Subgroups — #14271321

Order 1856.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₅₈	C₂	1	1	yes	maximal, characteristic
2	#11745286	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₁₁₆	C₂	1	2	yes	maximal, complemented
4	C₂₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#11745164	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₉	—	2	1	no	—
8	C₂×Dic₅₈	—	2	1	no	—
9	C₂×Dic₅₈	—	2	4	no	—
10	C₂×Dic₅₈	C₂²	1	1	yes	characteristic
11	C₂×Dic₅₈	C₂²	1	2	yes	—
12	C₂×C₈×C₂₉	C₂²	1	2	yes	—
13	C₂²⋊Dic₂₉	—	2	1	no	—
14	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
15	#90779	—	2	1	no	—
16	Dic₁₁₆	—	2	4	no	—
17	C₂³×C₂₉	D₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	—	2	2	no	—
19	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
21	C₂×Dic₂₉	—	2	4	no	—
22	C₂×Dic₂₉	—	2	2	no	—
23	C₂×Dic₂₉	—	2	1	no	—
24	C₂×Dic₂₉	—	2	1	no	—
25	Dic₅₈	—	2	4	no	—
26	Dic₅₈	—	2	2	no	—
27	Dic₅₈	—	2	2	no	—
28	Dic₅₈	D₄	1	4	yes	—
29	C₈×C₂₉	—	2	2	no	—
30	C₂²×C₂₉	—	2	1	no	—
31	C₂²×C₂₉	—	2	1	no	—
32	C₂²×C₂₉	Q₁₆	1	2	yes	complemented
33	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
34	C₄×C₂₉	—	2	1	no	—
35	C₄×C₂₉	C₂×D₄	1	2	yes	—
36	Dic₂₉	—	2	4	no	—
37	Dic₂₉	—	4	1	no	—
38	Dic₂₉	—	4	1	no	—
39	#451	—	29	1	no	maximal, Sylow
40	C₂×C₂₉	—	2	2	no	—
41	C₂×C₂₉	#120	1	1	yes	characteristic
42	C₂×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
43	C₂×C₂₉	#137	1	1	yes	characteristic
44	C₂²×Q₈	—	29	1	no	—
45	C₂×Q₁₆	—	29	2	no	—
46	C₂²⋊Q₈	—	29	1	no	—
47	#103	—	29	2	no	—
48	C₂²⋊C₈	D₂₉	1	1	yes	characteristic
49	C₂₉	#451	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₈	—	29	2	no	—
51	C₂×Q₈	—	29	1	no	—
52	C₂×Q₈	—	58	4	no	—
53	C₂×Q₈	—	58	1	no	—
54	C₂²×C₄	—	58	1	no	—
55	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
56	Q₁₆	—	58	4	no	—
57	C₂×C₈	C₂×D₂₉	1	2	yes	—
58	C₄⋊C₄	—	29	1	no	—
59	C₄⋊C₄	—	58	1	no	—
60	C₂²⋊C₄	—	58	1	no	—
61	C₂³	D₁₁₆	1	1	yes	characteristic
62	Q₈	—	29	4	no	—
63	Q₈	—	58	4	no	—
64	Q₈	—	58	2	no	—
65	Q₈	—	58	2	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	58	4	no	—
68	C₂×C₄	—	58	2	no	—
69	C₂×C₄	—	58	1	no	—
70	C₂×C₄	—	58	1	no	—
71	C₂×C₄	D₁₁₆	1	1	yes	characteristic
72	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
73	C₈	—	2	2	no	—
74	C₂²	—	2	1	no	—
75	C₂²	—	2	1	no	—
76	C₂²	Dic₁₁₆	1	2	yes	complemented
77	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	58	4	no	—
80	C₄	—	116	1	no	—
81	C₄	—	116	1	no	—
82	C₄	D₄×D₂₉	1	2	yes	—
83	C₂	—	2	2	no	—
84	C₂	#11745244	1	1	yes	characteristic
85	C₂	C₂×Dic₁₁₆	1	1	yes	characteristic
86	C₂	#11745271	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	C₂³×C₂₉	D₄
hypercenter	C₂²⋊C₈	D₂₉
hypocenter	C₂₉	#451
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
3. C₂×Dic₁₁₆	C₂	semidirect
5. #11745164	C₂	semidirect
32. C₂²×C₂₉	Q₁₆	semidirect
49. C₂₉	#451	semidirect
76. C₂²	Dic₁₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₅₈	2
#11745286	2
C₂×Dic₁₁₆	2
C₂₉×C₂²⋊C₈	2
#11745164	2
#451	29