Subgroups — #14271606

Order 1856.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745266	C₂	1	1	yes	maximal, characteristic
3	C₂₉×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₂₃₂	C₂	1	2	yes	maximal, complemented
5	#11745148	C₂	1	2	yes	maximal, complemented
6	#90805	—	2	1	no	—
7	C₂×Dic₅₈	—	2	1	no	—
8	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	Dic₁₁₆	—	2	1	no	—
10	Dic₁₁₆	C₂²	1	2	yes	—
11	Dic₁₁₆	C₂²	1	1	yes	characteristic
12	D₂₃₂	C₂²	1	1	yes	characteristic
13	#90773	—	2	1	no	—
14	C₁₆×C₂₉	C₂²	1	2	yes	—
15	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
16	C₂²⋊D₂₉	—	4	1	no	—
17	C₂×Dic₂₉	—	4	1	no	—
18	D₁₁₆	—	2	1	no	—
19	C₄×D₂₉	—	4	1	no	—
20	Dic₅₈	—	2	1	no	—
21	Dic₅₈	—	2	2	no	—
22	Dic₅₈	—	4	1	no	—
23	C₈×C₂₉	D₄	1	1	yes	characteristic
24	C₈×C₂₉	C₂³	1	1	yes	characteristic
25	C₂²×C₂₉	D₈	1	1	yes	characteristic
26	C₂×D₂₉	—	4	1	no	—
27	C₄×C₂₉	D₈	1	1	yes	characteristic
28	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
29	Dic₂₉	—	4	2	no	—
30	Dic₂₉	—	4	1	no	—
31	#510	—	29	1	no	maximal, Sylow
32	C₂×C₂₉	—	2	1	no	—
33	C₂×C₂₉	C₂×D₈	1	1	yes	characteristic
34	D₂₉	—	8	1	no	—
35	#135	—	29	1	no	—
36	C₂×Q₁₆	—	29	1	no	—
37	Q₃₂	—	29	2	no	—
38	SD₃₂	—	29	2	no	—
39	M₃₂	D₂₉	1	1	yes	characteristic, complemented
40	C₂₉	#510	1	1	yes	characteristic, complemented, Sylow
41	#41	—	58	1	no	—
42	C₂×Q₈	—	58	1	no	—
43	Q₁₆	—	29	2	no	—
44	Q₁₆	—	29	1	no	—
45	Q₁₆	—	58	1	no	—
46	SD₁₆	—	58	1	no	—
47	D₈	—	29	1	no	—
48	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
49	C₁₆	C₂×D₂₉	1	2	yes	—
50	Q₈	—	58	1	no	—
51	Q₈	—	58	2	no	—
52	Q₈	—	116	1	no	—
53	D₄	—	58	1	no	—
54	D₄	—	116	1	no	—
55	C₂×C₄	—	116	1	no	—
56	C₂×C₄	—	116	1	no	—
57	C₂×C₄	D₁₁₆	1	1	yes	characteristic
58	C₈	D₁₁₆	1	1	yes	characteristic
59	C₈	C₂²×D₂₉	1	1	yes	characteristic
60	C₂²	—	116	1	no	—
61	C₂²	D₂₃₂	1	1	yes	characteristic
62	C₄	—	116	1	no	—
63	C₄	—	116	2	no	—
64	C₄	D₂₃₂	1	1	yes	characteristic
65	C₄	C₂×D₁₁₆	1	1	yes	characteristic
66	C₂	—	2	1	no	—
67	C₂	—	232	1	no	—
68	C₂	C₂×D₂₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₂₃₂
commutator, cosocle	C₈×C₂₉	C₂³
Frattini	C₈	C₂²×D₂₉
Fitting	C₂₉×M₃₂	C₂
socle	C₂×C₂₉	C₂×D₈
prime radical	#11745266	C₂
hypercenter	M₃₂	D₂₉
hypocenter	C₂₉	#510
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₁₆	C₂	semidirect
3. C₂₉×M₃₂	C₂	semidirect
4. Dic₂₃₂	C₂	semidirect
5. #11745148	C₂	semidirect
39. M₃₂	D₂₉	semidirect
40. C₂₉	#510	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₁₆	2
#11745266	2
C₂₉×M₃₂	2
Dic₂₃₂	2
#11745148	2
#510	29