Subgroups — C₂×#4461 #69740

Order 384.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃⋊C₁₆	C₂	1	2	yes	maximal
3	#4461	C₂	1	4	yes	maximal, direct product factor
4	C₂×#346	—	3	1	no	maximal, Sylow
5	C₂²×C₃×C₈	C₄	1	1	yes	characteristic
6	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄²	C₄	1	1	yes	characteristic
8	C₃×C₄×C₈	C₄	1	2	yes	—
9	C₃×C₄×C₈	C₂²	1	2	yes	—
10	C₂×C₃⋊C₁₆	C₄	1	8	yes	complemented
11	C₂×C₃⋊C₁₆	C₂²	1	4	yes	—
12	C₂²×C₁₆	—	3	2	no	—
13	C₂×C₄×C₈	D₃	1	1	yes	characteristic
14	#346	—	3	4	no	—
15	C₂²×C₃×C₄	C₈	1	2	yes	—
16	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃×C₈	C₈	1	4	yes	—
18	C₂×C₃×C₈	C₂×C₄	1	4	yes	—
19	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
20	C₂×C₃×C₈	C₂×C₄	1	2	yes	—
21	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
22	C₃×C₄²	C₈	1	2	yes	—
23	C₃×C₄²	C₂×C₄	1	2	yes	—
24	C₃⋊C₁₆	C₂×C₄	1	8	yes	complemented
25	C₂²×C₈	Dic₃	1	1	yes	characteristic
26	C₂²×C₈	C₂×D₃	1	1	yes	characteristic
27	C₂×C₄²	Dic₃	1	1	yes	characteristic
28	C₂×C₁₆	—	3	8	no	—
29	C₂×C₁₆	—	3	4	no	—
30	C₄×C₈	Dic₃	1	2	yes	—
31	C₄×C₈	C₂×D₃	1	2	yes	—
32	C₂³×C₃	C₂×C₈	1	1	yes	characteristic
33	C₂×C₃×C₄	—	2	4	no	—
34	C₂×C₃×C₄	C₄²	1	2	yes	—
35	C₂×C₃×C₄	C₂×C₈	1	4	yes	—
36	C₂×C₃×C₄	C₂×C₈	1	1	yes	characteristic
37	C₂×C₃×C₄	C₂×C₈	1	2	yes	—
38	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
39	C₃×C₈	C₄²	1	2	yes	—
40	C₃×C₈	C₂×C₈	1	4	yes	—
41	C₃×C₈	C₂²×C₄	1	2	yes	—
42	C₂²×C₄	C₃⋊C₈	1	2	yes	—
43	C₂²×C₄	C₂×Dic₃	1	1	yes	characteristic
44	C₂×C₈	C₃⋊C₈	1	4	yes	—
45	C₂×C₈	C₄×D₃	1	4	yes	—
46	C₂×C₈	C₂×Dic₃	1	2	yes	—
47	C₂×C₈	C₂×Dic₃	1	1	yes	characteristic
48	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
49	C₄²	C₃⋊C₈	1	2	yes	—
50	C₄²	C₂×Dic₃	1	2	yes	—
51	C₁₆	—	3	8	no	—
52	C₂²×C₃	C₄×C₈	1	2	yes	—
53	C₂²×C₃	M₃₂	1	4	yes	—
54	C₂²×C₃	C₂²×C₈	1	1	yes	characteristic
55	C₃×C₄	—	2	4	no	—
56	C₃×C₄	C₄×C₈	1	2	yes	—
57	C₃×C₄	C₂×C₄²	1	1	yes	characteristic
58	C₃×C₄	C₂²×C₈	1	1	yes	characteristic
59	C₂³	C₂×C₃⋊C₈	1	1	yes	characteristic
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	C₂×C₃⋊C₈	1	4	yes	—
62	C₂×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
63	C₂×C₄	C₂×C₃⋊C₈	1	2	yes	—
64	C₂×C₄	C₄×Dic₃	1	2	yes	—
65	C₂×C₄	C₂²×Dic₃	1	1	yes	characteristic
66	C₈	C₂×C₃⋊C₈	1	4	yes	—
67	C₈	C₄×Dic₃	1	2	yes	—
68	C₈	C₂×C₄×D₃	1	2	yes	—
69	C₂×C₃	#346	1	4	yes	complemented
70	C₂×C₃	C₂×C₄×C₈	1	1	yes	characteristic
71	C₂×C₃	C₂×M₃₂	1	2	yes	—
72	C₂²	C₄×C₃⋊C₈	1	2	yes	—
73	C₂²	#812	1	4	yes	—
74	C₂²	C₂²×C₃⋊C₈	1	1	yes	characteristic
75	C₄	—	2	4	no	—
76	C₄	C₄×C₃⋊C₈	1	2	yes	—
77	C₄	C₂²×C₃⋊C₈	1	1	yes	characteristic
78	C₄	C₂×C₄×Dic₃	1	1	yes	characteristic
79	C₃	C₂×#346	1	1	yes	characteristic, complemented, Sylow
80	C₂	#4461	1	4	yes	direct product factor
81	C₂	C₂×C₄×C₃⋊C₈	1	1	yes	characteristic
82	C₂	C₂×#812	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂×D₃
commutator	C₂×C₃	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×D₃
Fitting	C₂×C₃×C₄×C₈	C₂
socle, prime radical	C₂³×C₃	C₂×C₈
cosocle	C₂×C₃×C₈	C₂³
hypercenter	C₂×C₄×C₈	D₃
hypocenter	C₃	C₂×#346
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #4461	C₂	direct (N × H)
10. C₂×C₃⋊C₁₆	C₄	semidirect
24. C₃⋊C₁₆	C₂×C₄	semidirect
69. C₂×C₃	#346	semidirect
79. C₃	C₂×#346	semidirect
80. C₂	#4461	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×C₄×C₈	2
C₂²×C₃⋊C₁₆	2
#4461	2
C₂×#346	3

Subgroups — C2×#4461 #69740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4461 #69740