Subgroups — C₂×#3674 #63503

Order 288.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₈	C₂	1	1	yes	maximal, characteristic
3	#3674	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×#216	—	3	1	no	maximal
6	Q₈×C₉	—	2	1	no	—
7	Q₈×C₉	C₂²	1	2	yes	—
8	C₂×C₄×C₉	—	2	1	no	—
9	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₉	—	2	1	no	—
11	Dic₁₈	—	2	1	no	—
12	Dic₁₈	C₂²	1	2	yes	—
13	C₉⋊C₈	C₂²	1	2	yes	—
14	C₂×C₃×Q₈	D₃	1	1	yes	characteristic
15	C₂×Dic₆	—	3	1	no	—
16	#216	—	3	4	no	—
17	C₂×C₃⋊C₈	—	3	1	no	—
18	C₂²×C₉	D₄	1	1	yes	characteristic
19	C₄×C₉	—	2	2	no	—
20	C₄×C₉	D₄	1	1	yes	characteristic
21	C₄×C₉	C₂³	1	1	yes	characteristic
22	Dic₉	—	2	2	no	—
23	C₂×Q₁₆	—	9	1	no	Sylow
24	C₃×Q₈	—	2	1	no	—
25	C₃×Q₈	C₂×D₃	1	2	yes	—
26	C₂×C₃×C₄	—	2	1	no	—
27	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
28	C₂×Dic₃	—	6	1	no	—
29	Dic₆	—	3	2	no	—
30	Dic₆	—	6	1	no	—
31	C₃⋊C₈	—	3	2	no	—
32	C₂×C₉	Q₁₆	1	2	yes	complemented
33	C₂×C₉	C₂×D₄	1	1	yes	characteristic
34	C₂×Q₈	—	9	1	no	—
35	C₂×Q₈	D₉	1	1	yes	characteristic
36	Q₁₆	—	9	4	no	—
37	C₂×C₈	—	9	1	no	—
38	C₂²×C₃	#67	1	1	yes	characteristic
39	C₃×C₄	—	2	2	no	—
40	C₃×C₄	#67	1	1	yes	characteristic
41	C₃×C₄	C₂²×D₃	1	1	yes	characteristic
42	Dic₃	—	6	2	no	—
43	C₉	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
44	Q₈	—	2	1	no	—
45	Q₈	—	9	2	no	—
46	Q₈	—	18	1	no	—
47	Q₈	C₂×D₉	1	2	yes	—
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	—	18	1	no	—
50	C₂×C₄	C₂×D₉	1	1	yes	characteristic
51	C₈	—	9	2	no	—
52	C₂×C₃	#216	1	2	yes	—
53	C₂×C₃	C₂×#67	1	1	yes	characteristic
54	C₂²	#611	1	1	yes	characteristic
55	C₄	—	2	2	no	—
56	C₄	—	18	2	no	—
57	C₄	#611	1	1	yes	characteristic
58	C₄	C₂²×D₉	1	1	yes	characteristic
59	C₃	C₂×#216	1	1	yes	characteristic
60	C₂	#3674	1	2	yes	direct product factor
61	C₂	C₂×#611	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#611
commutator, cosocle	C₄×C₉	C₂³
Frattini	C₃×C₄	C₂²×D₃
Fitting	C₂×Q₈×C₉	C₂
socle, prime radical	C₂²×C₃	#67
hypercenter	C₂×Q₈	D₉
hypocenter	C₉	C₂×Q₁₆
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
3. #3674	C₂	direct (N × H)
32. C₂×C₉	Q₁₆	semidirect
43. C₉	C₂×Q₁₆	semidirect
60. C₂	#3674	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×Q₈×C₉	2
C₂×Dic₁₈	2
#3674	2
C₂×C₉⋊C₈	2
C₂×#216	3

Subgroups — C2×#3674 #63503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3674 #63503