Subgroups — C₂²×D₃₀₄ #14576741

Order 2432.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₅₂	C₂	1	2	yes	maximal, complemented
2	C₂×D₃₀₄	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₇₆	—	2	2	no	—
5	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×D₁₅₂	—	2	6	no	—
7	C₂×D₁₅₂	C₂²	1	12	yes	complemented
8	C₂×C₁₆×C₁₉	C₂²	1	6	yes	complemented
9	D₃₀₄	C₂²	1	16	yes	direct product factor
10	C₂³×D₁₉	—	4	2	no	—
11	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
12	C₂×D₇₆	—	2	12	no	—
13	C₂×D₇₆	—	4	6	no	—
14	C₂×C₈×C₁₉	D₄	1	3	yes	—
15	C₂×C₈×C₁₉	C₂³	1	3	yes	—
16	D₁₅₂	—	2	12	no	—
17	D₁₅₂	C₂³	1	8	yes	complemented
18	C₁₆×C₁₉	C₂³	1	4	yes	complemented
19	C₂³×C₁₉	D₈	1	1	yes	characteristic
20	C₂²×D₁₉	—	4	12	no	—
21	C₂²×D₁₉	—	8	8	no	—
22	C₂×C₄×C₁₉	D₈	1	3	yes	—
23	C₂×C₄×C₁₉	C₂×D₄	1	3	yes	—
24	D₇₆	—	2	8	no	—
25	D₇₆	—	4	12	no	—
26	C₈×C₁₉	C₂×D₄	1	3	yes	—
27	C₈×C₁₉	C₂⁴	1	1	yes	characteristic
28	C₂²×D₁₆	—	19	1	no	maximal, Sylow
29	C₂²×C₁₉	D₁₆	1	4	yes	complemented
30	C₂²×C₁₉	C₂×D₈	1	3	yes	—
31	C₂×D₁₉	—	4	8	no	—
32	C₂×D₁₉	—	8	24	no	—
33	C₄×C₁₉	C₂×D₈	1	3	yes	—
34	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
35	C₂²×D₈	—	19	2	no	—
36	C₂×D₁₆	—	19	12	no	—
37	C₂²×C₁₆	D₁₉	1	1	yes	characteristic, complemented
38	C₂×C₁₉	C₂×D₁₆	1	6	yes	complemented
39	C₂×C₁₉	C₂²×D₈	1	1	yes	characteristic
40	D₁₉	—	8	8	no	—
41	C₂²×D₄	—	38	2	no	—
42	C₂×D₈	—	19	12	no	—
43	C₂×D₈	—	38	6	no	—
44	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
45	D₁₆	—	19	16	no	—
46	C₂×C₁₆	C₂×D₁₉	1	6	yes	complemented
47	C₁₉	C₂²×D₁₆	1	1	yes	characteristic, complemented, Sylow
48	C₂⁴	—	76	2	no	—
49	C₂×D₄	—	38	12	no	—
50	C₂×D₄	—	76	6	no	—
51	C₂²×C₄	D₇₆	1	1	yes	characteristic
52	D₈	—	19	8	no	—
53	D₈	—	38	12	no	—
54	C₂×C₈	D₇₆	1	3	yes	—
55	C₂×C₈	C₂²×D₁₉	1	3	yes	—
56	C₁₆	C₂²×D₁₉	1	4	yes	complemented
57	C₂³	—	76	12	no	—
58	C₂³	—	152	8	no	—
59	C₂³	D₁₅₂	1	1	yes	characteristic
60	D₄	—	38	8	no	—
61	D₄	—	76	12	no	—
62	C₂×C₄	D₁₅₂	1	3	yes	—
63	C₂×C₄	C₂×D₇₆	1	3	yes	—
64	C₈	C₂×D₇₆	1	3	yes	—
65	C₈	C₂³×D₁₉	1	1	yes	characteristic
66	C₂²	—	76	8	no	—
67	C₂²	—	152	24	no	—
68	C₂²	D₃₀₄	1	4	yes	direct product factor
69	C₂²	C₂×D₁₅₂	1	3	yes	—
70	C₄	C₂×D₁₅₂	1	3	yes	—
71	C₄	C₂²×D₇₆	1	1	yes	characteristic
72	C₂	—	152	8	no	—
73	C₂	C₂×D₃₀₄	1	6	yes	direct product factor
74	C₂	C₂²×D₁₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₅₂
commutator, cosocle	C₈×C₁₉	C₂⁴
Frattini	C₈	C₂³×D₁₉
Fitting	C₂²×C₁₆×C₁₉	C₂
socle	C₂³×C₁₉	D₈
hypercenter	C₂²×C₁₆	D₁₉
hypocenter	C₁₉	C₂²×D₁₆
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×D₁₅₂	C₂	semidirect
2. C₂×D₃₀₄	C₂	direct (N × H)
3. C₂²×C₁₆×C₁₉	C₂	semidirect
7. C₂×D₁₅₂	C₂²	semidirect
8. C₂×C₁₆×C₁₉	C₂²	semidirect
9. D₃₀₄	C₂²	direct (N × H)
17. D₁₅₂	C₂³	semidirect
18. C₁₆×C₁₉	C₂³	semidirect
29. C₂²×C₁₉	D₁₆	semidirect
37. C₂²×C₁₆	D₁₉	semidirect
38. C₂×C₁₉	C₂×D₁₆	semidirect
46. C₂×C₁₆	C₂×D₁₉	semidirect
47. C₁₉	C₂²×D₁₆	semidirect
56. C₁₆	C₂²×D₁₉	semidirect
68. C₂²	D₃₀₄	direct (N × H)
73. C₂	C₂×D₃₀₄	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×D₁₅₂	2
C₂×D₃₀₄	2
C₂²×C₁₆×C₁₉	2
C₂²×D₁₆	19

Subgroups — C22×D304 #14576741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₃₀₄ #14576741