Subgroups — C₉×#3211 #11767932

Order 1152.

615 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	C₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#124	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×#464	C₂	1	2	yes	maximal, complemented
6	C₉×#463	C₂	1	2	yes	maximal, complemented
7	C₉×#451	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#447	C₂	1	1	yes	maximal, characteristic
11	C₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3211	C₃	1	1	yes	maximal, characteristic
13	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×Q₁₆	C₂²	1	2	yes	complemented
16	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
17	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
18	C₂×C₉×D₈	C₂²	1	2	yes	—
19	C₉×#126	—	2	1	no	—
20	C₉×#125	C₂²	1	1	yes	characteristic, complemented
21	C₉×#124	—	2	1	no	—
22	C₉×#124	—	2	1	no	—
23	C₉×#124	C₂²	1	2	yes	—
24	C₉×#124	C₂²	1	2	yes	—
25	C₉×#124	C₂²	1	1	yes	characteristic, complemented
26	C₉×#123	—	2	1	no	—
27	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₉×#121	C₂²	1	1	yes	characteristic
29	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
30	C₄×D₄×C₉	—	2	1	no	—
31	C₄×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
32	C₉×#117	—	2	1	no	—
33	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
34	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
35	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
36	C₉×C₄⋊C₈	C₂²	1	2	yes	complemented
37	C₉×#103	C₂²	1	2	yes	complemented
38	C₉×#103	C₂²	1	2	yes	complemented
39	C₉×#102	C₂²	1	2	yes	—
40	C₉×#102	C₂²	1	2	yes	—
41	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₄×C₈×C₉	C₂²	1	2	yes	complemented
44	C₃×#529	C₂×C₃	1	1	yes	characteristic
45	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic
46	C₃×#495	C₂×C₃	1	2	yes	—
47	C₃×#488	C₂×C₃	1	2	yes	—
48	C₃×#464	C₂×C₃	1	2	yes	—
49	C₃×#463	C₂×C₃	1	2	yes	—
50	C₃×#451	C₂×C₃	1	1	yes	characteristic
51	C₃×#450	C₂×C₃	1	1	yes	characteristic
52	C₃×#448	C₂×C₃	1	1	yes	characteristic
53	C₃×#447	C₂×C₃	1	1	yes	characteristic
54	C₃×#431	C₂×C₃	1	1	yes	characteristic
55	C₂⁴×C₉	—	2	1	no	—
56	C₂×Q₈×C₉	—	2	1	no	—
57	C₂×Q₈×C₉	—	4	2	no	—
58	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
59	C₂×Q₈×C₉	C₂³	1	2	yes	—
60	C₂×D₄×C₉	—	2	1	no	—
61	C₂×D₄×C₉	—	2	1	no	—
62	C₂×D₄×C₉	—	4	2	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	1	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	C₂³	1	1	yes	characteristic
81	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₉×C₂²⋊C₄	—	2	1	no	—
83	C₉×C₂²⋊C₄	—	2	2	no	—
84	C₉×C₂²⋊C₄	—	2	2	no	—
85	C₉×C₂²⋊C₄	—	2	2	no	—
86	C₉×C₂²⋊C₄	—	2	2	no	—
87	C₉×C₂²⋊C₄	—	2	1	no	—
88	C₉×C₂²⋊C₄	—	2	1	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	#3211	C₉	1	1	yes	characteristic, direct product factor, Sylow
97	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
98	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
100	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
101	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
102	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
103	C₃×#126	—	2	1	no	—
104	C₃×#125	C₂²×C₃	1	1	yes	characteristic
105	C₃×#124	—	2	1	no	—
106	C₃×#124	—	2	1	no	—
107	C₃×#124	C₂²×C₃	1	2	yes	—
108	C₃×#124	C₂²×C₃	1	2	yes	—
109	C₃×#124	C₂²×C₃	1	1	yes	characteristic
110	C₃×#123	—	2	1	no	—
111	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
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	C₂²×C₃	1	1	yes	characteristic
116	C₃×#117	—	2	1	no	—
117	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₃×C₂²⋊C₄	—	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	1	yes	characteristic
126	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
127	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
128	C₂³×C₉	—	2	1	no	—
129	C₂³×C₉	—	2	2	no	—
130	C₂³×C₉	—	4	2	no	—
131	C₂³×C₉	—	4	2	no	—
132	C₂³×C₉	—	4	2	no	—
133	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
134	Q₈×C₉	—	2	2	no	—
135	Q₈×C₉	—	2	2	no	—
136	Q₈×C₉	—	2	2	no	—
137	Q₈×C₉	—	4	2	no	—
138	D₄×C₉	—	2	2	no	—
139	D₄×C₉	—	2	2	no	—
140	D₄×C₉	—	2	2	no	—
141	D₄×C₉	—	4	2	no	—
142	D₄×C₉	—	4	2	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	2	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	—	4	1	no	—
150	C₂×C₄×C₉	—	4	2	no	—
151	C₂×C₄×C₉	—	4	2	no	—
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	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
158	C₈×C₉	—	2	2	no	—
159	C₈×C₉	—	2	2	no	—
160	#529	C₂×C₉	1	1	yes	characteristic, complemented
161	C₂×#124	C₂×C₉	1	1	yes	characteristic, complemented
162	#495	C₂×C₉	1	2	yes	complemented
163	#488	C₂×C₉	1	2	yes	complemented
164	#464	C₂×C₉	1	2	yes	complemented
165	#463	C₂×C₉	1	2	yes	complemented
166	#451	C₂×C₉	1	1	yes	characteristic, complemented
167	#450	C₂×C₉	1	1	yes	characteristic, complemented
168	#448	C₂×C₉	1	1	yes	characteristic, complemented
169	#447	C₂×C₉	1	1	yes	characteristic
170	#431	C₂×C₉	1	1	yes	characteristic, complemented
171	C₂⁴×C₃	—	2	1	no	—
172	C₂×C₃×Q₈	—	2	1	no	—
173	C₂×C₃×Q₈	—	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	1	no	—
178	C₂×C₃×D₄	—	4	2	no	—
179	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
180	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
181	C₂²×C₃×C₄	—	2	1	no	—
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₃×Q₁₆	—	4	2	no	—
187	C₃×SD₁₆	—	4	2	no	—
188	C₃×SD₁₆	—	4	2	no	—
189	C₃×D₈	—	4	2	no	—
190	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
191	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
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	2	no	—
200	C₃×C₂²⋊C₄	—	2	2	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×C₂²⋊C₄	—	2	1	no	—
206	C₃×C₂²⋊C₄	—	2	1	no	—
207	C₃×C₄²	—	2	1	no	—
208	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
209	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
210	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
211	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
212	C₂²×C₉	—	2	1	no	—
213	C₂²×C₉	—	2	1	no	—
214	C₂²×C₉	—	4	2	no	—
215	C₂²×C₉	—	4	1	no	—
216	C₂²×C₉	—	4	1	no	—
217	C₂²×C₉	—	4	2	no	—
218	C₂²×C₉	—	4	1	no	—
219	C₂²×C₉	—	4	2	no	—
220	C₂²×C₉	—	8	4	no	—
221	C₂²×C₉	#135	1	2	yes	—
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	—	2	1	no	—
228	C₄×C₉	—	4	2	no	—
229	C₄×C₉	—	4	1	no	—
230	C₄×C₉	—	4	1	no	—
231	C₄×C₉	—	4	1	no	—
232	C₄×C₉	H(5,𝔽₂)	1	2	yes	—
233	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
234	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
235	C₂×Q₁₆	C₂²×C₉	1	2	yes	complemented
236	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
237	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
238	C₂×D₈	C₂²×C₉	1	2	yes	—
239	#126	—	2	1	no	—
240	#125	C₂²×C₉	1	1	yes	characteristic, complemented
241	#124	—	2	1	no	—
242	#124	—	2	1	no	—
243	#124	C₂²×C₉	1	2	yes	—
244	#124	C₂²×C₉	1	2	yes	—
245	#124	C₂²×C₉	1	1	yes	characteristic, complemented
246	#123	—	2	1	no	—
247	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
248	#121	C₂²×C₉	1	1	yes	characteristic
249	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
252	#117	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
256	C₄⋊C₈	C₂²×C₉	1	2	yes	complemented
257	#103	C₂²×C₉	1	2	yes	complemented
258	#103	C₂²×C₉	1	2	yes	complemented
259	#102	C₂²×C₉	1	2	yes	—
260	#102	C₂²×C₉	1	2	yes	—
261	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
262	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
263	C₄×C₈	C₂²×C₉	1	2	yes	complemented
264	C₂³×C₃	—	2	1	no	—
265	C₂³×C₃	—	2	2	no	—
266	C₂³×C₃	—	4	2	no	—
267	C₂³×C₃	—	4	2	no	—
268	C₂³×C₃	—	4	2	no	—
269	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
270	C₃×Q₈	—	2	2	no	—
271	C₃×Q₈	—	2	2	no	—
272	C₃×Q₈	—	2	2	no	—
273	C₃×Q₈	—	4	2	no	—
274	C₃×D₄	—	2	2	no	—
275	C₃×D₄	—	2	2	no	—
276	C₃×D₄	—	2	2	no	—
277	C₃×D₄	—	4	2	no	—
278	C₃×D₄	—	4	2	no	—
279	C₂×C₃×C₄	—	2	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	2	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	4	1	no	—
286	C₂×C₃×C₄	—	4	2	no	—
287	C₂×C₃×C₄	—	4	2	no	—
288	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
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	C₂⁴×C₃	1	1	yes	characteristic
294	C₃×C₈	—	2	2	no	—
295	C₃×C₈	—	2	2	no	—
296	C₂×C₉	—	2	2	no	—
297	C₂×C₉	—	8	1	no	—
298	C₂×C₉	—	8	2	no	—
299	C₂×C₉	#535	1	1	yes	characteristic
300	C₂×C₉	C₂×#135	1	1	yes	characteristic
301	C₂×C₉	#575	1	1	yes	characteristic
302	C₂⁴	—	2	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	4	2	no	—
305	C₂×Q₈	C₂³×C₉	1	2	yes	—
306	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	C₂³×C₉	1	2	yes	—
311	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
315	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
316	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
317	Q₁₆	—	4	2	no	—
318	SD₁₆	—	4	2	no	—
319	SD₁₆	—	4	2	no	—
320	D₈	—	4	2	no	—
321	C₂×C₈	C₂³×C₉	1	2	yes	—
322	C₂×C₈	C₂³×C₉	1	2	yes	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
328	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
329	C₂²⋊C₄	—	2	1	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	2	1	no	—
337	C₂²⋊C₄	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	D₄×C₉	1	1	yes	characteristic
340	C₄²	D₄×C₉	1	1	yes	characteristic
341	C₄²	C₂³×C₉	1	1	yes	characteristic
342	C₄²	C₂³×C₉	1	1	yes	characteristic
343	C₂²×C₃	—	2	1	no	—
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	4	1	no	—
346	C₂²×C₃	—	4	2	no	—
347	C₂²×C₃	—	4	1	no	—
348	C₂²×C₃	—	4	2	no	—
349	C₂²×C₃	—	4	2	no	—
350	C₂²×C₃	—	4	1	no	—
351	C₂²×C₃	—	8	4	no	—
352	C₂²×C₃	C₃×#135	1	2	yes	—
353	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
354	C₃×C₄	—	2	1	no	—
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×H(5,𝔽₂)	1	2	yes	—
364	C₉	#3211	1	1	yes	characteristic, direct product factor, Sylow
365	C₂³	—	2	1	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	—	2	2	no	—
373	Q₈	—	2	2	no	—
374	Q₈	—	4	2	no	—
375	D₄	—	2	2	no	—
376	D₄	—	2	2	no	—
377	D₄	—	2	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
390	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
391	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
392	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
394	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₂×C₃	—	2	2	no	—
398	C₂×C₃	—	8	2	no	—
399	C₂×C₃	—	8	1	no	—
400	C₂×C₃	C₃×#535	1	1	yes	characteristic
401	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
402	C₂×C₃	C₃×#575	1	1	yes	characteristic
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	8	4	no	—
412	C₂²	C₉×#135	1	2	yes	—
413	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	C₉×H(5,𝔽₂)	1	2	yes	—
424	C₃	C₃×#3211	1	1	yes	characteristic
425	C₂	—	2	2	no	—
426	C₂	—	8	2	no	—
427	C₂	—	8	1	no	—
428	C₂	C₉×#535	1	1	yes	characteristic
429	C₂	C₂×C₉×#135	1	1	yes	characteristic
430	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×#447	C₂×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×#529	C₂	semidirect
2. C₂×C₉×#124	C₂	semidirect
3. C₉×#495	C₂	semidirect
4. C₉×#488	C₂	semidirect
5. C₉×#464	C₂	semidirect
6. C₉×#463	C₂	semidirect
7. C₉×#451	C₂	semidirect
8. C₉×#450	C₂	semidirect
9. C₉×#448	C₂	semidirect
11. C₉×#431	C₂	semidirect
15. C₂×C₉×Q₁₆	C₂²	semidirect
17. C₂×C₉×SD₁₆	C₂²	semidirect
20. C₉×#125	C₂²	semidirect
25. C₉×#124	C₂²	semidirect
29. C₄×Q₈×C₉	C₂²	semidirect
31. C₄×D₄×C₉	C₂²	semidirect
36. C₉×C₄⋊C₈	C₂²	semidirect
37. C₉×#103	C₂²	semidirect
38. C₉×#103	C₂²	semidirect
43. C₄×C₈×C₉	C₂²	semidirect
96. #3211	C₉	direct (N × H)
160. #529	C₂×C₉	semidirect
161. C₂×#124	C₂×C₉	semidirect
162. #495	C₂×C₉	semidirect
163. #488	C₂×C₉	semidirect
164. #464	C₂×C₉	semidirect
165. #463	C₂×C₉	semidirect
166. #451	C₂×C₉	semidirect
167. #450	C₂×C₉	semidirect
168. #448	C₂×C₉	semidirect
170. #431	C₂×C₉	semidirect
235. C₂×Q₁₆	C₂²×C₉	semidirect
237. C₂×SD₁₆	C₂²×C₉	semidirect
240. #125	C₂²×C₉	semidirect
245. #124	C₂²×C₉	semidirect
249. C₄×Q₈	C₂²×C₉	semidirect
251. C₄×D₄	C₂²×C₉	semidirect
256. C₄⋊C₈	C₂²×C₉	semidirect
257. #103	C₂²×C₉	semidirect
258. #103	C₂²×C₉	semidirect
263. C₄×C₈	C₂²×C₉	semidirect
364. C₉	#3211	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×#529	2
C₂×C₉×#124	2
C₉×#495	2
C₉×#488	2
C₉×#464	2
C₉×#463	2
C₉×#451	2
C₉×#450	2
C₉×#448	2
C₉×#447	2
C₉×#431	2
C₃×#3211	3

Subgroups — C9×#3211 #11767932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3211 #11767932