Subgroups — C₃×D₃×#441 #11860094

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×D₃×Q₈	C₂	1	2	yes	maximal
3	C₃²×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5184	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5030	C₂	1	2	yes	maximal, complemented
6	C₃×D₃×#106	C₂	1	1	yes	maximal, characteristic
7	C₃×#4853	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₃×#103	C₂	1	2	yes	maximal
9	C₃×#4789	C₂	1	2	yes	maximal, complemented
10	C₃×#4716	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₃×#97	C₂	1	1	yes	maximal, characteristic
12	C₂×C₃×#441	—	3	1	no	maximal
13	D₃×#441	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	—
15	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
16	C₃²×C₄×Q₈	C₂²	1	2	yes	—
17	C₃×Q₈×Dic₃	C₂²	1	2	yes	—
18	C₂×C₃×#216	C₂²	1	2	yes	—
19	C₃×D₃×Q₁₆	C₄	1	8	yes	complemented
20	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
23	C₃×D₃×C₄⋊C₄	—	2	2	no	—
24	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₃×#887	—	2	2	no	—
26	C₃×#887	C₂²	1	2	yes	—
27	C₃×C₄²×D₃	—	2	2	no	—
28	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
29	C₃×C₄×Dic₆	—	2	2	no	—
30	C₃×C₄×Dic₆	C₂²	1	2	yes	—
31	C₃²×#106	C₂²	1	1	yes	characteristic
32	C₃²×#103	C₂²	1	2	yes	—
33	C₃²×#97	C₂²	1	1	yes	characteristic
34	C₃×#835	C₂²	1	2	yes	—
35	C₃×#817	C₂²	1	1	yes	characteristic
36	C₃×#816	C₂²	1	2	yes	—
37	C₃×#815	C₂²	1	1	yes	characteristic
38	C₃×#815	C₂²	1	1	yes	characteristic
39	C₃×#810	C₂²	1	2	yes	—
40	C₃×#808	C₂²	1	2	yes	—
41	C₃×#803	C₂²	1	1	yes	characteristic
42	C₂²×C₃×Q₁₆	—	3	1	no	—
43	C₂×C₃×C₄×Q₈	—	3	2	no	—
44	C₂×D₃×Q₁₆	C₂×C₃	1	1	yes	characteristic
45	C₄×D₃×Q₈	C₂×C₃	1	2	yes	—
46	C₃×#441	—	2	1	no	—
47	C₃×#441	—	3	1	no	—
48	C₃×#441	—	3	2	no	—
49	C₃×#441	—	3	1	no	—
50	C₃×#441	—	3	2	no	—
51	C₃×#441	—	3	1	no	—
52	C₃×#441	D₃	1	1	yes	characteristic, direct product factor
53	C₃×#441	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×#106	—	3	1	no	—
55	C₂×C₃×#103	—	3	2	no	—
56	C₂×C₃×#97	—	3	1	no	—
57	#5184	C₂×C₃	1	1	yes	characteristic, complemented
58	#5030	C₂×C₃	1	2	yes	complemented
59	D₃×#106	C₂×C₃	1	1	yes	characteristic
60	#4853	C₂×C₃	1	1	yes	characteristic, complemented
61	D₃×#103	C₂×C₃	1	2	yes	—
62	#4789	C₂×C₃	1	2	yes	complemented
63	#4716	C₂×C₃	1	1	yes	characteristic, complemented
64	D₃×#97	C₂×C₃	1	1	yes	characteristic
65	C₂×C₃²×Q₈	C₂³	1	2	yes	—
66	C₃×D₃×Q₈	—	2	4	no	—
67	C₃×D₃×Q₈	C₂×C₄	1	8	yes	—
68	C₂×C₃×C₄×D₃	—	2	2	no	—
69	C₂×C₃×C₄×D₃	—	2	2	no	—
70	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
71	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
72	C₂×C₃×Dic₆	—	2	2	no	—
73	C₂×C₃×Dic₆	C₂³	1	2	yes	—
74	C₃²×Q₁₆	C₂×C₄	1	4	yes	complemented
75	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
76	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
77	C₃²×C₄⋊C₄	—	2	2	no	—
78	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
79	C₃²×C₄²	—	2	2	no	—
80	C₃²×C₄²	C₂³	1	1	yes	characteristic
81	C₃×#216	C₂×C₄	1	8	yes	complemented
82	C₃×C₄⋊Dic₃	—	2	2	no	—
83	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
84	C₃×Dic₃⋊C₄	—	2	2	no	—
85	C₃×Dic₃⋊C₄	—	2	2	no	—
86	C₃×Dic₃⋊C₄	—	2	2	no	—
87	C₃×C₄×Dic₃	—	2	2	no	—
88	C₃×C₄×Dic₃	—	2	2	no	—
89	C₃×C₄×Dic₃	—	2	2	no	—
90	C₃×C₄×Dic₃	D₄	1	2	yes	—
91	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₃×Dic₁₂	C₂×C₄	1	4	yes	complemented
95	C₃×D₃×C₈	—	2	2	no	—
96	C₃×D₃×C₈	C₂×C₄	1	4	yes	—
97	C₂×#441	—	3	1	no	Sylow
98	C₂²×C₃×Q₈	—	3	2	no	—
99	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	—
100	C₂×C₃×Q₁₆	—	2	1	no	—
101	C₂×C₃×Q₁₆	—	3	2	no	—
102	C₂×C₃×Q₁₆	—	3	8	no	—
103	C₂×C₃×Q₁₆	—	3	1	no	—
104	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic
105	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
106	C₂²×C₃×C₈	—	3	1	no	—
107	C₂²×C₃×C₈	—	3	1	no	—
108	C₃×C₄×Q₈	—	2	2	no	—
109	C₃×C₄×Q₈	—	3	2	no	—
110	C₃×C₄×Q₈	—	3	2	no	—
111	C₃×C₄×Q₈	—	3	2	no	—
112	C₃×C₄×Q₈	—	6	2	no	—
113	C₃×C₄×Q₈	—	6	2	no	—
114	C₃×C₄×Q₈	C₂×D₃	1	2	yes	—
115	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
116	C₂×C₃×C₄⋊C₄	—	3	2	no	—
117	C₂×C₃×C₄⋊C₄	—	6	2	no	—
118	C₂×C₃×C₄²	—	3	1	no	—
119	C₂×C₃×C₄²	—	6	2	no	—
120	Q₈×Dic₃	C₂²×C₃	1	2	yes	—
121	C₂×#216	C₂²×C₃	1	2	yes	—
122	D₃×Q₁₆	C₃×C₄	1	8	yes	complemented
123	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
124	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
125	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
126	D₃×C₄⋊C₄	—	2	2	no	—
127	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
128	#887	—	2	2	no	—
129	#887	C₂²×C₃	1	2	yes	—
130	C₄²×D₃	—	2	2	no	—
131	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
132	C₄×Dic₆	—	2	2	no	—
133	C₄×Dic₆	C₂²×C₃	1	2	yes	—
134	C₃×#106	—	2	1	no	—
135	C₃×#106	—	3	1	no	—
136	C₃×#106	—	3	2	no	—
137	C₃×#106	C₂×D₃	1	1	yes	characteristic
138	C₃×#106	C₂²×C₃	1	1	yes	characteristic
139	C₃×#103	—	2	2	no	—
140	C₃×#103	—	3	2	no	—
141	C₃×#103	—	3	2	no	—
142	C₃×#103	—	3	2	no	—
143	C₃×#103	C₂×D₃	1	2	yes	—
144	C₃×#103	C₂²×C₃	1	2	yes	—
145	C₃×#97	—	2	1	no	—
146	C₃×#97	—	3	1	no	—
147	C₃×#97	—	3	1	no	—
148	C₃×#97	—	3	1	no	—
149	C₃×#97	C₂×D₃	1	1	yes	characteristic
150	C₃×#97	C₂²×C₃	1	1	yes	characteristic
151	#835	C₂²×C₃	1	2	yes	—
152	#817	C₂²×C₃	1	1	yes	characteristic
153	#816	C₂²×C₃	1	2	yes	—
154	#815	C₂²×C₃	1	1	yes	characteristic
155	#815	C₂²×C₃	1	1	yes	characteristic
156	#810	C₂²×C₃	1	2	yes	—
157	#808	C₂²×C₃	1	2	yes	—
158	#803	C₂²×C₃	1	1	yes	characteristic
159	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
160	C₃²×Q₈	—	2	2	no	—
161	C₃²×Q₈	C₂²×C₄	1	4	yes	—
162	C₂×C₃²×C₄	—	2	2	no	—
163	C₂×C₃²×C₄	—	2	2	no	—
164	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
165	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
166	C₂×C₃×Dic₃	—	2	2	no	—
167	C₂×C₃×Dic₃	—	2	2	no	—
168	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
169	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
170	C₃×C₄×D₃	—	2	8	no	—
171	C₃×C₄×D₃	—	2	4	no	—
172	C₃×C₄×D₃	—	4	4	no	—
173	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
174	C₃×C₄×D₃	#41	1	2	yes	—
175	C₃×Dic₆	—	2	2	no	—
176	C₃×Dic₆	—	2	8	no	—
177	C₃×Dic₆	C₂²×C₄	1	4	yes	—
178	C₃²×C₈	—	2	1	no	—
179	C₃²×C₈	C₂²×C₄	1	2	yes	—
180	C₃×C₃⋊C₈	—	2	1	no	—
181	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
182	C₂²×Q₁₆	—	3	1	no	—
183	C₂×C₄×Q₈	—	3	2	no	—
184	#441	—	3	1	no	—
185	#441	—	3	2	no	—
186	#441	—	3	1	no	—
187	#441	—	3	2	no	—
188	#441	—	3	1	no	—
189	#441	C₃×D₃	1	1	yes	characteristic, direct product factor
190	C₂×#106	—	3	1	no	—
191	C₂×#103	—	3	2	no	—
192	C₂×#97	—	3	1	no	—
193	C₂×C₃×Q₈	—	2	2	no	—
194	C₂×C₃×Q₈	—	3	8	no	—
195	C₂×C₃×Q₈	—	3	2	no	—
196	C₂×C₃×Q₈	—	6	2	no	—
197	C₂×C₃×Q₈	—	6	4	no	—
198	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
199	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
200	C₂²×C₃×C₄	—	3	1	no	—
201	C₂²×C₃×C₄	—	3	2	no	—
202	C₂²×C₃×C₄	—	6	2	no	—
203	C₂²×C₃×C₄	—	6	2	no	—
204	D₃×Q₈	—	2	4	no	—
205	D₃×Q₈	C₂×C₃×C₄	1	8	yes	—
206	C₂×C₄×D₃	—	2	2	no	—
207	C₂×C₄×D₃	—	2	2	no	—
208	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
209	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
210	C₂×Dic₆	—	2	2	no	—
211	C₂×Dic₆	C₂³×C₃	1	2	yes	—
212	C₃×Q₁₆	—	2	4	no	—
213	C₃×Q₁₆	—	3	8	no	—
214	C₃×Q₁₆	—	3	4	no	—
215	C₃×Q₁₆	C₄×D₃	1	4	yes	complemented
216	C₃×Q₁₆	C₂×C₃×C₄	1	4	yes	complemented
217	C₂×C₃×C₈	—	2	1	no	—
218	C₂×C₃×C₈	—	2	1	no	—
219	C₂×C₃×C₈	—	3	1	no	—
220	C₂×C₃×C₈	—	3	4	no	—
221	C₂×C₃×C₈	—	3	1	no	—
222	C₂×C₃×C₈	—	6	2	no	—
223	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
224	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
225	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
226	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
227	C₃×C₄⋊C₄	—	2	2	no	—
228	C₃×C₄⋊C₄	—	2	2	no	—
229	C₃×C₄⋊C₄	—	2	2	no	—
230	C₃×C₄⋊C₄	—	3	2	no	—
231	C₃×C₄⋊C₄	—	4	2	no	—
232	C₃×C₄⋊C₄	—	6	2	no	—
233	C₃×C₄⋊C₄	—	6	2	no	—
234	C₃×C₄⋊C₄	—	6	2	no	—
235	C₃×C₄⋊C₄	—	6	2	no	—
236	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
237	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
238	C₃×C₄²	—	2	2	no	—
239	C₃×C₄²	—	2	2	no	—
240	C₃×C₄²	—	2	1	no	—
241	C₃×C₄²	—	3	2	no	—
242	C₃×C₄²	—	3	1	no	—
243	C₃×C₄²	—	4	2	no	—
244	C₃×C₄²	—	6	2	no	—
245	C₃×C₄²	—	6	2	no	—
246	C₃×C₄²	—	6	2	no	—
247	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
248	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
249	#216	C₂×C₃×C₄	1	8	yes	complemented
250	C₄⋊Dic₃	—	2	2	no	—
251	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
252	Dic₃⋊C₄	—	2	2	no	—
253	Dic₃⋊C₄	—	2	2	no	—
254	Dic₃⋊C₄	—	2	2	no	—
255	C₄×Dic₃	—	2	2	no	—
256	C₄×Dic₃	—	2	2	no	—
257	C₄×Dic₃	—	2	2	no	—
258	C₄×Dic₃	C₃×D₄	1	2	yes	—
259	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
260	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
261	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
262	Dic₁₂	C₂×C₃×C₄	1	4	yes	complemented
263	D₃×C₈	—	2	2	no	—
264	D₃×C₈	C₂×C₃×C₄	1	4	yes	—
265	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₃×D₃	C₄×D₄	1	2	yes	—
267	C₂×C₃×D₃	#137	1	4	yes	—
268	C₃²×C₄	—	2	4	no	—
269	C₃²×C₄	—	2	2	no	—
270	C₃²×C₄	—	4	2	no	—
271	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
272	C₃²×C₄	C₂×#41	1	1	yes	characteristic
273	C₃×Dic₃	—	2	4	no	—
274	C₃×Dic₃	—	2	2	no	—
275	C₃×Dic₃	—	4	2	no	—
276	C₃×Dic₃	C₄×D₄	1	2	yes	—
277	C₂²×Q₈	—	3	2	no	—
278	C₂×Q₁₆	—	3	2	no	—
279	C₂×Q₁₆	—	3	8	no	—
280	C₂×Q₁₆	—	3	1	no	—
281	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
282	C₂²×C₈	—	3	1	no	—
283	C₂²×C₈	—	3	1	no	—
284	C₄×Q₈	—	3	2	no	—
285	C₄×Q₈	—	3	2	no	—
286	C₄×Q₈	—	3	2	no	—
287	C₄×Q₈	—	6	2	no	—
288	C₄×Q₈	—	6	2	no	—
289	C₄×Q₈	C₂×C₃×D₃	1	2	yes	—
290	C₂×C₄⋊C₄	—	3	2	no	—
291	C₂×C₄⋊C₄	—	6	2	no	—
292	C₂×C₄²	—	3	1	no	—
293	C₂×C₄²	—	6	2	no	—
294	#106	—	3	1	no	—
295	#106	—	3	2	no	—
296	#106	C₂×C₃×D₃	1	1	yes	characteristic
297	#103	—	3	2	no	—
298	#103	—	3	2	no	—
299	#103	—	3	2	no	—
300	#103	C₂×C₃×D₃	1	2	yes	—
301	#97	—	3	1	no	—
302	#97	—	3	1	no	—
303	#97	—	3	1	no	—
304	#97	C₂×C₃×D₃	1	1	yes	characteristic
305	C₂³×C₃	—	3	1	no	—
306	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
307	C₃×Q₈	—	2	2	no	—
308	C₃×Q₈	—	2	2	no	—
309	C₃×Q₈	—	2	4	no	—
310	C₃×Q₈	—	3	4	no	—
311	C₃×Q₈	—	4	2	no	—
312	C₃×Q₈	—	6	8	no	—
313	C₃×Q₈	—	6	2	no	—
314	C₃×Q₈	C₂×C₄×D₃	1	4	yes	—
315	C₃×Q₈	C₂²×C₃×C₄	1	4	yes	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	3	1	no	—
323	C₂×C₃×C₄	—	3	2	no	—
324	C₂×C₃×C₄	—	3	2	no	—
325	C₂×C₃×C₄	—	3	2	no	—
326	C₂×C₃×C₄	—	4	2	no	—
327	C₂×C₃×C₄	—	4	2	no	—
328	C₂×C₃×C₄	—	6	4	no	—
329	C₂×C₃×C₄	—	6	8	no	—
330	C₂×C₃×C₄	—	6	2	no	—
331	C₂×C₃×C₄	—	6	2	no	—
332	C₂×C₃×C₄	—	12	4	no	—
333	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
334	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
335	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
337	C₂×Dic₃	—	2	2	no	—
338	C₂×Dic₃	—	2	2	no	—
339	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
340	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
341	C₄×D₃	—	2	8	no	—
342	C₄×D₃	—	2	4	no	—
343	C₄×D₃	—	4	4	no	—
344	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
345	C₄×D₃	C₃×#41	1	2	yes	—
346	Dic₆	—	2	2	no	—
347	Dic₆	—	2	8	no	—
348	Dic₆	C₂²×C₃×C₄	1	4	yes	—
349	C₃×C₈	—	2	1	no	—
350	C₃×C₈	—	2	1	no	—
351	C₃×C₈	—	2	2	no	—
352	C₃×C₈	—	3	2	no	—
353	C₃×C₈	—	4	1	no	—
354	C₃×C₈	—	6	1	no	—
355	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
356	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
357	C₃⋊C₈	—	2	1	no	—
358	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	—
359	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
360	C₂×C₃²	C₂×#137	1	2	yes	—
361	C₃×D₃	#441	1	4	yes	direct product factor
362	C₂×Q₈	—	3	8	no	—
363	C₂×Q₈	—	3	2	no	—
364	C₂×Q₈	—	6	2	no	—
365	C₂×Q₈	—	6	4	no	—
366	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
367	C₂²×C₄	—	3	1	no	—
368	C₂²×C₄	—	3	2	no	—
369	C₂²×C₄	—	6	2	no	—
370	C₂²×C₄	—	6	2	no	—
371	Q₁₆	—	3	8	no	—
372	Q₁₆	—	3	4	no	—
373	Q₁₆	C₃×C₄×D₃	1	4	yes	complemented
374	C₂×C₈	—	3	1	no	—
375	C₂×C₈	—	3	4	no	—
376	C₂×C₈	—	3	1	no	—
377	C₂×C₈	—	6	2	no	—
378	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
379	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	3	2	no	—
382	C₄⋊C₄	—	6	2	no	—
383	C₄⋊C₄	—	6	2	no	—
384	C₄⋊C₄	—	6	2	no	—
385	C₄⋊C₄	—	6	2	no	—
386	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
387	C₄²	—	2	2	no	—
388	C₄²	—	3	1	no	—
389	C₄²	—	3	2	no	—
390	C₄²	—	6	2	no	—
391	C₄²	—	6	2	no	—
392	C₄²	—	6	2	no	—
393	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
394	C₂²×C₃	—	2	1	no	—
395	C₂²×C₃	—	3	4	no	—
396	C₂²×C₃	—	3	2	no	—
397	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
398	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
399	C₂×D₃	C₃×C₄×D₄	1	2	yes	—
400	C₂×D₃	C₃×#137	1	4	yes	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	2	2	no	—
403	C₃×C₄	—	2	4	no	—
404	C₃×C₄	—	2	4	no	—
405	C₃×C₄	—	2	1	no	—
406	C₃×C₄	—	2	1	no	—
407	C₃×C₄	—	3	2	no	—
408	C₃×C₄	—	4	2	no	—
409	C₃×C₄	—	4	4	no	—
410	C₃×C₄	—	4	2	no	—
411	C₃×C₄	—	4	2	no	—
412	C₃×C₄	—	6	2	no	—
413	C₃×C₄	—	6	4	no	—
414	C₃×C₄	—	8	2	no	—
415	C₃×C₄	—	12	2	no	—
416	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
417	C₃×C₄	D₃×#41	1	1	yes	characteristic
418	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
419	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
420	Dic₃	—	2	2	no	—
421	Dic₃	—	2	4	no	—
422	Dic₃	—	4	2	no	—
423	Dic₃	C₃×C₄×D₄	1	2	yes	—
424	C₃²	C₂×#441	1	1	yes	characteristic, complemented, Sylow
425	C₂³	—	3	1	no	—
426	Q₈	—	2	2	no	—
427	Q₈	—	3	4	no	—
428	Q₈	—	6	8	no	—
429	Q₈	—	6	2	no	—
430	Q₈	C₂×C₃×C₄×D₃	1	4	yes	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	3	1	no	—
434	C₂×C₄	—	3	2	no	—
435	C₂×C₄	—	3	2	no	—
436	C₂×C₄	—	3	2	no	—
437	C₂×C₄	—	6	4	no	—
438	C₂×C₄	—	6	8	no	—
439	C₂×C₄	—	6	2	no	—
440	C₂×C₄	—	6	2	no	—
441	C₂×C₄	—	12	4	no	—
442	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
443	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
444	C₈	—	2	1	no	—
445	C₈	—	3	2	no	—
446	C₈	—	6	1	no	—
447	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
448	C₂×C₃	—	2	2	no	—
449	C₂×C₃	—	2	1	no	—
450	C₂×C₃	—	3	4	no	—
451	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
452	C₂×C₃	D₃×#137	1	2	yes	—
453	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
454	C₂×C₃	C₂×C₃×#137	1	2	yes	—
455	D₃	C₃×#441	1	4	yes	direct product factor
456	C₂²	—	3	4	no	—
457	C₂²	—	3	2	no	—
458	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
459	C₄	—	2	2	no	—
460	C₄	—	2	4	no	—
461	C₄	—	3	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	6	2	no	—
464	C₄	—	6	4	no	—
465	C₄	—	12	2	no	—
466	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
467	C₄	C₃×D₃×#41	1	1	yes	characteristic
468	C₃	—	2	1	no	—
469	C₃	D₃×#441	1	1	yes	characteristic, direct product factor
470	C₃	C₂×C₃×#441	1	1	yes	characteristic, complemented
471	C₂	—	3	4	no	—
472	C₂	C₃×C₄×D₃×D₄	1	1	yes	characteristic
473	C₂	C₃×D₃×#137	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#441	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂²×C₃×D₃	C₂×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#441	D₃
hypocenter	C₃	C₂×C₃×#441
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#441

Complements

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

N	H ≅ G/N	type
3. C₃²×#441	C₂	semidirect
4. C₃×#5184	C₂	semidirect
5. C₃×#5030	C₂	semidirect
7. C₃×#4853	C₂	semidirect
9. C₃×#4789	C₂	semidirect
10. C₃×#4716	C₂	semidirect
13. D₃×#441	C₃	direct (N × H)
19. C₃×D₃×Q₁₆	C₄	semidirect
52. C₃×#441	D₃	direct (N × H)
53. C₃×#441	C₂×C₃	semidirect
57. #5184	C₂×C₃	semidirect
58. #5030	C₂×C₃	semidirect
60. #4853	C₂×C₃	semidirect
62. #4789	C₂×C₃	semidirect
63. #4716	C₂×C₃	semidirect
74. C₃²×Q₁₆	C₂×C₄	semidirect
81. C₃×#216	C₂×C₄	semidirect
94. C₃×Dic₁₂	C₂×C₄	semidirect
122. D₃×Q₁₆	C₃×C₄	semidirect
189. #441	C₃×D₃	direct (N × H)
215. C₃×Q₁₆	C₄×D₃	semidirect
216. C₃×Q₁₆	C₂×C₃×C₄	semidirect
249. #216	C₂×C₃×C₄	semidirect
262. Dic₁₂	C₂×C₃×C₄	semidirect
361. C₃×D₃	#441	direct (N × H)
373. Q₁₆	C₃×C₄×D₃	semidirect
424. C₃²	C₂×#441	semidirect
455. D₃	C₃×#441	direct (N × H)
469. C₃	D₃×#441	direct (N × H)
470. C₃	C₂×C₃×#441	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×Q₁₆	2
C₃×C₄×D₃×Q₈	2
C₃²×#441	2
C₃×#5184	2
C₃×#5030	2
C₃×D₃×#106	2
C₃×#4853	2
C₃×D₃×#103	2
C₃×#4789	2
C₃×#4716	2
C₃×D₃×#97	2
C₂×C₃×#441	3
D₃×#441	3

Subgroups — C3×D3×#441 #11860094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#441 #11860094