Subgroups — C₃×#2177 #72892

Order 384.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×D₈	C₂	1	2	yes	maximal, complemented
3	C₃×#367	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#357	C₂	1	2	yes	maximal, complemented
5	C₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	#2177	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×D₈	C₂²	1	2	yes	—
8	C₃×C₄×D₄	—	2	2	no	—
9	C₃×D₁₆	C₄	1	4	yes	complemented
10	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
12	C₃×#107	C₂²	1	2	yes	—
13	C₃×#102	—	2	2	no	—
14	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
15	C₂×D₁₆	C₂×C₃	1	1	yes	characteristic
16	C₄×D₈	C₂×C₃	1	2	yes	complemented
17	#367	C₂×C₃	1	1	yes	characteristic, complemented
18	#357	C₂×C₃	1	2	yes	complemented
19	#346	C₂×C₃	1	1	yes	characteristic, complemented
20	C₂×C₃×D₄	—	2	2	no	—
21	C₂²×C₃×C₄	—	4	2	no	—
22	C₃×D₈	—	2	2	no	—
23	C₃×D₈	C₂×C₄	1	4	yes	complemented
24	C₂×C₃×C₈	D₄	1	1	yes	characteristic
25	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
26	C₃×C₄⋊C₄	—	2	2	no	—
27	C₃×C₂²⋊C₄	—	4	2	no	—
28	C₃×C₄²	D₄	1	1	yes	characteristic
29	C₃×C₁₆	—	2	1	no	—
30	C₃×C₁₆	C₂×C₄	1	2	yes	complemented
31	C₂×D₈	C₂²×C₃	1	2	yes	—
32	C₄×D₄	—	2	2	no	—
33	D₁₆	C₃×C₄	1	4	yes	complemented
34	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
35	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
36	#107	C₂²×C₃	1	2	yes	—
37	#102	—	2	2	no	—
38	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
39	C₂³×C₃	—	4	2	no	—
40	C₃×D₄	—	2	4	no	—
41	C₃×D₄	—	4	2	no	—
42	C₂×C₃×C₄	—	4	2	no	—
43	C₂×C₃×C₄	—	8	4	no	—
44	C₂×C₃×C₄	D₈	1	2	yes	—
45	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
46	C₃×C₈	—	2	1	no	—
47	C₃×C₈	C₂²×C₄	1	1	yes	characteristic
48	C₃×C₈	#41	1	1	yes	characteristic
49	C₂×D₄	—	2	2	no	—
50	C₂²×C₄	—	4	2	no	—
51	D₈	—	2	2	no	—
52	D₈	C₂×C₃×C₄	1	4	yes	complemented
53	C₂×C₈	C₃×D₄	1	1	yes	characteristic
54	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
55	C₄⋊C₄	—	2	2	no	—
56	C₂²⋊C₄	—	4	2	no	—
57	C₄²	C₃×D₄	1	1	yes	characteristic
58	C₁₆	—	2	1	no	—
59	C₁₆	C₂×C₃×C₄	1	2	yes	complemented
60	C₂²×C₃	—	4	4	no	—
61	C₂²×C₃	—	8	2	no	—
62	C₂²×C₃	—	8	2	no	—
63	C₂²×C₃	C₂×D₈	1	1	yes	characteristic
64	C₃×C₄	—	2	2	no	—
65	C₃×C₄	—	8	2	no	—
66	C₃×C₄	C₄×D₄	1	1	yes	characteristic
67	C₃×C₄	#135	1	1	yes	characteristic
68	C₂³	—	4	2	no	—
69	D₄	—	2	4	no	—
70	D₄	—	4	2	no	—
71	C₂×C₄	—	4	2	no	—
72	C₂×C₄	—	8	4	no	—
73	C₂×C₄	C₃×D₈	1	2	yes	—
74	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
75	C₈	—	2	1	no	—
76	C₈	C₂²×C₃×C₄	1	1	yes	characteristic
77	C₈	C₃×#41	1	1	yes	characteristic
78	C₂×C₃	—	8	4	no	—
79	C₂×C₃	C₄×D₈	1	1	yes	characteristic
80	C₂×C₃	#509	1	2	yes	—
81	C₂²	—	4	4	no	—
82	C₂²	—	8	2	no	—
83	C₂²	—	8	2	no	—
84	C₂²	C₂×C₃×D₈	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	—	8	2	no	—
87	C₄	C₃×C₄×D₄	1	1	yes	characteristic
88	C₄	C₃×#135	1	1	yes	characteristic
89	C₃	#2177	1	1	yes	characteristic, direct product factor, Sylow
90	C₂	—	8	4	no	—
91	C₂	C₃×C₄×D₈	1	1	yes	characteristic
92	C₂	C₃×#509	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₈
commutator	C₈	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₈	C₂³×C₃
prime radical	C₂×C₃×D₁₆	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×D₈	C₂	semidirect
3. C₃×#367	C₂	semidirect
4. C₃×#357	C₂	semidirect
5. C₃×#346	C₂	semidirect
6. #2177	C₃	direct (N × H)
9. C₃×D₁₆	C₄	semidirect
16. C₄×D₈	C₂×C₃	semidirect
17. #367	C₂×C₃	semidirect
18. #357	C₂×C₃	semidirect
19. #346	C₂×C₃	semidirect
23. C₃×D₈	C₂×C₄	semidirect
30. C₃×C₁₆	C₂×C₄	semidirect
33. D₁₆	C₃×C₄	semidirect
52. D₈	C₂×C₃×C₄	semidirect
59. C₁₆	C₂×C₃×C₄	semidirect
89. C₃	#2177	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×D₁₆	2
C₃×C₄×D₈	2
C₃×#367	2
C₃×#357	2
C₃×#346	2
#2177	3

Subgroups — C3×#2177 #72892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2177 #72892