Subgroups — C₉×#5170 #13143356

Order 1728.

542 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×Q₈×C₉	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
4	C₂×C₉×#214	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#816	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5170	C₃	1	1	yes	maximal, characteristic
9	C₉×#448	—	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	D₃×Q₈×C₉	—	2	2	no	—
14	D₃×Q₈×C₉	—	2	2	no	—
15	C₂×C₄×D₃×C₉	—	2	1	no	—
16	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×Dic₆	—	2	1	no	—
18	C₂×C₉×Dic₆	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×#214	—	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×D₃×Q₈	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×#214	C₂×C₃	1	1	yes	characteristic
29	C₂²×Q₈×C₉	—	3	1	no	—
30	C₃×#835	C₂×C₃	1	1	yes	characteristic
31	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic
32	C₃×#816	C₂×C₃	1	1	yes	characteristic
33	C₂×C₉×SD₁₆	—	2	1	no	—
34	C₂×C₉×SD₁₆	—	3	1	no	—
35	C₂×C₉×SD₁₆	D₃	1	1	yes	characteristic, complemented
36	C₉×#121	—	3	1	no	—
37	C₉×#103	—	3	1	no	—
38	C₉×#103	—	3	1	no	—
39	C₉×C₂²⋊C₈	—	3	1	no	—
40	C₂³×C₃×C₉	—	2	1	no	—
41	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
42	C₃×Q₈×C₉	—	2	1	no	—
43	C₃×Q₈×C₉	D₄	1	2	yes	complemented
44	C₃×D₄×C₉	—	2	1	no	—
45	C₃×D₄×C₉	—	2	1	no	—
46	C₂×C₃×C₄×C₉	—	2	1	no	—
47	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
48	C₉×#67	—	4	2	no	—
49	C₂×C₉×Dic₃	—	2	1	no	—
50	C₂×C₉×Dic₃	—	2	1	no	—
51	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
52	C₄×D₃×C₉	—	2	4	no	—
53	C₄×D₃×C₉	—	2	1	no	—
54	C₄×D₃×C₉	—	2	1	no	—
55	C₉×Dic₆	—	2	4	no	—
56	C₉×Dic₆	—	2	1	no	—
57	C₉×Dic₆	D₄	1	2	yes	complemented
58	C₃×C₈×C₉	—	2	1	no	—
59	C₉×C₃⋊C₈	—	2	1	no	—
60	C₃×#448	—	3	1	no	—
61	#5170	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×D₃×Q₈	—	2	2	no	—
66	C₃×D₃×Q₈	—	2	2	no	—
67	C₂×C₃×C₄×D₃	—	2	1	no	—
68	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₃×Dic₆	—	2	1	no	—
70	C₂×C₃×Dic₆	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×#214	—	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	C₂×Q₈×C₉	—	2	1	no	—
78	C₂×Q₈×C₉	—	3	1	no	—
79	C₂×Q₈×C₉	—	6	1	no	—
80	C₂×Q₈×C₉	—	6	2	no	—
81	C₂×Q₈×C₉	—	6	2	no	—
82	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
83	C₂×D₄×C₉	—	2	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×SD₁₆	—	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	1	no	—
102	C₂×D₃×C₉	SD₁₆	1	2	yes	complemented
103	C₃×C₄×C₉	—	2	2	no	—
104	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
105	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
106	C₉×Dic₃	—	2	1	no	—
107	C₉×Dic₃	—	2	2	no	—
108	C₉×Dic₃	—	4	1	no	—
109	C₂²×C₃×Q₈	—	3	1	no	—
110	C₂×D₃×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
111	C₂×C₃×SD₁₆	—	2	1	no	—
112	C₂×C₃×SD₁₆	—	3	1	no	—
113	C₂×C₃×SD₁₆	C₂×C₉	1	1	yes	characteristic, complemented
114	C₂×C₃×SD₁₆	C₃×D₃	1	1	yes	characteristic
115	C₃×#121	—	3	1	no	—
116	#938	C₂×C₉	1	1	yes	characteristic
117	C₂×#214	C₂×C₉	1	1	yes	characteristic, complemented
118	C₃×#103	—	3	1	no	—
119	C₃×#103	—	3	1	no	—
120	C₃×C₂²⋊C₈	—	3	1	no	—
121	#835	C₂×C₉	1	1	yes	characteristic, complemented
122	(C₂×D₃)⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
123	#816	C₂×C₉	1	1	yes	characteristic, complemented
124	C₂³×C₃²	—	2	1	no	—
125	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
126	C₃²×Q₈	—	2	1	no	—
127	C₃²×Q₈	C₃×D₄	1	2	yes	—
128	C₃²×D₄	—	2	1	no	—
129	C₃²×D₄	—	2	1	no	—
130	C₂×C₃²×C₄	—	2	1	no	—
131	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
132	C₃×#67	—	4	2	no	—
133	C₂×C₃×Dic₃	—	2	1	no	—
134	C₂×C₃×Dic₃	—	2	1	no	—
135	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
136	C₃×C₄×D₃	—	2	4	no	—
137	C₃×C₄×D₃	—	2	1	no	—
138	C₃×C₄×D₃	—	2	1	no	—
139	C₃×Dic₆	—	2	4	no	—
140	C₃×Dic₆	—	2	1	no	—
141	C₃×Dic₆	C₃×D₄	1	2	yes	—
142	C₂³×C₉	—	2	1	no	—
143	C₂³×C₉	—	3	1	no	—
144	C₂³×C₉	—	4	1	no	—
145	C₃²×C₈	—	2	1	no	—
146	C₃×C₃⋊C₈	—	2	1	no	—
147	Q₈×C₉	—	2	1	no	—
148	Q₈×C₉	—	2	2	no	—
149	Q₈×C₉	—	3	2	no	—
150	Q₈×C₉	—	4	1	no	—
151	Q₈×C₉	—	6	4	no	—
152	Q₈×C₉	—	6	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	—	4	1	no	—
158	D₄×C₉	—	12	2	no	—
159	C₂×C₄×C₉	—	2	1	no	—
160	C₂×C₄×C₉	—	2	1	no	—
161	C₂×C₄×C₉	—	3	1	no	—
162	C₂×C₄×C₉	—	4	1	no	—
163	C₂×C₄×C₉	—	6	4	no	—
164	C₂×C₄×C₉	—	6	1	no	—
165	C₂×C₄×C₉	—	6	1	no	—
166	C₂×C₄×C₉	—	6	1	no	—
167	C₂×C₄×C₉	—	6	1	no	—
168	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
169	C₈×C₉	—	2	2	no	—
170	C₈×C₉	—	2	1	no	—
171	C₈×C₉	—	6	1	no	—
172	#448	—	3	1	no	Sylow
173	C₂×C₃×C₉	—	8	1	no	—
174	C₂×C₃×C₉	#120	1	1	yes	characteristic
175	C₂×C₃×C₉	C₂×SD₁₆	1	1	yes	characteristic
176	C₂×C₃×C₉	#137	1	1	yes	characteristic
177	D₃×C₉	—	2	2	no	—
178	C₂×C₃×Q₈	—	2	1	no	—
179	C₂×C₃×Q₈	—	3	1	no	—
180	C₂×C₃×Q₈	—	6	1	no	—
181	C₂×C₃×Q₈	—	6	2	no	—
182	C₂×C₃×Q₈	—	6	2	no	—
183	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
184	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
185	C₂×C₃×D₄	—	2	1	no	—
186	C₂×C₃×D₄	—	6	1	no	—
187	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
188	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
189	C₂²×C₃×C₄	—	3	1	no	—
190	C₂²×C₃×C₄	—	6	1	no	—
191	C₂×#67	—	2	1	no	—
192	D₃×Q₈	—	2	2	no	—
193	D₃×Q₈	—	2	2	no	—
194	C₂×C₄×D₃	—	2	1	no	—
195	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
196	C₂×Dic₆	—	2	1	no	—
197	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
198	C₃×SD₁₆	—	2	4	no	—
199	C₃×SD₁₆	—	2	2	no	—
200	C₃×SD₁₆	—	2	2	no	—
201	C₃×SD₁₆	—	6	2	no	—
202	C₂×C₃×C₈	—	2	1	no	—
203	C₂×C₃×C₈	—	3	1	no	—
204	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
205	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
206	C₃×C₄⋊C₄	—	3	1	no	—
207	C₃×C₂²⋊C₄	—	6	1	no	—
208	#217	—	2	1	no	—
209	#214	—	2	2	no	—
210	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
211	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
212	C₂²×C₃²	—	4	1	no	—
213	C₂²×C₃²	—	4	1	no	—
214	C₂²×C₃²	—	4	1	no	—
215	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
216	C₂×C₃×D₃	—	2	1	no	—
217	C₂×C₃×D₃	—	2	1	no	—
218	C₂×C₃×D₃	C₃×SD₁₆	1	2	yes	—
219	C₃²×C₄	—	2	2	no	—
220	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
221	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
222	C₃×Dic₃	—	2	1	no	—
223	C₃×Dic₃	—	2	2	no	—
224	C₃×Dic₃	—	4	1	no	—
225	C₂²×C₉	—	2	1	no	—
226	C₂²×C₉	—	3	2	no	—
227	C₂²×C₉	—	4	2	no	—
228	C₂²×C₉	—	4	1	no	—
229	C₂²×C₉	—	4	1	no	—
230	C₂²×C₉	—	4	1	no	—
231	C₂²×C₉	—	6	1	no	—
232	C₂²×C₉	—	6	1	no	—
233	C₂²×C₉	—	8	1	no	—
234	C₂²×C₉	—	8	1	no	—
235	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
236	C₄×C₉	—	2	2	no	—
237	C₄×C₉	—	2	1	no	—
238	C₄×C₉	—	2	1	no	—
239	C₄×C₉	—	4	2	no	—
240	C₄×C₉	—	6	1	no	—
241	C₄×C₉	—	6	2	no	—
242	C₄×C₉	—	12	1	no	—
243	C₄×C₉	D₃×D₄	1	1	yes	characteristic
244	C₄×C₉	C₂×#67	1	1	yes	characteristic
245	C₂²×Q₈	—	3	1	no	—
246	C₂×SD₁₆	—	3	1	no	—
247	C₂×SD₁₆	D₃×C₉	1	1	yes	characteristic, complemented
248	#121	—	3	1	no	—
249	#103	—	3	1	no	—
250	#103	—	3	1	no	—
251	C₂²⋊C₈	—	3	1	no	—
252	C₃×C₉	#448	1	1	yes	characteristic, complemented, Sylow
253	C₂³×C₃	—	2	1	no	—
254	C₂³×C₃	—	2	1	no	—
255	C₂³×C₃	—	3	1	no	—
256	C₂³×C₃	—	4	1	no	—
257	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
258	C₃×Q₈	—	2	1	no	—
259	C₃×Q₈	—	2	1	no	—
260	C₃×Q₈	—	2	2	no	—
261	C₃×Q₈	—	3	2	no	—
262	C₃×Q₈	—	4	1	no	—
263	C₃×Q₈	—	6	4	no	—
264	C₃×Q₈	—	6	1	no	—
265	C₃×Q₈	D₄×C₉	1	2	yes	complemented
266	C₃×Q₈	C₃×#67	1	2	yes	—
267	C₃×D₄	—	2	2	no	—
268	C₃×D₄	—	2	1	no	—
269	C₃×D₄	—	2	1	no	—
270	C₃×D₄	—	2	1	no	—
271	C₃×D₄	—	2	1	no	—
272	C₃×D₄	—	4	1	no	—
273	C₃×D₄	—	12	2	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	3	1	no	—
278	C₂×C₃×C₄	—	4	1	no	—
279	C₂×C₃×C₄	—	6	4	no	—
280	C₂×C₃×C₄	—	6	1	no	—
281	C₂×C₃×C₄	—	6	1	no	—
282	C₂×C₃×C₄	—	6	1	no	—
283	C₂×C₃×C₄	—	6	1	no	—
284	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
286	#67	—	4	2	no	—
287	C₂×Dic₃	—	2	1	no	—
288	C₂×Dic₃	—	2	1	no	—
289	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
290	C₄×D₃	—	2	4	no	—
291	C₄×D₃	—	2	1	no	—
292	C₄×D₃	—	2	1	no	—
293	Dic₆	—	2	4	no	—
294	Dic₆	—	2	1	no	—
295	Dic₆	D₄×C₉	1	2	yes	complemented
296	C₃×C₈	—	2	2	no	—
297	C₃×C₈	—	2	1	no	—
298	C₃×C₈	—	2	1	no	—
299	C₃×C₈	—	6	1	no	—
300	C₃⋊C₈	—	2	1	no	—
301	C₂×C₃²	—	8	1	no	—
302	C₂×C₃²	C₃×#120	1	1	yes	characteristic
303	C₂×C₃²	C₂×C₃×SD₁₆	1	1	yes	characteristic
304	C₂×C₃²	C₃×#137	1	1	yes	characteristic
305	C₃×D₃	—	2	2	no	—
306	C₂×C₉	—	2	1	no	—
307	C₂×C₉	—	2	1	no	—
308	C₂×C₉	—	2	1	no	—
309	C₂×C₉	—	6	2	no	—
310	C₂×C₉	—	8	2	no	—
311	C₂×C₉	—	8	1	no	—
312	C₂×C₉	D₃×SD₁₆	1	1	yes	characteristic
313	C₂×C₉	#915	1	1	yes	characteristic
314	C₂×C₉	#937	1	1	yes	characteristic
315	C₂×Q₈	—	3	1	no	—
316	C₂×Q₈	—	6	1	no	—
317	C₂×Q₈	—	6	2	no	—
318	C₂×Q₈	—	6	2	no	—
319	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
320	C₂×D₄	—	6	1	no	—
321	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
322	C₂²×C₄	—	3	1	no	—
323	C₂²×C₄	—	6	1	no	—
324	SD₁₆	—	2	2	no	—
325	SD₁₆	—	6	2	no	—
326	C₂×C₈	—	3	1	no	—
327	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
328	C₄⋊C₄	—	3	1	no	—
329	C₂²⋊C₄	—	6	1	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	3	2	no	—
332	C₂²×C₃	—	4	2	no	—
333	C₂²×C₃	—	4	1	no	—
334	C₂²×C₃	—	4	1	no	—
335	C₂²×C₃	—	4	1	no	—
336	C₂²×C₃	—	4	1	no	—
337	C₂²×C₃	—	4	1	no	—
338	C₂²×C₃	—	4	1	no	—
339	C₂²×C₃	—	6	1	no	—
340	C₂²×C₃	—	6	1	no	—
341	C₂²×C₃	—	8	1	no	—
342	C₂²×C₃	—	8	1	no	—
343	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
344	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
345	C₂×D₃	—	2	1	no	—
346	C₂×D₃	—	2	1	no	—
347	C₂×D₃	C₉×SD₁₆	1	2	yes	complemented
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	4	2	no	—
353	C₃×C₄	—	6	1	no	—
354	C₃×C₄	—	6	2	no	—
355	C₃×C₄	—	12	1	no	—
356	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
357	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
358	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
359	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
360	Dic₃	—	2	1	no	—
361	Dic₃	—	2	2	no	—
362	Dic₃	—	4	1	no	—
363	C₃²	C₃×#448	1	1	yes	characteristic
364	C₉	—	2	1	no	—
365	C₉	#5170	1	1	yes	characteristic, direct product factor
366	C₂³	—	2	1	no	—
367	C₂³	—	3	1	no	—
368	Q₈	—	2	1	no	—
369	Q₈	—	3	2	no	—
370	Q₈	—	6	4	no	—
371	Q₈	—	6	1	no	—
372	Q₈	C₉×#67	1	2	yes	complemented
373	D₄	—	2	1	no	—
374	D₄	—	2	1	no	—
375	D₄	—	12	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	3	1	no	—
378	C₂×C₄	—	6	4	no	—
379	C₂×C₄	—	6	1	no	—
380	C₂×C₄	—	6	1	no	—
381	C₂×C₄	—	6	1	no	—
382	C₂×C₄	—	6	1	no	—
383	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
384	C₈	—	2	1	no	—
385	C₈	—	6	1	no	—
386	C₂×C₃	—	2	1	no	—
387	C₂×C₃	—	2	1	no	—
388	C₂×C₃	—	2	1	no	—
389	C₂×C₃	—	6	2	no	—
390	C₂×C₃	—	8	2	no	—
391	C₂×C₃	—	8	1	no	—
392	C₂×C₃	—	8	1	no	—
393	C₂×C₃	C₉×#120	1	1	yes	characteristic
394	C₂×C₃	C₂×C₉×SD₁₆	1	1	yes	characteristic
395	C₂×C₃	C₉×#137	1	1	yes	characteristic
396	C₂×C₃	C₃×D₃×SD₁₆	1	1	yes	characteristic
397	C₂×C₃	C₃×#915	1	1	yes	characteristic
398	C₂×C₃	C₃×#937	1	1	yes	characteristic
399	D₃	—	2	2	no	—
400	C₂²	—	3	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	6	1	no	—
405	C₂²	—	6	1	no	—
406	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	6	1	no	—
409	C₄	—	6	2	no	—
410	C₄	—	12	1	no	—
411	C₄	D₃×D₄×C₉	1	1	yes	characteristic
412	C₄	C₂×C₉×#67	1	1	yes	characteristic
413	C₃	—	2	1	no	—
414	C₃	C₉×#448	1	1	yes	characteristic, complemented
415	C₃	C₃×#5170	1	1	yes	characteristic
416	C₂	—	6	2	no	—
417	C₂	—	8	1	no	—
418	C₂	D₃×C₉×SD₁₆	1	1	yes	characteristic
419	C₂	C₉×#915	1	1	yes	characteristic
420	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×#938	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₉×SD₁₆	D₃
hypocenter	C₃	C₉×#448
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×D₃×Q₈×C₉	C₂	semidirect
2. C₂×C₃×C₉×SD₁₆	C₂	semidirect
4. C₂×C₉×#214	C₂	semidirect
5. C₉×#835	C₂	semidirect
6. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
7. C₉×#816	C₂	semidirect
35. C₂×C₉×SD₁₆	D₃	semidirect
43. C₃×Q₈×C₉	D₄	semidirect
57. C₉×Dic₆	D₄	semidirect
61. #5170	C₉	direct (N × H)
102. C₂×D₃×C₉	SD₁₆	semidirect
110. C₂×D₃×Q₈	C₂×C₉	semidirect
113. C₂×C₃×SD₁₆	C₂×C₉	semidirect
117. C₂×#214	C₂×C₉	semidirect
121. #835	C₂×C₉	semidirect
122. (C₂×D₃)⋊C₈	C₂×C₉	semidirect
123. #816	C₂×C₉	semidirect
153. Q₈×C₉	#67	semidirect
247. C₂×SD₁₆	D₃×C₉	semidirect
252. C₃×C₉	#448	semidirect
265. C₃×Q₈	D₄×C₉	semidirect
295. Dic₆	D₄×C₉	semidirect
347. C₂×D₃	C₉×SD₁₆	semidirect
365. C₉	#5170	direct (N × H)
372. Q₈	C₉×#67	semidirect
414. C₃	C₉×#448	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×Q₈×C₉	2
C₂×C₃×C₉×SD₁₆	2
C₉×#938	2
C₂×C₉×#214	2
C₉×#835	2
C₉×(C₂×D₃)⋊C₈	2
C₉×#816	2
C₃×#5170	3
C₉×#448	3

Subgroups — C9×#5170 #13143356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5170 #13143356