Subgroups — C₂×C₄×C₉×D₁₂ #13152290

Order 1728.

1386 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₃×C₉	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₉×D₁₂	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×C₄×D₁₂	C₃	1	1	yes	maximal, characteristic
8	C₂×C₄×D₄×C₉	—	3	1	no	maximal
9	C₂³×D₃×C₉	C₂²	1	2	yes	—
10	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
14	C₂×C₉×D₁₂	C₄	1	8	yes	direct product factor
15	C₂×C₉×D₁₂	C₂²	1	4	yes	—
16	C₂×C₄×D₃×C₉	—	2	8	no	—
17	C₂×C₄×D₃×C₉	C₂²	1	8	yes	complemented
18	C₃×C₄²×C₉	C₂²	1	4	yes	complemented
19	C₉×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
20	C₉×C₄⋊Dic₃	C₂²	1	4	yes	complemented
21	C₂²×C₃×D₁₂	C₂×C₃	1	1	yes	characteristic
22	C₂²×C₃×C₄×D₃	C₂×C₃	1	2	yes	—
23	C₂×C₃²×C₄²	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	—
25	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
26	C₃×C₄×D₁₂	C₂×C₃	1	8	yes	—
27	C₂²×D₄×C₉	—	3	1	no	—
28	C₂³×C₄×C₉	—	3	2	no	—
29	C₄×D₄×C₉	—	3	8	no	—
30	C₂×C₉×C₄⋊C₄	—	3	1	no	—
31	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
32	C₂×C₄²×C₉	—	2	1	no	—
33	C₂×C₄²×C₉	D₃	1	1	yes	characteristic, complemented
34	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
35	C₂²×D₃×C₉	—	2	4	no	—
36	C₂²×D₃×C₉	—	2	4	no	—
37	C₂²×D₃×C₉	C₂×C₄	1	8	yes	complemented
38	C₂²×D₃×C₉	C₂³	1	4	yes	—
39	C₂×C₃×C₄×C₉	—	2	2	no	—
40	C₂×C₃×C₄×C₉	C₂×C₄	1	4	yes	complemented
41	C₂×C₃×C₄×C₉	D₄	1	4	yes	complemented
42	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
43	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
44	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
45	C₂×C₉×Dic₃	—	2	4	no	—
46	C₂×C₉×Dic₃	C₂³	1	4	yes	—
47	C₉×D₁₂	C₂×C₄	1	16	yes	direct product factor
48	C₄×D₃×C₉	—	2	16	no	—
49	C₂×C₃×C₄×D₄	—	3	1	no	—
50	C₂×C₄×D₁₂	C₉	1	1	yes	characteristic, direct product factor
51	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
52	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
53	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
54	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
55	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
56	C₂×C₃×D₁₂	C₃×C₄	1	8	yes	—
57	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
58	C₂×C₃×C₄×D₃	—	2	8	no	—
59	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
60	C₂⁴×C₉	—	3	2	no	—
61	C₃²×C₄²	C₂²×C₃	1	4	yes	—
62	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
63	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
64	C₂×D₄×C₉	—	3	8	no	—
65	C₂×D₄×C₉	—	3	4	no	—
66	C₂²×C₄×C₉	—	2	1	no	—
67	C₂²×C₄×C₉	—	2	1	no	—
68	C₂²×C₄×C₉	—	2	1	no	—
69	C₂²×C₄×C₉	—	3	2	no	—
70	C₂²×C₄×C₉	—	3	8	no	—
71	C₂²×C₄×C₉	—	6	8	no	—
72	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
73	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
74	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
75	C₉×C₄⋊C₄	—	3	4	no	—
76	C₉×C₂²⋊C₄	—	3	8	no	—
77	C₄²×C₉	—	2	4	no	—
78	C₄²×C₉	C₂×D₃	1	4	yes	complemented
79	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
80	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
81	C₂²×C₃×C₉	#41	1	2	yes	—
82	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
83	C₂×D₃×C₉	—	2	16	no	—
84	C₂×D₃×C₉	—	2	4	no	—
85	C₂×D₃×C₉	—	2	4	no	—
86	C₂×D₃×C₉	C₂²×C₄	1	8	yes	complemented
87	C₃×C₄×C₉	—	2	2	no	—
88	C₃×C₄×C₉	C₂²×C₄	1	4	yes	complemented
89	C₃×C₄×C₉	C₂×D₄	1	4	yes	complemented
90	C₉×Dic₃	—	2	4	no	—
91	C₂²×C₃×D₄	—	3	1	no	—
92	C₂³×C₃×C₄	—	3	2	no	—
93	C₂²×D₁₂	C₂×C₉	1	1	yes	characteristic
94	C₂²×C₄×D₃	C₂×C₉	1	2	yes	complemented
95	C₃×C₄×D₄	—	3	8	no	—
96	C₂×C₃×C₄⋊C₄	—	3	1	no	—
97	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
98	C₂×C₃×C₄²	—	2	1	no	—
99	C₂×C₃×C₄²	C₂×C₉	1	1	yes	characteristic, complemented
100	C₂×C₃×C₄²	C₃×D₃	1	1	yes	characteristic
101	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	2	yes	complemented
102	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
103	C₄×D₁₂	C₂×C₉	1	8	yes	direct product factor
104	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
105	C₂²×C₃×D₃	—	2	4	no	—
106	C₂²×C₃×D₃	—	2	4	no	—
107	C₂²×C₃×D₃	C₂×C₃×C₄	1	8	yes	—
108	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
109	C₂×C₃²×C₄	—	2	2	no	—
110	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
111	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
112	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
113	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
114	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
115	C₂×C₃×Dic₃	—	2	4	no	—
116	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
117	C₃×D₁₂	C₂×C₃×C₄	1	16	yes	—
118	C₃×C₄×D₃	—	2	16	no	—
119	C₂³×C₉	—	2	1	no	—
120	C₂³×C₉	—	3	8	no	—
121	C₂³×C₉	—	3	4	no	—
122	C₂³×C₉	—	6	4	no	—
123	C₂³×C₉	—	6	4	no	—
124	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
125	D₄×C₉	—	3	16	no	—
126	C₂×C₄×C₉	—	2	4	no	—
127	C₂×C₄×C₉	—	2	2	no	—
128	C₂×C₄×C₉	—	2	4	no	—
129	C₂×C₄×C₉	—	2	4	no	—
130	C₂×C₄×C₉	—	2	2	no	—
131	C₂×C₄×C₉	—	2	2	no	—
132	C₂×C₄×C₉	—	2	2	no	—
133	C₂×C₄×C₉	—	3	4	no	—
134	C₂×C₄×C₉	—	6	4	no	—
135	C₂×C₄×C₉	—	6	16	no	—
136	C₂×C₄×C₉	C₄×D₃	1	4	yes	complemented
137	C₂×C₄×C₉	D₁₂	1	4	yes	direct product factor
138	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
139	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
140	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
141	C₂×C₄×D₄	—	3	1	no	Sylow
142	C₂×C₃×C₉	C₄×D₄	1	4	yes	complemented
143	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
146	D₃×C₉	—	2	8	no	—
147	C₂⁴×C₃	—	3	2	no	—
148	C₂³×D₃	C₂²×C₉	1	2	yes	—
149	C₂×C₃×D₄	—	3	8	no	—
150	C₂×C₃×D₄	—	3	4	no	—
151	C₂²×C₃×C₄	—	2	1	no	—
152	C₂²×C₃×C₄	—	2	1	no	—
153	C₂²×C₃×C₄	—	2	1	no	—
154	C₂²×C₃×C₄	—	3	2	no	—
155	C₂²×C₃×C₄	—	3	8	no	—
156	C₂²×C₃×C₄	—	6	8	no	—
157	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
163	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
164	C₂×D₁₂	C₄×C₉	1	8	yes	direct product factor
165	C₂×D₁₂	C₂²×C₉	1	4	yes	—
166	C₂×C₄×D₃	—	2	8	no	—
167	C₂×C₄×D₃	C₂²×C₉	1	8	yes	complemented
168	C₃×C₄⋊C₄	—	3	4	no	—
169	C₃×C₂²⋊C₄	—	3	8	no	—
170	C₃×C₄²	—	2	4	no	—
171	C₃×C₄²	C₂²×C₉	1	4	yes	complemented
172	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
173	(C₂×D₃)⋊C₄	C₂²×C₉	1	8	yes	complemented
174	C₄⋊Dic₃	C₂²×C₉	1	4	yes	complemented
175	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
176	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
177	C₂²×C₃²	C₃×#41	1	2	yes	—
178	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
179	C₂×C₃×D₃	—	2	16	no	—
180	C₂×C₃×D₃	—	2	4	no	—
181	C₂×C₃×D₃	—	2	4	no	—
182	C₂×C₃×D₃	C₂²×C₃×C₄	1	8	yes	—
183	C₃²×C₄	—	2	2	no	—
184	C₃²×C₄	C₂²×C₃×C₄	1	4	yes	—
185	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
186	C₃×Dic₃	—	2	4	no	—
187	C₂²×C₉	—	2	1	no	—
188	C₂²×C₉	—	2	2	no	—
189	C₂²×C₉	—	2	2	no	—
190	C₂²×C₉	—	2	2	no	—
191	C₂²×C₉	—	3	8	no	—
192	C₂²×C₉	—	6	16	no	—
193	C₂²×C₉	—	6	4	no	—
194	C₂²×C₉	—	6	4	no	—
195	C₂²×C₉	C₂×C₄×D₃	1	2	yes	—
196	C₂²×C₉	C₂×D₁₂	1	2	yes	—
197	C₂²×C₉	#235	1	2	yes	—
198	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
199	C₄×C₉	—	2	4	no	—
200	C₄×C₉	—	2	2	no	—
201	C₄×C₉	—	2	4	no	—
202	C₄×C₉	—	2	4	no	—
203	C₄×C₉	—	6	4	no	—
204	C₄×C₉	C₂×C₄×D₃	1	4	yes	complemented
205	C₄×C₉	C₂×D₁₂	1	4	yes	direct product factor
206	C₂²×D₄	—	3	1	no	—
207	C₂³×C₄	—	3	2	no	—
208	C₄×D₄	—	3	8	no	—
209	C₂×C₄⋊C₄	—	3	1	no	—
210	C₂×C₂²⋊C₄	—	3	2	no	—
211	C₂×C₄²	D₃×C₉	1	1	yes	characteristic, complemented
212	C₃×C₉	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
213	C₂³×C₃	—	2	1	no	—
214	C₂³×C₃	—	3	4	no	—
215	C₂³×C₃	—	3	8	no	—
216	C₂³×C₃	—	6	4	no	—
217	C₂³×C₃	—	6	4	no	—
218	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
219	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
220	C₂²×D₃	—	2	4	no	—
221	C₂²×D₃	—	2	4	no	—
222	C₂²×D₃	C₂×C₄×C₉	1	8	yes	complemented
223	C₂²×D₃	C₂³×C₉	1	4	yes	—
224	C₃×D₄	—	3	16	no	—
225	C₂×C₃×C₄	—	2	4	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	3	4	no	—
234	C₂×C₃×C₄	—	6	4	no	—
235	C₂×C₃×C₄	—	6	16	no	—
236	C₂×C₃×C₄	C₂×C₄×C₉	1	4	yes	complemented
237	C₂×C₃×C₄	D₄×C₉	1	4	yes	complemented
238	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
239	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
240	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
241	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
242	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
243	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
244	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
245	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
246	C₂×Dic₃	—	2	4	no	—
247	C₂×Dic₃	C₂³×C₉	1	4	yes	—
248	D₁₂	C₂×C₄×C₉	1	16	yes	direct product factor
249	C₄×D₃	—	2	16	no	—
250	C₂×C₃²	C₃×C₄×D₄	1	4	yes	—
251	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
252	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
253	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
254	C₃×D₃	—	2	8	no	—
255	C₂×C₉	—	2	1	no	—
256	C₂×C₉	—	2	1	no	—
257	C₂×C₉	—	2	1	no	—
258	C₂×C₉	—	2	4	no	—
259	C₂×C₉	—	6	8	no	—
260	C₂×C₉	C₄×D₁₂	1	4	yes	direct product factor
261	C₂×C₉	C₂²×C₄×D₃	1	1	yes	characteristic
262	C₂×C₉	C₂²×D₁₂	1	1	yes	characteristic
263	C₂×C₉	C₂×#235	1	1	yes	characteristic
264	C₂⁴	—	3	2	no	—
265	C₂×D₄	—	3	8	no	—
266	C₂×D₄	—	3	4	no	—
267	C₂²×C₄	—	3	2	no	—
268	C₂²×C₄	—	3	8	no	—
269	C₂²×C₄	—	6	8	no	—
270	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
273	C₄⋊C₄	—	3	4	no	—
274	C₂²⋊C₄	—	3	8	no	—
275	C₄²	C₂×D₃×C₉	1	4	yes	complemented
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	2	2	no	—
278	C₂²×C₃	—	2	2	no	—
279	C₂²×C₃	—	2	2	no	—
280	C₂²×C₃	—	3	8	no	—
281	C₂²×C₃	—	6	4	no	—
282	C₂²×C₃	—	6	4	no	—
283	C₂²×C₃	—	6	16	no	—
284	C₂²×C₃	C₂²×C₄×C₉	1	2	yes	—
285	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
286	C₂²×C₃	C₉×#41	1	2	yes	—
287	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
288	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
289	C₂²×C₃	C₂×C₃×D₁₂	1	2	yes	—
290	C₂²×C₃	C₃×#235	1	2	yes	—
291	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
292	C₂×D₃	—	2	16	no	—
293	C₂×D₃	—	2	4	no	—
294	C₂×D₃	—	2	4	no	—
295	C₂×D₃	C₂²×C₄×C₉	1	8	yes	complemented
296	C₃×C₄	—	2	4	no	—
297	C₃×C₄	—	2	2	no	—
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	2	4	no	—
300	C₃×C₄	—	2	4	no	—
301	C₃×C₄	—	6	4	no	—
302	C₃×C₄	C₂²×C₄×C₉	1	4	yes	complemented
303	C₃×C₄	C₂×D₄×C₉	1	4	yes	complemented
304	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
305	C₃×C₄	C₂×C₃×D₁₂	1	4	yes	—
306	Dic₃	—	2	4	no	—
307	C₃²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
308	C₉	—	2	1	no	—
309	C₉	C₂×C₄×D₁₂	1	1	yes	characteristic, direct product factor
310	C₂³	—	3	4	no	—
311	C₂³	—	3	8	no	—
312	C₂³	—	6	4	no	—
313	C₂³	—	6	4	no	—
314	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
315	D₄	—	3	16	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	3	4	no	—
318	C₂×C₄	—	6	4	no	—
319	C₂×C₄	—	6	16	no	—
320	C₂×C₄	C₄×D₃×C₉	1	4	yes	complemented
321	C₂×C₄	C₉×D₁₂	1	4	yes	direct product factor
322	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
323	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
324	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
325	C₂×C₃	—	2	1	no	—
326	C₂×C₃	—	2	1	no	—
327	C₂×C₃	—	2	1	no	—
328	C₂×C₃	—	2	4	no	—
329	C₂×C₃	—	6	8	no	—
330	C₂×C₃	C₄×D₄×C₉	1	4	yes	complemented
331	C₂×C₃	C₂³×C₄×C₉	1	1	yes	characteristic
332	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
333	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
334	C₂×C₃	C₃×C₄×D₁₂	1	4	yes	—
335	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
336	C₂×C₃	C₂²×C₃×D₁₂	1	1	yes	characteristic
337	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
338	D₃	—	2	8	no	—
339	C₂²	—	3	8	no	—
340	C₂²	—	6	4	no	—
341	C₂²	—	6	4	no	—
342	C₂²	—	6	16	no	—
343	C₂²	C₂×C₄×D₃×C₉	1	2	yes	—
344	C₂²	C₂×C₉×D₁₂	1	2	yes	—
345	C₂²	C₉×#235	1	2	yes	—
346	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
347	C₄	—	2	2	no	—
348	C₄	—	6	4	no	—
349	C₄	C₂×C₄×D₃×C₉	1	4	yes	complemented
350	C₄	C₂×C₉×D₁₂	1	4	yes	direct product factor
351	C₃	—	2	1	no	—
352	C₃	C₂×C₄×D₄×C₉	1	1	yes	characteristic, complemented
353	C₃	C₂×C₃×C₄×D₁₂	1	1	yes	characteristic
354	C₂	—	6	8	no	—
355	C₂	C₄×C₉×D₁₂	1	4	yes	direct product factor
356	C₂	C₂²×C₄×D₃×C₉	1	1	yes	characteristic
357	C₂	C₂²×C₉×D₁₂	1	1	yes	characteristic
358	C₂	C₂×C₉×#235	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₉	C₂×D₃
commutator	C₂×C₃	C₂³×C₄×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₄²×C₉	C₂
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂²×C₃×D₁₂	C₂×C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₄²×C₉	D₃
hypocenter	C₃	C₂×C₄×D₄×C₉
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₉ ◁ C₂×C₄²×C₉

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₃×C₉	C₂	semidirect
3. C₂×C₃×C₄²×C₉	C₂	semidirect
4. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
5. C₂×C₉×C₄⋊Dic₃	C₂	semidirect
6. C₄×C₉×D₁₂	C₂	direct (N × H)
14. C₂×C₉×D₁₂	C₄	direct (N × H)
17. C₂×C₄×D₃×C₉	C₂²	semidirect
18. C₃×C₄²×C₉	C₂²	semidirect
19. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
20. C₉×C₄⋊Dic₃	C₂²	semidirect
33. C₂×C₄²×C₉	D₃	semidirect
37. C₂²×D₃×C₉	C₂×C₄	semidirect
40. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
41. C₂×C₃×C₄×C₉	D₄	semidirect
47. C₉×D₁₂	C₂×C₄	direct (N × H)
50. C₂×C₄×D₁₂	C₉	direct (N × H)
78. C₄²×C₉	C₂×D₃	semidirect
86. C₂×D₃×C₉	C₂²×C₄	semidirect
88. C₃×C₄×C₉	C₂²×C₄	semidirect
89. C₃×C₄×C₉	C₂×D₄	semidirect
94. C₂²×C₄×D₃	C₂×C₉	semidirect
99. C₂×C₃×C₄²	C₂×C₉	semidirect
101. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
102. C₂×C₄⋊Dic₃	C₂×C₉	semidirect
103. C₄×D₁₂	C₂×C₉	direct (N × H)
136. C₂×C₄×C₉	C₄×D₃	semidirect
137. C₂×C₄×C₉	D₁₂	direct (N × H)
142. C₂×C₃×C₉	C₄×D₄	semidirect
164. C₂×D₁₂	C₄×C₉	direct (N × H)
167. C₂×C₄×D₃	C₂²×C₉	semidirect
171. C₃×C₄²	C₂²×C₉	semidirect
173. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
174. C₄⋊Dic₃	C₂²×C₉	semidirect
204. C₄×C₉	C₂×C₄×D₃	semidirect
205. C₄×C₉	C₂×D₁₂	direct (N × H)
211. C₂×C₄²	D₃×C₉	semidirect
212. C₃×C₉	C₂×C₄×D₄	semidirect
222. C₂²×D₃	C₂×C₄×C₉	semidirect
236. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
237. C₂×C₃×C₄	D₄×C₉	semidirect
248. D₁₂	C₂×C₄×C₉	direct (N × H)
260. C₂×C₉	C₄×D₁₂	direct (N × H)
275. C₄²	C₂×D₃×C₉	semidirect
295. C₂×D₃	C₂²×C₄×C₉	semidirect
302. C₃×C₄	C₂²×C₄×C₉	semidirect
303. C₃×C₄	C₂×D₄×C₉	semidirect
309. C₉	C₂×C₄×D₁₂	direct (N × H)
320. C₂×C₄	C₄×D₃×C₉	semidirect
321. C₂×C₄	C₉×D₁₂	direct (N × H)
330. C₂×C₃	C₄×D₄×C₉	semidirect
349. C₄	C₂×C₄×D₃×C₉	semidirect
350. C₄	C₂×C₉×D₁₂	direct (N × H)
352. C₃	C₂×C₄×D₄×C₉	semidirect
355. C₂	C₄×C₉×D₁₂	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×D₁₂	2
C₂²×C₄×D₃×C₉	2
C₂×C₃×C₄²×C₉	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×C₄⋊Dic₃	2
C₄×C₉×D₁₂	2
C₂×C₃×C₄×D₁₂	3
C₂×C₄×D₄×C₉	3

Subgroups — C2×C4×C9×D12 #13152290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₉×D₁₂ #13152290