Subgroups — C₂×#4522 #71494

Order 384.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₄	C₂	1	1	yes	maximal, characteristic
3	#4522	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₆₄	—	3	1	no	maximal, Sylow
6	C₂×C₃×Q₁₆	—	2	1	no	—
7	C₂×Dic₁₂	—	2	1	no	—
8	C₃×Q₃₂	—	2	1	no	—
9	C₃×Q₃₂	C₂²	1	2	yes	—
10	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
11	Dic₂₄	—	2	1	no	—
12	Dic₂₄	C₂²	1	2	yes	—
13	C₃⋊C₃₂	C₂²	1	2	yes	—
14	C₂×Q₃₂	—	3	1	no	—
15	C₂×Q₃₂	D₃	1	1	yes	characteristic
16	Q₆₄	—	3	4	no	—
17	C₂×C₃₂	—	3	1	no	—
18	C₂×C₃×Q₈	—	4	1	no	—
19	C₂×Dic₆	—	4	1	no	—
20	C₃×Q₁₆	—	2	2	no	—
21	C₃×Q₁₆	—	4	1	no	—
22	C₂×C₃×C₈	D₄	1	1	yes	characteristic
23	Dic₁₂	—	2	2	no	—
24	Dic₁₂	—	4	1	no	—
25	C₃×C₁₆	D₄	1	1	yes	characteristic
26	C₃×C₁₆	C₂³	1	1	yes	characteristic
27	C₂×Q₁₆	—	2	1	no	—
28	C₂×Q₁₆	—	6	1	no	—
29	Q₃₂	—	2	1	no	—
30	Q₃₂	—	3	2	no	—
31	Q₃₂	—	6	1	no	—
32	Q₃₂	C₂×D₃	1	2	yes	—
33	C₂×C₁₆	C₂×D₃	1	1	yes	characteristic
34	C₃₂	—	3	2	no	—
35	C₃×Q₈	—	4	2	no	—
36	C₃×Q₈	—	8	1	no	—
37	C₂×C₃×C₄	—	8	1	no	—
38	C₂×C₃×C₄	D₈	1	1	yes	characteristic
39	C₂×Dic₃	—	8	1	no	—
40	Dic₆	—	4	2	no	—
41	Dic₆	—	8	1	no	—
42	C₃×C₈	D₈	1	1	yes	characteristic
43	C₃×C₈	C₂×D₄	1	1	yes	characteristic
44	C₂×Q₈	—	4	1	no	—
45	C₂×Q₈	—	12	1	no	—
46	Q₁₆	—	2	2	no	—
47	Q₁₆	—	4	1	no	—
48	Q₁₆	—	6	2	no	—
49	Q₁₆	—	12	1	no	—
50	C₂×C₈	#67	1	1	yes	characteristic
51	C₁₆	#67	1	1	yes	characteristic
52	C₁₆	C₂²×D₃	1	1	yes	characteristic
53	C₂²×C₃	D₁₆	1	1	yes	characteristic
54	C₃×C₄	—	8	2	no	—
55	C₃×C₄	D₁₆	1	1	yes	characteristic
56	C₃×C₄	C₂×D₈	1	1	yes	characteristic
57	Dic₃	—	8	2	no	—
58	Q₈	—	4	2	no	—
59	Q₈	—	8	1	no	—
60	Q₈	—	12	2	no	—
61	Q₈	—	24	1	no	—
62	C₂×C₄	—	8	1	no	—
63	C₂×C₄	—	24	1	no	—
64	C₂×C₄	#213	1	1	yes	characteristic
65	C₈	#213	1	1	yes	characteristic
66	C₈	C₂×#67	1	1	yes	characteristic
67	C₂×C₃	Q₆₄	1	2	yes	complemented
68	C₂×C₃	C₂×D₁₆	1	1	yes	characteristic
69	C₂²	#826	1	1	yes	characteristic
70	C₄	—	8	2	no	—
71	C₄	—	24	2	no	—
72	C₄	#826	1	1	yes	characteristic
73	C₄	C₂×#213	1	1	yes	characteristic
74	C₃	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
75	C₂	#4522	1	2	yes	direct product factor
76	C₂	C₂×#826	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#826
commutator, cosocle	C₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₃
Fitting	C₂×C₃×Q₃₂	C₂
socle, prime radical	C₂²×C₃	D₁₆
hypercenter	C₂×Q₃₂	D₃
hypocenter	C₃	C₂×Q₆₄
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
3. #4522	C₂	direct (N × H)
67. C₂×C₃	Q₆₄	semidirect
74. C₃	C₂×Q₆₄	semidirect
75. C₂	#4522	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×Q₃₂	2
C₂×Dic₂₄	2
#4522	2
C₂×C₃⋊C₃₂	2
C₂×Q₆₄	3

Subgroups — C2×#4522 #71494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4522 #71494