Subgroups — C₃×#2248 #72963

Order 384.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×SD₃₂	C₂	1	4	yes	maximal, complemented
2	C₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#493	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#2248	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×Q₁₆	—	2	1	no	—
7	C₂×C₃×Q₁₆	C₂²	1	2	yes	—
8	C₂×C₃×D₈	—	2	1	no	—
9	C₂×C₃×D₈	C₂²	1	2	yes	—
10	C₃×C₄⋊Q₈	—	2	1	no	—
11	C₃×#127	—	2	1	no	—
12	C₃×SD₃₂	—	2	8	no	—
13	C₂×C₃×C₁₆	C₂²	1	2	yes	—
14	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
15	C₂×SD₃₂	C₂×C₃	1	4	yes	complemented
16	#494	C₂×C₃	1	1	yes	characteristic, complemented
17	#493	C₂×C₃	1	1	yes	characteristic
18	C₄×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂×C₃×Q₈	—	2	2	no	—
20	C₂×C₃×D₄	—	2	2	no	—
21	C₂×C₃×D₄	—	4	2	no	—
22	C₃×Q₁₆	—	2	4	no	—
23	C₃×Q₁₆	—	4	2	no	—
24	C₃×D₈	—	2	4	no	—
25	C₃×D₈	—	4	2	no	—
26	C₂×C₃×C₈	D₄	1	1	yes	characteristic
27	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
28	C₃×C₄⋊C₄	—	4	2	no	—
29	C₃×C₄²	D₄	1	1	yes	characteristic
30	C₃×C₁₆	D₄	1	4	yes	complemented
31	C₂×Q₁₆	—	2	1	no	—
32	C₂×Q₁₆	C₂²×C₃	1	2	yes	—
33	C₂×D₈	—	2	1	no	—
34	C₂×D₈	C₂²×C₃	1	2	yes	—
35	C₄⋊Q₈	—	2	1	no	—
36	#127	—	2	1	no	—
37	SD₃₂	—	2	8	no	—
38	C₂×C₁₆	C₂²×C₃	1	2	yes	—
39	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
40	C₂³×C₃	—	4	2	no	—
41	C₃×Q₈	—	4	2	no	—
42	C₃×Q₈	—	4	2	no	—
43	C₃×D₄	—	4	2	no	—
44	C₃×D₄	—	4	2	no	—
45	C₃×D₄	—	8	4	no	—
46	C₂×C₃×C₄	—	4	2	no	—
47	C₂×C₃×C₄	D₈	1	2	yes	—
48	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
49	C₃×C₈	D₈	1	2	yes	—
50	C₃×C₈	C₂×D₄	1	2	yes	—
51	C₂×Q₈	—	2	2	no	—
52	C₂×D₄	—	2	2	no	—
53	C₂×D₄	—	4	2	no	—
54	Q₁₆	—	2	4	no	—
55	Q₁₆	—	4	2	no	—
56	D₈	—	2	4	no	—
57	D₈	—	4	2	no	—
58	C₂×C₈	C₃×D₄	1	1	yes	characteristic
59	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
60	C₄⋊C₄	—	4	2	no	—
61	C₄²	C₃×D₄	1	1	yes	characteristic
62	C₁₆	C₃×D₄	1	4	yes	complemented
63	C₂²×C₃	—	8	2	no	—
64	C₂²×C₃	—	8	4	no	—
65	C₂²×C₃	C₂×D₈	1	1	yes	characteristic
66	C₃×C₄	—	8	2	no	—
67	C₃×C₄	SD₃₂	1	4	yes	complemented
68	C₃×C₄	#127	1	1	yes	characteristic
69	C₃×C₄	C₂×D₈	1	1	yes	characteristic
70	C₂³	—	4	2	no	—
71	Q₈	—	4	2	no	—
72	Q₈	—	4	2	no	—
73	D₄	—	4	2	no	—
74	D₄	—	4	2	no	—
75	D₄	—	8	4	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	C₃×D₈	1	2	yes	—
78	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
79	C₈	C₃×D₈	1	2	yes	—
80	C₈	C₂×C₃×D₄	1	2	yes	—
81	C₂×C₃	—	16	2	no	—
82	C₂×C₃	#493	1	1	yes	characteristic
83	C₂×C₃	C₂×SD₃₂	1	2	yes	—
84	C₂²	—	8	4	no	—
85	C₂²	—	8	2	no	—
86	C₂²	C₂×C₃×D₈	1	1	yes	characteristic
87	C₄	—	8	2	no	—
88	C₄	C₃×SD₃₂	1	4	yes	complemented
89	C₄	C₃×#127	1	1	yes	characteristic
90	C₄	C₂×C₃×D₈	1	1	yes	characteristic
91	C₃	#2248	1	1	yes	characteristic, direct product factor, Sylow
92	C₂	—	16	2	no	—
93	C₂	C₃×#493	1	1	yes	characteristic
94	C₂	C₂×C₃×SD₃₂	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃
prime radical	C₃×#493	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×SD₃₂	C₂	semidirect
2. C₃×#494	C₂	semidirect
4. C₃×C₄×C₁₆	C₂	semidirect
5. #2248	C₃	direct (N × H)
15. C₂×SD₃₂	C₂×C₃	semidirect
16. #494	C₂×C₃	semidirect
18. C₄×C₁₆	C₂×C₃	semidirect
30. C₃×C₁₆	D₄	semidirect
62. C₁₆	C₃×D₄	semidirect
67. C₃×C₄	SD₃₂	semidirect
88. C₄	C₃×SD₃₂	semidirect
91. C₃	#2248	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×C₃×SD₃₂	2
C₃×#494	2
C₃×#493	2
C₃×C₄×C₁₆	2
#2248	3

Subgroups — C3×#2248 #72963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2248 #72963