Subgroups — #14271374

Order 1856.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₆	C₂	1	2	yes	maximal
2	#11745231	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₅₈	C₂	1	1	yes	maximal, characteristic
4	C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#11745164	C₂	1	2	yes	maximal
6	C₂×Dic₅₈	C₂²	1	2	yes	—
7	C₂×Dic₅₈	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₉	C₂²	1	2	yes	—
9	C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₂₉	—	2	1	no	—
11	C₄⋊Dic₂₉	—	2	1	no	—
12	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
13	#90779	—	2	1	no	—
14	C₄×Dic₂₉	—	2	1	no	—
15	Dic₁₁₆	—	2	4	no	—
16	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₉	—	2	1	no	—
20	C₂×Dic₂₉	—	2	1	no	—
21	C₂×Dic₂₉	—	2	2	no	—
22	Dic₅₈	—	2	1	no	—
23	Dic₅₈	—	2	2	no	—
24	Dic₅₈	—	2	2	no	—
25	Dic₅₈	D₄	1	2	yes	—
26	C₈×C₂₉	—	2	2	no	—
27	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
28	C₄×C₂₉	—	2	1	no	—
29	C₄×C₂₉	Q₁₆	1	2	yes	complemented
30	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
31	C₄×C₂₉	#41	1	1	yes	characteristic
32	Dic₂₉	—	2	2	no	—
33	Dic₂₉	—	4	2	no	—
34	Dic₂₉	—	4	1	no	—
35	#462	—	29	1	no	maximal, Sylow
36	C₂×C₂₉	#121	1	1	yes	characteristic
37	C₂×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
38	C₂×C₂₉	#137	1	1	yes	characteristic
39	C₂×Q₁₆	—	29	2	no	—
40	C₄⋊Q₈	—	29	1	no	—
41	C₄×Q₈	—	29	1	no	—
42	C₄⋊C₈	D₂₉	1	1	yes	characteristic
43	#103	—	29	2	no	—
44	C₂₉	#462	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	29	1	no	—
46	C₂×Q₈	—	29	2	no	—
47	Q₁₆	—	58	4	no	—
48	C₂×C₈	C₂×D₂₉	1	2	yes	—
49	C₄⋊C₄	—	29	1	no	—
50	C₄⋊C₄	—	58	1	no	—
51	C₄⋊C₄	—	58	1	no	—
52	C₄⋊C₄	—	58	1	no	—
53	C₄²	—	58	1	no	—
54	C₄²	C₂×D₂₉	1	1	yes	characteristic
55	Q₈	—	29	2	no	—
56	Q₈	—	58	1	no	—
57	Q₈	—	58	2	no	—
58	Q₈	—	58	2	no	—
59	C₂×C₄	—	58	1	no	—
60	C₂×C₄	—	58	1	no	—
61	C₂×C₄	—	58	2	no	—
62	C₂×C₄	D₁₁₆	1	1	yes	characteristic
63	C₂×C₄	D₁₁₆	1	1	yes	characteristic
64	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
65	C₈	—	2	2	no	—
66	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	58	2	no	—
69	C₄	—	116	2	no	—
70	C₄	—	116	1	no	—
71	C₄	Dic₁₁₆	1	2	yes	complemented
72	C₄	D₄×D₂₉	1	1	yes	characteristic
73	C₄	#90809	1	1	yes	characteristic
74	C₂	#11745257	1	1	yes	characteristic
75	C₂	C₂×Dic₁₁₆	1	1	yes	characteristic
76	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×C₄⋊C₈	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₄
hypercenter	C₄⋊C₈	D₂₉
hypocenter	C₂₉	#462
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
29. C₄×C₂₉	Q₁₆	semidirect
44. C₂₉	#462	semidirect
71. C₄	Dic₁₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₁₆	2
#11745231	2
C₄×Dic₅₈	2
C₂₉×C₄⋊C₈	2
#11745164	2
#462	29