Subgroups — C₂×C₃×#63511 #13153679

Order 1728.

938 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×#41	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63511	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×#3674	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#3672	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#3667	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#951	—	3	1	no	maximal
8	C₂×#63511	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₃×C₉×#41	—	2	2	no	—
10	C₃×C₉×#41	C₂²	1	4	yes	—
11	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₃×D₄×C₉	—	2	1	no	—
13	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×C₉	—	2	1	no	—
15	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₃×Dic₉	—	2	1	no	—
17	C₂×C₃×Dic₁₈	—	2	2	no	—
18	C₂×C₃×Dic₁₈	—	2	1	no	—
19	C₂×C₃×Dic₁₈	C₂²	1	2	yes	—
20	C₂×C₃×Dic₁₈	C₂²	1	4	yes	complemented
21	C₃×#3674	C₂²	1	8	yes	complemented
22	C₃×#3672	C₂²	1	8	yes	complemented
23	C₃×#3667	C₂²	1	4	yes	complemented
24	C₂×C₃×C₉⋊C₈	C₂²	1	2	yes	—
25	C₂×C₃²×#41	D₃	1	1	yes	characteristic
26	C₂²×C₃×Dic₆	—	3	1	no	—
27	C₃×#951	—	3	8	no	—
28	C₂×C₃×#216	—	3	2	no	—
29	C₂×C₃×#214	—	3	2	no	—
30	C₂×C₃×#208	—	3	1	no	—
31	C₂×C₉×#41	—	2	1	no	—
32	C₂×C₉×#41	C₂×C₃	1	1	yes	characteristic
33	C₂²×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
34	#63511	C₂×C₃	1	8	yes	direct product factor
35	C₂×#3674	C₂×C₃	1	2	yes	complemented
36	C₂×#3672	C₂×C₃	1	2	yes	complemented
37	C₂×#3667	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂³×C₃×C₉	—	2	1	no	—
39	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
40	C₃×Q₈×C₉	—	2	1	no	—
41	C₃×Q₈×C₉	C₂³	1	2	yes	—
42	C₃×D₄×C₉	—	2	4	no	—
43	C₃×D₄×C₉	—	2	1	no	—
44	C₃×D₄×C₉	C₂³	1	2	yes	—
45	C₂×C₃×C₄×C₉	—	2	1	no	—
46	C₂×C₃×C₄×C₉	—	2	4	no	—
47	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
48	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
51	C₂×C₃×Dic₉	—	2	2	no	—
52	C₂×C₃×Dic₉	—	2	4	no	—
53	C₃×Dic₁₈	—	2	2	no	—
54	C₃×Dic₁₈	—	2	4	no	—
55	C₃×Dic₁₈	C₂³	1	4	yes	—
56	C₃×C₉⋊C₈	C₂³	1	4	yes	—
57	C₂×C₃×#137	—	9	1	no	—
58	C₂×#951	—	3	1	no	—
59	C₃²×#41	—	2	2	no	—
60	C₃²×#41	C₂×D₃	1	4	yes	—
61	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
62	C₂×C₃²×D₄	—	2	1	no	—
63	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
64	C₂²×C₃²×C₄	—	2	1	no	—
65	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
66	C₂²×C₃×Dic₃	—	6	1	no	—
67	C₂×C₃×Dic₆	—	3	2	no	—
68	C₂×C₃×Dic₆	—	3	4	no	—
69	C₂×C₃×Dic₆	—	6	1	no	—
70	C₂×C₃×Dic₆	—	6	2	no	—
71	C₃×#216	—	3	8	no	—
72	C₃×#214	—	3	8	no	—
73	C₃×#208	—	3	4	no	—
74	C₂×C₃×C₃⋊C₈	—	3	2	no	—
75	C₉×#41	—	2	4	no	—
76	C₉×#41	—	2	4	no	—
77	C₉×#41	—	2	2	no	—
78	C₉×#41	C₂²×C₃	1	4	yes	—
79	C₂×Q₈×C₉	—	2	1	no	—
80	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
81	C₂×D₄×C₉	—	2	2	no	—
82	C₂×D₄×C₉	—	2	1	no	—
83	C₂×D₄×C₉	—	2	1	no	—
84	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
85	C₂²×C₄×C₉	—	2	2	no	—
86	C₂²×C₄×C₉	—	2	1	no	—
87	C₂²×C₄×C₉	—	2	1	no	—
88	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
89	C₂²×Dic₉	—	2	1	no	—
90	C₂×Dic₁₈	—	2	2	no	—
91	C₂×Dic₁₈	—	2	1	no	—
92	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
93	C₂×Dic₁₈	C₂²×C₃	1	4	yes	complemented
94	#3674	C₂²×C₃	1	8	yes	complemented
95	#3672	C₂²×C₃	1	8	yes	complemented
96	#3667	C₂²×C₃	1	4	yes	complemented
97	C₂×C₉⋊C₈	C₂²×C₃	1	2	yes	—
98	C₂²×C₃×C₉	—	2	2	no	—
99	C₂²×C₃×C₉	—	2	2	no	—
100	C₂²×C₃×C₉	—	4	2	no	—
101	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
102	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
103	C₃×C₄×C₉	—	2	2	no	—
104	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
105	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
106	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
107	C₃×Dic₉	—	2	4	no	—
108	C₂×C₃×#41	—	2	1	no	—
109	C₂×C₃×#41	D₉	1	1	yes	characteristic
110	C₂×C₃×#41	C₃×D₃	1	1	yes	characteristic
111	C₂²×C₃×Q₈	—	9	1	no	—
112	C₂²×Dic₆	—	3	1	no	—
113	C₃×#137	—	9	8	no	—
114	C₂×C₃×Q₁₆	—	9	2	no	—
115	C₂×C₃×SD₁₆	—	9	2	no	—
116	C₂×C₃×M₁₆	—	9	1	no	—
117	#951	—	3	8	no	—
118	C₂×#216	—	3	2	no	—
119	C₂×#214	—	3	2	no	—
120	C₂×#208	—	3	1	no	—
121	C₂³×C₃²	—	2	1	no	—
122	C₂³×C₃²	#67	1	1	yes	characteristic
123	C₃²×Q₈	—	2	1	no	—
124	C₃²×Q₈	C₂²×D₃	1	2	yes	—
125	C₃²×D₄	—	2	4	no	—
126	C₃²×D₄	—	2	1	no	—
127	C₃²×D₄	C₂²×D₃	1	2	yes	—
128	C₂×C₃²×C₄	—	2	1	no	—
129	C₂×C₃²×C₄	—	2	4	no	—
130	C₂×C₃²×C₄	#67	1	1	yes	characteristic
131	C₂×C₃²×C₄	#67	1	2	yes	—
132	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
133	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
134	C₂×C₃×Dic₃	—	6	4	no	—
135	C₂×C₃×Dic₃	—	6	2	no	—
136	C₃×Dic₆	—	3	4	no	—
137	C₃×Dic₆	—	6	4	no	—
138	C₃×Dic₆	—	6	2	no	—
139	C₂³×C₉	—	2	2	no	—
140	C₂³×C₉	—	2	1	no	—
141	C₂³×C₉	—	2	1	no	—
142	C₂³×C₉	C₃×D₄	1	1	yes	characteristic
143	C₃×C₃⋊C₈	—	3	4	no	—
144	Q₈×C₉	—	2	2	no	—
145	Q₈×C₉	—	2	1	no	—
146	Q₈×C₉	—	2	2	no	—
147	Q₈×C₉	C₂³×C₃	1	2	yes	—
148	D₄×C₉	—	2	8	no	—
149	D₄×C₉	—	2	2	no	—
150	D₄×C₉	—	2	4	no	—
151	D₄×C₉	—	2	1	no	—
152	D₄×C₉	—	2	2	no	—
153	D₄×C₉	C₂³×C₃	1	2	yes	—
154	C₂×C₄×C₉	—	2	2	no	—
155	C₂×C₄×C₉	—	2	8	no	—
156	C₂×C₄×C₉	—	2	1	no	—
157	C₂×C₄×C₉	—	2	4	no	—
158	C₂×C₄×C₉	—	2	1	no	—
159	C₂×C₄×C₉	—	2	2	no	—
160	C₂×C₄×C₉	—	2	1	no	—
161	C₂×C₄×C₉	—	2	2	no	—
162	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
163	C₂×C₄×C₉	C₃×D₄	1	2	yes	—
164	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
165	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
166	C₂×Dic₉	—	2	2	no	—
167	C₂×Dic₉	—	2	4	no	—
168	Dic₁₈	—	2	2	no	—
169	Dic₁₈	—	2	4	no	—
170	Dic₁₈	C₂³×C₃	1	4	yes	—
171	C₉⋊C₈	C₂³×C₃	1	4	yes	—
172	C₂×#137	—	9	1	no	Sylow
173	C₂×C₃×C₉	—	2	2	no	—
174	C₂×C₃×C₉	—	4	2	no	—
175	C₂×C₃×C₉	#137	1	2	yes	complemented
176	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
177	C₃×#41	—	2	4	no	—
178	C₃×#41	—	2	2	no	—
179	C₃×#41	—	2	2	no	—
180	C₃×#41	—	2	4	no	—
181	C₃×#41	C₂×D₉	1	4	yes	—
182	C₃×#41	C₂×C₃×D₃	1	4	yes	—
183	C₂×C₃×Q₈	—	2	1	no	—
184	C₂×C₃×Q₈	—	9	2	no	—
185	C₂×C₃×Q₈	—	9	4	no	—
186	C₂×C₃×Q₈	—	18	2	no	—
187	C₂×C₃×Q₈	—	18	1	no	—
188	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic
189	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
190	C₂×C₃×D₄	—	2	2	no	—
191	C₂×C₃×D₄	—	2	1	no	—
192	C₂×C₃×D₄	—	2	1	no	—
193	C₂×C₃×D₄	—	2	1	no	—
194	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
195	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
196	C₂²×C₃×C₄	—	2	2	no	—
197	C₂²×C₃×C₄	—	2	1	no	—
198	C₂²×C₃×C₄	—	2	1	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	—	18	1	no	—
201	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
202	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
203	C₂²×Dic₃	—	6	1	no	—
204	C₂×Dic₆	—	3	2	no	—
205	C₂×Dic₆	—	3	4	no	—
206	C₂×Dic₆	—	6	1	no	—
207	C₂×Dic₆	—	6	2	no	—
208	C₃×Q₁₆	—	9	8	no	—
209	C₃×SD₁₆	—	9	8	no	—
210	C₃×M₁₆	—	9	4	no	—
211	C₂×C₃×C₈	—	9	2	no	—
212	#216	—	3	8	no	—
213	#214	—	3	8	no	—
214	#208	—	3	4	no	—
215	C₂×C₃⋊C₈	—	3	2	no	—
216	C₂²×C₃²	—	2	2	no	—
217	C₂²×C₃²	—	2	2	no	—
218	C₂²×C₃²	—	4	2	no	—
219	C₂²×C₃²	C₂×#67	1	2	yes	—
220	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
221	C₃²×C₄	—	2	2	no	—
222	C₃²×C₄	C₂×#67	1	2	yes	—
223	C₃²×C₄	C₂×#67	1	1	yes	characteristic
224	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
225	C₃×Dic₃	—	6	4	no	—
226	C₂²×C₉	—	2	2	no	—
227	C₂²×C₉	—	2	4	no	—
228	C₂²×C₉	—	2	2	no	—
229	C₂²×C₉	—	2	1	no	—
230	C₂²×C₉	—	2	2	no	—
231	C₂²×C₉	—	4	2	no	—
232	C₂²×C₉	—	4	4	no	—
233	C₂²×C₉	—	4	2	no	—
234	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
235	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
236	C₄×C₉	—	2	4	no	—
237	C₄×C₉	—	2	2	no	—
238	C₄×C₉	—	2	1	no	—
239	C₄×C₉	—	2	2	no	—
240	C₄×C₉	—	2	1	no	—
241	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
242	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
243	C₄×C₉	C₂⁴×C₃	1	1	yes	characteristic
244	Dic₉	—	2	4	no	—
245	C₂×#41	C₃×D₉	1	1	yes	characteristic
246	C₂²×Q₈	—	9	1	no	—
247	#137	—	9	8	no	—
248	C₂×Q₁₆	—	9	2	no	—
249	C₂×SD₁₆	—	9	2	no	—
250	C₂×M₁₆	—	9	1	no	—
251	C₃×C₉	C₂×#137	1	1	yes	characteristic, complemented, Sylow
252	C₂³×C₃	—	2	2	no	—
253	C₂³×C₃	—	2	1	no	—
254	C₂³×C₃	—	2	1	no	—
255	C₂³×C₃	—	2	1	no	—
256	C₂³×C₃	#611	1	1	yes	characteristic
257	C₂³×C₃	C₃×#67	1	1	yes	characteristic
258	C₃×Q₈	—	2	2	no	—
259	C₃×Q₈	—	2	1	no	—
260	C₃×Q₈	—	2	1	no	—
261	C₃×Q₈	—	2	2	no	—
262	C₃×Q₈	—	9	4	no	—
263	C₃×Q₈	—	18	4	no	—
264	C₃×Q₈	—	18	2	no	—
265	C₃×Q₈	C₂²×D₉	1	2	yes	—
266	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
267	C₃×D₄	—	2	8	no	—
268	C₃×D₄	—	2	2	no	—
269	C₃×D₄	—	2	4	no	—
270	C₃×D₄	—	2	4	no	—
271	C₃×D₄	—	2	1	no	—
272	C₃×D₄	—	2	1	no	—
273	C₃×D₄	—	2	2	no	—
274	C₃×D₄	C₂²×D₉	1	2	yes	—
275	C₃×D₄	C₂²×C₃×D₃	1	2	yes	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	8	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	2	4	no	—
281	C₂×C₃×C₄	—	2	4	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	18	4	no	—
287	C₂×C₃×C₄	—	18	2	no	—
288	C₂×C₃×C₄	#611	1	2	yes	—
289	C₂×C₃×C₄	#611	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
291	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
292	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
293	C₂×C₃×C₄	C₃×#67	1	2	yes	—
294	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
296	C₂×Dic₃	—	6	4	no	—
297	C₂×Dic₃	—	6	2	no	—
298	Dic₆	—	3	4	no	—
299	Dic₆	—	6	4	no	—
300	Dic₆	—	6	2	no	—
301	C₃×C₈	—	9	4	no	—
302	C₃⋊C₈	—	3	4	no	—
303	C₂×C₃²	—	2	2	no	—
304	C₂×C₃²	—	4	2	no	—
305	C₂×C₃²	#951	1	2	yes	—
306	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
307	C₂×C₉	—	2	2	no	—
308	C₂×C₉	—	2	2	no	—
309	C₂×C₉	—	2	1	no	—
310	C₂×C₉	—	4	2	no	—
311	C₂×C₉	—	4	4	no	—
312	C₂×C₉	—	4	2	no	—
313	C₂×C₉	C₃×#137	1	2	yes	complemented
314	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
315	#41	—	2	2	no	—
316	#41	C₂×C₃×D₉	1	4	yes	—
317	C₂×Q₈	—	9	2	no	—
318	C₂×Q₈	—	9	4	no	—
319	C₂×Q₈	—	18	1	no	—
320	C₂×Q₈	—	18	2	no	—
321	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	18	1	no	—
326	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
327	Q₁₆	—	9	8	no	—
328	SD₁₆	—	9	8	no	—
329	M₁₆	—	9	4	no	—
330	C₂×C₈	—	9	2	no	—
331	C₂²×C₃	—	2	2	no	—
332	C₂²×C₃	—	2	2	no	—
333	C₂²×C₃	—	2	4	no	—
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	2	2	no	—
336	C₂²×C₃	—	2	1	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	4	2	no	—
339	C₂²×C₃	—	4	4	no	—
340	C₂²×C₃	—	4	2	no	—
341	C₂²×C₃	—	4	2	no	—
342	C₂²×C₃	C₂×#611	1	2	yes	—
343	C₂²×C₃	C₂×#611	1	1	yes	characteristic
344	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
345	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
346	C₃×C₄	—	2	4	no	—
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	2	1	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	18	4	no	—
353	C₃×C₄	C₂×#611	1	2	yes	—
354	C₃×C₄	C₂×#611	1	1	yes	characteristic
355	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
356	C₃×C₄	C₂×C₃×#67	1	2	yes	—
357	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
358	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
359	Dic₃	—	6	4	no	—
360	C₃²	C₂×#951	1	1	yes	characteristic
361	C₉	—	2	1	no	—
362	C₉	C₂×C₃×#137	1	1	yes	characteristic, complemented
363	C₂³	—	2	1	no	—
364	C₂³	C₃×#611	1	1	yes	characteristic
365	Q₈	—	2	1	no	—
366	Q₈	—	9	4	no	—
367	Q₈	—	18	4	no	—
368	Q₈	—	18	2	no	—
369	Q₈	C₂²×C₃×D₉	1	2	yes	—
370	D₄	—	2	4	no	—
371	D₄	—	2	1	no	—
372	D₄	C₂²×C₃×D₉	1	2	yes	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	18	4	no	—
376	C₂×C₄	—	18	2	no	—
377	C₂×C₄	C₃×#611	1	1	yes	characteristic
378	C₂×C₄	C₃×#611	1	2	yes	—
379	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
381	C₈	—	9	4	no	—
382	C₂×C₃	—	2	2	no	—
383	C₂×C₃	—	2	2	no	—
384	C₂×C₃	—	2	1	no	—
385	C₂×C₃	—	2	2	no	—
386	C₂×C₃	—	4	2	no	—
387	C₂×C₃	—	4	4	no	—
388	C₂×C₃	—	4	2	no	—
389	C₂×C₃	—	4	2	no	—
390	C₂×C₃	#63511	1	2	yes	direct product factor
391	C₂×C₃	C₂²×#611	1	1	yes	characteristic
392	C₂×C₃	C₃×#951	1	2	yes	—
393	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	C₂×C₃×#611	1	2	yes	—
398	C₂²	C₂×C₃×#611	1	1	yes	characteristic
399	C₄	—	2	2	no	—
400	C₄	—	18	4	no	—
401	C₄	C₂×C₃×#611	1	2	yes	—
402	C₄	C₂×C₃×#611	1	1	yes	characteristic
403	C₄	C₂³×C₃×D₉	1	1	yes	characteristic
404	C₃	—	2	1	no	—
405	C₃	C₂×#63511	1	1	yes	characteristic, direct product factor
406	C₃	C₂×C₃×#951	1	1	yes	characteristic
407	C₂	—	2	2	no	—
408	C₂	—	4	2	no	—
409	C₂	C₃×#63511	1	2	yes	direct product factor
410	C₂	C₂²×C₃×#611	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×#611
commutator, cosocle	C₄×C₉	C₂⁴×C₃
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×#41	C₂
socle	C₂²×C₃²	C₂×#67
prime radical	C₂×C₃²×#41	D₃
hypercenter	C₂×C₃×#41	D₉
hypocenter	C₉	C₂×C₃×#137
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#41

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×Dic₁₈	C₂	semidirect
3. C₃×#63511	C₂	direct (N × H)
4. C₂×C₃×#3674	C₂	semidirect
5. C₂×C₃×#3672	C₂	semidirect
6. C₂×C₃×#3667	C₂	semidirect
8. C₂×#63511	C₃	direct (N × H)
20. C₂×C₃×Dic₁₈	C₂²	semidirect
21. C₃×#3674	C₂²	semidirect
22. C₃×#3672	C₂²	semidirect
23. C₃×#3667	C₂²	semidirect
33. C₂²×Dic₁₈	C₂×C₃	semidirect
34. #63511	C₂×C₃	direct (N × H)
35. C₂×#3674	C₂×C₃	semidirect
36. C₂×#3672	C₂×C₃	semidirect
37. C₂×#3667	C₂×C₃	semidirect
93. C₂×Dic₁₈	C₂²×C₃	semidirect
94. #3674	C₂²×C₃	semidirect
95. #3672	C₂²×C₃	semidirect
96. #3667	C₂²×C₃	semidirect
175. C₂×C₃×C₉	#137	semidirect
251. C₃×C₉	C₂×#137	semidirect
313. C₂×C₉	C₃×#137	semidirect
362. C₉	C₂×C₃×#137	semidirect
390. C₂×C₃	#63511	direct (N × H)
405. C₃	C₂×#63511	direct (N × H)
409. C₂	C₃×#63511	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₉×#41	2
C₂²×C₃×Dic₁₈	2
C₃×#63511	2
C₂×C₃×#3674	2
C₂×C₃×#3672	2
C₂×C₃×#3667	2
C₂×C₃×#951	3
C₂×#63511	3

Subgroups — C2×C3×#63511 #13153679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#63511 #13153679