Subgroups — C₂²×#11745166 #16828067

Order 3712.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Dic₂₉	C₂	1	2	yes	maximal
2	C₂×#11745166	C₂	1	12	yes	maximal, direct product factor
3	C₂³×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
5	C₂³×Dic₂₉	—	2	2	no	—
6	C₂²×C₈×C₂₉	C₄	1	8	yes	complemented
7	C₂²×C₈×C₂₉	C₂²	1	6	yes	—
8	C₂×C₄⋊Dic₂₉	—	2	6	no	—
9	C₂×C₄⋊Dic₂₉	C₂²	1	12	yes	—
10	#11745166	C₂²	1	16	yes	direct product factor
11	C₂⁴×C₂₉	D₄	1	1	yes	characteristic
12	C₂²×C₄×C₂₉	C₂×C₄	1	4	yes	—
13	C₂²×C₄×C₂₉	D₄	1	3	yes	—
14	C₂²×C₄×C₂₉	Q₈	1	4	yes	—
15	C₂²×C₄×C₂₉	C₂³	1	3	yes	—
16	C₂²×Dic₂₉	—	2	12	no	—
17	C₂²×Dic₂₉	—	4	8	no	—
18	C₂×C₈×C₂₉	C₂×C₄	1	24	yes	complemented
19	C₂×C₈×C₂₉	C₂³	1	4	yes	—
20	C₄⋊Dic₂₉	—	2	12	no	—
21	C₄⋊Dic₂₉	C₂³	1	8	yes	—
22	C₂³×C₂₉	C₄⋊C₄	1	4	yes	—
23	C₂³×C₂₉	D₈	1	4	yes	—
24	C₂³×C₂₉	Q₁₆	1	4	yes	—
25	C₂³×C₂₉	C₂×D₄	1	3	yes	—
26	C₂×C₄×C₂₉	C₄⋊C₄	1	12	yes	—
27	C₂×C₄×C₂₉	C₂²×C₄	1	6	yes	—
28	C₂×C₄×C₂₉	C₂×D₄	1	3	yes	—
29	C₂×C₄×C₂₉	C₂×Q₈	1	6	yes	—
30	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
31	C₂×Dic₂₉	—	2	8	no	—
32	C₂×Dic₂₉	—	4	24	no	—
33	C₈×C₂₉	C₂²×C₄	1	8	yes	complemented
34	C₂²×#107	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	#107	1	16	yes	complemented
36	C₂²×C₂₉	C₂×C₄⋊C₄	1	6	yes	—
37	C₂²×C₂₉	C₂×D₈	1	6	yes	—
38	C₂²×C₂₉	C₂×Q₁₆	1	6	yes	—
39	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
40	C₄×C₂₉	C₂×C₄⋊C₄	1	6	yes	—
41	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
42	C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
43	Dic₂₉	—	4	8	no	—
44	C₂³×C₈	D₂₉	1	1	yes	characteristic
45	C₂²×C₄⋊C₄	—	29	2	no	—
46	C₂×#107	—	29	12	no	—
47	C₂×C₂₉	C₂×#107	1	12	yes	complemented
48	C₂×C₂₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₂₉	C₂²×D₈	1	1	yes	characteristic
50	C₂×C₂₉	C₂²×Q₁₆	1	1	yes	characteristic
51	C₂³×C₄	—	58	2	no	—
52	C₂³×C₄	C₂×D₂₉	1	1	yes	characteristic
53	C₂²×C₈	Dic₂₉	1	8	yes	complemented
54	C₂²×C₈	C₂×D₂₉	1	6	yes	—
55	C₂×C₄⋊C₄	—	29	12	no	—
56	C₂×C₄⋊C₄	—	58	6	no	—
57	#107	—	29	16	no	—
58	C₂₉	C₂²×#107	1	1	yes	characteristic, complemented, Sylow
59	C₂⁴	D₁₁₆	1	1	yes	characteristic
60	C₂²×C₄	—	58	12	no	—
61	C₂²×C₄	—	116	8	no	—
62	C₂²×C₄	Dic₅₈	1	4	yes	—
63	C₂²×C₄	D₁₁₆	1	3	yes	—
64	C₂²×C₄	C₂×Dic₂₉	1	4	yes	—
65	C₂²×C₄	C₂²×D₂₉	1	3	yes	—
66	C₂×C₈	C₂×Dic₂₉	1	24	yes	complemented
67	C₂×C₈	C₂²×D₂₉	1	4	yes	—
68	C₄⋊C₄	—	29	8	no	—
69	C₄⋊C₄	—	58	12	no	—
70	C₂³	D₂₃₂	1	4	yes	—
71	C₂³	Dic₁₁₆	1	4	yes	—
72	C₂³	C₄⋊Dic₂₉	1	4	yes	—
73	C₂³	C₂×D₁₁₆	1	3	yes	—
74	C₂×C₄	—	58	8	no	—
75	C₂×C₄	—	116	24	no	—
76	C₂×C₄	C₄⋊Dic₂₉	1	12	yes	—
77	C₂×C₄	C₂×Dic₅₈	1	6	yes	—
78	C₂×C₄	C₂×D₁₁₆	1	3	yes	—
79	C₂×C₄	C₂²×Dic₂₉	1	6	yes	—
80	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
81	C₈	C₂²×Dic₂₉	1	8	yes	complemented
82	C₂²	#11745166	1	16	yes	direct product factor
83	C₂²	C₂×D₂₃₂	1	6	yes	—
84	C₂²	C₂×Dic₁₁₆	1	6	yes	—
85	C₂²	C₂×C₄⋊Dic₂₉	1	6	yes	—
86	C₂²	C₂²×D₁₁₆	1	1	yes	characteristic
87	C₄	—	116	8	no	—
88	C₄	C₂×C₄⋊Dic₂₉	1	6	yes	—
89	C₄	C₂²×Dic₅₈	1	1	yes	characteristic
90	C₄	C₂³×Dic₂₉	1	1	yes	characteristic
91	C₂	C₂×#11745166	1	12	yes	direct product factor
92	C₂	C₂²×C₄⋊Dic₂₉	1	1	yes	characteristic
93	C₂	C₂²×D₂₃₂	1	1	yes	characteristic
94	C₂	C₂²×Dic₁₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₁₁₆
commutator	C₄×C₂₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂³×C₈×C₂₉	C₂
socle, prime radical	C₂⁴×C₂₉	D₄
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	C₂³×C₈	D₂₉
hypocenter	C₂₉	C₂²×#107
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#11745166	C₂	direct (N × H)
6. C₂²×C₈×C₂₉	C₄	semidirect
10. #11745166	C₂²	direct (N × H)
18. C₂×C₈×C₂₉	C₂×C₄	semidirect
33. C₈×C₂₉	C₂²×C₄	semidirect
35. C₂²×C₂₉	#107	semidirect
47. C₂×C₂₉	C₂×#107	semidirect
53. C₂²×C₈	Dic₂₉	semidirect
58. C₂₉	C₂²×#107	semidirect
66. C₂×C₈	C₂×Dic₂₉	semidirect
81. C₈	C₂²×Dic₂₉	semidirect
82. C₂²	#11745166	direct (N × H)
91. C₂	C₂×#11745166	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Dic₂₉	2
C₂×#11745166	2
C₂³×C₈×C₂₉	2
C₂²×#107	29

Subgroups — C22×#11745166 #16828067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11745166 #16828067