Subgroups — #11704208

Order 768.

7474 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3459	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
3	#86572	C₂	1	1	yes	maximal, characteristic, complemented
4	#86454	C₂	1	6	yes	maximal, complemented
5	#86453	C₂	1	6	yes	maximal, complemented
6	#86415	C₂	1	6	yes	maximal, complemented
7	#86414	C₂	1	6	yes	maximal, complemented
8	D₃×#534	C₂	1	3	yes	maximal, complemented
9	#86295	C₂	1	3	yes	maximal, complemented
10	#86158	C₂	1	6	yes	maximal, complemented
11	#86155	C₂	1	6	yes	maximal, complemented
12	#86044	C₂	1	6	yes	maximal, complemented
13	#86043	C₂	1	6	yes	maximal, complemented
14	#85776	C₂	1	3	yes	maximal, complemented
15	C₂×#5545	C₂	1	3	yes	maximal, complemented
16	#62844	—	3	1	no	maximal, Sylow
17	C₂²×D₃×D₄	C₂²	1	3	yes	—
18	C₃×#543	C₂²	1	1	yes	characteristic, complemented
19	C₃×#539	C₂²	1	6	yes	complemented
20	C₃×#538	C₂²	1	6	yes	complemented
21	C₃×#534	C₂²	1	3	yes	complemented
22	C₃×#529	C₂²	1	6	yes	complemented
23	C₃×#525	C₂²	1	6	yes	complemented
24	C₂×C₃×C₄×D₄	C₂²	1	3	yes	complemented
25	#5831	C₂²	1	2	yes	complemented
26	#5829	C₂²	1	6	yes	complemented
27	#5804	C₂²	1	6	yes	complemented
28	C₂×D₄×Dic₃	C₂²	1	3	yes	complemented
29	#5791	C₂²	1	6	yes	complemented
30	C₂×C₄×#67	C₂²	1	3	yes	complemented
31	C₂×C₄×#67	C₂²	1	3	yes	complemented
32	C₂²×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×(C₂×D₃)⋊C₄	C₂²	1	3	yes	complemented
34	#5709	C₂²	1	12	yes	complemented
35	#5708	C₂²	1	12	yes	complemented
36	#5705	C₂²	1	12	yes	complemented
37	#5705	C₂²	1	12	yes	complemented
38	#5695	C₂²	1	6	yes	complemented
39	#5694	C₂²	1	6	yes	complemented
40	#5693	C₂²	1	12	yes	complemented
41	#5679	C₂²	1	12	yes	complemented
42	#5677	C₂²	1	6	yes	complemented
43	#5676	C₂²	1	6	yes	complemented
44	#5665	C₂²	1	12	yes	complemented
45	#5661	C₂²	1	12	yes	complemented
46	#5659	C₂²	1	12	yes	complemented
47	#5658	C₂²	1	12	yes	complemented
48	#5654	C₂²	1	12	yes	complemented
49	#5653	C₂²	1	12	yes	complemented
50	D₃×#123	C₂²	1	12	yes	complemented
51	#5649	C₂²	1	12	yes	complemented
52	#5645	C₂²	1	6	yes	complemented
53	#5644	C₂²	1	6	yes	complemented
54	#5639	C₂²	1	6	yes	complemented
55	#5637	C₂²	1	12	yes	complemented
56	#5634	C₂²	1	6	yes	complemented
57	#5634	C₂²	1	6	yes	complemented
58	#5633	C₂²	1	6	yes	complemented
59	#5627	C₂²	1	6	yes	complemented
60	D₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
61	D₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
62	#5624	C₂²	1	6	yes	complemented
63	#5617	C₂²	1	6	yes	complemented
64	#5614	C₂²	1	6	yes	complemented
65	#5612	C₂²	1	6	yes	complemented
66	#5610	C₂²	1	12	yes	complemented
67	#5606	C₂²	1	6	yes	complemented
68	#5605	C₂²	1	6	yes	—
69	#5605	C₂²	1	6	yes	—
70	D₃×#121	C₂²	1	6	yes	complemented
71	D₃×#121	C₂²	1	6	yes	complemented
72	#5602	C₂²	1	6	yes	complemented
73	#5600	C₂²	1	6	yes	complemented
74	#5593	C₂²	1	12	yes	complemented
75	#5589	C₂²	1	12	yes	complemented
76	D₃×#120	C₂²	1	12	yes	complemented
77	#5586	C₂²	1	12	yes	complemented
78	#5581	C₂²	1	6	yes	complemented
79	#5576	C₂²	1	2	yes	complemented
80	#5564	C₂²	1	12	yes	complemented
81	#5560	C₂²	1	12	yes	complemented
82	#5558	C₂²	1	6	yes	complemented
83	#5556	C₂²	1	12	yes	complemented
84	#5554	C₂²	1	6	yes	complemented
85	#5547	C₂²	1	12	yes	complemented
86	#5545	C₂²	1	12	yes	complemented
87	#5545	C₂²	1	12	yes	complemented
88	#5545	C₂²	1	12	yes	complemented
89	#5545	C₂²	1	12	yes	complemented
90	#5538	C₂²	1	12	yes	complemented
91	#5530	C₂²	1	6	yes	complemented
92	#5529	C₂²	1	6	yes	complemented
93	#5527	C₂²	1	12	yes	complemented
94	#5515	C₂²	1	6	yes	complemented
95	C₂×#893	C₂²	1	3	yes	complemented
96	C₂×#892	C₂²	1	3	yes	complemented
97	#5494	C₂²	1	6	yes	complemented
98	#5493	C₂²	1	3	yes	complemented
99	C₂×#67⋊C₄	C₂²	1	3	yes	complemented
100	C₂×#67⋊C₄	C₂²	1	3	yes	complemented
101	C₂×D₃×C₂²⋊C₄	C₂²	1	3	yes	—
102	C₂×D₃×C₂²⋊C₄	C₂²	1	3	yes	complemented
103	#5483	C₂²	1	3	yes	complemented
104	#5479	C₂²	1	6	yes	complemented
105	C₂×C₄×D₁₂	C₂²	1	3	yes	complemented
106	C₂×#872	C₂²	1	3	yes	complemented
107	#3505	—	3	6	no	—
108	#3505	—	3	6	no	—
109	#3505	—	3	6	no	—
110	#3505	—	3	6	no	—
111	#3491	—	3	6	no	—
112	#3491	—	3	6	no	—
113	#3490	—	3	6	no	—
114	#3490	—	3	6	no	—
115	#3459	—	3	1	no	—
116	#3459	—	3	3	no	—
117	#3459	—	3	3	no	—
118	#3459	D₃	1	1	yes	characteristic, complemented
119	C₂×#543	—	3	1	no	—
120	C₂×#534	—	3	3	no	—
121	C₂×#518	—	3	3	no	—
122	C₂⁴×D₃	C₂³	1	3	yes	—
123	C₂⁴×D₃	C₂³	1	1	yes	characteristic
124	C₂×C₃×#41	C₂³	1	2	yes	complemented
125	C₂²×C₃×D₄	C₂³	1	3	yes	—
126	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
127	C₂³×C₃×C₄	C₂³	1	3	yes	complemented
128	C₂²×#67	C₂³	1	3	yes	—
129	C₂²×#67	C₂³	1	3	yes	—
130	C₂³×Dic₃	C₂³	1	1	yes	characteristic
131	C₂³×Dic₃	C₂³	1	3	yes	complemented
132	C₂×#239	C₂³	1	2	yes	complemented
133	C₂×D₃×Q₈	C₂³	1	2	yes	complemented
134	C₂×D₃×Q₈	C₂³	1	2	yes	complemented
135	C₂×#237	C₂³	1	6	yes	complemented
136	C₂×D₃×D₄	—	2	24	no	—
137	C₂×D₃×D₄	C₂³	1	12	yes	—
138	C₂×D₃×D₄	C₂³	1	12	yes	—
139	C₂×D₃×D₄	C₂³	1	6	yes	complemented
140	C₂×D₃×D₄	C₂³	1	6	yes	complemented
141	C₂×#235	C₂³	1	6	yes	complemented
142	C₂²×D₁₂	C₂³	1	3	yes	—
143	C₂²×C₄×D₃	C₂³	1	3	yes	—
144	C₂²×C₄×D₃	C₂³	1	3	yes	—
145	C₂²×C₄×D₃	C₂³	1	3	yes	—
146	C₂²×C₄×D₃	C₂³	1	3	yes	complemented
147	C₂²×C₄×D₃	C₂³	1	3	yes	complemented
148	C₃×#126	C₂³	1	12	yes	complemented
149	C₃×#125	C₂³	1	6	yes	complemented
150	C₃×#124	C₂³	1	6	yes	complemented
151	C₃×#123	C₂³	1	12	yes	complemented
152	C₃×#123	C₂³	1	12	yes	complemented
153	C₃×C₂²⋊Q₈	C₂³	1	6	yes	complemented
154	C₃×C₂²⋊Q₈	C₂³	1	6	yes	complemented
155	C₃×C₂²⋊Q₈	C₂³	1	6	yes	complemented
156	C₃×#121	C₂³	1	6	yes	—
157	C₃×#121	C₂³	1	6	yes	—
158	C₃×#121	C₂³	1	6	yes	complemented
159	C₃×#120	C₂³	1	12	yes	complemented
160	C₃×C₄×Q₈	C₂³	1	2	yes	complemented
161	C₃×C₄×D₄	C₂³	1	12	yes	complemented
162	C₃×C₄×D₄	C₂³	1	12	yes	complemented
163	C₃×C₄×D₄	C₂³	1	6	yes	complemented
164	C₃×#117	C₂³	1	6	yes	complemented
165	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	complemented
166	C₂×C₃×C₂²⋊C₄	C₂³	1	3	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	3	yes	complemented
168	C₂×C₃×C₄²	C₂³	1	3	yes	complemented
169	#953	C₂³	1	12	yes	complemented
170	C₂×#217	C₂³	1	3	yes	—
171	C₂×#217	C₂³	1	3	yes	complemented
172	#947	C₂³	1	6	yes	complemented
173	#946	C₂³	1	6	yes	complemented
174	#946	C₂³	1	6	yes	complemented
175	#946	C₂³	1	6	yes	complemented
176	Q₈×Dic₃	C₂³	1	2	yes	complemented
177	#939	C₂³	1	12	yes	—
178	#939	C₂³	1	12	yes	—
179	#939	C₂³	1	12	yes	complemented
180	#938	C₂³	1	6	yes	complemented
181	#938	C₂³	1	6	yes	complemented
182	#938	C₂³	1	6	yes	complemented
183	#937	C₂³	1	12	yes	—
184	#937	C₂³	1	12	yes	—
185	#937	C₂³	1	12	yes	complemented
186	#936	C₂³	1	6	yes	complemented
187	#935	C₂³	1	12	yes	complemented
188	#935	C₂³	1	12	yes	complemented
189	D₄×Dic₃	C₂³	1	12	yes	complemented
190	D₄×Dic₃	C₂³	1	6	yes	complemented
191	D₄×Dic₃	C₂³	1	12	yes	complemented
192	#930	C₂³	1	6	yes	—
193	#930	C₂³	1	6	yes	—
194	#930	C₂³	1	6	yes	complemented
195	#929	C₂³	1	12	yes	complemented
196	#929	C₂³	1	12	yes	complemented
197	C₄×#67	C₂³	1	6	yes	—
198	C₄×#67	C₂³	1	6	yes	—
199	C₄×#67	C₂³	1	6	yes	complemented
200	C₄×#67	C₂³	1	12	yes	complemented
201	C₄×#67	C₂³	1	12	yes	complemented
202	C₄×#67	C₂³	1	12	yes	complemented
203	C₄×#67	C₂³	1	6	yes	complemented
204	C₂×(C₂×D₃)⋊C₄	C₂³	1	3	yes	—
205	C₂×(C₂×D₃)⋊C₄	C₂³	1	3	yes	—
206	C₂×(C₂×D₃)⋊C₄	C₂³	1	3	yes	—
207	C₂×(C₂×D₃)⋊C₄	C₂³	1	3	yes	—
208	C₂×(C₂×D₃)⋊C₄	C₂³	1	3	yes	—
209	C₂×(C₂×D₃)⋊C₄	C₂³	1	3	yes	—
210	C₂×(C₂×D₃)⋊C₄	C₂³	1	12	yes	complemented
211	C₂×(C₂×D₃)⋊C₄	C₂³	1	3	yes	complemented
212	C₂×(C₂×D₃)⋊C₄	C₂³	1	3	yes	complemented
213	C₂×(C₂×D₃)⋊C₄	C₂³	1	12	yes	complemented
214	#926	C₂³	1	6	yes	complemented
215	C₂×C₄⋊Dic₃	C₂³	1	3	yes	complemented
216	#924	C₂³	1	6	yes	complemented
217	#924	C₂³	1	6	yes	complemented
218	#924	C₂³	1	6	yes	complemented
219	C₂×Dic₃⋊C₄	C₂³	1	3	yes	complemented
220	C₂×Dic₃⋊C₄	C₂³	1	3	yes	complemented
221	C₂×C₄×Dic₃	C₂³	1	3	yes	complemented
222	C₂×C₄×Dic₃	C₂³	1	3	yes	complemented
223	C₂×C₄×Dic₃	C₂³	1	3	yes	complemented
224	#898	C₂³	1	12	yes	complemented
225	#898	C₂³	1	12	yes	complemented
226	#898	C₂³	1	12	yes	complemented
227	#897	C₂³	1	6	yes	complemented
228	#897	C₂³	1	6	yes	complemented
229	#897	C₂³	1	6	yes	complemented
230	#896	C₂³	1	12	yes	complemented
231	#896	C₂³	1	12	yes	complemented
232	#896	C₂³	1	12	yes	complemented
233	#895	C₂³	1	6	yes	complemented
234	#895	C₂³	1	6	yes	complemented
235	#895	C₂³	1	6	yes	complemented
236	#894	C₂³	1	12	yes	—
237	#894	C₂³	1	12	yes	—
238	#894	C₂³	1	12	yes	complemented
239	#894	C₂³	1	12	yes	complemented
240	#893	C₂³	1	12	yes	—
241	#893	C₂³	1	12	yes	complemented
242	#893	C₂³	1	6	yes	complemented
243	#892	C₂³	1	12	yes	complemented
244	#892	C₂³	1	12	yes	complemented
245	#892	C₂³	1	6	yes	complemented
246	#892	C₂³	1	6	yes	complemented
247	D₃×C₄⋊C₄	C₂³	1	6	yes	complemented
248	D₃×C₄⋊C₄	C₂³	1	6	yes	complemented
249	D₃×C₄⋊C₄	C₂³	1	6	yes	complemented
250	D₃×C₄⋊C₄	C₂³	1	6	yes	complemented
251	#890	C₂³	1	6	yes	complemented
252	#890	C₂³	1	6	yes	complemented
253	#889	C₂³	1	12	yes	complemented
254	#889	C₂³	1	12	yes	complemented
255	#887	C₂³	1	6	yes	complemented
256	#886	C₂³	1	12	yes	complemented
257	#886	C₂³	1	12	yes	complemented
258	#885	C₂³	1	12	yes	complemented
259	#885	C₂³	1	12	yes	complemented
260	#884	C₂³	1	12	yes	complemented
261	#884	C₂³	1	12	yes	complemented
262	#884	C₂³	1	12	yes	complemented
263	#883	C₂³	1	12	yes	—
264	#883	C₂³	1	12	yes	—
265	#883	C₂³	1	12	yes	complemented
266	#883	C₂³	1	12	yes	complemented
267	#882	C₂³	1	12	yes	—
268	#882	C₂³	1	12	yes	—
269	#882	C₂³	1	12	yes	complemented
270	#67⋊C₄	C₂³	1	12	yes	—
271	#67⋊C₄	C₂³	1	12	yes	complemented
272	#67⋊C₄	C₂³	1	12	yes	complemented
273	#67⋊C₄	C₂³	1	12	yes	complemented
274	#67⋊C₄	C₂³	1	12	yes	complemented
275	D₃×C₂²⋊C₄	C₂³	1	12	yes	—
276	D₃×C₂²⋊C₄	C₂³	1	12	yes	—
277	D₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
278	D₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
279	D₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
280	D₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
281	#879	C₂³	1	12	yes	complemented
282	#879	C₂³	1	12	yes	complemented
283	#879	C₂³	1	12	yes	complemented
284	#878	C₂³	1	12	yes	complemented
285	#878	C₂³	1	12	yes	complemented
286	#878	C₂³	1	12	yes	complemented
287	#877	C₂³	1	12	yes	complemented
288	#876	C₂³	1	12	yes	complemented
289	#875	C₂³	1	6	yes	complemented
290	C₄×D₁₂	C₂³	1	6	yes	—
291	C₄×D₁₂	C₂³	1	6	yes	—
292	C₄×D₁₂	C₂³	1	6	yes	complemented
293	C₄×D₁₂	C₂³	1	6	yes	complemented
294	C₄×D₁₂	C₂³	1	6	yes	complemented
295	#872	C₂³	1	12	yes	complemented
296	#872	C₂³	1	12	yes	complemented
297	#872	C₂³	1	12	yes	complemented
298	#870	C₂³	1	6	yes	complemented
299	C₄×Dic₆	C₂³	1	6	yes	complemented
300	C₂³×D₄	—	3	3	no	—
301	#553	—	3	12	no	—
302	#553	—	3	6	no	—
303	#553	—	3	12	no	—
304	#553	—	3	6	no	—
305	#553	—	3	6	no	—
306	#553	—	3	6	no	—
307	#552	—	3	12	no	—
308	#552	—	3	12	no	—
309	#552	—	3	6	no	—
310	#552	—	3	6	no	—
311	#552	—	3	6	no	—
312	#552	—	3	6	no	—
313	#551	—	3	12	no	—
314	#551	—	3	12	no	—
315	#551	—	3	12	no	—
316	#551	—	3	12	no	—
317	#551	—	3	12	no	—
318	#551	—	3	12	no	—
319	#551	—	3	12	no	—
320	#551	—	3	12	no	—
321	#548	—	3	2	no	—
322	#548	—	3	6	no	—
323	#548	—	3	6	no	—
324	#548	—	3	2	no	—
325	#546	—	3	6	no	—
326	#546	—	3	6	no	—
327	#546	—	3	12	no	—
328	#546	—	3	12	no	—
329	#546	—	3	6	no	—
330	#546	—	3	6	no	—
331	#543	—	3	6	no	—
332	#543	—	3	6	no	—
333	#543	—	3	3	no	—
334	#543	C₂×D₃	1	1	yes	characteristic, complemented
335	#539	—	3	12	no	—
336	#539	—	3	6	no	—
337	#539	—	3	6	no	—
338	#539	—	3	12	no	—
339	#539	—	3	6	no	—
340	#539	C₂×D₃	1	6	yes	complemented
341	#538	—	3	6	no	—
342	#538	—	3	6	no	—
343	#538	—	3	12	no	—
344	#538	—	3	12	no	—
345	#538	—	3	6	no	—
346	#538	C₂×D₃	1	6	yes	complemented
347	#534	—	3	6	no	—
348	#534	—	3	12	no	—
349	#534	—	3	6	no	—
350	#534	—	3	6	no	—
351	#534	—	3	12	no	—
352	#534	—	3	3	no	—
353	#534	C₂×D₃	1	3	yes	complemented
354	#529	—	3	12	no	—
355	#529	—	3	6	no	—
356	#529	—	3	6	no	—
357	#529	—	3	12	no	—
358	#529	—	3	6	no	—
359	#529	C₂×D₃	1	6	yes	complemented
360	#525	—	3	6	no	—
361	#525	—	3	6	no	—
362	#525	—	3	6	no	—
363	#525	—	3	12	no	—
364	#525	—	3	12	no	—
365	#525	C₂×D₃	1	6	yes	complemented
366	C₂×#123	—	3	12	no	—
367	C₂×C₂²⋊Q₈	—	3	6	no	—
368	C₂×C₂²⋊Q₈	—	3	6	no	—
369	C₂×#121	—	3	6	no	—
370	C₂×#121	—	3	6	no	—
371	C₂×#120	—	3	12	no	—
372	#518	—	3	12	no	—
373	#518	—	3	12	no	—
374	#518	—	3	12	no	—
375	#518	—	3	12	no	—
376	C₂×C₄×D₄	—	3	3	no	—
377	C₂×C₄×D₄	—	3	3	no	—
378	C₂×C₄×D₄	—	3	3	no	—
379	C₂×C₄×D₄	—	3	3	no	—
380	C₂×C₄×D₄	—	3	3	no	—
381	C₂×C₄×D₄	—	3	3	no	—
382	C₂×C₄×D₄	—	3	3	no	—
383	C₂×C₄×D₄	C₂×D₃	1	3	yes	complemented
384	C₂×#117	—	3	3	no	—
385	C₂×#117	—	3	3	no	—
386	C₂²×C₂²⋊C₄	—	3	1	no	—
387	C₂²×C₂²⋊C₄	—	3	3	no	—
388	C₂²×C₂²⋊C₄	—	3	3	no	—
389	C₂²×C₂²⋊C₄	—	3	3	no	—
390	C₂⁴×C₃	C₂⁴	1	3	yes	—
391	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
392	C₂³×D₃	—	2	12	no	—
393	C₂³×D₃	—	8	1	no	—
394	C₂³×D₃	—	8	1	no	—
395	C₂³×D₃	—	8	3	no	—
396	C₂³×D₃	—	8	3	no	—
397	C₂³×D₃	#41	1	8	yes	complemented
398	C₂³×D₃	C₂⁴	1	12	yes	—
399	C₂³×D₃	C₂⁴	1	3	yes	—
400	C₂³×D₃	C₂⁴	1	3	yes	—
401	C₂³×D₃	C₂⁴	1	3	yes	—
402	C₃×#41	—	8	2	no	—
403	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
404	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
405	C₂×C₃×D₄	—	2	12	no	—
406	C₂×C₃×D₄	C₂⁴	1	12	yes	—
407	C₂×C₃×D₄	C₂⁴	1	6	yes	—
408	C₂×C₃×D₄	C₂⁴	1	6	yes	—
409	C₂²×C₃×C₄	—	8	1	no	—
410	C₂²×C₃×C₄	—	8	3	no	—
411	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
412	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
413	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
414	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
415	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
416	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
417	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
418	C₂×#67	—	2	12	no	—
419	C₂×#67	—	2	12	no	—
420	C₂×#67	C₂⁴	1	6	yes	—
421	C₂×#67	C₂⁴	1	12	yes	—
422	C₂×#67	C₂⁴	1	6	yes	—
423	C₂×#67	C₂⁴	1	12	yes	—
424	C₂×#67	C₂⁴	1	12	yes	—
425	C₂²×Dic₃	—	8	1	no	—
426	C₂²×Dic₃	—	8	3	no	—
427	C₂²×Dic₃	C₂⁴	1	3	yes	—
428	C₂²×Dic₃	C₂⁴	1	12	yes	—
429	C₂²×Dic₃	C₂⁴	1	3	yes	—
430	C₂²×Dic₃	C₂⁴	1	3	yes	—
431	C₂²×Dic₃	C₂⁴	1	3	yes	—
432	C₂²×Dic₃	C₂⁴	1	3	yes	—
433	#239	—	8	2	no	—
434	D₃×Q₈	—	8	2	no	—
435	D₃×Q₈	—	8	2	no	—
436	#237	—	8	6	no	—
437	D₃×D₄	—	2	48	no	—
438	D₃×D₄	—	2	48	no	—
439	D₃×D₄	—	8	6	no	—
440	D₃×D₄	—	8	6	no	—
441	#235	—	8	6	no	—
442	C₂×D₁₂	—	2	12	no	—
443	C₂×D₁₂	C₂⁴	1	6	yes	—
444	C₂×D₁₂	C₂⁴	1	6	yes	—
445	C₂×D₁₂	C₂⁴	1	6	yes	—
446	C₂×D₁₂	C₂⁴	1	6	yes	—
447	C₂×C₄×D₃	—	2	12	no	—
448	C₂×C₄×D₃	—	8	3	no	—
449	C₂×C₄×D₃	—	8	3	no	—
450	C₂×C₄×D₃	—	8	3	no	—
451	C₂×C₄×D₃	—	8	3	no	—
452	C₂×C₄×D₃	C₂⁴	1	12	yes	—
453	C₂×C₄×D₃	C₂⁴	1	12	yes	—
454	C₂×C₄×D₃	C₂⁴	1	6	yes	—
455	C₂×C₄×D₃	C₂⁴	1	6	yes	—
456	C₂×C₄×D₃	C₂⁴	1	6	yes	—
457	C₂×C₄×D₃	C₂⁴	1	6	yes	—
458	C₂×C₄×D₃	C₂⁴	1	6	yes	—
459	C₂×C₄×D₃	C₂⁴	1	6	yes	—
460	C₂×Dic₆	C₂⁴	1	6	yes	—
461	C₂×Dic₆	C₂⁴	1	6	yes	—
462	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
463	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
464	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
465	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
466	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
467	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
468	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
469	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
470	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
471	C₃×C₄²	C₂⁴	1	6	yes	—
472	C₃×C₄²	C₂⁴	1	6	yes	—
473	#217	C₂⁴	1	12	yes	—
474	#217	C₂⁴	1	12	yes	—
475	#217	C₂⁴	1	12	yes	—
476	#217	C₂⁴	1	6	yes	—
477	#217	C₂⁴	1	6	yes	—
478	(C₂×D₃)⋊C₄	C₂⁴	1	3	yes	—
479	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
480	(C₂×D₃)⋊C₄	C₂⁴	1	6	yes	—
481	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
482	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
483	(C₂×D₃)⋊C₄	C₂⁴	1	3	yes	—
484	(C₂×D₃)⋊C₄	C₂⁴	1	6	yes	—
485	(C₂×D₃)⋊C₄	C₂⁴	1	6	yes	—
486	(C₂×D₃)⋊C₄	C₂⁴	1	1	yes	characteristic
487	(C₂×D₃)⋊C₄	C₂⁴	1	3	yes	—
488	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
489	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
490	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
491	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
492	C₄⋊Dic₃	C₂⁴	1	6	yes	—
493	C₄⋊Dic₃	C₂⁴	1	6	yes	—
494	C₄⋊Dic₃	C₂⁴	1	6	yes	—
495	C₄⋊Dic₃	C₂⁴	1	6	yes	—
496	C₄⋊Dic₃	C₂⁴	1	6	yes	—
497	C₄⋊Dic₃	C₂⁴	1	6	yes	—
498	Dic₃⋊C₄	C₂⁴	1	12	yes	—
499	Dic₃⋊C₄	C₂⁴	1	6	yes	—
500	Dic₃⋊C₄	C₂⁴	1	12	yes	—
501	Dic₃⋊C₄	C₂⁴	1	12	yes	—
502	Dic₃⋊C₄	C₂⁴	1	6	yes	—
503	Dic₃⋊C₄	C₂⁴	1	12	yes	—
504	Dic₃⋊C₄	C₂⁴	1	12	yes	—
505	C₄×Dic₃	C₂⁴	1	12	yes	—
506	C₄×Dic₃	C₂⁴	1	12	yes	—
507	C₄×Dic₃	C₂⁴	1	6	yes	—
508	C₄×Dic₃	C₂⁴	1	6	yes	—
509	C₂⁵	—	3	1	no	—
510	C₂⁵	—	3	3	no	—
511	C₂×#41	—	3	2	no	—
512	C₂×#41	—	3	6	no	—
513	C₂×#41	—	3	6	no	—
514	C₂×#41	C₂²×D₃	1	2	yes	complemented
515	C₂²×Q₈	—	3	2	no	—
516	C₂²×Q₈	—	3	2	no	—
517	C₂²×D₄	—	3	3	no	—
518	C₂²×D₄	—	3	3	no	—
519	C₂²×D₄	—	3	12	no	—
520	C₂²×D₄	—	3	12	no	—
521	C₂²×D₄	—	3	6	no	—
522	C₂²×D₄	—	3	6	no	—
523	C₂²×D₄	—	3	3	no	—
524	C₂²×D₄	—	6	24	no	—
525	C₂²×D₄	C₂²×D₃	1	3	yes	—
526	C₂³×C₄	—	3	1	no	—
527	C₂³×C₄	—	3	3	no	—
528	C₂³×C₄	—	3	3	no	—
529	C₂³×C₄	—	3	3	no	—
530	C₂³×C₄	—	3	3	no	—
531	C₂³×C₄	—	3	3	no	—
532	C₂³×C₄	—	3	3	no	—
533	C₂³×C₄	C₂²×D₃	1	1	yes	characteristic
534	C₂³×C₄	C₂²×D₃	1	3	yes	complemented
535	#126	—	3	12	no	—
536	#126	—	3	12	no	—
537	#126	—	3	12	no	—
538	#126	—	3	12	no	—
539	#126	—	3	12	no	—
540	#126	—	3	12	no	—
541	#126	—	3	12	no	—
542	#126	C₂²×D₃	1	12	yes	complemented
543	#125	—	3	12	no	—
544	#125	—	3	12	no	—
545	#125	—	3	6	no	—
546	#125	—	3	6	no	—
547	#125	—	3	6	no	—
548	#125	C₂²×D₃	1	6	yes	complemented
549	#124	—	3	6	no	—
550	#124	—	3	6	no	—
551	#124	—	3	12	no	—
552	#124	—	3	12	no	—
553	#124	—	3	6	no	—
554	#124	C₂²×D₃	1	6	yes	complemented
555	#123	—	3	12	no	—
556	#123	—	3	12	no	—
557	#123	—	3	12	no	—
558	#123	—	3	12	no	—
559	#123	—	3	12	no	—
560	#123	—	3	12	no	—
561	#123	—	3	12	no	—
562	#123	—	3	12	no	—
563	#123	—	3	12	no	—
564	#123	—	3	12	no	—
565	#123	—	3	12	no	—
566	#123	—	3	12	no	—
567	#123	—	3	12	no	—
568	#123	—	3	12	no	—
569	#123	C₂²×D₃	1	12	yes	complemented
570	#123	C₂²×D₃	1	12	yes	complemented
571	C₂²⋊Q₈	—	3	6	no	—
572	C₂²⋊Q₈	—	3	6	no	—
573	C₂²⋊Q₈	—	3	6	no	—
574	C₂²⋊Q₈	—	3	6	no	—
575	C₂²⋊Q₈	—	3	6	no	—
576	C₂²⋊Q₈	—	3	6	no	—
577	C₂²⋊Q₈	—	3	12	no	—
578	C₂²⋊Q₈	—	3	12	no	—
579	C₂²⋊Q₈	—	3	6	no	—
580	C₂²⋊Q₈	—	3	6	no	—
581	C₂²⋊Q₈	—	3	12	no	—
582	C₂²⋊Q₈	—	3	6	no	—
583	C₂²⋊Q₈	—	3	12	no	—
584	C₂²⋊Q₈	—	3	12	no	—
585	C₂²⋊Q₈	—	3	12	no	—
586	C₂²⋊Q₈	C₂²×D₃	1	6	yes	complemented
587	C₂²⋊Q₈	C₂²×D₃	1	6	yes	complemented
588	C₂²⋊Q₈	C₂²×D₃	1	6	yes	complemented
589	#121	—	3	12	no	—
590	#121	—	3	12	no	—
591	#121	—	3	6	no	—
592	#121	—	3	6	no	—
593	#121	—	3	6	no	—
594	#121	—	3	12	no	—
595	#121	—	3	6	no	—
596	#121	—	3	6	no	—
597	#121	—	3	6	no	—
598	#121	—	3	6	no	—
599	#121	—	3	6	no	—
600	#121	—	3	6	no	—
601	#121	—	3	12	no	—
602	#121	—	3	12	no	—
603	#121	—	3	12	no	—
604	#121	C₂²×D₃	1	6	yes	—
605	#121	C₂²×D₃	1	6	yes	—
606	#121	C₂²×D₃	1	6	yes	complemented
607	#120	—	3	12	no	—
608	#120	—	3	12	no	—
609	#120	—	3	12	no	—
610	#120	—	3	12	no	—
611	#120	—	3	12	no	—
612	#120	—	3	12	no	—
613	#120	—	3	12	no	—
614	#120	C₂²×D₃	1	12	yes	complemented
615	C₄×Q₈	—	3	2	no	—
616	C₄×Q₈	—	3	6	no	—
617	C₄×Q₈	—	3	6	no	—
618	C₄×Q₈	C₂²×D₃	1	2	yes	complemented
619	C₄×D₄	—	3	12	no	—
620	C₄×D₄	—	3	12	no	—
621	C₄×D₄	—	3	6	no	—
622	C₄×D₄	—	3	12	no	—
623	C₄×D₄	—	3	12	no	—
624	C₄×D₄	—	3	6	no	—
625	C₄×D₄	—	3	6	no	—
626	C₄×D₄	—	3	6	no	—
627	C₄×D₄	—	3	6	no	—
628	C₄×D₄	—	3	12	no	—
629	C₄×D₄	—	3	12	no	—
630	C₄×D₄	—	3	12	no	—
631	C₄×D₄	—	3	6	no	—
632	C₄×D₄	—	3	12	no	—
633	C₄×D₄	—	3	12	no	—
634	C₄×D₄	—	3	12	no	—
635	C₄×D₄	—	3	12	no	—
636	C₄×D₄	—	3	12	no	—
637	C₄×D₄	—	3	6	no	—
638	C₄×D₄	—	3	6	no	—
639	C₄×D₄	—	3	6	no	—
640	C₄×D₄	—	3	6	no	—
641	C₄×D₄	—	3	6	no	—
642	C₄×D₄	C₂²×D₃	1	12	yes	complemented
643	C₄×D₄	C₂²×D₃	1	12	yes	complemented
644	C₄×D₄	C₂²×D₃	1	6	yes	complemented
645	#117	—	3	6	no	—
646	#117	—	3	12	no	—
647	#117	—	3	12	no	—
648	#117	—	3	6	no	—
649	#117	—	3	6	no	—
650	#117	—	3	12	no	—
651	#117	—	3	12	no	—
652	#117	—	3	12	no	—
653	#117	—	3	12	no	—
654	#117	C₂²×D₃	1	6	yes	complemented
655	C₂×C₄⋊C₄	—	3	3	no	—
656	C₂×C₄⋊C₄	—	3	3	no	—
657	C₂×C₄⋊C₄	—	3	3	no	—
658	C₂×C₄⋊C₄	—	3	6	no	—
659	C₂×C₄⋊C₄	—	3	6	no	—
660	C₂×C₄⋊C₄	—	3	6	no	—
661	C₂×C₄⋊C₄	—	3	6	no	—
662	C₂×C₄⋊C₄	C₂²×D₃	1	3	yes	complemented
663	C₂×C₂²⋊C₄	—	3	3	no	—
664	C₂×C₂²⋊C₄	—	3	3	no	—
665	C₂×C₂²⋊C₄	—	3	3	no	—
666	C₂×C₂²⋊C₄	—	3	3	no	—
667	C₂×C₂²⋊C₄	—	3	3	no	—
668	C₂×C₂²⋊C₄	—	3	3	no	—
669	C₂×C₂²⋊C₄	—	3	3	no	—
670	C₂×C₂²⋊C₄	—	3	3	no	—
671	C₂×C₂²⋊C₄	—	3	3	no	—
672	C₂×C₂²⋊C₄	—	3	3	no	—
673	C₂×C₂²⋊C₄	—	3	12	no	—
674	C₂×C₂²⋊C₄	—	3	12	no	—
675	C₂×C₂²⋊C₄	—	3	12	no	—
676	C₂×C₂²⋊C₄	—	3	12	no	—
677	C₂×C₂²⋊C₄	—	3	12	no	—
678	C₂×C₂²⋊C₄	—	3	12	no	—
679	C₂×C₂²⋊C₄	—	3	12	no	—
680	C₂×C₂²⋊C₄	—	3	12	no	—
681	C₂×C₂²⋊C₄	C₂²×D₃	1	3	yes	—
682	C₂×C₂²⋊C₄	C₂²×D₃	1	3	yes	complemented
683	C₂×C₄²	—	3	3	no	—
684	C₂×C₄²	—	3	3	no	—
685	C₂×C₄²	—	3	3	no	—
686	C₂×C₄²	C₂²×D₃	1	3	yes	complemented
687	C₂³×C₃	—	2	6	no	—
688	C₂³×C₃	—	4	1	no	—
689	C₂³×C₃	—	4	3	no	—
690	C₂³×C₃	—	4	1	no	—
691	C₂³×C₃	—	4	3	no	—
692	C₂³×C₃	C₂×#41	1	4	yes	—
693	C₂³×C₃	C₂⁵	1	6	yes	—
694	C₂³×C₃	C₂⁵	1	3	yes	—
695	C₂²×D₃	—	2	6	no	—
696	C₂²×D₃	—	2	24	no	—
697	C₂²×D₃	—	4	3	no	—
698	C₂²×D₃	—	4	3	no	—
699	C₂²×D₃	—	4	3	no	—
700	C₂²×D₃	—	4	3	no	—
701	C₂²×D₃	—	4	3	no	—
702	C₂²×D₃	—	4	3	no	—
703	C₂²×D₃	—	4	12	no	—
704	C₂²×D₃	—	4	12	no	—
705	C₂²×D₃	—	8	8	no	—
706	C₂²×D₃	—	8	24	no	—
707	C₂²×D₃	C₂×#41	1	12	yes	—
708	C₂²×D₃	C₂×#41	1	12	yes	—
709	C₂²×D₃	C₂⁵	1	6	yes	—
710	C₂²×D₃	C₂⁵	1	3	yes	—
711	C₂²×D₃	C₂⁵	1	1	yes	characteristic
712	C₃×Q₈	—	4	2	no	—
713	C₃×Q₈	—	4	2	no	—
714	C₃×D₄	—	2	24	no	—
715	C₃×D₄	—	4	6	no	—
716	C₃×D₄	—	4	6	no	—
717	C₂×C₃×C₄	—	2	6	no	—
718	C₂×C₃×C₄	—	4	3	no	—
719	C₂×C₃×C₄	—	4	3	no	—
720	C₂×C₃×C₄	—	4	3	no	—
721	C₂×C₃×C₄	—	4	6	no	—
722	C₂×C₃×C₄	—	4	3	no	—
723	C₂×C₃×C₄	—	4	6	no	—
724	C₂×C₃×C₄	C₂⁵	1	3	yes	—
725	C₂×C₃×C₄	C₂⁵	1	6	yes	—
726	C₂×C₃×C₄	C₂⁵	1	6	yes	—
727	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
728	C₂×C₃×C₄	C₂⁵	1	6	yes	—
729	#67	—	2	24	no	—
730	#67	—	2	12	no	—
731	#67	—	2	12	no	—
732	#67	—	4	12	no	—
733	#67	—	4	12	no	—
734	C₂×Dic₃	—	2	6	no	—
735	C₂×Dic₃	—	4	3	no	—
736	C₂×Dic₃	—	4	3	no	—
737	C₂×Dic₃	—	4	3	no	—
738	C₂×Dic₃	—	4	12	no	—
739	C₂×Dic₃	—	4	3	no	—
740	C₂×Dic₃	C₂⁵	1	3	yes	—
741	C₂×Dic₃	C₂⁵	1	1	yes	characteristic
742	C₂×Dic₃	C₂⁵	1	6	yes	—
743	C₂×Dic₃	C₂⁵	1	6	yes	—
744	C₂×Dic₃	C₂⁵	1	6	yes	—
745	D₁₂	—	2	12	no	—
746	D₁₂	—	2	12	no	—
747	D₁₂	—	4	6	no	—
748	D₁₂	—	4	6	no	—
749	C₄×D₃	—	2	24	no	—
750	C₄×D₃	—	4	12	no	—
751	C₄×D₃	—	4	6	no	—
752	C₄×D₃	—	4	6	no	—
753	C₄×D₃	—	4	6	no	—
754	C₄×D₃	—	4	6	no	—
755	C₄×D₃	—	4	6	no	—
756	C₄×D₃	—	4	6	no	—
757	Dic₆	—	4	6	no	—
758	Dic₆	—	4	6	no	—
759	C₂⁴	—	3	3	no	—
760	C₂⁴	—	3	3	no	—
761	C₂⁴	—	3	8	no	—
762	C₂⁴	—	3	12	no	—
763	C₂⁴	—	3	3	no	—
764	C₂⁴	—	6	12	no	—
765	C₂⁴	—	24	1	no	—
766	C₂⁴	—	24	3	no	—
767	C₂⁴	—	24	1	no	—
768	C₂⁴	—	24	3	no	—
769	C₂⁴	C₂³×D₃	1	3	yes	—
770	C₂⁴	C₂³×D₃	1	1	yes	characteristic
771	#41	—	8	2	no	—
772	#41	—	24	6	no	—
773	#41	—	24	6	no	—
774	#41	—	24	2	no	—
775	C₂×Q₈	—	3	6	no	—
776	C₂×Q₈	—	3	6	no	—
777	C₂×Q₈	—	24	2	no	—
778	C₂×Q₈	—	24	2	no	—
779	C₂×Q₈	C₂³×D₃	1	2	yes	—
780	C₂×Q₈	C₂³×D₃	1	2	yes	—
781	C₂×D₄	—	2	12	no	—
782	C₂×D₄	—	3	6	no	—
783	C₂×D₄	—	3	12	no	—
784	C₂×D₄	—	3	6	no	—
785	C₂×D₄	—	3	12	no	—
786	C₂×D₄	—	3	12	no	—
787	C₂×D₄	—	3	6	no	—
788	C₂×D₄	—	3	6	no	—
789	C₂×D₄	—	3	6	no	—
790	C₂×D₄	—	3	6	no	—
791	C₂×D₄	—	6	12	no	—
792	C₂×D₄	—	6	48	no	—
793	C₂×D₄	—	6	48	no	—
794	C₂×D₄	—	6	12	no	—
795	C₂×D₄	—	6	12	no	—
796	C₂×D₄	—	24	6	no	—
797	C₂×D₄	—	24	6	no	—
798	C₂×D₄	C₂³×D₃	1	12	yes	—
799	C₂×D₄	C₂³×D₃	1	6	yes	—
800	C₂×D₄	C₂³×D₃	1	6	yes	—
801	C₂²×C₄	—	3	3	no	—
802	C₂²×C₄	—	3	3	no	—
803	C₂²×C₄	—	3	3	no	—
804	C₂²×C₄	—	3	3	no	—
805	C₂²×C₄	—	3	3	no	—
806	C₂²×C₄	—	3	12	no	—
807	C₂²×C₄	—	3	12	no	—
808	C₂²×C₄	—	3	6	no	—
809	C₂²×C₄	—	3	6	no	—
810	C₂²×C₄	—	3	6	no	—
811	C₂²×C₄	—	3	6	no	—
812	C₂²×C₄	—	3	6	no	—
813	C₂²×C₄	—	3	6	no	—
814	C₂²×C₄	—	3	12	no	—
815	C₂²×C₄	—	6	12	no	—
816	C₂²×C₄	—	8	1	no	—
817	C₂²×C₄	—	8	3	no	—
818	C₂²×C₄	—	24	3	no	—
819	C₂²×C₄	—	24	3	no	—
820	C₂²×C₄	—	24	3	no	—
821	C₂²×C₄	—	24	3	no	—
822	C₂²×C₄	—	24	1	no	—
823	C₂²×C₄	—	24	3	no	—
824	C₂²×C₄	C₂³×D₃	1	3	yes	—
825	C₂²×C₄	C₂³×D₃	1	3	yes	—
826	C₂²×C₄	C₂³×D₃	1	3	yes	—
827	C₂²×C₄	C₂³×D₃	1	3	yes	—
828	C₂²×C₄	C₂³×D₃	1	3	yes	—
829	C₂²×C₄	C₂³×D₃	1	6	yes	—
830	C₂²×C₄	C₂³×D₃	1	6	yes	—
831	C₄⋊C₄	—	3	12	no	—
832	C₄⋊C₄	—	3	6	no	—
833	C₄⋊C₄	—	3	6	no	—
834	C₄⋊C₄	—	3	6	no	—
835	C₄⋊C₄	—	3	6	no	—
836	C₄⋊C₄	—	3	12	no	—
837	C₄⋊C₄	—	3	12	no	—
838	C₄⋊C₄	—	3	6	no	—
839	C₄⋊C₄	—	3	6	no	—
840	C₄⋊C₄	—	3	12	no	—
841	C₄⋊C₄	—	3	12	no	—
842	C₄⋊C₄	—	3	6	no	—
843	C₄⋊C₄	—	3	6	no	—
844	C₄⋊C₄	C₂³×D₃	1	6	yes	—
845	C₄⋊C₄	C₂³×D₃	1	6	yes	—
846	C₄⋊C₄	C₂³×D₃	1	6	yes	—
847	C₄⋊C₄	C₂³×D₃	1	6	yes	—
848	C₄⋊C₄	C₂³×D₃	1	12	yes	—
849	C₂²⋊C₄	—	3	12	no	—
850	C₂²⋊C₄	—	3	6	no	—
851	C₂²⋊C₄	—	3	6	no	—
852	C₂²⋊C₄	—	3	12	no	—
853	C₂²⋊C₄	—	3	12	no	—
854	C₂²⋊C₄	—	3	6	no	—
855	C₂²⋊C₄	—	3	3	no	—
856	C₂²⋊C₄	—	3	3	no	—
857	C₂²⋊C₄	—	3	12	no	—
858	C₂²⋊C₄	—	3	12	no	—
859	C₂²⋊C₄	—	3	3	no	—
860	C₂²⋊C₄	—	3	1	no	—
861	C₂²⋊C₄	—	3	12	no	—
862	C₂²⋊C₄	—	3	6	no	—
863	C₂²⋊C₄	—	3	6	no	—
864	C₂²⋊C₄	—	3	12	no	—
865	C₂²⋊C₄	—	3	12	no	—
866	C₂²⋊C₄	—	3	12	no	—
867	C₂²⋊C₄	—	3	12	no	—
868	C₂²⋊C₄	C₂³×D₃	1	12	yes	—
869	C₂²⋊C₄	C₂³×D₃	1	12	yes	—
870	C₂²⋊C₄	C₂³×D₃	1	12	yes	—
871	C₂²⋊C₄	C₂³×D₃	1	12	yes	—
872	C₄²	—	3	6	no	—
873	C₄²	—	3	6	no	—
874	C₄²	—	3	12	no	—
875	C₄²	—	3	12	no	—
876	C₄²	C₂³×D₃	1	6	yes	—
877	C₄²	C₂³×D₃	1	6	yes	—
878	C₂²×C₃	—	2	3	no	—
879	C₂²×C₃	—	2	3	no	—
880	C₂²×C₃	—	2	6	no	—
881	C₂²×C₃	—	2	6	no	—
882	C₂²×C₃	—	2	6	no	—
883	C₂²×C₃	—	4	4	no	—
884	C₂²×C₃	—	4	12	no	—
885	C₂²×C₃	C₂²×#41	1	6	yes	—
886	C₂²×C₃	C₂⁶	1	1	yes	characteristic
887	C₂×D₃	—	2	1	no	—
888	C₂×D₃	—	2	1	no	—
889	C₂×D₃	—	2	3	no	—
890	C₂×D₃	—	2	3	no	—
891	C₂×D₃	—	2	6	no	—
892	C₂×D₃	—	2	6	no	—
893	C₂×D₃	—	2	6	no	—
894	C₂×D₃	—	4	12	no	—
895	C₂×D₃	—	4	12	no	—
896	C₂×D₃	—	4	12	no	—
897	C₂×D₃	—	8	24	no	—
898	C₂×D₃	C₂²×#41	1	6	yes	—
899	C₂×D₃	C₂²×#41	1	2	yes	—
900	C₃×C₄	—	2	6	no	—
901	C₃×C₄	—	2	6	no	—
902	C₃×C₄	—	2	6	no	—
903	C₃×C₄	—	2	3	no	—
904	C₃×C₄	—	2	1	no	—
905	Dic₃	—	2	6	no	—
906	Dic₃	—	2	6	no	—
907	Dic₃	—	2	6	no	—
908	Dic₃	—	2	1	no	—
909	Dic₃	—	2	3	no	—
910	C₂³	—	2	6	no	—
911	C₂³	—	3	3	no	—
912	C₂³	—	3	1	no	—
913	C₂³	—	3	12	no	—
914	C₂³	—	3	12	no	—
915	C₂³	—	3	6	no	—
916	C₂³	—	4	1	no	—
917	C₂³	—	4	3	no	—
918	C₂³	—	4	1	no	—
919	C₂³	—	4	3	no	—
920	C₂³	—	6	24	no	—
921	C₂³	—	6	6	no	—
922	C₂³	—	12	3	no	—
923	C₂³	—	12	3	no	—
924	C₂³	—	12	3	no	—
925	C₂³	—	12	3	no	—
926	C₂³	—	12	3	no	—
927	C₂³	—	12	3	no	—
928	C₂³	—	12	12	no	—
929	C₂³	—	12	12	no	—
930	C₂³	—	24	8	no	—
931	C₂³	—	24	24	no	—
932	C₂³	D₃×#41	1	4	yes	—
933	C₂³	C₂⁴×D₃	1	6	yes	—
934	C₂³	C₂⁴×D₃	1	3	yes	—
935	Q₈	—	4	2	no	—
936	Q₈	—	4	2	no	—
937	Q₈	—	12	6	no	—
938	Q₈	—	12	6	no	—
939	D₄	—	2	24	no	—
940	D₄	—	4	6	no	—
941	D₄	—	4	6	no	—
942	D₄	—	6	12	no	—
943	D₄	—	6	12	no	—
944	D₄	—	6	12	no	—
945	D₄	—	6	12	no	—
946	D₄	—	6	24	no	—
947	D₄	—	12	6	no	—
948	D₄	—	12	6	no	—
949	D₄	—	12	12	no	—
950	D₄	—	12	12	no	—
951	C₂×C₄	—	2	6	no	—
952	C₂×C₄	—	3	1	no	—
953	C₂×C₄	—	3	3	no	—
954	C₂×C₄	—	3	6	no	—
955	C₂×C₄	—	3	6	no	—
956	C₂×C₄	—	3	6	no	—
957	C₂×C₄	—	4	3	no	—
958	C₂×C₄	—	4	3	no	—
959	C₂×C₄	—	4	3	no	—
960	C₂×C₄	—	4	6	no	—
961	C₂×C₄	—	4	6	no	—
962	C₂×C₄	—	4	3	no	—
963	C₂×C₄	—	6	24	no	—
964	C₂×C₄	—	6	6	no	—
965	C₂×C₄	—	12	6	no	—
966	C₂×C₄	—	12	6	no	—
967	C₂×C₄	—	12	6	no	—
968	C₂×C₄	—	12	6	no	—
969	C₂×C₄	—	12	12	no	—
970	C₂×C₄	—	12	6	no	—
971	C₂×C₄	—	12	6	no	—
972	C₂×C₄	—	12	3	no	—
973	C₂×C₄	—	12	3	no	—
974	C₂×C₄	—	12	3	no	—
975	C₂×C₄	—	12	3	no	—
976	C₂×C₄	—	12	12	no	—
977	C₂×C₄	C₂⁴×D₃	1	3	yes	—
978	C₂×C₄	C₂⁴×D₃	1	6	yes	—
979	C₂×C₄	C₂⁴×D₃	1	6	yes	—
980	C₂×C₄	C₂⁴×D₃	1	1	yes	characteristic
981	C₂×C₄	C₂⁴×D₃	1	6	yes	—
982	C₂×C₃	—	2	6	no	—
983	C₂×C₃	—	4	6	no	—
984	C₂×C₃	C₂³×#41	1	1	yes	characteristic
985	C₂×C₃	H(7,𝔽₂)	1	1	yes	characteristic
986	C₂×C₃	H(7,𝔽₂)	1	1	yes	characteristic
987	D₃	—	2	6	no	—
988	D₃	—	2	2	no	—
989	D₃	—	4	6	no	—
990	C₂²	—	2	3	no	—
991	C₂²	—	2	3	no	—
992	C₂²	—	2	6	no	—
993	C₂²	—	2	6	no	—
994	C₂²	—	2	6	no	—
995	C₂²	—	3	6	no	—
996	C₂²	—	3	2	no	—
997	C₂²	—	4	4	no	—
998	C₂²	—	4	12	no	—
999	C₂²	—	6	1	no	—
1000	C₂²	—	6	3	no	—
1001	C₂²	—	6	1	no	—
1002	C₂²	—	6	3	no	—
1003	C₂²	—	6	6	no	—
1004	C₂²	—	6	6	no	—
1005	C₂²	—	6	6	no	—
1006	C₂²	—	12	12	no	—
1007	C₂²	—	12	12	no	—
1008	C₂²	—	12	12	no	—
1009	C₂²	—	24	24	no	—
1010	C₂²	C₂×D₃×#41	1	6	yes	—
1011	C₂²	C₂⁵×D₃	1	1	yes	characteristic
1012	C₄	—	2	6	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	3	no	—
1015	C₄	—	2	6	no	—
1016	C₄	—	2	6	no	—
1017	C₄	—	6	6	no	—
1018	C₄	—	6	6	no	—
1019	C₄	—	6	1	no	—
1020	C₄	—	6	3	no	—
1021	C₄	—	6	6	no	—
1022	C₃	#62844	1	1	yes	characteristic, complemented, Sylow
1023	C₂	—	2	6	no	—
1024	C₂	—	4	6	no	—
1025	C₂	—	6	6	no	—
1026	C₂	—	6	2	no	—
1027	C₂	—	12	6	no	—
1028	C₂	C₂²×D₃×#41	1	1	yes	characteristic
1029	C₂	#87568	1	1	yes	characteristic
1030	C₂	#87574	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁶
Fitting	C₃×#3459	C₂
hypercenter	#3459	D₃
hypocenter	C₃	#62844
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #3459

Complements

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

N	H ≅ G/N	type
1. C₃×#3459	C₂	semidirect
2. D₃×#543	C₂	semidirect
3. #86572	C₂	semidirect
4. #86454	C₂	semidirect
5. #86453	C₂	semidirect
6. #86415	C₂	semidirect
7. #86414	C₂	semidirect
8. D₃×#534	C₂	semidirect
9. #86295	C₂	semidirect
10. #86158	C₂	semidirect
11. #86155	C₂	semidirect
12. #86044	C₂	semidirect
13. #86043	C₂	semidirect
14. #85776	C₂	semidirect
15. C₂×#5545	C₂	semidirect
18. C₃×#543	C₂²	semidirect
19. C₃×#539	C₂²	semidirect
20. C₃×#538	C₂²	semidirect
21. C₃×#534	C₂²	semidirect
22. C₃×#529	C₂²	semidirect
23. C₃×#525	C₂²	semidirect
24. C₂×C₃×C₄×D₄	C₂²	semidirect
25. #5831	C₂²	semidirect
26. #5829	C₂²	semidirect
27. #5804	C₂²	semidirect
28. C₂×D₄×Dic₃	C₂²	semidirect
29. #5791	C₂²	semidirect
30. C₂×C₄×#67	C₂²	semidirect
31. C₂×C₄×#67	C₂²	semidirect
33. C₂²×(C₂×D₃)⋊C₄	C₂²	semidirect
34. #5709	C₂²	semidirect
35. #5708	C₂²	semidirect
36. #5705	C₂²	semidirect
37. #5705	C₂²	semidirect
38. #5695	C₂²	semidirect
39. #5694	C₂²	semidirect
40. #5693	C₂²	semidirect
41. #5679	C₂²	semidirect
42. #5677	C₂²	semidirect
43. #5676	C₂²	semidirect
44. #5665	C₂²	semidirect
45. #5661	C₂²	semidirect
46. #5659	C₂²	semidirect
47. #5658	C₂²	semidirect
48. #5654	C₂²	semidirect
49. #5653	C₂²	semidirect
50. D₃×#123	C₂²	semidirect
51. #5649	C₂²	semidirect
52. #5645	C₂²	semidirect
53. #5644	C₂²	semidirect
54. #5639	C₂²	semidirect
55. #5637	C₂²	semidirect
56. #5634	C₂²	semidirect
57. #5634	C₂²	semidirect
58. #5633	C₂²	semidirect
59. #5627	C₂²	semidirect
60. D₃×C₂²⋊Q₈	C₂²	semidirect
61. D₃×C₂²⋊Q₈	C₂²	semidirect
62. #5624	C₂²	semidirect
63. #5617	C₂²	semidirect
64. #5614	C₂²	semidirect
65. #5612	C₂²	semidirect
66. #5610	C₂²	semidirect
67. #5606	C₂²	semidirect
70. D₃×#121	C₂²	semidirect
71. D₃×#121	C₂²	semidirect
72. #5602	C₂²	semidirect
73. #5600	C₂²	semidirect
74. #5593	C₂²	semidirect
75. #5589	C₂²	semidirect
76. D₃×#120	C₂²	semidirect
77. #5586	C₂²	semidirect
78. #5581	C₂²	semidirect
79. #5576	C₂²	semidirect
80. #5564	C₂²	semidirect
81. #5560	C₂²	semidirect
82. #5558	C₂²	semidirect
83. #5556	C₂²	semidirect
84. #5554	C₂²	semidirect
85. #5547	C₂²	semidirect
86. #5545	C₂²	semidirect
87. #5545	C₂²	semidirect
88. #5545	C₂²	semidirect
89. #5545	C₂²	semidirect
90. #5538	C₂²	semidirect
91. #5530	C₂²	semidirect
92. #5529	C₂²	semidirect
93. #5527	C₂²	semidirect
94. #5515	C₂²	semidirect
95. C₂×#893	C₂²	semidirect
96. C₂×#892	C₂²	semidirect
97. #5494	C₂²	semidirect
98. #5493	C₂²	semidirect
99. C₂×#67⋊C₄	C₂²	semidirect
100. C₂×#67⋊C₄	C₂²	semidirect
102. C₂×D₃×C₂²⋊C₄	C₂²	semidirect
103. #5483	C₂²	semidirect
104. #5479	C₂²	semidirect
105. C₂×C₄×D₁₂	C₂²	semidirect
106. C₂×#872	C₂²	semidirect
118. #3459	D₃	semidirect
124. C₂×C₃×#41	C₂³	semidirect
127. C₂³×C₃×C₄	C₂³	semidirect
131. C₂³×Dic₃	C₂³	semidirect
132. C₂×#239	C₂³	semidirect
133. C₂×D₃×Q₈	C₂³	semidirect
134. C₂×D₃×Q₈	C₂³	semidirect
135. C₂×#237	C₂³	semidirect
139. C₂×D₃×D₄	C₂³	semidirect
140. C₂×D₃×D₄	C₂³	semidirect
141. C₂×#235	C₂³	semidirect
146. C₂²×C₄×D₃	C₂³	semidirect
147. C₂²×C₄×D₃	C₂³	semidirect
148. C₃×#126	C₂³	semidirect
149. C₃×#125	C₂³	semidirect
150. C₃×#124	C₂³	semidirect
151. C₃×#123	C₂³	semidirect
152. C₃×#123	C₂³	semidirect
153. C₃×C₂²⋊Q₈	C₂³	semidirect
154. C₃×C₂²⋊Q₈	C₂³	semidirect
155. C₃×C₂²⋊Q₈	C₂³	semidirect
158. C₃×#121	C₂³	semidirect
159. C₃×#120	C₂³	semidirect
160. C₃×C₄×Q₈	C₂³	semidirect
161. C₃×C₄×D₄	C₂³	semidirect
162. C₃×C₄×D₄	C₂³	semidirect
163. C₃×C₄×D₄	C₂³	semidirect
164. C₃×#117	C₂³	semidirect
165. C₂×C₃×C₄⋊C₄	C₂³	semidirect
167. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
168. C₂×C₃×C₄²	C₂³	semidirect
169. #953	C₂³	semidirect
171. C₂×#217	C₂³	semidirect
172. #947	C₂³	semidirect
173. #946	C₂³	semidirect
174. #946	C₂³	semidirect
175. #946	C₂³	semidirect
176. Q₈×Dic₃	C₂³	semidirect
179. #939	C₂³	semidirect
180. #938	C₂³	semidirect
181. #938	C₂³	semidirect
182. #938	C₂³	semidirect
185. #937	C₂³	semidirect
186. #936	C₂³	semidirect
187. #935	C₂³	semidirect
188. #935	C₂³	semidirect
189. D₄×Dic₃	C₂³	semidirect
190. D₄×Dic₃	C₂³	semidirect
191. D₄×Dic₃	C₂³	semidirect
194. #930	C₂³	semidirect
195. #929	C₂³	semidirect
196. #929	C₂³	semidirect
199. C₄×#67	C₂³	semidirect
200. C₄×#67	C₂³	semidirect
201. C₄×#67	C₂³	semidirect
202. C₄×#67	C₂³	semidirect
203. C₄×#67	C₂³	semidirect
210. C₂×(C₂×D₃)⋊C₄	C₂³	semidirect
211. C₂×(C₂×D₃)⋊C₄	C₂³	semidirect
212. C₂×(C₂×D₃)⋊C₄	C₂³	semidirect
213. C₂×(C₂×D₃)⋊C₄	C₂³	semidirect
214. #926	C₂³	semidirect
215. C₂×C₄⋊Dic₃	C₂³	semidirect
216. #924	C₂³	semidirect
217. #924	C₂³	semidirect
218. #924	C₂³	semidirect
219. C₂×Dic₃⋊C₄	C₂³	semidirect
220. C₂×Dic₃⋊C₄	C₂³	semidirect
221. C₂×C₄×Dic₃	C₂³	semidirect
222. C₂×C₄×Dic₃	C₂³	semidirect
223. C₂×C₄×Dic₃	C₂³	semidirect
224. #898	C₂³	semidirect
225. #898	C₂³	semidirect
226. #898	C₂³	semidirect
227. #897	C₂³	semidirect
228. #897	C₂³	semidirect
229. #897	C₂³	semidirect
230. #896	C₂³	semidirect
231. #896	C₂³	semidirect
232. #896	C₂³	semidirect
233. #895	C₂³	semidirect
234. #895	C₂³	semidirect
235. #895	C₂³	semidirect
238. #894	C₂³	semidirect
239. #894	C₂³	semidirect
241. #893	C₂³	semidirect
242. #893	C₂³	semidirect
243. #892	C₂³	semidirect
244. #892	C₂³	semidirect
245. #892	C₂³	semidirect
246. #892	C₂³	semidirect
247. D₃×C₄⋊C₄	C₂³	semidirect
248. D₃×C₄⋊C₄	C₂³	semidirect
249. D₃×C₄⋊C₄	C₂³	semidirect
250. D₃×C₄⋊C₄	C₂³	semidirect
251. #890	C₂³	semidirect
252. #890	C₂³	semidirect
253. #889	C₂³	semidirect
254. #889	C₂³	semidirect
255. #887	C₂³	semidirect
256. #886	C₂³	semidirect
257. #886	C₂³	semidirect
258. #885	C₂³	semidirect
259. #885	C₂³	semidirect
260. #884	C₂³	semidirect
261. #884	C₂³	semidirect
262. #884	C₂³	semidirect
265. #883	C₂³	semidirect
266. #883	C₂³	semidirect
269. #882	C₂³	semidirect
271. #67⋊C₄	C₂³	semidirect
272. #67⋊C₄	C₂³	semidirect
273. #67⋊C₄	C₂³	semidirect
274. #67⋊C₄	C₂³	semidirect
277. D₃×C₂²⋊C₄	C₂³	semidirect
278. D₃×C₂²⋊C₄	C₂³	semidirect
279. D₃×C₂²⋊C₄	C₂³	semidirect
280. D₃×C₂²⋊C₄	C₂³	semidirect
281. #879	C₂³	semidirect
282. #879	C₂³	semidirect
283. #879	C₂³	semidirect
284. #878	C₂³	semidirect
285. #878	C₂³	semidirect
286. #878	C₂³	semidirect
287. #877	C₂³	semidirect
288. #876	C₂³	semidirect
289. #875	C₂³	semidirect
292. C₄×D₁₂	C₂³	semidirect
293. C₄×D₁₂	C₂³	semidirect
294. C₄×D₁₂	C₂³	semidirect
295. #872	C₂³	semidirect
296. #872	C₂³	semidirect
297. #872	C₂³	semidirect
298. #870	C₂³	semidirect
299. C₄×Dic₆	C₂³	semidirect
334. #543	C₂×D₃	semidirect
340. #539	C₂×D₃	semidirect
346. #538	C₂×D₃	semidirect
353. #534	C₂×D₃	semidirect
359. #529	C₂×D₃	semidirect
365. #525	C₂×D₃	semidirect
383. C₂×C₄×D₄	C₂×D₃	semidirect
397. C₂³×D₃	#41	semidirect
514. C₂×#41	C₂²×D₃	semidirect
534. C₂³×C₄	C₂²×D₃	semidirect
542. #126	C₂²×D₃	semidirect
548. #125	C₂²×D₃	semidirect
554. #124	C₂²×D₃	semidirect
569. #123	C₂²×D₃	semidirect
570. #123	C₂²×D₃	semidirect
586. C₂²⋊Q₈	C₂²×D₃	semidirect
587. C₂²⋊Q₈	C₂²×D₃	semidirect
588. C₂²⋊Q₈	C₂²×D₃	semidirect
606. #121	C₂²×D₃	semidirect
614. #120	C₂²×D₃	semidirect
618. C₄×Q₈	C₂²×D₃	semidirect
642. C₄×D₄	C₂²×D₃	semidirect
643. C₄×D₄	C₂²×D₃	semidirect
644. C₄×D₄	C₂²×D₃	semidirect
654. #117	C₂²×D₃	semidirect
662. C₂×C₄⋊C₄	C₂²×D₃	semidirect
682. C₂×C₂²⋊C₄	C₂²×D₃	semidirect
686. C₂×C₄²	C₂²×D₃	semidirect
1022. C₃	#62844	semidirect

Maximal subgroups

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

subgroup	index
C₃×#3459	2
D₃×#543	2
#86572	2
#86454	2
#86453	2
#86415	2
#86414	2
D₃×#534	2
#86295	2
#86158	2
#86155	2
#86044	2
#86043	2
#85776	2
C₂×#5545	2
#62844	3