Subgroups — #14272045

Order 1856.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745345	C₂	1	1	yes	maximal, characteristic
2	D₂₉⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×#90772	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
5	C₂²⋊#1181	C₄	1	2	yes	—
6	#90800	C₄	1	2	yes	complemented
7	C₄⋊#1181	—	2	1	no	—
8	C₄×#1181	—	2	1	no	—
9	#90796	—	2	1	no	—
10	D₂₉⋊C₈	—	2	1	no	—
11	C₂×C₈×C₂₉	C₄	1	1	yes	characteristic, complemented
12	C₂×#6597	C₄	1	1	yes	characteristic, complemented
13	#90772	—	2	1	no	—
14	#90772	—	2	1	no	—
15	C₂²×D₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×#1181	—	2	2	no	—
17	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
19	C₄×D₂₉	D₄	1	1	yes	characteristic
20	C₄×D₂₉	D₄	1	1	yes	characteristic
21	C₄×D₂₉	D₄	1	1	yes	characteristic
22	C₄×D₂₉	Q₈	1	1	yes	characteristic
23	#6599	—	2	2	no	—
24	C₈×C₂₉	—	2	1	no	—
25	#6597	—	2	1	no	—
26	C₂²×C₂₉	C₄²	1	1	yes	characteristic
27	C₂×D₂₉	—	4	1	no	—
28	C₂×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×D₂₉	C₄⋊C₄	1	1	yes	characteristic
30	#1181	—	4	2	no	—
31	C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
33	Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
34	Dic₂₉	C₄⋊C₄	1	1	yes	characteristic
35	#344	—	29	1	no	maximal, Sylow
36	C₂×C₂₉	—	2	1	no	—
37	C₂×C₂₉	#95	1	1	yes	characteristic
38	D₂₉	—	2	1	no	—
39	D₂₉	—	2	1	no	—
40	C₂×M₁₆	—	29	1	no	—
41	C₂×M₁₆	—	29	1	no	—
42	#117	—	29	1	no	—
43	C₂₉	#344	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₄	—	29	1	no	—
45	M₁₆	—	29	2	no	—
46	M₁₆	—	58	1	no	—
47	M₁₆	—	58	1	no	—
48	M₁₆	—	58	1	no	—
49	C₂×C₈	—	29	1	no	—
50	C₂×C₈	—	58	1	no	—
51	C₂×C₈	#1181	1	1	yes	characteristic, complemented
52	C₄⋊C₄	—	58	1	no	—
53	C₂²⋊C₄	—	29	2	no	—
54	C₄²	—	58	1	no	—
55	C₂³	—	29	1	no	—
56	C₂×C₄	—	29	1	no	—
57	C₂×C₄	—	29	1	no	—
58	C₂×C₄	—	29	1	no	—
59	C₂×C₄	—	29	1	no	—
60	C₂×C₄	—	29	1	no	—
61	C₂×C₄	—	58	2	no	—
62	C₂×C₄	C₂×#1181	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	58	2	no	—
65	C₈	—	58	1	no	—
66	C₂²	—	29	1	no	—
67	C₂²	—	29	1	no	—
68	C₂²	—	116	1	no	—
69	C₂²	C₄×#1181	1	1	yes	characteristic
70	C₄	—	29	1	no	—
71	C₄	—	29	1	no	—
72	C₄	—	116	2	no	—
73	C₄	C₄⋊#1181	1	1	yes	characteristic
74	C₄	C₂²⋊#1181	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	58	1	no	—
77	C₂	—	58	1	no	—
78	C₂	(C₂×#1181)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#1181
commutator	C₂²×C₂₉	C₄²
Frattini	C₂×C₄	C₂×#1181
Fitting	C₂×C₈×C₂₉	C₄
socle	C₂×C₂₉	#95
prime radical	C₂²×D₂₉	C₂×C₄
cosocle	C₂×C₄×D₂₉	C₂²
hypercenter	C₂×C₈	#1181
hypocenter	C₂₉	#344
LCS	G ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
6. #90800	C₄	semidirect
11. C₂×C₈×C₂₉	C₄	semidirect
12. C₂×#6597	C₄	semidirect
43. C₂₉	#344	semidirect
51. C₂×C₈	#1181	semidirect

Maximal subgroups

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

subgroup	index
#11745345	2
D₂₉⋊M₁₆	2
C₂×#90772	2
#344	29