Subgroups — #14271404

Order 1856.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
2	#11745286	C₂	1	2	yes	maximal
3	C₂×Dic₁₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745166	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745164	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×Dic₅₈	C₂²	1	2	yes	—
8	C₂×C₈×C₂₉	—	2	2	no	—
9	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₂²⋊Dic₂₉	—	2	2	no	—
12	C₄⋊Dic₂₉	C₂²	1	2	yes	—
13	#90779	—	2	2	no	—
14	Dic₁₁₆	—	2	2	no	—
15	C₂³×C₂₉	D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₉	—	2	1	no	—
17	C₂×C₄×C₂₉	—	2	1	no	—
18	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
19	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
20	C₂×Dic₂₉	—	2	2	no	—
21	C₂×Dic₂₉	—	2	2	no	—
22	Dic₅₈	—	2	2	no	—
23	Dic₅₈	—	2	2	no	—
24	C₈×C₂₉	—	2	1	no	—
25	C₈×C₂₉	D₄	1	2	yes	—
26	C₂²×C₂₉	—	2	1	no	—
27	C₂²×C₂₉	—	2	1	no	—
28	C₂²×C₂₉	Q₁₆	1	2	yes	complemented
29	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
30	C₄×C₂₉	—	2	1	no	—
31	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
32	C₄×C₂₉	#41	1	1	yes	characteristic
33	Dic₂₉	—	4	2	no	—
34	Dic₂₉	—	4	2	no	—
35	#467	—	29	1	no	maximal, Sylow
36	C₂×C₂₉	—	2	2	no	—
37	C₂×C₂₉	#121	1	1	yes	characteristic
38	C₂×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
39	C₂×C₂₉	#135	1	1	yes	characteristic
40	C₂×Q₁₆	—	29	1	no	—
41	C₂²×C₈	D₂₉	1	1	yes	characteristic
42	C₂²⋊Q₈	—	29	2	no	—
43	#107	—	29	1	no	—
44	#103	—	29	2	no	—
45	C₂₉	#467	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₈	—	29	2	no	—
47	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
48	Q₁₆	—	58	2	no	—
49	C₂×C₈	—	2	2	no	—
50	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
51	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
52	C₄⋊C₄	—	29	2	no	—
53	C₄⋊C₄	—	58	2	no	—
54	C₂²⋊C₄	—	58	2	no	—
55	C₂³	D₁₁₆	1	1	yes	characteristic
56	Q₈	—	58	2	no	—
57	Q₈	—	58	2	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	58	2	no	—
61	C₂×C₄	—	58	2	no	—
62	C₂×C₄	D₁₁₆	1	1	yes	characteristic
63	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
64	C₈	—	2	1	no	—
65	C₈	C₂²⋊D₂₉	1	2	yes	—
66	C₂²	—	2	1	no	—
67	C₂²	—	2	1	no	—
68	C₂²	Dic₁₁₆	1	2	yes	complemented
69	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	116	2	no	—
72	C₄	—	116	2	no	—
73	C₄	#90805	1	1	yes	characteristic
74	C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
75	C₂	—	2	2	no	—
76	C₂	#11745266	1	1	yes	characteristic
77	C₂	C₂×Dic₁₁₆	1	1	yes	characteristic
78	C₂	#11745292	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₁₆
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂²×C₈×C₂₉	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	C₂³×C₂₉	D₄
hypercenter	C₂²×C₈	D₂₉
hypocenter	C₂₉	#467
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₁₁₆	C₂	semidirect
4. #11745166	C₂	semidirect
5. #11745164	C₂	semidirect
28. C₂²×C₂₉	Q₁₆	semidirect
45. C₂₉	#467	semidirect
68. C₂²	Dic₁₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₂₉	2
#11745286	2
C₂×Dic₁₁₆	2
#11745166	2
#11745164	2
#467	29