Subgroups — C₃×#493226 #72226273

Order 1536.

1328 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#33443	C₂	1	2	yes	maximal
2	C₃×#33329	C₂	1	2	yes	maximal, complemented
3	C₃×#20512	C₂	1	1	yes	maximal, characteristic
4	C₃×#12667	C₂	1	2	yes	maximal, complemented
5	C₃×#12659	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#12618	C₂	1	4	yes	maximal, complemented
7	C₃×#12609	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×#347	C₂	1	1	yes	maximal, characteristic, complemented
9	#493226	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₃×#3407	C₂²	1	4	yes	—
11	C₂×C₃×#444	C₄	1	1	yes	characteristic
12	C₂×C₃×#443	C₂²	1	1	yes	characteristic
13	C₃×#2943	C₄	1	1	yes	characteristic
14	C₃×#2875	C₂²	1	2	yes	—
15	C₃×#2171	C₄	1	8	yes	complemented
16	C₃×#2170	C₄	1	8	yes	complemented
17	C₂×C₃×#364	C₂²	1	2	yes	—
18	C₃×#2117	C₂²	1	4	yes	—
19	C₃×#2110	—	2	4	no	—
20	C₃×#2110	C₂²	1	4	yes	—
21	C₂×C₃×#347	—	2	4	no	—
22	C₂×C₃×#347	C₂²	1	2	yes	—
23	C₂×C₃×#347	C₂²	1	1	yes	characteristic
24	C₂×C₃×#347	C₂²	1	2	yes	—
25	C₂×C₃×#347	C₂²	1	1	yes	characteristic
26	C₃×C₄×M₃₂	C₂²	1	2	yes	—
27	C₃×#1778	C₄	1	1	yes	characteristic
28	C₃×#1773	C₄	1	1	yes	characteristic
29	C₃×#1772	C₂²	1	1	yes	characteristic
30	C₃×#1765	C₂²	1	2	yes	—
31	C₃×#1764	C₄	1	2	yes	—
32	C₃×C₄×#104	C₄	1	2	yes	—
33	C₃×C₄×#97	C₂²	1	1	yes	characteristic
34	C₃×#1378	C₂²	1	4	yes	—
35	C₃×#1377	C₂²	1	2	yes	—
36	#33443	C₂×C₃	1	2	yes	—
37	#33329	C₂×C₃	1	2	yes	complemented
38	#20512	C₂×C₃	1	1	yes	characteristic
39	#12667	C₂×C₃	1	2	yes	complemented
40	#12659	C₂×C₃	1	1	yes	characteristic, complemented
41	#12618	C₂×C₃	1	4	yes	complemented
42	#12609	C₂×C₃	1	2	yes	complemented
43	C₄×#347	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×C₃×#135	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×#131	C₂×C₄	1	2	yes	—
46	C₂×C₃×#131	C₂³	1	2	yes	—
47	C₃×C₄×#41	C₂×C₄	1	2	yes	—
48	C₃×#504	—	2	8	no	—
49	C₃×#504	C₂×C₄	1	16	yes	complemented
50	C₂×C₃×M₃₂	—	2	8	no	—
51	C₂×C₃×M₃₂	C₂³	1	4	yes	—
52	C₂×C₃×M₃₂	C₂³	1	2	yes	—
53	C₂×C₃×M₃₂	C₂³	1	2	yes	—
54	C₃×#444	—	2	4	no	—
55	C₃×#443	C₂×C₄	1	4	yes	—
56	C₃×#443	C₂×C₄	1	4	yes	—
57	C₃×#442	—	2	1	no	—
58	C₃×#441	—	2	1	no	—
59	C₃×#440	—	2	2	no	—
60	C₂×C₃×#108	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×#108	C₂×C₄	1	1	yes	characteristic
62	C₃×#427	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×#104	C₂×C₄	1	2	yes	—
64	C₂×C₃×#104	C₂×C₄	1	2	yes	—
65	C₃×#416	C₂×C₄	1	2	yes	—
66	C₃×#405	—	2	2	no	—
67	C₃×#405	—	2	2	no	—
68	C₃×#405	C₂×C₄	1	2	yes	—
69	C₃×#405	C₂³	1	2	yes	—
70	C₃×C₄×M₁₆	—	2	2	no	—
71	C₃×C₄×M₁₆	C₂×C₄	1	2	yes	—
72	C₂×C₃×#97	—	2	2	no	—
73	C₂×C₃×#97	C₂×C₄	1	1	yes	characteristic
74	C₂×C₃×#97	C₂×C₄	1	1	yes	characteristic
75	C₂×C₃×#97	C₂³	1	1	yes	characteristic
76	C₂×C₃×#97	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
78	C₂×C₃×C₄×C₈	C₂³	1	1	yes	characteristic
79	C₃×C₄³	C₂×C₄	1	1	yes	characteristic
80	C₃×#364	C₂×C₄	1	4	yes	complemented
81	C₃×#364	C₂×C₄	1	4	yes	complemented
82	C₃×#350	C₂×C₄	1	16	yes	complemented
83	C₃×#347	—	2	8	no	—
84	C₃×#347	—	2	4	no	—
85	C₃×#347	—	2	2	no	—
86	C₃×#347	—	2	2	no	—
87	C₃×#347	—	2	2	no	—
88	C₃×#347	D₄	1	4	yes	—
89	C₃×#346	C₂×C₄	1	4	yes	complemented
90	C₃×C₄×C₁₆	C₂×C₄	1	4	yes	complemented
91	C₃×#341	C₂×C₄	1	2	yes	—
92	C₃×#339	C₂×C₄	1	2	yes	—
93	C₃×#339	C₂×C₄	1	2	yes	—
94	#3407	C₂²×C₃	1	4	yes	—
95	C₂×#444	C₃×C₄	1	1	yes	characteristic
96	C₂×#443	C₂²×C₃	1	1	yes	characteristic
97	#2943	C₃×C₄	1	1	yes	characteristic
98	#2875	C₂²×C₃	1	2	yes	—
99	#2171	C₃×C₄	1	8	yes	complemented
100	#2170	C₃×C₄	1	8	yes	complemented
101	C₂×#364	C₂²×C₃	1	2	yes	—
102	#2117	C₂²×C₃	1	4	yes	—
103	#2110	—	2	4	no	—
104	#2110	C₂²×C₃	1	4	yes	—
105	C₂×#347	—	2	4	no	—
106	C₂×#347	C₂²×C₃	1	2	yes	—
107	C₂×#347	C₂²×C₃	1	1	yes	characteristic
108	C₂×#347	C₂²×C₃	1	2	yes	—
109	C₂×#347	C₂²×C₃	1	1	yes	characteristic
110	C₄×M₃₂	C₂²×C₃	1	2	yes	—
111	#1778	C₃×C₄	1	1	yes	characteristic
112	#1773	C₃×C₄	1	1	yes	characteristic
113	#1772	C₂²×C₃	1	1	yes	characteristic
114	#1765	C₂²×C₃	1	2	yes	—
115	#1764	C₃×C₄	1	2	yes	—
116	C₄×#104	C₃×C₄	1	2	yes	—
117	C₄×#97	C₂²×C₃	1	1	yes	characteristic
118	#1378	C₂²×C₃	1	4	yes	—
119	#1377	C₂²×C₃	1	2	yes	—
120	C₂×C₃×#41	C₂²×C₄	1	2	yes	—
121	C₃×#135	C₄²	1	4	yes	—
122	C₃×#135	M₁₆	1	4	yes	—
123	C₂×C₃×Q₁₆	M₁₆	1	1	yes	characteristic
124	C₂×C₃×SD₁₆	M₁₆	1	2	yes	—
125	C₂×C₃×D₈	M₁₆	1	1	yes	characteristic
126	C₃×#131	—	2	4	no	—
127	C₃×#131	—	2	4	no	—
128	C₃×#131	—	4	2	no	—
129	C₃×#131	C₂²×C₄	1	8	yes	—
130	C₂×C₃×M₁₆	—	2	2	no	—
131	C₂×C₃×M₁₆	—	2	2	no	—
132	C₂×C₃×M₁₆	C₂²×C₄	1	2	yes	—
133	C₂×C₃×M₁₆	C₂²×C₄	1	2	yes	—
134	C₂²×C₃×C₈	—	2	2	no	—
135	C₂²×C₃×C₈	—	2	2	no	—
136	C₂²×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₃×C₈	C₂⁴	1	1	yes	characteristic
140	C₃×C₄×Q₈	—	2	2	no	—
141	C₃×C₄×D₄	—	2	2	no	—
142	C₃×C₄×D₄	—	4	2	no	—
143	C₃×#117	—	2	2	no	—
144	C₃×#117	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄²	—	2	2	no	—
146	C₂×C₃×C₄²	—	4	1	no	—
147	C₂×C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
150	C₃×M₃₂	—	2	4	no	—
151	C₃×M₃₂	—	2	2	no	—
152	C₃×M₃₂	—	2	2	no	—
153	C₃×M₃₂	—	2	16	no	—
154	C₃×M₃₂	C₂²×C₄	1	8	yes	—
155	C₃×M₃₂	C₂×D₄	1	4	yes	—
156	C₃×M₃₂	#41	1	4	yes	—
157	C₂×C₃×C₁₆	—	2	4	no	—
158	C₂×C₃×C₁₆	—	2	16	no	—
159	C₂×C₃×C₁₆	C₂²×C₄	1	4	yes	—
160	C₂×C₃×C₁₆	C₂²×C₄	1	4	yes	—
161	C₃×#108	—	2	2	no	—
162	C₃×#108	C₄²	1	4	yes	—
163	C₃×#107	—	2	1	no	—
164	C₃×#106	—	2	1	no	—
165	C₃×#104	—	2	4	no	—
166	C₃×#104	C₄²	1	4	yes	—
167	C₃×#104	C₄²	1	4	yes	—
168	C₃×#103	—	2	2	no	—
169	C₃×#102	—	2	2	no	—
170	C₃×#97	—	2	2	no	—
171	C₃×#97	—	2	1	no	—
172	C₃×#97	—	2	1	no	—
173	C₃×#97	—	2	2	no	—
174	C₃×#97	—	2	2	no	—
175	C₃×#97	—	2	2	no	—
176	C₃×#97	—	2	2	no	—
177	C₃×#97	C₂×D₄	1	2	yes	—
178	C₃×#97	#41	1	2	yes	—
179	C₃×C₄×C₈	—	2	2	no	—
180	C₃×C₄×C₈	—	2	2	no	—
181	C₃×C₄×C₈	—	2	2	no	—
182	C₃×C₄×C₈	—	4	1	no	—
183	C₃×C₄×C₈	C₂²×C₄	1	2	yes	—
184	C₃×C₄×C₈	C₂²×C₄	1	2	yes	—
185	C₂×#135	C₂×C₃×C₄	1	1	yes	characteristic
186	C₂×#131	C₂×C₃×C₄	1	2	yes	—
187	C₂×#131	C₂³×C₃	1	2	yes	—
188	C₄×#41	C₂×C₃×C₄	1	2	yes	—
189	#504	—	2	8	no	—
190	#504	C₂×C₃×C₄	1	16	yes	complemented
191	C₂×M₃₂	—	2	8	no	—
192	C₂×M₃₂	C₂³×C₃	1	4	yes	—
193	C₂×M₃₂	C₂³×C₃	1	2	yes	—
194	C₂×M₃₂	C₂³×C₃	1	2	yes	—
195	#444	—	2	4	no	—
196	#443	C₂×C₃×C₄	1	4	yes	—
197	#443	C₂×C₃×C₄	1	4	yes	—
198	#442	—	2	1	no	—
199	#441	—	2	1	no	—
200	#440	—	2	2	no	—
201	C₂×#108	C₂×C₃×C₄	1	1	yes	characteristic
202	C₂×#108	C₂×C₃×C₄	1	1	yes	characteristic
203	#427	C₂×C₃×C₄	1	1	yes	characteristic
204	C₂×#104	C₂×C₃×C₄	1	2	yes	—
205	C₂×#104	C₂×C₃×C₄	1	2	yes	—
206	#416	C₂×C₃×C₄	1	2	yes	—
207	#405	—	2	2	no	—
208	#405	—	2	2	no	—
209	#405	C₂×C₃×C₄	1	2	yes	—
210	#405	C₂³×C₃	1	2	yes	—
211	C₄×M₁₆	—	2	2	no	—
212	C₄×M₁₆	C₂×C₃×C₄	1	2	yes	—
213	C₂×#97	—	2	2	no	—
214	C₂×#97	C₂×C₃×C₄	1	1	yes	characteristic
215	C₂×#97	C₂×C₃×C₄	1	1	yes	characteristic
216	C₂×#97	C₂³×C₃	1	1	yes	characteristic
217	C₂×#97	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₄×C₈	C₂×C₃×C₄	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂³×C₃	1	1	yes	characteristic
220	C₄³	C₂×C₃×C₄	1	1	yes	characteristic
221	#364	C₂×C₃×C₄	1	4	yes	complemented
222	#364	C₂×C₃×C₄	1	4	yes	complemented
223	#350	C₂×C₃×C₄	1	16	yes	complemented
224	#347	—	2	8	no	—
225	#347	—	2	4	no	—
226	#347	—	2	2	no	—
227	#347	—	2	2	no	—
228	#347	—	2	2	no	—
229	#347	C₃×D₄	1	4	yes	—
230	#346	C₂×C₃×C₄	1	4	yes	complemented
231	C₄×C₁₆	C₂×C₃×C₄	1	4	yes	complemented
232	#341	C₂×C₃×C₄	1	2	yes	—
233	#339	C₂×C₃×C₄	1	2	yes	—
234	#339	C₂×C₃×C₄	1	2	yes	—
235	C₃×#41	—	2	2	no	—
236	C₃×#41	—	2	2	no	—
237	C₃×#41	C₂×C₄²	1	4	yes	—
238	C₃×#41	C₂×M₁₆	1	4	yes	—
239	C₂×C₃×Q₈	C₂×M₁₆	1	2	yes	—
240	C₂×C₃×D₄	—	2	2	no	—
241	C₂×C₃×D₄	C₂×M₁₆	1	2	yes	—
242	C₂²×C₃×C₄	—	2	2	no	—
243	C₂²×C₃×C₄	—	2	1	no	—
244	C₂²×C₃×C₄	—	2	1	no	—
245	C₂²×C₃×C₄	—	2	1	no	—
246	C₂²×C₃×C₄	—	4	2	no	—
247	C₂²×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
248	C₃×Q₁₆	#97	1	4	yes	—
249	C₃×SD₁₆	#97	1	8	yes	—
250	C₃×D₈	#97	1	4	yes	—
251	C₃×M₁₆	—	2	2	no	—
252	C₃×M₁₆	—	2	8	no	—
253	C₃×M₁₆	—	2	2	no	—
254	C₃×M₁₆	—	2	2	no	—
255	C₃×M₁₆	—	4	4	no	—
256	C₃×M₁₆	C₂×C₄²	1	4	yes	—
257	C₂×C₃×C₈	—	2	2	no	—
258	C₂×C₃×C₈	—	2	1	no	—
259	C₂×C₃×C₈	—	2	1	no	—
260	C₂×C₃×C₈	—	2	8	no	—
261	C₂×C₃×C₈	—	2	2	no	—
262	C₂×C₃×C₈	—	2	1	no	—
263	C₂×C₃×C₈	—	2	1	no	—
264	C₂×C₃×C₈	—	2	1	no	—
265	C₂×C₃×C₈	—	4	4	no	—
266	C₂×C₃×C₈	C₂×C₄²	1	2	yes	—
267	C₂×C₃×C₈	C₄×D₄	1	2	yes	—
268	C₂×C₃×C₈	C₂×M₁₆	1	1	yes	characteristic
269	C₂×C₃×C₈	C₂×M₁₆	1	1	yes	characteristic
270	C₂×C₃×C₈	C₂×M₁₆	1	2	yes	—
271	C₂×C₃×C₈	C₂³×C₄	1	2	yes	—
272	C₂×C₃×C₈	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₃×C₈	C₂×#41	1	2	yes	—
274	C₂×C₃×C₈	C₂×#41	1	1	yes	characteristic
275	C₃×C₄⋊C₄	—	2	2	no	—
276	C₃×C₄⋊C₄	—	4	2	no	—
277	C₃×C₂²⋊C₄	—	2	2	no	—
278	C₃×C₂²⋊C₄	—	4	2	no	—
279	C₃×C₄²	—	2	1	no	—
280	C₃×C₄²	—	2	1	no	—
281	C₃×C₄²	—	2	2	no	—
282	C₃×C₄²	—	2	1	no	—
283	C₃×C₄²	—	2	1	no	—
284	C₃×C₄²	—	4	2	no	—
285	C₃×C₄²	—	8	2	no	—
286	C₃×C₄²	C₂×C₄²	1	1	yes	characteristic
287	C₃×C₄²	C₂×C₄²	1	1	yes	characteristic
288	C₃×C₄²	C₄×D₄	1	2	yes	—
289	C₃×C₁₆	—	2	8	no	—
290	C₃×C₁₆	—	2	4	no	—
291	C₃×C₁₆	C₄×D₄	1	8	yes	—
292	C₂×#41	C₂²×C₃×C₄	1	2	yes	—
293	#135	C₃×C₄²	1	4	yes	—
294	#135	C₃×M₁₆	1	4	yes	—
295	C₂×Q₁₆	C₃×M₁₆	1	1	yes	characteristic
296	C₂×SD₁₆	C₃×M₁₆	1	2	yes	—
297	C₂×D₈	C₃×M₁₆	1	1	yes	characteristic
298	#131	—	2	4	no	—
299	#131	—	2	4	no	—
300	#131	—	4	2	no	—
301	#131	C₂²×C₃×C₄	1	8	yes	—
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	C₂²×C₃×C₄	1	2	yes	—
305	C₂×M₁₆	C₂²×C₃×C₄	1	2	yes	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
309	C₂²×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
310	C₂²×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
311	C₂²×C₈	C₂⁴×C₃	1	1	yes	characteristic
312	C₄×Q₈	—	2	2	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	4	2	no	—
315	#117	—	2	2	no	—
316	#117	C₂²×C₃×C₄	1	2	yes	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	4	1	no	—
319	C₂×C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
320	C₂×C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
321	C₂×C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
322	M₃₂	—	2	4	no	—
323	M₃₂	—	2	2	no	—
324	M₃₂	—	2	2	no	—
325	M₃₂	—	2	16	no	—
326	M₃₂	C₂²×C₃×C₄	1	8	yes	—
327	M₃₂	C₂×C₃×D₄	1	4	yes	—
328	M₃₂	C₃×#41	1	4	yes	—
329	C₂×C₁₆	—	2	4	no	—
330	C₂×C₁₆	—	2	16	no	—
331	C₂×C₁₆	C₂²×C₃×C₄	1	4	yes	—
332	C₂×C₁₆	C₂²×C₃×C₄	1	4	yes	—
333	#108	—	2	2	no	—
334	#108	C₃×C₄²	1	4	yes	—
335	#107	—	2	1	no	—
336	#106	—	2	1	no	—
337	#104	—	2	4	no	—
338	#104	C₃×C₄²	1	4	yes	—
339	#104	C₃×C₄²	1	4	yes	—
340	#103	—	2	2	no	—
341	#102	—	2	2	no	—
342	#97	—	2	2	no	—
343	#97	—	2	1	no	—
344	#97	—	2	1	no	—
345	#97	—	2	2	no	—
346	#97	—	2	2	no	—
347	#97	—	2	2	no	—
348	#97	—	2	2	no	—
349	#97	C₂×C₃×D₄	1	2	yes	—
350	#97	C₃×#41	1	2	yes	—
351	C₄×C₈	—	2	2	no	—
352	C₄×C₈	—	2	2	no	—
353	C₄×C₈	—	2	2	no	—
354	C₄×C₈	—	4	1	no	—
355	C₄×C₈	C₂²×C₃×C₄	1	2	yes	—
356	C₄×C₈	C₂²×C₃×C₄	1	2	yes	—
357	C₂³×C₃	—	2	2	no	—
358	C₂³×C₃	#568	1	1	yes	characteristic
359	C₃×Q₈	—	2	2	no	—
360	C₃×Q₈	C₂×#97	1	4	yes	—
361	C₃×D₄	—	2	4	no	—
362	C₃×D₄	—	2	4	no	—
363	C₃×D₄	—	2	2	no	—
364	C₃×D₄	C₂×#97	1	4	yes	—
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	4	no	—
368	C₂×C₃×C₄	—	2	4	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	4	2	no	—
372	C₂×C₃×C₄	—	4	2	no	—
373	C₂×C₃×C₄	—	4	1	no	—
374	C₂×C₃×C₄	—	8	1	no	—
375	C₂×C₃×C₄	—	8	1	no	—
376	C₂×C₃×C₄	—	16	2	no	—
377	C₂×C₃×C₄	C₂²×C₄²	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂×C₄×D₄	1	1	yes	characteristic
379	C₂×C₃×C₄	C₄×#41	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂²×M₁₆	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂²×M₁₆	1	1	yes	characteristic
382	C₂×C₃×C₄	#568	1	1	yes	characteristic
383	C₃×C₈	—	2	2	no	—
384	C₃×C₈	—	2	4	no	—
385	C₃×C₈	—	4	2	no	—
386	C₃×C₈	—	4	1	no	—
387	C₃×C₈	C₂×#97	1	2	yes	—
388	C₃×C₈	C₂×#97	1	2	yes	—
389	C₃×C₈	C₂×C₄×D₄	1	2	yes	—
390	C₃×C₈	C₄×#41	1	2	yes	—
391	#41	—	2	2	no	—
392	#41	—	2	2	no	—
393	#41	C₂×C₃×C₄²	1	4	yes	—
394	#41	C₂×C₃×M₁₆	1	4	yes	—
395	C₂×Q₈	C₂×C₃×M₁₆	1	2	yes	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	C₂×C₃×M₁₆	1	2	yes	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
404	Q₁₆	C₃×#97	1	4	yes	—
405	SD₁₆	C₃×#97	1	8	yes	—
406	D₈	C₃×#97	1	4	yes	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	8	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	4	4	no	—
412	M₁₆	C₂×C₃×C₄²	1	4	yes	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	8	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	4	4	no	—
422	C₂×C₈	C₂×C₃×C₄²	1	2	yes	—
423	C₂×C₈	C₃×C₄×D₄	1	2	yes	—
424	C₂×C₈	C₂×C₃×M₁₆	1	1	yes	characteristic
425	C₂×C₈	C₂×C₃×M₁₆	1	1	yes	characteristic
426	C₂×C₈	C₂×C₃×M₁₆	1	2	yes	—
427	C₂×C₈	C₂³×C₃×C₄	1	2	yes	—
428	C₂×C₈	C₂²×C₃×D₄	1	1	yes	characteristic
429	C₂×C₈	C₂×C₃×#41	1	2	yes	—
430	C₂×C₈	C₂×C₃×#41	1	1	yes	characteristic
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	4	2	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	4	2	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	4	2	no	—
441	C₄²	—	8	2	no	—
442	C₄²	C₂×C₃×C₄²	1	1	yes	characteristic
443	C₄²	C₂×C₃×C₄²	1	1	yes	characteristic
444	C₄²	C₃×C₄×D₄	1	2	yes	—
445	C₁₆	—	2	8	no	—
446	C₁₆	—	2	4	no	—
447	C₁₆	C₃×C₄×D₄	1	8	yes	—
448	C₂²×C₃	—	2	4	no	—
449	C₂²×C₃	—	4	1	no	—
450	C₂²×C₃	—	8	2	no	—
451	C₂²×C₃	#2875	1	1	yes	characteristic
452	C₂²×C₃	D₄×M₁₆	1	1	yes	characteristic
453	C₂²×C₃	#2970	1	1	yes	characteristic
454	C₃×C₄	—	2	2	no	—
455	C₃×C₄	—	2	4	no	—
456	C₃×C₄	—	4	1	no	—
457	C₃×C₄	—	4	2	no	—
458	C₃×C₄	—	8	1	no	—
459	C₃×C₄	—	8	2	no	—
460	C₃×C₄	C₄²×D₄	1	1	yes	characteristic
461	C₃×C₄	C₂²×#97	1	1	yes	characteristic
462	C₃×C₄	D₄×M₁₆	1	1	yes	characteristic
463	C₃×C₄	#2970	1	1	yes	characteristic
464	C₂³	—	2	2	no	—
465	C₂³	C₃×#568	1	1	yes	characteristic
466	Q₈	—	2	2	no	—
467	Q₈	C₂×C₃×#97	1	4	yes	—
468	D₄	—	2	4	no	—
469	D₄	—	2	4	no	—
470	D₄	—	2	2	no	—
471	D₄	C₂×C₃×#97	1	4	yes	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	8	1	no	—
482	C₂×C₄	—	8	1	no	—
483	C₂×C₄	—	16	2	no	—
484	C₂×C₄	C₂²×C₃×C₄²	1	1	yes	characteristic
485	C₂×C₄	C₂×C₃×C₄×D₄	1	1	yes	characteristic
486	C₂×C₄	C₃×C₄×#41	1	1	yes	characteristic
487	C₂×C₄	C₂²×C₃×M₁₆	1	1	yes	characteristic
488	C₂×C₄	C₂²×C₃×M₁₆	1	1	yes	characteristic
489	C₂×C₄	C₃×#568	1	1	yes	characteristic
490	C₈	—	2	2	no	—
491	C₈	—	2	4	no	—
492	C₈	—	4	2	no	—
493	C₈	—	4	1	no	—
494	C₈	C₂×C₃×#97	1	2	yes	—
495	C₈	C₂×C₃×#97	1	2	yes	—
496	C₈	C₂×C₃×C₄×D₄	1	2	yes	—
497	C₈	C₃×C₄×#41	1	2	yes	—
498	C₂×C₃	—	2	1	no	—
499	C₂×C₃	—	2	1	no	—
500	C₂×C₃	—	2	1	no	—
501	C₂×C₃	—	4	4	no	—
502	C₂×C₃	D₄×#97	1	1	yes	characteristic
503	C₂²	—	2	4	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	8	2	no	—
506	C₂²	C₃×#2875	1	1	yes	characteristic
507	C₂²	C₃×D₄×M₁₆	1	1	yes	characteristic
508	C₂²	C₃×#2970	1	1	yes	characteristic
509	C₄	—	2	2	no	—
510	C₄	—	2	4	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	8	1	no	—
514	C₄	—	8	2	no	—
515	C₄	C₃×C₄²×D₄	1	1	yes	characteristic
516	C₄	C₂²×C₃×#97	1	1	yes	characteristic
517	C₄	C₃×D₄×M₁₆	1	1	yes	characteristic
518	C₄	C₃×#2970	1	1	yes	characteristic
519	C₃	#493226	1	1	yes	characteristic, direct product factor, Sylow
520	C₂	—	2	1	no	—
521	C₂	—	2	1	no	—
522	C₂	—	2	1	no	—
523	C₂	—	4	4	no	—
524	C₂	C₃×D₄×#97	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₄²×D₄
commutator	C₂×C₄	C₂²×C₃×C₄²
Frattini, cosocle	C₂²×C₈	C₂⁴×C₃
socle	C₂×C₃	D₄×#97
prime radical	C₂×C₃×#135	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×#347 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#33329	C₂	semidirect
4. C₃×#12667	C₂	semidirect
5. C₃×#12659	C₂	semidirect
6. C₃×#12618	C₂	semidirect
7. C₃×#12609	C₂	semidirect
8. C₃×C₄×#347	C₂	semidirect
9. #493226	C₃	direct (N × H)
15. C₃×#2171	C₄	semidirect
16. C₃×#2170	C₄	semidirect
37. #33329	C₂×C₃	semidirect
39. #12667	C₂×C₃	semidirect
40. #12659	C₂×C₃	semidirect
41. #12618	C₂×C₃	semidirect
42. #12609	C₂×C₃	semidirect
43. C₄×#347	C₂×C₃	semidirect
49. C₃×#504	C₂×C₄	semidirect
80. C₃×#364	C₂×C₄	semidirect
81. C₃×#364	C₂×C₄	semidirect
82. C₃×#350	C₂×C₄	semidirect
89. C₃×#346	C₂×C₄	semidirect
90. C₃×C₄×C₁₆	C₂×C₄	semidirect
99. #2171	C₃×C₄	semidirect
100. #2170	C₃×C₄	semidirect
190. #504	C₂×C₃×C₄	semidirect
221. #364	C₂×C₃×C₄	semidirect
222. #364	C₂×C₃×C₄	semidirect
223. #350	C₂×C₃×C₄	semidirect
230. #346	C₂×C₃×C₄	semidirect
231. C₄×C₁₆	C₂×C₃×C₄	semidirect
519. C₃	#493226	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#33443	2
C₃×#33329	2
C₃×#20512	2
C₃×#12667	2
C₃×#12659	2
C₃×#12618	2
C₃×#12609	2
C₃×C₄×#347	2
#493226	3

Subgroups — C3×#493226 #72226273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#493226 #72226273