Subgroups — C₉×#3219 #11767940

Order 1152.

594 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#491	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#464	C₂	1	2	yes	maximal, complemented
8	C₉×#463	C₂	1	2	yes	maximal, complemented
9	C₉×#452	C₂	1	2	yes	maximal, complemented
10	C₉×#449	C₂	1	2	yes	maximal, complemented
11	C₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3219	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	2	yes	—
14	C₂×C₉×Q₁₆	C₂²	1	2	yes	—
15	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
17	C₂×C₉×D₈	C₂²	1	2	yes	—
18	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₉×#127	C₂²	1	1	yes	characteristic
20	C₉×#126	—	2	1	no	—
21	C₉×#125	C₂²	1	1	yes	characteristic
22	C₉×#124	C₂²	1	1	yes	characteristic
23	C₉×#124	C₂²	1	2	yes	—
24	C₉×#123	—	2	1	no	—
25	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₉×#121	—	2	1	no	—
27	C₉×#121	—	2	1	no	—
28	C₉×#121	C₂²	1	1	yes	characteristic
29	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
30	C₄×D₄×C₉	—	2	1	no	—
31	C₄×D₄×C₉	—	2	1	no	—
32	C₄×D₄×C₉	—	2	1	no	—
33	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
34	C₉×#117	—	2	1	no	—
35	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
36	C₉×C₄⋊C₈	C₂²	1	2	yes	—
37	C₉×#103	C₂²	1	2	yes	—
38	C₉×#103	C₂²	1	2	yes	—
39	C₉×#102	C₂²	1	2	yes	—
40	C₉×#102	C₂²	1	2	yes	—
41	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
42	C₉×#97	C₂²	1	1	yes	characteristic
43	C₉×#97	C₂²	1	1	yes	characteristic
44	C₃×#532	C₂×C₃	1	1	yes	characteristic
45	C₃×#529	C₂×C₃	1	1	yes	characteristic
46	C₃×#497	C₂×C₃	1	1	yes	characteristic
47	C₃×#496	C₂×C₃	1	1	yes	characteristic
48	C₃×#491	C₂×C₃	1	1	yes	characteristic
49	C₃×#490	C₂×C₃	1	1	yes	characteristic
50	C₃×#464	C₂×C₃	1	2	yes	—
51	C₃×#463	C₂×C₃	1	2	yes	—
52	C₃×#452	C₂×C₃	1	2	yes	—
53	C₃×#449	C₂×C₃	1	2	yes	—
54	C₃×#432	C₂×C₃	1	1	yes	characteristic
55	C₉×#41	—	4	2	no	—
56	C₉×#41	—	4	2	no	—
57	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
58	C₂×Q₈×C₉	C₂³	1	2	yes	—
59	C₂×D₄×C₉	—	2	1	no	—
60	C₂×D₄×C₉	—	2	2	no	—
61	C₂×D₄×C₉	—	2	1	no	—
62	C₂×D₄×C₉	—	2	1	no	—
63	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₉	C₂³	1	2	yes	—
65	C₂²×C₄×C₉	—	2	1	no	—
66	C₂²×C₄×C₉	—	2	2	no	—
67	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
68	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
69	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₉×Q₁₆	—	4	2	no	—
71	C₉×SD₁₆	—	4	2	no	—
72	C₉×SD₁₆	—	4	2	no	—
73	C₉×D₈	—	4	2	no	—
74	C₂×C₈×C₉	C₂³	1	2	yes	—
75	C₂×C₈×C₉	C₂³	1	2	yes	—
76	C₉×C₄⋊C₄	—	2	1	no	—
77	C₉×C₄⋊C₄	—	2	1	no	—
78	C₉×C₄⋊C₄	—	2	1	no	—
79	C₉×C₄⋊C₄	—	2	1	no	—
80	C₉×C₄⋊C₄	—	2	1	no	—
81	C₉×C₄⋊C₄	—	2	1	no	—
82	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₉×C₂²⋊C₄	—	2	1	no	—
85	C₉×C₂²⋊C₄	—	2	1	no	—
86	C₉×C₂²⋊C₄	—	2	1	no	—
87	C₉×C₂²⋊C₄	—	2	2	no	—
88	C₉×C₂²⋊C₄	—	2	2	no	—
89	C₉×C₂²⋊C₄	—	2	1	no	—
90	C₉×C₂²⋊C₄	—	2	1	no	—
91	C₄²×C₉	—	2	1	no	—
92	C₄²×C₉	D₄	1	1	yes	characteristic
93	C₄²×C₉	D₄	1	1	yes	characteristic
94	C₄²×C₉	C₂³	1	1	yes	characteristic
95	C₄²×C₉	C₂³	1	1	yes	characteristic
96	#3219	C₉	1	1	yes	characteristic, direct product factor, Sylow
97	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
98	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
99	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
100	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
101	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
102	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
103	C₃×#127	C₂²×C₃	1	1	yes	characteristic
104	C₃×#126	—	2	1	no	—
105	C₃×#125	C₂²×C₃	1	1	yes	characteristic
106	C₃×#124	C₂²×C₃	1	2	yes	—
107	C₃×#124	C₂²×C₃	1	1	yes	characteristic
108	C₃×#123	—	2	1	no	—
109	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
110	C₃×#121	—	2	1	no	—
111	C₃×#121	—	2	1	no	—
112	C₃×#121	C₂²×C₃	1	1	yes	characteristic
113	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
114	C₃×C₄×D₄	—	2	1	no	—
115	C₃×C₄×D₄	—	2	1	no	—
116	C₃×C₄×D₄	—	2	1	no	—
117	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
118	C₃×#117	—	2	1	no	—
119	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
120	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
121	C₃×#103	C₂²×C₃	1	2	yes	—
122	C₃×#103	C₂²×C₃	1	2	yes	—
123	C₃×#102	C₂²×C₃	1	2	yes	—
124	C₃×#102	C₂²×C₃	1	2	yes	—
125	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
126	C₃×#97	C₂²×C₃	1	1	yes	characteristic
127	C₃×#97	C₂²×C₃	1	1	yes	characteristic
128	C₂³×C₉	—	2	1	no	—
129	C₂³×C₉	—	2	2	no	—
130	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
131	Q₈×C₉	—	2	2	no	—
132	Q₈×C₉	—	2	2	no	—
133	Q₈×C₉	—	2	2	no	—
134	D₄×C₉	—	2	2	no	—
135	D₄×C₉	—	2	2	no	—
136	D₄×C₉	—	2	2	no	—
137	D₄×C₉	—	4	2	no	—
138	D₄×C₉	—	4	2	no	—
139	D₄×C₉	—	4	2	no	—
140	D₄×C₉	—	4	4	no	—
141	C₂×C₄×C₉	—	2	2	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	2	no	—
146	C₂×C₄×C₉	—	4	1	no	—
147	C₂×C₄×C₉	—	4	1	no	—
148	C₂×C₄×C₉	—	4	2	no	—
149	C₂×C₄×C₉	—	4	4	no	—
150	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
156	C₈×C₉	—	2	2	no	—
157	C₈×C₉	—	2	2	no	—
158	#532	C₂×C₉	1	1	yes	characteristic, complemented
159	#529	C₂×C₉	1	1	yes	characteristic, complemented
160	#497	C₂×C₉	1	1	yes	characteristic, complemented
161	#496	C₂×C₉	1	1	yes	characteristic, complemented
162	#491	C₂×C₉	1	1	yes	characteristic, complemented
163	#490	C₂×C₉	1	1	yes	characteristic, complemented
164	#464	C₂×C₉	1	2	yes	complemented
165	#463	C₂×C₉	1	2	yes	complemented
166	#452	C₂×C₉	1	2	yes	complemented
167	#449	C₂×C₉	1	2	yes	complemented
168	#432	C₂×C₉	1	1	yes	characteristic, complemented
169	C₃×#41	—	4	2	no	—
170	C₃×#41	—	4	2	no	—
171	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
172	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
173	C₂×C₃×D₄	—	2	1	no	—
174	C₂×C₃×D₄	—	2	2	no	—
175	C₂×C₃×D₄	—	2	1	no	—
176	C₂×C₃×D₄	—	2	1	no	—
177	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
178	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₂²×C₃×C₄	—	2	2	no	—
181	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
184	C₃×Q₁₆	—	4	2	no	—
185	C₃×SD₁₆	—	4	2	no	—
186	C₃×SD₁₆	—	4	2	no	—
187	C₃×D₈	—	4	2	no	—
188	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
189	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
190	C₃×C₄⋊C₄	—	2	1	no	—
191	C₃×C₄⋊C₄	—	2	1	no	—
192	C₃×C₄⋊C₄	—	2	1	no	—
193	C₃×C₄⋊C₄	—	2	1	no	—
194	C₃×C₄⋊C₄	—	2	1	no	—
195	C₃×C₄⋊C₄	—	2	1	no	—
196	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
197	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
198	C₃×C₂²⋊C₄	—	2	1	no	—
199	C₃×C₂²⋊C₄	—	2	1	no	—
200	C₃×C₂²⋊C₄	—	2	1	no	—
201	C₃×C₂²⋊C₄	—	2	2	no	—
202	C₃×C₂²⋊C₄	—	2	2	no	—
203	C₃×C₂²⋊C₄	—	2	1	no	—
204	C₃×C₂²⋊C₄	—	2	1	no	—
205	C₃×C₄²	—	2	1	no	—
206	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
207	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
208	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
209	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
210	C₂²×C₉	—	2	1	no	—
211	C₂²×C₉	—	2	1	no	—
212	C₂²×C₉	—	2	1	no	—
213	C₂²×C₉	—	4	2	no	—
214	C₂²×C₉	—	4	1	no	—
215	C₂²×C₉	—	4	1	no	—
216	C₂²×C₉	—	4	2	no	—
217	C₂²×C₉	—	4	2	no	—
218	C₂²×C₉	—	4	1	no	—
219	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
220	C₄×C₉	—	2	1	no	—
221	C₄×C₉	—	2	1	no	—
222	C₄×C₉	—	2	1	no	—
223	C₄×C₉	—	2	1	no	—
224	C₄×C₉	—	2	1	no	—
225	C₄×C₉	—	4	2	no	—
226	C₄×C₉	—	4	1	no	—
227	C₄×C₉	—	4	1	no	—
228	C₄×C₉	—	4	1	no	—
229	C₄×C₉	H(5,𝔽₂)	1	2	yes	—
230	C₂×#41	C₂²×C₉	1	2	yes	—
231	C₂×Q₁₆	C₂²×C₉	1	2	yes	—
232	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
233	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
234	C₂×D₈	C₂²×C₉	1	2	yes	—
235	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
236	#127	C₂²×C₉	1	1	yes	characteristic
237	#126	—	2	1	no	—
238	#125	C₂²×C₉	1	1	yes	characteristic
239	#124	C₂²×C₉	1	1	yes	characteristic
240	#124	C₂²×C₉	1	2	yes	—
241	#123	—	2	1	no	—
242	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
243	#121	—	2	1	no	—
244	#121	—	2	1	no	—
245	#121	C₂²×C₉	1	1	yes	characteristic
246	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
251	#117	—	2	1	no	—
252	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
253	C₄⋊C₈	C₂²×C₉	1	2	yes	—
254	#103	C₂²×C₉	1	2	yes	—
255	#103	C₂²×C₉	1	2	yes	—
256	#102	C₂²×C₉	1	2	yes	—
257	#102	C₂²×C₉	1	2	yes	—
258	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
259	#97	C₂²×C₉	1	1	yes	characteristic
260	#97	C₂²×C₉	1	1	yes	characteristic
261	C₂³×C₃	—	2	1	no	—
262	C₂³×C₃	—	2	2	no	—
263	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
264	C₃×Q₈	—	2	2	no	—
265	C₃×Q₈	—	2	2	no	—
266	C₃×Q₈	—	2	2	no	—
267	C₃×D₄	—	2	2	no	—
268	C₃×D₄	—	2	2	no	—
269	C₃×D₄	—	2	2	no	—
270	C₃×D₄	—	4	2	no	—
271	C₃×D₄	—	4	2	no	—
272	C₃×D₄	—	4	2	no	—
273	C₃×D₄	—	4	4	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	4	1	no	—
280	C₂×C₃×C₄	—	4	1	no	—
281	C₂×C₃×C₄	—	4	2	no	—
282	C₂×C₃×C₄	—	4	4	no	—
283	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
289	C₃×C₈	—	2	2	no	—
290	C₃×C₈	—	2	2	no	—
291	C₂×C₉	—	4	1	no	—
292	C₂×C₉	—	8	2	no	—
293	C₂×C₉	—	8	1	no	—
294	C₂×C₉	#535	1	1	yes	characteristic
295	C₂×C₉	#575	1	1	yes	characteristic
296	C₂×C₉	#575	1	1	yes	characteristic
297	#41	—	4	2	no	—
298	#41	—	4	2	no	—
299	C₂×Q₈	C₂³×C₉	1	2	yes	—
300	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	C₂³×C₉	1	2	yes	—
306	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
310	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
311	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
312	Q₁₆	—	4	2	no	—
313	SD₁₆	—	4	2	no	—
314	SD₁₆	—	4	2	no	—
315	D₈	—	4	2	no	—
316	C₂×C₈	C₂³×C₉	1	2	yes	—
317	C₂×C₈	C₂³×C₉	1	2	yes	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
325	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
326	C₂²⋊C₄	—	2	1	no	—
327	C₂²⋊C₄	—	2	1	no	—
328	C₂²⋊C₄	—	2	1	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	D₄×C₉	1	1	yes	characteristic
335	C₄²	D₄×C₉	1	1	yes	characteristic
336	C₄²	C₂³×C₉	1	1	yes	characteristic
337	C₄²	C₂³×C₉	1	1	yes	characteristic
338	C₂²×C₃	—	2	1	no	—
339	C₂²×C₃	—	2	1	no	—
340	C₂²×C₃	—	2	1	no	—
341	C₂²×C₃	—	4	1	no	—
342	C₂²×C₃	—	4	2	no	—
343	C₂²×C₃	—	4	2	no	—
344	C₂²×C₃	—	4	1	no	—
345	C₂²×C₃	—	4	2	no	—
346	C₂²×C₃	—	4	1	no	—
347	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
348	C₃×C₄	—	2	1	no	—
349	C₃×C₄	—	2	1	no	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	4	1	no	—
354	C₃×C₄	—	4	1	no	—
355	C₃×C₄	—	4	2	no	—
356	C₃×C₄	—	4	1	no	—
357	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
358	C₉	#3219	1	1	yes	characteristic, direct product factor, Sylow
359	C₂³	—	2	1	no	—
360	C₂³	—	2	2	no	—
361	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
362	Q₈	—	2	2	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	2	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	4	no	—
371	D₄	—	4	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
382	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
383	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
384	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
385	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
386	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₂×C₃	—	4	1	no	—
390	C₂×C₃	—	8	1	no	—
391	C₂×C₃	—	8	2	no	—
392	C₂×C₃	C₃×#535	1	1	yes	characteristic
393	C₂×C₃	C₃×#575	1	1	yes	characteristic
394	C₂×C₃	C₃×#575	1	1	yes	characteristic
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	1	no	—
404	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	C₉×H(5,𝔽₂)	1	2	yes	—
415	C₃	C₃×#3219	1	1	yes	characteristic
416	C₂	—	4	1	no	—
417	C₂	—	8	2	no	—
418	C₂	—	8	1	no	—
419	C₂	C₉×#535	1	1	yes	characteristic
420	C₂	C₉×#575	1	1	yes	characteristic
421	C₂	C₉×#575	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×#3219	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#532	C₂	semidirect
2. C₉×#529	C₂	semidirect
3. C₉×#497	C₂	semidirect
4. C₉×#496	C₂	semidirect
5. C₉×#491	C₂	semidirect
6. C₉×#490	C₂	semidirect
7. C₉×#464	C₂	semidirect
8. C₉×#463	C₂	semidirect
9. C₉×#452	C₂	semidirect
10. C₉×#449	C₂	semidirect
11. C₉×#432	C₂	semidirect
96. #3219	C₉	direct (N × H)
158. #532	C₂×C₉	semidirect
159. #529	C₂×C₉	semidirect
160. #497	C₂×C₉	semidirect
161. #496	C₂×C₉	semidirect
162. #491	C₂×C₉	semidirect
163. #490	C₂×C₉	semidirect
164. #464	C₂×C₉	semidirect
165. #463	C₂×C₉	semidirect
166. #452	C₂×C₉	semidirect
167. #449	C₂×C₉	semidirect
168. #432	C₂×C₉	semidirect
358. C₉	#3219	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#532	2
C₉×#529	2
C₉×#497	2
C₉×#496	2
C₉×#491	2
C₉×#490	2
C₉×#464	2
C₉×#463	2
C₉×#452	2
C₉×#449	2
C₉×#432	2
C₃×#3219	3

Subgroups — C9×#3219 #11767940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3219 #11767940