Subgroups — C₉×#5169 #13143355

Order 1728.

632 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₉×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#215	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#832	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#821	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5169	C₃	1	1	yes	maximal, characteristic
9	C₉×#450	—	3	1	no	maximal
10	C₂³×D₃×C₉	—	2	1	no	—
11	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₉×#67	—	2	1	no	—
14	D₃×D₄×C₉	—	2	2	no	—
15	D₃×D₄×C₉	—	2	2	no	—
16	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
18	C₃×C₉×SD₁₆	—	2	2	no	—
19	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
20	C₉×#215	—	2	2	no	—
21	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
22	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
23	C₉×Dic₃⋊C₄	—	2	1	no	—
24	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃²×SD₁₆	C₂×C₃	1	1	yes	characteristic
27	C₃×#946	C₂×C₃	1	1	yes	characteristic
28	C₂×C₃×#215	C₂×C₃	1	1	yes	characteristic
29	C₂²×D₄×C₉	—	3	1	no	—
30	C₃×#832	C₂×C₃	1	1	yes	characteristic
31	C₃×#821	C₂×C₃	1	1	yes	characteristic
32	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic
33	C₂×C₉×SD₁₆	—	2	1	no	—
34	C₂×C₉×SD₁₆	—	3	1	no	—
35	C₂×C₉×SD₁₆	D₃	1	1	yes	characteristic, complemented
36	C₉×C₂²⋊Q₈	—	3	1	no	—
37	C₉×#102	—	3	1	no	—
38	C₉×#102	—	3	1	no	—
39	C₉×C₂²⋊C₈	—	3	1	no	—
40	C₂³×C₃×C₉	—	2	1	no	—
41	C₂²×D₃×C₉	—	2	4	no	—
42	C₂²×D₃×C₉	—	2	1	no	—
43	C₂²×D₃×C₉	—	4	2	no	—
44	C₂²×D₃×C₉	—	4	2	no	—
45	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
46	C₃×Q₈×C₉	—	2	1	no	—
47	C₃×Q₈×C₉	—	2	1	no	—
48	C₃×D₄×C₉	—	2	1	no	—
49	C₃×D₄×C₉	D₄	1	2	yes	—
50	C₂×C₃×C₄×C₉	—	2	1	no	—
51	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₉×#67	—	2	4	no	—
53	C₂×C₉×Dic₃	—	2	1	no	—
54	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
55	C₉×D₁₂	—	2	1	no	—
56	C₉×D₁₂	D₄	1	2	yes	—
57	C₄×D₃×C₉	—	2	1	no	—
58	C₄×D₃×C₉	—	2	1	no	—
59	C₃×C₈×C₉	—	2	1	no	—
60	C₉×C₃⋊C₈	—	2	1	no	—
61	C₃×#450	—	3	1	no	—
62	#5169	C₉	1	1	yes	characteristic, direct product factor
63	C₂³×C₃×D₃	—	2	1	no	—
64	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₃×#67	—	2	1	no	—
67	C₃×D₃×D₄	—	2	2	no	—
68	C₃×D₃×D₄	—	2	2	no	—
69	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
71	C₂⁴×C₉	—	6	1	no	—
72	C₃²×SD₁₆	—	2	2	no	—
73	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
74	C₃×#215	—	2	2	no	—
75	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
76	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
77	C₃×Dic₃⋊C₄	—	2	1	no	—
78	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
79	C₂×Q₈×C₉	—	2	1	no	—
80	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
81	C₂×D₄×C₉	—	2	1	no	—
82	C₂×D₄×C₉	—	3	1	no	—
83	C₂×D₄×C₉	—	6	1	no	—
84	C₂×D₄×C₉	—	6	2	no	—
85	C₂×D₄×C₉	—	6	2	no	—
86	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
87	C₂²×C₄×C₉	—	3	1	no	—
88	C₉×SD₁₆	—	2	4	no	—
89	C₉×SD₁₆	—	2	2	no	—
90	C₉×SD₁₆	—	6	2	no	—
91	C₂×C₈×C₉	—	2	1	no	—
92	C₂×C₈×C₉	—	3	1	no	—
93	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
94	C₉×C₄⋊C₄	—	3	1	no	—
95	C₉×C₄⋊C₄	—	6	1	no	—
96	C₉×C₂²⋊C₄	—	6	1	no	—
97	C₂²×C₃×C₉	—	2	2	no	—
98	C₂²×C₃×C₉	—	4	1	no	—
99	C₂²×C₃×C₉	—	4	1	no	—
100	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
101	C₂×D₃×C₉	—	2	1	no	—
102	C₂×D₃×C₉	—	2	1	no	—
103	C₂×D₃×C₉	—	2	2	no	—
104	C₂×D₃×C₉	—	4	8	no	—
105	C₂×D₃×C₉	—	4	1	no	—
106	C₂×D₃×C₉	—	4	1	no	—
107	C₂×D₃×C₉	SD₁₆	1	2	yes	complemented
108	C₃×C₄×C₉	—	4	1	no	—
109	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
110	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
111	C₉×Dic₃	—	2	1	no	—
112	C₉×Dic₃	—	4	1	no	—
113	C₂²×C₃×D₄	—	3	1	no	—
114	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic
115	C₂×C₃×SD₁₆	—	2	1	no	—
116	C₂×C₃×SD₁₆	—	3	1	no	—
117	C₂×C₃×SD₁₆	C₂×C₉	1	1	yes	characteristic, complemented
118	C₂×C₃×SD₁₆	C₃×D₃	1	1	yes	characteristic
119	C₃×C₂²⋊Q₈	—	3	1	no	—
120	#946	C₂×C₉	1	1	yes	characteristic, complemented
121	C₂×#215	C₂×C₉	1	1	yes	characteristic, complemented
122	C₃×#102	—	3	1	no	—
123	C₃×#102	—	3	1	no	—
124	C₃×C₂²⋊C₈	—	3	1	no	—
125	#832	C₂×C₉	1	1	yes	characteristic, complemented
126	#821	C₂×C₉	1	1	yes	characteristic, complemented
127	(C₂×D₃)⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
128	C₂³×C₃²	—	2	1	no	—
129	C₂²×C₃×D₃	—	2	4	no	—
130	C₂²×C₃×D₃	—	2	1	no	—
131	C₂²×C₃×D₃	—	4	2	no	—
132	C₂²×C₃×D₃	—	4	2	no	—
133	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
134	C₃²×Q₈	—	2	1	no	—
135	C₃²×Q₈	—	2	1	no	—
136	C₃²×D₄	—	2	1	no	—
137	C₃²×D₄	C₃×D₄	1	2	yes	—
138	C₂×C₃²×C₄	—	2	1	no	—
139	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
140	C₃×#67	—	2	4	no	—
141	C₂×C₃×Dic₃	—	2	1	no	—
142	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
143	C₃×D₁₂	—	2	1	no	—
144	C₃×D₁₂	C₃×D₄	1	2	yes	—
145	C₃×C₄×D₃	—	2	1	no	—
146	C₃×C₄×D₃	—	2	1	no	—
147	C₂³×C₉	—	2	1	no	—
148	C₂³×C₉	—	3	1	no	—
149	C₂³×C₉	—	4	1	no	—
150	C₂³×C₉	—	6	4	no	—
151	C₂³×C₉	—	6	1	no	—
152	C₂³×C₉	—	12	2	no	—
153	C₂³×C₉	—	12	2	no	—
154	C₃²×C₈	—	2	1	no	—
155	C₃×C₃⋊C₈	—	2	1	no	—
156	Q₈×C₉	—	2	2	no	—
157	Q₈×C₉	—	2	1	no	—
158	Q₈×C₉	—	2	1	no	—
159	Q₈×C₉	—	4	1	no	—
160	D₄×C₉	—	2	1	no	—
161	D₄×C₉	—	2	2	no	—
162	D₄×C₉	—	3	2	no	—
163	D₄×C₉	—	4	1	no	—
164	D₄×C₉	—	6	4	no	—
165	D₄×C₉	—	6	1	no	—
166	D₄×C₉	#67	1	2	yes	—
167	C₂×C₄×C₉	—	2	1	no	—
168	C₂×C₄×C₉	—	2	1	no	—
169	C₂×C₄×C₉	—	3	1	no	—
170	C₂×C₄×C₉	—	4	1	no	—
171	C₂×C₄×C₉	—	6	1	no	—
172	C₂×C₄×C₉	—	6	1	no	—
173	C₂×C₄×C₉	—	6	1	no	—
174	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
175	C₈×C₉	—	2	2	no	—
176	C₈×C₉	—	2	1	no	—
177	C₈×C₉	—	6	1	no	—
178	#450	—	3	1	no	Sylow
179	C₂×C₃×C₉	—	4	2	no	—
180	C₂×C₃×C₉	#120	1	1	yes	characteristic
181	C₂×C₃×C₉	C₂×SD₁₆	1	1	yes	characteristic
182	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
183	D₃×C₉	—	2	2	no	—
184	D₃×C₉	—	4	2	no	—
185	C₂⁴×C₃	—	6	1	no	—
186	C₂³×D₃	—	2	1	no	—
187	C₂×C₃×Q₈	—	2	1	no	—
188	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
189	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
190	C₂×C₃×D₄	—	2	1	no	—
191	C₂×C₃×D₄	—	3	1	no	—
192	C₂×C₃×D₄	—	6	1	no	—
193	C₂×C₃×D₄	—	6	2	no	—
194	C₂×C₃×D₄	—	6	2	no	—
195	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
196	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
197	C₂²×C₃×C₄	—	3	1	no	—
198	C₂×#67	—	2	1	no	—
199	D₃×D₄	—	2	2	no	—
200	D₃×D₄	—	2	2	no	—
201	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
202	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
203	C₃×SD₁₆	—	2	4	no	—
204	C₃×SD₁₆	—	2	2	no	—
205	C₃×SD₁₆	—	2	2	no	—
206	C₃×SD₁₆	—	6	2	no	—
207	C₂×C₃×C₈	—	2	1	no	—
208	C₂×C₃×C₈	—	3	1	no	—
209	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
210	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
211	C₃×C₄⋊C₄	—	3	1	no	—
212	C₃×C₄⋊C₄	—	6	1	no	—
213	C₃×C₂²⋊C₄	—	6	1	no	—
214	#215	—	2	2	no	—
215	(C₂×D₃)⋊C₄	—	2	1	no	—
216	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
217	Dic₃⋊C₄	—	2	1	no	—
218	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
219	C₂²×C₃²	—	2	2	no	—
220	C₂²×C₃²	—	4	1	no	—
221	C₂²×C₃²	—	4	1	no	—
222	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
223	C₂×C₃×D₃	—	2	1	no	—
224	C₂×C₃×D₃	—	2	1	no	—
225	C₂×C₃×D₃	—	2	2	no	—
226	C₂×C₃×D₃	—	4	8	no	—
227	C₂×C₃×D₃	—	4	1	no	—
228	C₂×C₃×D₃	—	4	1	no	—
229	C₂×C₃×D₃	C₃×SD₁₆	1	2	yes	—
230	C₃²×C₄	—	4	1	no	—
231	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
232	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
233	C₃×Dic₃	—	2	1	no	—
234	C₃×Dic₃	—	4	1	no	—
235	C₂²×C₉	—	2	2	no	—
236	C₂²×C₉	—	2	1	no	—
237	C₂²×C₉	—	3	2	no	—
238	C₂²×C₉	—	4	2	no	—
239	C₂²×C₉	—	4	1	no	—
240	C₂²×C₉	—	4	1	no	—
241	C₂²×C₉	—	6	1	no	—
242	C₂²×C₉	—	6	1	no	—
243	C₂²×C₉	—	6	2	no	—
244	C₂²×C₉	—	8	1	no	—
245	C₂²×C₉	—	8	1	no	—
246	C₂²×C₉	—	12	8	no	—
247	C₂²×C₉	—	12	1	no	—
248	C₂²×C₉	—	12	1	no	—
249	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
250	C₄×C₉	—	2	1	no	—
251	C₄×C₉	—	2	1	no	—
252	C₄×C₉	—	4	2	no	—
253	C₄×C₉	—	4	1	no	—
254	C₄×C₉	—	6	1	no	—
255	C₄×C₉	—	12	1	no	—
256	C₄×C₉	D₃×D₄	1	1	yes	characteristic
257	C₄×C₉	C₂×#67	1	1	yes	characteristic
258	C₂²×D₄	—	3	1	no	—
259	C₂×SD₁₆	—	3	1	no	—
260	C₂×SD₁₆	D₃×C₉	1	1	yes	characteristic, complemented
261	C₂²⋊Q₈	—	3	1	no	—
262	#102	—	3	1	no	—
263	#102	—	3	1	no	—
264	C₂²⋊C₈	—	3	1	no	—
265	C₃×C₉	#450	1	1	yes	characteristic, complemented, Sylow
266	C₂³×C₃	—	2	1	no	—
267	C₂³×C₃	—	2	1	no	—
268	C₂³×C₃	—	3	1	no	—
269	C₂³×C₃	—	4	1	no	—
270	C₂³×C₃	—	6	4	no	—
271	C₂³×C₃	—	6	1	no	—
272	C₂³×C₃	—	12	2	no	—
273	C₂³×C₃	—	12	2	no	—
274	C₂²×D₃	—	2	4	no	—
275	C₂²×D₃	—	2	1	no	—
276	C₂²×D₃	—	4	2	no	—
277	C₂²×D₃	—	4	2	no	—
278	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
279	C₃×Q₈	—	2	2	no	—
280	C₃×Q₈	—	2	1	no	—
281	C₃×Q₈	—	2	1	no	—
282	C₃×Q₈	—	2	1	no	—
283	C₃×Q₈	—	2	1	no	—
284	C₃×Q₈	—	4	1	no	—
285	C₃×D₄	—	2	1	no	—
286	C₃×D₄	—	2	1	no	—
287	C₃×D₄	—	2	2	no	—
288	C₃×D₄	—	3	2	no	—
289	C₃×D₄	—	4	1	no	—
290	C₃×D₄	—	6	4	no	—
291	C₃×D₄	—	6	1	no	—
292	C₃×D₄	D₄×C₉	1	2	yes	—
293	C₃×D₄	C₃×#67	1	2	yes	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	3	1	no	—
298	C₂×C₃×C₄	—	4	1	no	—
299	C₂×C₃×C₄	—	6	1	no	—
300	C₂×C₃×C₄	—	6	1	no	—
301	C₂×C₃×C₄	—	6	1	no	—
302	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
304	#67	—	2	4	no	—
305	C₂×Dic₃	—	2	1	no	—
306	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
307	D₁₂	—	2	1	no	—
308	D₁₂	D₄×C₉	1	2	yes	—
309	C₄×D₃	—	2	1	no	—
310	C₄×D₃	—	2	1	no	—
311	C₃×C₈	—	2	2	no	—
312	C₃×C₈	—	2	1	no	—
313	C₃×C₈	—	2	1	no	—
314	C₃×C₈	—	6	1	no	—
315	C₃⋊C₈	—	2	1	no	—
316	C₂×C₃²	—	4	2	no	—
317	C₂×C₃²	C₃×#120	1	1	yes	characteristic
318	C₂×C₃²	C₂×C₃×SD₁₆	1	1	yes	characteristic
319	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
320	C₃×D₃	—	2	2	no	—
321	C₃×D₃	—	4	2	no	—
322	C₂×C₉	—	2	1	no	—
323	C₂×C₉	—	2	1	no	—
324	C₂×C₉	—	2	1	no	—
325	C₂×C₉	—	4	2	no	—
326	C₂×C₉	—	6	2	no	—
327	C₂×C₉	—	8	2	no	—
328	C₂×C₉	—	12	2	no	—
329	C₂×C₉	D₃×SD₁₆	1	1	yes	characteristic
330	C₂×C₉	#914	1	1	yes	characteristic
331	C₂×C₉	#937	1	1	yes	characteristic
332	C₂⁴	—	6	1	no	—
333	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
334	C₂×D₄	—	3	1	no	—
335	C₂×D₄	—	6	1	no	—
336	C₂×D₄	—	6	2	no	—
337	C₂×D₄	—	6	2	no	—
338	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
339	C₂²×C₄	—	3	1	no	—
340	SD₁₆	—	2	2	no	—
341	SD₁₆	—	6	2	no	—
342	C₂×C₈	—	3	1	no	—
343	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
344	C₄⋊C₄	—	3	1	no	—
345	C₄⋊C₄	—	6	1	no	—
346	C₂²⋊C₄	—	6	1	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	2	2	no	—
349	C₂²×C₃	—	2	1	no	—
350	C₂²×C₃	—	3	2	no	—
351	C₂²×C₃	—	4	2	no	—
352	C₂²×C₃	—	4	1	no	—
353	C₂²×C₃	—	4	1	no	—
354	C₂²×C₃	—	4	1	no	—
355	C₂²×C₃	—	4	1	no	—
356	C₂²×C₃	—	6	1	no	—
357	C₂²×C₃	—	6	1	no	—
358	C₂²×C₃	—	6	2	no	—
359	C₂²×C₃	—	8	1	no	—
360	C₂²×C₃	—	8	1	no	—
361	C₂²×C₃	—	12	8	no	—
362	C₂²×C₃	—	12	1	no	—
363	C₂²×C₃	—	12	1	no	—
364	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
365	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
366	C₂×D₃	—	2	1	no	—
367	C₂×D₃	—	2	1	no	—
368	C₂×D₃	—	2	2	no	—
369	C₂×D₃	—	4	8	no	—
370	C₂×D₃	—	4	1	no	—
371	C₂×D₃	—	4	1	no	—
372	C₂×D₃	C₉×SD₁₆	1	2	yes	complemented
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	4	2	no	—
376	C₃×C₄	—	4	1	no	—
377	C₃×C₄	—	4	1	no	—
378	C₃×C₄	—	6	1	no	—
379	C₃×C₄	—	12	1	no	—
380	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
381	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
382	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
383	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
384	Dic₃	—	2	1	no	—
385	Dic₃	—	4	1	no	—
386	C₃²	C₃×#450	1	1	yes	characteristic
387	C₉	—	2	1	no	—
388	C₉	#5169	1	1	yes	characteristic, direct product factor
389	C₂³	—	2	1	no	—
390	C₂³	—	3	1	no	—
391	C₂³	—	6	4	no	—
392	C₂³	—	6	1	no	—
393	C₂³	—	12	2	no	—
394	C₂³	—	12	2	no	—
395	Q₈	—	2	1	no	—
396	Q₈	—	2	1	no	—
397	D₄	—	2	1	no	—
398	D₄	—	3	2	no	—
399	D₄	—	6	4	no	—
400	D₄	—	6	1	no	—
401	D₄	C₉×#67	1	2	yes	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	3	1	no	—
404	C₂×C₄	—	6	1	no	—
405	C₂×C₄	—	6	1	no	—
406	C₂×C₄	—	6	1	no	—
407	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
408	C₈	—	2	1	no	—
409	C₈	—	6	1	no	—
410	C₂×C₃	—	2	1	no	—
411	C₂×C₃	—	2	1	no	—
412	C₂×C₃	—	2	1	no	—
413	C₂×C₃	—	4	2	no	—
414	C₂×C₃	—	4	2	no	—
415	C₂×C₃	—	6	2	no	—
416	C₂×C₃	—	8	2	no	—
417	C₂×C₃	—	12	2	no	—
418	C₂×C₃	C₉×#120	1	1	yes	characteristic
419	C₂×C₃	C₂×C₉×SD₁₆	1	1	yes	characteristic
420	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
421	C₂×C₃	C₃×D₃×SD₁₆	1	1	yes	characteristic
422	C₂×C₃	C₃×#914	1	1	yes	characteristic
423	C₂×C₃	C₃×#937	1	1	yes	characteristic
424	D₃	—	2	2	no	—
425	D₃	—	4	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	3	2	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	6	1	no	—
431	C₂²	—	6	1	no	—
432	C₂²	—	6	2	no	—
433	C₂²	—	12	8	no	—
434	C₂²	—	12	1	no	—
435	C₂²	—	12	1	no	—
436	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
437	C₄	—	4	1	no	—
438	C₄	—	6	1	no	—
439	C₄	—	12	1	no	—
440	C₄	D₃×D₄×C₉	1	1	yes	characteristic
441	C₄	C₂×C₉×#67	1	1	yes	characteristic
442	C₃	—	2	1	no	—
443	C₃	C₉×#450	1	1	yes	characteristic, complemented
444	C₃	C₃×#5169	1	1	yes	characteristic
445	C₂	—	4	2	no	—
446	C₂	—	6	2	no	—
447	C₂	—	12	2	no	—
448	C₂	D₃×C₉×SD₁₆	1	1	yes	characteristic
449	C₂	C₉×#914	1	1	yes	characteristic
450	C₂	C₉×#937	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₂×C₃×C₄	C₂³×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃×C₉×SD₁₆	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃×D₃×D₄	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₉×SD₁₆	D₃
hypocenter	C₃	C₉×#450
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₂×C₉×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₉×SD₁₆	C₂	semidirect
3. C₉×#946	C₂	semidirect
4. C₂×C₉×#215	C₂	semidirect
5. C₉×#832	C₂	semidirect
6. C₉×#821	C₂	semidirect
7. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
11. C₂×C₃×Q₈×C₉	C₂²	semidirect
19. C₂×C₃×C₈×C₉	C₂²	semidirect
22. C₉×C₄⋊Dic₃	C₂²	semidirect
24. C₂×C₉×C₃⋊C₈	C₂²	semidirect
35. C₂×C₉×SD₁₆	D₃	semidirect
62. #5169	C₉	direct (N × H)
80. C₂×Q₈×C₉	C₂×D₃	semidirect
93. C₂×C₈×C₉	C₂×D₃	semidirect
107. C₂×D₃×C₉	SD₁₆	semidirect
117. C₂×C₃×SD₁₆	C₂×C₉	semidirect
120. #946	C₂×C₉	semidirect
121. C₂×#215	C₂×C₉	semidirect
125. #832	C₂×C₉	semidirect
126. #821	C₂×C₉	semidirect
127. (C₂×D₃)⋊C₈	C₂×C₉	semidirect
188. C₂×C₃×Q₈	C₂²×C₉	semidirect
209. C₂×C₃×C₈	C₂²×C₉	semidirect
216. C₄⋊Dic₃	C₂²×C₉	semidirect
218. C₂×C₃⋊C₈	C₂²×C₉	semidirect
260. C₂×SD₁₆	D₃×C₉	semidirect
265. C₃×C₉	#450	semidirect
333. C₂×Q₈	C₂×D₃×C₉	semidirect
343. C₂×C₈	C₂×D₃×C₉	semidirect
372. C₂×D₃	C₉×SD₁₆	semidirect
388. C₉	#5169	direct (N × H)
443. C₃	C₉×#450	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×D₄×C₉	2
C₂×C₃×C₉×SD₁₆	2
C₉×#946	2
C₂×C₉×#215	2
C₉×#832	2
C₉×#821	2
C₉×(C₂×D₃)⋊C₈	2
C₃×#5169	3
C₉×#450	3

Subgroups — C9×#5169 #13143355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5169 #13143355