Subgroups — C₂×D₉×2₋¹⁺⁴ #11919228

Order 1152.

8808 conjugacy classes of subgroups.

The subgroup lattice has 222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	D₉×2₋¹⁺⁴	C₂	1	32	yes	maximal, direct product factor
3	C₂×#63716	C₂	1	10	yes	maximal, complemented
4	C₂×#41×D₉	C₂	1	10	yes	maximal, complemented
5	C₂×#63713	C₂	1	5	yes	maximal, complemented
6	C₂²×Q₈×D₉	C₂	1	5	yes	maximal, complemented
7	C₂×D₃×2₋¹⁺⁴	—	3	1	no	maximal
8	C₉×2₋¹⁺⁴	C₂²	1	16	yes	complemented
9	C₂×C₉×#41	C₂²	1	10	yes	complemented
10	C₂²×Q₈×C₉	C₂²	1	5	yes	complemented
11	#63716	C₂²	1	160	yes	complemented
12	#41×D₉	C₂²	1	160	yes	complemented
13	#63713	C₂²	1	80	yes	complemented
14	C₂×#3701	C₂²	1	10	yes	complemented
15	C₂×Q₈×D₉	C₂²	1	10	yes	—
16	C₂×Q₈×D₉	C₂²	1	20	yes	complemented
17	C₂×Q₈×D₉	C₂²	1	80	yes	complemented
18	C₂×#3699	C₂²	1	30	yes	complemented
19	C₂×D₄×D₉	C₂²	1	10	yes	—
20	C₂×#3697	C₂²	1	30	yes	complemented
21	C₂²×C₄×D₉	C₂²	1	15	yes	—
22	C₂²×Dic₁₈	C₂²	1	15	yes	complemented
23	C₂×C₃×2₋¹⁺⁴	D₃	1	1	yes	characteristic
24	D₃×2₋¹⁺⁴	—	3	32	no	—
25	C₂×#1010	—	3	10	no	—
26	C₂×D₃×#41	—	3	10	no	—
27	C₂×#1007	—	3	5	no	—
28	C₂²×D₃×Q₈	—	3	5	no	—
29	C₂³×D₉	C₂³	1	5	yes	—
30	C₉×#41	C₂³	1	80	yes	complemented
31	C₂×Q₈×C₉	C₂³	1	10	yes	—
32	C₂×Q₈×C₉	C₂³	1	40	yes	complemented
33	C₂×D₄×C₉	C₂³	1	10	yes	—
34	C₂²×C₄×C₉	C₂³	1	15	yes	—
35	C₂×#611	C₂³	1	20	yes	—
36	C₂²×Dic₉	C₂³	1	15	yes	—
37	#3701	C₂³	1	80	yes	complemented
38	Q₈×D₉	C₂³	1	80	yes	—
39	Q₈×D₉	C₂³	1	160	yes	complemented
40	#3699	C₂³	1	240	yes	complemented
41	D₄×D₉	C₂³	1	80	yes	—
42	#3697	C₂³	1	240	yes	complemented
43	C₂×D₃₆	C₂³	1	10	yes	—
44	C₂×C₄×D₉	C₂³	1	10	yes	—
45	C₂×C₄×D₉	C₂³	1	30	yes	—
46	C₂×C₄×D₉	C₂³	1	120	yes	—
47	C₂×Dic₁₈	C₂³	1	30	yes	—
48	C₂×Dic₁₈	C₂³	1	120	yes	complemented
49	C₂²×2₋¹⁺⁴	—	9	1	no	Sylow
50	C₃×2₋¹⁺⁴	C₂×D₃	1	16	yes	—
51	C₂×C₃×#41	C₂×D₃	1	10	yes	—
52	C₂²×C₃×Q₈	C₂×D₃	1	5	yes	—
53	#1010	—	3	160	no	—
54	D₃×#41	—	3	160	no	—
55	#1007	—	3	80	no	—
56	C₂×#239	—	3	10	no	—
57	C₂×D₃×Q₈	—	3	10	no	—
58	C₂×D₃×Q₈	—	3	20	no	—
59	C₂×D₃×Q₈	—	3	80	no	—
60	C₂×#237	—	3	30	no	—
61	C₂×D₃×D₄	—	3	10	no	—
62	C₂×#235	—	3	30	no	—
63	C₂²×C₄×D₃	—	3	15	no	—
64	C₂²×Dic₆	—	3	15	no	—
65	C₂³×C₉	C₂⁴	1	5	yes	—
66	C₂²×D₉	—	2	20	no	—
67	C₂²×D₉	C₂⁴	1	5	yes	—
68	C₂²×D₉	C₂⁴	1	20	yes	—
69	C₂²×D₉	C₂⁴	1	1	yes	characteristic
70	Q₈×C₉	C₂⁴	1	40	yes	—
71	D₄×C₉	C₂⁴	1	40	yes	—
72	C₂×C₄×C₉	C₂⁴	1	10	yes	—
73	C₂×C₄×C₉	C₂⁴	1	60	yes	—
74	#611	C₂⁴	1	80	yes	—
75	C₂×Dic₉	C₂⁴	1	10	yes	—
76	C₂×Dic₉	C₂⁴	1	60	yes	—
77	D₃₆	C₂⁴	1	40	yes	—
78	C₄×D₉	C₂⁴	1	40	yes	—
79	C₄×D₉	C₂⁴	1	120	yes	—
80	Dic₁₈	C₂⁴	1	120	yes	—
81	C₂×2₋¹⁺⁴	—	9	32	no	—
82	C₂×2₋¹⁺⁴	—	9	10	no	—
83	C₂×2₋¹⁺⁴	—	9	5	no	—
84	C₂×2₋¹⁺⁴	D₉	1	1	yes	characteristic, direct product factor
85	C₂²×#41	—	9	10	no	—
86	C₂³×Q₈	—	9	5	no	—
87	C₂³×D₃	—	3	5	no	—
88	C₃×#41	C₂²×D₃	1	80	yes	—
89	C₂×C₃×Q₈	C₂²×D₃	1	10	yes	—
90	C₂×C₃×Q₈	C₂²×D₃	1	40	yes	—
91	C₂×C₃×D₄	C₂²×D₃	1	10	yes	—
92	C₂²×C₃×C₄	C₂²×D₃	1	15	yes	—
93	C₂×#67	—	3	20	no	—
94	C₂²×Dic₃	—	3	15	no	—
95	#239	—	3	80	no	—
96	D₃×Q₈	—	3	80	no	—
97	D₃×Q₈	—	3	160	no	—
98	#237	—	3	240	no	—
99	D₃×D₄	—	3	80	no	—
100	#235	—	3	240	no	—
101	C₂×D₁₂	—	3	10	no	—
102	C₂×C₄×D₃	—	3	10	no	—
103	C₂×C₄×D₃	—	3	30	no	—
104	C₂×C₄×D₃	—	3	120	no	—
105	C₂×Dic₆	—	3	30	no	—
106	C₂×Dic₆	—	3	120	no	—
107	C₂²×C₉	—	2	10	no	—
108	C₂²×C₉	C₂⁵	1	10	yes	—
109	C₂²×C₉	C₂⁵	1	1	yes	characteristic
110	C₂×D₉	—	2	10	no	—
111	C₂×D₉	—	2	40	no	—
112	C₂×D₉	2₋¹⁺⁴	1	4	yes	direct product factor
113	C₂×D₉	C₂⁵	1	10	yes	—
114	C₂×D₉	C₂⁵	1	2	yes	—
115	C₄×C₉	C₂⁵	1	20	yes	—
116	Dic₉	C₂⁵	1	20	yes	—
117	2₋¹⁺⁴	—	9	160	no	—
118	2₋¹⁺⁴	—	9	80	no	—
119	2₋¹⁺⁴	C₂×D₉	1	16	yes	direct product factor
120	C₂×#41	—	9	160	no	—
121	C₂×#41	—	9	10	no	—
122	C₂×#41	—	9	30	no	—
123	C₂×#41	—	9	30	no	—
124	C₂×#41	C₂×D₉	1	10	yes	complemented
125	C₂²×Q₈	—	9	10	no	—
126	C₂²×Q₈	—	9	20	no	—
127	C₂²×Q₈	—	9	80	no	—
128	C₂²×Q₈	—	9	15	no	—
129	C₂²×Q₈	C₂×D₉	1	5	yes	complemented
130	C₂²×D₄	—	9	10	no	—
131	C₂³×C₄	—	9	15	no	—
132	C₂³×C₃	C₂³×D₃	1	5	yes	—
133	C₂²×D₃	—	3	1	no	—
134	C₂²×D₃	—	3	5	no	—
135	C₂²×D₃	—	3	20	no	—
136	C₂²×D₃	—	6	20	no	—
137	C₃×Q₈	C₂³×D₃	1	40	yes	—
138	C₃×D₄	C₂³×D₃	1	40	yes	—
139	C₂×C₃×C₄	C₂³×D₃	1	10	yes	—
140	C₂×C₃×C₄	C₂³×D₃	1	60	yes	—
141	#67	—	3	80	no	—
142	C₂×Dic₃	—	3	10	no	—
143	C₂×Dic₃	—	3	60	no	—
144	D₁₂	—	3	40	no	—
145	C₄×D₃	—	3	40	no	—
146	C₄×D₃	—	3	120	no	—
147	Dic₆	—	3	120	no	—
148	C₂×C₉	—	2	10	no	—
149	C₂×C₉	C₂×2₋¹⁺⁴	1	2	yes	complemented
150	C₂×C₉	C₂⁶	1	1	yes	characteristic
151	D₉	—	2	10	no	—
152	D₉	C₂×2₋¹⁺⁴	1	4	yes	direct product factor
153	C₂⁴	—	9	5	no	—
154	#41	—	9	80	no	—
155	#41	—	9	240	no	—
156	#41	—	9	240	no	—
157	#41	C₂²×D₉	1	80	yes	complemented
158	C₂×Q₈	—	9	80	no	—
159	C₂×Q₈	—	9	160	no	—
160	C₂×Q₈	—	9	30	no	—
161	C₂×Q₈	—	9	120	no	—
162	C₂×Q₈	C₂²×D₉	1	10	yes	—
163	C₂×Q₈	C₂²×D₉	1	40	yes	complemented
164	C₂×D₄	—	9	20	no	—
165	C₂×D₄	—	9	80	no	—
166	C₂×D₄	—	9	10	no	—
167	C₂×D₄	C₂²×D₉	1	10	yes	—
168	C₂²×C₄	—	9	15	no	—
169	C₂²×C₄	—	9	10	no	—
170	C₂²×C₄	—	9	120	no	—
171	C₂²×C₄	—	9	30	no	—
172	C₂²×C₄	C₂²×D₉	1	15	yes	—
173	C₂²×C₃	—	2	10	no	—
174	C₂²×C₃	C₂⁴×D₃	1	10	yes	—
175	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
176	C₂×D₃	—	3	4	no	—
177	C₂×D₃	—	3	2	no	—
178	C₂×D₃	—	3	10	no	—
179	C₂×D₃	—	6	40	no	—
180	C₂×D₃	—	6	10	no	—
181	C₃×C₄	C₂⁴×D₃	1	20	yes	—
182	Dic₃	—	3	20	no	—
183	C₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
184	C₂³	—	9	1	no	—
185	C₂³	—	9	20	no	—
186	C₂³	—	9	5	no	—
187	C₂³	—	18	20	no	—
188	C₂³	C₂³×D₉	1	5	yes	—
189	Q₈	—	9	120	no	—
190	Q₈	C₂³×D₉	1	40	yes	—
191	D₄	—	9	80	no	—
192	D₄	—	9	40	no	—
193	D₄	C₂³×D₉	1	40	yes	—
194	C₂×C₄	—	9	60	no	—
195	C₂×C₄	—	9	10	no	—
196	C₂×C₄	—	9	40	no	—
197	C₂×C₄	—	9	120	no	—
198	C₂×C₄	C₂³×D₉	1	60	yes	—
199	C₂×C₄	C₂³×D₉	1	10	yes	—
200	C₂×C₃	—	2	10	no	—
201	C₂×C₃	D₃×2₋¹⁺⁴	1	2	yes	—
202	C₂×C₃	C₂⁵×D₃	1	1	yes	characteristic
203	D₃	—	3	4	no	—
204	D₃	—	6	10	no	—
205	C₂²	—	2	10	no	—
206	C₂²	—	9	2	no	—
207	C₂²	—	9	4	no	—
208	C₂²	—	9	10	no	—
209	C₂²	—	18	40	no	—
210	C₂²	—	18	10	no	—
211	C₂²	C₂⁴×D₉	1	10	yes	—
212	C₂²	C₂⁴×D₉	1	1	yes	characteristic
213	C₄	—	9	20	no	—
214	C₄	C₂⁴×D₉	1	20	yes	—
215	C₃	C₂×D₃×2₋¹⁺⁴	1	1	yes	characteristic
216	C₂	—	2	10	no	—
217	C₂	—	9	4	no	—
218	C₂	—	18	10	no	—
219	C₂	D₉×2₋¹⁺⁴	1	2	yes	direct product factor
220	C₂	C₂⁵×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂⁴×D₉
commutator, cosocle	C₂×C₉	C₂⁶
Frattini	C₂×C₃	C₂⁵×D₃
Fitting	C₂×C₉×2₋¹⁺⁴	C₂
socle	C₂²×C₃	C₂⁴×D₃
hypercenter	C₂×2₋¹⁺⁴	D₉
hypocenter	C₉	C₂²×2₋¹⁺⁴
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×2₋¹⁺⁴	C₂	semidirect
2. D₉×2₋¹⁺⁴	C₂	direct (N × H)
3. C₂×#63716	C₂	semidirect
4. C₂×#41×D₉	C₂	semidirect
5. C₂×#63713	C₂	semidirect
6. C₂²×Q₈×D₉	C₂	semidirect
8. C₉×2₋¹⁺⁴	C₂²	semidirect
9. C₂×C₉×#41	C₂²	semidirect
10. C₂²×Q₈×C₉	C₂²	semidirect
11. #63716	C₂²	semidirect
12. #41×D₉	C₂²	semidirect
13. #63713	C₂²	semidirect
14. C₂×#3701	C₂²	semidirect
16. C₂×Q₈×D₉	C₂²	semidirect
17. C₂×Q₈×D₉	C₂²	semidirect
18. C₂×#3699	C₂²	semidirect
20. C₂×#3697	C₂²	semidirect
22. C₂²×Dic₁₈	C₂²	semidirect
30. C₉×#41	C₂³	semidirect
32. C₂×Q₈×C₉	C₂³	semidirect
37. #3701	C₂³	semidirect
39. Q₈×D₉	C₂³	semidirect
40. #3699	C₂³	semidirect
42. #3697	C₂³	semidirect
48. C₂×Dic₁₈	C₂³	semidirect
84. C₂×2₋¹⁺⁴	D₉	direct (N × H)
112. C₂×D₉	2₋¹⁺⁴	direct (N × H)
119. 2₋¹⁺⁴	C₂×D₉	direct (N × H)
124. C₂×#41	C₂×D₉	semidirect
129. C₂²×Q₈	C₂×D₉	semidirect
149. C₂×C₉	C₂×2₋¹⁺⁴	semidirect
152. D₉	C₂×2₋¹⁺⁴	direct (N × H)
157. #41	C₂²×D₉	semidirect
163. C₂×Q₈	C₂²×D₉	semidirect
183. C₉	C₂²×2₋¹⁺⁴	semidirect
219. C₂	D₉×2₋¹⁺⁴	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×2₋¹⁺⁴	2
D₉×2₋¹⁺⁴	2
C₂×#63716	2
C₂×#41×D₉	2
C₂×#63713	2
C₂²×Q₈×D₉	2
C₂×D₃×2₋¹⁺⁴	3

Subgroups — C2×D9×2−1+4 #11919228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₉×2₋¹⁺⁴ #11919228