Subgroups — #14270933

Order 1856.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×#90777	C₂	1	1	yes	maximal, characteristic
3	C₂×#90777	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
5	C₄⋊C₄×C₂₉	—	2	1	no	—
6	C₂²⋊C₄×C₂₉	C₄	1	2	yes	—
7	C₄²×C₂₉	—	2	1	no	—
8	#90777	—	2	1	no	—
9	#90777	—	2	1	no	—
10	#90777	—	2	1	no	—
11	#90777	C₄	1	2	yes	complemented
12	C₂×#6597	—	2	1	no	—
13	C₂×#6597	C₄	1	2	yes	complemented
14	C₂³×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₉	—	2	2	no	—
16	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
19	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
21	C₂×C₄×C₂₉	Q₈	1	1	yes	characteristic
22	#6597	—	2	2	no	—
23	#6597	—	2	2	no	—
24	C₂²×C₂₉	—	4	1	no	—
25	C₂²×C₂₉	C₄²	1	1	yes	characteristic
26	C₂²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
28	C₄×C₂₉	—	4	2	no	—
29	C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
33	#344	—	29	1	no	maximal, Sylow
34	C₂×C₂₉	—	2	1	no	—
35	C₂×C₂₉	—	2	1	no	—
36	C₂×C₂₉	—	2	1	no	—
37	C₂×C₂₉	#95	1	1	yes	characteristic
38	C₂×M₁₆	—	29	1	no	—
39	C₂×M₁₆	—	29	1	no	—
40	#117	D₂₉	1	1	yes	characteristic
41	C₂₉	#344	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
43	M₁₆	—	29	2	no	—
44	M₁₆	—	58	1	no	—
45	M₁₆	—	58	1	no	—
46	M₁₆	—	58	1	no	—
47	C₂×C₈	—	29	2	no	—
48	C₂×C₈	—	58	1	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₂²⋊C₄	Dic₂₉	1	2	yes	—
51	C₄²	—	2	1	no	—
52	C₂³	C₂×Dic₂₉	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	Dic₅₈	1	1	yes	characteristic
55	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
56	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
57	C₂×C₄	D₁₁₆	1	1	yes	characteristic
58	C₂×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
59	C₂×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
60	C₈	—	58	2	no	—
61	C₈	—	58	2	no	—
62	C₂²	—	4	1	no	—
63	C₂²	C₄×Dic₂₉	1	1	yes	characteristic
64	C₂²	C₄⋊Dic₂₉	1	1	yes	characteristic
65	C₂²	C₂²⋊Dic₂₉	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	#90779	1	1	yes	characteristic
68	C₄	#90779	1	1	yes	characteristic
69	C₄	#90781	1	1	yes	characteristic
70	C₄	#90781	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	—	2	1	no	—
73	C₂	—	2	1	no	—
74	C₂	#11745179	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#90781
commutator	C₂²×C₂₉	C₄²
Frattini	C₂²×C₄	C₂×D₂₉
Fitting	C₂₉×#117	C₂
socle	C₂×C₂₉	#95
prime radical	C₂³×C₂₉	C₂×C₄
cosocle	C₂²×C₄×C₂₉	C₂²
hypercenter	#117	D₂₉
hypocenter	C₂₉	#344
LCS	G ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
11. #90777	C₄	semidirect
13. C₂×#6597	C₄	semidirect
41. C₂₉	#344	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#117	2
C₂×#90777	2
#344	29