Subgroups — #14271439

Order 1856.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745271	C₂	1	2	yes	maximal
2	C₂×Dic₁₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745263	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745172	C₂	1	2	yes	maximal, complemented
6	#90805	C₂²	1	1	yes	characteristic
7	C₂×Dic₅₈	C₂²	1	2	yes	—
8	M₁₆×C₂₉	C₂²	1	2	yes	—
9	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	#90777	C₂²	1	1	yes	characteristic
11	Dic₁₁₆	—	2	2	no	—
12	Dic₁₁₆	—	2	1	no	—
13	Dic₁₁₆	—	2	1	no	—
14	#90773	—	2	2	no	—
15	#90772	—	2	1	no	—
16	C₈×D₂₉	—	2	1	no	—
17	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	C₂²⋊D₂₉	—	2	1	no	—
19	C₂×Dic₂₉	—	2	2	no	—
20	D₁₁₆	D₄	1	1	yes	characteristic
21	C₄×D₂₉	—	2	1	no	—
22	Dic₅₈	—	2	2	no	—
23	Dic₅₈	—	2	2	no	—
24	Dic₅₈	D₄	1	1	yes	characteristic
25	C₈×C₂₉	—	2	2	no	—
26	C₈×C₂₉	D₄	1	1	yes	characteristic
27	C₈×C₂₉	D₄	1	1	yes	characteristic
28	#6597	—	2	1	no	—
29	C₂²×C₂₉	#41	1	1	yes	characteristic
30	C₂×D₂₉	—	2	1	no	—
31	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
32	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
33	Dic₂₉	—	2	1	no	—
34	Dic₂₉	—	4	2	no	—
35	#473	—	29	1	no	maximal, Sylow
36	C₂×C₂₉	—	2	1	no	—
37	C₂×C₂₉	#121	1	1	yes	characteristic
38	D₂₉	—	4	1	no	—
39	#137	—	29	2	no	—
40	C₂×Q₁₆	—	29	1	no	—
41	#131	—	29	1	no	—
42	#108	D₂₉	1	1	yes	characteristic, complemented
43	#101	—	29	2	no	—
44	C₂₉	#473	1	1	yes	characteristic, complemented, Sylow
45	#41	—	29	1	no	—
46	C₂×Q₈	—	29	2	no	—
47	Q₁₆	—	58	2	no	—
48	Q₁₆	—	58	1	no	—
49	Q₁₆	—	58	1	no	—
50	SD₁₆	—	58	2	no	—
51	M₁₆	—	29	1	no	—
52	M₁₆	—	58	1	no	—
53	M₁₆	C₂×D₂₉	1	2	yes	—
54	C₂×C₈	—	58	1	no	—
55	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
56	Q₈	—	29	1	no	—
57	Q₈	—	58	2	no	—
58	Q₈	—	58	2	no	—
59	D₄	—	29	1	no	—
60	D₄	—	58	1	no	—
61	C₂×C₄	—	58	1	no	—
62	C₂×C₄	—	58	2	no	—
63	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
64	C₈	—	2	2	no	—
65	C₈	—	58	1	no	—
66	C₈	D₁₁₆	1	1	yes	characteristic
67	C₈	D₁₁₆	1	1	yes	characteristic
68	C₂²	—	58	1	no	—
69	C₂²	#90809	1	1	yes	characteristic
70	C₄	—	58	1	no	—
71	C₄	—	116	2	no	—
72	C₄	C₂×D₁₁₆	1	1	yes	characteristic
73	C₄	D₄×D₂₉	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	116	1	no	—
76	C₂	#11745257	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11745257
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#108	C₂
socle	C₂×C₂₉	#121
prime radical	#90805	C₂²
hypercenter	#108	D₂₉
hypocenter	C₂₉	#473
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₁₆	C₂	semidirect
4. C₂₉×#108	C₂	semidirect
5. #11745172	C₂	semidirect
42. #108	D₂₉	semidirect
44. C₂₉	#473	semidirect

Maximal subgroups

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

subgroup	index
#11745271	2
C₂×Dic₁₁₆	2
#11745263	2
C₂₉×#108	2
#11745172	2
#473	29