Subgroups — #14271281

Order 1856.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745266	C₂	1	1	yes	maximal, characteristic
2	#11745263	C₂	1	2	yes	maximal, complemented
3	C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745167	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745153	C₂	1	2	yes	maximal, complemented
6	#90805	C₂²	1	2	yes	—
7	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	#90777	C₂²	1	2	yes	—
11	Dic₁₁₆	C₄	1	1	yes	characteristic, complemented
12	D₂₃₂	C₄	1	1	yes	characteristic, complemented
13	#90773	C₄	1	2	yes	complemented
14	#90772	—	2	2	no	—
15	C₈×D₂₉	—	2	2	no	—
16	C₂×C₄×C₂₉	—	2	1	no	—
17	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	C₂²⋊D₂₉	—	2	2	no	—
19	D₁₁₆	C₂×C₄	1	2	yes	—
20	C₄×D₂₉	—	2	2	no	—
21	Dic₅₈	C₂×C₄	1	2	yes	—
22	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
23	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
24	C₈×C₂₉	D₄	1	1	yes	characteristic
25	C₈×C₂₉	D₄	1	1	yes	characteristic
26	#6597	—	2	2	no	—
27	C₂²×C₂₉	#41	1	1	yes	characteristic
28	C₂×D₂₉	—	2	2	no	—
29	C₄×C₂₉	—	2	2	no	—
30	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
32	Dic₂₉	—	2	2	no	—
33	#443	—	29	1	no	maximal, Sylow
34	C₂×C₂₉	—	2	1	no	—
35	C₂×C₂₉	C₄×D₄	1	1	yes	characteristic
36	D₂₉	—	4	2	no	—
37	#135	—	29	1	no	—
38	#131	—	29	2	no	—
39	#108	—	29	1	no	—
40	#104	—	29	2	no	—
41	C₄×C₈	D₂₉	1	1	yes	characteristic, complemented
42	C₂₉	#443	1	1	yes	characteristic, complemented, Sylow
43	#41	—	29	2	no	—
44	Q₁₆	—	29	1	no	—
45	SD₁₆	—	29	2	no	—
46	D₈	—	29	1	no	—
47	M₁₆	—	29	2	no	—
48	M₁₆	—	58	2	no	—
49	C₂×C₈	—	58	2	no	—
50	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
51	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
52	C₄²	C₂×D₂₉	1	1	yes	characteristic
53	Q₈	—	29	2	no	—
54	D₄	—	29	2	no	—
55	D₄	—	58	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	58	2	no	—
58	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
59	C₈	—	58	2	no	—
60	C₈	C₄×D₂₉	1	1	yes	characteristic
61	C₈	C₄×D₂₉	1	1	yes	characteristic
62	C₈	D₁₁₆	1	1	yes	characteristic
63	C₈	D₁₁₆	1	1	yes	characteristic
64	C₂²	—	58	2	no	—
65	C₂²	#90805	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	—	58	2	no	—
68	C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
69	C₄	C₂×D₁₁₆	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	116	2	no	—
72	C₂	C₄×D₁₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₁₁₆
commutator	C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₄×C₈×C₂₉	C₂
socle	C₂×C₂₉	C₄×D₄
prime radical	#11745266	C₂
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₄×C₈	D₂₉
hypocenter	C₂₉	#443
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #11745263	C₂	semidirect
3. C₄×C₈×C₂₉	C₂	semidirect
4. #11745167	C₂	semidirect
5. #11745153	C₂	semidirect
11. Dic₁₁₆	C₄	semidirect
12. D₂₃₂	C₄	semidirect
13. #90773	C₄	semidirect
41. C₄×C₈	D₂₉	semidirect
42. C₂₉	#443	semidirect

Maximal subgroups

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

subgroup	index
#11745266	2
#11745263	2
C₄×C₈×C₂₉	2
#11745167	2
#11745153	2
#443	29