Subgroups — #14271521

Order 1856.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745298	C₂	1	1	yes	maximal, characteristic
2	#11745250	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#102	C₂	1	1	yes	maximal, characteristic
4	#11745180	C₂	1	1	yes	maximal, characteristic
5	#11745164	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745163	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745158	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₅₈	—	2	1	no	—
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	C₂²⋊Dic₂₉	—	2	1	no	—
14	C₂²⋊Dic₂₉	—	2	1	no	—
15	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
16	#90779	—	2	1	no	—
17	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
18	C₂×#6597	C₂²	1	1	yes	characteristic
19	C₂³×C₂₉	—	2	1	no	—
20	D₄×C₂₉	—	2	1	no	—
21	D₄×C₂₉	—	2	1	no	—
22	C₂×C₄×C₂₉	—	2	1	no	—
23	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
24	C₂×Dic₂₉	—	2	1	no	—
25	C₂×Dic₂₉	—	2	1	no	—
26	C₂×Dic₂₉	D₄	1	1	yes	characteristic
27	C₂×Dic₂₉	D₄	1	1	yes	characteristic
28	Dic₅₈	—	2	1	no	—
29	Dic₅₈	—	2	1	no	—
30	Dic₅₈	—	4	2	no	—
31	C₈×C₂₉	—	2	1	no	—
32	#6597	—	2	1	no	—
33	C₂²×C₂₉	—	4	1	no	—
34	C₂²×C₂₉	—	4	1	no	—
35	C₂²×C₂₉	—	4	1	no	—
36	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
37	C₄×C₂₉	—	4	1	no	—
38	C₄×C₂₉	#41	1	1	yes	characteristic
39	C₄×C₂₉	#41	1	1	yes	characteristic
40	Dic₂₉	—	2	1	no	—
41	Dic₂₉	—	2	1	no	—
42	Dic₂₉	—	4	1	no	—
43	Dic₂₉	—	4	1	no	—
44	#489	—	29	1	no	maximal, Sylow
45	C₂×C₂₉	—	8	1	no	—
46	C₂×C₂₉	#124	1	1	yes	characteristic
47	C₂×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
48	C₂×C₂₉	#137	1	1	yes	characteristic
49	C₄⋊Q₈	—	29	1	no	—
50	#124	—	29	1	no	—
51	#103	—	29	1	no	—
52	#103	—	29	1	no	—
53	#102	—	29	1	no	—
54	#102	D₂₉	1	1	yes	characteristic
55	#97	—	29	1	no	—
56	C₂₉	#489	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	29	1	no	—
58	C₂×Q₈	—	58	1	no	—
59	C₂×D₄	C₂×D₂₉	1	1	yes	characteristic
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	C₂×D₂₉	1	1	yes	characteristic
65	C₂²⋊C₄	—	58	1	no	—
66	C₂²⋊C₄	—	58	1	no	—
67	C₄²	—	29	1	no	—
68	C₂³	—	2	1	no	—
69	Q₈	—	58	1	no	—
70	Q₈	—	58	1	no	—
71	Q₈	—	116	2	no	—
72	D₄	—	2	1	no	—
73	D₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	29	1	no	—
76	C₂×C₄	—	29	1	no	—
77	C₂×C₄	—	58	1	no	—
78	C₂×C₄	—	58	1	no	—
79	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	58	1	no	—
82	C₂²	—	4	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	D₄×D₂₉	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	58	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	#90807	1	1	yes	characteristic
93	C₂	—	8	1	no	—
94	C₂	#11745247	1	1	yes	characteristic
95	C₂	#11745273	1	1	yes	characteristic
96	C₂	#11745277	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#102	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	C₂×D₄×C₂₉	C₂²
hypercenter	#102	D₂₉
hypocenter	C₂₉	#489
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

Complements

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

N	H ≅ G/N	type
2. #11745250	C₂	semidirect
5. #11745164	C₂	semidirect
6. #11745163	C₂	semidirect
7. #11745158	C₂	semidirect
56. C₂₉	#489	semidirect

Maximal subgroups

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

subgroup	index
#11745298	2
#11745250	2
C₂₉×#102	2
#11745180	2
#11745164	2
#11745163	2
#11745158	2
#489	29