Subgroups — C₉×#3105 #11767826

Order 1152.

681 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×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#484	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#481	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#478	C₂	1	2	yes	maximal, complemented
6	C₉×#463	C₂	1	2	yes	maximal, complemented
7	C₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#447	C₂	1	1	yes	maximal, characteristic
9	C₄×C₉×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₄×C₉×D₈	C₂	1	2	yes	maximal, complemented
11	C₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3105	C₃	1	1	yes	maximal, characteristic
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₉	—	2	1	no	—
15	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₉×D₈	C₂²	1	2	yes	—
17	C₉×#126	—	2	1	no	—
18	C₉×#125	C₂²	1	1	yes	characteristic, complemented
19	C₉×#124	C₂²	1	1	yes	characteristic, complemented
20	C₉×#123	—	2	1	no	—
21	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₉×#121	C₂²	1	1	yes	characteristic
23	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
24	C₄×D₄×C₉	—	2	1	no	—
25	C₄×D₄×C₉	—	2	1	no	—
26	C₄×D₄×C₉	—	2	1	no	—
27	C₄×D₄×C₉	C₂²	1	2	yes	—
28	C₄×D₄×C₉	C₂²	1	2	yes	—
29	C₄×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
30	C₉×#117	—	2	1	no	—
31	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
33	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
34	C₉×#107	C₂²	1	2	yes	complemented
35	C₉×#106	C₂²	1	2	yes	complemented
36	C₉×C₄⋊C₈	C₂²	1	2	yes	complemented
37	C₉×#103	C₂²	1	2	yes	complemented
38	C₉×#102	C₂²	1	2	yes	—
39	C₉×#102	C₂²	1	2	yes	—
40	C₉×#102	C₂²	1	2	yes	complemented
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×C₄×D₄	C₂×C₃	1	1	yes	characteristic
46	C₃×#484	C₂×C₃	1	1	yes	characteristic
47	C₃×#481	C₂×C₃	1	1	yes	characteristic
48	C₃×#478	C₂×C₃	1	2	yes	—
49	C₃×#463	C₂×C₃	1	2	yes	—
50	C₃×#450	C₂×C₃	1	1	yes	characteristic
51	C₃×#447	C₂×C₃	1	1	yes	characteristic
52	C₃×C₄×SD₁₆	C₂×C₃	1	2	yes	—
53	C₃×C₄×D₈	C₂×C₃	1	2	yes	—
54	C₃×#431	C₂×C₃	1	1	yes	characteristic
55	C₂⁴×C₉	—	2	1	no	—
56	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
57	C₂×D₄×C₉	—	2	4	no	—
58	C₂×D₄×C₉	—	2	1	no	—
59	C₂×D₄×C₉	—	2	1	no	—
60	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
61	C₂×D₄×C₉	C₂³	1	2	yes	—
62	C₂²×C₄×C₉	—	2	1	no	—
63	C₂²×C₄×C₉	—	2	2	no	—
64	C₂²×C₄×C₉	—	2	1	no	—
65	C₂²×C₄×C₉	—	2	2	no	—
66	C₂²×C₄×C₉	—	4	4	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×SD₁₆	—	2	4	no	—
71	C₉×D₈	—	2	4	no	—
72	C₂×C₈×C₉	C₂³	1	2	yes	—
73	C₂×C₈×C₉	C₂³	1	2	yes	—
74	C₉×C₄⋊C₄	—	2	1	no	—
75	C₉×C₄⋊C₄	—	2	1	no	—
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	C₂³	1	2	yes	—
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	1	no	—
86	C₉×C₂²⋊C₄	—	2	1	no	—
87	C₉×C₂²⋊C₄	—	2	1	no	—
88	C₉×C₂²⋊C₄	—	2	1	no	—
89	C₄²×C₉	—	2	1	no	—
90	C₄²×C₉	D₄	1	1	yes	characteristic
91	C₄²×C₉	D₄	1	1	yes	characteristic
92	C₄²×C₉	C₂³	1	1	yes	characteristic
93	C₄²×C₉	C₂³	1	1	yes	characteristic
94	#3105	C₉	1	1	yes	characteristic, direct product factor, Sylow
95	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
96	C₂³×C₃×C₄	—	2	1	no	—
97	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
98	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
99	C₃×#126	—	2	1	no	—
100	C₃×#125	C₂²×C₃	1	1	yes	characteristic
101	C₃×#124	C₂²×C₃	1	1	yes	characteristic
102	C₃×#123	—	2	1	no	—
103	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
104	C₃×#121	C₂²×C₃	1	1	yes	characteristic
105	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
106	C₃×C₄×D₄	—	2	1	no	—
107	C₃×C₄×D₄	—	2	1	no	—
108	C₃×C₄×D₄	—	2	1	no	—
109	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
110	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
111	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
112	C₃×#117	—	2	1	no	—
113	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
116	C₃×#107	C₂²×C₃	1	2	yes	—
117	C₃×#106	C₂²×C₃	1	2	yes	—
118	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
119	C₃×#103	C₂²×C₃	1	2	yes	—
120	C₃×#102	C₂²×C₃	1	2	yes	—
121	C₃×#102	C₂²×C₃	1	2	yes	—
122	C₃×#102	C₂²×C₃	1	2	yes	—
123	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
124	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
125	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
126	C₂³×C₉	—	2	4	no	—
127	C₂³×C₉	—	2	2	no	—
128	C₂³×C₉	—	2	1	no	—
129	C₂³×C₉	—	4	2	no	—
130	C₂³×C₉	—	4	2	no	—
131	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
132	Q₈×C₉	—	2	2	no	—
133	D₄×C₉	—	2	4	no	—
134	D₄×C₉	—	2	2	no	—
135	D₄×C₉	—	2	2	no	—
136	D₄×C₉	—	4	2	no	—
137	D₄×C₉	#41	1	4	yes	—
138	C₂×C₄×C₉	—	2	2	no	—
139	C₂×C₄×C₉	—	2	2	no	—
140	C₂×C₄×C₉	—	2	2	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	4	4	no	—
146	C₂×C₄×C₉	—	4	2	no	—
147	C₂×C₄×C₉	—	4	2	no	—
148	C₂×C₄×C₉	—	4	4	no	—
149	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
155	C₈×C₉	—	2	2	no	—
156	C₈×C₉	—	2	2	no	—
157	#529	C₂×C₉	1	1	yes	characteristic, complemented
158	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
159	#484	C₂×C₉	1	1	yes	characteristic, complemented
160	#481	C₂×C₉	1	1	yes	characteristic, complemented
161	#478	C₂×C₉	1	2	yes	complemented
162	#463	C₂×C₉	1	2	yes	complemented
163	#450	C₂×C₉	1	1	yes	characteristic, complemented
164	#447	C₂×C₉	1	1	yes	characteristic
165	C₄×SD₁₆	C₂×C₉	1	2	yes	complemented
166	C₄×D₈	C₂×C₉	1	2	yes	complemented
167	#431	C₂×C₉	1	1	yes	characteristic, complemented
168	C₂⁴×C₃	—	2	1	no	—
169	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₃×D₄	—	2	4	no	—
171	C₂×C₃×D₄	—	2	1	no	—
172	C₂×C₃×D₄	—	2	1	no	—
173	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
174	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
175	C₂²×C₃×C₄	—	2	1	no	—
176	C₂²×C₃×C₄	—	2	1	no	—
177	C₂²×C₃×C₄	—	2	2	no	—
178	C₂²×C₃×C₄	—	2	2	no	—
179	C₂²×C₃×C₄	—	4	4	no	—
180	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₃×SD₁₆	—	2	4	no	—
184	C₃×D₈	—	2	4	no	—
185	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
186	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
187	C₃×C₄⋊C₄	—	2	1	no	—
188	C₃×C₄⋊C₄	—	2	1	no	—
189	C₃×C₄⋊C₄	—	2	1	no	—
190	C₃×C₄⋊C₄	—	2	1	no	—
191	C₃×C₄⋊C₄	—	2	1	no	—
192	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
193	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
194	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
195	C₃×C₂²⋊C₄	—	2	1	no	—
196	C₃×C₂²⋊C₄	—	2	2	no	—
197	C₃×C₂²⋊C₄	—	2	2	no	—
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	1	no	—
202	C₃×C₄²	—	2	1	no	—
203	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
204	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
205	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
206	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
207	C₂²×C₉	—	2	1	no	—
208	C₂²×C₉	—	2	1	no	—
209	C₂²×C₉	—	2	4	no	—
210	C₂²×C₉	—	4	8	no	—
211	C₂²×C₉	—	4	2	no	—
212	C₂²×C₉	—	4	2	no	—
213	C₂²×C₉	—	4	1	no	—
214	C₂²×C₉	—	4	1	no	—
215	C₂²×C₉	—	4	1	no	—
216	C₂²×C₉	#135	1	2	yes	—
217	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
218	C₄×C₉	—	2	1	no	—
219	C₄×C₉	—	2	1	no	—
220	C₄×C₉	—	2	1	no	—
221	C₄×C₉	—	2	1	no	—
222	C₄×C₉	—	4	1	no	—
223	C₄×C₉	—	4	1	no	—
224	C₄×C₉	—	4	1	no	—
225	C₄×C₉	—	4	2	no	—
226	C₄×C₉	AGL(1,ℤ/8)	1	2	yes	—
227	C₄×C₉	C₂×#41	1	2	yes	—
228	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
229	C₂³×C₄	—	2	1	no	—
230	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
231	C₂×D₈	C₂²×C₉	1	2	yes	—
232	#126	—	2	1	no	—
233	#125	C₂²×C₉	1	1	yes	characteristic, complemented
234	#124	C₂²×C₉	1	1	yes	characteristic, complemented
235	#123	—	2	1	no	—
236	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
237	#121	C₂²×C₉	1	1	yes	characteristic
238	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	C₂²×C₉	1	2	yes	—
243	C₄×D₄	C₂²×C₉	1	2	yes	—
244	C₄×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
245	#117	—	2	1	no	—
246	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
249	#107	C₂²×C₉	1	2	yes	complemented
250	#106	C₂²×C₉	1	2	yes	complemented
251	C₄⋊C₈	C₂²×C₉	1	2	yes	complemented
252	#103	C₂²×C₉	1	2	yes	complemented
253	#102	C₂²×C₉	1	2	yes	—
254	#102	C₂²×C₉	1	2	yes	—
255	#102	C₂²×C₉	1	2	yes	complemented
256	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
257	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
258	C₄×C₈	C₂²×C₉	1	2	yes	complemented
259	C₂³×C₃	—	2	4	no	—
260	C₂³×C₃	—	2	2	no	—
261	C₂³×C₃	—	2	1	no	—
262	C₂³×C₃	—	4	2	no	—
263	C₂³×C₃	—	4	2	no	—
264	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
265	C₃×Q₈	—	2	2	no	—
266	C₃×D₄	—	2	4	no	—
267	C₃×D₄	—	2	2	no	—
268	C₃×D₄	—	2	2	no	—
269	C₃×D₄	—	4	2	no	—
270	C₃×D₄	C₃×#41	1	4	yes	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	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	—	2	2	no	—
278	C₂×C₃×C₄	—	4	4	no	—
279	C₂×C₃×C₄	—	4	2	no	—
280	C₂×C₃×C₄	—	4	2	no	—
281	C₂×C₃×C₄	—	4	4	no	—
282	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
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	C₂⁴×C₃	1	1	yes	characteristic
288	C₃×C₈	—	2	2	no	—
289	C₃×C₈	—	2	2	no	—
290	C₂×C₉	—	2	2	no	—
291	C₂×C₉	—	4	4	no	—
292	C₂×C₉	—	8	1	no	—
293	C₂×C₉	#525	1	1	yes	characteristic
294	C₂×C₉	C₂×#135	1	1	yes	characteristic
295	C₂×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
296	C₂⁴	—	2	1	no	—
297	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
302	C₂×D₄	C₂³×C₉	1	2	yes	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
309	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
310	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
311	SD₁₆	—	2	4	no	—
312	D₈	—	2	4	no	—
313	C₂×C₈	C₂³×C₉	1	2	yes	—
314	C₂×C₈	C₂³×C₉	1	2	yes	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
321	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
322	C₄⋊C₄	C₂³×C₉	1	2	yes	—
323	C₂²⋊C₄	—	2	1	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	1	no	—
327	C₂²⋊C₄	—	2	1	no	—
328	C₂²⋊C₄	—	2	1	no	—
329	C₂²⋊C₄	—	2	1	no	—
330	C₄²	—	2	1	no	—
331	C₄²	D₄×C₉	1	1	yes	characteristic
332	C₄²	D₄×C₉	1	1	yes	characteristic
333	C₄²	C₂³×C₉	1	1	yes	characteristic
334	C₄²	C₂³×C₉	1	1	yes	characteristic
335	C₂²×C₃	—	2	1	no	—
336	C₂²×C₃	—	2	1	no	—
337	C₂²×C₃	—	2	4	no	—
338	C₂²×C₃	—	4	8	no	—
339	C₂²×C₃	—	4	2	no	—
340	C₂²×C₃	—	4	2	no	—
341	C₂²×C₃	—	4	1	no	—
342	C₂²×C₃	—	4	1	no	—
343	C₂²×C₃	—	4	1	no	—
344	C₂²×C₃	C₃×#135	1	2	yes	—
345	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
346	C₃×C₄	—	2	1	no	—
347	C₃×C₄	—	2	1	no	—
348	C₃×C₄	—	2	1	no	—
349	C₃×C₄	—	2	1	no	—
350	C₃×C₄	—	4	1	no	—
351	C₃×C₄	—	4	2	no	—
352	C₃×C₄	—	4	1	no	—
353	C₃×C₄	—	4	1	no	—
354	C₃×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
355	C₃×C₄	C₂×C₃×#41	1	2	yes	—
356	C₉	#3105	1	1	yes	characteristic, direct product factor, Sylow
357	C₂³	—	2	4	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
363	Q₈	—	2	2	no	—
364	D₄	—	2	4	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	2	no	—
367	D₄	—	4	2	no	—
368	D₄	C₉×#41	1	4	yes	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
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	C₂⁴×C₉	1	1	yes	characteristic
386	C₈	—	2	2	no	—
387	C₈	—	2	2	no	—
388	C₂×C₃	—	2	2	no	—
389	C₂×C₃	—	4	4	no	—
390	C₂×C₃	—	8	1	no	—
391	C₂×C₃	C₃×#525	1	1	yes	characteristic
392	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
393	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	4	8	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	C₉×#135	1	2	yes	—
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	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	1	no	—
413	C₄	C₉×AGL(1,ℤ/8)	1	2	yes	—
414	C₄	C₂×C₉×#41	1	2	yes	—
415	C₃	C₃×#3105	1	1	yes	characteristic
416	C₂	—	2	2	no	—
417	C₂	—	4	4	no	—
418	C₂	—	8	1	no	—
419	C₂	C₉×#525	1	1	yes	characteristic
420	C₂	C₂×C₉×#135	1	1	yes	characteristic
421	C₂	C₂×C₉×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂×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 ◁ C₂×C₄×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×C₄×D₄×C₉	C₂	semidirect
3. C₉×#484	C₂	semidirect
4. C₉×#481	C₂	semidirect
5. C₉×#478	C₂	semidirect
6. C₉×#463	C₂	semidirect
7. C₉×#450	C₂	semidirect
9. C₄×C₉×SD₁₆	C₂	semidirect
10. C₄×C₉×D₈	C₂	semidirect
11. C₉×#431	C₂	semidirect
18. C₉×#125	C₂²	semidirect
19. C₉×#124	C₂²	semidirect
23. C₄×Q₈×C₉	C₂²	semidirect
29. C₄×D₄×C₉	C₂²	semidirect
34. C₉×#107	C₂²	semidirect
35. C₉×#106	C₂²	semidirect
36. C₉×C₄⋊C₈	C₂²	semidirect
37. C₉×#103	C₂²	semidirect
40. C₉×#102	C₂²	semidirect
43. C₄×C₈×C₉	C₂²	semidirect
94. #3105	C₉	direct (N × H)
157. #529	C₂×C₉	semidirect
158. C₂×C₄×D₄	C₂×C₉	semidirect
159. #484	C₂×C₉	semidirect
160. #481	C₂×C₉	semidirect
161. #478	C₂×C₉	semidirect
162. #463	C₂×C₉	semidirect
163. #450	C₂×C₉	semidirect
165. C₄×SD₁₆	C₂×C₉	semidirect
166. C₄×D₈	C₂×C₉	semidirect
167. #431	C₂×C₉	semidirect
233. #125	C₂²×C₉	semidirect
234. #124	C₂²×C₉	semidirect
238. C₄×Q₈	C₂²×C₉	semidirect
244. C₄×D₄	C₂²×C₉	semidirect
249. #107	C₂²×C₉	semidirect
250. #106	C₂²×C₉	semidirect
251. C₄⋊C₈	C₂²×C₉	semidirect
252. #103	C₂²×C₉	semidirect
255. #102	C₂²×C₉	semidirect
258. C₄×C₈	C₂²×C₉	semidirect
356. C₉	#3105	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×C₄×D₄×C₉	2
C₉×#484	2
C₉×#481	2
C₉×#478	2
C₉×#463	2
C₉×#450	2
C₉×#447	2
C₄×C₉×SD₁₆	2
C₄×C₉×D₈	2
C₉×#431	2
C₃×#3105	3

Subgroups — C9×#3105 #11767826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3105 #11767826