Subgroups — C₃×#61819 #10680426

Order 768.

1770 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3381	C₂	1	4	yes	maximal, complemented
4	C₃×#3380	C₂	1	4	yes	maximal, complemented
5	C₃×#3361	C₂	1	4	yes	maximal, complemented
6	C₃×#3360	C₂	1	4	yes	maximal, complemented
7	C₃×#3232	C₂	1	4	yes	maximal, complemented
8	C₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3105	C₂	1	4	yes	maximal, complemented
11	C₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3100	C₂	1	1	yes	maximal, characteristic
13	C₃×#2982	C₂	1	1	yes	maximal, characteristic, complemented
14	#61819	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃×#559	C₂²	1	2	yes	complemented
16	C₃×#557	C₂²	1	2	yes	complemented
17	C₃×#556	—	2	2	no	—
18	C₃×#556	C₂²	1	2	yes	complemented
19	C₃×#554	—	2	2	no	—
20	C₃×#554	—	2	2	no	—
21	C₃×#554	C₂²	1	4	yes	—
22	C₃×#554	C₂²	1	4	yes	—
23	C₃×#554	C₂²	1	2	yes	complemented
24	C₃×#552	—	2	2	no	—
25	C₃×#539	—	2	2	no	—
26	C₃×#536	—	2	1	no	—
27	C₃×#533	C₂²	1	1	yes	characteristic
28	C₃×#532	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₃×#529	C₂²	1	4	yes	—
31	C₂×C₃×#125	C₂²	1	2	yes	—
32	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
33	C₂×C₃×C₂²⋊Q₈	—	2	2	no	—
34	C₃×#520	—	2	1	no	—
35	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
38	C₂²×C₃×C₄⋊C₄	—	2	1	no	—
39	C₃×#500	C₂²	1	2	yes	complemented
40	C₃×#499	C₂²	1	8	yes	complemented
41	C₃×#498	C₂²	1	2	yes	complemented
42	C₃×#488	C₂²	1	8	yes	complemented
43	C₃×#487	C₂²	1	2	yes	complemented
44	C₃×#486	C₂²	1	2	yes	complemented
45	C₃×#484	C₂²	1	4	yes	—
46	C₃×#483	C₂²	1	2	yes	—
47	C₃×#481	C₂²	1	4	yes	—
48	C₃×#480	C₂²	1	2	yes	—
49	C₃×#479	C₂²	1	8	yes	complemented
50	C₃×#478	C₂²	1	8	yes	—
51	C₃×#478	C₂²	1	8	yes	complemented
52	C₃×#477	C₂²	1	4	yes	complemented
53	C₃×#476	C₂²	1	2	yes	—
54	C₃×#476	C₂²	1	4	yes	complemented
55	C₃×#474	C₂²	1	2	yes	—
56	C₃×#463	C₂²	1	8	yes	—
57	C₃×#461	C₂²	1	2	yes	—
58	C₃×#459	C₂²	1	2	yes	—
59	C₃×#450	C₂²	1	2	yes	—
60	C₃×#447	C₂²	1	2	yes	—
61	C₃×C₈×Q₈	C₂²	1	4	yes	complemented
62	C₃×C₈×Q₈	C₂²	1	4	yes	complemented
63	C₃×C₄×SD₁₆	C₂²	1	4	yes	—
64	C₃×C₄×SD₁₆	C₂²	1	8	yes	—
65	C₃×C₄×D₈	C₂²	1	4	yes	—
66	C₃×C₄×D₈	C₂²	1	8	yes	—
67	C₃×#431	C₂²	1	1	yes	characteristic
68	C₃×#431	C₂²	1	1	yes	characteristic
69	C₃×#431	C₂²	1	4	yes	—
70	#3507	C₂×C₃	1	1	yes	characteristic, complemented
71	C₂×#554	C₂×C₃	1	1	yes	characteristic, complemented
72	#3381	C₂×C₃	1	4	yes	complemented
73	#3380	C₂×C₃	1	4	yes	complemented
74	#3361	C₂×C₃	1	4	yes	complemented
75	#3360	C₂×C₃	1	4	yes	complemented
76	#3232	C₂×C₃	1	4	yes	complemented
77	#3230	C₂×C₃	1	1	yes	characteristic, complemented
78	#3227	C₂×C₃	1	1	yes	characteristic, complemented
79	#3105	C₂×C₃	1	4	yes	complemented
80	#3101	C₂×C₃	1	1	yes	characteristic, complemented
81	#3100	C₂×C₃	1	1	yes	characteristic
82	#2982	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×C₃×#41	—	2	1	no	—
84	C₂²×C₃×Q₈	—	2	1	no	—
85	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
86	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
87	C₂³×C₃×C₄	—	2	1	no	—
88	C₂³×C₃×C₄	—	2	2	no	—
89	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
90	C₂×C₃×D₈	C₂³	1	4	yes	—
91	C₃×C₄⋊Q₈	—	2	2	no	—
92	C₃×C₄⋊Q₈	—	2	1	no	—
93	C₃×C₄⋊Q₈	—	2	1	no	—
94	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
95	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
96	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₃×#127	C₂³	1	1	yes	characteristic
100	C₃×#126	—	2	4	no	—
101	C₃×#126	—	2	4	no	—
102	C₃×#125	—	2	4	no	—
103	C₃×#125	—	2	4	no	—
104	C₃×#125	—	2	1	no	—
105	C₃×#125	C₂³	1	8	yes	—
106	C₃×#125	C₂³	1	4	yes	—
107	C₃×#124	—	2	2	no	—
108	C₃×#124	—	2	1	no	—
109	C₃×#124	C₂³	1	4	yes	—
110	C₃×#123	—	2	4	no	—
111	C₃×#123	—	2	4	no	—
112	C₃×C₂²⋊Q₈	—	2	4	no	—
113	C₃×C₂²⋊Q₈	—	2	4	no	—
114	C₃×C₂²⋊Q₈	—	2	2	no	—
115	C₃×C₂²⋊Q₈	—	2	2	no	—
116	C₃×C₂²⋊Q₈	—	2	1	no	—
117	C₃×C₂²⋊Q₈	—	2	8	no	—
118	C₃×C₂²⋊Q₈	—	2	8	no	—
119	C₃×C₂²⋊Q₈	—	2	4	no	—
120	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
121	C₃×#121	—	2	1	no	—
122	C₃×#121	C₂³	1	2	yes	—
123	C₃×C₄×Q₈	—	2	2	no	—
124	C₃×C₄×Q₈	—	2	1	no	—
125	C₃×C₄×Q₈	D₄	1	2	yes	—
126	C₃×C₄×Q₈	D₄	1	2	yes	—
127	C₃×C₄×Q₈	C₂³	1	2	yes	—
128	C₃×C₄×Q₈	C₂³	1	4	yes	—
129	C₃×C₄×Q₈	C₂³	1	2	yes	—
130	C₃×C₄×Q₈	C₂³	1	2	yes	—
131	C₃×C₄×D₄	—	2	4	no	—
132	C₃×C₄×D₄	—	2	2	no	—
133	C₃×C₄×D₄	—	2	4	no	—
134	C₃×C₄×D₄	—	2	1	no	—
135	C₃×C₄×D₄	—	2	1	no	—
136	C₃×C₄×D₄	—	2	1	no	—
137	C₃×C₄×D₄	C₂³	1	4	yes	—
138	C₃×C₄×D₄	C₂³	1	2	yes	—
139	C₃×C₄×D₄	C₂³	1	2	yes	—
140	C₃×C₄×D₄	C₂³	1	8	yes	—
141	C₃×C₄×D₄	C₂³	1	2	yes	—
142	C₃×#117	—	2	1	no	—
143	C₃×#117	—	2	2	no	—
144	C₃×#117	—	2	4	no	—
145	C₂×C₃×C₄⋊C₄	—	2	2	no	—
146	C₂×C₃×C₄⋊C₄	—	2	1	no	—
147	C₂×C₃×C₄⋊C₄	—	2	2	no	—
148	C₂×C₃×C₄⋊C₄	—	2	4	no	—
149	C₂×C₃×C₄⋊C₄	—	2	4	no	—
150	C₂×C₃×C₄⋊C₄	—	2	2	no	—
151	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
152	C₂×C₃×C₄⋊C₄	D₄	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
156	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
157	C₂×C₃×C₄²	C₂³	1	2	yes	—
158	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
159	C₃×#107	C₂³	1	4	yes	—
160	C₃×#107	C₂³	1	8	yes	—
161	C₃×#106	C₂³	1	4	yes	—
162	C₃×#106	C₂³	1	8	yes	—
163	C₃×C₄⋊C₈	C₂³	1	2	yes	—
164	C₃×C₄⋊C₈	C₂³	1	2	yes	—
165	C₃×C₄⋊C₈	C₂³	1	8	yes	—
166	C₃×#103	C₂³	1	4	yes	—
167	C₃×#103	C₂³	1	8	yes	—
168	C₃×#102	C₂³	1	4	yes	—
169	C₃×#102	C₂³	1	4	yes	—
170	C₃×#102	C₂³	1	4	yes	—
171	C₃×#102	C₂³	1	8	yes	—
172	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
173	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
174	C₃×C₄×C₈	C₂³	1	2	yes	—
175	C₃×C₄×C₈	C₂³	1	8	yes	—
176	C₃×C₄×C₈	C₂³	1	2	yes	—
177	#559	C₂²×C₃	1	2	yes	complemented
178	#557	C₂²×C₃	1	2	yes	complemented
179	#556	—	2	2	no	—
180	#556	C₂²×C₃	1	2	yes	complemented
181	#554	—	2	2	no	—
182	#554	—	2	2	no	—
183	#554	C₂²×C₃	1	4	yes	—
184	#554	C₂²×C₃	1	4	yes	—
185	#554	C₂²×C₃	1	2	yes	complemented
186	#552	—	2	2	no	—
187	#539	—	2	2	no	—
188	#536	—	2	1	no	—
189	#533	C₂²×C₃	1	1	yes	characteristic
190	#532	C₂²×C₃	1	1	yes	characteristic
191	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
192	#529	C₂²×C₃	1	4	yes	—
193	C₂×#125	C₂²×C₃	1	2	yes	—
194	C₂×C₂²⋊Q₈	—	2	1	no	—
195	C₂×C₂²⋊Q₈	—	2	2	no	—
196	#520	—	2	1	no	—
197	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
198	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
199	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
200	C₂²×C₄⋊C₄	—	2	1	no	—
201	#500	C₂²×C₃	1	2	yes	complemented
202	#499	C₂²×C₃	1	8	yes	complemented
203	#498	C₂²×C₃	1	2	yes	complemented
204	#488	C₂²×C₃	1	8	yes	complemented
205	#487	C₂²×C₃	1	2	yes	complemented
206	#486	C₂²×C₃	1	2	yes	complemented
207	#484	C₂²×C₃	1	4	yes	—
208	#483	C₂²×C₃	1	2	yes	—
209	#481	C₂²×C₃	1	4	yes	—
210	#480	C₂²×C₃	1	2	yes	—
211	#479	C₂²×C₃	1	8	yes	complemented
212	#478	C₂²×C₃	1	8	yes	—
213	#478	C₂²×C₃	1	8	yes	complemented
214	#477	C₂²×C₃	1	4	yes	complemented
215	#476	C₂²×C₃	1	2	yes	—
216	#476	C₂²×C₃	1	4	yes	complemented
217	#474	C₂²×C₃	1	2	yes	—
218	#463	C₂²×C₃	1	8	yes	—
219	#461	C₂²×C₃	1	2	yes	—
220	#459	C₂²×C₃	1	2	yes	—
221	#450	C₂²×C₃	1	2	yes	—
222	#447	C₂²×C₃	1	2	yes	—
223	C₈×Q₈	C₂²×C₃	1	4	yes	complemented
224	C₈×Q₈	C₂²×C₃	1	4	yes	complemented
225	C₄×SD₁₆	C₂²×C₃	1	4	yes	—
226	C₄×SD₁₆	C₂²×C₃	1	8	yes	—
227	C₄×D₈	C₂²×C₃	1	4	yes	—
228	C₄×D₈	C₂²×C₃	1	8	yes	—
229	#431	C₂²×C₃	1	1	yes	characteristic
230	#431	C₂²×C₃	1	1	yes	characteristic
231	#431	C₂²×C₃	1	4	yes	—
232	C₂⁴×C₃	—	2	1	no	—
233	C₃×#41	—	4	4	no	—
234	C₂×C₃×Q₈	—	2	4	no	—
235	C₂×C₃×Q₈	—	2	1	no	—
236	C₂×C₃×Q₈	—	2	1	no	—
237	C₂×C₃×Q₈	—	2	2	no	—
238	C₂×C₃×Q₈	—	2	2	no	—
239	C₂×C₃×Q₈	—	8	2	no	—
240	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
241	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
242	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
243	C₂×C₃×D₄	—	2	4	no	—
244	C₂×C₃×D₄	—	2	2	no	—
245	C₂×C₃×D₄	—	2	1	no	—
246	C₂×C₃×D₄	—	2	1	no	—
247	C₂×C₃×D₄	—	2	1	no	—
248	C₂×C₃×D₄	C₂⁴	1	2	yes	—
249	C₂×C₃×D₄	C₂⁴	1	2	yes	—
250	C₂²×C₃×C₄	—	2	1	no	—
251	C₂²×C₃×C₄	—	2	2	no	—
252	C₂²×C₃×C₄	—	2	2	no	—
253	C₂²×C₃×C₄	—	2	2	no	—
254	C₂²×C₃×C₄	—	2	2	no	—
255	C₂²×C₃×C₄	—	2	8	no	—
256	C₂²×C₃×C₄	—	2	4	no	—
257	C₂²×C₃×C₄	—	4	4	no	—
258	C₂²×C₃×C₄	—	8	4	no	—
259	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
260	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
262	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
264	C₃×SD₁₆	—	2	8	no	—
265	C₃×D₈	—	2	8	no	—
266	C₂×C₃×C₈	C₂⁴	1	4	yes	—
267	C₂×C₃×C₈	C₂⁴	1	4	yes	—
268	C₃×C₄⋊C₄	—	2	8	no	—
269	C₃×C₄⋊C₄	—	2	2	no	—
270	C₃×C₄⋊C₄	—	2	2	no	—
271	C₃×C₄⋊C₄	—	2	1	no	—
272	C₃×C₄⋊C₄	—	2	4	no	—
273	C₃×C₄⋊C₄	—	2	8	no	—
274	C₃×C₄⋊C₄	—	2	1	no	—
275	C₃×C₄⋊C₄	—	2	2	no	—
276	C₃×C₄⋊C₄	—	2	1	no	—
277	C₃×C₄⋊C₄	—	2	2	no	—
278	C₃×C₄⋊C₄	—	2	4	no	—
279	C₃×C₄⋊C₄	—	2	1	no	—
280	C₃×C₄⋊C₄	—	2	1	no	—
281	C₃×C₄⋊C₄	—	2	2	no	—
282	C₃×C₄⋊C₄	—	2	4	no	—
283	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
284	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
285	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
286	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
287	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
288	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
289	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
290	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
291	C₃×C₂²⋊C₄	—	2	2	no	—
292	C₃×C₂²⋊C₄	—	2	2	no	—
293	C₃×C₂²⋊C₄	—	2	2	no	—
294	C₃×C₂²⋊C₄	—	2	8	no	—
295	C₃×C₂²⋊C₄	—	2	2	no	—
296	C₃×C₂²⋊C₄	—	2	4	no	—
297	C₃×C₂²⋊C₄	—	2	4	no	—
298	C₃×C₂²⋊C₄	—	2	2	no	—
299	C₃×C₂²⋊C₄	—	2	4	no	—
300	C₃×C₄²	—	2	4	no	—
301	C₃×C₄²	—	2	2	no	—
302	C₃×C₄²	C₂×D₄	1	4	yes	—
303	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
304	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
305	C₃×C₄²	C₂⁴	1	1	yes	characteristic
306	C₃×C₄²	C₂⁴	1	4	yes	—
307	C₃×C₄²	C₂⁴	1	1	yes	characteristic
308	C₂×#41	—	2	1	no	—
309	C₂²×Q₈	—	2	1	no	—
310	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
311	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
312	C₂³×C₄	—	2	1	no	—
313	C₂³×C₄	—	2	2	no	—
314	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
315	C₂×D₈	C₂³×C₃	1	4	yes	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
320	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
321	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
322	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
323	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
324	#127	C₂³×C₃	1	1	yes	characteristic
325	#126	—	2	4	no	—
326	#126	—	2	4	no	—
327	#125	—	2	4	no	—
328	#125	—	2	4	no	—
329	#125	—	2	1	no	—
330	#125	C₂³×C₃	1	8	yes	—
331	#125	C₂³×C₃	1	4	yes	—
332	#124	—	2	2	no	—
333	#124	—	2	1	no	—
334	#124	C₂³×C₃	1	4	yes	—
335	#123	—	2	4	no	—
336	#123	—	2	4	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	—	2	2	no	—
340	C₂²⋊Q₈	—	2	2	no	—
341	C₂²⋊Q₈	—	2	1	no	—
342	C₂²⋊Q₈	—	2	8	no	—
343	C₂²⋊Q₈	—	2	8	no	—
344	C₂²⋊Q₈	—	2	4	no	—
345	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
346	#121	—	2	1	no	—
347	#121	C₂³×C₃	1	2	yes	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×Q₈	C₃×D₄	1	2	yes	—
351	C₄×Q₈	C₃×D₄	1	2	yes	—
352	C₄×Q₈	C₂³×C₃	1	4	yes	—
353	C₄×Q₈	C₂³×C₃	1	2	yes	—
354	C₄×Q₈	C₂³×C₃	1	2	yes	—
355	C₄×Q₈	C₂³×C₃	1	2	yes	—
356	C₄×D₄	—	2	4	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	4	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	C₂³×C₃	1	2	yes	—
363	C₄×D₄	C₂³×C₃	1	8	yes	—
364	C₄×D₄	C₂³×C₃	1	2	yes	—
365	C₄×D₄	C₂³×C₃	1	4	yes	—
366	C₄×D₄	C₂³×C₃	1	2	yes	—
367	#117	—	2	1	no	—
368	#117	—	2	2	no	—
369	#117	—	2	4	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	4	no	—
374	C₂×C₄⋊C₄	—	2	4	no	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₃×D₄	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₄²	C₂³×C₃	1	2	yes	—
383	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
384	#107	C₂³×C₃	1	4	yes	—
385	#107	C₂³×C₃	1	8	yes	—
386	#106	C₂³×C₃	1	4	yes	—
387	#106	C₂³×C₃	1	8	yes	—
388	C₄⋊C₈	C₂³×C₃	1	2	yes	—
389	C₄⋊C₈	C₂³×C₃	1	2	yes	—
390	C₄⋊C₈	C₂³×C₃	1	8	yes	—
391	#103	C₂³×C₃	1	4	yes	—
392	#103	C₂³×C₃	1	8	yes	—
393	#102	C₂³×C₃	1	4	yes	—
394	#102	C₂³×C₃	1	4	yes	—
395	#102	C₂³×C₃	1	4	yes	—
396	#102	C₂³×C₃	1	8	yes	—
397	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
398	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
399	C₄×C₈	C₂³×C₃	1	2	yes	—
400	C₄×C₈	C₂³×C₃	1	8	yes	—
401	C₄×C₈	C₂³×C₃	1	2	yes	—
402	C₂³×C₃	—	2	4	no	—
403	C₂³×C₃	—	2	2	no	—
404	C₂³×C₃	—	2	2	no	—
405	C₂³×C₃	—	4	2	no	—
406	C₂³×C₃	—	4	2	no	—
407	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
408	C₃×Q₈	—	2	4	no	—
409	C₃×Q₈	—	2	4	no	—
410	C₃×Q₈	—	2	4	no	—
411	C₃×Q₈	—	4	2	no	—
412	C₃×Q₈	—	8	1	no	—
413	C₃×Q₈	—	8	2	no	—
414	C₃×Q₈	—	8	2	no	—
415	C₃×D₄	—	2	4	no	—
416	C₃×D₄	—	2	2	no	—
417	C₃×D₄	—	2	4	no	—
418	C₃×D₄	—	4	4	no	—
419	C₃×D₄	—	4	2	no	—
420	C₃×D₄	—	8	1	no	—
421	C₃×D₄	2₋¹⁺⁴	1	4	yes	—
422	C₂×C₃×C₄	—	2	4	no	—
423	C₂×C₃×C₄	—	2	2	no	—
424	C₂×C₃×C₄	—	2	2	no	—
425	C₂×C₃×C₄	—	2	2	no	—
426	C₂×C₃×C₄	—	2	2	no	—
427	C₂×C₃×C₄	—	2	2	no	—
428	C₂×C₃×C₄	—	2	4	no	—
429	C₂×C₃×C₄	—	4	2	no	—
430	C₂×C₃×C₄	—	4	1	no	—
431	C₂×C₃×C₄	—	4	4	no	—
432	C₂×C₃×C₄	—	4	2	no	—
433	C₂×C₃×C₄	—	4	4	no	—
434	C₂×C₃×C₄	—	4	4	no	—
435	C₂×C₃×C₄	—	4	4	no	—
436	C₂×C₃×C₄	—	8	4	no	—
437	C₂×C₃×C₄	—	8	8	no	—
438	C₂×C₃×C₄	#135	1	4	yes	—
439	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
440	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
442	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
447	C₃×C₈	—	2	4	no	—
448	C₃×C₈	—	2	4	no	—
449	C₂⁴	—	2	1	no	—
450	#41	—	4	4	no	—
451	C₂×Q₈	—	2	4	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	8	2	no	—
457	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
458	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
459	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	C₂⁴×C₃	1	2	yes	—
466	C₂×D₄	C₂⁴×C₃	1	2	yes	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	4	4	no	—
475	C₂²×C₄	—	8	4	no	—
476	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
477	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
479	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
481	SD₁₆	—	2	8	no	—
482	D₈	—	2	8	no	—
483	C₂×C₈	C₂⁴×C₃	1	4	yes	—
484	C₂×C₈	C₂⁴×C₃	1	4	yes	—
485	C₄⋊C₄	—	2	8	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	8	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
501	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
502	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
503	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
504	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
505	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
506	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
507	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₄²	—	2	4	no	—
518	C₄²	—	2	2	no	—
519	C₄²	C₂×C₃×D₄	1	4	yes	—
520	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
521	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
522	C₄²	C₂⁴×C₃	1	1	yes	characteristic
523	C₄²	C₂⁴×C₃	1	4	yes	—
524	C₄²	C₂⁴×C₃	1	1	yes	characteristic
525	C₂²×C₃	—	2	1	no	—
526	C₂²×C₃	—	2	1	no	—
527	C₂²×C₃	—	2	4	no	—
528	C₂²×C₃	—	4	8	no	—
529	C₂²×C₃	—	4	2	no	—
530	C₂²×C₃	—	4	2	no	—
531	C₂²×C₃	—	4	2	no	—
532	C₂²×C₃	—	4	2	no	—
533	C₂²×C₃	—	4	2	no	—
534	C₂²×C₃	C₂×#135	1	2	yes	—
535	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
536	C₃×C₄	—	2	4	no	—
537	C₃×C₄	—	2	1	no	—
538	C₃×C₄	—	2	1	no	—
539	C₃×C₄	—	2	1	no	—
540	C₃×C₄	—	2	4	no	—
541	C₃×C₄	—	4	4	no	—
542	C₃×C₄	—	4	2	no	—
543	C₃×C₄	—	4	2	no	—
544	C₃×C₄	—	4	2	no	—
545	C₃×C₄	—	4	2	no	—
546	C₃×C₄	C₂×#135	1	2	yes	—
547	C₃×C₄	C₂×#135	1	2	yes	—
548	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
549	C₂³	—	2	4	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
555	Q₈	—	2	4	no	—
556	Q₈	—	2	4	no	—
557	Q₈	—	2	4	no	—
558	Q₈	—	4	2	no	—
559	Q₈	—	8	2	no	—
560	Q₈	—	8	2	no	—
561	Q₈	—	8	1	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	4	no	—
565	D₄	—	4	4	no	—
566	D₄	—	4	2	no	—
567	D₄	—	8	1	no	—
568	D₄	C₃×2₋¹⁺⁴	1	4	yes	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	4	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	—	8	8	no	—
584	C₂×C₄	—	8	4	no	—
585	C₂×C₄	C₃×#135	1	4	yes	—
586	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
587	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
588	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
589	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
590	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
591	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
592	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
593	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
594	C₈	—	2	4	no	—
595	C₈	—	2	4	no	—
596	C₂×C₃	—	2	2	no	—
597	C₂×C₃	—	4	4	no	—
598	C₂×C₃	—	8	2	no	—
599	C₂×C₃	#3486	1	1	yes	characteristic
600	C₂×C₃	C₂²×#135	1	1	yes	characteristic
601	C₂×C₃	#3585	1	1	yes	characteristic
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	4	no	—
605	C₂²	—	4	8	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	C₂×C₃×#135	1	2	yes	—
612	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
613	C₄	—	2	1	no	—
614	C₄	—	2	4	no	—
615	C₄	—	2	4	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	4	no	—
622	C₄	—	4	2	no	—
623	C₄	C₂×C₃×#135	1	2	yes	—
624	C₄	C₂×C₃×#135	1	2	yes	—
625	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
626	C₃	#61819	1	1	yes	characteristic, direct product factor, Sylow
627	C₂	—	2	2	no	—
628	C₂	—	4	4	no	—
629	C₂	—	8	2	no	—
630	C₂	C₃×#3486	1	1	yes	characteristic
631	C₂	C₂²×C₃×#135	1	1	yes	characteristic
632	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×#3100	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3507	C₂	semidirect
2. C₂×C₃×#554	C₂	semidirect
3. C₃×#3381	C₂	semidirect
4. C₃×#3380	C₂	semidirect
5. C₃×#3361	C₂	semidirect
6. C₃×#3360	C₂	semidirect
7. C₃×#3232	C₂	semidirect
8. C₃×#3230	C₂	semidirect
9. C₃×#3227	C₂	semidirect
10. C₃×#3105	C₂	semidirect
11. C₃×#3101	C₂	semidirect
13. C₃×#2982	C₂	semidirect
14. #61819	C₃	direct (N × H)
15. C₃×#559	C₂²	semidirect
16. C₃×#557	C₂²	semidirect
18. C₃×#556	C₂²	semidirect
23. C₃×#554	C₂²	semidirect
39. C₃×#500	C₂²	semidirect
40. C₃×#499	C₂²	semidirect
41. C₃×#498	C₂²	semidirect
42. C₃×#488	C₂²	semidirect
43. C₃×#487	C₂²	semidirect
44. C₃×#486	C₂²	semidirect
49. C₃×#479	C₂²	semidirect
51. C₃×#478	C₂²	semidirect
52. C₃×#477	C₂²	semidirect
54. C₃×#476	C₂²	semidirect
61. C₃×C₈×Q₈	C₂²	semidirect
62. C₃×C₈×Q₈	C₂²	semidirect
70. #3507	C₂×C₃	semidirect
71. C₂×#554	C₂×C₃	semidirect
72. #3381	C₂×C₃	semidirect
73. #3380	C₂×C₃	semidirect
74. #3361	C₂×C₃	semidirect
75. #3360	C₂×C₃	semidirect
76. #3232	C₂×C₃	semidirect
77. #3230	C₂×C₃	semidirect
78. #3227	C₂×C₃	semidirect
79. #3105	C₂×C₃	semidirect
80. #3101	C₂×C₃	semidirect
82. #2982	C₂×C₃	semidirect
177. #559	C₂²×C₃	semidirect
178. #557	C₂²×C₃	semidirect
180. #556	C₂²×C₃	semidirect
185. #554	C₂²×C₃	semidirect
201. #500	C₂²×C₃	semidirect
202. #499	C₂²×C₃	semidirect
203. #498	C₂²×C₃	semidirect
204. #488	C₂²×C₃	semidirect
205. #487	C₂²×C₃	semidirect
206. #486	C₂²×C₃	semidirect
211. #479	C₂²×C₃	semidirect
213. #478	C₂²×C₃	semidirect
214. #477	C₂²×C₃	semidirect
216. #476	C₂²×C₃	semidirect
223. C₈×Q₈	C₂²×C₃	semidirect
224. C₈×Q₈	C₂²×C₃	semidirect
626. C₃	#61819	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×#3507	2
C₂×C₃×#554	2
C₃×#3381	2
C₃×#3380	2
C₃×#3361	2
C₃×#3360	2
C₃×#3232	2
C₃×#3230	2
C₃×#3227	2
C₃×#3105	2
C₃×#3101	2
C₃×#3100	2
C₃×#2982	2
#61819	3

Subgroups — C3×#61819 #10680426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61819 #10680426