Subgroups — C₃²×#1355 #11768404

Order 1152.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#490	C₂	1	1	yes	maximal, characteristic
2	C₃²×#347	C₂	1	2	yes	maximal, complemented
3	C₃×#1355	C₃	1	4	yes	maximal, direct product factor
4	C₃²×#127	C₄	1	1	yes	characteristic
5	C₃²×#125	C₄	1	1	yes	characteristic
6	C₃²×M₃₂	—	2	2	no	—
7	C₃²×#102	—	2	2	no	—
8	C₃²×#97	C₂²	1	1	yes	characteristic
9	C₃×#490	C₂×C₃	1	4	yes	—
10	C₃×#347	C₂×C₃	1	8	yes	complemented
11	C₂×C₃²×D₄	—	2	1	no	—
12	C₂×C₃²×D₄	—	4	1	no	—
13	C₂×C₃²×C₈	D₄	1	2	yes	—
14	C₃²×C₄⋊C₄	—	2	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	#1355	C₃²	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×#127	C₃×C₄	1	4	yes	—
20	C₃×#125	C₃×C₄	1	4	yes	—
21	C₃×M₃₂	—	2	8	no	—
22	C₃×#102	—	2	8	no	—
23	C₃×#97	C₂²×C₃	1	4	yes	—
24	C₂³×C₃²	—	4	1	no	—
25	C₃²×D₄	—	4	2	no	—
26	C₃²×D₄	—	8	2	no	—
27	C₂×C₃²×C₄	—	2	1	no	—
28	C₂×C₃²×C₄	—	4	1	no	—
29	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
30	C₃²×C₈	—	2	2	no	—
31	#490	C₂×C₃²	1	1	yes	characteristic
32	#347	C₂×C₃²	1	2	yes	complemented
33	C₂×C₃×D₄	—	2	4	no	—
34	C₂×C₃×D₄	—	4	4	no	—
35	C₂×C₃×C₈	C₃×D₄	1	8	yes	—
36	C₃×C₄⋊C₄	—	2	4	no	—
37	C₃×C₄⋊C₄	—	4	4	no	—
38	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
39	C₃×C₁₆	—	2	16	no	—
40	C₂²×C₃²	—	8	2	no	—
41	C₂²×C₃²	—	8	1	no	—
42	C₂²×C₃²	#100	1	1	yes	characteristic
43	C₃²×C₄	—	4	1	no	—
44	C₃²×C₄	—	8	1	no	—
45	C₃²×C₄	#104	1	2	yes	—
46	#127	C₃²×C₄	1	1	yes	characteristic
47	#125	C₃²×C₄	1	1	yes	characteristic
48	M₃₂	—	2	2	no	—
49	#102	—	2	2	no	—
50	#97	C₂²×C₃²	1	1	yes	characteristic
51	C₂³×C₃	—	4	4	no	—
52	C₃×D₄	—	4	8	no	—
53	C₃×D₄	—	8	8	no	—
54	C₂×C₃×C₄	—	2	4	no	—
55	C₂×C₃×C₄	—	4	4	no	—
56	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	4	yes	—
57	C₃×C₈	—	2	8	no	—
58	C₂×C₃²	—	2	1	no	—
59	C₂×C₃²	—	16	1	no	—
60	C₂×C₃²	#329	1	1	yes	characteristic
61	C₂×D₄	—	2	1	no	—
62	C₂×D₄	—	4	1	no	—
63	C₂×C₈	C₃²×D₄	1	2	yes	—
64	C₄⋊C₄	—	2	1	no	—
65	C₄⋊C₄	—	4	1	no	—
66	C₄²	C₂×C₃²×C₄	1	1	yes	characteristic
67	C₁₆	—	2	4	no	—
68	C₂²×C₃	—	8	8	no	—
69	C₂²×C₃	—	8	4	no	—
70	C₂²×C₃	C₃×#100	1	4	yes	—
71	C₃×C₄	—	4	4	no	—
72	C₃×C₄	—	8	4	no	—
73	C₃×C₄	C₃×#104	1	8	yes	—
74	C₃²	#1355	1	1	yes	characteristic, direct product factor, Sylow
75	C₂³	—	4	1	no	—
76	D₄	—	4	2	no	—
77	D₄	—	8	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	4	1	no	—
80	C₂×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₂×C₃	—	2	4	no	—
83	C₂×C₃	—	16	4	no	—
84	C₂×C₃	C₃×#329	1	4	yes	—
85	C₂²	—	8	2	no	—
86	C₂²	—	8	1	no	—
87	C₂²	C₃²×#100	1	1	yes	characteristic
88	C₄	—	4	1	no	—
89	C₄	—	8	1	no	—
90	C₄	C₃²×#104	1	2	yes	—
91	C₃	C₃×#1355	1	4	yes	direct product factor
92	C₂	—	2	1	no	—
93	C₂	—	16	1	no	—
94	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	C₃²×#127	C₄
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
2. C₃²×#347	C₂	semidirect
3. C₃×#1355	C₃	direct (N × H)
10. C₃×#347	C₂×C₃	semidirect
18. #1355	C₃²	direct (N × H)
32. #347	C₂×C₃²	semidirect
74. C₃²	#1355	direct (N × H)
91. C₃	C₃×#1355	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×#490	2
C₃²×#347	2
C₃×#1355	3

Subgroups — C32×#1355 #11768404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#1355 #11768404