Subgroups — C₂×#4543 #71734

Order 384.

232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×#803	C₂	1	2	yes	maximal
3	#4543	C₂	1	4	yes	maximal, direct product factor
4	C₂×#330	—	3	1	no	maximal, Sylow
5	C₃×#125	—	2	2	no	—
6	C₃×#125	C₄	1	2	yes	—
7	C₃×#125	C₂²	1	2	yes	—
8	C₂×C₃×C₄⋊C₄	—	2	2	no	—
9	C₂×C₃×C₄⋊C₄	C₄	1	2	yes	—
10	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
11	C₂²×C₃⋊C₈	—	2	2	no	—
12	#803	—	2	2	no	—
13	#803	C₂²	1	4	yes	—
14	C₂×#125	D₃	1	1	yes	characteristic
15	C₂×#97	—	3	2	no	—
16	#330	—	3	4	no	—
17	C₂²×C₃×C₄	—	2	2	no	—
18	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₃×C₄	D₄	1	2	yes	—
20	C₃×C₄⋊C₄	—	2	4	no	—
21	C₃×C₄⋊C₄	—	2	2	no	—
22	C₃×C₄⋊C₄	—	2	4	no	—
23	C₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
24	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
25	C₃×C₄²	D₄	1	2	yes	—
26	C₃×C₄²	C₂³	1	1	yes	characteristic
27	C₂×C₃⋊C₈	—	2	8	no	—
28	C₂×C₃⋊C₈	—	2	4	no	—
29	C₂²×C₈	—	6	2	no	—
30	#125	—	2	2	no	—
31	#125	Dic₃	1	2	yes	—
32	#125	C₂×D₃	1	2	yes	—
33	C₂×C₄⋊C₄	—	2	2	no	—
34	C₂×C₄⋊C₄	Dic₃	1	2	yes	—
35	C₂×C₄²	C₂×D₃	1	1	yes	characteristic
36	#97	—	3	4	no	—
37	#97	—	6	2	no	—
38	C₂³×C₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₃×C₄	—	2	2	no	—
40	C₂×C₃×C₄	—	2	4	no	—
41	C₂×C₃×C₄	—	2	4	no	—
42	C₂×C₃×C₄	—	4	4	no	—
43	C₂×C₃×C₄	C₂²⋊C₄	1	2	yes	—
44	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
47	C₃⋊C₈	—	2	8	no	—
48	C₂²×C₄	—	2	2	no	—
49	C₂²×C₄	C₂×Dic₃	1	1	yes	characteristic
50	C₂²×C₄	#67	1	2	yes	—
51	C₂×C₈	—	6	8	no	—
52	C₂×C₈	—	6	4	no	—
53	C₄⋊C₄	—	2	4	no	—
54	C₄⋊C₄	—	2	2	no	—
55	C₄⋊C₄	—	2	4	no	—
56	C₄⋊C₄	C₂×Dic₃	1	4	yes	—
57	C₄²	C₂×Dic₃	1	1	yes	characteristic
58	C₄²	#67	1	2	yes	—
59	C₄²	C₂²×D₃	1	1	yes	characteristic
60	C₂²×C₃	#101	1	2	yes	—
61	C₂²×C₃	#104	1	4	yes	—
62	C₂²×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₃×C₄	—	2	1	no	—
64	C₃×C₄	—	2	1	no	—
65	C₃×C₄	—	2	2	no	—
66	C₃×C₄	—	2	2	no	—
67	C₃×C₄	—	4	4	no	—
68	C₂³	#217	1	1	yes	characteristic
69	C₂×C₄	—	2	2	no	—
70	C₂×C₄	—	2	4	no	—
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	—	4	4	no	—
73	C₂×C₄	#217	1	2	yes	—
74	C₂×C₄	#217	1	1	yes	characteristic
75	C₂×C₄	C₂²×Dic₃	1	1	yes	characteristic
76	C₂×C₄	C₂×#67	1	2	yes	—
77	C₈	—	6	8	no	—
78	C₂×C₃	#330	1	4	yes	complemented
79	C₂×C₃	C₂×#101	1	1	yes	characteristic
80	C₂×C₃	C₂×#104	1	2	yes	—
81	C₂²	#836	1	2	yes	—
82	C₂²	#837	1	4	yes	—
83	C₂²	C₂×#217	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	2	1	no	—
86	C₄	—	2	2	no	—
87	C₄	—	2	2	no	—
88	C₄	—	4	4	no	—
89	C₃	C₂×#330	1	1	yes	characteristic, complemented, Sylow
90	C₂	#4543	1	4	yes	direct product factor
91	C₂	C₂×#836	1	1	yes	characteristic
92	C₂	C₂×#837	1	2	yes	—

	subgroup	G/H
center	C₂³	#217
commutator	C₂×C₃×C₄	C₂²×C₄
Frattini	C₄²	C₂²×D₃
Fitting	C₂×C₃×#125	C₂
socle, prime radical	C₂³×C₃	C₂²⋊C₄
cosocle	C₃×C₄²	C₂³
hypercenter	C₂×#125	D₃
hypocenter	C₃	C₂×#330
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
3. #4543	C₂	direct (N × H)
78. C₂×C₃	#330	semidirect
89. C₃	C₂×#330	semidirect
90. C₂	#4543	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×#125	2
C₂×#803	2
#4543	2
C₂×#330	3

Subgroups — C2×#4543 #71734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4543 #71734