Subgroups — C₃²×#2253 #11769302

Order 1152.

348 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#499	C₂	1	2	yes	maximal
2	C₃²×#367	C₂	1	2	yes	maximal
3	C₃²×#366	C₂	1	2	yes	maximal
4	C₃²×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₃×#2253	C₃	1	4	yes	maximal, direct product factor
6	C₃²×#125	—	2	2	no	—
7	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
9	C₃²×#107	C₂²	1	4	yes	—
10	C₃²×#106	—	2	2	no	—
11	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
12	C₃×#499	C₂×C₃	1	8	yes	—
13	C₃×#367	C₂×C₃	1	8	yes	—
14	C₃×#366	C₂×C₃	1	8	yes	—
15	C₃×C₄×C₁₆	C₂×C₃	1	4	yes	—
16	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
17	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
18	C₃²×C₄⋊C₄	—	2	4	no	—
19	C₃²×C₄⋊C₄	—	4	4	no	—
20	C₃²×C₄²	D₄	1	1	yes	characteristic
21	C₃²×C₁₆	Q₈	1	2	yes	—
22	C₃²×C₁₆	Q₈	1	2	yes	—
23	#2253	C₃²	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×#125	—	2	8	no	—
25	C₂×C₃×C₁₆	C₂²×C₃	1	4	yes	—
26	C₂×C₃×C₁₆	C₂²×C₃	1	4	yes	—
27	C₃×#107	C₂²×C₃	1	16	yes	—
28	C₃×#106	—	2	8	no	—
29	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
30	C₂×C₃²×C₄	—	4	4	no	—
31	C₂×C₃²×C₄	D₈	1	2	yes	—
32	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
33	C₃²×C₈	Q₁₆	1	2	yes	—
34	C₃²×C₈	C₂×Q₈	1	1	yes	characteristic
35	C₃²×C₈	C₂×Q₈	1	1	yes	characteristic
36	#499	C₂×C₃²	1	2	yes	—
37	#367	C₂×C₃²	1	2	yes	—
38	#366	C₂×C₃²	1	2	yes	—
39	C₄×C₁₆	C₂×C₃²	1	1	yes	characteristic
40	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
41	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
42	C₃×C₄⋊C₄	—	2	16	no	—
43	C₃×C₄⋊C₄	—	4	16	no	—
44	C₃×C₄²	C₃×D₄	1	4	yes	—
45	C₃×C₁₆	C₃×Q₈	1	8	yes	—
46	C₃×C₁₆	C₃×Q₈	1	8	yes	—
47	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
48	C₃²×C₄	—	2	2	no	—
49	C₃²×C₄	—	8	4	no	—
50	C₃²×C₄	C₄⋊Q₈	1	1	yes	characteristic
51	C₃²×C₄	C₂×Q₁₆	1	1	yes	characteristic
52	#125	—	2	2	no	—
53	C₂×C₁₆	C₂²×C₃²	1	1	yes	characteristic
54	C₂×C₁₆	C₂²×C₃²	1	1	yes	characteristic
55	#107	C₂²×C₃²	1	4	yes	—
56	#106	—	2	2	no	—
57	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic
58	C₂×C₃×C₄	—	4	16	no	—
59	C₂×C₃×C₄	C₃×D₈	1	8	yes	—
60	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
61	C₃×C₈	C₃×Q₁₆	1	8	yes	—
62	C₃×C₈	C₂×C₃×Q₈	1	4	yes	—
63	C₃×C₈	C₂×C₃×Q₈	1	4	yes	—
64	C₂×C₃²	#500	1	1	yes	characteristic
65	C₂×C₃²	#508	1	2	yes	—
66	C₂×C₈	C₃²×D₄	1	1	yes	characteristic
67	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
68	C₄⋊C₄	—	2	4	no	—
69	C₄⋊C₄	—	4	4	no	—
70	C₄²	C₃²×D₄	1	1	yes	characteristic
71	C₁₆	C₃²×Q₈	1	2	yes	—
72	C₁₆	C₃²×Q₈	1	2	yes	—
73	C₂²×C₃	C₂×C₃×D₈	1	4	yes	—
74	C₃×C₄	—	2	8	no	—
75	C₃×C₄	—	8	16	no	—
76	C₃×C₄	C₃×C₄⋊Q₈	1	4	yes	—
77	C₃×C₄	C₂×C₃×Q₁₆	1	4	yes	—
78	C₃²	#2253	1	1	yes	characteristic, direct product factor, Sylow
79	C₂×C₄	—	4	4	no	—
80	C₂×C₄	C₃²×D₈	1	2	yes	—
81	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
82	C₈	C₃²×Q₁₆	1	2	yes	—
83	C₈	C₂×C₃²×Q₈	1	1	yes	characteristic
84	C₈	C₂×C₃²×Q₈	1	1	yes	characteristic
85	C₂×C₃	C₃×#500	1	4	yes	—
86	C₂×C₃	C₃×#508	1	8	yes	—
87	C₂²	C₂×C₃²×D₈	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	8	4	no	—
90	C₄	C₃²×C₄⋊Q₈	1	1	yes	characteristic
91	C₄	C₂×C₃²×Q₁₆	1	1	yes	characteristic
92	C₃	C₃×#2253	1	4	yes	direct product factor
93	C₂	C₃²×#500	1	1	yes	characteristic
94	C₂	C₃²×#508	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃²	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄² ◁ C₃²×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₃×#2253	C₃	direct (N × H)
23. #2253	C₃²	direct (N × H)
78. C₃²	#2253	direct (N × H)
92. C₃	C₃×#2253	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×#499	2
C₃²×#367	2
C₃²×#366	2
C₃²×C₄×C₁₆	2
C₃×#2253	3

Subgroups — C32×#2253 #11769302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#2253 #11769302