Subgroups — C₂×#3699 #63709

Order 288.

246 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#611	C₂	1	2	yes	maximal, complemented
3	C₂²×Dic₉	C₂	1	2	yes	maximal, complemented
4	#3699	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄×D₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#237	—	3	1	no	maximal
8	C₂³×C₉	C₂²	1	2	yes	—
9	C₂²×D₉	C₂²	1	1	yes	characteristic
10	D₄×C₉	C₂²	1	4	yes	complemented
11	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
12	#611	C₂²	1	8	yes	complemented
13	C₂×Dic₉	C₂²	1	2	yes	—
14	C₂×Dic₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₉	C₂²	1	8	yes	complemented
16	C₄×D₉	C₂²	1	4	yes	complemented
17	Dic₁₈	C₂²	1	4	yes	complemented
18	C₂×C₃×D₄	D₃	1	1	yes	characteristic
19	C₂×#67	—	3	2	no	—
20	C₂²×Dic₃	—	3	2	no	—
21	#237	—	3	8	no	—
22	C₂×C₄×D₃	—	3	1	no	—
23	C₂×Dic₆	—	3	1	no	—
24	C₂²×C₉	—	2	4	no	—
25	C₂²×C₉	C₂³	1	4	yes	—
26	C₂²×C₉	C₂³	1	1	yes	characteristic
27	C₂×D₉	—	2	2	no	—
28	C₂×D₉	C₂³	1	2	yes	—
29	C₄×C₉	C₂³	1	2	yes	—
30	Dic₉	C₂³	1	4	yes	—
31	Dic₉	C₂³	1	2	yes	—
32	C₂×#41	—	9	1	no	Sylow
33	C₂³×C₃	C₂×D₃	1	2	yes	—
34	C₂²×D₃	—	3	1	no	—
35	C₃×D₄	C₂×D₃	1	4	yes	—
36	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
37	#67	—	3	8	no	—
38	C₂×Dic₃	—	3	2	no	—
39	C₂×Dic₃	—	3	1	no	—
40	C₂×Dic₃	—	3	8	no	—
41	C₄×D₃	—	3	4	no	—
42	Dic₆	—	3	4	no	—
43	C₂×C₉	—	2	4	no	—
44	C₂×C₉	#41	1	2	yes	complemented
45	C₂×C₉	C₂⁴	1	1	yes	characteristic
46	D₉	—	2	2	no	—
47	#41	—	9	8	no	—
48	C₂×Q₈	—	9	1	no	—
49	C₂×D₄	—	9	2	no	—
50	C₂×D₄	D₉	1	1	yes	characteristic, complemented
51	C₂²×C₄	—	9	2	no	—
52	C₂²×C₄	—	9	1	no	—
53	C₂²×C₃	—	2	4	no	—
54	C₂²×C₃	C₂²×D₃	1	4	yes	—
55	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
56	C₂×D₃	—	3	2	no	—
57	C₂×D₃	—	6	2	no	—
58	C₃×C₄	C₂²×D₃	1	2	yes	—
59	Dic₃	—	3	4	no	—
60	Dic₃	—	3	2	no	—
61	C₉	C₂×#41	1	1	yes	characteristic, complemented, Sylow
62	C₂³	—	9	1	no	—
63	C₂³	C₂×D₉	1	2	yes	—
64	Q₈	—	9	4	no	—
65	D₄	—	9	8	no	—
66	D₄	C₂×D₉	1	4	yes	complemented
67	C₂×C₄	—	9	8	no	—
68	C₂×C₄	—	9	1	no	—
69	C₂×C₄	—	9	2	no	—
70	C₂×C₄	—	9	4	no	—
71	C₂×C₄	C₂×D₉	1	1	yes	characteristic
72	C₂×C₃	—	2	4	no	—
73	C₂×C₃	#237	1	2	yes	—
74	C₂×C₃	C₂³×D₃	1	1	yes	characteristic
75	D₃	—	6	2	no	—
76	C₂²	—	2	4	no	—
77	C₂²	—	9	2	no	—
78	C₂²	—	18	2	no	—
79	C₂²	C₂²×D₉	1	4	yes	—
80	C₂²	C₂²×D₉	1	1	yes	characteristic
81	C₄	—	9	2	no	—
82	C₄	—	9	4	no	—
83	C₄	C₂²×D₉	1	2	yes	—
84	C₃	C₂×#237	1	1	yes	characteristic
85	C₂	—	2	4	no	—
86	C₂	—	18	2	no	—
87	C₂	#3699	1	2	yes	direct product factor
88	C₂	C₂³×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₉
commutator, cosocle	C₂×C₉	C₂⁴
Frattini	C₂×C₃	C₂³×D₃
Fitting	C₂×D₄×C₉	C₂
socle	C₂²×C₃	C₂²×D₃
hypercenter	C₂×D₄	D₉
hypocenter	C₉	C₂×#41
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×C₉	C₂	semidirect
2. C₂×#611	C₂	semidirect
3. C₂²×Dic₉	C₂	semidirect
4. #3699	C₂	direct (N × H)
5. C₂×C₄×D₉	C₂	semidirect
6. C₂×Dic₁₈	C₂	semidirect
10. D₄×C₉	C₂²	semidirect
12. #611	C₂²	semidirect
15. C₂×Dic₉	C₂²	semidirect
16. C₄×D₉	C₂²	semidirect
17. Dic₁₈	C₂²	semidirect
44. C₂×C₉	#41	semidirect
50. C₂×D₄	D₉	semidirect
61. C₉	C₂×#41	semidirect
66. D₄	C₂×D₉	semidirect
87. C₂	#3699	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×D₄×C₉	2
C₂×#611	2
C₂²×Dic₉	2
#3699	2
C₂×C₄×D₉	2
C₂×Dic₁₈	2
C₂×#237	3

Subgroups — C2×#3699 #63709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3699 #63709