Subgroups — C₉×#5163 #13143340

Order 1728.

452 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	C₂×C₃×C₉×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#215	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#940	C₂	1	1	yes	maximal, characteristic
5	C₉×#832	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#821	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5163	C₃	1	1	yes	maximal, characteristic
9	C₉×#460	—	3	1	no	maximal
10	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₉×#67	—	2	1	no	—
13	C₂×C₉×#67	—	2	1	no	—
14	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
15	C₃×C₉×SD₁₆	—	2	2	no	—
16	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
17	C₉×#215	—	2	2	no	—
18	C₉×C₄⋊Dic₃	—	2	1	no	—
19	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₄×C₉×Dic₃	—	2	1	no	—
21	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₃²×SD₁₆	C₂×C₃	1	1	yes	characteristic
24	C₃×Q₈×Dic₃	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×#215	C₂×C₃	1	1	yes	characteristic
26	C₃×#940	C₂×C₃	1	1	yes	characteristic
27	C₃×#832	C₂×C₃	1	1	yes	characteristic
28	C₃×#821	C₂×C₃	1	1	yes	characteristic
29	C₃×Dic₃⋊C₈	C₂×C₃	1	1	yes	characteristic
30	C₂×C₉×SD₁₆	—	2	1	no	—
31	C₂×C₉×SD₁₆	—	3	1	no	—
32	C₂×C₉×SD₁₆	D₃	1	1	yes	characteristic, complemented
33	C₉×#127	—	3	1	no	—
34	C₄×Q₈×C₉	—	3	1	no	—
35	C₉×C₄⋊C₈	—	3	1	no	—
36	C₉×#102	—	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×Q₈×C₉	—	2	1	no	—
41	C₃×Q₈×C₉	D₄	1	2	yes	complemented
42	C₃×D₄×C₉	—	2	1	no	—
43	C₃×D₄×C₉	—	2	1	no	—
44	C₂×C₃×C₄×C₉	—	2	1	no	—
45	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
46	C₉×#67	—	4	2	no	—
47	C₉×#67	—	4	2	no	—
48	C₂×C₉×Dic₃	—	2	1	no	—
49	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
50	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
51	C₉×D₁₂	—	2	1	no	—
52	C₉×D₁₂	—	2	1	no	—
53	C₃×C₈×C₉	—	2	1	no	—
54	C₉×C₃⋊C₈	—	2	1	no	—
55	C₃×#460	—	3	1	no	—
56	#5163	C₉	1	1	yes	characteristic, direct product factor
57	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₃×#67	—	2	1	no	—
60	C₂×C₃×#67	—	2	1	no	—
61	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
62	C₃²×SD₁₆	—	2	2	no	—
63	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
64	C₃×#215	—	2	2	no	—
65	C₃×C₄⋊Dic₃	—	2	1	no	—
66	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
67	C₃×C₄×Dic₃	—	2	1	no	—
68	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
70	C₂×Q₈×C₉	—	2	1	no	—
71	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
72	C₂×D₄×C₉	—	2	1	no	—
73	C₂×D₄×C₉	—	3	1	no	—
74	C₂×D₄×C₉	—	6	1	no	—
75	C₂×D₄×C₉	—	6	1	no	—
76	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
77	C₉×SD₁₆	—	2	4	no	—
78	C₉×SD₁₆	—	2	2	no	—
79	C₉×SD₁₆	—	6	2	no	—
80	C₂×C₈×C₉	—	2	1	no	—
81	C₂×C₈×C₉	—	3	1	no	—
82	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
83	C₉×C₄⋊C₄	—	3	1	no	—
84	C₉×C₄⋊C₄	—	6	1	no	—
85	C₄²×C₉	—	3	1	no	—
86	C₄²×C₉	—	6	1	no	—
87	C₂²×C₃×C₉	—	4	1	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	2	no	—
95	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
96	C₃×C₄×C₉	#41	1	1	yes	characteristic
97	C₉×Dic₃	—	2	1	no	—
98	C₉×Dic₃	—	4	1	no	—
99	C₉×Dic₃	SD₁₆	1	2	yes	complemented
100	C₂×C₃×SD₁₆	—	2	1	no	—
101	C₂×C₃×SD₁₆	—	3	1	no	—
102	C₂×C₃×SD₁₆	C₂×C₉	1	1	yes	characteristic, complemented
103	C₂×C₃×SD₁₆	C₃×D₃	1	1	yes	characteristic
104	C₃×#127	—	3	1	no	—
105	C₃×C₄×Q₈	—	3	1	no	—
106	Q₈×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
107	C₂×#215	C₂×C₉	1	1	yes	characteristic, complemented
108	#940	C₂×C₉	1	1	yes	characteristic
109	C₃×C₄⋊C₈	—	3	1	no	—
110	C₃×#102	—	3	1	no	—
111	C₃×#102	—	3	1	no	—
112	#832	C₂×C₉	1	1	yes	characteristic, complemented
113	#821	C₂×C₉	1	1	yes	characteristic, complemented
114	Dic₃⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
115	C₂³×C₃²	—	2	1	no	—
116	C₂²×C₃×D₃	—	2	1	no	—
117	C₃²×Q₈	—	2	1	no	—
118	C₃²×Q₈	C₃×D₄	1	2	yes	—
119	C₃²×D₄	—	2	1	no	—
120	C₃²×D₄	—	2	1	no	—
121	C₂×C₃²×C₄	—	2	1	no	—
122	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
123	C₃×#67	—	4	2	no	—
124	C₃×#67	—	4	2	no	—
125	C₂×C₃×Dic₃	—	2	1	no	—
126	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
127	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
128	C₃×D₁₂	—	2	1	no	—
129	C₃×D₁₂	—	2	1	no	—
130	C₂³×C₉	—	2	1	no	—
131	C₂³×C₉	—	4	1	no	—
132	C₂³×C₉	—	6	1	no	—
133	C₃²×C₈	—	2	1	no	—
134	C₃×C₃⋊C₈	—	2	1	no	—
135	Q₈×C₉	—	2	1	no	—
136	Q₈×C₉	—	2	2	no	—
137	Q₈×C₉	—	4	1	no	—
138	Q₈×C₉	#67	1	2	yes	complemented
139	D₄×C₉	—	2	2	no	—
140	D₄×C₉	—	2	1	no	—
141	D₄×C₉	—	2	1	no	—
142	D₄×C₉	—	4	1	no	—
143	D₄×C₉	—	6	1	no	—
144	D₄×C₉	—	6	1	no	—
145	D₄×C₉	—	12	2	no	—
146	D₄×C₉	—	12	2	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	—	3	1	no	—
150	C₂×C₄×C₉	—	3	1	no	—
151	C₂×C₄×C₉	—	4	1	no	—
152	C₂×C₄×C₉	—	6	1	no	—
153	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
154	C₈×C₉	—	2	2	no	—
155	C₈×C₉	—	2	1	no	—
156	C₈×C₉	—	6	1	no	—
157	#460	—	3	1	no	Sylow
158	C₂×C₃×C₉	—	8	1	no	—
159	C₂×C₃×C₉	#121	1	1	yes	characteristic
160	C₂×C₃×C₉	C₂×SD₁₆	1	1	yes	characteristic
161	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
162	D₃×C₉	—	8	1	no	—
163	C₂×C₃×Q₈	—	2	1	no	—
164	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
165	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
166	C₂×C₃×D₄	—	2	1	no	—
167	C₂×C₃×D₄	—	3	1	no	—
168	C₂×C₃×D₄	—	6	1	no	—
169	C₂×C₃×D₄	—	6	1	no	—
170	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
171	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
172	C₂×#67	—	2	1	no	—
173	C₂×#67	—	2	1	no	—
174	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
175	C₃×SD₁₆	—	2	4	no	—
176	C₃×SD₁₆	—	2	2	no	—
177	C₃×SD₁₆	—	2	2	no	—
178	C₃×SD₁₆	—	6	2	no	—
179	C₂×C₃×C₈	—	2	1	no	—
180	C₂×C₃×C₈	—	3	1	no	—
181	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
182	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
183	C₃×C₄⋊C₄	—	3	1	no	—
184	C₃×C₄⋊C₄	—	6	1	no	—
185	C₃×C₄²	—	3	1	no	—
186	C₃×C₄²	—	6	1	no	—
187	#215	—	2	2	no	—
188	C₄⋊Dic₃	—	2	1	no	—
189	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
190	C₄×Dic₃	—	2	1	no	—
191	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
192	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
193	C₂²×C₃²	—	4	1	no	—
194	C₂²×C₃²	—	4	1	no	—
195	C₂²×C₃²	—	4	1	no	—
196	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
197	C₂×C₃×D₃	—	4	1	no	—
198	C₂×C₃×D₃	—	4	1	no	—
199	C₂×C₃×D₃	—	4	1	no	—
200	C₃²×C₄	—	2	2	no	—
201	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
202	C₃²×C₄	C₃×#41	1	1	yes	characteristic
203	C₃×Dic₃	—	2	1	no	—
204	C₃×Dic₃	—	4	1	no	—
205	C₃×Dic₃	C₃×SD₁₆	1	2	yes	—
206	C₂²×C₉	—	2	1	no	—
207	C₂²×C₉	—	4	2	no	—
208	C₂²×C₉	—	4	1	no	—
209	C₂²×C₉	—	4	1	no	—
210	C₂²×C₉	—	4	1	no	—
211	C₂²×C₉	—	8	1	no	—
212	C₂²×C₉	—	8	1	no	—
213	C₂²×C₉	—	12	1	no	—
214	C₂²×C₉	—	12	1	no	—
215	C₂²×C₉	—	12	1	no	—
216	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
217	C₄×C₉	—	2	2	no	—
218	C₄×C₉	—	2	1	no	—
219	C₄×C₉	—	2	1	no	—
220	C₄×C₉	—	3	2	no	—
221	C₄×C₉	—	4	2	no	—
222	C₄×C₉	—	6	1	no	—
223	C₄×C₉	—	12	1	no	—
224	C₄×C₉	#237	1	1	yes	characteristic
225	C₄×C₉	C₂×#67	1	1	yes	characteristic
226	C₂×SD₁₆	—	3	1	no	—
227	C₂×SD₁₆	D₃×C₉	1	1	yes	characteristic, complemented
228	#127	—	3	1	no	—
229	C₄×Q₈	—	3	1	no	—
230	C₄⋊C₈	—	3	1	no	—
231	#102	—	3	1	no	—
232	#102	—	3	1	no	—
233	C₃×C₉	#460	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₃	—	2	1	no	—
235	C₂³×C₃	—	2	1	no	—
236	C₂³×C₃	—	4	1	no	—
237	C₂³×C₃	—	6	1	no	—
238	C₂²×D₃	—	2	1	no	—
239	C₃×Q₈	—	2	1	no	—
240	C₃×Q₈	—	2	1	no	—
241	C₃×Q₈	—	2	2	no	—
242	C₃×Q₈	—	4	1	no	—
243	C₃×Q₈	D₄×C₉	1	2	yes	complemented
244	C₃×Q₈	C₃×#67	1	2	yes	—
245	C₃×D₄	—	2	2	no	—
246	C₃×D₄	—	2	1	no	—
247	C₃×D₄	—	2	1	no	—
248	C₃×D₄	—	2	1	no	—
249	C₃×D₄	—	2	1	no	—
250	C₃×D₄	—	4	1	no	—
251	C₃×D₄	—	6	1	no	—
252	C₃×D₄	—	6	1	no	—
253	C₃×D₄	—	12	2	no	—
254	C₃×D₄	—	12	2	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	3	1	no	—
259	C₂×C₃×C₄	—	3	1	no	—
260	C₂×C₃×C₄	—	4	1	no	—
261	C₂×C₃×C₄	—	6	1	no	—
262	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
264	#67	—	4	2	no	—
265	#67	—	4	2	no	—
266	C₂×Dic₃	—	2	1	no	—
267	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
268	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
269	D₁₂	—	2	1	no	—
270	D₁₂	—	2	1	no	—
271	C₃×C₈	—	2	2	no	—
272	C₃×C₈	—	2	1	no	—
273	C₃×C₈	—	2	1	no	—
274	C₃×C₈	—	6	1	no	—
275	C₃⋊C₈	—	2	1	no	—
276	C₂×C₃²	—	8	1	no	—
277	C₂×C₃²	C₃×#121	1	1	yes	characteristic
278	C₂×C₃²	C₂×C₃×SD₁₆	1	1	yes	characteristic
279	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
280	C₃×D₃	—	8	1	no	—
281	C₂×C₉	—	2	1	no	—
282	C₂×C₉	—	2	1	no	—
283	C₂×C₉	—	2	1	no	—
284	C₂×C₉	—	8	2	no	—
285	C₂×C₉	—	8	1	no	—
286	C₂×C₉	—	24	1	no	—
287	C₂×C₉	D₃×SD₁₆	1	1	yes	characteristic
288	C₂×C₉	#914	1	1	yes	characteristic
289	C₂×C₉	#939	1	1	yes	characteristic
290	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
291	C₂×D₄	—	3	1	no	—
292	C₂×D₄	—	6	1	no	—
293	C₂×D₄	—	6	1	no	—
294	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
295	SD₁₆	—	2	2	no	—
296	SD₁₆	—	6	2	no	—
297	C₂×C₈	—	3	1	no	—
298	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
299	C₄⋊C₄	—	3	1	no	—
300	C₄⋊C₄	—	6	1	no	—
301	C₄²	—	3	1	no	—
302	C₄²	—	6	1	no	—
303	C₂²×C₃	—	2	1	no	—
304	C₂²×C₃	—	4	2	no	—
305	C₂²×C₃	—	4	1	no	—
306	C₂²×C₃	—	4	1	no	—
307	C₂²×C₃	—	4	1	no	—
308	C₂²×C₃	—	4	1	no	—
309	C₂²×C₃	—	4	1	no	—
310	C₂²×C₃	—	4	1	no	—
311	C₂²×C₃	—	8	1	no	—
312	C₂²×C₃	—	8	1	no	—
313	C₂²×C₃	—	12	1	no	—
314	C₂²×C₃	—	12	1	no	—
315	C₂²×C₃	—	12	1	no	—
316	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
317	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
318	C₂×D₃	—	4	1	no	—
319	C₂×D₃	—	4	1	no	—
320	C₂×D₃	—	4	1	no	—
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	2	2	no	—
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	3	2	no	—
326	C₃×C₄	—	4	2	no	—
327	C₃×C₄	—	6	1	no	—
328	C₃×C₄	—	12	1	no	—
329	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
330	C₃×C₄	C₉×#41	1	1	yes	characteristic
331	C₃×C₄	C₃×#237	1	1	yes	characteristic
332	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
333	Dic₃	—	2	1	no	—
334	Dic₃	—	4	1	no	—
335	Dic₃	C₉×SD₁₆	1	2	yes	complemented
336	C₃²	C₃×#460	1	1	yes	characteristic
337	C₉	—	2	1	no	—
338	C₉	#5163	1	1	yes	characteristic, direct product factor
339	C₂³	—	2	1	no	—
340	C₂³	—	6	1	no	—
341	Q₈	—	2	1	no	—
342	Q₈	C₉×#67	1	2	yes	complemented
343	D₄	—	2	1	no	—
344	D₄	—	2	1	no	—
345	D₄	—	6	1	no	—
346	D₄	—	6	1	no	—
347	D₄	—	12	2	no	—
348	D₄	—	12	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	3	1	no	—
351	C₂×C₄	—	3	1	no	—
352	C₂×C₄	—	6	1	no	—
353	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
354	C₈	—	2	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	—	8	2	no	—
360	C₂×C₃	—	8	1	no	—
361	C₂×C₃	—	8	1	no	—
362	C₂×C₃	—	24	1	no	—
363	C₂×C₃	C₉×#121	1	1	yes	characteristic
364	C₂×C₃	C₂×C₉×SD₁₆	1	1	yes	characteristic
365	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
366	C₂×C₃	C₃×D₃×SD₁₆	1	1	yes	characteristic
367	C₂×C₃	C₃×#914	1	1	yes	characteristic
368	C₂×C₃	C₃×#939	1	1	yes	characteristic
369	D₃	—	8	1	no	—
370	C₂²	—	4	1	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	D₃×D₄×C₉	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	3	2	no	—
379	C₄	—	6	1	no	—
380	C₄	—	12	1	no	—
381	C₄	C₉×#237	1	1	yes	characteristic
382	C₄	C₂×C₉×#67	1	1	yes	characteristic
383	C₃	—	2	1	no	—
384	C₃	C₉×#460	1	1	yes	characteristic, complemented
385	C₃	C₃×#5163	1	1	yes	characteristic
386	C₂	—	8	1	no	—
387	C₂	—	24	1	no	—
388	C₂	D₃×C₉×SD₁₆	1	1	yes	characteristic
389	C₂	C₉×#914	1	1	yes	characteristic
390	C₂	C₉×#939	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₂×C₃×C₄	C₂³×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃×C₉×SD₁₆	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₃×#940	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₉×SD₁₆	D₃
hypocenter	C₃	C₉×#460
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₂×C₉×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×SD₁₆	C₂	semidirect
2. Q₈×C₉×Dic₃	C₂	semidirect
3. C₂×C₉×#215	C₂	semidirect
5. C₉×#832	C₂	semidirect
6. C₉×#821	C₂	semidirect
7. C₉×Dic₃⋊C₈	C₂	semidirect
32. C₂×C₉×SD₁₆	D₃	semidirect
41. C₃×Q₈×C₉	D₄	semidirect
56. #5163	C₉	direct (N × H)
99. C₉×Dic₃	SD₁₆	semidirect
102. C₂×C₃×SD₁₆	C₂×C₉	semidirect
106. Q₈×Dic₃	C₂×C₉	semidirect
107. C₂×#215	C₂×C₉	semidirect
112. #832	C₂×C₉	semidirect
113. #821	C₂×C₉	semidirect
114. Dic₃⋊C₈	C₂×C₉	semidirect
138. Q₈×C₉	#67	semidirect
227. C₂×SD₁₆	D₃×C₉	semidirect
233. C₃×C₉	#460	semidirect
243. C₃×Q₈	D₄×C₉	semidirect
335. Dic₃	C₉×SD₁₆	semidirect
338. C₉	#5163	direct (N × H)
342. Q₈	C₉×#67	semidirect
384. C₃	C₉×#460	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₉×SD₁₆	2
Q₈×C₉×Dic₃	2
C₂×C₉×#215	2
C₉×#940	2
C₉×#832	2
C₉×#821	2
C₉×Dic₃⋊C₈	2
C₃×#5163	3
C₉×#460	3

Subgroups — C9×#5163 #13143340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5163 #13143340