Subgroups — C₃×#35314 #10653921

Order 768.

1566 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2864	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2863	C₂	1	2	yes	maximal, complemented
3	C₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2628	C₂	1	1	yes	maximal, characteristic
5	C₃×#2625	C₂	1	2	yes	maximal
6	C₃×#2621	C₂	1	1	yes	maximal, characteristic
7	C₃×#2524	C₂	1	4	yes	maximal, complemented
8	C₃×#2523	C₂	1	4	yes	maximal
9	C₃×#2520	C₂	1	4	yes	maximal, complemented
10	C₃×#2517	C₂	1	4	yes	maximal
11	C₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2327	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2320	C₂	1	2	yes	maximal, complemented
14	C₃×C₄×C₂²⋊Q₈	C₂	1	2	yes	maximal
15	C₃×C₄×#117	C₂	1	1	yes	maximal, characteristic
16	#35314	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
21	C₂×C₃×#117	C₂²	1	1	yes	characteristic
22	C₂×C₃×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
24	C₃×#400	C₂²	1	4	yes	—
25	C₃×#400	C₂²	1	2	yes	—
26	C₃×#399	C₂²	1	2	yes	—
27	C₃×#398	C₂²	1	2	yes	—
28	C₃×#398	C₂²	1	2	yes	—
29	C₃×#398	C₂²	1	4	yes	—
30	C₃×#397	C₂²	1	2	yes	—
31	C₃×#397	C₂²	1	2	yes	—
32	C₃×#397	C₂²	1	4	yes	—
33	C₃×#397	C₂²	1	4	yes	—
34	C₃×#395	C₂²	1	2	yes	—
35	C₃×#393	C₂²	1	2	yes	—
36	C₃×#391	C₂²	1	2	yes	—
37	C₃×#391	C₂²	1	2	yes	—
38	C₃×#391	C₂²	1	2	yes	—
39	C₃×#391	C₂²	1	4	yes	—
40	C₃×#391	C₂²	1	4	yes	—
41	C₃×#391	C₂²	1	2	yes	—
42	C₃×#389	C₂²	1	2	yes	—
43	C₃×#389	C₂²	1	2	yes	—
44	C₃×#389	C₂²	1	2	yes	—
45	C₃×#389	C₂²	1	2	yes	—
46	C₃×#387	C₂²	1	4	yes	—
47	C₃×#387	C₂²	1	4	yes	—
48	C₃×#387	C₂²	1	4	yes	—
49	C₃×#387	C₂²	1	4	yes	—
50	C₃×#387	C₂²	1	4	yes	—
51	C₃×#387	C₂²	1	4	yes	—
52	C₃×#387	C₂²	1	4	yes	—
53	C₃×#387	C₂²	1	4	yes	—
54	C₃×#387	C₂²	1	4	yes	—
55	C₃×#387	C₂²	1	4	yes	—
56	C₃×#387	C₂²	1	4	yes	—
57	C₃×#385	C₂²	1	4	yes	—
58	C₃×#383	C₂²	1	4	yes	—
59	C₃×#383	C₂²	1	4	yes	—
60	C₃×#382	C₂²	1	1	yes	characteristic
61	C₃×#382	C₂²	1	1	yes	characteristic
62	C₃×#382	C₂²	1	4	yes	—
63	C₃×#382	C₂²	1	4	yes	—
64	C₃×#380	C₂²	1	2	yes	—
65	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
66	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
67	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
68	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
69	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
70	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
71	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₃×#376	C₂²	1	1	yes	characteristic
73	C₃×#376	C₂²	1	1	yes	characteristic
74	C₃×C₄³	C₂²	1	1	yes	characteristic
75	C₃×C₄³	C₂²	1	1	yes	characteristic
76	#2864	C₂×C₃	1	1	yes	characteristic, complemented
77	#2863	C₂×C₃	1	2	yes	complemented
78	#2862	C₂×C₃	1	1	yes	characteristic, complemented
79	#2628	C₂×C₃	1	1	yes	characteristic
80	#2625	C₂×C₃	1	2	yes	—
81	#2621	C₂×C₃	1	1	yes	characteristic
82	#2524	C₂×C₃	1	4	yes	complemented
83	#2523	C₂×C₃	1	4	yes	—
84	#2520	C₂×C₃	1	4	yes	complemented
85	#2517	C₂×C₃	1	4	yes	—
86	#2331	C₂×C₃	1	1	yes	characteristic, complemented
87	#2327	C₂×C₃	1	1	yes	characteristic, complemented
88	#2320	C₂×C₃	1	2	yes	complemented
89	C₄×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
90	C₄×#117	C₂×C₃	1	1	yes	characteristic
91	C₂²×C₃×Q₈	C₂³	1	2	yes	—
92	C₂²×C₃×Q₈	C₂³	1	2	yes	—
93	C₂³×C₃×C₄	C₂³	1	2	yes	—
94	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
95	C₃×C₄⋊Q₈	—	2	4	no	—
96	C₃×C₄⋊Q₈	—	2	4	no	—
97	C₃×C₂²⋊Q₈	—	2	8	no	—
98	C₃×C₄×Q₈	—	2	8	no	—
99	C₃×#117	—	2	4	no	—
100	C₃×#117	—	2	4	no	—
101	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₃×C₄²	—	2	4	no	—
122	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
123	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
124	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
125	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
126	C₂×C₃×C₄²	C₂³	1	2	yes	—
127	C₂×C₃×C₄²	C₂³	1	2	yes	—
128	C₂×C₃×C₄²	C₂³	1	4	yes	—
129	C₂×C₃×C₄²	C₂³	1	2	yes	—
130	C₂×C₃×C₄²	C₂³	1	2	yes	—
131	C₂×C₃×C₄²	C₂³	1	2	yes	—
132	C₂×C₃×C₄²	C₂³	1	4	yes	—
133	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
134	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
135	C₃×#95	C₂³	1	2	yes	—
136	C₃×#95	C₂³	1	2	yes	—
137	C₃×#95	C₂³	1	2	yes	—
138	C₃×#95	C₂³	1	2	yes	—
139	C₃×#95	C₂³	1	4	yes	—
140	C₃×#95	C₂³	1	4	yes	—
141	C₃×#95	C₂³	1	4	yes	—
142	C₃×#95	C₂³	1	4	yes	—
143	C₃×#95	C₂³	1	4	yes	—
144	C₃×#95	C₂³	1	4	yes	—
145	C₃×#95	C₂³	1	4	yes	—
146	C₃×#95	C₂³	1	2	yes	—
147	C₃×#95	C₂³	1	2	yes	—
148	C₃×#95	C₂³	1	2	yes	—
149	C₃×#95	C₂³	1	4	yes	—
150	C₃×#95	C₂³	1	2	yes	—
151	C₃×#95	C₂³	1	4	yes	—
152	C₃×#95	C₂³	1	4	yes	—
153	C₃×#95	C₂³	1	4	yes	—
154	C₃×#95	C₂³	1	4	yes	—
155	C₃×#95	C₂³	1	4	yes	—
156	C₃×#95	C₂³	1	4	yes	—
157	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
160	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
161	C₂×#117	C₂²×C₃	1	1	yes	characteristic
162	C₂×#117	C₂²×C₃	1	1	yes	characteristic
163	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
164	#400	C₂²×C₃	1	4	yes	—
165	#400	C₂²×C₃	1	2	yes	—
166	#399	C₂²×C₃	1	2	yes	—
167	#398	C₂²×C₃	1	2	yes	—
168	#398	C₂²×C₃	1	2	yes	—
169	#398	C₂²×C₃	1	4	yes	—
170	#397	C₂²×C₃	1	2	yes	—
171	#397	C₂²×C₃	1	2	yes	—
172	#397	C₂²×C₃	1	4	yes	—
173	#397	C₂²×C₃	1	4	yes	—
174	#395	C₂²×C₃	1	2	yes	—
175	#393	C₂²×C₃	1	2	yes	—
176	#391	C₂²×C₃	1	2	yes	—
177	#391	C₂²×C₃	1	2	yes	—
178	#391	C₂²×C₃	1	2	yes	—
179	#391	C₂²×C₃	1	4	yes	—
180	#391	C₂²×C₃	1	2	yes	—
181	#391	C₂²×C₃	1	4	yes	—
182	#389	C₂²×C₃	1	2	yes	—
183	#389	C₂²×C₃	1	2	yes	—
184	#389	C₂²×C₃	1	2	yes	—
185	#389	C₂²×C₃	1	2	yes	—
186	#387	C₂²×C₃	1	4	yes	—
187	#387	C₂²×C₃	1	4	yes	—
188	#387	C₂²×C₃	1	4	yes	—
189	#387	C₂²×C₃	1	4	yes	—
190	#387	C₂²×C₃	1	4	yes	—
191	#387	C₂²×C₃	1	4	yes	—
192	#387	C₂²×C₃	1	4	yes	—
193	#387	C₂²×C₃	1	4	yes	—
194	#387	C₂²×C₃	1	4	yes	—
195	#387	C₂²×C₃	1	4	yes	—
196	#387	C₂²×C₃	1	4	yes	—
197	#385	C₂²×C₃	1	4	yes	—
198	#383	C₂²×C₃	1	4	yes	—
199	#383	C₂²×C₃	1	4	yes	—
200	#382	C₂²×C₃	1	4	yes	—
201	#382	C₂²×C₃	1	1	yes	characteristic
202	#382	C₂²×C₃	1	1	yes	characteristic
203	#382	C₂²×C₃	1	4	yes	—
204	#380	C₂²×C₃	1	2	yes	—
205	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
206	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
207	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
208	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
209	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
210	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
211	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
212	#376	C₂²×C₃	1	1	yes	characteristic
213	#376	C₂²×C₃	1	1	yes	characteristic
214	C₄³	C₂²×C₃	1	1	yes	characteristic
215	C₄³	C₂²×C₃	1	1	yes	characteristic
216	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
217	C₂×C₃×Q₈	—	2	4	no	—
218	C₂×C₃×Q₈	—	2	4	no	—
219	C₂×C₃×Q₈	—	2	4	no	—
220	C₂×C₃×Q₈	—	2	4	no	—
221	C₂×C₃×Q₈	—	4	4	no	—
222	C₂²×C₃×C₄	—	2	2	no	—
223	C₂²×C₃×C₄	—	2	2	no	—
224	C₂²×C₃×C₄	—	2	4	no	—
225	C₂²×C₃×C₄	—	2	4	no	—
226	C₂²×C₃×C₄	—	4	2	no	—
227	C₂²×C₃×C₄	#41	1	4	yes	—
228	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
230	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
231	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
232	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
233	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
234	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
235	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
237	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
241	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
242	C₃×C₄⋊C₄	—	2	2	no	—
243	C₃×C₄⋊C₄	—	2	2	no	—
244	C₃×C₄⋊C₄	—	2	4	no	—
245	C₃×C₄⋊C₄	—	2	4	no	—
246	C₃×C₄⋊C₄	—	2	8	no	—
247	C₃×C₄⋊C₄	—	2	4	no	—
248	C₃×C₄⋊C₄	—	2	8	no	—
249	C₃×C₄⋊C₄	—	2	4	no	—
250	C₃×C₄⋊C₄	—	2	4	no	—
251	C₃×C₄⋊C₄	—	2	4	no	—
252	C₃×C₄⋊C₄	—	2	4	no	—
253	C₃×C₄⋊C₄	—	2	8	no	—
254	C₃×C₄⋊C₄	—	4	4	no	—
255	C₃×C₄⋊C₄	—	4	4	no	—
256	C₃×C₄⋊C₄	—	4	4	no	—
257	C₃×C₂²⋊C₄	—	2	4	no	—
258	C₃×C₂²⋊C₄	—	2	8	no	—
259	C₃×C₂²⋊C₄	—	2	2	no	—
260	C₃×C₂²⋊C₄	—	2	2	no	—
261	C₃×C₂²⋊C₄	—	4	4	no	—
262	C₃×C₄²	—	2	4	no	—
263	C₃×C₄²	—	2	2	no	—
264	C₃×C₄²	—	2	2	no	—
265	C₃×C₄²	—	2	2	no	—
266	C₃×C₄²	—	2	2	no	—
267	C₃×C₄²	—	2	8	no	—
268	C₃×C₄²	—	2	4	no	—
269	C₃×C₄²	—	2	4	no	—
270	C₃×C₄²	—	4	2	no	—
271	C₃×C₄²	—	4	2	no	—
272	C₃×C₄²	—	4	4	no	—
273	C₃×C₄²	#41	1	4	yes	—
274	C₃×C₄²	#41	1	4	yes	—
275	C₂²×Q₈	C₂³×C₃	1	2	yes	—
276	C₂²×Q₈	C₂³×C₃	1	2	yes	—
277	C₂³×C₄	C₂³×C₃	1	2	yes	—
278	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
279	C₄⋊Q₈	—	2	4	no	—
280	C₄⋊Q₈	—	2	4	no	—
281	C₂²⋊Q₈	—	2	8	no	—
282	C₄×Q₈	—	2	8	no	—
283	#117	—	2	4	no	—
284	#117	—	2	4	no	—
285	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
290	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
292	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
297	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
298	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
299	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
305	C₂×C₄²	—	2	4	no	—
306	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₃	1	4	yes	—
310	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₃	1	2	yes	—
312	C₂×C₄²	C₂³×C₃	1	2	yes	—
313	C₂×C₄²	C₂³×C₃	1	2	yes	—
314	C₂×C₄²	C₂³×C₃	1	2	yes	—
315	C₂×C₄²	C₂³×C₃	1	2	yes	—
316	C₂×C₄²	C₂³×C₃	1	4	yes	—
317	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
319	#95	C₂³×C₃	1	2	yes	—
320	#95	C₂³×C₃	1	2	yes	—
321	#95	C₂³×C₃	1	2	yes	—
322	#95	C₂³×C₃	1	2	yes	—
323	#95	C₂³×C₃	1	4	yes	—
324	#95	C₂³×C₃	1	4	yes	—
325	#95	C₂³×C₃	1	4	yes	—
326	#95	C₂³×C₃	1	4	yes	—
327	#95	C₂³×C₃	1	4	yes	—
328	#95	C₂³×C₃	1	4	yes	—
329	#95	C₂³×C₃	1	4	yes	—
330	#95	C₂³×C₃	1	2	yes	—
331	#95	C₂³×C₃	1	2	yes	—
332	#95	C₂³×C₃	1	2	yes	—
333	#95	C₂³×C₃	1	4	yes	—
334	#95	C₂³×C₃	1	2	yes	—
335	#95	C₂³×C₃	1	4	yes	—
336	#95	C₂³×C₃	1	4	yes	—
337	#95	C₂³×C₃	1	4	yes	—
338	#95	C₂³×C₃	1	4	yes	—
339	#95	C₂³×C₃	1	4	yes	—
340	#95	C₂³×C₃	1	4	yes	—
341	C₂³×C₃	—	2	1	no	—
342	C₂³×C₃	—	2	1	no	—
343	C₂³×C₃	—	2	2	no	—
344	C₂³×C₃	—	2	2	no	—
345	C₂³×C₃	C₂×#41	1	2	yes	—
346	C₂³×C₃	C₂⁵	1	1	yes	characteristic
347	C₃×Q₈	—	4	8	no	—
348	C₃×Q₈	—	8	4	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	8	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	2	4	no	—
363	C₂×C₃×C₄	—	2	4	no	—
364	C₂×C₃×C₄	—	2	4	no	—
365	C₂×C₃×C₄	—	2	4	no	—
366	C₂×C₃×C₄	—	2	4	no	—
367	C₂×C₃×C₄	—	2	4	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	4	no	—
372	C₂×C₃×C₄	—	2	4	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	4	no	—
376	C₂×C₃×C₄	—	2	2	no	—
377	C₂×C₃×C₄	—	2	4	no	—
378	C₂×C₃×C₄	—	2	4	no	—
379	C₂×C₃×C₄	—	2	4	no	—
380	C₂×C₃×C₄	—	4	8	no	—
381	C₂×C₃×C₄	C₂×#41	1	4	yes	—
382	C₂×C₃×C₄	C₂×#41	1	2	yes	—
383	C₂×C₃×C₄	C₂×#41	1	2	yes	—
384	C₂×C₃×C₄	C₂×#41	1	2	yes	—
385	C₂×C₃×C₄	C₂×#41	1	2	yes	—
386	C₂×C₃×C₄	C₂×#41	1	2	yes	—
387	C₂×C₃×C₄	C₂×#41	1	2	yes	—
388	C₂×C₃×C₄	2₋¹⁺⁴	1	4	yes	—
389	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	—	4	4	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	C₃×#41	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
403	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
404	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
405	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
406	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
407	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	8	no	—
427	C₄⋊C₄	—	4	4	no	—
428	C₄⋊C₄	—	4	4	no	—
429	C₄⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₂²⋊C₄	—	2	8	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	4	4	no	—
435	C₄²	—	2	4	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	8	no	—
441	C₄²	—	2	4	no	—
442	C₄²	—	2	4	no	—
443	C₄²	—	4	2	no	—
444	C₄²	—	4	2	no	—
445	C₄²	—	4	4	no	—
446	C₄²	C₃×#41	1	4	yes	—
447	C₄²	C₃×#41	1	4	yes	—
448	C₂²×C₃	—	2	2	no	—
449	C₂²×C₃	—	2	4	no	—
450	C₂²×C₃	—	4	2	no	—
451	C₂²×C₃	—	4	1	no	—
452	C₂²×C₃	—	4	1	no	—
453	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
454	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
455	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
456	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
457	C₂²×C₃	#585	1	2	yes	—
458	C₃×C₄	—	2	2	no	—
459	C₃×C₄	—	2	4	no	—
460	C₃×C₄	—	2	4	no	—
461	C₃×C₄	—	2	2	no	—
462	C₃×C₄	—	2	2	no	—
463	C₃×C₄	—	4	4	no	—
464	C₃×C₄	—	4	2	no	—
465	C₃×C₄	—	4	2	no	—
466	C₃×C₄	—	4	4	no	—
467	C₃×C₄	—	4	4	no	—
468	C₃×C₄	—	4	1	no	—
469	C₃×C₄	—	4	1	no	—
470	C₃×C₄	—	4	4	no	—
471	C₃×C₄	#529	1	4	yes	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	C₂×C₃×#41	1	2	yes	—
477	C₂³	C₂⁵×C₃	1	1	yes	characteristic
478	Q₈	—	4	8	no	—
479	Q₈	—	8	4	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	4	8	no	—
512	C₂×C₄	C₂×C₃×#41	1	4	yes	—
513	C₂×C₄	C₂×C₃×#41	1	2	yes	—
514	C₂×C₄	C₂×C₃×#41	1	2	yes	—
515	C₂×C₄	C₂×C₃×#41	1	2	yes	—
516	C₂×C₄	C₂×C₃×#41	1	2	yes	—
517	C₂×C₄	C₂×C₃×#41	1	2	yes	—
518	C₂×C₄	C₂×C₃×#41	1	2	yes	—
519	C₂×C₄	C₃×2₋¹⁺⁴	1	4	yes	—
520	C₂×C₃	—	4	2	no	—
521	C₂×C₃	C₂×#529	1	1	yes	characteristic
522	C₂×C₃	#3461	1	2	yes	—
523	C₂×C₃	#3495	1	2	yes	—
524	C₂×C₃	#3509	1	1	yes	characteristic
525	C₂×C₃	#3510	1	1	yes	characteristic
526	C₂²	—	2	2	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
532	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
533	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
534	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
535	C₂²	C₃×#585	1	2	yes	—
536	C₄	—	2	2	no	—
537	C₄	—	2	4	no	—
538	C₄	—	2	4	no	—
539	C₄	—	2	2	no	—
540	C₄	—	2	2	no	—
541	C₄	—	4	4	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	4	no	—
545	C₄	—	4	4	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	4	no	—
548	C₄	—	4	1	no	—
549	C₄	C₃×#529	1	4	yes	—
550	C₃	#35314	1	1	yes	characteristic, direct product factor, Sylow
551	C₂	—	4	2	no	—
552	C₂	C₂×C₃×#529	1	1	yes	characteristic
553	C₂	C₃×#3461	1	2	yes	—
554	C₂	C₃×#3495	1	2	yes	—
555	C₂	C₃×#3509	1	1	yes	characteristic
556	C₂	C₃×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂⁴×C₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#2864	C₂	semidirect
2. C₃×#2863	C₂	semidirect
3. C₃×#2862	C₂	semidirect
7. C₃×#2524	C₂	semidirect
9. C₃×#2520	C₂	semidirect
11. C₃×#2331	C₂	semidirect
12. C₃×#2327	C₂	semidirect
13. C₃×#2320	C₂	semidirect
16. #35314	C₃	direct (N × H)
76. #2864	C₂×C₃	semidirect
77. #2863	C₂×C₃	semidirect
78. #2862	C₂×C₃	semidirect
82. #2524	C₂×C₃	semidirect
84. #2520	C₂×C₃	semidirect
86. #2331	C₂×C₃	semidirect
87. #2327	C₂×C₃	semidirect
88. #2320	C₂×C₃	semidirect
550. C₃	#35314	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×#2864	2
C₃×#2863	2
C₃×#2862	2
C₃×#2628	2
C₃×#2625	2
C₃×#2621	2
C₃×#2524	2
C₃×#2523	2
C₃×#2520	2
C₃×#2517	2
C₃×#2331	2
C₃×#2327	2
C₃×#2320	2
C₃×C₄×C₂²⋊Q₈	2
C₃×C₄×#117	2
#35314	3

Subgroups — C3×#35314 #10653921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35314 #10653921