Subgroups — C₃×#3458 #87342

Order 384.

996 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#544	C₂	1	12	yes	maximal, complemented
2	C₃×#543	C₂	1	4	yes	maximal
3	C₃×#533	C₂	1	12	yes	maximal, complemented
4	C₂×C₃×#117	C₂	1	3	yes	maximal
5	#3458	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₃×C₄⋊Q₈	C₂²	1	24	yes	complemented
8	C₃×#125	C₂²	1	24	yes	complemented
9	C₃×C₂²⋊Q₈	C₂²	1	48	yes	—
10	C₃×C₄×Q₈	C₂²	1	16	yes	complemented
11	C₃×#117	C₂²	1	12	yes	—
12	C₃×#117	C₂²	1	12	yes	—
13	C₂×C₃×C₄⋊C₄	C₂²	1	6	yes	—
14	C₂×C₃×C₂²⋊C₄	C₂²	1	6	yes	—
15	C₂×C₃×C₄²	C₂²	1	6	yes	—
16	#544	C₂×C₃	1	12	yes	complemented
17	#543	C₂×C₃	1	4	yes	—
18	#533	C₂×C₃	1	12	yes	complemented
19	C₂×#117	C₂×C₃	1	3	yes	—
20	C₂⁴×C₃	C₂³	1	1	yes	characteristic
21	C₂×C₃×Q₈	C₂³	1	16	yes	—
22	C₂²×C₃×C₄	Q₈	1	8	yes	complemented
23	C₂²×C₃×C₄	C₂³	1	12	yes	—
24	C₂²×C₃×C₄	C₂³	1	3	yes	—
25	C₂²×C₃×C₄	C₂³	1	3	yes	—
26	C₃×C₄⋊C₄	C₂³	1	24	yes	—
27	C₃×C₄⋊C₄	C₂³	1	48	yes	—
28	C₃×C₂²⋊C₄	C₂³	1	24	yes	—
29	C₃×C₄²	C₂³	1	12	yes	—
30	C₃×C₄²	C₂³	1	12	yes	—
31	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
32	C₄⋊Q₈	C₂²×C₃	1	24	yes	complemented
33	#125	C₂²×C₃	1	24	yes	complemented
34	C₂²⋊Q₈	C₂²×C₃	1	48	yes	—
35	C₄×Q₈	C₂²×C₃	1	16	yes	complemented
36	#117	C₂²×C₃	1	12	yes	—
37	#117	C₂²×C₃	1	12	yes	—
38	C₂×C₄⋊C₄	C₂²×C₃	1	6	yes	—
39	C₂×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
40	C₂×C₄²	C₂²×C₃	1	6	yes	—
41	C₂³×C₃	—	4	2	no	—
42	C₂³×C₃	C₂×Q₈	1	4	yes	—
43	C₂³×C₃	C₂⁴	1	3	yes	—
44	C₃×Q₈	—	4	16	no	—
45	C₂×C₃×C₄	—	4	12	no	—
46	C₂×C₃×C₄	C₂×Q₈	1	12	yes	—
47	C₂×C₃×C₄	C₂×Q₈	1	12	yes	—
48	C₂×C₃×C₄	C₂⁴	1	24	yes	—
49	C₂×C₃×C₄	C₂⁴	1	3	yes	—
50	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
51	C₂⁴	C₂³×C₃	1	1	yes	characteristic
52	C₂×Q₈	C₂³×C₃	1	16	yes	—
53	C₂²×C₄	C₃×Q₈	1	8	yes	complemented
54	C₂²×C₄	C₂³×C₃	1	12	yes	—
55	C₂²×C₄	C₂³×C₃	1	3	yes	—
56	C₂²×C₄	C₂³×C₃	1	3	yes	—
57	C₄⋊C₄	C₂³×C₃	1	24	yes	—
58	C₄⋊C₄	C₂³×C₃	1	48	yes	—
59	C₂²⋊C₄	C₂³×C₃	1	24	yes	—
60	C₄²	C₂³×C₃	1	12	yes	—
61	C₄²	C₂³×C₃	1	12	yes	—
62	C₂²×C₃	—	2	6	no	—
63	C₂²×C₃	—	4	4	no	—
64	C₂²×C₃	C₂²×Q₈	1	6	yes	—
65	C₂²×C₃	C₂⁵	1	1	yes	characteristic
66	C₃×C₄	—	2	24	no	—
67	C₃×C₄	C₂²×Q₈	1	6	yes	—
68	C₃×C₄	C₂²×Q₈	1	2	yes	—
69	C₂³	—	4	2	no	—
70	C₂³	C₂×C₃×Q₈	1	4	yes	—
71	C₂³	C₂⁴×C₃	1	3	yes	—
72	Q₈	—	4	16	no	—
73	C₂×C₄	—	4	12	no	—
74	C₂×C₄	C₂×C₃×Q₈	1	12	yes	—
75	C₂×C₄	C₂×C₃×Q₈	1	12	yes	—
76	C₂×C₄	C₂⁴×C₃	1	24	yes	—
77	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
78	C₂×C₄	C₂⁴×C₃	1	3	yes	—
79	C₂×C₃	—	2	6	no	—
80	C₂×C₃	C₂³×Q₈	1	1	yes	characteristic
81	C₂×C₃	#585	1	2	yes	—
82	C₂²	—	2	6	no	—
83	C₂²	—	4	4	no	—
84	C₂²	C₂²×C₃×Q₈	1	6	yes	—
85	C₂²	C₂⁵×C₃	1	1	yes	characteristic
86	C₄	—	2	24	no	—
87	C₄	C₂²×C₃×Q₈	1	2	yes	—
88	C₄	C₂²×C₃×Q₈	1	6	yes	—
89	C₃	#3458	1	1	yes	characteristic, direct product factor, Sylow
90	C₂	—	2	6	no	—
91	C₂	C₂³×C₃×Q₈	1	1	yes	characteristic
92	C₂	C₃×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
socle	C₂²×C₃	C₂⁵
prime radical	C₂⁴×C₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#544	C₂	semidirect
3. C₃×#533	C₂	semidirect
5. #3458	C₃	direct (N × H)
7. C₃×C₄⋊Q₈	C₂²	semidirect
8. C₃×#125	C₂²	semidirect
10. C₃×C₄×Q₈	C₂²	semidirect
16. #544	C₂×C₃	semidirect
18. #533	C₂×C₃	semidirect
22. C₂²×C₃×C₄	Q₈	semidirect
32. C₄⋊Q₈	C₂²×C₃	semidirect
33. #125	C₂²×C₃	semidirect
35. C₄×Q₈	C₂²×C₃	semidirect
53. C₂²×C₄	C₃×Q₈	semidirect
89. C₃	#3458	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#544	2
C₃×#543	2
C₃×#533	2
C₂×C₃×#117	2
#3458	3

Subgroups — C3×#3458 #87342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3458 #87342