Subgroups — C₄×#11745163 #16819176

Order 3712.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745163	C₂	1	4	yes	maximal
2	C₂×C₄×#6597	C₂	1	1	yes	maximal, characteristic
3	C₄²×Dic₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
6	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₂₉	C₄	1	4	yes	—
8	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
9	C₂²×#6597	C₂²	1	2	yes	—
10	C₄×C₈×C₂₉	C₄	1	4	yes	complemented
11	#11745163	C₄	1	16	yes	direct product factor
12	C₄×#6597	C₄	1	4	yes	complemented
13	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
15	C₂²×Dic₂₉	C₂×C₄	1	4	yes	—
16	C₂×C₈×C₂₉	C₂×C₄	1	8	yes	—
17	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
18	C₄²×C₂₉	C₂×C₄	1	2	yes	—
19	C₄²×C₂₉	C₂×C₄	1	2	yes	—
20	C₄×Dic₂₉	—	2	8	no	—
21	C₄×Dic₂₉	C₂×C₄	1	8	yes	—
22	C₂×#6597	C₂×C₄	1	4	yes	—
23	C₂×#6597	C₂×C₄	1	8	yes	—
24	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₉	C₄²	1	4	yes	—
26	C₂×C₄×C₂₉	M₁₆	1	8	yes	—
27	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
29	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₂₉	—	2	8	no	—
31	C₂×Dic₂₉	C₄²	1	8	yes	—
32	C₈×C₂₉	C₄²	1	8	yes	complemented
33	#6597	C₄²	1	8	yes	complemented
34	C₄×#97	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
36	C₂²×C₂₉	C₂×C₄²	1	2	yes	—
37	C₂²×C₂₉	C₂×M₁₆	1	4	yes	—
38	C₄×C₂₉	#97	1	8	yes	complemented
39	C₄×C₂₉	C₂×C₄²	1	2	yes	—
40	C₄×C₂₉	C₂×C₄²	1	2	yes	—
41	Dic₂₉	—	2	8	no	—
42	C₂×#97	—	29	4	no	—
43	C₂×C₄×C₈	—	29	1	no	—
44	C₂×C₄×C₈	D₂₉	1	1	yes	characteristic
45	C₄³	—	29	1	no	—
46	C₂×C₂₉	C₄³	1	1	yes	characteristic
47	C₂×C₂₉	C₂×#97	1	2	yes	—
48	C₂×C₂₉	C₄×M₁₆	1	4	yes	—
49	C₂²×C₈	—	29	2	no	—
50	C₂²×C₈	C₂×D₂₉	1	2	yes	—
51	C₂×C₄²	—	29	2	no	—
52	C₂×C₄²	—	29	4	no	—
53	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
54	#97	—	29	16	no	—
55	C₄×C₈	—	29	4	no	—
56	C₄×C₈	Dic₂₉	1	4	yes	complemented
57	C₂₉	C₄×#97	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	—	29	4	no	—
59	C₂²×C₄	C₄×D₂₉	1	2	yes	—
60	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
61	C₂×C₈	—	29	4	no	—
62	C₂×C₈	—	29	8	no	—
63	C₂×C₈	C₄×D₂₉	1	8	yes	—
64	C₂×C₈	C₂×Dic₂₉	1	4	yes	—
65	C₄²	—	29	8	no	—
66	C₄²	—	58	8	no	—
67	C₄²	C₄×D₂₉	1	2	yes	—
68	C₄²	C₂×Dic₂₉	1	2	yes	—
69	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
70	C₂×C₄	—	29	8	no	—
71	C₂×C₄	—	58	8	no	—
72	C₂×C₄	#90772	1	8	yes	—
73	C₂×C₄	C₄×Dic₂₉	1	4	yes	—
74	C₂×C₄	C₂×C₄×D₂₉	1	4	yes	—
75	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
76	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
77	C₈	—	29	8	no	—
78	C₈	C₄×Dic₂₉	1	8	yes	complemented
79	C₂²	C₄²×D₂₉	1	2	yes	—
80	C₂²	C₂×#90772	1	4	yes	—
81	C₂²	C₂×C₄×Dic₂₉	1	1	yes	characteristic
82	C₄	—	58	8	no	—
83	C₄	#11745163	1	8	yes	direct product factor
84	C₄	C₄²×D₂₉	1	2	yes	—
85	C₄	C₂×C₄×Dic₂₉	1	2	yes	—
86	C₂	C₄²×Dic₂₉	1	1	yes	characteristic
87	C₂	C₂×#11745163	1	2	yes	—
88	C₂	C₄×#90772	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂×D₂₉
commutator	C₂×C₂₉	C₄³
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₄×C₈×C₂₉	C₂
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×C₄×C₈	D₂₉
hypocenter	C₂₉	C₄×#97
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
10. C₄×C₈×C₂₉	C₄	semidirect
11. #11745163	C₄	direct (N × H)
12. C₄×#6597	C₄	semidirect
32. C₈×C₂₉	C₄²	semidirect
33. #6597	C₄²	semidirect
38. C₄×C₂₉	#97	semidirect
56. C₄×C₈	Dic₂₉	semidirect
57. C₂₉	C₄×#97	semidirect
78. C₈	C₄×Dic₂₉	semidirect
83. C₄	#11745163	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11745163	2
C₂×C₄×#6597	2
C₄²×Dic₂₉	2
C₂×C₄×C₈×C₂₉	2
C₄×#97	29

Subgroups — C4×#11745163 #16819176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11745163 #16819176