Subgroups — C₃×#37142 #10655749

Order 768.

1472 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2860	C₂	1	1	yes	maximal, characteristic
3	C₃×#2809	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2808	C₂	1	1	yes	maximal, characteristic
5	C₃×#2806	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2804	C₂	1	1	yes	maximal, characteristic
7	C₃×#2766	C₂	1	2	yes	maximal, complemented
8	C₃×#2761	C₂	1	2	yes	maximal
9	C₃×#2759	C₂	1	2	yes	maximal, complemented
10	C₃×#2729	C₂	1	2	yes	maximal, complemented
11	C₃×#2716	C₂	1	2	yes	maximal, complemented
12	C₃×#2689	C₂	1	2	yes	maximal, complemented
13	C₃×#2637	C₂	1	2	yes	maximal, complemented
14	C₃×#2588	C₂	1	2	yes	maximal, complemented
15	C₃×#2560	C₂	1	2	yes	maximal
16	C₃×#2532	C₂	1	2	yes	maximal, complemented
17	C₃×#2527	C₂	1	2	yes	maximal, complemented
18	C₃×#2334	C₂	1	2	yes	maximal, complemented
19	C₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
20	#37142	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×#126	C₂²	1	2	yes	—
24	C₂×C₃×#126	C₂²	1	2	yes	—
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
27	C₃×#401	C₂²	1	2	yes	—
28	C₃×#400	C₂²	1	2	yes	—
29	C₃×#400	C₂²	1	2	yes	—
30	C₃×#400	C₂²	1	2	yes	—
31	C₃×#400	C₂²	1	2	yes	—
32	C₃×#398	C₂²	1	2	yes	—
33	C₃×#398	C₂²	1	2	yes	—
34	C₃×#398	C₂²	1	2	yes	—
35	C₃×#398	C₂²	1	2	yes	—
36	C₃×#398	C₂²	1	2	yes	—
37	C₃×#398	C₂²	1	2	yes	—
38	C₃×#397	C₂²	1	2	yes	—
39	C₃×#397	C₂²	1	2	yes	—
40	C₃×#397	C₂²	1	2	yes	—
41	C₃×#397	C₂²	1	2	yes	—
42	C₃×#396	C₂²	1	2	yes	—
43	C₃×#396	C₂²	1	2	yes	—
44	C₃×#395	C₂²	1	2	yes	—
45	C₃×#395	C₂²	1	2	yes	—
46	C₃×#394	C₂²	1	2	yes	—
47	C₃×#393	C₂²	1	2	yes	—
48	C₃×#393	C₂²	1	2	yes	—
49	C₃×#393	C₂²	1	2	yes	—
50	C₃×#393	C₂²	1	2	yes	—
51	C₃×#391	C₂²	1	2	yes	—
52	C₃×#391	C₂²	1	2	yes	—
53	C₃×#391	C₂²	1	2	yes	—
54	C₃×#391	C₂²	1	2	yes	—
55	C₃×#391	C₂²	1	1	yes	characteristic
56	C₃×#391	C₂²	1	1	yes	characteristic
57	C₃×#391	C₂²	1	1	yes	characteristic
58	C₃×#391	C₂²	1	1	yes	characteristic
59	C₃×#391	C₂²	1	1	yes	characteristic
60	C₃×#391	C₂²	1	1	yes	characteristic
61	C₃×#391	C₂²	1	2	yes	—
62	C₃×#390	C₂²	1	1	yes	characteristic
63	C₃×#390	C₂²	1	1	yes	characteristic
64	C₃×#390	C₂²	1	1	yes	characteristic
65	C₃×#389	C₂²	1	1	yes	characteristic
66	C₃×#389	C₂²	1	2	yes	—
67	C₃×#389	C₂²	1	2	yes	—
68	C₃×#389	C₂²	1	1	yes	characteristic
69	C₃×#389	C₂²	1	1	yes	characteristic
70	C₃×#389	C₂²	1	1	yes	characteristic
71	C₃×#389	C₂²	1	1	yes	characteristic
72	C₃×#388	C₂²	1	2	yes	—
73	C₃×#388	C₂²	1	2	yes	—
74	C₃×#388	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	—
76	C₃×#388	C₂²	1	2	yes	—
77	C₃×#388	C₂²	1	2	yes	—
78	C₃×#388	C₂²	1	2	yes	—
79	C₃×#388	C₂²	1	2	yes	—
80	C₃×#388	C₂²	1	2	yes	—
81	C₃×#388	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#387	C₂²	1	2	yes	—
84	C₃×#387	C₂²	1	2	yes	—
85	C₃×#387	C₂²	1	2	yes	—
86	C₃×#387	C₂²	1	2	yes	—
87	C₃×#387	C₂²	1	2	yes	—
88	C₃×#387	C₂²	1	2	yes	—
89	C₃×#387	C₂²	1	2	yes	—
90	C₃×#387	C₂²	1	2	yes	—
91	C₃×#387	C₂²	1	2	yes	—
92	C₃×#387	C₂²	1	2	yes	—
93	C₃×#387	C₂²	1	2	yes	—
94	C₃×#386	C₂²	1	2	yes	—
95	C₃×#385	C₂²	1	2	yes	—
96	C₃×#385	C₂²	1	2	yes	—
97	C₃×#385	C₂²	1	2	yes	—
98	C₃×#383	C₂²	1	2	yes	—
99	C₃×#382	C₂²	1	2	yes	—
100	C₃×#382	C₂²	1	2	yes	—
101	C₃×#381	C₂²	1	2	yes	—
102	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
103	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
104	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₃×#376	C₂²	1	2	yes	—
107	C₃×C₄³	C₂²	1	1	yes	characteristic
108	#2862	C₂×C₃	1	1	yes	characteristic, complemented
109	#2860	C₂×C₃	1	1	yes	characteristic
110	#2809	C₂×C₃	1	1	yes	characteristic, complemented
111	#2808	C₂×C₃	1	1	yes	characteristic
112	#2806	C₂×C₃	1	1	yes	characteristic, complemented
113	#2804	C₂×C₃	1	1	yes	characteristic
114	#2766	C₂×C₃	1	2	yes	complemented
115	#2761	C₂×C₃	1	2	yes	—
116	#2759	C₂×C₃	1	2	yes	complemented
117	#2729	C₂×C₃	1	2	yes	complemented
118	#2716	C₂×C₃	1	2	yes	complemented
119	#2689	C₂×C₃	1	2	yes	complemented
120	#2637	C₂×C₃	1	2	yes	complemented
121	#2588	C₂×C₃	1	2	yes	complemented
122	#2560	C₂×C₃	1	2	yes	—
123	#2532	C₂×C₃	1	2	yes	complemented
124	#2527	C₂×C₃	1	2	yes	complemented
125	#2334	C₂×C₃	1	2	yes	complemented
126	#2295	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
128	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
129	C₂²×C₃×Q₈	C₂³	1	2	yes	—
130	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
131	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
132	C₂³×C₃×C₄	C₂³	1	2	yes	—
133	C₃×C₄⋊Q₈	—	4	2	no	—
134	C₃×C₄⋊Q₈	—	4	2	no	—
135	C₃×#126	—	2	8	no	—
136	C₃×#126	—	4	4	no	—
137	C₃×C₂²⋊Q₈	—	4	4	no	—
138	C₃×C₄×Q₈	—	2	4	no	—
139	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄²	C₂³	1	2	yes	—
180	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
183	C₂×C₃×C₄²	C₂³	1	2	yes	—
184	C₂×C₃×C₄²	C₂³	1	2	yes	—
185	C₂×C₃×C₄²	C₂³	1	2	yes	—
186	C₂×C₃×C₄²	C₂³	1	2	yes	—
187	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
188	C₃×#95	C₂³	1	2	yes	—
189	C₃×#95	C₂³	1	2	yes	—
190	C₃×#95	C₂³	1	2	yes	—
191	C₃×#95	C₂³	1	2	yes	—
192	C₃×#95	C₂³	1	2	yes	—
193	C₃×#95	C₂³	1	2	yes	—
194	C₃×#95	C₂³	1	2	yes	—
195	C₃×#95	C₂³	1	2	yes	—
196	C₃×#95	C₂³	1	2	yes	—
197	C₃×#95	C₂³	1	2	yes	—
198	C₃×#95	C₂³	1	2	yes	—
199	C₃×#95	C₂³	1	2	yes	—
200	C₃×#95	C₂³	1	2	yes	—
201	C₃×#95	C₂³	1	2	yes	—
202	C₃×#95	C₂³	1	2	yes	—
203	C₃×#95	C₂³	1	2	yes	—
204	C₃×#95	C₂³	1	2	yes	—
205	C₃×#95	C₂³	1	2	yes	—
206	C₃×#95	C₂³	1	2	yes	—
207	C₃×#95	C₂³	1	2	yes	—
208	C₃×#95	C₂³	1	2	yes	—
209	C₃×#95	C₂³	1	2	yes	—
210	C₃×#95	C₂³	1	2	yes	—
211	C₃×#95	C₂³	1	2	yes	—
212	C₃×#95	C₂³	1	2	yes	—
213	C₃×#95	C₂³	1	2	yes	—
214	C₃×#95	C₂³	1	2	yes	—
215	C₃×#95	C₂³	1	2	yes	—
216	C₃×#95	C₂³	1	2	yes	—
217	C₃×#95	C₂³	1	2	yes	—
218	C₃×#95	C₂³	1	2	yes	—
219	C₃×#95	C₂³	1	2	yes	—
220	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
221	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
222	C₂×#126	C₂²×C₃	1	2	yes	—
223	C₂×#126	C₂²×C₃	1	2	yes	—
224	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
225	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
226	#401	C₂²×C₃	1	2	yes	—
227	#400	C₂²×C₃	1	2	yes	—
228	#400	C₂²×C₃	1	2	yes	—
229	#400	C₂²×C₃	1	2	yes	—
230	#400	C₂²×C₃	1	2	yes	—
231	#398	C₂²×C₃	1	2	yes	—
232	#398	C₂²×C₃	1	2	yes	—
233	#398	C₂²×C₃	1	2	yes	—
234	#398	C₂²×C₃	1	2	yes	—
235	#398	C₂²×C₃	1	2	yes	—
236	#398	C₂²×C₃	1	2	yes	—
237	#397	C₂²×C₃	1	2	yes	—
238	#397	C₂²×C₃	1	2	yes	—
239	#397	C₂²×C₃	1	2	yes	—
240	#397	C₂²×C₃	1	2	yes	—
241	#396	C₂²×C₃	1	2	yes	—
242	#396	C₂²×C₃	1	2	yes	—
243	#395	C₂²×C₃	1	2	yes	—
244	#395	C₂²×C₃	1	2	yes	—
245	#394	C₂²×C₃	1	2	yes	—
246	#393	C₂²×C₃	1	2	yes	—
247	#393	C₂²×C₃	1	2	yes	—
248	#393	C₂²×C₃	1	2	yes	—
249	#393	C₂²×C₃	1	2	yes	—
250	#391	C₂²×C₃	1	2	yes	—
251	#391	C₂²×C₃	1	2	yes	—
252	#391	C₂²×C₃	1	2	yes	—
253	#391	C₂²×C₃	1	1	yes	characteristic
254	#391	C₂²×C₃	1	1	yes	characteristic
255	#391	C₂²×C₃	1	1	yes	characteristic
256	#391	C₂²×C₃	1	1	yes	characteristic
257	#391	C₂²×C₃	1	2	yes	—
258	#391	C₂²×C₃	1	2	yes	—
259	#391	C₂²×C₃	1	1	yes	characteristic
260	#391	C₂²×C₃	1	1	yes	characteristic
261	#390	C₂²×C₃	1	1	yes	characteristic
262	#390	C₂²×C₃	1	1	yes	characteristic
263	#390	C₂²×C₃	1	1	yes	characteristic
264	#389	C₂²×C₃	1	1	yes	characteristic
265	#389	C₂²×C₃	1	2	yes	—
266	#389	C₂²×C₃	1	2	yes	—
267	#389	C₂²×C₃	1	1	yes	characteristic
268	#389	C₂²×C₃	1	1	yes	characteristic
269	#389	C₂²×C₃	1	1	yes	characteristic
270	#389	C₂²×C₃	1	1	yes	characteristic
271	#388	C₂²×C₃	1	2	yes	—
272	#388	C₂²×C₃	1	2	yes	—
273	#388	C₂²×C₃	1	2	yes	—
274	#388	C₂²×C₃	1	2	yes	—
275	#388	C₂²×C₃	1	2	yes	—
276	#388	C₂²×C₃	1	2	yes	—
277	#388	C₂²×C₃	1	2	yes	—
278	#388	C₂²×C₃	1	2	yes	—
279	#388	C₂²×C₃	1	2	yes	—
280	#388	C₂²×C₃	1	2	yes	—
281	#387	C₂²×C₃	1	2	yes	—
282	#387	C₂²×C₃	1	2	yes	—
283	#387	C₂²×C₃	1	2	yes	—
284	#387	C₂²×C₃	1	2	yes	—
285	#387	C₂²×C₃	1	2	yes	—
286	#387	C₂²×C₃	1	2	yes	—
287	#387	C₂²×C₃	1	2	yes	—
288	#387	C₂²×C₃	1	2	yes	—
289	#387	C₂²×C₃	1	2	yes	—
290	#387	C₂²×C₃	1	2	yes	—
291	#387	C₂²×C₃	1	2	yes	—
292	#387	C₂²×C₃	1	2	yes	—
293	#386	C₂²×C₃	1	2	yes	—
294	#385	C₂²×C₃	1	2	yes	—
295	#385	C₂²×C₃	1	2	yes	—
296	#385	C₂²×C₃	1	2	yes	—
297	#383	C₂²×C₃	1	2	yes	—
298	#382	C₂²×C₃	1	2	yes	—
299	#382	C₂²×C₃	1	2	yes	—
300	#381	C₂²×C₃	1	2	yes	—
301	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
302	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
303	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
304	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
305	#376	C₂²×C₃	1	2	yes	—
306	C₄³	C₂²×C₃	1	1	yes	characteristic
307	C₂⁴×C₃	C₂⁴	1	2	yes	—
308	C₂×C₃×Q₈	—	2	2	no	—
309	C₂×C₃×Q₈	—	2	4	no	—
310	C₂×C₃×Q₈	—	2	2	no	—
311	C₂×C₃×Q₈	—	2	2	no	—
312	C₂×C₃×Q₈	—	4	1	no	—
313	C₂×C₃×Q₈	—	4	1	no	—
314	C₂×C₃×Q₈	—	4	1	no	—
315	C₂×C₃×Q₈	—	4	1	no	—
316	C₂×C₃×Q₈	—	4	1	no	—
317	C₂×C₃×Q₈	—	4	2	no	—
318	C₂×C₃×Q₈	—	4	1	no	—
319	C₂×C₃×Q₈	—	4	2	no	—
320	C₂×C₃×D₄	—	2	2	no	—
321	C₂×C₃×D₄	—	4	1	no	—
322	C₂×C₃×D₄	—	4	1	no	—
323	C₂²×C₃×C₄	—	4	2	no	—
324	C₂²×C₃×C₄	—	4	2	no	—
325	C₂²×C₃×C₄	—	4	2	no	—
326	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
327	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
328	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
329	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
330	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
331	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
332	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
333	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
334	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
335	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
336	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
337	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
338	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
339	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
340	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
341	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
342	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
343	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
344	C₃×C₄⋊C₄	—	2	2	no	—
345	C₃×C₄⋊C₄	—	2	4	no	—
346	C₃×C₄⋊C₄	—	2	4	no	—
347	C₃×C₄⋊C₄	—	2	4	no	—
348	C₃×C₄⋊C₄	—	2	4	no	—
349	C₃×C₄⋊C₄	—	2	4	no	—
350	C₃×C₄⋊C₄	—	2	4	no	—
351	C₃×C₄⋊C₄	—	2	4	no	—
352	C₃×C₄⋊C₄	—	2	2	no	—
353	C₃×C₄⋊C₄	—	4	1	no	—
354	C₃×C₄⋊C₄	—	4	1	no	—
355	C₃×C₄⋊C₄	—	4	1	no	—
356	C₃×C₄⋊C₄	—	4	1	no	—
357	C₃×C₄⋊C₄	—	4	2	no	—
358	C₃×C₄⋊C₄	—	4	2	no	—
359	C₃×C₄⋊C₄	—	4	2	no	—
360	C₃×C₄⋊C₄	—	4	2	no	—
361	C₃×C₄⋊C₄	—	4	2	no	—
362	C₃×C₄⋊C₄	—	4	2	no	—
363	C₃×C₄⋊C₄	—	4	2	no	—
364	C₃×C₄⋊C₄	—	4	2	no	—
365	C₃×C₄⋊C₄	—	4	2	no	—
366	C₃×C₄⋊C₄	—	4	1	no	—
367	C₃×C₄⋊C₄	—	4	1	no	—
368	C₃×C₂²⋊C₄	—	2	4	no	—
369	C₃×C₂²⋊C₄	—	2	4	no	—
370	C₃×C₂²⋊C₄	—	2	4	no	—
371	C₃×C₂²⋊C₄	—	2	4	no	—
372	C₃×C₂²⋊C₄	—	2	4	no	—
373	C₃×C₂²⋊C₄	—	4	2	no	—
374	C₃×C₂²⋊C₄	—	4	2	no	—
375	C₃×C₂²⋊C₄	—	4	2	no	—
376	C₃×C₂²⋊C₄	—	4	2	no	—
377	C₃×C₂²⋊C₄	—	4	2	no	—
378	C₃×C₂²⋊C₄	—	4	2	no	—
379	C₃×C₂²⋊C₄	—	4	2	no	—
380	C₃×C₂²⋊C₄	—	4	2	no	—
381	C₃×C₄²	—	2	4	no	—
382	C₃×C₄²	—	2	2	no	—
383	C₃×C₄²	—	2	2	no	—
384	C₃×C₄²	—	2	2	no	—
385	C₃×C₄²	—	4	1	no	—
386	C₃×C₄²	—	4	2	no	—
387	C₃×C₄²	—	4	1	no	—
388	C₃×C₄²	—	4	1	no	—
389	C₃×C₄²	—	4	2	no	—
390	C₃×C₄²	—	4	2	no	—
391	C₃×C₄²	—	4	2	no	—
392	C₃×C₄²	#41	1	4	yes	—
393	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
394	C₂²×Q₈	C₂³×C₃	1	2	yes	—
395	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
396	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
397	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₃	1	2	yes	—
399	C₄⋊Q₈	—	4	2	no	—
400	C₄⋊Q₈	—	4	2	no	—
401	#126	—	2	8	no	—
402	#126	—	4	4	no	—
403	C₂²⋊Q₈	—	4	4	no	—
404	C₄×Q₈	—	2	4	no	—
405	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
442	C₂×C₄²	C₂³×C₃	1	2	yes	—
443	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
446	C₂×C₄²	C₂³×C₃	1	2	yes	—
447	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₃	1	2	yes	—
451	C₂×C₄²	C₂³×C₃	1	2	yes	—
452	C₂×C₄²	C₂³×C₃	1	2	yes	—
453	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
454	#95	C₂³×C₃	1	2	yes	—
455	#95	C₂³×C₃	1	2	yes	—
456	#95	C₂³×C₃	1	2	yes	—
457	#95	C₂³×C₃	1	2	yes	—
458	#95	C₂³×C₃	1	2	yes	—
459	#95	C₂³×C₃	1	2	yes	—
460	#95	C₂³×C₃	1	2	yes	—
461	#95	C₂³×C₃	1	2	yes	—
462	#95	C₂³×C₃	1	2	yes	—
463	#95	C₂³×C₃	1	2	yes	—
464	#95	C₂³×C₃	1	2	yes	—
465	#95	C₂³×C₃	1	2	yes	—
466	#95	C₂³×C₃	1	2	yes	—
467	#95	C₂³×C₃	1	2	yes	—
468	#95	C₂³×C₃	1	2	yes	—
469	#95	C₂³×C₃	1	2	yes	—
470	#95	C₂³×C₃	1	2	yes	—
471	#95	C₂³×C₃	1	2	yes	—
472	#95	C₂³×C₃	1	2	yes	—
473	#95	C₂³×C₃	1	2	yes	—
474	#95	C₂³×C₃	1	2	yes	—
475	#95	C₂³×C₃	1	2	yes	—
476	#95	C₂³×C₃	1	2	yes	—
477	#95	C₂³×C₃	1	2	yes	—
478	#95	C₂³×C₃	1	2	yes	—
479	#95	C₂³×C₃	1	2	yes	—
480	#95	C₂³×C₃	1	2	yes	—
481	#95	C₂³×C₃	1	2	yes	—
482	#95	C₂³×C₃	1	2	yes	—
483	#95	C₂³×C₃	1	2	yes	—
484	#95	C₂³×C₃	1	2	yes	—
485	#95	C₂³×C₃	1	2	yes	—
486	C₂³×C₃	—	2	2	no	—
487	C₂³×C₃	—	2	2	no	—
488	C₂³×C₃	—	2	2	no	—
489	C₂³×C₃	—	2	2	no	—
490	C₂³×C₃	—	2	2	no	—
491	C₂³×C₃	—	2	2	no	—
492	C₂³×C₃	—	2	2	no	—
493	C₂³×C₃	C₂⁵	1	1	yes	characteristic
494	C₃×Q₈	—	4	4	no	—
495	C₃×Q₈	—	8	4	no	—
496	C₃×Q₈	—	8	2	no	—
497	C₃×Q₈	—	8	2	no	—
498	C₃×D₄	—	8	2	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	1	no	—
501	C₂×C₃×C₄	—	2	1	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	1	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	2	no	—
512	C₂×C₃×C₄	—	2	2	no	—
513	C₂×C₃×C₄	—	2	2	no	—
514	C₂×C₃×C₄	—	2	2	no	—
515	C₂×C₃×C₄	—	2	2	no	—
516	C₂×C₃×C₄	—	2	2	no	—
517	C₂×C₃×C₄	—	2	2	no	—
518	C₂×C₃×C₄	—	2	2	no	—
519	C₂×C₃×C₄	—	2	2	no	—
520	C₂×C₃×C₄	—	2	2	no	—
521	C₂×C₃×C₄	—	2	2	no	—
522	C₂×C₃×C₄	—	2	2	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	1	no	—
525	C₂×C₃×C₄	—	2	2	no	—
526	C₂×C₃×C₄	—	2	2	no	—
527	C₂×C₃×C₄	—	2	2	no	—
528	C₂×C₃×C₄	—	2	2	no	—
529	C₂×C₃×C₄	—	2	2	no	—
530	C₂×C₃×C₄	—	2	2	no	—
531	C₂×C₃×C₄	—	2	2	no	—
532	C₂×C₃×C₄	—	2	1	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	2	2	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	—	2	2	no	—
539	C₂×C₃×C₄	—	2	2	no	—
540	C₂×C₃×C₄	—	2	2	no	—
541	C₂×C₃×C₄	—	2	2	no	—
542	C₂×C₃×C₄	—	2	2	no	—
543	C₂×C₃×C₄	—	2	2	no	—
544	C₂×C₃×C₄	—	2	2	no	—
545	C₂×C₃×C₄	—	2	2	no	—
546	C₂×C₃×C₄	—	2	2	no	—
547	C₂×C₃×C₄	—	8	4	no	—
548	C₂×C₃×C₄	C₂×#41	1	2	yes	—
549	C₂×C₃×C₄	C₂×#41	1	2	yes	—
550	C₂×C₃×C₄	C₂×#41	1	2	yes	—
551	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
552	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
553	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
554	C₂⁴	C₂⁴×C₃	1	2	yes	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	4	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	4	1	no	—
560	C₂×Q₈	—	4	1	no	—
561	C₂×Q₈	—	4	1	no	—
562	C₂×Q₈	—	4	1	no	—
563	C₂×Q₈	—	4	1	no	—
564	C₂×Q₈	—	4	2	no	—
565	C₂×Q₈	—	4	1	no	—
566	C₂×Q₈	—	4	2	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	4	1	no	—
569	C₂×D₄	—	4	1	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	4	2	no	—
601	C₄⋊C₄	—	4	2	no	—
602	C₄⋊C₄	—	4	2	no	—
603	C₄⋊C₄	—	4	2	no	—
604	C₄⋊C₄	—	4	2	no	—
605	C₄⋊C₄	—	4	1	no	—
606	C₄⋊C₄	—	4	1	no	—
607	C₄⋊C₄	—	4	1	no	—
608	C₄⋊C₄	—	4	1	no	—
609	C₄⋊C₄	—	4	1	no	—
610	C₄⋊C₄	—	4	1	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₂²⋊C₄	—	4	2	no	—
624	C₂²⋊C₄	—	4	2	no	—
625	C₂²⋊C₄	—	4	2	no	—
626	C₂²⋊C₄	—	4	2	no	—
627	C₂²⋊C₄	—	4	2	no	—
628	C₄²	—	2	4	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	4	2	no	—
633	C₄²	—	4	1	no	—
634	C₄²	—	4	2	no	—
635	C₄²	—	4	1	no	—
636	C₄²	—	4	1	no	—
637	C₄²	—	4	2	no	—
638	C₄²	—	4	2	no	—
639	C₄²	C₃×#41	1	4	yes	—
640	C₂²×C₃	—	4	2	no	—
641	C₂²×C₃	—	4	2	no	—
642	C₂²×C₃	—	4	2	no	—
643	C₂²×C₃	—	4	2	no	—
644	C₂²×C₃	—	4	2	no	—
645	C₂²×C₃	—	4	2	no	—
646	C₂²×C₃	—	4	2	no	—
647	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
648	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
649	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
650	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
651	C₂²×C₃	#585	1	1	yes	characteristic
652	C₂²×C₃	#585	1	1	yes	characteristic
653	C₂²×C₃	#585	1	1	yes	characteristic
654	C₃×C₄	—	2	2	no	—
655	C₃×C₄	—	2	2	no	—
656	C₃×C₄	—	2	2	no	—
657	C₃×C₄	—	2	2	no	—
658	C₃×C₄	—	2	2	no	—
659	C₃×C₄	—	2	2	no	—
660	C₃×C₄	—	4	2	no	—
661	C₃×C₄	—	4	2	no	—
662	C₃×C₄	—	4	2	no	—
663	C₃×C₄	—	4	2	no	—
664	C₃×C₄	—	4	2	no	—
665	C₃×C₄	—	4	2	no	—
666	C₃×C₄	—	4	2	no	—
667	C₃×C₄	—	4	2	no	—
668	C₃×C₄	—	4	1	no	—
669	C₃×C₄	—	4	2	no	—
670	C₃×C₄	—	4	2	no	—
671	C₃×C₄	—	4	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	C₂⁵×C₃	1	1	yes	characteristic
680	Q₈	—	4	4	no	—
681	Q₈	—	8	4	no	—
682	Q₈	—	8	2	no	—
683	Q₈	—	8	2	no	—
684	D₄	—	8	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	8	4	no	—
734	C₂×C₄	C₂×C₃×#41	1	2	yes	—
735	C₂×C₄	C₂×C₃×#41	1	2	yes	—
736	C₂×C₄	C₂×C₃×#41	1	2	yes	—
737	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
738	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
739	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
740	C₂×C₃	—	8	2	no	—
741	C₂×C₃	#3455	1	1	yes	characteristic
742	C₂×C₃	#3507	1	1	yes	characteristic
743	C₂×C₃	#3511	1	1	yes	characteristic
744	C₂×C₃	#3545	1	1	yes	characteristic
745	C₂×C₃	#3555	1	1	yes	characteristic
746	C₂×C₃	#3561	1	1	yes	characteristic
747	C₂×C₃	#3564	1	1	yes	characteristic
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
756	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
757	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
758	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
759	C₂²	C₃×#585	1	1	yes	characteristic
760	C₂²	C₃×#585	1	1	yes	characteristic
761	C₂²	C₃×#585	1	1	yes	characteristic
762	C₄	—	2	2	no	—
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	1	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₃	#37142	1	1	yes	characteristic, direct product factor, Sylow
781	C₂	—	8	2	no	—
782	C₂	C₃×#3455	1	1	yes	characteristic
783	C₂	C₃×#3507	1	1	yes	characteristic
784	C₂	C₃×#3511	1	1	yes	characteristic
785	C₂	C₃×#3545	1	1	yes	characteristic
786	C₂	C₃×#3555	1	1	yes	characteristic
787	C₂	C₃×#3561	1	1	yes	characteristic
788	C₂	C₃×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
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×#2862	C₂	semidirect
3. C₃×#2809	C₂	semidirect
5. C₃×#2806	C₂	semidirect
7. C₃×#2766	C₂	semidirect
9. C₃×#2759	C₂	semidirect
10. C₃×#2729	C₂	semidirect
11. C₃×#2716	C₂	semidirect
12. C₃×#2689	C₂	semidirect
13. C₃×#2637	C₂	semidirect
14. C₃×#2588	C₂	semidirect
16. C₃×#2532	C₂	semidirect
17. C₃×#2527	C₂	semidirect
18. C₃×#2334	C₂	semidirect
19. C₃×#2295	C₂	semidirect
20. #37142	C₃	direct (N × H)
108. #2862	C₂×C₃	semidirect
110. #2809	C₂×C₃	semidirect
112. #2806	C₂×C₃	semidirect
114. #2766	C₂×C₃	semidirect
116. #2759	C₂×C₃	semidirect
117. #2729	C₂×C₃	semidirect
118. #2716	C₂×C₃	semidirect
119. #2689	C₂×C₃	semidirect
120. #2637	C₂×C₃	semidirect
121. #2588	C₂×C₃	semidirect
123. #2532	C₂×C₃	semidirect
124. #2527	C₂×C₃	semidirect
125. #2334	C₂×C₃	semidirect
126. #2295	C₂×C₃	semidirect
780. C₃	#37142	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×#2862	2
C₃×#2860	2
C₃×#2809	2
C₃×#2808	2
C₃×#2806	2
C₃×#2804	2
C₃×#2766	2
C₃×#2761	2
C₃×#2759	2
C₃×#2729	2
C₃×#2716	2
C₃×#2689	2
C₃×#2637	2
C₃×#2588	2
C₃×#2560	2
C₃×#2532	2
C₃×#2527	2
C₃×#2334	2
C₃×#2295	2
#37142	3

Subgroups — C3×#37142 #10655749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37142 #10655749