Subgroups — Q₈×C₉⋊C₁₆ #11797995

Order 1152.

201 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₉⋊C₁₆)	C₂	1	3	yes	maximal
3	C₄×C₉⋊C₁₆	C₂	1	3	yes	maximal
4	Q₈×C₃⋊C₁₆	—	3	1	no	maximal
5	C₄×Q₈×C₉	C₄	1	1	yes	characteristic
6	C₉×C₄⋊C₈	C₄	1	3	yes	—
7	C₄×C₈×C₉	C₂²	1	3	yes	—
8	C₂×C₉⋊C₁₆	C₂²	1	3	yes	—
9	C₂×C₉⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₃×C₈×Q₈	D₃	1	1	yes	characteristic
11	C₄⋊(C₃⋊C₁₆)	—	3	3	no	—
12	C₄×C₃⋊C₁₆	—	3	3	no	—
13	C₂×Q₈×C₉	C₈	1	1	yes	characteristic
14	C₂×C₈×C₉	C₂×C₄	1	3	yes	—
15	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
16	C₉×C₄⋊C₄	C₈	1	3	yes	—
17	C₄²×C₉	C₂×C₄	1	3	yes	—
18	C₉⋊C₁₆	—	2	3	no	—
19	C₉⋊C₁₆	Q₈	1	2	yes	direct product factor
20	Q₈×C₁₆	—	9	1	no	Sylow
21	C₃×C₄×Q₈	Dic₃	1	1	yes	characteristic
22	C₃×C₄⋊C₈	Dic₃	1	3	yes	—
23	C₃×C₄×C₈	C₂×D₃	1	3	yes	—
24	C₂×C₃⋊C₁₆	—	3	1	no	—
25	C₂×C₃⋊C₁₆	—	3	3	no	—
26	Q₈×C₉	C₁₆	1	4	yes	complemented
27	C₂×C₄×C₉	C₂×C₈	1	3	yes	—
28	C₂×C₄×C₉	C₂×C₈	1	3	yes	—
29	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
30	C₈×C₉	—	2	3	no	—
31	C₈×C₉	C₂×Q₈	1	1	yes	characteristic
32	C₈×C₉	#41	1	1	yes	characteristic
33	C₈×Q₈	D₉	1	1	yes	characteristic
34	C₄⋊C₁₆	—	9	3	no	—
35	C₄×C₁₆	—	9	3	no	—
36	C₂×C₃×Q₈	C₃⋊C₈	1	1	yes	characteristic
37	C₂×C₃×C₈	C₂×Dic₃	1	3	yes	—
38	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
39	C₃×C₄⋊C₄	C₃⋊C₈	1	3	yes	—
40	C₃×C₄²	C₂×Dic₃	1	3	yes	—
41	C₃⋊C₁₆	—	3	2	no	—
42	C₃⋊C₁₆	—	6	3	no	—
43	C₂²×C₉	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₉	—	2	3	no	—
45	C₄×C₉	C₂×C₁₆	1	6	yes	—
46	C₄×C₉	C₄×Q₈	1	1	yes	characteristic
47	C₄×C₉	#131	1	1	yes	characteristic
48	C₄×Q₈	Dic₉	1	1	yes	characteristic
49	C₂×C₁₆	—	9	1	no	—
50	C₂×C₁₆	—	9	3	no	—
51	C₄⋊C₈	Dic₉	1	3	yes	—
52	C₄×C₈	C₂×D₉	1	3	yes	—
53	C₃×Q₈	C₃⋊C₁₆	1	4	yes	—
54	C₂×C₃×C₄	C₂×C₃⋊C₈	1	3	yes	—
55	C₂×C₃×C₄	C₂×C₃⋊C₈	1	3	yes	—
56	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
57	C₃×C₈	—	2	3	no	—
58	C₃×C₈	D₃×Q₈	1	1	yes	characteristic
59	C₃×C₈	#239	1	1	yes	characteristic
60	C₂×C₉	C₈×Q₈	1	1	yes	characteristic
61	C₂×C₉	C₂²×C₁₆	1	1	yes	characteristic
62	C₂×C₉	#504	1	1	yes	characteristic
63	C₂×Q₈	C₉⋊C₈	1	1	yes	characteristic
64	C₂×C₈	C₂×Dic₉	1	3	yes	—
65	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
66	C₄⋊C₄	C₉⋊C₈	1	3	yes	—
67	C₄²	C₂×Dic₉	1	3	yes	—
68	C₁₆	—	9	2	no	—
69	C₁₆	—	18	3	no	—
70	C₂²×C₃	C₂²×C₃⋊C₈	1	1	yes	characteristic
71	C₃×C₄	—	2	3	no	—
72	C₃×C₄	C₂×C₃⋊C₁₆	1	6	yes	—
73	C₃×C₄	Q₈×Dic₃	1	1	yes	characteristic
74	C₃×C₄	#948	1	1	yes	characteristic
75	C₉	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
76	Q₈	C₉⋊C₁₆	1	4	yes	direct product factor
77	C₂×C₄	C₂×C₉⋊C₈	1	3	yes	—
78	C₂×C₄	C₂×C₉⋊C₈	1	3	yes	—
79	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
80	C₈	—	2	3	no	—
81	C₈	Q₈×D₉	1	1	yes	characteristic
82	C₈	#3701	1	1	yes	characteristic
83	C₂×C₃	Q₈×C₃⋊C₈	1	1	yes	characteristic
84	C₂×C₃	C₂²×C₃⋊C₁₆	1	1	yes	characteristic
85	C₂×C₃	#5140	1	1	yes	characteristic
86	C₂²	C₂²×C₉⋊C₈	1	1	yes	characteristic
87	C₄	—	2	3	no	—
88	C₄	C₂×C₉⋊C₁₆	1	6	yes	—
89	C₄	Q₈×Dic₉	1	1	yes	characteristic
90	C₄	#63510	1	1	yes	characteristic
91	C₃	Q₈×C₃⋊C₁₆	1	1	yes	characteristic
92	C₂	Q₈×C₉⋊C₈	1	1	yes	characteristic
93	C₂	C₂²×C₉⋊C₁₆	1	1	yes	characteristic
94	C₂	#10588820	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₉
commutator	C₂×C₉	C₂²×C₁₆
Frattini	C₂×C₃×C₈	C₂²×D₃
Fitting	C₈×Q₈×C₉	C₂
socle, prime radical	C₂²×C₃	C₂²×C₃⋊C₈
cosocle	C₂×C₈×C₉	C₂³
hypercenter	C₈×Q₈	D₉
hypocenter	C₉	Q₈×C₁₆
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
19. C₉⋊C₁₆	Q₈	direct (N × H)
26. Q₈×C₉	C₁₆	semidirect
75. C₉	Q₈×C₁₆	semidirect
76. Q₈	C₉⋊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
C₈×Q₈×C₉	2
C₄⋊(C₉⋊C₁₆)	2
C₄×C₉⋊C₁₆	2
Q₈×C₃⋊C₁₆	3

Subgroups — Q8×C9⋊C16 #11797995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₉⋊C₁₆ #11797995