Subgroups — C₃×D₃×#473 #11867953

Order 1152.

946 conjugacy classes of subgroups.

The subgroup lattice has 699 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×#137	C₂	1	2	yes	maximal
2	C₂×C₃×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×#131	C₂	1	1	yes	maximal, characteristic
4	C₃²×#473	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5204	C₂	1	2	yes	maximal, complemented
6	C₃×#5192	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5143	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4896	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4755	C₂	1	2	yes	maximal, complemented
11	C₃×D₃×#101	C₂	1	2	yes	maximal, complemented
12	C₂×C₃×#473	—	3	1	no	maximal
13	D₃×#473	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃×D₃×#41	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	—
16	C₃²×#137	C₂²	1	2	yes	—
17	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
18	C₃²×#131	C₂²	1	1	yes	characteristic
19	C₃×#951	C₂²	1	2	yes	—
20	C₃×#948	C₂²	1	1	yes	characteristic
21	C₂×C₃×#216	C₂²	1	2	yes	complemented
22	C₃×#942	C₂²	1	2	yes	—
23	C₃×#918	—	2	2	no	—
24	C₃×D₃×Q₁₆	—	2	2	no	—
25	C₃×D₃×Q₁₆	—	2	1	no	—
26	C₃×D₃×Q₁₆	—	2	1	no	—
27	C₃×D₃×Q₁₆	—	2	1	no	—
28	C₃×D₃×Q₁₆	—	2	1	no	—
29	C₃×#915	—	2	2	no	—
30	C₃×D₃×SD₁₆	—	2	2	no	—
31	C₃×#909	C₂²	1	2	yes	—
32	C₃×#907	—	2	1	no	—
33	C₃×#907	C₂²	1	1	yes	characteristic
34	C₃×D₃×M₁₆	—	2	1	no	—
35	C₃×D₃×M₁₆	C₂²	1	1	yes	characteristic
36	C₃×D₃×M₁₆	C₂²	1	2	yes	—
37	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
38	C₃×#901	—	2	1	no	—
39	C₃×#901	C₂²	1	1	yes	characteristic
40	C₂×C₃×D₃×C₈	—	2	1	no	—
41	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
42	C₃²×#108	C₂²	1	1	yes	characteristic, complemented
43	C₃²×#101	C₂²	1	2	yes	complemented
44	C₃×#836	C₂²	1	2	yes	complemented
45	C₃×#824	C₂²	1	2	yes	complemented
46	C₃×#824	C₂²	1	2	yes	complemented
47	C₃×#822	C₂²	1	2	yes	complemented
48	C₃×#819	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃×#137	—	3	2	no	—
50	C₂²×C₃×Q₁₆	—	3	1	no	—
51	C₂×C₃×#131	—	3	1	no	—
52	D₃×#137	C₂×C₃	1	2	yes	—
53	C₂×D₃×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
54	D₃×#131	C₂×C₃	1	1	yes	characteristic
55	C₃×#473	—	2	1	no	—
56	C₃×#473	—	3	2	no	—
57	C₃×#473	—	3	1	no	—
58	C₃×#473	—	3	1	no	—
59	C₃×#473	—	3	1	no	—
60	C₃×#473	—	3	2	no	—
61	C₃×#473	D₃	1	1	yes	characteristic, direct product factor
62	C₃×#473	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂×C₃×#108	—	3	1	no	—
64	C₂×C₃×#101	—	3	2	no	—
65	#5204	C₂×C₃	1	2	yes	complemented
66	#5192	C₂×C₃	1	1	yes	characteristic, complemented
67	#5143	C₂×C₃	1	1	yes	characteristic, complemented
68	#4896	C₂×C₃	1	1	yes	characteristic, complemented
69	D₃×#108	C₂×C₃	1	1	yes	characteristic, complemented
70	#4755	C₂×C₃	1	2	yes	complemented
71	D₃×#101	C₂×C₃	1	2	yes	complemented
72	C₃²×#41	C₂³	1	1	yes	characteristic
73	C₂×C₃²×Q₈	C₂³	1	2	yes	—
74	C₃×#239	D₄	1	1	yes	characteristic
75	C₃×D₃×Q₈	—	2	2	no	—
76	C₃×D₃×Q₈	—	2	2	no	—
77	C₃×D₃×Q₈	—	2	2	no	—
78	C₃×D₃×Q₈	—	2	2	no	—
79	C₃×D₃×Q₈	D₄	1	1	yes	characteristic
80	C₃×#237	—	2	1	no	—
81	C₃×#237	D₄	1	1	yes	characteristic
82	C₃×D₃×D₄	—	2	1	no	—
83	C₃×D₃×D₄	D₄	1	1	yes	characteristic
84	C₃×#235	—	2	1	no	—
85	C₃×#235	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₄×D₃	—	2	1	no	—
87	C₂×C₃×C₄×D₃	—	2	2	no	—
88	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
89	C₂×C₃×Dic₆	—	2	2	no	—
90	C₂×C₃×Dic₆	C₂³	1	2	yes	—
91	C₃²×Q₁₆	—	2	2	no	—
92	C₃²×Q₁₆	—	2	1	no	—
93	C₃²×Q₁₆	—	2	1	no	—
94	C₃²×SD₁₆	—	2	2	no	—
95	C₃²×M₁₆	—	2	1	no	—
96	C₃²×M₁₆	C₂³	1	1	yes	characteristic
97	C₃²×M₁₆	C₂³	1	2	yes	—
98	C₂×C₃²×C₈	—	2	1	no	—
99	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
100	C₃×#216	—	2	2	no	—
101	C₃×#216	—	2	2	no	—
102	C₃×#216	—	2	2	no	—
103	C₃×#216	—	2	2	no	—
104	C₃×#215	—	2	2	no	—
105	C₃×#214	—	2	2	no	—
106	C₃×#208	—	2	1	no	—
107	C₃×#208	C₂³	1	1	yes	characteristic
108	C₃×#208	C₂³	1	2	yes	—
109	C₂×C₃×C₃⋊C₈	—	2	1	no	—
110	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
111	C₃×Dic₁₂	—	2	2	no	—
112	C₃×Dic₁₂	—	2	1	no	—
113	C₃×Dic₁₂	—	2	1	no	—
114	C₃×#204	—	2	2	no	—
115	C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
116	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
117	C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
118	C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
119	C₃×D₃×C₈	—	2	1	no	—
120	C₃×D₃×C₈	—	2	2	no	—
121	C₃×D₃×C₈	—	2	1	no	—
122	C₃×D₃×C₈	—	2	1	no	—
123	C₃×D₃×C₈	D₄	1	1	yes	characteristic
124	C₃×D₃×C₈	D₄	1	1	yes	characteristic
125	C₃×D₃×C₈	D₄	1	1	yes	characteristic
126	C₃×D₃×C₈	D₄	1	1	yes	characteristic
127	C₂×#473	—	3	1	no	Sylow
128	C₂×C₃×#41	—	3	1	no	—
129	C₂²×C₃×Q₈	—	3	2	no	—
130	D₃×#41	C₂²×C₃	1	1	yes	characteristic
131	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	—
132	C₃×#137	—	2	2	no	—
133	C₃×#137	—	3	2	no	—
134	C₃×#137	—	3	2	no	—
135	C₃×#137	—	3	2	no	—
136	C₃×#137	—	6	2	no	—
137	C₃×#137	—	6	2	no	—
138	C₃×#137	C₂×D₃	1	2	yes	—
139	C₃×#137	C₂²×C₃	1	2	yes	—
140	C₂×C₃×Q₁₆	—	2	1	no	—
141	C₂×C₃×Q₁₆	—	3	2	no	—
142	C₂×C₃×Q₁₆	—	3	1	no	—
143	C₂×C₃×Q₁₆	—	6	1	no	—
144	C₂×C₃×Q₁₆	—	6	1	no	—
145	C₂×C₃×Q₁₆	—	6	1	no	—
146	C₂×C₃×Q₁₆	—	6	1	no	—
147	C₂×C₃×Q₁₆	—	6	2	no	—
148	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
149	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
150	C₂×C₃×SD₁₆	—	6	2	no	—
151	C₃×#131	—	2	1	no	—
152	C₃×#131	—	3	1	no	—
153	C₃×#131	—	3	1	no	—
154	C₃×#131	—	3	1	no	—
155	C₃×#131	—	6	1	no	—
156	C₃×#131	—	6	1	no	—
157	C₃×#131	C₂×D₃	1	1	yes	characteristic
158	C₃×#131	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₃×M₁₆	—	3	1	no	—
160	C₂×C₃×M₁₆	—	3	2	no	—
161	C₂×C₃×M₁₆	—	6	1	no	—
162	C₂²×C₃×C₈	—	3	1	no	—
163	C₂²×C₃×C₈	—	6	1	no	—
164	#951	C₂²×C₃	1	2	yes	—
165	#948	C₂²×C₃	1	1	yes	characteristic
166	C₂×#216	C₂²×C₃	1	2	yes	complemented
167	#942	C₂²×C₃	1	2	yes	—
168	#918	—	2	2	no	—
169	D₃×Q₁₆	—	2	2	no	—
170	D₃×Q₁₆	—	2	1	no	—
171	D₃×Q₁₆	—	2	1	no	—
172	D₃×Q₁₆	—	2	1	no	—
173	D₃×Q₁₆	—	2	1	no	—
174	#915	—	2	2	no	—
175	D₃×SD₁₆	—	2	2	no	—
176	#909	C₂²×C₃	1	2	yes	—
177	#907	—	2	1	no	—
178	#907	C₂²×C₃	1	1	yes	characteristic
179	D₃×M₁₆	—	2	1	no	—
180	D₃×M₁₆	C₂²×C₃	1	2	yes	—
181	D₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
182	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
183	#901	—	2	1	no	—
184	#901	C₂²×C₃	1	1	yes	characteristic
185	C₂×D₃×C₈	—	2	1	no	—
186	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
187	C₃×#108	—	2	1	no	—
188	C₃×#108	—	3	2	no	—
189	C₃×#108	—	3	1	no	—
190	C₃×#108	C₂×D₃	1	1	yes	characteristic, complemented
191	C₃×#108	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₃×#101	—	2	2	no	—
193	C₃×#101	—	3	2	no	—
194	C₃×#101	—	3	2	no	—
195	C₃×#101	—	3	2	no	—
196	C₃×#101	C₂×D₃	1	2	yes	complemented
197	C₃×#101	C₂²×C₃	1	2	yes	complemented
198	#836	C₂²×C₃	1	2	yes	complemented
199	#824	C₂²×C₃	1	2	yes	complemented
200	#824	C₂²×C₃	1	2	yes	complemented
201	#822	C₂²×C₃	1	2	yes	complemented
202	#819	C₂²×C₃	1	1	yes	characteristic, complemented
203	C₂²×C₃×D₃	—	2	1	no	—
204	C₂²×C₃×D₃	#41	1	1	yes	characteristic
205	C₃²×Q₈	—	2	2	no	—
206	C₃²×Q₈	—	2	2	no	—
207	C₃²×Q₈	C₂×D₄	1	1	yes	characteristic
208	C₃²×D₄	—	2	1	no	—
209	C₃²×D₄	C₂×D₄	1	1	yes	characteristic
210	C₂×C₃²×C₄	—	2	1	no	—
211	C₂×C₃²×C₄	—	2	2	no	—
212	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
213	C₃×#67	—	2	1	no	—
214	C₃×#67	—	2	1	no	—
215	C₃×#67	—	2	1	no	—
216	C₂×C₃×Dic₃	—	2	1	no	—
217	C₂×C₃×Dic₃	—	2	2	no	—
218	C₂×C₃×Dic₃	#41	1	1	yes	characteristic
219	C₃×D₁₂	—	2	1	no	—
220	C₃×D₁₂	C₂×D₄	1	1	yes	characteristic
221	C₃×C₄×D₃	—	2	1	no	—
222	C₃×C₄×D₃	—	2	1	no	—
223	C₃×C₄×D₃	—	2	1	no	—
224	C₃×C₄×D₃	—	4	2	no	—
225	C₃×C₄×D₃	—	4	2	no	—
226	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
227	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
228	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
229	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
230	C₃×Dic₆	—	2	1	no	—
231	C₃×Dic₆	—	2	2	no	—
232	C₃×Dic₆	—	2	2	no	—
233	C₃×Dic₆	—	4	2	no	—
234	C₃×Dic₆	—	4	2	no	—
235	C₃×Dic₆	C₂×D₄	1	1	yes	characteristic
236	C₃²×C₈	—	2	1	no	—
237	C₃²×C₈	—	2	2	no	—
238	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
239	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
240	C₃×C₃⋊C₈	—	2	1	no	—
241	C₃×C₃⋊C₈	—	2	2	no	—
242	C₃×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
243	C₃×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
244	C₂×#137	—	3	2	no	—
245	C₂²×Q₁₆	—	3	1	no	—
246	C₂×#131	—	3	1	no	—
247	#473	—	3	2	no	—
248	#473	—	3	1	no	—
249	#473	—	3	1	no	—
250	#473	—	3	1	no	—
251	#473	—	3	2	no	—
252	#473	C₃×D₃	1	1	yes	characteristic, direct product factor
253	C₂×#108	—	3	1	no	—
254	C₂×#101	—	3	2	no	—
255	C₃×#41	—	2	1	no	—
256	C₃×#41	—	3	1	no	—
257	C₃×#41	—	3	1	no	—
258	C₃×#41	—	3	1	no	—
259	C₃×#41	—	6	1	no	—
260	C₃×#41	—	6	1	no	—
261	C₃×#41	C₂²×D₃	1	1	yes	characteristic
262	C₃×#41	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₃×Q₈	—	2	2	no	—
264	C₂×C₃×Q₈	—	3	1	no	—
265	C₂×C₃×Q₈	—	3	2	no	—
266	C₂×C₃×Q₈	—	6	2	no	—
267	C₂×C₃×Q₈	—	6	2	no	—
268	C₂×C₃×Q₈	—	6	2	no	—
269	C₂×C₃×Q₈	—	6	2	no	—
270	C₂×C₃×Q₈	—	6	2	no	—
271	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
272	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
273	C₂×C₃×D₄	—	3	1	no	—
274	C₂×C₃×D₄	—	6	1	no	—
275	C₂²×C₃×C₄	—	3	1	no	—
276	C₂²×C₃×C₄	—	6	1	no	—
277	C₂²×C₃×C₄	—	6	2	no	—
278	#239	C₃×D₄	1	1	yes	characteristic
279	D₃×Q₈	—	2	2	no	—
280	D₃×Q₈	—	2	2	no	—
281	D₃×Q₈	—	2	2	no	—
282	D₃×Q₈	—	2	2	no	—
283	D₃×Q₈	C₃×D₄	1	1	yes	characteristic
284	#237	—	2	1	no	—
285	#237	C₃×D₄	1	1	yes	characteristic
286	D₃×D₄	—	2	1	no	—
287	D₃×D₄	C₃×D₄	1	1	yes	characteristic
288	#235	—	2	1	no	—
289	#235	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₄×D₃	—	2	1	no	—
291	C₂×C₄×D₃	—	2	2	no	—
292	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
293	C₂×Dic₆	—	2	2	no	—
294	C₂×Dic₆	C₂³×C₃	1	2	yes	—
295	C₃×Q₁₆	—	2	2	no	—
296	C₃×Q₁₆	—	2	2	no	—
297	C₃×Q₁₆	—	2	1	no	—
298	C₃×Q₁₆	—	2	1	no	—
299	C₃×Q₁₆	—	2	1	no	—
300	C₃×Q₁₆	—	2	1	no	—
301	C₃×Q₁₆	—	4	1	no	—
302	C₃×Q₁₆	—	4	1	no	—
303	C₃×Q₁₆	—	4	2	no	—
304	C₃×Q₁₆	—	6	2	no	—
305	C₃×Q₁₆	—	6	2	no	—
306	C₃×Q₁₆	—	6	2	no	—
307	C₃×Q₁₆	—	6	2	no	—
308	C₃×Q₁₆	—	6	2	no	—
309	C₃×Q₁₆	—	6	1	no	—
310	C₃×Q₁₆	—	6	1	no	—
311	C₃×SD₁₆	—	2	2	no	—
312	C₃×SD₁₆	—	2	2	no	—
313	C₃×SD₁₆	—	4	2	no	—
314	C₃×SD₁₆	—	6	2	no	—
315	C₃×SD₁₆	—	6	2	no	—
316	C₃×SD₁₆	—	6	2	no	—
317	C₃×M₁₆	—	2	1	no	—
318	C₃×M₁₆	—	2	1	no	—
319	C₃×M₁₆	—	2	1	no	—
320	C₃×M₁₆	—	2	2	no	—
321	C₃×M₁₆	—	3	1	no	—
322	C₃×M₁₆	—	3	2	no	—
323	C₃×M₁₆	—	4	1	no	—
324	C₃×M₁₆	—	6	1	no	—
325	C₃×M₁₆	—	6	1	no	—
326	C₃×M₁₆	—	6	2	no	—
327	C₃×M₁₆	—	6	1	no	—
328	C₃×M₁₆	—	6	1	no	—
329	C₃×M₁₆	C₂²×D₃	1	1	yes	characteristic
330	C₃×M₁₆	C₂²×D₃	1	2	yes	—
331	C₃×M₁₆	C₂³×C₃	1	2	yes	—
332	C₃×M₁₆	C₂³×C₃	1	1	yes	characteristic
333	C₂×C₃×C₈	—	2	1	no	—
334	C₂×C₃×C₈	—	2	1	no	—
335	C₂×C₃×C₈	—	2	1	no	—
336	C₂×C₃×C₈	—	3	1	no	—
337	C₂×C₃×C₈	—	3	1	no	—
338	C₂×C₃×C₈	—	3	1	no	—
339	C₂×C₃×C₈	—	3	1	no	—
340	C₂×C₃×C₈	—	3	1	no	—
341	C₂×C₃×C₈	—	4	1	no	—
342	C₂×C₃×C₈	—	6	1	no	—
343	C₂×C₃×C₈	—	6	1	no	—
344	C₂×C₃×C₈	—	6	2	no	—
345	C₂×C₃×C₈	—	6	1	no	—
346	C₂×C₃×C₈	—	6	1	no	—
347	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
348	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
349	#216	—	2	2	no	—
350	#216	—	2	2	no	—
351	#216	—	2	2	no	—
352	#216	—	2	2	no	—
353	#215	—	2	2	no	—
354	#214	—	2	2	no	—
355	#208	—	2	1	no	—
356	#208	C₂³×C₃	1	2	yes	—
357	#208	C₂³×C₃	1	1	yes	characteristic
358	C₂×C₃⋊C₈	—	2	1	no	—
359	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
360	Dic₁₂	—	2	2	no	—
361	Dic₁₂	—	2	1	no	—
362	Dic₁₂	—	2	1	no	—
363	#204	—	2	2	no	—
364	ΓL(1,𝔽₂₅)	—	2	1	no	—
365	ΓL(1,𝔽₂₅)	—	2	2	no	—
366	ΓL(1,𝔽₂₅)	—	2	1	no	—
367	ΓL(1,𝔽₂₅)	—	2	1	no	—
368	D₃×C₈	—	2	1	no	—
369	D₃×C₈	—	2	2	no	—
370	D₃×C₈	—	2	1	no	—
371	D₃×C₈	—	2	1	no	—
372	D₃×C₈	C₃×D₄	1	1	yes	characteristic
373	D₃×C₈	C₃×D₄	1	1	yes	characteristic
374	D₃×C₈	C₃×D₄	1	1	yes	characteristic
375	D₃×C₈	C₃×D₄	1	1	yes	characteristic
376	C₂²×C₃²	—	2	1	no	—
377	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
378	C₂×C₃×D₃	—	2	2	no	—
379	C₂×C₃×D₃	—	2	1	no	—
380	C₂×C₃×D₃	—	4	2	no	—
381	C₂×C₃×D₃	#121	1	1	yes	characteristic
382	C₂×C₃×D₃	#121	1	1	yes	characteristic
383	C₃²×C₄	—	2	1	no	—
384	C₃²×C₄	—	4	2	no	—
385	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
386	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
387	C₃×Dic₃	—	2	1	no	—
388	C₃×Dic₃	—	4	2	no	—
389	C₃×Dic₃	#121	1	1	yes	characteristic
390	C₃×Dic₃	#121	1	1	yes	characteristic
391	C₂×#41	—	3	1	no	—
392	C₂²×Q₈	—	3	2	no	—
393	#137	—	3	2	no	—
394	#137	—	3	2	no	—
395	#137	—	3	2	no	—
396	#137	—	6	2	no	—
397	#137	—	6	2	no	—
398	#137	C₂×C₃×D₃	1	2	yes	—
399	C₂×Q₁₆	—	3	2	no	—
400	C₂×Q₁₆	—	3	1	no	—
401	C₂×Q₁₆	—	6	1	no	—
402	C₂×Q₁₆	—	6	1	no	—
403	C₂×Q₁₆	—	6	1	no	—
404	C₂×Q₁₆	—	6	1	no	—
405	C₂×Q₁₆	—	6	2	no	—
406	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic, complemented
407	C₂×SD₁₆	—	6	2	no	—
408	#131	—	3	1	no	—
409	#131	—	3	1	no	—
410	#131	—	3	1	no	—
411	#131	—	6	1	no	—
412	#131	—	6	1	no	—
413	#131	C₂×C₃×D₃	1	1	yes	characteristic
414	C₂×M₁₆	—	3	1	no	—
415	C₂×M₁₆	—	3	2	no	—
416	C₂×M₁₆	—	6	1	no	—
417	C₂²×C₈	—	3	1	no	—
418	C₂²×C₈	—	6	1	no	—
419	#108	—	3	2	no	—
420	#108	—	3	1	no	—
421	#108	C₂×C₃×D₃	1	1	yes	characteristic, complemented
422	#101	—	3	2	no	—
423	#101	—	3	2	no	—
424	#101	—	3	2	no	—
425	#101	C₂×C₃×D₃	1	2	yes	complemented
426	C₂³×C₃	—	3	1	no	—
427	C₂³×C₃	—	6	1	no	—
428	C₂²×D₃	—	2	1	no	—
429	C₂²×D₃	C₃×#41	1	1	yes	characteristic
430	C₃×Q₈	—	2	2	no	—
431	C₃×Q₈	—	2	2	no	—
432	C₃×Q₈	—	2	2	no	—
433	C₃×Q₈	—	2	2	no	—
434	C₃×Q₈	—	2	1	no	—
435	C₃×Q₈	—	3	1	no	—
436	C₃×Q₈	—	4	2	no	—
437	C₃×Q₈	—	4	2	no	—
438	C₃×Q₈	—	6	1	no	—
439	C₃×Q₈	—	6	2	no	—
440	C₃×Q₈	—	6	2	no	—
441	C₃×Q₈	—	12	2	no	—
442	C₃×Q₈	—	12	2	no	—
443	C₃×Q₈	D₃×D₄	1	1	yes	characteristic
444	C₃×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
445	C₃×D₄	—	2	1	no	—
446	C₃×D₄	—	2	1	no	—
447	C₃×D₄	—	2	1	no	—
448	C₃×D₄	—	3	1	no	—
449	C₃×D₄	—	4	1	no	—
450	C₃×D₄	—	6	1	no	—
451	C₃×D₄	—	6	1	no	—
452	C₃×D₄	—	6	1	no	—
453	C₃×D₄	—	6	1	no	—
454	C₃×D₄	D₃×D₄	1	1	yes	characteristic
455	C₃×D₄	C₂×C₃×D₄	1	1	yes	characteristic
456	C₂×C₃×C₄	—	2	1	no	—
457	C₂×C₃×C₄	—	2	1	no	—
458	C₂×C₃×C₄	—	2	2	no	—
459	C₂×C₃×C₄	—	2	2	no	—
460	C₂×C₃×C₄	—	2	1	no	—
461	C₂×C₃×C₄	—	3	1	no	—
462	C₂×C₃×C₄	—	3	1	no	—
463	C₂×C₃×C₄	—	3	1	no	—
464	C₂×C₃×C₄	—	3	1	no	—
465	C₂×C₃×C₄	—	3	1	no	—
466	C₂×C₃×C₄	—	4	1	no	—
467	C₂×C₃×C₄	—	4	2	no	—
468	C₂×C₃×C₄	—	6	1	no	—
469	C₂×C₃×C₄	—	6	1	no	—
470	C₂×C₃×C₄	—	6	1	no	—
471	C₂×C₃×C₄	—	6	1	no	—
472	C₂×C₃×C₄	—	6	2	no	—
473	C₂×C₃×C₄	—	12	2	no	—
474	C₂×C₃×C₄	—	12	2	no	—
475	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
476	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
477	#67	—	2	1	no	—
478	#67	—	2	1	no	—
479	#67	—	2	1	no	—
480	C₂×Dic₃	—	2	1	no	—
481	C₂×Dic₃	—	2	2	no	—
482	C₂×Dic₃	C₃×#41	1	1	yes	characteristic
483	D₁₂	—	2	1	no	—
484	D₁₂	C₂×C₃×D₄	1	1	yes	characteristic
485	C₄×D₃	—	2	1	no	—
486	C₄×D₃	—	2	1	no	—
487	C₄×D₃	—	2	1	no	—
488	C₄×D₃	—	4	2	no	—
489	C₄×D₃	—	4	2	no	—
490	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
491	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
492	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
493	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
494	Dic₆	—	2	1	no	—
495	Dic₆	—	2	2	no	—
496	Dic₆	—	2	2	no	—
497	Dic₆	—	4	2	no	—
498	Dic₆	—	4	2	no	—
499	Dic₆	C₂×C₃×D₄	1	1	yes	characteristic
500	C₃×C₈	—	2	1	no	—
501	C₃×C₈	—	2	2	no	—
502	C₃×C₈	—	2	1	no	—
503	C₃×C₈	—	2	2	no	—
504	C₃×C₈	—	2	1	no	—
505	C₃×C₈	—	2	1	no	—
506	C₃×C₈	—	3	1	no	—
507	C₃×C₈	—	3	1	no	—
508	C₃×C₈	—	4	1	no	—
509	C₃×C₈	—	4	2	no	—
510	C₃×C₈	—	6	1	no	—
511	C₃×C₈	—	6	2	no	—
512	C₃×C₈	D₃×D₄	1	1	yes	characteristic
513	C₃×C₈	D₃×D₄	1	1	yes	characteristic
514	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
515	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
516	C₃⋊C₈	—	2	1	no	—
517	C₃⋊C₈	—	2	2	no	—
518	C₃⋊C₈	C₂×C₃×D₄	1	1	yes	characteristic
519	C₃⋊C₈	C₂×C₃×D₄	1	1	yes	characteristic
520	C₂×C₃²	—	2	1	no	—
521	C₂×C₃²	—	4	1	no	—
522	C₂×C₃²	C₂×#121	1	1	yes	characteristic
523	C₃×D₃	—	2	1	no	—
524	C₃×D₃	—	4	1	no	—
525	C₃×D₃	#473	1	2	yes	direct product factor
526	#41	—	3	1	no	—
527	#41	—	3	1	no	—
528	#41	—	3	1	no	—
529	#41	—	6	1	no	—
530	#41	—	6	1	no	—
531	#41	C₂²×C₃×D₃	1	1	yes	characteristic
532	C₂×Q₈	—	3	1	no	—
533	C₂×Q₈	—	3	2	no	—
534	C₂×Q₈	—	6	2	no	—
535	C₂×Q₈	—	6	2	no	—
536	C₂×Q₈	—	6	2	no	—
537	C₂×Q₈	—	6	2	no	—
538	C₂×Q₈	—	6	2	no	—
539	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
540	C₂×D₄	—	3	1	no	—
541	C₂×D₄	—	6	1	no	—
542	C₂²×C₄	—	3	1	no	—
543	C₂²×C₄	—	6	1	no	—
544	C₂²×C₄	—	6	2	no	—
545	Q₁₆	—	2	2	no	—
546	Q₁₆	—	2	1	no	—
547	Q₁₆	—	2	1	no	—
548	Q₁₆	—	6	2	no	—
549	Q₁₆	—	6	2	no	—
550	Q₁₆	—	6	2	no	—
551	Q₁₆	—	6	2	no	—
552	Q₁₆	—	6	2	no	—
553	Q₁₆	—	6	1	no	—
554	Q₁₆	—	6	1	no	—
555	SD₁₆	—	2	2	no	—
556	SD₁₆	—	6	2	no	—
557	SD₁₆	—	6	2	no	—
558	SD₁₆	—	6	2	no	—
559	M₁₆	—	2	1	no	—
560	M₁₆	—	3	1	no	—
561	M₁₆	—	3	2	no	—
562	M₁₆	—	6	1	no	—
563	M₁₆	—	6	1	no	—
564	M₁₆	—	6	2	no	—
565	M₁₆	—	6	1	no	—
566	M₁₆	—	6	1	no	—
567	M₁₆	C₂²×C₃×D₃	1	1	yes	characteristic
568	M₁₆	C₂²×C₃×D₃	1	2	yes	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	3	1	no	—
571	C₂×C₈	—	3	1	no	—
572	C₂×C₈	—	3	1	no	—
573	C₂×C₈	—	3	1	no	—
574	C₂×C₈	—	3	1	no	—
575	C₂×C₈	—	6	1	no	—
576	C₂×C₈	—	6	1	no	—
577	C₂×C₈	—	6	2	no	—
578	C₂×C₈	—	6	1	no	—
579	C₂×C₈	—	6	1	no	—
580	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
581	C₂²×C₃	—	2	1	no	—
582	C₂²×C₃	—	2	1	no	—
583	C₂²×C₃	—	2	1	no	—
584	C₂²×C₃	—	3	1	no	—
585	C₂²×C₃	—	3	1	no	—
586	C₂²×C₃	—	4	1	no	—
587	C₂²×C₃	—	6	2	no	—
588	C₂²×C₃	—	6	1	no	—
589	C₂²×C₃	—	12	2	no	—
590	C₂²×C₃	D₃×#41	1	1	yes	characteristic
591	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
592	C₂×D₃	—	2	2	no	—
593	C₂×D₃	—	2	1	no	—
594	C₂×D₃	—	4	2	no	—
595	C₂×D₃	C₃×#121	1	1	yes	characteristic
596	C₂×D₃	C₃×#121	1	1	yes	characteristic
597	C₃×C₄	—	2	1	no	—
598	C₃×C₄	—	2	1	no	—
599	C₃×C₄	—	2	1	no	—
600	C₃×C₄	—	2	1	no	—
601	C₃×C₄	—	3	1	no	—
602	C₃×C₄	—	3	1	no	—
603	C₃×C₄	—	4	1	no	—
604	C₃×C₄	—	4	2	no	—
605	C₃×C₄	—	4	2	no	—
606	C₃×C₄	—	6	1	no	—
607	C₃×C₄	—	8	2	no	—
608	C₃×C₄	—	12	2	no	—
609	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
610	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
611	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
612	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
613	Dic₃	—	2	1	no	—
614	Dic₃	—	4	2	no	—
615	Dic₃	C₃×#121	1	1	yes	characteristic
616	Dic₃	C₃×#121	1	1	yes	characteristic
617	C₃²	C₂×#473	1	1	yes	characteristic, complemented, Sylow
618	C₂³	—	3	1	no	—
619	C₂³	—	6	1	no	—
620	Q₈	—	2	2	no	—
621	Q₈	—	2	2	no	—
622	Q₈	—	3	1	no	—
623	Q₈	—	6	1	no	—
624	Q₈	—	6	2	no	—
625	Q₈	—	6	2	no	—
626	Q₈	—	12	2	no	—
627	Q₈	—	12	2	no	—
628	Q₈	C₃×D₃×D₄	1	1	yes	characteristic
629	D₄	—	2	1	no	—
630	D₄	—	3	1	no	—
631	D₄	—	6	1	no	—
632	D₄	—	6	1	no	—
633	D₄	—	6	1	no	—
634	D₄	—	6	1	no	—
635	D₄	C₃×D₃×D₄	1	1	yes	characteristic
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	3	1	no	—
639	C₂×C₄	—	3	1	no	—
640	C₂×C₄	—	3	1	no	—
641	C₂×C₄	—	3	1	no	—
642	C₂×C₄	—	3	1	no	—
643	C₂×C₄	—	6	1	no	—
644	C₂×C₄	—	6	1	no	—
645	C₂×C₄	—	6	1	no	—
646	C₂×C₄	—	6	1	no	—
647	C₂×C₄	—	6	2	no	—
648	C₂×C₄	—	12	2	no	—
649	C₂×C₄	—	12	2	no	—
650	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
651	C₈	—	2	1	no	—
652	C₈	—	2	2	no	—
653	C₈	—	3	1	no	—
654	C₈	—	3	1	no	—
655	C₈	—	6	1	no	—
656	C₈	—	6	2	no	—
657	C₈	C₃×D₃×D₄	1	1	yes	characteristic
658	C₈	C₃×D₃×D₄	1	1	yes	characteristic
659	C₂×C₃	—	2	1	no	—
660	C₂×C₃	—	2	1	no	—
661	C₂×C₃	—	2	1	no	—
662	C₂×C₃	—	3	2	no	—
663	C₂×C₃	—	4	1	no	—
664	C₂×C₃	—	4	1	no	—
665	C₂×C₃	—	4	1	no	—
666	C₂×C₃	—	6	1	no	—
667	C₂×C₃	—	8	1	no	—
668	C₂×C₃	—	12	1	no	—
669	C₂×C₃	D₃×#121	1	1	yes	characteristic
670	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
671	D₃	—	2	1	no	—
672	D₃	—	4	1	no	—
673	D₃	C₃×#473	1	2	yes	direct product factor
674	C₂²	—	2	1	no	—
675	C₂²	—	3	1	no	—
676	C₂²	—	3	1	no	—
677	C₂²	—	6	2	no	—
678	C₂²	—	6	1	no	—
679	C₂²	—	12	2	no	—
680	C₂²	C₃×D₃×#41	1	1	yes	characteristic
681	C₄	—	2	1	no	—
682	C₄	—	3	1	no	—
683	C₄	—	3	1	no	—
684	C₄	—	4	2	no	—
685	C₄	—	6	1	no	—
686	C₄	—	12	2	no	—
687	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
688	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
689	C₃	—	2	1	no	—
690	C₃	D₃×#473	1	1	yes	characteristic, direct product factor
691	C₃	C₂×C₃×#473	1	1	yes	characteristic, complemented
692	C₂	—	2	1	no	—
693	C₂	—	3	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	6	1	no	—
696	C₂	—	12	1	no	—
697	C₂	C₃×D₃×#121	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₃×#121
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#473	C₂
socle	C₂×C₃²	C₂×#121
prime radical	C₃×D₃×#41	C₂²
hypercenter	C₃×#473	D₃
hypocenter	C₃	C₂×C₃×#473
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#473

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×D₃×Q₁₆	C₂	semidirect
4. C₃²×#473	C₂	semidirect
5. C₃×#5204	C₂	semidirect
6. C₃×#5192	C₂	semidirect
7. C₃×#5143	C₂	semidirect
8. C₃×#4896	C₂	semidirect
9. C₃×D₃×#108	C₂	semidirect
10. C₃×#4755	C₂	semidirect
11. C₃×D₃×#101	C₂	semidirect
13. D₃×#473	C₃	direct (N × H)
17. C₂×C₃²×Q₁₆	C₂²	semidirect
21. C₂×C₃×#216	C₂²	semidirect
37. C₂×C₃×Dic₁₂	C₂²	semidirect
42. C₃²×#108	C₂²	semidirect
43. C₃²×#101	C₂²	semidirect
44. C₃×#836	C₂²	semidirect
45. C₃×#824	C₂²	semidirect
46. C₃×#824	C₂²	semidirect
47. C₃×#822	C₂²	semidirect
48. C₃×#819	C₂²	semidirect
53. C₂×D₃×Q₁₆	C₂×C₃	semidirect
61. C₃×#473	D₃	direct (N × H)
62. C₃×#473	C₂×C₃	semidirect
65. #5204	C₂×C₃	semidirect
66. #5192	C₂×C₃	semidirect
67. #5143	C₂×C₃	semidirect
68. #4896	C₂×C₃	semidirect
69. D₃×#108	C₂×C₃	semidirect
70. #4755	C₂×C₃	semidirect
71. D₃×#101	C₂×C₃	semidirect
148. C₂×C₃×Q₁₆	C₂×D₃	semidirect
149. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
166. C₂×#216	C₂²×C₃	semidirect
182. C₂×Dic₁₂	C₂²×C₃	semidirect
190. C₃×#108	C₂×D₃	semidirect
191. C₃×#108	C₂²×C₃	semidirect
196. C₃×#101	C₂×D₃	semidirect
197. C₃×#101	C₂²×C₃	semidirect
198. #836	C₂²×C₃	semidirect
199. #824	C₂²×C₃	semidirect
200. #824	C₂²×C₃	semidirect
201. #822	C₂²×C₃	semidirect
202. #819	C₂²×C₃	semidirect
252. #473	C₃×D₃	direct (N × H)
406. C₂×Q₁₆	C₂×C₃×D₃	semidirect
421. #108	C₂×C₃×D₃	semidirect
425. #101	C₂×C₃×D₃	semidirect
525. C₃×D₃	#473	direct (N × H)
617. C₃²	C₂×#473	semidirect
673. D₃	C₃×#473	direct (N × H)
690. C₃	D₃×#473	direct (N × H)
691. C₃	C₂×C₃×#473	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×#137	2
C₂×C₃×D₃×Q₁₆	2
C₃×D₃×#131	2
C₃²×#473	2
C₃×#5204	2
C₃×#5192	2
C₃×#5143	2
C₃×#4896	2
C₃×D₃×#108	2
C₃×#4755	2
C₃×D₃×#101	2
C₂×C₃×#473	3
D₃×#473	3

Subgroups — C3×D3×#473 #11867953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#473 #11867953