Subgroups — #14271218

Order 1856.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745168	C₂	1	2	yes	maximal
4	#11745162	C₂	1	2	yes	maximal, complemented
5	#11745151	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₂₉	C₄	1	1	yes	characteristic
7	C₂×C₄×D₂₉	C₄	1	1	yes	characteristic
8	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₂₉	C₂²	1	2	yes	—
10	C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	C₄×Dic₂₉	C₄	1	1	yes	characteristic
12	C₄×Dic₂₉	C₄	1	1	yes	characteristic
13	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
14	C₂×#6597	C₂²	1	2	yes	—
15	C₂²×D₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
22	C₄×D₂₉	—	2	2	no	—
23	C₄×D₂₉	—	2	2	no	—
24	C₄×D₂₉	—	2	2	no	—
25	C₈×C₂₉	—	2	2	no	—
26	#6597	—	2	2	no	—
27	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₂₉	—	2	1	no	—
29	C₂×D₂₉	—	2	1	no	—
30	C₂×D₂₉	M₁₆	1	2	yes	—
31	C₄×C₂₉	—	2	1	no	—
32	C₄×C₂₉	—	2	1	no	—
33	C₄×C₂₉	#41	1	2	yes	—
34	Dic₂₉	—	2	1	no	—
35	Dic₂₉	—	2	1	no	—
36	Dic₂₉	M₁₆	1	2	yes	—
37	#432	—	29	1	no	maximal, Sylow
38	C₂×C₂₉	#117	1	1	yes	characteristic
39	C₂×C₂₉	C₂×M₁₆	1	1	yes	characteristic
40	C₂×C₂₉	C₂×M₁₆	1	1	yes	characteristic
41	D₂₉	—	2	2	no	—
42	C₂×C₄²	—	29	1	no	—
43	C₄⋊C₈	—	29	2	no	—
44	C₂²⋊C₈	—	29	2	no	—
45	#97	—	29	1	no	—
46	#97	D₂₉	1	1	yes	characteristic, complemented
47	C₂₉	#432	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₄	—	29	1	no	—
49	C₂²×C₄	—	29	1	no	—
50	C₂²×C₄	—	29	1	no	—
51	C₂×C₈	—	29	2	no	—
52	C₂×C₈	C₂×D₂₉	1	2	yes	—
53	C₄²	—	29	1	no	—
54	C₄²	—	29	1	no	—
55	C₄²	—	29	1	no	—
56	C₄²	C₂×D₂₉	1	1	yes	characteristic
57	C₂³	—	29	1	no	—
58	C₂×C₄	—	29	1	no	—
59	C₂×C₄	—	29	1	no	—
60	C₂×C₄	—	29	1	no	—
61	C₂×C₄	—	58	2	no	—
62	C₂×C₄	—	58	2	no	—
63	C₂×C₄	—	58	2	no	—
64	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
65	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
66	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
67	C₈	—	2	2	no	—
68	C₈	—	58	2	no	—
69	C₂²	—	29	2	no	—
70	C₂²	—	58	1	no	—
71	C₂²	—	58	1	no	—
72	C₂²	C₂×C₄×D₂₉	1	1	yes	characteristic
73	C₄	—	2	1	no	—
74	C₄	—	2	1	no	—
75	C₄	—	29	2	no	—
76	C₄	—	58	1	no	—
77	C₄	—	58	1	no	—
78	C₄	#90805	1	2	yes	—
79	C₂	—	58	2	no	—
80	C₂	#11745234	1	1	yes	characteristic
81	C₂	M₁₆×D₂₉	1	1	yes	characteristic
82	C₂	M₁₆×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂²×C₄
Fitting	C₂₉×#97	C₂
prime radical	C₂²×D₂₉	C₂×C₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	#97	D₂₉
hypocenter	C₂₉	#432
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

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

N	H ≅ G/N	type
2. C₂₉×#97	C₂	semidirect
4. #11745162	C₂	semidirect
5. #11745151	C₂	semidirect
46. #97	D₂₉	semidirect
47. C₂₉	#432	semidirect

Maximal subgroups

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

subgroup	index
C₄²×D₂₉	2
C₂₉×#97	2
#11745168	2
#11745162	2
#11745151	2
#432	29