Subgroups — C₃²×#1356 #11768405

Order 1152.

234 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#491	C₂	1	1	yes	maximal, characteristic
2	C₃²×#347	C₂	1	2	yes	maximal
3	C₃×#1356	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₄⋊Q₈	C₄	1	1	yes	characteristic
5	C₃²×#125	C₄	1	1	yes	characteristic
6	C₃²×M₃₂	—	2	2	no	—
7	C₃²×#103	—	2	2	no	—
8	C₃²×#97	C₂²	1	1	yes	characteristic
9	C₃×#491	C₂×C₃	1	4	yes	—
10	C₃×#347	C₂×C₃	1	8	yes	—
11	C₂×C₃²×Q₈	—	2	1	no	—
12	C₂×C₃²×C₈	D₄	1	2	yes	—
13	C₃²×C₄⋊C₄	—	2	1	no	—
14	C₃²×C₄⋊C₄	—	4	1	no	—
15	C₃²×C₄⋊C₄	—	4	1	no	—
16	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
17	C₃²×C₁₆	—	2	4	no	—
18	#1356	C₃²	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₄⋊Q₈	C₃×C₄	1	4	yes	—
20	C₃×#125	C₃×C₄	1	4	yes	—
21	C₃×M₃₂	—	2	8	no	—
22	C₃×#103	—	2	8	no	—
23	C₃×#97	C₂²×C₃	1	4	yes	—
24	C₃²×Q₈	—	4	2	no	—
25	C₂×C₃²×C₄	—	2	1	no	—
26	C₂×C₃²×C₄	—	4	1	no	—
27	C₂×C₃²×C₄	—	4	1	no	—
28	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
29	C₃²×C₈	—	2	2	no	—
30	#491	C₂×C₃²	1	1	yes	characteristic
31	#347	C₂×C₃²	1	2	yes	—
32	C₂×C₃×Q₈	—	2	4	no	—
33	C₂×C₃×C₈	C₃×D₄	1	8	yes	—
34	C₃×C₄⋊C₄	—	2	4	no	—
35	C₃×C₄⋊C₄	—	4	4	no	—
36	C₃×C₄⋊C₄	—	4	4	no	—
37	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
38	C₃×C₁₆	—	2	16	no	—
39	C₂²×C₃²	#100	1	1	yes	characteristic
40	C₃²×C₄	—	4	1	no	—
41	C₃²×C₄	—	8	1	no	—
42	C₃²×C₄	—	8	1	no	—
43	C₃²×C₄	#104	1	2	yes	—
44	C₄⋊Q₈	C₃²×C₄	1	1	yes	characteristic
45	#125	C₃²×C₄	1	1	yes	characteristic
46	M₃₂	—	2	2	no	—
47	#103	—	2	2	no	—
48	#97	C₂²×C₃²	1	1	yes	characteristic
49	C₃×Q₈	—	4	8	no	—
50	C₂×C₃×C₄	—	2	4	no	—
51	C₂×C₃×C₄	—	4	4	no	—
52	C₂×C₃×C₄	—	4	4	no	—
53	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	4	yes	—
54	C₃×C₈	—	2	8	no	—
55	C₂×C₃²	—	2	1	no	—
56	C₂×C₃²	#329	1	1	yes	characteristic
57	C₂×Q₈	—	2	1	no	—
58	C₂×C₈	C₃²×D₄	1	2	yes	—
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	—	4	1	no	—
61	C₄⋊C₄	—	4	1	no	—
62	C₄²	C₂×C₃²×C₄	1	1	yes	characteristic
63	C₁₆	—	2	4	no	—
64	C₂²×C₃	C₃×#100	1	4	yes	—
65	C₃×C₄	—	4	4	no	—
66	C₃×C₄	—	8	4	no	—
67	C₃×C₄	—	8	4	no	—
68	C₃×C₄	C₃×#104	1	8	yes	—
69	C₃²	#1356	1	1	yes	characteristic, direct product factor, Sylow
70	Q₈	—	4	2	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	4	1	no	—
73	C₂×C₄	—	4	1	no	—
74	C₂×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
75	C₈	—	2	2	no	—
76	C₂×C₃	—	2	4	no	—
77	C₂×C₃	C₃×#329	1	4	yes	—
78	C₂²	C₃²×#100	1	1	yes	characteristic
79	C₄	—	4	1	no	—
80	C₄	—	8	1	no	—
81	C₄	—	8	1	no	—
82	C₄	C₃²×#104	1	2	yes	—
83	C₃	C₃×#1356	1	4	yes	direct product factor
84	C₂	—	2	1	no	—
85	C₂	C₃²×#329	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃²	#329
commutator	C₄²	C₂×C₃²×C₄
Frattini, cosocle	#97	C₂²×C₃²
prime radical	C₂²×C₃²	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ C₂×C₃²×C₄ ◁ C₃²×#97 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×#1356	C₃	direct (N × H)
18. #1356	C₃²	direct (N × H)
69. C₃²	#1356	direct (N × H)
83. C₃	C₃×#1356	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×#491	2
C₃²×#347	2
C₃×#1356	3

Subgroups — C32×#1356 #11768405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#1356 #11768405