Subgroups — #31736683

Order 17152.

1758 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574035	C₂	1	1	yes	maximal, characteristic, complemented
2	#22574010	C₂	1	1	yes	maximal, characteristic, complemented
3	#22573167	C₂	1	2	yes	maximal, complemented
4	#22573162	C₂	1	2	yes	maximal, complemented
5	#22573161	C₂	1	2	yes	maximal, complemented
6	#22573152	C₂	1	2	yes	maximal, complemented
7	#22573133	C₂	1	2	yes	maximal, complemented
8	#22573103	C₂	1	2	yes	maximal, complemented
9	#22573087	C₂	1	2	yes	maximal, complemented
10	#22573071	C₂	1	2	yes	maximal, complemented
11	#22570762	C₂	1	1	yes	maximal, characteristic, complemented
12	#22570749	C₂	1	1	yes	maximal, characteristic, complemented
13	#22570741	C₂	1	1	yes	maximal, characteristic, complemented
14	#22570069	C₂	1	1	yes	maximal, characteristic, complemented
15	#22570058	C₂	1	1	yes	maximal, characteristic, complemented
16	#22570043	C₂	1	1	yes	maximal, characteristic, complemented
17	#22570043	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16863697	C₂	1	1	yes	maximal, characteristic, complemented
19	#22569152	C₂	1	1	yes	maximal, characteristic, complemented
20	#22569044	C₂	1	1	yes	maximal, characteristic
21	#22569044	C₂	1	1	yes	maximal, characteristic
22	C₄×#14524068	C₂	1	1	yes	maximal, characteristic
23	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14524068	C₂²	1	1	yes	characteristic
25	#16864122	C₂²	1	2	yes	complemented
26	#16864122	C₂²	1	2	yes	complemented
27	#16864107	C₂²	1	2	yes	—
28	#16864106	—	2	1	no	—
29	#16864106	—	2	1	no	—
30	#16864106	—	2	1	no	—
31	#16864105	—	2	2	no	—
32	#16864105	—	2	2	no	—
33	#16864105	C₂²	1	2	yes	complemented
34	#16864105	C₂²	1	2	yes	complemented
35	#16864102	C₂²	1	2	yes	—
36	#16864102	C₂²	1	2	yes	—
37	Q₈×D₂₆₈	—	2	1	no	—
38	#16864061	C₂²	1	2	yes	—
39	#16864024	—	2	1	no	—
40	#16864024	—	2	1	no	—
41	#16864024	C₂²	1	1	yes	characteristic
42	#16864024	C₂²	1	1	yes	characteristic
43	#16864024	C₂²	1	1	yes	characteristic
44	#16864024	C₂²	1	1	yes	characteristic
45	#16864021	—	2	2	no	—
46	#16863953	—	2	1	no	—
47	#16863953	C₂²	1	1	yes	characteristic
48	C₂×#14524035	—	2	1	no	—
49	C₂×#14524035	C₂²	1	1	yes	characteristic
50	C₂²⋊Q₈×D₆₇	—	2	2	no	—
51	#16863879	C₂²	1	1	yes	characteristic
52	#16863879	C₂²	1	1	yes	characteristic
53	#16863870	C₂²	1	1	yes	characteristic
54	#16863870	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
56	#16863804	C₂²	1	2	yes	complemented
57	#16863804	C₂²	1	2	yes	complemented
58	#16863803	C₂²	1	2	yes	complemented
59	#16863803	C₂²	1	2	yes	complemented
60	#16863802	C₂²	1	2	yes	complemented
61	#16863802	C₂²	1	2	yes	complemented
62	#16863800	C₂²	1	2	yes	complemented
63	#16863797	C₂²	1	2	yes	complemented
64	#16863796	C₂²	1	2	yes	complemented
65	#16863795	C₂²	1	2	yes	complemented
66	#16863795	C₂²	1	2	yes	complemented
67	#16863793	C₂²	1	2	yes	complemented
68	#16863705	C₂²	1	2	yes	complemented
69	#16863701	C₂²	1	2	yes	complemented
70	#16863699	C₂²	1	2	yes	—
71	#16863699	C₂²	1	2	yes	—
72	#16863698	C₂²	1	2	yes	complemented
73	#16863697	C₂²	1	2	yes	—
74	#16863697	C₂²	1	2	yes	—
75	#16863697	C₂²	1	2	yes	—
76	#16863697	C₂²	1	2	yes	—
77	#16863695	C₂²	1	2	yes	—
78	#16863695	C₂²	1	2	yes	—
79	#16863694	C₂²	1	2	yes	complemented
80	#16863689	C₂²	1	2	yes	complemented
81	#16863685	C₂²	1	2	yes	—
82	#16863685	C₂²	1	2	yes	—
83	#16863684	C₂²	1	2	yes	complemented
84	#16863679	C₂²	1	2	yes	complemented
85	#16863675	C₂²	1	2	yes	—
86	#16863675	C₂²	1	2	yes	—
87	#16863674	C₂²	1	2	yes	complemented
88	#16863525	C₂²	1	2	yes	complemented
89	#16863525	C₂²	1	2	yes	complemented
90	#16863523	C₂²	1	2	yes	complemented
91	#16863520	C₂²	1	2	yes	complemented
92	#16863506	C₂²	1	2	yes	—
93	#16863505	C₂²	1	2	yes	—
94	#16863505	C₂²	1	2	yes	—
95	#16863499	C₂²	1	2	yes	—
96	#16863499	C₂²	1	2	yes	—
97	#16863494	C₂²	1	2	yes	—
98	C₄×#11761615	C₂²	1	2	yes	—
99	#16863481	C₂²	1	2	yes	—
100	#16863481	C₂²	1	2	yes	—
101	C₄×#11761613	C₂²	1	2	yes	—
102	#16863476	C₂²	1	2	yes	—
103	#16863476	C₂²	1	2	yes	—
104	#16863439	C₂²	1	1	yes	characteristic
105	#16863439	C₂²	1	1	yes	characteristic
106	#16863439	C₂²	1	1	yes	characteristic
107	#16863439	C₂²	1	1	yes	characteristic
108	#16863439	C₂²	1	1	yes	characteristic
109	C₂×#14523977	C₂²	1	1	yes	characteristic
110	C₂×#14523975	C₂²	1	1	yes	characteristic
111	#16863422	C₂²	1	1	yes	characteristic
112	#16863422	C₂²	1	1	yes	characteristic
113	#16863400	C₂²	1	1	yes	characteristic
114	#16863397	C₂²	1	1	yes	characteristic
115	C₂×#14523965	C₂²	1	1	yes	characteristic
116	C₂×#14523965	C₂²	1	1	yes	characteristic
117	#16863351	C₂²	1	1	yes	characteristic
118	#16863351	C₂²	1	1	yes	characteristic
119	C₄×#11761612	C₂²	1	1	yes	characteristic
120	#533×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
122	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#478×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#478×C₆₇	C₂²	1	1	yes	characteristic, complemented
126	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	#427×C₆₇	C₂²	1	1	yes	characteristic
131	#427×C₆₇	C₂²	1	1	yes	characteristic
132	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
133	#416×C₆₇	C₂²	1	1	yes	characteristic
134	#416×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×Q₈×D₆₇	—	2	2	no	—
136	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
137	C₂²×C₄×D₆₇	—	2	1	no	—
138	#14524068	Q₈	1	8	yes	complemented
139	C₂×#11761615	C₂³	1	2	yes	—
140	C₂×#11761613	C₂³	1	2	yes	—
141	C₂×#11761612	C₂³	1	1	yes	characteristic
142	C₂×#11761612	C₂³	1	1	yes	characteristic
143	#14524043	—	2	1	no	—
144	#14524043	—	2	1	no	—
145	#14524043	—	2	1	no	—
146	#14524043	—	2	1	no	—
147	#14524043	D₄	1	1	yes	characteristic
148	#14524043	D₄	1	1	yes	characteristic
149	#14524042	—	2	2	no	—
150	#14524042	—	2	2	no	—
151	#14524042	C₂³	1	2	yes	—
152	#14524042	C₂³	1	2	yes	—
153	#14524042	C₂³	1	2	yes	—
154	#14524042	C₂³	1	2	yes	—
155	#14524035	—	2	1	no	—
156	#14524035	—	2	1	no	—
157	#14524035	—	2	1	no	—
158	#14524035	—	2	1	no	—
159	#14524035	—	2	2	no	—
160	#14524035	—	2	2	no	—
161	#14524035	—	2	1	no	—
162	#14524035	—	2	1	no	—
163	#14524035	D₄	1	1	yes	characteristic
164	#14524035	D₄	1	1	yes	characteristic
165	#14524035	C₂³	1	2	yes	—
166	#14524035	C₂³	1	2	yes	—
167	#14524034	—	2	2	no	—
168	#14524034	—	2	2	no	—
169	#14524034	C₂³	1	2	yes	—
170	#14524034	C₂³	1	2	yes	—
171	#14524034	C₂³	1	2	yes	—
172	#14524034	C₂³	1	2	yes	—
173	#14524023	—	2	2	no	—
174	#14524023	—	2	2	no	—
175	#14524023	—	2	2	no	—
176	#14524022	—	2	2	no	—
177	#14524022	—	2	2	no	—
178	#14524022	D₄	1	2	yes	—
179	#14524022	D₄	1	2	yes	—
180	#14524021	—	2	2	no	—
181	#14524021	—	2	2	no	—
182	#14524021	—	2	2	no	—
183	#14524021	—	2	2	no	—
184	#14524021	—	2	2	no	—
185	#14524021	—	2	2	no	—
186	#14524020	—	2	2	no	—
187	#14524020	—	2	2	no	—
188	#14524020	—	2	2	no	—
189	#14524020	—	2	2	no	—
190	#14524020	—	2	2	no	—
191	#14524020	—	2	2	no	—
192	#14524020	—	2	2	no	—
193	#14524020	—	2	2	no	—
194	#14524019	—	2	2	no	—
195	#14524019	—	2	2	no	—
196	#14524019	—	2	2	no	—
197	Q₈×Dic₆₇	C₂³	1	2	yes	—
198	Q₈×Dic₆₇	C₂³	1	2	yes	—
199	C₄×Dic₁₃₄	—	2	2	no	—
200	C₄×Dic₁₃₄	—	2	2	no	—
201	C₄×Dic₁₃₄	C₂³	1	2	yes	—
202	C₄×Dic₁₃₄	C₂³	1	2	yes	—
203	C₄×D₂₆₈	—	2	1	no	—
204	C₄×D₂₆₈	—	2	1	no	—
205	C₄×D₂₆₈	—	2	1	no	—
206	C₄×D₂₆₈	—	2	1	no	—
207	C₄×D₂₆₈	—	2	1	no	—
208	C₄×D₂₆₈	—	2	1	no	—
209	C₄×D₂₆₈	C₂³	1	2	yes	—
210	C₄×D₂₆₈	C₂³	1	2	yes	—
211	D₄×Dic₆₇	—	2	2	no	—
212	D₄×Dic₆₇	—	2	2	no	—
213	D₄×Dic₆₇	C₂³	1	2	yes	—
214	D₄×Dic₆₇	C₂³	1	2	yes	—
215	#14524005	C₂³	1	2	yes	—
216	#14524005	C₂³	1	2	yes	—
217	#14524005	C₂³	1	2	yes	—
218	#14524005	C₂³	1	2	yes	—
219	#14524002	—	2	1	no	—
220	#14524002	—	2	1	no	—
221	#14524002	C₂³	1	1	yes	characteristic
222	#14524002	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₆₇	—	2	1	no	—
224	C₂×C₄⋊Dic₆₇	—	2	1	no	—
225	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
228	C₂×Dic₆₇⋊C₄	—	2	2	no	—
229	C₂×Dic₆₇⋊C₄	—	2	2	no	—
230	C₂×Dic₆₇⋊C₄	—	2	1	no	—
231	C₂×Dic₆₇⋊C₄	—	2	1	no	—
232	C₄⋊C₄×D₆₇	—	2	2	no	—
233	C₄⋊C₄×D₆₇	—	2	2	no	—
234	C₄⋊C₄×D₆₇	—	2	2	no	—
235	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
236	C₂²⋊C₄×D₆₇	—	2	2	no	—
237	C₂²⋊C₄×D₆₇	—	2	2	no	—
238	#14523977	C₂³	1	2	yes	—
239	#14523977	C₂³	1	2	yes	—
240	#14523976	C₂³	1	2	yes	—
241	#14523976	C₂³	1	2	yes	—
242	#14523976	C₂³	1	2	yes	—
243	#14523976	C₂³	1	2	yes	—
244	#14523976	C₂³	1	2	yes	—
245	#14523975	C₂³	1	2	yes	—
246	#14523975	C₂³	1	2	yes	—
247	#14523974	C₂³	1	2	yes	—
248	#14523974	C₂³	1	2	yes	—
249	#14523974	C₂³	1	2	yes	—
250	#14523974	C₂³	1	2	yes	—
251	#14523974	C₂³	1	2	yes	—
252	Dic₆₇⋊C₈	C₂³	1	2	yes	—
253	Dic₆₇⋊C₈	C₂³	1	2	yes	—
254	Dic₆₇⋊C₈	C₂³	1	2	yes	—
255	Dic₆₇⋊C₈	C₂³	1	2	yes	—
256	#14523967	C₂³	1	2	yes	—
257	#14523965	C₂³	1	2	yes	—
258	#14523965	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	#14523954	C₂³	1	2	yes	—
265	#14523953	C₂³	1	2	yes	—
266	#14523953	C₂³	1	2	yes	—
267	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
268	C₈×Dic₆₇	C₂³	1	2	yes	—
269	C₈×Dic₆₇	C₂³	1	2	yes	—
270	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
273	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
274	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
275	#125×C₆₇	C₂³	1	1	yes	characteristic
276	#125×C₆₇	C₂³	1	1	yes	characteristic
277	C₂²⋊Q₈×C₆₇	—	2	1	no	—
278	C₂²⋊Q₈×C₆₇	—	2	1	no	—
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×D₄×C₆₇	—	2	1	no	—
284	C₄×D₄×C₆₇	—	2	1	no	—
285	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
287	#117×C₆₇	—	2	1	no	—
288	#117×C₆₇	C₂³	1	1	yes	characteristic
289	#117×C₆₇	C₂³	1	1	yes	characteristic
290	#117×C₆₇	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₆₇	—	2	1	no	—
292	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
293	#107×C₆₇	C₂³	1	1	yes	characteristic
294	#107×C₆₇	C₂³	1	1	yes	characteristic
295	#107×C₆₇	C₂³	1	1	yes	characteristic
296	#107×C₆₇	C₂³	1	1	yes	characteristic
297	#106×C₆₇	C₂³	1	1	yes	characteristic
298	#106×C₆₇	C₂³	1	1	yes	characteristic
299	#106×C₆₇	C₂³	1	1	yes	characteristic
300	#106×C₆₇	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
304	C₄⋊C₈×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	#103×C₆₇	C₂³	1	1	yes	characteristic
309	#102×C₆₇	C₂³	1	1	yes	characteristic
310	#102×C₆₇	C₂³	1	1	yes	characteristic
311	#102×C₆₇	C₂³	1	1	yes	characteristic
312	#102×C₆₇	C₂³	1	1	yes	characteristic
313	C₂³×D₆₇	—	2	1	no	—
314	C₂×Dic₁₃₄	—	2	2	no	—
315	C₂×Dic₁₃₄	—	2	2	no	—
316	C₂×Dic₁₃₄	—	2	2	no	—
317	C₂×Dic₁₃₄	—	2	2	no	—
318	C₂×Dic₁₃₄	C₂×D₄	1	2	yes	—
319	C₂×Dic₁₃₄	C₂×D₄	1	2	yes	—
320	Q₈×D₆₇	—	8	4	no	—
321	C₂×D₂₆₈	—	2	1	no	—
322	C₂×D₂₆₈	—	2	2	no	—
323	C₂×D₂₆₈	C₂×Q₈	1	4	yes	—
324	C₂×D₂₆₈	C₂⁴	1	2	yes	—
325	C₂²×Dic₆₇	—	2	1	no	—
326	C₂²×Dic₆₇	—	2	1	no	—
327	C₂²×Dic₆₇	—	2	1	no	—
328	C₂²×Dic₆₇	—	2	2	no	—
329	C₂²×Dic₆₇	—	2	2	no	—
330	C₂×C₄×D₆₇	—	2	2	no	—
331	C₂×C₄×D₆₇	—	2	2	no	—
332	C₂×C₄×D₆₇	—	2	2	no	—
333	C₂×C₄×D₆₇	—	2	2	no	—
334	C₂×C₄×D₆₇	—	2	2	no	—
335	C₂×C₄×D₆₇	—	2	2	no	—
336	C₂×C₄×D₆₇	—	8	2	no	—
337	#11761615	C₂×Q₈	1	8	yes	complemented
338	#11761613	C₂×Q₈	1	8	yes	complemented
339	#11761612	—	2	2	no	—
340	#11761612	C₂×Q₈	1	4	yes	complemented
341	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
342	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
343	C₄⋊Dic₆₇	—	2	1	no	—
344	C₄⋊Dic₆₇	—	2	1	no	—
345	C₄⋊Dic₆₇	—	2	1	no	—
346	C₄⋊Dic₆₇	—	2	2	no	—
347	C₄⋊Dic₆₇	—	2	2	no	—
348	C₄⋊Dic₆₇	—	2	2	no	—
349	C₄⋊Dic₆₇	—	2	2	no	—
350	C₄⋊Dic₆₇	—	2	2	no	—
351	C₄⋊Dic₆₇	—	2	2	no	—
352	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
353	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
354	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
355	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
356	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
357	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
358	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
359	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
360	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
361	Dic₆₇⋊C₄	—	2	2	no	—
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	—	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	—	2	2	no	—
379	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
380	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
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	C₄×Dic₆₇	—	2	2	no	—
388	C₄×Dic₆₇	—	2	2	no	—
389	C₄×Dic₆₇	C₂⁴	1	2	yes	—
390	C₄×Dic₆₇	C₂⁴	1	2	yes	—
391	#41×C₆₇	—	2	2	no	—
392	#41×C₆₇	C₂×Q₈	1	4	yes	complemented
393	C₂×Q₈×C₆₇	—	2	1	no	—
394	C₂×Q₈×C₆₇	—	2	1	no	—
395	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×D₄×C₆₇	—	2	1	no	—
397	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₆₇	—	2	1	no	—
399	C₂²×C₄×C₆₇	—	2	1	no	—
400	C₂²×C₄×C₆₇	—	2	1	no	—
401	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₆₇	—	2	2	no	—
405	C₂×C₈×C₆₇	—	2	2	no	—
406	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₆₇	—	2	1	no	—
411	C₄⋊C₄×C₆₇	—	2	1	no	—
412	C₄⋊C₄×C₆₇	—	2	1	no	—
413	C₄⋊C₄×C₆₇	—	2	1	no	—
414	C₄⋊C₄×C₆₇	—	2	1	no	—
415	C₄⋊C₄×C₆₇	—	2	1	no	—
416	C₄⋊C₄×C₆₇	—	2	1	no	—
417	C₄⋊C₄×C₆₇	—	2	1	no	—
418	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₆₇	—	2	1	no	—
425	C₂²⋊C₄×C₆₇	—	2	1	no	—
426	C₂²⋊C₄×C₆₇	—	2	1	no	—
427	C₂²⋊C₄×C₆₇	—	2	1	no	—
428	C₂²⋊C₄×C₆₇	—	2	1	no	—
429	C₄²×C₆₇	—	2	1	no	—
430	C₄²×C₆₇	—	2	1	no	—
431	C₄²×C₆₇	—	2	1	no	—
432	C₄²×C₆₇	—	2	1	no	—
433	C₄²×C₆₇	—	2	1	no	—
434	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₂³×C₆₇	—	2	1	no	—
439	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
440	C₂²×D₆₇	—	2	2	no	—
441	C₂²×D₆₇	—	2	4	no	—
442	C₂²×D₆₇	—	8	1	no	—
443	C₂²×D₆₇	—	8	1	no	—
444	Q₈×C₆₇	—	2	1	no	—
445	Q₈×C₆₇	—	4	2	no	—
446	Q₈×C₆₇	—	8	1	no	—
447	Q₈×C₆₇	C₂²×Q₈	1	2	yes	—
448	D₄×C₆₇	—	2	4	no	—
449	D₄×C₆₇	—	2	1	no	—
450	D₄×C₆₇	C₂²×Q₈	1	2	yes	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	2	4	no	—
453	C₂×C₄×C₆₇	—	2	1	no	—
454	C₂×C₄×C₆₇	—	2	1	no	—
455	C₂×C₄×C₆₇	—	2	1	no	—
456	C₂×C₄×C₆₇	—	2	1	no	—
457	C₂×C₄×C₆₇	—	2	1	no	—
458	C₂×C₄×C₆₇	—	2	1	no	—
459	C₂×C₄×C₆₇	—	4	1	no	—
460	C₂×C₄×C₆₇	—	4	1	no	—
461	C₂×C₄×C₆₇	—	8	1	no	—
462	C₂×C₄×C₆₇	—	8	1	no	—
463	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
469	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
470	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
471	C₂×Dic₆₇	—	2	2	no	—
472	C₂×Dic₆₇	—	2	2	no	—
473	C₂×Dic₆₇	—	2	2	no	—
474	C₂×Dic₆₇	—	8	2	no	—
475	C₂×Dic₆₇	—	8	2	no	—
476	C₂×Dic₆₇	—	8	1	no	—
477	C₂×Dic₆₇	—	8	1	no	—
478	C₂×Dic₆₇	—	8	1	no	—
479	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
480	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
481	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
482	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
483	D₂₆₈	—	2	4	no	—
484	D₂₆₈	—	2	2	no	—
485	D₂₆₈	C₂²×Q₈	1	4	yes	—
486	C₄×D₆₇	—	4	4	no	—
487	C₄×D₆₇	—	8	2	no	—
488	C₄×D₆₇	—	8	2	no	—
489	C₄×D₆₇	—	8	2	no	—
490	C₄×D₆₇	—	8	2	no	—
491	C₄×D₆₇	—	8	2	no	—
492	Dic₁₃₄	—	4	2	no	—
493	Dic₁₃₄	—	4	2	no	—
494	Dic₁₃₄	—	8	2	no	—
495	Dic₁₃₄	—	8	2	no	—
496	Dic₁₃₄	—	8	2	no	—
497	Dic₁₃₄	—	8	2	no	—
498	C₈×C₆₇	—	2	1	no	—
499	C₈×C₆₇	—	2	1	no	—
500	C₈×C₆₇	—	2	1	no	—
501	C₈×C₆₇	—	2	1	no	—
502	C₆₇⋊C₈	—	2	2	no	—
503	C₆₇⋊C₈	C₂²×Q₈	1	4	yes	—
504	C₂²×C₆₇	—	2	1	no	—
505	C₂²×C₆₇	—	2	1	no	—
506	C₂²×C₆₇	—	2	2	no	—
507	C₂²×C₆₇	—	4	1	no	—
508	C₂²×C₆₇	—	4	1	no	—
509	C₂²×C₆₇	D₄×Q₈	1	2	yes	—
510	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
511	C₂×D₆₇	—	2	4	no	—
512	C₂×D₆₇	—	4	2	no	—
513	C₂×D₆₇	—	4	2	no	—
514	C₂×D₆₇	—	8	4	no	—
515	C₄×C₆₇	—	2	1	no	—
516	C₄×C₆₇	—	2	1	no	—
517	C₄×C₆₇	—	2	1	no	—
518	C₄×C₆₇	—	2	1	no	—
519	C₄×C₆₇	—	2	2	no	—
520	C₄×C₆₇	—	4	1	no	—
521	C₄×C₆₇	—	4	1	no	—
522	C₄×C₆₇	—	4	1	no	—
523	C₄×C₆₇	—	4	1	no	—
524	C₄×C₆₇	—	4	1	no	—
525	C₄×C₆₇	—	4	1	no	—
526	C₄×C₆₇	D₄×Q₈	1	2	yes	—
527	C₄×C₆₇	C₂³×Q₈	1	1	yes	characteristic
528	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
529	Dic₆₇	—	2	2	no	—
530	Dic₆₇	—	2	2	no	—
531	Dic₆₇	—	2	2	no	—
532	Dic₆₇	—	2	2	no	—
533	Dic₆₇	—	4	2	no	—
534	Dic₆₇	—	4	2	no	—
535	Dic₆₇	—	4	2	no	—
536	#61385	—	67	1	no	maximal, Sylow
537	C₂×C₆₇	—	2	2	no	—
538	C₂×C₆₇	—	4	2	no	—
539	C₂×C₆₇	C₂×D₄×Q₈	1	1	yes	characteristic
540	C₂×C₆₇	#3584	1	1	yes	characteristic
541	C₂×C₆₇	#3585	1	1	yes	characteristic
542	D₆₇	—	4	4	no	—
543	#3504	—	67	1	no	—
544	#3501	—	67	1	no	—
545	#3389	—	67	2	no	—
546	#3389	—	67	2	no	—
547	#3388	—	67	2	no	—
548	#3388	—	67	2	no	—
549	#3386	—	67	2	no	—
550	#3384	—	67	2	no	—
551	#3381	—	67	2	no	—
552	#3380	—	67	2	no	—
553	#3166	—	67	1	no	—
554	#3164	—	67	1	no	—
555	#3163	—	67	1	no	—
556	#3084	—	67	1	no	—
557	#3083	—	67	1	no	—
558	#3081	—	67	1	no	—
559	#3081	—	67	1	no	—
560	#3076	D₆₇	1	1	yes	characteristic, complemented
561	C₂×#478	—	67	1	no	—
562	#2962	—	67	1	no	—
563	#2946	—	67	1	no	—
564	#2946	—	67	1	no	—
565	C₄×AGL(1,ℤ/8)	—	67	1	no	—
566	C₆₇	#61385	1	1	yes	characteristic, complemented, Sylow
567	C₂×AGL(1,ℤ/8)	—	67	1	no	—
568	#557	—	67	2	no	—
569	#557	—	67	2	no	—
570	#554	—	67	2	no	—
571	#554	—	67	2	no	—
572	#554	—	67	2	no	—
573	#554	—	67	2	no	—
574	#554	—	67	2	no	—
575	#554	—	134	2	no	—
576	#554	—	134	2	no	—
577	#554	—	134	1	no	—
578	#554	—	134	1	no	—
579	#554	—	134	1	no	—
580	D₄×Q₈	—	67	2	no	—
581	D₄×Q₈	—	134	1	no	—
582	#544	—	67	1	no	—
583	#544	—	67	1	no	—
584	#544	—	67	1	no	—
585	#544	—	67	1	no	—
586	#544	—	134	1	no	—
587	#544	—	134	1	no	—
588	#543	—	134	2	no	—
589	#533	—	67	1	no	—
590	#533	—	134	1	no	—
591	#533	C₂×D₆₇	1	1	yes	characteristic
592	C₂×#125	—	67	1	no	—
593	C₂×#125	—	134	1	no	—
594	C₂×C₂²⋊Q₈	—	134	2	no	—
595	#520	—	67	1	no	—
596	#520	—	67	1	no	—
597	#518	—	67	1	no	—
598	#518	—	67	1	no	—
599	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
600	C₂×C₄×D₄	—	67	1	no	—
601	#501	—	67	2	no	—
602	#501	—	67	2	no	—
603	#501	—	67	2	no	—
604	#501	—	67	2	no	—
605	#501	—	67	2	no	—
606	#501	—	67	2	no	—
607	#500	—	67	2	no	—
608	#499	—	67	2	no	—
609	#499	—	67	2	no	—
610	#499	—	67	2	no	—
611	#499	—	67	2	no	—
612	#498	—	67	2	no	—
613	#479	—	67	2	no	—
614	#479	—	67	2	no	—
615	#479	C₂×D₆₇	1	1	yes	characteristic, complemented
616	#479	C₂×D₆₇	1	1	yes	characteristic, complemented
617	#478	—	67	2	no	—
618	#478	—	67	2	no	—
619	#478	—	67	2	no	—
620	#478	—	67	2	no	—
621	#478	—	67	2	no	—
622	#478	—	67	2	no	—
623	#478	—	67	2	no	—
624	#478	—	67	2	no	—
625	#478	—	67	2	no	—
626	#478	—	67	2	no	—
627	#478	C₂×D₆₇	1	1	yes	characteristic, complemented
628	#478	C₂×D₆₇	1	1	yes	characteristic, complemented
629	#477	—	67	2	no	—
630	#477	C₂×D₆₇	1	1	yes	characteristic, complemented
631	#476	—	67	2	no	—
632	#476	—	67	2	no	—
633	#476	—	67	2	no	—
634	#476	C₂×D₆₇	1	1	yes	characteristic, complemented
635	#475	—	67	2	no	—
636	#475	C₂×D₆₇	1	1	yes	characteristic, complemented
637	#474	—	67	2	no	—
638	#474	—	67	2	no	—
639	#474	—	67	2	no	—
640	#474	C₂×D₆₇	1	1	yes	characteristic, complemented
641	#446	—	67	2	no	—
642	#446	—	67	2	no	—
643	#446	—	67	2	no	—
644	C₈×Q₈	—	67	2	no	—
645	#442	—	67	2	no	—
646	#442	—	67	2	no	—
647	#442	—	67	2	no	—
648	#440	—	67	2	no	—
649	#440	—	67	2	no	—
650	#440	—	67	2	no	—
651	C₄×SD₁₆	—	67	2	no	—
652	C₄×SD₁₆	—	67	2	no	—
653	C₄×SD₁₆	—	67	2	no	—
654	C₄×D₈	—	67	2	no	—
655	C₄×D₈	—	67	2	no	—
656	C₄×D₈	—	67	2	no	—
657	#428	—	67	1	no	—
658	#428	—	67	1	no	—
659	#428	—	67	1	no	—
660	#428	—	67	1	no	—
661	#428	—	67	1	no	—
662	#427	C₂×D₆₇	1	1	yes	characteristic
663	#427	C₂×D₆₇	1	1	yes	characteristic
664	C₂×#107	—	67	1	no	—
665	C₂×#106	—	67	1	no	—
666	#424	—	67	1	no	—
667	#424	—	67	1	no	—
668	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
669	#418	—	67	1	no	—
670	#417	—	67	1	no	—
671	#416	C₂×D₆₇	1	1	yes	characteristic
672	#416	C₂×D₆₇	1	1	yes	characteristic
673	C₂×#102	—	67	1	no	—
674	C₂×#102	—	67	1	no	—
675	#405	—	67	1	no	—
676	#405	—	67	1	no	—
677	C₄×M₁₆	—	67	1	no	—
678	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
679	C₂²×Q₈	—	134	2	no	—
680	C₂²×D₄	—	67	1	no	—
681	C₂³×C₄	—	134	1	no	—
682	AGL(1,ℤ/8)	—	67	8	no	—
683	C₂×SD₁₆	—	67	2	no	—
684	C₂×D₈	—	67	2	no	—
685	C₂×M₁₆	—	67	1	no	—
686	C₂×M₁₆	—	67	1	no	—
687	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
688	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
689	C₄⋊Q₈	—	67	2	no	—
690	C₄⋊Q₈	—	67	2	no	—
691	C₄⋊Q₈	—	67	2	no	—
692	C₄⋊Q₈	—	67	2	no	—
693	C₄⋊Q₈	—	67	1	no	—
694	C₄⋊Q₈	—	67	1	no	—
695	C₄⋊Q₈	—	134	1	no	—
696	C₄⋊Q₈	—	134	1	no	—
697	C₄⋊Q₈	—	134	1	no	—
698	C₄⋊Q₈	—	134	1	no	—
699	C₄⋊Q₈	—	134	2	no	—
700	C₄⋊Q₈	—	134	2	no	—
701	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
702	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
703	#125	—	67	2	no	—
704	#125	—	67	2	no	—
705	#125	—	67	2	no	—
706	#125	—	67	2	no	—
707	#125	—	67	1	no	—
708	#125	—	67	1	no	—
709	#125	—	67	2	no	—
710	#125	—	67	2	no	—
711	#125	—	134	1	no	—
712	#125	—	134	1	no	—
713	#125	—	134	2	no	—
714	#125	—	134	2	no	—
715	#125	—	134	1	no	—
716	#125	—	134	1	no	—
717	#125	—	134	2	no	—
718	#125	—	134	2	no	—
719	#125	—	134	1	no	—
720	#125	—	134	1	no	—
721	#125	C₂²×D₆₇	1	1	yes	characteristic
722	#125	C₂²×D₆₇	1	1	yes	characteristic
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	67	2	no	—
726	C₂²⋊Q₈	—	67	2	no	—
727	C₂²⋊Q₈	—	134	2	no	—
728	C₂²⋊Q₈	—	134	2	no	—
729	C₂²⋊Q₈	—	134	2	no	—
730	C₂²⋊Q₈	—	134	2	no	—
731	C₂²⋊Q₈	—	134	2	no	—
732	C₂²⋊Q₈	—	134	2	no	—
733	C₂²⋊Q₈	—	134	2	no	—
734	C₂²⋊Q₈	—	134	2	no	—
735	C₂²⋊Q₈	—	134	2	no	—
736	C₂²⋊Q₈	—	134	2	no	—
737	C₂²⋊Q₈	—	134	2	no	—
738	C₂²⋊Q₈	—	134	2	no	—
739	C₂²⋊Q₈	—	134	2	no	—
740	C₂²⋊Q₈	—	134	2	no	—
741	C₂²⋊Q₈	—	134	2	no	—
742	C₂²⋊Q₈	—	134	2	no	—
743	C₂²⋊Q₈	—	134	2	no	—
744	C₂²⋊Q₈	—	134	2	no	—
745	C₂²⋊Q₈	—	134	2	no	—
746	C₂²⋊Q₈	—	134	2	no	—
747	C₂²⋊Q₈	—	134	2	no	—
748	C₂²⋊Q₈	—	134	2	no	—
749	C₄×Q₈	—	2	1	no	—
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	—	67	2	no	—
752	C₄×Q₈	—	67	2	no	—
753	C₄×Q₈	—	67	2	no	—
754	C₄×Q₈	—	67	2	no	—
755	C₄×Q₈	—	134	2	no	—
756	C₄×Q₈	—	134	2	no	—
757	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
758	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	67	2	no	—
762	C₄×D₄	—	67	2	no	—
763	C₄×D₄	—	67	2	no	—
764	C₄×D₄	—	67	2	no	—
765	C₄×D₄	—	67	2	no	—
766	C₄×D₄	—	67	2	no	—
767	C₄×D₄	—	67	2	no	—
768	C₄×D₄	—	67	2	no	—
769	C₄×D₄	—	134	1	no	—
770	C₄×D₄	—	134	1	no	—
771	C₄×D₄	—	134	1	no	—
772	C₄×D₄	—	134	1	no	—
773	C₄×D₄	—	134	2	no	—
774	C₄×D₄	—	134	2	no	—
775	C₄×D₄	—	134	1	no	—
776	C₄×D₄	—	134	1	no	—
777	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
778	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
779	#117	—	2	1	no	—
780	#117	—	67	1	no	—
781	#117	—	67	1	no	—
782	#117	—	134	1	no	—
783	#117	—	134	1	no	—
784	#117	C₂²×D₆₇	1	1	yes	characteristic
785	#117	C₂²×D₆₇	1	1	yes	characteristic
786	#117	C₂²×D₆₇	1	1	yes	characteristic
787	C₂×C₄⋊C₄	—	67	1	no	—
788	C₂×C₄⋊C₄	—	67	1	no	—
789	C₂×C₄⋊C₄	—	67	1	no	—
790	C₂×C₄⋊C₄	—	134	2	no	—
791	C₂×C₄⋊C₄	—	134	2	no	—
792	C₂×C₄⋊C₄	—	134	2	no	—
793	C₂×C₄⋊C₄	—	134	1	no	—
794	C₂×C₄⋊C₄	—	134	1	no	—
795	C₂×C₄⋊C₄	—	134	2	no	—
796	C₂×C₄⋊C₄	—	134	2	no	—
797	C₂×C₄⋊C₄	—	134	1	no	—
798	C₂×C₄⋊C₄	—	134	1	no	—
799	C₂×C₂²⋊C₄	—	134	2	no	—
800	C₂×C₂²⋊C₄	—	134	2	no	—
801	C₂×C₂²⋊C₄	—	134	1	no	—
802	C₂×C₄²	—	2	1	no	—
803	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
804	#107	—	67	2	no	—
805	#107	—	67	2	no	—
806	#107	—	67	2	no	—
807	#107	—	67	2	no	—
808	#107	—	67	2	no	—
809	#107	—	67	2	no	—
810	#107	—	67	2	no	—
811	#107	C₂²×D₆₇	1	1	yes	characteristic
812	#107	C₂²×D₆₇	1	1	yes	characteristic
813	#107	C₂²×D₆₇	1	1	yes	characteristic
814	#107	C₂²×D₆₇	1	1	yes	characteristic
815	#106	—	67	2	no	—
816	#106	—	67	2	no	—
817	#106	—	67	2	no	—
818	#106	—	67	2	no	—
819	#106	—	67	2	no	—
820	#106	—	67	2	no	—
821	#106	—	67	2	no	—
822	#106	C₂²×D₆₇	1	1	yes	characteristic
823	#106	C₂²×D₆₇	1	1	yes	characteristic
824	#106	C₂²×D₆₇	1	1	yes	characteristic
825	#106	C₂²×D₆₇	1	1	yes	characteristic
826	C₄⋊C₈	—	67	2	no	—
827	C₄⋊C₈	—	67	2	no	—
828	C₄⋊C₈	—	67	2	no	—
829	C₄⋊C₈	—	67	2	no	—
830	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
831	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
832	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
833	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
834	#103	—	67	2	no	—
835	#103	C₂²×D₆₇	1	1	yes	characteristic
836	#103	C₂²×D₆₇	1	1	yes	characteristic
837	#103	C₂²×D₆₇	1	1	yes	characteristic
838	#103	C₂²×D₆₇	1	1	yes	characteristic
839	#102	—	67	2	no	—
840	#102	—	67	2	no	—
841	#102	—	67	2	no	—
842	#102	—	67	2	no	—
843	#102	—	67	2	no	—
844	#102	—	67	2	no	—
845	#102	—	67	2	no	—
846	#102	C₂²×D₆₇	1	1	yes	characteristic
847	#102	C₂²×D₆₇	1	1	yes	characteristic
848	#102	C₂²×D₆₇	1	1	yes	characteristic
849	#102	C₂²×D₆₇	1	1	yes	characteristic
850	#97	—	67	2	no	—
851	#97	—	67	2	no	—
852	#97	—	67	2	no	—
853	C₄×C₈	—	67	2	no	—
854	C₄×C₈	—	67	2	no	—
855	C₄×C₈	—	67	2	no	—
856	C₂⁴	—	134	1	no	—
857	#41	—	2	2	no	—
858	#41	Q₈×D₆₇	1	4	yes	complemented
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	536	4	no	—
862	C₂×Q₈	—	67	2	no	—
863	C₂×Q₈	—	67	2	no	—
864	C₂×Q₈	—	134	2	no	—
865	C₂×Q₈	—	134	2	no	—
866	C₂×Q₈	—	134	2	no	—
867	C₂×Q₈	—	134	2	no	—
868	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	—	67	4	no	—
871	C₂×D₄	—	67	2	no	—
872	C₂×D₄	—	134	1	no	—
873	C₂×D₄	—	134	2	no	—
874	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	536	2	no	—
879	C₂²×C₄	—	134	2	no	—
880	C₂²×C₄	—	134	2	no	—
881	C₂²×C₄	—	134	2	no	—
882	C₂²×C₄	—	134	2	no	—
883	C₂²×C₄	—	134	2	no	—
884	C₂²×C₄	—	134	2	no	—
885	C₂²×C₄	—	134	2	no	—
886	C₂²×C₄	—	134	1	no	—
887	C₂²×C₄	—	134	1	no	—
888	C₂²×C₄	—	134	1	no	—
889	C₂²×C₄	—	134	2	no	—
890	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
891	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
892	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
893	SD₁₆	—	67	8	no	—
894	D₈	—	67	8	no	—
895	M₁₆	—	67	4	no	—
896	M₁₆	—	134	2	no	—
897	C₂×C₈	—	2	2	no	—
898	C₂×C₈	—	2	2	no	—
899	C₂×C₈	—	67	2	no	—
900	C₂×C₈	—	67	2	no	—
901	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
902	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
903	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
904	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	67	2	no	—
914	C₄⋊C₄	—	67	1	no	—
915	C₄⋊C₄	—	67	1	no	—
916	C₄⋊C₄	—	67	2	no	—
917	C₄⋊C₄	—	67	2	no	—
918	C₄⋊C₄	—	67	2	no	—
919	C₄⋊C₄	—	67	1	no	—
920	C₄⋊C₄	—	67	1	no	—
921	C₄⋊C₄	—	67	2	no	—
922	C₄⋊C₄	—	67	2	no	—
923	C₄⋊C₄	—	67	2	no	—
924	C₄⋊C₄	—	67	2	no	—
925	C₄⋊C₄	—	67	2	no	—
926	C₄⋊C₄	—	134	2	no	—
927	C₄⋊C₄	—	134	2	no	—
928	C₄⋊C₄	—	134	2	no	—
929	C₄⋊C₄	—	134	2	no	—
930	C₄⋊C₄	—	134	2	no	—
931	C₄⋊C₄	—	134	2	no	—
932	C₄⋊C₄	—	134	2	no	—
933	C₄⋊C₄	—	134	2	no	—
934	C₄⋊C₄	—	134	2	no	—
935	C₄⋊C₄	—	134	2	no	—
936	C₄⋊C₄	—	134	2	no	—
937	C₄⋊C₄	—	134	2	no	—
938	C₄⋊C₄	—	134	2	no	—
939	C₄⋊C₄	—	134	2	no	—
940	C₄⋊C₄	—	134	1	no	—
941	C₄⋊C₄	—	134	1	no	—
942	C₄⋊C₄	—	134	1	no	—
943	C₄⋊C₄	—	134	2	no	—
944	C₄⋊C₄	—	134	2	no	—
945	C₄⋊C₄	—	134	2	no	—
946	C₄⋊C₄	—	134	2	no	—
947	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
948	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
949	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
950	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
951	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
952	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	67	2	no	—
959	C₂²⋊C₄	—	67	2	no	—
960	C₂²⋊C₄	—	134	2	no	—
961	C₂²⋊C₄	—	134	2	no	—
962	C₂²⋊C₄	—	134	2	no	—
963	C₂²⋊C₄	—	134	2	no	—
964	C₂²⋊C₄	—	134	2	no	—
965	C₂²⋊C₄	—	134	2	no	—
966	C₂²⋊C₄	—	134	2	no	—
967	C₂²⋊C₄	—	134	2	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	67	2	no	—
974	C₄²	—	67	2	no	—
975	C₄²	—	134	2	no	—
976	C₄²	—	134	2	no	—
977	C₄²	D₄×D₆₇	1	1	yes	characteristic
978	C₄²	D₄×D₆₇	1	1	yes	characteristic
979	C₄²	C₂³×D₆₇	1	1	yes	characteristic
980	C₄²	C₂³×D₆₇	1	1	yes	characteristic
981	C₂³	—	2	1	no	—
982	C₂³	—	536	1	no	—
983	C₂³	—	536	1	no	—
984	C₂³	—	134	2	no	—
985	C₂³	—	134	4	no	—
986	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
987	Q₈	—	2	1	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	8	1	no	—
990	Q₈	—	268	2	no	—
991	Q₈	—	268	2	no	—
992	Q₈	—	536	2	no	—
993	Q₈	—	536	2	no	—
994	Q₈	—	536	2	no	—
995	Q₈	—	536	2	no	—
996	Q₈	C₂×Q₈×D₆₇	1	2	yes	—
997	D₄	—	2	4	no	—
998	D₄	—	2	1	no	—
999	D₄	—	67	4	no	—
1000	D₄	—	134	4	no	—
1001	D₄	—	134	2	no	—
1002	D₄	C₂×Q₈×D₆₇	1	2	yes	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	4	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	8	1	no	—
1014	C₂×C₄	—	8	1	no	—
1015	C₂×C₄	—	268	4	no	—
1016	C₂×C₄	—	536	2	no	—
1017	C₂×C₄	—	536	2	no	—
1018	C₂×C₄	—	536	2	no	—
1019	C₂×C₄	—	536	2	no	—
1020	C₂×C₄	—	536	2	no	—
1021	C₂×C₄	—	536	1	no	—
1022	C₂×C₄	—	536	1	no	—
1023	C₂×C₄	—	536	1	no	—
1024	C₂×C₄	—	536	2	no	—
1025	C₂×C₄	—	536	2	no	—
1026	C₂×C₄	—	67	2	no	—
1027	C₂×C₄	—	67	2	no	—
1028	C₂×C₄	—	67	2	no	—
1029	C₂×C₄	—	67	2	no	—
1030	C₂×C₄	—	134	2	no	—
1031	C₂×C₄	—	134	2	no	—
1032	C₂×C₄	—	134	2	no	—
1033	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1034	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1035	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1036	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1037	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1038	C₂×C₄	C₂×Q₈×D₆₇	1	2	yes	—
1039	C₂×C₄	#14524090	1	2	yes	—
1040	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1041	C₈	—	2	1	no	—
1042	C₈	—	2	1	no	—
1043	C₈	—	2	1	no	—
1044	C₈	—	2	1	no	—
1045	C₈	—	67	4	no	—
1046	C₈	—	134	2	no	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	4	1	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	268	2	no	—
1053	C₂²	—	268	2	no	—
1054	C₂²	—	536	4	no	—
1055	C₂²	—	134	4	no	—
1056	C₂²	#16864059	1	2	yes	—
1057	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1058	C₄	—	2	2	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	268	2	no	—
1070	C₄	—	268	2	no	—
1071	C₄	—	268	2	no	—
1072	C₄	—	134	2	no	—
1073	C₄	—	134	2	no	—
1074	C₄	—	134	2	no	—
1075	C₄	—	134	2	no	—
1076	C₄	#16864059	1	2	yes	—
1077	C₄	C₂²×Q₈×D₆₇	1	1	yes	characteristic
1078	C₄	C₂×#14524090	1	1	yes	characteristic
1079	C₂	—	2	2	no	—
1080	C₂	—	4	2	no	—
1081	C₂	—	268	4	no	—
1082	C₂	C₂×#16864059	1	1	yes	characteristic
1083	C₂	#22574978	1	1	yes	characteristic
1084	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	C₆₇×#3076	C₂
socle	C₂²×C₆₇	C₂³×D₄
prime radical	C₂×#14524068	C₂²
hypercenter	#3076	D₆₇
hypocenter	C₆₇	#61385
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #22574035	C₂	semidirect
2. #22574010	C₂	semidirect
3. #22573167	C₂	semidirect
4. #22573162	C₂	semidirect
5. #22573161	C₂	semidirect
6. #22573152	C₂	semidirect
7. #22573133	C₂	semidirect
8. #22573103	C₂	semidirect
9. #22573087	C₂	semidirect
10. #22573071	C₂	semidirect
11. #22570762	C₂	semidirect
12. #22570749	C₂	semidirect
13. #22570741	C₂	semidirect
14. #22570069	C₂	semidirect
15. #22570058	C₂	semidirect
16. #22570043	C₂	semidirect
17. #22570043	C₂	semidirect
18. C₂×#16863697	C₂	semidirect
19. #22569152	C₂	semidirect
23. C₆₇×#3076	C₂	semidirect
25. #16864122	C₂²	semidirect
26. #16864122	C₂²	semidirect
33. #16864105	C₂²	semidirect
34. #16864105	C₂²	semidirect
56. #16863804	C₂²	semidirect
57. #16863804	C₂²	semidirect
58. #16863803	C₂²	semidirect
59. #16863803	C₂²	semidirect
60. #16863802	C₂²	semidirect
61. #16863802	C₂²	semidirect
62. #16863800	C₂²	semidirect
63. #16863797	C₂²	semidirect
64. #16863796	C₂²	semidirect
65. #16863795	C₂²	semidirect
66. #16863795	C₂²	semidirect
67. #16863793	C₂²	semidirect
68. #16863705	C₂²	semidirect
69. #16863701	C₂²	semidirect
72. #16863698	C₂²	semidirect
79. #16863694	C₂²	semidirect
80. #16863689	C₂²	semidirect
83. #16863684	C₂²	semidirect
84. #16863679	C₂²	semidirect
87. #16863674	C₂²	semidirect
88. #16863525	C₂²	semidirect
89. #16863525	C₂²	semidirect
90. #16863523	C₂²	semidirect
91. #16863520	C₂²	semidirect
122. #479×C₆₇	C₂²	semidirect
123. #479×C₆₇	C₂²	semidirect
124. #478×C₆₇	C₂²	semidirect
125. #478×C₆₇	C₂²	semidirect
126. #477×C₆₇	C₂²	semidirect
127. #476×C₆₇	C₂²	semidirect
128. #475×C₆₇	C₂²	semidirect
129. #474×C₆₇	C₂²	semidirect
138. #14524068	Q₈	semidirect
337. #11761615	C₂×Q₈	semidirect
338. #11761613	C₂×Q₈	semidirect
340. #11761612	C₂×Q₈	semidirect
392. #41×C₆₇	C₂×Q₈	semidirect
560. #3076	D₆₇	semidirect
566. C₆₇	#61385	semidirect
615. #479	C₂×D₆₇	semidirect
616. #479	C₂×D₆₇	semidirect
627. #478	C₂×D₆₇	semidirect
628. #478	C₂×D₆₇	semidirect
630. #477	C₂×D₆₇	semidirect
634. #476	C₂×D₆₇	semidirect
636. #475	C₂×D₆₇	semidirect
640. #474	C₂×D₆₇	semidirect
858. #41	Q₈×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574035	2
#22574010	2
#22573167	2
#22573162	2
#22573161	2
#22573152	2
#22573133	2
#22573103	2
#22573087	2
#22573071	2
#22570762	2
#22570749	2
#22570741	2
#22570069	2
#22570058	2
#22570043	2
C₂×#16863697	2
#22569152	2
#22569044	2
C₄×#14524068	2
C₆₇×#3076	2
#61385	67