Subgroups — C₃×#2150 #72865

Order 384.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×M₃₂	C₂	1	2	yes	maximal
2	C₂×C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊C₁₆	C₂	1	4	yes	maximal, complemented
4	#2150	C₃	1	1	yes	maximal, characteristic, direct product factor, 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×M₃₂	—	2	4	no	—
9	C₂×C₃×C₁₆	C₂²	1	4	yes	—
10	C₃×C₄×C₈	C₄	1	2	yes	—
11	C₃×C₄×C₈	C₂²	1	2	yes	—
12	C₂×M₃₂	C₂×C₃	1	2	yes	—
13	C₂×C₄×C₈	C₂×C₃	1	1	yes	characteristic
14	C₄⋊C₁₆	C₂×C₃	1	4	yes	complemented
15	C₂²×C₃×C₄	C₈	1	2	yes	—
16	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃×C₈	—	2	2	no	—
18	C₂×C₃×C₈	C₂×C₄	1	2	yes	—
19	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
20	C₂×C₃×C₈	D₄	1	2	yes	—
21	C₂×C₃×C₈	Q₈	1	2	yes	—
22	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
23	C₃×C₄²	C₈	1	1	yes	characteristic
24	C₃×C₄²	C₈	1	1	yes	characteristic
25	C₃×C₄²	C₂×C₄	1	2	yes	—
26	C₃×C₁₆	—	2	4	no	—
27	C₂²×C₈	C₃×C₄	1	1	yes	characteristic
28	C₂²×C₈	C₂²×C₃	1	1	yes	characteristic
29	C₂×C₄²	C₃×C₄	1	1	yes	characteristic
30	M₃₂	—	2	4	no	—
31	C₂×C₁₆	C₂²×C₃	1	4	yes	—
32	C₄×C₈	C₃×C₄	1	2	yes	—
33	C₄×C₈	C₂²×C₃	1	2	yes	—
34	C₂³×C₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₃×C₄	—	2	4	no	—
36	C₂×C₃×C₄	C₄⋊C₄	1	2	yes	—
37	C₂×C₃×C₄	C₂×C₈	1	2	yes	—
38	C₂×C₃×C₄	C₂×C₈	1	1	yes	characteristic
39	C₂×C₃×C₄	C₂×C₈	1	2	yes	—
40	C₂×C₃×C₄	M₁₆	1	2	yes	—
41	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
42	C₃×C₈	—	2	2	no	—
43	C₃×C₈	C₄⋊C₄	1	2	yes	—
44	C₃×C₈	C₂×D₄	1	1	yes	characteristic
45	C₃×C₈	C₂×Q₈	1	1	yes	characteristic
46	C₂²×C₄	C₃×C₈	1	2	yes	—
47	C₂²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
48	C₂×C₈	—	2	2	no	—
49	C₂×C₈	C₂×C₃×C₄	1	2	yes	—
50	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
51	C₂×C₈	C₃×D₄	1	2	yes	—
52	C₂×C₈	C₃×Q₈	1	2	yes	—
53	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
54	C₄²	C₃×C₈	1	1	yes	characteristic
55	C₄²	C₃×C₈	1	1	yes	characteristic
56	C₄²	C₂×C₃×C₄	1	2	yes	—
57	C₁₆	—	2	4	no	—
58	C₂²×C₃	—	2	2	no	—
59	C₂²×C₃	C₄⋊C₈	1	2	yes	—
60	C₂²×C₃	C₂²×C₈	1	1	yes	characteristic
61	C₃×C₄	—	2	2	no	—
62	C₃×C₄	C₄⋊C₈	1	2	yes	—
63	C₃×C₄	M₃₂	1	4	yes	complemented
64	C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₃×C₄	C₂×M₁₆	1	1	yes	characteristic
66	C₂³	C₂×C₃×C₈	1	1	yes	characteristic
67	C₂×C₄	—	2	4	no	—
68	C₂×C₄	C₃×C₄⋊C₄	1	2	yes	—
69	C₂×C₄	C₂×C₃×C₈	1	2	yes	—
70	C₂×C₄	C₂×C₃×C₈	1	1	yes	characteristic
71	C₂×C₄	C₂×C₃×C₈	1	2	yes	—
72	C₂×C₄	C₃×M₁₆	1	2	yes	—
73	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
74	C₈	—	2	2	no	—
75	C₈	C₃×C₄⋊C₄	1	2	yes	—
76	C₈	C₂×C₃×D₄	1	1	yes	characteristic
77	C₈	C₂×C₃×Q₈	1	1	yes	characteristic
78	C₂×C₃	—	2	2	no	—
79	C₂×C₃	C₂×C₄⋊C₈	1	1	yes	characteristic
80	C₂×C₃	C₂×M₃₂	1	2	yes	—
81	C₂²	—	2	2	no	—
82	C₂²	C₃×C₄⋊C₈	1	2	yes	—
83	C₂²	C₂²×C₃×C₈	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	C₃×C₄⋊C₈	1	2	yes	—
86	C₄	C₃×M₃₂	1	4	yes	complemented
87	C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
88	C₄	C₂×C₃×M₁₆	1	1	yes	characteristic
89	C₃	#2150	1	1	yes	characteristic, direct product factor, Sylow
90	C₂	—	2	2	no	—
91	C₂	C₂×C₃×C₄⋊C₈	1	1	yes	characteristic
92	C₂	C₂×C₃×M₃₂	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₈	C₂³
commutator	C₂²	C₂²×C₃×C₈
Frattini, cosocle	C₂×C₈	C₂³×C₃
socle	C₂²×C₃	C₂²×C₈
prime radical	C₂³×C₃	C₂×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₄⋊C₁₆	C₂	semidirect
4. #2150	C₃	direct (N × H)
14. C₄⋊C₁₆	C₂×C₃	semidirect
63. C₃×C₄	M₃₂	semidirect
86. C₄	C₃×M₃₂	semidirect
89. C₃	#2150	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×M₃₂	2
C₂×C₃×C₄×C₈	2
C₃×C₄⋊C₁₆	2
#2150	3

Subgroups — C3×#2150 #72865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2150 #72865