Subgroups — C₃²×Q₈×C₁₆ #11769231

Order 1152.

402 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄⋊C₁₆	C₂	1	3	yes	maximal
3	C₃²×C₄×C₁₆	C₂	1	3	yes	maximal
4	C₃×Q₈×C₁₆	C₃	1	4	yes	maximal, direct product factor
5	C₃²×C₄×Q₈	C₄	1	1	yes	characteristic
6	C₂×C₃²×C₁₆	C₂²	1	3	yes	—
7	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
8	C₃²×C₄⋊C₈	C₄	1	3	yes	—
9	C₃²×C₄×C₈	C₂²	1	3	yes	—
10	C₃×C₈×Q₈	C₂×C₃	1	4	yes	—
11	C₃×C₄⋊C₁₆	C₂×C₃	1	12	yes	—
12	C₃×C₄×C₁₆	C₂×C₃	1	12	yes	—
13	C₂×C₃²×Q₈	C₈	1	1	yes	characteristic
14	C₂×C₃²×C₈	C₂×C₄	1	3	yes	—
15	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
16	C₃²×C₄⋊C₄	C₈	1	3	yes	—
17	C₃²×C₄²	C₂×C₄	1	3	yes	—
18	C₃²×C₁₆	—	2	3	no	—
19	C₃²×C₁₆	Q₈	1	2	yes	direct product factor
20	Q₈×C₁₆	C₃²	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₄×Q₈	C₃×C₄	1	4	yes	—
22	C₂×C₃×C₁₆	C₂²×C₃	1	12	yes	—
23	C₂×C₃×C₁₆	C₂²×C₃	1	4	yes	—
24	C₃×C₄⋊C₈	C₃×C₄	1	12	yes	—
25	C₃×C₄×C₈	C₂²×C₃	1	12	yes	—
26	C₃²×Q₈	C₁₆	1	4	yes	direct product factor
27	C₂×C₃²×C₄	C₂×C₈	1	3	yes	—
28	C₂×C₃²×C₄	C₂×C₈	1	3	yes	—
29	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
30	C₃²×C₈	—	2	3	no	—
31	C₃²×C₈	C₂×Q₈	1	1	yes	characteristic
32	C₃²×C₈	#41	1	1	yes	characteristic
33	C₈×Q₈	C₂×C₃²	1	1	yes	characteristic
34	C₄⋊C₁₆	C₂×C₃²	1	3	yes	—
35	C₄×C₁₆	C₂×C₃²	1	3	yes	—
36	C₂×C₃×Q₈	C₃×C₈	1	4	yes	—
37	C₂×C₃×C₈	C₂×C₃×C₄	1	12	yes	—
38	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
39	C₃×C₄⋊C₄	C₃×C₈	1	12	yes	—
40	C₃×C₄²	C₂×C₃×C₄	1	12	yes	—
41	C₃×C₁₆	—	2	12	no	—
42	C₃×C₁₆	C₃×Q₈	1	8	yes	direct product factor
43	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
44	C₃²×C₄	—	2	3	no	—
45	C₃²×C₄	C₂×C₁₆	1	6	yes	—
46	C₃²×C₄	C₄×Q₈	1	1	yes	characteristic
47	C₃²×C₄	#131	1	1	yes	characteristic
48	C₄×Q₈	C₃²×C₄	1	1	yes	characteristic
49	C₂×C₁₆	C₂²×C₃²	1	3	yes	—
50	C₂×C₁₆	C₂²×C₃²	1	1	yes	characteristic
51	C₄⋊C₈	C₃²×C₄	1	3	yes	—
52	C₄×C₈	C₂²×C₃²	1	3	yes	—
53	C₃×Q₈	C₃×C₁₆	1	16	yes	direct product factor
54	C₂×C₃×C₄	C₂×C₃×C₈	1	12	yes	—
55	C₂×C₃×C₄	C₂×C₃×C₈	1	12	yes	—
56	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
57	C₃×C₈	—	2	12	no	—
58	C₃×C₈	C₂×C₃×Q₈	1	4	yes	—
59	C₃×C₈	C₃×#41	1	4	yes	—
60	C₂×C₃²	C₈×Q₈	1	1	yes	characteristic
61	C₂×C₃²	C₂²×C₁₆	1	1	yes	characteristic
62	C₂×C₃²	#504	1	1	yes	characteristic
63	C₂×Q₈	C₃²×C₈	1	1	yes	characteristic
64	C₂×C₈	C₂×C₃²×C₄	1	3	yes	—
65	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
66	C₄⋊C₄	C₃²×C₈	1	3	yes	—
67	C₄²	C₂×C₃²×C₄	1	3	yes	—
68	C₁₆	—	2	3	no	—
69	C₁₆	C₃²×Q₈	1	2	yes	direct product factor
70	C₂²×C₃	C₂²×C₃×C₈	1	4	yes	—
71	C₃×C₄	—	2	12	no	—
72	C₃×C₄	C₂×C₃×C₁₆	1	24	yes	—
73	C₃×C₄	C₃×C₄×Q₈	1	4	yes	—
74	C₃×C₄	C₃×#131	1	4	yes	—
75	C₃²	Q₈×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
76	Q₈	C₃²×C₁₆	1	4	yes	direct product factor
77	C₂×C₄	C₂×C₃²×C₈	1	3	yes	—
78	C₂×C₄	C₂×C₃²×C₈	1	3	yes	—
79	C₂×C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
80	C₈	—	2	3	no	—
81	C₈	C₂×C₃²×Q₈	1	1	yes	characteristic
82	C₈	C₃²×#41	1	1	yes	characteristic
83	C₂×C₃	C₃×C₈×Q₈	1	4	yes	—
84	C₂×C₃	C₂²×C₃×C₁₆	1	4	yes	—
85	C₂×C₃	C₃×#504	1	4	yes	—
86	C₂²	C₂²×C₃²×C₈	1	1	yes	characteristic
87	C₄	—	2	3	no	—
88	C₄	C₂×C₃²×C₁₆	1	6	yes	—
89	C₄	C₃²×C₄×Q₈	1	1	yes	characteristic
90	C₄	C₃²×#131	1	1	yes	characteristic
91	C₃	C₃×Q₈×C₁₆	1	4	yes	direct product factor
92	C₂	C₃²×C₈×Q₈	1	1	yes	characteristic
93	C₂	C₂²×C₃²×C₁₆	1	1	yes	characteristic
94	C₂	C₃²×#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₁₆	C₂²
commutator	C₂	C₂²×C₃²×C₁₆
Frattini, cosocle	C₂×C₈	C₂³×C₃²
socle, prime radical	C₂²×C₃²	C₂²×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃²×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃×Q₈×C₁₆	C₃	direct (N × H)
19. C₃²×C₁₆	Q₈	direct (N × H)
20. Q₈×C₁₆	C₃²	direct (N × H)
26. C₃²×Q₈	C₁₆	direct (N × H)
42. C₃×C₁₆	C₃×Q₈	direct (N × H)
53. C₃×Q₈	C₃×C₁₆	direct (N × H)
69. C₁₆	C₃²×Q₈	direct (N × H)
75. C₃²	Q₈×C₁₆	direct (N × H)
76. Q₈	C₃²×C₁₆	direct (N × H)
91. C₃	C₃×Q₈×C₁₆	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×C₈×Q₈	2
C₃²×C₄⋊C₁₆	2
C₃²×C₄×C₁₆	2
C₃×Q₈×C₁₆	3

Subgroups — C32×Q8×C16 #11769231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×Q₈×C₁₆ #11769231