Subgroups — C₂×#4506 #71405

Order 384.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#819	C₂	1	2	yes	maximal
3	#4506	C₂	1	4	yes	maximal, direct product factor
4	C₂×#368	—	3	1	no	maximal, Sylow
5	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
6	C₂×#208	—	2	2	no	—
7	C₂×C₃×C₁₆	C₄	1	2	yes	—
8	C₂×C₃×C₁₆	C₄	1	2	yes	—
9	C₂×C₃×C₁₆	C₂²	1	2	yes	—
10	#819	—	2	2	no	—
11	#819	C₂²	1	4	yes	—
12	C₂²×C₁₆	D₃	1	1	yes	characteristic
13	C₂×#108	—	3	2	no	—
14	#368	—	3	4	no	—
15	C₂²×C₃×C₄	D₄	1	1	yes	characteristic
16	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃×C₈	D₄	1	1	yes	characteristic
19	C₂×C₃×C₈	Q₈	1	1	yes	characteristic
20	C₂×C₃×C₈	Q₈	1	1	yes	characteristic
21	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
22	#208	—	2	4	no	—
23	#208	—	4	2	no	—
24	C₂×C₃⋊C₈	—	4	2	no	—
25	C₃×C₁₆	C₂×C₄	1	4	yes	—
26	C₂×M₁₆	—	6	2	no	—
27	C₂²×C₈	C₂×D₃	1	1	yes	characteristic
28	C₂×C₁₆	Dic₃	1	2	yes	—
29	C₂×C₁₆	Dic₃	1	2	yes	—
30	C₂×C₁₆	C₂×D₃	1	2	yes	—
31	#108	—	3	4	no	—
32	#108	—	6	2	no	—
33	C₂³×C₃	Q₁₆	1	1	yes	characteristic
34	C₂×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₃×C₄	D₈	1	1	yes	characteristic
37	C₂×C₃×C₄	D₈	1	1	yes	characteristic
38	C₂×C₃×C₄	Q₁₆	1	1	yes	characteristic
39	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
40	C₃×C₈	C₄⋊C₄	1	1	yes	characteristic
41	C₃×C₈	C₄⋊C₄	1	1	yes	characteristic
42	C₃×C₈	C₂²×C₄	1	1	yes	characteristic
43	C₃×C₈	C₂×Q₈	1	1	yes	characteristic
44	C₃⋊C₈	—	4	4	no	—
45	C₂²×C₄	D₁₂	1	1	yes	characteristic
46	M₁₆	—	6	4	no	—
47	M₁₆	—	12	2	no	—
48	C₂×C₈	—	12	2	no	—
49	C₂×C₈	Dic₆	1	1	yes	characteristic
50	C₂×C₈	Dic₆	1	1	yes	characteristic
51	C₂×C₈	D₁₂	1	1	yes	characteristic
52	C₂×C₈	C₂×Dic₃	1	1	yes	characteristic
53	C₂×C₈	C₂×Dic₃	1	1	yes	characteristic
54	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
55	C₁₆	C₂×Dic₃	1	4	yes	—
56	C₂²×C₃	—	2	2	no	—
57	C₂²×C₃	#107	1	1	yes	characteristic
58	C₂²×C₃	#107	1	1	yes	characteristic
59	C₂²×C₃	C₂×Q₁₆	1	1	yes	characteristic
60	C₃×C₄	#107	1	1	yes	characteristic
61	C₃×C₄	#107	1	1	yes	characteristic
62	C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₃×C₄	C₂×D₈	1	1	yes	characteristic
64	C₂³	Dic₁₂	1	1	yes	characteristic
65	C₂×C₄	D₂₄	1	1	yes	characteristic
66	C₂×C₄	D₂₄	1	1	yes	characteristic
67	C₂×C₄	Dic₁₂	1	1	yes	characteristic
68	C₂×C₄	C₄⋊Dic₃	1	1	yes	characteristic
69	C₂×C₄	C₄⋊Dic₃	1	1	yes	characteristic
70	C₂×C₄	C₂×D₁₂	1	1	yes	characteristic
71	C₈	—	12	4	no	—
72	C₈	C₄⋊Dic₃	1	1	yes	characteristic
73	C₈	C₄⋊Dic₃	1	1	yes	characteristic
74	C₈	C₂×Dic₆	1	1	yes	characteristic
75	C₈	C₂²×Dic₃	1	1	yes	characteristic
76	C₂×C₃	—	2	1	no	—
77	C₂×C₃	—	2	1	no	—
78	C₂×C₃	#368	1	2	yes	complemented
79	C₂×C₃	C₂×#107	1	1	yes	characteristic
80	C₂²	—	2	2	no	—
81	C₂²	#818	1	1	yes	characteristic
82	C₂²	#818	1	1	yes	characteristic
83	C₂²	C₂×Dic₁₂	1	1	yes	characteristic
84	C₄	#818	1	1	yes	characteristic
85	C₄	#818	1	1	yes	characteristic
86	C₄	C₂×D₂₄	1	1	yes	characteristic
87	C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
88	C₃	C₂×#368	1	1	yes	characteristic, complemented, Sylow
89	C₂	—	2	1	no	—
90	C₂	—	2	1	no	—
91	C₂	#4506	1	2	yes	direct product factor
92	C₂	C₂×#818	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₂₄
commutator	C₃×C₈	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃
Fitting	C₂²×C₃×C₁₆	C₂
socle	C₂²×C₃	#107
prime radical	C₂³×C₃	Q₁₆
cosocle	C₂×C₃×C₈	C₂³
hypercenter	C₂²×C₁₆	D₃
hypocenter	C₃	C₂×#368
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
3. #4506	C₂	direct (N × H)
78. C₂×C₃	#368	semidirect
88. C₃	C₂×#368	semidirect
91. C₂	#4506	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×C₁₆	2
C₂×#819	2
#4506	2
C₂×#368	3

Subgroups — C2×#4506 #71405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4506 #71405