Subgroups — C₂²×D₉×#67 #13164807

Order 1728.

4322 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×D₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₃×D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#6233	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₉×#67	C₂	1	24	yes	maximal, direct product factor
6	C₂²×#6194	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6192	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₃×D₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₃×#67	—	3	1	no	maximal
10	C₂²×D₄×D₉	—	3	1	no	maximal
11	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic, complemented
12	C₂³×C₃⋊D₉	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
14	C₂³×C₃×D₉	—	2	8	no	—
15	C₂³×C₃×D₉	C₂²	1	1	yes	characteristic
16	C₂³×C₃×D₉	C₂²	1	12	yes	complemented
17	C₂³×C₃×D₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₃×D₉	—	2	8	no	—
19	C₂²×D₃×D₉	C₂²	1	12	yes	complemented
20	C₂×#6233	C₂²	1	12	yes	complemented
21	C₂²×C₃⋊Dic₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₉×#67	C₂²	1	12	yes	complemented
23	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
24	D₉×#67	C₂²	1	64	yes	direct product factor
25	C₂×#6194	C₂²	1	12	yes	complemented
26	C₂×#6192	C₂²	1	12	yes	complemented
27	C₂×Dic₃×D₉	C₂²	1	12	yes	complemented
28	C₂⁴×C₃×D₃	—	3	1	no	—
29	C₂³×D₃²	—	3	1	no	—
30	C₂²×#638	—	3	1	no	—
31	C₂²×C₃×#67	D₃	1	1	yes	characteristic
32	C₂×D₃×#67	—	3	24	no	—
33	C₂²×#626	—	3	1	no	—
34	C₂²×#625	—	3	1	no	—
35	C₂²×D₃×Dic₃	—	3	1	no	—
36	C₂⁴×D₉	—	3	1	no	—
37	C₂⁴×D₉	D₃	1	1	yes	characteristic, complemented
38	C₂²×D₄×C₉	—	3	1	no	—
39	C₂²×#611	—	3	1	no	—
40	C₂²×#611	—	3	1	no	—
41	C₂²×#611	—	6	1	no	—
42	C₂×D₄×D₉	—	3	24	no	—
43	C₂²×D₃₆	—	3	1	no	—
44	C₂²×C₄×D₉	—	3	1	no	—
45	C₂³×C₃×C₉	—	2	4	no	—
46	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
47	C₂³×C₃×C₉	C₂³	1	6	yes	complemented
48	C₂²×C₃⋊D₉	—	2	4	no	—
49	C₂²×C₃⋊D₉	C₂³	1	6	yes	complemented
50	C₂²×D₃×C₉	—	2	4	no	—
51	C₂²×D₃×C₉	C₂³	1	6	yes	complemented
52	C₂²×C₃×D₉	—	2	4	no	—
53	C₂²×C₃×D₉	—	2	48	no	—
54	C₂²×C₃×D₉	D₄	1	8	yes	complemented
55	C₂²×C₃×D₉	C₂³	1	6	yes	—
56	C₂²×C₃×D₉	C₂³	1	16	yes	complemented
57	C₂²×C₃×D₉	C₂³	1	6	yes	complemented
58	C₂×D₃×D₉	—	2	48	no	—
59	C₂×D₃×D₉	C₂³	1	16	yes	complemented
60	#6233	C₂³	1	16	yes	complemented
61	C₂×C₃⋊Dic₉	C₂³	1	6	yes	complemented
62	C₉×#67	C₂³	1	16	yes	complemented
63	C₂×C₉×Dic₃	C₂³	1	6	yes	complemented
64	#6194	C₂³	1	16	yes	complemented
65	#6192	C₂³	1	16	yes	complemented
66	Dic₃×D₉	C₂³	1	16	yes	complemented
67	C₂³×#67	—	9	1	no	—
68	C₂²×D₃×D₄	—	9	1	no	—
69	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic
70	C₂³×C₃⋊D₃	—	3	1	no	—
71	C₂³×C₃×D₃	—	3	1	no	—
72	C₂³×C₃×D₃	—	3	1	no	—
73	C₂³×C₃×D₃	—	3	12	no	—
74	C₂³×C₃×D₃	—	6	8	no	—
75	C₂³×C₃×D₃	C₂×D₃	1	1	yes	characteristic
76	C₂²×D₃²	—	3	12	no	—
77	C₂²×D₃²	—	6	8	no	—
78	C₂×#638	—	3	12	no	—
79	C₂²×C₃⋊Dic₃	—	3	1	no	—
80	C₂×C₃×#67	C₂×D₃	1	12	yes	—
81	C₂²×C₃×Dic₃	C₂×D₃	1	1	yes	characteristic
82	D₃×#67	—	3	64	no	—
83	C₂×#626	—	3	12	no	—
84	C₂×#625	—	3	12	no	—
85	C₂×D₃×Dic₃	—	3	12	no	—
86	C₂⁴×C₉	—	2	1	no	—
87	C₂⁴×C₉	—	3	1	no	—
88	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic, complemented
89	C₂³×D₉	—	2	8	no	—
90	C₂³×D₉	—	3	1	no	—
91	C₂³×D₉	—	3	12	no	—
92	C₂³×D₉	—	6	8	no	—
93	C₂³×D₉	—	6	1	no	—
94	C₂³×D₉	C₂×D₃	1	1	yes	characteristic
95	C₂³×D₉	C₂×D₃	1	12	yes	complemented
96	C₂³×D₉	C₂×D₃	1	1	yes	characteristic, complemented
97	C₂×D₄×C₉	—	3	12	no	—
98	C₂²×C₄×C₉	—	3	1	no	—
99	C₂×#611	—	3	12	no	—
100	C₂×#611	—	3	12	no	—
101	C₂×#611	—	6	12	no	—
102	C₂²×Dic₉	—	3	1	no	—
103	C₂²×Dic₉	—	6	1	no	—
104	D₄×D₉	—	3	64	no	—
105	C₂×D₃₆	—	3	12	no	—
106	C₂×C₄×D₉	—	3	12	no	—
107	C₂²×C₃×C₉	—	2	12	no	—
108	C₂²×C₃×C₉	C₂×D₄	1	4	yes	complemented
109	C₂²×C₃×C₉	C₂⁴	1	3	yes	—
110	C₂²×C₃×C₉	C₂⁴	1	4	yes	complemented
111	C₂×C₃⋊D₉	—	2	12	no	—
112	C₂×C₃⋊D₉	C₂⁴	1	4	yes	complemented
113	C₂×D₃×C₉	—	2	12	no	—
114	C₂×D₃×C₉	C₂⁴	1	4	yes	complemented
115	C₂×C₃×D₉	—	2	12	no	—
116	C₂×C₃×D₉	—	2	32	no	—
117	C₂×C₃×D₉	C₂×D₄	1	24	yes	complemented
118	C₂×C₃×D₉	C₂⁴	1	4	yes	—
119	C₂×C₃×D₉	C₂⁴	1	4	yes	complemented
120	D₃×D₉	—	2	32	no	—
121	C₃⋊Dic₉	C₂⁴	1	4	yes	complemented
122	C₉×Dic₃	C₂⁴	1	4	yes	complemented
123	C₂⁵×C₃	—	9	1	no	—
124	C₂⁴×D₃	—	3	1	no	—
125	C₂⁴×D₃	—	9	1	no	—
126	C₂⁴×D₃	—	9	1	no	—
127	C₂²×C₃×D₄	—	3	1	no	—
128	C₂²×#67	—	9	1	no	—
129	C₂²×#67	—	9	1	no	—
130	C₂²×#67	—	9	1	no	—
131	C₂²×#67	—	9	1	no	—
132	C₂²×#67	—	9	24	no	—
133	C₂²×#67	—	9	1	no	—
134	C₂²×#67	—	18	1	no	—
135	C₂²×#67	D₉	1	1	yes	characteristic, direct product factor
136	C₂³×Dic₃	—	9	1	no	—
137	C₂×D₃×D₄	—	9	24	no	—
138	C₂²×D₁₂	—	9	1	no	—
139	C₂²×C₄×D₃	—	9	1	no	—
140	C₂³×C₃²	—	2	4	no	—
141	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
142	C₂³×C₃²	C₂²×D₃	1	6	yes	—
143	C₂²×C₃⋊D₃	—	3	6	no	—
144	C₂²×C₃⋊D₃	—	6	4	no	—
145	C₂²×C₃×D₃	—	2	4	no	—
146	C₂²×C₃×D₃	—	3	8	no	—
147	C₂²×C₃×D₃	—	3	6	no	—
148	C₂²×C₃×D₃	—	3	6	no	—
149	C₂²×C₃×D₃	—	3	16	no	—
150	C₂²×C₃×D₃	—	6	48	no	—
151	C₂²×C₃×D₃	—	6	4	no	—
152	C₂²×C₃×D₃	C₂²×D₃	1	6	yes	—
153	C₂×D₃²	—	3	16	no	—
154	C₂×D₃²	—	6	48	no	—
155	#638	—	3	16	no	—
156	C₂×C₃⋊Dic₃	—	3	6	no	—
157	C₃×#67	C₂²×D₃	1	16	yes	—
158	C₂×C₃×Dic₃	C₂²×D₃	1	6	yes	—
159	#626	—	3	16	no	—
160	#625	—	3	16	no	—
161	D₃×Dic₃	—	3	16	no	—
162	C₂³×C₉	—	2	4	no	—
163	C₂³×C₉	—	2	1	no	—
164	C₂³×C₉	—	2	6	no	—
165	C₂³×C₉	—	3	6	no	—
166	C₂³×C₉	—	4	4	no	—
167	C₂³×C₉	—	6	4	no	—
168	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
169	C₂³×C₉	C₂²×D₃	1	6	yes	complemented
170	C₂²×D₉	—	2	4	no	—
171	C₂²×D₉	—	2	48	no	—
172	C₂²×D₉	—	3	6	no	—
173	C₂²×D₉	—	3	16	no	—
174	C₂²×D₉	—	6	6	no	—
175	C₂²×D₉	—	6	4	no	—
176	C₂²×D₉	—	6	48	no	—
177	C₂²×D₉	—	12	4	no	—
178	C₂²×D₉	#67	1	8	yes	direct product factor
179	C₂²×D₉	C₂²×D₃	1	6	yes	—
180	C₂²×D₉	C₂²×D₃	1	16	yes	complemented
181	C₂²×D₉	C₂²×D₃	1	6	yes	complemented
182	D₄×C₉	—	3	16	no	—
183	C₂×C₄×C₉	—	3	6	no	—
184	#611	—	3	16	no	—
185	#611	—	3	16	no	—
186	#611	—	6	16	no	—
187	C₂×Dic₉	—	3	6	no	—
188	C₂×Dic₉	—	6	6	no	—
189	D₃₆	—	3	16	no	—
190	C₄×D₉	—	3	16	no	—
191	C₂³×D₄	—	27	1	no	Sylow
192	C₂×C₃×C₉	—	2	4	no	—
193	C₂×C₃×C₉	C₂²×D₄	1	6	yes	complemented
194	C₂×C₃×C₉	C₂⁵	1	1	yes	characteristic
195	C₃⋊D₉	—	2	4	no	—
196	D₃×C₉	—	2	4	no	—
197	C₃×D₉	—	2	4	no	—
198	C₃×D₉	C₂²×D₄	1	8	yes	complemented
199	C₂⁴×C₃	—	2	1	no	—
200	C₂⁴×C₃	—	3	1	no	—
201	C₂⁴×C₃	—	9	1	no	—
202	C₂⁴×C₃	—	9	1	no	—
203	C₂⁴×C₃	—	9	12	no	—
204	C₂⁴×C₃	—	18	8	no	—
205	C₂⁴×C₃	C₂×D₉	1	1	yes	characteristic, complemented
206	C₂⁴×C₃	D₃²	1	1	yes	characteristic
207	C₂³×D₃	—	3	1	no	—
208	C₂³×D₃	—	3	1	no	—
209	C₂³×D₃	—	3	12	no	—
210	C₂³×D₃	—	6	8	no	—
211	C₂³×D₃	—	9	12	no	—
212	C₂³×D₃	—	9	1	no	—
213	C₂³×D₃	—	9	1	no	—
214	C₂³×D₃	—	9	12	no	—
215	C₂³×D₃	—	18	1	no	—
216	C₂³×D₃	—	18	8	no	—
217	C₂³×D₃	—	18	8	no	—
218	C₂³×D₃	C₂×D₉	1	1	yes	characteristic, complemented
219	C₂×C₃×D₄	—	3	12	no	—
220	C₂²×C₃×C₄	—	3	1	no	—
221	C₂×#67	—	9	12	no	—
222	C₂×#67	—	9	12	no	—
223	C₂×#67	—	9	12	no	—
224	C₂×#67	—	9	12	no	—
225	C₂×#67	—	9	64	no	—
226	C₂×#67	—	9	12	no	—
227	C₂×#67	—	18	12	no	—
228	C₂×#67	C₂×D₉	1	12	yes	direct product factor
229	C₂²×Dic₃	—	9	1	no	—
230	C₂²×Dic₃	—	9	1	no	—
231	C₂²×Dic₃	—	9	12	no	—
232	C₂²×Dic₃	—	18	1	no	—
233	C₂²×Dic₃	C₂×D₉	1	1	yes	characteristic, complemented
234	D₃×D₄	—	9	64	no	—
235	C₂×D₁₂	—	9	12	no	—
236	C₂×C₄×D₃	—	9	12	no	—
237	C₂²×C₃²	—	2	12	no	—
238	C₂²×C₃²	D₃×D₄	1	4	yes	—
239	C₂²×C₃²	C₂³×D₃	1	3	yes	—
240	C₂²×C₃²	C₂³×D₃	1	4	yes	—
241	C₂×C₃⋊D₃	—	3	4	no	—
242	C₂×C₃⋊D₃	—	6	12	no	—
243	C₂×C₃×D₃	—	2	12	no	—
244	C₂×C₃×D₃	—	3	24	no	—
245	C₂×C₃×D₃	—	3	4	no	—
246	C₂×C₃×D₃	—	3	4	no	—
247	C₂×C₃×D₃	—	6	32	no	—
248	C₂×C₃×D₃	—	6	12	no	—
249	C₂×C₃×D₃	C₂³×D₃	1	4	yes	—
250	D₃²	—	6	32	no	—
251	C₃⋊Dic₃	—	3	4	no	—
252	C₃×Dic₃	C₂³×D₃	1	4	yes	—
253	C₂²×C₉	—	2	12	no	—
254	C₂²×C₉	—	2	3	no	—
255	C₂²×C₉	—	2	4	no	—
256	C₂²×C₉	—	2	4	no	—
257	C₂²×C₉	—	3	4	no	—
258	C₂²×C₉	—	4	12	no	—
259	C₂²×C₉	—	6	12	no	—
260	C₂²×C₉	C₂×#67	1	4	yes	complemented
261	C₂²×C₉	C₂³×D₃	1	3	yes	—
262	C₂²×C₉	C₂³×D₃	1	4	yes	complemented
263	C₂×D₉	—	2	12	no	—
264	C₂×D₉	—	2	32	no	—
265	C₂×D₉	—	3	4	no	—
266	C₂×D₉	—	6	4	no	—
267	C₂×D₉	—	6	12	no	—
268	C₂×D₉	—	6	32	no	—
269	C₂×D₉	—	12	12	no	—
270	C₂×D₉	C₂×#67	1	24	yes	direct product factor
271	C₂×D₉	C₂³×D₃	1	4	yes	—
272	C₂×D₉	C₂³×D₃	1	4	yes	complemented
273	C₄×C₉	—	3	4	no	—
274	Dic₉	—	3	4	no	—
275	Dic₉	—	6	4	no	—
276	C₂⁵	—	9	1	no	—
277	C₂⁵	—	27	1	no	—
278	C₂²×D₄	—	3	1	no	—
279	C₂²×D₄	—	27	1	no	—
280	C₂²×D₄	—	27	24	no	—
281	C₂²×D₄	—	27	1	no	—
282	C₂²×D₄	—	27	1	no	—
283	C₂³×C₄	—	27	1	no	—
284	C₃×C₉	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
285	C₂³×C₃	—	2	4	no	—
286	C₂³×C₃	—	2	4	no	—
287	C₂³×C₃	—	2	1	no	—
288	C₂³×C₃	—	2	6	no	—
289	C₂³×C₃	—	3	6	no	—
290	C₂³×C₃	—	4	4	no	—
291	C₂³×C₃	—	6	4	no	—
292	C₂³×C₃	—	9	8	no	—
293	C₂³×C₃	—	9	6	no	—
294	C₂³×C₃	—	9	6	no	—
295	C₂³×C₃	—	9	16	no	—
296	C₂³×C₃	—	18	48	no	—
297	C₂³×C₃	—	18	4	no	—
298	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
299	C₂³×C₃	C₂²×D₉	1	6	yes	complemented
300	C₂³×C₃	C₂×D₃²	1	1	yes	characteristic
301	C₂³×C₃	C₂×D₃²	1	6	yes	—
302	C₂²×D₃	—	2	4	no	—
303	C₂²×D₃	—	3	6	no	—
304	C₂²×D₃	—	3	8	no	—
305	C₂²×D₃	—	3	6	no	—
306	C₂²×D₃	—	3	16	no	—
307	C₂²×D₃	—	6	48	no	—
308	C₂²×D₃	—	6	4	no	—
309	C₂²×D₃	—	9	16	no	—
310	C₂²×D₃	—	9	6	no	—
311	C₂²×D₃	—	9	6	no	—
312	C₂²×D₃	—	9	16	no	—
313	C₂²×D₃	—	18	6	no	—
314	C₂²×D₃	—	18	48	no	—
315	C₂²×D₃	—	18	48	no	—
316	C₂²×D₃	—	18	4	no	—
317	C₂²×D₃	—	18	4	no	—
318	C₂²×D₃	—	36	4	no	—
319	C₂²×D₃	C₂²×D₉	1	6	yes	complemented
320	C₃×D₄	—	3	16	no	—
321	C₂×C₃×C₄	—	3	6	no	—
322	#67	—	9	16	no	—
323	#67	—	9	16	no	—
324	#67	—	9	16	no	—
325	#67	—	9	16	no	—
326	#67	—	9	16	no	—
327	#67	—	18	16	no	—
328	#67	C₂²×D₉	1	16	yes	direct product factor
329	C₂×Dic₃	—	9	6	no	—
330	C₂×Dic₃	—	9	6	no	—
331	C₂×Dic₃	—	9	16	no	—
332	C₂×Dic₃	—	18	6	no	—
333	C₂×Dic₃	C₂²×D₉	1	6	yes	complemented
334	D₁₂	—	9	16	no	—
335	C₄×D₃	—	9	16	no	—
336	C₂×C₃²	—	2	4	no	—
337	C₂×C₃²	C₂×D₃×D₄	1	6	yes	—
338	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
339	C₃⋊D₃	—	6	4	no	—
340	C₃×D₃	—	2	4	no	—
341	C₃×D₃	—	3	8	no	—
342	C₃×D₃	—	6	4	no	—
343	C₂×C₉	—	2	4	no	—
344	C₂×C₉	—	2	6	no	—
345	C₂×C₉	—	2	1	no	—
346	C₂×C₉	—	4	4	no	—
347	C₂×C₉	—	6	4	no	—
348	C₂×C₉	C₂²×#67	1	6	yes	complemented
349	C₂×C₉	C₂⁴×D₃	1	1	yes	characteristic
350	D₉	—	2	4	no	—
351	D₉	—	6	4	no	—
352	D₉	—	12	4	no	—
353	D₉	C₂²×#67	1	8	yes	direct product factor
354	C₂⁴	—	3	1	no	—
355	C₂⁴	—	9	1	no	—
356	C₂⁴	—	9	1	no	—
357	C₂⁴	—	9	12	no	—
358	C₂⁴	—	18	8	no	—
359	C₂⁴	—	27	12	no	—
360	C₂⁴	—	27	1	no	—
361	C₂⁴	—	54	8	no	—
362	C₂⁴	D₃×D₉	1	1	yes	characteristic, complemented
363	C₂×D₄	—	3	12	no	—
364	C₂×D₄	—	27	12	no	—
365	C₂×D₄	—	27	64	no	—
366	C₂×D₄	—	27	12	no	—
367	C₂×D₄	—	27	12	no	—
368	C₂²×C₄	—	3	1	no	—
369	C₂²×C₄	—	27	12	no	—
370	C₂²×C₄	—	27	1	no	—
371	C₂²×C₃	—	2	12	no	—
372	C₂²×C₃	—	2	12	no	—
373	C₂²×C₃	—	2	3	no	—
374	C₂²×C₃	—	2	4	no	—
375	C₂²×C₃	—	2	4	no	—
376	C₂²×C₃	—	3	4	no	—
377	C₂²×C₃	—	4	12	no	—
378	C₂²×C₃	—	6	12	no	—
379	C₂²×C₃	—	9	4	no	—
380	C₂²×C₃	—	9	24	no	—
381	C₂²×C₃	—	9	4	no	—
382	C₂²×C₃	—	18	32	no	—
383	C₂²×C₃	—	18	12	no	—
384	C₂²×C₃	D₄×D₉	1	4	yes	complemented
385	C₂²×C₃	C₂³×D₉	1	3	yes	—
386	C₂²×C₃	C₂³×D₉	1	4	yes	complemented
387	C₂²×C₃	D₃×#67	1	4	yes	—
388	C₂²×C₃	C₂²×D₃²	1	3	yes	—
389	C₂²×C₃	C₂²×D₃²	1	4	yes	—
390	C₂×D₃	—	2	12	no	—
391	C₂×D₃	—	3	24	no	—
392	C₂×D₃	—	3	4	no	—
393	C₂×D₃	—	3	4	no	—
394	C₂×D₃	—	6	32	no	—
395	C₂×D₃	—	6	12	no	—
396	C₂×D₃	—	9	4	no	—
397	C₂×D₃	—	9	4	no	—
398	C₂×D₃	—	18	4	no	—
399	C₂×D₃	—	18	32	no	—
400	C₂×D₃	—	18	32	no	—
401	C₂×D₃	—	18	12	no	—
402	C₂×D₃	—	18	12	no	—
403	C₂×D₃	—	36	12	no	—
404	C₂×D₃	C₂³×D₉	1	4	yes	complemented
405	C₃×C₄	—	3	4	no	—
406	Dic₃	—	9	4	no	—
407	Dic₃	—	9	4	no	—
408	Dic₃	—	18	4	no	—
409	Dic₃	C₂³×D₉	1	4	yes	complemented
410	C₃²	C₂²×D₃×D₄	1	1	yes	characteristic
411	C₉	—	2	1	no	—
412	C₉	C₂³×#67	1	1	yes	characteristic, complemented
413	C₂³	—	2	4	no	—
414	C₂³	—	3	6	no	—
415	C₂³	—	6	4	no	—
416	C₂³	—	9	6	no	—
417	C₂³	—	9	8	no	—
418	C₂³	—	9	6	no	—
419	C₂³	—	9	16	no	—
420	C₂³	—	18	48	no	—
421	C₂³	—	18	4	no	—
422	C₂³	—	27	16	no	—
423	C₂³	—	27	6	no	—
424	C₂³	—	54	48	no	—
425	C₂³	—	54	4	no	—
426	C₂³	C₂×D₃×D₉	1	1	yes	characteristic
427	C₂³	C₂×D₃×D₉	1	6	yes	complemented
428	D₄	—	3	16	no	—
429	D₄	—	27	16	no	—
430	D₄	—	27	16	no	—
431	D₄	—	27	16	no	—
432	C₂×C₄	—	3	6	no	—
433	C₂×C₄	—	27	16	no	—
434	C₂×C₄	—	27	6	no	—
435	C₂×C₃	—	2	4	no	—
436	C₂×C₃	—	2	4	no	—
437	C₂×C₃	—	2	1	no	—
438	C₂×C₃	—	2	6	no	—
439	C₂×C₃	—	4	4	no	—
440	C₂×C₃	—	6	4	no	—
441	C₂×C₃	—	9	8	no	—
442	C₂×C₃	—	18	4	no	—
443	C₂×C₃	C₂×D₄×D₉	1	6	yes	complemented
444	C₂×C₃	C₂⁴×D₉	1	1	yes	characteristic
445	C₂×C₃	C₂×D₃×#67	1	6	yes	—
446	C₂×C₃	C₂³×D₃²	1	1	yes	characteristic
447	D₃	—	2	4	no	—
448	D₃	—	3	8	no	—
449	D₃	—	6	4	no	—
450	D₃	—	18	4	no	—
451	D₃	—	18	4	no	—
452	D₃	—	36	4	no	—
453	C₂²	—	2	12	no	—
454	C₂²	—	3	4	no	—
455	C₂²	—	6	12	no	—
456	C₂²	—	9	4	no	—
457	C₂²	—	9	24	no	—
458	C₂²	—	9	4	no	—
459	C₂²	—	18	32	no	—
460	C₂²	—	18	12	no	—
461	C₂²	—	27	4	no	—
462	C₂²	—	54	32	no	—
463	C₂²	—	54	12	no	—
464	C₂²	D₉×#67	1	4	yes	direct product factor
465	C₂²	C₂²×D₃×D₉	1	3	yes	—
466	C₂²	C₂²×D₃×D₉	1	4	yes	complemented
467	C₄	—	3	4	no	—
468	C₄	—	27	4	no	—
469	C₃	—	2	1	no	—
470	C₃	C₂²×D₄×D₉	1	1	yes	characteristic, complemented
471	C₃	C₂²×D₃×#67	1	1	yes	characteristic
472	C₂	—	2	4	no	—
473	C₂	—	6	4	no	—
474	C₂	—	9	8	no	—
475	C₂	—	18	4	no	—
476	C₂	—	54	4	no	—
477	C₂	C₂×D₉×#67	1	6	yes	direct product factor
478	C₂	C₂³×D₃×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃×D₉
commutator, cosocle	C₂×C₃×C₉	C₂⁵
Frattini	C₂×C₃	C₂³×D₃²
Fitting	C₂⁴×C₃×C₉	C₂²
socle	C₂³×C₃²	C₂²×D₃
hypercenter	C₂⁴	D₃×D₉
hypocenter	C₃×C₉	C₂³×D₄
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×D₉	C₂	semidirect
2. C₂³×D₃×D₉	C₂	semidirect
3. C₂²×#6233	C₂	semidirect
4. C₂²×C₉×#67	C₂	semidirect
5. C₂×D₉×#67	C₂	direct (N × H)
6. C₂²×#6194	C₂	semidirect
7. C₂²×#6192	C₂	semidirect
8. C₂²×Dic₃×D₉	C₂	semidirect
11. C₂⁴×C₃×C₉	C₂²	semidirect
12. C₂³×C₃⋊D₉	C₂²	semidirect
13. C₂³×D₃×C₉	C₂²	semidirect
16. C₂³×C₃×D₉	C₂²	semidirect
17. C₂³×C₃×D₉	C₂²	semidirect
19. C₂²×D₃×D₉	C₂²	semidirect
20. C₂×#6233	C₂²	semidirect
21. C₂²×C₃⋊Dic₉	C₂²	semidirect
22. C₂×C₉×#67	C₂²	semidirect
23. C₂²×C₉×Dic₃	C₂²	semidirect
24. D₉×#67	C₂²	direct (N × H)
25. C₂×#6194	C₂²	semidirect
26. C₂×#6192	C₂²	semidirect
27. C₂×Dic₃×D₉	C₂²	semidirect
37. C₂⁴×D₉	D₃	semidirect
47. C₂³×C₃×C₉	C₂³	semidirect
49. C₂²×C₃⋊D₉	C₂³	semidirect
51. C₂²×D₃×C₉	C₂³	semidirect
54. C₂²×C₃×D₉	D₄	semidirect
56. C₂²×C₃×D₉	C₂³	semidirect
57. C₂²×C₃×D₉	C₂³	semidirect
59. C₂×D₃×D₉	C₂³	semidirect
60. #6233	C₂³	semidirect
61. C₂×C₃⋊Dic₉	C₂³	semidirect
62. C₉×#67	C₂³	semidirect
63. C₂×C₉×Dic₃	C₂³	semidirect
64. #6194	C₂³	semidirect
65. #6192	C₂³	semidirect
66. Dic₃×D₉	C₂³	semidirect
88. C₂⁴×C₉	C₂×D₃	semidirect
95. C₂³×D₉	C₂×D₃	semidirect
96. C₂³×D₉	C₂×D₃	semidirect
108. C₂²×C₃×C₉	C₂×D₄	semidirect
110. C₂²×C₃×C₉	C₂⁴	semidirect
112. C₂×C₃⋊D₉	C₂⁴	semidirect
114. C₂×D₃×C₉	C₂⁴	semidirect
117. C₂×C₃×D₉	C₂×D₄	semidirect
119. C₂×C₃×D₉	C₂⁴	semidirect
121. C₃⋊Dic₉	C₂⁴	semidirect
122. C₉×Dic₃	C₂⁴	semidirect
135. C₂²×#67	D₉	direct (N × H)
169. C₂³×C₉	C₂²×D₃	semidirect
178. C₂²×D₉	#67	direct (N × H)
180. C₂²×D₉	C₂²×D₃	semidirect
181. C₂²×D₉	C₂²×D₃	semidirect
193. C₂×C₃×C₉	C₂²×D₄	semidirect
198. C₃×D₉	C₂²×D₄	semidirect
205. C₂⁴×C₃	C₂×D₉	semidirect
218. C₂³×D₃	C₂×D₉	semidirect
228. C₂×#67	C₂×D₉	direct (N × H)
233. C₂²×Dic₃	C₂×D₉	semidirect
260. C₂²×C₉	C₂×#67	semidirect
262. C₂²×C₉	C₂³×D₃	semidirect
270. C₂×D₉	C₂×#67	direct (N × H)
272. C₂×D₉	C₂³×D₃	semidirect
284. C₃×C₉	C₂³×D₄	semidirect
299. C₂³×C₃	C₂²×D₉	semidirect
319. C₂²×D₃	C₂²×D₉	semidirect
328. #67	C₂²×D₉	direct (N × H)
333. C₂×Dic₃	C₂²×D₉	semidirect
348. C₂×C₉	C₂²×#67	semidirect
353. D₉	C₂²×#67	direct (N × H)
362. C₂⁴	D₃×D₉	semidirect
384. C₂²×C₃	D₄×D₉	semidirect
386. C₂²×C₃	C₂³×D₉	semidirect
404. C₂×D₃	C₂³×D₉	semidirect
409. Dic₃	C₂³×D₉	semidirect
412. C₉	C₂³×#67	semidirect
427. C₂³	C₂×D₃×D₉	semidirect
443. C₂×C₃	C₂×D₄×D₉	semidirect
464. C₂²	D₉×#67	direct (N × H)
466. C₂²	C₂²×D₃×D₉	semidirect
470. C₃	C₂²×D₄×D₉	semidirect
477. C₂	C₂×D₉×#67	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×D₉	2
C₂³×D₃×D₉	2
C₂²×#6233	2
C₂²×C₉×#67	2
C₂×D₉×#67	2
C₂²×#6194	2
C₂²×#6192	2
C₂²×Dic₃×D₉	2
C₂²×D₃×#67	3
C₂²×D₄×D₉	3

Subgroups — C22×D9×#67 #13164807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₉×#67 #13164807