1	yes	characteristic
84	C₂	#11745270	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₁₆
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×C₂²⋊C₈	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	#11745292	C₂
hypercenter	C₂²⋊C₈	D₂₉
hypocenter	C₂₉	#481
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊Dic₂₉	C₂	semidirect
3. C₂₉×C₂²⋊C₈	C₂	semidirect
4. #11745169	C₂	semidirect
5. #11745165	C₂	semidirect
47. C₂²⋊C₈	D₂₉	semidirect
48. C₂₉	#481	semidirect

Maximal subgroups

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

subgroup	index
#11745292	2
C₂×C₄⋊Dic₂₉	2
C₂₉×C₂²⋊C₈	2
#11745169	2
#11745165	2
#481	29