Subgroups — C₂×Q₈×C₃⋊Dic₃ #10596282

Order 576.

894 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×Q₈	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₃⋊Dic₃	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊(C₃⋊Dic₃)	C₂	1	3	yes	maximal
4	C₂×C₄×C₃⋊Dic₃	C₂	1	3	yes	maximal
5	C₂×Q₈×Dic₃	—	3	4	no	maximal
6	C₂×C₃²×Q₈	C₄	1	8	yes	complemented
7	C₂×C₃²×Q₈	C₂²	1	4	yes	—
8	C₂²×C₃²×C₄	C₂²	1	3	yes	—
9	C₂²×C₃⋊Dic₃	C₂²	1	3	yes	—
10	C₂²×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
11	C₄⋊(C₃⋊Dic₃)	C₂²	1	12	yes	—
12	C₄×C₃⋊Dic₃	C₂²	1	12	yes	—
13	C₂²×C₃×Q₈	D₃	1	4	yes	—
14	Q₈×Dic₃	—	3	32	no	—
15	C₂×C₄⋊Dic₃	—	3	12	no	—
16	C₂×C₄×Dic₃	—	3	12	no	—
17	C₂³×C₃²	C₂³	1	1	yes	characteristic
18	C₃²×Q₈	C₂×C₄	1	16	yes	complemented
19	C₂×C₃²×C₄	C₂×C₄	1	12	yes	—
20	C₂×C₃²×C₄	C₂³	1	6	yes	—
21	C₂×C₃⋊Dic₃	—	2	6	no	—
22	C₂×C₃⋊Dic₃	Q₈	1	4	yes	direct product factor
23	C₂×C₃⋊Dic₃	C₂³	1	6	yes	—
24	C₂×C₃⋊Dic₃	C₂³	1	2	yes	—
25	C₂×C₄×Q₈	—	9	1	no	Sylow
26	C₂×C₃×Q₈	Dic₃	1	32	yes	complemented
27	C₂×C₃×Q₈	C₂×D₃	1	16	yes	—
28	C₂²×C₃×C₄	C₂×D₃	1	12	yes	—
29	C₂²×Dic₃	—	3	4	no	—
30	C₂²×Dic₃	—	3	12	no	—
31	C₄⋊Dic₃	—	3	48	no	—
32	C₄×Dic₃	—	3	48	no	—
33	C₂²×C₃²	C₂²×C₄	1	2	yes	—
34	C₂²×C₃²	C₂×Q₈	1	2	yes	—
35	C₂²×C₃²	#41	1	2	yes	—
36	C₂²×C₃²	C₂⁴	1	1	yes	characteristic
37	C₃²×C₄	C₂²×C₄	1	12	yes	—
38	C₃⋊Dic₃	—	2	6	no	—
39	C₃⋊Dic₃	C₂×Q₈	1	4	yes	direct product factor
40	C₂²×Q₈	C₃⋊D₃	1	1	yes	characteristic
41	C₄×Q₈	—	9	8	no	—
42	C₂×C₄⋊C₄	—	9	3	no	—
43	C₂×C₄²	—	9	3	no	—
44	C₂³×C₃	C₂²×D₃	1	4	yes	—
45	C₃×Q₈	C₂×Dic₃	1	64	yes	complemented
46	C₂×C₃×C₄	C₂×Dic₃	1	48	yes	—
47	C₂×C₃×C₄	C₂²×D₃	1	24	yes	—
48	C₂×Dic₃	—	3	16	no	—
49	C₂×Dic₃	—	3	8	no	—
50	C₂×Dic₃	—	3	24	no	—
51	C₂×Dic₃	—	6	24	no	—
52	C₂×C₃²	C₄×Q₈	1	4	yes	complemented
53	C₂×C₃²	C₂³×C₄	1	1	yes	characteristic
54	C₂×C₃²	C₂²×Q₈	1	1	yes	characteristic
55	C₂×C₃²	C₂×#41	1	1	yes	characteristic
56	C₂×Q₈	C₃⋊Dic₃	1	8	yes	direct product factor
57	C₂×Q₈	C₂×C₃⋊D₃	1	4	yes	—
58	C₂²×C₄	—	9	1	no	—
59	C₂²×C₄	—	9	3	no	—
60	C₂²×C₄	C₂×C₃⋊D₃	1	3	yes	—
61	C₄⋊C₄	—	9	12	no	—
62	C₄²	—	9	12	no	—
63	C₂²×C₃	D₃×Q₈	1	8	yes	—
64	C₂²×C₃	#239	1	8	yes	—
65	C₂²×C₃	C₂²×Dic₃	1	8	yes	—
66	C₂²×C₃	C₂³×D₃	1	4	yes	—
67	C₃×C₄	C₂²×Dic₃	1	48	yes	—
68	Dic₃	—	3	16	no	—
69	Dic₃	—	6	24	no	—
70	C₃²	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
71	C₂³	C₂²×C₃⋊D₃	1	1	yes	characteristic
72	Q₈	C₂×C₃⋊Dic₃	1	16	yes	direct product factor
73	C₂×C₄	—	9	2	no	—
74	C₂×C₄	—	9	4	no	—
75	C₂×C₄	—	9	6	no	—
76	C₂×C₄	—	18	6	no	—
77	C₂×C₄	C₂×C₃⋊Dic₃	1	12	yes	—
78	C₂×C₄	C₂²×C₃⋊D₃	1	6	yes	—
79	C₂×C₃	Q₈×Dic₃	1	16	yes	complemented
80	C₂×C₃	C₂×D₃×Q₈	1	4	yes	—
81	C₂×C₃	C₂×#239	1	4	yes	—
82	C₂×C₃	C₂³×Dic₃	1	4	yes	—
83	C₂²	Q₈×C₃⋊D₃	1	2	yes	—
84	C₂²	#3832	1	2	yes	—
85	C₂²	C₂²×C₃⋊Dic₃	1	2	yes	—
86	C₂²	C₂³×C₃⋊D₃	1	1	yes	characteristic
87	C₄	—	9	4	no	—
88	C₄	—	18	6	no	—
89	C₄	C₂²×C₃⋊Dic₃	1	12	yes	—
90	C₃	C₂×Q₈×Dic₃	1	4	yes	complemented
91	C₂	Q₈×C₃⋊Dic₃	1	4	yes	direct product factor
92	C₂	C₂×Q₈×C₃⋊D₃	1	1	yes	characteristic
93	C₂	C₂×#3832	1	1	yes	characteristic
94	C₂	C₂³×C₃⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₃⋊D₃
commutator	C₂×C₃²	C₂³×C₄
Frattini	C₂²	C₂³×C₃⋊D₃
Fitting	C₂²×C₃²×Q₈	C₂
socle, prime radical	C₂³×C₃²	C₂³
cosocle	C₂²×C₃²	C₂⁴
hypercenter	C₂²×Q₈	C₃⋊D₃
hypocenter	C₃²	C₂×C₄×Q₈
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. Q₈×C₃⋊Dic₃	C₂	direct (N × H)
6. C₂×C₃²×Q₈	C₄	semidirect
18. C₃²×Q₈	C₂×C₄	semidirect
22. C₂×C₃⋊Dic₃	Q₈	direct (N × H)
26. C₂×C₃×Q₈	Dic₃	semidirect
39. C₃⋊Dic₃	C₂×Q₈	direct (N × H)
45. C₃×Q₈	C₂×Dic₃	semidirect
52. C₂×C₃²	C₄×Q₈	semidirect
56. C₂×Q₈	C₃⋊Dic₃	direct (N × H)
70. C₃²	C₂×C₄×Q₈	semidirect
72. Q₈	C₂×C₃⋊Dic₃	direct (N × H)
79. C₂×C₃	Q₈×Dic₃	semidirect
90. C₃	C₂×Q₈×Dic₃	semidirect
91. C₂	Q₈×C₃⋊Dic₃	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×C₃²×Q₈	2
Q₈×C₃⋊Dic₃	2
C₂×C₄⋊(C₃⋊Dic₃)	2
C₂×C₄×C₃⋊Dic₃	2
C₂×Q₈×Dic₃	3

Subgroups — C2×Q8×C3⋊Dic3 #10596282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×C₃⋊Dic₃ #10596282