Subgroups — C₃×#18672 #10637279

Order 768.

906 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#1652	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#1651	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1646	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1645	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#1628	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1627	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#1624	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#1623	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#1554	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
16	#18672	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×Q₈²	C₂²	1	1	yes	characteristic
18	C₃×#556	—	2	1	no	—
19	C₃×#556	—	2	2	no	—
20	C₃×#556	—	2	1	no	—
21	C₃×#556	C₂²	1	1	yes	characteristic
22	C₃×#555	—	2	1	no	—
23	C₃×#555	C₂²	1	1	yes	characteristic
24	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic
25	C₃×#548	—	2	1	no	—
26	C₃×#542	—	2	2	no	—
27	C₃×#542	—	2	1	no	—
28	C₃×#533	—	2	1	no	—
29	C₃×#533	C₂²	1	1	yes	characteristic
30	C₃×#532	C₂²	1	1	yes	characteristic
31	C₃×#529	—	2	1	no	—
32	C₃×#529	C₂²	1	1	yes	characteristic
33	C₃×#519	—	2	1	no	—
34	C₃×C₄×#41	C₂²	1	1	yes	characteristic
35	C₃×#498	C₂²	1	1	yes	characteristic
36	C₃×#495	—	2	1	no	—
37	C₃×#492	C₂²	1	1	yes	characteristic
38	C₃×#488	—	2	1	no	—
39	C₃×#487	C₂²	1	1	yes	characteristic
40	C₃×#486	C₂²	1	1	yes	characteristic
41	C₃×#482	—	2	1	no	—
42	C₃×#475	C₂²	1	1	yes	characteristic
43	C₃×#474	C₂²	1	1	yes	characteristic
44	C₃×#465	—	2	2	no	—
45	C₃×#462	C₂²	1	1	yes	characteristic
46	C₃×#461	C₂²	1	1	yes	characteristic
47	C₃×#460	C₂²	1	1	yes	characteristic
48	C₃×#460	C₂²	1	1	yes	characteristic
49	C₃×#459	C₂²	1	1	yes	characteristic
50	C₃×#459	C₂²	1	1	yes	characteristic
51	C₃×#452	—	2	1	no	—
52	C₃×#449	—	2	1	no	—
53	C₃×#449	—	2	1	no	—
54	C₃×#442	—	2	1	no	—
55	C₃×#440	—	2	1	no	—
56	C₃×C₄×SD₁₆	—	2	2	no	—
57	C₃×#432	C₂²	1	1	yes	characteristic
58	C₃×#431	C₂²	1	1	yes	characteristic
59	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
60	C₃×#333	C₂²	1	1	yes	characteristic
61	C₃×#333	C₂²	1	1	yes	characteristic
62	C₃×#332	C₂²	1	1	yes	characteristic
63	C₃×#332	C₂²	1	1	yes	characteristic
64	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
72	#3518	C₂×C₃	1	1	yes	characteristic, complemented
73	#3212	C₂×C₃	1	1	yes	characteristic, complemented
74	#3167	C₂×C₃	1	1	yes	characteristic, complemented
75	#3115	C₂×C₃	1	1	yes	characteristic, complemented
76	#1652	C₂×C₃	1	1	yes	characteristic, complemented
77	#1651	C₂×C₃	1	1	yes	characteristic, complemented
78	#1646	C₂×C₃	1	1	yes	characteristic, complemented
79	#1645	C₂×C₃	1	1	yes	characteristic, complemented
80	#1628	C₂×C₃	1	1	yes	characteristic, complemented
81	#1627	C₂×C₃	1	1	yes	characteristic, complemented
82	#1624	C₂×C₃	1	1	yes	characteristic, complemented
83	#1623	C₂×C₃	1	1	yes	characteristic, complemented
84	#1554	C₂×C₃	1	1	yes	characteristic, complemented
85	#1494	C₂×C₃	1	1	yes	characteristic, complemented
86	#1476	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×C₃×#41	—	2	1	no	—
88	C₂×C₃×#41	D₄	1	1	yes	characteristic
89	C₂²×C₃×Q₈	—	2	1	no	—
90	C₂×C₃×Q₁₆	—	2	1	no	—
91	C₂×C₃×SD₁₆	—	2	2	no	—
92	C₂×C₃×SD₁₆	—	2	1	no	—
93	C₂×C₃×SD₁₆	—	2	1	no	—
94	C₂×C₃×SD₁₆	—	2	1	no	—
95	C₂×C₃×D₈	—	2	1	no	—
96	C₂×C₃×D₈	—	2	1	no	—
97	C₂²×C₃×C₈	—	2	1	no	—
98	C₃×C₄⋊Q₈	—	2	2	no	—
99	C₃×C₄⋊Q₈	—	2	1	no	—
100	C₃×C₄⋊Q₈	—	2	1	no	—
101	C₃×C₄⋊Q₈	—	2	1	no	—
102	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₃×#127	C₂³	1	1	yes	characteristic
106	C₃×#126	—	2	2	no	—
107	C₃×#126	—	2	2	no	—
108	C₃×#126	—	2	2	no	—
109	C₃×#126	—	2	2	no	—
110	C₃×#126	—	2	1	no	—
111	C₃×#125	—	2	1	no	—
112	C₃×#125	D₄	1	1	yes	characteristic
113	C₃×#124	—	2	2	no	—
114	C₃×#124	—	2	2	no	—
115	C₃×#124	—	2	2	no	—
116	C₃×#124	—	2	2	no	—
117	C₃×#124	—	2	1	no	—
118	C₃×#124	—	2	1	no	—
119	C₃×#124	D₄	1	1	yes	characteristic
120	C₃×#123	—	2	2	no	—
121	C₃×#123	—	2	1	no	—
122	C₃×C₂²⋊Q₈	—	2	2	no	—
123	C₃×C₂²⋊Q₈	—	2	2	no	—
124	C₃×C₂²⋊Q₈	—	2	1	no	—
125	C₃×C₂²⋊Q₈	—	2	1	no	—
126	C₃×C₂²⋊Q₈	—	2	1	no	—
127	C₃×C₂²⋊Q₈	—	2	2	no	—
128	C₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
129	C₃×C₂²⋊Q₈	D₄	1	2	yes	—
130	C₃×#121	—	2	2	no	—
131	C₃×#121	—	2	1	no	—
132	C₃×#121	—	2	1	no	—
133	C₃×#121	—	2	1	no	—
134	C₃×#121	—	2	1	no	—
135	C₃×#121	D₄	1	1	yes	characteristic
136	C₃×C₄×Q₈	—	2	2	no	—
137	C₃×C₄×Q₈	—	2	2	no	—
138	C₃×C₄×Q₈	—	2	2	no	—
139	C₃×C₄×Q₈	—	2	1	no	—
140	C₃×C₄×Q₈	—	2	1	no	—
141	C₃×C₄×Q₈	—	2	1	no	—
142	C₃×C₄×Q₈	—	2	1	no	—
143	C₃×C₄×Q₈	D₄	1	2	yes	—
144	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
145	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
146	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
147	C₃×C₄×D₄	—	2	2	no	—
148	C₃×C₄×D₄	—	2	1	no	—
149	C₃×C₄×D₄	—	2	1	no	—
150	C₃×C₄×D₄	—	2	1	no	—
151	C₃×C₄×D₄	—	2	1	no	—
152	C₃×C₄×D₄	—	2	1	no	—
153	C₃×C₄×D₄	—	2	1	no	—
154	C₃×C₄×D₄	D₄	1	1	yes	characteristic
155	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
156	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
157	C₃×#117	—	2	2	no	—
158	C₃×#117	—	2	2	no	—
159	C₃×#117	—	2	1	no	—
160	C₃×#117	—	2	1	no	—
161	C₃×#117	—	2	1	no	—
162	C₃×#117	—	2	1	no	—
163	C₃×#117	—	2	1	no	—
164	C₃×#117	—	2	1	no	—
165	C₃×#117	D₄	1	1	yes	characteristic
166	C₂×C₃×C₄²	—	2	1	no	—
167	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
168	C₃×#107	—	2	1	no	—
169	C₃×#106	—	2	2	no	—
170	C₃×#106	—	2	1	no	—
171	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
172	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
173	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
174	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₃×#103	—	2	2	no	—
176	C₃×#103	—	2	1	no	—
177	C₃×#103	—	2	1	no	—
178	C₃×#103	—	2	1	no	—
179	C₃×#102	—	2	1	no	—
180	C₃×#102	—	2	2	no	—
181	C₃×#102	—	2	1	no	—
182	C₃×#102	—	2	1	no	—
183	C₃×#102	—	2	1	no	—
184	C₃×#102	—	2	1	no	—
185	C₃×C₂²⋊C₈	—	2	1	no	—
186	C₃×C₂²⋊C₈	—	2	1	no	—
187	C₃×#97	—	2	1	no	—
188	C₃×C₄×C₈	—	2	1	no	—
189	C₃×C₄×C₈	—	2	1	no	—
190	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
191	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
192	Q₈²	C₂²×C₃	1	1	yes	characteristic
193	#556	—	2	1	no	—
194	#556	—	2	2	no	—
195	#556	—	2	1	no	—
196	#556	C₂²×C₃	1	1	yes	characteristic
197	#555	—	2	1	no	—
198	#555	C₂²×C₃	1	1	yes	characteristic
199	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic
200	#548	—	2	1	no	—
201	#542	—	2	2	no	—
202	#542	—	2	1	no	—
203	#533	—	2	1	no	—
204	#533	C₂²×C₃	1	1	yes	characteristic
205	#532	C₂²×C₃	1	1	yes	characteristic
206	#529	—	2	1	no	—
207	#529	C₂²×C₃	1	1	yes	characteristic
208	#519	—	2	1	no	—
209	C₄×#41	C₂²×C₃	1	1	yes	characteristic
210	#498	C₂²×C₃	1	1	yes	characteristic
211	#495	—	2	1	no	—
212	#492	C₂²×C₃	1	1	yes	characteristic
213	#488	—	2	1	no	—
214	#487	C₂²×C₃	1	1	yes	characteristic
215	#486	C₂²×C₃	1	1	yes	characteristic
216	#482	—	2	1	no	—
217	#475	C₂²×C₃	1	1	yes	characteristic
218	#474	C₂²×C₃	1	1	yes	characteristic
219	#465	—	2	2	no	—
220	#462	C₂²×C₃	1	1	yes	characteristic
221	#461	C₂²×C₃	1	1	yes	characteristic
222	#460	C₂²×C₃	1	1	yes	characteristic
223	#460	C₂²×C₃	1	1	yes	characteristic
224	#459	C₂²×C₃	1	1	yes	characteristic
225	#459	C₂²×C₃	1	1	yes	characteristic
226	#452	—	2	1	no	—
227	#449	—	2	1	no	—
228	#449	—	2	1	no	—
229	#442	—	2	1	no	—
230	#440	—	2	1	no	—
231	C₄×SD₁₆	—	2	2	no	—
232	#432	C₂²×C₃	1	1	yes	characteristic
233	#431	C₂²×C₃	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
235	#333	C₂²×C₃	1	1	yes	characteristic
236	#333	C₂²×C₃	1	1	yes	characteristic
237	#332	C₂²×C₃	1	1	yes	characteristic
238	#332	C₂²×C₃	1	1	yes	characteristic
239	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
240	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
241	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
242	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
243	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
244	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
245	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
246	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
247	C₃×#41	—	2	2	no	—
248	C₃×#41	—	4	1	no	—
249	C₃×#41	—	8	1	no	—
250	C₃×#41	—	8	1	no	—
251	C₂×C₃×Q₈	—	2	2	no	—
252	C₂×C₃×Q₈	—	2	2	no	—
253	C₂×C₃×Q₈	—	2	1	no	—
254	C₂×C₃×Q₈	—	2	1	no	—
255	C₂×C₃×Q₈	—	4	2	no	—
256	C₂×C₃×Q₈	—	4	2	no	—
257	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
258	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
259	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
260	C₂×C₃×D₄	—	2	1	no	—
261	C₂×C₃×D₄	—	2	2	no	—
262	C₂×C₃×D₄	—	2	1	no	—
263	C₂×C₃×D₄	—	2	1	no	—
264	C₂×C₃×D₄	—	2	1	no	—
265	C₂×C₃×D₄	—	2	1	no	—
266	C₂×C₃×D₄	—	4	1	no	—
267	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
268	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₃×C₄	—	2	2	no	—
270	C₂²×C₃×C₄	—	2	1	no	—
271	C₂²×C₃×C₄	—	2	1	no	—
272	C₂²×C₃×C₄	—	2	1	no	—
273	C₂²×C₃×C₄	—	2	1	no	—
274	C₂²×C₃×C₄	—	4	1	no	—
275	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
278	C₃×Q₁₆	—	8	1	no	—
279	C₃×SD₁₆	—	4	4	no	—
280	C₃×SD₁₆	—	4	2	no	—
281	C₃×SD₁₆	—	8	1	no	—
282	C₃×SD₁₆	—	8	1	no	—
283	C₃×D₈	—	4	2	no	—
284	C₃×D₈	—	8	1	no	—
285	C₂×C₃×C₈	—	2	1	no	—
286	C₂×C₃×C₈	—	2	1	no	—
287	C₂×C₃×C₈	—	2	1	no	—
288	C₂×C₃×C₈	—	2	1	no	—
289	C₂×C₃×C₈	—	2	1	no	—
290	C₂×C₃×C₈	—	2	1	no	—
291	C₂×C₃×C₈	—	4	2	no	—
292	C₃×C₄⋊C₄	—	2	2	no	—
293	C₃×C₄⋊C₄	—	2	2	no	—
294	C₃×C₄⋊C₄	—	2	2	no	—
295	C₃×C₄⋊C₄	—	2	2	no	—
296	C₃×C₄⋊C₄	—	2	1	no	—
297	C₃×C₄⋊C₄	—	2	1	no	—
298	C₃×C₄⋊C₄	—	2	2	no	—
299	C₃×C₄⋊C₄	—	2	1	no	—
300	C₃×C₄⋊C₄	—	2	1	no	—
301	C₃×C₄⋊C₄	—	2	2	no	—
302	C₃×C₄⋊C₄	—	2	1	no	—
303	C₃×C₄⋊C₄	—	2	1	no	—
304	C₃×C₄⋊C₄	—	2	1	no	—
305	C₃×C₄⋊C₄	—	2	1	no	—
306	C₃×C₄⋊C₄	—	2	1	no	—
307	C₃×C₄⋊C₄	—	2	1	no	—
308	C₃×C₄⋊C₄	—	2	1	no	—
309	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
310	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
311	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
312	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
313	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
314	C₃×C₂²⋊C₄	—	2	2	no	—
315	C₃×C₂²⋊C₄	—	2	2	no	—
316	C₃×C₂²⋊C₄	—	2	2	no	—
317	C₃×C₂²⋊C₄	—	2	2	no	—
318	C₃×C₂²⋊C₄	—	2	2	no	—
319	C₃×C₂²⋊C₄	—	2	2	no	—
320	C₃×C₂²⋊C₄	—	2	1	no	—
321	C₃×C₂²⋊C₄	—	2	1	no	—
322	C₃×C₂²⋊C₄	—	2	1	no	—
323	C₃×C₂²⋊C₄	—	2	1	no	—
324	C₃×C₂²⋊C₄	—	2	1	no	—
325	C₃×C₂²⋊C₄	—	2	1	no	—
326	C₃×C₂²⋊C₄	—	2	1	no	—
327	C₃×C₂²⋊C₄	—	2	1	no	—
328	C₃×C₂²⋊C₄	—	4	1	no	—
329	C₃×C₂²⋊C₄	—	4	1	no	—
330	C₃×C₄²	—	2	2	no	—
331	C₃×C₄²	—	2	2	no	—
332	C₃×C₄²	—	2	2	no	—
333	C₃×C₄²	—	2	1	no	—
334	C₃×C₄²	—	2	1	no	—
335	C₃×C₄²	—	2	2	no	—
336	C₃×C₄²	—	2	1	no	—
337	C₃×C₄²	—	2	1	no	—
338	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
339	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
340	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
341	C₃×C₄²	C₂⁴	1	1	yes	characteristic
342	C₂×#41	—	2	1	no	—
343	C₂×#41	C₃×D₄	1	1	yes	characteristic
344	C₂²×Q₈	—	2	1	no	—
345	C₂×Q₁₆	—	2	1	no	—
346	C₂×SD₁₆	—	2	2	no	—
347	C₂×SD₁₆	—	2	1	no	—
348	C₂×SD₁₆	—	2	1	no	—
349	C₂×SD₁₆	—	2	1	no	—
350	C₂×D₈	—	2	1	no	—
351	C₂×D₈	—	2	1	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₄⋊Q₈	—	2	2	no	—
354	C₄⋊Q₈	—	2	1	no	—
355	C₄⋊Q₈	—	2	1	no	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
358	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
360	#127	C₂³×C₃	1	1	yes	characteristic
361	#126	—	2	2	no	—
362	#126	—	2	2	no	—
363	#126	—	2	2	no	—
364	#126	—	2	2	no	—
365	#126	—	2	1	no	—
366	#125	—	2	1	no	—
367	#125	C₃×D₄	1	1	yes	characteristic
368	#124	—	2	2	no	—
369	#124	—	2	2	no	—
370	#124	—	2	2	no	—
371	#124	—	2	2	no	—
372	#124	—	2	1	no	—
373	#124	—	2	1	no	—
374	#124	C₃×D₄	1	1	yes	characteristic
375	#123	—	2	2	no	—
376	#123	—	2	1	no	—
377	C₂²⋊Q₈	—	2	2	no	—
378	C₂²⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	C₃×D₄	1	1	yes	characteristic
384	C₂²⋊Q₈	C₃×D₄	1	2	yes	—
385	#121	—	2	2	no	—
386	#121	—	2	1	no	—
387	#121	—	2	1	no	—
388	#121	—	2	1	no	—
389	#121	—	2	1	no	—
390	#121	C₃×D₄	1	1	yes	characteristic
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	—	2	1	no	—
396	C₄×Q₈	—	2	1	no	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
399	C₄×Q₈	C₃×D₄	1	2	yes	—
400	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
401	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	C₃×D₄	1	1	yes	characteristic
410	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
411	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
412	#117	—	2	2	no	—
413	#117	—	2	2	no	—
414	#117	—	2	1	no	—
415	#117	—	2	1	no	—
416	#117	—	2	1	no	—
417	#117	—	2	1	no	—
418	#117	—	2	1	no	—
419	#117	—	2	1	no	—
420	#117	C₃×D₄	1	1	yes	characteristic
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
423	#107	—	2	1	no	—
424	#106	—	2	2	no	—
425	#106	—	2	1	no	—
426	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
427	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
428	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
429	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
430	#103	—	2	2	no	—
431	#103	—	2	1	no	—
432	#103	—	2	1	no	—
433	#103	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	2	no	—
436	#102	—	2	1	no	—
437	#102	—	2	1	no	—
438	#102	—	2	1	no	—
439	#102	—	2	1	no	—
440	C₂²⋊C₈	—	2	1	no	—
441	C₂²⋊C₈	—	2	1	no	—
442	#97	—	2	1	no	—
443	C₄×C₈	—	2	1	no	—
444	C₄×C₈	—	2	1	no	—
445	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
446	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
447	C₂³×C₃	—	2	1	no	—
448	C₂³×C₃	—	2	1	no	—
449	C₂³×C₃	—	4	1	no	—
450	C₂³×C₃	#120	1	1	yes	characteristic
451	C₃×Q₈	—	2	1	no	—
452	C₃×Q₈	—	2	1	no	—
453	C₃×Q₈	—	2	1	no	—
454	C₃×Q₈	—	4	2	no	—
455	C₃×Q₈	—	4	4	no	—
456	C₃×Q₈	—	4	1	no	—
457	C₃×Q₈	—	4	1	no	—
458	C₃×Q₈	—	4	1	no	—
459	C₃×Q₈	—	4	1	no	—
460	C₃×Q₈	—	8	2	no	—
461	C₃×Q₈	#135	1	2	yes	—
462	C₃×D₄	—	2	1	no	—
463	C₃×D₄	—	2	1	no	—
464	C₃×D₄	—	2	1	no	—
465	C₃×D₄	—	2	1	no	—
466	C₃×D₄	—	4	2	no	—
467	C₃×D₄	—	4	2	no	—
468	C₃×D₄	—	4	1	no	—
469	C₃×D₄	—	4	1	no	—
470	C₃×D₄	—	4	1	no	—
471	C₃×D₄	—	4	1	no	—
472	C₃×D₄	—	8	1	no	—
473	C₃×D₄	—	8	2	no	—
474	C₃×D₄	—	8	2	no	—
475	C₂×C₃×C₄	—	2	1	no	—
476	C₂×C₃×C₄	—	2	1	no	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	2	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	2	2	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	4	1	no	—
488	C₂×C₃×C₄	—	4	2	no	—
489	C₂×C₃×C₄	—	4	4	no	—
490	C₂×C₃×C₄	—	4	1	no	—
491	C₂×C₃×C₄	—	4	1	no	—
492	C₂×C₃×C₄	—	4	1	no	—
493	C₂×C₃×C₄	—	4	1	no	—
494	C₂×C₃×C₄	—	4	1	no	—
495	C₂×C₃×C₄	—	8	1	no	—
496	C₂×C₃×C₄	—	8	2	no	—
497	C₂×C₃×C₄	#120	1	1	yes	characteristic
498	C₂×C₃×C₄	#120	1	1	yes	characteristic
499	C₂×C₃×C₄	#120	1	1	yes	characteristic
500	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
503	C₃×C₈	—	2	2	no	—
504	C₃×C₈	—	4	1	no	—
505	C₃×C₈	—	4	1	no	—
506	C₃×C₈	—	4	1	no	—
507	C₃×C₈	—	4	1	no	—
508	C₃×C₈	—	4	1	no	—
509	#41	—	2	2	no	—
510	#41	—	4	1	no	—
511	#41	—	8	1	no	—
512	#41	—	8	1	no	—
513	C₂×Q₈	—	2	2	no	—
514	C₂×Q₈	—	2	2	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	4	2	no	—
518	C₂×Q₈	—	4	2	no	—
519	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
520	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
521	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	4	1	no	—
529	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
530	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	4	1	no	—
537	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
538	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
539	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
540	Q₁₆	—	8	1	no	—
541	SD₁₆	—	4	4	no	—
542	SD₁₆	—	4	2	no	—
543	SD₁₆	—	8	1	no	—
544	SD₁₆	—	8	1	no	—
545	D₈	—	4	2	no	—
546	D₈	—	8	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	4	2	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
572	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
573	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
574	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
575	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	2	1	no	—
583	C₂²⋊C₄	—	2	1	no	—
584	C₂²⋊C₄	—	2	1	no	—
585	C₂²⋊C₄	—	2	1	no	—
586	C₂²⋊C₄	—	2	1	no	—
587	C₂²⋊C₄	—	2	1	no	—
588	C₂²⋊C₄	—	2	1	no	—
589	C₂²⋊C₄	—	2	1	no	—
590	C₂²⋊C₄	—	4	1	no	—
591	C₂²⋊C₄	—	4	1	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	2	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	2	1	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	2	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	2	1	no	—
600	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
601	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
602	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
603	C₄²	C₂⁴×C₃	1	1	yes	characteristic
604	C₂²×C₃	—	2	1	no	—
605	C₂²×C₃	—	2	1	no	—
606	C₂²×C₃	—	2	1	no	—
607	C₂²×C₃	—	4	1	no	—
608	C₂²×C₃	—	4	1	no	—
609	C₂²×C₃	—	4	1	no	—
610	C₂²×C₃	—	4	1	no	—
611	C₂²×C₃	—	4	1	no	—
612	C₂²×C₃	—	4	1	no	—
613	C₂²×C₃	—	8	1	no	—
614	C₂²×C₃	—	8	1	no	—
615	C₂²×C₃	—	8	1	no	—
616	C₂²×C₃	C₂×#120	1	1	yes	characteristic
617	C₃×C₄	—	2	1	no	—
618	C₃×C₄	—	2	2	no	—
619	C₃×C₄	—	2	1	no	—
620	C₃×C₄	—	2	1	no	—
621	C₃×C₄	—	2	1	no	—
622	C₃×C₄	—	4	2	no	—
623	C₃×C₄	—	4	1	no	—
624	C₃×C₄	—	4	1	no	—
625	C₃×C₄	—	4	1	no	—
626	C₃×C₄	—	4	1	no	—
627	C₃×C₄	—	4	2	no	—
628	C₃×C₄	—	4	1	no	—
629	C₃×C₄	—	8	1	no	—
630	C₃×C₄	C₂×#135	1	1	yes	characteristic
631	C₃×C₄	#575	1	1	yes	characteristic
632	C₃×C₄	#577	1	1	yes	characteristic
633	C₃×C₄	#577	1	1	yes	characteristic
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	C₃×#120	1	1	yes	characteristic
638	Q₈	—	2	1	no	—
639	Q₈	—	2	1	no	—
640	Q₈	—	2	1	no	—
641	Q₈	—	4	2	no	—
642	Q₈	—	4	4	no	—
643	Q₈	—	4	1	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	4	1	no	—
646	Q₈	—	4	1	no	—
647	Q₈	—	8	2	no	—
648	Q₈	C₃×#135	1	2	yes	—
649	D₄	—	2	1	no	—
650	D₄	—	2	1	no	—
651	D₄	—	2	1	no	—
652	D₄	—	2	1	no	—
653	D₄	—	4	2	no	—
654	D₄	—	4	2	no	—
655	D₄	—	4	1	no	—
656	D₄	—	4	1	no	—
657	D₄	—	4	1	no	—
658	D₄	—	4	1	no	—
659	D₄	—	8	1	no	—
660	D₄	—	8	2	no	—
661	D₄	—	8	2	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	2	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	8	1	no	—
683	C₂×C₄	—	8	2	no	—
684	C₂×C₄	C₃×#120	1	1	yes	characteristic
685	C₂×C₄	C₃×#120	1	1	yes	characteristic
686	C₂×C₄	C₃×#120	1	1	yes	characteristic
687	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
688	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
689	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
690	C₈	—	2	2	no	—
691	C₈	—	4	1	no	—
692	C₈	—	4	1	no	—
693	C₈	—	4	1	no	—
694	C₈	—	4	1	no	—
695	C₈	—	4	1	no	—
696	C₂×C₃	—	4	1	no	—
697	C₂×C₃	—	8	1	no	—
698	C₂×C₃	—	8	1	no	—
699	C₂×C₃	—	16	1	no	—
700	C₂×C₃	#3002	1	1	yes	characteristic
701	C₂×C₃	#3010	1	1	yes	characteristic
702	C₂×C₃	#3018	1	1	yes	characteristic
703	C₂²	—	2	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	8	1	no	—
713	C₂²	—	8	1	no	—
714	C₂²	—	8	1	no	—
715	C₂²	C₂×C₃×#120	1	1	yes	characteristic
716	C₄	—	2	1	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	1	no	—
728	C₄	—	8	1	no	—
729	C₄	C₂×C₃×#135	1	1	yes	characteristic
730	C₄	C₃×#575	1	1	yes	characteristic
731	C₄	C₃×#577	1	1	yes	characteristic
732	C₄	C₃×#577	1	1	yes	characteristic
733	C₃	#18672	1	1	yes	characteristic, direct product factor, Sylow
734	C₂	—	4	1	no	—
735	C₂	—	8	1	no	—
736	C₂	—	8	1	no	—
737	C₂	—	16	1	no	—
738	C₂	C₃×#3002	1	1	yes	characteristic
739	C₂	C₃×#3010	1	1	yes	characteristic
740	C₂	C₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3518	C₂	semidirect
2. C₃×#3212	C₂	semidirect
3. C₃×#3167	C₂	semidirect
4. C₃×#3115	C₂	semidirect
5. C₃×#1652	C₂	semidirect
6. C₃×#1651	C₂	semidirect
7. C₃×#1646	C₂	semidirect
8. C₃×#1645	C₂	semidirect
9. C₃×#1628	C₂	semidirect
10. C₃×#1627	C₂	semidirect
11. C₃×#1624	C₂	semidirect
12. C₃×#1623	C₂	semidirect
13. C₃×#1554	C₂	semidirect
14. C₃×#1494	C₂	semidirect
15. C₃×#1476	C₂	semidirect
16. #18672	C₃	direct (N × H)
72. #3518	C₂×C₃	semidirect
73. #3212	C₂×C₃	semidirect
74. #3167	C₂×C₃	semidirect
75. #3115	C₂×C₃	semidirect
76. #1652	C₂×C₃	semidirect
77. #1651	C₂×C₃	semidirect
78. #1646	C₂×C₃	semidirect
79. #1645	C₂×C₃	semidirect
80. #1628	C₂×C₃	semidirect
81. #1627	C₂×C₃	semidirect
82. #1624	C₂×C₃	semidirect
83. #1623	C₂×C₃	semidirect
84. #1554	C₂×C₃	semidirect
85. #1494	C₂×C₃	semidirect
86. #1476	C₂×C₃	semidirect
733. C₃	#18672	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×#3518	2
C₃×#3212	2
C₃×#3167	2
C₃×#3115	2
C₃×#1652	2
C₃×#1651	2
C₃×#1646	2
C₃×#1645	2
C₃×#1628	2
C₃×#1627	2
C₃×#1624	2
C₃×#1623	2
C₃×#1554	2
C₃×#1494	2
C₃×#1476	2
#18672	3

Subgroups — C3×#18672 #10637279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#18672 #10637279