Subgroups — #31740049

Order 17152.

1820 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574305	C₂	1	1	yes	maximal, characteristic, complemented
2	#22574170	C₂	1	1	yes	maximal, characteristic
3	#22573260	C₂	1	1	yes	maximal, characteristic, complemented
4	#22573128	C₂	1	1	yes	maximal, characteristic, complemented
5	#22572903	C₂	1	1	yes	maximal, characteristic, complemented
6	#22572849	C₂	1	1	yes	maximal, characteristic, complemented
7	#22572725	C₂	1	2	yes	maximal, complemented
8	#22572641	C₂	1	1	yes	maximal, characteristic, complemented
9	#22572499	C₂	1	2	yes	maximal, complemented
10	#22572494	C₂	1	1	yes	maximal, characteristic, complemented
11	#22572442	C₂	1	1	yes	maximal, characteristic, complemented
12	#22572426	C₂	1	2	yes	maximal, complemented
13	SD₁₆×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#22571713	C₂	1	2	yes	maximal, complemented
15	#22570927	C₂	1	1	yes	maximal, characteristic, complemented
16	#22570883	C₂	1	2	yes	maximal, complemented
17	#22570460	C₂	1	2	yes	maximal, complemented
18	#22570442	C₂	1	2	yes	maximal, complemented
19	#22570280	C₂	1	1	yes	maximal, characteristic, complemented
20	#22570240	C₂	1	1	yes	maximal, characteristic, complemented
21	#22569213	C₂	1	1	yes	maximal, characteristic, complemented
22	#22569065	C₂	1	2	yes	maximal, complemented
23	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×SD₁₆×D₆₇	C₂²	1	2	yes	—
25	#16864131	C₂²	1	1	yes	characteristic
26	#16864125	C₂²	1	1	yes	characteristic, complemented
27	#16864124	—	2	1	no	—
28	#16864124	C₂²	1	1	yes	characteristic, complemented
29	#16864119	—	2	1	no	—
30	#16864119	C₂²	1	1	yes	characteristic
31	#16864119	C₂²	1	1	yes	characteristic
32	#16864109	C₂²	1	2	yes	—
33	#16864081	—	2	2	no	—
34	#16864081	C₂²	1	2	yes	complemented
35	#16864070	—	2	2	no	—
36	Q₈×D₂₆₈	C₂²	1	1	yes	characteristic
37	D₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
38	Q₈×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
39	#16864055	—	2	1	no	—
40	#16864042	—	2	1	no	—
41	#16864034	C₂²	1	2	yes	—
42	D₄×D₂₆₈	C₂²	1	1	yes	characteristic
43	#16864018	C₂²	1	2	yes	—
44	#16864004	—	2	2	no	—
45	#16864004	C₂²	1	2	yes	complemented
46	#16863979	—	2	2	no	—
47	#16863953	—	2	1	no	—
48	#16863953	C₂²	1	1	yes	characteristic, complemented
49	#16863946	C₂²	1	1	yes	characteristic
50	#16863930	—	2	1	no	—
51	#16863930	—	2	1	no	—
52	#16863930	C₂²	1	1	yes	characteristic
53	C₂×#14524031	—	2	1	no	—
54	#16863872	C₂²	1	2	yes	complemented
55	#16863868	C₂²	1	2	yes	—
56	#16863803	C₂²	1	2	yes	complemented
57	#16863801	C₂²	1	1	yes	characteristic, complemented
58	#16863789	C₂²	1	2	yes	complemented
59	#16863769	C₂²	1	1	yes	characteristic
60	#16863752	C₂²	1	2	yes	complemented
61	#16863747	C₂²	1	1	yes	characteristic, complemented
62	#16863745	C₂²	1	2	yes	complemented
63	#16863743	C₂²	1	1	yes	characteristic
64	#16863739	C₂²	1	2	yes	complemented
65	#16863737	C₂²	1	2	yes	complemented
66	#16863736	C₂²	1	2	yes	complemented
67	#16863736	C₂²	1	2	yes	complemented
68	#16863722	C₂²	1	2	yes	—
69	#16863714	C₂²	1	2	yes	complemented
70	#16863699	C₂²	1	2	yes	complemented
71	#16863694	C₂²	1	2	yes	—
72	#16863689	C₂²	1	2	yes	complemented
73	#16863681	C₂²	1	1	yes	characteristic, complemented
74	#16863681	C₂²	1	1	yes	characteristic, complemented
75	#16863681	C₂²	1	1	yes	characteristic, complemented
76	#16863680	C₂²	1	2	yes	complemented
77	#16863676	C₂²	1	1	yes	characteristic
78	#16863653	C₂²	1	2	yes	complemented
79	#16863645	C₂²	1	2	yes	—
80	#16863642	C₂²	1	2	yes	complemented
81	#16863642	C₂²	1	2	yes	complemented
82	#16863634	C₂²	1	2	yes	complemented
83	#16863626	C₂²	1	2	yes	—
84	#16863621	C₂²	1	2	yes	complemented
85	#16863620	C₂²	1	2	yes	complemented
86	#16863606	C₂²	1	1	yes	characteristic, complemented
87	#16863601	C₂²	1	1	yes	characteristic
88	#16863600	C₂²	1	2	yes	complemented
89	#16863599	C₂²	1	2	yes	—
90	#16863596	C₂²	1	1	yes	characteristic
91	#16863596	C₂²	1	1	yes	characteristic
92	#16863558	C₂²	1	2	yes	—
93	#16863550	C₂²	1	2	yes	complemented
94	#16863548	C₂²	1	2	yes	—
95	#16863545	C₂²	1	2	yes	—
96	#16863536	C₂²	1	2	yes	—
97	#16863535	C₂²	1	2	yes	complemented
98	#16863526	C₂²	1	1	yes	characteristic, complemented
99	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
100	#16863498	C₂²	1	2	yes	complemented
101	#16863498	C₂²	1	2	yes	complemented
102	#16863497	C₂²	1	2	yes	—
103	#16863495	C₂²	1	2	yes	complemented
104	C₄×#11761618	C₂²	1	2	yes	complemented
105	#16863487	C₂²	1	2	yes	—
106	C₄×#11761615	C₂²	1	2	yes	complemented
107	C₄×#11761615	C₂²	1	2	yes	complemented
108	C₄×#11761616	C₂²	1	2	yes	—
109	#16863481	C₂²	1	2	yes	complemented
110	#16863475	C₂²	1	1	yes	characteristic
111	#16863472	C₂²	1	2	yes	complemented
112	#16863465	C₂²	1	2	yes	complemented
113	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
114	#16863458	C₂²	1	2	yes	complemented
115	#16863449	C₂²	1	1	yes	characteristic, complemented
116	#16863433	C₂²	1	2	yes	complemented
117	#16863403	C₂²	1	2	yes	complemented
118	#16863399	C₂²	1	2	yes	—
119	#16863353	C₂²	1	2	yes	complemented
120	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#440×C₆₇	C₂²	1	1	yes	characteristic
126	#440×C₆₇	C₂²	1	1	yes	characteristic
127	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
130	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
131	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#417×C₆₇	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#11761628	—	2	1	no	—
136	C₂²×Dic₁₃₄	—	2	1	no	—
137	C₂×Q₈×D₆₇	C₂³	1	2	yes	—
138	C₂²×D₂₆₈	—	2	1	no	—
139	C₂×D₄×D₆₇	C₂³	1	2	yes	—
140	C₂×#11761618	C₂³	1	2	yes	—
141	C₂×#11761617	C₂³	1	2	yes	—
142	C₂×#11761617	C₂³	1	2	yes	—
143	C₂×#11761616	C₂³	1	2	yes	—
144	C₂×#11761615	C₂³	1	2	yes	—
145	C₂×#11761615	C₂³	1	2	yes	—
146	SD₁₆×D₆₇	—	2	8	no	—
147	C₂×#11761611	C₂³	1	2	yes	—
148	C₂×C₈×D₆₇	C₂³	1	2	yes	—
149	#14524043	—	2	1	no	—
150	#14524043	—	2	1	no	—
151	#14524043	C₂³	1	1	yes	characteristic
152	#14524043	C₂³	1	1	yes	characteristic
153	#14524043	C₂³	1	1	yes	characteristic
154	#14524042	C₂³	1	2	yes	—
155	#14524041	—	2	2	no	—
156	#14524041	C₂³	1	2	yes	—
157	#14524040	C₂³	1	1	yes	characteristic
158	#14524038	—	2	2	no	—
159	#14524038	—	2	2	no	—
160	#14524038	—	2	2	no	—
161	#14524038	—	2	2	no	—
162	#14524037	—	2	2	no	—
163	#14524037	—	2	2	no	—
164	#14524037	D₄	1	2	yes	—
165	#14524035	—	2	1	no	—
166	#14524035	—	2	2	no	—
167	#14524035	—	2	1	no	—
168	#14524035	D₄	1	1	yes	characteristic
169	#14524034	—	2	2	no	—
170	#14524034	C₂³	1	2	yes	—
171	#14524033	—	2	2	no	—
172	#14524033	—	2	2	no	—
173	#14524033	—	2	2	no	—
174	#14524032	C₂³	1	2	yes	—
175	#14524031	—	2	1	no	—
176	#14524031	—	2	1	no	—
177	#14524031	—	2	1	no	—
178	#14524031	—	2	2	no	—
179	#14524031	—	2	2	no	—
180	#14524031	—	2	1	no	—
181	#14524031	D₄	1	1	yes	characteristic
182	#14524029	—	2	2	no	—
183	#14524028	—	2	2	no	—
184	#14524028	—	2	2	no	—
185	#14524026	—	2	2	no	—
186	#14524026	—	2	2	no	—
187	#14524026	D₄	1	2	yes	—
188	#14524023	—	2	2	no	—
189	#14524023	C₂³	1	2	yes	—
190	#14524022	—	2	1	no	—
191	#14524022	—	2	2	no	—
192	#14524022	—	2	1	no	—
193	#14524022	D₄	1	1	yes	characteristic
194	#14524022	C₂³	1	2	yes	—
195	#14524021	—	2	2	no	—
196	#14524020	—	2	2	no	—
197	#14524019	—	2	2	no	—
198	#14524019	C₂³	1	2	yes	—
199	#14524019	C₂³	1	2	yes	—
200	#14524018	C₂³	1	2	yes	—
201	#14524017	—	2	1	no	—
202	#14524017	—	2	1	no	—
203	#14524017	D₄	1	1	yes	characteristic
204	#14524017	C₂³	1	2	yes	—
205	#14524016	—	2	2	no	—
206	#14524015	—	2	2	no	—
207	#14524013	—	2	2	no	—
208	#14524011	—	2	2	no	—
209	Q₈×Dic₆₇	C₂³	1	2	yes	—
210	C₄×Dic₁₃₄	—	2	1	no	—
211	C₄×Dic₁₃₄	—	2	1	no	—
212	C₄×Dic₁₃₄	—	2	1	no	—
213	C₄×Dic₁₃₄	—	2	1	no	—
214	C₄×Dic₁₃₄	—	2	2	no	—
215	C₄×Dic₁₃₄	—	2	1	no	—
216	C₄×Dic₁₃₄	C₂³	1	2	yes	—
217	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
218	#14524008	—	2	2	no	—
219	#14524008	C₂³	1	2	yes	—
220	C₄×D₂₆₈	—	2	1	no	—
221	C₄×D₂₆₈	—	2	1	no	—
222	C₄×D₂₆₈	—	2	1	no	—
223	C₄×D₂₆₈	C₂³	1	2	yes	—
224	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
225	D₄×Dic₆₇	C₂³	1	2	yes	—
226	#14524005	C₂³	1	2	yes	—
227	C₄×C₂²⋊D₆₇	—	2	2	no	—
228	C₄×C₂²⋊D₆₇	—	2	2	no	—
229	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
230	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
231	#14524002	—	2	2	no	—
232	#14524002	—	2	1	no	—
233	#14524001	—	2	2	no	—
234	#14524001	C₂³	1	2	yes	—
235	#14524001	C₂³	1	2	yes	—
236	#14524000	—	2	2	no	—
237	#14524000	—	2	2	no	—
238	#14524000	C₂³	1	2	yes	—
239	C₂×(C₂×D₆₇)⋊C₄	—	2	2	no	—
240	C₂×(C₂×D₆₇)⋊C₄	—	2	2	no	—
241	C₂²⋊C₄×D₆₇	—	2	2	no	—
242	#14523977	C₂³	1	2	yes	—
243	#14523977	C₂³	1	2	yes	—
244	#14523976	C₂³	1	2	yes	—
245	#14523974	C₂³	1	2	yes	—
246	#14523974	C₂³	1	2	yes	—
247	#14523974	C₂³	1	2	yes	—
248	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
249	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
250	Dic₆₇⋊C₈	C₂³	1	2	yes	—
251	Dic₆₇⋊C₈	C₂³	1	2	yes	—
252	#14523968	C₂³	1	2	yes	—
253	#14523968	C₂³	1	2	yes	—
254	#14523967	C₂³	1	2	yes	—
255	#14523967	C₂³	1	2	yes	—
256	#14523967	C₂³	1	2	yes	—
257	#14523966	C₂³	1	2	yes	—
258	#14523966	C₂³	1	2	yes	—
259	#14523965	C₂³	1	2	yes	—
260	#14523965	C₂³	1	2	yes	—
261	#14523964	C₂³	1	2	yes	—
262	#14523963	C₂³	1	2	yes	—
263	#14523963	C₂³	1	2	yes	—
264	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
265	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
267	#14523953	C₂³	1	2	yes	—
268	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
269	C₈×Dic₆₇	C₂³	1	2	yes	—
270	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
271	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
272	#137×C₆₇	—	2	4	no	—
273	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
274	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
277	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
278	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
279	C₄×Q₈×C₆₇	—	2	1	no	—
280	C₄×Q₈×C₆₇	—	2	1	no	—
281	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₆₇	—	2	1	no	—
288	C₄×D₄×C₆₇	—	2	1	no	—
289	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
291	#117×C₆₇	—	2	1	no	—
292	#117×C₆₇	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
294	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₆₇	—	2	1	no	—
296	C₂×C₄²×C₆₇	—	2	1	no	—
297	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
298	#107×C₆₇	C₂³	1	1	yes	characteristic
299	#107×C₆₇	C₂³	1	1	yes	characteristic
300	#106×C₆₇	C₂³	1	1	yes	characteristic
301	#106×C₆₇	C₂³	1	1	yes	characteristic
302	#103×C₆₇	C₂³	1	1	yes	characteristic
303	#103×C₆₇	C₂³	1	1	yes	characteristic
304	#103×C₆₇	C₂³	1	1	yes	characteristic
305	#103×C₆₇	C₂³	1	1	yes	characteristic
306	#103×C₆₇	C₂³	1	1	yes	characteristic
307	#103×C₆₇	C₂³	1	1	yes	characteristic
308	#102×C₆₇	C₂³	1	1	yes	characteristic
309	#102×C₆₇	C₂³	1	1	yes	characteristic
310	#97×C₆₇	C₂³	1	1	yes	characteristic
311	#97×C₆₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₂³×D₆₇	—	2	2	no	—
315	#11761628	—	8	2	no	—
316	C₂×Dic₁₃₄	—	2	1	no	—
317	C₂×Dic₁₃₄	—	2	1	no	—
318	C₂×Dic₁₃₄	—	2	2	no	—
319	C₂×Dic₁₃₄	—	2	2	no	—
320	C₂×Dic₁₃₄	—	8	2	no	—
321	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
322	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
323	Q₈×D₆₇	—	2	4	no	—
324	Q₈×D₆₇	—	4	2	no	—
325	C₂×D₂₆₈	—	2	1	no	—
326	C₂×D₂₆₈	—	2	2	no	—
327	C₂×D₂₆₈	—	2	1	no	—
328	C₂×D₂₆₈	—	8	2	no	—
329	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
330	C₂×D₂₆₈	C₂⁴	1	2	yes	—
331	C₂×C₂²⋊D₆₇	—	2	2	no	—
332	C₂×C₂²⋊D₆₇	—	2	2	no	—
333	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
334	D₄×D₆₇	—	2	4	no	—
335	D₄×D₆₇	—	4	2	no	—
336	C₂²×Dic₆₇	—	2	2	no	—
337	C₂×C₄×D₆₇	—	2	2	no	—
338	C₂×C₄×D₆₇	—	2	2	no	—
339	C₂×C₄×D₆₇	—	2	2	no	—
340	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
341	#11761618	—	4	2	no	—
342	#11761617	—	2	4	no	—
343	#11761617	—	4	2	no	—
344	#11761616	—	2	4	no	—
345	#11761615	—	2	4	no	—
346	#11761615	—	4	2	no	—
347	#11761611	—	4	2	no	—
348	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
349	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
350	C₈×D₆₇	—	2	4	no	—
351	C₄⋊Dic₆₇	—	2	1	no	—
352	C₄⋊Dic₆₇	—	2	1	no	—
353	C₄⋊Dic₆₇	—	2	1	no	—
354	C₄⋊Dic₆₇	—	2	1	no	—
355	C₄⋊Dic₆₇	—	2	2	no	—
356	C₄⋊Dic₆₇	—	2	2	no	—
357	C₄⋊Dic₆₇	—	2	2	no	—
358	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
359	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
360	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
361	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
362	Dic₆₇⋊C₄	—	2	2	no	—
363	Dic₆₇⋊C₄	—	2	2	no	—
364	Dic₆₇⋊C₄	—	2	2	no	—
365	Dic₆₇⋊C₄	—	2	2	no	—
366	Dic₆₇⋊C₄	—	2	2	no	—
367	Dic₆₇⋊C₄	—	2	2	no	—
368	Dic₆₇⋊C₄	—	2	2	no	—
369	Dic₆₇⋊C₄	—	2	2	no	—
370	Dic₆₇⋊C₄	—	2	2	no	—
371	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
372	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
373	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
374	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
375	C₂²⋊Dic₆₇	—	2	2	no	—
376	C₂²⋊Dic₆₇	—	2	2	no	—
377	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
378	(C₂×D₆₇)⋊C₄	—	2	2	no	—
379	(C₂×D₆₇)⋊C₄	—	2	2	no	—
380	(C₂×D₆₇)⋊C₄	—	2	2	no	—
381	(C₂×D₆₇)⋊C₄	—	2	2	no	—
382	(C₂×D₆₇)⋊C₄	—	2	2	no	—
383	(C₂×D₆₇)⋊C₄	—	2	2	no	—
384	(C₂×D₆₇)⋊C₄	—	2	2	no	—
385	(C₂×D₆₇)⋊C₄	—	2	2	no	—
386	(C₂×D₆₇)⋊C₄	—	2	2	no	—
387	(C₂×D₆₇)⋊C₄	—	2	2	no	—
388	(C₂×D₆₇)⋊C₄	—	2	2	no	—
389	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
390	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
391	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
392	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
393	C₄×Dic₆₇	—	2	2	no	—
394	C₄×Dic₆₇	—	2	2	no	—
395	C₄×Dic₆₇	—	2	2	no	—
396	C₄×Dic₆₇	—	2	2	no	—
397	C₄×Dic₆₇	—	2	2	no	—
398	C₄×Dic₆₇	C₂⁴	1	2	yes	—
399	#41×C₆₇	—	2	2	no	—
400	#41×C₆₇	—	4	1	no	—
401	C₂×Q₈×C₆₇	—	2	1	no	—
402	C₂×Q₈×C₆₇	—	2	2	no	—
403	C₂×Q₈×C₆₇	—	4	1	no	—
404	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
406	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
407	C₂×D₄×C₆₇	—	2	1	no	—
408	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₆₇	—	2	1	no	—
410	C₂²×C₄×C₆₇	—	2	1	no	—
411	C₂²×C₄×C₆₇	—	2	1	no	—
412	C₂²×C₄×C₆₇	—	2	1	no	—
413	C₂²×C₄×C₆₇	—	2	1	no	—
414	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
415	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
416	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
417	Q₁₆×C₆₇	—	2	2	no	—
418	Q₁₆×C₆₇	—	2	2	no	—
419	SD₁₆×C₆₇	—	2	2	no	—
420	SD₁₆×C₆₇	#41	1	4	yes	complemented
421	M₁₆×C₆₇	—	2	2	no	—
422	M₁₆×C₆₇	—	4	1	no	—
423	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₆₇	—	2	1	no	—
428	C₄⋊C₄×C₆₇	—	2	1	no	—
429	C₄⋊C₄×C₆₇	—	2	1	no	—
430	C₄⋊C₄×C₆₇	—	2	1	no	—
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	—	2	1	no	—
433	C₄⋊C₄×C₆₇	—	2	1	no	—
434	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₂²⋊C₄×C₆₇	—	2	1	no	—
439	C₂²⋊C₄×C₆₇	—	2	1	no	—
440	C₂²⋊C₄×C₆₇	—	2	1	no	—
441	C₄²×C₆₇	—	2	1	no	—
442	C₄²×C₆₇	—	2	1	no	—
443	C₄²×C₆₇	—	2	1	no	—
444	C₄²×C₆₇	—	2	1	no	—
445	C₄²×C₆₇	—	2	1	no	—
446	C₄²×C₆₇	—	2	1	no	—
447	C₄²×C₆₇	—	2	1	no	—
448	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
451	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₂³×C₆₇	—	2	1	no	—
453	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
454	C₂²×D₆₇	—	2	2	no	—
455	C₂²×D₆₇	—	4	4	no	—
456	C₂²×D₆₇	—	8	2	no	—
457	C₂²×D₆₇	—	8	2	no	—
458	C₂²×D₆₇	C₂²×D₄	1	2	yes	—
459	Q₈×C₆₇	—	2	1	no	—
460	Q₈×C₆₇	—	2	1	no	—
461	Q₈×C₆₇	—	2	1	no	—
462	Q₈×C₆₇	—	2	1	no	—
463	Q₈×C₆₇	—	2	1	no	—
464	Q₈×C₆₇	—	4	2	no	—
465	Q₈×C₆₇	C₂×#41	1	2	yes	—
466	D₄×C₆₇	—	2	1	no	—
467	D₄×C₆₇	—	4	2	no	—
468	D₄×C₆₇	C₂×#41	1	2	yes	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	2	no	—
471	C₂×C₄×C₆₇	—	2	1	no	—
472	C₂×C₄×C₆₇	—	2	1	no	—
473	C₂×C₄×C₆₇	—	2	1	no	—
474	C₂×C₄×C₆₇	—	2	1	no	—
475	C₂×C₄×C₆₇	—	2	1	no	—
476	C₂×C₄×C₆₇	—	2	1	no	—
477	C₂×C₄×C₆₇	—	2	1	no	—
478	C₂×C₄×C₆₇	—	2	1	no	—
479	C₂×C₄×C₆₇	—	4	1	no	—
480	C₂×C₄×C₆₇	—	4	2	no	—
481	C₂×C₄×C₆₇	—	4	2	no	—
482	C₂×C₄×C₆₇	—	4	2	no	—
483	C₂×C₄×C₆₇	—	4	2	no	—
484	C₂×C₄×C₆₇	—	8	1	no	—
485	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
491	C₂²⋊D₆₇	—	4	2	no	—
492	C₂²⋊D₆₇	—	4	4	no	—
493	C₂²⋊D₆₇	—	8	2	no	—
494	C₂×Dic₆₇	—	2	2	no	—
495	C₂×Dic₆₇	—	2	2	no	—
496	C₂×Dic₆₇	—	2	2	no	—
497	C₂×Dic₆₇	—	8	2	no	—
498	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
499	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
500	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
501	D₂₆₈	—	2	2	no	—
502	D₂₆₈	—	2	2	no	—
503	D₂₆₈	—	2	2	no	—
504	D₂₆₈	—	4	2	no	—
505	D₂₆₈	—	8	1	no	—
506	D₂₆₈	—	8	2	no	—
507	C₄×D₆₇	—	2	2	no	—
508	C₄×D₆₇	—	2	2	no	—
509	C₄×D₆₇	—	4	4	no	—
510	C₄×D₆₇	—	8	2	no	—
511	C₄×D₆₇	—	8	2	no	—
512	Dic₁₃₄	—	2	2	no	—
513	Dic₁₃₄	—	2	2	no	—
514	Dic₁₃₄	—	2	2	no	—
515	Dic₁₃₄	—	4	4	no	—
516	Dic₁₃₄	—	4	2	no	—
517	Dic₁₃₄	—	4	2	no	—
518	Dic₁₃₄	—	8	2	no	—
519	C₈×C₆₇	—	2	1	no	—
520	C₈×C₆₇	—	2	1	no	—
521	C₈×C₆₇	—	2	1	no	—
522	C₈×C₆₇	C₂×#41	1	2	yes	—
523	C₆₇⋊C₈	—	2	2	no	—
524	C₆₇⋊C₈	—	2	2	no	—
525	C₂²×C₆₇	—	2	1	no	—
526	C₂²×C₆₇	—	2	2	no	—
527	C₂²×C₆₇	—	2	1	no	—
528	C₂²×C₆₇	—	2	1	no	—
529	C₂²×C₆₇	—	4	1	no	—
530	C₂²×C₆₇	—	4	1	no	—
531	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
532	C₂×D₆₇	—	2	2	no	—
533	C₂×D₆₇	—	2	2	no	—
534	C₂×D₆₇	—	2	2	no	—
535	C₂×D₆₇	—	4	2	no	—
536	C₂×D₆₇	—	4	2	no	—
537	C₂×D₆₇	—	4	2	no	—
538	C₂×D₆₇	—	16	4	no	—
539	C₄×C₆₇	—	2	1	no	—
540	C₄×C₆₇	—	2	1	no	—
541	C₄×C₆₇	—	2	2	no	—
542	C₄×C₆₇	—	2	1	no	—
543	C₄×C₆₇	—	2	1	no	—
544	C₄×C₆₇	—	4	1	no	—
545	C₄×C₆₇	—	4	1	no	—
546	C₄×C₆₇	—	4	1	no	—
547	C₄×C₆₇	—	4	1	no	—
548	C₄×C₆₇	—	4	1	no	—
549	C₄×C₆₇	—	4	1	no	—
550	C₄×C₆₇	#577	1	2	yes	—
551	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
552	C₄×C₆₇	#585	1	1	yes	characteristic
553	Dic₆₇	—	2	2	no	—
554	Dic₆₇	—	2	2	no	—
555	Dic₆₇	—	2	2	no	—
556	Dic₆₇	—	4	2	no	—
557	Dic₆₇	—	4	2	no	—
558	Dic₆₇	—	4	2	no	—
559	#61540	—	67	1	no	maximal, Sylow
560	C₂×C₆₇	—	4	2	no	—
561	C₂×C₆₇	—	4	1	no	—
562	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
563	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
564	C₂×C₆₇	#3586	1	1	yes	characteristic
565	D₆₇	—	4	2	no	—
566	D₆₇	—	8	2	no	—
567	#3523	—	67	1	no	—
568	#3514	—	67	1	no	—
569	#3400	—	67	1	no	—
570	#3386	—	67	1	no	—
571	#3365	—	67	1	no	—
572	#3359	—	67	1	no	—
573	#3348	—	67	2	no	—
574	#3342	—	67	1	no	—
575	#3329	—	67	2	no	—
576	#3328	—	67	1	no	—
577	#3324	—	67	1	no	—
578	#3323	—	67	2	no	—
579	D₄×SD₁₆	—	67	1	no	—
580	#3266	—	67	2	no	—
581	#3182	—	67	1	no	—
582	#3178	—	67	2	no	—
583	#3123	—	67	2	no	—
584	#3121	—	67	2	no	—
585	#3107	—	67	1	no	—
586	#3103	—	67	1	no	—
587	#2969	—	67	1	no	—
588	#2949	—	67	2	no	—
589	C₄×#137	D₆₇	1	1	yes	characteristic, complemented
590	C₆₇	#61540	1	1	yes	characteristic, complemented, Sylow
591	C₂×#137	C₂×D₆₇	1	1	yes	characteristic
592	C₂²×SD₁₆	—	67	2	no	—
593	#559	—	67	1	no	—
594	#557	—	67	1	no	—
595	#557	—	67	1	no	—
596	#557	—	134	1	no	—
597	#556	—	67	1	no	—
598	#556	—	67	1	no	—
599	#556	—	134	1	no	—
600	#555	—	67	2	no	—
601	#552	—	67	2	no	—
602	#552	—	134	2	no	—
603	#551	—	134	2	no	—
604	D₄×Q₈	—	67	1	no	—
605	D₄×Q₈	—	67	2	no	—
606	D₄×Q₈	—	67	1	no	—
607	#548	—	134	1	no	—
608	#546	—	67	2	no	—
609	#546	—	134	1	no	—
610	D₄²	—	67	1	no	—
611	#542	—	67	2	no	—
612	#541	—	67	2	no	—
613	#541	—	134	2	no	—
614	#538	—	134	2	no	—
615	#533	—	67	1	no	—
616	#533	—	134	1	no	—
617	#532	—	67	1	no	—
618	#529	—	67	1	no	—
619	#529	—	134	1	no	—
620	#529	—	134	1	no	—
621	C₂×#124	—	134	1	no	—
622	#519	—	67	2	no	—
623	#518	—	67	2	no	—
624	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
625	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
626	#501	—	67	2	no	—
627	#500	—	67	1	no	—
628	#497	—	67	2	no	—
629	#492	—	67	1	no	—
630	#488	—	67	2	no	—
631	#487	—	67	2	no	—
632	#487	—	67	1	no	—
633	#486	—	67	1	no	—
634	#485	—	67	2	no	—
635	#485	—	67	2	no	—
636	#485	—	67	2	no	—
637	#485	—	67	2	no	—
638	#482	—	67	2	no	—
639	#481	—	67	2	no	—
640	#478	—	67	2	no	—
641	#478	—	67	2	no	—
642	#477	—	67	2	no	—
643	#475	—	67	1	no	—
644	#475	—	67	1	no	—
645	#475	—	67	1	no	—
646	#475	—	67	2	no	—
647	#474	—	67	1	no	—
648	#470	—	67	2	no	—
649	#468	—	67	2	no	—
650	#468	—	67	2	no	—
651	#468	—	67	2	no	—
652	#467	—	67	2	no	—
653	#465	—	67	2	no	—
654	#464	—	67	2	no	—
655	#464	—	67	2	no	—
656	#462	—	67	1	no	—
657	#461	—	67	2	no	—
658	#461	—	67	1	no	—
659	#461	—	67	2	no	—
660	#460	—	67	1	no	—
661	#460	—	67	1	no	—
662	#452	—	67	2	no	—
663	#451	—	67	2	no	—
664	#450	—	67	2	no	—
665	#450	—	67	2	no	—
666	#448	—	67	2	no	—
667	#448	—	67	2	no	—
668	#446	—	67	1	no	—
669	C₈×Q₈	—	67	1	no	—
670	#441	C₂×D₆₇	1	1	yes	characteristic, complemented
671	#441	C₂×D₆₇	1	1	yes	characteristic, complemented
672	#440	—	67	2	no	—
673	#440	—	67	2	no	—
674	#440	—	67	2	no	—
675	#440	—	67	2	no	—
676	#440	C₂×D₆₇	1	1	yes	characteristic
677	#440	C₂×D₆₇	1	1	yes	characteristic
678	C₄×Q₁₆	—	67	2	no	—
679	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
680	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
681	C₄×SD₁₆	—	67	2	no	—
682	C₄×SD₁₆	—	67	2	no	—
683	C₄×SD₁₆	—	67	2	no	—
684	C₄×SD₁₆	—	67	2	no	—
685	C₄×SD₁₆	—	67	2	no	—
686	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic
687	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic
688	#436	—	67	2	no	—
689	#436	—	67	1	no	—
690	#435	—	67	2	no	—
691	C₈×D₄	—	67	1	no	—
692	#433	—	67	2	no	—
693	#431	—	67	1	no	—
694	#428	C₂×D₆₇	1	1	yes	characteristic, complemented
695	#427	—	67	2	no	—
696	#419	—	67	2	no	—
697	#419	C₂×D₆₇	1	1	yes	characteristic, complemented
698	#418	—	67	2	no	—
699	#417	C₂×D₆₇	1	1	yes	characteristic
700	#405	—	67	2	no	—
701	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
702	C₂×#41	—	134	1	no	—
703	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
704	C₂²×Q₈	—	67	2	no	—
705	C₂²×Q₈	—	134	1	no	—
706	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
707	C₂²×D₄	—	67	2	no	—
708	C₂²×D₄	—	134	1	no	—
709	#137	—	2	4	no	—
710	C₂×Q₁₆	—	67	2	no	—
711	C₂×Q₁₆	C₂²×D₆₇	1	1	yes	characteristic
712	C₂×Q₁₆	C₂²×D₆₇	1	1	yes	characteristic
713	C₂×SD₁₆	—	67	2	no	—
714	C₂×SD₁₆	—	67	2	no	—
715	C₂×SD₁₆	—	67	2	no	—
716	C₂×SD₁₆	—	67	2	no	—
717	C₂×SD₁₆	—	67	2	no	—
718	C₂×SD₁₆	—	134	8	no	—
719	C₂×SD₁₆	C₂²×D₆₇	1	1	yes	characteristic
720	C₂×SD₁₆	C₂²×D₆₇	1	1	yes	characteristic
721	C₂×M₁₆	—	67	2	no	—
722	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
723	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
724	C₂²×C₈	—	67	2	no	—
725	C₄⋊Q₈	—	67	2	no	—
726	C₄⋊Q₈	—	67	2	no	—
727	C₄⋊Q₈	—	67	1	no	—
728	C₄⋊Q₈	—	67	1	no	—
729	C₄⋊Q₈	—	67	1	no	—
730	C₄⋊Q₈	—	134	1	no	—
731	C₄⋊Q₈	—	134	1	no	—
732	C₄⋊Q₈	—	134	2	no	—
733	#127	—	67	1	no	—
734	#126	—	67	2	no	—
735	#126	—	134	2	no	—
736	#126	—	134	2	no	—
737	#126	—	134	2	no	—
738	#126	—	134	2	no	—
739	#126	—	134	2	no	—
740	#126	—	134	2	no	—
741	#125	—	67	2	no	—
742	#125	—	67	1	no	—
743	#125	—	134	1	no	—
744	#125	—	134	2	no	—
745	#125	—	134	2	no	—
746	#125	—	134	2	no	—
747	#125	—	134	2	no	—
748	#125	—	134	2	no	—
749	#125	—	134	1	no	—
750	#124	—	67	2	no	—
751	#124	—	67	1	no	—
752	#124	—	134	2	no	—
753	#124	—	134	2	no	—
754	#124	—	134	1	no	—
755	#124	—	134	1	no	—
756	#124	—	134	1	no	—
757	#124	—	134	2	no	—
758	#124	—	134	1	no	—
759	#123	—	67	2	no	—
760	#123	—	134	2	no	—
761	#123	—	134	2	no	—
762	#123	—	134	2	no	—
763	#123	—	134	2	no	—
764	C₂²⋊Q₈	—	67	1	no	—
765	C₂²⋊Q₈	—	67	2	no	—
766	C₂²⋊Q₈	—	67	2	no	—
767	C₂²⋊Q₈	—	67	2	no	—
768	C₂²⋊Q₈	—	67	2	no	—
769	C₂²⋊Q₈	—	134	2	no	—
770	C₂²⋊Q₈	—	134	2	no	—
771	C₂²⋊Q₈	—	134	2	no	—
772	C₂²⋊Q₈	—	134	2	no	—
773	C₂²⋊Q₈	—	134	2	no	—
774	C₂²⋊Q₈	—	134	1	no	—
775	C₂²⋊Q₈	—	134	1	no	—
776	#121	—	67	1	no	—
777	#121	—	67	2	no	—
778	#121	—	67	2	no	—
779	#121	—	134	2	no	—
780	#121	—	134	2	no	—
781	#121	—	134	1	no	—
782	#121	—	134	1	no	—
783	#120	—	134	2	no	—
784	#120	—	134	2	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	67	1	no	—
788	C₄×Q₈	—	67	2	no	—
789	C₄×Q₈	—	67	2	no	—
790	C₄×Q₈	—	67	2	no	—
791	C₄×Q₈	—	134	2	no	—
792	C₄×Q₈	—	134	1	no	—
793	C₄×Q₈	—	134	1	no	—
794	C₄×Q₈	—	134	1	no	—
795	C₄×Q₈	—	134	1	no	—
796	C₄×Q₈	—	134	2	no	—
797	C₄×Q₈	—	134	1	no	—
798	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
799	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
800	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
801	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
802	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
803	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	67	2	no	—
807	C₄×D₄	—	67	2	no	—
808	C₄×D₄	—	67	2	no	—
809	C₄×D₄	—	67	1	no	—
810	C₄×D₄	—	67	2	no	—
811	C₄×D₄	—	134	1	no	—
812	C₄×D₄	—	134	1	no	—
813	C₄×D₄	—	134	2	no	—
814	C₄×D₄	—	134	2	no	—
815	C₄×D₄	—	134	2	no	—
816	C₄×D₄	—	134	1	no	—
817	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
818	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
819	#117	—	2	1	no	—
820	#117	—	67	2	no	—
821	#117	—	67	2	no	—
822	#117	—	67	2	no	—
823	#117	—	134	2	no	—
824	#117	—	134	2	no	—
825	#117	—	134	2	no	—
826	#117	—	134	2	no	—
827	#117	—	134	1	no	—
828	#117	C₂²×D₆₇	1	1	yes	characteristic
829	C₂×C₄⋊C₄	—	2	1	no	—
830	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
831	C₂×C₂²⋊C₄	—	134	2	no	—
832	C₂×C₂²⋊C₄	—	134	2	no	—
833	C₂×C₂²⋊C₄	—	134	2	no	—
834	C₂×C₄²	—	2	1	no	—
835	C₂×C₄²	—	2	1	no	—
836	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
837	#107	—	67	2	no	—
838	#107	—	67	2	no	—
839	#107	—	67	2	no	—
840	#107	C₂²×D₆₇	1	1	yes	characteristic
841	#107	C₂²×D₆₇	1	1	yes	characteristic
842	#106	—	67	2	no	—
843	#106	—	67	2	no	—
844	#106	—	67	2	no	—
845	#106	C₂²×D₆₇	1	1	yes	characteristic
846	#106	C₂²×D₆₇	1	1	yes	characteristic
847	C₄⋊C₈	—	67	2	no	—
848	C₄⋊C₈	—	67	2	no	—
849	C₄⋊C₈	—	67	1	no	—
850	C₄⋊C₈	—	67	1	no	—
851	#103	—	67	2	no	—
852	#103	—	67	2	no	—
853	#103	—	67	2	no	—
854	#103	—	67	2	no	—
855	#103	—	67	2	no	—
856	#103	—	67	2	no	—
857	#103	—	67	2	no	—
858	#103	C₂²×D₆₇	1	1	yes	characteristic
859	#103	C₂²×D₆₇	1	1	yes	characteristic
860	#103	C₂²×D₆₇	1	1	yes	characteristic
861	#103	C₂²×D₆₇	1	1	yes	characteristic
862	#103	C₂²×D₆₇	1	1	yes	characteristic
863	#103	C₂²×D₆₇	1	1	yes	characteristic
864	#102	—	67	2	no	—
865	#102	—	67	2	no	—
866	#102	—	67	2	no	—
867	#102	—	67	2	no	—
868	#102	—	67	2	no	—
869	#102	C₂²×D₆₇	1	1	yes	characteristic
870	#102	C₂²×D₆₇	1	1	yes	characteristic
871	C₂²⋊C₈	—	67	2	no	—
872	C₂²⋊C₈	—	67	2	no	—
873	C₂²⋊C₈	—	67	2	no	—
874	#97	—	67	2	no	—
875	#97	C₂²×D₆₇	1	1	yes	characteristic
876	#97	C₂²×D₆₇	1	1	yes	characteristic
877	C₄×C₈	—	67	2	no	—
878	C₄×C₈	—	67	2	no	—
879	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
880	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
881	C₂⁴	—	134	2	no	—
882	#41	—	2	2	no	—
883	#41	—	4	1	no	—
884	#41	—	536	2	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	4	1	no	—
888	C₂×Q₈	—	268	2	no	—
889	C₂×Q₈	—	536	2	no	—
890	C₂×Q₈	—	67	1	no	—
891	C₂×Q₈	—	67	2	no	—
892	C₂×Q₈	—	134	2	no	—
893	C₂×Q₈	—	134	2	no	—
894	C₂×Q₈	—	134	4	no	—
895	C₂×Q₈	—	134	1	no	—
896	C₂×Q₈	—	134	1	no	—
897	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
898	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
899	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	268	2	no	—
902	C₂×D₄	—	536	2	no	—
903	C₂×D₄	—	67	2	no	—
904	C₂×D₄	—	67	1	no	—
905	C₂×D₄	—	67	2	no	—
906	C₂×D₄	—	134	2	no	—
907	C₂×D₄	—	134	2	no	—
908	C₂×D₄	—	134	4	no	—
909	C₂×D₄	—	134	2	no	—
910	C₂×D₄	—	134	1	no	—
911	C₂×D₄	—	134	1	no	—
912	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	67	2	no	—
919	C₂²×C₄	—	134	2	no	—
920	C₂²×C₄	—	134	2	no	—
921	C₂²×C₄	—	134	2	no	—
922	C₂²×C₄	—	134	2	no	—
923	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
924	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
925	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
926	Q₁₆	—	2	2	no	—
927	Q₁₆	—	2	2	no	—
928	Q₁₆	—	268	2	no	—
929	SD₁₆	—	2	2	no	—
930	SD₁₆	—	268	2	no	—
931	SD₁₆	—	268	2	no	—
932	SD₁₆	—	134	4	no	—
933	SD₁₆	—	134	4	no	—
934	SD₁₆	—	134	4	no	—
935	SD₁₆	#11761628	1	4	yes	complemented
936	M₁₆	—	2	2	no	—
937	M₁₆	—	4	1	no	—
938	M₁₆	—	268	2	no	—
939	C₂×C₈	—	67	2	no	—
940	C₂×C₈	—	67	2	no	—
941	C₂×C₈	—	134	4	no	—
942	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
943	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
944	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
945	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	67	2	no	—
954	C₄⋊C₄	—	67	2	no	—
955	C₄⋊C₄	—	67	2	no	—
956	C₄⋊C₄	—	67	1	no	—
957	C₄⋊C₄	—	67	1	no	—
958	C₄⋊C₄	—	67	2	no	—
959	C₄⋊C₄	—	67	2	no	—
960	C₄⋊C₄	—	67	2	no	—
961	C₄⋊C₄	—	134	2	no	—
962	C₄⋊C₄	—	134	2	no	—
963	C₄⋊C₄	—	134	2	no	—
964	C₄⋊C₄	—	134	2	no	—
965	C₄⋊C₄	—	134	2	no	—
966	C₄⋊C₄	—	134	2	no	—
967	C₄⋊C₄	—	134	2	no	—
968	C₄⋊C₄	—	134	2	no	—
969	C₄⋊C₄	—	134	2	no	—
970	C₄⋊C₄	—	134	2	no	—
971	C₄⋊C₄	—	134	2	no	—
972	C₄⋊C₄	—	134	1	no	—
973	C₄⋊C₄	—	134	1	no	—
974	C₄⋊C₄	—	134	1	no	—
975	C₄⋊C₄	—	134	1	no	—
976	C₄⋊C₄	—	134	2	no	—
977	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
978	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
979	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
980	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	67	2	no	—
985	C₂²⋊C₄	—	67	2	no	—
986	C₂²⋊C₄	—	67	2	no	—
987	C₂²⋊C₄	—	67	2	no	—
988	C₂²⋊C₄	—	67	2	no	—
989	C₂²⋊C₄	—	134	2	no	—
990	C₂²⋊C₄	—	134	2	no	—
991	C₂²⋊C₄	—	134	2	no	—
992	C₂²⋊C₄	—	134	2	no	—
993	C₂²⋊C₄	—	134	2	no	—
994	C₂²⋊C₄	—	134	2	no	—
995	C₂²⋊C₄	—	134	2	no	—
996	C₂²⋊C₄	—	134	2	no	—
997	C₂²⋊C₄	—	134	2	no	—
998	C₂²⋊C₄	—	134	2	no	—
999	C₂²⋊C₄	—	134	2	no	—
1000	C₂²⋊C₄	—	134	2	no	—
1001	C₂²⋊C₄	—	134	2	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	67	2	no	—
1010	C₄²	—	134	2	no	—
1011	C₄²	—	134	2	no	—
1012	C₄²	—	134	2	no	—
1013	C₄²	—	134	2	no	—
1014	C₄²	—	134	2	no	—
1015	C₄²	D₄×D₆₇	1	1	yes	characteristic
1016	C₄²	D₄×D₆₇	1	1	yes	characteristic
1017	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1018	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1019	C₂³	—	2	1	no	—
1020	C₂³	—	268	4	no	—
1021	C₂³	—	536	2	no	—
1022	C₂³	—	536	2	no	—
1023	C₂³	—	67	2	no	—
1024	C₂³	—	134	2	no	—
1025	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	2	1	no	—
1030	Q₈	—	2	1	no	—
1031	Q₈	—	4	2	no	—
1032	Q₈	—	268	4	no	—
1033	Q₈	—	268	2	no	—
1034	Q₈	—	268	2	no	—
1035	Q₈	—	536	2	no	—
1036	Q₈	—	134	2	no	—
1037	Q₈	—	134	2	no	—
1038	Q₈	—	134	2	no	—
1039	Q₈	C₂×#11761628	1	2	yes	—
1040	D₄	—	2	1	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	268	4	no	—
1043	D₄	—	268	2	no	—
1044	D₄	—	268	2	no	—
1045	D₄	—	536	1	no	—
1046	D₄	—	536	2	no	—
1047	D₄	—	536	2	no	—
1048	D₄	—	134	2	no	—
1049	D₄	—	134	2	no	—
1050	D₄	—	134	2	no	—
1051	D₄	C₂×#11761628	1	2	yes	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	4	1	no	—
1063	C₂×C₄	—	4	2	no	—
1064	C₂×C₄	—	4	2	no	—
1065	C₂×C₄	—	4	2	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	8	1	no	—
1068	C₂×C₄	—	268	4	no	—
1069	C₂×C₄	—	536	2	no	—
1070	C₂×C₄	—	536	2	no	—
1071	C₂×C₄	—	536	2	no	—
1072	C₂×C₄	—	67	2	no	—
1073	C₂×C₄	—	67	2	no	—
1074	C₂×C₄	—	67	2	no	—
1075	C₂×C₄	—	134	2	no	—
1076	C₂×C₄	—	134	2	no	—
1077	C₂×C₄	—	134	2	no	—
1078	C₂×C₄	—	134	2	no	—
1079	C₂×C₄	—	134	2	no	—
1080	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1081	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1082	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1083	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1084	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1085	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1086	C₈	—	2	1	no	—
1087	C₈	—	2	1	no	—
1088	C₈	—	2	1	no	—
1089	C₈	—	134	2	no	—
1090	C₈	—	134	2	no	—
1091	C₈	C₂×#11761628	1	2	yes	—
1092	C₂²	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	268	2	no	—
1099	C₂²	—	268	2	no	—
1100	C₂²	—	268	2	no	—
1101	C₂²	—	1072	4	no	—
1102	C₂²	—	134	2	no	—
1103	C₂²	—	134	2	no	—
1104	C₂²	—	134	2	no	—
1105	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	2	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	268	2	no	—
1118	C₄	—	268	2	no	—
1119	C₄	—	268	2	no	—
1120	C₄	—	134	2	no	—
1121	C₄	—	134	2	no	—
1122	C₄	—	134	2	no	—
1123	C₄	#16864205	1	2	yes	—
1124	C₄	C₂²×#11761628	1	1	yes	characteristic
1125	C₄	#16864232	1	1	yes	characteristic
1126	C₂	—	4	1	no	—
1127	C₂	—	4	2	no	—
1128	C₂	—	268	2	no	—
1129	C₂	—	536	2	no	—
1130	C₂	D₄×#11761628	1	1	yes	characteristic
1131	C₂	C₂×#16864205	1	1	yes	characteristic
1132	C₂	#22574993	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₆₇
commutator, cosocle	C₂×C₄×C₆₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₄×#137×C₆₇	C₂
socle	C₂²×C₆₇	C₂³×D₄
prime radical	#22574170	C₂
hypercenter	C₄×#137	D₆₇
hypocenter	C₆₇	#61540
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#137

Complements

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

N	H ≅ G/N	type
1. #22574305	C₂	semidirect
3. #22573260	C₂	semidirect
4. #22573128	C₂	semidirect
5. #22572903	C₂	semidirect
6. #22572849	C₂	semidirect
7. #22572725	C₂	semidirect
8. #22572641	C₂	semidirect
9. #22572499	C₂	semidirect
10. #22572494	C₂	semidirect
11. #22572442	C₂	semidirect
12. #22572426	C₂	semidirect
13. SD₁₆×D₂₆₈	C₂	semidirect
14. #22571713	C₂	semidirect
15. #22570927	C₂	semidirect
16. #22570883	C₂	semidirect
17. #22570460	C₂	semidirect
18. #22570442	C₂	semidirect
19. #22570280	C₂	semidirect
20. #22570240	C₂	semidirect
21. #22569213	C₂	semidirect
22. #22569065	C₂	semidirect
23. C₄×#137×C₆₇	C₂	semidirect
26. #16864125	C₂²	semidirect
28. #16864124	C₂²	semidirect
34. #16864081	C₂²	semidirect
38. Q₈×C₂²⋊D₆₇	C₂²	semidirect
45. #16864004	C₂²	semidirect
48. #16863953	C₂²	semidirect
54. #16863872	C₂²	semidirect
56. #16863803	C₂²	semidirect
57. #16863801	C₂²	semidirect
58. #16863789	C₂²	semidirect
60. #16863752	C₂²	semidirect
61. #16863747	C₂²	semidirect
62. #16863745	C₂²	semidirect
64. #16863739	C₂²	semidirect
65. #16863737	C₂²	semidirect
66. #16863736	C₂²	semidirect
67. #16863736	C₂²	semidirect
69. #16863714	C₂²	semidirect
70. #16863699	C₂²	semidirect
72. #16863689	C₂²	semidirect
73. #16863681	C₂²	semidirect
74. #16863681	C₂²	semidirect
75. #16863681	C₂²	semidirect
76. #16863680	C₂²	semidirect
78. #16863653	C₂²	semidirect
80. #16863642	C₂²	semidirect
81. #16863642	C₂²	semidirect
82. #16863634	C₂²	semidirect
84. #16863621	C₂²	semidirect
85. #16863620	C₂²	semidirect
86. #16863606	C₂²	semidirect
88. #16863600	C₂²	semidirect
93. #16863550	C₂²	semidirect
97. #16863535	C₂²	semidirect
98. #16863526	C₂²	semidirect
99. C₈×Dic₁₃₄	C₂²	semidirect
100. #16863498	C₂²	semidirect
101. #16863498	C₂²	semidirect
103. #16863495	C₂²	semidirect
104. C₄×#11761618	C₂²	semidirect
106. C₄×#11761615	C₂²	semidirect
107. C₄×#11761615	C₂²	semidirect
109. #16863481	C₂²	semidirect
111. #16863472	C₂²	semidirect
112. #16863465	C₂²	semidirect
114. #16863458	C₂²	semidirect
115. #16863449	C₂²	semidirect
116. #16863433	C₂²	semidirect
117. #16863403	C₂²	semidirect
119. #16863353	C₂²	semidirect
122. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
123. #441×C₆₇	C₂²	semidirect
124. #441×C₆₇	C₂²	semidirect
127. C₄×Q₁₆×C₆₇	C₂²	semidirect
128. C₄×Q₁₆×C₆₇	C₂²	semidirect
131. #428×C₆₇	C₂²	semidirect
132. #419×C₆₇	C₂²	semidirect
134. C₄×M₁₆×C₆₇	C₂²	semidirect
420. SD₁₆×C₆₇	#41	semidirect
589. C₄×#137	D₆₇	semidirect
590. C₆₇	#61540	semidirect
625. C₂×C₄×Q₈	C₂×D₆₇	semidirect
670. #441	C₂×D₆₇	semidirect
671. #441	C₂×D₆₇	semidirect
679. C₄×Q₁₆	C₂×D₆₇	semidirect
680. C₄×Q₁₆	C₂×D₆₇	semidirect
694. #428	C₂×D₆₇	semidirect
697. #419	C₂×D₆₇	semidirect
701. C₄×M₁₆	C₂×D₆₇	semidirect
935. SD₁₆	#11761628	semidirect

Maximal subgroups

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

subgroup	index
#22574305	2
#22574170	2
#22573260	2
#22573128	2
#22572903	2
#22572849	2
#22572725	2
#22572641	2
#22572499	2
#22572494	2
#22572442	2
#22572426	2
SD₁₆×D₂₆₈	2
#22571713	2
#22570927	2
#22570883	2
#22570460	2
#22570442	2
#22570280	2
#22570240	2
#22569213	2
#22569065	2
C₄×#137×C₆₇	2
#61540	67