Subgroups — C₂×D₉×#106 #11858370

Order 1152.

900 conjugacy classes of subgroups.

The subgroup lattice has 237 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×D₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×D₉	C₂	1	2	yes	maximal
3	C₂×C₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#63377	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#63367	C₂	1	2	yes	maximal, complemented
6	D₉×#106	C₂	1	8	yes	maximal, direct product factor
7	C₂×D₃×#106	—	3	1	no	maximal
8	C₂²×C₄×D₉	—	2	2	no	—
9	C₂²×C₄×D₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
13	C₂×Dic₉⋊C₄	—	2	2	no	—
14	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₈×D₉	C₄	1	8	yes	complemented
16	C₂×C₈×D₉	C₂²	1	4	yes	—
17	C₄⋊C₄×D₉	—	2	4	no	—
18	C₄⋊C₄×D₉	C₂²	1	8	yes	—
19	C₉×#106	C₂²	1	4	yes	complemented
20	#63377	C₂²	1	4	yes	complemented
21	#63367	C₂²	1	8	yes	complemented
22	C₂²×D₃×C₈	—	3	1	no	—
23	C₂×D₃×C₄⋊C₄	—	3	2	no	—
24	C₂×C₃×#106	D₃	1	1	yes	characteristic
25	C₂×#817	—	3	1	no	—
26	C₂×#808	—	3	2	no	—
27	D₃×#106	—	3	8	no	—
28	C₂³×D₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×C₉	—	2	2	no	—
30	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₉	—	2	2	no	—
32	C₂²×Dic₉	D₄	1	1	yes	characteristic
33	C₂×C₄×D₉	—	2	8	no	—
34	C₂×C₄×D₉	—	4	8	no	—
35	C₂×C₄×D₉	C₂×C₄	1	4	yes	—
36	C₂×C₄×D₉	D₄	1	2	yes	—
37	C₂×C₄×D₉	Q₈	1	4	yes	—
38	C₂×C₄×D₉	C₂³	1	2	yes	—
39	C₂×C₈×C₉	C₂×C₄	1	4	yes	complemented
40	C₂×C₈×C₉	C₂³	1	2	yes	—
41	C₉×C₄⋊C₄	—	2	2	no	—
42	C₉×C₄⋊C₄	C₂³	1	4	yes	—
43	C₄⋊Dic₉	—	2	2	no	—
44	C₄⋊Dic₉	C₂³	1	4	yes	—
45	Dic₉⋊C₄	—	2	8	no	—
46	C₂×C₉⋊C₈	C₂×C₄	1	4	yes	complemented
47	C₂×C₉⋊C₈	C₂³	1	2	yes	—
48	C₈×D₉	C₂×C₄	1	16	yes	complemented
49	C₂²×#106	—	9	1	no	Sylow
50	C₂²×C₄×D₃	—	3	1	no	—
51	C₂²×C₄×D₃	—	6	2	no	—
52	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
53	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
54	C₂×C₄⋊Dic₃	—	3	2	no	—
55	C₂×Dic₃⋊C₄	—	6	2	no	—
56	C₂²×C₃⋊C₈	—	3	1	no	—
57	C₂×D₃×C₈	—	3	8	no	—
58	C₂×D₃×C₈	—	3	4	no	—
59	D₃×C₄⋊C₄	—	3	8	no	—
60	D₃×C₄⋊C₄	—	6	4	no	—
61	C₃×#106	C₂×D₃	1	4	yes	—
62	#817	—	3	4	no	—
63	#808	—	3	8	no	—
64	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×D₉	C₄⋊C₄	1	4	yes	—
66	C₂²×D₉	SD₁₆	1	8	yes	—
67	C₂²×D₉	C₂×D₄	1	2	yes	—
68	C₂×C₄×C₉	—	2	4	no	—
69	C₂×C₄×C₉	—	4	4	no	—
70	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
71	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
72	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
73	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
74	C₂×Dic₉	—	2	4	no	—
75	C₂×Dic₉	—	4	4	no	—
76	C₂×Dic₉	C₄⋊C₄	1	4	yes	—
77	C₂×Dic₉	C₂×D₄	1	2	yes	—
78	C₄×D₉	—	4	16	no	—
79	C₄×D₉	C₄⋊C₄	1	8	yes	—
80	C₄×D₉	C₂²×C₄	1	4	yes	—
81	C₄×D₉	C₂×Q₈	1	4	yes	—
82	C₈×C₉	C₂²×C₄	1	4	yes	complemented
83	C₉⋊C₈	C₂²×C₄	1	4	yes	complemented
84	C₂³×C₈	—	9	1	no	—
85	C₂²×C₄⋊C₄	—	9	2	no	—
86	C₂×#106	—	9	1	no	—
87	C₂×#106	—	9	2	no	—
88	C₂×#106	—	9	8	no	—
89	C₂×#106	D₉	1	1	yes	characteristic, direct product factor
90	C₂³×D₃	—	3	1	no	—
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	—	6	2	no	—
95	C₂×C₄×D₃	—	3	4	no	—
96	C₂×C₄×D₃	—	3	2	no	—
97	C₂×C₄×D₃	—	3	4	no	—
98	C₂×C₄×D₃	—	3	2	no	—
99	C₂×C₄×D₃	—	6	8	no	—
100	C₂×C₄×D₃	—	12	8	no	—
101	C₂×C₃×C₈	C₄×D₃	1	4	yes	—
102	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
103	C₃×C₄⋊C₄	—	2	2	no	—
104	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
105	C₄⋊Dic₃	—	3	4	no	—
106	C₄⋊Dic₃	—	6	2	no	—
107	Dic₃⋊C₄	—	6	8	no	—
108	C₂×C₃⋊C₈	—	3	4	no	—
109	C₂×C₃⋊C₈	—	3	2	no	—
110	D₃×C₈	—	3	16	no	—
111	C₂²×C₉	C₂×C₄⋊C₄	1	2	yes	—
112	C₂²×C₉	C₂×SD₁₆	1	4	yes	—
113	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
114	C₂×D₉	#106	1	16	yes	direct product factor
115	C₂×D₉	C₂×C₄⋊C₄	1	4	yes	—
116	C₂×D₉	C₂×SD₁₆	1	8	yes	—
117	C₄×C₉	—	4	4	no	—
118	C₄×C₉	C₂×C₄⋊C₄	1	2	yes	—
119	C₄×C₉	C₂³×C₄	1	1	yes	characteristic
120	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
121	Dic₉	—	4	4	no	—
122	Dic₉	C₂×C₄⋊C₄	1	4	yes	—
123	C₂³×C₄	—	9	1	no	—
124	C₂³×C₄	—	18	2	no	—
125	C₂²×C₈	—	9	1	no	—
126	C₂²×C₈	—	9	8	no	—
127	C₂²×C₈	—	9	4	no	—
128	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
129	C₂×C₄⋊C₄	—	9	2	no	—
130	C₂×C₄⋊C₄	—	9	8	no	—
131	C₂×C₄⋊C₄	—	18	4	no	—
132	C₂×C₄⋊C₄	—	18	2	no	—
133	C₂×C₄⋊C₄	C₂×D₉	1	2	yes	—
134	#106	—	9	4	no	—
135	#106	—	9	8	no	—
136	#106	C₂×D₉	1	4	yes	direct product factor
137	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
138	C₂²×D₃	—	3	4	no	—
139	C₂²×D₃	—	3	8	no	—
140	C₂²×D₃	—	3	2	no	—
141	C₂×C₃×C₄	—	2	4	no	—
142	C₂×C₃×C₄	—	4	4	no	—
143	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
144	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
146	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
147	C₂×Dic₃	—	3	4	no	—
148	C₂×Dic₃	—	3	2	no	—
149	C₂×Dic₃	—	6	4	no	—
150	C₂×Dic₃	—	12	4	no	—
151	C₄×D₃	—	3	8	no	—
152	C₄×D₃	—	3	4	no	—
153	C₄×D₃	—	3	4	no	—
154	C₄×D₃	—	12	16	no	—
155	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
156	C₃⋊C₈	—	3	4	no	—
157	C₂×C₉	C₂×#106	1	4	yes	complemented
158	C₂×C₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₉	C₂²×SD₁₆	1	2	yes	—
160	D₉	C₂×#106	1	8	yes	direct product factor
161	C₂⁴	—	9	1	no	—
162	C₂²×C₄	—	2	2	no	—
163	C₂²×C₄	—	9	1	no	—
164	C₂²×C₄	—	9	4	no	—
165	C₂²×C₄	—	9	2	no	—
166	C₂²×C₄	—	9	4	no	—
167	C₂²×C₄	—	9	2	no	—
168	C₂²×C₄	—	18	8	no	—
169	C₂²×C₄	—	18	2	no	—
170	C₂²×C₄	—	36	8	no	—
171	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
172	C₂×C₈	—	9	4	no	—
173	C₂×C₈	—	9	2	no	—
174	C₂×C₈	—	9	16	no	—
175	C₂×C₈	C₄×D₉	1	4	yes	complemented
176	C₂×C₈	C₂²×D₉	1	2	yes	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	9	4	no	—
179	C₄⋊C₄	—	18	8	no	—
180	C₄⋊C₄	—	18	2	no	—
181	C₄⋊C₄	C₂²×D₉	1	4	yes	—
182	C₂²×C₃	D₃×C₄⋊C₄	1	2	yes	—
183	C₂²×C₃	D₃×SD₁₆	1	4	yes	—
184	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
185	C₂×D₃	—	3	4	no	—
186	C₂×D₃	—	3	8	no	—
187	C₂×D₃	—	3	16	no	—
188	C₃×C₄	—	4	4	no	—
189	C₃×C₄	D₃×C₄⋊C₄	1	2	yes	—
190	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
191	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
192	Dic₃	—	3	4	no	—
193	Dic₃	—	12	4	no	—
194	C₉	C₂²×#106	1	1	yes	characteristic, complemented, Sylow
195	C₂³	—	9	2	no	—
196	C₂³	—	9	4	no	—
197	C₂³	—	9	8	no	—
198	C₂³	D₄×D₉	1	1	yes	characteristic
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	9	2	no	—
202	C₂×C₄	—	9	4	no	—
203	C₂×C₄	—	9	4	no	—
204	C₂×C₄	—	9	8	no	—
205	C₂×C₄	—	9	4	no	—
206	C₂×C₄	—	18	4	no	—
207	C₂×C₄	—	36	16	no	—
208	C₂×C₄	—	36	4	no	—
209	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
210	C₂×C₄	D₄×D₉	1	1	yes	characteristic
211	C₂×C₄	Q₈×D₉	1	2	yes	—
212	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
213	C₈	—	9	4	no	—
214	C₈	C₂×C₄×D₉	1	4	yes	complemented
215	C₂×C₃	D₃×#106	1	4	yes	—
216	C₂×C₃	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
217	C₂×C₃	C₂×D₃×SD₁₆	1	2	yes	—
218	D₃	—	3	8	no	—
219	C₂²	—	9	16	no	—
220	C₂²	—	9	4	no	—
221	C₂²	—	9	8	no	—
222	C₂²	C₄⋊C₄×D₉	1	2	yes	—
223	C₂²	SD₁₆×D₉	1	4	yes	—
224	C₂²	C₂×D₄×D₉	1	1	yes	characteristic
225	C₄	—	4	4	no	—
226	C₄	—	9	4	no	—
227	C₄	—	36	4	no	—
228	C₄	C₄⋊C₄×D₉	1	2	yes	—
229	C₄	C₂²×C₄×D₉	1	1	yes	characteristic
230	C₄	C₂×Q₈×D₉	1	1	yes	characteristic
231	C₃	C₂×D₃×#106	1	1	yes	characteristic
232	C₂	—	9	8	no	—
233	C₂	D₉×#106	1	4	yes	direct product factor
234	C₂	C₂×C₄⋊C₄×D₉	1	1	yes	characteristic
235	C₂	C₂×SD₁₆×D₉	1	2	yes	—

	subgroup	G/H
center	C₂³	D₄×D₉
commutator	C₄×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂×C₉×#106	C₂
socle	C₂³×C₃	D₃×D₄
prime radical	C₂³×D₉	D₄
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂×#106	D₉
hypocenter	C₉	C₂²×#106
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

Complements

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

N	H ≅ G/N	type
3. C₂×C₉×#106	C₂	semidirect
4. C₂×#63377	C₂	semidirect
5. C₂×#63367	C₂	semidirect
6. D₉×#106	C₂	direct (N × H)
15. C₂×C₈×D₉	C₄	semidirect
19. C₉×#106	C₂²	semidirect
20. #63377	C₂²	semidirect
21. #63367	C₂²	semidirect
39. C₂×C₈×C₉	C₂×C₄	semidirect
46. C₂×C₉⋊C₈	C₂×C₄	semidirect
48. C₈×D₉	C₂×C₄	semidirect
82. C₈×C₉	C₂²×C₄	semidirect
83. C₉⋊C₈	C₂²×C₄	semidirect
89. C₂×#106	D₉	direct (N × H)
114. C₂×D₉	#106	direct (N × H)
136. #106	C₂×D₉	direct (N × H)
157. C₂×C₉	C₂×#106	semidirect
160. D₉	C₂×#106	direct (N × H)
175. C₂×C₈	C₄×D₉	semidirect
194. C₉	C₂²×#106	semidirect
214. C₈	C₂×C₄×D₉	semidirect
233. C₂	D₉×#106	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×C₈×D₉	2
C₂×C₄⋊C₄×D₉	2
C₂×C₉×#106	2
C₂×#63377	2
C₂×#63367	2
D₉×#106	2
C₂×D₃×#106	3

Subgroups — C2×D9×#106 #11858370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₉×#106 #11858370