Subgroups — C₃²×#2252 #11769301

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×#366	C₂	1	4	yes	maximal
3	C₃²×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×#2252	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×#366	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	#2252	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	1	yes	characteristic
29	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
30	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
31	C₃²×C₈	Q₁₆	1	2	yes	—
32	C₃²×C₈	C₂×Q₈	1	2	yes	—
33	#500	C₂×C₃²	1	2	yes	—
34	#366	C₂×C₃²	1	4	yes	—
35	C₄×C₁₆	C₂×C₃²	1	1	yes	characteristic
36	C₂×C₃×Q₈	—	4	8	no	—
37	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
38	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
39	C₃×C₄⋊C₄	—	2	16	no	—
40	C₃×C₄⋊C₄	—	4	8	no	—
41	C₃×C₄²	C₃×D₄	1	4	yes	—
42	C₃×C₁₆	C₃×Q₈	1	16	yes	complemented
43	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
44	C₃²×C₄	—	8	4	no	—
45	C₃²×C₄	D₁₆	1	2	yes	—
46	C₃²×C₄	Q₃₂	1	2	yes	—
47	C₃²×C₄	C₄⋊Q₈	1	1	yes	characteristic
48	C₃²×C₄	C₂×Q₁₆	1	1	yes	characteristic
49	C₄⋊Q₈	—	2	2	no	—
50	C₂×C₁₆	C₂²×C₃²	1	2	yes	—
51	#107	—	2	2	no	—
52	#107	C₂²×C₃²	1	4	yes	—
53	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic
54	C₃×Q₈	—	8	16	no	—
55	C₂×C₃×C₄	—	4	16	no	—
56	C₂×C₃×C₄	C₃×D₈	1	4	yes	—
57	C₂×C₃×C₄	C₃×D₈	1	4	yes	—
58	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
59	C₃×C₈	C₃×Q₁₆	1	8	yes	—
60	C₃×C₈	C₂×C₃×Q₈	1	8	yes	—
61	C₂×C₃²	#500	1	1	yes	characteristic
62	C₂×C₃²	C₂×D₁₆	1	1	yes	characteristic
63	C₂×C₃²	C₂×Q₃₂	1	1	yes	characteristic
64	C₂×Q₈	—	4	2	no	—
65	C₂×C₈	C₃²×D₄	1	1	yes	characteristic
66	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
67	C₄⋊C₄	—	2	4	no	—
68	C₄⋊C₄	—	4	2	no	—
69	C₄²	C₃²×D₄	1	1	yes	characteristic
70	C₁₆	C₃²×Q₈	1	4	yes	complemented
71	C₂²×C₃	C₂×C₃×D₈	1	4	yes	—
72	C₃×C₄	—	8	16	no	—
73	C₃×C₄	C₃×D₁₆	1	8	yes	—
74	C₃×C₄	C₃×Q₃₂	1	8	yes	—
75	C₃×C₄	C₃×C₄⋊Q₈	1	4	yes	—
76	C₃×C₄	C₂×C₃×Q₁₆	1	4	yes	—
77	C₃²	#2252	1	1	yes	characteristic, direct product factor, Sylow
78	Q₈	—	8	4	no	—
79	C₂×C₄	—	4	4	no	—
80	C₂×C₄	C₃²×D₈	1	1	yes	characteristic
81	C₂×C₄	C₃²×D₈	1	1	yes	characteristic
82	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
83	C₈	C₃²×Q₁₆	1	2	yes	—
84	C₈	C₂×C₃²×Q₈	1	2	yes	—
85	C₂×C₃	C₃×#500	1	4	yes	—
86	C₂×C₃	C₂×C₃×D₁₆	1	4	yes	—
87	C₂×C₃	C₂×C₃×Q₃₂	1	4	yes	—
88	C₂²	C₂×C₃²×D₈	1	1	yes	characteristic
89	C₄	—	8	4	no	—
90	C₄	C₃²×D₁₆	1	2	yes	—
91	C₄	C₃²×Q₃₂	1	2	yes	—
92	C₄	C₃²×C₄⋊Q₈	1	1	yes	characteristic
93	C₄	C₂×C₃²×Q₁₆	1	1	yes	characteristic
94	C₃	C₃×#2252	1	4	yes	direct product factor
95	C₂	C₃²×#500	1	1	yes	characteristic
96	C₂	C₂×C₃²×D₁₆	1	1	yes	characteristic
97	C₂	C₂×C₃²×Q₃₂	1	1	yes	characteristic

	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×#2252	C₃	direct (N × H)
19. C₃²×C₁₆	Q₈	semidirect
20. #2252	C₃²	direct (N × H)
42. C₃×C₁₆	C₃×Q₈	semidirect
70. C₁₆	C₃²×Q₈	semidirect
77. C₃²	#2252	direct (N × H)
94. C₃	C₃×#2252	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×#366	2
C₃²×C₄×C₁₆	2
C₃×#2252	3

Subgroups — C32×#2252 #11769301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#2252 #11769301