Subgroups — C₂×Q₁₆×Dic₉ #11859927

Order 1152.

732 conjugacy classes of subgroups.

The subgroup lattice has 225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×Dic₉	C₂	1	2	yes	maximal
3	C₂×#63395	C₂	1	2	yes	maximal
4	Q₁₆×Dic₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×#63378	C₂	1	1	yes	maximal, characteristic
6	C₂×C₈×Dic₉	C₂	1	1	yes	maximal, characteristic
7	C₂×Dic₃×Q₁₆	—	3	1	no	maximal
8	C₂²×Q₈×C₉	C₂²	1	2	yes	—
9	C₂×C₉×Q₁₆	C₄	1	8	yes	complemented
10	C₂×C₉×Q₁₆	C₂²	1	4	yes	—
11	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
12	Q₈×Dic₉	—	2	4	no	—
13	Q₈×Dic₉	C₂²	1	8	yes	—
14	C₂×C₄⋊Dic₉	—	2	2	no	—
15	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
16	C₂×C₄×Dic₉	—	2	2	no	—
17	C₂×C₄×Dic₉	C₂²	1	1	yes	characteristic
18	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
19	#63395	C₂²	1	8	yes	—
20	#63378	C₂²	1	4	yes	—
21	C₈×Dic₉	C₂²	1	4	yes	—
22	C₂²×C₃×Q₁₆	D₃	1	1	yes	characteristic
23	C₂×Q₈×Dic₃	—	3	2	no	—
24	C₂×#835	—	3	2	no	—
25	Dic₃×Q₁₆	—	3	8	no	—
26	C₂×#818	—	3	1	no	—
27	C₂×C₈×Dic₃	—	3	1	no	—
28	C₂×Q₈×C₉	—	2	2	no	—
29	C₂×Q₈×C₉	—	2	4	no	—
30	C₂×Q₈×C₉	C₂×C₄	1	8	yes	—
31	C₂×Q₈×C₉	C₂³	1	4	yes	—
32	C₂²×C₄×C₉	—	2	2	no	—
33	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
34	C₂²×Dic₉	—	2	2	no	—
35	C₂²×Dic₉	D₄	1	1	yes	characteristic
36	C₂²×Dic₉	D₄	1	1	yes	characteristic
37	C₉×Q₁₆	C₂×C₄	1	16	yes	complemented
38	C₂×C₈×C₉	C₂×C₄	1	4	yes	—
39	C₂×C₈×C₉	C₂³	1	2	yes	—
40	C₄⋊Dic₉	—	2	2	no	—
41	C₄⋊Dic₉	—	2	8	no	—
42	C₄⋊Dic₉	C₂³	1	4	yes	—
43	C₄×Dic₉	—	2	8	no	—
44	C₄×Dic₉	D₄	1	2	yes	—
45	C₄×Dic₉	C₂³	1	2	yes	—
46	C₂×C₉⋊C₈	—	2	2	no	—
47	C₂×C₉⋊C₈	C₂³	1	2	yes	—
48	C₂×C₄×Q₁₆	—	9	1	no	Sylow
49	C₂²×C₃×Q₈	C₂×D₃	1	2	yes	—
50	C₂×C₃×Q₁₆	Dic₃	1	8	yes	—
51	C₂×C₃×Q₁₆	C₂×D₃	1	4	yes	—
52	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
53	Q₈×Dic₃	—	3	8	no	—
54	Q₈×Dic₃	—	6	4	no	—
55	C₂×C₄⋊Dic₃	—	3	2	no	—
56	C₂×C₄⋊Dic₃	—	6	2	no	—
57	C₂×C₄×Dic₃	—	3	1	no	—
58	C₂×C₄×Dic₃	—	6	2	no	—
59	C₂²×C₃⋊C₈	—	3	1	no	—
60	#835	—	3	8	no	—
61	#818	—	3	4	no	—
62	C₈×Dic₃	—	3	4	no	—
63	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
64	Q₈×C₉	—	2	8	no	—
65	Q₈×C₉	—	2	4	no	—
66	Q₈×C₉	C₂²×C₄	1	8	yes	—
67	C₂×C₄×C₉	—	2	8	no	—
68	C₂×C₄×C₉	—	2	4	no	—
69	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
70	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₉	#41	1	2	yes	—
72	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
73	C₂×Dic₉	—	2	2	no	—
74	C₂×Dic₉	—	2	4	no	—
75	C₂×Dic₉	—	4	4	no	—
76	C₂×Dic₉	Q₁₆	1	4	yes	direct product factor
77	C₂×Dic₉	C₂×D₄	1	2	yes	—
78	C₂×Dic₉	C₂×D₄	1	2	yes	—
79	C₈×C₉	C₂²×C₄	1	4	yes	—
80	C₉⋊C₈	—	2	2	no	—
81	C₂²×Q₁₆	D₉	1	1	yes	characteristic
82	C₂×C₄×Q₈	—	9	2	no	—
83	C₄×Q₁₆	—	9	8	no	—
84	C₂×#107	—	9	1	no	—
85	C₂×#103	—	9	2	no	—
86	C₂×C₄×C₈	—	9	1	no	—
87	C₂×C₃×Q₈	—	2	2	no	—
88	C₂×C₃×Q₈	—	2	4	no	—
89	C₂×C₃×Q₈	C₂×Dic₃	1	8	yes	—
90	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
91	C₂²×C₃×C₄	—	2	2	no	—
92	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
93	C₂²×Dic₃	—	3	1	no	—
94	C₂²×Dic₃	—	3	1	no	—
95	C₂²×Dic₃	—	6	2	no	—
96	C₃×Q₁₆	C₂×Dic₃	1	16	yes	—
97	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	—
98	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
99	C₄⋊Dic₃	—	3	4	no	—
100	C₄⋊Dic₃	—	6	8	no	—
101	C₄⋊Dic₃	—	6	2	no	—
102	C₄×Dic₃	—	3	2	no	—
103	C₄×Dic₃	—	3	2	no	—
104	C₄×Dic₃	—	6	8	no	—
105	C₂×C₃⋊C₈	—	3	2	no	—
106	C₂×C₃⋊C₈	—	6	2	no	—
107	C₂²×C₉	C₄×D₄	1	2	yes	—
108	C₂²×C₉	C₂×Q₁₆	1	2	yes	—
109	C₂²×C₉	#135	1	2	yes	—
110	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
111	C₄×C₉	—	2	8	no	—
112	C₄×C₉	C₄×D₄	1	2	yes	—
113	C₄×C₉	C₂³×C₄	1	1	yes	characteristic
114	C₄×C₉	C₂×#41	1	1	yes	characteristic
115	Dic₉	—	2	2	no	—
116	Dic₉	—	4	4	no	—
117	Dic₉	C₂×Q₁₆	1	4	yes	direct product factor
118	C₂²×Q₈	C₂×D₉	1	2	yes	—
119	C₂×Q₁₆	Dic₉	1	8	yes	direct product factor
120	C₂×Q₁₆	C₂×D₉	1	4	yes	—
121	C₂²×C₈	—	9	1	no	—
122	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
123	C₄×Q₈	—	9	8	no	—
124	C₄×Q₈	—	18	4	no	—
125	C₂×C₄⋊C₄	—	9	2	no	—
126	C₂×C₄⋊C₄	—	18	2	no	—
127	C₂×C₄²	—	9	1	no	—
128	C₂×C₄²	—	18	2	no	—
129	#107	—	9	4	no	—
130	#103	—	9	8	no	—
131	C₄×C₈	—	9	4	no	—
132	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
133	C₃×Q₈	—	2	8	no	—
134	C₃×Q₈	—	2	4	no	—
135	C₃×Q₈	C₂²×Dic₃	1	8	yes	—
136	C₂×C₃×C₄	—	2	8	no	—
137	C₂×C₃×C₄	—	2	4	no	—
138	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄	#237	1	2	yes	—
140	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
141	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
142	C₂×Dic₃	—	3	4	no	—
143	C₂×Dic₃	—	3	2	no	—
144	C₂×Dic₃	—	3	2	no	—
145	C₂×Dic₃	—	6	2	no	—
146	C₂×Dic₃	—	6	4	no	—
147	C₂×Dic₃	—	12	4	no	—
148	C₃×C₈	C₂²×Dic₃	1	4	yes	—
149	C₃⋊C₈	—	6	2	no	—
150	C₂×C₉	C₄×Q₁₆	1	4	yes	complemented
151	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
152	C₂×C₉	C₂²×Q₁₆	1	1	yes	characteristic
153	C₂×C₉	C₂×#135	1	1	yes	characteristic
154	C₂×Q₈	—	2	2	no	—
155	C₂×Q₈	—	2	4	no	—
156	C₂×Q₈	C₂×Dic₉	1	8	yes	—
157	C₂×Q₈	C₂²×D₉	1	4	yes	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	9	1	no	—
160	C₂²×C₄	—	9	1	no	—
161	C₂²×C₄	—	18	2	no	—
162	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
163	Q₁₆	C₂×Dic₉	1	16	yes	direct product factor
164	C₂×C₈	—	9	2	no	—
165	C₂×C₈	—	18	2	no	—
166	C₂×C₈	C₂×Dic₉	1	4	yes	—
167	C₂×C₈	C₂²×D₉	1	2	yes	—
168	C₄⋊C₄	—	9	4	no	—
169	C₄⋊C₄	—	18	8	no	—
170	C₄⋊C₄	—	18	2	no	—
171	C₄²	—	9	2	no	—
172	C₄²	—	9	2	no	—
173	C₄²	—	18	8	no	—
174	C₂²×C₃	D₃×Q₁₆	1	2	yes	—
175	C₂²×C₃	#919	1	2	yes	—
176	C₂²×C₃	D₄×Dic₃	1	2	yes	—
177	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
178	C₃×C₄	—	2	8	no	—
179	C₃×C₄	D₄×Dic₃	1	2	yes	—
180	C₃×C₄	C₂×#237	1	1	yes	characteristic
181	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
182	Dic₃	—	3	4	no	—
183	Dic₃	—	6	2	no	—
184	Dic₃	—	12	4	no	—
185	C₉	C₂×C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
186	C₂³	D₄×D₉	1	1	yes	characteristic
187	Q₈	—	2	8	no	—
188	Q₈	—	2	4	no	—
189	Q₈	C₂²×Dic₉	1	8	yes	—
190	C₂×C₄	—	2	8	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	9	2	no	—
193	C₂×C₄	—	9	4	no	—
194	C₂×C₄	—	9	2	no	—
195	C₂×C₄	—	18	2	no	—
196	C₂×C₄	—	18	4	no	—
197	C₂×C₄	—	36	4	no	—
198	C₂×C₄	D₄×D₉	1	1	yes	characteristic
199	C₂×C₄	#3699	1	2	yes	—
200	C₂×C₄	C₂²×Dic₉	1	2	yes	—
201	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
202	C₈	—	18	2	no	—
203	C₈	C₂²×Dic₉	1	4	yes	—
204	C₂×C₃	Dic₃×Q₁₆	1	4	yes	—
205	C₂×C₃	C₂×D₃×Q₁₆	1	1	yes	characteristic
206	C₂×C₃	C₂×#919	1	1	yes	characteristic
207	C₂×C₃	C₂×D₄×Dic₃	1	1	yes	characteristic
208	C₂²	Q₁₆×D₉	1	2	yes	—
209	C₂²	#63481	1	2	yes	—
210	C₂²	D₄×Dic₉	1	2	yes	—
211	C₂²	C₂×D₄×D₉	1	1	yes	characteristic
212	C₄	—	2	8	no	—
213	C₄	—	9	4	no	—
214	C₄	—	18	2	no	—
215	C₄	—	36	4	no	—
216	C₄	D₄×Dic₉	1	2	yes	—
217	C₄	C₂×#3699	1	1	yes	characteristic
218	C₄	C₂³×Dic₉	1	1	yes	characteristic
219	C₃	C₂×Dic₃×Q₁₆	1	1	yes	characteristic
220	C₂	Q₁₆×Dic₉	1	4	yes	direct product factor
221	C₂	C₂×Q₁₆×D₉	1	1	yes	characteristic
222	C₂	C₂×#63481	1	1	yes	characteristic
223	C₂	C₂×D₄×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄×D₉
commutator	C₄×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂²×C₉×Q₁₆	C₂
socle, prime radical	C₂³×C₃	D₃×D₄
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂²×Q₁₆	D₉
hypocenter	C₉	C₂×C₄×Q₁₆
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

Complements

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

N	H ≅ G/N	type
4. Q₁₆×Dic₉	C₂	direct (N × H)
9. C₂×C₉×Q₁₆	C₄	semidirect
37. C₉×Q₁₆	C₂×C₄	semidirect
76. C₂×Dic₉	Q₁₆	direct (N × H)
117. Dic₉	C₂×Q₁₆	direct (N × H)
119. C₂×Q₁₆	Dic₉	direct (N × H)
150. C₂×C₉	C₄×Q₁₆	semidirect
163. Q₁₆	C₂×Dic₉	direct (N × H)
185. C₉	C₂×C₄×Q₁₆	semidirect
220. C₂	Q₁₆×Dic₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×Q₁₆	2
C₂×Q₈×Dic₉	2
C₂×#63395	2
Q₁₆×Dic₉	2
C₂×#63378	2
C₂×C₈×Dic₉	2
C₂×Dic₃×Q₁₆	3

Subgroups — C2×Q16×Dic9 #11859927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₁₆×Dic₉ #11859927