Subgroups — C₉×#3212 #11767933

Order 1152.

600 conjugacy classes of subgroups.

The subgroup lattice has 435 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×#495	C₂	1	2	yes	maximal, complemented
4	C₉×#488	C₂	1	2	yes	maximal, complemented
5	C₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#452	C₂	1	2	yes	maximal, complemented
10	C₉×#449	C₂	1	2	yes	maximal, complemented
11	C₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3212	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	1	yes	characteristic
37	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₉×#103	C₂²	1	2	yes	—
39	C₉×#103	C₂²	1	2	yes	—
40	C₉×#102	C₂²	1	2	yes	—
41	C₉×#102	C₂²	1	2	yes	—
42	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₄×C₈×C₉	C₂²	1	2	yes	—
44	C₃×#532	C₂×C₃	1	1	yes	characteristic
45	C₃×#529	C₂×C₃	1	1	yes	characteristic
46	C₃×#495	C₂×C₃	1	2	yes	—
47	C₃×#488	C₂×C₃	1	2	yes	—
48	C₃×#462	C₂×C₃	1	1	yes	characteristic
49	C₃×#461	C₂×C₃	1	1	yes	characteristic
50	C₃×#460	C₂×C₃	1	1	yes	characteristic
51	C₃×#459	C₂×C₃	1	1	yes	characteristic
52	C₃×#452	C₂×C₃	1	2	yes	—
53	C₃×#449	C₂×C₃	1	2	yes	—
54	C₃×#431	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	#3212	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	1	yes	characteristic
107	C₃×#124	C₂²×C₃	1	2	yes	—
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	1	yes	characteristic
121	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
122	C₃×#103	C₂²×C₃	1	2	yes	—
123	C₃×#103	C₂²×C₃	1	2	yes	—
124	C₃×#102	C₂²×C₃	1	2	yes	—
125	C₃×#102	C₂²×C₃	1	2	yes	—
126	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
127	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
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	1	no	—
132	Q₈×C₉	—	2	2	no	—
133	Q₈×C₉	—	2	1	no	—
134	Q₈×C₉	—	2	2	no	—
135	D₄×C₉	—	2	1	no	—
136	D₄×C₉	—	2	2	no	—
137	D₄×C₉	—	2	1	no	—
138	D₄×C₉	—	2	2	no	—
139	D₄×C₉	—	4	2	no	—
140	D₄×C₉	—	4	2	no	—
141	D₄×C₉	—	4	4	no	—
142	D₄×C₉	—	4	2	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	—	2	2	no	—
150	C₂×C₄×C₉	—	4	1	no	—
151	C₂×C₄×C₉	—	4	4	no	—
152	C₂×C₄×C₉	—	4	2	no	—
153	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
159	C₈×C₉	—	2	2	no	—
160	C₈×C₉	—	2	2	no	—
161	#532	C₂×C₉	1	1	yes	characteristic, complemented
162	#529	C₂×C₉	1	1	yes	characteristic, complemented
163	#495	C₂×C₉	1	2	yes	complemented
164	#488	C₂×C₉	1	2	yes	complemented
165	#462	C₂×C₉	1	1	yes	characteristic, complemented
166	#461	C₂×C₉	1	1	yes	characteristic, complemented
167	#460	C₂×C₉	1	1	yes	characteristic, complemented
168	#459	C₂×C₉	1	1	yes	characteristic, complemented
169	#452	C₂×C₉	1	2	yes	complemented
170	#449	C₂×C₉	1	2	yes	complemented
171	#431	C₂×C₉	1	1	yes	characteristic, complemented
172	C₃×#41	—	4	2	no	—
173	C₃×#41	—	4	2	no	—
174	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
175	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
176	C₂×C₃×D₄	—	2	1	no	—
177	C₂×C₃×D₄	—	2	2	no	—
178	C₂×C₃×D₄	—	2	1	no	—
179	C₂×C₃×D₄	—	2	1	no	—
180	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
181	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	—	2	2	no	—
184	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
187	C₃×Q₁₆	—	4	2	no	—
188	C₃×SD₁₆	—	4	2	no	—
189	C₃×SD₁₆	—	4	2	no	—
190	C₃×D₈	—	4	2	no	—
191	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
192	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
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	—	2	1	no	—
197	C₃×C₄⋊C₄	—	2	1	no	—
198	C₃×C₄⋊C₄	—	2	1	no	—
199	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
200	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
201	C₃×C₂²⋊C₄	—	2	1	no	—
202	C₃×C₂²⋊C₄	—	2	1	no	—
203	C₃×C₂²⋊C₄	—	2	1	no	—
204	C₃×C₂²⋊C₄	—	2	2	no	—
205	C₃×C₂²⋊C₄	—	2	2	no	—
206	C₃×C₂²⋊C₄	—	2	1	no	—
207	C₃×C₂²⋊C₄	—	2	1	no	—
208	C₃×C₄²	—	2	1	no	—
209	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
210	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
211	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
212	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
213	C₂²×C₉	—	2	1	no	—
214	C₂²×C₉	—	2	1	no	—
215	C₂²×C₉	—	2	1	no	—
216	C₂²×C₉	—	4	2	no	—
217	C₂²×C₉	—	4	1	no	—
218	C₂²×C₉	—	4	1	no	—
219	C₂²×C₉	—	4	2	no	—
220	C₂²×C₉	—	4	2	no	—
221	C₂²×C₉	—	4	1	no	—
222	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
223	C₄×C₉	—	2	1	no	—
224	C₄×C₉	—	2	1	no	—
225	C₄×C₉	—	2	1	no	—
226	C₄×C₉	—	2	1	no	—
227	C₄×C₉	—	4	2	no	—
228	C₄×C₉	—	4	1	no	—
229	C₄×C₉	—	4	1	no	—
230	C₄×C₉	—	4	1	no	—
231	C₄×C₉	#135	1	2	yes	—
232	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
233	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×#41	C₂²×C₉	1	2	yes	—
235	C₂×Q₁₆	C₂²×C₉	1	2	yes	—
236	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
237	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
238	C₂×D₈	C₂²×C₉	1	2	yes	—
239	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
240	#127	C₂²×C₉	1	1	yes	characteristic
241	#126	—	2	1	no	—
242	#125	C₂²×C₉	1	1	yes	characteristic
243	#124	C₂²×C₉	1	1	yes	characteristic
244	#124	C₂²×C₉	1	2	yes	—
245	#123	—	2	1	no	—
246	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
247	#121	—	2	1	no	—
248	#121	—	2	1	no	—
249	#121	C₂²×C₉	1	1	yes	characteristic
250	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
255	#117	—	2	1	no	—
256	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
257	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
258	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
259	#103	C₂²×C₉	1	2	yes	—
260	#103	C₂²×C₉	1	2	yes	—
261	#102	C₂²×C₉	1	2	yes	—
262	#102	C₂²×C₉	1	2	yes	—
263	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
264	C₄×C₈	C₂²×C₉	1	2	yes	—
265	C₂³×C₃	—	2	1	no	—
266	C₂³×C₃	—	2	2	no	—
267	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
268	C₃×Q₈	—	2	1	no	—
269	C₃×Q₈	—	2	2	no	—
270	C₃×Q₈	—	2	1	no	—
271	C₃×Q₈	—	2	2	no	—
272	C₃×D₄	—	2	1	no	—
273	C₃×D₄	—	2	2	no	—
274	C₃×D₄	—	2	1	no	—
275	C₃×D₄	—	2	2	no	—
276	C₃×D₄	—	4	2	no	—
277	C₃×D₄	—	4	2	no	—
278	C₃×D₄	—	4	4	no	—
279	C₃×D₄	—	4	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	1	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	4	1	no	—
288	C₂×C₃×C₄	—	4	4	no	—
289	C₂×C₃×C₄	—	4	2	no	—
290	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
296	C₃×C₈	—	2	2	no	—
297	C₃×C₈	—	2	2	no	—
298	C₂×C₉	—	4	1	no	—
299	C₂×C₉	—	8	2	no	—
300	C₂×C₉	—	8	1	no	—
301	C₂×C₉	#535	1	1	yes	characteristic
302	C₂×C₉	C₂×#135	1	1	yes	characteristic
303	C₂×C₉	#575	1	1	yes	characteristic
304	#41	—	4	2	no	—
305	#41	—	4	2	no	—
306	C₂×Q₈	C₂³×C₉	1	2	yes	—
307	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	C₂³×C₉	1	2	yes	—
313	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
317	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
318	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
319	Q₁₆	—	4	2	no	—
320	SD₁₆	—	4	2	no	—
321	SD₁₆	—	4	2	no	—
322	D₈	—	4	2	no	—
323	C₂×C₈	C₂³×C₉	1	2	yes	—
324	C₂×C₈	C₂³×C₉	1	2	yes	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
332	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	1	no	—
339	C₂²⋊C₄	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	D₄×C₉	1	1	yes	characteristic
342	C₄²	D₄×C₉	1	1	yes	characteristic
343	C₄²	C₂³×C₉	1	1	yes	characteristic
344	C₄²	C₂³×C₉	1	1	yes	characteristic
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	4	1	no	—
349	C₂²×C₃	—	4	2	no	—
350	C₂²×C₃	—	4	2	no	—
351	C₂²×C₃	—	4	1	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	—	4	1	no	—
354	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	2	1	no	—
357	C₃×C₄	—	2	1	no	—
358	C₃×C₄	—	2	1	no	—
359	C₃×C₄	—	4	1	no	—
360	C₃×C₄	—	4	1	no	—
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	—	4	1	no	—
363	C₃×C₄	C₃×#135	1	2	yes	—
364	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
365	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
366	C₉	#3212	1	1	yes	characteristic, direct product factor, Sylow
367	C₂³	—	2	1	no	—
368	C₂³	—	2	2	no	—
369	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
370	Q₈	—	2	1	no	—
371	Q₈	—	2	2	no	—
372	Q₈	—	2	1	no	—
373	Q₈	—	2	2	no	—
374	D₄	—	2	1	no	—
375	D₄	—	2	2	no	—
376	D₄	—	2	1	no	—
377	D₄	—	2	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	4	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
394	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
395	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
397	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₂×C₃	—	4	1	no	—
401	C₂×C₃	—	8	1	no	—
402	C₂×C₃	—	8	2	no	—
403	C₂×C₃	C₃×#535	1	1	yes	characteristic
404	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
405	C₂×C₃	C₃×#575	1	1	yes	characteristic
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	1	no	—
415	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	1	no	—
424	C₄	C₉×#135	1	2	yes	—
425	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
426	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
427	C₃	C₃×#3212	1	1	yes	characteristic
428	C₂	—	4	1	no	—
429	C₂	—	8	2	no	—
430	C₂	—	8	1	no	—
431	C₂	C₉×#535	1	1	yes	characteristic
432	C₂	C₂×C₉×#135	1	1	yes	characteristic
433	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×#3212	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×#495	C₂	semidirect
4. C₉×#488	C₂	semidirect
5. C₉×#462	C₂	semidirect
6. C₉×#461	C₂	semidirect
7. C₉×#460	C₂	semidirect
8. C₉×#459	C₂	semidirect
9. C₉×#452	C₂	semidirect
10. C₉×#449	C₂	semidirect
11. C₉×#431	C₂	semidirect
96. #3212	C₉	direct (N × H)
161. #532	C₂×C₉	semidirect
162. #529	C₂×C₉	semidirect
163. #495	C₂×C₉	semidirect
164. #488	C₂×C₉	semidirect
165. #462	C₂×C₉	semidirect
166. #461	C₂×C₉	semidirect
167. #460	C₂×C₉	semidirect
168. #459	C₂×C₉	semidirect
169. #452	C₂×C₉	semidirect
170. #449	C₂×C₉	semidirect
171. #431	C₂×C₉	semidirect
366. C₉	#3212	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×#495	2
C₉×#488	2
C₉×#462	2
C₉×#461	2
C₉×#460	2
C₉×#459	2
C₉×#452	2
C₉×#449	2
C₉×#431	2
C₃×#3212	3

Subgroups — C9×#3212 #11767933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3212 #11767933