Subgroups — D₃×#499269 #72271666

Order 3072.

At least 7962 conjugacy classes of subgroups; only the 859 normal subgroups are shown.

The subgroup lattice has 809 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72271660	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×#13310	C₂	1	1	yes	maximal, characteristic, complemented
3	#72271651	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×#13318	C₂	1	1	yes	maximal, characteristic, complemented
5	#72271643	C₂	1	1	yes	maximal, characteristic, complemented
6	#72271642	C₂	1	1	yes	maximal, characteristic, complemented
7	#72271639	C₂	1	1	yes	maximal, characteristic, complemented
8	#72271634	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×#13417	C₂	1	1	yes	maximal, characteristic, complemented
10	#72271630	C₂	1	1	yes	maximal, characteristic, complemented
11	#72271627	C₂	1	1	yes	maximal, characteristic, complemented
12	#72271621	C₂	1	1	yes	maximal, characteristic, complemented
13	D₃×#13334	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#499269	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×#13374	C₂	1	1	yes	maximal, characteristic, complemented
16	D₃×#13460	C₂	1	1	yes	maximal, characteristic, complemented
17	#72271510	C₂	1	1	yes	maximal, characteristic, complemented
18	#72271482	C₂	1	1	yes	maximal, characteristic, complemented
19	#72271409	C₂	1	1	yes	maximal, characteristic, complemented
20	D₃×#13400	C₂	1	1	yes	maximal, characteristic, complemented
21	#72270440	C₂	1	1	yes	maximal, characteristic, complemented
22	D₃×#13396	C₂	1	1	yes	maximal, characteristic, complemented
23	#72270254	C₂	1	1	yes	maximal, characteristic, complemented
24	#72270166	C₂	1	1	yes	maximal, characteristic, complemented
25	D₃×#21559	C₂	1	1	yes	maximal, characteristic, complemented
26	D₃×#12609	C₂	1	1	yes	maximal, characteristic, complemented
27	D₃×#12649	C₂	1	1	yes	maximal, characteristic, complemented
28	D₃×#33468	C₂	1	1	yes	maximal, characteristic, complemented
29	D₃×#60698	C₂	1	1	yes	maximal, characteristic, complemented
30	D₃×#12647	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×D₃×AGL(1,ℤ/16)	C₂	1	1	yes	maximal, characteristic, complemented
32	D₃×#3414	C₂²	1	1	yes	characteristic
33	C₂×D₃×#509	C₂²	1	1	yes	characteristic
34	#11665268	C₂²	1	1	yes	characteristic, complemented
35	#11665267	C₂²	1	1	yes	characteristic, complemented
36	#11665266	C₂²	1	1	yes	characteristic, complemented
37	#11665265	C₂²	1	1	yes	characteristic, complemented
38	#11665260	C₂²	1	1	yes	characteristic, complemented
39	#11665259	C₂²	1	1	yes	characteristic, complemented
40	#11665253	C₂²	1	1	yes	characteristic, complemented
41	D₃×#3163	C₂²	1	1	yes	characteristic
42	D₃×#3155	C₂²	1	1	yes	characteristic
43	D₃×#3067	C₂²	1	1	yes	characteristic
44	D₃×#3060	C₂²	1	1	yes	characteristic
45	D₃×#3058	C₂²	1	1	yes	characteristic
46	C₂×D₃×#444	C₂²	1	1	yes	characteristic
47	D₃×#2943	C₂²	1	1	yes	characteristic
48	C₂×D₃×#442	C₂²	1	1	yes	characteristic
49	D₃×#2875	C₂²	1	1	yes	characteristic
50	#10948640	C₂²	1	1	yes	characteristic, complemented
51	#10948639	C₂²	1	1	yes	characteristic, complemented
52	#10948638	C₂²	1	1	yes	characteristic, complemented
53	#10948637	C₂²	1	1	yes	characteristic, complemented
54	#10948636	C₂²	1	1	yes	characteristic, complemented
55	#10948635	C₂²	1	1	yes	characteristic, complemented
56	#10948633	C₂²	1	1	yes	characteristic, complemented
57	C₂×#69254	C₂²	1	1	yes	characteristic, complemented
58	C₂×#69091	C₂²	1	1	yes	characteristic, complemented
59	C₂×#71515	C₂²	1	1	yes	characteristic, complemented
60	C₂×#70929	C₂²	1	1	yes	characteristic, complemented
61	C₂×#69310	C₂²	1	1	yes	characteristic, complemented
62	C₂×#70918	C₂²	1	1	yes	characteristic, complemented
63	C₂×#69249	C₂²	1	1	yes	characteristic, complemented
64	D₃×#2155	C₂²	1	1	yes	characteristic
65	C₂×D₃×#365	C₂²	1	1	yes	characteristic
66	D₃×#2148	C₂²	1	1	yes	characteristic
67	C₂×D₃×#361	C₂²	1	1	yes	characteristic
68	C₂×D₃×#361	C₂²	1	1	yes	characteristic
69	D₃×#2145	C₂²	1	1	yes	characteristic
70	D₃×#2145	C₂²	1	1	yes	characteristic
71	C₂×D₃×#360	C₂²	1	1	yes	characteristic
72	D₃×#2143	C₂²	1	1	yes	characteristic
73	D₃×#2140	C₂²	1	1	yes	characteristic
74	D₃×#2117	C₂²	1	1	yes	characteristic
75	D₃×#2117	C₂²	1	1	yes	characteristic
76	C₂×D₃×#347	C₂²	1	1	yes	characteristic
77	C₂×D₃×#347	C₂²	1	1	yes	characteristic
78	#10802140	C₂²	1	1	yes	characteristic, complemented
79	#10802139	C₂²	1	1	yes	characteristic, complemented
80	#10802138	C₂²	1	1	yes	characteristic, complemented
81	#10802137	C₂²	1	1	yes	characteristic, complemented
82	#10802132	C₂²	1	1	yes	characteristic, complemented
83	#10802131	C₂²	1	1	yes	characteristic, complemented
84	#10802130	C₂²	1	1	yes	characteristic, complemented
85	D₃×#1976	C₂²	1	1	yes	characteristic
86	D₃×#1953	C₂²	1	1	yes	characteristic
87	D₃×#1814	C₂²	1	1	yes	characteristic
88	D₃×#1773	C₂²	1	1	yes	characteristic
89	#10714853	C₂²	1	1	yes	characteristic, complemented
90	#10714852	C₂²	1	1	yes	characteristic, complemented
91	#10714851	C₂²	1	1	yes	characteristic, complemented
92	#10714850	C₂²	1	1	yes	characteristic, complemented
93	#10714849	C₂²	1	1	yes	characteristic, complemented
94	#10714848	C₂²	1	1	yes	characteristic, complemented
95	#10714847	C₂²	1	1	yes	characteristic, complemented
96	#10714592	C₂²	1	1	yes	characteristic, complemented
97	#10714591	C₂²	1	1	yes	characteristic, complemented
98	#10714590	C₂²	1	1	yes	characteristic, complemented
99	#10714589	C₂²	1	1	yes	characteristic, complemented
100	#10714588	C₂²	1	1	yes	characteristic, complemented
101	#10714587	C₂²	1	1	yes	characteristic, complemented
102	#10714586	C₂²	1	1	yes	characteristic, complemented
103	#10714485	C₂²	1	1	yes	characteristic, complemented
104	#10714484	C₂²	1	1	yes	characteristic, complemented
105	#10714483	C₂²	1	1	yes	characteristic, complemented
106	#10714482	C₂²	1	1	yes	characteristic, complemented
107	#10714481	C₂²	1	1	yes	characteristic, complemented
108	#10714480	C₂²	1	1	yes	characteristic, complemented
109	#10714479	C₂²	1	1	yes	characteristic, complemented
110	#10714457	C₂²	1	1	yes	characteristic, complemented
111	#10714456	C₂²	1	1	yes	characteristic, complemented
112	#10714455	C₂²	1	1	yes	characteristic, complemented
113	#10714454	C₂²	1	1	yes	characteristic, complemented
114	#10714453	C₂²	1	1	yes	characteristic, complemented
115	#10714452	C₂²	1	1	yes	characteristic, complemented
116	#10714451	C₂²	1	1	yes	characteristic, complemented
117	#10714313	C₂²	1	1	yes	characteristic, complemented
118	#10714312	C₂²	1	1	yes	characteristic, complemented
119	#10714311	C₂²	1	1	yes	characteristic, complemented
120	#10714310	C₂²	1	1	yes	characteristic, complemented
121	#10714309	C₂²	1	1	yes	characteristic, complemented
122	#10714308	C₂²	1	1	yes	characteristic, complemented
123	#10714307	C₂²	1	1	yes	characteristic, complemented
124	#10714073	C₂²	1	1	yes	characteristic, complemented
125	#10714072	C₂²	1	1	yes	characteristic, complemented
126	#10714071	C₂²	1	1	yes	characteristic, complemented
127	#10714070	C₂²	1	1	yes	characteristic, complemented
128	#10714069	C₂²	1	1	yes	characteristic, complemented
129	#10714068	C₂²	1	1	yes	characteristic, complemented
130	#10714067	C₂²	1	1	yes	characteristic, complemented
131	#10713973	C₂²	1	1	yes	characteristic, complemented
132	#10713972	C₂²	1	1	yes	characteristic, complemented
133	#10713971	C₂²	1	1	yes	characteristic, complemented
134	#10713970	C₂²	1	1	yes	characteristic, complemented
135	#10713969	C₂²	1	1	yes	characteristic, complemented
136	#10713968	C₂²	1	1	yes	characteristic, complemented
137	#10713967	C₂²	1	1	yes	characteristic, complemented
138	#10713923	C₂²	1	1	yes	characteristic, complemented
139	#10713922	C₂²	1	1	yes	characteristic, complemented
140	#10713921	C₂²	1	1	yes	characteristic, complemented
141	#10713920	C₂²	1	1	yes	characteristic, complemented
142	#10713919	C₂²	1	1	yes	characteristic, complemented
143	#10713918	C₂²	1	1	yes	characteristic, complemented
144	#10713917	C₂²	1	1	yes	characteristic, complemented
145	#10710476	C₂²	1	1	yes	characteristic, complemented
146	#10710475	C₂²	1	1	yes	characteristic, complemented
147	#10710474	C₂²	1	1	yes	characteristic, complemented
148	#10710473	C₂²	1	1	yes	characteristic, complemented
149	#10710472	C₂²	1	1	yes	characteristic, complemented
150	#10710471	C₂²	1	1	yes	characteristic, complemented
151	#10710470	C₂²	1	1	yes	characteristic, complemented
152	#10710462	C₂²	1	1	yes	characteristic, complemented
153	#10710461	C₂²	1	1	yes	characteristic, complemented
154	#10710460	C₂²	1	1	yes	characteristic, complemented
155	#10710459	C₂²	1	1	yes	characteristic, complemented
156	#10710458	C₂²	1	1	yes	characteristic, complemented
157	#10710457	C₂²	1	1	yes	characteristic, complemented
158	#10710456	C₂²	1	1	yes	characteristic, complemented
159	#10710264	C₂²	1	1	yes	characteristic, complemented
160	#10710263	C₂²	1	1	yes	characteristic, complemented
161	#10710263	C₂²	1	1	yes	characteristic, complemented
162	#10710262	C₂²	1	1	yes	characteristic, complemented
163	#10710261	C₂²	1	1	yes	characteristic, complemented
164	#10710260	C₂²	1	1	yes	characteristic, complemented
165	#10710260	C₂²	1	1	yes	characteristic, complemented
166	D₃×#1389	C₂²	1	1	yes	characteristic
167	D₃×#1386	C₂²	1	1	yes	characteristic
168	D₃×#1384	C₂²	1	1	yes	characteristic
169	D₃×#1383	C₂²	1	1	yes	characteristic
170	D₃×#1378	C₂²	1	1	yes	characteristic
171	D₃×#1378	C₂²	1	1	yes	characteristic
172	C₃×#60698	C₂²	1	1	yes	characteristic, complemented
173	C₃×#33468	C₂²	1	1	yes	characteristic, complemented
174	C₂×C₃×AGL(1,ℤ/16)	C₂²	1	1	yes	characteristic, complemented
175	C₃×#21559	C₂²	1	1	yes	characteristic, complemented
176	C₃×#13460	C₂²	1	1	yes	characteristic, complemented
177	C₃×#13417	C₂²	1	1	yes	characteristic, complemented
178	C₃×#13400	C₂²	1	1	yes	characteristic, complemented
179	C₃×#13396	C₂²	1	1	yes	characteristic, complemented
180	C₃×#13374	C₂²	1	1	yes	characteristic, complemented
181	C₃×#13334	C₂²	1	1	yes	characteristic, complemented
182	C₃×#13318	C₂²	1	1	yes	characteristic, complemented
183	C₃×#13310	C₂²	1	1	yes	characteristic, complemented
184	C₃×#12649	C₂²	1	1	yes	characteristic, complemented
185	C₃×#12647	C₂²	1	1	yes	characteristic, complemented
186	C₃×#12609	C₂²	1	1	yes	characteristic, complemented
187	#499269	D₃	1	1	yes	characteristic, direct product factor
188	C₂×D₃×#135	C₂³	1	1	yes	characteristic
189	C₂×D₃×#135	C₂³	1	1	yes	characteristic
190	C₂²×D₃×D₈	C₂³	1	1	yes	characteristic
191	C₂×D₃×#131	D₄	1	1	yes	characteristic
192	C₂×D₃×#131	C₂³	1	1	yes	characteristic
193	C₄×D₃×#41	D₄	1	1	yes	characteristic
194	C₃×#3414	C₂³	1	1	yes	characteristic
195	C₂×C₃×#509	C₂³	1	1	yes	characteristic
196	C₃×#3163	C₂³	1	1	yes	characteristic
197	C₃×#3155	C₂³	1	1	yes	characteristic
198	C₃×#3067	C₂³	1	1	yes	characteristic
199	C₃×#3060	C₂³	1	1	yes	characteristic
200	C₃×#3058	C₂³	1	1	yes	characteristic
201	C₂×C₃×#444	C₂³	1	1	yes	characteristic
202	C₃×#2943	C₂³	1	1	yes	characteristic
203	C₂×C₃×#442	C₂³	1	1	yes	characteristic
204	C₃×#2875	C₂³	1	1	yes	characteristic
205	#83928	C₂³	1	1	yes	characteristic
206	#83916	C₂³	1	1	yes	characteristic
207	C₂×#5197	C₂³	1	1	yes	characteristic
208	#83906	C₂³	1	1	yes	characteristic
209	#83897	C₂³	1	1	yes	characteristic
210	#83894	C₂³	1	1	yes	characteristic
211	#83894	C₂³	1	1	yes	characteristic
212	C₂×#5193	C₂³	1	1	yes	characteristic
213	#83836	C₂³	1	1	yes	characteristic
214	#83830	C₂³	1	1	yes	characteristic
215	C₂×#5152	C₂³	1	1	yes	characteristic
216	C₂×#5147	C₂³	1	1	yes	characteristic
217	#83805	C₂³	1	1	yes	characteristic
218	#83800	C₂³	1	1	yes	characteristic
219	#83799	C₂³	1	1	yes	characteristic
220	#83782	D₄	1	1	yes	characteristic
221	#83782	C₂³	1	1	yes	characteristic
222	#82511	D₄	1	1	yes	characteristic
223	#82009	C₂³	1	1	yes	characteristic
224	C₂×#4908	C₂³	1	1	yes	characteristic
225	C₂×D₃×M₃₂	C₂³	1	1	yes	characteristic
226	C₂×D₃×M₃₂	C₂³	1	1	yes	characteristic
227	C₂×D₃×M₃₂	C₂³	1	1	yes	characteristic
228	C₂×D₃×M₃₂	C₂³	1	1	yes	characteristic
229	#79864	D₄	1	1	yes	characteristic
230	#79864	D₄	1	1	yes	characteristic
231	D₃×#442	D₄	1	2	yes	—
232	D₃×#442	D₄	1	2	yes	—
233	D₃×#442	D₄	1	1	yes	characteristic
234	D₃×#442	D₄	1	2	yes	—
235	D₃×#442	D₄	1	2	yes	—
236	D₃×#442	D₄	1	1	yes	characteristic
237	#79828	D₄	1	1	yes	characteristic
238	#79828	D₄	1	1	yes	characteristic
239	D₃×#441	D₄	1	1	yes	characteristic
240	D₃×#441	D₄	1	1	yes	characteristic
241	#79256	C₂³	1	1	yes	characteristic
242	C₂×D₃×#108	C₂³	1	1	yes	characteristic
243	C₂×D₃×#108	C₂³	1	1	yes	characteristic
244	C₂×#4894	C₂³	1	1	yes	characteristic
245	#79183	C₂³	1	1	yes	characteristic
246	D₃×#427	C₂³	1	1	yes	characteristic
247	D₃×#427	C₂³	1	1	yes	characteristic
248	#79172	C₂³	1	1	yes	characteristic
249	#79166	C₂³	1	1	yes	characteristic
250	#79120	C₂³	1	1	yes	characteristic
251	C₂×D₃×#106	C₂³	1	1	yes	characteristic
252	#79110	C₂³	1	1	yes	characteristic
253	C₂×#4869	C₂³	1	1	yes	characteristic
254	#78565	C₂³	1	1	yes	characteristic
255	#78550	D₄	1	1	yes	characteristic
256	#78550	C₂³	1	1	yes	characteristic
257	D₃×#405	D₄	1	1	yes	characteristic
258	D₃×#405	C₂³	1	1	yes	characteristic
259	#78545	C₂³	1	1	yes	characteristic
260	#78516	D₄	1	1	yes	characteristic
261	C₄×D₃×M₁₆	D₄	1	1	yes	characteristic
262	C₂×#4717	C₂³	1	1	yes	characteristic
263	#78494	C₂³	1	1	yes	characteristic
264	C₂×#4711	C₂³	1	1	yes	characteristic
265	#78486	C₂³	1	1	yes	characteristic
266	C₂×D₃×#97	C₂³	1	1	yes	characteristic
267	C₃×#2155	C₂³	1	1	yes	characteristic
268	C₂×C₃×#365	C₂³	1	1	yes	characteristic
269	C₃×#2148	C₂³	1	1	yes	characteristic
270	C₂×C₃×#361	C₂³	1	1	yes	characteristic
271	C₂×C₃×#361	C₂³	1	1	yes	characteristic
272	C₃×#2145	C₂³	1	1	yes	characteristic
273	C₃×#2145	C₂³	1	1	yes	characteristic
274	C₂×C₃×#360	C₂³	1	1	yes	characteristic
275	C₃×#2143	C₂³	1	1	yes	characteristic
276	C₃×#2140	C₂³	1	1	yes	characteristic
277	C₃×#2117	C₂³	1	1	yes	characteristic
278	C₃×#2117	C₂³	1	1	yes	characteristic
279	C₂×C₃×#347	C₂³	1	1	yes	characteristic
280	C₂×C₃×#347	C₂³	1	1	yes	characteristic
281	C₃×#1976	C₂³	1	1	yes	characteristic
282	C₃×#1953	C₂³	1	1	yes	characteristic
283	C₃×#1814	C₂³	1	1	yes	characteristic
284	C₃×#1773	C₂³	1	1	yes	characteristic
285	#72086	C₂³	1	1	yes	characteristic
286	#72081	C₂³	1	1	yes	characteristic
287	#72080	C₂³	1	1	yes	characteristic
288	#72076	C₂³	1	1	yes	characteristic
289	#72076	C₂³	1	1	yes	characteristic
290	C₂×#4566	C₂³	1	1	yes	characteristic
291	C₂×#4563	C₂³	1	1	yes	characteristic
292	C₂×#4563	C₂³	1	1	yes	characteristic
293	#72033	C₂³	1	1	yes	characteristic
294	#72013	C₂³	1	1	yes	characteristic
295	#72006	C₂³	1	1	yes	characteristic
296	#72006	C₂³	1	1	yes	characteristic
297	#71450	C₂³	1	1	yes	characteristic
298	#71450	C₂³	1	1	yes	characteristic
299	C₂×#4518	C₂³	1	1	yes	characteristic
300	#71448	C₂³	1	1	yes	characteristic
301	#71442	C₂³	1	1	yes	characteristic
302	C₂×#4516	C₂³	1	1	yes	characteristic
303	C₂×#4516	C₂³	1	1	yes	characteristic
304	#71440	C₂³	1	1	yes	characteristic
305	#71438	C₂³	1	1	yes	characteristic
306	#71438	C₂³	1	1	yes	characteristic
307	#71437	C₂³	1	1	yes	characteristic
308	#71437	C₂³	1	1	yes	characteristic
309	#71427	C₂³	1	1	yes	characteristic
310	C₂×#4513	C₂³	1	1	yes	characteristic
311	C₂×#4512	C₂³	1	1	yes	characteristic
312	C₂×#4512	C₂³	1	1	yes	characteristic
313	C₂×#4512	C₂³	1	1	yes	characteristic
314	C₂×#4512	C₂³	1	1	yes	characteristic
315	#70719	C₂³	1	1	yes	characteristic
316	#70707	C₂³	1	1	yes	characteristic
317	#70706	C₂³	1	1	yes	characteristic
318	#70703	C₂³	1	1	yes	characteristic
319	#70690	C₂³	1	1	yes	characteristic
320	#70687	C₂³	1	1	yes	characteristic
321	C₂×#4495	C₂³	1	1	yes	characteristic
322	C₂×#4495	C₂³	1	1	yes	characteristic
323	#70685	C₂³	1	1	yes	characteristic
324	C₂×#4494	C₂³	1	1	yes	characteristic
325	#70665	C₂³	1	1	yes	characteristic
326	#70660	C₂³	1	1	yes	characteristic
327	#70658	C₂³	1	1	yes	characteristic
328	#70656	C₂³	1	1	yes	characteristic
329	#70656	C₂³	1	1	yes	characteristic
330	#70652	C₂³	1	1	yes	characteristic
331	#70650	C₂³	1	1	yes	characteristic
332	C₂×#4488	C₂³	1	1	yes	characteristic
333	C₂×#4487	C₂³	1	1	yes	characteristic
334	#69901	C₂³	1	1	yes	characteristic
335	#69897	C₂³	1	1	yes	characteristic
336	#69829	C₂³	1	1	yes	characteristic
337	C₂×#4466	C₂³	1	1	yes	characteristic
338	C₂×#4466	C₂³	1	1	yes	characteristic
339	C₃×#1389	C₂³	1	1	yes	characteristic
340	C₃×#1386	C₂³	1	1	yes	characteristic
341	C₃×#1384	C₂³	1	1	yes	characteristic
342	C₃×#1383	C₂³	1	1	yes	characteristic
343	C₃×#1378	C₂³	1	1	yes	characteristic
344	C₃×#1378	C₂³	1	1	yes	characteristic
345	#67822	C₂³	1	1	yes	characteristic
346	#67819	C₂³	1	1	yes	characteristic
347	#67818	C₂³	1	1	yes	characteristic
348	#67816	C₂³	1	1	yes	characteristic
349	#67814	C₂³	1	1	yes	characteristic
350	#67814	C₂³	1	1	yes	characteristic
351	#67813	C₂³	1	1	yes	characteristic
352	#67813	C₂³	1	1	yes	characteristic
353	#67735	C₂³	1	1	yes	characteristic
354	#67730	C₂³	1	1	yes	characteristic
355	#67727	C₂³	1	1	yes	characteristic
356	#67726	C₂³	1	1	yes	characteristic
357	#67725	C₂³	1	1	yes	characteristic
358	#67725	C₂³	1	1	yes	characteristic
359	#67721	C₂³	1	1	yes	characteristic
360	#67720	C₂³	1	1	yes	characteristic
361	#67672	C₂³	1	1	yes	characteristic
362	#67672	C₂³	1	1	yes	characteristic
363	#60698	C₂×D₃	1	1	yes	characteristic, complemented
364	#33468	C₂×D₃	1	1	yes	characteristic, complemented
365	C₂×AGL(1,ℤ/16)	C₂×D₃	1	1	yes	characteristic, complemented
366	#21559	C₂×D₃	1	1	yes	characteristic, complemented
367	#13460	C₂×D₃	1	1	yes	characteristic, complemented
368	#13417	C₂×D₃	1	1	yes	characteristic, complemented
369	#13400	C₂×D₃	1	1	yes	characteristic, complemented
370	#13396	C₂×D₃	1	1	yes	characteristic, complemented
371	#13374	C₂×D₃	1	1	yes	characteristic, complemented
372	#13334	C₂×D₃	1	1	yes	characteristic, complemented
373	#13318	C₂×D₃	1	1	yes	characteristic, complemented
374	#13310	C₂×D₃	1	1	yes	characteristic, complemented
375	#12649	C₂×D₃	1	1	yes	characteristic, complemented
376	#12647	C₂×D₃	1	1	yes	characteristic, complemented
377	#12609	C₂×D₃	1	1	yes	characteristic, complemented
378	C₂×D₃×#41	C₂×D₄	1	1	yes	characteristic
379	C₂×C₃×#135	C₂⁴	1	1	yes	characteristic
380	C₂×C₃×#135	C₂⁴	1	1	yes	characteristic
381	C₂²×C₃×D₈	C₂⁴	1	1	yes	characteristic
382	C₂×C₃×#131	C₂×D₄	1	1	yes	characteristic
383	C₂×C₃×#131	C₂⁴	1	1	yes	characteristic
384	C₃×C₄×#41	C₂×D₄	1	1	yes	characteristic
385	Dic₃×#41	C₂×D₄	1	1	yes	characteristic
386	C₂×#948	C₂×D₄	1	1	yes	characteristic
387	C₂×#948	C₂×D₄	1	1	yes	characteristic
388	C₂×#919	C₂×D₄	1	1	yes	characteristic
389	C₂×#919	#41	1	1	yes	characteristic, complemented
390	C₂×D₃×Q₁₆	C₂×D₄	1	1	yes	characteristic
391	C₂×D₃×Q₁₆	#41	1	1	yes	characteristic, complemented
392	C₂×#912	C₂×D₄	1	1	yes	characteristic
393	C₂×#912	#41	1	1	yes	characteristic, complemented
394	C₂×D₃×D₈	C₂×D₄	1	2	yes	—
395	C₂×D₃×D₈	C₂×D₄	1	2	yes	—
396	C₂×D₃×D₈	C₂×D₄	1	1	yes	characteristic
397	C₂×D₃×D₈	#41	1	1	yes	characteristic, complemented
398	C₂×#907	C₂×D₄	1	1	yes	characteristic
399	C₂×#907	C₂×D₄	1	1	yes	characteristic
400	C₂×D₃×M₁₆	C₂×D₄	1	1	yes	characteristic
401	C₂×D₃×M₁₆	C₂×D₄	1	1	yes	characteristic
402	C₂×#904	C₂⁴	1	1	yes	characteristic
403	C₂×#904	C₂⁴	1	1	yes	characteristic
404	C₂²×D₂₄	C₂⁴	1	1	yes	characteristic
405	C₂×#901	C₂×D₄	1	1	yes	characteristic
406	C₂×#901	C₂⁴	1	1	yes	characteristic
407	C₂²×D₃×C₈	C₂×D₄	1	1	yes	characteristic
408	C₂²×D₃×C₈	C₂⁴	1	1	yes	characteristic
409	#5522	C₂×D₄	1	1	yes	characteristic
410	D₃×#117	C₂×D₄	1	1	yes	characteristic
411	C₄×#235	C₂×D₄	1	1	yes	characteristic
412	C₂×C₄²×D₃	C₂×D₄	1	1	yes	characteristic
413	C₂×C₃×M₃₂	C₂⁴	1	1	yes	characteristic
414	C₂×C₃×M₃₂	C₂⁴	1	1	yes	characteristic
415	C₂×C₃×M₃₂	C₂⁴	1	1	yes	characteristic
416	C₂×C₃×M₃₂	C₂⁴	1	1	yes	characteristic
417	C₃×#442	C₂×D₄	1	2	yes	—
418	C₃×#442	C₂×D₄	1	1	yes	characteristic
419	C₃×#442	C₂×D₄	1	1	yes	characteristic
420	C₃×#442	C₂×D₄	1	2	yes	—
421	C₃×#441	C₂×D₄	1	1	yes	characteristic
422	C₃×#441	C₂×D₄	1	1	yes	characteristic
423	C₂×C₃×#108	C₂⁴	1	1	yes	characteristic
424	C₂×C₃×#108	C₂⁴	1	1	yes	characteristic
425	C₃×#427	C₂⁴	1	1	yes	characteristic
426	C₃×#427	C₂⁴	1	1	yes	characteristic
427	C₂×C₃×#106	C₂⁴	1	1	yes	characteristic
428	C₃×#405	C₂×D₄	1	1	yes	characteristic
429	C₃×#405	C₂⁴	1	1	yes	characteristic
430	C₃×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
431	C₂×C₃×#97	C₂⁴	1	1	yes	characteristic
432	#5184	C₂×D₄	1	1	yes	characteristic
433	#5184	C₂×D₄	1	1	yes	characteristic
434	#5152	C₂×D₄	1	2	yes	—
435	#5152	C₂×D₄	1	2	yes	—
436	#5152	C₂×D₄	1	1	yes	characteristic
437	#5152	C₂×D₄	1	1	yes	characteristic
438	#5122	C₂×D₄	1	1	yes	characteristic
439	#5122	C₂×D₄	1	1	yes	characteristic
440	Dic₃×M₁₆	C₂×D₄	1	1	yes	characteristic
441	Dic₃×M₁₆	C₂×D₄	1	1	yes	characteristic
442	C₂×#819	C₂⁴	1	1	yes	characteristic
443	C₂×#819	C₂⁴	1	1	yes	characteristic
444	#5106	C₂⁴	1	1	yes	characteristic
445	#5106	C₂⁴	1	1	yes	characteristic
446	C₂×#817	C₂⁴	1	1	yes	characteristic
447	#5101	C₂×D₄	1	1	yes	characteristic
448	#5101	C₂⁴	1	1	yes	characteristic
449	C₂×#815	C₂×D₄	1	1	yes	characteristic
450	C₂×#815	C₂⁴	1	1	yes	characteristic
451	C₂×#812	C₂⁴	1	1	yes	characteristic
452	C₂×#812	C₂⁴	1	1	yes	characteristic
453	C₂×#812	C₂⁴	1	1	yes	characteristic
454	C₂×#812	C₂⁴	1	1	yes	characteristic
455	#4997	C₂×D₄	1	1	yes	characteristic
456	#4997	C₂×D₄	1	1	yes	characteristic
457	C₄×#208	C₂×D₄	1	1	yes	characteristic
458	C₂×#803	C₂×D₄	1	1	yes	characteristic
459	D₃×M₃₂	#41	1	2	yes	complemented
460	D₃×M₃₂	#41	1	2	yes	complemented
461	C₂×#798	#41	1	2	yes	complemented
462	C₂×D₃×C₁₆	#41	1	2	yes	complemented
463	D₃×#108	#41	1	2	yes	complemented
464	D₃×#108	#41	1	2	yes	complemented
465	#4869	C₂×D₄	1	2	yes	—
466	#4869	C₂×D₄	1	2	yes	—
467	#4869	C₂×D₄	1	1	yes	characteristic
468	#4869	C₂×D₄	1	1	yes	characteristic
469	#4860	C₂×D₄	1	1	yes	characteristic
470	#4860	C₂×D₄	1	1	yes	characteristic
471	D₃×#106	C₂×D₄	1	2	yes	—
472	D₃×#106	C₂×D₄	1	2	yes	—
473	D₃×#106	C₂×D₄	1	1	yes	characteristic
474	D₃×#106	C₂×D₄	1	1	yes	characteristic
475	#4853	C₂×D₄	1	1	yes	characteristic
476	#4853	C₂×D₄	1	1	yes	characteristic
477	#4716	C₂×D₄	1	1	yes	characteristic
478	#4716	C₂×D₄	1	1	yes	characteristic
479	#4711	C₂×D₄	1	1	yes	characteristic
480	#4711	C₂×D₄	1	2	yes	—
481	#4711	C₂×D₄	1	2	yes	—
482	#4711	C₂×D₄	1	1	yes	characteristic
483	D₃×#97	C₂×D₄	1	1	yes	characteristic
484	D₃×#97	C₂×D₄	1	1	yes	characteristic
485	D₃×#97	C₂×D₄	1	1	yes	characteristic
486	D₃×#97	C₂×D₄	1	1	yes	characteristic
487	D₃×#97	C₂×D₄	1	1	yes	characteristic
488	D₃×#97	C₂×D₄	1	1	yes	characteristic
489	D₃×#97	C₂×D₄	1	1	yes	characteristic
490	D₃×#97	C₂×D₄	1	1	yes	characteristic
491	#3414	C₂²×D₃	1	1	yes	characteristic
492	C₂×#509	C₂²×D₃	1	1	yes	characteristic
493	#3163	C₂²×D₃	1	1	yes	characteristic
494	#3155	C₂²×D₃	1	1	yes	characteristic
495	#3067	C₂²×D₃	1	1	yes	characteristic
496	#3060	C₂²×D₃	1	1	yes	characteristic
497	#3058	C₂²×D₃	1	1	yes	characteristic
498	C₂×#444	C₂²×D₃	1	1	yes	characteristic
499	#2943	C₂²×D₃	1	1	yes	characteristic
500	C₂×#442	C₂²×D₃	1	1	yes	characteristic
501	#2875	C₂²×D₃	1	1	yes	characteristic
502	#2155	C₂²×D₃	1	1	yes	characteristic
503	C₂×#365	C₂²×D₃	1	1	yes	characteristic
504	#2148	C₂²×D₃	1	1	yes	characteristic
505	C₂×#361	C₂²×D₃	1	1	yes	characteristic
506	C₂×#361	C₂²×D₃	1	1	yes	characteristic
507	#2145	C₂²×D₃	1	1	yes	characteristic
508	#2145	C₂²×D₃	1	1	yes	characteristic
509	C₂×#360	C₂²×D₃	1	1	yes	characteristic
510	#2143	C₂²×D₃	1	1	yes	characteristic
511	#2140	C₂²×D₃	1	1	yes	characteristic
512	#2117	C₂²×D₃	1	1	yes	characteristic
513	#2117	C₂²×D₃	1	1	yes	characteristic
514	C₂×#347	C₂²×D₃	1	1	yes	characteristic
515	C₂×#347	C₂²×D₃	1	1	yes	characteristic
516	#1976	C₂²×D₃	1	1	yes	characteristic
517	#1953	C₂²×D₃	1	1	yes	characteristic
518	#1814	C₂²×D₃	1	1	yes	characteristic
519	#1773	C₂²×D₃	1	1	yes	characteristic
520	#1389	C₂²×D₃	1	1	yes	characteristic
521	#1386	C₂²×D₃	1	1	yes	characteristic
522	#1384	C₂²×D₃	1	1	yes	characteristic
523	#1383	C₂²×D₃	1	1	yes	characteristic
524	#1378	C₂²×D₃	1	1	yes	characteristic
525	#1378	C₂²×D₃	1	1	yes	characteristic
526	C₂×C₃×#41	C₂²×D₄	1	1	yes	characteristic
527	C₂×#239	AGL(1,ℤ/8)	1	1	yes	characteristic
528	C₂×D₃×Q₈	AGL(1,ℤ/8)	1	1	yes	characteristic
529	C₂×#237	AGL(1,ℤ/8)	1	1	yes	characteristic
530	C₂×D₃×D₄	AGL(1,ℤ/8)	1	1	yes	characteristic
531	C₂×#235	C₂²×D₄	1	1	yes	characteristic
532	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₃×Q₁₆	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₃×Q₁₆	C₂×#41	1	1	yes	characteristic, complemented
535	C₂×C₃×D₈	C₂²×D₄	1	2	yes	—
536	C₂×C₃×D₈	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₃×D₈	C₂×#41	1	1	yes	characteristic, complemented
538	C₂×C₃×M₁₆	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₃×M₁₆	C₂²×D₄	1	1	yes	characteristic
540	C₂²×C₃×C₈	C₂²×D₄	1	1	yes	characteristic
541	C₂²×C₃×C₈	C₂⁵	1	1	yes	characteristic
542	C₃×#117	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₃×C₄²	C₂²×D₄	1	1	yes	characteristic
544	#926	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×Dic₃	C₂²×D₄	1	1	yes	characteristic
546	C₂×#208	C₂²×D₄	1	1	yes	characteristic
547	C₂×#208	C₂²×D₄	1	1	yes	characteristic
548	C₂²×C₃⋊C₈	C₂²×D₄	1	1	yes	characteristic
549	C₂²×C₃⋊C₈	C₂²×D₄	1	1	yes	characteristic
550	D₃×M₁₆	AGL(1,ℤ/8)	1	2	yes	—
551	D₃×M₁₆	AGL(1,ℤ/8)	1	2	yes	—
552	C₂×Dic₁₂	C₂²×D₄	1	1	yes	characteristic
553	C₂×Dic₁₂	C₂×#41	1	1	yes	characteristic, complemented
554	C₂×D₂₄	C₂²×D₄	1	1	yes	characteristic
555	C₂×D₂₄	C₂²×D₄	1	2	yes	—
556	C₂×D₂₄	C₂×#41	1	1	yes	characteristic, complemented
557	C₂×D₃×C₈	#120	1	1	yes	characteristic
558	C₂×D₃×C₈	#120	1	1	yes	characteristic
559	C₂×D₃×C₈	#120	1	1	yes	characteristic
560	C₂×D₃×C₈	#120	1	1	yes	characteristic
561	C₂×D₃×C₈	C₂²×D₄	1	1	yes	characteristic
562	C₂×D₃×C₈	C₂²×D₄	1	1	yes	characteristic
563	C₂×D₃×C₈	C₂²×D₄	1	1	yes	characteristic
564	C₂×D₃×C₈	C₂²×D₄	1	1	yes	characteristic
565	C₂×D₃×C₈	C₂×#41	1	1	yes	characteristic
566	C₂×D₃×C₈	C₂×#41	1	1	yes	characteristic
567	C₂×D₃×C₈	C₂×#41	1	1	yes	characteristic
568	C₂×D₃×C₈	C₂×#41	1	1	yes	characteristic
569	C₂×D₃×C₈	C₂×#41	1	1	yes	characteristic
570	C₂×D₃×C₈	C₂×#41	1	1	yes	characteristic
571	C₂×D₃×C₈	C₂×#41	1	1	yes	characteristic
572	C₂×D₃×C₈	C₂×#41	1	1	yes	characteristic
573	D₃×C₂²⋊C₄	AGL(1,ℤ/8)	1	2	yes	—
574	#877	AGL(1,ℤ/8)	1	2	yes	—
575	C₄²×D₃	#120	1	1	yes	characteristic
576	C₄²×D₃	#120	1	1	yes	characteristic
577	C₄²×D₃	#120	1	1	yes	characteristic
578	C₄²×D₃	#120	1	1	yes	characteristic
579	C₃×M₃₂	C₂×#41	1	2	yes	complemented
580	C₂×C₃×C₁₆	C₂×#41	1	2	yes	complemented
581	C₃×#108	C₂×#41	1	2	yes	complemented
582	C₃×#106	C₂²×D₄	1	2	yes	—
583	C₃×#106	C₂²×D₄	1	1	yes	characteristic
584	C₃×#106	C₂²×D₄	1	1	yes	characteristic
585	C₃×#97	C₂²×D₄	1	1	yes	characteristic
586	C₃×#97	C₂²×D₄	1	1	yes	characteristic
587	C₃×#97	C₂²×D₄	1	1	yes	characteristic
588	C₃×#97	C₂²×D₄	1	1	yes	characteristic
589	#819	C₂×#41	1	2	yes	complemented
590	#817	C₂²×D₄	1	2	yes	—
591	#817	C₂²×D₄	1	1	yes	characteristic
592	#817	C₂²×D₄	1	1	yes	characteristic
593	#815	#120	1	1	yes	characteristic
594	#815	#120	1	1	yes	characteristic
595	#815	#120	1	1	yes	characteristic
596	#815	#120	1	1	yes	characteristic
597	#815	C₂²×D₄	1	1	yes	characteristic
598	#815	C₂²×D₄	1	1	yes	characteristic
599	#815	C₂²×D₄	1	1	yes	characteristic
600	#815	C₂²×D₄	1	1	yes	characteristic
601	#812	C₂×#41	1	2	yes	complemented
602	C₂×C₃⋊C₁₆	C₂×#41	1	2	yes	complemented
603	#803	#120	1	1	yes	characteristic
604	#803	#120	1	1	yes	characteristic
605	#803	#120	1	1	yes	characteristic
606	#803	#120	1	1	yes	characteristic
607	C₂×#135	C₂³×D₃	1	1	yes	characteristic
608	C₂×#135	C₂³×D₃	1	1	yes	characteristic
609	C₂²×D₈	C₂³×D₃	1	1	yes	characteristic
610	C₂×#131	D₃×D₄	1	1	yes	characteristic
611	C₂×#131	C₂³×D₃	1	1	yes	characteristic
612	C₄×#41	D₃×D₄	1	1	yes	characteristic
613	C₂×M₃₂	C₂³×D₃	1	1	yes	characteristic
614	C₂×M₃₂	C₂³×D₃	1	1	yes	characteristic
615	C₂×M₃₂	C₂³×D₃	1	1	yes	characteristic
616	C₂×M₃₂	C₂³×D₃	1	1	yes	characteristic
617	#442	D₃×D₄	1	1	yes	characteristic
618	#442	D₃×D₄	1	2	yes	—
619	#442	D₃×D₄	1	2	yes	—
620	#442	D₃×D₄	1	1	yes	characteristic
621	#441	D₃×D₄	1	1	yes	characteristic
622	#441	D₃×D₄	1	1	yes	characteristic
623	C₂×#108	C₂³×D₃	1	1	yes	characteristic
624	C₂×#108	C₂³×D₃	1	1	yes	characteristic
625	#427	C₂³×D₃	1	1	yes	characteristic
626	#427	C₂³×D₃	1	1	yes	characteristic
627	C₂×#106	C₂³×D₃	1	1	yes	characteristic
628	#405	D₃×D₄	1	1	yes	characteristic
629	#405	C₂³×D₃	1	1	yes	characteristic
630	C₄×M₁₆	D₃×D₄	1	1	yes	characteristic
631	C₂×#97	C₂³×D₃	1	1	yes	characteristic
632	C₂³×D₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
633	C₂×C₃×Q₈	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
634	C₂×C₃×D₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
635	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
636	C₂²×Dic₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
637	C₂×D₁₂	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
638	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
639	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
640	C₂×C₄×D₃	#525	1	1	yes	characteristic
641	C₂×C₄×D₃	#525	1	1	yes	characteristic
642	C₂×C₄×D₃	#532	1	1	yes	characteristic
643	C₂×C₄×D₃	#532	1	1	yes	characteristic
644	C₂×C₄×D₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
645	C₂×C₄×D₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
646	C₂×C₄×D₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
647	C₂×C₄×D₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
648	C₂×C₄×D₃	#575	1	1	yes	characteristic
649	C₂×C₄×D₃	#575	1	1	yes	characteristic
650	C₂×Dic₆	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
651	C₃×M₁₆	C₂×AGL(1,ℤ/8)	1	2	yes	—
652	C₂×C₃×C₈	C₂×#120	1	1	yes	characteristic
653	C₂×C₃×C₈	C₂×#120	1	1	yes	characteristic
654	C₂×C₃×C₈	C₂³×D₄	1	1	yes	characteristic
655	C₂×C₃×C₈	C₂³×D₄	1	1	yes	characteristic
656	C₂×C₃×C₈	C₂²×#41	1	1	yes	characteristic
657	C₂×C₃×C₈	C₂²×#41	1	1	yes	characteristic
658	C₂×C₃×C₈	C₂²×#41	1	1	yes	characteristic
659	C₂×C₃×C₈	C₂²×#41	1	1	yes	characteristic
660	C₃×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
661	C₃×C₄²	C₂×#120	1	1	yes	characteristic
662	C₃×C₄²	C₂×#120	1	1	yes	characteristic
663	#217	C₂×AGL(1,ℤ/8)	1	2	yes	—
664	C₄×Dic₃	C₂×#120	1	1	yes	characteristic
665	C₄×Dic₃	C₂×#120	1	1	yes	characteristic
666	#208	C₂×AGL(1,ℤ/8)	1	2	yes	—
667	C₂×C₃⋊C₈	C₂×#120	1	1	yes	characteristic
668	C₂×C₃⋊C₈	C₂×#120	1	1	yes	characteristic
669	C₂×C₃⋊C₈	C₂×#120	1	1	yes	characteristic
670	C₂×C₃⋊C₈	C₂×#120	1	1	yes	characteristic
671	C₂×C₃⋊C₈	#525	1	1	yes	characteristic
672	C₂×C₃⋊C₈	#525	1	1	yes	characteristic
673	C₂×C₃⋊C₈	#532	1	1	yes	characteristic
674	C₂×C₃⋊C₈	#532	1	1	yes	characteristic
675	D₃×C₈	#525	1	1	yes	characteristic
676	D₃×C₈	#525	1	1	yes	characteristic
677	D₃×C₈	#525	1	1	yes	characteristic
678	D₃×C₈	#525	1	1	yes	characteristic
679	D₃×C₈	#525	1	1	yes	characteristic
680	D₃×C₈	#525	1	1	yes	characteristic
681	D₃×C₈	#525	1	1	yes	characteristic
682	D₃×C₈	#525	1	1	yes	characteristic
683	D₃×C₈	#532	1	1	yes	characteristic
684	D₃×C₈	#532	1	1	yes	characteristic
685	D₃×C₈	#532	1	1	yes	characteristic
686	D₃×C₈	#532	1	1	yes	characteristic
687	D₃×C₈	#532	1	1	yes	characteristic
688	D₃×C₈	#532	1	1	yes	characteristic
689	D₃×C₈	#532	1	1	yes	characteristic
690	D₃×C₈	#532	1	1	yes	characteristic
691	C₂×#41	C₂×D₃×D₄	1	1	yes	characteristic
692	C₂×Q₁₆	C₂×D₃×D₄	1	1	yes	characteristic
693	C₂×Q₁₆	D₃×#41	1	1	yes	characteristic, complemented
694	C₂×D₈	C₂×D₃×D₄	1	2	yes	—
695	C₂×D₈	C₂×D₃×D₄	1	1	yes	characteristic
696	C₂×D₈	D₃×#41	1	1	yes	characteristic, complemented
697	C₂×M₁₆	C₂×D₃×D₄	1	1	yes	characteristic
698	C₂×M₁₆	C₂×D₃×D₄	1	1	yes	characteristic
699	C₂²×C₈	C₂×D₃×D₄	1	1	yes	characteristic
700	C₂²×C₈	C₂⁴×D₃	1	1	yes	characteristic
701	#117	C₂×D₃×D₄	1	1	yes	characteristic
702	C₂×C₄²	C₂×D₃×D₄	1	1	yes	characteristic
703	M₃₂	D₃×#41	1	2	yes	complemented
704	C₂×C₁₆	D₃×#41	1	2	yes	complemented
705	#108	D₃×#41	1	2	yes	complemented
706	#106	C₂×D₃×D₄	1	2	yes	—
707	#106	C₂×D₃×D₄	1	1	yes	characteristic
708	#106	C₂×D₃×D₄	1	1	yes	characteristic
709	#97	C₂×D₃×D₄	1	1	yes	characteristic
710	#97	C₂×D₃×D₄	1	1	yes	characteristic
711	#97	C₂×D₃×D₄	1	1	yes	characteristic
712	#97	C₂×D₃×D₄	1	1	yes	characteristic
713	C₂³×C₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
714	C₂²×D₃	#3003	1	1	yes	characteristic
715	C₂²×D₃	#3003	1	1	yes	characteristic
716	C₂²×D₃	#3115	1	1	yes	characteristic
717	C₂²×D₃	#3115	1	1	yes	characteristic
718	C₂²×D₃	#3184	1	1	yes	characteristic
719	C₂²×D₃	#3184	1	1	yes	characteristic
720	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
721	C₂×C₃×C₄	C₂×#525	1	1	yes	characteristic
722	C₂×C₃×C₄	C₂×#532	1	1	yes	characteristic
723	C₂×C₃×C₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
724	C₂×C₃×C₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
725	C₂×C₃×C₄	C₂×#575	1	1	yes	characteristic
726	C₂×Dic₃	#3003	1	1	yes	characteristic
727	C₂×Dic₃	#3003	1	1	yes	characteristic
728	C₂×Dic₃	#3115	1	1	yes	characteristic
729	C₂×Dic₃	#3115	1	1	yes	characteristic
730	C₂×Dic₃	#3184	1	1	yes	characteristic
731	C₂×Dic₃	#3184	1	1	yes	characteristic
732	C₄×D₃	#2388	1	1	yes	characteristic
733	C₄×D₃	#2388	1	1	yes	characteristic
734	C₄×D₃	#2388	1	1	yes	characteristic
735	C₄×D₃	#2388	1	1	yes	characteristic
736	C₄×D₃	#3006	1	1	yes	characteristic
737	C₄×D₃	#3006	1	1	yes	characteristic
738	C₄×D₃	#3006	1	1	yes	characteristic
739	C₄×D₃	#3006	1	1	yes	characteristic
740	C₄×D₃	#3109	1	1	yes	characteristic
741	C₄×D₃	#3109	1	1	yes	characteristic
742	C₄×D₃	#3109	1	1	yes	characteristic
743	C₄×D₃	#3109	1	1	yes	characteristic
744	C₄×D₃	#3180	1	1	yes	characteristic
745	C₄×D₃	#3180	1	1	yes	characteristic
746	C₄×D₃	#3180	1	1	yes	characteristic
747	C₄×D₃	#3180	1	1	yes	characteristic
748	C₃×C₈	C₂×#525	1	1	yes	characteristic
749	C₃×C₈	C₂×#525	1	1	yes	characteristic
750	C₃×C₈	C₂×#532	1	1	yes	characteristic
751	C₃×C₈	C₂×#532	1	1	yes	characteristic
752	C₃⋊C₈	#2388	1	1	yes	characteristic
753	C₃⋊C₈	#2388	1	1	yes	characteristic
754	C₃⋊C₈	#2388	1	1	yes	characteristic
755	C₃⋊C₈	#2388	1	1	yes	characteristic
756	C₂×Q₈	D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
757	C₂×D₄	D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
758	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
759	M₁₆	D₃×AGL(1,ℤ/8)	1	2	yes	—
760	C₂×C₈	D₃×#120	1	1	yes	characteristic
761	C₂×C₈	D₃×#120	1	1	yes	characteristic
762	C₂×C₈	C₂²×D₃×D₄	1	1	yes	characteristic
763	C₂×C₈	C₂²×D₃×D₄	1	1	yes	characteristic
764	C₂×C₈	C₂×D₃×#41	1	1	yes	characteristic
765	C₂×C₈	C₂×D₃×#41	1	1	yes	characteristic
766	C₂×C₈	C₂×D₃×#41	1	1	yes	characteristic
767	C₂×C₈	C₂×D₃×#41	1	1	yes	characteristic
768	C₂²⋊C₄	D₃×AGL(1,ℤ/8)	1	2	yes	—
769	C₄²	D₃×#120	1	1	yes	characteristic
770	C₄²	D₃×#120	1	1	yes	characteristic
771	C₂²×C₃	C₂×#3003	1	1	yes	characteristic
772	C₂²×C₃	C₂×#3115	1	1	yes	characteristic
773	C₂²×C₃	C₂×#3184	1	1	yes	characteristic
774	C₂×D₃	#23573	1	1	yes	characteristic
775	C₂×D₃	#23573	1	1	yes	characteristic
776	C₂×D₃	#23573	1	1	yes	characteristic
777	C₂×D₃	#23573	1	1	yes	characteristic
778	C₃×C₄	C₂×#2388	1	1	yes	characteristic
779	C₃×C₄	C₂×#3006	1	1	yes	characteristic
780	C₃×C₄	C₂×#3109	1	1	yes	characteristic
781	C₃×C₄	C₂×#3180	1	1	yes	characteristic
782	Dic₃	#23573	1	1	yes	characteristic
783	Dic₃	#23573	1	1	yes	characteristic
784	Dic₃	#23573	1	1	yes	characteristic
785	Dic₃	#23573	1	1	yes	characteristic
786	C₂³	C₂×D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
787	C₂×C₄	C₂×D₃×#120	1	1	yes	characteristic
788	C₂×C₄	D₃×#525	1	1	yes	characteristic
789	C₂×C₄	D₃×#532	1	1	yes	characteristic
790	C₂×C₄	C₂×D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
791	C₂×C₄	C₂×D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
792	C₂×C₄	D₃×#575	1	1	yes	characteristic
793	C₈	D₃×#525	1	1	yes	characteristic
794	C₈	D₃×#525	1	1	yes	characteristic
795	C₈	D₃×#532	1	1	yes	characteristic
796	C₈	D₃×#532	1	1	yes	characteristic
797	C₂×C₃	C₂×#23573	1	1	yes	characteristic
798	D₃	#499269	1	2	yes	direct product factor
799	C₂²	D₃×#3003	1	1	yes	characteristic
800	C₂²	D₃×#3115	1	1	yes	characteristic
801	C₂²	D₃×#3184	1	1	yes	characteristic
802	C₄	D₃×#2388	1	1	yes	characteristic
803	C₄	D₃×#3006	1	1	yes	characteristic
804	C₄	D₃×#3109	1	1	yes	characteristic
805	C₄	D₃×#3180	1	1	yes	characteristic
806	C₃	C₂×#499269	1	1	yes	characteristic, complemented, Sylow
807	C₂	D₃×#23573	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃×#23573
commutator, cosocle	C₂²×C₃×C₈	C₂⁵
Frattini	C₂²×C₈	C₂⁴×D₃
Fitting	C₃×#499269	C₂
socle	C₂×C₃	C₂×#23573
hypercenter	#499269	D₃
hypocenter	C₃	C₂×#499269
LCS	G ▷ C₂²×C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2875 ◁ #499269

Complements

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

N	H ≅ G/N	type
1. #72271660	C₂	semidirect
2. D₃×#13310	C₂	semidirect
3. #72271651	C₂	semidirect
4. D₃×#13318	C₂	semidirect
5. #72271643	C₂	semidirect
6. #72271642	C₂	semidirect
7. #72271639	C₂	semidirect
8. #72271634	C₂	semidirect
9. D₃×#13417	C₂	semidirect
10. #72271630	C₂	semidirect
11. #72271627	C₂	semidirect
12. #72271621	C₂	semidirect
13. D₃×#13334	C₂	semidirect
14. C₃×#499269	C₂	semidirect
15. D₃×#13374	C₂	semidirect
16. D₃×#13460	C₂	semidirect
17. #72271510	C₂	semidirect
18. #72271482	C₂	semidirect
19. #72271409	C₂	semidirect
20. D₃×#13400	C₂	semidirect
21. #72270440	C₂	semidirect
22. D₃×#13396	C₂	semidirect
23. #72270254	C₂	semidirect
24. #72270166	C₂	semidirect
25. D₃×#21559	C₂	semidirect
26. D₃×#12609	C₂	semidirect
27. D₃×#12649	C₂	semidirect
28. D₃×#33468	C₂	semidirect
29. D₃×#60698	C₂	semidirect
30. D₃×#12647	C₂	semidirect
31. C₂×D₃×AGL(1,ℤ/16)	C₂	semidirect
34. #11665268	C₂²	semidirect
35. #11665267	C₂²	semidirect
36. #11665266	C₂²	semidirect
37. #11665265	C₂²	semidirect
38. #11665260	C₂²	semidirect
39. #11665259	C₂²	semidirect
40. #11665253	C₂²	semidirect
50. #10948640	C₂²	semidirect
51. #10948639	C₂²	semidirect
52. #10948638	C₂²	semidirect
53. #10948637	C₂²	semidirect
54. #10948636	C₂²	semidirect
55. #10948635	C₂²	semidirect
56. #10948633	C₂²	semidirect
57. C₂×#69254	C₂²	semidirect
58. C₂×#69091	C₂²	semidirect
59. C₂×#71515	C₂²	semidirect
60. C₂×#70929	C₂²	semidirect
61. C₂×#69310	C₂²	semidirect
62. C₂×#70918	C₂²	semidirect
63. C₂×#69249	C₂²	semidirect
78. #10802140	C₂²	semidirect
79. #10802139	C₂²	semidirect
80. #10802138	C₂²	semidirect
81. #10802137	C₂²	semidirect
82. #10802132	C₂²	semidirect
83. #10802131	C₂²	semidirect
84. #10802130	C₂²	semidirect
89. #10714853	C₂²	semidirect
90. #10714852	C₂²	semidirect
91. #10714851	C₂²	semidirect
92. #10714850	C₂²	semidirect
93. #10714849	C₂²	semidirect
94. #10714848	C₂²	semidirect
95. #10714847	C₂²	semidirect
96. #10714592	C₂²	semidirect
97. #10714591	C₂²	semidirect
98. #10714590	C₂²	semidirect
99. #10714589	C₂²	semidirect
100. #10714588	C₂²	semidirect
101. #10714587	C₂²	semidirect
102. #10714586	C₂²	semidirect
103. #10714485	C₂²	semidirect
104. #10714484	C₂²	semidirect
105. #10714483	C₂²	semidirect
106. #10714482	C₂²	semidirect
107. #10714481	C₂²	semidirect
108. #10714480	C₂²	semidirect
109. #10714479	C₂²	semidirect
110. #10714457	C₂²	semidirect
111. #10714456	C₂²	semidirect
112. #10714455	C₂²	semidirect
113. #10714454	C₂²	semidirect
114. #10714453	C₂²	semidirect
115. #10714452	C₂²	semidirect
116. #10714451	C₂²	semidirect
117. #10714313	C₂²	semidirect
118. #10714312	C₂²	semidirect
119. #10714311	C₂²	semidirect
120. #10714310	C₂²	semidirect
121. #10714309	C₂²	semidirect
122. #10714308	C₂²	semidirect
123. #10714307	C₂²	semidirect
124. #10714073	C₂²	semidirect
125. #10714072	C₂²	semidirect
126. #10714071	C₂²	semidirect
127. #10714070	C₂²	semidirect
128. #10714069	C₂²	semidirect
129. #10714068	C₂²	semidirect
130. #10714067	C₂²	semidirect
131. #10713973	C₂²	semidirect
132. #10713972	C₂²	semidirect
133. #10713971	C₂²	semidirect
134. #10713970	C₂²	semidirect
135. #10713969	C₂²	semidirect
136. #10713968	C₂²	semidirect
137. #10713967	C₂²	semidirect
138. #10713923	C₂²	semidirect
139. #10713922	C₂²	semidirect
140. #10713921	C₂²	semidirect
141. #10713920	C₂²	semidirect
142. #10713919	C₂²	semidirect
143. #10713918	C₂²	semidirect
144. #10713917	C₂²	semidirect
145. #10710476	C₂²	semidirect
146. #10710475	C₂²	semidirect
147. #10710474	C₂²	semidirect
148. #10710473	C₂²	semidirect
149. #10710472	C₂²	semidirect
150. #10710471	C₂²	semidirect
151. #10710470	C₂²	semidirect
152. #10710462	C₂²	semidirect
153. #10710461	C₂²	semidirect
154. #10710460	C₂²	semidirect
155. #10710459	C₂²	semidirect
156. #10710458	C₂²	semidirect
157. #10710457	C₂²	semidirect
158. #10710456	C₂²	semidirect
159. #10710264	C₂²	semidirect
160. #10710263	C₂²	semidirect
161. #10710263	C₂²	semidirect
162. #10710262	C₂²	semidirect
163. #10710261	C₂²	semidirect
164. #10710260	C₂²	semidirect
165. #10710260	C₂²	semidirect
172. C₃×#60698	C₂²	semidirect
173. C₃×#33468	C₂²	semidirect
174. C₂×C₃×AGL(1,ℤ/16)	C₂²	semidirect
175. C₃×#21559	C₂²	semidirect
176. C₃×#13460	C₂²	semidirect
177. C₃×#13417	C₂²	semidirect
178. C₃×#13400	C₂²	semidirect
179. C₃×#13396	C₂²	semidirect
180. C₃×#13374	C₂²	semidirect
181. C₃×#13334	C₂²	semidirect
182. C₃×#13318	C₂²	semidirect
183. C₃×#13310	C₂²	semidirect
184. C₃×#12649	C₂²	semidirect
185. C₃×#12647	C₂²	semidirect
186. C₃×#12609	C₂²	semidirect
187. #499269	D₃	direct (N × H)
363. #60698	C₂×D₃	semidirect
364. #33468	C₂×D₃	semidirect
365. C₂×AGL(1,ℤ/16)	C₂×D₃	semidirect
366. #21559	C₂×D₃	semidirect
367. #13460	C₂×D₃	semidirect
368. #13417	C₂×D₃	semidirect
369. #13400	C₂×D₃	semidirect
370. #13396	C₂×D₃	semidirect
371. #13374	C₂×D₃	semidirect
372. #13334	C₂×D₃	semidirect
373. #13318	C₂×D₃	semidirect
374. #13310	C₂×D₃	semidirect
375. #12649	C₂×D₃	semidirect
376. #12647	C₂×D₃	semidirect
377. #12609	C₂×D₃	semidirect
389. C₂×#919	#41	semidirect
391. C₂×D₃×Q₁₆	#41	semidirect
393. C₂×#912	#41	semidirect
397. C₂×D₃×D₈	#41	semidirect
459. D₃×M₃₂	#41	semidirect
460. D₃×M₃₂	#41	semidirect
461. C₂×#798	#41	semidirect
462. C₂×D₃×C₁₆	#41	semidirect
463. D₃×#108	#41	semidirect
464. D₃×#108	#41	semidirect
534. C₂×C₃×Q₁₆	C₂×#41	semidirect
537. C₂×C₃×D₈	C₂×#41	semidirect
553. C₂×Dic₁₂	C₂×#41	semidirect
556. C₂×D₂₄	C₂×#41	semidirect
579. C₃×M₃₂	C₂×#41	semidirect
580. C₂×C₃×C₁₆	C₂×#41	semidirect
581. C₃×#108	C₂×#41	semidirect
589. #819	C₂×#41	semidirect
601. #812	C₂×#41	semidirect
602. C₂×C₃⋊C₁₆	C₂×#41	semidirect
693. C₂×Q₁₆	D₃×#41	semidirect
696. C₂×D₈	D₃×#41	semidirect
703. M₃₂	D₃×#41	semidirect
704. C₂×C₁₆	D₃×#41	semidirect
705. #108	D₃×#41	semidirect
798. D₃	#499269	direct (N × H)
806. C₃	C₂×#499269	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#72271660	2
D₃×#13310	2
#72271651	2
D₃×#13318	2
#72271643	2
#72271642	2
#72271639	2
#72271634	2
D₃×#13417	2
#72271630	2
#72271627	2
#72271621	2
D₃×#13334	2
C₃×#499269	2
D₃×#13374	2
D₃×#13460	2
#72271510	2
#72271482	2
#72271409	2
D₃×#13400	2
#72270440	2
D₃×#13396	2
#72270254	2
#72270166	2
D₃×#21559	2
D₃×#12609	2
D₃×#12649	2
D₃×#33468	2
D₃×#60698	2
C₂×#499269	3
D₃×#12647	2
C₂×D₃×AGL(1,ℤ/16)	2

Subgroups — D3×#499269 #72271666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#499269 #72271666