Subgroups — C₃×#2158 #72873

Order 384.

152 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	C₃×#427	C₂	1	2	yes	maximal
3	C₃×#367	C₂	1	2	yes	maximal, complemented
4	C₃×#366	C₂	1	2	yes	maximal, complemented
5	#2158	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
7	C₃×#117	—	2	2	no	—
8	C₂×C₃×C₁₆	C₄	1	4	yes	complemented
9	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
11	C₃×#107	C₂²	1	4	yes	—
12	C₃×#106	—	2	2	no	—
13	C₂²×C₁₆	C₂×C₃	1	1	yes	characteristic
14	#427	C₂×C₃	1	2	yes	—
15	#367	C₂×C₃	1	2	yes	complemented
16	#366	C₂×C₃	1	2	yes	complemented
17	C₂²×C₃×C₄	D₄	1	1	yes	characteristic
18	C₂×C₃×C₈	C₂×C₄	1	2	yes	—
19	C₂×C₃×C₈	D₄	1	1	yes	characteristic
20	C₂×C₃×C₈	Q₈	1	2	yes	—
21	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
22	C₃×C₄⋊C₄	—	2	4	no	—
23	C₃×C₂²⋊C₄	—	4	2	no	—
24	C₃×C₄²	—	4	2	no	—
25	C₃×C₁₆	C₂×C₄	1	2	yes	—
26	C₃×C₁₆	C₂×C₄	1	2	yes	—
27	C₂²×C₈	C₂²×C₃	1	1	yes	characteristic
28	#117	—	2	2	no	—
29	C₂×C₁₆	C₃×C₄	1	4	yes	complemented
30	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
32	#107	C₂²×C₃	1	4	yes	—
33	#106	—	2	2	no	—
34	C₂³×C₃	D₈	1	1	yes	characteristic
35	C₂×C₃×C₄	—	4	4	no	—
36	C₂×C₃×C₄	C₄⋊C₄	1	2	yes	—
37	C₂×C₃×C₄	D₈	1	1	yes	characteristic
38	C₂×C₃×C₄	Q₁₆	1	2	yes	—
39	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
40	C₃×C₈	C₄⋊C₄	1	2	yes	—
41	C₃×C₈	C₂²×C₄	1	1	yes	characteristic
42	C₃×C₈	C₂×Q₈	1	1	yes	characteristic
43	C₂²×C₄	C₃×D₄	1	1	yes	characteristic
44	C₂×C₈	C₂×C₃×C₄	1	2	yes	—
45	C₂×C₈	C₃×D₄	1	1	yes	characteristic
46	C₂×C₈	C₃×Q₈	1	2	yes	—
47	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
48	C₄⋊C₄	—	2	4	no	—
49	C₂²⋊C₄	—	4	2	no	—
50	C₄²	—	4	2	no	—
51	C₁₆	C₂×C₃×C₄	1	2	yes	—
52	C₁₆	C₂×C₃×C₄	1	2	yes	—
53	C₂²×C₃	—	2	2	no	—
54	C₂²×C₃	#107	1	2	yes	—
55	C₂²×C₃	C₂×D₈	1	1	yes	characteristic
56	C₃×C₄	—	8	4	no	—
57	C₃×C₄	#107	1	2	yes	—
58	C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₃×C₄	C₂×Q₁₆	1	1	yes	characteristic
60	C₂³	C₃×D₈	1	1	yes	characteristic
61	C₂×C₄	—	4	4	no	—
62	C₂×C₄	C₃×C₄⋊C₄	1	2	yes	—
63	C₂×C₄	C₃×D₈	1	1	yes	characteristic
64	C₂×C₄	C₃×Q₁₆	1	2	yes	—
65	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
66	C₈	C₃×C₄⋊C₄	1	2	yes	—
67	C₈	C₂²×C₃×C₄	1	1	yes	characteristic
68	C₈	C₂×C₃×Q₈	1	1	yes	characteristic
69	C₂×C₃	—	2	2	no	—
70	C₂×C₃	C₂×#107	1	1	yes	characteristic
71	C₂×C₃	#508	1	2	yes	—
72	C₂²	—	2	2	no	—
73	C₂²	C₃×#107	1	2	yes	—
74	C₂²	C₂×C₃×D₈	1	1	yes	characteristic
75	C₄	—	8	4	no	—
76	C₄	C₃×#107	1	2	yes	—
77	C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
78	C₄	C₂×C₃×Q₁₆	1	1	yes	characteristic
79	C₃	#2158	1	1	yes	characteristic, direct product factor, Sylow
80	C₂	—	2	2	no	—
81	C₂	C₂×C₃×#107	1	1	yes	characteristic
82	C₂	C₃×#508	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₈
commutator	C₈	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₈	C₂³×C₃
socle	C₂²×C₃	C₂×D₈
prime radical	C₂³×C₃	D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×#367	C₂	semidirect
4. C₃×#366	C₂	semidirect
5. #2158	C₃	direct (N × H)
8. C₂×C₃×C₁₆	C₄	semidirect
15. #367	C₂×C₃	semidirect
16. #366	C₂×C₃	semidirect
29. C₂×C₁₆	C₃×C₄	semidirect
79. C₃	#2158	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
C₃×#427	2
C₃×#367	2
C₃×#366	2
#2158	3

Subgroups — C3×#2158 #72873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2158 #72873