Subgroups — #63441

Order 288.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
2	#3676	C₂	1	1	yes	maximal, characteristic
3	#3676	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₉⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₉⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#879	—	3	1	no	maximal
9	C₂³×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂×Dic₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₉	C₂²	1	1	yes	characteristic
14	C₂×Dic₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₉	C₂²	1	1	yes	characteristic
16	C₃×C₂²⋊C₄	D₃	1	1	yes	characteristic
17	#217	—	3	1	no	—
18	#217	—	3	1	no	—
19	C₄⋊Dic₃	—	3	1	no	—
20	Dic₃⋊C₄	—	3	1	no	—
21	Dic₃⋊C₄	—	3	1	no	—
22	C₄×Dic₃	—	3	1	no	—
23	C₂²×C₉	—	2	1	no	—
24	C₂²×C₉	—	2	1	no	—
25	C₂²×C₉	—	2	1	no	—
26	C₂²×C₉	C₂³	1	1	yes	characteristic
27	C₄×C₉	—	2	1	no	—
28	C₄×C₉	—	2	1	no	—
29	Dic₉	—	2	1	no	—
30	Dic₉	—	2	1	no	—
31	Dic₉	—	2	1	no	—
32	Dic₉	—	2	1	no	—
33	#126	—	9	1	no	Sylow
34	C₂³×C₃	C₂×D₃	1	1	yes	characteristic
35	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
36	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
37	C₂×Dic₃	—	3	1	no	—
38	C₂×Dic₃	—	3	1	no	—
39	C₂×Dic₃	—	3	1	no	—
40	C₂×Dic₃	—	3	1	no	—
41	C₂×C₉	—	4	1	no	—
42	C₂×C₉	#41	1	1	yes	characteristic
43	C₂×C₉	#41	1	1	yes	characteristic
44	C₂×C₉	#41	1	1	yes	characteristic
45	C₄⋊C₄	—	9	1	no	—
46	C₄⋊C₄	—	9	1	no	—
47	C₄⋊C₄	—	9	1	no	—
48	C₂²⋊C₄	—	9	1	no	—
49	C₂²⋊C₄	—	9	1	no	—
50	C₂²⋊C₄	D₉	1	1	yes	characteristic
51	C₄²	—	9	1	no	—
52	C₂²×C₃	—	2	1	no	—
53	C₂²×C₃	—	2	1	no	—
54	C₂²×C₃	—	2	1	no	—
55	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
56	C₃×C₄	—	2	1	no	—
57	C₃×C₄	—	2	1	no	—
58	Dic₃	—	6	1	no	—
59	Dic₃	—	6	1	no	—
60	Dic₃	—	6	1	no	—
61	Dic₃	—	6	1	no	—
62	C₉	#126	1	1	yes	characteristic, complemented, Sylow
63	C₂³	C₂×D₉	1	1	yes	characteristic
64	C₂×C₄	—	9	1	no	—
65	C₂×C₄	—	9	1	no	—
66	C₂×C₄	—	9	1	no	—
67	C₂×C₄	—	9	1	no	—
68	C₂×C₄	C₂×D₉	1	1	yes	characteristic
69	C₂×C₄	C₂×D₉	1	1	yes	characteristic
70	C₂×C₃	—	4	1	no	—
71	C₂×C₃	#235	1	1	yes	characteristic
72	C₂×C₃	#237	1	1	yes	characteristic
73	C₂×C₃	#237	1	1	yes	characteristic
74	C₂²	—	2	1	no	—
75	C₂²	—	2	1	no	—
76	C₂²	—	2	1	no	—
77	C₂²	C₂²×D₉	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	2	1	no	—
80	C₄	—	18	1	no	—
81	C₄	—	18	1	no	—
82	C₄	—	18	1	no	—
83	C₄	—	18	1	no	—
84	C₃	#879	1	1	yes	characteristic
85	C₂	—	4	1	no	—
86	C₂	#3697	1	1	yes	characteristic
87	C₂	#3699	1	1	yes	characteristic
88	C₂	#3699	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₉
commutator, cosocle	C₂²×C₉	C₂³
Frattini, socle	C₂²×C₃	C₂²×D₃
Fitting	C₉×C₂²⋊C₄	C₂
prime radical	C₂³×C₃	C₂×D₃
hypercenter	C₂²⋊C₄	D₉
hypocenter	C₉	#126
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
4. C₄⋊Dic₉	C₂	semidirect
5. Dic₉⋊C₄	C₂	semidirect
6. Dic₉⋊C₄	C₂	semidirect
7. C₄×Dic₉	C₂	semidirect
62. C₉	#126	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₂²⋊C₄	2
#3676	2
C₄⋊Dic₉	2
Dic₉⋊C₄	2
C₄×Dic₉	2
#879	3