Subgroups — #16819125

Order 3712.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271561	C₂	1	2	yes	maximal
2	#14271561	C₂	1	1	yes	maximal, characteristic
3	#14271543	C₂	1	1	yes	maximal, characteristic
4	#14271514	C₂	1	2	yes	maximal
5	C₂₉×#322	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₁₆	—	2	2	no	—
7	#11745231	C₂²	1	1	yes	characteristic
8	#11745231	C₂²	1	2	yes	—
9	#11745231	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₂₉	C₂²	1	2	yes	—
11	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	#11745165	—	2	4	no	—
13	#11745165	—	2	2	no	—
14	#11745164	—	2	4	no	—
15	C₂×Dic₅₈	—	2	2	no	—
16	C₂×Dic₅₈	—	2	1	no	—
17	C₂×Dic₅₈	—	2	1	no	—
18	C₂×C₈×C₂₉	D₄	1	4	yes	—
19	C₂×C₈×C₂₉	D₄	1	2	yes	—
20	C₄²×C₂₉	C₂³	1	1	yes	characteristic
21	C₄⋊Dic₂₉	—	2	2	no	—
22	C₄⋊Dic₂₉	—	2	2	no	—
23	C₄⋊Dic₂₉	—	2	2	no	—
24	C₄⋊Dic₂₉	—	2	2	no	—
25	Dic₁₁₆	—	4	4	no	—
26	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
28	C₂×Dic₂₉	—	4	1	no	—
29	C₂×Dic₂₉	—	4	1	no	—
30	C₂×Dic₂₉	—	4	2	no	—
31	Dic₅₈	—	4	2	no	—
32	Dic₅₈	—	4	2	no	—
33	Dic₅₈	—	4	4	no	—
34	C₈×C₂₉	—	2	4	no	—
35	C₈×C₂₉	SD₁₆	1	4	yes	—
36	#1716	—	29	1	no	maximal, Sylow
37	C₂²×C₂₉	#127	1	1	yes	characteristic
38	C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
39	C₄×C₂₉	#137	1	4	yes	—
40	Dic₂₉	—	8	1	no	—
41	Dic₂₉	—	8	1	no	—
42	Dic₂₉	—	8	2	no	—
43	#498	—	29	2	no	—
44	#498	—	29	1	no	—
45	#494	—	29	1	no	—
46	#487	—	29	2	no	—
47	#322	D₂₉	1	1	yes	characteristic
48	C₂×C₂₉	#492	1	1	yes	characteristic
49	C₂×C₂₉	#497	1	2	yes	—
50	C₂×Q₁₆	—	58	2	no	—
51	C₄⋊Q₈	—	29	1	no	—
52	C₄⋊Q₈	—	29	2	no	—
53	C₄⋊Q₈	—	29	1	no	—
54	#106	—	58	4	no	—
55	#106	—	58	2	no	—
56	#103	—	58	4	no	—
57	C₄×C₈	C₂×D₂₉	1	2	yes	—
58	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
59	C₂₉	#1716	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	58	2	no	—
61	C₂×Q₈	—	58	1	no	—
62	C₂×Q₈	—	58	1	no	—
63	Q₁₆	—	116	4	no	—
64	C₂×C₈	D₁₁₆	1	4	yes	—
65	C₂×C₈	D₁₁₆	1	2	yes	—
66	C₄⋊C₄	—	58	2	no	—
67	C₄⋊C₄	—	58	2	no	—
68	C₄⋊C₄	—	58	2	no	—
69	C₄⋊C₄	—	58	2	no	—
70	C₄²	C₂²×D₂₉	1	1	yes	characteristic
71	Q₈	—	116	2	no	—
72	Q₈	—	116	2	no	—
73	Q₈	—	116	4	no	—
74	C₂×C₄	—	116	1	no	—
75	C₂×C₄	—	116	1	no	—
76	C₂×C₄	—	116	2	no	—
77	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
78	C₂×C₄	C₂×D₁₁₆	1	2	yes	—
79	C₈	—	2	4	no	—
80	C₈	#90773	1	4	yes	—
81	C₂²	#11745236	1	1	yes	characteristic
82	C₄	—	232	1	no	—
83	C₄	—	232	1	no	—
84	C₄	—	232	2	no	—
85	C₄	C₂×#90773	1	2	yes	—
86	C₄	#11745271	1	4	yes	—
87	C₂	#14271536	1	1	yes	characteristic
88	C₂	#14271557	1	2	yes	—

	subgroup	G/H
center	C₂²	#11745236
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#322	C₂
socle, prime radical	C₂²×C₂₉	#127
hypercenter	#322	D₂₉
hypocenter	C₂₉	#1716
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
59. C₂₉	#1716	semidirect

Maximal subgroups

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

subgroup	index
#14271561	2
#14271543	2
#14271514	2
C₂₉×#322	2
#1716	29