Subgroups — C₃×C₄×#95 #72147

Order 384.

752 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄²	C₂	1	3	yes	maximal
2	C₂×C₃×#95	C₂	1	4	yes	maximal
3	C₄×#95	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂³×C₃×C₄	C₂²	1	6	yes	—
5	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄²	—	2	12	no	—
7	C₂×C₃×C₄²	C₄	1	12	yes	complemented
8	C₃×#95	C₄	1	16	yes	direct product factor
9	C₂²×C₄²	C₂×C₃	1	3	yes	—
10	C₂×#95	C₂×C₃	1	4	yes	—
11	C₂⁴×C₃	C₂³	1	1	yes	characteristic
12	C₂²×C₃×C₄	—	2	12	no	—
13	C₂²×C₃×C₄	—	2	12	no	—
14	C₂²×C₃×C₄	C₂×C₄	1	24	yes	—
15	C₂²×C₃×C₄	C₂×C₄	1	12	yes	—
16	C₂²×C₃×C₄	C₂×C₄	1	6	yes	—
17	C₂²×C₃×C₄	D₄	1	6	yes	—
18	C₂²×C₃×C₄	Q₈	1	2	yes	—
19	C₃×C₄²	—	2	24	no	—
20	C₂³×C₄	C₂²×C₃	1	6	yes	—
21	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
22	C₂×C₄²	—	2	12	no	—
23	C₂×C₄²	C₃×C₄	1	12	yes	complemented
24	#95	C₃×C₄	1	16	yes	direct product factor
25	C₂³×C₃	C₂²×C₄	1	3	yes	—
26	C₂³×C₃	C₂²×C₄	1	4	yes	—
27	C₂³×C₃	C₂×D₄	1	3	yes	—
28	C₂³×C₃	C₂×Q₈	1	1	yes	characteristic
29	C₂³×C₃	#41	1	4	yes	—
30	C₂×C₃×C₄	—	2	12	no	—
31	C₂×C₃×C₄	—	2	12	no	—
32	C₂×C₃×C₄	—	2	48	no	—
33	C₂×C₃×C₄	C₄²	1	4	yes	—
34	C₂×C₃×C₄	C₄²	1	24	yes	complemented
35	C₂×C₃×C₄	C₂²⋊C₄	1	12	yes	—
36	C₂×C₃×C₄	C₄⋊C₄	1	12	yes	—
37	C₂⁴	C₂³×C₃	1	1	yes	characteristic
38	C₂²×C₄	—	2	12	no	—
39	C₂²×C₄	—	2	12	no	—
40	C₂²×C₄	C₂×C₃×C₄	1	24	yes	—
41	C₂²×C₄	C₂×C₃×C₄	1	12	yes	—
42	C₂²×C₄	C₂×C₃×C₄	1	6	yes	—
43	C₂²×C₄	C₃×D₄	1	6	yes	—
44	C₂²×C₄	C₃×Q₈	1	2	yes	—
45	C₄²	—	2	24	no	—
46	C₂²×C₃	C₂×C₄²	1	1	yes	characteristic
47	C₂²×C₃	C₂×C₄²	1	6	yes	—
48	C₂²×C₃	C₂×C₂²⋊C₄	1	3	yes	—
49	C₂²×C₃	C₂×C₄⋊C₄	1	3	yes	—
50	C₂²×C₃	#117	1	6	yes	—
51	C₂²×C₃	C₄×D₄	1	12	yes	—
52	C₂²×C₃	C₄×Q₈	1	4	yes	—
53	C₃×C₄	—	2	24	no	—
54	C₃×C₄	#95	1	8	yes	direct product factor
55	C₂³	C₂²×C₃×C₄	1	3	yes	—
56	C₂³	C₂²×C₃×C₄	1	4	yes	—
57	C₂³	C₂×C₃×D₄	1	3	yes	—
58	C₂³	C₂×C₃×Q₈	1	1	yes	characteristic
59	C₂³	C₃×#41	1	4	yes	—
60	C₂×C₄	—	2	12	no	—
61	C₂×C₄	—	2	12	no	—
62	C₂×C₄	—	2	48	no	—
63	C₂×C₄	C₃×C₄²	1	4	yes	—
64	C₂×C₄	C₃×C₄²	1	24	yes	complemented
65	C₂×C₄	C₃×C₂²⋊C₄	1	12	yes	—
66	C₂×C₄	C₃×C₄⋊C₄	1	12	yes	—
67	C₂×C₃	C₄³	1	1	yes	characteristic
68	C₂×C₃	C₂×#95	1	1	yes	characteristic
69	C₂×C₃	#376	1	1	yes	characteristic
70	C₂×C₃	C₄×C₂²⋊C₄	1	6	yes	—
71	C₂×C₃	C₄×C₄⋊C₄	1	6	yes	—
72	C₂²	C₂×C₃×C₄²	1	1	yes	characteristic
73	C₂²	C₂×C₃×C₄²	1	6	yes	—
74	C₂²	C₂×C₃×C₂²⋊C₄	1	3	yes	—
75	C₂²	C₂×C₃×C₄⋊C₄	1	3	yes	—
76	C₂²	C₃×#117	1	6	yes	—
77	C₂²	C₃×C₄×D₄	1	12	yes	—
78	C₂²	C₃×C₄×Q₈	1	4	yes	—
79	C₄	—	2	24	no	—
80	C₄	C₃×#95	1	8	yes	direct product factor
81	C₃	C₄×#95	1	1	yes	characteristic, direct product factor, Sylow
82	C₂	C₃×C₄³	1	1	yes	characteristic
83	C₂	C₂×C₃×#95	1	1	yes	characteristic
84	C₂	C₃×#376	1	1	yes	characteristic
85	C₂	C₃×C₄×C₂²⋊C₄	1	6	yes	—
86	C₂	C₃×C₄×C₄⋊C₄	1	6	yes	—

	subgroup	G/H
center	C₂³×C₃×C₄	C₂²
commutator	C₂	C₃×C₄³
Frattini, cosocle	C₂⁴	C₂³×C₃
socle, prime radical	C₂⁴×C₃	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×#95	C₃	direct (N × H)
7. C₂×C₃×C₄²	C₄	semidirect
8. C₃×#95	C₄	direct (N × H)
23. C₂×C₄²	C₃×C₄	semidirect
24. #95	C₃×C₄	direct (N × H)
34. C₂×C₃×C₄	C₄²	semidirect
54. C₃×C₄	#95	direct (N × H)
64. C₂×C₄	C₃×C₄²	semidirect
80. C₄	C₃×#95	direct (N × H)
81. C₃	C₄×#95	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×C₄²	2
C₂×C₃×#95	2
C₄×#95	3

Subgroups — C3×C4×#95 #72147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#95 #72147