Subgroups — C₂×#63378 #10588786

Order 576.

195 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₉	C₂	1	2	yes	maximal
3	#63378	C₂	1	4	yes	maximal, direct product factor
4	C₂×#818	—	3	1	no	maximal
5	C₂²×C₄×C₉	C₂²	1	1	yes	characteristic
6	C₂²×Dic₉	—	2	2	no	—
7	C₂×C₈×C₉	C₄	1	4	yes	complemented
8	C₂×C₈×C₉	C₂²	1	2	yes	—
9	C₄⋊Dic₉	—	2	2	no	—
10	C₄⋊Dic₉	C₂²	1	4	yes	—
11	C₂²×C₃×C₈	D₃	1	1	yes	characteristic
12	C₂×C₄⋊Dic₃	—	3	2	no	—
13	#818	—	3	4	no	—
14	C₂³×C₉	D₄	1	1	yes	characteristic
15	C₂×C₄×C₉	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₉	Q₈	1	2	yes	—
18	C₂×C₄×C₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₉	—	2	4	no	—
20	C₂×Dic₉	—	4	4	no	—
21	C₈×C₉	C₂×C₄	1	4	yes	complemented
22	C₂×#107	—	9	1	no	Sylow
23	C₂²×C₃×C₄	C₂×D₃	1	1	yes	characteristic
24	C₂²×Dic₃	—	6	2	no	—
25	C₂×C₃×C₈	Dic₃	1	4	yes	—
26	C₂×C₃×C₈	C₂×D₃	1	2	yes	—
27	C₄⋊Dic₃	—	3	4	no	—
28	C₄⋊Dic₃	—	6	2	no	—
29	C₂²×C₉	C₄⋊C₄	1	2	yes	—
30	C₂²×C₉	D₈	1	2	yes	—
31	C₂²×C₉	Q₁₆	1	2	yes	—
32	C₂²×C₉	C₂×D₄	1	1	yes	characteristic
33	C₄×C₉	C₄⋊C₄	1	2	yes	—
34	C₄×C₉	C₂²×C₄	1	1	yes	characteristic
35	C₄×C₉	C₂×Q₈	1	1	yes	characteristic
36	Dic₉	—	4	4	no	—
37	C₂²×C₈	D₉	1	1	yes	characteristic
38	C₂×C₄⋊C₄	—	9	2	no	—
39	#107	—	9	4	no	—
40	C₂³×C₃	D₁₂	1	1	yes	characteristic
41	C₂×C₃×C₄	Dic₆	1	2	yes	—
42	C₂×C₃×C₄	D₁₂	1	1	yes	characteristic
43	C₂×C₃×C₄	C₂×Dic₃	1	2	yes	—
44	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
45	C₂×Dic₃	—	6	4	no	—
46	C₂×Dic₃	—	12	4	no	—
47	C₃×C₈	C₂×Dic₃	1	4	yes	—
48	C₂×C₉	#107	1	4	yes	complemented
49	C₂×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₉	C₂×D₈	1	1	yes	characteristic
51	C₂×C₉	C₂×Q₁₆	1	1	yes	characteristic
52	C₂²×C₄	—	18	2	no	—
53	C₂²×C₄	C₂×D₉	1	1	yes	characteristic
54	C₂×C₈	Dic₉	1	4	yes	complemented
55	C₂×C₈	C₂×D₉	1	2	yes	—
56	C₄⋊C₄	—	9	4	no	—
57	C₄⋊C₄	—	18	2	no	—
58	C₂²×C₃	D₂₄	1	2	yes	—
59	C₂²×C₃	Dic₁₂	1	2	yes	—
60	C₂²×C₃	C₄⋊Dic₃	1	2	yes	—
61	C₂²×C₃	C₂×D₁₂	1	1	yes	characteristic
62	C₃×C₄	C₄⋊Dic₃	1	2	yes	—
63	C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
64	C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
65	Dic₃	—	12	4	no	—
66	C₉	C₂×#107	1	1	yes	characteristic, complemented, Sylow
67	C₂³	D₃₆	1	1	yes	characteristic
68	C₂×C₄	—	18	4	no	—
69	C₂×C₄	—	36	4	no	—
70	C₂×C₄	Dic₁₈	1	2	yes	—
71	C₂×C₄	D₃₆	1	1	yes	characteristic
72	C₂×C₄	C₂×Dic₉	1	2	yes	—
73	C₂×C₄	C₂²×D₉	1	1	yes	characteristic
74	C₈	C₂×Dic₉	1	4	yes	complemented
75	C₂×C₃	#818	1	4	yes	—
76	C₂×C₃	C₂×D₂₄	1	1	yes	characteristic
77	C₂×C₃	C₂×Dic₁₂	1	1	yes	characteristic
78	C₂×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
79	C₂²	Dic₃₆	1	2	yes	—
80	C₂²	D₇₂	1	2	yes	—
81	C₂²	C₄⋊Dic₉	1	2	yes	—
82	C₂²	C₂×D₃₆	1	1	yes	characteristic
83	C₄	—	36	4	no	—
84	C₄	C₄⋊Dic₉	1	2	yes	—
85	C₄	C₂×Dic₁₈	1	1	yes	characteristic
86	C₄	C₂²×Dic₉	1	1	yes	characteristic
87	C₃	C₂×#818	1	1	yes	characteristic
88	C₂	#63378	1	4	yes	direct product factor
89	C₂	C₂×Dic₃₆	1	1	yes	characteristic
90	C₂	C₂×D₇₂	1	1	yes	characteristic
91	C₂	C₂×C₄⋊Dic₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₃₆
commutator	C₄×C₉	C₂²×C₄
Frattini	C₂×C₃×C₄	C₂²×D₃
Fitting	C₂²×C₈×C₉	C₂
socle, prime radical	C₂³×C₃	D₁₂
cosocle	C₂×C₄×C₉	C₂³
hypercenter	C₂²×C₈	D₉
hypocenter	C₉	C₂×#107
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. #63378	C₂	direct (N × H)
7. C₂×C₈×C₉	C₄	semidirect
21. C₈×C₉	C₂×C₄	semidirect
48. C₂×C₉	#107	semidirect
54. C₂×C₈	Dic₉	semidirect
66. C₉	C₂×#107	semidirect
74. C₈	C₂×Dic₉	semidirect
88. C₂	#63378	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×C₈×C₉	2
C₂×C₄⋊Dic₉	2
#63378	2
C₂×#818	3

Subgroups — C2×#63378 #10588786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#63378 #10588786