Subgroups — C₉×#3063 #11767784

Order 1152.

708 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#537	C₂	1	1	yes	maximal, characteristic
4	C₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#470	C₂	1	2	yes	maximal, complemented
6	C₉×#468	C₂	1	2	yes	maximal, complemented
7	C₉×#467	C₂	1	2	yes	maximal, complemented
8	C₉×#465	C₂	1	2	yes	maximal, complemented
9	C₉×#428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#416	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3063	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic
14	C₂×C₉×#41	C₂²	1	1	yes	characteristic
15	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
16	C₉×#137	—	2	4	no	—
17	C₂×C₉×Q₁₆	C₂²	1	2	yes	—
18	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
19	C₉×#131	—	2	4	no	—
20	C₂×C₉×M₁₆	C₂²	1	2	yes	—
21	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
23	C₂²×C₈×C₉	C₂²	1	2	yes	—
24	C₉×C₄⋊Q₈	—	2	1	no	—
25	C₉×#124	—	2	1	no	—
26	C₉×#123	—	2	2	no	—
27	C₉×C₂²⋊Q₈	—	2	1	no	—
28	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₉×#121	—	2	1	no	—
32	C₉×#121	—	2	2	no	—
33	C₉×#121	C₂²	1	2	yes	—
34	C₉×#117	C₂²	1	1	yes	characteristic
35	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₉×#107	C₂²	1	2	yes	—
37	C₉×#106	C₂²	1	2	yes	—
38	C₉×#103	C₂²	1	2	yes	—
39	C₉×#103	C₂²	1	2	yes	—
40	C₉×#103	C₂²	1	1	yes	characteristic
41	C₉×#103	C₂²	1	1	yes	characteristic
42	C₉×#102	C₂²	1	1	yes	characteristic
43	C₉×#102	C₂²	1	1	yes	characteristic
44	C₂×C₃×#137	C₂×C₃	1	1	yes	characteristic
45	C₂×C₃×#131	C₂×C₃	1	1	yes	characteristic
46	C₃×#537	C₂×C₃	1	1	yes	characteristic
47	C₃×#536	C₂×C₃	1	1	yes	characteristic
48	C₃×#470	C₂×C₃	1	2	yes	—
49	C₃×#468	C₂×C₃	1	2	yes	—
50	C₃×#467	C₂×C₃	1	2	yes	—
51	C₃×#465	C₂×C₃	1	2	yes	—
52	C₃×#428	C₂×C₃	1	1	yes	characteristic
53	C₃×#416	C₂×C₃	1	1	yes	characteristic
54	C₂×C₃×#103	C₂×C₃	1	1	yes	characteristic
55	C₉×#41	—	2	2	no	—
56	C₉×#41	—	2	2	no	—
57	C₉×#41	—	2	2	no	—
58	C₉×#41	—	2	2	no	—
59	C₂×Q₈×C₉	—	2	1	no	—
60	C₂×Q₈×C₉	—	2	2	no	—
61	C₂×Q₈×C₉	—	2	2	no	—
62	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
63	C₂×Q₈×C₉	C₂³	1	2	yes	—
64	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
65	C₂×D₄×C₉	—	2	1	no	—
66	C₂×D₄×C₉	—	2	2	no	—
67	C₂×D₄×C₉	D₄	1	2	yes	—
68	C₂×D₄×C₉	D₄	1	1	yes	characteristic
69	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₉	—	2	1	no	—
71	C₂²×C₄×C₉	—	2	1	no	—
72	C₂²×C₄×C₉	—	2	1	no	—
73	C₂²×C₄×C₉	C₂³	1	2	yes	—
74	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₉×Q₁₆	—	2	4	no	—
76	C₉×SD₁₆	—	2	4	no	—
77	C₉×M₁₆	—	2	4	no	—
78	C₉×M₁₆	D₄	1	4	yes	complemented
79	C₂×C₈×C₉	—	2	2	no	—
80	C₂×C₈×C₉	—	2	4	no	—
81	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
82	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
83	C₂×C₈×C₉	C₂³	1	2	yes	—
84	C₉×C₄⋊C₄	—	2	1	no	—
85	C₉×C₄⋊C₄	—	2	2	no	—
86	C₉×C₄⋊C₄	—	2	2	no	—
87	C₉×C₄⋊C₄	—	2	2	no	—
88	C₉×C₄⋊C₄	C₂³	1	2	yes	—
89	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₉×C₂²⋊C₄	—	2	1	no	—
92	C₉×C₂²⋊C₄	—	2	2	no	—
93	C₉×C₂²⋊C₄	—	2	2	no	—
94	C₉×C₂²⋊C₄	—	2	2	no	—
95	C₉×C₂²⋊C₄	—	2	2	no	—
96	C₄²×C₉	—	2	1	no	—
97	#3063	C₉	1	1	yes	characteristic, direct product factor, Sylow
98	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
100	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
101	C₃×#137	—	2	4	no	—
102	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
103	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
104	C₃×#131	—	2	4	no	—
105	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
106	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
107	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
109	C₃×C₄⋊Q₈	—	2	1	no	—
110	C₃×#124	—	2	1	no	—
111	C₃×#123	—	2	2	no	—
112	C₃×C₂²⋊Q₈	—	2	1	no	—
113	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
114	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
115	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
116	C₃×#121	—	2	1	no	—
117	C₃×#121	—	2	2	no	—
118	C₃×#121	C₂²×C₃	1	2	yes	—
119	C₃×#117	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₃×#107	C₂²×C₃	1	2	yes	—
122	C₃×#106	C₂²×C₃	1	2	yes	—
123	C₃×#103	C₂²×C₃	1	2	yes	—
124	C₃×#103	C₂²×C₃	1	2	yes	—
125	C₃×#103	C₂²×C₃	1	1	yes	characteristic
126	C₃×#103	C₂²×C₃	1	1	yes	characteristic
127	C₃×#102	C₂²×C₃	1	1	yes	characteristic
128	C₃×#102	C₂²×C₃	1	1	yes	characteristic
129	C₂³×C₉	—	2	1	no	—
130	C₂³×C₉	C₂×D₄	1	2	yes	—
131	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
132	Q₈×C₉	—	2	2	no	—
133	Q₈×C₉	—	2	2	no	—
134	Q₈×C₉	—	2	1	no	—
135	Q₈×C₉	—	2	2	no	—
136	Q₈×C₉	—	2	1	no	—
137	Q₈×C₉	—	4	2	no	—
138	D₄×C₉	—	2	4	no	—
139	D₄×C₉	—	2	2	no	—
140	D₄×C₉	—	2	1	no	—
141	D₄×C₉	—	2	1	no	—
142	D₄×C₉	—	4	2	no	—
143	D₄×C₉	—	8	2	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	2	2	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	2	2	no	—
149	C₂×C₄×C₉	—	2	1	no	—
150	C₂×C₄×C₉	—	2	2	no	—
151	C₂×C₄×C₉	—	4	2	no	—
152	C₂×C₄×C₉	—	4	2	no	—
153	C₂×C₄×C₉	—	8	1	no	—
154	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
155	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
157	C₂×C₄×C₉	#41	1	2	yes	—
158	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
159	C₈×C₉	—	2	1	no	—
160	C₈×C₉	—	2	1	no	—
161	C₈×C₉	C₂×D₄	1	4	yes	—
162	C₂×#137	C₂×C₉	1	1	yes	characteristic, complemented
163	C₂×#131	C₂×C₉	1	1	yes	characteristic, complemented
164	#537	C₂×C₉	1	1	yes	characteristic
165	#536	C₂×C₉	1	1	yes	characteristic, complemented
166	#470	C₂×C₉	1	2	yes	complemented
167	#468	C₂×C₉	1	2	yes	complemented
168	#467	C₂×C₉	1	2	yes	complemented
169	#465	C₂×C₉	1	2	yes	complemented
170	#428	C₂×C₉	1	1	yes	characteristic, complemented
171	#416	C₂×C₉	1	1	yes	characteristic, complemented
172	C₂×#103	C₂×C₉	1	1	yes	characteristic, complemented
173	C₃×#41	—	2	2	no	—
174	C₃×#41	—	2	2	no	—
175	C₃×#41	—	2	2	no	—
176	C₃×#41	—	2	2	no	—
177	C₂×C₃×Q₈	—	2	1	no	—
178	C₂×C₃×Q₈	—	2	2	no	—
179	C₂×C₃×Q₈	—	2	2	no	—
180	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
181	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
182	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₃×D₄	—	2	1	no	—
184	C₂×C₃×D₄	—	2	2	no	—
185	C₂×C₃×D₄	C₃×D₄	1	2	yes	—
186	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
187	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
188	C₂²×C₃×C₄	—	2	1	no	—
189	C₂²×C₃×C₄	—	2	1	no	—
190	C₂²×C₃×C₄	—	2	1	no	—
191	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
192	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
193	C₃×Q₁₆	—	2	4	no	—
194	C₃×SD₁₆	—	2	4	no	—
195	C₃×M₁₆	—	2	4	no	—
196	C₃×M₁₆	C₃×D₄	1	4	yes	—
197	C₂×C₃×C₈	—	2	2	no	—
198	C₂×C₃×C₈	—	2	4	no	—
199	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
200	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
202	C₃×C₄⋊C₄	—	2	1	no	—
203	C₃×C₄⋊C₄	—	2	2	no	—
204	C₃×C₄⋊C₄	—	2	2	no	—
205	C₃×C₄⋊C₄	—	2	2	no	—
206	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
207	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
208	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
209	C₃×C₂²⋊C₄	—	2	1	no	—
210	C₃×C₂²⋊C₄	—	2	2	no	—
211	C₃×C₂²⋊C₄	—	2	2	no	—
212	C₃×C₂²⋊C₄	—	2	2	no	—
213	C₃×C₂²⋊C₄	—	2	2	no	—
214	C₃×C₄²	—	2	1	no	—
215	C₂²×C₉	—	2	1	no	—
216	C₂²×C₉	—	2	1	no	—
217	C₂²×C₉	—	2	2	no	—
218	C₂²×C₉	—	2	2	no	—
219	C₂²×C₉	—	2	2	no	—
220	C₂²×C₉	—	4	1	no	—
221	C₂²×C₉	—	4	1	no	—
222	C₂²×C₉	—	4	1	no	—
223	C₂²×C₉	#121	1	2	yes	—
224	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
225	C₄×C₉	—	2	2	no	—
226	C₄×C₉	—	4	1	no	—
227	C₄×C₉	—	4	2	no	—
228	C₄×C₉	—	4	1	no	—
229	C₄×C₉	—	4	2	no	—
230	C₄×C₉	—	4	1	no	—
231	C₄×C₉	#121	1	2	yes	—
232	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
233	C₄×C₉	C₂×#41	1	1	yes	characteristic
234	C₂×#41	C₂²×C₉	1	1	yes	characteristic
235	C₂×#41	C₂²×C₉	1	1	yes	characteristic
236	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
237	#137	—	2	4	no	—
238	C₂×Q₁₆	C₂²×C₉	1	2	yes	—
239	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
240	#131	—	2	4	no	—
241	C₂×M₁₆	C₂²×C₉	1	2	yes	—
242	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
243	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
244	C₂²×C₈	C₂²×C₉	1	2	yes	—
245	C₄⋊Q₈	—	2	1	no	—
246	#124	—	2	1	no	—
247	#123	—	2	2	no	—
248	C₂²⋊Q₈	—	2	1	no	—
249	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
250	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
251	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
252	#121	—	2	1	no	—
253	#121	—	2	2	no	—
254	#121	C₂²×C₉	1	2	yes	—
255	#117	C₂²×C₉	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
257	#107	C₂²×C₉	1	2	yes	—
258	#106	C₂²×C₉	1	2	yes	—
259	#103	C₂²×C₉	1	2	yes	—
260	#103	C₂²×C₉	1	2	yes	—
261	#103	C₂²×C₉	1	1	yes	characteristic
262	#103	C₂²×C₉	1	1	yes	characteristic
263	#102	C₂²×C₉	1	1	yes	characteristic
264	#102	C₂²×C₉	1	1	yes	characteristic
265	C₂³×C₃	—	2	1	no	—
266	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
267	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
268	C₃×Q₈	—	2	2	no	—
269	C₃×Q₈	—	2	2	no	—
270	C₃×Q₈	—	2	1	no	—
271	C₃×Q₈	—	2	2	no	—
272	C₃×Q₈	—	2	1	no	—
273	C₃×Q₈	—	4	2	no	—
274	C₃×D₄	—	2	4	no	—
275	C₃×D₄	—	2	2	no	—
276	C₃×D₄	—	2	1	no	—
277	C₃×D₄	—	2	1	no	—
278	C₃×D₄	—	4	2	no	—
279	C₃×D₄	—	8	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	4	2	no	—
288	C₂×C₃×C₄	—	4	2	no	—
289	C₂×C₃×C₄	—	8	1	no	—
290	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
291	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
293	C₂×C₃×C₄	C₃×#41	1	2	yes	—
294	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
295	C₃×C₈	—	2	1	no	—
296	C₃×C₈	—	2	1	no	—
297	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
298	C₂×C₉	—	2	2	no	—
299	C₂×C₉	—	4	2	no	—
300	C₂×C₉	—	8	1	no	—
301	C₂×C₉	C₂×#121	1	1	yes	characteristic
302	C₂×C₉	#577	1	1	yes	characteristic
303	C₂×C₉	#578	1	1	yes	characteristic
304	#41	—	2	2	no	—
305	#41	—	2	2	no	—
306	#41	—	2	2	no	—
307	#41	—	2	2	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
312	C₂×Q₈	C₂³×C₉	1	2	yes	—
313	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	D₄×C₉	1	2	yes	—
317	C₂×D₄	D₄×C₉	1	1	yes	characteristic
318	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	C₂³×C₉	1	2	yes	—
323	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
324	Q₁₆	—	2	4	no	—
325	SD₁₆	—	2	4	no	—
326	M₁₆	—	2	4	no	—
327	M₁₆	D₄×C₉	1	4	yes	complemented
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	4	no	—
330	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
331	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
332	C₂×C₈	C₂³×C₉	1	2	yes	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
338	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
339	C₄⋊C₄	C₂³×C₉	1	2	yes	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₄²	—	2	1	no	—
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	2	2	no	—
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	4	1	no	—
352	C₂²×C₃	—	4	1	no	—
353	C₂²×C₃	—	4	1	no	—
354	C₂²×C₃	C₃×#121	1	2	yes	—
355	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
356	C₃×C₄	—	2	2	no	—
357	C₃×C₄	—	4	2	no	—
358	C₃×C₄	—	4	1	no	—
359	C₃×C₄	—	4	1	no	—
360	C₃×C₄	—	4	1	no	—
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	C₃×#121	1	2	yes	—
363	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
364	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
365	C₉	#3063	1	1	yes	characteristic, direct product factor, Sylow
366	C₂³	—	2	1	no	—
367	C₂³	C₂×D₄×C₉	1	2	yes	—
368	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
369	Q₈	—	2	2	no	—
370	Q₈	—	2	2	no	—
371	Q₈	—	2	1	no	—
372	Q₈	—	2	2	no	—
373	Q₈	—	2	1	no	—
374	Q₈	—	4	2	no	—
375	D₄	—	2	4	no	—
376	D₄	—	2	2	no	—
377	D₄	—	2	1	no	—
378	D₄	—	2	1	no	—
379	D₄	—	4	2	no	—
380	D₄	—	8	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
392	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
394	C₂×C₄	C₉×#41	1	2	yes	—
395	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	C₂×D₄×C₉	1	4	yes	—
399	C₂×C₃	—	2	2	no	—
400	C₂×C₃	—	4	2	no	—
401	C₂×C₃	—	8	1	no	—
402	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
403	C₂×C₃	C₃×#577	1	1	yes	characteristic
404	C₂×C₃	C₃×#578	1	1	yes	characteristic
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	C₉×#121	1	2	yes	—
414	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	C₉×#121	1	2	yes	—
422	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
423	C₄	C₂×C₉×#41	1	1	yes	characteristic
424	C₃	C₃×#3063	1	1	yes	characteristic
425	C₂	—	2	2	no	—
426	C₂	—	4	2	no	—
427	C₂	—	8	1	no	—
428	C₂	C₂×C₉×#121	1	1	yes	characteristic
429	C₂	C₉×#577	1	1	yes	characteristic
430	C₂	C₉×#578	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#537	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#137	C₂	semidirect
2. C₂×C₉×#131	C₂	semidirect
4. C₉×#536	C₂	semidirect
5. C₉×#470	C₂	semidirect
6. C₉×#468	C₂	semidirect
7. C₉×#467	C₂	semidirect
8. C₉×#465	C₂	semidirect
9. C₉×#428	C₂	semidirect
10. C₉×#416	C₂	semidirect
11. C₂×C₉×#103	C₂	semidirect
78. C₉×M₁₆	D₄	semidirect
97. #3063	C₉	direct (N × H)
162. C₂×#137	C₂×C₉	semidirect
163. C₂×#131	C₂×C₉	semidirect
165. #536	C₂×C₉	semidirect
166. #470	C₂×C₉	semidirect
167. #468	C₂×C₉	semidirect
168. #467	C₂×C₉	semidirect
169. #465	C₂×C₉	semidirect
170. #428	C₂×C₉	semidirect
171. #416	C₂×C₉	semidirect
172. C₂×#103	C₂×C₉	semidirect
327. M₁₆	D₄×C₉	semidirect
365. C₉	#3063	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×#137	2
C₂×C₉×#131	2
C₉×#537	2
C₉×#536	2
C₉×#470	2
C₉×#468	2
C₉×#467	2
C₉×#465	2
C₉×#428	2
C₉×#416	2
C₂×C₉×#103	2
C₃×#3063	3

Subgroups — C9×#3063 #11767784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3063 #11767784