Subgroups — C₂²×Dic₃₆ #10589838

Order 576.

387 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₈	C₂	1	2	yes	maximal
2	C₂²×C₈×C₉	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₃₆	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Dic₁₂	—	3	1	no	maximal
5	C₂²×C₄×C₉	C₂²	1	1	yes	characteristic
6	C₂²×Dic₉	—	2	2	no	—
7	C₂×Dic₁₈	—	2	6	no	—
8	C₂×Dic₁₈	C₂²	1	12	yes	—
9	C₂×C₈×C₉	C₂²	1	6	yes	—
10	Dic₃₆	C₂²	1	16	yes	direct product factor
11	C₂²×Dic₆	—	3	2	no	—
12	C₂²×C₃×C₈	D₃	1	1	yes	characteristic
13	C₂×Dic₁₂	—	3	12	no	—
14	C₂³×C₉	D₄	1	1	yes	characteristic
15	C₂×C₄×C₉	D₄	1	3	yes	—
16	C₂×C₄×C₉	C₂³	1	3	yes	—
17	C₂×Dic₉	—	2	12	no	—
18	Dic₁₈	—	2	12	no	—
19	Dic₁₈	C₂³	1	8	yes	—
20	C₈×C₉	C₂³	1	4	yes	—
21	C₂²×Q₁₆	—	9	1	no	Sylow
22	C₂²×C₃×C₄	C₂×D₃	1	1	yes	characteristic
23	C₂²×Dic₃	—	6	2	no	—
24	C₂×Dic₆	—	3	12	no	—
25	C₂×Dic₆	—	6	6	no	—
26	C₂×C₃×C₈	C₂×D₃	1	6	yes	—
27	Dic₁₂	—	3	16	no	—
28	C₂²×C₉	Q₁₆	1	4	yes	complemented
29	C₂²×C₉	C₂×D₄	1	3	yes	—
30	C₄×C₉	C₂×D₄	1	3	yes	—
31	C₄×C₉	C₂⁴	1	1	yes	characteristic
32	Dic₉	—	2	8	no	—
33	C₂²×Q₈	—	9	2	no	—
34	C₂×Q₁₆	—	9	12	no	—
35	C₂²×C₈	D₉	1	1	yes	characteristic
36	C₂³×C₃	D₁₂	1	1	yes	characteristic
37	C₂×C₃×C₄	D₁₂	1	3	yes	—
38	C₂×C₃×C₄	C₂²×D₃	1	3	yes	—
39	C₂×Dic₃	—	6	12	no	—
40	Dic₆	—	3	8	no	—
41	Dic₆	—	6	12	no	—
42	C₃×C₈	C₂²×D₃	1	4	yes	—
43	C₂×C₉	C₂×Q₁₆	1	6	yes	complemented
44	C₂×C₉	C₂²×D₄	1	1	yes	characteristic
45	C₂×Q₈	—	9	12	no	—
46	C₂×Q₈	—	18	6	no	—
47	C₂²×C₄	—	18	2	no	—
48	C₂²×C₄	C₂×D₉	1	1	yes	characteristic
49	Q₁₆	—	9	16	no	—
50	C₂×C₈	C₂×D₉	1	6	yes	—
51	C₂²×C₃	Dic₁₂	1	4	yes	—
52	C₂²×C₃	C₂×D₁₂	1	3	yes	—
53	C₃×C₄	C₂×D₁₂	1	3	yes	—
54	C₃×C₄	C₂³×D₃	1	1	yes	characteristic
55	Dic₃	—	6	8	no	—
56	C₉	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
57	C₂³	D₃₆	1	1	yes	characteristic
58	Q₈	—	9	8	no	—
59	Q₈	—	18	12	no	—
60	C₂×C₄	—	18	12	no	—
61	C₂×C₄	D₃₆	1	3	yes	—
62	C₂×C₄	C₂²×D₉	1	3	yes	—
63	C₈	C₂²×D₉	1	4	yes	—
64	C₂×C₃	C₂×Dic₁₂	1	6	yes	—
65	C₂×C₃	C₂²×D₁₂	1	1	yes	characteristic
66	C₂²	Dic₃₆	1	4	yes	direct product factor
67	C₂²	C₂×D₃₆	1	3	yes	—
68	C₄	—	18	8	no	—
69	C₄	C₂×D₃₆	1	3	yes	—
70	C₄	C₂³×D₉	1	1	yes	characteristic
71	C₃	C₂²×Dic₁₂	1	1	yes	characteristic
72	C₂	C₂×Dic₃₆	1	6	yes	direct product factor
73	C₂	C₂²×D₃₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₃₆
commutator, cosocle	C₄×C₉	C₂⁴
Frattini	C₃×C₄	C₂³×D₃
Fitting	C₂²×C₈×C₉	C₂
socle, prime radical	C₂³×C₃	D₁₂
hypercenter	C₂²×C₈	D₉
hypocenter	C₉	C₂²×Q₁₆
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₃₆	C₂	direct (N × H)
10. Dic₃₆	C₂²	direct (N × H)
28. C₂²×C₉	Q₁₆	semidirect
43. C₂×C₉	C₂×Q₁₆	semidirect
56. C₉	C₂²×Q₁₆	semidirect
66. C₂²	Dic₃₆	direct (N × H)
72. C₂	C₂×Dic₃₆	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×Dic₁₈	2
C₂²×C₈×C₉	2
C₂×Dic₃₆	2
C₂²×Dic₁₂	3

Subgroups — C22×Dic36 #10589838

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₃₆ #10589838