Subgroups — #14271438

Order 1856.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#131	C₂	1	1	yes	maximal, characteristic
2	#11745313	C₂	1	2	yes	maximal
3	C₂×Dic₁₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745172	C₂	1	2	yes	maximal, complemented
5	#11745167	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×Dic₅₈	C₂²	1	2	yes	—
8	M₁₆×C₂₉	—	2	1	no	—
9	M₁₆×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₂₉	—	2	1	no	—
11	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	#90785	—	2	2	no	—
13	#90783	—	2	2	no	—
14	#90777	C₂²	1	2	yes	—
15	Dic₁₁₆	—	2	1	no	—
16	Dic₁₁₆	—	2	1	no	—
17	Q₈×C₂₉	D₄	1	1	yes	characteristic
18	D₄×C₂₉	—	2	1	no	—
19	D₄×C₂₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	—	2	1	no	—
21	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
22	C₂×Dic₂₉	—	2	2	no	—
23	Dic₅₈	—	2	2	no	—
24	Dic₅₈	—	2	2	no	—
25	C₈×C₂₉	—	2	1	no	—
26	C₈×C₂₉	D₄	1	1	yes	characteristic
27	C₈×C₂₉	D₄	1	1	yes	characteristic
28	#6597	—	2	2	no	—
29	C₂²×C₂₉	—	2	1	no	—
30	C₂²×C₂₉	#41	1	1	yes	characteristic
31	C₄×C₂₉	—	2	1	no	—
32	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
33	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
34	Dic₂₉	—	4	2	no	—
35	#473	—	29	1	no	maximal, Sylow
36	C₂×C₂₉	—	2	1	no	—
37	C₂×C₂₉	—	4	1	no	—
38	C₂×C₂₉	#121	1	1	yes	characteristic
39	#137	—	29	2	no	—
40	C₂×Q₁₆	—	29	1	no	—
41	#131	D₂₉	1	1	yes	characteristic
42	#108	—	29	1	no	—
43	#101	—	29	2	no	—
44	C₂₉	#473	1	1	yes	characteristic, complemented, Sylow
45	#41	C₂×D₂₉	1	1	yes	characteristic
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	—	2	1	no	—
52	M₁₆	—	29	2	no	—
53	M₁₆	C₂×D₂₉	1	1	yes	characteristic
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
56	Q₈	—	58	2	no	—
57	Q₈	—	58	2	no	—
58	Q₈	D₁₁₆	1	1	yes	characteristic
59	D₄	—	2	1	no	—
60	D₄	D₁₁₆	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	58	2	no	—
63	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
64	C₈	—	2	1	no	—
65	C₈	—	58	2	no	—
66	C₈	C₂²⋊D₂₉	1	1	yes	characteristic
67	C₈	C₂²⋊D₂₉	1	1	yes	characteristic
68	C₂²	—	2	1	no	—
69	C₂²	#90805	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	116	2	no	—
72	C₄	C₂×D₁₁₆	1	1	yes	characteristic
73	C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	4	1	no	—
76	C₂	#11745292	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11745292
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#131	C₂
socle	C₂×C₂₉	#121
prime radical	#41×C₂₉	C₂²
hypercenter	#131	D₂₉
hypocenter	C₂₉	#473
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₁₁₆	C₂	semidirect
4. #11745172	C₂	semidirect
5. #11745167	C₂	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
C₂₉×#131	2
#11745313	2
C₂×Dic₁₁₆	2
#11745172	2
#11745167	2
#473	29