Subgroups — #14271369

Order 1856.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#90773	C₂	1	2	yes	maximal
2	C₄×D₁₁₆	C₂	1	1	yes	maximal, characteristic
3	#11745231	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745164	C₂	1	2	yes	maximal, complemented
6	C₂×D₁₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₂₉	—	2	1	no	—
8	C₂×Dic₅₈	C₂²	1	2	yes	—
9	C₂×C₈×C₂₉	C₂²	1	2	yes	—
10	C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	#90781	—	2	1	no	—
12	C₄⋊Dic₂₉	—	2	1	no	—
13	C₄⋊Dic₂₉	—	2	1	no	—
14	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
15	#90773	—	2	4	no	—
16	C₂²×D₂₉	—	2	1	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	2	no	—
21	C₂×Dic₂₉	—	2	1	no	—
22	D₁₁₆	—	2	1	no	—
23	D₁₁₆	D₄	1	2	yes	—
24	C₄×D₂₉	—	4	2	no	—
25	Dic₅₈	—	2	2	no	—
26	Dic₅₈	—	2	2	no	—
27	C₈×C₂₉	—	2	2	no	—
28	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
29	C₂×D₂₉	—	2	2	no	—
30	C₂×D₂₉	—	4	1	no	—
31	C₂×D₂₉	—	4	1	no	—
32	C₄×C₂₉	—	2	1	no	—
33	C₄×C₂₉	SD₁₆	1	2	yes	complemented
34	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
35	C₄×C₂₉	#41	1	1	yes	characteristic
36	Dic₂₉	—	4	2	no	—
37	Dic₂₉	—	4	1	no	—
38	#461	—	29	1	no	maximal, Sylow
39	C₂×C₂₉	#121	1	1	yes	characteristic
40	C₂×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
41	C₂×C₂₉	#137	1	1	yes	characteristic
42	D₂₉	—	4	2	no	—
43	C₂×SD₁₆	—	29	2	no	—
44	C₄⋊Q₈	—	29	1	no	—
45	C₄×D₄	—	29	1	no	—
46	C₄⋊C₈	D₂₉	1	1	yes	characteristic, complemented
47	#103	—	29	2	no	—
48	C₂₉	#461	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₈	—	29	2	no	—
50	C₂×D₄	—	29	1	no	—
51	C₂²×C₄	—	58	1	no	—
52	SD₁₆	—	58	4	no	—
53	C₂×C₈	C₂×D₂₉	1	2	yes	—
54	C₄⋊C₄	—	29	1	no	—
55	C₄⋊C₄	—	58	1	no	—
56	C₄⋊C₄	—	58	1	no	—
57	C₂²⋊C₄	—	58	1	no	—
58	C₄²	C₂×D₂₉	1	1	yes	characteristic
59	C₂³	—	58	1	no	—
60	Q₈	—	58	2	no	—
61	Q₈	—	58	2	no	—
62	D₄	—	29	2	no	—
63	D₄	—	58	1	no	—
64	C₂×C₄	—	58	1	no	—
65	C₂×C₄	—	58	2	no	—
66	C₂×C₄	—	116	2	no	—
67	C₂×C₄	D₁₁₆	1	1	yes	characteristic
68	C₂×C₄	D₁₁₆	1	1	yes	characteristic
69	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₂²	—	58	2	no	—
72	C₂²	—	116	1	no	—
73	C₂²	—	116	1	no	—
74	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	116	2	no	—
77	C₄	—	116	1	no	—
78	C₄	#90773	1	2	yes	complemented
79	C₄	D₄×D₂₉	1	1	yes	characteristic
80	C₄	#90809	1	1	yes	characteristic
81	C₂	—	116	2	no	—
82	C₂	#11745257	1	1	yes	characteristic
83	C₂	C₂×#90773	1	1	yes	characteristic
84	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	C₂²×C₂₉	C₂×D₄
prime radical	C₂×D₁₁₆	C₂²
hypercenter	C₄⋊C₈	D₂₉
hypocenter	C₂₉	#461
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
3. #11745231	C₂	semidirect
4. C₂₉×C₄⋊C₈	C₂	semidirect
5. #11745164	C₂	semidirect
33. C₄×C₂₉	SD₁₆	semidirect
46. C₄⋊C₈	D₂₉	semidirect
48. C₂₉	#461	semidirect
78. 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
C₄×D₁₁₆	2
#11745231	2
C₂₉×C₄⋊C₈	2
#11745164	2
#461	29