Subgroups — C₃×#37255 #10655862

Order 768.

1396 conjugacy classes of subgroups.

The subgroup lattice has 728 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
2	C₃×#2864	C₂	1	1	yes	maximal, characteristic
3	C₃×#2810	C₂	1	1	yes	maximal, characteristic
4	C₃×#2791	C₂	1	2	yes	maximal
5	C₃×#2766	C₂	1	2	yes	maximal
6	C₃×#2762	C₂	1	2	yes	maximal
7	C₃×#2755	C₂	1	2	yes	maximal
8	C₃×#2726	C₂	1	1	yes	maximal, characteristic
9	C₃×#2726	C₂	1	1	yes	maximal, characteristic
10	C₃×#2726	C₂	1	1	yes	maximal, characteristic
11	C₃×#2719	C₂	1	2	yes	maximal
12	C₃×#2713	C₂	1	2	yes	maximal
13	C₃×#2655	C₂	1	2	yes	maximal
14	C₃×#2590	C₂	1	2	yes	maximal
15	C₃×#2585	C₂	1	2	yes	maximal
16	C₃×#2462	C₂	1	2	yes	maximal
17	C₃×#2453	C₂	1	2	yes	maximal
18	C₃×#2336	C₂	1	2	yes	maximal
19	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
20	#37255	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×#125	C₂²	1	2	yes	—
23	C₂×C₃×#125	C₂²	1	2	yes	—
24	C₂×C₃×#125	C₂²	1	2	yes	—
25	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
26	C₃×#401	C₂²	1	2	yes	—
27	C₃×#400	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×#400	C₂²	1	2	yes	—
33	C₃×#400	C₂²	1	2	yes	—
34	C₃×#400	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×#398	C₂²	1	2	yes	—
39	C₃×#398	C₂²	1	2	yes	—
40	C₃×#398	C₂²	1	2	yes	—
41	C₃×#398	C₂²	1	2	yes	—
42	C₃×#398	C₂²	1	2	yes	—
43	C₃×#398	C₂²	1	2	yes	—
44	C₃×#398	C₂²	1	2	yes	—
45	C₃×#398	C₂²	1	2	yes	—
46	C₃×#398	C₂²	1	2	yes	—
47	C₃×#398	C₂²	1	2	yes	—
48	C₃×#395	C₂²	1	2	yes	—
49	C₃×#395	C₂²	1	2	yes	—
50	C₃×#391	C₂²	1	2	yes	—
51	C₃×#391	C₂²	1	2	yes	—
52	C₃×#391	C₂²	1	2	yes	—
53	C₃×#389	C₂²	1	2	yes	—
54	C₃×#389	C₂²	1	1	yes	characteristic
55	C₃×#389	C₂²	1	2	yes	—
56	C₃×#389	C₂²	1	2	yes	—
57	C₃×#389	C₂²	1	2	yes	—
58	C₃×#389	C₂²	1	1	yes	characteristic
59	C₃×#389	C₂²	1	2	yes	—
60	C₃×#389	C₂²	1	2	yes	—
61	C₃×#389	C₂²	1	1	yes	characteristic
62	C₃×#389	C₂²	1	1	yes	characteristic
63	C₃×#389	C₂²	1	1	yes	characteristic
64	C₃×#389	C₂²	1	2	yes	—
65	C₃×#389	C₂²	1	2	yes	—
66	C₃×#389	C₂²	1	1	yes	characteristic
67	C₃×#389	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	2	yes	—
72	C₃×#387	C₂²	1	2	yes	—
73	C₃×#387	C₂²	1	2	yes	—
74	C₃×#387	C₂²	1	2	yes	—
75	C₃×#387	C₂²	1	2	yes	—
76	C₃×#387	C₂²	1	2	yes	—
77	C₃×#387	C₂²	1	2	yes	—
78	C₃×#387	C₂²	1	2	yes	—
79	C₃×#387	C₂²	1	2	yes	—
80	C₃×#387	C₂²	1	2	yes	—
81	C₃×#387	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×#387	C₂²	1	2	yes	—
95	C₃×#387	C₂²	1	2	yes	—
96	C₃×#384	C₂²	1	1	yes	characteristic
97	C₃×#383	C₂²	1	2	yes	—
98	C₃×#382	C₂²	1	1	yes	characteristic
99	C₃×#382	C₂²	1	1	yes	characteristic
100	C₃×#382	C₂²	1	1	yes	characteristic
101	C₃×#382	C₂²	1	1	yes	characteristic
102	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
104	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
105	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
106	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₃×C₄³	C₂²	1	1	yes	characteristic
108	#2864	C₂×C₃	1	1	yes	characteristic
109	#2864	C₂×C₃	1	1	yes	characteristic
110	#2810	C₂×C₃	1	1	yes	characteristic
111	#2791	C₂×C₃	1	2	yes	—
112	#2766	C₂×C₃	1	2	yes	—
113	#2762	C₂×C₃	1	2	yes	—
114	#2755	C₂×C₃	1	2	yes	—
115	#2726	C₂×C₃	1	1	yes	characteristic
116	#2726	C₂×C₃	1	1	yes	characteristic
117	#2726	C₂×C₃	1	1	yes	characteristic
118	#2719	C₂×C₃	1	2	yes	—
119	#2713	C₂×C₃	1	2	yes	—
120	#2655	C₂×C₃	1	2	yes	—
121	#2590	C₂×C₃	1	2	yes	—
122	#2585	C₂×C₃	1	2	yes	—
123	#2462	C₂×C₃	1	2	yes	—
124	#2453	C₂×C₃	1	2	yes	—
125	#2336	C₂×C₃	1	2	yes	—
126	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
127	C₂²×C₃×Q₈	C₂³	1	2	yes	—
128	C₃×C₄⋊Q₈	—	2	4	no	—
129	C₃×#125	—	2	8	no	—
130	C₃×#125	—	4	4	no	—
131	C₃×#125	—	4	4	no	—
132	C₃×C₄×Q₈	—	4	4	no	—
133	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
154	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄²	C₂³	1	2	yes	—
177	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄²	C₂³	1	2	yes	—
179	C₂×C₃×C₄²	C₂³	1	2	yes	—
180	C₂×C₃×C₄²	C₂³	1	2	yes	—
181	C₂×C₃×C₄²	C₂³	1	2	yes	—
182	C₂×C₃×C₄²	C₂³	1	2	yes	—
183	C₃×#95	C₂³	1	2	yes	—
184	C₃×#95	C₂³	1	2	yes	—
185	C₃×#95	C₂³	1	2	yes	—
186	C₃×#95	C₂³	1	2	yes	—
187	C₃×#95	C₂³	1	2	yes	—
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	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
220	C₂×#125	C₂²×C₃	1	2	yes	—
221	C₂×#125	C₂²×C₃	1	2	yes	—
222	C₂×#125	C₂²×C₃	1	2	yes	—
223	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
224	#401	C₂²×C₃	1	2	yes	—
225	#400	C₂²×C₃	1	2	yes	—
226	#400	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	#400	C₂²×C₃	1	2	yes	—
232	#400	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	#398	C₂²×C₃	1	2	yes	—
238	#398	C₂²×C₃	1	2	yes	—
239	#398	C₂²×C₃	1	2	yes	—
240	#398	C₂²×C₃	1	2	yes	—
241	#398	C₂²×C₃	1	2	yes	—
242	#398	C₂²×C₃	1	2	yes	—
243	#398	C₂²×C₃	1	2	yes	—
244	#398	C₂²×C₃	1	2	yes	—
245	#398	C₂²×C₃	1	2	yes	—
246	#395	C₂²×C₃	1	2	yes	—
247	#395	C₂²×C₃	1	2	yes	—
248	#391	C₂²×C₃	1	2	yes	—
249	#391	C₂²×C₃	1	2	yes	—
250	#391	C₂²×C₃	1	2	yes	—
251	#389	C₂²×C₃	1	2	yes	—
252	#389	C₂²×C₃	1	1	yes	characteristic
253	#389	C₂²×C₃	1	1	yes	characteristic
254	#389	C₂²×C₃	1	1	yes	characteristic
255	#389	C₂²×C₃	1	2	yes	—
256	#389	C₂²×C₃	1	2	yes	—
257	#389	C₂²×C₃	1	1	yes	characteristic
258	#389	C₂²×C₃	1	2	yes	—
259	#389	C₂²×C₃	1	2	yes	—
260	#389	C₂²×C₃	1	2	yes	—
261	#389	C₂²×C₃	1	1	yes	characteristic
262	#389	C₂²×C₃	1	1	yes	characteristic
263	#389	C₂²×C₃	1	1	yes	characteristic
264	#389	C₂²×C₃	1	1	yes	characteristic
265	#389	C₂²×C₃	1	1	yes	characteristic
266	#389	C₂²×C₃	1	1	yes	characteristic
267	#389	C₂²×C₃	1	2	yes	—
268	#389	C₂²×C₃	1	2	yes	—
269	#387	C₂²×C₃	1	2	yes	—
270	#387	C₂²×C₃	1	2	yes	—
271	#387	C₂²×C₃	1	2	yes	—
272	#387	C₂²×C₃	1	2	yes	—
273	#387	C₂²×C₃	1	2	yes	—
274	#387	C₂²×C₃	1	2	yes	—
275	#387	C₂²×C₃	1	2	yes	—
276	#387	C₂²×C₃	1	2	yes	—
277	#387	C₂²×C₃	1	2	yes	—
278	#387	C₂²×C₃	1	2	yes	—
279	#387	C₂²×C₃	1	2	yes	—
280	#387	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	#387	C₂²×C₃	1	2	yes	—
294	#384	C₂²×C₃	1	1	yes	characteristic
295	#383	C₂²×C₃	1	2	yes	—
296	#382	C₂²×C₃	1	1	yes	characteristic
297	#382	C₂²×C₃	1	1	yes	characteristic
298	#382	C₂²×C₃	1	1	yes	characteristic
299	#382	C₂²×C₃	1	1	yes	characteristic
300	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
301	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
302	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
303	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
304	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
305	C₄³	C₂²×C₃	1	1	yes	characteristic
306	C₂×C₃×Q₈	—	2	4	no	—
307	C₂×C₃×Q₈	—	2	4	no	—
308	C₂×C₃×Q₈	—	4	2	no	—
309	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
310	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
311	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
312	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
313	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
314	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
315	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
316	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
317	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
318	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
319	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
320	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
321	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
322	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
323	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
324	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
325	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
326	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
327	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
328	C₃×C₄⋊C₄	—	2	4	no	—
329	C₃×C₄⋊C₄	—	2	4	no	—
330	C₃×C₄⋊C₄	—	2	4	no	—
331	C₃×C₄⋊C₄	—	2	4	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	—	2	4	no	—
336	C₃×C₄⋊C₄	—	2	4	no	—
337	C₃×C₄⋊C₄	—	2	2	no	—
338	C₃×C₄⋊C₄	—	2	2	no	—
339	C₃×C₄⋊C₄	—	2	4	no	—
340	C₃×C₄⋊C₄	—	2	4	no	—
341	C₃×C₄⋊C₄	—	2	4	no	—
342	C₃×C₄⋊C₄	—	2	4	no	—
343	C₃×C₄⋊C₄	—	2	2	no	—
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	—	4	1	no	—
349	C₃×C₄⋊C₄	—	4	1	no	—
350	C₃×C₄⋊C₄	—	4	1	no	—
351	C₃×C₄⋊C₄	—	4	1	no	—
352	C₃×C₄⋊C₄	—	4	1	no	—
353	C₃×C₄⋊C₄	—	4	1	no	—
354	C₃×C₄⋊C₄	—	4	2	no	—
355	C₃×C₄⋊C₄	—	4	2	no	—
356	C₃×C₄⋊C₄	—	4	2	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	#41	1	4	yes	—
365	C₃×C₄²	—	2	4	no	—
366	C₃×C₄²	—	2	2	no	—
367	C₃×C₄²	—	2	2	no	—
368	C₃×C₄²	—	2	2	no	—
369	C₃×C₄²	—	2	2	no	—
370	C₃×C₄²	—	2	2	no	—
371	C₃×C₄²	—	2	2	no	—
372	C₃×C₄²	—	4	1	no	—
373	C₃×C₄²	—	4	2	no	—
374	C₃×C₄²	—	4	2	no	—
375	C₃×C₄²	—	4	2	no	—
376	C₃×C₄²	—	4	2	no	—
377	C₃×C₄²	—	4	2	no	—
378	C₂²×Q₈	C₂³×C₃	1	2	yes	—
379	C₄⋊Q₈	—	2	4	no	—
380	#125	—	2	8	no	—
381	#125	—	4	4	no	—
382	#125	—	4	4	no	—
383	C₄×Q₈	—	4	4	no	—
384	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₃	1	2	yes	—
423	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₃	1	2	yes	—
429	C₂×C₄²	C₂³×C₃	1	2	yes	—
430	C₂×C₄²	C₂³×C₃	1	2	yes	—
431	C₂×C₄²	C₂³×C₃	1	2	yes	—
432	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₃	1	2	yes	—
434	#95	C₂³×C₃	1	2	yes	—
435	#95	C₂³×C₃	1	2	yes	—
436	#95	C₂³×C₃	1	2	yes	—
437	#95	C₂³×C₃	1	2	yes	—
438	#95	C₂³×C₃	1	2	yes	—
439	#95	C₂³×C₃	1	2	yes	—
440	#95	C₂³×C₃	1	2	yes	—
441	#95	C₂³×C₃	1	2	yes	—
442	#95	C₂³×C₃	1	2	yes	—
443	#95	C₂³×C₃	1	2	yes	—
444	#95	C₂³×C₃	1	2	yes	—
445	#95	C₂³×C₃	1	2	yes	—
446	#95	C₂³×C₃	1	2	yes	—
447	#95	C₂³×C₃	1	2	yes	—
448	#95	C₂³×C₃	1	2	yes	—
449	#95	C₂³×C₃	1	2	yes	—
450	#95	C₂³×C₃	1	2	yes	—
451	#95	C₂³×C₃	1	2	yes	—
452	#95	C₂³×C₃	1	2	yes	—
453	#95	C₂³×C₃	1	2	yes	—
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	C₂³×C₃	C₂⁵	1	1	yes	characteristic
471	C₃×Q₈	—	4	8	no	—
472	C₂×C₃×C₄	—	2	1	no	—
473	C₂×C₃×C₄	—	2	1	no	—
474	C₂×C₃×C₄	—	2	1	no	—
475	C₂×C₃×C₄	—	2	1	no	—
476	C₂×C₃×C₄	—	2	2	no	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	2	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	2	no	—
487	C₂×C₃×C₄	—	2	2	no	—
488	C₂×C₃×C₄	—	2	2	no	—
489	C₂×C₃×C₄	—	2	2	no	—
490	C₂×C₃×C₄	—	2	2	no	—
491	C₂×C₃×C₄	—	2	2	no	—
492	C₂×C₃×C₄	—	2	2	no	—
493	C₂×C₃×C₄	—	2	2	no	—
494	C₂×C₃×C₄	—	2	2	no	—
495	C₂×C₃×C₄	—	2	2	no	—
496	C₂×C₃×C₄	—	2	2	no	—
497	C₂×C₃×C₄	—	2	2	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	1	no	—
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	—	2	2	no	—
510	C₂×C₃×C₄	—	2	2	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	C₂×#41	1	2	yes	—
523	C₂×C₃×C₄	C₂×#41	1	4	yes	—
524	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
525	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
526	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
527	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
528	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
529	C₂×Q₈	—	2	4	no	—
530	C₂×Q₈	—	2	4	no	—
531	C₂×Q₈	—	4	2	no	—
532	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
537	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
545	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	4	2	no	—
572	C₄⋊C₄	—	4	2	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	2	no	—
575	C₄⋊C₄	—	4	2	no	—
576	C₄⋊C₄	—	4	2	no	—
577	C₄⋊C₄	—	4	2	no	—
578	C₄⋊C₄	—	4	1	no	—
579	C₄⋊C₄	—	4	1	no	—
580	C₄⋊C₄	—	4	1	no	—
581	C₄⋊C₄	—	4	1	no	—
582	C₄⋊C₄	—	4	1	no	—
583	C₄⋊C₄	—	4	1	no	—
584	C₄⋊C₄	—	4	2	no	—
585	C₄⋊C₄	—	4	2	no	—
586	C₄⋊C₄	—	4	2	no	—
587	C₄⋊C₄	C₃×#41	1	4	yes	—
588	C₄²	—	2	4	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	2	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	4	2	no	—
596	C₄²	—	4	2	no	—
597	C₄²	—	4	2	no	—
598	C₄²	—	4	2	no	—
599	C₄²	—	4	1	no	—
600	C₄²	—	4	2	no	—
601	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
602	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
603	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
604	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
605	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
606	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
607	C₂²×C₃	#585	1	1	yes	characteristic
608	C₃×C₄	—	2	2	no	—
609	C₃×C₄	—	2	4	no	—
610	C₃×C₄	—	2	2	no	—
611	C₃×C₄	—	2	2	no	—
612	C₃×C₄	—	2	2	no	—
613	C₃×C₄	—	2	2	no	—
614	C₃×C₄	—	2	2	no	—
615	C₃×C₄	—	4	2	no	—
616	C₃×C₄	—	4	2	no	—
617	C₃×C₄	—	4	2	no	—
618	C₃×C₄	—	4	2	no	—
619	C₃×C₄	—	4	2	no	—
620	C₃×C₄	—	4	2	no	—
621	C₃×C₄	—	4	2	no	—
622	C₃×C₄	—	4	1	no	—
623	C₃×C₄	—	4	2	no	—
624	C₃×C₄	—	4	2	no	—
625	C₃×C₄	—	4	2	no	—
626	C₃×C₄	—	4	2	no	—
627	C₂³	C₂⁵×C₃	1	1	yes	characteristic
628	Q₈	—	4	8	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
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	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	C₂×C₃×#41	1	2	yes	—
680	C₂×C₄	C₂×C₃×#41	1	4	yes	—
681	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
682	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
683	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
684	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
685	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
686	C₂×C₃	#3461	1	1	yes	characteristic
687	C₂×C₃	#3520	1	1	yes	characteristic
688	C₂×C₃	#3523	1	1	yes	characteristic
689	C₂×C₃	#3552	1	1	yes	characteristic
690	C₂×C₃	#3556	1	1	yes	characteristic
691	C₂×C₃	#3559	1	1	yes	characteristic
692	C₂×C₃	#3563	1	1	yes	characteristic
693	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
694	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
695	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
696	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
697	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
698	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
699	C₂²	C₃×#585	1	1	yes	characteristic
700	C₄	—	2	2	no	—
701	C₄	—	2	4	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	1	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₃	#37255	1	1	yes	characteristic, direct product factor, Sylow
720	C₂	C₃×#3461	1	1	yes	characteristic
721	C₂	C₃×#3520	1	1	yes	characteristic
722	C₂	C₃×#3523	1	1	yes	characteristic
723	C₂	C₃×#3552	1	1	yes	characteristic
724	C₂	C₃×#3556	1	1	yes	characteristic
725	C₂	C₃×#3559	1	1	yes	characteristic
726	C₂	C₃×#3563	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
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
20. #37255	C₃	direct (N × H)
719. C₃	#37255	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×#2810	2
C₃×#2791	2
C₃×#2766	2
C₃×#2762	2
C₃×#2755	2
C₃×#2726	2
C₃×#2719	2
C₃×#2713	2
C₃×#2655	2
C₃×#2590	2
C₃×#2585	2
C₃×#2462	2
C₃×#2453	2
C₃×#2336	2
C₃×C₄×C₄⋊Q₈	2
#37255	3

Subgroups — C3×#37255 #10655862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37255 #10655862