Subgroups — C₂³×C₄×#1181 #16836462

Order 3712.

3000 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×#1181	C₂	1	2	yes	maximal
2	C₂²×C₄×#1181	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₄×D₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂⁴×D₂₉	C₂²	1	1	yes	characteristic
5	C₂³×#1181	C₄	1	32	yes	direct product factor
6	C₂³×#1181	C₂²	1	28	yes	—
7	C₂³×C₄×C₂₉	C₄	1	1	yes	characteristic, complemented
8	C₂³×Dic₂₉	C₄	1	1	yes	characteristic, complemented
9	C₂²×C₄×D₂₉	C₄	1	14	yes	complemented
10	C₂²×C₄×D₂₉	C₂²	1	14	yes	—
11	C₂×C₄×#1181	C₂²	1	112	yes	direct product factor
12	C₂⁴×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂³×D₂₉	C₂×C₄	1	7	yes	—
14	C₂³×D₂₉	C₂×C₄	1	16	yes	—
15	C₂³×D₂₉	C₂³	1	7	yes	—
16	C₂²×#1181	C₂×C₄	1	224	yes	direct product factor
17	C₂²×#1181	C₂³	1	56	yes	—
18	C₂²×C₄×C₂₉	C₂×C₄	1	14	yes	complemented
19	C₂²×Dic₂₉	C₂×C₄	1	14	yes	complemented
20	C₂×C₄×D₂₉	C₂×C₄	1	84	yes	complemented
21	C₂×C₄×D₂₉	C₂³	1	28	yes	—
22	C₄×#1181	C₂³	1	64	yes	direct product factor
23	C₂³×C₂₉	C₄²	1	8	yes	complemented
24	C₂³×C₂₉	C₂²×C₄	1	7	yes	—
25	C₂²×D₂₉	C₄²	1	56	yes	complemented
26	C₂²×D₂₉	C₂²×C₄	1	21	yes	—
27	C₂²×D₂₉	C₂²×C₄	1	56	yes	—
28	C₂²×D₂₉	C₂⁴	1	7	yes	—
29	C₂×#1181	C₂²×C₄	1	224	yes	direct product factor
30	C₂×#1181	C₂⁴	1	16	yes	—
31	C₂×C₄×C₂₉	C₂²×C₄	1	28	yes	complemented
32	C₂×Dic₂₉	C₂²×C₄	1	28	yes	complemented
33	C₄×D₂₉	C₂²×C₄	1	56	yes	complemented
34	C₄×D₂₉	C₂⁴	1	8	yes	—
35	C₂³×C₄²	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	C₂×C₄²	1	28	yes	complemented
37	C₂²×C₂₉	C₂³×C₄	1	7	yes	—
38	C₂×D₂₉	C₂×C₄²	1	84	yes	complemented
39	C₂×D₂₉	C₂³×C₄	1	28	yes	—
40	C₂×D₂₉	C₂³×C₄	1	7	yes	—
41	C₂×D₂₉	C₂⁵	1	1	yes	characteristic
42	#1181	C₂³×C₄	1	32	yes	direct product factor
43	C₄×C₂₉	C₂³×C₄	1	8	yes	complemented
44	Dic₂₉	C₂³×C₄	1	8	yes	complemented
45	C₂⁴×C₄	—	29	2	no	—
46	C₂⁴×C₄	—	29	1	no	—
47	C₂²×C₄²	—	29	28	no	—
48	C₂×C₂₉	C₂²×C₄²	1	14	yes	complemented
49	C₂×C₂₉	C₂⁴×C₄	1	1	yes	characteristic
50	D₂₉	C₂²×C₄²	1	14	yes	complemented
51	D₂₉	C₂⁴×C₄	1	2	yes	—
52	C₂⁵	—	29	1	no	—
53	C₂³×C₄	—	29	32	no	—
54	C₂³×C₄	—	29	28	no	—
55	C₂³×C₄	—	29	1	no	—
56	C₂³×C₄	—	29	14	no	—
57	C₂³×C₄	—	29	14	no	—
58	C₂³×C₄	#1181	1	1	yes	characteristic, direct product factor
59	C₂×C₄²	—	29	112	no	—
60	C₂₉	C₂³×C₄²	1	1	yes	characteristic, complemented, Sylow
61	C₂⁴	—	29	16	no	—
62	C₂⁴	—	29	7	no	—
63	C₂⁴	—	29	7	no	—
64	C₂⁴	C₂×#1181	1	1	yes	characteristic
65	C₂²×C₄	—	29	56	no	—
66	C₂²×C₄	—	29	224	no	—
67	C₂²×C₄	—	29	14	no	—
68	C₂²×C₄	—	29	28	no	—
69	C₂²×C₄	—	29	84	no	—
70	C₂²×C₄	C₂×#1181	1	14	yes	direct product factor
71	C₄²	—	29	64	no	—
72	C₂³	—	29	56	no	—
73	C₂³	—	29	56	no	—
74	C₂³	—	29	7	no	—
75	C₂³	—	29	21	no	—
76	C₂³	C₄×#1181	1	8	yes	direct product factor
77	C₂³	C₂²×#1181	1	7	yes	—
78	C₂×C₄	—	29	16	no	—
79	C₂×C₄	—	29	224	no	—
80	C₂×C₄	—	29	28	no	—
81	C₂×C₄	—	29	8	no	—
82	C₂×C₄	—	29	56	no	—
83	C₂×C₄	C₂²×#1181	1	28	yes	direct product factor
84	C₂²	—	29	28	no	—
85	C₂²	—	29	84	no	—
86	C₂²	—	29	1	no	—
87	C₂²	—	29	7	no	—
88	C₂²	C₂×C₄×#1181	1	28	yes	direct product factor
89	C₂²	C₂³×#1181	1	7	yes	—
90	C₄	—	29	32	no	—
91	C₄	—	29	8	no	—
92	C₄	C₂³×#1181	1	8	yes	direct product factor
93	C₂	—	29	2	no	—
94	C₂	—	29	14	no	—
95	C₂	C₂²×C₄×#1181	1	14	yes	direct product factor
96	C₂	C₂⁴×#1181	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	#1181
commutator, hypocenter	C₂₉	C₂³×C₄²
Frattini	C₂	C₂⁴×#1181
Fitting	C₂³×C₄×C₂₉	C₄
socle	C₂⁴×C₂₉	C₂×C₄
prime radical	C₂⁴×D₂₉	C₂²
cosocle	C₂×D₂₉	C₂⁵
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×#1181	C₂	direct (N × H)
5. C₂³×#1181	C₄	direct (N × H)
7. C₂³×C₄×C₂₉	C₄	semidirect
8. C₂³×Dic₂₉	C₄	semidirect
9. C₂²×C₄×D₂₉	C₄	semidirect
11. C₂×C₄×#1181	C₂²	direct (N × H)
16. C₂²×#1181	C₂×C₄	direct (N × H)
18. C₂²×C₄×C₂₉	C₂×C₄	semidirect
19. C₂²×Dic₂₉	C₂×C₄	semidirect
20. C₂×C₄×D₂₉	C₂×C₄	semidirect
22. C₄×#1181	C₂³	direct (N × H)
23. C₂³×C₂₉	C₄²	semidirect
25. C₂²×D₂₉	C₄²	semidirect
29. C₂×#1181	C₂²×C₄	direct (N × H)
31. C₂×C₄×C₂₉	C₂²×C₄	semidirect
32. C₂×Dic₂₉	C₂²×C₄	semidirect
33. C₄×D₂₉	C₂²×C₄	semidirect
36. C₂²×C₂₉	C₂×C₄²	semidirect
38. C₂×D₂₉	C₂×C₄²	semidirect
42. #1181	C₂³×C₄	direct (N × H)
43. C₄×C₂₉	C₂³×C₄	semidirect
44. Dic₂₉	C₂³×C₄	semidirect
48. C₂×C₂₉	C₂²×C₄²	semidirect
50. D₂₉	C₂²×C₄²	semidirect
58. C₂³×C₄	#1181	direct (N × H)
60. C₂₉	C₂³×C₄²	semidirect
70. C₂²×C₄	C₂×#1181	direct (N × H)
76. C₂³	C₄×#1181	direct (N × H)
83. C₂×C₄	C₂²×#1181	direct (N × H)
88. C₂²	C₂×C₄×#1181	direct (N × H)
92. C₄	C₂³×#1181	direct (N × H)
95. C₂	C₂²×C₄×#1181	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×#1181	2
C₂²×C₄×#1181	2
C₂³×C₄×D₂₉	2
C₂³×C₄²	29

Subgroups — C23×C4×#1181 #16836462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×#1181 #16836462