Subgroups — C₃²×#1839 #11768888

Order 1152.

720 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄³	C₂	1	1	yes	maximal, characteristic
2	C₃²×#336	C₂	1	6	yes	maximal
3	C₃×#1839	C₃	1	4	yes	maximal, direct product factor
4	C₂²×C₃²×C₈	C₂²	1	4	yes	—
5	C₂×C₃²×C₄²	C₄	1	3	yes	—
6	C₂×C₃²×C₄²	C₄	1	1	yes	characteristic
7	C₂×C₃²×C₄²	C₂²	1	3	yes	—
8	C₃×C₄³	C₂×C₃	1	4	yes	—
9	C₃×#336	C₂×C₃	1	24	yes	—
10	C₂²×C₃²×C₄	C₂×C₄	1	3	yes	—
11	C₂²×C₃²×C₄	C₂×C₄	1	3	yes	—
12	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
13	C₂×C₃²×C₈	—	2	12	no	—
14	C₃²×C₄²	—	2	6	no	—
15	C₃²×C₄²	—	2	6	no	—
16	C₃²×C₄²	C₈	1	4	yes	complemented
17	#1839	C₃²	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²×C₃×C₈	C₂²×C₃	1	16	yes	—
19	C₂×C₃×C₄²	C₃×C₄	1	12	yes	—
20	C₂×C₃×C₄²	C₃×C₄	1	4	yes	—
21	C₂×C₃×C₄²	C₂²×C₃	1	12	yes	—
22	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₃²×C₄	—	2	3	no	—
24	C₂×C₃²×C₄	—	2	3	no	—
25	C₂×C₃²×C₄	—	2	3	no	—
26	C₂×C₃²×C₄	—	2	3	no	—
27	C₂×C₃²×C₄	C₂×C₈	1	6	yes	—
28	C₂×C₃²×C₄	M₁₆	1	6	yes	—
29	C₂×C₃²×C₄	#41	1	6	yes	—
30	C₃²×C₈	—	4	4	no	—
31	C₄³	C₂×C₃²	1	1	yes	characteristic
32	#336	C₂×C₃²	1	6	yes	—
33	C₂²×C₃×C₄	C₂×C₃×C₄	1	12	yes	—
34	C₂²×C₃×C₄	C₂×C₃×C₄	1	12	yes	—
35	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
36	C₂×C₃×C₈	—	2	48	no	—
37	C₃×C₄²	—	2	24	no	—
38	C₃×C₄²	—	2	24	no	—
39	C₃×C₄²	C₃×C₈	1	16	yes	complemented
40	C₂²×C₃²	#117	1	3	yes	—
41	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
42	C₂²×C₃²	C₂×M₁₆	1	3	yes	—
43	C₃²×C₄	—	2	6	no	—
44	C₃²×C₄	—	2	6	no	—
45	C₃²×C₄	#126	1	4	yes	—
46	C₂²×C₈	C₂²×C₃²	1	4	yes	—
47	C₂×C₄²	C₃²×C₄	1	3	yes	—
48	C₂×C₄²	C₃²×C₄	1	1	yes	characteristic
49	C₂×C₄²	C₂²×C₃²	1	3	yes	—
50	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
51	C₂×C₃×C₄	—	2	12	no	—
52	C₂×C₃×C₄	—	2	12	no	—
53	C₂×C₃×C₄	—	2	12	no	—
54	C₂×C₃×C₄	—	2	12	no	—
55	C₂×C₃×C₄	C₂×C₃×C₈	1	24	yes	—
56	C₂×C₃×C₄	C₃×M₁₆	1	24	yes	—
57	C₂×C₃×C₄	C₃×#41	1	24	yes	—
58	C₃×C₈	—	4	16	no	—
59	C₂×C₃²	#383	1	1	yes	characteristic
60	C₂×C₃²	#431	1	3	yes	—
61	C₂×C₃²	#432	1	3	yes	—
62	C₂²×C₄	C₂×C₃²×C₄	1	3	yes	—
63	C₂²×C₄	C₂×C₃²×C₄	1	3	yes	—
64	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
65	C₂×C₈	—	2	12	no	—
66	C₄²	—	2	6	no	—
67	C₄²	—	2	6	no	—
68	C₄²	C₃²×C₈	1	4	yes	complemented
69	C₂²×C₃	C₃×#117	1	12	yes	—
70	C₂²×C₃	C₂²×C₃×C₈	1	4	yes	—
71	C₂²×C₃	C₂×C₃×M₁₆	1	12	yes	—
72	C₃×C₄	—	2	24	no	—
73	C₃×C₄	—	2	24	no	—
74	C₃×C₄	C₃×#126	1	16	yes	—
75	C₃²	#1839	1	1	yes	characteristic, direct product factor, Sylow
76	C₂³	C₂²×C₃²×C₄	1	1	yes	characteristic
77	C₂×C₄	—	2	3	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	C₂×C₃²×C₈	1	6	yes	—
82	C₂×C₄	C₃²×M₁₆	1	6	yes	—
83	C₂×C₄	C₃²×#41	1	6	yes	—
84	C₈	—	4	4	no	—
85	C₂×C₃	C₃×#383	1	4	yes	—
86	C₂×C₃	C₃×#431	1	12	yes	—
87	C₂×C₃	C₃×#432	1	12	yes	—
88	C₂²	C₃²×#117	1	3	yes	—
89	C₂²	C₂²×C₃²×C₈	1	1	yes	characteristic
90	C₂²	C₂×C₃²×M₁₆	1	3	yes	—
91	C₄	—	2	6	no	—
92	C₄	—	2	6	no	—
93	C₄	C₃²×#126	1	4	yes	—
94	C₃	C₃×#1839	1	4	yes	direct product factor
95	C₂	C₃²×#383	1	1	yes	characteristic
96	C₂	C₃²×#431	1	3	yes	—
97	C₂	C₃²×#432	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃²×C₄	C₂³
commutator	C₂²	C₂²×C₃²×C₈
Frattini, cosocle	C₂²×C₄	C₂³×C₃²
socle, prime radical	C₂³×C₃²	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃²×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×#1839	C₃	direct (N × H)
16. C₃²×C₄²	C₈	semidirect
17. #1839	C₃²	direct (N × H)
39. C₃×C₄²	C₃×C₈	semidirect
68. C₄²	C₃²×C₈	semidirect
75. C₃²	#1839	direct (N × H)
94. C₃	C₃×#1839	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₄³	2
C₃²×#336	2
C₃×#1839	3

Subgroups — C32×#1839 #11768888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#1839 #11768888