Subgroups — #14271435

Order 1856.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745304	C₂	1	2	yes	maximal
3	#11745263	C₂	1	1	yes	maximal, characteristic
4	#11745184	C₂	1	2	yes	maximal, complemented
5	#11745167	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₂₉	C₂²	1	2	yes	—
7	#90805	C₂²	1	1	yes	characteristic
8	Q₁₆×C₂₉	—	2	1	no	—
9	Q₁₆×C₂₉	—	2	1	no	—
10	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	#90785	—	2	2	no	—
12	#90784	—	2	2	no	—
13	#90777	C₂²	1	2	yes	—
14	#90777	C₂²	1	1	yes	characteristic
15	#90772	—	2	1	no	—
16	C₈×D₂₉	—	2	1	no	—
17	Q₈×C₂₉	—	2	2	no	—
18	Q₈×C₂₉	—	2	2	no	—
19	C₂×C₄×C₂₉	—	2	2	no	—
20	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
21	C₂²⋊D₂₉	—	2	1	no	—
22	D₁₁₆	D₄	1	1	yes	characteristic
23	C₄×D₂₉	—	2	1	no	—
24	Dic₅₈	D₄	1	1	yes	characteristic
25	C₈×C₂₉	D₄	1	1	yes	characteristic
26	C₈×C₂₉	D₄	1	1	yes	characteristic
27	#6597	—	2	1	no	—
28	#6597	—	2	2	no	—
29	C₂²×C₂₉	#41	1	1	yes	characteristic
30	C₂×D₂₉	—	2	1	no	—
31	C₄×C₂₉	—	4	2	no	—
32	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
33	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
34	Dic₂₉	—	2	1	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	D₂₉	1	1	yes	characteristic, complemented
41	#131	—	29	1	no	—
42	#108	—	29	1	no	—
43	#101	—	29	2	no	—
44	C₂₉	#473	1	1	yes	characteristic, complemented, Sylow
45	#41	—	29	1	no	—
46	C₂×Q₈	C₂×D₂₉	1	2	yes	—
47	Q₁₆	—	2	1	no	—
48	Q₁₆	—	2	1	no	—
49	Q₁₆	—	58	2	no	—
50	SD₁₆	—	58	2	no	—
51	M₁₆	—	29	1	no	—
52	M₁₆	—	29	2	no	—
53	M₁₆	—	58	1	no	—
54	C₂×C₈	—	58	1	no	—
55	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
56	Q₈	—	2	2	no	—
57	Q₈	—	2	2	no	—
58	Q₈	—	29	1	no	—
59	D₄	—	29	1	no	—
60	D₄	—	58	1	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	58	1	no	—
63	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
64	C₈	—	58	2	no	—
65	C₈	—	58	1	no	—
66	C₈	C₂²⋊D₂₉	1	1	yes	characteristic
67	C₈	C₂²⋊D₂₉	1	1	yes	characteristic
68	C₂²	—	58	1	no	—
69	C₂²	#90807	1	1	yes	characteristic
70	C₄	—	4	2	no	—
71	C₄	—	58	1	no	—
72	C₄	D₄×D₂₉	1	1	yes	characteristic
73	C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	116	1	no	—
76	C₂	#11745300	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11745300
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂×Q₁₆×C₂₉	C₂
socle	C₂×C₂₉	#121
prime radical	#90805	C₂²
hypercenter	C₂×Q₁₆	D₂₉
hypocenter	C₂₉	#473
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×C₂₉	C₂	semidirect
4. #11745184	C₂	semidirect
5. #11745167	C₂	semidirect
40. C₂×Q₁₆	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
C₂×Q₁₆×C₂₉	2
#11745304	2
#11745263	2
#11745184	2
#11745167	2
#473	29