Subgroups — #14271364

Order 1856.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#90773	C₂	1	2	yes	maximal, complemented
2	#11745236	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₅₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745169	C₂	1	2	yes	maximal, complemented
6	C₂×D₁₁₆	—	2	1	no	—
7	C₂×D₁₁₆	—	2	1	no	—
8	C₂×D₁₁₆	C₂²	1	2	yes	—
9	C₂×Dic₅₈	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₂₉	C₂²	1	2	yes	—
11	C₄²×C₂₉	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
13	#90779	—	2	1	no	—
14	C₄×Dic₂₉	—	2	1	no	—
15	#90773	—	2	4	no	—
16	C₂²×D₂₉	—	2	2	no	—
17	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
19	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
20	C₂×Dic₂₉	—	2	1	no	—
21	C₂×Dic₂₉	—	2	1	no	—
22	D₁₁₆	—	2	2	no	—
23	D₁₁₆	—	2	2	no	—
24	D₁₁₆	—	4	2	no	—
25	D₁₁₆	—	4	2	no	—
26	Dic₅₈	—	2	1	no	—
27	Dic₅₈	D₄	1	2	yes	complemented
28	C₈×C₂₉	—	2	2	no	—
29	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
30	C₂×D₂₉	—	4	2	no	—
31	C₂×D₂₉	—	4	2	no	—
32	C₂×D₂₉	—	4	2	no	—
33	C₄×C₂₉	—	2	1	no	—
34	C₄×C₂₉	SD₁₆	1	2	yes	complemented
35	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
36	C₄×C₂₉	#41	1	1	yes	characteristic
37	Dic₂₉	—	2	2	no	—
38	Dic₂₉	—	4	1	no	—
39	#460	—	29	1	no	maximal, Sylow
40	C₂×C₂₉	#121	1	1	yes	characteristic
41	C₂×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
43	D₂₉	—	8	2	no	—
44	C₂×SD₁₆	—	29	2	no	—
45	#127	—	29	1	no	—
46	C₄×Q₈	—	29	1	no	—
47	C₄⋊C₈	D₂₉	1	1	yes	characteristic, complemented
48	#102	—	29	2	no	—
49	C₂₉	#460	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₈	—	29	1	no	—
51	C₂×D₄	—	29	2	no	—
52	C₂×D₄	—	58	1	no	—
53	C₂×D₄	—	58	1	no	—
54	SD₁₆	—	58	4	no	—
55	C₂×C₈	C₂×D₂₉	1	2	yes	—
56	C₄⋊C₄	—	29	1	no	—
57	C₄⋊C₄	—	58	1	no	—
58	C₄²	—	58	1	no	—
59	C₄²	C₂×D₂₉	1	1	yes	characteristic
60	C₂³	—	58	2	no	—
61	Q₈	—	29	2	no	—
62	Q₈	—	58	1	no	—
63	D₄	—	58	2	no	—
64	D₄	—	58	2	no	—
65	D₄	—	116	2	no	—
66	D₄	—	116	2	no	—
67	C₂×C₄	—	58	1	no	—
68	C₂×C₄	—	58	1	no	—
69	C₂×C₄	D₁₁₆	1	1	yes	characteristic
70	C₂×C₄	D₁₁₆	1	1	yes	characteristic
71	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₂²	—	116	2	no	—
74	C₂²	—	116	2	no	—
75	C₂²	—	116	2	no	—
76	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	58	2	no	—
79	C₄	—	116	1	no	—
80	C₄	#90773	1	2	yes	complemented
81	C₄	D₄×D₂₉	1	1	yes	characteristic
82	C₄	#90809	1	1	yes	characteristic
83	C₂	—	232	2	no	—
84	C₂	#11745257	1	1	yes	characteristic
85	C₂	C₂×#90773	1	1	yes	characteristic
86	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×C₄⋊C₈	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	#11745236	C₂
hypercenter	C₄⋊C₈	D₂₉
hypocenter	C₂₉	#460
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#90773	C₂	semidirect
3. C₄×Dic₅₈	C₂	semidirect
4. C₂₉×C₄⋊C₈	C₂	semidirect
5. #11745169	C₂	semidirect
27. Dic₅₈	D₄	semidirect
34. C₄×C₂₉	SD₁₆	semidirect
47. C₄⋊C₈	D₂₉	semidirect
49. C₂₉	#460	semidirect
80. C₄	#90773	semidirect

Maximal subgroups

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

subgroup	index
C₂×#90773	2
#11745236	2
C₄×Dic₅₈	2
C₂₉×C₄⋊C₈	2
#11745169	2
#460	29