Subgroups — D₄×C₉⋊C₁₆ #11797434

Order 1152.

261 conjugacy classes of subgroups.

The subgroup lattice has 162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₉⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	#10588226	C₂	1	2	yes	maximal, complemented
4	C₄⋊(C₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₃⋊C₁₆	—	3	1	no	maximal
7	C₂²×C₈×C₉	C₂²	1	2	yes	—
8	C₄×D₄×C₉	C₄	1	1	yes	characteristic
9	C₉×C₄⋊C₈	C₄	1	1	yes	characteristic
10	C₉×C₂²⋊C₈	C₄	1	2	yes	—
11	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₉⋊C₁₆	—	2	4	no	—
13	C₂×C₉⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₉⋊C₁₆	C₂²	1	2	yes	—
15	C₂×C₉⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₃×C₈×D₄	D₃	1	1	yes	characteristic
17	C₂²×C₃⋊C₁₆	—	3	2	no	—
18	#4549	—	3	2	no	—
19	C₄⋊(C₃⋊C₁₆)	—	3	1	no	—
20	C₄×C₃⋊C₁₆	—	3	1	no	—
21	C₂×D₄×C₉	C₈	1	1	yes	characteristic
22	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₉	—	2	2	no	—
24	C₂×C₈×C₉	—	2	2	no	—
25	C₂×C₈×C₉	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
28	C₉×C₄⋊C₄	C₈	1	1	yes	characteristic
29	C₉×C₂²⋊C₄	C₈	1	2	yes	—
30	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
31	C₉⋊C₁₆	—	2	2	no	—
32	C₉⋊C₁₆	—	2	1	no	—
33	C₉⋊C₁₆	D₄	1	2	yes	direct product factor
34	D₄×C₁₆	—	9	1	no	Sylow
35	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
36	C₃×C₄×D₄	Dic₃	1	1	yes	characteristic
37	C₃×C₄⋊C₈	Dic₃	1	1	yes	characteristic
38	C₃×C₂²⋊C₈	Dic₃	1	2	yes	—
39	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
40	C₂×C₃⋊C₁₆	—	3	1	no	—
41	C₂×C₃⋊C₁₆	—	3	1	no	—
42	C₂×C₃⋊C₁₆	—	3	2	no	—
43	C₂×C₃⋊C₁₆	—	6	4	no	—
44	C₂³×C₉	C₂×C₈	1	2	yes	—
45	D₄×C₉	C₁₆	1	4	yes	complemented
46	C₂×C₄×C₉	—	2	2	no	—
47	C₂×C₄×C₉	—	2	2	no	—
48	C₂×C₄×C₉	C₂×C₈	1	1	yes	characteristic
49	C₂×C₄×C₉	C₂×C₈	1	2	yes	—
50	C₂×C₄×C₉	C₂×C₈	1	1	yes	characteristic
51	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
52	C₈×C₉	—	2	2	no	—
53	C₈×C₉	—	2	1	no	—
54	C₈×C₉	C₂×D₄	1	1	yes	characteristic
55	C₈×C₉	#41	1	1	yes	characteristic
56	C₂²×C₁₆	—	9	2	no	—
57	C₈×D₄	D₉	1	1	yes	characteristic
58	C₄⋊C₁₆	—	9	1	no	—
59	C₂²⋊C₁₆	—	9	2	no	—
60	C₄×C₁₆	—	9	1	no	—
61	C₂×C₃×D₄	C₃⋊C₈	1	1	yes	characteristic
62	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
63	C₂×C₃×C₈	—	2	2	no	—
64	C₂×C₃×C₈	—	2	2	no	—
65	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
66	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
67	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
68	C₃×C₄⋊C₄	C₃⋊C₈	1	1	yes	characteristic
69	C₃×C₂²⋊C₄	C₃⋊C₈	1	2	yes	—
70	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
71	C₃⋊C₁₆	—	3	2	no	—
72	C₃⋊C₁₆	—	6	2	no	—
73	C₃⋊C₁₆	—	6	1	no	—
74	C₂²×C₉	—	2	2	no	—
75	C₂²×C₉	—	2	2	no	—
76	C₂²×C₉	C₂×C₁₆	1	4	yes	complemented
77	C₂²×C₉	C₂²×C₈	1	1	yes	characteristic
78	C₄×C₉	—	2	2	no	—
79	C₄×C₉	—	2	1	no	—
80	C₄×C₉	C₂×C₁₆	1	2	yes	complemented
81	C₄×C₉	C₄×D₄	1	1	yes	characteristic
82	C₄×C₉	#131	1	1	yes	characteristic
83	C₂²×C₈	C₂×D₉	1	2	yes	—
84	C₄×D₄	Dic₉	1	1	yes	characteristic
85	C₂×C₁₆	—	9	1	no	—
86	C₂×C₁₆	—	9	1	no	—
87	C₂×C₁₆	—	9	2	no	—
88	C₂×C₁₆	—	18	4	no	—
89	C₄⋊C₈	Dic₉	1	1	yes	characteristic
90	C₂²⋊C₈	Dic₉	1	2	yes	—
91	C₄×C₈	C₂×D₉	1	1	yes	characteristic
92	C₂³×C₃	C₂×C₃⋊C₈	1	2	yes	—
93	C₃×D₄	C₃⋊C₁₆	1	4	yes	—
94	C₂×C₃×C₄	—	2	2	no	—
95	C₂×C₃×C₄	—	2	2	no	—
96	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
97	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
98	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
99	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
100	C₃×C₈	—	2	2	no	—
101	C₃×C₈	—	2	1	no	—
102	C₃×C₈	D₃×D₄	1	1	yes	characteristic
103	C₃×C₈	#237	1	1	yes	characteristic
104	C₂×C₉	—	2	4	no	—
105	C₂×C₉	C₈×D₄	1	1	yes	characteristic
106	C₂×C₉	C₂²×C₁₆	1	1	yes	characteristic
107	C₂×C₉	#504	1	1	yes	characteristic
108	C₂×D₄	C₉⋊C₈	1	1	yes	characteristic
109	C₂²×C₄	C₂×Dic₉	1	2	yes	—
110	C₂×C₈	—	2	2	no	—
111	C₂×C₈	—	2	2	no	—
112	C₂×C₈	C₂×Dic₉	1	1	yes	characteristic
113	C₂×C₈	C₂×Dic₉	1	2	yes	—
114	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
115	C₄⋊C₄	C₉⋊C₈	1	1	yes	characteristic
116	C₂²⋊C₄	C₉⋊C₈	1	2	yes	—
117	C₄²	C₂×Dic₉	1	1	yes	characteristic
118	C₁₆	—	9	2	no	—
119	C₁₆	—	18	2	no	—
120	C₁₆	—	18	1	no	—
121	C₂²×C₃	—	2	2	no	—
122	C₂²×C₃	—	2	2	no	—
123	C₂²×C₃	C₂×C₃⋊C₁₆	1	4	yes	—
124	C₂²×C₃	C₂²×C₃⋊C₈	1	1	yes	characteristic
125	C₃×C₄	—	2	1	no	—
126	C₃×C₄	—	2	2	no	—
127	C₃×C₄	C₂×C₃⋊C₁₆	1	2	yes	—
128	C₃×C₄	D₄×Dic₃	1	1	yes	characteristic
129	C₃×C₄	#948	1	1	yes	characteristic
130	C₉	D₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
131	C₂³	C₂×C₉⋊C₈	1	2	yes	—
132	D₄	C₉⋊C₁₆	1	4	yes	direct product factor
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	C₂×C₉⋊C₈	1	1	yes	characteristic
136	C₂×C₄	C₂×C₉⋊C₈	1	2	yes	—
137	C₂×C₄	C₂×C₉⋊C₈	1	1	yes	characteristic
138	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
139	C₈	—	2	2	no	—
140	C₈	—	2	1	no	—
141	C₈	D₄×D₉	1	1	yes	characteristic
142	C₈	#3699	1	1	yes	characteristic
143	C₂×C₃	—	2	4	no	—
144	C₂×C₃	D₄×C₃⋊C₈	1	1	yes	characteristic
145	C₂×C₃	C₂²×C₃⋊C₁₆	1	1	yes	characteristic
146	C₂×C₃	#5140	1	1	yes	characteristic
147	C₂²	—	2	2	no	—
148	C₂²	—	2	2	no	—
149	C₂²	C₂×C₉⋊C₁₆	1	4	yes	complemented
150	C₂²	C₂²×C₉⋊C₈	1	1	yes	characteristic
151	C₄	—	2	2	no	—
152	C₄	—	2	1	no	—
153	C₄	C₂×C₉⋊C₁₆	1	2	yes	complemented
154	C₄	D₄×Dic₉	1	1	yes	characteristic
155	C₄	#63510	1	1	yes	characteristic
156	C₃	D₄×C₃⋊C₁₆	1	1	yes	characteristic
157	C₂	—	2	4	no	—
158	C₂	D₄×C₉⋊C₈	1	1	yes	characteristic
159	C₂	C₂²×C₉⋊C₁₆	1	1	yes	characteristic
160	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×D₄×C₉	C₂
socle	C₂²×C₃	C₂²×C₃⋊C₈
prime radical	C₂×C₃×D₄	C₃⋊C₈
cosocle	C₂×C₈×C₉	C₂³
hypercenter	C₈×D₄	D₉
hypocenter	C₉	D₄×C₁₆
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₉⋊C₁₆	C₂	semidirect
3. #10588226	C₂	semidirect
4. C₄⋊(C₉⋊C₁₆)	C₂	semidirect
5. C₄×C₉⋊C₁₆	C₂	semidirect
33. C₉⋊C₁₆	D₄	direct (N × H)
45. D₄×C₉	C₁₆	semidirect
76. C₂²×C₉	C₂×C₁₆	semidirect
80. C₄×C₉	C₂×C₁₆	semidirect
130. C₉	D₄×C₁₆	semidirect
132. D₄	C₉⋊C₁₆	direct (N × H)
149. C₂²	C₂×C₉⋊C₁₆	semidirect
153. C₄	C₂×C₉⋊C₁₆	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₈×D₄×C₉	2
C₂²×C₉⋊C₁₆	2
#10588226	2
C₄⋊(C₉⋊C₁₆)	2
C₄×C₉⋊C₁₆	2
D₄×C₃⋊C₁₆	3

Subgroups — D4×C9⋊C16 #11797434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₉⋊C₁₆ #11797434