Subgroups — C₃×D₉×#124 #13153087

Order 1728.

1066 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×D₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×D₉	C₂	1	1	yes	maximal, characteristic
3	C₃×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63509	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63498	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63447	C₂	1	4	yes	maximal, complemented
7	C₃×C₂²⋊C₄×D₉	C₂	1	4	yes	maximal, complemented
8	C₃×#63437	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄²×D₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×D₃×#124	—	3	1	no	maximal
11	D₉×#124	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂³×C₃×D₉	C₂²	1	2	yes	—
13	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×#611	C₂²	1	2	yes	—
16	C₃×Q₈×D₉	—	2	4	no	—
17	C₃×D₄×D₉	—	2	4	no	—
18	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
20	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
21	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
22	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×Dic₁₈	C₂²	1	2	yes	complemented
24	C₃×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
25	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
26	C₃×#3676	C₂²	1	4	yes	complemented
27	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	complemented
28	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	complemented
29	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₄×Dic₉	C₂²	1	2	yes	complemented
31	C₂×C₃×D₃×Q₈	—	3	1	no	—
32	C₂×C₃×D₃×D₄	—	3	1	no	—
33	C₃²×#124	D₃	1	1	yes	characteristic
34	C₃×#947	—	3	1	no	—
35	C₃×#936	—	3	1	no	—
36	C₃×#885	—	3	4	no	—
37	C₃×D₃×C₂²⋊C₄	—	3	4	no	—
38	C₃×#875	—	3	1	no	—
39	C₃×C₄²×D₃	—	3	1	no	—
40	C₂×Q₈×D₉	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×D₄×D₉	C₂×C₃	1	1	yes	characteristic
42	C₉×#124	—	2	1	no	—
43	C₉×#124	C₂×C₃	1	1	yes	characteristic, complemented
44	#63509	C₂×C₃	1	1	yes	characteristic, complemented
45	#63498	C₂×C₃	1	1	yes	characteristic, complemented
46	#63447	C₂×C₃	1	4	yes	complemented
47	C₂²⋊C₄×D₉	C₂×C₃	1	4	yes	complemented
48	#63437	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄²×D₉	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂³×C₃×C₉	C₂³	1	2	yes	—
51	C₂²×C₃×D₉	—	2	4	no	—
52	C₂²×C₃×D₉	—	2	8	no	—
53	C₂²×C₃×D₉	C₂³	1	2	yes	—
54	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
55	C₃×Q₈×C₉	—	2	2	no	—
56	C₃×D₄×C₉	—	2	2	no	—
57	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
58	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
59	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₃×#611	—	2	4	no	—
61	C₂×C₃×Dic₉	C₂³	1	2	yes	—
62	C₂×C₃×Dic₉	C₂³	1	2	yes	—
63	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
64	C₃×D₃₆	—	2	2	no	—
65	C₃×C₄×D₉	—	2	4	no	—
66	C₃×C₄×D₉	—	2	4	no	—
67	C₃×C₄×D₉	D₄	1	4	yes	—
68	C₃×Dic₁₈	—	2	2	no	—
69	C₃×Dic₁₈	—	2	4	no	—
70	C₂×C₃×#124	—	9	1	no	—
71	D₃×#124	—	3	1	no	—
72	C₂³×C₃×D₃	—	3	2	no	—
73	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
74	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
75	C₂×C₃×#67	—	3	2	no	—
76	C₃×D₃×Q₈	—	6	4	no	—
77	C₃×D₃×D₄	—	6	4	no	—
78	C₂×C₃×D₁₂	—	3	1	no	—
79	C₂×C₃×C₄×D₃	—	3	1	no	—
80	C₂×C₃×C₄×D₃	—	3	2	no	—
81	C₂×C₃×C₄×D₃	—	3	2	no	—
82	C₂×C₃×Dic₆	—	3	2	no	—
83	C₂×C₃×Dic₆	—	3	1	no	—
84	C₂³×D₉	C₂²×C₃	1	2	yes	—
85	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	—
86	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
87	C₃×#217	—	3	4	no	—
88	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
89	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
90	C₃×C₄×Dic₃	—	3	2	no	—
91	C₃×C₄×Dic₃	—	3	1	no	—
92	C₂×Q₈×C₉	—	2	1	no	—
93	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
94	C₂×D₄×C₉	—	2	1	no	—
95	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
96	C₂×#611	C₂²×C₃	1	2	yes	—
97	Q₈×D₉	—	2	4	no	—
98	D₄×D₉	—	2	4	no	—
99	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
101	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
102	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
103	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₂×Dic₁₈	C₂²×C₃	1	2	yes	complemented
105	C₉×C₂²⋊C₄	—	2	4	no	—
106	C₉×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
107	C₄²×C₉	—	2	1	no	—
108	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
109	#3676	C₂²×C₃	1	4	yes	complemented
110	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	complemented
111	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	complemented
112	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₄×Dic₉	C₂²×C₃	1	2	yes	complemented
114	C₂²×C₃×C₉	—	2	2	no	—
115	C₂²×C₃×C₉	—	2	4	no	—
116	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
117	C₂×C₃×D₉	—	2	2	no	—
118	C₂×C₃×D₉	—	2	4	no	—
119	C₂×C₃×D₉	—	4	8	no	—
120	C₂×C₃×D₉	C₂×D₄	1	2	yes	—
121	C₂×C₃×D₉	#41	1	4	yes	—
122	C₃×C₄×C₉	—	2	2	no	—
123	C₃×C₄×C₉	—	2	2	no	—
124	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
125	C₃×Dic₉	—	2	2	no	—
126	C₃×Dic₉	—	2	2	no	—
127	C₃×Dic₉	C₂×D₄	1	2	yes	—
128	C₂²×C₃×Q₈	—	9	1	no	—
129	C₂²×C₃×D₄	—	9	1	no	—
130	C₂×D₃×Q₈	—	3	1	no	—
131	C₂×D₃×D₄	—	3	1	no	—
132	C₃×#124	—	2	1	no	—
133	C₃×#124	—	9	1	no	—
134	C₃×#124	—	9	1	no	—
135	C₃×#124	—	9	4	no	—
136	C₃×#124	—	9	1	no	—
137	C₃×#124	D₉	1	1	yes	characteristic, direct product factor
138	C₃×#124	C₃×D₃	1	1	yes	characteristic
139	C₂×C₃×C₂²⋊C₄	—	9	4	no	—
140	C₂×C₃×C₄²	—	9	1	no	—
141	#947	—	3	1	no	—
142	#936	—	3	1	no	—
143	#885	—	3	4	no	—
144	D₃×C₂²⋊C₄	—	3	4	no	—
145	#875	—	3	1	no	—
146	C₄²×D₃	—	3	1	no	—
147	C₂³×C₃²	C₂²×D₃	1	2	yes	—
148	C₂²×C₃×D₃	—	3	1	no	—
149	C₂²×C₃×D₃	—	3	2	no	—
150	C₂²×C₃×D₃	—	6	8	no	—
151	C₂²×C₃×D₃	—	6	4	no	—
152	C₃²×Q₈	—	2	2	no	—
153	C₃²×D₄	—	2	2	no	—
154	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
155	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
156	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
157	C₃×#67	—	6	4	no	—
158	C₂×C₃×Dic₃	—	3	1	no	—
159	C₂×C₃×Dic₃	—	3	2	no	—
160	C₂×C₃×Dic₃	—	3	2	no	—
161	C₃×D₁₂	—	6	2	no	—
162	C₃×C₄×D₃	—	3	4	no	—
163	C₃×C₄×D₃	—	6	4	no	—
164	C₃×C₄×D₃	—	6	4	no	—
165	C₃×Dic₆	—	6	4	no	—
166	C₃×Dic₆	—	6	2	no	—
167	C₂³×C₉	—	2	2	no	—
168	C₂³×C₉	C₂³×C₃	1	2	yes	—
169	C₂²×D₉	—	2	4	no	—
170	C₂²×D₉	—	2	8	no	—
171	C₂²×D₉	C₂³×C₃	1	2	yes	—
172	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
173	Q₈×C₉	—	2	2	no	—
174	Q₈×C₉	—	4	2	no	—
175	D₄×C₉	—	2	2	no	—
176	D₄×C₉	—	4	2	no	—
177	C₂×C₄×C₉	—	2	1	no	—
178	C₂×C₄×C₉	—	2	2	no	—
179	C₂×C₄×C₉	—	2	2	no	—
180	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
181	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
182	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
183	#611	—	2	4	no	—
184	C₂×Dic₉	C₂³×C₃	1	2	yes	—
185	C₂×Dic₉	C₂³×C₃	1	2	yes	—
186	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
187	D₃₆	—	2	2	no	—
188	C₄×D₉	—	2	4	no	—
189	C₄×D₉	—	2	4	no	—
190	C₄×D₉	C₃×D₄	1	4	yes	—
191	Dic₁₈	—	2	2	no	—
192	Dic₁₈	—	2	4	no	—
193	C₂×#124	—	9	1	no	Sylow
194	C₂×C₃×C₉	—	4	2	no	—
195	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₃×C₉	C₂×#41	1	2	yes	—
197	C₃×D₉	—	4	2	no	—
198	C₃×D₉	#124	1	4	yes	direct product factor
199	C₂⁴×C₃	—	9	2	no	—
200	C₂³×D₃	—	3	2	no	—
201	C₂×C₃×Q₈	—	2	1	no	—
202	C₂×C₃×Q₈	—	9	2	no	—
203	C₂×C₃×Q₈	—	9	1	no	—
204	C₂×C₃×Q₈	—	18	4	no	—
205	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic, complemented
206	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
207	C₂×C₃×D₄	—	2	1	no	—
208	C₂×C₃×D₄	—	9	2	no	—
209	C₂×C₃×D₄	—	9	1	no	—
210	C₂×C₃×D₄	—	18	4	no	—
211	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
212	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
213	C₂²×C₃×C₄	—	9	1	no	—
214	C₂²×C₃×C₄	—	9	2	no	—
215	C₂²×C₃×C₄	—	9	2	no	—
216	C₂×#67	—	3	2	no	—
217	D₃×Q₈	—	6	4	no	—
218	D₃×D₄	—	6	4	no	—
219	C₂×D₁₂	—	3	1	no	—
220	C₂×C₄×D₃	—	3	1	no	—
221	C₂×C₄×D₃	—	3	2	no	—
222	C₂×C₄×D₃	—	3	2	no	—
223	C₂×Dic₆	—	3	1	no	—
224	C₂×Dic₆	—	3	2	no	—
225	C₃×C₂²⋊C₄	—	2	4	no	—
226	C₃×C₂²⋊C₄	—	9	4	no	—
227	C₃×C₂²⋊C₄	—	9	4	no	—
228	C₃×C₂²⋊C₄	—	9	4	no	—
229	C₃×C₂²⋊C₄	C₂×D₉	1	4	yes	complemented
230	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
231	C₃×C₄²	—	2	1	no	—
232	C₃×C₄²	—	9	2	no	—
233	C₃×C₄²	—	9	1	no	—
234	C₃×C₄²	C₂×D₉	1	1	yes	characteristic, complemented
235	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
236	#217	—	3	4	no	—
237	(C₂×D₃)⋊C₄	—	3	4	no	—
238	(C₂×D₃)⋊C₄	—	3	4	no	—
239	C₄×Dic₃	—	3	2	no	—
240	C₄×Dic₃	—	3	1	no	—
241	C₂²×C₃²	—	2	2	no	—
242	C₂²×C₃²	—	2	4	no	—
243	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
244	C₂×C₃×D₃	—	3	2	no	—
245	C₂×C₃×D₃	—	3	4	no	—
246	C₂×C₃×D₃	—	6	2	no	—
247	C₂×C₃×D₃	—	6	4	no	—
248	C₂×C₃×D₃	—	12	8	no	—
249	C₃²×C₄	—	2	2	no	—
250	C₃²×C₄	—	2	2	no	—
251	C₃²×C₄	D₃×D₄	1	2	yes	—
252	C₃×Dic₃	—	3	2	no	—
253	C₃×Dic₃	—	6	2	no	—
254	C₃×Dic₃	—	6	2	no	—
255	C₂²×C₉	—	2	2	no	—
256	C₂²×C₉	—	2	4	no	—
257	C₂²×C₉	—	2	1	no	—
258	C₂²×C₉	—	4	2	no	—
259	C₂²×C₉	—	4	4	no	—
260	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
261	C₂×D₉	—	2	2	no	—
262	C₂×D₉	—	2	4	no	—
263	C₂×D₉	—	4	8	no	—
264	C₂×D₉	C₂×C₃×D₄	1	2	yes	—
265	C₂×D₉	C₃×#41	1	4	yes	—
266	C₄×C₉	—	2	2	no	—
267	C₄×C₉	—	2	2	no	—
268	C₄×C₉	—	2	2	no	—
269	C₄×C₉	—	4	2	no	—
270	C₄×C₉	—	4	2	no	—
271	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
272	Dic₉	—	2	2	no	—
273	Dic₉	—	2	2	no	—
274	Dic₉	C₂×C₃×D₄	1	2	yes	—
275	C₂²×Q₈	—	9	1	no	—
276	C₂²×D₄	—	9	1	no	—
277	#124	—	9	1	no	—
278	#124	—	9	1	no	—
279	#124	—	9	4	no	—
280	#124	—	9	1	no	—
281	#124	C₃×D₉	1	1	yes	characteristic, direct product factor
282	C₂×C₂²⋊C₄	—	9	4	no	—
283	C₂×C₄²	—	9	1	no	—
284	C₃×C₉	C₂×#124	1	1	yes	characteristic, complemented, Sylow
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	—	9	1	no	—
287	C₂³×C₃	—	9	2	no	—
288	C₂³×C₃	—	18	4	no	—
289	C₂³×C₃	—	18	8	no	—
290	C₂³×C₃	C₂²×D₉	1	2	yes	—
291	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
292	C₂²×D₃	—	3	1	no	—
293	C₂²×D₃	—	3	2	no	—
294	C₂²×D₃	—	6	4	no	—
295	C₂²×D₃	—	6	8	no	—
296	C₃×Q₈	—	2	2	no	—
297	C₃×Q₈	—	2	2	no	—
298	C₃×Q₈	—	4	2	no	—
299	C₃×Q₈	—	18	4	no	—
300	C₃×Q₈	—	18	2	no	—
301	C₃×D₄	—	2	2	no	—
302	C₃×D₄	—	2	2	no	—
303	C₃×D₄	—	4	2	no	—
304	C₃×D₄	—	18	4	no	—
305	C₃×D₄	—	18	2	no	—
306	C₂×C₃×C₄	—	2	1	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	9	1	no	—
310	C₂×C₃×C₄	—	9	4	no	—
311	C₂×C₃×C₄	—	9	2	no	—
312	C₂×C₃×C₄	—	9	2	no	—
313	C₂×C₃×C₄	—	18	4	no	—
314	C₂×C₃×C₄	—	18	4	no	—
315	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
316	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
317	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
319	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
320	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
321	#67	—	6	4	no	—
322	C₂×Dic₃	—	3	1	no	—
323	C₂×Dic₃	—	3	2	no	—
324	C₂×Dic₃	—	3	2	no	—
325	D₁₂	—	6	2	no	—
326	C₄×D₃	—	3	4	no	—
327	C₄×D₃	—	6	4	no	—
328	C₄×D₃	—	6	4	no	—
329	Dic₆	—	6	4	no	—
330	Dic₆	—	6	2	no	—
331	C₂×C₃²	—	4	2	no	—
332	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
333	C₂×C₃²	D₃×#41	1	2	yes	—
334	C₃×D₃	—	3	4	no	—
335	C₃×D₃	—	12	2	no	—
336	C₂×C₉	—	2	1	no	—
337	C₂×C₉	—	2	2	no	—
338	C₂×C₉	—	4	2	no	—
339	C₂×C₉	—	8	2	no	—
340	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
341	C₂×C₉	C₂×C₃×#41	1	2	yes	—
342	D₉	—	4	2	no	—
343	D₉	C₃×#124	1	4	yes	direct product factor
344	C₂⁴	—	9	2	no	—
345	C₂×Q₈	—	9	2	no	—
346	C₂×Q₈	—	9	1	no	—
347	C₂×Q₈	—	18	4	no	—
348	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic, complemented
349	C₂×D₄	—	9	2	no	—
350	C₂×D₄	—	9	1	no	—
351	C₂×D₄	—	18	4	no	—
352	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
353	C₂²×C₄	—	9	1	no	—
354	C₂²×C₄	—	9	2	no	—
355	C₂²×C₄	—	9	2	no	—
356	C₂²⋊C₄	—	9	4	no	—
357	C₂²⋊C₄	—	9	4	no	—
358	C₂²⋊C₄	—	9	4	no	—
359	C₂²⋊C₄	C₂×C₃×D₉	1	4	yes	complemented
360	C₄²	—	9	2	no	—
361	C₄²	—	9	1	no	—
362	C₄²	C₂×C₃×D₉	1	1	yes	characteristic, complemented
363	C₂²×C₃	—	2	2	no	—
364	C₂²×C₃	—	2	4	no	—
365	C₂²×C₃	—	2	2	no	—
366	C₂²×C₃	—	2	4	no	—
367	C₂²×C₃	—	2	1	no	—
368	C₂²×C₃	—	4	2	no	—
369	C₂²×C₃	—	4	4	no	—
370	C₂²×C₃	—	9	2	no	—
371	C₂²×C₃	—	9	4	no	—
372	C₂²×C₃	—	18	2	no	—
373	C₂²×C₃	—	18	4	no	—
374	C₂²×C₃	—	36	8	no	—
375	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
376	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
377	C₂×D₃	—	3	2	no	—
378	C₂×D₃	—	3	4	no	—
379	C₂×D₃	—	6	2	no	—
380	C₂×D₃	—	6	4	no	—
381	C₂×D₃	—	12	8	no	—
382	C₃×C₄	—	2	2	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	—	2	2	no	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	4	2	no	—
388	C₃×C₄	—	4	2	no	—
389	C₃×C₄	—	9	2	no	—
390	C₃×C₄	—	18	2	no	—
391	C₃×C₄	—	18	2	no	—
392	C₃×C₄	D₄×D₉	1	2	yes	—
393	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
394	Dic₃	—	3	2	no	—
395	Dic₃	—	6	2	no	—
396	Dic₃	—	6	2	no	—
397	C₃²	D₃×#124	1	1	yes	characteristic
398	C₉	—	2	1	no	—
399	C₉	C₂×C₃×#124	1	1	yes	characteristic, complemented
400	C₂³	—	9	1	no	—
401	C₂³	—	9	2	no	—
402	C₂³	—	18	4	no	—
403	C₂³	—	18	8	no	—
404	C₂³	C₂²×C₃×D₉	1	2	yes	—
405	Q₈	—	2	2	no	—
406	Q₈	—	18	4	no	—
407	Q₈	—	18	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	18	4	no	—
410	D₄	—	18	2	no	—
411	C₂×C₄	—	9	1	no	—
412	C₂×C₄	—	9	4	no	—
413	C₂×C₄	—	9	2	no	—
414	C₂×C₄	—	9	2	no	—
415	C₂×C₄	—	18	4	no	—
416	C₂×C₄	—	18	4	no	—
417	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
418	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
419	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	2	2	no	—
422	C₂×C₃	—	4	2	no	—
423	C₂×C₃	—	4	2	no	—
424	C₂×C₃	—	8	2	no	—
425	C₂×C₃	—	9	4	no	—
426	C₂×C₃	—	36	2	no	—
427	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
428	C₂×C₃	#41×D₉	1	2	yes	—
429	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
430	C₂×C₃	C₃×D₃×#41	1	2	yes	—
431	D₃	—	3	4	no	—
432	D₃	—	12	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	9	2	no	—
436	C₂²	—	9	4	no	—
437	C₂²	—	18	2	no	—
438	C₂²	—	18	4	no	—
439	C₂²	—	36	8	no	—
440	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	9	2	no	—
444	C₄	—	18	2	no	—
445	C₄	—	18	2	no	—
446	C₄	C₃×D₄×D₉	1	2	yes	—
447	C₃	—	2	1	no	—
448	C₃	D₉×#124	1	1	yes	characteristic, direct product factor
449	C₃	C₃×D₃×#124	1	1	yes	characteristic
450	C₂	—	4	2	no	—
451	C₂	—	9	4	no	—
452	C₂	—	36	2	no	—
453	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic
454	C₂	C₃×#41×D₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#124	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂×C₃×D₄×D₉	C₂
hypercenter	C₃×#124	D₉
hypocenter	C₉	C₂×C₃×#124
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₈×D₉	C₂	semidirect
3. C₃×C₉×#124	C₂	semidirect
4. C₃×#63509	C₂	semidirect
5. C₃×#63498	C₂	semidirect
6. C₃×#63447	C₂	semidirect
7. C₃×C₂²⋊C₄×D₉	C₂	semidirect
8. C₃×#63437	C₂	semidirect
9. C₃×C₄²×D₉	C₂	semidirect
11. D₉×#124	C₃	direct (N × H)
13. C₂×C₃×Q₈×C₉	C₂²	semidirect
22. C₂×C₃×Dic₁₈	C₂²	semidirect
23. C₂×C₃×Dic₁₈	C₂²	semidirect
24. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
25. C₃×C₄²×C₉	C₂²	semidirect
26. C₃×#3676	C₂²	semidirect
27. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
28. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
29. C₃×C₄×Dic₉	C₂²	semidirect
30. C₃×C₄×Dic₉	C₂²	semidirect
40. C₂×Q₈×D₉	C₂×C₃	semidirect
43. C₉×#124	C₂×C₃	semidirect
44. #63509	C₂×C₃	semidirect
45. #63498	C₂×C₃	semidirect
46. #63447	C₂×C₃	semidirect
47. C₂²⋊C₄×D₉	C₂×C₃	semidirect
48. #63437	C₂×C₃	semidirect
49. C₄²×D₉	C₂×C₃	semidirect
93. C₂×Q₈×C₉	C₂²×C₃	semidirect
103. C₂×Dic₁₈	C₂²×C₃	semidirect
104. C₂×Dic₁₈	C₂²×C₃	semidirect
106. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
108. C₄²×C₉	C₂²×C₃	semidirect
109. #3676	C₂²×C₃	semidirect
110. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
111. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
112. C₄×Dic₉	C₂²×C₃	semidirect
113. C₄×Dic₉	C₂²×C₃	semidirect
137. C₃×#124	D₉	direct (N × H)
198. C₃×D₉	#124	direct (N × H)
205. C₂×C₃×Q₈	C₂×D₉	semidirect
229. C₃×C₂²⋊C₄	C₂×D₉	semidirect
234. C₃×C₄²	C₂×D₉	semidirect
281. #124	C₃×D₉	direct (N × H)
284. C₃×C₉	C₂×#124	semidirect
343. D₉	C₃×#124	direct (N × H)
348. C₂×Q₈	C₂×C₃×D₉	semidirect
359. C₂²⋊C₄	C₂×C₃×D₉	semidirect
362. C₄²	C₂×C₃×D₉	semidirect
399. C₉	C₂×C₃×#124	semidirect
448. C₃	D₉×#124	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×Q₈×D₉	2
C₂×C₃×D₄×D₉	2
C₃×C₉×#124	2
C₃×#63509	2
C₃×#63498	2
C₃×#63447	2
C₃×C₂²⋊C₄×D₉	2
C₃×#63437	2
C₃×C₄²×D₉	2
C₃×D₃×#124	3
D₉×#124	3

Subgroups — C3×D9×#124 #13153087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₉×#124 #13153087