Subgroups — #14271500

Order 1856.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745259	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745168	C₂	1	1	yes	maximal, characteristic
5	#11745164	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745158	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745155	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₂₉	—	2	1	no	—
9	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₅₈	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
14	#90781	—	2	1	no	—
15	C₄⋊Dic₂₉	—	2	1	no	—
16	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
17	#90779	—	2	1	no	—
18	C₂×#6597	C₂²	1	1	yes	characteristic
19	C₂²×D₂₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	—	2	1	no	—
21	C₂×C₄×C₂₉	—	2	1	no	—
22	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
23	C₂×Dic₂₉	—	2	1	no	—
24	C₂×Dic₂₉	—	2	1	no	—
25	C₂×Dic₂₉	D₄	1	1	yes	characteristic
26	C₄×D₂₉	—	2	1	no	—
27	C₄×D₂₉	—	2	1	no	—
28	C₄×D₂₉	—	4	2	no	—
29	Dic₅₈	—	2	1	no	—
30	Dic₅₈	—	2	1	no	—
31	C₈×C₂₉	—	2	1	no	—
32	#6597	—	2	1	no	—
33	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
34	C₂×D₂₉	—	2	1	no	—
35	C₂×D₂₉	—	2	1	no	—
36	C₂×D₂₉	Q₁₆	1	2	yes	—
37	C₄×C₂₉	—	4	1	no	—
38	C₄×C₂₉	—	4	1	no	—
39	C₄×C₂₉	#41	1	1	yes	characteristic
40	C₄×C₂₉	#41	1	1	yes	characteristic
41	Dic₂₉	—	2	1	no	—
42	Dic₂₉	—	4	1	no	—
43	Dic₂₉	—	4	1	no	—
44	#484	—	29	1	no	maximal, Sylow
45	C₂×C₂₉	#123	1	1	yes	characteristic
46	C₂×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
47	C₂×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
48	D₂₉	—	2	2	no	—
49	C₂²⋊Q₈	—	29	1	no	—
50	C₂×C₄⋊C₄	—	29	1	no	—
51	#107	—	29	1	no	—
52	#107	D₂₉	1	1	yes	characteristic, complemented
53	#103	—	29	1	no	—
54	#103	—	29	1	no	—
55	C₂²⋊C₈	—	29	1	no	—
56	C₂₉	#484	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	29	1	no	—
58	C₂²×C₄	—	29	1	no	—
59	C₂²×C₄	—	58	1	no	—
60	C₂×C₈	—	29	1	no	—
61	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
62	C₄⋊C₄	—	29	1	no	—
63	C₄⋊C₄	—	58	1	no	—
64	C₄⋊C₄	—	58	1	no	—
65	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
66	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
67	C₂²⋊C₄	—	58	1	no	—
68	C₂³	—	29	1	no	—
69	Q₈	—	58	1	no	—
70	Q₈	—	58	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	29	1	no	—
74	C₂×C₄	—	58	1	no	—
75	C₂×C₄	—	58	1	no	—
76	C₂×C₄	—	58	1	no	—
77	C₂×C₄	—	58	1	no	—
78	C₂×C₄	—	116	2	no	—
79	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	58	1	no	—
82	C₂²	—	29	2	no	—
83	C₂²	—	58	1	no	—
84	C₂²	—	58	1	no	—
85	C₂²	D₄×D₂₉	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	58	1	no	—
89	C₄	—	116	1	no	—
90	C₄	—	116	1	no	—
91	C₄	#90805	1	1	yes	characteristic
92	C₄	#90809	1	1	yes	characteristic
93	C₂	—	58	2	no	—
94	C₂	#11745256	1	1	yes	characteristic
95	C₂	#11745273	1	1	yes	characteristic
96	C₂	Q₁₆×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#107	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	C₂²×D₂₉	D₄
hypercenter	#107	D₂₉
hypocenter	C₂₉	#484
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
3. C₂₉×#107	C₂	semidirect
5. #11745164	C₂	semidirect
6. #11745158	C₂	semidirect
7. #11745155	C₂	semidirect
52. #107	D₂₉	semidirect
56. C₂₉	#484	semidirect

Maximal subgroups

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

subgroup	index
#11745259	2
C₄⋊C₄×D₂₉	2
C₂₉×#107	2
#11745168	2
#11745164	2
#11745158	2
#11745155	2
#484	29