Subgroups — C₃×#1837 #72552

Order 384.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#423	C₂	1	2	yes	maximal
2	C₂×C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#341	C₂	1	4	yes	maximal
4	#1837	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×M₁₆	C₂²	1	4	yes	—
6	C₂²×C₃×C₈	C₂²	1	2	yes	—
7	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
8	C₃×C₄⋊C₈	—	2	4	no	—
9	C₃×C₄×C₈	C₄	1	2	yes	—
10	C₃×C₄×C₈	C₄	1	2	yes	—
11	#423	C₂×C₃	1	2	yes	—
12	C₂×C₄×C₈	C₂×C₃	1	1	yes	characteristic
13	#341	C₂×C₃	1	4	yes	—
14	C₂²×C₃×C₄	Q₈	1	2	yes	—
15	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
16	C₃×M₁₆	—	2	8	no	—
17	C₂×C₃×C₈	—	2	4	no	—
18	C₂×C₃×C₈	—	2	4	no	—
19	C₂×C₃×C₈	C₂×C₄	1	4	yes	—
20	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
21	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
22	C₃×C₄²	D₄	1	2	yes	—
23	C₂×M₁₆	C₂²×C₃	1	4	yes	—
24	C₂²×C₈	C₂²×C₃	1	2	yes	—
25	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
26	C₄⋊C₈	—	2	4	no	—
27	C₄×C₈	C₃×C₄	1	2	yes	—
28	C₄×C₈	C₃×C₄	1	2	yes	—
29	C₂³×C₃	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₃×C₄	—	2	4	no	—
31	C₂×C₃×C₄	C₄⋊C₄	1	2	yes	—
32	C₂×C₃×C₄	C₄⋊C₄	1	2	yes	—
33	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
35	C₂×C₃×C₄	#41	1	4	yes	—
36	C₃×C₈	—	2	4	no	—
37	C₃×C₈	—	4	4	no	—
38	C₂²×C₄	C₃×Q₈	1	2	yes	—
39	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
40	M₁₆	—	2	8	no	—
41	C₂×C₈	—	2	4	no	—
42	C₂×C₈	—	2	4	no	—
43	C₂×C₈	C₂×C₃×C₄	1	4	yes	—
44	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
45	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
46	C₄²	C₃×D₄	1	2	yes	—
47	C₂²×C₃	—	2	2	no	—
48	C₂²×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂²×C₃	#125	1	2	yes	—
50	C₃×C₄	—	2	2	no	—
51	C₃×C₄	#108	1	4	yes	—
52	C₃×C₄	#117	1	2	yes	—
53	C₃×C₄	#124	1	2	yes	—
54	C₂³	C₂×C₃×Q₈	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	C₃×C₄⋊C₄	1	2	yes	—
57	C₂×C₄	C₃×C₄⋊C₄	1	2	yes	—
58	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
59	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
60	C₂×C₄	C₃×#41	1	4	yes	—
61	C₈	—	2	4	no	—
62	C₈	—	4	4	no	—
63	C₂×C₃	—	2	2	no	—
64	C₂×C₃	#382	1	1	yes	characteristic
65	C₂×C₃	C₂×#108	1	2	yes	—
66	C₂²	—	2	2	no	—
67	C₂²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
68	C₂²	C₃×#125	1	2	yes	—
69	C₄	—	2	2	no	—
70	C₄	C₃×#108	1	4	yes	—
71	C₄	C₃×#117	1	2	yes	—
72	C₄	C₃×#124	1	2	yes	—
73	C₃	#1837	1	1	yes	characteristic, direct product factor, Sylow
74	C₂	—	2	2	no	—
75	C₂	C₃×#382	1	1	yes	characteristic
76	C₂	C₂×C₃×#108	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄
Frattini, cosocle	C₂²×C₄	C₂³×C₃
socle	C₂²×C₃	C₂×C₄⋊C₄
prime radical	C₂³×C₃	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
4. #1837	C₃	direct (N × H)
73. C₃	#1837	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×#423	2
C₂×C₃×C₄×C₈	2
C₃×#341	2
#1837	3

Subgroups — C3×#1837 #72552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1837 #72552