Subgroups — C₂×C₃⋊#401 #73348

Order 384.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#95	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊#95	C₂	1	3	yes	maximal
3	C₂×C₃⋊#95	C₂	1	3	yes	maximal
4	C₃⋊#401	C₂	1	8	yes	maximal, direct product factor
5	C₂×#401	—	3	1	no	maximal, Sylow
6	C₂³×C₃×C₄	C₂²	1	3	yes	—
7	C₂³×Dic₃	C₂²	1	1	yes	characteristic
8	C₂³×Dic₃	C₂²	1	3	yes	—
9	C₃×#95	C₂²	1	4	yes	—
10	C₃⋊#95	C₂²	1	12	yes	—
11	C₃⋊#95	C₂²	1	12	yes	—
12	#401	—	3	8	no	—
13	C₂×#95	—	3	3	no	—
14	C₂×#95	—	3	3	no	—
15	C₂×#95	D₃	1	1	yes	characteristic
16	C₂⁴×C₃	C₂³	1	1	yes	characteristic
17	C₂²×C₃×C₄	—	2	6	no	—
18	C₂²×C₃×C₄	—	2	12	no	—
19	C₂²×C₃×C₄	C₂³	1	6	yes	—
20	C₂²×Dic₃	—	2	6	no	—
21	C₂²×Dic₃	—	2	6	no	—
22	C₂²×Dic₃	—	2	6	no	—
23	C₂²×Dic₃	—	2	6	no	—
24	C₂²×Dic₃	C₂³	1	2	yes	—
25	C₂²×Dic₃	C₂³	1	6	yes	—
26	C₂³×C₄	—	3	1	no	—
27	C₂³×C₄	—	3	3	no	—
28	C₂³×C₄	C₂×D₃	1	3	yes	—
29	#95	—	3	12	no	—
30	#95	—	3	12	no	—
31	#95	C₂×D₃	1	4	yes	—
32	C₂³×C₃	#41	1	6	yes	—
33	C₂³×C₃	#41	1	6	yes	—
34	C₂³×C₃	#41	1	2	yes	—
35	C₂³×C₃	C₂⁴	1	1	yes	characteristic
36	C₂×C₃×C₄	—	2	6	no	—
37	C₂×C₃×C₄	—	2	12	no	—
38	C₂×C₃×C₄	—	4	12	no	—
39	C₂×Dic₃	—	2	6	no	—
40	C₂×Dic₃	—	2	6	no	—
41	C₂×Dic₃	—	2	6	no	—
42	C₂×Dic₃	—	2	6	no	—
43	C₂×Dic₃	—	4	4	no	—
44	C₂×Dic₃	—	4	12	no	—
45	C₂⁴	C₂²×D₃	1	1	yes	characteristic
46	C₂²×C₄	—	2	6	no	—
47	C₂²×C₄	—	2	12	no	—
48	C₂²×C₄	—	3	2	no	—
49	C₂²×C₄	—	3	6	no	—
50	C₂²×C₄	—	6	6	no	—
51	C₂²×C₄	—	6	6	no	—
52	C₂²×C₄	—	6	6	no	—
53	C₂²×C₄	—	6	6	no	—
54	C₂²×C₄	C₂²×D₃	1	6	yes	—
55	C₂²×C₃	#126	1	4	yes	—
56	C₂²×C₃	#126	1	12	yes	—
57	C₂²×C₃	#126	1	12	yes	—
58	C₂²×C₃	C₂×#41	1	3	yes	—
59	C₂²×C₃	C₂×#41	1	3	yes	—
60	C₂²×C₃	C₂×#41	1	1	yes	characteristic
61	C₃×C₄	—	4	6	no	—
62	Dic₃	—	4	2	no	—
63	Dic₃	—	4	6	no	—
64	C₂³	#235	1	6	yes	—
65	C₂³	#237	1	6	yes	—
66	C₂³	#239	1	2	yes	—
67	C₂³	C₂³×D₃	1	1	yes	characteristic
68	C₂×C₄	—	2	6	no	—
69	C₂×C₄	—	2	12	no	—
70	C₂×C₄	—	4	12	no	—
71	C₂×C₄	—	6	6	no	—
72	C₂×C₄	—	6	6	no	—
73	C₂×C₄	—	6	6	no	—
74	C₂×C₄	—	6	6	no	—
75	C₂×C₄	—	12	4	no	—
76	C₂×C₄	—	12	12	no	—
77	C₂×C₃	#401	1	8	yes	complemented
78	C₂×C₃	C₂×#126	1	1	yes	characteristic
79	C₂×C₃	C₂×#126	1	3	yes	—
80	C₂×C₃	C₂×#126	1	3	yes	—
81	C₂²	#876	1	4	yes	—
82	C₂²	#879	1	12	yes	—
83	C₂²	#898	1	12	yes	—
84	C₂²	C₂×#235	1	3	yes	—
85	C₂²	C₂×#237	1	3	yes	—
86	C₂²	C₂×#239	1	1	yes	characteristic
87	C₄	—	4	6	no	—
88	C₄	—	12	2	no	—
89	C₄	—	12	6	no	—
90	C₃	C₂×#401	1	1	yes	characteristic, complemented, Sylow
91	C₂	C₃⋊#401	1	8	yes	direct product factor
92	C₂	C₂×#876	1	1	yes	characteristic
93	C₂	C₂×#879	1	3	yes	—
94	C₂	C₂×#898	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₃
commutator, cosocle	C₂³×C₃	C₂⁴
Frattini	C₂³	C₂³×D₃
Fitting	C₂×C₃×#95	C₂
socle, prime radical	C₂⁴×C₃	C₂³
hypercenter	C₂×#95	D₃
hypocenter	C₃	C₂×#401
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

Complements

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

N	H ≅ G/N	type
4. C₃⋊#401	C₂	direct (N × H)
77. C₂×C₃	#401	semidirect
90. C₃	C₂×#401	semidirect
91. C₂	C₃⋊#401	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×#95	2
C₂×C₃⋊#95	2
C₃⋊#401	2
C₂×#401	3

Subgroups — C2×C3⋊#401 #73348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊#401 #73348