Subgroups — C₃²×#2254 #11769303

Order 1152.

384 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#500	C₂	1	2	yes	maximal
2	C₃²×#367	C₂	1	4	yes	maximal
3	C₃²×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×#2254	C₃	1	4	yes	maximal, direct product factor
5	C₃²×C₄⋊Q₈	—	2	2	no	—
6	C₂×C₃²×C₁₆	C₂²	1	2	yes	—
7	C₃²×#107	—	2	2	no	—
8	C₃²×#107	C₂²	1	4	yes	—
9	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
10	C₃×#500	C₂×C₃	1	8	yes	—
11	C₃×#367	C₂×C₃	1	16	yes	—
12	C₃×C₄×C₁₆	C₂×C₃	1	4	yes	—
13	C₂×C₃²×Q₈	—	4	2	no	—
14	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
15	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
16	C₃²×C₄⋊C₄	—	2	4	no	—
17	C₃²×C₄⋊C₄	—	4	2	no	—
18	C₃²×C₄²	D₄	1	1	yes	characteristic
19	C₃²×C₁₆	Q₈	1	4	yes	complemented
20	#2254	C₃²	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₄⋊Q₈	—	2	8	no	—
22	C₂×C₃×C₁₆	C₂²×C₃	1	8	yes	—
23	C₃×#107	—	2	8	no	—
24	C₃×#107	C₂²×C₃	1	16	yes	—
25	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
26	C₃²×Q₈	—	8	4	no	—
27	C₂×C₃²×C₄	—	4	4	no	—
28	C₂×C₃²×C₄	D₈	1	2	yes	—
29	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
30	C₃²×C₈	Q₁₆	1	2	yes	—
31	C₃²×C₈	C₂×Q₈	1	2	yes	—
32	#500	C₂×C₃²	1	2	yes	—
33	#367	C₂×C₃²	1	4	yes	—
34	C₄×C₁₆	C₂×C₃²	1	1	yes	characteristic
35	C₂×C₃×Q₈	—	4	8	no	—
36	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
37	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
38	C₃×C₄⋊C₄	—	2	16	no	—
39	C₃×C₄⋊C₄	—	4	8	no	—
40	C₃×C₄²	C₃×D₄	1	4	yes	—
41	C₃×C₁₆	C₃×Q₈	1	16	yes	complemented
42	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
43	C₃²×C₄	—	8	4	no	—
44	C₃²×C₄	SD₃₂	1	4	yes	—
45	C₃²×C₄	C₄⋊Q₈	1	1	yes	characteristic
46	C₃²×C₄	C₂×Q₁₆	1	1	yes	characteristic
47	C₄⋊Q₈	—	2	2	no	—
48	C₂×C₁₆	C₂²×C₃²	1	2	yes	—
49	#107	—	2	2	no	—
50	#107	C₂²×C₃²	1	4	yes	—
51	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic
52	C₃×Q₈	—	8	16	no	—
53	C₂×C₃×C₄	—	4	16	no	—
54	C₂×C₃×C₄	C₃×D₈	1	8	yes	—
55	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
56	C₃×C₈	C₃×Q₁₆	1	8	yes	—
57	C₃×C₈	C₂×C₃×Q₈	1	8	yes	—
58	C₂×C₃²	#500	1	1	yes	characteristic
59	C₂×C₃²	C₂×SD₃₂	1	2	yes	—
60	C₂×Q₈	—	4	2	no	—
61	C₂×C₈	C₃²×D₄	1	1	yes	characteristic
62	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
63	C₄⋊C₄	—	2	4	no	—
64	C₄⋊C₄	—	4	2	no	—
65	C₄²	C₃²×D₄	1	1	yes	characteristic
66	C₁₆	C₃²×Q₈	1	4	yes	complemented
67	C₂²×C₃	C₂×C₃×D₈	1	4	yes	—
68	C₃×C₄	—	8	16	no	—
69	C₃×C₄	C₃×SD₃₂	1	16	yes	—
70	C₃×C₄	C₃×C₄⋊Q₈	1	4	yes	—
71	C₃×C₄	C₂×C₃×Q₁₆	1	4	yes	—
72	C₃²	#2254	1	1	yes	characteristic, direct product factor, Sylow
73	Q₈	—	8	4	no	—
74	C₂×C₄	—	4	4	no	—
75	C₂×C₄	C₃²×D₈	1	2	yes	—
76	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
77	C₈	C₃²×Q₁₆	1	2	yes	—
78	C₈	C₂×C₃²×Q₈	1	2	yes	—
79	C₂×C₃	C₃×#500	1	4	yes	—
80	C₂×C₃	C₂×C₃×SD₃₂	1	8	yes	—
81	C₂²	C₂×C₃²×D₈	1	1	yes	characteristic
82	C₄	—	8	4	no	—
83	C₄	C₃²×SD₃₂	1	4	yes	—
84	C₄	C₃²×C₄⋊Q₈	1	1	yes	characteristic
85	C₄	C₂×C₃²×Q₁₆	1	1	yes	characteristic
86	C₃	C₃×#2254	1	4	yes	direct product factor
87	C₂	C₃²×#500	1	1	yes	characteristic
88	C₂	C₂×C₃²×SD₃₂	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
4. C₃×#2254	C₃	direct (N × H)
19. C₃²×C₁₆	Q₈	semidirect
20. #2254	C₃²	direct (N × H)
41. C₃×C₁₆	C₃×Q₈	semidirect
66. C₁₆	C₃²×Q₈	semidirect
72. C₃²	#2254	direct (N × H)
86. C₃	C₃×#2254	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×#500	2
C₃²×#367	2
C₃²×C₄×C₁₆	2
C₃×#2254	3

Subgroups — C32×#2254 #11769303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#2254 #11769303