Subgroups — C₃×D₃×#471 #11867841

Order 1152.

988 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×D₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#471	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5203	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5200	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5177	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4898	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4754	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×D₃×#101	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#4748	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₃×#100	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#471	—	3	1	no	maximal
17	D₃×#471	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₃×D₃×#41	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
21	C₃²×#137	C₂²	1	1	yes	characteristic, complemented
22	C₃²×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
23	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₃²×#131	C₂²	1	1	yes	characteristic, complemented
25	C₃×#951	C₂²	1	1	yes	characteristic, complemented
26	C₃×#949	C₂²	1	1	yes	characteristic
27	C₃×#948	C₂²	1	1	yes	characteristic, complemented
28	C₃×#942	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×#215	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×#214	C₂²	1	1	yes	characteristic, complemented
31	C₃×#932	C₂²	1	1	yes	characteristic
32	C₃×#918	—	2	1	no	—
33	C₃×D₃×Q₁₆	—	2	1	no	—
34	C₃×#915	—	2	1	no	—
35	C₃×#914	—	2	1	no	—
36	C₃×D₃×SD₁₆	—	2	1	no	—
37	C₃×D₃×SD₁₆	—	2	1	no	—
38	C₃×D₃×SD₁₆	—	2	1	no	—
39	C₃×D₃×SD₁₆	—	2	1	no	—
40	C₃×D₃×SD₁₆	—	2	1	no	—
41	C₃×D₃×SD₁₆	—	2	1	no	—
42	C₃×#911	—	2	1	no	—
43	C₃×D₃×D₈	—	2	1	no	—
44	C₃×#909	C₂²	1	1	yes	characteristic, complemented
45	C₃×#908	C₂²	1	1	yes	characteristic
46	C₃×#907	—	2	1	no	—
47	C₃×#907	C₂²	1	1	yes	characteristic, complemented
48	C₃×D₃×M₁₆	—	2	1	no	—
49	C₃×D₃×M₁₆	C₂²	1	1	yes	characteristic
50	C₃×D₃×M₁₆	C₂²	1	1	yes	characteristic
51	C₃×D₃×M₁₆	C₂²	1	1	yes	characteristic
52	C₂×C₃×#204	C₂²	1	1	yes	characteristic, complemented
53	C₃×#901	—	2	1	no	—
54	C₃×#901	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×D₃×C₈	—	2	1	no	—
56	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
57	C₃²×#108	C₂²	1	1	yes	characteristic, complemented
58	C₃²×#101	C₂²	1	1	yes	characteristic, complemented
59	C₃²×#100	C₂²	1	1	yes	characteristic, complemented
60	C₃×#836	C₂²	1	1	yes	characteristic, complemented
61	C₃×#833	C₂²	1	1	yes	characteristic, complemented
62	C₃×#824	C₂²	1	1	yes	characteristic, complemented
63	C₃×#824	C₂²	1	1	yes	characteristic, complemented
64	C₃×#823	C₂²	1	1	yes	characteristic, complemented
65	C₃×#823	C₂²	1	1	yes	characteristic, complemented
66	C₃×#822	C₂²	1	1	yes	characteristic, complemented
67	C₃×#822	C₂²	1	1	yes	characteristic, complemented
68	C₃×#819	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₃×#137	—	3	1	no	—
70	C₂×C₃×AGL(1,ℤ/8)	—	3	1	no	—
71	C₂²×C₃×SD₁₆	—	3	1	no	—
72	C₂×C₃×#131	—	3	1	no	—
73	D₃×#137	C₂×C₃	1	1	yes	characteristic, complemented
74	D₃×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
75	C₂×D₃×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
76	D₃×#131	C₂×C₃	1	1	yes	characteristic, complemented
77	C₃×#471	—	2	1	no	—
78	C₃×#471	—	3	1	no	—
79	C₃×#471	—	3	1	no	—
80	C₃×#471	—	3	1	no	—
81	C₃×#471	—	3	1	no	—
82	C₃×#471	—	3	1	no	—
83	C₃×#471	—	3	1	no	—
84	C₃×#471	—	3	1	no	—
85	C₃×#471	D₃	1	1	yes	characteristic, direct product factor
86	C₃×#471	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×C₃×#108	—	3	1	no	—
88	C₂×C₃×#101	—	3	1	no	—
89	C₂×C₃×#100	—	3	1	no	—
90	#5203	C₂×C₃	1	1	yes	characteristic, complemented
91	#5200	C₂×C₃	1	1	yes	characteristic, complemented
92	#5177	C₂×C₃	1	1	yes	characteristic, complemented
93	#5141	C₂×C₃	1	1	yes	characteristic, complemented
94	#4898	C₂×C₃	1	1	yes	characteristic, complemented
95	D₃×#108	C₂×C₃	1	1	yes	characteristic, complemented
96	#4754	C₂×C₃	1	1	yes	characteristic, complemented
97	D₃×#101	C₂×C₃	1	1	yes	characteristic, complemented
98	#4748	C₂×C₃	1	1	yes	characteristic, complemented
99	D₃×#100	C₂×C₃	1	1	yes	characteristic, complemented
100	C₂³×C₃×D₃	—	2	1	no	—
101	C₃²×#41	C₂³	1	1	yes	characteristic
102	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
103	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
104	C₂×C₃×#67	—	2	1	no	—
105	C₃×#239	D₄	1	1	yes	characteristic
106	C₃×D₃×Q₈	—	2	1	no	—
107	C₃×D₃×Q₈	—	2	1	no	—
108	C₃×D₃×Q₈	—	2	1	no	—
109	C₃×D₃×Q₈	—	2	1	no	—
110	C₃×D₃×Q₈	D₄	1	1	yes	characteristic
111	C₃×#237	—	2	1	no	—
112	C₃×#237	D₄	1	1	yes	characteristic
113	C₃×D₃×D₄	—	2	1	no	—
114	C₃×D₃×D₄	—	2	1	no	—
115	C₃×D₃×D₄	—	2	1	no	—
116	C₃×D₃×D₄	—	2	1	no	—
117	C₃×D₃×D₄	—	2	1	no	—
118	C₃×D₃×D₄	D₄	1	1	yes	characteristic
119	C₃×#235	—	2	1	no	—
120	C₃×#235	C₂³	1	1	yes	characteristic
121	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₄×D₃	—	2	1	no	—
123	C₂×C₃×C₄×D₃	—	2	1	no	—
124	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
125	C₂×C₃×Dic₆	—	2	1	no	—
126	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
127	C₃²×Q₁₆	—	2	1	no	—
128	C₃²×SD₁₆	—	2	1	no	—
129	C₃²×SD₁₆	—	2	1	no	—
130	C₃²×SD₁₆	—	2	1	no	—
131	C₃²×SD₁₆	—	2	1	no	—
132	C₃²×D₈	—	2	1	no	—
133	C₃²×M₁₆	—	2	1	no	—
134	C₃²×M₁₆	C₂³	1	1	yes	characteristic
135	C₃²×M₁₆	C₂³	1	1	yes	characteristic
136	C₃²×M₁₆	C₂³	1	1	yes	characteristic
137	C₂×C₃²×C₈	—	2	1	no	—
138	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
139	C₃×#216	—	2	1	no	—
140	C₃×#216	—	2	1	no	—
141	C₃×#215	—	2	1	no	—
142	C₃×#215	—	2	1	no	—
143	C₃×#215	—	2	1	no	—
144	C₃×#215	—	2	1	no	—
145	C₃×#214	—	2	1	no	—
146	C₃×#214	—	2	1	no	—
147	C₃×#214	—	2	1	no	—
148	C₃×#214	—	2	1	no	—
149	C₃×#213	—	2	1	no	—
150	C₃×#213	—	2	1	no	—
151	C₃×#208	—	2	1	no	—
152	C₃×#208	C₂³	1	1	yes	characteristic
153	C₃×#208	C₂³	1	1	yes	characteristic
154	C₃×#208	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₃⋊C₈	—	2	1	no	—
156	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
157	C₃×Dic₁₂	—	2	1	no	—
158	C₃×D₂₄	—	2	1	no	—
159	C₃×#204	—	2	1	no	—
160	C₃×#204	—	2	1	no	—
161	C₃×#204	—	2	1	no	—
162	C₃×#204	—	2	1	no	—
163	C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
164	C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
165	C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
166	C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
167	C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
168	C₃×D₃×C₈	—	2	1	no	—
169	C₃×D₃×C₈	—	2	1	no	—
170	C₃×D₃×C₈	—	2	1	no	—
171	C₃×D₃×C₈	—	2	1	no	—
172	C₃×D₃×C₈	—	2	1	no	—
173	C₃×D₃×C₈	D₄	1	1	yes	characteristic
174	C₃×D₃×C₈	D₄	1	1	yes	characteristic
175	C₃×D₃×C₈	D₄	1	1	yes	characteristic
176	C₃×D₃×C₈	D₄	1	1	yes	characteristic
177	C₂×#471	—	3	1	no	Sylow
178	C₂×C₃×#41	—	3	1	no	—
179	C₂²×C₃×Q₈	—	3	1	no	—
180	C₂²×C₃×D₄	—	3	1	no	—
181	D₃×#41	C₂²×C₃	1	1	yes	characteristic
182	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
183	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
184	C₃×#137	—	2	1	no	—
185	C₃×#137	—	3	1	no	—
186	C₃×#137	—	3	1	no	—
187	C₃×#137	—	3	1	no	—
188	C₃×#137	—	6	1	no	—
189	C₃×#137	—	6	1	no	—
190	C₃×#137	C₂×D₃	1	1	yes	characteristic, complemented
191	C₃×#137	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₃×AGL(1,ℤ/8)	—	2	1	no	—
193	C₃×AGL(1,ℤ/8)	—	3	1	no	—
194	C₃×AGL(1,ℤ/8)	—	3	1	no	—
195	C₃×AGL(1,ℤ/8)	—	3	1	no	—
196	C₃×AGL(1,ℤ/8)	—	6	1	no	—
197	C₃×AGL(1,ℤ/8)	—	6	1	no	—
198	C₃×AGL(1,ℤ/8)	C₂×D₃	1	1	yes	characteristic
199	C₃×AGL(1,ℤ/8)	C₂²×C₃	1	1	yes	characteristic
200	C₂×C₃×Q₁₆	—	6	1	no	—
201	C₂×C₃×SD₁₆	—	2	1	no	—
202	C₂×C₃×SD₁₆	—	3	1	no	—
203	C₂×C₃×SD₁₆	—	3	1	no	—
204	C₂×C₃×SD₁₆	—	3	1	no	—
205	C₂×C₃×SD₁₆	—	6	1	no	—
206	C₂×C₃×SD₁₆	—	6	1	no	—
207	C₂×C₃×SD₁₆	—	6	1	no	—
208	C₂×C₃×SD₁₆	—	6	1	no	—
209	C₂×C₃×SD₁₆	—	6	1	no	—
210	C₂×C₃×SD₁₆	—	6	1	no	—
211	C₂×C₃×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
212	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
213	C₂×C₃×D₈	—	6	1	no	—
214	C₃×#131	—	2	1	no	—
215	C₃×#131	—	3	1	no	—
216	C₃×#131	—	3	1	no	—
217	C₃×#131	—	3	1	no	—
218	C₃×#131	—	6	1	no	—
219	C₃×#131	—	6	1	no	—
220	C₃×#131	C₂×D₃	1	1	yes	characteristic, complemented
221	C₃×#131	C₂²×C₃	1	1	yes	characteristic, complemented
222	C₂×C₃×M₁₆	—	3	1	no	—
223	C₂×C₃×M₁₆	—	3	1	no	—
224	C₂×C₃×M₁₆	—	3	1	no	—
225	C₂×C₃×M₁₆	—	6	1	no	—
226	C₂²×C₃×C₈	—	3	1	no	—
227	C₂²×C₃×C₈	—	6	1	no	—
228	#951	C₂²×C₃	1	1	yes	characteristic, complemented
229	#949	C₂²×C₃	1	1	yes	characteristic
230	#948	C₂²×C₃	1	1	yes	characteristic, complemented
231	#942	C₂²×C₃	1	1	yes	characteristic, complemented
232	C₂×#215	C₂²×C₃	1	1	yes	characteristic, complemented
233	C₂×#214	C₂²×C₃	1	1	yes	characteristic, complemented
234	#932	C₂²×C₃	1	1	yes	characteristic
235	#918	—	2	1	no	—
236	D₃×Q₁₆	—	2	1	no	—
237	#915	—	2	1	no	—
238	#914	—	2	1	no	—
239	D₃×SD₁₆	—	2	1	no	—
240	D₃×SD₁₆	—	2	1	no	—
241	D₃×SD₁₆	—	2	1	no	—
242	D₃×SD₁₆	—	2	1	no	—
243	D₃×SD₁₆	—	2	1	no	—
244	D₃×SD₁₆	—	2	1	no	—
245	#911	—	2	1	no	—
246	D₃×D₈	—	2	1	no	—
247	#909	C₂²×C₃	1	1	yes	characteristic, complemented
248	#908	C₂²×C₃	1	1	yes	characteristic
249	#907	—	2	1	no	—
250	#907	C₂²×C₃	1	1	yes	characteristic, complemented
251	D₃×M₁₆	—	2	1	no	—
252	D₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
253	D₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
254	D₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
255	C₂×#204	C₂²×C₃	1	1	yes	characteristic, complemented
256	#901	—	2	1	no	—
257	#901	C₂²×C₃	1	1	yes	characteristic, complemented
258	C₂×D₃×C₈	—	2	1	no	—
259	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
260	C₃×#108	—	2	1	no	—
261	C₃×#108	—	3	1	no	—
262	C₃×#108	—	3	1	no	—
263	C₃×#108	—	3	1	no	—
264	C₃×#108	C₂×D₃	1	1	yes	characteristic, complemented
265	C₃×#108	C₂²×C₃	1	1	yes	characteristic, complemented
266	C₃×#101	—	2	1	no	—
267	C₃×#101	—	3	1	no	—
268	C₃×#101	—	3	1	no	—
269	C₃×#101	—	3	1	no	—
270	C₃×#101	C₂×D₃	1	1	yes	characteristic, complemented
271	C₃×#101	C₂²×C₃	1	1	yes	characteristic, complemented
272	C₃×#100	—	2	1	no	—
273	C₃×#100	—	3	1	no	—
274	C₃×#100	—	3	1	no	—
275	C₃×#100	—	3	1	no	—
276	C₃×#100	C₂×D₃	1	1	yes	characteristic, complemented
277	C₃×#100	C₂²×C₃	1	1	yes	characteristic, complemented
278	#836	C₂²×C₃	1	1	yes	characteristic, complemented
279	#833	C₂²×C₃	1	1	yes	characteristic, complemented
280	#824	C₂²×C₃	1	1	yes	characteristic, complemented
281	#824	C₂²×C₃	1	1	yes	characteristic, complemented
282	#823	C₂²×C₃	1	1	yes	characteristic, complemented
283	#823	C₂²×C₃	1	1	yes	characteristic, complemented
284	#822	C₂²×C₃	1	1	yes	characteristic, complemented
285	#822	C₂²×C₃	1	1	yes	characteristic, complemented
286	#819	C₂²×C₃	1	1	yes	characteristic, complemented
287	C₂³×C₃²	—	2	1	no	—
288	C₂²×C₃×D₃	—	2	1	no	—
289	C₂²×C₃×D₃	—	2	1	no	—
290	C₂²×C₃×D₃	—	4	1	no	—
291	C₂²×C₃×D₃	—	4	1	no	—
292	C₂²×C₃×D₃	—	8	2	no	—
293	C₂²×C₃×D₃	#41	1	1	yes	characteristic
294	C₃²×Q₈	—	2	1	no	—
295	C₃²×Q₈	—	2	1	no	—
296	C₃²×Q₈	C₂×D₄	1	1	yes	characteristic
297	C₃²×D₄	—	2	1	no	—
298	C₃²×D₄	—	2	1	no	—
299	C₃²×D₄	—	2	1	no	—
300	C₃²×D₄	C₂×D₄	1	1	yes	characteristic
301	C₂×C₃²×C₄	—	2	1	no	—
302	C₂×C₃²×C₄	—	2	1	no	—
303	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
304	C₃×#67	—	2	1	no	—
305	C₃×#67	—	2	1	no	—
306	C₃×#67	—	2	1	no	—
307	C₃×#67	—	4	1	no	—
308	C₃×#67	—	4	1	no	—
309	C₂×C₃×Dic₃	—	2	1	no	—
310	C₂×C₃×Dic₃	—	2	1	no	—
311	C₂×C₃×Dic₃	#41	1	1	yes	characteristic
312	C₃×D₁₂	—	2	1	no	—
313	C₃×D₁₂	—	2	1	no	—
314	C₃×D₁₂	—	2	1	no	—
315	C₃×D₁₂	C₂×D₄	1	1	yes	characteristic
316	C₃×C₄×D₃	—	2	1	no	—
317	C₃×C₄×D₃	—	2	1	no	—
318	C₃×C₄×D₃	—	2	1	no	—
319	C₃×C₄×D₃	—	4	1	no	—
320	C₃×C₄×D₃	—	4	1	no	—
321	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
322	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
323	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
324	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
325	C₃×Dic₆	—	2	1	no	—
326	C₃×Dic₆	—	2	1	no	—
327	C₃×Dic₆	—	2	1	no	—
328	C₃×Dic₆	—	4	1	no	—
329	C₃×Dic₆	—	4	1	no	—
330	C₃×Dic₆	C₂×D₄	1	1	yes	characteristic
331	C₃²×C₈	—	2	1	no	—
332	C₃²×C₈	—	2	1	no	—
333	C₃²×C₈	—	2	1	no	—
334	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
335	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
336	C₃×C₃⋊C₈	—	2	1	no	—
337	C₃×C₃⋊C₈	—	2	1	no	—
338	C₃×C₃⋊C₈	—	2	1	no	—
339	C₃×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
340	C₃×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
341	C₂×#137	—	3	1	no	—
342	C₂×AGL(1,ℤ/8)	—	3	1	no	—
343	C₂²×SD₁₆	—	3	1	no	—
344	C₂×#131	—	3	1	no	—
345	#471	—	3	1	no	—
346	#471	—	3	1	no	—
347	#471	—	3	1	no	—
348	#471	—	3	1	no	—
349	#471	—	3	1	no	—
350	#471	—	3	1	no	—
351	#471	—	3	1	no	—
352	#471	C₃×D₃	1	1	yes	characteristic, direct product factor
353	C₂×#108	—	3	1	no	—
354	C₂×#101	—	3	1	no	—
355	C₂×#100	—	3	1	no	—
356	C₂⁴×C₃	—	6	1	no	—
357	C₂³×D₃	—	2	1	no	—
358	C₃×#41	—	2	1	no	—
359	C₃×#41	—	3	1	no	—
360	C₃×#41	—	3	1	no	—
361	C₃×#41	—	3	1	no	—
362	C₃×#41	—	6	1	no	—
363	C₃×#41	—	6	1	no	—
364	C₃×#41	C₂²×D₃	1	1	yes	characteristic
365	C₃×#41	C₂³×C₃	1	1	yes	characteristic
366	C₂×C₃×Q₈	—	2	1	no	—
367	C₂×C₃×Q₈	—	3	1	no	—
368	C₂×C₃×Q₈	—	3	1	no	—
369	C₂×C₃×Q₈	—	6	1	no	—
370	C₂×C₃×Q₈	—	6	1	no	—
371	C₂×C₃×Q₈	—	6	1	no	—
372	C₂×C₃×Q₈	—	6	1	no	—
373	C₂×C₃×Q₈	—	6	1	no	—
374	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
375	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
376	C₂×C₃×D₄	—	2	1	no	—
377	C₂×C₃×D₄	—	3	1	no	—
378	C₂×C₃×D₄	—	3	1	no	—
379	C₂×C₃×D₄	—	6	1	no	—
380	C₂×C₃×D₄	—	6	1	no	—
381	C₂×C₃×D₄	—	6	1	no	—
382	C₂×C₃×D₄	—	6	1	no	—
383	C₂×C₃×D₄	—	6	1	no	—
384	C₂×C₃×D₄	—	6	1	no	—
385	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
386	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
387	C₂²×C₃×C₄	—	3	1	no	—
388	C₂²×C₃×C₄	—	6	1	no	—
389	C₂²×C₃×C₄	—	6	1	no	—
390	C₂×#67	—	2	1	no	—
391	#239	C₃×D₄	1	1	yes	characteristic
392	D₃×Q₈	—	2	1	no	—
393	D₃×Q₈	—	2	1	no	—
394	D₃×Q₈	—	2	1	no	—
395	D₃×Q₈	—	2	1	no	—
396	D₃×Q₈	C₃×D₄	1	1	yes	characteristic
397	#237	—	2	1	no	—
398	#237	C₃×D₄	1	1	yes	characteristic
399	D₃×D₄	—	2	1	no	—
400	D₃×D₄	—	2	1	no	—
401	D₃×D₄	—	2	1	no	—
402	D₃×D₄	—	2	1	no	—
403	D₃×D₄	—	2	1	no	—
404	D₃×D₄	C₃×D₄	1	1	yes	characteristic
405	#235	—	2	1	no	—
406	#235	C₂³×C₃	1	1	yes	characteristic
407	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
408	C₂×C₄×D₃	—	2	1	no	—
409	C₂×C₄×D₃	—	2	1	no	—
410	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
411	C₂×Dic₆	—	2	1	no	—
412	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
413	C₃×Q₁₆	—	2	1	no	—
414	C₃×Q₁₆	—	2	1	no	—
415	C₃×Q₁₆	—	4	1	no	—
416	C₃×Q₁₆	—	6	1	no	—
417	C₃×Q₁₆	—	6	1	no	—
418	C₃×Q₁₆	—	6	1	no	—
419	C₃×SD₁₆	—	2	1	no	—
420	C₃×SD₁₆	—	2	1	no	—
421	C₃×SD₁₆	—	2	1	no	—
422	C₃×SD₁₆	—	2	1	no	—
423	C₃×SD₁₆	—	2	1	no	—
424	C₃×SD₁₆	—	2	1	no	—
425	C₃×SD₁₆	—	2	1	no	—
426	C₃×SD₁₆	—	2	1	no	—
427	C₃×SD₁₆	—	4	1	no	—
428	C₃×SD₁₆	—	4	1	no	—
429	C₃×SD₁₆	—	4	1	no	—
430	C₃×SD₁₆	—	4	1	no	—
431	C₃×SD₁₆	—	6	1	no	—
432	C₃×SD₁₆	—	6	1	no	—
433	C₃×SD₁₆	—	6	1	no	—
434	C₃×SD₁₆	—	6	1	no	—
435	C₃×SD₁₆	—	6	1	no	—
436	C₃×SD₁₆	—	6	1	no	—
437	C₃×SD₁₆	—	6	1	no	—
438	C₃×SD₁₆	—	6	1	no	—
439	C₃×SD₁₆	—	6	1	no	—
440	C₃×SD₁₆	—	6	1	no	—
441	C₃×SD₁₆	—	6	1	no	—
442	C₃×SD₁₆	—	6	1	no	—
443	C₃×D₈	—	2	1	no	—
444	C₃×D₈	—	2	1	no	—
445	C₃×D₈	—	4	1	no	—
446	C₃×D₈	—	6	1	no	—
447	C₃×D₈	—	6	1	no	—
448	C₃×D₈	—	6	1	no	—
449	C₃×M₁₆	—	2	1	no	—
450	C₃×M₁₆	—	2	1	no	—
451	C₃×M₁₆	—	2	1	no	—
452	C₃×M₁₆	—	2	1	no	—
453	C₃×M₁₆	—	2	1	no	—
454	C₃×M₁₆	—	3	1	no	—
455	C₃×M₁₆	—	3	1	no	—
456	C₃×M₁₆	—	3	1	no	—
457	C₃×M₁₆	—	4	1	no	—
458	C₃×M₁₆	—	6	1	no	—
459	C₃×M₁₆	—	6	1	no	—
460	C₃×M₁₆	—	6	1	no	—
461	C₃×M₁₆	—	6	1	no	—
462	C₃×M₁₆	—	6	1	no	—
463	C₃×M₁₆	—	6	1	no	—
464	C₃×M₁₆	C₂²×D₃	1	1	yes	characteristic
465	C₃×M₁₆	C₂²×D₃	1	1	yes	characteristic
466	C₃×M₁₆	C₂²×D₃	1	1	yes	characteristic
467	C₃×M₁₆	C₂³×C₃	1	1	yes	characteristic
468	C₃×M₁₆	C₂³×C₃	1	1	yes	characteristic
469	C₃×M₁₆	C₂³×C₃	1	1	yes	characteristic
470	C₂×C₃×C₈	—	2	1	no	—
471	C₂×C₃×C₈	—	2	1	no	—
472	C₂×C₃×C₈	—	2	1	no	—
473	C₂×C₃×C₈	—	3	1	no	—
474	C₂×C₃×C₈	—	3	1	no	—
475	C₂×C₃×C₈	—	3	1	no	—
476	C₂×C₃×C₈	—	3	1	no	—
477	C₂×C₃×C₈	—	3	1	no	—
478	C₂×C₃×C₈	—	4	1	no	—
479	C₂×C₃×C₈	—	6	1	no	—
480	C₂×C₃×C₈	—	6	1	no	—
481	C₂×C₃×C₈	—	6	1	no	—
482	C₂×C₃×C₈	—	6	1	no	—
483	C₂×C₃×C₈	—	6	1	no	—
484	C₂×C₃×C₈	—	6	1	no	—
485	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
486	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
487	#216	—	2	1	no	—
488	#216	—	2	1	no	—
489	#215	—	2	1	no	—
490	#215	—	2	1	no	—
491	#215	—	2	1	no	—
492	#215	—	2	1	no	—
493	#214	—	2	1	no	—
494	#214	—	2	1	no	—
495	#214	—	2	1	no	—
496	#214	—	2	1	no	—
497	#213	—	2	1	no	—
498	#213	—	2	1	no	—
499	#208	—	2	1	no	—
500	#208	C₂³×C₃	1	1	yes	characteristic
501	#208	C₂³×C₃	1	1	yes	characteristic
502	#208	C₂³×C₃	1	1	yes	characteristic
503	C₂×C₃⋊C₈	—	2	1	no	—
504	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
505	Dic₁₂	—	2	1	no	—
506	D₂₄	—	2	1	no	—
507	#204	—	2	1	no	—
508	#204	—	2	1	no	—
509	#204	—	2	1	no	—
510	#204	—	2	1	no	—
511	ΓL(1,𝔽₂₅)	—	2	1	no	—
512	ΓL(1,𝔽₂₅)	—	2	1	no	—
513	ΓL(1,𝔽₂₅)	—	2	1	no	—
514	ΓL(1,𝔽₂₅)	—	2	1	no	—
515	ΓL(1,𝔽₂₅)	—	2	1	no	—
516	D₃×C₈	—	2	1	no	—
517	D₃×C₈	—	2	1	no	—
518	D₃×C₈	—	2	1	no	—
519	D₃×C₈	—	2	1	no	—
520	D₃×C₈	—	2	1	no	—
521	D₃×C₈	C₃×D₄	1	1	yes	characteristic
522	D₃×C₈	C₃×D₄	1	1	yes	characteristic
523	D₃×C₈	C₃×D₄	1	1	yes	characteristic
524	D₃×C₈	C₃×D₄	1	1	yes	characteristic
525	C₂²×C₃²	—	2	1	no	—
526	C₂²×C₃²	—	4	1	no	—
527	C₂²×C₃²	—	8	1	no	—
528	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
529	C₂×C₃×D₃	—	2	2	no	—
530	C₂×C₃×D₃	—	2	1	no	—
531	C₂×C₃×D₃	—	4	2	no	—
532	C₂×C₃×D₃	—	4	1	no	—
533	C₂×C₃×D₃	—	8	2	no	—
534	C₂×C₃×D₃	—	8	2	no	—
535	C₂×C₃×D₃	—	8	1	no	—
536	C₂×C₃×D₃	#121	1	1	yes	characteristic
537	C₂×C₃×D₃	#121	1	1	yes	characteristic
538	C₃²×C₄	—	2	1	no	—
539	C₃²×C₄	—	4	1	no	—
540	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
541	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
542	C₃×Dic₃	—	2	1	no	—
543	C₃×Dic₃	—	4	1	no	—
544	C₃×Dic₃	#121	1	1	yes	characteristic
545	C₃×Dic₃	#121	1	1	yes	characteristic
546	C₂×#41	—	3	1	no	—
547	C₂²×Q₈	—	3	1	no	—
548	C₂²×D₄	—	3	1	no	—
549	#137	—	3	1	no	—
550	#137	—	3	1	no	—
551	#137	—	3	1	no	—
552	#137	—	6	1	no	—
553	#137	—	6	1	no	—
554	#137	C₂×C₃×D₃	1	1	yes	characteristic, complemented
555	AGL(1,ℤ/8)	—	3	1	no	—
556	AGL(1,ℤ/8)	—	3	1	no	—
557	AGL(1,ℤ/8)	—	3	1	no	—
558	AGL(1,ℤ/8)	—	6	1	no	—
559	AGL(1,ℤ/8)	—	6	1	no	—
560	AGL(1,ℤ/8)	C₂×C₃×D₃	1	1	yes	characteristic
561	C₂×Q₁₆	—	6	1	no	—
562	C₂×SD₁₆	—	3	1	no	—
563	C₂×SD₁₆	—	3	1	no	—
564	C₂×SD₁₆	—	3	1	no	—
565	C₂×SD₁₆	—	6	1	no	—
566	C₂×SD₁₆	—	6	1	no	—
567	C₂×SD₁₆	—	6	1	no	—
568	C₂×SD₁₆	—	6	1	no	—
569	C₂×SD₁₆	—	6	1	no	—
570	C₂×SD₁₆	—	6	1	no	—
571	C₂×SD₁₆	C₂×C₃×D₃	1	1	yes	characteristic, complemented
572	C₂×D₈	—	6	1	no	—
573	#131	—	3	1	no	—
574	#131	—	3	1	no	—
575	#131	—	3	1	no	—
576	#131	—	6	1	no	—
577	#131	—	6	1	no	—
578	#131	C₂×C₃×D₃	1	1	yes	characteristic, complemented
579	C₂×M₁₆	—	3	1	no	—
580	C₂×M₁₆	—	3	1	no	—
581	C₂×M₁₆	—	3	1	no	—
582	C₂×M₁₆	—	6	1	no	—
583	C₂²×C₈	—	3	1	no	—
584	C₂²×C₈	—	6	1	no	—
585	#108	—	3	1	no	—
586	#108	—	3	1	no	—
587	#108	—	3	1	no	—
588	#108	C₂×C₃×D₃	1	1	yes	characteristic, complemented
589	#101	—	3	1	no	—
590	#101	—	3	1	no	—
591	#101	—	3	1	no	—
592	#101	C₂×C₃×D₃	1	1	yes	characteristic, complemented
593	#100	—	3	1	no	—
594	#100	—	3	1	no	—
595	#100	—	3	1	no	—
596	#100	C₂×C₃×D₃	1	1	yes	characteristic, complemented
597	C₂³×C₃	—	2	1	no	—
598	C₂³×C₃	—	2	1	no	—
599	C₂³×C₃	—	3	1	no	—
600	C₂³×C₃	—	4	1	no	—
601	C₂³×C₃	—	6	1	no	—
602	C₂³×C₃	—	6	1	no	—
603	C₂³×C₃	—	12	1	no	—
604	C₂³×C₃	—	12	1	no	—
605	C₂³×C₃	—	24	2	no	—
606	C₂²×D₃	—	2	1	no	—
607	C₂²×D₃	—	2	1	no	—
608	C₂²×D₃	—	4	1	no	—
609	C₂²×D₃	—	4	1	no	—
610	C₂²×D₃	—	8	2	no	—
611	C₂²×D₃	C₃×#41	1	1	yes	characteristic
612	C₃×Q₈	—	2	1	no	—
613	C₃×Q₈	—	2	1	no	—
614	C₃×Q₈	—	2	1	no	—
615	C₃×Q₈	—	2	1	no	—
616	C₃×Q₈	—	2	1	no	—
617	C₃×Q₈	—	3	1	no	—
618	C₃×Q₈	—	4	1	no	—
619	C₃×Q₈	—	4	1	no	—
620	C₃×Q₈	—	6	1	no	—
621	C₃×Q₈	—	6	1	no	—
622	C₃×Q₈	—	6	1	no	—
623	C₃×Q₈	—	12	1	no	—
624	C₃×Q₈	—	12	1	no	—
625	C₃×Q₈	D₃×D₄	1	1	yes	characteristic
626	C₃×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
627	C₃×D₄	—	2	1	no	—
628	C₃×D₄	—	2	1	no	—
629	C₃×D₄	—	2	1	no	—
630	C₃×D₄	—	2	1	no	—
631	C₃×D₄	—	2	1	no	—
632	C₃×D₄	—	2	1	no	—
633	C₃×D₄	—	2	1	no	—
634	C₃×D₄	—	3	1	no	—
635	C₃×D₄	—	4	1	no	—
636	C₃×D₄	—	4	1	no	—
637	C₃×D₄	—	4	1	no	—
638	C₃×D₄	—	6	1	no	—
639	C₃×D₄	—	6	1	no	—
640	C₃×D₄	—	6	1	no	—
641	C₃×D₄	—	6	1	no	—
642	C₃×D₄	—	6	1	no	—
643	C₃×D₄	—	6	1	no	—
644	C₃×D₄	—	12	1	no	—
645	C₃×D₄	—	12	1	no	—
646	C₃×D₄	D₃×D₄	1	1	yes	characteristic
647	C₃×D₄	C₂×C₃×D₄	1	1	yes	characteristic
648	C₂×C₃×C₄	—	2	1	no	—
649	C₂×C₃×C₄	—	2	1	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	1	no	—
653	C₂×C₃×C₄	—	3	1	no	—
654	C₂×C₃×C₄	—	3	1	no	—
655	C₂×C₃×C₄	—	3	1	no	—
656	C₂×C₃×C₄	—	3	1	no	—
657	C₂×C₃×C₄	—	3	1	no	—
658	C₂×C₃×C₄	—	4	1	no	—
659	C₂×C₃×C₄	—	4	1	no	—
660	C₂×C₃×C₄	—	6	1	no	—
661	C₂×C₃×C₄	—	6	1	no	—
662	C₂×C₃×C₄	—	6	1	no	—
663	C₂×C₃×C₄	—	6	1	no	—
664	C₂×C₃×C₄	—	6	1	no	—
665	C₂×C₃×C₄	—	12	1	no	—
666	C₂×C₃×C₄	—	12	1	no	—
667	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
668	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
669	#67	—	2	1	no	—
670	#67	—	2	1	no	—
671	#67	—	2	1	no	—
672	#67	—	4	1	no	—
673	#67	—	4	1	no	—
674	C₂×Dic₃	—	2	1	no	—
675	C₂×Dic₃	—	2	1	no	—
676	C₂×Dic₃	C₃×#41	1	1	yes	characteristic
677	D₁₂	—	2	1	no	—
678	D₁₂	—	2	1	no	—
679	D₁₂	—	2	1	no	—
680	D₁₂	C₂×C₃×D₄	1	1	yes	characteristic
681	C₄×D₃	—	2	1	no	—
682	C₄×D₃	—	2	1	no	—
683	C₄×D₃	—	2	1	no	—
684	C₄×D₃	—	4	1	no	—
685	C₄×D₃	—	4	1	no	—
686	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
687	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
688	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
689	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
690	Dic₆	—	2	1	no	—
691	Dic₆	—	2	1	no	—
692	Dic₆	—	2	1	no	—
693	Dic₆	—	4	1	no	—
694	Dic₆	—	4	1	no	—
695	Dic₆	C₂×C₃×D₄	1	1	yes	characteristic
696	C₃×C₈	—	2	1	no	—
697	C₃×C₈	—	2	1	no	—
698	C₃×C₈	—	2	1	no	—
699	C₃×C₈	—	2	1	no	—
700	C₃×C₈	—	2	1	no	—
701	C₃×C₈	—	2	1	no	—
702	C₃×C₈	—	2	1	no	—
703	C₃×C₈	—	2	1	no	—
704	C₃×C₈	—	3	1	no	—
705	C₃×C₈	—	3	1	no	—
706	C₃×C₈	—	4	1	no	—
707	C₃×C₈	—	4	1	no	—
708	C₃×C₈	—	4	1	no	—
709	C₃×C₈	—	6	1	no	—
710	C₃×C₈	—	6	1	no	—
711	C₃×C₈	—	6	1	no	—
712	C₃×C₈	D₃×D₄	1	1	yes	characteristic
713	C₃×C₈	D₃×D₄	1	1	yes	characteristic
714	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
715	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
716	C₃⋊C₈	—	2	1	no	—
717	C₃⋊C₈	—	2	1	no	—
718	C₃⋊C₈	—	2	1	no	—
719	C₃⋊C₈	C₂×C₃×D₄	1	1	yes	characteristic
720	C₃⋊C₈	C₂×C₃×D₄	1	1	yes	characteristic
721	C₂×C₃²	—	2	1	no	—
722	C₂×C₃²	—	4	1	no	—
723	C₂×C₃²	—	8	1	no	—
724	C₂×C₃²	C₂×#121	1	1	yes	characteristic
725	C₃×D₃	—	2	1	no	—
726	C₃×D₃	—	4	1	no	—
727	C₃×D₃	—	8	1	no	—
728	C₃×D₃	#471	1	2	yes	direct product factor
729	C₂⁴	—	6	1	no	—
730	#41	—	3	1	no	—
731	#41	—	3	1	no	—
732	#41	—	3	1	no	—
733	#41	—	6	1	no	—
734	#41	—	6	1	no	—
735	#41	C₂²×C₃×D₃	1	1	yes	characteristic
736	C₂×Q₈	—	3	1	no	—
737	C₂×Q₈	—	3	1	no	—
738	C₂×Q₈	—	6	1	no	—
739	C₂×Q₈	—	6	1	no	—
740	C₂×Q₈	—	6	1	no	—
741	C₂×Q₈	—	6	1	no	—
742	C₂×Q₈	—	6	1	no	—
743	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
744	C₂×D₄	—	3	1	no	—
745	C₂×D₄	—	3	1	no	—
746	C₂×D₄	—	6	1	no	—
747	C₂×D₄	—	6	1	no	—
748	C₂×D₄	—	6	1	no	—
749	C₂×D₄	—	6	1	no	—
750	C₂×D₄	—	6	1	no	—
751	C₂×D₄	—	6	1	no	—
752	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
753	C₂²×C₄	—	3	1	no	—
754	C₂²×C₄	—	6	1	no	—
755	C₂²×C₄	—	6	1	no	—
756	Q₁₆	—	2	1	no	—
757	Q₁₆	—	6	1	no	—
758	Q₁₆	—	6	1	no	—
759	Q₁₆	—	6	1	no	—
760	SD₁₆	—	2	1	no	—
761	SD₁₆	—	2	1	no	—
762	SD₁₆	—	2	1	no	—
763	SD₁₆	—	2	1	no	—
764	SD₁₆	—	6	1	no	—
765	SD₁₆	—	6	1	no	—
766	SD₁₆	—	6	1	no	—
767	SD₁₆	—	6	1	no	—
768	SD₁₆	—	6	1	no	—
769	SD₁₆	—	6	1	no	—
770	SD₁₆	—	6	1	no	—
771	SD₁₆	—	6	1	no	—
772	SD₁₆	—	6	1	no	—
773	SD₁₆	—	6	1	no	—
774	SD₁₆	—	6	1	no	—
775	SD₁₆	—	6	1	no	—
776	D₈	—	2	1	no	—
777	D₈	—	6	1	no	—
778	D₈	—	6	1	no	—
779	D₈	—	6	1	no	—
780	M₁₆	—	2	1	no	—
781	M₁₆	—	3	1	no	—
782	M₁₆	—	3	1	no	—
783	M₁₆	—	3	1	no	—
784	M₁₆	—	6	1	no	—
785	M₁₆	—	6	1	no	—
786	M₁₆	—	6	1	no	—
787	M₁₆	—	6	1	no	—
788	M₁₆	—	6	1	no	—
789	M₁₆	—	6	1	no	—
790	M₁₆	C₂²×C₃×D₃	1	1	yes	characteristic
791	M₁₆	C₂²×C₃×D₃	1	1	yes	characteristic
792	M₁₆	C₂²×C₃×D₃	1	1	yes	characteristic
793	C₂×C₈	—	2	1	no	—
794	C₂×C₈	—	3	1	no	—
795	C₂×C₈	—	3	1	no	—
796	C₂×C₈	—	3	1	no	—
797	C₂×C₈	—	3	1	no	—
798	C₂×C₈	—	3	1	no	—
799	C₂×C₈	—	6	1	no	—
800	C₂×C₈	—	6	1	no	—
801	C₂×C₈	—	6	1	no	—
802	C₂×C₈	—	6	1	no	—
803	C₂×C₈	—	6	1	no	—
804	C₂×C₈	—	6	1	no	—
805	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
806	C₂²×C₃	—	2	1	no	—
807	C₂²×C₃	—	2	1	no	—
808	C₂²×C₃	—	2	1	no	—
809	C₂²×C₃	—	3	1	no	—
810	C₂²×C₃	—	3	1	no	—
811	C₂²×C₃	—	4	1	no	—
812	C₂²×C₃	—	4	1	no	—
813	C₂²×C₃	—	4	1	no	—
814	C₂²×C₃	—	6	2	no	—
815	C₂²×C₃	—	6	1	no	—
816	C₂²×C₃	—	8	1	no	—
817	C₂²×C₃	—	8	1	no	—
818	C₂²×C₃	—	8	1	no	—
819	C₂²×C₃	—	12	2	no	—
820	C₂²×C₃	—	12	1	no	—
821	C₂²×C₃	—	16	1	no	—
822	C₂²×C₃	—	24	1	no	—
823	C₂²×C₃	—	24	2	no	—
824	C₂²×C₃	—	24	2	no	—
825	C₂²×C₃	D₃×#41	1	1	yes	characteristic
826	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
827	C₂×D₃	—	2	2	no	—
828	C₂×D₃	—	2	1	no	—
829	C₂×D₃	—	4	2	no	—
830	C₂×D₃	—	4	1	no	—
831	C₂×D₃	—	8	2	no	—
832	C₂×D₃	—	8	2	no	—
833	C₂×D₃	—	8	1	no	—
834	C₂×D₃	C₃×#121	1	1	yes	characteristic
835	C₂×D₃	C₃×#121	1	1	yes	characteristic
836	C₃×C₄	—	2	1	no	—
837	C₃×C₄	—	2	1	no	—
838	C₃×C₄	—	2	1	no	—
839	C₃×C₄	—	2	1	no	—
840	C₃×C₄	—	3	1	no	—
841	C₃×C₄	—	3	1	no	—
842	C₃×C₄	—	4	1	no	—
843	C₃×C₄	—	4	1	no	—
844	C₃×C₄	—	4	1	no	—
845	C₃×C₄	—	6	1	no	—
846	C₃×C₄	—	8	1	no	—
847	C₃×C₄	—	12	1	no	—
848	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
849	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
850	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
851	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
852	Dic₃	—	2	1	no	—
853	Dic₃	—	4	1	no	—
854	Dic₃	C₃×#121	1	1	yes	characteristic
855	Dic₃	C₃×#121	1	1	yes	characteristic
856	C₃²	C₂×#471	1	1	yes	characteristic, complemented, Sylow
857	C₂³	—	2	1	no	—
858	C₂³	—	3	1	no	—
859	C₂³	—	6	1	no	—
860	C₂³	—	6	1	no	—
861	C₂³	—	12	1	no	—
862	C₂³	—	12	1	no	—
863	C₂³	—	24	2	no	—
864	Q₈	—	2	1	no	—
865	Q₈	—	2	1	no	—
866	Q₈	—	3	1	no	—
867	Q₈	—	6	1	no	—
868	Q₈	—	6	1	no	—
869	Q₈	—	6	1	no	—
870	Q₈	—	12	1	no	—
871	Q₈	—	12	1	no	—
872	Q₈	C₃×D₃×D₄	1	1	yes	characteristic
873	D₄	—	2	1	no	—
874	D₄	—	2	1	no	—
875	D₄	—	2	1	no	—
876	D₄	—	3	1	no	—
877	D₄	—	6	1	no	—
878	D₄	—	6	1	no	—
879	D₄	—	6	1	no	—
880	D₄	—	6	1	no	—
881	D₄	—	6	1	no	—
882	D₄	—	6	1	no	—
883	D₄	—	12	1	no	—
884	D₄	—	12	1	no	—
885	D₄	C₃×D₃×D₄	1	1	yes	characteristic
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	3	1	no	—
889	C₂×C₄	—	3	1	no	—
890	C₂×C₄	—	3	1	no	—
891	C₂×C₄	—	3	1	no	—
892	C₂×C₄	—	3	1	no	—
893	C₂×C₄	—	6	1	no	—
894	C₂×C₄	—	6	1	no	—
895	C₂×C₄	—	6	1	no	—
896	C₂×C₄	—	6	1	no	—
897	C₂×C₄	—	6	1	no	—
898	C₂×C₄	—	12	1	no	—
899	C₂×C₄	—	12	1	no	—
900	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
901	C₈	—	2	1	no	—
902	C₈	—	2	1	no	—
903	C₈	—	2	1	no	—
904	C₈	—	3	1	no	—
905	C₈	—	3	1	no	—
906	C₈	—	6	1	no	—
907	C₈	—	6	1	no	—
908	C₈	—	6	1	no	—
909	C₈	C₃×D₃×D₄	1	1	yes	characteristic
910	C₈	C₃×D₃×D₄	1	1	yes	characteristic
911	C₂×C₃	—	2	1	no	—
912	C₂×C₃	—	2	1	no	—
913	C₂×C₃	—	2	1	no	—
914	C₂×C₃	—	3	2	no	—
915	C₂×C₃	—	4	1	no	—
916	C₂×C₃	—	4	1	no	—
917	C₂×C₃	—	4	1	no	—
918	C₂×C₃	—	6	1	no	—
919	C₂×C₃	—	8	1	no	—
920	C₂×C₃	—	8	1	no	—
921	C₂×C₃	—	8	1	no	—
922	C₂×C₃	—	12	1	no	—
923	C₂×C₃	—	16	1	no	—
924	C₂×C₃	—	24	1	no	—
925	C₂×C₃	D₃×#121	1	1	yes	characteristic
926	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
927	D₃	—	2	1	no	—
928	D₃	—	4	1	no	—
929	D₃	—	8	1	no	—
930	D₃	C₃×#471	1	2	yes	direct product factor
931	C₂²	—	2	1	no	—
932	C₂²	—	3	1	no	—
933	C₂²	—	3	1	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	6	2	no	—
936	C₂²	—	6	1	no	—
937	C₂²	—	8	1	no	—
938	C₂²	—	12	2	no	—
939	C₂²	—	12	1	no	—
940	C₂²	—	24	1	no	—
941	C₂²	—	24	2	no	—
942	C₂²	—	24	2	no	—
943	C₂²	C₃×D₃×#41	1	1	yes	characteristic
944	C₄	—	2	1	no	—
945	C₄	—	3	1	no	—
946	C₄	—	3	1	no	—
947	C₄	—	4	1	no	—
948	C₄	—	6	1	no	—
949	C₄	—	12	1	no	—
950	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
951	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
952	C₃	—	2	1	no	—
953	C₃	D₃×#471	1	1	yes	characteristic, direct product factor
954	C₃	C₂×C₃×#471	1	1	yes	characteristic, complemented
955	C₂	—	2	1	no	—
956	C₂	—	3	2	no	—
957	C₂	—	4	1	no	—
958	C₂	—	6	1	no	—
959	C₂	—	8	1	no	—
960	C₂	—	12	1	no	—
961	C₂	—	24	1	no	—
962	C₂	C₃×D₃×#121	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₃×#121
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#471	C₂
socle	C₂×C₃²	C₂×#121
prime radical	C₃×D₃×AGL(1,ℤ/8)	C₂
hypercenter	C₃×#471	D₃
hypocenter	C₃	C₂×C₃×#471
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#471

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×#137	C₂	semidirect
3. C₂×C₃×D₃×SD₁₆	C₂	semidirect
4. C₃×D₃×#131	C₂	semidirect
5. C₃²×#471	C₂	semidirect
6. C₃×#5203	C₂	semidirect
7. C₃×#5200	C₂	semidirect
8. C₃×#5177	C₂	semidirect
9. C₃×#5141	C₂	semidirect
10. C₃×#4898	C₂	semidirect
11. C₃×D₃×#108	C₂	semidirect
12. C₃×#4754	C₂	semidirect
13. C₃×D₃×#101	C₂	semidirect
14. C₃×#4748	C₂	semidirect
15. C₃×D₃×#100	C₂	semidirect
17. D₃×#471	C₃	direct (N × H)
21. C₃²×#137	C₂²	semidirect
23. C₂×C₃²×SD₁₆	C₂²	semidirect
24. C₃²×#131	C₂²	semidirect
25. C₃×#951	C₂²	semidirect
27. C₃×#948	C₂²	semidirect
28. C₃×#942	C₂²	semidirect
29. C₂×C₃×#215	C₂²	semidirect
30. C₂×C₃×#214	C₂²	semidirect
44. C₃×#909	C₂²	semidirect
47. C₃×#907	C₂²	semidirect
52. C₂×C₃×#204	C₂²	semidirect
54. C₃×#901	C₂²	semidirect
57. C₃²×#108	C₂²	semidirect
58. C₃²×#101	C₂²	semidirect
59. C₃²×#100	C₂²	semidirect
60. C₃×#836	C₂²	semidirect
61. C₃×#833	C₂²	semidirect
62. C₃×#824	C₂²	semidirect
63. C₃×#824	C₂²	semidirect
64. C₃×#823	C₂²	semidirect
65. C₃×#823	C₂²	semidirect
66. C₃×#822	C₂²	semidirect
67. C₃×#822	C₂²	semidirect
68. C₃×#819	C₂²	semidirect
73. D₃×#137	C₂×C₃	semidirect
75. C₂×D₃×SD₁₆	C₂×C₃	semidirect
76. D₃×#131	C₂×C₃	semidirect
85. C₃×#471	D₃	direct (N × H)
86. C₃×#471	C₂×C₃	semidirect
90. #5203	C₂×C₃	semidirect
91. #5200	C₂×C₃	semidirect
92. #5177	C₂×C₃	semidirect
93. #5141	C₂×C₃	semidirect
94. #4898	C₂×C₃	semidirect
95. D₃×#108	C₂×C₃	semidirect
96. #4754	C₂×C₃	semidirect
97. D₃×#101	C₂×C₃	semidirect
98. #4748	C₂×C₃	semidirect
99. D₃×#100	C₂×C₃	semidirect
190. C₃×#137	C₂×D₃	semidirect
191. C₃×#137	C₂²×C₃	semidirect
211. C₂×C₃×SD₁₆	C₂×D₃	semidirect
212. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
220. C₃×#131	C₂×D₃	semidirect
221. C₃×#131	C₂²×C₃	semidirect
228. #951	C₂²×C₃	semidirect
230. #948	C₂²×C₃	semidirect
231. #942	C₂²×C₃	semidirect
232. C₂×#215	C₂²×C₃	semidirect
233. C₂×#214	C₂²×C₃	semidirect
247. #909	C₂²×C₃	semidirect
250. #907	C₂²×C₃	semidirect
255. C₂×#204	C₂²×C₃	semidirect
257. #901	C₂²×C₃	semidirect
264. C₃×#108	C₂×D₃	semidirect
265. C₃×#108	C₂²×C₃	semidirect
270. C₃×#101	C₂×D₃	semidirect
271. C₃×#101	C₂²×C₃	semidirect
276. C₃×#100	C₂×D₃	semidirect
277. C₃×#100	C₂²×C₃	semidirect
278. #836	C₂²×C₃	semidirect
279. #833	C₂²×C₃	semidirect
280. #824	C₂²×C₃	semidirect
281. #824	C₂²×C₃	semidirect
282. #823	C₂²×C₃	semidirect
283. #823	C₂²×C₃	semidirect
284. #822	C₂²×C₃	semidirect
285. #822	C₂²×C₃	semidirect
286. #819	C₂²×C₃	semidirect
352. #471	C₃×D₃	direct (N × H)
554. #137	C₂×C₃×D₃	semidirect
571. C₂×SD₁₆	C₂×C₃×D₃	semidirect
578. #131	C₂×C₃×D₃	semidirect
588. #108	C₂×C₃×D₃	semidirect
592. #101	C₂×C₃×D₃	semidirect
596. #100	C₂×C₃×D₃	semidirect
728. C₃×D₃	#471	direct (N × H)
856. C₃²	C₂×#471	semidirect
930. D₃	C₃×#471	direct (N × H)
953. C₃	D₃×#471	direct (N × H)
954. C₃	C₂×C₃×#471	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×#137	2
C₃×D₃×AGL(1,ℤ/8)	2
C₂×C₃×D₃×SD₁₆	2
C₃×D₃×#131	2
C₃²×#471	2
C₃×#5203	2
C₃×#5200	2
C₃×#5177	2
C₃×#5141	2
C₃×#4898	2
C₃×D₃×#108	2
C₃×#4754	2
C₃×D₃×#101	2
C₃×#4748	2
C₃×D₃×#100	2
C₂×C₃×#471	3
D₃×#471	3

Subgroups — C3×D3×#471 #11867841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#471 #11867841