Subgroups — C₉×#4810 #13141897

Order 1728.

528 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#215	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#895	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#809	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4810	C₃	1	1	yes	maximal, characteristic
9	C₉×#449	—	3	1	no	maximal
10	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
11	C₉×#239	—	2	2	no	—
12	C₉×#239	—	2	2	no	—
13	C₂×C₉×D₁₂	—	2	1	no	—
14	C₂×C₉×D₁₂	—	2	1	no	—
15	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₃×C₉	—	2	1	no	—
18	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₉×#215	—	2	2	no	—
22	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
23	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₉×D₂₄	—	2	2	no	—
25	C₂×C₃×#239	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×#215	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×D₂₄	C₂×C₃	1	1	yes	characteristic
28	C₃×#895	C₂×C₃	1	1	yes	characteristic
29	C₂×C₉×#41	—	3	1	no	—
30	C₃²×#103	C₂×C₃	1	1	yes	characteristic
31	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic
32	C₃×#809	C₂×C₃	1	1	yes	characteristic
33	C₂×C₉×SD₁₆	—	3	1	no	—
34	C₂×C₉×D₈	—	3	1	no	—
35	C₉×#121	—	3	1	no	—
36	C₉×#103	—	2	1	no	—
37	C₉×#103	D₃	1	1	yes	characteristic, complemented
38	C₉×#102	—	3	1	no	—
39	C₉×C₂²⋊C₈	—	3	1	no	—
40	C₂²×D₃×C₉	—	2	1	no	—
41	C₂²×D₃×C₉	—	2	1	no	—
42	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
43	C₃×Q₈×C₉	—	2	1	no	—
44	C₃×Q₈×C₉	D₄	1	2	yes	complemented
45	C₂×C₃×C₄×C₉	—	2	1	no	—
46	C₂×C₃×C₄×C₉	—	2	1	no	—
47	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
48	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
49	C₉×D₁₂	—	2	4	no	—
50	C₉×D₁₂	—	2	1	no	—
51	C₉×D₁₂	—	2	1	no	—
52	C₉×D₁₂	—	2	1	no	—
53	C₉×D₁₂	—	4	2	no	—
54	C₉×D₁₂	D₄	1	2	yes	complemented
55	C₄×D₃×C₉	—	2	4	no	—
56	C₄×D₃×C₉	—	2	1	no	—
57	C₄×D₃×C₉	—	2	1	no	—
58	C₃×C₈×C₉	—	2	1	no	—
59	C₉×C₃⋊C₈	—	2	1	no	—
60	C₃×#449	—	3	1	no	—
61	#4810	C₉	1	1	yes	characteristic, direct product factor
62	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
63	C₃×#239	—	2	2	no	—
64	C₃×#239	—	2	2	no	—
65	C₂×C₃×D₁₂	—	2	1	no	—
66	C₂×C₃×D₁₂	—	2	1	no	—
67	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₃×C₄×D₃	—	2	1	no	—
70	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
72	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
73	C₃×#215	—	2	2	no	—
74	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
75	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
76	C₃×D₂₄	—	2	2	no	—
77	C₉×#41	—	6	2	no	—
78	C₉×#41	—	6	2	no	—
79	C₂×Q₈×C₉	—	2	1	no	—
80	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
81	C₂×D₄×C₉	—	3	1	no	—
82	C₂×D₄×C₉	—	3	1	no	—
83	C₂×D₄×C₉	—	6	1	no	—
84	C₂×D₄×C₉	—	6	1	no	—
85	C₂²×C₄×C₉	—	3	1	no	—
86	C₂²×C₄×C₉	—	6	1	no	—
87	C₉×SD₁₆	—	6	2	no	—
88	C₉×D₈	—	6	2	no	—
89	C₂×C₈×C₉	—	2	1	no	—
90	C₂×C₈×C₉	—	3	1	no	—
91	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
92	C₉×C₄⋊C₄	—	2	1	no	—
93	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
94	C₉×C₂²⋊C₄	—	6	1	no	—
95	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
96	C₂×D₃×C₉	—	2	1	no	—
97	C₂×D₃×C₉	—	2	2	no	—
98	C₂×D₃×C₉	—	2	1	no	—
99	C₂×D₃×C₉	—	2	1	no	—
100	C₂×D₃×C₉	—	4	1	no	—
101	C₂×D₃×C₉	—	4	1	no	—
102	C₂×D₃×C₉	—	4	1	no	—
103	C₂×D₃×C₉	—	4	1	no	—
104	C₂×D₃×C₉	—	4	1	no	—
105	C₃×C₄×C₉	—	2	2	no	—
106	C₃×C₄×C₉	—	4	1	no	—
107	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
108	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
109	C₉×Dic₃	—	2	1	no	—
110	C₂×C₃×#41	—	3	1	no	—
111	C₂×#239	C₂×C₉	1	1	yes	characteristic, complemented
112	C₂×C₃×SD₁₆	—	3	1	no	—
113	C₂×C₃×D₈	—	3	1	no	—
114	C₃×#121	—	3	1	no	—
115	C₂×#215	C₂×C₉	1	1	yes	characteristic, complemented
116	C₂×D₂₄	C₂×C₉	1	1	yes	characteristic, complemented
117	#895	C₂×C₉	1	1	yes	characteristic, complemented
118	C₃×#103	—	2	1	no	—
119	C₃×#103	C₂×C₉	1	1	yes	characteristic, complemented
120	C₃×#103	C₃×D₃	1	1	yes	characteristic
121	C₃×#102	—	3	1	no	—
122	C₃×C₂²⋊C₈	—	3	1	no	—
123	(C₂×D₃)⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
124	#809	C₂×C₉	1	1	yes	characteristic, complemented
125	C₂²×C₃×D₃	—	2	1	no	—
126	C₂²×C₃×D₃	—	2	1	no	—
127	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
128	C₃²×Q₈	—	2	1	no	—
129	C₃²×Q₈	C₃×D₄	1	2	yes	—
130	C₂×C₃²×C₄	—	2	1	no	—
131	C₂×C₃²×C₄	—	2	1	no	—
132	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
133	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
134	C₃×D₁₂	—	2	4	no	—
135	C₃×D₁₂	—	2	1	no	—
136	C₃×D₁₂	—	2	1	no	—
137	C₃×D₁₂	—	2	1	no	—
138	C₃×D₁₂	—	4	2	no	—
139	C₃×D₁₂	C₃×D₄	1	2	yes	—
140	C₃×C₄×D₃	—	2	4	no	—
141	C₃×C₄×D₃	—	2	1	no	—
142	C₃×C₄×D₃	—	2	1	no	—
143	C₂³×C₉	—	3	1	no	—
144	C₂³×C₉	—	6	1	no	—
145	C₂³×C₉	—	6	1	no	—
146	C₃²×C₈	—	2	1	no	—
147	C₃×C₃⋊C₈	—	2	1	no	—
148	Q₈×C₉	—	2	1	no	—
149	Q₈×C₉	—	2	2	no	—
150	Q₈×C₉	—	4	1	no	—
151	Q₈×C₉	D₁₂	1	2	yes	complemented
152	D₄×C₉	—	3	2	no	—
153	D₄×C₉	—	6	4	no	—
154	D₄×C₉	—	6	1	no	—
155	D₄×C₉	—	6	1	no	—
156	D₄×C₉	—	6	1	no	—
157	D₄×C₉	—	12	2	no	—
158	C₂×C₄×C₉	—	2	1	no	—
159	C₂×C₄×C₉	—	2	1	no	—
160	C₂×C₄×C₉	—	2	1	no	—
161	C₂×C₄×C₉	—	3	1	no	—
162	C₂×C₄×C₉	—	4	1	no	—
163	C₂×C₄×C₉	—	4	1	no	—
164	C₂×C₄×C₉	—	6	4	no	—
165	C₂×C₄×C₉	—	6	1	no	—
166	C₂×C₄×C₉	—	6	1	no	—
167	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
168	C₈×C₉	—	2	1	no	—
169	C₈×C₉	—	4	1	no	—
170	C₈×C₉	—	6	1	no	—
171	#449	—	3	1	no	Sylow
172	C₂×C₃×C₉	#120	1	1	yes	characteristic
173	C₂×C₃×C₉	#135	1	1	yes	characteristic
174	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
175	D₃×C₉	—	4	1	no	—
176	D₃×C₉	—	4	2	no	—
177	D₃×C₉	—	8	1	no	—
178	C₃×#41	—	6	2	no	—
179	C₃×#41	—	6	2	no	—
180	C₂×C₃×Q₈	—	2	1	no	—
181	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
182	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
183	C₂×C₃×D₄	—	3	1	no	—
184	C₂×C₃×D₄	—	3	1	no	—
185	C₂×C₃×D₄	—	6	1	no	—
186	C₂×C₃×D₄	—	6	1	no	—
187	C₂²×C₃×C₄	—	3	1	no	—
188	C₂²×C₃×C₄	—	6	1	no	—
189	#239	—	2	2	no	—
190	#239	—	2	2	no	—
191	C₂×D₁₂	—	2	1	no	—
192	C₂×D₁₂	—	2	1	no	—
193	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
194	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
195	C₂×C₄×D₃	—	2	1	no	—
196	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
197	C₃×SD₁₆	—	6	2	no	—
198	C₃×D₈	—	6	2	no	—
199	C₂×C₃×C₈	—	2	1	no	—
200	C₂×C₃×C₈	—	3	1	no	—
201	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
202	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
203	C₃×C₄⋊C₄	—	2	1	no	—
204	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
205	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
206	C₃×C₂²⋊C₄	—	6	1	no	—
207	#215	—	2	2	no	—
208	(C₂×D₃)⋊C₄	—	2	1	no	—
209	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
210	D₂₄	—	2	2	no	—
211	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
212	C₂×C₃×D₃	—	2	1	no	—
213	C₂×C₃×D₃	—	2	2	no	—
214	C₂×C₃×D₃	—	2	1	no	—
215	C₂×C₃×D₃	—	2	1	no	—
216	C₂×C₃×D₃	—	4	1	no	—
217	C₂×C₃×D₃	—	4	1	no	—
218	C₂×C₃×D₃	—	4	1	no	—
219	C₂×C₃×D₃	—	4	1	no	—
220	C₂×C₃×D₃	—	4	1	no	—
221	C₃²×C₄	—	2	2	no	—
222	C₃²×C₄	—	4	1	no	—
223	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
224	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
225	C₃×Dic₃	—	2	1	no	—
226	C₂²×C₉	—	2	1	no	—
227	C₂²×C₉	—	6	2	no	—
228	C₂²×C₉	—	6	1	no	—
229	C₂²×C₉	—	6	1	no	—
230	C₂²×C₉	—	6	1	no	—
231	C₂²×C₉	—	12	1	no	—
232	C₂²×C₉	—	12	1	no	—
233	C₂²×C₉	—	12	1	no	—
234	C₂²×C₉	—	12	1	no	—
235	C₂²×C₉	—	12	1	no	—
236	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
237	C₄×C₉	—	2	2	no	—
238	C₄×C₉	—	2	1	no	—
239	C₄×C₉	—	2	1	no	—
240	C₄×C₉	—	4	2	no	—
241	C₄×C₉	—	4	1	no	—
242	C₄×C₉	—	6	1	no	—
243	C₄×C₉	—	8	1	no	—
244	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
245	C₄×C₉	D₃×D₄	1	1	yes	characteristic
246	C₂×#41	—	3	1	no	—
247	C₂×SD₁₆	—	3	1	no	—
248	C₂×D₈	—	3	1	no	—
249	#121	—	3	1	no	—
250	#103	D₃×C₉	1	1	yes	characteristic, complemented
251	#102	—	3	1	no	—
252	C₂²⋊C₈	—	3	1	no	—
253	C₃×C₉	#449	1	1	yes	characteristic, complemented, Sylow
254	C₂³×C₃	—	3	1	no	—
255	C₂³×C₃	—	6	1	no	—
256	C₂³×C₃	—	6	1	no	—
257	C₂²×D₃	—	2	1	no	—
258	C₂²×D₃	—	2	1	no	—
259	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
260	C₃×Q₈	—	2	1	no	—
261	C₃×Q₈	—	2	1	no	—
262	C₃×Q₈	—	2	2	no	—
263	C₃×Q₈	—	4	1	no	—
264	C₃×Q₈	D₄×C₉	1	2	yes	complemented
265	C₃×Q₈	C₃×D₁₂	1	2	yes	—
266	C₃×D₄	—	3	2	no	—
267	C₃×D₄	—	6	4	no	—
268	C₃×D₄	—	6	1	no	—
269	C₃×D₄	—	6	1	no	—
270	C₃×D₄	—	6	1	no	—
271	C₃×D₄	—	12	2	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	3	1	no	—
278	C₂×C₃×C₄	—	4	1	no	—
279	C₂×C₃×C₄	—	4	1	no	—
280	C₂×C₃×C₄	—	6	4	no	—
281	C₂×C₃×C₄	—	6	1	no	—
282	C₂×C₃×C₄	—	6	1	no	—
283	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
285	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
286	D₁₂	—	2	4	no	—
287	D₁₂	—	2	1	no	—
288	D₁₂	—	2	1	no	—
289	D₁₂	—	2	1	no	—
290	D₁₂	—	4	2	no	—
291	D₁₂	D₄×C₉	1	2	yes	complemented
292	C₄×D₃	—	2	4	no	—
293	C₄×D₃	—	2	1	no	—
294	C₄×D₃	—	2	1	no	—
295	C₃×C₈	—	2	1	no	—
296	C₃×C₈	—	2	1	no	—
297	C₃×C₈	—	4	1	no	—
298	C₃×C₈	—	6	1	no	—
299	C₃⋊C₈	—	2	1	no	—
300	C₂×C₃²	C₃×#120	1	1	yes	characteristic
301	C₂×C₃²	C₃×#135	1	1	yes	characteristic
302	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
303	C₃×D₃	—	4	1	no	—
304	C₃×D₃	—	4	2	no	—
305	C₃×D₃	—	8	1	no	—
306	C₂×C₉	—	2	1	no	—
307	C₂×C₉	—	2	1	no	—
308	C₂×C₉	—	2	1	no	—
309	C₂×C₉	—	12	1	no	—
310	C₂×C₉	—	12	2	no	—
311	C₂×C₉	—	24	1	no	—
312	C₂×C₉	#882	1	1	yes	characteristic
313	C₂×C₉	#914	1	1	yes	characteristic
314	C₂×C₉	#919	1	1	yes	characteristic
315	#41	—	6	2	no	—
316	#41	—	6	2	no	—
317	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
318	C₂×D₄	—	3	1	no	—
319	C₂×D₄	—	3	1	no	—
320	C₂×D₄	—	6	1	no	—
321	C₂×D₄	—	6	1	no	—
322	C₂²×C₄	—	3	1	no	—
323	C₂²×C₄	—	6	1	no	—
324	SD₁₆	—	6	2	no	—
325	D₈	—	6	2	no	—
326	C₂×C₈	—	3	1	no	—
327	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
328	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
329	C₂²⋊C₄	—	6	1	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	6	2	no	—
332	C₂²×C₃	—	6	1	no	—
333	C₂²×C₃	—	6	1	no	—
334	C₂²×C₃	—	6	1	no	—
335	C₂²×C₃	—	12	1	no	—
336	C₂²×C₃	—	12	1	no	—
337	C₂²×C₃	—	12	1	no	—
338	C₂²×C₃	—	12	1	no	—
339	C₂²×C₃	—	12	1	no	—
340	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
341	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
342	C₂×D₃	—	2	1	no	—
343	C₂×D₃	—	2	2	no	—
344	C₂×D₃	—	2	1	no	—
345	C₂×D₃	—	2	1	no	—
346	C₂×D₃	—	4	1	no	—
347	C₂×D₃	—	4	1	no	—
348	C₂×D₃	—	4	1	no	—
349	C₂×D₃	—	4	1	no	—
350	C₂×D₃	—	4	1	no	—
351	C₃×C₄	—	2	2	no	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	4	2	no	—
356	C₃×C₄	—	4	1	no	—
357	C₃×C₄	—	4	1	no	—
358	C₃×C₄	—	6	1	no	—
359	C₃×C₄	—	8	1	no	—
360	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
361	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
362	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
363	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
364	Dic₃	—	2	1	no	—
365	C₃²	C₃×#449	1	1	yes	characteristic
366	C₉	—	2	1	no	—
367	C₉	#4810	1	1	yes	characteristic, direct product factor
368	C₂³	—	3	1	no	—
369	C₂³	—	6	1	no	—
370	C₂³	—	6	1	no	—
371	Q₈	—	2	1	no	—
372	Q₈	C₉×D₁₂	1	2	yes	complemented
373	D₄	—	3	2	no	—
374	D₄	—	6	4	no	—
375	D₄	—	6	1	no	—
376	D₄	—	6	1	no	—
377	D₄	—	6	1	no	—
378	D₄	—	12	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	3	1	no	—
382	C₂×C₄	—	6	4	no	—
383	C₂×C₄	—	6	1	no	—
384	C₂×C₄	—	6	1	no	—
385	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
386	C₈	—	2	1	no	—
387	C₈	—	6	1	no	—
388	C₂×C₃	—	2	1	no	—
389	C₂×C₃	—	2	1	no	—
390	C₂×C₃	—	2	1	no	—
391	C₂×C₃	—	12	1	no	—
392	C₂×C₃	—	12	2	no	—
393	C₂×C₃	—	24	1	no	—
394	C₂×C₃	C₉×#120	1	1	yes	characteristic
395	C₂×C₃	C₉×#135	1	1	yes	characteristic
396	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
397	C₂×C₃	C₃×#882	1	1	yes	characteristic
398	C₂×C₃	C₃×#914	1	1	yes	characteristic
399	C₂×C₃	C₃×#919	1	1	yes	characteristic
400	D₃	—	4	1	no	—
401	D₃	—	4	2	no	—
402	D₃	—	8	1	no	—
403	C₂²	—	6	1	no	—
404	C₂²	—	6	1	no	—
405	C₂²	—	6	2	no	—
406	C₂²	—	6	1	no	—
407	C₂²	—	12	1	no	—
408	C₂²	—	12	1	no	—
409	C₂²	—	12	1	no	—
410	C₂²	—	12	1	no	—
411	C₂²	—	12	1	no	—
412	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	6	1	no	—
416	C₄	C₂×C₉×D₁₂	1	1	yes	characteristic
417	C₄	D₃×D₄×C₉	1	1	yes	characteristic
418	C₃	—	2	1	no	—
419	C₃	C₉×#449	1	1	yes	characteristic, complemented
420	C₃	C₃×#4810	1	1	yes	characteristic
421	C₂	—	12	1	no	—
422	C₂	—	12	2	no	—
423	C₂	—	24	1	no	—
424	C₂	C₉×#882	1	1	yes	characteristic
425	C₂	C₉×#914	1	1	yes	characteristic
426	C₂	C₉×#919	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	C₃×C₉×#103	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₃×#4810	C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#103	D₃
hypocenter	C₃	C₉×#449
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#103

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#239	C₂	semidirect
2. C₂×C₉×#215	C₂	semidirect
3. C₂×C₉×D₂₄	C₂	semidirect
4. C₉×#895	C₂	semidirect
5. C₃×C₉×#103	C₂	semidirect
6. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
7. C₉×#809	C₂	semidirect
37. C₉×#103	D₃	semidirect
44. C₃×Q₈×C₉	D₄	semidirect
54. C₉×D₁₂	D₄	semidirect
61. #4810	C₉	direct (N × H)
111. C₂×#239	C₂×C₉	semidirect
115. C₂×#215	C₂×C₉	semidirect
116. C₂×D₂₄	C₂×C₉	semidirect
117. #895	C₂×C₉	semidirect
119. C₃×#103	C₂×C₉	semidirect
123. (C₂×D₃)⋊C₈	C₂×C₉	semidirect
124. #809	C₂×C₉	semidirect
151. Q₈×C₉	D₁₂	semidirect
250. #103	D₃×C₉	semidirect
253. C₃×C₉	#449	semidirect
264. C₃×Q₈	D₄×C₉	semidirect
291. D₁₂	D₄×C₉	semidirect
367. C₉	#4810	direct (N × H)
372. Q₈	C₉×D₁₂	semidirect
419. C₃	C₉×#449	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#239	2
C₂×C₉×#215	2
C₂×C₉×D₂₄	2
C₉×#895	2
C₃×C₉×#103	2
C₉×(C₂×D₃)⋊C₈	2
C₉×#809	2
C₃×#4810	3
C₉×#449	3

Subgroups — C9×#4810 #13141897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4810 #13141897