Subgroups — C₃×#37136 #10655743

Order 768.

1588 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2806	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2804	C₂	1	1	yes	maximal, characteristic
5	C₃×#2768	C₂	1	2	yes	maximal, complemented
6	C₃×#2763	C₂	1	2	yes	maximal, complemented
7	C₃×#2755	C₂	1	2	yes	maximal, complemented
8	C₃×#2734	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2732	C₂	1	1	yes	maximal, characteristic
10	C₃×#2729	C₂	1	2	yes	maximal, complemented
11	C₃×#2692	C₂	1	2	yes	maximal
12	C₃×#2677	C₂	1	2	yes	maximal, complemented
13	C₃×#2666	C₂	1	2	yes	maximal, complemented
14	C₃×#2607	C₂	1	2	yes	maximal, complemented
15	C₃×#2549	C₂	1	2	yes	maximal, complemented
16	C₃×#2439	C₂	1	2	yes	maximal, complemented
17	C₃×#2438	C₂	1	2	yes	maximal, complemented
18	C₃×#2318	C₂	1	2	yes	maximal
19	C₃×#2293	C₂	1	1	yes	maximal, characteristic
20	#37136	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	2	yes	—
23	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×#117	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×#399	C₂²	1	2	yes	—
33	C₃×#399	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×#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×#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×#395	C₂²	1	2	yes	—
47	C₃×#395	C₂²	1	2	yes	—
48	C₃×#395	C₂²	1	2	yes	—
49	C₃×#393	C₂²	1	2	yes	—
50	C₃×#393	C₂²	1	2	yes	—
51	C₃×#393	C₂²	1	2	yes	—
52	C₃×#393	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	2	yes	—
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×#391	C₂²	1	1	yes	characteristic
63	C₃×#391	C₂²	1	2	yes	—
64	C₃×#391	C₂²	1	1	yes	characteristic
65	C₃×#390	C₂²	1	1	yes	characteristic
66	C₃×#390	C₂²	1	1	yes	characteristic
67	C₃×#389	C₂²	1	2	yes	—
68	C₃×#389	C₂²	1	2	yes	—
69	C₃×#389	C₂²	1	2	yes	—
70	C₃×#389	C₂²	1	1	yes	characteristic
71	C₃×#389	C₂²	1	1	yes	characteristic
72	C₃×#389	C₂²	1	1	yes	characteristic
73	C₃×#389	C₂²	1	1	yes	characteristic
74	C₃×#389	C₂²	1	1	yes	characteristic
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×#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×#386	C₂²	1	2	yes	—
89	C₃×#386	C₂²	1	2	yes	—
90	C₃×#385	C₂²	1	2	yes	—
91	C₃×#385	C₂²	1	2	yes	—
92	C₃×#385	C₂²	1	2	yes	—
93	C₃×#385	C₂²	1	2	yes	—
94	C₃×#385	C₂²	1	2	yes	—
95	C₃×#385	C₂²	1	2	yes	—
96	C₃×#383	C₂²	1	2	yes	—
97	C₃×#382	C₂²	1	2	yes	—
98	C₃×#382	C₂²	1	2	yes	—
99	C₃×#382	C₂²	1	2	yes	—
100	C₃×#381	C₂²	1	2	yes	—
101	C₃×#380	C₂²	1	2	yes	—
102	C₃×#380	C₂²	1	2	yes	—
103	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₂×C₃×#95	C₂²	1	2	yes	—
107	C₃×C₄³	C₂²	1	1	yes	characteristic
108	#2863	C₂×C₃	1	1	yes	characteristic, complemented
109	#2862	C₂×C₃	1	1	yes	characteristic, complemented
110	#2806	C₂×C₃	1	1	yes	characteristic, complemented
111	#2804	C₂×C₃	1	1	yes	characteristic
112	#2768	C₂×C₃	1	2	yes	complemented
113	#2763	C₂×C₃	1	2	yes	complemented
114	#2755	C₂×C₃	1	2	yes	complemented
115	#2734	C₂×C₃	1	1	yes	characteristic, complemented
116	#2732	C₂×C₃	1	1	yes	characteristic
117	#2729	C₂×C₃	1	2	yes	complemented
118	#2692	C₂×C₃	1	2	yes	—
119	#2677	C₂×C₃	1	2	yes	complemented
120	#2666	C₂×C₃	1	2	yes	complemented
121	#2607	C₂×C₃	1	2	yes	complemented
122	#2549	C₂×C₃	1	2	yes	complemented
123	#2439	C₂×C₃	1	2	yes	complemented
124	#2438	C₂×C₃	1	2	yes	complemented
125	#2318	C₂×C₃	1	2	yes	—
126	#2293	C₂×C₃	1	1	yes	characteristic
127	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
128	C₂²×C₃×Q₈	C₂³	1	2	yes	—
129	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
130	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
131	C₂²×C₃×Q₈	C₂³	1	2	yes	—
132	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
133	C₂³×C₃×C₄	C₂³	1	2	yes	—
134	C₂³×C₃×C₄	C₂³	1	2	yes	—
135	C₂³×C₃×C₄	C₂³	1	2	yes	—
136	C₃×C₄⋊Q₈	—	4	2	no	—
137	C₃×C₄⋊Q₈	—	4	2	no	—
138	C₃×C₄⋊Q₈	—	4	4	no	—
139	C₃×C₂²⋊Q₈	—	4	4	no	—
140	C₃×C₂²⋊Q₈	—	4	4	no	—
141	C₃×C₂²⋊Q₈	—	4	4	no	—
142	C₃×C₄×D₄	Q₈	1	8	yes	complemented
143	C₃×#117	—	4	4	no	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
169	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
183	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
184	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
186	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
187	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₄²	C₂³	1	2	yes	—
189	C₂×C₃×C₄²	C₂³	1	2	yes	—
190	C₂×C₃×C₄²	C₂³	1	2	yes	—
191	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	C₃×#95	C₂³	1	2	yes	—
221	C₃×#95	C₂³	1	2	yes	—
222	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
224	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
225	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
226	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
227	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
228	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
229	C₂×#117	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	#399	C₂²×C₃	1	2	yes	—
234	#399	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	#396	C₂²×C₃	1	2	yes	—
244	#396	C₂²×C₃	1	2	yes	—
245	#395	C₂²×C₃	1	2	yes	—
246	#395	C₂²×C₃	1	2	yes	—
247	#395	C₂²×C₃	1	2	yes	—
248	#395	C₂²×C₃	1	2	yes	—
249	#395	C₂²×C₃	1	2	yes	—
250	#393	C₂²×C₃	1	2	yes	—
251	#393	C₂²×C₃	1	2	yes	—
252	#393	C₂²×C₃	1	2	yes	—
253	#393	C₂²×C₃	1	2	yes	—
254	#391	C₂²×C₃	1	2	yes	—
255	#391	C₂²×C₃	1	2	yes	—
256	#391	C₂²×C₃	1	1	yes	characteristic
257	#391	C₂²×C₃	1	1	yes	characteristic
258	#391	C₂²×C₃	1	1	yes	characteristic
259	#391	C₂²×C₃	1	1	yes	characteristic
260	#391	C₂²×C₃	1	1	yes	characteristic
261	#391	C₂²×C₃	1	2	yes	—
262	#391	C₂²×C₃	1	2	yes	—
263	#391	C₂²×C₃	1	1	yes	characteristic
264	#391	C₂²×C₃	1	1	yes	characteristic
265	#391	C₂²×C₃	1	2	yes	—
266	#390	C₂²×C₃	1	1	yes	characteristic
267	#390	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	#389	C₂²×C₃	1	2	yes	—
272	#389	C₂²×C₃	1	2	yes	—
273	#389	C₂²×C₃	1	2	yes	—
274	#389	C₂²×C₃	1	1	yes	characteristic
275	#389	C₂²×C₃	1	1	yes	characteristic
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	#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	#386	C₂²×C₃	1	2	yes	—
290	#386	C₂²×C₃	1	2	yes	—
291	#385	C₂²×C₃	1	2	yes	—
292	#385	C₂²×C₃	1	2	yes	—
293	#385	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	#382	C₂²×C₃	1	2	yes	—
301	#381	C₂²×C₃	1	2	yes	—
302	#380	C₂²×C₃	1	2	yes	—
303	#380	C₂²×C₃	1	2	yes	—
304	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
305	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
306	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
307	C₂×#95	C₂²×C₃	1	2	yes	—
308	C₄³	C₂²×C₃	1	1	yes	characteristic
309	C₂⁴×C₃	C₂⁴	1	2	yes	—
310	C₂×C₃×Q₈	—	2	2	no	—
311	C₂×C₃×Q₈	—	2	4	no	—
312	C₂×C₃×Q₈	—	2	2	no	—
313	C₂×C₃×Q₈	—	2	2	no	—
314	C₂×C₃×Q₈	—	4	2	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	1	no	—
320	C₂×C₃×Q₈	—	4	2	no	—
321	C₂×C₃×Q₈	—	4	2	no	—
322	C₂×C₃×Q₈	—	4	1	no	—
323	C₂×C₃×Q₈	—	4	1	no	—
324	C₂×C₃×Q₈	—	4	2	no	—
325	C₂×C₃×D₄	—	4	1	no	—
326	C₂×C₃×D₄	—	4	1	no	—
327	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
328	C₂²×C₃×C₄	—	4	2	no	—
329	C₂²×C₃×C₄	—	4	2	no	—
330	C₂²×C₃×C₄	—	4	2	no	—
331	C₂²×C₃×C₄	—	4	2	no	—
332	C₂²×C₃×C₄	—	4	2	no	—
333	C₂²×C₃×C₄	—	4	2	no	—
334	C₂²×C₃×C₄	—	4	2	no	—
335	C₂²×C₃×C₄	—	4	2	no	—
336	C₂²×C₃×C₄	C₂×Q₈	1	8	yes	—
337	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
338	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
339	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
340	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
341	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
342	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
343	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
344	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
345	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
346	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
347	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
348	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
349	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
350	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
351	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
352	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
353	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
354	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
355	C₃×C₄⋊C₄	—	2	4	no	—
356	C₃×C₄⋊C₄	—	2	4	no	—
357	C₃×C₄⋊C₄	—	2	4	no	—
358	C₃×C₄⋊C₄	—	2	4	no	—
359	C₃×C₄⋊C₄	—	2	2	no	—
360	C₃×C₄⋊C₄	—	4	2	no	—
361	C₃×C₄⋊C₄	—	4	1	no	—
362	C₃×C₄⋊C₄	—	4	1	no	—
363	C₃×C₄⋊C₄	—	4	1	no	—
364	C₃×C₄⋊C₄	—	4	1	no	—
365	C₃×C₄⋊C₄	—	4	2	no	—
366	C₃×C₄⋊C₄	—	4	2	no	—
367	C₃×C₄⋊C₄	—	4	2	no	—
368	C₃×C₄⋊C₄	—	4	2	no	—
369	C₃×C₄⋊C₄	—	4	2	no	—
370	C₃×C₄⋊C₄	—	4	2	no	—
371	C₃×C₄⋊C₄	—	4	2	no	—
372	C₃×C₄⋊C₄	—	4	2	no	—
373	C₃×C₄⋊C₄	—	4	2	no	—
374	C₃×C₄⋊C₄	—	4	2	no	—
375	C₃×C₄⋊C₄	—	4	2	no	—
376	C₃×C₄⋊C₄	—	4	2	no	—
377	C₃×C₄⋊C₄	—	4	1	no	—
378	C₃×C₄⋊C₄	—	4	1	no	—
379	C₃×C₄⋊C₄	—	4	2	no	—
380	C₃×C₄⋊C₄	—	4	2	no	—
381	C₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
382	C₃×C₂²⋊C₄	—	2	4	no	—
383	C₃×C₂²⋊C₄	—	2	4	no	—
384	C₃×C₂²⋊C₄	—	2	4	no	—
385	C₃×C₂²⋊C₄	—	4	2	no	—
386	C₃×C₂²⋊C₄	—	4	2	no	—
387	C₃×C₂²⋊C₄	—	4	2	no	—
388	C₃×C₂²⋊C₄	—	4	2	no	—
389	C₃×C₂²⋊C₄	—	4	2	no	—
390	C₃×C₂²⋊C₄	—	4	2	no	—
391	C₃×C₂²⋊C₄	—	4	2	no	—
392	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
393	C₃×C₄²	—	2	2	no	—
394	C₃×C₄²	—	2	2	no	—
395	C₃×C₄²	—	2	2	no	—
396	C₃×C₄²	—	4	2	no	—
397	C₃×C₄²	—	4	1	no	—
398	C₃×C₄²	—	4	1	no	—
399	C₃×C₄²	—	4	1	no	—
400	C₃×C₄²	—	4	2	no	—
401	C₃×C₄²	—	4	2	no	—
402	C₃×C₄²	C₂×Q₈	1	4	yes	—
403	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
404	C₂²×Q₈	C₂³×C₃	1	2	yes	—
405	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
406	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
407	C₂²×Q₈	C₂³×C₃	1	2	yes	—
408	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
409	C₂³×C₄	C₂³×C₃	1	2	yes	—
410	C₂³×C₄	C₂³×C₃	1	2	yes	—
411	C₂³×C₄	C₂³×C₃	1	2	yes	—
412	C₄⋊Q₈	—	4	2	no	—
413	C₄⋊Q₈	—	4	2	no	—
414	C₄⋊Q₈	—	4	4	no	—
415	C₂²⋊Q₈	—	4	4	no	—
416	C₂²⋊Q₈	—	4	4	no	—
417	C₂²⋊Q₈	—	4	4	no	—
418	C₄×D₄	C₃×Q₈	1	8	yes	complemented
419	#117	—	4	4	no	—
420	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
447	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
458	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
461	C₂×C₄²	C₂³×C₃	1	2	yes	—
462	C₂×C₄²	C₂³×C₃	1	2	yes	—
463	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
466	C₂×C₄²	C₂³×C₃	1	2	yes	—
467	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
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	#95	C₂³×C₃	1	2	yes	—
487	#95	C₂³×C₃	1	2	yes	—
488	#95	C₂³×C₃	1	2	yes	—
489	#95	C₂³×C₃	1	2	yes	—
490	#95	C₂³×C₃	1	2	yes	—
491	#95	C₂³×C₃	1	2	yes	—
492	#95	C₂³×C₃	1	2	yes	—
493	#95	C₂³×C₃	1	2	yes	—
494	#95	C₂³×C₃	1	2	yes	—
495	#95	C₂³×C₃	1	2	yes	—
496	#95	C₂³×C₃	1	2	yes	—
497	#95	C₂³×C₃	1	2	yes	—
498	C₂³×C₃	—	2	2	no	—
499	C₂³×C₃	—	2	2	no	—
500	C₂³×C₃	—	2	2	no	—
501	C₂³×C₃	—	2	2	no	—
502	C₂³×C₃	—	2	2	no	—
503	C₂³×C₃	—	2	2	no	—
504	C₂³×C₃	C₂²×Q₈	1	4	yes	—
505	C₂³×C₃	C₂⁵	1	1	yes	characteristic
506	C₃×Q₈	—	8	4	no	—
507	C₃×Q₈	—	8	2	no	—
508	C₃×Q₈	—	8	2	no	—
509	C₃×Q₈	—	8	2	no	—
510	C₃×Q₈	—	8	4	no	—
511	C₃×D₄	—	4	4	no	—
512	C₂×C₃×C₄	—	2	1	no	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	—	2	1	no	—
515	C₂×C₃×C₄	—	2	2	no	—
516	C₂×C₃×C₄	—	2	1	no	—
517	C₂×C₃×C₄	—	2	2	no	—
518	C₂×C₃×C₄	—	2	1	no	—
519	C₂×C₃×C₄	—	2	1	no	—
520	C₂×C₃×C₄	—	2	1	no	—
521	C₂×C₃×C₄	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	1	no	—
525	C₂×C₃×C₄	—	2	1	no	—
526	C₂×C₃×C₄	—	2	1	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	2	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	1	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	1	no	—
546	C₂×C₃×C₄	—	2	2	no	—
547	C₂×C₃×C₄	—	2	2	no	—
548	C₂×C₃×C₄	—	2	2	no	—
549	C₂×C₃×C₄	—	2	2	no	—
550	C₂×C₃×C₄	—	2	2	no	—
551	C₂×C₃×C₄	—	2	2	no	—
552	C₂×C₃×C₄	—	2	2	no	—
553	C₂×C₃×C₄	—	2	2	no	—
554	C₂×C₃×C₄	—	2	2	no	—
555	C₂×C₃×C₄	—	2	2	no	—
556	C₂×C₃×C₄	—	2	2	no	—
557	C₂×C₃×C₄	—	2	2	no	—
558	C₂×C₃×C₄	—	2	2	no	—
559	C₂×C₃×C₄	—	4	8	no	—
560	C₂×C₃×C₄	—	8	4	no	—
561	C₂×C₃×C₄	—	8	4	no	—
562	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
563	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
564	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
565	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
566	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
567	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
568	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
569	C₂⁴	C₂⁴×C₃	1	2	yes	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	4	2	no	—
575	C₂×Q₈	—	4	1	no	—
576	C₂×Q₈	—	4	1	no	—
577	C₂×Q₈	—	4	2	no	—
578	C₂×Q₈	—	4	1	no	—
579	C₂×Q₈	—	4	1	no	—
580	C₂×Q₈	—	4	2	no	—
581	C₂×Q₈	—	4	2	no	—
582	C₂×Q₈	—	4	1	no	—
583	C₂×Q₈	—	4	1	no	—
584	C₂×Q₈	—	4	2	no	—
585	C₂×D₄	—	4	1	no	—
586	C₂×D₄	—	4	1	no	—
587	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	C₂×C₃×Q₈	1	8	yes	—
597	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	1	no	—
629	C₄⋊C₄	—	4	1	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	—	4	2	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	—	4	1	no	—
634	C₄⋊C₄	—	4	1	no	—
635	C₄⋊C₄	—	4	1	no	—
636	C₄⋊C₄	—	4	1	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	2	no	—
656	C₄²	—	4	2	no	—
657	C₄²	—	4	2	no	—
658	C₄²	—	4	2	no	—
659	C₄²	—	4	1	no	—
660	C₄²	—	4	1	no	—
661	C₄²	—	4	1	no	—
662	C₄²	C₂×C₃×Q₈	1	4	yes	—
663	C₂²×C₃	—	2	4	no	—
664	C₂²×C₃	—	2	4	no	—
665	C₂²×C₃	—	2	4	no	—
666	C₂²×C₃	—	4	2	no	—
667	C₂²×C₃	—	4	2	no	—
668	C₂²×C₃	—	4	2	no	—
669	C₂²×C₃	—	4	2	no	—
670	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
671	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
672	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
674	C₂²×C₃	#585	1	1	yes	characteristic
675	C₂²×C₃	#585	1	1	yes	characteristic
676	C₂²×C₃	#585	1	1	yes	characteristic
677	C₃×C₄	—	2	2	no	—
678	C₃×C₄	—	2	2	no	—
679	C₃×C₄	—	2	4	no	—
680	C₃×C₄	—	2	2	no	—
681	C₃×C₄	—	2	2	no	—
682	C₃×C₄	—	2	2	no	—
683	C₃×C₄	—	2	2	no	—
684	C₃×C₄	—	4	2	no	—
685	C₃×C₄	—	4	2	no	—
686	C₃×C₄	—	4	2	no	—
687	C₃×C₄	—	4	1	no	—
688	C₃×C₄	—	4	2	no	—
689	C₃×C₄	—	4	2	no	—
690	C₃×C₄	—	4	2	no	—
691	C₃×C₄	—	4	2	no	—
692	C₃×C₄	—	4	2	no	—
693	C₃×C₄	—	4	2	no	—
694	C₃×C₄	—	4	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	C₂²×C₃×Q₈	1	4	yes	—
702	C₂³	C₂⁵×C₃	1	1	yes	characteristic
703	Q₈	—	8	4	no	—
704	Q₈	—	8	2	no	—
705	Q₈	—	8	2	no	—
706	Q₈	—	8	2	no	—
707	Q₈	—	8	4	no	—
708	D₄	—	4	4	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	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	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	4	8	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
760	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
761	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
762	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
763	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
764	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
765	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
766	C₂×C₃	—	4	4	no	—
767	C₂×C₃	#3458	1	1	yes	characteristic
768	C₂×C₃	#3501	1	1	yes	characteristic
769	C₂×C₃	#3503	1	1	yes	characteristic
770	C₂×C₃	#3545	1	1	yes	characteristic
771	C₂×C₃	#3554	1	1	yes	characteristic
772	C₂×C₃	#3558	1	1	yes	characteristic
773	C₂×C₃	#3564	1	1	yes	characteristic
774	C₂²	—	2	4	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
782	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
783	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
784	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
785	C₂²	C₃×#585	1	1	yes	characteristic
786	C₂²	C₃×#585	1	1	yes	characteristic
787	C₂²	C₃×#585	1	1	yes	characteristic
788	C₄	—	2	2	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	4	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	2	no	—
806	C₃	#37136	1	1	yes	characteristic, direct product factor, Sylow
807	C₂	—	4	4	no	—
808	C₂	C₃×#3458	1	1	yes	characteristic
809	C₂	C₃×#3501	1	1	yes	characteristic
810	C₂	C₃×#3503	1	1	yes	characteristic
811	C₂	C₃×#3545	1	1	yes	characteristic
812	C₂	C₃×#3554	1	1	yes	characteristic
813	C₂	C₃×#3558	1	1	yes	characteristic
814	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×#2863	C₂	semidirect
2. C₃×#2862	C₂	semidirect
3. C₃×#2806	C₂	semidirect
5. C₃×#2768	C₂	semidirect
6. C₃×#2763	C₂	semidirect
7. C₃×#2755	C₂	semidirect
8. C₃×#2734	C₂	semidirect
10. C₃×#2729	C₂	semidirect
12. C₃×#2677	C₂	semidirect
13. C₃×#2666	C₂	semidirect
14. C₃×#2607	C₂	semidirect
15. C₃×#2549	C₂	semidirect
16. C₃×#2439	C₂	semidirect
17. C₃×#2438	C₂	semidirect
20. #37136	C₃	direct (N × H)
108. #2863	C₂×C₃	semidirect
109. #2862	C₂×C₃	semidirect
110. #2806	C₂×C₃	semidirect
112. #2768	C₂×C₃	semidirect
113. #2763	C₂×C₃	semidirect
114. #2755	C₂×C₃	semidirect
115. #2734	C₂×C₃	semidirect
117. #2729	C₂×C₃	semidirect
119. #2677	C₂×C₃	semidirect
120. #2666	C₂×C₃	semidirect
121. #2607	C₂×C₃	semidirect
122. #2549	C₂×C₃	semidirect
123. #2439	C₂×C₃	semidirect
124. #2438	C₂×C₃	semidirect
142. C₃×C₄×D₄	Q₈	semidirect
418. C₄×D₄	C₃×Q₈	semidirect
806. C₃	#37136	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×#2863	2
C₃×#2862	2
C₃×#2806	2
C₃×#2804	2
C₃×#2768	2
C₃×#2763	2
C₃×#2755	2
C₃×#2734	2
C₃×#2732	2
C₃×#2729	2
C₃×#2692	2
C₃×#2677	2
C₃×#2666	2
C₃×#2607	2
C₃×#2549	2
C₃×#2439	2
C₃×#2438	2
C₃×#2318	2
C₃×#2293	2
#37136	3

Subgroups — C3×#37136 #10655743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37136 #10655743