Subgroups — C₃×#61850 #10680457

Order 768.

1716 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3385	C₂	1	2	yes	maximal, complemented
4	C₃×#3384	C₂	1	4	yes	maximal, complemented
5	C₃×Q₈×SD₁₆	C₂	1	2	yes	maximal, complemented
6	C₃×#3376	C₂	1	4	yes	maximal, complemented
7	C₃×#3373	C₂	1	2	yes	maximal, complemented
8	C₃×#3361	C₂	1	2	yes	maximal, complemented
9	C₃×#3244	C₂	1	4	yes	maximal, complemented
10	C₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3118	C₂	1	4	yes	maximal, complemented
13	C₃×#3109	C₂	1	1	yes	maximal, characteristic
14	C₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	#61850	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×#563	—	2	2	no	—
18	C₃×#559	C₂²	1	2	yes	complemented
19	C₃×Q₈²	C₂²	1	2	yes	complemented
20	C₃×#556	—	2	1	no	—
21	C₃×#556	C₂²	1	2	yes	complemented
22	C₃×#554	—	2	1	no	—
23	C₃×#554	—	2	2	no	—
24	C₃×#554	C₂²	1	4	yes	—
25	C₃×#554	C₂²	1	2	yes	—
26	C₃×D₄×Q₈	—	2	1	no	—
27	C₃×D₄×Q₈	—	2	1	no	—
28	C₃×D₄×Q₈	C₂²	1	2	yes	—
29	C₃×D₄×Q₈	C₂²	1	2	yes	complemented
30	C₃×#544	C₂²	1	2	yes	—
31	C₃×#543	—	2	2	no	—
32	C₃×#542	—	2	2	no	—
33	C₃×#542	C₂²	1	4	yes	—
34	C₃×#536	—	2	2	no	—
35	C₃×#533	C₂²	1	1	yes	characteristic
36	C₃×#533	C₂²	1	1	yes	characteristic
37	C₃×#533	C₂²	1	1	yes	characteristic
38	C₃×#532	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₂²⋊Q₈	—	2	2	no	—
40	C₃×#518	C₂²	1	2	yes	—
41	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
42	C₃×#501	C₂²	1	2	yes	complemented
43	C₃×#501	C₂²	1	4	yes	complemented
44	C₃×#500	C₂²	1	1	yes	characteristic, complemented
45	C₃×#498	C₂²	1	4	yes	complemented
46	C₃×#498	C₂²	1	1	yes	characteristic, complemented
47	C₃×#491	C₂²	1	2	yes	complemented
48	C₃×#489	C₂²	1	4	yes	complemented
49	C₃×#488	C₂²	1	4	yes	complemented
50	C₃×#486	C₂²	1	1	yes	characteristic, complemented
51	C₃×#486	C₂²	1	1	yes	characteristic, complemented
52	C₃×#485	C₂²	1	4	yes	—
53	C₃×#483	C₂²	1	2	yes	—
54	C₃×#482	C₂²	1	4	yes	—
55	C₃×#481	C₂²	1	2	yes	—
56	C₃×#479	C₂²	1	4	yes	complemented
57	C₃×#478	C₂²	1	4	yes	complemented
58	C₃×#478	C₂²	1	4	yes	complemented
59	C₃×#477	C₂²	1	2	yes	complemented
60	C₃×#476	C₂²	1	2	yes	—
61	C₃×#476	C₂²	1	4	yes	—
62	C₃×#476	C₂²	1	2	yes	—
63	C₃×#476	C₂²	1	4	yes	complemented
64	C₃×#475	C₂²	1	2	yes	complemented
65	C₃×#475	C₂²	1	4	yes	complemented
66	C₃×#474	C₂²	1	4	yes	—
67	C₃×#463	C₂²	1	4	yes	—
68	C₃×#463	C₂²	1	4	yes	—
69	C₃×#461	C₂²	1	2	yes	—
70	C₃×#459	C₂²	1	2	yes	—
71	C₃×#450	C₂²	1	2	yes	—
72	C₃×#447	C₂²	1	2	yes	—
73	C₃×#446	C₂²	1	4	yes	complemented
74	C₃×#446	C₂²	1	2	yes	complemented
75	C₃×C₈×Q₈	C₂²	1	2	yes	complemented
76	C₃×#442	C₂²	1	4	yes	—
77	C₃×#442	C₂²	1	4	yes	—
78	C₃×#440	C₂²	1	4	yes	—
79	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
80	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
81	C₃×C₄×SD₁₆	C₂²	1	4	yes	—
82	C₃×C₄×D₈	C₂²	1	4	yes	—
83	C₃×#433	C₂²	1	4	yes	—
84	C₃×#432	C₂²	1	1	yes	characteristic
85	C₃×#431	C₂²	1	1	yes	characteristic
86	#3550	C₂×C₃	1	1	yes	characteristic, complemented
87	#3501	C₂×C₃	1	1	yes	characteristic, complemented
88	#3385	C₂×C₃	1	2	yes	complemented
89	#3384	C₂×C₃	1	4	yes	complemented
90	Q₈×SD₁₆	C₂×C₃	1	2	yes	complemented
91	#3376	C₂×C₃	1	4	yes	complemented
92	#3373	C₂×C₃	1	2	yes	complemented
93	#3361	C₂×C₃	1	2	yes	complemented
94	#3244	C₂×C₃	1	4	yes	complemented
95	#3237	C₂×C₃	1	1	yes	characteristic, complemented
96	#3228	C₂×C₃	1	1	yes	characteristic, complemented
97	#3118	C₂×C₃	1	4	yes	complemented
98	#3109	C₂×C₃	1	1	yes	characteristic
99	#3101	C₂×C₃	1	1	yes	characteristic, complemented
100	#2985	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂×C₃×#41	—	2	1	no	—
102	C₂²×C₃×Q₈	—	2	2	no	—
103	C₂²×C₃×Q₈	—	2	2	no	—
104	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
105	C₂³×C₃×C₄	—	2	1	no	—
106	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
107	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
108	C₂×C₃×D₈	C₂³	1	4	yes	—
109	C₃×C₄⋊Q₈	—	2	4	no	—
110	C₃×C₄⋊Q₈	—	2	2	no	—
111	C₃×C₄⋊Q₈	—	2	2	no	—
112	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
114	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
119	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₃×#127	C₂³	1	1	yes	characteristic
122	C₃×#126	—	2	4	no	—
123	C₃×#126	—	2	4	no	—
124	C₃×#125	—	2	2	no	—
125	C₃×#125	—	2	1	no	—
126	C₃×#125	D₄	1	2	yes	—
127	C₃×#125	C₂³	1	2	yes	—
128	C₃×#125	C₂³	1	4	yes	—
129	C₃×#124	—	2	2	no	—
130	C₃×#124	—	2	4	no	—
131	C₃×#124	—	2	1	no	—
132	C₃×#124	C₂³	1	4	yes	—
133	C₃×#123	—	2	4	no	—
134	C₃×#123	—	2	4	no	—
135	C₃×C₂²⋊Q₈	—	2	2	no	—
136	C₃×C₂²⋊Q₈	—	2	2	no	—
137	C₃×C₂²⋊Q₈	—	2	4	no	—
138	C₃×C₂²⋊Q₈	—	2	1	no	—
139	C₃×C₂²⋊Q₈	—	2	1	no	—
140	C₃×C₂²⋊Q₈	—	2	1	no	—
141	C₃×C₂²⋊Q₈	—	2	4	no	—
142	C₃×C₂²⋊Q₈	—	2	4	no	—
143	C₃×C₂²⋊Q₈	—	2	2	no	—
144	C₃×C₂²⋊Q₈	—	2	4	no	—
145	C₃×C₂²⋊Q₈	—	2	2	no	—
146	C₃×C₂²⋊Q₈	—	2	4	no	—
147	C₃×C₂²⋊Q₈	—	2	4	no	—
148	C₃×C₂²⋊Q₈	—	2	4	no	—
149	C₃×C₂²⋊Q₈	—	2	4	no	—
150	C₃×C₂²⋊Q₈	D₄	1	2	yes	—
151	C₃×C₂²⋊Q₈	D₄	1	2	yes	—
152	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₃×#121	—	2	1	no	—
154	C₃×#121	C₂³	1	2	yes	—
155	C₃×C₄×Q₈	—	2	2	no	—
156	C₃×C₄×Q₈	—	2	1	no	—
157	C₃×C₄×Q₈	—	2	1	no	—
158	C₃×C₄×Q₈	—	2	1	no	—
159	C₃×C₄×Q₈	C₂³	1	2	yes	—
160	C₃×C₄×Q₈	C₂³	1	4	yes	—
161	C₃×C₄×Q₈	C₂³	1	2	yes	—
162	C₃×C₄×Q₈	C₂³	1	2	yes	—
163	C₃×C₄×D₄	—	2	2	no	—
164	C₃×C₄×D₄	—	2	2	no	—
165	C₃×C₄×D₄	—	2	2	no	—
166	C₃×C₄×D₄	—	2	1	no	—
167	C₃×C₄×D₄	—	2	1	no	—
168	C₃×C₄×D₄	—	2	1	no	—
169	C₃×C₄×D₄	C₂³	1	4	yes	—
170	C₃×C₄×D₄	C₂³	1	4	yes	—
171	C₃×C₄×D₄	C₂³	1	2	yes	—
172	C₃×C₄×D₄	C₂³	1	4	yes	—
173	C₃×C₄×D₄	C₂³	1	2	yes	—
174	C₃×C₄×D₄	C₂³	1	2	yes	—
175	C₃×#117	—	2	1	no	—
176	C₃×#117	—	2	2	no	—
177	C₃×#117	C₂³	1	2	yes	—
178	C₃×#117	C₂³	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	—	2	4	no	—
180	C₂×C₃×C₄⋊C₄	—	2	2	no	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
184	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
185	C₃×#107	C₂³	1	4	yes	—
186	C₃×#107	C₂³	1	4	yes	—
187	C₃×#106	C₂³	1	4	yes	—
188	C₃×#106	C₂³	1	2	yes	—
189	C₃×#106	C₂³	1	2	yes	—
190	C₃×#106	C₂³	1	4	yes	—
191	C₃×#106	C₂³	1	4	yes	—
192	C₃×C₄⋊C₈	C₂³	1	2	yes	—
193	C₃×C₄⋊C₈	C₂³	1	2	yes	—
194	C₃×C₄⋊C₈	C₂³	1	4	yes	—
195	C₃×C₄⋊C₈	C₂³	1	4	yes	—
196	C₃×#103	C₂³	1	2	yes	—
197	C₃×#103	C₂³	1	2	yes	—
198	C₃×#103	C₂³	1	4	yes	—
199	C₃×#103	C₂³	1	4	yes	—
200	C₃×#102	C₂³	1	2	yes	—
201	C₃×#102	C₂³	1	4	yes	—
202	C₃×#102	C₂³	1	4	yes	—
203	C₃×#102	C₂³	1	2	yes	—
204	C₃×#102	C₂³	1	4	yes	—
205	C₃×#102	C₂³	1	4	yes	—
206	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
207	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₃×#97	C₂³	1	2	yes	—
209	C₃×#97	C₂³	1	4	yes	—
210	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
211	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
212	C₃×C₄×C₈	C₂³	1	4	yes	—
213	#563	—	2	2	no	—
214	#559	C₂²×C₃	1	2	yes	complemented
215	Q₈²	C₂²×C₃	1	2	yes	complemented
216	#556	—	2	1	no	—
217	#556	C₂²×C₃	1	2	yes	complemented
218	#554	—	2	1	no	—
219	#554	—	2	2	no	—
220	#554	C₂²×C₃	1	2	yes	—
221	#554	C₂²×C₃	1	4	yes	—
222	D₄×Q₈	—	2	1	no	—
223	D₄×Q₈	—	2	1	no	—
224	D₄×Q₈	C₂²×C₃	1	2	yes	—
225	D₄×Q₈	C₂²×C₃	1	2	yes	complemented
226	#544	C₂²×C₃	1	2	yes	—
227	#543	—	2	2	no	—
228	#542	—	2	2	no	—
229	#542	C₂²×C₃	1	4	yes	—
230	#536	—	2	2	no	—
231	#533	C₂²×C₃	1	1	yes	characteristic
232	#533	C₂²×C₃	1	1	yes	characteristic
233	#533	C₂²×C₃	1	1	yes	characteristic
234	#532	C₂²×C₃	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	—	2	2	no	—
236	#518	C₂²×C₃	1	2	yes	—
237	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
238	#501	C₂²×C₃	1	2	yes	complemented
239	#501	C₂²×C₃	1	4	yes	complemented
240	#500	C₂²×C₃	1	1	yes	characteristic, complemented
241	#498	C₂²×C₃	1	1	yes	characteristic, complemented
242	#498	C₂²×C₃	1	4	yes	complemented
243	#491	C₂²×C₃	1	2	yes	complemented
244	#489	C₂²×C₃	1	4	yes	complemented
245	#488	C₂²×C₃	1	4	yes	complemented
246	#486	C₂²×C₃	1	1	yes	characteristic, complemented
247	#486	C₂²×C₃	1	1	yes	characteristic, complemented
248	#485	C₂²×C₃	1	4	yes	—
249	#483	C₂²×C₃	1	2	yes	—
250	#482	C₂²×C₃	1	4	yes	—
251	#481	C₂²×C₃	1	2	yes	—
252	#479	C₂²×C₃	1	4	yes	complemented
253	#478	C₂²×C₃	1	4	yes	complemented
254	#478	C₂²×C₃	1	4	yes	complemented
255	#477	C₂²×C₃	1	2	yes	complemented
256	#476	C₂²×C₃	1	2	yes	—
257	#476	C₂²×C₃	1	2	yes	—
258	#476	C₂²×C₃	1	4	yes	—
259	#476	C₂²×C₃	1	4	yes	complemented
260	#475	C₂²×C₃	1	2	yes	complemented
261	#475	C₂²×C₃	1	4	yes	complemented
262	#474	C₂²×C₃	1	4	yes	—
263	#463	C₂²×C₃	1	4	yes	—
264	#463	C₂²×C₃	1	4	yes	—
265	#461	C₂²×C₃	1	2	yes	—
266	#459	C₂²×C₃	1	2	yes	—
267	#450	C₂²×C₃	1	2	yes	—
268	#447	C₂²×C₃	1	2	yes	—
269	#446	C₂²×C₃	1	2	yes	complemented
270	#446	C₂²×C₃	1	4	yes	complemented
271	C₈×Q₈	C₂²×C₃	1	2	yes	complemented
272	#442	C₂²×C₃	1	4	yes	—
273	#442	C₂²×C₃	1	4	yes	—
274	#440	C₂²×C₃	1	4	yes	—
275	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
276	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
277	C₄×SD₁₆	C₂²×C₃	1	4	yes	—
278	C₄×D₈	C₂²×C₃	1	4	yes	—
279	#433	C₂²×C₃	1	4	yes	—
280	#432	C₂²×C₃	1	1	yes	characteristic
281	#431	C₂²×C₃	1	1	yes	characteristic
282	C₂⁴×C₃	—	2	1	no	—
283	C₃×#41	—	8	2	no	—
284	C₂×C₃×Q₈	—	2	1	no	—
285	C₂×C₃×Q₈	—	2	1	no	—
286	C₂×C₃×Q₈	—	2	1	no	—
287	C₂×C₃×Q₈	—	2	4	no	—
288	C₂×C₃×Q₈	—	2	4	no	—
289	C₂×C₃×Q₈	—	2	1	no	—
290	C₂×C₃×Q₈	—	8	4	no	—
291	C₂×C₃×Q₈	—	8	4	no	—
292	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
293	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
294	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
295	C₂×C₃×D₄	—	2	4	no	—
296	C₂×C₃×D₄	—	2	2	no	—
297	C₂×C₃×D₄	—	2	1	no	—
298	C₂×C₃×D₄	—	2	1	no	—
299	C₂×C₃×D₄	—	2	1	no	—
300	C₂×C₃×D₄	C₂⁴	1	2	yes	—
301	C₂×C₃×D₄	C₂⁴	1	2	yes	—
302	C₂²×C₃×C₄	—	2	1	no	—
303	C₂²×C₃×C₄	—	2	2	no	—
304	C₂²×C₃×C₄	—	2	2	no	—
305	C₂²×C₃×C₄	—	2	4	no	—
306	C₂²×C₃×C₄	—	2	4	no	—
307	C₂²×C₃×C₄	—	2	2	no	—
308	C₂²×C₃×C₄	—	2	4	no	—
309	C₂²×C₃×C₄	—	8	2	no	—
310	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
313	C₃×SD₁₆	—	2	4	no	—
314	C₃×SD₁₆	—	2	4	no	—
315	C₃×D₈	—	2	8	no	—
316	C₂×C₃×C₈	C₂⁴	1	2	yes	—
317	C₂×C₃×C₈	C₂⁴	1	2	yes	—
318	C₂×C₃×C₈	C₂⁴	1	4	yes	—
319	C₃×C₄⋊C₄	—	2	2	no	—
320	C₃×C₄⋊C₄	—	2	1	no	—
321	C₃×C₄⋊C₄	—	2	4	no	—
322	C₃×C₄⋊C₄	—	2	4	no	—
323	C₃×C₄⋊C₄	—	2	4	no	—
324	C₃×C₄⋊C₄	—	2	1	no	—
325	C₃×C₄⋊C₄	—	2	1	no	—
326	C₃×C₄⋊C₄	—	2	1	no	—
327	C₃×C₄⋊C₄	—	2	1	no	—
328	C₃×C₄⋊C₄	—	2	1	no	—
329	C₃×C₄⋊C₄	—	2	2	no	—
330	C₃×C₄⋊C₄	—	2	1	no	—
331	C₃×C₄⋊C₄	—	2	2	no	—
332	C₃×C₄⋊C₄	—	2	4	no	—
333	C₃×C₄⋊C₄	—	2	4	no	—
334	C₃×C₄⋊C₄	—	2	2	no	—
335	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
336	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
337	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
338	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
339	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
340	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
341	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
342	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
343	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
344	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
345	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
346	C₃×C₂²⋊C₄	—	2	2	no	—
347	C₃×C₂²⋊C₄	—	2	2	no	—
348	C₃×C₂²⋊C₄	—	2	4	no	—
349	C₃×C₂²⋊C₄	—	2	4	no	—
350	C₃×C₂²⋊C₄	—	2	2	no	—
351	C₃×C₂²⋊C₄	—	2	2	no	—
352	C₃×C₂²⋊C₄	—	2	4	no	—
353	C₃×C₂²⋊C₄	—	2	2	no	—
354	C₃×C₂²⋊C₄	—	2	4	no	—
355	C₃×C₂²⋊C₄	—	2	2	no	—
356	C₃×C₂²⋊C₄	—	2	4	no	—
357	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
358	C₃×C₄²	—	2	2	no	—
359	C₃×C₄²	—	2	4	no	—
360	C₃×C₄²	—	2	2	no	—
361	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
362	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
363	C₃×C₄²	C₂⁴	1	1	yes	characteristic
364	C₃×C₄²	C₂⁴	1	4	yes	—
365	C₃×C₄²	C₂⁴	1	1	yes	characteristic
366	C₂×#41	—	2	1	no	—
367	C₂²×Q₈	—	2	2	no	—
368	C₂²×Q₈	—	2	2	no	—
369	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
370	C₂³×C₄	—	2	1	no	—
371	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
372	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
373	C₂×D₈	C₂³×C₃	1	4	yes	—
374	C₄⋊Q₈	—	2	4	no	—
375	C₄⋊Q₈	—	2	2	no	—
376	C₄⋊Q₈	—	2	2	no	—
377	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
378	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
379	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
380	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
381	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
382	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
383	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
384	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
385	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
386	#127	C₂³×C₃	1	1	yes	characteristic
387	#126	—	2	4	no	—
388	#126	—	2	4	no	—
389	#125	—	2	2	no	—
390	#125	—	2	1	no	—
391	#125	C₃×D₄	1	2	yes	—
392	#125	C₂³×C₃	1	2	yes	—
393	#125	C₂³×C₃	1	4	yes	—
394	#124	—	2	2	no	—
395	#124	—	2	4	no	—
396	#124	—	2	1	no	—
397	#124	C₂³×C₃	1	4	yes	—
398	#123	—	2	4	no	—
399	#123	—	2	4	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	—	2	4	no	—
403	C₂²⋊Q₈	—	2	1	no	—
404	C₂²⋊Q₈	—	2	1	no	—
405	C₂²⋊Q₈	—	2	1	no	—
406	C₂²⋊Q₈	—	2	2	no	—
407	C₂²⋊Q₈	—	2	4	no	—
408	C₂²⋊Q₈	—	2	2	no	—
409	C₂²⋊Q₈	—	2	4	no	—
410	C₂²⋊Q₈	—	2	4	no	—
411	C₂²⋊Q₈	—	2	4	no	—
412	C₂²⋊Q₈	—	2	4	no	—
413	C₂²⋊Q₈	—	2	4	no	—
414	C₂²⋊Q₈	—	2	4	no	—
415	C₂²⋊Q₈	C₃×D₄	1	2	yes	—
416	C₂²⋊Q₈	C₃×D₄	1	2	yes	—
417	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
418	#121	—	2	1	no	—
419	#121	C₂³×C₃	1	2	yes	—
420	C₄×Q₈	—	2	2	no	—
421	C₄×Q₈	—	2	1	no	—
422	C₄×Q₈	—	2	1	no	—
423	C₄×Q₈	—	2	1	no	—
424	C₄×Q₈	C₂³×C₃	1	2	yes	—
425	C₄×Q₈	C₂³×C₃	1	4	yes	—
426	C₄×Q₈	C₂³×C₃	1	2	yes	—
427	C₄×Q₈	C₂³×C₃	1	2	yes	—
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	—	2	2	no	—
431	C₄×D₄	—	2	1	no	—
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	2	1	no	—
434	C₄×D₄	C₂³×C₃	1	2	yes	—
435	C₄×D₄	C₂³×C₃	1	2	yes	—
436	C₄×D₄	C₂³×C₃	1	4	yes	—
437	C₄×D₄	C₂³×C₃	1	4	yes	—
438	C₄×D₄	C₂³×C₃	1	2	yes	—
439	C₄×D₄	C₂³×C₃	1	4	yes	—
440	#117	—	2	1	no	—
441	#117	—	2	2	no	—
442	#117	C₂³×C₃	1	2	yes	—
443	#117	C₂³×C₃	1	2	yes	—
444	C₂×C₄⋊C₄	—	2	4	no	—
445	C₂×C₄⋊C₄	—	2	2	no	—
446	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	4	no	—
449	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
450	#107	C₂³×C₃	1	4	yes	—
451	#107	C₂³×C₃	1	4	yes	—
452	#106	C₂³×C₃	1	4	yes	—
453	#106	C₂³×C₃	1	2	yes	—
454	#106	C₂³×C₃	1	2	yes	—
455	#106	C₂³×C₃	1	4	yes	—
456	#106	C₂³×C₃	1	4	yes	—
457	C₄⋊C₈	C₂³×C₃	1	2	yes	—
458	C₄⋊C₈	C₂³×C₃	1	2	yes	—
459	C₄⋊C₈	C₂³×C₃	1	4	yes	—
460	C₄⋊C₈	C₂³×C₃	1	4	yes	—
461	#103	C₂³×C₃	1	2	yes	—
462	#103	C₂³×C₃	1	2	yes	—
463	#103	C₂³×C₃	1	4	yes	—
464	#103	C₂³×C₃	1	4	yes	—
465	#102	C₂³×C₃	1	2	yes	—
466	#102	C₂³×C₃	1	4	yes	—
467	#102	C₂³×C₃	1	4	yes	—
468	#102	C₂³×C₃	1	2	yes	—
469	#102	C₂³×C₃	1	4	yes	—
470	#102	C₂³×C₃	1	4	yes	—
471	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
472	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
473	#97	C₂³×C₃	1	2	yes	—
474	#97	C₂³×C₃	1	4	yes	—
475	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
476	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
477	C₄×C₈	C₂³×C₃	1	4	yes	—
478	C₂³×C₃	—	2	4	no	—
479	C₂³×C₃	—	2	2	no	—
480	C₂³×C₃	—	2	2	no	—
481	C₂³×C₃	—	8	1	no	—
482	C₂³×C₃	—	8	1	no	—
483	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
484	C₃×Q₈	—	2	4	no	—
485	C₃×Q₈	—	2	2	no	—
486	C₃×Q₈	—	2	2	no	—
487	C₃×Q₈	—	4	2	no	—
488	C₃×Q₈	—	4	2	no	—
489	C₃×Q₈	—	4	2	no	—
490	C₃×Q₈	—	8	1	no	—
491	C₃×Q₈	—	8	4	no	—
492	C₃×Q₈	—	8	4	no	—
493	C₃×Q₈	—	8	1	no	—
494	C₃×D₄	—	2	4	no	—
495	C₃×D₄	—	2	2	no	—
496	C₃×D₄	—	2	4	no	—
497	C₃×D₄	—	4	2	no	—
498	C₃×D₄	—	8	1	no	—
499	C₃×D₄	—	8	2	no	—
500	C₃×D₄	2₋¹⁺⁴	1	4	yes	—
501	C₂×C₃×C₄	—	2	2	no	—
502	C₂×C₃×C₄	—	2	2	no	—
503	C₂×C₃×C₄	—	2	2	no	—
504	C₂×C₃×C₄	—	2	2	no	—
505	C₂×C₃×C₄	—	2	2	no	—
506	C₂×C₃×C₄	—	2	2	no	—
507	C₂×C₃×C₄	—	2	2	no	—
508	C₂×C₃×C₄	—	2	2	no	—
509	C₂×C₃×C₄	—	4	1	no	—
510	C₂×C₃×C₄	—	4	4	no	—
511	C₂×C₃×C₄	—	4	4	no	—
512	C₂×C₃×C₄	—	8	4	no	—
513	C₂×C₃×C₄	—	8	2	no	—
514	C₂×C₃×C₄	—	8	4	no	—
515	C₂×C₃×C₄	—	8	4	no	—
516	C₂×C₃×C₄	—	8	1	no	—
517	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
519	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
523	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
525	C₃×C₈	—	2	4	no	—
526	C₃×C₈	—	2	2	no	—
527	C₃×C₈	—	2	2	no	—
528	C₂⁴	—	2	1	no	—
529	#41	—	8	2	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	4	no	—
534	C₂×Q₈	—	2	4	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	8	4	no	—
537	C₂×Q₈	—	8	4	no	—
538	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
539	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
540	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	C₂⁴×C₃	1	2	yes	—
547	C₂×D₄	C₂⁴×C₃	1	2	yes	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	8	2	no	—
556	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
557	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
559	SD₁₆	—	2	4	no	—
560	SD₁₆	—	2	4	no	—
561	D₈	—	2	8	no	—
562	C₂×C₈	C₂⁴×C₃	1	2	yes	—
563	C₂×C₈	C₂⁴×C₃	1	2	yes	—
564	C₂×C₈	C₂⁴×C₃	1	4	yes	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
582	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
583	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
584	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
585	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
586	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
587	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
588	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
589	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
590	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
591	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
604	C₄²	—	2	2	no	—
605	C₄²	—	2	4	no	—
606	C₄²	—	2	2	no	—
607	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
608	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
609	C₄²	C₂⁴×C₃	1	1	yes	characteristic
610	C₄²	C₂⁴×C₃	1	4	yes	—
611	C₄²	C₂⁴×C₃	1	1	yes	characteristic
612	C₂²×C₃	—	2	1	no	—
613	C₂²×C₃	—	2	1	no	—
614	C₂²×C₃	—	2	4	no	—
615	C₂²×C₃	—	2	1	no	—
616	C₂²×C₃	—	4	2	no	—
617	C₂²×C₃	—	4	2	no	—
618	C₂²×C₃	—	4	2	no	—
619	C₂²×C₃	—	4	2	no	—
620	C₂²×C₃	—	4	2	no	—
621	C₂²×C₃	—	8	4	no	—
622	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
623	C₃×C₄	—	2	1	no	—
624	C₃×C₄	—	2	1	no	—
625	C₃×C₄	—	2	4	no	—
626	C₃×C₄	—	2	1	no	—
627	C₃×C₄	—	2	1	no	—
628	C₃×C₄	—	2	4	no	—
629	C₃×C₄	—	4	2	no	—
630	C₃×C₄	—	4	2	no	—
631	C₃×C₄	—	4	2	no	—
632	C₃×C₄	—	4	2	no	—
633	C₃×C₄	—	4	2	no	—
634	C₃×C₄	—	4	2	no	—
635	C₃×C₄	#577	1	2	yes	—
636	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	8	1	no	—
641	C₂³	—	8	1	no	—
642	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
643	Q₈	—	2	4	no	—
644	Q₈	—	2	2	no	—
645	Q₈	—	2	2	no	—
646	Q₈	—	4	2	no	—
647	Q₈	—	4	2	no	—
648	Q₈	—	4	2	no	—
649	Q₈	—	8	4	no	—
650	Q₈	—	8	4	no	—
651	Q₈	—	8	1	no	—
652	Q₈	—	8	1	no	—
653	D₄	—	2	4	no	—
654	D₄	—	2	2	no	—
655	D₄	—	2	4	no	—
656	D₄	—	4	2	no	—
657	D₄	—	8	1	no	—
658	D₄	—	8	2	no	—
659	D₄	C₃×2₋¹⁺⁴	1	4	yes	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	4	no	—
670	C₂×C₄	—	4	4	no	—
671	C₂×C₄	—	8	2	no	—
672	C₂×C₄	—	8	4	no	—
673	C₂×C₄	—	8	4	no	—
674	C₂×C₄	—	8	4	no	—
675	C₂×C₄	—	8	1	no	—
676	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
677	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
678	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
679	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
680	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
681	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
682	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
683	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
684	C₈	—	2	4	no	—
685	C₈	—	2	2	no	—
686	C₈	—	2	2	no	—
687	C₂×C₃	—	4	1	no	—
688	C₂×C₃	—	4	4	no	—
689	C₂×C₃	—	8	2	no	—
690	C₂×C₃	#3486	1	1	yes	characteristic
691	C₂×C₃	C₂×#577	1	1	yes	characteristic
692	C₂×C₃	#3585	1	1	yes	characteristic
693	C₂²	—	2	1	no	—
694	C₂²	—	2	4	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	8	4	no	—
703	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
704	C₄	—	2	1	no	—
705	C₄	—	2	1	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	4	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	C₃×#577	1	2	yes	—
717	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
718	C₃	#61850	1	1	yes	characteristic, direct product factor, Sylow
719	C₂	—	4	1	no	—
720	C₂	—	4	4	no	—
721	C₂	—	8	2	no	—
722	C₂	C₃×#3486	1	1	yes	characteristic
723	C₂	C₂×C₃×#577	1	1	yes	characteristic
724	C₂	C₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₃×#3109	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3550	C₂	semidirect
2. C₃×#3501	C₂	semidirect
3. C₃×#3385	C₂	semidirect
4. C₃×#3384	C₂	semidirect
5. C₃×Q₈×SD₁₆	C₂	semidirect
6. C₃×#3376	C₂	semidirect
7. C₃×#3373	C₂	semidirect
8. C₃×#3361	C₂	semidirect
9. C₃×#3244	C₂	semidirect
10. C₃×#3237	C₂	semidirect
11. C₃×#3228	C₂	semidirect
12. C₃×#3118	C₂	semidirect
14. C₃×#3101	C₂	semidirect
15. C₃×#2985	C₂	semidirect
16. #61850	C₃	direct (N × H)
18. C₃×#559	C₂²	semidirect
19. C₃×Q₈²	C₂²	semidirect
21. C₃×#556	C₂²	semidirect
29. C₃×D₄×Q₈	C₂²	semidirect
42. C₃×#501	C₂²	semidirect
43. C₃×#501	C₂²	semidirect
44. C₃×#500	C₂²	semidirect
45. C₃×#498	C₂²	semidirect
46. C₃×#498	C₂²	semidirect
47. C₃×#491	C₂²	semidirect
48. C₃×#489	C₂²	semidirect
49. C₃×#488	C₂²	semidirect
50. C₃×#486	C₂²	semidirect
51. C₃×#486	C₂²	semidirect
56. C₃×#479	C₂²	semidirect
57. C₃×#478	C₂²	semidirect
58. C₃×#478	C₂²	semidirect
59. C₃×#477	C₂²	semidirect
63. C₃×#476	C₂²	semidirect
64. C₃×#475	C₂²	semidirect
65. C₃×#475	C₂²	semidirect
73. C₃×#446	C₂²	semidirect
74. C₃×#446	C₂²	semidirect
75. C₃×C₈×Q₈	C₂²	semidirect
86. #3550	C₂×C₃	semidirect
87. #3501	C₂×C₃	semidirect
88. #3385	C₂×C₃	semidirect
89. #3384	C₂×C₃	semidirect
90. Q₈×SD₁₆	C₂×C₃	semidirect
91. #3376	C₂×C₃	semidirect
92. #3373	C₂×C₃	semidirect
93. #3361	C₂×C₃	semidirect
94. #3244	C₂×C₃	semidirect
95. #3237	C₂×C₃	semidirect
96. #3228	C₂×C₃	semidirect
97. #3118	C₂×C₃	semidirect
99. #3101	C₂×C₃	semidirect
100. #2985	C₂×C₃	semidirect
214. #559	C₂²×C₃	semidirect
215. Q₈²	C₂²×C₃	semidirect
217. #556	C₂²×C₃	semidirect
225. D₄×Q₈	C₂²×C₃	semidirect
238. #501	C₂²×C₃	semidirect
239. #501	C₂²×C₃	semidirect
240. #500	C₂²×C₃	semidirect
241. #498	C₂²×C₃	semidirect
242. #498	C₂²×C₃	semidirect
243. #491	C₂²×C₃	semidirect
244. #489	C₂²×C₃	semidirect
245. #488	C₂²×C₃	semidirect
246. #486	C₂²×C₃	semidirect
247. #486	C₂²×C₃	semidirect
252. #479	C₂²×C₃	semidirect
253. #478	C₂²×C₃	semidirect
254. #478	C₂²×C₃	semidirect
255. #477	C₂²×C₃	semidirect
259. #476	C₂²×C₃	semidirect
260. #475	C₂²×C₃	semidirect
261. #475	C₂²×C₃	semidirect
269. #446	C₂²×C₃	semidirect
270. #446	C₂²×C₃	semidirect
271. C₈×Q₈	C₂²×C₃	semidirect
718. C₃	#61850	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×#3550	2
C₃×#3501	2
C₃×#3385	2
C₃×#3384	2
C₃×Q₈×SD₁₆	2
C₃×#3376	2
C₃×#3373	2
C₃×#3361	2
C₃×#3244	2
C₃×#3237	2
C₃×#3228	2
C₃×#3118	2
C₃×#3109	2
C₃×#3101	2
C₃×#2985	2
#61850	3

Subgroups — C3×#61850 #10680457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61850 #10680457