Subgroups — #31740403

Order 17152.

1876 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574294	C₂	1	1	yes	maximal, characteristic, complemented
2	#22574170	C₂	1	1	yes	maximal, characteristic, complemented
3	#22573219	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₁₆×Dic₁₃₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#22573021	C₂	1	1	yes	maximal, characteristic, complemented
6	#22572999	C₂	1	1	yes	maximal, characteristic, complemented
7	#22572826	C₂	1	1	yes	maximal, characteristic, complemented
8	#22572800	C₂	1	2	yes	maximal, complemented
9	#22572396	C₂	1	2	yes	maximal, complemented
10	#22572171	C₂	1	2	yes	maximal, complemented
11	#22572150	C₂	1	1	yes	maximal, characteristic, complemented
12	#22572035	C₂	1	1	yes	maximal, characteristic, complemented
13	#22571834	C₂	1	2	yes	maximal, complemented
14	#22571830	C₂	1	1	yes	maximal, characteristic, complemented
15	#22570947	C₂	1	1	yes	maximal, characteristic, complemented
16	#22570829	C₂	1	2	yes	maximal, complemented
17	#22570484	C₂	1	2	yes	maximal, complemented
18	#22570397	C₂	1	2	yes	maximal, complemented
19	#22570269	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	#22569040	C₂	1	2	yes	maximal, complemented
23	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14524070	C₂²	1	2	yes	—
25	#16864131	—	2	1	no	—
26	#16864131	C₂²	1	1	yes	characteristic
27	#16864131	C₂²	1	1	yes	characteristic, complemented
28	Q₈×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
29	#16864119	C₂²	1	1	yes	characteristic
30	#16864109	C₂²	1	2	yes	—
31	#16864106	—	2	1	no	—
32	#16864106	C₂²	1	1	yes	characteristic
33	#16864070	—	2	2	no	—
34	#16864068	C₂²	1	1	yes	characteristic
35	D₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
36	#16864057	C₂²	1	2	yes	complemented
37	#16864055	—	2	1	no	—
38	#16864047	—	2	2	no	—
39	#16864047	C₂²	1	2	yes	complemented
40	#16864042	—	2	1	no	—
41	#16864034	C₂²	1	2	yes	—
42	D₄×D₂₆₈	C₂²	1	1	yes	characteristic
43	#16864018	—	2	2	no	—
44	#16864018	C₂²	1	2	yes	—
45	#16864018	C₂²	1	2	yes	complemented
46	#16863979	—	2	2	no	—
47	#16863946	—	2	1	no	—
48	#16863946	C₂²	1	1	yes	characteristic
49	#16863946	C₂²	1	1	yes	characteristic, complemented
50	#16863930	—	2	1	no	—
51	#16863930	—	2	1	no	—
52	#16863930	C₂²	1	1	yes	characteristic
53	C₂×#14524031	—	2	1	no	—
54	#16863878	C₂²	1	2	yes	complemented
55	#16863868	C₂²	1	2	yes	—
56	#16863794	C₂²	1	1	yes	characteristic, complemented
57	#16863793	C₂²	1	2	yes	complemented
58	#16863781	C₂²	1	2	yes	complemented
59	#16863773	C₂²	1	1	yes	characteristic
60	#16863757	C₂²	1	2	yes	complemented
61	#16863757	C₂²	1	2	yes	complemented
62	#16863743	C₂²	1	1	yes	characteristic
63	#16863743	C₂²	1	1	yes	characteristic, complemented
64	#16863735	C₂²	1	2	yes	complemented
65	#16863725	C₂²	1	2	yes	complemented
66	#16863723	C₂²	1	2	yes	complemented
67	#16863720	C₂²	1	2	yes	complemented
68	#16863716	C₂²	1	2	yes	—
69	#16863714	C₂²	1	2	yes	complemented
70	#16863691	C₂²	1	1	yes	characteristic, complemented
71	#16863686	C₂²	1	1	yes	characteristic
72	#16863685	C₂²	1	2	yes	complemented
73	#16863684	C₂²	1	2	yes	—
74	#16863681	C₂²	1	1	yes	characteristic, complemented
75	#16863681	C₂²	1	1	yes	characteristic, complemented
76	#16863679	C₂²	1	2	yes	complemented
77	#16863675	C₂²	1	2	yes	complemented
78	#16863651	C₂²	1	2	yes	complemented
79	#16863650	C₂²	1	2	yes	—
80	#16863649	C₂²	1	2	yes	complemented
81	#16863649	C₂²	1	2	yes	complemented
82	#16863628	C₂²	1	2	yes	—
83	#16863628	C₂²	1	2	yes	complemented
84	#16863620	C₂²	1	2	yes	complemented
85	#16863614	C₂²	1	2	yes	complemented
86	#16863614	C₂²	1	2	yes	complemented
87	#16863613	C₂²	1	2	yes	—
88	#16863596	C₂²	1	1	yes	characteristic
89	#16863596	C₂²	1	1	yes	characteristic
90	#16863596	C₂²	1	1	yes	characteristic, complemented
91	#16863591	C₂²	1	1	yes	characteristic
92	#16863557	C₂²	1	2	yes	complemented
93	#16863545	C₂²	1	2	yes	—
94	#16863544	C₂²	1	2	yes	—
95	#16863541	C₂²	1	2	yes	—
96	#16863535	C₂²	1	2	yes	complemented
97	#16863531	C₂²	1	2	yes	—
98	#16863526	C₂²	1	1	yes	characteristic, complemented
99	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
100	#16863509	C₂²	1	2	yes	complemented
101	#16863509	C₂²	1	2	yes	complemented
102	#16863505	C₂²	1	2	yes	—
103	#16863499	C₂²	1	2	yes	complemented
104	SD₁₆×Dic₆₇	C₂²	1	2	yes	—
105	C₄×#11761615	C₂²	1	2	yes	complemented
106	C₄×#11761615	C₂²	1	2	yes	complemented
107	C₄×#11761615	C₂²	1	2	yes	complemented
108	#16863478	C₂²	1	2	yes	complemented
109	C₄×#11761613	C₂²	1	2	yes	—
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	#16863437	C₂²	1	2	yes	complemented
117	#16863391	C₂²	1	2	yes	complemented
118	#102×D₆₇	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×#11761629	C₂³	1	2	yes	—
136	C₂×#11761628	—	2	2	no	—
137	C₂×#11761628	—	2	1	no	—
138	C₂×#11761628	—	2	1	no	—
139	C₂²×Dic₁₃₄	—	2	1	no	—
140	C₂²×D₂₆₈	—	2	1	no	—
141	C₂×D₄×D₆₇	C₂³	1	2	yes	—
142	#14524070	—	2	8	no	—
143	C₂×#11761615	C₂³	1	2	yes	—
144	C₂×#11761615	C₂³	1	2	yes	—
145	C₂×#11761615	C₂³	1	2	yes	—
146	C₂×D₅₃₆	C₂³	1	2	yes	—
147	C₂×D₅₃₆	C₂³	1	2	yes	—
148	C₂×#11761613	C₂³	1	2	yes	—
149	C₂×#11761611	C₂³	1	2	yes	—
150	C₂×C₈×D₆₇	C₂³	1	2	yes	—
151	#14524043	—	2	1	no	—
152	#14524043	C₂³	1	1	yes	characteristic
153	#14524043	C₂³	1	1	yes	characteristic
154	#14524042	—	2	2	no	—
155	#14524042	C₂³	1	2	yes	—
156	#14524042	C₂³	1	2	yes	—
157	#14524040	—	2	1	no	—
158	#14524040	C₂³	1	1	yes	characteristic
159	#14524040	C₂³	1	1	yes	characteristic
160	#14524038	—	2	2	no	—
161	#14524037	—	2	2	no	—
162	#14524037	—	2	2	no	—
163	#14524037	D₄	1	2	yes	—
164	#14524035	—	2	1	no	—
165	#14524035	D₄	1	1	yes	characteristic
166	#14524032	—	2	2	no	—
167	#14524032	C₂³	1	2	yes	—
168	#14524032	C₂³	1	2	yes	—
169	#14524031	—	2	1	no	—
170	#14524031	—	2	1	no	—
171	#14524031	—	2	1	no	—
172	#14524031	—	2	2	no	—
173	#14524031	—	2	2	no	—
174	#14524031	—	2	2	no	—
175	#14524031	—	2	1	no	—
176	#14524031	—	2	1	no	—
177	#14524031	D₄	1	1	yes	characteristic
178	#14524029	—	2	2	no	—
179	#14524028	—	2	2	no	—
180	#14524028	—	2	2	no	—
181	#14524028	—	2	2	no	—
182	#14524028	—	2	2	no	—
183	#14524028	—	2	2	no	—
184	#14524026	—	2	2	no	—
185	#14524026	—	2	2	no	—
186	#14524026	D₄	1	2	yes	—
187	#14524022	—	2	1	no	—
188	#14524022	D₄	1	1	yes	characteristic
189	#14524021	—	2	2	no	—
190	#14524021	—	2	2	no	—
191	#14524021	—	2	2	no	—
192	#14524021	—	2	2	no	—
193	#14524020	—	2	2	no	—
194	#14524019	—	2	2	no	—
195	#14524019	C₂³	1	2	yes	—
196	#14524019	C₂³	1	2	yes	—
197	#14524018	—	2	2	no	—
198	#14524018	C₂³	1	2	yes	—
199	#14524018	C₂³	1	2	yes	—
200	#14524017	—	2	2	no	—
201	#14524017	—	2	1	no	—
202	#14524017	—	2	1	no	—
203	#14524017	—	2	1	no	—
204	#14524017	D₄	1	1	yes	characteristic
205	#14524017	C₂³	1	2	yes	—
206	#14524017	C₂³	1	2	yes	—
207	#14524016	—	2	2	no	—
208	#14524015	—	2	2	no	—
209	#14524013	—	2	2	no	—
210	#14524011	—	2	2	no	—
211	Q₈×Dic₆₇	C₂³	1	2	yes	—
212	C₄×Dic₁₃₄	—	2	1	no	—
213	C₄×Dic₁₃₄	—	2	1	no	—
214	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
215	C₄×D₂₆₈	—	2	1	no	—
216	C₄×D₂₆₈	—	2	1	no	—
217	C₄×D₂₆₈	—	2	1	no	—
218	C₄×D₂₆₈	—	2	1	no	—
219	C₄×D₂₆₈	—	2	2	no	—
220	C₄×D₂₆₈	—	2	1	no	—
221	C₄×D₂₆₈	—	2	1	no	—
222	C₄×D₂₆₈	C₂³	1	2	yes	—
223	C₄×D₂₆₈	C₂³	1	2	yes	—
224	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
225	D₄×Dic₆₇	C₂³	1	2	yes	—
226	#14524005	—	2	2	no	—
227	#14524005	C₂³	1	2	yes	—
228	#14524005	C₂³	1	2	yes	—
229	C₄×C₂²⋊D₆₇	—	2	2	no	—
230	C₄×C₂²⋊D₆₇	—	2	2	no	—
231	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
232	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
233	#14524001	C₂³	1	2	yes	—
234	#14524000	—	2	2	no	—
235	#14524000	—	2	2	no	—
236	#14524000	C₂³	1	2	yes	—
237	C₄⋊C₄×D₆₇	—	2	2	no	—
238	C₄⋊C₄×D₆₇	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	#14523976	C₂³	1	2	yes	—
243	#14523975	C₂³	1	2	yes	—
244	#14523975	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	#14523967	C₂³	1	2	yes	—
253	#14523967	C₂³	1	2	yes	—
254	#14523967	C₂³	1	2	yes	—
255	#14523965	C₂³	1	2	yes	—
256	#14523965	C₂³	1	2	yes	—
257	#14523965	C₂³	1	2	yes	—
258	#14523965	C₂³	1	2	yes	—
259	#14523964	C₂³	1	2	yes	—
260	#14523963	C₂³	1	2	yes	—
261	#14523963	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	#11761629	—	2	4	no	—
316	#11761629	—	4	2	no	—
317	#11761628	—	8	2	no	—
318	#11761628	—	8	4	no	—
319	#11761628	—	8	2	no	—
320	C₂×Dic₁₃₄	—	2	1	no	—
321	C₂×Dic₁₃₄	—	2	1	no	—
322	C₂×Dic₁₃₄	—	2	2	no	—
323	C₂×Dic₁₃₄	—	2	2	no	—
324	C₂×Dic₁₃₄	—	8	2	no	—
325	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
326	C₂×D₂₆₈	—	2	2	no	—
327	C₂×D₂₆₈	—	2	1	no	—
328	C₂×D₂₆₈	—	2	1	no	—
329	C₂×D₂₆₈	—	2	2	no	—
330	C₂×D₂₆₈	—	2	2	no	—
331	C₂×D₂₆₈	—	2	1	no	—
332	C₂×D₂₆₈	—	2	1	no	—
333	C₂×D₂₆₈	—	8	2	no	—
334	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
335	C₂×D₂₆₈	C₂⁴	1	2	yes	—
336	C₂×D₂₆₈	C₂⁴	1	2	yes	—
337	C₂×C₂²⋊D₆₇	—	2	2	no	—
338	C₂×C₂²⋊D₆₇	—	2	2	no	—
339	C₂×C₂²⋊D₆₇	—	2	2	no	—
340	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
341	D₄×D₆₇	—	2	4	no	—
342	D₄×D₆₇	—	4	2	no	—
343	C₂²×Dic₆₇	—	2	2	no	—
344	C₂×C₄×D₆₇	—	2	2	no	—
345	C₂×C₄×D₆₇	—	2	2	no	—
346	C₂×C₄×D₆₇	—	2	2	no	—
347	C₂×C₄×D₆₇	—	2	2	no	—
348	C₂×C₄×D₆₇	—	2	2	no	—
349	C₂×C₄×D₆₇	—	2	2	no	—
350	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
351	#11761615	—	2	4	no	—
352	#11761615	—	4	2	no	—
353	#11761615	—	4	2	no	—
354	D₅₃₆	—	2	4	no	—
355	D₅₃₆	—	4	2	no	—
356	#11761613	—	2	4	no	—
357	#11761611	—	2	4	no	—
358	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
359	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
360	C₈×D₆₇	—	4	2	no	—
361	C₄⋊Dic₆₇	—	2	1	no	—
362	C₄⋊Dic₆₇	—	2	1	no	—
363	C₄⋊Dic₆₇	—	2	2	no	—
364	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
365	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
366	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
367	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
368	Dic₆₇⋊C₄	—	2	2	no	—
369	Dic₆₇⋊C₄	—	2	2	no	—
370	Dic₆₇⋊C₄	—	2	2	no	—
371	Dic₆₇⋊C₄	—	2	2	no	—
372	Dic₆₇⋊C₄	—	2	2	no	—
373	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
374	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
375	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
376	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
377	C₂²⋊Dic₆₇	—	2	2	no	—
378	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
390	(C₂×D₆₇)⋊C₄	—	2	2	no	—
391	(C₂×D₆₇)⋊C₄	—	2	2	no	—
392	(C₂×D₆₇)⋊C₄	—	2	2	no	—
393	(C₂×D₆₇)⋊C₄	—	2	2	no	—
394	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
395	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
396	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
397	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
398	C₄×Dic₆₇	—	2	2	no	—
399	C₄×Dic₆₇	—	2	2	no	—
400	C₄×Dic₆₇	C₂⁴	1	2	yes	—
401	#41×C₆₇	—	2	2	no	—
402	#41×C₆₇	—	4	1	no	—
403	C₂×Q₈×C₆₇	—	2	1	no	—
404	C₂×Q₈×C₆₇	—	2	2	no	—
405	C₂×Q₈×C₆₇	—	4	1	no	—
406	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
407	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂×D₄×C₆₇	—	2	1	no	—
410	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
415	C₂²×C₄×C₆₇	—	2	1	no	—
416	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
417	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
418	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	Q₁₆×C₆₇	—	2	2	no	—
420	Q₁₆×C₆₇	—	2	2	no	—
421	SD₁₆×C₆₇	—	2	2	no	—
422	SD₁₆×C₆₇	#41	1	4	yes	complemented
423	M₁₆×C₆₇	—	2	2	no	—
424	M₁₆×C₆₇	—	4	1	no	—
425	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
427	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
428	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
435	C₄⋊C₄×C₆₇	—	2	1	no	—
436	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄×C₆₇	—	2	1	no	—
441	C₂²⋊C₄×C₆₇	—	2	1	no	—
442	C₂²⋊C₄×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	—	2	1	no	—
449	C₄²×C₆₇	—	2	1	no	—
450	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
453	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₂³×C₆₇	—	2	1	no	—
455	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
456	C₂²×D₆₇	—	2	2	no	—
457	C₂²×D₆₇	—	2	2	no	—
458	C₂²×D₆₇	—	4	4	no	—
459	C₂²×D₆₇	—	8	2	no	—
460	C₂²×D₆₇	—	8	2	no	—
461	C₂²×D₆₇	C₂²×D₄	1	2	yes	—
462	Q₈×C₆₇	—	2	1	no	—
463	Q₈×C₆₇	—	2	1	no	—
464	Q₈×C₆₇	—	2	1	no	—
465	Q₈×C₆₇	—	2	1	no	—
466	Q₈×C₆₇	—	2	1	no	—
467	Q₈×C₆₇	—	4	2	no	—
468	Q₈×C₆₇	C₂×#41	1	2	yes	—
469	D₄×C₆₇	—	2	1	no	—
470	D₄×C₆₇	—	4	2	no	—
471	D₄×C₆₇	C₂×#41	1	2	yes	—
472	C₂×C₄×C₆₇	—	2	1	no	—
473	C₂×C₄×C₆₇	—	2	2	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	—	2	1	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	1	no	—
482	C₂×C₄×C₆₇	—	4	1	no	—
483	C₂×C₄×C₆₇	—	4	2	no	—
484	C₂×C₄×C₆₇	—	4	2	no	—
485	C₂×C₄×C₆₇	—	4	2	no	—
486	C₂×C₄×C₆₇	—	4	2	no	—
487	C₂×C₄×C₆₇	—	8	1	no	—
488	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
494	C₂²⋊D₆₇	—	4	2	no	—
495	C₂²⋊D₆₇	—	4	4	no	—
496	C₂²⋊D₆₇	—	4	4	no	—
497	C₂²⋊D₆₇	—	8	2	no	—
498	C₂×Dic₆₇	—	2	2	no	—
499	C₂×Dic₆₇	—	2	2	no	—
500	C₂×Dic₆₇	—	8	2	no	—
501	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
502	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
503	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
504	D₂₆₈	—	2	2	no	—
505	D₂₆₈	—	2	2	no	—
506	D₂₆₈	—	2	2	no	—
507	D₂₆₈	—	2	2	no	—
508	D₂₆₈	—	2	2	no	—
509	D₂₆₈	—	4	4	no	—
510	D₂₆₈	—	4	2	no	—
511	D₂₆₈	—	4	2	no	—
512	D₂₆₈	—	8	1	no	—
513	D₂₆₈	—	8	1	no	—
514	D₂₆₈	—	8	2	no	—
515	D₂₆₈	—	8	2	no	—
516	C₄×D₆₇	—	2	2	no	—
517	C₄×D₆₇	—	2	2	no	—
518	C₄×D₆₇	—	4	4	no	—
519	C₄×D₆₇	—	8	2	no	—
520	C₄×D₆₇	—	8	2	no	—
521	C₄×D₆₇	—	8	2	no	—
522	C₄×D₆₇	—	8	2	no	—
523	C₄×D₆₇	—	8	2	no	—
524	Dic₁₃₄	—	2	2	no	—
525	Dic₁₃₄	—	4	2	no	—
526	Dic₁₃₄	—	8	2	no	—
527	Dic₁₃₄	—	8	2	no	—
528	Dic₁₃₄	—	8	1	no	—
529	C₈×C₆₇	—	2	1	no	—
530	C₈×C₆₇	—	2	1	no	—
531	C₈×C₆₇	—	2	1	no	—
532	C₈×C₆₇	C₂×#41	1	2	yes	—
533	C₆₇⋊C₈	—	2	2	no	—
534	C₆₇⋊C₈	—	2	2	no	—
535	C₂²×C₆₇	—	2	1	no	—
536	C₂²×C₆₇	—	2	2	no	—
537	C₂²×C₆₇	—	2	1	no	—
538	C₂²×C₆₇	—	2	1	no	—
539	C₂²×C₆₇	—	4	1	no	—
540	C₂²×C₆₇	—	4	1	no	—
541	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
542	C₂×D₆₇	—	2	2	no	—
543	C₂×D₆₇	—	2	2	no	—
544	C₂×D₆₇	—	2	2	no	—
545	C₂×D₆₇	—	4	2	no	—
546	C₂×D₆₇	—	4	2	no	—
547	C₂×D₆₇	—	4	2	no	—
548	C₂×D₆₇	—	4	2	no	—
549	C₂×D₆₇	—	4	2	no	—
550	C₂×D₆₇	—	4	2	no	—
551	C₂×D₆₇	—	16	4	no	—
552	C₄×C₆₇	—	2	1	no	—
553	C₄×C₆₇	—	2	1	no	—
554	C₄×C₆₇	—	2	2	no	—
555	C₄×C₆₇	—	2	1	no	—
556	C₄×C₆₇	—	2	1	no	—
557	C₄×C₆₇	—	4	1	no	—
558	C₄×C₆₇	—	4	1	no	—
559	C₄×C₆₇	—	4	1	no	—
560	C₄×C₆₇	—	4	1	no	—
561	C₄×C₆₇	—	4	1	no	—
562	C₄×C₆₇	—	4	1	no	—
563	C₄×C₆₇	#577	1	2	yes	—
564	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
565	C₄×C₆₇	#585	1	1	yes	characteristic
566	Dic₆₇	—	2	2	no	—
567	Dic₆₇	—	2	2	no	—
568	Dic₆₇	—	2	2	no	—
569	Dic₆₇	—	4	2	no	—
570	Dic₆₇	—	4	2	no	—
571	#61554	—	67	1	no	maximal, Sylow
572	C₂×C₆₇	—	4	2	no	—
573	C₂×C₆₇	—	4	1	no	—
574	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
575	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
576	C₂×C₆₇	#3585	1	1	yes	characteristic
577	D₆₇	—	4	2	no	—
578	D₆₇	—	8	2	no	—
579	D₆₇	—	8	2	no	—
580	#3522	—	67	1	no	—
581	#3514	—	67	1	no	—
582	#3396	—	67	1	no	—
583	Q₈×SD₁₆	—	67	1	no	—
584	#3375	—	67	1	no	—
585	#3373	—	67	1	no	—
586	#3356	—	67	1	no	—
587	#3354	—	67	2	no	—
588	#3321	—	67	2	no	—
589	#3306	—	67	2	no	—
590	#3304	—	67	1	no	—
591	#3295	—	67	1	no	—
592	#3275	—	67	2	no	—
593	#3274	—	67	1	no	—
594	#3184	—	67	1	no	—
595	#3173	—	67	2	no	—
596	#3125	—	67	2	no	—
597	#3118	—	67	2	no	—
598	#3106	—	67	1	no	—
599	#3103	—	67	1	no	—
600	#2969	—	67	1	no	—
601	#2946	—	67	2	no	—
602	C₄×#137	D₆₇	1	1	yes	characteristic, complemented
603	C₆₇	#61554	1	1	yes	characteristic, complemented, Sylow
604	C₂×#137	C₂×D₆₇	1	1	yes	characteristic
605	C₂×AGL(1,ℤ/8)	—	67	2	no	—
606	#559	—	67	1	no	—
607	#559	—	67	1	no	—
608	#559	—	134	1	no	—
609	Q₈²	—	67	1	no	—
610	#556	—	67	1	no	—
611	#555	—	67	2	no	—
612	#554	—	67	1	no	—
613	#554	—	134	1	no	—
614	#551	—	134	2	no	—
615	#550	—	67	1	no	—
616	D₄×Q₈	—	67	1	no	—
617	#548	—	67	2	no	—
618	#548	—	134	1	no	—
619	#547	—	67	2	no	—
620	#547	—	134	2	no	—
621	#546	—	67	2	no	—
622	#546	—	134	1	no	—
623	D₄²	—	67	1	no	—
624	#542	—	67	2	no	—
625	#542	—	67	2	no	—
626	#542	—	134	2	no	—
627	#538	—	134	2	no	—
628	#532	—	67	1	no	—
629	#532	—	67	1	no	—
630	#532	—	134	1	no	—
631	#529	—	67	1	no	—
632	#529	—	134	1	no	—
633	#529	—	134	1	no	—
634	C₂×#124	—	134	1	no	—
635	#520	—	67	2	no	—
636	#518	—	67	2	no	—
637	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
638	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
639	#498	—	67	2	no	—
640	#498	—	67	1	no	—
641	#495	—	67	2	no	—
642	#493	—	67	1	no	—
643	#489	—	67	2	no	—
644	#489	—	67	2	no	—
645	#486	—	67	1	no	—
646	#486	—	67	1	no	—
647	#485	—	67	2	no	—
648	#483	—	67	2	no	—
649	#482	—	67	2	no	—
650	#482	—	67	2	no	—
651	#481	—	67	2	no	—
652	#481	—	67	2	no	—
653	#477	—	67	1	no	—
654	#476	—	67	1	no	—
655	#476	—	67	2	no	—
656	#476	—	67	2	no	—
657	#475	—	67	1	no	—
658	#475	—	67	1	no	—
659	#475	—	67	2	no	—
660	#474	—	67	2	no	—
661	#470	—	67	2	no	—
662	#469	—	67	2	no	—
663	#469	—	67	2	no	—
664	#469	—	67	2	no	—
665	#465	—	67	2	no	—
666	#465	—	67	2	no	—
667	#464	—	67	2	no	—
668	#463	—	67	2	no	—
669	#463	—	67	2	no	—
670	#463	—	67	2	no	—
671	#460	—	67	1	no	—
672	#460	—	67	1	no	—
673	#460	—	67	1	no	—
674	#459	—	67	1	no	—
675	#452	—	67	2	no	—
676	#450	—	67	2	no	—
677	#449	—	67	2	no	—
678	#449	—	67	2	no	—
679	#448	—	67	2	no	—
680	#447	—	67	2	no	—
681	#446	—	67	1	no	—
682	C₈×Q₈	—	67	1	no	—
683	#442	—	67	2	no	—
684	#442	—	67	2	no	—
685	#442	—	67	2	no	—
686	#441	C₂×D₆₇	1	1	yes	characteristic, complemented
687	#441	C₂×D₆₇	1	1	yes	characteristic, complemented
688	#440	—	67	2	no	—
689	#440	C₂×D₆₇	1	1	yes	characteristic
690	#440	C₂×D₆₇	1	1	yes	characteristic
691	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
692	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
693	C₄×SD₁₆	—	67	2	no	—
694	C₄×SD₁₆	—	67	2	no	—
695	C₄×SD₁₆	—	67	2	no	—
696	C₄×SD₁₆	—	67	2	no	—
697	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic
698	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic
699	C₄×D₈	—	67	2	no	—
700	C₄×D₈	—	67	2	no	—
701	#436	—	67	2	no	—
702	#436	—	67	1	no	—
703	#435	—	67	2	no	—
704	C₈×D₄	—	67	1	no	—
705	#433	—	67	2	no	—
706	#431	—	67	1	no	—
707	#428	—	67	2	no	—
708	#428	C₂×D₆₇	1	1	yes	characteristic, complemented
709	#419	C₂×D₆₇	1	1	yes	characteristic, complemented
710	#417	C₂×D₆₇	1	1	yes	characteristic
711	#416	—	67	2	no	—
712	C₂×#102	—	67	2	no	—
713	#405	—	67	2	no	—
714	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
715	C₂×#41	—	67	2	no	—
716	C₂×#41	—	134	2	no	—
717	C₂×#41	—	134	1	no	—
718	C₂×#41	—	134	1	no	—
719	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
720	C₂²×Q₈	—	134	1	no	—
721	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
722	C₂²×D₄	—	67	2	no	—
723	C₂²×D₄	—	134	1	no	—
724	#137	—	2	4	no	—
725	AGL(1,ℤ/8)	—	134	8	no	—
726	C₂×Q₁₆	C₂²×D₆₇	1	1	yes	characteristic
727	C₂×Q₁₆	C₂²×D₆₇	1	1	yes	characteristic
728	C₂×SD₁₆	—	67	2	no	—
729	C₂×SD₁₆	—	67	2	no	—
730	C₂×SD₁₆	—	67	2	no	—
731	C₂×SD₁₆	C₂²×D₆₇	1	1	yes	characteristic
732	C₂×SD₁₆	C₂²×D₆₇	1	1	yes	characteristic
733	C₂×D₈	—	67	2	no	—
734	C₂×D₈	—	67	2	no	—
735	C₂×D₈	—	67	2	no	—
736	C₂×M₁₆	—	67	2	no	—
737	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
738	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
739	C₂²×C₈	—	67	2	no	—
740	C₄⋊Q₈	—	67	2	no	—
741	C₄⋊Q₈	—	67	2	no	—
742	C₄⋊Q₈	—	67	1	no	—
743	C₄⋊Q₈	—	67	1	no	—
744	C₄⋊Q₈	—	134	1	no	—
745	C₄⋊Q₈	—	134	2	no	—
746	#127	—	67	1	no	—
747	#127	—	67	1	no	—
748	#127	—	134	1	no	—
749	#126	—	67	2	no	—
750	#126	—	134	2	no	—
751	#126	—	134	2	no	—
752	#126	—	134	2	no	—
753	#125	—	67	1	no	—
754	#125	—	134	1	no	—
755	#124	—	67	2	no	—
756	#124	—	67	2	no	—
757	#124	—	67	1	no	—
758	#124	—	134	2	no	—
759	#124	—	134	2	no	—
760	#124	—	134	2	no	—
761	#124	—	134	1	no	—
762	#124	—	134	1	no	—
763	#124	—	134	1	no	—
764	#124	—	134	2	no	—
765	#124	—	134	2	no	—
766	#124	—	134	1	no	—
767	#124	—	134	1	no	—
768	#123	—	67	2	no	—
769	#123	—	134	2	no	—
770	#123	—	134	2	no	—
771	#123	—	134	2	no	—
772	#123	—	134	2	no	—
773	#123	—	134	2	no	—
774	#123	—	134	2	no	—
775	#123	—	134	2	no	—
776	C₂²⋊Q₈	—	67	1	no	—
777	C₂²⋊Q₈	—	67	2	no	—
778	C₂²⋊Q₈	—	67	2	no	—
779	C₂²⋊Q₈	—	134	2	no	—
780	C₂²⋊Q₈	—	134	2	no	—
781	C₂²⋊Q₈	—	134	2	no	—
782	C₂²⋊Q₈	—	134	2	no	—
783	C₂²⋊Q₈	—	134	2	no	—
784	C₂²⋊Q₈	—	134	1	no	—
785	C₂²⋊Q₈	—	134	2	no	—
786	#121	—	67	1	no	—
787	#121	—	67	2	no	—
788	#121	—	67	2	no	—
789	#121	—	67	2	no	—
790	#121	—	67	2	no	—
791	#121	—	134	2	no	—
792	#121	—	134	2	no	—
793	#121	—	134	2	no	—
794	#121	—	134	1	no	—
795	#121	—	134	2	no	—
796	#121	—	134	1	no	—
797	#121	—	134	1	no	—
798	#120	—	134	2	no	—
799	#120	—	134	2	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	67	1	no	—
803	C₄×Q₈	—	67	2	no	—
804	C₄×Q₈	—	134	1	no	—
805	C₄×Q₈	—	134	1	no	—
806	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
807	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
808	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
809	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
810	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
811	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	67	2	no	—
815	C₄×D₄	—	67	2	no	—
816	C₄×D₄	—	67	2	no	—
817	C₄×D₄	—	67	2	no	—
818	C₄×D₄	—	67	1	no	—
819	C₄×D₄	—	67	2	no	—
820	C₄×D₄	—	67	2	no	—
821	C₄×D₄	—	134	2	no	—
822	C₄×D₄	—	134	1	no	—
823	C₄×D₄	—	134	1	no	—
824	C₄×D₄	—	134	1	no	—
825	C₄×D₄	—	134	1	no	—
826	C₄×D₄	—	134	2	no	—
827	C₄×D₄	—	134	2	no	—
828	C₄×D₄	—	134	2	no	—
829	C₄×D₄	—	134	2	no	—
830	C₄×D₄	—	134	1	no	—
831	C₄×D₄	—	134	1	no	—
832	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
833	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
834	#117	—	2	1	no	—
835	#117	—	67	2	no	—
836	#117	—	67	2	no	—
837	#117	—	134	2	no	—
838	#117	—	134	2	no	—
839	#117	C₂²×D₆₇	1	1	yes	characteristic
840	C₂×C₄⋊C₄	—	2	1	no	—
841	C₂×C₄⋊C₄	—	67	2	no	—
842	C₂×C₄⋊C₄	—	134	2	no	—
843	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
844	C₂×C₂²⋊C₄	—	134	2	no	—
845	C₂×C₂²⋊C₄	—	134	2	no	—
846	C₂×C₂²⋊C₄	—	134	2	no	—
847	C₂×C₄²	—	2	1	no	—
848	C₂×C₄²	—	2	1	no	—
849	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
850	#107	—	67	2	no	—
851	#107	C₂²×D₆₇	1	1	yes	characteristic
852	#107	C₂²×D₆₇	1	1	yes	characteristic
853	#106	—	67	2	no	—
854	#106	—	67	2	no	—
855	#106	—	67	2	no	—
856	#106	—	67	2	no	—
857	#106	—	67	2	no	—
858	#106	C₂²×D₆₇	1	1	yes	characteristic
859	#106	C₂²×D₆₇	1	1	yes	characteristic
860	C₄⋊C₈	—	67	2	no	—
861	C₄⋊C₈	—	67	2	no	—
862	C₄⋊C₈	—	67	1	no	—
863	C₄⋊C₈	—	67	1	no	—
864	#103	—	67	2	no	—
865	#103	—	67	2	no	—
866	#103	—	67	2	no	—
867	#103	C₂²×D₆₇	1	1	yes	characteristic
868	#103	C₂²×D₆₇	1	1	yes	characteristic
869	#103	C₂²×D₆₇	1	1	yes	characteristic
870	#103	C₂²×D₆₇	1	1	yes	characteristic
871	#103	C₂²×D₆₇	1	1	yes	characteristic
872	#103	C₂²×D₆₇	1	1	yes	characteristic
873	#102	—	67	2	no	—
874	#102	—	67	2	no	—
875	#102	—	67	2	no	—
876	#102	—	67	2	no	—
877	#102	—	67	2	no	—
878	#102	—	67	2	no	—
879	#102	—	67	2	no	—
880	#102	—	67	2	no	—
881	#102	—	67	2	no	—
882	#102	C₂²×D₆₇	1	1	yes	characteristic
883	#102	C₂²×D₆₇	1	1	yes	characteristic
884	C₂²⋊C₈	—	67	2	no	—
885	C₂²⋊C₈	—	67	2	no	—
886	C₂²⋊C₈	—	67	2	no	—
887	#97	—	67	2	no	—
888	#97	C₂²×D₆₇	1	1	yes	characteristic
889	#97	C₂²×D₆₇	1	1	yes	characteristic
890	C₄×C₈	—	67	2	no	—
891	C₄×C₈	—	67	2	no	—
892	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
893	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
894	C₂⁴	—	134	2	no	—
895	#41	—	2	2	no	—
896	#41	—	4	1	no	—
897	#41	—	268	2	no	—
898	#41	—	536	2	no	—
899	#41	—	536	2	no	—
900	#41	—	536	4	no	—
901	#41	—	134	4	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	4	1	no	—
905	C₂×Q₈	—	536	2	no	—
906	C₂×Q₈	—	67	1	no	—
907	C₂×Q₈	—	134	2	no	—
908	C₂×Q₈	—	134	2	no	—
909	C₂×Q₈	—	134	1	no	—
910	C₂×Q₈	—	134	1	no	—
911	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
912	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
913	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	268	2	no	—
916	C₂×D₄	—	536	2	no	—
917	C₂×D₄	—	67	2	no	—
918	C₂×D₄	—	67	1	no	—
919	C₂×D₄	—	67	2	no	—
920	C₂×D₄	—	67	2	no	—
921	C₂×D₄	—	134	2	no	—
922	C₂×D₄	—	134	2	no	—
923	C₂×D₄	—	134	2	no	—
924	C₂×D₄	—	134	2	no	—
925	C₂×D₄	—	134	2	no	—
926	C₂×D₄	—	134	4	no	—
927	C₂×D₄	—	134	2	no	—
928	C₂×D₄	—	134	1	no	—
929	C₂×D₄	—	134	1	no	—
930	C₂×D₄	—	134	1	no	—
931	C₂×D₄	—	134	1	no	—
932	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	67	2	no	—
939	C₂²×C₄	—	134	2	no	—
940	C₂²×C₄	—	134	2	no	—
941	C₂²×C₄	—	134	2	no	—
942	C₂²×C₄	—	134	2	no	—
943	C₂²×C₄	—	134	2	no	—
944	C₂²×C₄	—	134	2	no	—
945	C₂²×C₄	—	134	2	no	—
946	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
947	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
948	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
949	Q₁₆	—	2	2	no	—
950	Q₁₆	—	2	2	no	—
951	SD₁₆	—	2	2	no	—
952	SD₁₆	—	268	2	no	—
953	SD₁₆	—	268	2	no	—
954	SD₁₆	—	134	4	no	—
955	SD₁₆	#11761628	1	4	yes	complemented
956	D₈	—	268	2	no	—
957	D₈	—	134	4	no	—
958	D₈	—	134	4	no	—
959	M₁₆	—	2	2	no	—
960	M₁₆	—	4	1	no	—
961	M₁₆	—	134	4	no	—
962	C₂×C₈	—	268	2	no	—
963	C₂×C₈	—	67	2	no	—
964	C₂×C₈	—	67	2	no	—
965	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
966	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
967	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
968	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	67	2	no	—
977	C₄⋊C₄	—	67	2	no	—
978	C₄⋊C₄	—	67	2	no	—
979	C₄⋊C₄	—	67	1	no	—
980	C₄⋊C₄	—	67	1	no	—
981	C₄⋊C₄	—	67	2	no	—
982	C₄⋊C₄	—	67	2	no	—
983	C₄⋊C₄	—	67	2	no	—
984	C₄⋊C₄	—	134	2	no	—
985	C₄⋊C₄	—	134	2	no	—
986	C₄⋊C₄	—	134	2	no	—
987	C₄⋊C₄	—	134	2	no	—
988	C₄⋊C₄	—	134	2	no	—
989	C₄⋊C₄	—	134	2	no	—
990	C₄⋊C₄	—	134	1	no	—
991	C₄⋊C₄	—	134	1	no	—
992	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
993	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
994	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
995	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	67	2	no	—
1000	C₂²⋊C₄	—	67	2	no	—
1001	C₂²⋊C₄	—	67	2	no	—
1002	C₂²⋊C₄	—	67	2	no	—
1003	C₂²⋊C₄	—	67	2	no	—
1004	C₂²⋊C₄	—	134	2	no	—
1005	C₂²⋊C₄	—	134	2	no	—
1006	C₂²⋊C₄	—	134	2	no	—
1007	C₂²⋊C₄	—	134	2	no	—
1008	C₂²⋊C₄	—	134	2	no	—
1009	C₂²⋊C₄	—	134	2	no	—
1010	C₂²⋊C₄	—	134	2	no	—
1011	C₂²⋊C₄	—	134	2	no	—
1012	C₂²⋊C₄	—	134	2	no	—
1013	C₂²⋊C₄	—	134	2	no	—
1014	C₂²⋊C₄	—	134	2	no	—
1015	C₂²⋊C₄	—	134	2	no	—
1016	C₂²⋊C₄	—	134	2	no	—
1017	C₂²⋊C₄	—	134	2	no	—
1018	C₂²⋊C₄	—	134	2	no	—
1019	C₂²⋊C₄	—	134	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	67	2	no	—
1028	C₄²	—	134	2	no	—
1029	C₄²	—	134	2	no	—
1030	C₄²	D₄×D₆₇	1	1	yes	characteristic
1031	C₄²	D₄×D₆₇	1	1	yes	characteristic
1032	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1033	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1034	C₂³	—	2	1	no	—
1035	C₂³	—	268	4	no	—
1036	C₂³	—	536	2	no	—
1037	C₂³	—	536	2	no	—
1038	C₂³	—	67	2	no	—
1039	C₂³	—	134	2	no	—
1040	C₂³	—	134	2	no	—
1041	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	4	2	no	—
1048	Q₈	—	268	2	no	—
1049	Q₈	—	536	1	no	—
1050	Q₈	—	536	2	no	—
1051	Q₈	—	536	2	no	—
1052	Q₈	—	134	2	no	—
1053	Q₈	C₂×#11761628	1	2	yes	—
1054	D₄	—	2	1	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	268	4	no	—
1057	D₄	—	268	4	no	—
1058	D₄	—	268	4	no	—
1059	D₄	—	268	2	no	—
1060	D₄	—	268	2	no	—
1061	D₄	—	268	2	no	—
1062	D₄	—	536	1	no	—
1063	D₄	—	536	1	no	—
1064	D₄	—	536	2	no	—
1065	D₄	—	536	2	no	—
1066	D₄	—	536	2	no	—
1067	D₄	—	134	2	no	—
1068	D₄	—	134	2	no	—
1069	D₄	—	134	2	no	—
1070	D₄	—	134	2	no	—
1071	D₄	—	134	2	no	—
1072	D₄	C₂×#11761628	1	2	yes	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	4	1	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	8	1	no	—
1089	C₂×C₄	—	268	4	no	—
1090	C₂×C₄	—	536	2	no	—
1091	C₂×C₄	—	536	2	no	—
1092	C₂×C₄	—	536	2	no	—
1093	C₂×C₄	—	536	2	no	—
1094	C₂×C₄	—	536	2	no	—
1095	C₂×C₄	—	536	2	no	—
1096	C₂×C₄	—	67	2	no	—
1097	C₂×C₄	—	67	2	no	—
1098	C₂×C₄	—	67	2	no	—
1099	C₂×C₄	—	134	2	no	—
1100	C₂×C₄	—	134	2	no	—
1101	C₂×C₄	—	134	2	no	—
1102	C₂×C₄	—	134	2	no	—
1103	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1104	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1105	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1106	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1107	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1108	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	134	2	no	—
1113	C₈	—	134	2	no	—
1114	C₈	C₂×#11761628	1	2	yes	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	268	2	no	—
1122	C₂²	—	268	2	no	—
1123	C₂²	—	268	2	no	—
1124	C₂²	—	268	2	no	—
1125	C₂²	—	268	2	no	—
1126	C₂²	—	268	2	no	—
1127	C₂²	—	1072	4	no	—
1128	C₂²	—	134	2	no	—
1129	C₂²	—	134	2	no	—
1130	C₂²	—	134	2	no	—
1131	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	268	2	no	—
1144	C₄	—	268	2	no	—
1145	C₄	—	134	2	no	—
1146	C₄	—	134	2	no	—
1147	C₄	—	134	2	no	—
1148	C₄	#16864205	1	2	yes	—
1149	C₄	C₂²×#11761628	1	1	yes	characteristic
1150	C₄	#16864232	1	1	yes	characteristic
1151	C₂	—	4	1	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	268	2	no	—
1154	C₂	—	536	2	no	—
1155	C₂	—	536	2	no	—
1156	C₂	D₄×#11761628	1	1	yes	characteristic
1157	C₂	C₂×#16864205	1	1	yes	characteristic
1158	C₂	#22574986	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
hypercenter	C₄×#137	D₆₇
hypocenter	C₆₇	#61554
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. #22574294	C₂	semidirect
2. #22574170	C₂	semidirect
3. #22573219	C₂	semidirect
4. SD₁₆×Dic₁₃₄	C₂	semidirect
5. #22573021	C₂	semidirect
6. #22572999	C₂	semidirect
7. #22572826	C₂	semidirect
8. #22572800	C₂	semidirect
9. #22572396	C₂	semidirect
10. #22572171	C₂	semidirect
11. #22572150	C₂	semidirect
12. #22572035	C₂	semidirect
13. #22571834	C₂	semidirect
14. #22571830	C₂	semidirect
15. #22570947	C₂	semidirect
16. #22570829	C₂	semidirect
17. #22570484	C₂	semidirect
18. #22570397	C₂	semidirect
19. #22570269	C₂	semidirect
20. #22570240	C₂	semidirect
21. #22569213	C₂	semidirect
22. #22569040	C₂	semidirect
23. C₄×#137×C₆₇	C₂	semidirect
27. #16864131	C₂²	semidirect
28. Q₈×Dic₁₃₄	C₂²	semidirect
36. #16864057	C₂²	semidirect
39. #16864047	C₂²	semidirect
45. #16864018	C₂²	semidirect
49. #16863946	C₂²	semidirect
54. #16863878	C₂²	semidirect
56. #16863794	C₂²	semidirect
57. #16863793	C₂²	semidirect
58. #16863781	C₂²	semidirect
60. #16863757	C₂²	semidirect
61. #16863757	C₂²	semidirect
63. #16863743	C₂²	semidirect
64. #16863735	C₂²	semidirect
65. #16863725	C₂²	semidirect
66. #16863723	C₂²	semidirect
67. #16863720	C₂²	semidirect
69. #16863714	C₂²	semidirect
70. #16863691	C₂²	semidirect
72. #16863685	C₂²	semidirect
74. #16863681	C₂²	semidirect
75. #16863681	C₂²	semidirect
76. #16863679	C₂²	semidirect
77. #16863675	C₂²	semidirect
78. #16863651	C₂²	semidirect
80. #16863649	C₂²	semidirect
81. #16863649	C₂²	semidirect
83. #16863628	C₂²	semidirect
84. #16863620	C₂²	semidirect
85. #16863614	C₂²	semidirect
86. #16863614	C₂²	semidirect
90. #16863596	C₂²	semidirect
92. #16863557	C₂²	semidirect
96. #16863535	C₂²	semidirect
98. #16863526	C₂²	semidirect
99. C₈×Dic₁₃₄	C₂²	semidirect
100. #16863509	C₂²	semidirect
101. #16863509	C₂²	semidirect
103. #16863499	C₂²	semidirect
105. C₄×#11761615	C₂²	semidirect
106. C₄×#11761615	C₂²	semidirect
107. C₄×#11761615	C₂²	semidirect
108. #16863478	C₂²	semidirect
111. #16863472	C₂²	semidirect
112. #16863465	C₂²	semidirect
114. #16863458	C₂²	semidirect
115. #16863449	C₂²	semidirect
116. #16863437	C₂²	semidirect
117. #16863391	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
422. SD₁₆×C₆₇	#41	semidirect
602. C₄×#137	D₆₇	semidirect
603. C₆₇	#61554	semidirect
638. C₂×C₄×Q₈	C₂×D₆₇	semidirect
686. #441	C₂×D₆₇	semidirect
687. #441	C₂×D₆₇	semidirect
691. C₄×Q₁₆	C₂×D₆₇	semidirect
692. C₄×Q₁₆	C₂×D₆₇	semidirect
708. #428	C₂×D₆₇	semidirect
709. #419	C₂×D₆₇	semidirect
714. C₄×M₁₆	C₂×D₆₇	semidirect
955. SD₁₆	#11761628	semidirect

Maximal subgroups

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

subgroup	index
#22574294	2
#22574170	2
#22573219	2
SD₁₆×Dic₁₃₄	2
#22573021	2
#22572999	2
#22572826	2
#22572800	2
#22572396	2
#22572171	2
#22572150	2
#22572035	2
#22571834	2
#22571830	2
#22570947	2
#22570829	2
#22570484	2
#22570397	2
#22570269	2
#22570240	2
#22569213	2
#22569040	2
C₄×#137×C₆₇	2
#61554	67