Subgroups — C₃×#61845 #10680452

Order 768.

1688 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×Q₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3389	C₂	1	2	yes	maximal, complemented
4	C₃×#3388	C₂	1	2	yes	maximal, complemented
5	C₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#3377	C₂	1	2	yes	maximal, complemented
10	C₃×#3376	C₂	1	2	yes	maximal, complemented
11	C₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3240	C₂	1	2	yes	maximal, complemented
16	C₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3233	C₂	1	2	yes	maximal, complemented
18	C₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#3115	C₂	1	1	yes	maximal, characteristic
20	C₃×#3111	C₂	1	2	yes	maximal, complemented
21	C₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#3102	C₂	1	2	yes	maximal, complemented
23	C₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
24	#61845	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#559	C₂²	1	1	yes	characteristic
26	C₃×#559	C₂²	1	1	yes	characteristic
27	C₃×Q₈²	C₂²	1	1	yes	characteristic
28	C₃×#557	C₂²	1	1	yes	characteristic
29	C₃×#557	C₂²	1	2	yes	—
30	C₃×#557	C₂²	1	1	yes	characteristic
31	C₃×#557	C₂²	1	1	yes	characteristic
32	C₃×#556	—	2	1	no	—
33	C₃×#556	—	2	1	no	—
34	C₃×#556	C₂²	1	2	yes	—
35	C₃×#554	—	2	1	no	—
36	C₃×#554	—	2	2	no	—
37	C₃×#554	C₂²	1	2	yes	—
38	C₃×#554	C₂²	1	2	yes	—
39	C₃×#554	C₂²	1	1	yes	characteristic
40	C₃×#552	—	2	2	no	—
41	C₃×D₄×Q₈	—	2	1	no	—
42	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic
43	C₃×#539	—	2	2	no	—
44	C₃×#536	—	2	1	no	—
45	C₃×#533	—	2	2	no	—
46	C₃×#533	—	2	1	no	—
47	C₃×#533	C₂²	1	1	yes	characteristic
48	C₃×#533	C₂²	1	1	yes	characteristic
49	C₃×#533	C₂²	1	2	yes	—
50	C₃×#532	C₂²	1	1	yes	characteristic
51	C₃×#529	C₂²	1	2	yes	—
52	C₃×#529	C₂²	1	2	yes	—
53	C₃×#520	—	2	1	no	—
54	C₃×C₄×#41	C₂²	1	2	yes	—
55	C₃×C₄×#41	C₂²	1	1	yes	characteristic
56	C₂×C₃×C₄×Q₈	—	2	1	no	—
57	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
58	C₃×#501	C₂²	1	2	yes	—
59	C₃×#501	C₂²	1	2	yes	—
60	C₃×#501	C₂²	1	2	yes	—
61	C₃×#500	C₂²	1	1	yes	characteristic
62	C₃×#499	C₂²	1	2	yes	—
63	C₃×#499	C₂²	1	2	yes	—
64	C₃×#498	C₂²	1	1	yes	characteristic
65	C₃×#491	C₂²	1	2	yes	—
66	C₃×#489	C₂²	1	2	yes	—
67	C₃×#489	C₂²	1	2	yes	—
68	C₃×#488	C₂²	1	2	yes	—
69	C₃×#488	C₂²	1	2	yes	—
70	C₃×#486	C₂²	1	1	yes	characteristic
71	C₃×#486	C₂²	1	1	yes	characteristic
72	C₃×#485	C₂²	1	1	yes	characteristic
73	C₃×#485	C₂²	1	2	yes	—
74	C₃×#485	C₂²	1	2	yes	—
75	C₃×#485	C₂²	1	1	yes	characteristic
76	C₃×#482	C₂²	1	2	yes	—
77	C₃×#482	C₂²	1	2	yes	—
78	C₃×#482	C₂²	1	2	yes	—
79	C₃×#479	C₂²	1	2	yes	—
80	C₃×#479	C₂²	1	2	yes	—
81	C₃×#479	C₂²	1	2	yes	—
82	C₃×#479	C₂²	1	2	yes	—
83	C₃×#478	C₂²	1	2	yes	—
84	C₃×#478	C₂²	1	2	yes	—
85	C₃×#478	C₂²	1	2	yes	—
86	C₃×#478	C₂²	1	2	yes	—
87	C₃×#478	C₂²	1	2	yes	—
88	C₃×#478	C₂²	1	2	yes	—
89	C₃×#477	C₂²	1	2	yes	—
90	C₃×#477	C₂²	1	1	yes	characteristic
91	C₃×#477	C₂²	1	1	yes	characteristic
92	C₃×#476	C₂²	1	2	yes	—
93	C₃×#475	C₂²	1	1	yes	characteristic
94	C₃×#475	C₂²	1	2	yes	—
95	C₃×#475	C₂²	1	1	yes	characteristic
96	C₃×#475	C₂²	1	1	yes	characteristic
97	C₃×#475	C₂²	1	1	yes	characteristic
98	C₃×#474	C₂²	1	1	yes	characteristic
99	C₃×#474	C₂²	1	1	yes	characteristic
100	C₃×#474	C₂²	1	2	yes	—
101	C₃×#464	C₂²	1	2	yes	—
102	C₃×#464	C₂²	1	2	yes	—
103	C₃×#463	C₂²	1	2	yes	—
104	C₃×#463	C₂²	1	2	yes	—
105	C₃×#462	C₂²	1	1	yes	characteristic
106	C₃×#461	C₂²	1	1	yes	characteristic
107	C₃×#460	C₂²	1	1	yes	characteristic
108	C₃×#459	C₂²	1	1	yes	characteristic
109	C₃×#452	C₂²	1	1	yes	characteristic
110	C₃×#452	C₂²	1	1	yes	characteristic
111	C₃×#449	C₂²	1	2	yes	—
112	C₃×#446	C₂²	1	1	yes	characteristic
113	C₃×#446	C₂²	1	1	yes	characteristic
114	C₃×#446	C₂²	1	2	yes	—
115	C₃×#446	C₂²	1	2	yes	—
116	C₃×C₈×Q₈	C₂²	1	1	yes	characteristic
117	C₃×C₈×Q₈	C₂²	1	1	yes	characteristic
118	C₃×#442	C₂²	1	2	yes	—
119	C₃×#442	C₂²	1	2	yes	—
120	C₃×#441	C₂²	1	2	yes	—
121	C₃×#440	C₂²	1	2	yes	—
122	C₃×#440	C₂²	1	2	yes	—
123	C₃×#440	C₂²	1	2	yes	—
124	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
125	C₃×C₄×Q₁₆	C₂²	1	2	yes	—
126	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
127	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
128	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
129	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
130	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
131	C₃×C₄×D₈	C₂²	1	2	yes	—
132	C₃×#432	C₂²	1	1	yes	characteristic
133	C₃×#432	C₂²	1	2	yes	—
134	C₃×#431	C₂²	1	1	yes	characteristic
135	C₃×#431	C₂²	1	2	yes	—
136	#3507	C₂×C₃	1	1	yes	characteristic, complemented
137	Q₈×#41	C₂×C₃	1	1	yes	characteristic, complemented
138	#3389	C₂×C₃	1	2	yes	complemented
139	#3388	C₂×C₃	1	2	yes	complemented
140	#3387	C₂×C₃	1	1	yes	characteristic, complemented
141	#3386	C₂×C₃	1	1	yes	characteristic, complemented
142	#3383	C₂×C₃	1	1	yes	characteristic, complemented
143	#3381	C₂×C₃	1	1	yes	characteristic, complemented
144	#3377	C₂×C₃	1	2	yes	complemented
145	#3376	C₂×C₃	1	2	yes	complemented
146	#3375	C₂×C₃	1	1	yes	characteristic, complemented
147	#3373	C₂×C₃	1	1	yes	characteristic, complemented
148	#3365	C₂×C₃	1	1	yes	characteristic, complemented
149	#3361	C₂×C₃	1	1	yes	characteristic, complemented
150	#3240	C₂×C₃	1	2	yes	complemented
151	#3237	C₂×C₃	1	1	yes	characteristic, complemented
152	#3233	C₂×C₃	1	2	yes	complemented
153	#3228	C₂×C₃	1	1	yes	characteristic, complemented
154	#3115	C₂×C₃	1	1	yes	characteristic
155	#3111	C₂×C₃	1	2	yes	complemented
156	#3107	C₂×C₃	1	1	yes	characteristic, complemented
157	#3102	C₂×C₃	1	2	yes	complemented
158	#2984	C₂×C₃	1	1	yes	characteristic, complemented
159	C₂×C₃×#41	—	2	1	no	—
160	C₂×C₃×#41	C₂³	1	1	yes	characteristic
161	C₂²×C₃×Q₈	—	2	1	no	—
162	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
163	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
164	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
166	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
168	C₂×C₃×D₈	C₂³	1	2	yes	—
169	C₃×C₄⋊Q₈	—	2	1	no	—
170	C₃×C₄⋊Q₈	—	2	2	no	—
171	C₃×C₄⋊Q₈	—	2	1	no	—
172	C₃×C₄⋊Q₈	—	2	1	no	—
173	C₃×C₄⋊Q₈	—	2	1	no	—
174	C₃×C₄⋊Q₈	—	2	2	no	—
175	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
176	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
177	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
178	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
181	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
182	C₃×#127	C₂³	1	1	yes	characteristic
183	C₃×#126	—	2	2	no	—
184	C₃×#126	—	2	2	no	—
185	C₃×#126	—	2	2	no	—
186	C₃×#126	—	2	2	no	—
187	C₃×#125	—	2	2	no	—
188	C₃×#125	—	2	2	no	—
189	C₃×#125	—	2	2	no	—
190	C₃×#125	—	2	2	no	—
191	C₃×#125	—	2	2	no	—
192	C₃×#125	—	2	1	no	—
193	C₃×#125	C₂³	1	2	yes	—
194	C₃×#125	C₂³	1	2	yes	—
195	C₃×#125	C₂³	1	2	yes	—
196	C₃×#125	C₂³	1	2	yes	—
197	C₃×#125	C₂³	1	2	yes	—
198	C₃×#124	—	2	1	no	—
199	C₃×#124	—	2	1	no	—
200	C₃×#124	—	2	1	no	—
201	C₃×#124	C₂³	1	2	yes	—
202	C₃×#124	C₂³	1	2	yes	—
203	C₃×#123	—	2	2	no	—
204	C₃×#123	—	2	2	no	—
205	C₃×#123	—	2	2	no	—
206	C₃×#123	—	2	2	no	—
207	C₃×C₂²⋊Q₈	—	2	1	no	—
208	C₃×C₂²⋊Q₈	—	2	2	no	—
209	C₃×C₂²⋊Q₈	—	2	2	no	—
210	C₃×C₂²⋊Q₈	—	2	2	no	—
211	C₃×C₂²⋊Q₈	—	2	1	no	—
212	C₃×C₂²⋊Q₈	—	2	1	no	—
213	C₃×C₂²⋊Q₈	—	2	2	no	—
214	C₃×C₂²⋊Q₈	—	2	2	no	—
215	C₃×C₂²⋊Q₈	—	2	1	no	—
216	C₃×C₂²⋊Q₈	—	2	1	no	—
217	C₃×C₂²⋊Q₈	—	2	2	no	—
218	C₃×C₂²⋊Q₈	—	2	2	no	—
219	C₃×C₂²⋊Q₈	—	2	2	no	—
220	C₃×C₂²⋊Q₈	—	2	2	no	—
221	C₃×C₂²⋊Q₈	—	2	2	no	—
222	C₃×C₂²⋊Q₈	—	2	2	no	—
223	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₃×#121	—	2	1	no	—
226	C₃×#121	C₂³	1	2	yes	—
227	C₃×C₄×Q₈	—	2	1	no	—
228	C₃×C₄×Q₈	—	2	1	no	—
229	C₃×C₄×Q₈	—	2	2	no	—
230	C₃×C₄×Q₈	—	2	1	no	—
231	C₃×C₄×Q₈	—	2	1	no	—
232	C₃×C₄×Q₈	—	2	2	no	—
233	C₃×C₄×Q₈	—	2	1	no	—
234	C₃×C₄×Q₈	—	2	2	no	—
235	C₃×C₄×Q₈	—	2	1	no	—
236	C₃×C₄×Q₈	—	2	1	no	—
237	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
238	C₃×C₄×Q₈	D₄	1	2	yes	—
239	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
240	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₃×C₄×Q₈	C₂³	1	2	yes	—
242	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
243	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
244	C₃×C₄×Q₈	C₂³	1	2	yes	—
245	C₃×C₄×Q₈	C₂³	1	2	yes	—
246	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
247	C₃×C₄×Q₈	C₂³	1	2	yes	—
248	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
249	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₃×C₄×Q₈	C₂³	1	2	yes	—
251	C₃×C₄×D₄	—	2	1	no	—
252	C₃×C₄×D₄	—	2	2	no	—
253	C₃×C₄×D₄	—	2	2	no	—
254	C₃×C₄×D₄	—	2	1	no	—
255	C₃×C₄×D₄	—	2	2	no	—
256	C₃×C₄×D₄	—	2	2	no	—
257	C₃×C₄×D₄	—	2	1	no	—
258	C₃×C₄×D₄	—	2	1	no	—
259	C₃×C₄×D₄	—	2	1	no	—
260	C₃×C₄×D₄	C₂³	1	2	yes	—
261	C₃×C₄×D₄	C₂³	1	2	yes	—
262	C₃×C₄×D₄	C₂³	1	2	yes	—
263	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
264	C₃×C₄×D₄	C₂³	1	2	yes	—
265	C₃×C₄×D₄	C₂³	1	2	yes	—
266	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
267	C₃×#117	—	2	1	no	—
268	C₃×#117	—	2	2	no	—
269	C₃×#117	—	2	2	no	—
270	C₃×#117	—	2	1	no	—
271	C₃×#117	—	2	2	no	—
272	C₃×#117	—	2	2	no	—
273	C₃×#117	C₂³	1	2	yes	—
274	C₃×#117	C₂³	1	1	yes	characteristic
275	C₂×C₃×C₄⋊C₄	—	2	1	no	—
276	C₂×C₃×C₄⋊C₄	—	2	2	no	—
277	C₂×C₃×C₄⋊C₄	—	2	2	no	—
278	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
279	C₂×C₃×C₄⋊C₄	D₄	1	2	yes	—
280	C₂×C₃×C₄²	—	2	2	no	—
281	C₂×C₃×C₄²	—	2	1	no	—
282	C₂×C₃×C₄²	C₂³	1	2	yes	—
283	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
284	C₃×#107	C₂³	1	2	yes	—
285	C₃×#107	C₂³	1	1	yes	characteristic
286	C₃×#107	C₂³	1	1	yes	characteristic
287	C₃×#107	C₂³	1	2	yes	—
288	C₃×#107	C₂³	1	2	yes	—
289	C₃×#107	C₂³	1	2	yes	—
290	C₃×#107	C₂³	1	2	yes	—
291	C₃×#106	C₂³	1	1	yes	characteristic
292	C₃×#106	C₂³	1	1	yes	characteristic
293	C₃×#106	C₂³	1	2	yes	—
294	C₃×#106	C₂³	1	2	yes	—
295	C₃×#106	C₂³	1	2	yes	—
296	C₃×#106	C₂³	1	2	yes	—
297	C₃×#106	C₂³	1	2	yes	—
298	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
299	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
300	C₃×C₄⋊C₈	C₂³	1	2	yes	—
301	C₃×C₄⋊C₈	C₂³	1	2	yes	—
302	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
303	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
304	C₃×C₄⋊C₈	C₂³	1	2	yes	—
305	C₃×C₄⋊C₈	C₂³	1	2	yes	—
306	C₃×#103	C₂³	1	1	yes	characteristic
307	C₃×#103	C₂³	1	1	yes	characteristic
308	C₃×#103	C₂³	1	1	yes	characteristic
309	C₃×#103	C₂³	1	2	yes	—
310	C₃×#103	C₂³	1	1	yes	characteristic
311	C₃×#103	C₂³	1	2	yes	—
312	C₃×#103	C₂³	1	1	yes	characteristic
313	C₃×#103	C₂³	1	1	yes	characteristic
314	C₃×#103	C₂³	1	2	yes	—
315	C₃×#103	C₂³	1	2	yes	—
316	C₃×#103	C₂³	1	2	yes	—
317	C₃×#102	C₂³	1	1	yes	characteristic
318	C₃×#102	C₂³	1	2	yes	—
319	C₃×#102	C₂³	1	2	yes	—
320	C₃×#102	C₂³	1	1	yes	characteristic
321	C₃×#102	C₂³	1	2	yes	—
322	C₃×#102	C₂³	1	2	yes	—
323	C₃×#102	C₂³	1	2	yes	—
324	C₃×#102	C₂³	1	2	yes	—
325	C₃×#102	C₂³	1	2	yes	—
326	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
327	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
328	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
329	C₃×#97	C₂³	1	2	yes	—
330	C₃×#97	C₂³	1	2	yes	—
331	C₃×#97	C₂³	1	2	yes	—
332	C₃×C₄×C₈	C₂³	1	2	yes	—
333	C₃×C₄×C₈	C₂³	1	2	yes	—
334	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
335	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
336	#559	C₂²×C₃	1	1	yes	characteristic
337	#559	C₂²×C₃	1	1	yes	characteristic
338	Q₈²	C₂²×C₃	1	1	yes	characteristic
339	#557	C₂²×C₃	1	1	yes	characteristic
340	#557	C₂²×C₃	1	2	yes	—
341	#557	C₂²×C₃	1	1	yes	characteristic
342	#557	C₂²×C₃	1	1	yes	characteristic
343	#556	—	2	1	no	—
344	#556	—	2	1	no	—
345	#556	C₂²×C₃	1	2	yes	—
346	#554	—	2	1	no	—
347	#554	—	2	2	no	—
348	#554	C₂²×C₃	1	1	yes	characteristic
349	#554	C₂²×C₃	1	2	yes	—
350	#554	C₂²×C₃	1	2	yes	—
351	#552	—	2	2	no	—
352	D₄×Q₈	—	2	1	no	—
353	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic
354	#539	—	2	2	no	—
355	#536	—	2	1	no	—
356	#533	—	2	2	no	—
357	#533	—	2	1	no	—
358	#533	C₂²×C₃	1	1	yes	characteristic
359	#533	C₂²×C₃	1	1	yes	characteristic
360	#533	C₂²×C₃	1	2	yes	—
361	#532	C₂²×C₃	1	1	yes	characteristic
362	#529	C₂²×C₃	1	2	yes	—
363	#529	C₂²×C₃	1	2	yes	—
364	#520	—	2	1	no	—
365	C₄×#41	C₂²×C₃	1	2	yes	—
366	C₄×#41	C₂²×C₃	1	1	yes	characteristic
367	C₂×C₄×Q₈	—	2	1	no	—
368	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
369	#501	C₂²×C₃	1	2	yes	—
370	#501	C₂²×C₃	1	2	yes	—
371	#501	C₂²×C₃	1	2	yes	—
372	#500	C₂²×C₃	1	1	yes	characteristic
373	#499	C₂²×C₃	1	2	yes	—
374	#499	C₂²×C₃	1	2	yes	—
375	#498	C₂²×C₃	1	1	yes	characteristic
376	#491	C₂²×C₃	1	2	yes	—
377	#489	C₂²×C₃	1	2	yes	—
378	#489	C₂²×C₃	1	2	yes	—
379	#488	C₂²×C₃	1	2	yes	—
380	#488	C₂²×C₃	1	2	yes	—
381	#486	C₂²×C₃	1	1	yes	characteristic
382	#486	C₂²×C₃	1	1	yes	characteristic
383	#485	C₂²×C₃	1	2	yes	—
384	#485	C₂²×C₃	1	1	yes	characteristic
385	#485	C₂²×C₃	1	1	yes	characteristic
386	#485	C₂²×C₃	1	2	yes	—
387	#482	C₂²×C₃	1	2	yes	—
388	#482	C₂²×C₃	1	2	yes	—
389	#482	C₂²×C₃	1	2	yes	—
390	#479	C₂²×C₃	1	2	yes	—
391	#479	C₂²×C₃	1	2	yes	—
392	#479	C₂²×C₃	1	2	yes	—
393	#479	C₂²×C₃	1	2	yes	—
394	#478	C₂²×C₃	1	2	yes	—
395	#478	C₂²×C₃	1	2	yes	—
396	#478	C₂²×C₃	1	2	yes	—
397	#478	C₂²×C₃	1	2	yes	—
398	#478	C₂²×C₃	1	2	yes	—
399	#478	C₂²×C₃	1	2	yes	—
400	#477	C₂²×C₃	1	1	yes	characteristic
401	#477	C₂²×C₃	1	1	yes	characteristic
402	#477	C₂²×C₃	1	2	yes	—
403	#476	C₂²×C₃	1	2	yes	—
404	#475	C₂²×C₃	1	1	yes	characteristic
405	#475	C₂²×C₃	1	1	yes	characteristic
406	#475	C₂²×C₃	1	1	yes	characteristic
407	#475	C₂²×C₃	1	1	yes	characteristic
408	#475	C₂²×C₃	1	2	yes	—
409	#474	C₂²×C₃	1	1	yes	characteristic
410	#474	C₂²×C₃	1	1	yes	characteristic
411	#474	C₂²×C₃	1	2	yes	—
412	#464	C₂²×C₃	1	2	yes	—
413	#464	C₂²×C₃	1	2	yes	—
414	#463	C₂²×C₃	1	2	yes	—
415	#463	C₂²×C₃	1	2	yes	—
416	#462	C₂²×C₃	1	1	yes	characteristic
417	#461	C₂²×C₃	1	1	yes	characteristic
418	#460	C₂²×C₃	1	1	yes	characteristic
419	#459	C₂²×C₃	1	1	yes	characteristic
420	#452	C₂²×C₃	1	1	yes	characteristic
421	#452	C₂²×C₃	1	1	yes	characteristic
422	#449	C₂²×C₃	1	2	yes	—
423	#446	C₂²×C₃	1	1	yes	characteristic
424	#446	C₂²×C₃	1	1	yes	characteristic
425	#446	C₂²×C₃	1	2	yes	—
426	#446	C₂²×C₃	1	2	yes	—
427	C₈×Q₈	C₂²×C₃	1	1	yes	characteristic
428	C₈×Q₈	C₂²×C₃	1	1	yes	characteristic
429	#442	C₂²×C₃	1	2	yes	—
430	#442	C₂²×C₃	1	2	yes	—
431	#441	C₂²×C₃	1	2	yes	—
432	#440	C₂²×C₃	1	2	yes	—
433	#440	C₂²×C₃	1	2	yes	—
434	#440	C₂²×C₃	1	2	yes	—
435	C₄×Q₁₆	C₂²×C₃	1	2	yes	—
436	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic
437	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic
438	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
439	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
440	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
441	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
442	C₄×D₈	C₂²×C₃	1	2	yes	—
443	#432	C₂²×C₃	1	2	yes	—
444	#432	C₂²×C₃	1	1	yes	characteristic
445	#431	C₂²×C₃	1	2	yes	—
446	#431	C₂²×C₃	1	1	yes	characteristic
447	C₃×#41	—	2	2	no	—
448	C₃×#41	—	2	2	no	—
449	C₃×#41	—	4	4	no	—
450	C₂×C₃×Q₈	—	2	2	no	—
451	C₂×C₃×Q₈	—	2	1	no	—
452	C₂×C₃×Q₈	—	2	1	no	—
453	C₂×C₃×Q₈	—	2	1	no	—
454	C₂×C₃×Q₈	—	2	2	no	—
455	C₂×C₃×Q₈	—	2	1	no	—
456	C₂×C₃×Q₈	—	4	2	no	—
457	C₂×C₃×Q₈	—	4	4	no	—
458	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
459	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
460	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
461	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
462	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
463	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
464	C₂×C₃×D₄	—	2	1	no	—
465	C₂×C₃×D₄	—	2	2	no	—
466	C₂×C₃×D₄	—	2	1	no	—
467	C₂×C₃×D₄	—	2	1	no	—
468	C₂×C₃×D₄	C₂⁴	1	2	yes	—
469	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
470	C₂²×C₃×C₄	—	2	1	no	—
471	C₂²×C₃×C₄	—	2	2	no	—
472	C₂²×C₃×C₄	—	2	1	no	—
473	C₂²×C₃×C₄	—	2	2	no	—
474	C₂²×C₃×C₄	—	2	2	no	—
475	C₂²×C₃×C₄	—	2	1	no	—
476	C₂²×C₃×C₄	—	2	2	no	—
477	C₂²×C₃×C₄	—	2	2	no	—
478	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
479	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
480	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
481	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
482	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
483	C₃×Q₁₆	—	2	2	no	—
484	C₃×Q₁₆	—	2	2	no	—
485	C₃×SD₁₆	—	2	4	no	—
486	C₃×SD₁₆	—	2	2	no	—
487	C₃×SD₁₆	—	2	2	no	—
488	C₃×D₈	—	2	4	no	—
489	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
490	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
491	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
492	C₂×C₃×C₈	C₂⁴	1	2	yes	—
493	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
494	C₂×C₃×C₈	C₂⁴	1	2	yes	—
495	C₃×C₄⋊C₄	—	2	1	no	—
496	C₃×C₄⋊C₄	—	2	2	no	—
497	C₃×C₄⋊C₄	—	2	2	no	—
498	C₃×C₄⋊C₄	—	2	2	no	—
499	C₃×C₄⋊C₄	—	2	2	no	—
500	C₃×C₄⋊C₄	—	2	2	no	—
501	C₃×C₄⋊C₄	—	2	2	no	—
502	C₃×C₄⋊C₄	—	2	1	no	—
503	C₃×C₄⋊C₄	—	2	1	no	—
504	C₃×C₄⋊C₄	—	2	1	no	—
505	C₃×C₄⋊C₄	—	2	1	no	—
506	C₃×C₄⋊C₄	—	2	2	no	—
507	C₃×C₄⋊C₄	—	2	2	no	—
508	C₃×C₄⋊C₄	—	2	1	no	—
509	C₃×C₄⋊C₄	—	2	1	no	—
510	C₃×C₄⋊C₄	—	2	2	no	—
511	C₃×C₄⋊C₄	—	2	2	no	—
512	C₃×C₄⋊C₄	—	2	1	no	—
513	C₃×C₄⋊C₄	—	2	2	no	—
514	C₃×C₄⋊C₄	—	2	1	no	—
515	C₃×C₄⋊C₄	—	2	2	no	—
516	C₃×C₄⋊C₄	—	2	2	no	—
517	C₃×C₄⋊C₄	—	2	2	no	—
518	C₃×C₄⋊C₄	—	2	1	no	—
519	C₃×C₄⋊C₄	—	2	1	no	—
520	C₃×C₄⋊C₄	—	2	1	no	—
521	C₃×C₄⋊C₄	—	2	2	no	—
522	C₃×C₄⋊C₄	—	2	2	no	—
523	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
524	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
525	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
526	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
527	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
528	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
529	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
530	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
531	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
532	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
533	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
534	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
535	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
536	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
537	C₃×C₂²⋊C₄	—	2	1	no	—
538	C₃×C₂²⋊C₄	—	2	1	no	—
539	C₃×C₂²⋊C₄	—	2	2	no	—
540	C₃×C₂²⋊C₄	—	2	1	no	—
541	C₃×C₂²⋊C₄	—	2	2	no	—
542	C₃×C₂²⋊C₄	—	2	2	no	—
543	C₃×C₂²⋊C₄	—	2	2	no	—
544	C₃×C₂²⋊C₄	—	2	2	no	—
545	C₃×C₂²⋊C₄	—	2	2	no	—
546	C₃×C₂²⋊C₄	—	2	1	no	—
547	C₃×C₂²⋊C₄	—	2	1	no	—
548	C₃×C₂²⋊C₄	—	2	2	no	—
549	C₃×C₂²⋊C₄	—	2	2	no	—
550	C₃×C₂²⋊C₄	—	2	2	no	—
551	C₃×C₂²⋊C₄	—	2	2	no	—
552	C₃×C₂²⋊C₄	—	2	2	no	—
553	C₃×C₄²	—	2	2	no	—
554	C₃×C₄²	—	2	1	no	—
555	C₃×C₄²	—	2	2	no	—
556	C₃×C₄²	—	2	1	no	—
557	C₃×C₄²	—	2	2	no	—
558	C₃×C₄²	—	2	1	no	—
559	C₃×C₄²	—	2	2	no	—
560	C₃×C₄²	—	2	2	no	—
561	C₃×C₄²	—	2	1	no	—
562	C₃×C₄²	—	2	1	no	—
563	C₃×C₄²	C₂×D₄	1	2	yes	—
564	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
565	C₃×C₄²	C₂×D₄	1	2	yes	—
566	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
567	C₃×C₄²	C₂⁴	1	2	yes	—
568	C₃×C₄²	C₂⁴	1	1	yes	characteristic
569	C₃×C₄²	C₂⁴	1	1	yes	characteristic
570	C₃×C₄²	C₂⁴	1	2	yes	—
571	C₂×#41	—	2	1	no	—
572	C₂×#41	C₂³×C₃	1	1	yes	characteristic
573	C₂²×Q₈	—	2	1	no	—
574	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
575	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
576	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
577	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
578	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
579	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
580	C₂×D₈	C₂³×C₃	1	2	yes	—
581	C₄⋊Q₈	—	2	1	no	—
582	C₄⋊Q₈	—	2	2	no	—
583	C₄⋊Q₈	—	2	1	no	—
584	C₄⋊Q₈	—	2	1	no	—
585	C₄⋊Q₈	—	2	1	no	—
586	C₄⋊Q₈	—	2	2	no	—
587	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
588	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
589	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
590	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
591	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
592	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
593	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
594	#127	C₂³×C₃	1	1	yes	characteristic
595	#126	—	2	2	no	—
596	#126	—	2	2	no	—
597	#126	—	2	2	no	—
598	#126	—	2	2	no	—
599	#125	—	2	2	no	—
600	#125	—	2	2	no	—
601	#125	—	2	2	no	—
602	#125	—	2	2	no	—
603	#125	—	2	2	no	—
604	#125	—	2	1	no	—
605	#125	C₂³×C₃	1	2	yes	—
606	#125	C₂³×C₃	1	2	yes	—
607	#125	C₂³×C₃	1	2	yes	—
608	#125	C₂³×C₃	1	2	yes	—
609	#125	C₂³×C₃	1	2	yes	—
610	#124	—	2	1	no	—
611	#124	—	2	1	no	—
612	#124	—	2	1	no	—
613	#124	C₂³×C₃	1	2	yes	—
614	#124	C₂³×C₃	1	2	yes	—
615	#123	—	2	2	no	—
616	#123	—	2	2	no	—
617	#123	—	2	2	no	—
618	#123	—	2	2	no	—
619	C₂²⋊Q₈	—	2	1	no	—
620	C₂²⋊Q₈	—	2	2	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	—	2	1	no	—
624	C₂²⋊Q₈	—	2	1	no	—
625	C₂²⋊Q₈	—	2	2	no	—
626	C₂²⋊Q₈	—	2	2	no	—
627	C₂²⋊Q₈	—	2	1	no	—
628	C₂²⋊Q₈	—	2	1	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
636	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
637	#121	—	2	1	no	—
638	#121	C₂³×C₃	1	2	yes	—
639	C₄×Q₈	—	2	1	no	—
640	C₄×Q₈	—	2	1	no	—
641	C₄×Q₈	—	2	2	no	—
642	C₄×Q₈	—	2	1	no	—
643	C₄×Q₈	—	2	1	no	—
644	C₄×Q₈	—	2	2	no	—
645	C₄×Q₈	—	2	1	no	—
646	C₄×Q₈	—	2	2	no	—
647	C₄×Q₈	—	2	1	no	—
648	C₄×Q₈	—	2	1	no	—
649	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
650	C₄×Q₈	C₃×D₄	1	2	yes	—
651	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
652	C₄×Q₈	C₂³×C₃	1	2	yes	—
653	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
654	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
655	C₄×Q₈	C₂³×C₃	1	2	yes	—
656	C₄×Q₈	C₂³×C₃	1	2	yes	—
657	C₄×Q₈	C₂³×C₃	1	2	yes	—
658	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
659	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
660	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
661	C₄×Q₈	C₂³×C₃	1	2	yes	—
662	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
663	C₄×D₄	—	2	1	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	1	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	1	no	—
670	C₄×D₄	—	2	1	no	—
671	C₄×D₄	—	2	1	no	—
672	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
673	C₄×D₄	C₂³×C₃	1	2	yes	—
674	C₄×D₄	C₂³×C₃	1	2	yes	—
675	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
676	C₄×D₄	C₂³×C₃	1	2	yes	—
677	C₄×D₄	C₂³×C₃	1	2	yes	—
678	C₄×D₄	C₂³×C₃	1	2	yes	—
679	#117	—	2	1	no	—
680	#117	—	2	2	no	—
681	#117	—	2	2	no	—
682	#117	—	2	1	no	—
683	#117	—	2	2	no	—
684	#117	—	2	2	no	—
685	#117	C₂³×C₃	1	2	yes	—
686	#117	C₂³×C₃	1	1	yes	characteristic
687	C₂×C₄⋊C₄	—	2	1	no	—
688	C₂×C₄⋊C₄	—	2	2	no	—
689	C₂×C₄⋊C₄	—	2	2	no	—
690	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₃×D₄	1	2	yes	—
692	C₂×C₄²	—	2	2	no	—
693	C₂×C₄²	—	2	1	no	—
694	C₂×C₄²	C₂³×C₃	1	2	yes	—
695	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
696	#107	C₂³×C₃	1	2	yes	—
697	#107	C₂³×C₃	1	1	yes	characteristic
698	#107	C₂³×C₃	1	1	yes	characteristic
699	#107	C₂³×C₃	1	2	yes	—
700	#107	C₂³×C₃	1	2	yes	—
701	#107	C₂³×C₃	1	2	yes	—
702	#107	C₂³×C₃	1	2	yes	—
703	#106	C₂³×C₃	1	1	yes	characteristic
704	#106	C₂³×C₃	1	2	yes	—
705	#106	C₂³×C₃	1	1	yes	characteristic
706	#106	C₂³×C₃	1	2	yes	—
707	#106	C₂³×C₃	1	2	yes	—
708	#106	C₂³×C₃	1	2	yes	—
709	#106	C₂³×C₃	1	2	yes	—
710	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
711	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
712	C₄⋊C₈	C₂³×C₃	1	2	yes	—
713	C₄⋊C₈	C₂³×C₃	1	2	yes	—
714	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
715	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
716	C₄⋊C₈	C₂³×C₃	1	2	yes	—
717	C₄⋊C₈	C₂³×C₃	1	2	yes	—
718	#103	C₂³×C₃	1	1	yes	characteristic
719	#103	C₂³×C₃	1	1	yes	characteristic
720	#103	C₂³×C₃	1	1	yes	characteristic
721	#103	C₂³×C₃	1	2	yes	—
722	#103	C₂³×C₃	1	1	yes	characteristic
723	#103	C₂³×C₃	1	2	yes	—
724	#103	C₂³×C₃	1	1	yes	characteristic
725	#103	C₂³×C₃	1	1	yes	characteristic
726	#103	C₂³×C₃	1	2	yes	—
727	#103	C₂³×C₃	1	2	yes	—
728	#103	C₂³×C₃	1	2	yes	—
729	#102	C₂³×C₃	1	1	yes	characteristic
730	#102	C₂³×C₃	1	2	yes	—
731	#102	C₂³×C₃	1	2	yes	—
732	#102	C₂³×C₃	1	1	yes	characteristic
733	#102	C₂³×C₃	1	2	yes	—
734	#102	C₂³×C₃	1	2	yes	—
735	#102	C₂³×C₃	1	2	yes	—
736	#102	C₂³×C₃	1	2	yes	—
737	#102	C₂³×C₃	1	2	yes	—
738	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
739	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
740	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
741	#97	C₂³×C₃	1	2	yes	—
742	#97	C₂³×C₃	1	2	yes	—
743	#97	C₂³×C₃	1	2	yes	—
744	C₄×C₈	C₂³×C₃	1	2	yes	—
745	C₄×C₈	C₂³×C₃	1	2	yes	—
746	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
747	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
748	C₂³×C₃	—	2	1	no	—
749	C₂³×C₃	—	2	2	no	—
750	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
751	C₃×Q₈	—	2	2	no	—
752	C₃×Q₈	—	2	2	no	—
753	C₃×Q₈	—	2	1	no	—
754	C₃×Q₈	—	2	1	no	—
755	C₃×Q₈	—	2	1	no	—
756	C₃×Q₈	—	2	1	no	—
757	C₃×Q₈	—	2	1	no	—
758	C₃×Q₈	—	4	2	no	—
759	C₃×Q₈	—	4	4	no	—
760	C₃×Q₈	—	4	2	no	—
761	C₃×Q₈	—	4	2	no	—
762	C₃×Q₈	—	8	1	no	—
763	C₃×Q₈	—	8	2	no	—
764	C₃×Q₈	—	8	1	no	—
765	C₃×Q₈	2₋¹⁺⁴	1	2	yes	—
766	C₃×D₄	—	2	4	no	—
767	C₃×D₄	—	2	1	no	—
768	C₃×D₄	—	2	2	no	—
769	C₃×D₄	—	2	2	no	—
770	C₃×D₄	—	4	4	no	—
771	C₃×D₄	—	4	2	no	—
772	C₃×D₄	—	8	1	no	—
773	C₃×D₄	2₋¹⁺⁴	1	2	yes	—
774	C₂×C₃×C₄	—	2	4	no	—
775	C₂×C₃×C₄	—	2	1	no	—
776	C₂×C₃×C₄	—	2	2	no	—
777	C₂×C₃×C₄	—	2	1	no	—
778	C₂×C₃×C₄	—	2	1	no	—
779	C₂×C₃×C₄	—	2	1	no	—
780	C₂×C₃×C₄	—	2	1	no	—
781	C₂×C₃×C₄	—	2	2	no	—
782	C₂×C₃×C₄	—	2	2	no	—
783	C₂×C₃×C₄	—	2	1	no	—
784	C₂×C₃×C₄	—	2	2	no	—
785	C₂×C₃×C₄	—	2	1	no	—
786	C₂×C₃×C₄	—	2	1	no	—
787	C₂×C₃×C₄	—	2	1	no	—
788	C₂×C₃×C₄	—	4	2	no	—
789	C₂×C₃×C₄	—	4	1	no	—
790	C₂×C₃×C₄	—	4	2	no	—
791	C₂×C₃×C₄	—	4	4	no	—
792	C₂×C₃×C₄	—	4	4	no	—
793	C₂×C₃×C₄	—	4	2	no	—
794	C₂×C₃×C₄	—	8	2	no	—
795	C₂×C₃×C₄	—	8	2	no	—
796	C₂×C₃×C₄	—	8	2	no	—
797	C₂×C₃×C₄	—	8	1	no	—
798	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
799	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
800	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
801	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
802	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
803	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
804	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
805	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
806	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
807	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
808	C₃×C₈	—	2	2	no	—
809	C₃×C₈	—	2	2	no	—
810	C₃×C₈	—	2	1	no	—
811	C₃×C₈	—	2	1	no	—
812	C₃×C₈	—	2	1	no	—
813	C₃×C₈	—	2	1	no	—
814	#41	—	2	2	no	—
815	#41	—	2	2	no	—
816	#41	—	4	4	no	—
817	C₂×Q₈	—	2	2	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	—	2	1	no	—
820	C₂×Q₈	—	2	1	no	—
821	C₂×Q₈	—	2	2	no	—
822	C₂×Q₈	—	2	1	no	—
823	C₂×Q₈	—	4	2	no	—
824	C₂×Q₈	—	4	4	no	—
825	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
826	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
827	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
828	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
829	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
830	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	1	no	—
835	C₂×D₄	C₂⁴×C₃	1	2	yes	—
836	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
846	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
847	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
848	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
850	Q₁₆	—	2	2	no	—
851	Q₁₆	—	2	2	no	—
852	SD₁₆	—	2	4	no	—
853	SD₁₆	—	2	2	no	—
854	SD₁₆	—	2	2	no	—
855	D₈	—	2	4	no	—
856	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
857	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
858	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
859	C₂×C₈	C₂⁴×C₃	1	2	yes	—
860	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
861	C₂×C₈	C₂⁴×C₃	1	2	yes	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	1	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
891	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
892	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
893	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
894	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
895	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
896	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
897	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
898	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
899	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
900	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
901	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
902	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
903	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
904	C₂²⋊C₄	—	2	1	no	—
905	C₂²⋊C₄	—	2	1	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	1	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	1	no	—
914	C₂²⋊C₄	—	2	1	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₄²	—	2	2	no	—
921	C₄²	—	2	1	no	—
922	C₄²	—	2	2	no	—
923	C₄²	—	2	1	no	—
924	C₄²	—	2	2	no	—
925	C₄²	—	2	1	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	—	2	1	no	—
929	C₄²	—	2	1	no	—
930	C₄²	C₂×C₃×D₄	1	2	yes	—
931	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
932	C₄²	C₂×C₃×D₄	1	2	yes	—
933	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
934	C₄²	C₂⁴×C₃	1	2	yes	—
935	C₄²	C₂⁴×C₃	1	1	yes	characteristic
936	C₄²	C₂⁴×C₃	1	1	yes	characteristic
937	C₄²	C₂⁴×C₃	1	2	yes	—
938	C₂²×C₃	—	2	1	no	—
939	C₂²×C₃	—	2	1	no	—
940	C₂²×C₃	—	2	2	no	—
941	C₂²×C₃	—	2	1	no	—
942	C₂²×C₃	—	4	1	no	—
943	C₂²×C₃	—	4	1	no	—
944	C₂²×C₃	—	4	2	no	—
945	C₂²×C₃	—	4	2	no	—
946	C₂²×C₃	—	4	2	no	—
947	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
948	C₃×C₄	—	2	2	no	—
949	C₃×C₄	—	2	2	no	—
950	C₃×C₄	—	2	1	no	—
951	C₃×C₄	—	2	1	no	—
952	C₃×C₄	—	2	1	no	—
953	C₃×C₄	—	2	2	no	—
954	C₃×C₄	—	2	1	no	—
955	C₃×C₄	—	2	2	no	—
956	C₃×C₄	—	2	2	no	—
957	C₃×C₄	—	4	1	no	—
958	C₃×C₄	—	4	1	no	—
959	C₃×C₄	—	4	2	no	—
960	C₃×C₄	—	4	1	no	—
961	C₃×C₄	—	4	1	no	—
962	C₃×C₄	—	4	1	no	—
963	C₃×C₄	—	4	2	no	—
964	C₃×C₄	—	4	2	no	—
965	C₃×C₄	—	4	1	no	—
966	C₃×C₄	#575	1	2	yes	—
967	C₃×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
968	C₃×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
969	C₂³	—	2	1	no	—
970	C₂³	—	2	2	no	—
971	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
972	Q₈	—	2	2	no	—
973	Q₈	—	2	2	no	—
974	Q₈	—	2	1	no	—
975	Q₈	—	2	1	no	—
976	Q₈	—	2	1	no	—
977	Q₈	—	2	1	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	4	2	no	—
980	Q₈	—	4	4	no	—
981	Q₈	—	4	2	no	—
982	Q₈	—	4	2	no	—
983	Q₈	—	8	1	no	—
984	Q₈	—	8	2	no	—
985	Q₈	—	8	1	no	—
986	Q₈	C₃×2₋¹⁺⁴	1	2	yes	—
987	D₄	—	2	4	no	—
988	D₄	—	2	1	no	—
989	D₄	—	2	2	no	—
990	D₄	—	2	2	no	—
991	D₄	—	4	4	no	—
992	D₄	—	4	2	no	—
993	D₄	—	8	1	no	—
994	D₄	C₃×2₋¹⁺⁴	1	2	yes	—
995	C₂×C₄	—	2	4	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	4	2	no	—
1010	C₂×C₄	—	4	2	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	4	4	no	—
1013	C₂×C₄	—	4	4	no	—
1014	C₂×C₄	—	4	2	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	—	8	1	no	—
1019	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1020	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1021	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1022	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1023	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1024	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1025	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1026	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1027	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1028	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1029	C₈	—	2	2	no	—
1030	C₈	—	2	2	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	1	no	—
1033	C₈	—	2	1	no	—
1034	C₈	—	2	1	no	—
1035	C₂×C₃	—	4	1	no	—
1036	C₂×C₃	—	4	2	no	—
1037	C₂×C₃	—	8	2	no	—
1038	C₂×C₃	#3486	1	1	yes	characteristic
1039	C₂×C₃	C₂×#575	1	1	yes	characteristic
1040	C₂×C₃	#3584	1	1	yes	characteristic
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	4	1	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1051	C₄	—	2	1	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	C₃×#575	1	2	yes	—
1070	C₄	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1071	C₄	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1072	C₃	#61845	1	1	yes	characteristic, direct product factor, Sylow
1073	C₂	—	4	1	no	—
1074	C₂	—	4	2	no	—
1075	C₂	—	8	2	no	—
1076	C₂	C₃×#3486	1	1	yes	characteristic
1077	C₂	C₂×C₃×#575	1	1	yes	characteristic
1078	C₂	C₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₃×#3115	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3507	C₂	semidirect
2. C₃×Q₈×#41	C₂	semidirect
3. C₃×#3389	C₂	semidirect
4. C₃×#3388	C₂	semidirect
5. C₃×#3387	C₂	semidirect
6. C₃×#3386	C₂	semidirect
7. C₃×#3383	C₂	semidirect
8. C₃×#3381	C₂	semidirect
9. C₃×#3377	C₂	semidirect
10. C₃×#3376	C₂	semidirect
11. C₃×#3375	C₂	semidirect
12. C₃×#3373	C₂	semidirect
13. C₃×#3365	C₂	semidirect
14. C₃×#3361	C₂	semidirect
15. C₃×#3240	C₂	semidirect
16. C₃×#3237	C₂	semidirect
17. C₃×#3233	C₂	semidirect
18. C₃×#3228	C₂	semidirect
20. C₃×#3111	C₂	semidirect
21. C₃×#3107	C₂	semidirect
22. C₃×#3102	C₂	semidirect
23. C₃×#2984	C₂	semidirect
24. #61845	C₃	direct (N × H)
136. #3507	C₂×C₃	semidirect
137. Q₈×#41	C₂×C₃	semidirect
138. #3389	C₂×C₃	semidirect
139. #3388	C₂×C₃	semidirect
140. #3387	C₂×C₃	semidirect
141. #3386	C₂×C₃	semidirect
142. #3383	C₂×C₃	semidirect
143. #3381	C₂×C₃	semidirect
144. #3377	C₂×C₃	semidirect
145. #3376	C₂×C₃	semidirect
146. #3375	C₂×C₃	semidirect
147. #3373	C₂×C₃	semidirect
148. #3365	C₂×C₃	semidirect
149. #3361	C₂×C₃	semidirect
150. #3240	C₂×C₃	semidirect
151. #3237	C₂×C₃	semidirect
152. #3233	C₂×C₃	semidirect
153. #3228	C₂×C₃	semidirect
155. #3111	C₂×C₃	semidirect
156. #3107	C₂×C₃	semidirect
157. #3102	C₂×C₃	semidirect
158. #2984	C₂×C₃	semidirect
1072. C₃	#61845	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×#3507	2
C₃×Q₈×#41	2
C₃×#3389	2
C₃×#3388	2
C₃×#3387	2
C₃×#3386	2
C₃×#3383	2
C₃×#3381	2
C₃×#3377	2
C₃×#3376	2
C₃×#3375	2
C₃×#3373	2
C₃×#3365	2
C₃×#3361	2
C₃×#3240	2
C₃×#3237	2
C₃×#3233	2
C₃×#3228	2
C₃×#3115	2
C₃×#3111	2
C₃×#3107	2
C₃×#3102	2
C₃×#2984	2
#61845	3

Subgroups — C3×#61845 #10680452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61845 #10680452