Subgroups — #11708410

Order 768.

7484 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
2	#87092	C₂	1	6	yes	maximal, complemented
3	#87092	C₂	1	6	yes	maximal, complemented
4	#87091	C₂	1	3	yes	maximal, complemented
5	#87090	C₂	1	6	yes	maximal, complemented
6	D₃×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
7	#87087	C₂	1	3	yes	maximal, complemented
8	#87086	C₂	1	6	yes	maximal, complemented
9	#87085	C₂	1	1	yes	maximal, characteristic, complemented
10	#86080	C₂	1	6	yes	maximal, complemented
11	#86079	C₂	1	3	yes	maximal, complemented
12	#86077	C₂	1	6	yes	maximal, complemented
13	#86076	C₂	1	3	yes	maximal, complemented
14	#85921	C₂	1	6	yes	maximal, complemented
15	#85919	C₂	1	6	yes	maximal, complemented
16	#63045	—	3	1	no	maximal, Sylow
17	C₂³×#67	C₂²	1	2	yes	complemented
18	C₂×#1007	C₂²	1	1	yes	characteristic, complemented
19	C₂×#1004	C₂²	1	3	yes	complemented
20	C₃×H(3,𝔽₄)	C₂²	1	1	yes	characteristic, complemented
21	C₃×H(3,𝔽₄)	C₂²	1	6	yes	complemented
22	C₃×H(3,𝔽₄)	C₂²	1	3	yes	complemented
23	C₃×H(3,𝔽₄)	C₂²	1	6	yes	complemented
24	C₂×C₃×#124	C₂²	1	3	yes	complemented
25	C₂×C₃×#124	C₂²	1	6	yes	complemented
26	C₂×C₃×#120	C₂²	1	6	yes	complemented
27	C₂×#953	C₂²	1	6	yes	complemented
28	#5817	C₂²	1	6	yes	complemented
29	#5816	C₂²	1	3	yes	complemented
30	Q₈×#67	C₂²	1	2	yes	complemented
31	#5806	C₂²	1	6	yes	complemented
32	#5805	C₂²	1	3	yes	complemented
33	#5804	C₂²	1	6	yes	complemented
34	D₄×#67	C₂²	1	6	yes	complemented
35	D₄×#67	C₂²	1	12	yes	complemented
36	#5684	C₂²	1	6	yes	complemented
37	#5684	C₂²	1	6	yes	complemented
38	#5684	C₂²	1	6	yes	complemented
39	#5683	C₂²	1	3	yes	complemented
40	#5683	C₂²	1	6	yes	complemented
41	#5683	C₂²	1	6	yes	complemented
42	#5682	C₂²	1	12	yes	complemented
43	#5681	C₂²	1	12	yes	complemented
44	#5681	C₂²	1	6	yes	complemented
45	#5680	C₂²	1	6	yes	complemented
46	#5680	C₂²	1	6	yes	complemented
47	#5679	C₂²	1	6	yes	complemented
48	#5679	C₂²	1	12	yes	complemented
49	#5678	C₂²	1	12	yes	complemented
50	#5678	C₂²	1	12	yes	complemented
51	#5678	C₂²	1	12	yes	complemented
52	#5678	C₂²	1	12	yes	complemented
53	#5677	C₂²	1	6	yes	complemented
54	#5677	C₂²	1	12	yes	complemented
55	#5676	C₂²	1	6	yes	complemented
56	#5676	C₂²	1	12	yes	complemented
57	#5676	C₂²	1	12	yes	complemented
58	#5675	C₂²	1	3	yes	complemented
59	#5675	C₂²	1	3	yes	complemented
60	#5674	C₂²	1	3	yes	complemented
61	#5674	C₂²	1	12	yes	complemented
62	#5674	C₂²	1	3	yes	complemented
63	D₃×#124	C₂²	1	3	yes	complemented
64	D₃×#124	C₂²	1	6	yes	complemented
65	D₃×#124	C₂²	1	3	yes	complemented
66	#5672	C₂²	1	3	yes	complemented
67	#5671	C₂²	1	6	yes	complemented
68	#5670	C₂²	1	12	yes	complemented
69	#5670	C₂²	1	6	yes	complemented
70	#5669	C₂²	1	12	yes	complemented
71	#5669	C₂²	1	12	yes	complemented
72	#5668	C₂²	1	3	yes	complemented
73	#5668	C₂²	1	6	yes	complemented
74	#5668	C₂²	1	3	yes	complemented
75	#5595	C₂²	1	6	yes	complemented
76	#5595	C₂²	1	12	yes	complemented
77	#5594	C₂²	1	6	yes	complemented
78	#5593	C₂²	1	12	yes	complemented
79	#5593	C₂²	1	12	yes	complemented
80	#5592	C₂²	1	6	yes	complemented
81	#5592	C₂²	1	6	yes	complemented
82	#5592	C₂²	1	12	yes	complemented
83	#5591	C₂²	1	12	yes	complemented
84	#5591	C₂²	1	12	yes	complemented
85	#5591	C₂²	1	12	yes	complemented
86	#5590	C₂²	1	12	yes	complemented
87	#5590	C₂²	1	6	yes	complemented
88	#5590	C₂²	1	12	yes	complemented
89	#5589	C₂²	1	6	yes	complemented
90	#5589	C₂²	1	12	yes	complemented
91	#5589	C₂²	1	6	yes	complemented
92	D₃×#120	C₂²	1	6	yes	complemented
93	D₃×#120	C₂²	1	6	yes	complemented
94	#5587	C₂²	1	6	yes	complemented
95	#5586	C₂²	1	6	yes	complemented
96	#5586	C₂²	1	6	yes	complemented
97	#5495	C₂²	1	12	yes	complemented
98	#5494	C₂²	1	12	yes	complemented
99	#5493	C₂²	1	6	yes	complemented
100	#5490	C₂²	1	12	yes	complemented
101	#5490	C₂²	1	12	yes	complemented
102	#5490	C₂²	1	12	yes	complemented
103	#5486	C₂²	1	6	yes	complemented
104	#5479	C₂²	1	6	yes	complemented
105	#5477	C₂²	1	3	yes	complemented
106	C₄×#235	C₂²	1	3	yes	complemented
107	#3558	—	3	6	no	—
108	#3558	—	3	6	no	—
109	#3558	—	3	6	no	—
110	#3549	—	3	3	no	—
111	#3545	—	3	3	no	—
112	#3545	—	3	3	no	—
113	#3540	—	3	6	no	—
114	#3532	—	3	6	no	—
115	#3532	—	3	6	no	—
116	#3529	—	3	1	no	—
117	C₂×H(3,𝔽₄)	—	3	1	no	—
118	C₂×H(3,𝔽₄)	D₃	1	1	yes	characteristic, complemented
119	#3514	—	3	6	no	—
120	#3500	—	3	3	no	—
121	#3484	—	3	6	no	—
122	C₂⁵×C₃	C₂³	1	2	yes	complemented
123	C₂⁴×D₃	C₂³	1	2	yes	complemented
124	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic, complemented
125	C₂²×C₃×Q₈	C₂³	1	2	yes	complemented
126	C₂²×C₃×D₄	C₂³	1	3	yes	—
127	C₂²×C₃×D₄	C₂³	1	6	yes	—
128	C₂²×#67	—	4	8	no	—
129	C₂²×#67	C₂³	1	6	yes	—
130	C₂²×#67	C₂³	1	6	yes	—
131	C₂²×#67	C₂³	1	6	yes	complemented
132	C₂²×#67	C₂³	1	6	yes	complemented
133	C₂²×#67	C₂³	1	6	yes	complemented
134	C₂²×#67	C₂³	1	12	yes	complemented
135	C₂³×Dic₃	C₂³	1	2	yes	complemented
136	#1007	—	4	4	no	—
137	C₂×#239	C₂³	1	1	yes	characteristic, complemented
138	C₂×#239	C₂³	1	3	yes	complemented
139	C₂×#239	C₂³	1	6	yes	complemented
140	C₂×D₃×Q₈	C₂³	1	1	yes	characteristic, complemented
141	C₂×D₃×Q₈	C₂³	1	3	yes	complemented
142	C₂×D₃×Q₈	C₂³	1	2	yes	complemented
143	#1004	—	4	12	no	—
144	C₂×#237	C₂³	1	3	yes	—
145	C₂×#237	C₂³	1	3	yes	—
146	C₂×#237	C₂³	1	6	yes	—
147	C₂×#237	C₂³	1	6	yes	complemented
148	C₂×D₃×D₄	C₂³	1	3	yes	—
149	C₂×D₃×D₄	C₂³	1	3	yes	—
150	C₂×D₃×D₄	C₂³	1	6	yes	—
151	C₂×D₃×D₄	C₂³	1	6	yes	—
152	C₂×D₃×D₄	C₂³	1	12	yes	complemented
153	C₂×#235	C₂³	1	3	yes	—
154	C₂×#235	C₂³	1	3	yes	—
155	C₂×#235	C₂³	1	3	yes	complemented
156	C₃×#124	C₂³	1	3	yes	—
157	C₃×#124	C₂³	1	6	yes	—
158	C₃×#124	C₂³	1	6	yes	—
159	C₃×#124	C₂³	1	3	yes	—
160	C₃×#124	C₂³	1	3	yes	complemented
161	C₃×#124	C₂³	1	6	yes	complemented
162	C₃×#124	C₂³	1	12	yes	complemented
163	C₃×#124	C₂³	1	12	yes	complemented
164	C₃×#124	C₂³	1	3	yes	complemented
165	C₃×#124	C₂³	1	12	yes	complemented
166	C₃×#124	C₂³	1	6	yes	complemented
167	C₃×#120	C₂³	1	6	yes	—
168	C₃×#120	C₂³	1	6	yes	—
169	C₃×#120	C₂³	1	12	yes	—
170	C₃×#120	C₂³	1	6	yes	complemented
171	C₃×#120	C₂³	1	6	yes	complemented
172	C₃×#120	C₂³	1	12	yes	complemented
173	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	complemented
174	C₂×C₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
175	C₂×C₃×C₄²	C₂³	1	3	yes	complemented
176	#953	C₂³	1	12	yes	—
177	#953	C₂³	1	12	yes	complemented
178	#953	C₂³	1	6	yes	complemented
179	#953	C₂³	1	6	yes	complemented
180	#953	C₂³	1	6	yes	complemented
181	#953	C₂³	1	6	yes	complemented
182	C₂×#217	C₂³	1	6	yes	complemented
183	C₂×#217	C₂³	1	12	yes	complemented
184	#947	C₂³	1	3	yes	complemented
185	#947	C₂³	1	12	yes	complemented
186	#947	C₂³	1	3	yes	complemented
187	#947	C₂³	1	6	yes	complemented
188	#946	C₂³	1	12	yes	complemented
189	#946	C₂³	1	12	yes	complemented
190	#946	C₂³	1	6	yes	complemented
191	#946	C₂³	1	6	yes	complemented
192	Q₈×Dic₃	C₂³	1	6	yes	complemented
193	Q₈×Dic₃	C₂³	1	2	yes	complemented
194	#944	C₂³	1	3	yes	complemented
195	#944	C₂³	1	6	yes	complemented
196	#944	C₂³	1	3	yes	complemented
197	#940	C₂³	1	3	yes	—
198	#940	C₂³	1	6	yes	—
199	#940	C₂³	1	12	yes	—
200	#940	C₂³	1	3	yes	complemented
201	#939	C₂³	1	12	yes	—
202	#939	C₂³	1	12	yes	—
203	#939	C₂³	1	12	yes	—
204	#939	C₂³	1	12	yes	complemented
205	#939	C₂³	1	12	yes	complemented
206	#939	C₂³	1	12	yes	complemented
207	#938	C₂³	1	6	yes	—
208	#938	C₂³	1	12	yes	—
209	#938	C₂³	1	6	yes	—
210	#938	C₂³	1	12	yes	complemented
211	#937	C₂³	1	12	yes	—
212	#937	C₂³	1	12	yes	—
213	#937	C₂³	1	6	yes	—
214	#937	C₂³	1	6	yes	complemented
215	#937	C₂³	1	12	yes	complemented
216	#936	C₂³	1	6	yes	—
217	#936	C₂³	1	3	yes	—
218	#936	C₂³	1	3	yes	complemented
219	#935	C₂³	1	6	yes	—
220	#935	C₂³	1	6	yes	complemented
221	#935	C₂³	1	12	yes	complemented
222	D₄×Dic₃	C₂³	1	6	yes	—
223	D₄×Dic₃	C₂³	1	6	yes	complemented
224	D₄×Dic₃	C₂³	1	12	yes	complemented
225	#930	C₂³	1	6	yes	—
226	#930	C₂³	1	12	yes	complemented
227	#929	C₂³	1	12	yes	complemented
228	C₄×#67	C₂³	1	6	yes	—
229	C₄×#67	C₂³	1	6	yes	complemented
230	C₄×#67	C₂³	1	12	yes	complemented
231	#926	C₂³	1	3	yes	complemented
232	#924	C₂³	1	6	yes	complemented
233	#886	C₂³	1	12	yes	complemented
234	#886	C₂³	1	6	yes	complemented
235	#886	C₂³	1	12	yes	complemented
236	#886	C₂³	1	6	yes	complemented
237	#885	C₂³	1	12	yes	complemented
238	#885	C₂³	1	12	yes	complemented
239	#885	C₂³	1	12	yes	complemented
240	#885	C₂³	1	12	yes	complemented
241	#885	C₂³	1	12	yes	complemented
242	#885	C₂³	1	12	yes	complemented
243	#884	C₂³	1	12	yes	complemented
244	#884	C₂³	1	12	yes	complemented
245	#884	C₂³	1	12	yes	complemented
246	#884	C₂³	1	12	yes	complemented
247	#884	C₂³	1	12	yes	complemented
248	#884	C₂³	1	12	yes	complemented
249	#884	C₂³	1	12	yes	complemented
250	#884	C₂³	1	12	yes	complemented
251	#883	C₂³	1	12	yes	complemented
252	#883	C₂³	1	12	yes	complemented
253	#883	C₂³	1	12	yes	complemented
254	#883	C₂³	1	12	yes	complemented
255	#883	C₂³	1	12	yes	complemented
256	#883	C₂³	1	12	yes	complemented
257	#882	C₂³	1	12	yes	complemented
258	#882	C₂³	1	6	yes	complemented
259	#882	C₂³	1	12	yes	complemented
260	#882	C₂³	1	12	yes	complemented
261	#882	C₂³	1	12	yes	complemented
262	#882	C₂³	1	6	yes	complemented
263	#67⋊C₄	C₂³	1	12	yes	complemented
264	#67⋊C₄	C₂³	1	12	yes	complemented
265	#67⋊C₄	C₂³	1	12	yes	complemented
266	#67⋊C₄	C₂³	1	12	yes	complemented
267	#67⋊C₄	C₂³	1	12	yes	complemented
268	#67⋊C₄	C₂³	1	12	yes	complemented
269	D₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
270	D₃×C₂²⋊C₄	C₂³	1	6	yes	complemented
271	D₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
272	D₃×C₂²⋊C₄	C₂³	1	6	yes	complemented
273	D₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
274	#879	C₂³	1	12	yes	complemented
275	#879	C₂³	1	12	yes	complemented
276	#879	C₂³	1	12	yes	complemented
277	#879	C₂³	1	12	yes	complemented
278	#878	C₂³	1	12	yes	complemented
279	#878	C₂³	1	12	yes	complemented
280	#878	C₂³	1	12	yes	complemented
281	#878	C₂³	1	12	yes	complemented
282	#877	C₂³	1	6	yes	complemented
283	#877	C₂³	1	12	yes	complemented
284	#877	C₂³	1	6	yes	complemented
285	#876	C₂³	1	12	yes	complemented
286	#875	C₂³	1	3	yes	complemented
287	#875	C₂³	1	6	yes	complemented
288	#875	C₂³	1	3	yes	complemented
289	#874	C₂³	1	3	yes	complemented
290	C₄×D₁₂	C₂³	1	6	yes	complemented
291	C₄×D₁₂	C₂³	1	6	yes	complemented
292	C₄×D₁₂	C₂³	1	12	yes	complemented
293	#872	C₂³	1	3	yes	complemented
294	#872	C₂³	1	12	yes	complemented
295	#872	C₂³	1	3	yes	complemented
296	C₄²×D₃	C₂³	1	3	yes	complemented
297	C₄²×D₃	C₂³	1	3	yes	complemented
298	#870	C₂³	1	6	yes	complemented
299	#869	C₂³	1	3	yes	complemented
300	C₄×Dic₆	C₂³	1	6	yes	complemented
301	C₄×Dic₆	C₂³	1	6	yes	complemented
302	C₂×2₋¹⁺⁴	—	3	1	no	—
303	C₂×H(5,𝔽₂)	—	3	3	no	—
304	C₂³×D₄	—	3	2	no	—
305	#563	—	3	3	no	—
306	#562	—	3	6	no	—
307	#562	—	3	6	no	—
308	#562	—	3	6	no	—
309	H(3,𝔽₄)	—	3	3	no	—
310	H(3,𝔽₄)	—	3	6	no	—
311	H(3,𝔽₄)	—	3	6	no	—
312	H(3,𝔽₄)	—	3	6	no	—
313	H(3,𝔽₄)	C₂×D₃	1	1	yes	characteristic, complemented
314	H(3,𝔽₄)	C₂×D₃	1	6	yes	complemented
315	H(3,𝔽₄)	C₂×D₃	1	3	yes	complemented
316	H(3,𝔽₄)	C₂×D₃	1	6	yes	complemented
317	#560	—	3	6	no	—
318	#560	—	3	12	no	—
319	#559	—	3	6	no	—
320	#559	—	3	12	no	—
321	#556	—	3	6	no	—
322	#555	—	3	12	no	—
323	#555	—	3	6	no	—
324	#551	—	3	6	no	—
325	#551	—	3	12	no	—
326	#551	—	3	6	no	—
327	#551	—	3	12	no	—
328	D₄×Q₈	—	3	2	no	—
329	#548	—	3	6	no	—
330	#548	—	3	12	no	—
331	#548	—	3	6	no	—
332	#546	—	3	6	no	—
333	#546	—	3	6	no	—
334	#546	—	3	12	no	—
335	#546	—	3	12	no	—
336	#546	—	3	12	no	—
337	#546	—	3	12	no	—
338	#546	—	3	12	no	—
339	#546	—	3	12	no	—
340	#546	—	3	12	no	—
341	#546	—	3	12	no	—
342	D₄²	—	3	6	no	—
343	D₄²	—	3	12	no	—
344	D₄²	—	3	12	no	—
345	D₄²	—	3	6	no	—
346	D₄²	—	3	12	no	—
347	#542	—	3	12	no	—
348	#542	—	3	12	no	—
349	#542	—	3	12	no	—
350	#538	—	3	12	no	—
351	#538	—	3	12	no	—
352	#538	—	3	12	no	—
353	#538	—	3	12	no	—
354	#538	—	3	12	no	—
355	#538	—	3	12	no	—
356	#538	—	3	12	no	—
357	#536	—	3	3	no	—
358	#536	—	3	3	no	—
359	#536	—	3	3	no	—
360	#535	—	3	3	no	—
361	#535	—	3	3	no	—
362	#535	—	3	3	no	—
363	#535	—	3	12	no	—
364	#535	—	3	6	no	—
365	#535	—	3	6	no	—
366	#535	—	3	12	no	—
367	#534	—	3	6	no	—
368	#534	—	3	6	no	—
369	#534	—	3	12	no	—
370	#534	—	3	6	no	—
371	#534	—	3	6	no	—
372	#532	—	3	3	no	—
373	#532	—	3	3	no	—
374	#532	—	3	6	no	—
375	#532	—	3	3	no	—
376	#529	—	3	6	no	—
377	#529	—	3	6	no	—
378	#529	—	3	6	no	—
379	C₂×#124	—	3	3	no	—
380	C₂×#124	—	3	6	no	—
381	C₂×#124	—	3	3	no	—
382	C₂×#124	C₂×D₃	1	3	yes	complemented
383	C₂×#124	C₂×D₃	1	6	yes	complemented
384	#525	—	3	6	no	—
385	#525	—	3	6	no	—
386	C₂×#120	—	3	6	no	—
387	C₂×#120	—	3	6	no	—
388	C₂×#120	—	3	6	no	—
389	C₂×#120	C₂×D₃	1	6	yes	complemented
390	#518	—	3	6	no	—
391	C₄×#41	—	3	3	no	—
392	C₂⁴×C₃	—	4	4	no	—
393	C₂⁴×C₃	—	8	4	no	—
394	C₂⁴×C₃	C₂⁴	1	6	yes	—
395	C₂⁴×C₃	C₂⁴	1	6	yes	—
396	C₂⁴×C₃	C₂⁴	1	2	yes	—
397	C₂³×D₃	—	4	4	no	—
398	C₂³×D₃	—	8	4	no	—
399	C₂³×D₃	C₂⁴	1	6	yes	—
400	C₂³×D₃	C₂⁴	1	6	yes	—
401	C₂³×D₃	C₂⁴	1	6	yes	—
402	C₂×C₃×Q₈	—	4	2	no	—
403	C₂×C₃×Q₈	—	8	2	no	—
404	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
405	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
406	C₂×C₃×Q₈	C₂⁴	1	3	yes	—
407	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
408	C₂×C₃×D₄	—	4	6	no	—
409	C₂×C₃×D₄	—	8	6	no	—
410	C₂×C₃×D₄	C₂⁴	1	6	yes	—
411	C₂×C₃×D₄	C₂⁴	1	12	yes	—
412	C₂×C₃×D₄	C₂⁴	1	6	yes	—
413	C₂×C₃×D₄	C₂⁴	1	3	yes	—
414	C₂×C₃×D₄	C₂⁴	1	6	yes	—
415	C₂×C₃×D₄	C₂⁴	1	3	yes	—
416	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
417	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
418	C₂×#67	—	2	24	no	—
419	C₂×#67	—	4	12	no	—
420	C₂×#67	—	4	12	no	—
421	C₂×#67	—	4	12	no	—
422	C₂×#67	—	4	12	no	—
423	C₂×#67	—	8	12	no	—
424	C₂×#67	C₂⁴	1	6	yes	—
425	C₂×#67	C₂⁴	1	6	yes	—
426	C₂×#67	C₂⁴	1	6	yes	—
427	C₂×#67	C₂⁴	1	3	yes	—
428	C₂×#67	C₂⁴	1	12	yes	—
429	C₂×#67	C₂⁴	1	12	yes	—
430	C₂×#67	C₂⁴	1	12	yes	—
431	C₂×#67	C₂⁴	1	12	yes	—
432	C₂×#67	C₂⁴	1	6	yes	—
433	C₂×#67	C₂⁴	1	12	yes	—
434	C₂×#67	C₂⁴	1	6	yes	—
435	C₂×#67	C₂⁴	1	1	yes	characteristic
436	C₂²×Dic₃	—	4	4	no	—
437	C₂²×Dic₃	C₂⁴	1	6	yes	—
438	C₂²×Dic₃	C₂⁴	1	12	yes	—
439	C₂²×Dic₃	C₂⁴	1	6	yes	—
440	C₂²×Dic₃	C₂⁴	1	6	yes	—
441	#239	—	4	2	no	—
442	#239	—	4	6	no	—
443	#239	—	8	6	no	—
444	D₃×Q₈	—	4	6	no	—
445	D₃×Q₈	—	4	2	no	—
446	D₃×Q₈	—	8	2	no	—
447	#237	—	4	12	no	—
448	#237	—	4	6	no	—
449	#237	—	4	6	no	—
450	#237	—	8	6	no	—
451	D₃×D₄	—	4	6	no	—
452	D₃×D₄	—	4	6	no	—
453	D₃×D₄	—	4	12	no	—
454	D₃×D₄	—	8	6	no	—
455	D₃×D₄	—	8	12	no	—
456	#235	—	2	12	no	—
457	#235	—	4	6	no	—
458	#235	—	4	6	no	—
459	C₂×D₁₂	C₂⁴	1	3	yes	—
460	C₂×D₁₂	C₂⁴	1	12	yes	—
461	C₂×D₁₂	C₂⁴	1	6	yes	—
462	C₂×D₁₂	C₂⁴	1	3	yes	—
463	C₂×D₁₂	C₂⁴	1	3	yes	—
464	C₂×C₄×D₃	C₂⁴	1	3	yes	—
465	C₂×C₄×D₃	C₂⁴	1	3	yes	—
466	C₂×C₄×D₃	C₂⁴	1	6	yes	—
467	C₂×C₄×D₃	C₂⁴	1	6	yes	—
468	C₂×C₄×D₃	C₂⁴	1	12	yes	—
469	C₂×C₄×D₃	C₂⁴	1	6	yes	—
470	C₂×C₄×D₃	C₂⁴	1	6	yes	—
471	C₂×Dic₆	C₂⁴	1	3	yes	—
472	C₂×Dic₆	C₂⁴	1	6	yes	—
473	C₂×Dic₆	C₂⁴	1	3	yes	—
474	C₂×Dic₆	C₂⁴	1	3	yes	—
475	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
476	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
477	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
478	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
479	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
480	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
481	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
482	C₃×C₄²	C₂⁴	1	6	yes	—
483	C₃×C₄²	C₂⁴	1	3	yes	—
484	C₃×C₄²	C₂⁴	1	3	yes	—
485	#217	C₂⁴	1	12	yes	—
486	#217	C₂⁴	1	6	yes	—
487	#217	C₂⁴	1	6	yes	—
488	#217	C₂⁴	1	12	yes	—
489	#217	C₂⁴	1	12	yes	—
490	#217	C₂⁴	1	12	yes	—
491	#217	C₂⁴	1	6	yes	—
492	(C₂×D₃)⋊C₄	C₂⁴	1	6	yes	—
493	(C₂×D₃)⋊C₄	C₂⁴	1	6	yes	—
494	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
495	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
496	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
497	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
498	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
499	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
500	C₄⋊Dic₃	C₂⁴	1	6	yes	—
501	C₄⋊Dic₃	C₂⁴	1	6	yes	—
502	C₄⋊Dic₃	C₂⁴	1	12	yes	—
503	C₄⋊Dic₃	C₂⁴	1	6	yes	—
504	Dic₃⋊C₄	C₂⁴	1	6	yes	—
505	Dic₃⋊C₄	C₂⁴	1	6	yes	—
506	Dic₃⋊C₄	C₂⁴	1	12	yes	—
507	Dic₃⋊C₄	C₂⁴	1	12	yes	—
508	Dic₃⋊C₄	C₂⁴	1	12	yes	—
509	Dic₃⋊C₄	C₂⁴	1	12	yes	—
510	C₄×Dic₃	C₂⁴	1	6	yes	—
511	C₄×Dic₃	C₂⁴	1	6	yes	—
512	C₄×Dic₃	C₂⁴	1	12	yes	—
513	C₄×Dic₃	C₂⁴	1	3	yes	—
514	C₄×Dic₃	C₂⁴	1	3	yes	—
515	C₂⁵	—	3	2	no	—
516	C₂⁵	C₂²×D₃	1	2	yes	complemented
517	2₋¹⁺⁴	—	12	4	no	—
518	H(5,𝔽₂)	—	12	12	no	—
519	C₂×#41	—	3	1	no	—
520	C₂×#41	—	3	3	no	—
521	C₂×#41	—	3	6	no	—
522	C₂×#41	—	3	3	no	—
523	C₂×#41	—	3	6	no	—
524	C₂×#41	—	3	3	no	—
525	C₂×#41	—	3	6	no	—
526	C₂×#41	—	3	3	no	—
527	C₂×#41	—	3	3	no	—
528	C₂×#41	—	3	3	no	—
529	C₂²×Q₈	—	3	1	no	—
530	C₂²×Q₈	—	3	3	no	—
531	C₂²×Q₈	—	3	2	no	—
532	C₂²×Q₈	C₂²×D₃	1	1	yes	characteristic, complemented
533	C₂²×Q₈	C₂²×D₃	1	2	yes	complemented
534	C₂²×D₄	—	3	6	no	—
535	C₂²×D₄	—	3	6	no	—
536	C₂²×D₄	—	3	6	no	—
537	C₂²×D₄	—	3	6	no	—
538	C₂²×D₄	—	3	6	no	—
539	C₂²×D₄	—	3	12	no	—
540	C₂²×D₄	—	3	3	no	—
541	C₂²×D₄	—	3	6	no	—
542	C₂²×D₄	—	3	3	no	—
543	C₂²×D₄	—	3	6	no	—
544	C₂²×D₄	—	3	12	no	—
545	C₂²×D₄	—	12	8	no	—
546	C₂²×D₄	C₂²×D₃	1	3	yes	—
547	C₂²×D₄	C₂²×D₃	1	6	yes	—
548	C₂³×C₄	—	3	2	no	—
549	C₄⋊Q₈	—	3	3	no	—
550	C₄⋊Q₈	—	3	3	no	—
551	C₄⋊Q₈	—	3	6	no	—
552	C₄⋊Q₈	—	3	3	no	—
553	#127	—	3	3	no	—
554	#127	—	3	6	no	—
555	#127	—	3	3	no	—
556	#127	—	3	12	no	—
557	#127	—	3	3	no	—
558	#126	—	3	12	no	—
559	#126	—	3	12	no	—
560	#126	—	3	12	no	—
561	#126	—	3	12	no	—
562	#126	—	3	12	no	—
563	#125	—	3	6	no	—
564	#124	—	3	3	no	—
565	#124	—	3	3	no	—
566	#124	—	3	6	no	—
567	#124	—	3	12	no	—
568	#124	—	3	3	no	—
569	#124	—	3	3	no	—
570	#124	—	3	6	no	—
571	#124	—	3	12	no	—
572	#124	—	3	12	no	—
573	#124	—	3	12	no	—
574	#124	—	3	12	no	—
575	#124	—	3	12	no	—
576	#124	—	3	12	no	—
577	#124	—	3	3	no	—
578	#124	—	3	6	no	—
579	#124	—	3	3	no	—
580	#124	C₂²×D₃	1	6	yes	—
581	#124	C₂²×D₃	1	3	yes	—
582	#124	C₂²×D₃	1	3	yes	—
583	#124	C₂²×D₃	1	6	yes	—
584	#124	C₂²×D₃	1	3	yes	complemented
585	#124	C₂²×D₃	1	6	yes	complemented
586	#124	C₂²×D₃	1	3	yes	complemented
587	#124	C₂²×D₃	1	12	yes	complemented
588	#124	C₂²×D₃	1	6	yes	complemented
589	#124	C₂²×D₃	1	12	yes	complemented
590	#124	C₂²×D₃	1	12	yes	complemented
591	#123	—	3	6	no	—
592	#123	—	3	6	no	—
593	#123	—	3	12	no	—
594	#123	—	3	12	no	—
595	#123	—	3	6	no	—
596	#123	—	3	6	no	—
597	#123	—	3	12	no	—
598	#123	—	3	12	no	—
599	#123	—	3	12	no	—
600	#123	—	3	12	no	—
601	#123	—	3	12	no	—
602	#123	—	3	12	no	—
603	#123	—	3	12	no	—
604	#123	—	3	12	no	—
605	C₂²⋊Q₈	—	3	6	no	—
606	C₂²⋊Q₈	—	3	6	no	—
607	C₂²⋊Q₈	—	3	12	no	—
608	C₂²⋊Q₈	—	3	12	no	—
609	C₂²⋊Q₈	—	3	6	no	—
610	C₂²⋊Q₈	—	3	12	no	—
611	C₂²⋊Q₈	—	3	12	no	—
612	C₂²⋊Q₈	—	3	12	no	—
613	C₂²⋊Q₈	—	3	12	no	—
614	#121	—	3	12	no	—
615	#121	—	3	12	no	—
616	#121	—	3	6	no	—
617	#121	—	3	6	no	—
618	#121	—	3	12	no	—
619	#121	—	3	12	no	—
620	#121	—	3	12	no	—
621	#121	—	3	12	no	—
622	#121	—	3	12	no	—
623	#121	—	3	12	no	—
624	#121	—	3	6	no	—
625	#121	—	3	12	no	—
626	#121	—	3	12	no	—
627	#121	—	3	12	no	—
628	#121	—	3	12	no	—
629	#121	—	3	12	no	—
630	#121	—	3	12	no	—
631	#121	—	3	12	no	—
632	#121	—	3	12	no	—
633	#121	—	3	12	no	—
634	#120	—	3	6	no	—
635	#120	—	3	6	no	—
636	#120	—	3	6	no	—
637	#120	—	3	6	no	—
638	#120	—	3	12	no	—
639	#120	—	3	12	no	—
640	#120	—	3	6	no	—
641	#120	—	3	6	no	—
642	#120	—	3	12	no	—
643	#120	—	3	12	no	—
644	#120	—	3	12	no	—
645	#120	—	3	6	no	—
646	#120	—	3	6	no	—
647	#120	—	3	12	no	—
648	#120	—	3	12	no	—
649	#120	—	3	12	no	—
650	#120	—	3	12	no	—
651	#120	C₂²×D₃	1	6	yes	—
652	#120	C₂²×D₃	1	6	yes	—
653	#120	C₂²×D₃	1	12	yes	—
654	#120	C₂²×D₃	1	6	yes	complemented
655	#120	C₂²×D₃	1	6	yes	complemented
656	#120	C₂²×D₃	1	12	yes	complemented
657	C₄×Q₈	—	3	2	no	—
658	C₄×Q₈	—	3	6	no	—
659	C₄×Q₈	—	3	6	no	—
660	C₄×Q₈	—	3	6	no	—
661	C₄×D₄	—	3	6	no	—
662	C₄×D₄	—	3	12	no	—
663	C₄×D₄	—	3	6	no	—
664	C₄×D₄	—	3	6	no	—
665	C₄×D₄	—	3	6	no	—
666	C₄×D₄	—	3	12	no	—
667	C₄×D₄	—	3	12	no	—
668	C₄×D₄	—	3	12	no	—
669	C₄×D₄	—	3	12	no	—
670	C₄×D₄	—	3	12	no	—
671	C₄×D₄	—	3	12	no	—
672	C₄×D₄	—	3	12	no	—
673	C₄×D₄	—	3	6	no	—
674	C₄×D₄	—	3	6	no	—
675	C₄×D₄	—	3	12	no	—
676	#117	—	3	3	no	—
677	#117	—	3	6	no	—
678	#117	—	3	6	no	—
679	#117	—	3	12	no	—
680	#117	—	3	3	no	—
681	#117	—	3	3	no	—
682	#117	—	3	12	no	—
683	C₂×C₂²⋊C₄	—	3	6	no	—
684	C₂×C₂²⋊C₄	—	3	12	no	—
685	C₂×C₂²⋊C₄	—	3	6	no	—
686	C₂×C₂²⋊C₄	—	3	6	no	—
687	C₂×C₂²⋊C₄	—	3	12	no	—
688	C₂×C₂²⋊C₄	—	3	12	no	—
689	C₂×C₂²⋊C₄	—	3	12	no	—
690	C₂×C₂²⋊C₄	C₂²×D₃	1	6	yes	complemented
691	C₂×C₂²⋊C₄	C₂²×D₃	1	12	yes	complemented
692	C₂×C₄²	—	3	3	no	—
693	C₂×C₄²	—	3	3	no	—
694	C₂×C₄²	C₂²×D₃	1	3	yes	complemented
695	C₂³×C₃	—	2	12	no	—
696	C₂³×C₃	—	4	2	no	—
697	C₂³×C₃	—	4	4	no	—
698	C₂³×C₃	—	4	6	no	—
699	C₂³×C₃	—	4	12	no	—
700	C₂³×C₃	—	4	12	no	—
701	C₂³×C₃	—	8	16	no	—
702	C₂³×C₃	C₂⁵	1	6	yes	—
703	C₂³×C₃	C₂⁵	1	6	yes	—
704	C₂³×C₃	C₂⁵	1	1	yes	characteristic
705	C₂²×D₃	—	2	12	no	—
706	C₂²×D₃	—	4	12	no	—
707	C₂²×D₃	—	4	12	no	—
708	C₂²×D₃	—	4	6	no	—
709	C₂²×D₃	—	4	6	no	—
710	C₂²×D₃	—	4	12	no	—
711	C₂²×D₃	—	8	16	no	—
712	C₂²×D₃	C₂⁵	1	6	yes	—
713	C₂²×D₃	C₂⁵	1	3	yes	—
714	C₂²×D₃	C₂⁵	1	1	yes	characteristic
715	C₃×Q₈	—	4	3	no	—
716	C₃×Q₈	—	4	1	no	—
717	C₃×Q₈	—	4	2	no	—
718	C₃×Q₈	—	4	6	no	—
719	C₃×D₄	—	4	6	no	—
720	C₃×D₄	—	4	3	no	—
721	C₃×D₄	—	4	3	no	—
722	C₃×D₄	—	4	6	no	—
723	C₃×D₄	—	4	12	no	—
724	C₃×D₄	—	4	6	no	—
725	C₂×C₃×C₄	—	2	6	no	—
726	C₂×C₃×C₄	—	4	6	no	—
727	C₂×C₃×C₄	C₂⁵	1	6	yes	—
728	C₂×C₃×C₄	C₂⁵	1	3	yes	—
729	C₂×C₃×C₄	C₂⁵	1	6	yes	—
730	C₂×C₃×C₄	C₂⁵	1	3	yes	—
731	#67	—	2	6	no	—
732	#67	—	2	12	no	—
733	#67	—	2	12	no	—
734	#67	—	2	12	no	—
735	#67	—	4	6	no	—
736	#67	—	4	6	no	—
737	#67	—	4	12	no	—
738	#67	—	4	12	no	—
739	#67	—	4	12	no	—
740	#67	—	4	12	no	—
741	#67	—	4	12	no	—
742	#67	H(5,𝔽₂)	1	4	yes	—
743	C₂×Dic₃	—	2	12	no	—
744	C₂×Dic₃	—	4	6	no	—
745	C₂×Dic₃	—	4	12	no	—
746	C₂×Dic₃	—	4	6	no	—
747	C₂×Dic₃	C₂⁵	1	6	yes	—
748	C₂×Dic₃	C₂⁵	1	6	yes	—
749	C₂×Dic₃	C₂⁵	1	6	yes	—
750	C₂×Dic₃	C₂⁵	1	3	yes	—
751	C₂×Dic₃	C₂⁵	1	1	yes	characteristic
752	D₁₂	—	2	6	no	—
753	D₁₂	—	4	3	no	—
754	D₁₂	—	4	3	no	—
755	D₁₂	—	4	6	no	—
756	D₁₂	—	4	12	no	—
757	C₄×D₃	—	2	6	no	—
758	C₄×D₃	—	2	6	no	—
759	C₄×D₃	—	4	6	no	—
760	C₄×D₃	—	4	6	no	—
761	C₄×D₃	—	4	6	no	—
762	C₄×D₃	—	4	12	no	—
763	C₄×D₃	—	4	6	no	—
764	Dic₆	—	2	6	no	—
765	Dic₆	—	4	3	no	—
766	Dic₆	—	4	3	no	—
767	Dic₆	—	4	6	no	—
768	C₂⁴	—	3	6	no	—
769	C₂⁴	—	3	6	no	—
770	C₂⁴	—	3	6	no	—
771	C₂⁴	—	4	4	no	—
772	C₂⁴	—	8	4	no	—
773	C₂⁴	—	12	4	no	—
774	C₂⁴	—	24	4	no	—
775	C₂⁴	C₂³×D₃	1	6	yes	—
776	C₂⁴	C₂³×D₃	1	6	yes	—
777	C₂⁴	C₂³×D₃	1	2	yes	—
778	#41	—	6	12	no	—
779	#41	—	12	6	no	—
780	#41	—	12	6	no	—
781	#41	—	12	6	no	—
782	#41	—	12	2	no	—
783	#41	—	12	6	no	—
784	#41	—	12	12	no	—
785	#41	—	12	6	no	—
786	#41	—	24	6	no	—
787	#41	—	24	6	no	—
788	C₂×Q₈	—	3	3	no	—
789	C₂×Q₈	—	3	6	no	—
790	C₂×Q₈	—	3	3	no	—
791	C₂×Q₈	—	3	3	no	—
792	C₂×Q₈	—	4	2	no	—
793	C₂×Q₈	—	8	2	no	—
794	C₂×Q₈	—	12	2	no	—
795	C₂×Q₈	—	12	6	no	—
796	C₂×Q₈	—	24	2	no	—
797	C₂×Q₈	C₂³×D₃	1	2	yes	—
798	C₂×Q₈	C₂³×D₃	1	6	yes	—
799	C₂×Q₈	C₂³×D₃	1	3	yes	—
800	C₂×Q₈	C₂³×D₃	1	1	yes	characteristic
801	C₂×D₄	—	3	1	no	—
802	C₂×D₄	—	3	3	no	—
803	C₂×D₄	—	3	6	no	—
804	C₂×D₄	—	3	6	no	—
805	C₂×D₄	—	3	6	no	—
806	C₂×D₄	—	3	12	no	—
807	C₂×D₄	—	3	12	no	—
808	C₂×D₄	—	3	12	no	—
809	C₂×D₄	—	3	12	no	—
810	C₂×D₄	—	3	6	no	—
811	C₂×D₄	—	3	6	no	—
812	C₂×D₄	—	3	12	no	—
813	C₂×D₄	—	3	3	no	—
814	C₂×D₄	—	3	6	no	—
815	C₂×D₄	—	3	12	no	—
816	C₂×D₄	—	3	3	no	—
817	C₂×D₄	—	3	3	no	—
818	C₂×D₄	—	4	6	no	—
819	C₂×D₄	—	6	24	no	—
820	C₂×D₄	—	8	6	no	—
821	C₂×D₄	—	12	6	no	—
822	C₂×D₄	—	12	6	no	—
823	C₂×D₄	—	12	12	no	—
824	C₂×D₄	—	12	12	no	—
825	C₂×D₄	—	12	12	no	—
826	C₂×D₄	—	12	12	no	—
827	C₂×D₄	—	12	12	no	—
828	C₂×D₄	—	24	6	no	—
829	C₂×D₄	—	24	12	no	—
830	C₂×D₄	—	24	12	no	—
831	C₂×D₄	C₂³×D₃	1	6	yes	—
832	C₂×D₄	C₂³×D₃	1	6	yes	—
833	C₂×D₄	C₂³×D₃	1	12	yes	—
834	C₂×D₄	C₂³×D₃	1	3	yes	—
835	C₂×D₄	C₂³×D₃	1	6	yes	—
836	C₂×D₄	C₂³×D₃	1	3	yes	—
837	C₂²×C₄	—	3	6	no	—
838	C₂²×C₄	—	3	12	no	—
839	C₂²×C₄	—	3	6	no	—
840	C₂²×C₄	—	3	6	no	—
841	C₂²×C₄	—	3	3	no	—
842	C₂²×C₄	—	3	3	no	—
843	C₂²×C₄	—	3	6	no	—
844	C₂²×C₄	—	3	6	no	—
845	C₂²×C₄	—	3	12	no	—
846	C₂²×C₄	—	3	6	no	—
847	C₂²×C₄	—	3	6	no	—
848	C₂²×C₄	—	12	4	no	—
849	C₂²×C₄	C₂³×D₃	1	3	yes	—
850	C₂²×C₄	C₂³×D₃	1	6	yes	—
851	C₄⋊C₄	—	3	6	no	—
852	C₄⋊C₄	—	3	12	no	—
853	C₄⋊C₄	—	3	12	no	—
854	C₄⋊C₄	—	3	12	no	—
855	C₄⋊C₄	—	3	6	no	—
856	C₄⋊C₄	—	3	6	no	—
857	C₄⋊C₄	—	3	12	no	—
858	C₄⋊C₄	—	3	12	no	—
859	C₄⋊C₄	—	3	6	no	—
860	C₄⋊C₄	—	3	6	no	—
861	C₂²⋊C₄	—	3	6	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	—	3	6	no	—
869	C₂²⋊C₄	—	3	12	no	—
870	C₂²⋊C₄	—	3	12	no	—
871	C₂²⋊C₄	—	3	12	no	—
872	C₂²⋊C₄	—	3	12	no	—
873	C₂²⋊C₄	—	3	12	no	—
874	C₂²⋊C₄	—	3	6	no	—
875	C₂²⋊C₄	—	3	12	no	—
876	C₂²⋊C₄	C₂³×D₃	1	6	yes	—
877	C₂²⋊C₄	C₂³×D₃	1	6	yes	—
878	C₂²⋊C₄	C₂³×D₃	1	12	yes	—
879	C₂²⋊C₄	C₂³×D₃	1	12	yes	—
880	C₂²⋊C₄	C₂³×D₃	1	12	yes	—
881	C₂²⋊C₄	C₂³×D₃	1	12	yes	—
882	C₂²⋊C₄	C₂³×D₃	1	12	yes	—
883	C₄²	—	3	3	no	—
884	C₄²	—	3	6	no	—
885	C₄²	—	3	3	no	—
886	C₄²	—	3	6	no	—
887	C₄²	—	3	12	no	—
888	C₄²	C₂³×D₃	1	3	yes	—
889	C₄²	C₂³×D₃	1	3	yes	—
890	C₄²	C₂³×D₃	1	6	yes	—
891	C₂²×C₃	—	2	2	no	—
892	C₂²×C₃	—	2	6	no	—
893	C₂²×C₃	—	2	6	no	—
894	C₂²×C₃	—	2	12	no	—
895	C₂²×C₃	—	2	12	no	—
896	C₂²×C₃	—	4	8	no	—
897	C₂²×C₃	—	8	12	no	—
898	C₂²×C₃	—	8	12	no	—
899	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
900	C₂²×C₃	C₂⁶	1	1	yes	characteristic
901	C₂×D₃	—	2	2	no	—
902	C₂×D₃	—	2	3	no	—
903	C₂×D₃	—	2	6	no	—
904	C₂×D₃	—	2	6	no	—
905	C₂×D₃	—	2	12	no	—
906	C₂×D₃	—	8	12	no	—
907	C₂×D₃	—	8	12	no	—
908	C₂×D₃	—	16	6	no	—
909	C₂×D₃	C₂×H(5,𝔽₂)	1	2	yes	—
910	C₃×C₄	—	2	3	no	—
911	C₃×C₄	—	2	3	no	—
912	C₃×C₄	—	2	6	no	—
913	C₃×C₄	—	2	6	no	—
914	Dic₃	—	2	3	no	—
915	Dic₃	—	2	6	no	—
916	Dic₃	—	2	6	no	—
917	Dic₃	—	2	6	no	—
918	Dic₃	C₂×H(5,𝔽₂)	1	2	yes	—
919	C₂³	—	2	12	no	—
920	C₂³	—	3	1	no	—
921	C₂³	—	3	6	no	—
922	C₂³	—	3	3	no	—
923	C₂³	—	4	2	no	—
924	C₂³	—	4	4	no	—
925	C₂³	—	4	12	no	—
926	C₂³	—	4	6	no	—
927	C₂³	—	4	12	no	—
928	C₂³	—	6	12	no	—
929	C₂³	—	8	16	no	—
930	C₂³	—	12	6	no	—
931	C₂³	—	12	12	no	—
932	C₂³	—	12	12	no	—
933	C₂³	—	12	6	no	—
934	C₂³	—	12	12	no	—
935	C₂³	—	24	16	no	—
936	C₂³	C₂⁴×D₃	1	6	yes	—
937	C₂³	C₂⁴×D₃	1	6	yes	—
938	C₂³	C₂⁴×D₃	1	1	yes	characteristic
939	Q₈	—	4	1	no	—
940	Q₈	—	4	3	no	—
941	Q₈	—	4	2	no	—
942	Q₈	—	4	6	no	—
943	Q₈	—	6	6	no	—
944	Q₈	—	12	3	no	—
945	Q₈	—	12	6	no	—
946	Q₈	—	12	3	no	—
947	D₄	—	3	4	no	—
948	D₄	—	4	3	no	—
949	D₄	—	4	3	no	—
950	D₄	—	4	6	no	—
951	D₄	—	4	12	no	—
952	D₄	—	4	6	no	—
953	D₄	—	4	6	no	—
954	D₄	—	6	6	no	—
955	D₄	—	6	12	no	—
956	D₄	—	6	12	no	—
957	D₄	—	6	12	no	—
958	D₄	—	6	6	no	—
959	D₄	—	12	3	no	—
960	D₄	—	12	12	no	—
961	D₄	—	12	6	no	—
962	D₄	—	12	3	no	—
963	D₄	—	12	12	no	—
964	D₄	—	12	6	no	—
965	D₄	—	12	6	no	—
966	D₄	—	12	12	no	—
967	D₄	—	12	12	no	—
968	D₄	—	12	12	no	—
969	D₄	—	12	12	no	—
970	C₂×C₄	—	2	6	no	—
971	C₂×C₄	—	3	1	no	—
972	C₂×C₄	—	3	6	no	—
973	C₂×C₄	—	3	3	no	—
974	C₂×C₄	—	3	6	no	—
975	C₂×C₄	—	3	6	no	—
976	C₂×C₄	—	4	6	no	—
977	C₂×C₄	—	6	6	no	—
978	C₂×C₄	—	6	6	no	—
979	C₂×C₄	—	6	12	no	—
980	C₂×C₄	—	12	6	no	—
981	C₂×C₄	—	12	6	no	—
982	C₂×C₄	—	12	12	no	—
983	C₂×C₄	—	12	6	no	—
984	C₂×C₄	—	12	6	no	—
985	C₂×C₄	—	12	6	no	—
986	C₂×C₄	—	12	6	no	—
987	C₂×C₄	—	12	12	no	—
988	C₂×C₄	C₂⁴×D₃	1	6	yes	—
989	C₂×C₄	C₂⁴×D₃	1	6	yes	—
990	C₂×C₄	C₂⁴×D₃	1	3	yes	—
991	C₂×C₄	C₂⁴×D₃	1	3	yes	—
992	C₂×C₃	—	2	2	no	—
993	C₂×C₃	—	4	6	no	—
994	C₂×C₃	—	4	6	no	—
995	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
996	C₂×C₃	H(7,𝔽₂)	1	2	yes	—
997	D₃	—	2	2	no	—
998	D₃	—	4	6	no	—
999	D₃	—	4	3	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	6	no	—
1002	C₂²	—	2	6	no	—
1003	C₂²	—	2	12	no	—
1004	C₂²	—	2	12	no	—
1005	C₂²	—	3	2	no	—
1006	C₂²	—	4	8	no	—
1007	C₂²	—	6	2	no	—
1008	C₂²	—	6	3	no	—
1009	C₂²	—	6	6	no	—
1010	C₂²	—	6	6	no	—
1011	C₂²	—	6	12	no	—
1012	C₂²	—	8	12	no	—
1013	C₂²	—	8	12	no	—
1014	C₂²	—	24	12	no	—
1015	C₂²	—	24	12	no	—
1016	C₂²	—	48	6	no	—
1017	C₂²	D₃×H(5,𝔽₂)	1	2	yes	—
1018	C₂²	C₂⁵×D₃	1	1	yes	characteristic
1019	C₄	—	2	3	no	—
1020	C₄	—	2	3	no	—
1021	C₄	—	2	6	no	—
1022	C₄	—	2	6	no	—
1023	C₄	—	3	2	no	—
1024	C₄	—	6	6	no	—
1025	C₄	—	6	3	no	—
1026	C₄	—	6	6	no	—
1027	C₄	—	6	6	no	—
1028	C₃	#63045	1	1	yes	characteristic, complemented, Sylow
1029	C₂	—	2	2	no	—
1030	C₂	—	4	6	no	—
1031	C₂	—	4	6	no	—
1032	C₂	—	6	2	no	—
1033	C₂	—	12	6	no	—
1034	C₂	—	12	3	no	—
1035	C₂	C₂×D₃×H(5,𝔽₂)	1	1	yes	characteristic
1036	C₂	#87568	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁶
Fitting	C₂×C₃×H(3,𝔽₄)	C₂
hypercenter	C₂×H(3,𝔽₄)	D₃
hypocenter	C₃	#63045
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×H(3,𝔽₄)	C₂	semidirect
2. #87092	C₂	semidirect
3. #87092	C₂	semidirect
4. #87091	C₂	semidirect
5. #87090	C₂	semidirect
6. D₃×H(3,𝔽₄)	C₂	semidirect
7. #87087	C₂	semidirect
8. #87086	C₂	semidirect
9. #87085	C₂	semidirect
10. #86080	C₂	semidirect
11. #86079	C₂	semidirect
12. #86077	C₂	semidirect
13. #86076	C₂	semidirect
14. #85921	C₂	semidirect
15. #85919	C₂	semidirect
17. C₂³×#67	C₂²	semidirect
18. C₂×#1007	C₂²	semidirect
19. C₂×#1004	C₂²	semidirect
20. C₃×H(3,𝔽₄)	C₂²	semidirect
21. C₃×H(3,𝔽₄)	C₂²	semidirect
22. C₃×H(3,𝔽₄)	C₂²	semidirect
23. C₃×H(3,𝔽₄)	C₂²	semidirect
24. C₂×C₃×#124	C₂²	semidirect
25. C₂×C₃×#124	C₂²	semidirect
26. C₂×C₃×#120	C₂²	semidirect
27. C₂×#953	C₂²	semidirect
28. #5817	C₂²	semidirect
29. #5816	C₂²	semidirect
30. Q₈×#67	C₂²	semidirect
31. #5806	C₂²	semidirect
32. #5805	C₂²	semidirect
33. #5804	C₂²	semidirect
34. D₄×#67	C₂²	semidirect
35. D₄×#67	C₂²	semidirect
36. #5684	C₂²	semidirect
37. #5684	C₂²	semidirect
38. #5684	C₂²	semidirect
39. #5683	C₂²	semidirect
40. #5683	C₂²	semidirect
41. #5683	C₂²	semidirect
42. #5682	C₂²	semidirect
43. #5681	C₂²	semidirect
44. #5681	C₂²	semidirect
45. #5680	C₂²	semidirect
46. #5680	C₂²	semidirect
47. #5679	C₂²	semidirect
48. #5679	C₂²	semidirect
49. #5678	C₂²	semidirect
50. #5678	C₂²	semidirect
51. #5678	C₂²	semidirect
52. #5678	C₂²	semidirect
53. #5677	C₂²	semidirect
54. #5677	C₂²	semidirect
55. #5676	C₂²	semidirect
56. #5676	C₂²	semidirect
57. #5676	C₂²	semidirect
58. #5675	C₂²	semidirect
59. #5675	C₂²	semidirect
60. #5674	C₂²	semidirect
61. #5674	C₂²	semidirect
62. #5674	C₂²	semidirect
63. D₃×#124	C₂²	semidirect
64. D₃×#124	C₂²	semidirect
65. D₃×#124	C₂²	semidirect
66. #5672	C₂²	semidirect
67. #5671	C₂²	semidirect
68. #5670	C₂²	semidirect
69. #5670	C₂²	semidirect
70. #5669	C₂²	semidirect
71. #5669	C₂²	semidirect
72. #5668	C₂²	semidirect
73. #5668	C₂²	semidirect
74. #5668	C₂²	semidirect
75. #5595	C₂²	semidirect
76. #5595	C₂²	semidirect
77. #5594	C₂²	semidirect
78. #5593	C₂²	semidirect
79. #5593	C₂²	semidirect
80. #5592	C₂²	semidirect
81. #5592	C₂²	semidirect
82. #5592	C₂²	semidirect
83. #5591	C₂²	semidirect
84. #5591	C₂²	semidirect
85. #5591	C₂²	semidirect
86. #5590	C₂²	semidirect
87. #5590	C₂²	semidirect
88. #5590	C₂²	semidirect
89. #5589	C₂²	semidirect
90. #5589	C₂²	semidirect
91. #5589	C₂²	semidirect
92. D₃×#120	C₂²	semidirect
93. D₃×#120	C₂²	semidirect
94. #5587	C₂²	semidirect
95. #5586	C₂²	semidirect
96. #5586	C₂²	semidirect
97. #5495	C₂²	semidirect
98. #5494	C₂²	semidirect
99. #5493	C₂²	semidirect
100. #5490	C₂²	semidirect
101. #5490	C₂²	semidirect
102. #5490	C₂²	semidirect
103. #5486	C₂²	semidirect
104. #5479	C₂²	semidirect
105. #5477	C₂²	semidirect
106. C₄×#235	C₂²	semidirect
118. C₂×H(3,𝔽₄)	D₃	semidirect
122. C₂⁵×C₃	C₂³	semidirect
123. C₂⁴×D₃	C₂³	semidirect
124. C₂²×C₃×Q₈	C₂³	semidirect
125. C₂²×C₃×Q₈	C₂³	semidirect
131. C₂²×#67	C₂³	semidirect
132. C₂²×#67	C₂³	semidirect
133. C₂²×#67	C₂³	semidirect
134. C₂²×#67	C₂³	semidirect
135. C₂³×Dic₃	C₂³	semidirect
137. C₂×#239	C₂³	semidirect
138. C₂×#239	C₂³	semidirect
139. C₂×#239	C₂³	semidirect
140. C₂×D₃×Q₈	C₂³	semidirect
141. C₂×D₃×Q₈	C₂³	semidirect
142. C₂×D₃×Q₈	C₂³	semidirect
147. C₂×#237	C₂³	semidirect
152. C₂×D₃×D₄	C₂³	semidirect
155. C₂×#235	C₂³	semidirect
160. C₃×#124	C₂³	semidirect
161. C₃×#124	C₂³	semidirect
162. C₃×#124	C₂³	semidirect
163. C₃×#124	C₂³	semidirect
164. C₃×#124	C₂³	semidirect
165. C₃×#124	C₂³	semidirect
166. C₃×#124	C₂³	semidirect
170. C₃×#120	C₂³	semidirect
171. C₃×#120	C₂³	semidirect
172. C₃×#120	C₂³	semidirect
173. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
174. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
175. C₂×C₃×C₄²	C₂³	semidirect
177. #953	C₂³	semidirect
178. #953	C₂³	semidirect
179. #953	C₂³	semidirect
180. #953	C₂³	semidirect
181. #953	C₂³	semidirect
182. C₂×#217	C₂³	semidirect
183. C₂×#217	C₂³	semidirect
184. #947	C₂³	semidirect
185. #947	C₂³	semidirect
186. #947	C₂³	semidirect
187. #947	C₂³	semidirect
188. #946	C₂³	semidirect
189. #946	C₂³	semidirect
190. #946	C₂³	semidirect
191. #946	C₂³	semidirect
192. Q₈×Dic₃	C₂³	semidirect
193. Q₈×Dic₃	C₂³	semidirect
194. #944	C₂³	semidirect
195. #944	C₂³	semidirect
196. #944	C₂³	semidirect
200. #940	C₂³	semidirect
204. #939	C₂³	semidirect
205. #939	C₂³	semidirect
206. #939	C₂³	semidirect
210. #938	C₂³	semidirect
214. #937	C₂³	semidirect
215. #937	C₂³	semidirect
218. #936	C₂³	semidirect
220. #935	C₂³	semidirect
221. #935	C₂³	semidirect
223. D₄×Dic₃	C₂³	semidirect
224. D₄×Dic₃	C₂³	semidirect
226. #930	C₂³	semidirect
227. #929	C₂³	semidirect
229. C₄×#67	C₂³	semidirect
230. C₄×#67	C₂³	semidirect
231. #926	C₂³	semidirect
232. #924	C₂³	semidirect
233. #886	C₂³	semidirect
234. #886	C₂³	semidirect
235. #886	C₂³	semidirect
236. #886	C₂³	semidirect
237. #885	C₂³	semidirect
238. #885	C₂³	semidirect
239. #885	C₂³	semidirect
240. #885	C₂³	semidirect
241. #885	C₂³	semidirect
242. #885	C₂³	semidirect
243. #884	C₂³	semidirect
244. #884	C₂³	semidirect
245. #884	C₂³	semidirect
246. #884	C₂³	semidirect
247. #884	C₂³	semidirect
248. #884	C₂³	semidirect
249. #884	C₂³	semidirect
250. #884	C₂³	semidirect
251. #883	C₂³	semidirect
252. #883	C₂³	semidirect
253. #883	C₂³	semidirect
254. #883	C₂³	semidirect
255. #883	C₂³	semidirect
256. #883	C₂³	semidirect
257. #882	C₂³	semidirect
258. #882	C₂³	semidirect
259. #882	C₂³	semidirect
260. #882	C₂³	semidirect
261. #882	C₂³	semidirect
262. #882	C₂³	semidirect
263. #67⋊C₄	C₂³	semidirect
264. #67⋊C₄	C₂³	semidirect
265. #67⋊C₄	C₂³	semidirect
266. #67⋊C₄	C₂³	semidirect
267. #67⋊C₄	C₂³	semidirect
268. #67⋊C₄	C₂³	semidirect
269. D₃×C₂²⋊C₄	C₂³	semidirect
270. D₃×C₂²⋊C₄	C₂³	semidirect
271. D₃×C₂²⋊C₄	C₂³	semidirect
272. D₃×C₂²⋊C₄	C₂³	semidirect
273. D₃×C₂²⋊C₄	C₂³	semidirect
274. #879	C₂³	semidirect
275. #879	C₂³	semidirect
276. #879	C₂³	semidirect
277. #879	C₂³	semidirect
278. #878	C₂³	semidirect
279. #878	C₂³	semidirect
280. #878	C₂³	semidirect
281. #878	C₂³	semidirect
282. #877	C₂³	semidirect
283. #877	C₂³	semidirect
284. #877	C₂³	semidirect
285. #876	C₂³	semidirect
286. #875	C₂³	semidirect
287. #875	C₂³	semidirect
288. #875	C₂³	semidirect
289. #874	C₂³	semidirect
290. C₄×D₁₂	C₂³	semidirect
291. C₄×D₁₂	C₂³	semidirect
292. C₄×D₁₂	C₂³	semidirect
293. #872	C₂³	semidirect
294. #872	C₂³	semidirect
295. #872	C₂³	semidirect
296. C₄²×D₃	C₂³	semidirect
297. C₄²×D₃	C₂³	semidirect
298. #870	C₂³	semidirect
299. #869	C₂³	semidirect
300. C₄×Dic₆	C₂³	semidirect
301. C₄×Dic₆	C₂³	semidirect
313. H(3,𝔽₄)	C₂×D₃	semidirect
314. H(3,𝔽₄)	C₂×D₃	semidirect
315. H(3,𝔽₄)	C₂×D₃	semidirect
316. H(3,𝔽₄)	C₂×D₃	semidirect
382. C₂×#124	C₂×D₃	semidirect
383. C₂×#124	C₂×D₃	semidirect
389. C₂×#120	C₂×D₃	semidirect
516. C₂⁵	C₂²×D₃	semidirect
532. C₂²×Q₈	C₂²×D₃	semidirect
533. C₂²×Q₈	C₂²×D₃	semidirect
584. #124	C₂²×D₃	semidirect
585. #124	C₂²×D₃	semidirect
586. #124	C₂²×D₃	semidirect
587. #124	C₂²×D₃	semidirect
588. #124	C₂²×D₃	semidirect
589. #124	C₂²×D₃	semidirect
590. #124	C₂²×D₃	semidirect
654. #120	C₂²×D₃	semidirect
655. #120	C₂²×D₃	semidirect
656. #120	C₂²×D₃	semidirect
690. C₂×C₂²⋊C₄	C₂²×D₃	semidirect
691. C₂×C₂²⋊C₄	C₂²×D₃	semidirect
694. C₂×C₄²	C₂²×D₃	semidirect
1028. C₃	#63045	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×H(3,𝔽₄)	2
#87092	2
#87091	2
#87090	2
D₃×H(3,𝔽₄)	2
#87087	2
#87086	2
#87085	2
#86080	2
#86079	2
#86077	2
#86076	2
#85921	2
#85919	2
#63045	3