Subgroups — C₃×#18765 #10637372

Order 768.

902 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3482	C₂	1	1	yes	maximal, characteristic
2	C₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#3076	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×#1648	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1647	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#1638	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1637	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#1636	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#1635	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#1552	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#1488	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#1477	C₂	1	1	yes	maximal, characteristic, complemented
16	#18765	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×#557	C₂²	1	1	yes	characteristic
18	C₃×#556	—	2	1	no	—
19	C₃×#556	C₂²	1	1	yes	characteristic
20	C₃×#552	—	2	2	no	—
21	C₃×#552	—	2	1	no	—
22	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic
23	C₃×#548	—	2	1	no	—
24	C₃×#547	—	2	1	no	—
25	C₃×#547	C₂²	1	1	yes	characteristic
26	C₃×#533	—	2	1	no	—
27	C₃×#533	C₂²	1	1	yes	characteristic
28	C₃×#533	C₂²	1	1	yes	characteristic
29	C₃×#529	—	2	1	no	—
30	C₃×#529	—	2	2	no	—
31	C₃×C₄×#41	—	2	1	no	—
32	C₃×C₄×#41	C₂²	1	1	yes	characteristic
33	C₃×C₄×#41	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×Q₈	—	2	1	no	—
35	C₃×#500	C₂²	1	1	yes	characteristic
36	C₃×#498	C₂²	1	1	yes	characteristic
37	C₃×#487	C₂²	1	1	yes	characteristic
38	C₃×#487	C₂²	1	1	yes	characteristic
39	C₃×#485	—	2	2	no	—
40	C₃×#485	—	2	1	no	—
41	C₃×#479	—	2	2	no	—
42	C₃×#479	—	2	1	no	—
43	C₃×#478	—	2	1	no	—
44	C₃×#477	C₂²	1	1	yes	characteristic
45	C₃×#477	C₂²	1	1	yes	characteristic
46	C₃×#476	C₂²	1	1	yes	characteristic
47	C₃×#476	C₂²	1	1	yes	characteristic
48	C₃×#475	C₂²	1	1	yes	characteristic
49	C₃×#474	C₂²	1	1	yes	characteristic
50	C₃×#462	C₂²	1	1	yes	characteristic
51	C₃×#461	C₂²	1	1	yes	characteristic
52	C₃×#452	—	2	1	no	—
53	C₃×#441	—	2	1	no	—
54	C₃×#440	—	2	1	no	—
55	C₃×#432	C₂²	1	1	yes	characteristic
56	C₃×#431	C₂²	1	1	yes	characteristic
57	C₃×#427	—	2	1	no	—
58	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
59	C₃×#416	—	2	1	no	—
60	C₃×#332	C₂²	1	1	yes	characteristic
61	C₃×#332	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	#3482	C₂×C₃	1	1	yes	characteristic
73	#3231	C₂×C₃	1	1	yes	characteristic, complemented
74	#3116	C₂×C₃	1	1	yes	characteristic, complemented
75	#3076	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	#1648	C₂×C₃	1	1	yes	characteristic, complemented
79	#1647	C₂×C₃	1	1	yes	characteristic, complemented
80	#1638	C₂×C₃	1	1	yes	characteristic, complemented
81	#1637	C₂×C₃	1	1	yes	characteristic, complemented
82	#1636	C₂×C₃	1	1	yes	characteristic, complemented
83	#1635	C₂×C₃	1	1	yes	characteristic, complemented
84	#1552	C₂×C₃	1	1	yes	characteristic, complemented
85	#1488	C₂×C₃	1	1	yes	characteristic, complemented
86	#1477	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×C₃×#41	—	2	1	no	—
88	C₂×C₃×#41	D₄	1	1	yes	characteristic
89	C₂×C₃×#41	D₄	1	1	yes	characteristic
90	C₂²×C₃×Q₈	—	2	1	no	—
91	C₂×C₃×Q₁₆	—	2	1	no	—
92	C₂×C₃×SD₁₆	—	2	1	no	—
93	C₂²×C₃×C₈	—	2	1	no	—
94	C₃×C₄⋊Q₈	—	2	1	no	—
95	C₃×C₄⋊Q₈	—	2	1	no	—
96	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
97	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
98	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₃×#126	—	2	2	no	—
101	C₃×#126	—	2	2	no	—
102	C₃×#126	—	2	2	no	—
103	C₃×#125	—	2	2	no	—
104	C₃×#125	—	2	2	no	—
105	C₃×#125	—	2	1	no	—
106	C₃×#125	—	2	1	no	—
107	C₃×#125	D₄	1	2	yes	—
108	C₃×#124	—	2	2	no	—
109	C₃×#124	—	2	1	no	—
110	C₃×#123	—	2	2	no	—
111	C₃×#123	—	2	2	no	—
112	C₃×#123	—	2	2	no	—
113	C₃×C₂²⋊Q₈	—	2	2	no	—
114	C₃×C₂²⋊Q₈	—	2	1	no	—
115	C₃×C₂²⋊Q₈	—	2	1	no	—
116	C₃×C₂²⋊Q₈	—	2	1	no	—
117	C₃×C₂²⋊Q₈	—	2	1	no	—
118	C₃×C₂²⋊Q₈	—	2	2	no	—
119	C₃×C₂²⋊Q₈	—	2	1	no	—
120	C₃×C₂²⋊Q₈	—	2	1	no	—
121	C₃×C₂²⋊Q₈	—	2	1	no	—
122	C₃×#121	—	2	2	no	—
123	C₃×#121	—	2	1	no	—
124	C₃×C₄×Q₈	—	2	2	no	—
125	C₃×C₄×Q₈	—	2	2	no	—
126	C₃×C₄×Q₈	—	2	1	no	—
127	C₃×C₄×Q₈	—	2	1	no	—
128	C₃×C₄×Q₈	—	2	1	no	—
129	C₃×C₄×Q₈	—	2	1	no	—
130	C₃×C₄×Q₈	—	2	1	no	—
131	C₃×C₄×Q₈	—	2	1	no	—
132	C₃×C₄×Q₈	—	2	1	no	—
133	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
134	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
135	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
136	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
137	C₃×C₄×D₄	—	2	2	no	—
138	C₃×C₄×D₄	—	2	2	no	—
139	C₃×C₄×D₄	—	2	1	no	—
140	C₃×C₄×D₄	—	2	1	no	—
141	C₃×C₄×D₄	—	2	1	no	—
142	C₃×C₄×D₄	—	2	1	no	—
143	C₃×C₄×D₄	—	2	1	no	—
144	C₃×C₄×D₄	D₄	1	1	yes	characteristic
145	C₃×C₄×D₄	D₄	1	1	yes	characteristic
146	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
147	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
148	C₃×#117	—	2	2	no	—
149	C₃×#117	—	2	2	no	—
150	C₃×#117	—	2	1	no	—
151	C₃×#117	—	2	1	no	—
152	C₃×#117	—	2	1	no	—
153	C₃×#117	—	2	1	no	—
154	C₃×#117	D₄	1	1	yes	characteristic
155	C₃×#117	D₄	1	1	yes	characteristic
156	C₃×#117	D₄	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	—	2	2	no	—
158	C₂×C₃×C₄⋊C₄	—	2	1	no	—
159	C₂×C₃×C₄²	—	2	2	no	—
160	C₂×C₃×C₄²	—	2	1	no	—
161	C₂×C₃×C₄²	—	2	1	no	—
162	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
163	C₃×#107	—	2	1	no	—
164	C₃×#107	—	2	1	no	—
165	C₃×#107	—	2	1	no	—
166	C₃×#107	—	2	2	no	—
167	C₃×#106	—	2	1	no	—
168	C₃×#106	—	2	1	no	—
169	C₃×#106	—	2	1	no	—
170	C₃×#106	—	2	2	no	—
171	C₃×C₄⋊C₈	—	2	1	no	—
172	C₃×C₄⋊C₈	—	2	1	no	—
173	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
174	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
177	C₃×#103	—	2	1	no	—
178	C₃×#103	—	2	1	no	—
179	C₃×#103	—	2	1	no	—
180	C₃×#103	—	2	1	no	—
181	C₃×#103	—	2	1	no	—
182	C₃×#103	—	2	2	no	—
183	C₃×#103	—	2	2	no	—
184	C₃×#102	—	2	1	no	—
185	C₃×#102	—	2	1	no	—
186	C₃×#102	—	2	1	no	—
187	C₃×C₂²⋊C₈	—	2	1	no	—
188	C₃×C₂²⋊C₈	—	2	1	no	—
189	C₃×#97	—	2	1	no	—
190	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
191	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
192	#557	C₂²×C₃	1	1	yes	characteristic
193	#556	—	2	1	no	—
194	#556	C₂²×C₃	1	1	yes	characteristic
195	#552	—	2	2	no	—
196	#552	—	2	1	no	—
197	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic
198	#548	—	2	1	no	—
199	#547	—	2	1	no	—
200	#547	C₂²×C₃	1	1	yes	characteristic
201	#533	—	2	1	no	—
202	#533	C₂²×C₃	1	1	yes	characteristic
203	#533	C₂²×C₃	1	1	yes	characteristic
204	#529	—	2	1	no	—
205	#529	—	2	2	no	—
206	C₄×#41	—	2	1	no	—
207	C₄×#41	C₂²×C₃	1	1	yes	characteristic
208	C₄×#41	C₂²×C₃	1	1	yes	characteristic
209	C₂×C₄×Q₈	—	2	1	no	—
210	#500	C₂²×C₃	1	1	yes	characteristic
211	#498	C₂²×C₃	1	1	yes	characteristic
212	#487	C₂²×C₃	1	1	yes	characteristic
213	#487	C₂²×C₃	1	1	yes	characteristic
214	#485	—	2	1	no	—
215	#485	—	2	2	no	—
216	#479	—	2	2	no	—
217	#479	—	2	1	no	—
218	#478	—	2	1	no	—
219	#477	C₂²×C₃	1	1	yes	characteristic
220	#477	C₂²×C₃	1	1	yes	characteristic
221	#476	C₂²×C₃	1	1	yes	characteristic
222	#476	C₂²×C₃	1	1	yes	characteristic
223	#475	C₂²×C₃	1	1	yes	characteristic
224	#474	C₂²×C₃	1	1	yes	characteristic
225	#462	C₂²×C₃	1	1	yes	characteristic
226	#461	C₂²×C₃	1	1	yes	characteristic
227	#452	—	2	1	no	—
228	#441	—	2	1	no	—
229	#440	—	2	1	no	—
230	#432	C₂²×C₃	1	1	yes	characteristic
231	#431	C₂²×C₃	1	1	yes	characteristic
232	#427	—	2	1	no	—
233	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
234	#416	—	2	1	no	—
235	#332	C₂²×C₃	1	1	yes	characteristic
236	#332	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	—	2	2	no	—
249	C₃×#41	—	4	1	no	—
250	C₃×#41	—	4	1	no	—
251	C₃×#41	—	4	2	no	—
252	C₃×#41	—	4	2	no	—
253	C₂×C₃×Q₈	—	2	2	no	—
254	C₂×C₃×Q₈	—	2	1	no	—
255	C₂×C₃×Q₈	—	2	1	no	—
256	C₂×C₃×Q₈	—	2	1	no	—
257	C₂×C₃×Q₈	—	2	1	no	—
258	C₂×C₃×Q₈	—	4	2	no	—
259	C₂×C₃×Q₈	—	4	2	no	—
260	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
261	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
262	C₂×C₃×D₄	—	2	2	no	—
263	C₂×C₃×D₄	—	2	1	no	—
264	C₂×C₃×D₄	—	2	1	no	—
265	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
266	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₃×C₄	—	2	2	no	—
268	C₂²×C₃×C₄	—	2	2	no	—
269	C₂²×C₃×C₄	—	2	1	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	—	2	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	—	4	2	no	—
279	C₃×SD₁₆	—	4	2	no	—
280	C₂×C₃×C₈	—	2	1	no	—
281	C₂×C₃×C₈	—	2	1	no	—
282	C₂×C₃×C₈	—	2	1	no	—
283	C₂×C₃×C₈	—	2	1	no	—
284	C₂×C₃×C₈	—	2	1	no	—
285	C₂×C₃×C₈	—	2	1	no	—
286	C₂×C₃×C₈	—	4	2	no	—
287	C₃×C₄⋊C₄	—	2	2	no	—
288	C₃×C₄⋊C₄	—	2	2	no	—
289	C₃×C₄⋊C₄	—	2	2	no	—
290	C₃×C₄⋊C₄	—	2	2	no	—
291	C₃×C₄⋊C₄	—	2	2	no	—
292	C₃×C₄⋊C₄	—	2	2	no	—
293	C₃×C₄⋊C₄	—	2	1	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	1	no	—
299	C₃×C₄⋊C₄	—	2	1	no	—
300	C₃×C₄⋊C₄	—	2	1	no	—
301	C₃×C₄⋊C₄	—	2	1	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	—	4	1	no	—
306	C₃×C₄⋊C₄	—	4	1	no	—
307	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
308	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
309	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
310	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
311	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
312	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
313	C₃×C₂²⋊C₄	—	2	2	no	—
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	1	no	—
318	C₃×C₂²⋊C₄	—	2	1	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	—	4	1	no	—
325	C₃×C₄²	—	2	2	no	—
326	C₃×C₄²	—	2	2	no	—
327	C₃×C₄²	—	2	1	no	—
328	C₃×C₄²	—	2	1	no	—
329	C₃×C₄²	—	2	1	no	—
330	C₃×C₄²	—	2	2	no	—
331	C₃×C₄²	—	2	1	no	—
332	C₃×C₄²	—	2	1	no	—
333	C₃×C₄²	—	2	1	no	—
334	C₃×C₄²	—	4	1	no	—
335	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
336	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
337	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
338	C₃×C₄²	C₂⁴	1	1	yes	characteristic
339	C₂×#41	—	2	1	no	—
340	C₂×#41	C₃×D₄	1	1	yes	characteristic
341	C₂×#41	C₃×D₄	1	1	yes	characteristic
342	C₂²×Q₈	—	2	1	no	—
343	C₂×Q₁₆	—	2	1	no	—
344	C₂×SD₁₆	—	2	1	no	—
345	C₂²×C₈	—	2	1	no	—
346	C₄⋊Q₈	—	2	1	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
349	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
350	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
351	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
352	#126	—	2	2	no	—
353	#126	—	2	2	no	—
354	#126	—	2	2	no	—
355	#125	—	2	2	no	—
356	#125	—	2	2	no	—
357	#125	—	2	1	no	—
358	#125	—	2	1	no	—
359	#125	C₃×D₄	1	2	yes	—
360	#124	—	2	2	no	—
361	#124	—	2	1	no	—
362	#123	—	2	2	no	—
363	#123	—	2	2	no	—
364	#123	—	2	2	no	—
365	C₂²⋊Q₈	—	2	2	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	#121	—	2	2	no	—
375	#121	—	2	1	no	—
376	C₄×Q₈	—	2	2	no	—
377	C₄×Q₈	—	2	2	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	—	2	1	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
386	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
387	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
388	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	C₃×D₄	1	1	yes	characteristic
397	C₄×D₄	C₃×D₄	1	1	yes	characteristic
398	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
399	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
400	#117	—	2	2	no	—
401	#117	—	2	2	no	—
402	#117	—	2	1	no	—
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	#117	—	2	1	no	—
406	#117	C₃×D₄	1	1	yes	characteristic
407	#117	C₃×D₄	1	1	yes	characteristic
408	#117	C₃×D₄	1	2	yes	—
409	C₂×C₄⋊C₄	—	2	2	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄²	—	2	2	no	—
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
415	#107	—	2	1	no	—
416	#107	—	2	1	no	—
417	#107	—	2	1	no	—
418	#107	—	2	2	no	—
419	#106	—	2	1	no	—
420	#106	—	2	1	no	—
421	#106	—	2	1	no	—
422	#106	—	2	2	no	—
423	C₄⋊C₈	—	2	1	no	—
424	C₄⋊C₈	—	2	1	no	—
425	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
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	#103	—	2	1	no	—
430	#103	—	2	1	no	—
431	#103	—	2	1	no	—
432	#103	—	2	1	no	—
433	#103	—	2	1	no	—
434	#103	—	2	2	no	—
435	#103	—	2	2	no	—
436	#102	—	2	1	no	—
437	#102	—	2	1	no	—
438	#102	—	2	1	no	—
439	C₂²⋊C₈	—	2	1	no	—
440	C₂²⋊C₈	—	2	1	no	—
441	#97	—	2	1	no	—
442	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
443	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
444	C₂³×C₃	—	2	1	no	—
445	C₂³×C₃	—	2	1	no	—
446	C₂³×C₃	#120	1	1	yes	characteristic
447	C₃×Q₈	—	2	1	no	—
448	C₃×Q₈	—	2	1	no	—
449	C₃×Q₈	—	2	1	no	—
450	C₃×Q₈	—	4	4	no	—
451	C₃×Q₈	—	4	2	no	—
452	C₃×Q₈	—	4	1	no	—
453	C₃×Q₈	—	4	1	no	—
454	C₃×Q₈	—	4	1	no	—
455	C₃×Q₈	—	4	1	no	—
456	C₃×Q₈	—	4	1	no	—
457	C₃×Q₈	—	4	1	no	—
458	C₃×Q₈	#137	1	2	yes	—
459	C₃×D₄	—	2	1	no	—
460	C₃×D₄	—	2	1	no	—
461	C₃×D₄	—	2	1	no	—
462	C₃×D₄	—	4	2	no	—
463	C₃×D₄	—	4	2	no	—
464	C₃×D₄	—	4	4	no	—
465	C₃×D₄	#135	1	2	yes	—
466	C₂×C₃×C₄	—	2	1	no	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	—	2	1	no	—
469	C₂×C₃×C₄	—	2	1	no	—
470	C₂×C₃×C₄	—	2	1	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	2	1	no	—
473	C₂×C₃×C₄	—	2	1	no	—
474	C₂×C₃×C₄	—	2	2	no	—
475	C₂×C₃×C₄	—	2	1	no	—
476	C₂×C₃×C₄	—	2	1	no	—
477	C₂×C₃×C₄	—	2	2	no	—
478	C₂×C₃×C₄	—	4	1	no	—
479	C₂×C₃×C₄	—	4	2	no	—
480	C₂×C₃×C₄	—	4	2	no	—
481	C₂×C₃×C₄	—	4	2	no	—
482	C₂×C₃×C₄	—	4	2	no	—
483	C₂×C₃×C₄	—	4	4	no	—
484	C₂×C₃×C₄	—	4	4	no	—
485	C₂×C₃×C₄	—	4	1	no	—
486	C₂×C₃×C₄	—	4	1	no	—
487	C₂×C₃×C₄	—	4	1	no	—
488	C₂×C₃×C₄	—	4	1	no	—
489	C₂×C₃×C₄	—	4	1	no	—
490	C₂×C₃×C₄	—	4	1	no	—
491	C₂×C₃×C₄	#120	1	1	yes	characteristic
492	C₂×C₃×C₄	#120	1	1	yes	characteristic
493	C₂×C₃×C₄	#120	1	1	yes	characteristic
494	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
497	C₃×C₈	—	4	1	no	—
498	C₃×C₈	—	4	1	no	—
499	C₃×C₈	—	4	1	no	—
500	C₃×C₈	—	4	1	no	—
501	C₃×C₈	—	4	1	no	—
502	C₃×C₈	—	4	1	no	—
503	#41	—	2	2	no	—
504	#41	—	2	2	no	—
505	#41	—	4	1	no	—
506	#41	—	4	1	no	—
507	#41	—	4	2	no	—
508	#41	—	4	2	no	—
509	C₂×Q₈	—	2	2	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	4	2	no	—
515	C₂×Q₈	—	4	2	no	—
516	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
517	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
522	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
532	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
533	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
534	Q₁₆	—	4	2	no	—
535	SD₁₆	—	4	2	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	4	2	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	4	1	no	—
562	C₄⋊C₄	—	4	1	no	—
563	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
564	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
565	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
566	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
567	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
568	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
569	C₂²⋊C₄	—	2	2	no	—
570	C₂²⋊C₄	—	2	2	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	2	1	no	—
574	C₂²⋊C₄	—	2	1	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	1	no	—
577	C₂²⋊C₄	—	2	1	no	—
578	C₂²⋊C₄	—	2	1	no	—
579	C₂²⋊C₄	—	2	1	no	—
580	C₂²⋊C₄	—	4	1	no	—
581	C₄²	—	2	2	no	—
582	C₄²	—	2	2	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	2	2	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	4	1	no	—
591	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
592	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
593	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
594	C₄²	C₂⁴×C₃	1	1	yes	characteristic
595	C₂²×C₃	—	2	1	no	—
596	C₂²×C₃	—	2	2	no	—
597	C₂²×C₃	—	2	1	no	—
598	C₂²×C₃	—	2	1	no	—
599	C₂²×C₃	—	4	1	no	—
600	C₂²×C₃	—	4	1	no	—
601	C₂²×C₃	—	4	1	no	—
602	C₂²×C₃	—	4	1	no	—
603	C₂²×C₃	—	4	1	no	—
604	C₂²×C₃	C₂×#120	1	1	yes	characteristic
605	C₃×C₄	—	2	1	no	—
606	C₃×C₄	—	2	1	no	—
607	C₃×C₄	—	2	2	no	—
608	C₃×C₄	—	2	1	no	—
609	C₃×C₄	—	2	1	no	—
610	C₃×C₄	—	4	1	no	—
611	C₃×C₄	—	4	1	no	—
612	C₃×C₄	—	4	2	no	—
613	C₃×C₄	—	4	2	no	—
614	C₃×C₄	—	4	1	no	—
615	C₃×C₄	—	4	1	no	—
616	C₃×C₄	—	4	1	no	—
617	C₃×C₄	—	8	1	no	—
618	C₃×C₄	—	8	1	no	—
619	C₃×C₄	C₂×#135	1	1	yes	characteristic
620	C₃×C₄	C₂×#137	1	1	yes	characteristic
621	C₃×C₄	#575	1	1	yes	characteristic
622	C₃×C₄	#575	1	1	yes	characteristic
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	C₃×#120	1	1	yes	characteristic
626	Q₈	—	2	1	no	—
627	Q₈	—	2	1	no	—
628	Q₈	—	2	1	no	—
629	Q₈	—	4	4	no	—
630	Q₈	—	4	2	no	—
631	Q₈	—	4	1	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	1	no	—
636	Q₈	—	4	1	no	—
637	Q₈	C₃×#137	1	2	yes	—
638	D₄	—	2	1	no	—
639	D₄	—	2	1	no	—
640	D₄	—	2	1	no	—
641	D₄	—	4	2	no	—
642	D₄	—	4	2	no	—
643	D₄	—	4	4	no	—
644	D₄	C₃×#135	1	2	yes	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	2	no	—
662	C₂×C₄	—	4	2	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	C₃×#120	1	1	yes	characteristic
671	C₂×C₄	C₃×#120	1	1	yes	characteristic
672	C₂×C₄	C₃×#120	1	1	yes	characteristic
673	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
674	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
675	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
676	C₈	—	4	1	no	—
677	C₈	—	4	1	no	—
678	C₈	—	4	1	no	—
679	C₈	—	4	1	no	—
680	C₈	—	4	1	no	—
681	C₈	—	4	1	no	—
682	C₂×C₃	—	4	1	no	—
683	C₂×C₃	—	4	2	no	—
684	C₂×C₃	—	8	1	no	—
685	C₂×C₃	#3002	1	1	yes	characteristic
686	C₂×C₃	#3007	1	1	yes	characteristic
687	C₂×C₃	#3020	1	1	yes	characteristic
688	C₂²	—	2	1	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	C₂×C₃×#120	1	1	yes	characteristic
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	1	no	—
702	C₄	—	2	1	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	8	1	no	—
711	C₄	—	8	1	no	—
712	C₄	C₂×C₃×#135	1	1	yes	characteristic
713	C₄	C₂×C₃×#137	1	1	yes	characteristic
714	C₄	C₃×#575	1	1	yes	characteristic
715	C₄	C₃×#575	1	1	yes	characteristic
716	C₃	#18765	1	1	yes	characteristic, direct product factor, Sylow
717	C₂	—	4	1	no	—
718	C₂	—	4	2	no	—
719	C₂	—	8	1	no	—
720	C₂	C₃×#3002	1	1	yes	characteristic
721	C₂	C₃×#3007	1	1	yes	characteristic
722	C₂	C₃×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃
prime radical	C₃×#3482	C₂
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
2. C₃×#3231	C₂	semidirect
3. C₃×#3116	C₂	semidirect
4. C₃×#3076	C₂	semidirect
5. C₃×#1652	C₂	semidirect
6. C₃×#1651	C₂	semidirect
7. C₃×#1648	C₂	semidirect
8. C₃×#1647	C₂	semidirect
9. C₃×#1638	C₂	semidirect
10. C₃×#1637	C₂	semidirect
11. C₃×#1636	C₂	semidirect
12. C₃×#1635	C₂	semidirect
13. C₃×#1552	C₂	semidirect
14. C₃×#1488	C₂	semidirect
15. C₃×#1477	C₂	semidirect
16. #18765	C₃	direct (N × H)
73. #3231	C₂×C₃	semidirect
74. #3116	C₂×C₃	semidirect
75. #3076	C₂×C₃	semidirect
76. #1652	C₂×C₃	semidirect
77. #1651	C₂×C₃	semidirect
78. #1648	C₂×C₃	semidirect
79. #1647	C₂×C₃	semidirect
80. #1638	C₂×C₃	semidirect
81. #1637	C₂×C₃	semidirect
82. #1636	C₂×C₃	semidirect
83. #1635	C₂×C₃	semidirect
84. #1552	C₂×C₃	semidirect
85. #1488	C₂×C₃	semidirect
86. #1477	C₂×C₃	semidirect
716. C₃	#18765	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×#3482	2
C₃×#3231	2
C₃×#3116	2
C₃×#3076	2
C₃×#1652	2
C₃×#1651	2
C₃×#1648	2
C₃×#1647	2
C₃×#1638	2
C₃×#1637	2
C₃×#1636	2
C₃×#1635	2
C₃×#1552	2
C₃×#1488	2
C₃×#1477	2
#18765	3

Subgroups — C3×#18765 #10637372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#18765 #10637372