Subgroups — #16821364

Order 3712.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₃₂	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₁₁₆	C₂	1	2	yes	maximal
3	#14270991	C₂	1	1	yes	maximal, characteristic
4	#14270968	C₂	1	2	yes	maximal
5	C₂₉×#346	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₁₆	C₂²	1	2	yes	—
7	C₄×Dic₅₈	—	2	2	no	—
8	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	#11745166	C₂²	1	2	yes	—
12	#11745164	—	2	2	no	—
13	Dic₂₃₂	C₄	1	4	yes	complemented
14	C₂×Dic₅₈	—	2	2	no	—
15	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
16	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
17	C₄²×C₂₉	D₄	1	1	yes	characteristic
18	C₄⋊Dic₂₉	—	2	2	no	—
19	#90779	—	4	2	no	—
20	C₄×Dic₂₉	—	4	2	no	—
21	Dic₁₁₆	—	2	2	no	—
22	Dic₁₁₆	C₂×C₄	1	4	yes	—
23	C₁₆×C₂₉	—	2	1	no	—
24	C₁₆×C₂₉	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₂₉	D₈	1	2	yes	—
26	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₂₉	—	4	2	no	—
28	C₂×Dic₂₉	—	4	2	no	—
29	Dic₅₈	—	2	4	no	—
30	Dic₅₈	—	4	2	no	—
31	C₈×C₂₉	—	2	1	no	—
32	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₂₉	#41	1	1	yes	characteristic
34	#2176	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
36	C₄×C₂₉	—	2	2	no	—
37	C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
38	C₄×C₂₉	#135	1	1	yes	characteristic
39	Dic₂₉	—	4	4	no	—
40	Dic₂₉	—	8	2	no	—
41	C₂×Q₃₂	—	29	1	no	—
42	C₄×Q₁₆	—	29	2	no	—
43	#367	—	29	1	no	—
44	#358	—	29	2	no	—
45	#346	D₂₉	1	1	yes	characteristic
46	C₂×C₂₉	C₄×D₈	1	1	yes	characteristic
47	C₂×C₂₉	#510	1	2	yes	—
48	C₂×Q₁₆	—	29	2	no	—
49	C₄×Q₈	—	58	2	no	—
50	Q₃₂	—	29	4	no	—
51	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
52	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
53	#107	—	29	2	no	—
54	#103	—	58	2	no	—
55	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
56	C₂₉	#2176	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	58	2	no	—
58	Q₁₆	—	29	4	no	—
59	Q₁₆	—	58	2	no	—
60	C₂×C₈	D₁₁₆	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
62	C₄⋊C₄	—	58	2	no	—
63	C₄⋊C₄	—	116	2	no	—
64	C₄²	—	116	2	no	—
65	C₄²	D₁₁₆	1	1	yes	characteristic
66	C₁₆	—	2	1	no	—
67	C₁₆	C₄×D₂₉	1	2	yes	—
68	Q₈	—	58	4	no	—
69	Q₈	—	116	2	no	—
70	C₂×C₄	—	116	2	no	—
71	C₂×C₄	—	116	2	no	—
72	C₂×C₄	D₂₃₂	1	2	yes	—
73	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	C₂×C₄×D₂₉	1	1	yes	characteristic
76	C₈	#90805	1	1	yes	characteristic
77	C₂²	C₂×D₂₃₂	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	116	4	no	—
80	C₄	—	232	2	no	—
81	C₄	C₄×D₁₁₆	1	1	yes	characteristic
82	C₄	#11745266	1	1	yes	characteristic
83	C₂	C₄×D₂₃₂	1	1	yes	characteristic
84	C₂	#14271606	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₂₃₂
commutator	C₈×C₂₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₂₉×#346	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₈
cosocle	C₂×C₈×C₂₉	C₂³
hypercenter	#346	D₂₉
hypocenter	C₂₉	#2176
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
13. Dic₂₃₂	C₄	semidirect
56. C₂₉	#2176	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₂₃₂	2
C₄×Dic₁₁₆	2
#14270991	2
#14270968	2
C₂₉×#346	2
#2176	29