Subgroups — C₉×#5172 #13143360

Order 1728.

554 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₉×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#938	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#213	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#821	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5172	C₃	1	1	yes	maximal, characteristic
9	C₉×#449	—	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	C₉×#239	—	2	2	no	—
14	C₉×#239	—	2	2	no	—
15	C₂×C₉×D₁₂	—	2	1	no	—
16	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₃×C₉	—	2	1	no	—
18	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
19	C₃×C₉×SD₁₆	—	2	2	no	—
20	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
21	C₉×#217	—	2	1	no	—
22	C₉×#213	—	2	2	no	—
23	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×#239	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃²×SD₁₆	C₂×C₃	1	1	yes	characteristic
27	C₃×#938	C₂×C₃	1	1	yes	characteristic
28	C₂×C₃×#213	C₂×C₃	1	1	yes	characteristic
29	C₂×C₉×#41	—	3	1	no	—
30	C₃×#835	C₂×C₃	1	1	yes	characteristic
31	C₃×#821	C₂×C₃	1	1	yes	characteristic
32	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic
33	C₂×C₉×SD₁₆	—	2	1	no	—
34	C₂×C₉×SD₁₆	D₃	1	1	yes	characteristic, complemented
35	C₂×C₉×D₈	—	3	1	no	—
36	C₉×#121	—	3	1	no	—
37	C₉×#103	—	3	1	no	—
38	C₉×#102	—	3	1	no	—
39	C₉×C₂²⋊C₈	—	3	1	no	—
40	C₂³×C₃×C₉	—	2	1	no	—
41	C₂²×D₃×C₉	—	2	1	no	—
42	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
43	C₃×Q₈×C₉	—	2	1	no	—
44	C₃×Q₈×C₉	D₄	1	2	yes	complemented
45	C₃×D₄×C₉	—	2	1	no	—
46	C₃×D₄×C₉	—	2	1	no	—
47	C₂×C₃×C₄×C₉	—	2	1	no	—
48	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
49	C₉×#67	—	4	2	no	—
50	C₂×C₉×Dic₃	—	2	1	no	—
51	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
52	C₉×D₁₂	—	2	4	no	—
53	C₉×D₁₂	—	2	1	no	—
54	C₉×D₁₂	D₄	1	2	yes	complemented
55	C₄×D₃×C₉	—	2	4	no	—
56	C₄×D₃×C₉	—	2	1	no	—
57	C₄×D₃×C₉	—	2	1	no	—
58	C₃×C₈×C₉	—	2	1	no	—
59	C₉×C₃⋊C₈	—	2	1	no	—
60	C₃×#449	—	3	1	no	—
61	#5172	C₉	1	1	yes	characteristic, direct product factor
62	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₃×#67	—	2	1	no	—
65	C₃×#239	—	2	2	no	—
66	C₃×#239	—	2	2	no	—
67	C₂×C₃×D₁₂	—	2	1	no	—
68	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₃×C₄×D₃	—	2	1	no	—
70	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
71	C₃²×SD₁₆	—	2	2	no	—
72	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₃×#217	—	2	1	no	—
74	C₃×#213	—	2	2	no	—
75	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
77	C₉×#41	—	6	2	no	—
78	C₉×#41	—	6	2	no	—
79	C₂×Q₈×C₉	—	2	1	no	—
80	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
81	C₂×D₄×C₉	—	2	1	no	—
82	C₂×D₄×C₉	—	3	1	no	—
83	C₂×D₄×C₉	—	6	1	no	—
84	C₂×D₄×C₉	—	6	1	no	—
85	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
86	C₂²×C₄×C₉	—	3	1	no	—
87	C₂²×C₄×C₉	—	6	1	no	—
88	C₉×SD₁₆	—	2	4	no	—
89	C₉×SD₁₆	—	2	2	no	—
90	C₉×D₈	—	6	2	no	—
91	C₂×C₈×C₉	—	2	1	no	—
92	C₂×C₈×C₉	—	3	1	no	—
93	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
94	C₉×C₄⋊C₄	—	3	1	no	—
95	C₉×C₂²⋊C₄	—	6	1	no	—
96	C₂²×C₃×C₉	—	4	1	no	—
97	C₂²×C₃×C₉	—	4	1	no	—
98	C₂²×C₃×C₉	—	4	1	no	—
99	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
100	C₂×D₃×C₉	—	2	1	no	—
101	C₂×D₃×C₉	—	2	2	no	—
102	C₂×D₃×C₉	—	2	1	no	—
103	C₂×D₃×C₉	—	2	1	no	—
104	C₂×D₃×C₉	—	4	1	no	—
105	C₂×D₃×C₉	—	4	1	no	—
106	C₃×C₄×C₉	—	2	2	no	—
107	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
108	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
109	C₉×Dic₃	—	2	1	no	—
110	C₉×Dic₃	—	4	1	no	—
111	C₂×C₃×#41	—	3	1	no	—
112	C₂×#239	C₂×C₉	1	1	yes	characteristic, complemented
113	C₂×C₃×SD₁₆	—	2	1	no	—
114	C₂×C₃×SD₁₆	C₂×C₉	1	1	yes	characteristic, complemented
115	C₂×C₃×SD₁₆	C₃×D₃	1	1	yes	characteristic
116	C₂×C₃×D₈	—	3	1	no	—
117	C₃×#121	—	3	1	no	—
118	#938	C₂×C₉	1	1	yes	characteristic, complemented
119	C₂×#213	C₂×C₉	1	1	yes	characteristic, complemented
120	C₃×#103	—	3	1	no	—
121	C₃×#102	—	3	1	no	—
122	C₃×C₂²⋊C₈	—	3	1	no	—
123	#835	C₂×C₉	1	1	yes	characteristic, complemented
124	#821	C₂×C₉	1	1	yes	characteristic, complemented
125	(C₂×D₃)⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
126	C₂³×C₃²	—	2	1	no	—
127	C₂²×C₃×D₃	—	2	1	no	—
128	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
129	C₃²×Q₈	—	2	1	no	—
130	C₃²×Q₈	C₃×D₄	1	2	yes	—
131	C₃²×D₄	—	2	1	no	—
132	C₃²×D₄	—	2	1	no	—
133	C₂×C₃²×C₄	—	2	1	no	—
134	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
135	C₃×#67	—	4	2	no	—
136	C₂×C₃×Dic₃	—	2	1	no	—
137	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
138	C₃×D₁₂	—	2	4	no	—
139	C₃×D₁₂	—	2	1	no	—
140	C₃×D₁₂	C₃×D₄	1	2	yes	—
141	C₃×C₄×D₃	—	2	4	no	—
142	C₃×C₄×D₃	—	2	1	no	—
143	C₃×C₄×D₃	—	2	1	no	—
144	C₂³×C₉	—	2	1	no	—
145	C₂³×C₉	—	3	1	no	—
146	C₂³×C₉	—	4	1	no	—
147	C₂³×C₉	—	6	1	no	—
148	C₃²×C₈	—	2	1	no	—
149	C₃×C₃⋊C₈	—	2	1	no	—
150	Q₈×C₉	—	2	1	no	—
151	Q₈×C₉	—	2	2	no	—
152	Q₈×C₉	—	4	1	no	—
153	Q₈×C₉	#67	1	2	yes	complemented
154	D₄×C₉	—	2	2	no	—
155	D₄×C₉	—	2	1	no	—
156	D₄×C₉	—	2	1	no	—
157	D₄×C₉	—	3	2	no	—
158	D₄×C₉	—	4	1	no	—
159	D₄×C₉	—	6	4	no	—
160	D₄×C₉	—	6	1	no	—
161	D₄×C₉	—	12	2	no	—
162	C₂×C₄×C₉	—	2	1	no	—
163	C₂×C₄×C₉	—	2	1	no	—
164	C₂×C₄×C₉	—	3	1	no	—
165	C₂×C₄×C₉	—	4	1	no	—
166	C₂×C₄×C₉	—	6	4	no	—
167	C₂×C₄×C₉	—	6	1	no	—
168	C₂×C₄×C₉	—	6	1	no	—
169	C₂×C₄×C₉	—	6	1	no	—
170	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
171	C₈×C₉	—	2	2	no	—
172	C₈×C₉	—	2	1	no	—
173	C₈×C₉	—	6	1	no	—
174	#449	—	3	1	no	Sylow
175	C₂×C₃×C₉	—	8	1	no	—
176	C₂×C₃×C₉	#120	1	1	yes	characteristic
177	C₂×C₃×C₉	#135	1	1	yes	characteristic
178	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
179	D₃×C₉	—	4	1	no	—
180	D₃×C₉	—	4	2	no	—
181	C₃×#41	—	6	2	no	—
182	C₃×#41	—	6	2	no	—
183	C₂×C₃×Q₈	—	2	1	no	—
184	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
185	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
186	C₂×C₃×D₄	—	2	1	no	—
187	C₂×C₃×D₄	—	3	1	no	—
188	C₂×C₃×D₄	—	6	1	no	—
189	C₂×C₃×D₄	—	6	1	no	—
190	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
191	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
192	C₂²×C₃×C₄	—	3	1	no	—
193	C₂²×C₃×C₄	—	6	1	no	—
194	C₂×#67	—	2	1	no	—
195	#239	—	2	2	no	—
196	#239	—	2	2	no	—
197	C₂×D₁₂	—	2	1	no	—
198	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
199	C₂×C₄×D₃	—	2	1	no	—
200	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
201	C₃×SD₁₆	—	2	4	no	—
202	C₃×SD₁₆	—	2	2	no	—
203	C₃×SD₁₆	—	2	2	no	—
204	C₃×D₈	—	6	2	no	—
205	C₂×C₃×C₈	—	2	1	no	—
206	C₂×C₃×C₈	—	3	1	no	—
207	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
208	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
209	C₃×C₄⋊C₄	—	3	1	no	—
210	C₃×C₂²⋊C₄	—	6	1	no	—
211	#217	—	2	1	no	—
212	#213	—	2	2	no	—
213	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
214	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
215	C₂²×C₃²	—	4	1	no	—
216	C₂²×C₃²	—	4	1	no	—
217	C₂²×C₃²	—	4	1	no	—
218	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
219	C₂×C₃×D₃	—	2	1	no	—
220	C₂×C₃×D₃	—	2	2	no	—
221	C₂×C₃×D₃	—	2	1	no	—
222	C₂×C₃×D₃	—	2	1	no	—
223	C₂×C₃×D₃	—	4	1	no	—
224	C₂×C₃×D₃	—	4	1	no	—
225	C₃²×C₄	—	2	2	no	—
226	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
227	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
228	C₃×Dic₃	—	2	1	no	—
229	C₃×Dic₃	—	4	1	no	—
230	C₂²×C₉	—	2	1	no	—
231	C₂²×C₉	—	4	2	no	—
232	C₂²×C₉	—	4	1	no	—
233	C₂²×C₉	—	4	1	no	—
234	C₂²×C₉	—	4	1	no	—
235	C₂²×C₉	—	6	1	no	—
236	C₂²×C₉	—	6	1	no	—
237	C₂²×C₉	—	6	2	no	—
238	C₂²×C₉	—	6	1	no	—
239	C₂²×C₉	—	8	1	no	—
240	C₂²×C₉	—	8	1	no	—
241	C₂²×C₉	—	12	1	no	—
242	C₂²×C₉	—	12	1	no	—
243	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
244	C₄×C₉	—	2	2	no	—
245	C₄×C₉	—	2	1	no	—
246	C₄×C₉	—	2	1	no	—
247	C₄×C₉	—	4	2	no	—
248	C₄×C₉	—	6	1	no	—
249	C₄×C₉	—	12	1	no	—
250	C₄×C₉	D₃×D₄	1	1	yes	characteristic
251	C₄×C₉	C₂×#67	1	1	yes	characteristic
252	C₂×#41	—	3	1	no	—
253	C₂×SD₁₆	D₃×C₉	1	1	yes	characteristic, complemented
254	C₂×D₈	—	3	1	no	—
255	#121	—	3	1	no	—
256	#103	—	3	1	no	—
257	#102	—	3	1	no	—
258	C₂²⋊C₈	—	3	1	no	—
259	C₃×C₉	#449	1	1	yes	characteristic, complemented, Sylow
260	C₂³×C₃	—	2	1	no	—
261	C₂³×C₃	—	2	1	no	—
262	C₂³×C₃	—	3	1	no	—
263	C₂³×C₃	—	4	1	no	—
264	C₂³×C₃	—	6	1	no	—
265	C₂²×D₃	—	2	1	no	—
266	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
267	C₃×Q₈	—	2	1	no	—
268	C₃×Q₈	—	2	1	no	—
269	C₃×Q₈	—	2	2	no	—
270	C₃×Q₈	—	4	1	no	—
271	C₃×Q₈	D₄×C₉	1	2	yes	complemented
272	C₃×Q₈	C₃×#67	1	2	yes	—
273	C₃×D₄	—	2	2	no	—
274	C₃×D₄	—	2	1	no	—
275	C₃×D₄	—	2	1	no	—
276	C₃×D₄	—	2	1	no	—
277	C₃×D₄	—	2	1	no	—
278	C₃×D₄	—	3	2	no	—
279	C₃×D₄	—	4	1	no	—
280	C₃×D₄	—	6	4	no	—
281	C₃×D₄	—	6	1	no	—
282	C₃×D₄	—	12	2	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	3	1	no	—
287	C₂×C₃×C₄	—	4	1	no	—
288	C₂×C₃×C₄	—	6	4	no	—
289	C₂×C₃×C₄	—	6	1	no	—
290	C₂×C₃×C₄	—	6	1	no	—
291	C₂×C₃×C₄	—	6	1	no	—
292	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
294	#67	—	4	2	no	—
295	C₂×Dic₃	—	2	1	no	—
296	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
297	D₁₂	—	2	4	no	—
298	D₁₂	—	2	1	no	—
299	D₁₂	D₄×C₉	1	2	yes	complemented
300	C₄×D₃	—	2	4	no	—
301	C₄×D₃	—	2	1	no	—
302	C₄×D₃	—	2	1	no	—
303	C₃×C₈	—	2	2	no	—
304	C₃×C₈	—	2	1	no	—
305	C₃×C₈	—	2	1	no	—
306	C₃×C₈	—	6	1	no	—
307	C₃⋊C₈	—	2	1	no	—
308	C₂×C₃²	—	8	1	no	—
309	C₂×C₃²	C₃×#120	1	1	yes	characteristic
310	C₂×C₃²	C₃×#135	1	1	yes	characteristic
311	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
312	C₃×D₃	—	4	1	no	—
313	C₃×D₃	—	4	2	no	—
314	C₂×C₉	—	2	1	no	—
315	C₂×C₉	—	2	1	no	—
316	C₂×C₉	—	2	1	no	—
317	C₂×C₉	—	8	2	no	—
318	C₂×C₉	—	8	1	no	—
319	C₂×C₉	—	12	1	no	—
320	C₂×C₉	—	12	2	no	—
321	C₂×C₉	#914	1	1	yes	characteristic
322	C₂×C₉	#916	1	1	yes	characteristic
323	C₂×C₉	#937	1	1	yes	characteristic
324	#41	—	6	2	no	—
325	#41	—	6	2	no	—
326	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
327	C₂×D₄	—	3	1	no	—
328	C₂×D₄	—	6	1	no	—
329	C₂×D₄	—	6	1	no	—
330	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
331	C₂²×C₄	—	3	1	no	—
332	C₂²×C₄	—	6	1	no	—
333	SD₁₆	—	2	2	no	—
334	D₈	—	6	2	no	—
335	C₂×C₈	—	3	1	no	—
336	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
337	C₄⋊C₄	—	3	1	no	—
338	C₂²⋊C₄	—	6	1	no	—
339	C₂²×C₃	—	2	1	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	—	4	1	no	—
345	C₂²×C₃	—	4	1	no	—
346	C₂²×C₃	—	4	1	no	—
347	C₂²×C₃	—	6	1	no	—
348	C₂²×C₃	—	6	1	no	—
349	C₂²×C₃	—	6	2	no	—
350	C₂²×C₃	—	6	1	no	—
351	C₂²×C₃	—	8	1	no	—
352	C₂²×C₃	—	8	1	no	—
353	C₂²×C₃	—	12	1	no	—
354	C₂²×C₃	—	12	1	no	—
355	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
356	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
357	C₂×D₃	—	2	1	no	—
358	C₂×D₃	—	2	2	no	—
359	C₂×D₃	—	2	1	no	—
360	C₂×D₃	—	2	1	no	—
361	C₂×D₃	—	4	1	no	—
362	C₂×D₃	—	4	1	no	—
363	C₃×C₄	—	2	2	no	—
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	2	1	no	—
366	C₃×C₄	—	2	1	no	—
367	C₃×C₄	—	4	2	no	—
368	C₃×C₄	—	6	1	no	—
369	C₃×C₄	—	12	1	no	—
370	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
371	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
372	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
373	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
374	Dic₃	—	2	1	no	—
375	Dic₃	—	4	1	no	—
376	C₃²	C₃×#449	1	1	yes	characteristic
377	C₉	—	2	1	no	—
378	C₉	#5172	1	1	yes	characteristic, direct product factor
379	C₂³	—	2	1	no	—
380	C₂³	—	3	1	no	—
381	C₂³	—	6	1	no	—
382	Q₈	—	2	1	no	—
383	Q₈	C₉×#67	1	2	yes	complemented
384	D₄	—	2	1	no	—
385	D₄	—	2	1	no	—
386	D₄	—	3	2	no	—
387	D₄	—	6	4	no	—
388	D₄	—	6	1	no	—
389	D₄	—	12	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	3	1	no	—
392	C₂×C₄	—	6	4	no	—
393	C₂×C₄	—	6	1	no	—
394	C₂×C₄	—	6	1	no	—
395	C₂×C₄	—	6	1	no	—
396	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
397	C₈	—	2	1	no	—
398	C₈	—	6	1	no	—
399	C₂×C₃	—	2	1	no	—
400	C₂×C₃	—	2	1	no	—
401	C₂×C₃	—	2	1	no	—
402	C₂×C₃	—	8	2	no	—
403	C₂×C₃	—	8	1	no	—
404	C₂×C₃	—	8	1	no	—
405	C₂×C₃	—	12	1	no	—
406	C₂×C₃	—	12	2	no	—
407	C₂×C₃	C₉×#120	1	1	yes	characteristic
408	C₂×C₃	C₉×#135	1	1	yes	characteristic
409	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
410	C₂×C₃	C₃×#914	1	1	yes	characteristic
411	C₂×C₃	C₃×#916	1	1	yes	characteristic
412	C₂×C₃	C₃×#937	1	1	yes	characteristic
413	D₃	—	4	1	no	—
414	D₃	—	4	2	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	6	1	no	—
419	C₂²	—	6	1	no	—
420	C₂²	—	6	2	no	—
421	C₂²	—	6	1	no	—
422	C₂²	—	12	1	no	—
423	C₂²	—	12	1	no	—
424	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
425	C₄	—	2	2	no	—
426	C₄	—	6	1	no	—
427	C₄	—	12	1	no	—
428	C₄	D₃×D₄×C₉	1	1	yes	characteristic
429	C₄	C₂×C₉×#67	1	1	yes	characteristic
430	C₃	—	2	1	no	—
431	C₃	C₉×#449	1	1	yes	characteristic, complemented
432	C₃	C₃×#5172	1	1	yes	characteristic
433	C₂	—	8	1	no	—
434	C₂	—	12	1	no	—
435	C₂	—	12	2	no	—
436	C₂	C₉×#914	1	1	yes	characteristic
437	C₂	C₉×#916	1	1	yes	characteristic
438	C₂	C₉×#937	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×#5172	C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₉×SD₁₆	D₃
hypocenter	C₃	C₉×#449
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×C₉×#239	C₂	semidirect
2. C₂×C₃×C₉×SD₁₆	C₂	semidirect
3. C₉×#938	C₂	semidirect
4. C₂×C₉×#213	C₂	semidirect
5. C₉×#835	C₂	semidirect
6. C₉×#821	C₂	semidirect
7. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
34. C₂×C₉×SD₁₆	D₃	semidirect
44. C₃×Q₈×C₉	D₄	semidirect
54. C₉×D₁₂	D₄	semidirect
61. #5172	C₉	direct (N × H)
112. C₂×#239	C₂×C₉	semidirect
114. C₂×C₃×SD₁₆	C₂×C₉	semidirect
118. #938	C₂×C₉	semidirect
119. C₂×#213	C₂×C₉	semidirect
123. #835	C₂×C₉	semidirect
124. #821	C₂×C₉	semidirect
125. (C₂×D₃)⋊C₈	C₂×C₉	semidirect
153. Q₈×C₉	#67	semidirect
253. C₂×SD₁₆	D₃×C₉	semidirect
259. C₃×C₉	#449	semidirect
271. C₃×Q₈	D₄×C₉	semidirect
299. D₁₂	D₄×C₉	semidirect
378. C₉	#5172	direct (N × H)
383. Q₈	C₉×#67	semidirect
431. C₃	C₉×#449	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#239	2
C₂×C₃×C₉×SD₁₆	2
C₉×#938	2
C₂×C₉×#213	2
C₉×#835	2
C₉×#821	2
C₉×(C₂×D₃)⋊C₈	2
C₃×#5172	3
C₉×#449	3

Subgroups — C9×#5172 #13143360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5172 #13143360