Subgroups — C₉×#5132 #13143189

Order 1728.

518 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#824	C₂	1	2	yes	maximal, complemented
5	C₉×#823	C₂	1	2	yes	maximal, complemented
6	C₃×#5132	C₃	1	1	yes	maximal, characteristic
7	C₉×#413	—	3	1	no	maximal
8	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₉×#67	C₄	1	2	yes	—
10	C₉×#235	—	2	1	no	—
11	C₉×#235	—	2	1	no	—
12	C₉×#235	—	2	1	no	—
13	C₉×#235	—	2	1	no	—
14	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₃×C₉	C₄	1	2	yes	—
16	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
17	C₃×C₉×M₁₆	—	2	1	no	—
18	C₃×C₉×M₁₆	C₂²	1	2	yes	—
19	C₂×C₃×C₈×C₉	—	2	1	no	—
20	C₉×#208	—	2	1	no	—
21	C₉×#208	C₂²	1	2	yes	—
22	C₂×C₉×C₃⋊C₈	—	2	1	no	—
23	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃²×M₁₆	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×#208	C₂×C₃	1	1	yes	characteristic
26	C₂×C₉×#41	—	3	1	no	—
27	C₃×#824	C₂×C₃	1	2	yes	—
28	C₃×#823	C₂×C₃	1	2	yes	—
29	C₂×C₉×M₁₆	—	2	1	no	—
30	C₂×C₉×M₁₆	—	3	1	no	—
31	C₂×C₉×M₁₆	D₃	1	1	yes	characteristic, complemented
32	C₉×#101	—	3	2	no	—
33	C₉×#100	—	3	2	no	—
34	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₃×C₉	C₂×C₄	1	2	yes	—
36	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
38	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
39	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
40	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
41	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
42	C₉×#67	—	2	2	no	—
43	C₉×#67	—	2	2	no	—
44	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	—
45	C₉×D₁₂	—	2	1	no	—
46	C₉×D₁₂	—	2	1	no	—
47	C₄×D₃×C₉	—	2	2	no	—
48	C₄×D₃×C₉	—	2	2	no	—
49	C₉×Dic₆	—	2	1	no	—
50	C₉×Dic₆	—	2	1	no	—
51	C₃×C₈×C₉	—	2	2	no	—
52	C₉×C₃⋊C₈	—	2	2	no	—
53	C₃×#413	—	3	1	no	—
54	#5132	C₉	1	1	yes	characteristic, direct product factor
55	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
56	C₂×C₃×#67	C₃×C₄	1	2	yes	—
57	C₃×#235	—	2	1	no	—
58	C₃×#235	—	2	1	no	—
59	C₃×#235	—	2	1	no	—
60	C₃×#235	—	2	1	no	—
61	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₃×C₄×D₃	C₃×C₄	1	2	yes	—
63	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
64	C₃²×M₁₆	—	2	1	no	—
65	C₃²×M₁₆	C₂²×C₃	1	2	yes	—
66	C₂×C₃²×C₈	—	2	1	no	—
67	C₃×#208	—	2	1	no	—
68	C₃×#208	C₂²×C₃	1	2	yes	—
69	C₂×C₃×C₃⋊C₈	—	2	1	no	—
70	C₉×#41	—	6	1	no	—
71	C₉×#41	—	6	1	no	—
72	C₉×#41	—	6	1	no	—
73	C₉×#41	—	6	1	no	—
74	C₂×Q₈×C₉	—	3	1	no	—
75	C₂×D₄×C₉	—	3	2	no	—
76	C₂×D₄×C₉	—	3	1	no	—
77	C₂²×C₄×C₉	—	2	1	no	—
78	C₂²×C₄×C₉	—	3	2	no	—
79	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
80	C₉×M₁₆	—	2	2	no	—
81	C₉×M₁₆	—	2	2	no	—
82	C₉×M₁₆	—	2	1	no	—
83	C₉×M₁₆	—	3	2	no	—
84	C₉×M₁₆	—	6	1	no	—
85	C₉×M₁₆	C₂×D₃	1	2	yes	—
86	C₂×C₈×C₉	—	2	2	no	—
87	C₂×C₈×C₉	—	2	1	no	—
88	C₂×C₈×C₉	—	6	1	no	—
89	C₂²×C₃×C₉	—	4	1	no	—
90	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
93	C₂×D₃×C₉	—	2	2	no	—
94	C₂×D₃×C₉	—	4	2	no	—
95	C₃×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₃×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
98	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
99	C₉×Dic₃	—	2	2	no	—
100	C₂×C₃×#41	—	3	1	no	—
101	C₂×#235	C₂×C₉	1	1	yes	characteristic
102	C₂×C₃×M₁₆	—	2	1	no	—
103	C₂×C₃×M₁₆	—	3	1	no	—
104	C₂×C₃×M₁₆	C₂×C₉	1	1	yes	characteristic, complemented
105	C₂×C₃×M₁₆	C₃×D₃	1	1	yes	characteristic
106	C₂×#208	C₂×C₉	1	1	yes	characteristic, complemented
107	C₃×#101	—	3	2	no	—
108	C₃×#100	—	3	2	no	—
109	#824	C₂×C₉	1	2	yes	complemented
110	#823	C₂×C₉	1	2	yes	complemented
111	C₂³×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
112	C₂²×C₃×D₃	C₂×C₃×C₄	1	2	yes	—
113	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
114	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
115	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
116	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
117	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
119	C₃×#67	—	2	2	no	—
120	C₃×#67	—	2	2	no	—
121	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
122	C₃×D₁₂	—	2	1	no	—
123	C₃×D₁₂	—	2	1	no	—
124	C₃×C₄×D₃	—	2	2	no	—
125	C₃×C₄×D₃	—	2	2	no	—
126	C₃×Dic₆	—	2	1	no	—
127	C₃×Dic₆	—	2	1	no	—
128	C₂³×C₉	—	2	1	no	—
129	C₂³×C₉	—	3	2	no	—
130	C₂³×C₉	C₄×D₃	1	1	yes	characteristic
131	C₃²×C₈	—	2	2	no	—
132	C₃×C₃⋊C₈	—	2	2	no	—
133	Q₈×C₉	—	6	1	no	—
134	Q₈×C₉	—	6	1	no	—
135	D₄×C₉	—	6	2	no	—
136	D₄×C₉	—	6	2	no	—
137	D₄×C₉	—	6	1	no	—
138	D₄×C₉	—	6	1	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	1	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	1	no	—
145	C₂×C₄×C₉	—	3	2	no	—
146	C₂×C₄×C₉	—	6	2	no	—
147	C₂×C₄×C₉	—	6	2	no	—
148	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
149	C₂×C₄×C₉	D₁₂	1	1	yes	characteristic
150	C₂×C₄×C₉	D₁₂	1	1	yes	characteristic
151	C₂×C₄×C₉	#67	1	1	yes	characteristic
152	C₂×C₄×C₉	#67	1	1	yes	characteristic
153	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
154	C₈×C₉	—	2	4	no	—
155	C₈×C₉	—	2	2	no	—
156	C₈×C₉	—	6	2	no	—
157	#413	—	3	1	no	Sylow
158	C₂×C₃×C₉	—	2	1	no	—
159	C₂×C₃×C₉	—	2	1	no	—
160	C₂×C₃×C₉	—	2	1	no	—
161	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	D₃×C₉	—	4	2	no	—
163	C₃×#41	—	6	1	no	—
164	C₃×#41	—	6	1	no	—
165	C₃×#41	—	6	1	no	—
166	C₃×#41	—	6	1	no	—
167	C₂×C₃×Q₈	—	3	1	no	—
168	C₂×C₃×D₄	—	3	2	no	—
169	C₂×C₃×D₄	—	3	1	no	—
170	C₂²×C₃×C₄	—	2	1	no	—
171	C₂²×C₃×C₄	—	3	2	no	—
172	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
174	C₂×#67	C₄×C₉	1	2	yes	—
175	#235	—	2	1	no	—
176	#235	—	2	1	no	—
177	#235	—	2	1	no	—
178	#235	—	2	1	no	—
179	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
180	C₂×C₄×D₃	C₄×C₉	1	2	yes	—
181	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
182	C₃×M₁₆	—	2	2	no	—
183	C₃×M₁₆	—	2	1	no	—
184	C₃×M₁₆	—	2	1	no	—
185	C₃×M₁₆	—	2	2	no	—
186	C₃×M₁₆	—	3	2	no	—
187	C₃×M₁₆	—	6	1	no	—
188	C₃×M₁₆	C₂²×C₉	1	2	yes	—
189	C₃×M₁₆	C₂×C₃×D₃	1	2	yes	—
190	C₂×C₃×C₈	—	2	2	no	—
191	C₂×C₃×C₈	—	2	1	no	—
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	—	6	1	no	—
194	#208	—	2	1	no	—
195	#208	C₂²×C₉	1	2	yes	—
196	C₂×C₃⋊C₈	—	2	1	no	—
197	C₂²×C₃²	—	4	1	no	—
198	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
201	C₂×C₃×D₃	—	2	2	no	—
202	C₂×C₃×D₃	—	4	2	no	—
203	C₃²×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
204	C₃²×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
205	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
206	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
207	C₃×Dic₃	—	2	2	no	—
208	C₂²×C₉	—	2	1	no	—
209	C₂²×C₉	—	2	1	no	—
210	C₂²×C₉	—	2	1	no	—
211	C₂²×C₉	—	4	1	no	—
212	C₂²×C₉	—	4	2	no	—
213	C₂²×C₉	—	6	2	no	—
214	C₂²×C₉	—	12	2	no	—
215	C₂²×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
216	C₂²×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
217	C₂²×C₉	C₂×C₄×D₃	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	—	6	2	no	—
223	C₄×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
224	C₄×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
225	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
226	C₄×C₉	C₂×#67	1	1	yes	characteristic
227	C₂×#41	—	3	1	no	—
228	C₂×M₁₆	—	3	1	no	—
229	C₂×M₁₆	D₃×C₉	1	1	yes	characteristic, complemented
230	#101	—	3	2	no	—
231	#100	—	3	2	no	—
232	C₃×C₉	#413	1	1	yes	characteristic, complemented, Sylow
233	C₂³×C₃	—	2	1	no	—
234	C₂³×C₃	—	3	2	no	—
235	C₂³×C₃	C₂×C₄×C₉	1	1	yes	characteristic
236	C₂³×C₃	C₃×C₄×D₃	1	1	yes	characteristic
237	C₂²×D₃	C₂×C₄×C₉	1	2	yes	—
238	C₃×Q₈	—	6	1	no	—
239	C₃×Q₈	—	6	1	no	—
240	C₃×D₄	—	6	2	no	—
241	C₃×D₄	—	6	2	no	—
242	C₃×D₄	—	6	1	no	—
243	C₃×D₄	—	6	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	3	2	no	—
251	C₂×C₃×C₄	—	6	2	no	—
252	C₂×C₃×C₄	—	6	2	no	—
253	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
254	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
255	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
256	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
257	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
259	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
260	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
261	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
262	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
263	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
265	#67	—	2	2	no	—
266	#67	—	2	2	no	—
267	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	—
268	D₁₂	—	2	1	no	—
269	D₁₂	—	2	1	no	—
270	C₄×D₃	—	2	2	no	—
271	C₄×D₃	—	2	2	no	—
272	Dic₆	—	2	1	no	—
273	Dic₆	—	2	1	no	—
274	C₃×C₈	—	2	4	no	—
275	C₃×C₈	—	2	2	no	—
276	C₃×C₈	—	2	2	no	—
277	C₃×C₈	—	6	2	no	—
278	C₃⋊C₈	—	2	2	no	—
279	C₂×C₃²	—	2	1	no	—
280	C₂×C₃²	—	2	1	no	—
281	C₂×C₃²	—	2	1	no	—
282	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
283	C₃×D₃	—	4	2	no	—
284	C₂×C₉	—	2	2	no	—
285	C₂×C₉	—	2	1	no	—
286	C₂×C₉	—	2	1	no	—
287	C₂×C₉	—	2	1	no	—
288	C₂×C₉	—	2	1	no	—
289	C₂×C₉	—	4	1	no	—
290	C₂×C₉	—	4	1	no	—
291	C₂×C₉	—	12	2	no	—
292	C₂×C₉	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
293	#41	—	6	1	no	—
294	#41	—	6	1	no	—
295	#41	—	6	1	no	—
296	#41	—	6	1	no	—
297	C₂×Q₈	—	3	1	no	—
298	C₂×D₄	—	3	2	no	—
299	C₂×D₄	—	3	1	no	—
300	C₂²×C₄	—	3	2	no	—
301	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
302	M₁₆	—	2	1	no	—
303	M₁₆	—	3	2	no	—
304	M₁₆	—	6	1	no	—
305	M₁₆	C₂×D₃×C₉	1	2	yes	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	6	1	no	—
308	C₂²×C₃	—	2	1	no	—
309	C₂²×C₃	—	2	1	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	4	1	no	—
312	C₂²×C₃	—	4	1	no	—
313	C₂²×C₃	—	4	2	no	—
314	C₂²×C₃	—	6	2	no	—
315	C₂²×C₃	—	12	2	no	—
316	C₂²×C₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
317	C₂²×C₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
318	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
319	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
320	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
321	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
322	C₂×D₃	—	2	2	no	—
323	C₂×D₃	—	4	2	no	—
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	6	2	no	—
329	C₃×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
330	C₃×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
331	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
332	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
333	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
334	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
335	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
336	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
337	Dic₃	—	2	2	no	—
338	C₃²	C₃×#413	1	1	yes	characteristic
339	C₉	—	2	1	no	—
340	C₉	#5132	1	1	yes	characteristic, direct product factor
341	C₂³	—	3	2	no	—
342	C₂³	C₄×D₃×C₉	1	1	yes	characteristic
343	Q₈	—	6	1	no	—
344	Q₈	—	6	1	no	—
345	D₄	—	6	2	no	—
346	D₄	—	6	2	no	—
347	D₄	—	6	1	no	—
348	D₄	—	6	1	no	—
349	C₂×C₄	—	3	2	no	—
350	C₂×C₄	—	6	2	no	—
351	C₂×C₄	—	6	2	no	—
352	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic
353	C₂×C₄	C₉×D₁₂	1	1	yes	characteristic
354	C₂×C₄	C₉×D₁₂	1	1	yes	characteristic
355	C₂×C₄	C₉×#67	1	1	yes	characteristic
356	C₂×C₄	C₉×#67	1	1	yes	characteristic
357	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
358	C₈	—	2	2	no	—
359	C₈	—	6	2	no	—
360	C₂×C₃	—	2	2	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	2	1	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	—	2	1	no	—
367	C₂×C₃	—	2	1	no	—
368	C₂×C₃	—	4	1	no	—
369	C₂×C₃	—	4	1	no	—
370	C₂×C₃	—	12	2	no	—
371	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
372	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
373	D₃	—	4	2	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	6	2	no	—
376	C₂²	—	12	2	no	—
377	C₂²	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
378	C₂²	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
379	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
380	C₄	—	6	2	no	—
381	C₄	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
382	C₄	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
383	C₄	C₂×C₉×D₁₂	1	1	yes	characteristic
384	C₄	C₂×C₉×#67	1	1	yes	characteristic
385	C₃	—	2	1	no	—
386	C₃	C₉×#413	1	1	yes	characteristic, complemented
387	C₃	C₃×#5132	1	1	yes	characteristic
388	C₂	—	2	1	no	—
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	12	2	no	—
392	C₂	C₂×C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃×C₉×M₁₆	C₂
socle	C₂×C₃²	C₂×C₃×C₂²⋊C₄
prime radical	C₂×C₃×#235	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₉×M₁₆	D₃
hypocenter	C₃	C₉×#413
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₉ ◁ C₂²×C₄×C₉ ◁ C₂×C₉×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₉×M₁₆	C₂	semidirect
3. C₂×C₉×#208	C₂	semidirect
4. C₉×#824	C₂	semidirect
5. C₉×#823	C₂	semidirect
31. C₂×C₉×M₁₆	D₃	semidirect
54. #5132	C₉	direct (N × H)
104. C₂×C₃×M₁₆	C₂×C₉	semidirect
106. C₂×#208	C₂×C₉	semidirect
109. #824	C₂×C₉	semidirect
110. #823	C₂×C₉	semidirect
229. C₂×M₁₆	D₃×C₉	semidirect
232. C₃×C₉	#413	semidirect
340. C₉	#5132	direct (N × H)
386. C₃	C₉×#413	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#235	2
C₂×C₃×C₉×M₁₆	2
C₂×C₉×#208	2
C₉×#824	2
C₉×#823	2
C₃×#5132	3
C₉×#413	3

Subgroups — C9×#5132 #13143189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5132 #13143189