Subgroups — #13138655

Order 1728.

524 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88640	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#3663	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11720542	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	(C₂×D₃)⋊(C₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	#11720282	C₂	1	1	yes	maximal, characteristic, complemented
8	#10590955	—	3	1	no	maximal
9	#10588409	—	3	1	no	maximal
10	C₂×C₄×C₃⋊D₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
13	C₂×#6195	C₄	1	1	yes	characteristic
14	C₂×#6194	C₄	1	1	yes	characteristic
15	C₂×#6192	C₄	1	1	yes	characteristic
16	C₂×#6189	C₄	1	1	yes	characteristic
17	#88640	—	2	2	no	—
18	#88640	—	2	2	no	—
19	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₃⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×#3663	—	2	2	no	—
24	D₉×C₃⋊C₈	—	2	2	no	—
25	C₂×#3798	—	3	1	no	—
26	C₂×C₃×ΓL(1,𝔽₂₅)	—	3	1	no	—
27	C₂×D₃×C₃⋊C₈	—	3	1	no	—
28	C₂×#3697	—	3	1	no	—
29	#63647	—	3	1	no	—
30	C₃×(C₂×D₃)⋊C₈	D₃	1	1	yes	characteristic
31	#63557	—	3	1	no	—
32	(C₂×D₃)⋊(C₃⋊C₈)	—	3	1	no	—
33	C₂×#3663	D₃	1	1	yes	characteristic, complemented
34	C₂×C₈×D₉	—	3	1	no	—
35	C₉×C₂²⋊C₈	—	3	1	no	—
36	#63389	—	3	1	no	—
37	(C₂×D₉)⋊C₈	—	3	1	no	—
38	(C₂×D₉)⋊C₈	—	3	1	no	—
39	(C₂×D₉)⋊C₈	—	6	1	no	—
40	C₂²×C₃⋊D₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×D₃×C₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×D₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
44	C₂×C₃⋊Dic₉	C₂×C₄	1	1	yes	characteristic
45	C₄×C₃⋊D₉	—	2	1	no	—
46	C₄×C₃⋊D₉	—	2	1	no	—
47	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×Dic₉	C₂×C₄	1	1	yes	characteristic
49	C₄×D₃×C₉	—	2	1	no	—
50	C₄×D₃×C₉	—	2	1	no	—
51	C₃×C₄×D₉	D₄	1	2	yes	—
52	C₃×C₄×D₉	D₄	1	2	yes	—
53	#6195	—	2	2	no	—
54	#6194	—	2	2	no	—
55	#6192	—	2	2	no	—
56	#6189	—	2	2	no	—
57	C₃×C₈×C₉	—	2	1	no	—
58	C₃⋊(C₉⋊C₈)	—	2	1	no	—
59	C₉×C₃⋊C₈	—	2	1	no	—
60	C₃×C₉⋊C₈	—	2	1	no	—
61	#5129	—	9	1	no	—
62	#4727	—	9	1	no	—
63	C₂×C₄×C₃⋊D₃	—	3	1	no	—
64	C₂×C₃×C₄×D₃	—	3	1	no	—
65	C₂×C₃×C₄×D₃	C₂×D₃	1	1	yes	characteristic
66	C₂×#627	—	3	1	no	—
67	C₂×#626	—	3	1	no	—
68	C₂×#626	—	3	1	no	—
69	C₂×#625	—	3	1	no	—
70	#3798	—	6	2	no	—
71	#3798	—	6	2	no	—
72	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
73	C₂×C₃⋊(C₃⋊C₈)	—	3	1	no	—
74	C₂×C₃×C₃⋊C₈	—	3	1	no	—
75	C₂×C₃×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
76	C₃×ΓL(1,𝔽₂₅)	—	6	2	no	—
77	D₃×C₃⋊C₈	—	6	2	no	—
78	C₂²×C₄×C₉	—	3	1	no	—
79	C₂×#611	—	3	1	no	—
80	C₂×#611	—	3	1	no	—
81	#3697	—	6	2	no	—
82	#3697	—	6	2	no	—
83	C₂×D₃₆	—	3	1	no	—
84	C₂×C₄×D₉	—	3	1	no	—
85	C₂×C₄×D₉	—	6	1	no	—
86	C₂×C₄×D₉	C₂×D₃	1	1	yes	characteristic
87	C₂×Dic₁₈	—	3	1	no	—
88	C₂×C₈×C₉	—	2	1	no	—
89	C₂×C₈×C₉	—	3	1	no	—
90	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
91	C₂×C₉⋊C₈	—	3	1	no	—
92	C₂×C₉⋊C₈	—	6	1	no	—
93	C₂×C₉⋊C₈	C₂×D₃	1	1	yes	characteristic
94	#3663	—	2	2	no	—
95	C₈×D₉	—	6	2	no	—
96	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃⋊D₉	—	2	1	no	—
98	C₂×C₃⋊D₉	—	2	1	no	—
99	C₂×C₃⋊D₉	—	2	1	no	—
100	C₂×D₃×C₉	—	2	1	no	—
101	C₂×D₃×C₉	—	2	1	no	—
102	C₂×D₃×C₉	—	2	1	no	—
103	C₂×C₃×D₉	—	2	1	no	—
104	C₂×C₃×D₉	—	2	1	no	—
105	C₂×C₃×D₉	C₂²⋊C₄	1	2	yes	—
106	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
107	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
108	C₃⋊Dic₉	—	2	1	no	—
109	C₉×Dic₃	—	2	1	no	—
110	C₃×Dic₉	C₂²⋊C₄	1	2	yes	—
111	C₂×#235	—	9	1	no	—
112	C₂×#235	—	9	1	no	—
113	C₂×C₃×M₁₆	—	9	1	no	—
114	C₂²×C₃⋊C₈	—	9	1	no	—
115	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
116	C₂×D₃×C₈	—	9	1	no	—
117	C₃×C₂²⋊C₈	—	3	1	no	—
118	#830	—	9	1	no	—
119	(C₂×D₃)⋊C₈	—	9	1	no	—
120	(C₂×D₃)⋊C₈	—	9	1	no	—
121	(C₂×D₃)⋊C₈	—	9	1	no	—
122	(C₂×D₃)⋊C₈	—	9	1	no	—
123	(C₂×D₃)⋊C₈	—	9	1	no	—
124	(C₂×D₃)⋊C₈	—	18	1	no	—
125	(C₂×D₃)⋊C₈	D₉	1	1	yes	characteristic, complemented
126	C₂²×C₃⋊D₃	—	3	1	no	—
127	C₂²×C₃×D₃	—	3	1	no	—
128	C₂²×C₃×D₃	C₄×D₃	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
130	C₂×C₃⋊Dic₃	—	3	1	no	—
131	C₄×C₃⋊D₃	—	6	1	no	—
132	C₄×C₃⋊D₃	—	6	1	no	—
133	C₂×C₃×Dic₃	—	3	1	no	—
134	C₂×C₃×Dic₃	C₄×D₃	1	1	yes	characteristic
135	C₃×C₄×D₃	—	2	1	no	—
136	C₃×C₄×D₃	—	2	1	no	—
137	C₃×C₄×D₃	—	3	2	no	—
138	C₃×C₄×D₃	—	3	2	no	—
139	#627	—	6	2	no	—
140	#626	—	6	2	no	—
141	#626	—	6	2	no	—
142	#625	—	6	2	no	—
143	C₂³×C₉	—	3	1	no	—
144	C₂²×D₉	—	3	1	no	—
145	C₂²×D₉	—	6	1	no	—
146	C₂²×D₉	C₄×D₃	1	1	yes	characteristic
147	C₃²×C₈	—	2	1	no	—
148	C₃⋊(C₃⋊C₈)	—	6	1	no	—
149	C₃×C₃⋊C₈	—	2	1	no	—
150	C₃×C₃⋊C₈	—	6	1	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	3	1	no	—
153	C₂×C₄×C₉	—	6	1	no	—
154	C₂×C₄×C₉	—	6	1	no	—
155	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
156	#611	—	6	2	no	—
157	#611	—	6	2	no	—
158	C₂×Dic₉	—	3	1	no	—
159	C₂×Dic₉	—	6	1	no	—
160	C₂×Dic₉	C₄×D₃	1	1	yes	characteristic
161	D₃₆	—	6	2	no	—
162	C₄×D₉	—	6	1	no	—
163	C₄×D₉	—	6	1	no	—
164	C₄×D₉	—	12	1	no	—
165	C₄×D₉	—	12	1	no	—
166	C₄×D₉	D₁₂	1	2	yes	—
167	C₄×D₉	#67	1	2	yes	—
168	Dic₁₈	—	6	2	no	—
169	C₈×C₉	—	2	1	no	—
170	C₈×C₉	—	4	1	no	—
171	C₈×C₉	—	6	1	no	—
172	C₉⋊C₈	—	2	1	no	—
173	C₉⋊C₈	—	6	1	no	—
174	C₉⋊C₈	—	12	1	no	—
175	#408	—	27	1	no	Sylow
176	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₃×C₉	#131	1	1	yes	characteristic
178	C₂×C₃×C₉	#131	1	1	yes	characteristic
179	C₃⋊D₉	—	4	1	no	—
180	D₃×C₉	—	4	1	no	—
181	C₃×D₉	—	2	2	no	—
182	C₂²×C₃×C₄	—	3	1	no	—
183	C₂²×C₃×C₄	—	9	1	no	—
184	C₂×#67	—	9	1	no	—
185	C₂×#67	—	9	1	no	—
186	C₂×#67	—	9	1	no	—
187	C₂×#67	—	9	1	no	—
188	#235	—	18	2	no	—
189	#235	—	18	2	no	—
190	#235	—	18	2	no	—
191	#235	—	18	2	no	—
192	C₂×D₁₂	—	9	1	no	—
193	C₂×D₁₂	—	9	1	no	—
194	C₂×C₄×D₃	—	3	1	no	—
195	C₂×C₄×D₃	—	9	1	no	—
196	C₂×C₄×D₃	—	9	1	no	—
197	C₂×C₄×D₃	—	18	1	no	—
198	C₂×C₄×D₃	C₂×D₉	1	1	yes	characteristic
199	C₂×Dic₆	—	9	1	no	—
200	C₂×Dic₆	—	9	1	no	—
201	C₃×M₁₆	—	18	2	no	—
202	C₂×C₃×C₈	—	2	1	no	—
203	C₂×C₃×C₈	—	3	1	no	—
204	C₂×C₃×C₈	—	9	1	no	—
205	C₂×C₃×C₈	C₂×D₉	1	1	yes	characteristic
206	C₂×C₃×C₈	D₃²	1	1	yes	characteristic
207	C₂×C₃⋊C₈	—	3	1	no	—
208	C₂×C₃⋊C₈	—	9	1	no	—
209	C₂×C₃⋊C₈	—	9	1	no	—
210	C₂×C₃⋊C₈	—	18	1	no	—
211	C₂×C₃⋊C₈	—	18	2	no	—
212	C₂×C₃⋊C₈	C₂×D₉	1	1	yes	characteristic
213	ΓL(1,𝔽₂₅)	—	6	2	no	—
214	D₃×C₈	—	18	2	no	—
215	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
216	C₂×C₃⋊D₃	—	6	1	no	—
217	C₂×C₃⋊D₃	—	6	1	no	—
218	C₂×C₃⋊D₃	—	6	1	no	—
219	C₂×C₃×D₃	—	2	1	no	—
220	C₂×C₃×D₃	—	2	1	no	—
221	C₂×C₃×D₃	—	2	1	no	—
222	C₂×C₃×D₃	—	3	2	no	—
223	C₂×C₃×D₃	—	6	1	no	—
224	C₂×C₃×D₃	—	6	1	no	—
225	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
226	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
227	C₃⋊Dic₃	—	6	1	no	—
228	C₃×Dic₃	—	2	1	no	—
229	C₃×Dic₃	—	3	2	no	—
230	C₂²×C₉	—	2	1	no	—
231	C₂²×C₉	—	6	1	no	—
232	C₂²×C₉	—	6	1	no	—
233	C₂²×C₉	—	6	1	no	—
234	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
235	C₂×D₉	—	2	1	no	—
236	C₂×D₉	—	2	1	no	—
237	C₂×D₉	—	6	2	no	—
238	C₂×D₉	—	6	1	no	—
239	C₂×D₉	—	6	1	no	—
240	C₂×D₉	—	6	1	no	—
241	C₂×D₉	—	12	1	no	—
242	C₂×D₉	—	12	1	no	—
243	C₂×D₉	(C₂×D₃)⋊C₄	1	2	yes	—
244	C₄×C₉	—	2	1	no	—
245	C₄×C₉	—	2	1	no	—
246	C₄×C₉	—	6	1	no	—
247	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
248	C₄×C₉	C₂×#67	1	1	yes	characteristic
249	Dic₉	—	6	1	no	—
250	Dic₉	—	12	1	no	—
251	Dic₉	(C₂×D₃)⋊C₄	1	2	yes	—
252	C₂×#41	—	27	1	no	—
253	C₂×M₁₆	—	9	1	no	—
254	C₂²×C₈	—	27	1	no	—
255	C₂²⋊C₈	—	3	1	no	—
256	C₂²⋊C₈	—	27	1	no	—
257	C₂²⋊C₈	—	27	1	no	—
258	C₂²⋊C₈	—	27	1	no	—
259	C₃×C₉	#408	1	1	yes	characteristic, complemented, Sylow
260	C₂³×C₃	—	3	1	no	—
261	C₂³×C₃	—	9	1	no	—
262	C₂²×D₃	—	3	1	no	—
263	C₂²×D₃	—	9	1	no	—
264	C₂²×D₃	—	9	1	no	—
265	C₂²×D₃	—	18	1	no	—
266	C₂²×D₃	C₄×D₉	1	1	yes	characteristic
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	3	1	no	—
269	C₂×C₃×C₄	—	6	1	no	—
270	C₂×C₃×C₄	—	6	1	no	—
271	C₂×C₃×C₄	—	9	1	no	—
272	C₂×C₃×C₄	—	9	2	no	—
273	C₂×C₃×C₄	—	9	2	no	—
274	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
276	#67	—	18	2	no	—
277	#67	—	18	2	no	—
278	#67	—	18	2	no	—
279	#67	—	18	2	no	—
280	C₂×Dic₃	—	3	1	no	—
281	C₂×Dic₃	—	9	1	no	—
282	C₂×Dic₃	—	9	1	no	—
283	C₂×Dic₃	—	18	1	no	—
284	C₂×Dic₃	C₄×D₉	1	1	yes	characteristic
285	D₁₂	—	18	2	no	—
286	D₁₂	—	18	2	no	—
287	C₄×D₃	—	2	1	no	—
288	C₄×D₃	—	2	1	no	—
289	C₄×D₃	—	3	2	no	—
290	C₄×D₃	—	3	2	no	—
291	C₄×D₃	—	18	1	no	—
292	C₄×D₃	—	18	1	no	—
293	C₄×D₃	—	18	1	no	—
294	C₄×D₃	—	18	1	no	—
295	C₄×D₃	—	36	1	no	—
296	C₄×D₃	—	36	1	no	—
297	Dic₆	—	18	2	no	—
298	Dic₆	—	18	2	no	—
299	C₃×C₈	—	2	1	no	—
300	C₃×C₈	—	2	1	no	—
301	C₃×C₈	—	4	1	no	—
302	C₃×C₈	—	6	1	no	—
303	C₃×C₈	—	18	1	no	—
304	C₃⋊C₈	—	2	1	no	—
305	C₃⋊C₈	—	6	1	no	—
306	C₃⋊C₈	—	18	1	no	—
307	C₃⋊C₈	—	18	1	no	—
308	C₃⋊C₈	—	36	1	no	—
309	C₂×C₃²	D₃×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₃²	#901	1	1	yes	characteristic
311	C₂×C₃²	#907	1	1	yes	characteristic
312	C₃⋊D₃	—	12	1	no	—
313	C₃×D₃	—	4	1	no	—
314	C₃×D₃	—	6	2	no	—
315	C₂×C₉	—	2	1	no	—
316	C₂×C₉	—	2	1	no	—
317	C₂×C₉	—	2	1	no	—
318	C₂×C₉	—	12	1	no	—
319	C₂×C₉	#907	1	1	yes	characteristic
320	C₂×C₉	#907	1	1	yes	characteristic
321	C₂×C₉	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
322	D₉	—	2	2	no	—
323	D₉	—	12	2	no	—
324	D₉	—	12	1	no	—
325	#41	—	54	2	no	—
326	#41	—	54	2	no	—
327	C₂×Q₈	—	27	1	no	—
328	C₂×D₄	—	27	1	no	—
329	C₂×D₄	—	27	1	no	—
330	C₂×D₄	—	27	1	no	—
331	C₂²×C₄	—	3	1	no	—
332	C₂²×C₄	—	9	1	no	—
333	C₂²×C₄	—	27	1	no	—
334	M₁₆	—	18	2	no	—
335	C₂×C₈	—	3	1	no	—
336	C₂×C₈	—	9	1	no	—
337	C₂×C₈	—	27	1	no	—
338	C₂×C₈	—	54	2	no	—
339	C₂×C₈	D₃×D₉	1	1	yes	characteristic
340	C₂²×C₃	—	2	1	no	—
341	C₂²×C₃	—	6	1	no	—
342	C₂²×C₃	—	6	1	no	—
343	C₂²×C₃	—	6	1	no	—
344	C₂²×C₃	—	9	2	no	—
345	C₂²×C₃	—	18	1	no	—
346	C₂²×C₃	—	18	1	no	—
347	C₂²×C₃	C₂×C₄×D₉	1	1	yes	characteristic
348	C₂²×C₃	C₄×D₃²	1	1	yes	characteristic
349	C₂×D₃	—	2	1	no	—
350	C₂×D₃	—	2	1	no	—
351	C₂×D₃	—	2	1	no	—
352	C₂×D₃	—	3	2	no	—
353	C₂×D₃	—	6	1	no	—
354	C₂×D₃	—	6	1	no	—
355	C₂×D₃	—	18	2	no	—
356	C₂×D₃	—	18	1	no	—
357	C₂×D₃	—	18	1	no	—
358	C₂×D₃	—	18	1	no	—
359	C₂×D₃	—	18	1	no	—
360	C₂×D₃	—	18	1	no	—
361	C₂×D₃	—	18	1	no	—
362	C₂×D₃	—	36	1	no	—
363	C₂×D₃	—	36	1	no	—
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	2	1	no	—
366	C₃×C₄	—	6	1	no	—
367	C₃×C₄	—	9	2	no	—
368	C₃×C₄	D₄×D₉	1	1	yes	characteristic
369	C₃×C₄	D₄×D₉	1	1	yes	characteristic
370	C₃×C₄	D₃×D₁₂	1	1	yes	characteristic
371	C₃×C₄	D₃×#67	1	1	yes	characteristic
372	Dic₃	—	2	1	no	—
373	Dic₃	—	3	2	no	—
374	Dic₃	—	18	1	no	—
375	Dic₃	—	18	1	no	—
376	Dic₃	—	36	1	no	—
377	C₃²	#4727	1	1	yes	characteristic
378	C₉	—	2	1	no	—
379	C₉	#5129	1	1	yes	characteristic, complemented
380	C₂³	—	3	1	no	—
381	C₂³	—	9	1	no	—
382	C₂³	—	27	1	no	—
383	Q₈	—	54	2	no	—
384	D₄	—	54	2	no	—
385	D₄	—	54	2	no	—
386	D₄	—	54	2	no	—
387	C₂×C₄	—	3	1	no	—
388	C₂×C₄	—	6	1	no	—
389	C₂×C₄	—	6	1	no	—
390	C₂×C₄	—	9	1	no	—
391	C₂×C₄	—	9	2	no	—
392	C₂×C₄	—	9	2	no	—
393	C₂×C₄	—	27	1	no	—
394	C₂×C₄	—	54	1	no	—
395	C₂×C₄	—	54	1	no	—
396	C₂×C₄	C₂×D₃×D₉	1	1	yes	characteristic
397	C₈	—	2	1	no	—
398	C₈	—	6	1	no	—
399	C₈	—	18	1	no	—
400	C₈	—	54	1	no	—
401	C₂×C₃	—	2	1	no	—
402	C₂×C₃	—	2	1	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	12	1	no	—
405	C₂×C₃	—	18	2	no	—
406	C₂×C₃	C₂²⋊C₄×D₉	1	1	yes	characteristic
407	C₂×C₃	#63464	1	1	yes	characteristic
408	C₂×C₃	#63469	1	1	yes	characteristic
409	C₂×C₃	#63804	1	1	yes	characteristic
410	C₂×C₃	#63805	1	1	yes	characteristic
411	C₂×C₃	D₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
412	D₃	—	4	1	no	—
413	D₃	—	6	2	no	—
414	D₃	—	36	2	no	—
415	D₃	—	36	1	no	—
416	D₃	—	36	1	no	—
417	C₂²	—	6	1	no	—
418	C₂²	—	6	1	no	—
419	C₂²	—	6	1	no	—
420	C₂²	—	9	2	no	—
421	C₂²	—	18	1	no	—
422	C₂²	—	18	1	no	—
423	C₂²	—	54	1	no	—
424	C₂²	—	54	1	no	—
425	C₂²	—	54	1	no	—
426	C₂²	C₄×D₃×D₉	1	1	yes	characteristic
427	C₄	—	6	1	no	—
428	C₄	—	9	2	no	—
429	C₄	—	54	1	no	—
430	C₄	D₉×D₁₂	1	1	yes	characteristic
431	C₄	D₉×#67	1	1	yes	characteristic
432	C₃	—	2	1	no	—
433	C₃	#10588409	1	1	yes	characteristic, complemented
434	C₃	#10590955	1	1	yes	characteristic
435	C₂	—	12	1	no	—
436	C₂	—	18	2	no	—
437	C₂	—	108	1	no	—
438	C₂	#11720808	1	1	yes	characteristic
439	C₂	#11720809	1	1	yes	characteristic
440	C₂	D₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×D₉
commutator	C₂²×C₃×C₉	C₂²×C₄
Frattini	C₂×C₃×C₄	C₂×D₃²
Fitting	C₂×C₃×C₈×C₉	C₂²
socle	C₂²×C₃²	C₂×C₄×D₃
prime radical	C₂×#88640	C₂
cosocle	C₂×C₃×C₄×C₉	C₂³
hypercenter	C₂×C₈	D₃×D₉
hypocenter	C₃×C₉	#408
LCS	G ▷ C₂²×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#3663	C₂	semidirect
3. C₂×D₉×C₃⋊C₈	C₂	semidirect
4. #11720542	C₂	semidirect
5. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
6. (C₂×D₃)⋊(C₉⋊C₈)	C₂	semidirect
7. #11720282	C₂	semidirect
33. C₂×#3663	D₃	semidirect
125. (C₂×D₃)⋊C₈	D₉	semidirect
259. C₃×C₉	#408	semidirect
379. C₉	#5129	semidirect
433. C₃	#10588409	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88640	2
C₂×C₃×#3663	2
C₂×D₉×C₃⋊C₈	2
#11720542	2
C₉×(C₂×D₃)⋊C₈	2
(C₂×D₃)⋊(C₉⋊C₈)	2
#11720282	2
#10590955	3
#10588409	3