Subgroups — #14272242

Order 1856.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×D₂₉	C₂	1	1	yes	maximal, characteristic
2	#11745348	C₂	1	2	yes	maximal, complemented
3	#11745346	C₂	1	6	yes	maximal, complemented
4	D₂₉⋊M₁₆	C₂	1	3	yes	maximal, complemented
5	C₂×#90796	C₂	1	3	yes	maximal, complemented
6	#41×C₂₉	C₄	1	1	yes	characteristic
7	#90809	C₂²	1	1	yes	characteristic
8	Q₈×D₂₉	C₄	1	1	yes	characteristic
9	#90807	C₂²	1	3	yes	—
10	D₄×D₂₉	C₄	1	3	yes	—
11	#90805	C₄	1	3	yes	—
12	C₂×C₄×D₂₉	C₂²	1	3	yes	—
13	#90800	C₂²	1	6	yes	complemented
14	C₂×#6599	C₂²	1	6	yes	complemented
15	#90796	C₂²	1	3	yes	—
16	#90796	C₂²	1	1	yes	characteristic
17	#90796	C₂²	1	6	yes	complemented
18	D₂₉⋊C₈	C₂²	1	6	yes	complemented
19	C₂²×D₂₉	C₂×C₄	1	3	yes	—
20	Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
21	D₄×C₂₉	C₂×C₄	1	3	yes	—
22	C₂×C₄×C₂₉	C₂×C₄	1	3	yes	—
23	C₂²⋊D₂₉	C₂×C₄	1	6	yes	—
24	C₂×Dic₂₉	C₂³	1	3	yes	—
25	D₁₁₆	C₂×C₄	1	3	yes	—
26	C₄×D₂₉	C₂×C₄	1	3	yes	—
27	C₄×D₂₉	C₂×C₄	1	3	yes	—
28	C₄×D₂₉	C₂³	1	3	yes	—
29	C₄×D₂₉	C₂³	1	1	yes	characteristic
30	Dic₅₈	C₂×C₄	1	3	yes	—
31	#6599	C₂³	1	2	yes	—
32	#6599	C₂³	1	6	yes	—
33	C₂²×C₂₉	C₂²×C₄	1	3	yes	—
34	C₂×D₂₉	—	4	3	no	—
35	C₂×D₂₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×D₂₉	C₂²×C₄	1	3	yes	—
37	C₄×C₂₉	C₂²×C₄	1	3	yes	—
38	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
39	Dic₂₉	C₂²×C₄	1	3	yes	—
40	Dic₂₉	C₂⁴	1	1	yes	characteristic
41	#568	—	29	1	no	maximal, Sylow
42	C₂×C₂₉	—	2	3	no	—
43	C₂×C₂₉	C₂³×C₄	1	1	yes	characteristic
44	D₂₉	—	2	1	no	—
45	D₂₉	—	2	3	no	—
46	C₂×#41	—	29	1	no	—
47	#131	—	29	6	no	—
48	#131	—	29	2	no	—
49	C₂×M₁₆	—	29	3	no	—
50	C₂×M₁₆	—	29	3	no	—
51	C₂₉	#568	1	1	yes	characteristic, complemented, Sylow
52	#41	—	29	1	no	—
53	#41	—	29	3	no	—
54	#41	—	29	3	no	—
55	#41	#1181	1	1	yes	characteristic
56	C₂×Q₈	—	29	1	no	—
57	C₂×D₄	—	29	3	no	—
58	C₂²×C₄	—	29	3	no	—
59	M₁₆	—	29	3	no	—
60	M₁₆	—	29	1	no	—
61	M₁₆	—	29	6	no	—
62	M₁₆	—	29	6	no	—
63	C₂×C₈	—	29	6	no	—
64	C₂×C₈	—	29	6	no	—
65	C₂³	—	29	3	no	—
66	Q₈	—	29	3	no	—
67	Q₈	C₂×#1181	1	1	yes	characteristic
68	D₄	—	29	6	no	—
69	D₄	—	29	3	no	—
70	D₄	C₂×#1181	1	3	yes	—
71	C₂×C₄	—	29	3	no	—
72	C₂×C₄	—	29	3	no	—
73	C₂×C₄	—	29	1	no	—
74	C₂×C₄	—	29	3	no	—
75	C₂×C₄	—	29	3	no	—
76	C₂×C₄	C₂×#1181	1	3	yes	—
77	C₈	—	29	2	no	—
78	C₈	—	29	6	no	—
79	C₂²	—	29	1	no	—
80	C₂²	—	29	3	no	—
81	C₂²	—	116	3	no	—
82	C₂²	C₂²×#1181	1	3	yes	—
83	C₄	—	29	1	no	—
84	C₄	—	29	3	no	—
85	C₄	C₂²×#1181	1	1	yes	characteristic
86	C₄	C₂²×#1181	1	3	yes	—
87	C₂	—	2	3	no	—
88	C₂	—	58	1	no	—
89	C₂	—	58	3	no	—
90	C₂	C₂³×#1181	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×#1181
commutator, socle	C₂×C₂₉	C₂³×C₄
Fitting	#41×C₂₉	C₄
prime radical	#41×D₂₉	C₂
cosocle	Dic₂₉	C₂⁴
hypercenter	#41	#1181
hypocenter	C₂₉	#568
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ #41

Complements

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

N	H ≅ G/N	type
2. #11745348	C₂	semidirect
3. #11745346	C₂	semidirect
4. D₂₉⋊M₁₆	C₂	semidirect
5. C₂×#90796	C₂	semidirect
13. #90800	C₂²	semidirect
14. C₂×#6599	C₂²	semidirect
17. #90796	C₂²	semidirect
18. D₂₉⋊C₈	C₂²	semidirect
51. C₂₉	#568	semidirect

Maximal subgroups

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

subgroup	index
#41×D₂₉	2
#11745348	2
#11745346	2
D₂₉⋊M₁₆	2
C₂×#90796	2
#568	29