Subgroups — C₉×#5016 #13142734

Order 1728.

466 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#214	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#213	C₂	1	1	yes	maximal, characteristic
4	C₉×#875	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#810	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#809	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5016	C₃	1	1	yes	maximal, characteristic
9	C₉×#463	—	3	1	no	maximal
10	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₉	—	2	1	no	—
12	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
13	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
14	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₃×C₉×C₂²⋊C₄	—	2	1	no	—
16	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
17	C₉×#214	—	2	2	no	—
18	C₉×#213	—	2	2	no	—
19	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
20	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
21	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×#214	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×#213	C₂×C₃	1	1	yes	characteristic
26	C₃×#875	C₂×C₃	1	1	yes	characteristic
27	C₃×#810	C₂×C₃	1	1	yes	characteristic
28	C₃×#809	C₂×C₃	1	1	yes	characteristic
29	C₃×C₄⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic
30	C₂×C₉×SD₁₆	—	3	1	no	—
31	C₂×C₉×D₈	—	3	1	no	—
32	C₉×#124	—	3	1	no	—
33	C₄×D₄×C₉	—	2	1	no	—
34	C₄×D₄×C₉	D₃	1	1	yes	characteristic, complemented
35	C₉×C₄⋊C₈	—	3	1	no	—
36	C₉×#103	—	3	1	no	—
37	C₉×#102	—	3	1	no	—
38	C₂³×C₃×C₉	—	2	1	no	—
39	C₂²×D₃×C₉	—	2	1	no	—
40	C₃×D₄×C₉	—	2	1	no	—
41	C₃×D₄×C₉	D₄	1	2	yes	—
42	C₂×C₃×C₄×C₉	—	2	1	no	—
43	C₂×C₃×C₄×C₉	—	4	2	no	—
44	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
45	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
46	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
47	C₂×C₉×Dic₃	—	2	1	no	—
48	C₉×D₁₂	—	2	1	no	—
49	C₉×D₁₂	—	2	1	no	—
50	C₉×Dic₆	—	2	1	no	—
51	C₉×Dic₆	—	2	1	no	—
52	C₉×C₃⋊C₈	—	2	1	no	—
53	C₉×C₃⋊C₈	—	2	1	no	—
54	C₃×#463	—	3	1	no	—
55	#5016	C₉	1	1	yes	characteristic, direct product factor
56	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
57	C₂²×C₃²×C₄	—	2	1	no	—
58	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
60	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
61	C₃²×C₂²⋊C₄	—	2	1	no	—
62	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
63	C₃×#214	—	2	2	no	—
64	C₃×#213	—	2	2	no	—
65	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
66	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
67	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
69	C₂×Q₈×C₉	—	3	1	no	—
70	C₂×D₄×C₉	—	2	1	no	—
71	C₂×D₄×C₉	—	3	1	no	—
72	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
73	C₂²×C₄×C₉	—	2	2	no	—
74	C₂²×C₄×C₉	—	2	1	no	—
75	C₉×SD₁₆	—	6	2	no	—
76	C₉×D₈	—	6	2	no	—
77	C₂×C₈×C₉	—	3	1	no	—
78	C₂×C₈×C₉	—	3	1	no	—
79	C₉×C₄⋊C₄	—	2	1	no	—
80	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
81	C₉×C₂²⋊C₄	—	2	2	no	—
82	C₉×C₂²⋊C₄	—	2	1	no	—
83	C₉×C₂²⋊C₄	—	6	1	no	—
84	C₉×C₂²⋊C₄	—	6	1	no	—
85	C₄²×C₉	—	2	1	no	—
86	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
87	C₂²×C₃×C₉	—	2	2	no	—
88	C₂²×C₃×C₉	—	4	1	no	—
89	C₂²×C₃×C₉	—	4	1	no	—
90	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
91	C₂×D₃×C₉	—	4	1	no	—
92	C₂×D₃×C₉	—	4	1	no	—
93	C₂×D₃×C₉	—	4	1	no	—
94	C₃×C₄×C₉	—	2	1	no	—
95	C₃×C₄×C₉	—	2	1	no	—
96	C₃×C₄×C₉	—	4	1	no	—
97	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
98	C₃×C₄×C₉	#41	1	1	yes	characteristic
99	C₉×Dic₃	—	4	1	no	—
100	C₂×C₃×SD₁₆	—	3	1	no	—
101	C₂×C₃×D₈	—	3	1	no	—
102	C₃×#124	—	3	1	no	—
103	C₃×C₄×D₄	—	2	1	no	—
104	C₃×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
105	C₃×C₄×D₄	C₃×D₃	1	1	yes	characteristic
106	C₂×#214	C₂×C₉	1	1	yes	characteristic, complemented
107	C₂×#213	C₂×C₉	1	1	yes	characteristic
108	#875	C₂×C₉	1	1	yes	characteristic, complemented
109	C₃×C₄⋊C₈	—	3	1	no	—
110	C₃×#103	—	3	1	no	—
111	C₃×#102	—	3	1	no	—
112	#810	C₂×C₉	1	1	yes	characteristic, complemented
113	#809	C₂×C₉	1	1	yes	characteristic, complemented
114	C₄⋊(C₃⋊C₈)	C₂×C₉	1	1	yes	characteristic, complemented
115	C₂³×C₃²	—	2	1	no	—
116	C₂²×C₃×D₃	—	2	1	no	—
117	C₃²×D₄	—	2	1	no	—
118	C₃²×D₄	C₃×D₄	1	2	yes	—
119	C₂×C₃²×C₄	—	2	1	no	—
120	C₂×C₃²×C₄	—	4	2	no	—
121	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
122	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
123	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
124	C₂×C₃×Dic₃	—	2	1	no	—
125	C₃×D₁₂	—	2	1	no	—
126	C₃×D₁₂	—	2	1	no	—
127	C₃×Dic₆	—	2	1	no	—
128	C₃×Dic₆	—	2	1	no	—
129	C₂³×C₉	—	2	2	no	—
130	C₂³×C₉	—	2	1	no	—
131	C₂³×C₉	—	6	1	no	—
132	C₃×C₃⋊C₈	—	2	1	no	—
133	C₃×C₃⋊C₈	—	2	1	no	—
134	Q₈×C₉	—	6	1	no	—
135	Q₈×C₉	—	6	1	no	—
136	D₄×C₉	—	2	2	no	—
137	D₄×C₉	—	2	1	no	—
138	D₄×C₉	—	2	2	no	—
139	D₄×C₉	—	6	1	no	—
140	D₄×C₉	—	6	1	no	—
141	D₄×C₉	D₁₂	1	2	yes	—
142	C₂×C₄×C₉	—	2	2	no	—
143	C₂×C₄×C₉	—	2	1	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	—	4	4	no	—
148	C₂×C₄×C₉	—	4	2	no	—
149	C₂×C₄×C₉	—	6	1	no	—
150	C₂×C₄×C₉	#67	1	1	yes	characteristic
151	C₂×C₄×C₉	#67	1	1	yes	characteristic
152	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
153	C₈×C₉	—	6	1	no	—
154	C₈×C₉	—	6	1	no	—
155	#463	—	3	1	no	Sylow
156	C₂×C₃×C₉	—	4	2	no	—
157	C₂×C₃×C₉	#121	1	1	yes	characteristic
158	C₂×C₃×C₉	#135	1	1	yes	characteristic
159	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
160	D₃×C₉	—	8	1	no	—
161	C₂×C₃×Q₈	—	3	1	no	—
162	C₂×C₃×D₄	—	2	1	no	—
163	C₂×C₃×D₄	—	3	1	no	—
164	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
165	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
166	C₂²×C₃×C₄	—	2	2	no	—
167	C₂²×C₃×C₄	—	2	1	no	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
170	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
171	C₃×SD₁₆	—	6	2	no	—
172	C₃×D₈	—	6	2	no	—
173	C₂×C₃×C₈	—	3	1	no	—
174	C₂×C₃×C₈	—	3	1	no	—
175	C₃×C₄⋊C₄	—	2	1	no	—
176	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
177	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
178	C₃×C₂²⋊C₄	—	2	2	no	—
179	C₃×C₂²⋊C₄	—	2	1	no	—
180	C₃×C₂²⋊C₄	—	2	1	no	—
181	C₃×C₂²⋊C₄	—	6	1	no	—
182	C₃×C₂²⋊C₄	—	6	1	no	—
183	C₃×C₄²	—	2	1	no	—
184	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
185	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
186	#214	—	2	2	no	—
187	#213	—	2	2	no	—
188	(C₂×D₃)⋊C₄	—	2	1	no	—
189	(C₂×D₃)⋊C₄	—	2	1	no	—
190	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
191	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
192	C₂²×C₃²	—	2	2	no	—
193	C₂²×C₃²	—	4	1	no	—
194	C₂²×C₃²	—	4	1	no	—
195	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
196	C₂×C₃×D₃	—	4	1	no	—
197	C₂×C₃×D₃	—	4	1	no	—
198	C₂×C₃×D₃	—	4	1	no	—
199	C₃²×C₄	—	2	1	no	—
200	C₃²×C₄	—	2	1	no	—
201	C₃²×C₄	—	4	1	no	—
202	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
203	C₃²×C₄	C₃×#41	1	1	yes	characteristic
204	C₃×Dic₃	—	4	1	no	—
205	C₂²×C₉	—	2	4	no	—
206	C₂²×C₉	—	2	2	no	—
207	C₂²×C₉	—	2	1	no	—
208	C₂²×C₉	—	4	2	no	—
209	C₂²×C₉	—	4	2	no	—
210	C₂²×C₉	—	4	1	no	—
211	C₂²×C₉	—	4	1	no	—
212	C₂²×C₉	—	12	1	no	—
213	C₂²×C₉	—	12	1	no	—
214	C₂²×C₉	—	12	1	no	—
215	C₂²×C₉	C₂×#67	1	1	yes	characteristic
216	C₄×C₉	—	2	2	no	—
217	C₄×C₉	—	2	1	no	—
218	C₄×C₉	—	2	1	no	—
219	C₄×C₉	—	2	1	no	—
220	C₄×C₉	—	2	1	no	—
221	C₄×C₉	—	4	1	no	—
222	C₄×C₉	—	4	2	no	—
223	C₄×C₉	—	4	1	no	—
224	C₄×C₉	—	12	1	no	—
225	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
226	C₄×C₉	#235	1	1	yes	characteristic
227	C₂×SD₁₆	—	3	1	no	—
228	C₂×D₈	—	3	1	no	—
229	#124	—	3	1	no	—
230	C₄×D₄	D₃×C₉	1	1	yes	characteristic, complemented
231	C₄⋊C₈	—	3	1	no	—
232	#103	—	3	1	no	—
233	#102	—	3	1	no	—
234	C₃×C₉	#463	1	1	yes	characteristic, complemented, Sylow
235	C₂³×C₃	—	2	2	no	—
236	C₂³×C₃	—	2	1	no	—
237	C₂³×C₃	—	2	1	no	—
238	C₂³×C₃	—	6	1	no	—
239	C₂²×D₃	—	2	1	no	—
240	C₃×Q₈	—	6	1	no	—
241	C₃×Q₈	—	6	1	no	—
242	C₃×D₄	—	2	2	no	—
243	C₃×D₄	—	2	1	no	—
244	C₃×D₄	—	2	1	no	—
245	C₃×D₄	—	2	2	no	—
246	C₃×D₄	—	6	1	no	—
247	C₃×D₄	—	6	1	no	—
248	C₃×D₄	D₄×C₉	1	2	yes	—
249	C₃×D₄	C₃×D₁₂	1	2	yes	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	4	2	no	—
257	C₂×C₃×C₄	—	4	4	no	—
258	C₂×C₃×C₄	—	4	2	no	—
259	C₂×C₃×C₄	—	6	1	no	—
260	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
261	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
263	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
264	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
266	C₂×Dic₃	—	2	1	no	—
267	D₁₂	—	2	1	no	—
268	D₁₂	—	2	1	no	—
269	Dic₆	—	2	1	no	—
270	Dic₆	—	2	1	no	—
271	C₃×C₈	—	6	1	no	—
272	C₃×C₈	—	6	1	no	—
273	C₃⋊C₈	—	2	1	no	—
274	C₃⋊C₈	—	2	1	no	—
275	C₂×C₃²	—	4	2	no	—
276	C₂×C₃²	C₃×#121	1	1	yes	characteristic
277	C₂×C₃²	C₃×#135	1	1	yes	characteristic
278	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
279	C₃×D₃	—	8	1	no	—
280	C₂×C₉	—	2	1	no	—
281	C₂×C₉	—	2	1	no	—
282	C₂×C₉	—	2	1	no	—
283	C₂×C₉	—	4	4	no	—
284	C₂×C₉	—	4	2	no	—
285	C₂×C₉	—	24	1	no	—
286	C₂×C₉	#930	1	1	yes	characteristic
287	C₂×C₉	#932	1	1	yes	characteristic
288	C₂×C₉	#950	1	1	yes	characteristic
289	C₂×Q₈	—	3	1	no	—
290	C₂×D₄	—	3	1	no	—
291	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
292	C₂²×C₄	—	2	1	no	—
293	SD₁₆	—	6	2	no	—
294	D₈	—	6	2	no	—
295	C₂×C₈	—	3	1	no	—
296	C₂×C₈	—	3	1	no	—
297	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
298	C₂²⋊C₄	—	2	1	no	—
299	C₂²⋊C₄	—	6	1	no	—
300	C₂²⋊C₄	—	6	1	no	—
301	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
302	C₂²×C₃	—	2	4	no	—
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	1	no	—
306	C₂²×C₃	—	4	2	no	—
307	C₂²×C₃	—	4	2	no	—
308	C₂²×C₃	—	4	1	no	—
309	C₂²×C₃	—	4	1	no	—
310	C₂²×C₃	—	4	1	no	—
311	C₂²×C₃	—	4	1	no	—
312	C₂²×C₃	—	12	1	no	—
313	C₂²×C₃	—	12	1	no	—
314	C₂²×C₃	—	12	1	no	—
315	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
316	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
317	C₂×D₃	—	4	1	no	—
318	C₂×D₃	—	4	1	no	—
319	C₂×D₃	—	4	1	no	—
320	C₃×C₄	—	2	2	no	—
321	C₃×C₄	—	2	1	no	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	4	1	no	—
328	C₃×C₄	—	4	2	no	—
329	C₃×C₄	—	4	1	no	—
330	C₃×C₄	—	4	1	no	—
331	C₃×C₄	—	12	1	no	—
332	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
333	C₃×C₄	C₉×#41	1	1	yes	characteristic
334	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
335	C₃×C₄	C₃×#235	1	1	yes	characteristic
336	Dic₃	—	4	1	no	—
337	C₃²	C₃×#463	1	1	yes	characteristic
338	C₉	—	2	1	no	—
339	C₉	#5016	1	1	yes	characteristic, direct product factor
340	C₂³	—	2	1	no	—
341	C₂³	—	6	1	no	—
342	Q₈	—	6	1	no	—
343	Q₈	—	6	1	no	—
344	D₄	—	2	1	no	—
345	D₄	—	6	1	no	—
346	D₄	—	6	1	no	—
347	D₄	C₉×D₁₂	1	2	yes	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	6	1	no	—
351	C₂×C₄	C₉×#67	1	1	yes	characteristic
352	C₂×C₄	C₉×#67	1	1	yes	characteristic
353	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
354	C₈	—	6	1	no	—
355	C₈	—	6	1	no	—
356	C₂×C₃	—	2	1	no	—
357	C₂×C₃	—	2	1	no	—
358	C₂×C₃	—	2	1	no	—
359	C₂×C₃	—	4	4	no	—
360	C₂×C₃	—	4	2	no	—
361	C₂×C₃	—	4	2	no	—
362	C₂×C₃	—	24	1	no	—
363	C₂×C₃	C₉×#121	1	1	yes	characteristic
364	C₂×C₃	C₉×#135	1	1	yes	characteristic
365	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
366	C₂×C₃	C₃×#930	1	1	yes	characteristic
367	C₂×C₃	C₃×#932	1	1	yes	characteristic
368	C₂×C₃	C₃×#950	1	1	yes	characteristic
369	D₃	—	8	1	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	12	1	no	—
374	C₂²	—	12	1	no	—
375	C₂²	—	12	1	no	—
376	C₂²	C₂×C₉×#67	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	4	1	no	—
380	C₄	—	12	1	no	—
381	C₄	C₂×C₉×D₁₂	1	1	yes	characteristic
382	C₄	C₉×#235	1	1	yes	characteristic
383	C₃	—	2	1	no	—
384	C₃	C₉×#463	1	1	yes	characteristic, complemented
385	C₃	C₃×#5016	1	1	yes	characteristic
386	C₂	—	4	2	no	—
387	C₂	—	24	1	no	—
388	C₂	C₉×#930	1	1	yes	characteristic
389	C₂	C₉×#932	1	1	yes	characteristic
390	C₂	C₉×#950	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂×#67
commutator	C₂×C₃×C₄	C₂³×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₄×D₄×C₉	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃×#213	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₄×D₄×C₉	D₃
hypocenter	C₃	C₉×#463
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₄²×C₉ ◁ C₄×D₄×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×D₄×C₉	C₂	semidirect
2. C₂×C₉×#214	C₂	semidirect
4. C₉×#875	C₂	semidirect
5. C₉×#810	C₂	semidirect
6. C₉×#809	C₂	semidirect
7. C₉×C₄⋊(C₃⋊C₈)	C₂	semidirect
34. C₄×D₄×C₉	D₃	semidirect
55. #5016	C₉	direct (N × H)
104. C₃×C₄×D₄	C₂×C₉	semidirect
106. C₂×#214	C₂×C₉	semidirect
108. #875	C₂×C₉	semidirect
112. #810	C₂×C₉	semidirect
113. #809	C₂×C₉	semidirect
114. C₄⋊(C₃⋊C₈)	C₂×C₉	semidirect
230. C₄×D₄	D₃×C₉	semidirect
234. C₃×C₉	#463	semidirect
339. C₉	#5016	direct (N × H)
384. C₃	C₉×#463	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×D₄×C₉	2
C₂×C₉×#214	2
C₂×C₉×#213	2
C₉×#875	2
C₉×#810	2
C₉×#809	2
C₉×C₄⋊(C₃⋊C₈)	2
C₃×#5016	3
C₉×#463	3

Subgroups — C9×#5016 #13142734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5016 #13142734