Subgroups — C₂²×#803 #82043

Order 384.

680 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃⋊C₈	C₂	1	2	yes	maximal
3	C₂×#803	C₂	1	12	yes	maximal, direct product factor
4	C₂²×#97	—	3	1	no	maximal, Sylow
5	C₂³×C₃×C₄	C₄	1	2	yes	—
6	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄²	C₄	1	6	yes	—
8	C₂×C₃×C₄²	C₂²	1	6	yes	—
9	C₂²×C₃⋊C₈	C₄	1	16	yes	complemented
10	C₂²×C₃⋊C₈	C₂²	1	12	yes	—
11	#803	C₂²	1	16	yes	direct product factor
12	C₂³×C₈	—	3	2	no	—
13	C₂²×C₄²	D₃	1	1	yes	characteristic
14	C₂×#97	—	3	12	no	—
15	C₂⁴×C₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₃×C₄	—	2	8	no	—
17	C₂²×C₃×C₄	C₂×C₄	1	8	yes	—
18	C₂²×C₃×C₄	C₂×C₄	1	12	yes	—
19	C₂²×C₃×C₄	C₂×C₄	1	3	yes	—
20	C₂²×C₃×C₄	C₂³	1	3	yes	—
21	C₃×C₄²	C₂×C₄	1	12	yes	—
22	C₃×C₄²	C₂³	1	4	yes	—
23	C₂×C₃⋊C₈	C₂×C₄	1	48	yes	complemented
24	C₂×C₃⋊C₈	C₂³	1	8	yes	—
25	C₂³×C₄	Dic₃	1	2	yes	—
26	C₂³×C₄	C₂×D₃	1	1	yes	characteristic
27	C₂²×C₈	—	3	16	no	—
28	C₂²×C₈	—	3	12	no	—
29	C₂×C₄²	Dic₃	1	6	yes	—
30	C₂×C₄²	C₂×D₃	1	6	yes	—
31	#97	—	3	16	no	—
32	C₂³×C₃	C₄²	1	4	yes	—
33	C₂³×C₃	M₁₆	1	8	yes	—
34	C₂³×C₃	C₂²×C₄	1	3	yes	—
35	C₂×C₃×C₄	—	2	24	no	—
36	C₂×C₃×C₄	C₄²	1	12	yes	—
37	C₂×C₃×C₄	C₂²×C₄	1	12	yes	—
38	C₂×C₃×C₄	C₂²×C₄	1	8	yes	—
39	C₂×C₃×C₄	C₂²×C₄	1	3	yes	—
40	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
41	C₃⋊C₈	C₂²×C₄	1	16	yes	complemented
42	C₂⁴	C₂×Dic₃	1	1	yes	characteristic
43	C₂²×C₄	—	2	8	no	—
44	C₂²×C₄	C₄×D₃	1	8	yes	—
45	C₂²×C₄	C₂×Dic₃	1	12	yes	—
46	C₂²×C₄	C₂×Dic₃	1	3	yes	—
47	C₂²×C₄	C₂²×D₃	1	3	yes	—
48	C₂×C₈	—	3	48	no	—
49	C₂×C₈	—	3	8	no	—
50	C₄²	C₂×Dic₃	1	12	yes	—
51	C₄²	C₂²×D₃	1	4	yes	—
52	C₂²×C₃	#97	1	16	yes	complemented
53	C₂²×C₃	C₂×C₄²	1	6	yes	—
54	C₂²×C₃	C₂×M₁₆	1	12	yes	—
55	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
56	C₃×C₄	—	2	8	no	—
57	C₃×C₄	C₂×C₄²	1	6	yes	—
58	C₃×C₄	C₂³×C₄	1	2	yes	—
59	C₂³	#208	1	8	yes	—
60	C₂³	C₄×Dic₃	1	4	yes	—
61	C₂³	C₂²×Dic₃	1	3	yes	—
62	C₂×C₄	—	2	24	no	—
63	C₂×C₄	C₄×Dic₃	1	12	yes	—
64	C₂×C₄	C₂×C₄×D₃	1	12	yes	—
65	C₂×C₄	C₂²×Dic₃	1	8	yes	—
66	C₂×C₄	C₂²×Dic₃	1	3	yes	—
67	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
68	C₈	—	3	16	no	—
69	C₂×C₃	C₂×#97	1	12	yes	complemented
70	C₂×C₃	C₂²×C₄²	1	1	yes	characteristic
71	C₂×C₃	C₂²×M₁₆	1	2	yes	—
72	C₂²	#803	1	16	yes	direct product factor
73	C₂²	C₂×#208	1	12	yes	—
74	C₂²	C₂×C₄×Dic₃	1	6	yes	—
75	C₂²	C₂³×Dic₃	1	1	yes	characteristic
76	C₄	—	2	8	no	—
77	C₄	C₂×C₄×Dic₃	1	6	yes	—
78	C₄	C₂²×C₄×D₃	1	2	yes	—
79	C₃	C₂²×#97	1	1	yes	characteristic, complemented, Sylow
80	C₂	C₂×#803	1	12	yes	direct product factor
81	C₂	C₂²×#208	1	2	yes	—
82	C₂	C₂²×C₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂×D₃
commutator	C₂×C₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₃
Fitting	C₂²×C₃×C₄²	C₂
socle, prime radical	C₂⁴×C₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴
hypercenter	C₂²×C₄²	D₃
hypocenter	C₃	C₂²×#97
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
3. C₂×#803	C₂	direct (N × H)
9. C₂²×C₃⋊C₈	C₄	semidirect
11. #803	C₂²	direct (N × H)
23. C₂×C₃⋊C₈	C₂×C₄	semidirect
41. C₃⋊C₈	C₂²×C₄	semidirect
52. C₂²×C₃	#97	semidirect
69. C₂×C₃	C₂×#97	semidirect
72. C₂²	#803	direct (N × H)
79. C₃	C₂²×#97	semidirect
80. C₂	C₂×#803	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×C₃×C₄²	2
C₂³×C₃⋊C₈	2
C₂×#803	2
C₂²×#97	3

Subgroups — C22×#803 #82043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#803 #82043