Subgroups — #31735967

Order 17152.

1792 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574105	C₂	1	1	yes	maximal, characteristic, complemented
2	#22574028	C₂	1	1	yes	maximal, characteristic, complemented
3	#22573056	C₂	1	2	yes	maximal, complemented
4	#22573041	C₂	1	2	yes	maximal, complemented
5	#22573024	C₂	1	2	yes	maximal, complemented
6	#22573002	C₂	1	2	yes	maximal, complemented
7	#22572982	C₂	1	2	yes	maximal, complemented
8	#22572967	C₂	1	2	yes	maximal, complemented
9	#22572950	C₂	1	2	yes	maximal, complemented
10	#22572928	C₂	1	2	yes	maximal, complemented
11	#22570578	C₂	1	1	yes	maximal, characteristic, complemented
12	#22570567	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16863756	C₂	1	1	yes	maximal, characteristic, complemented
14	#22570054	C₂	1	1	yes	maximal, characteristic, complemented
15	#22570043	C₂	1	1	yes	maximal, characteristic, complemented
16	#22570024	C₂	1	1	yes	maximal, characteristic, complemented
17	#22569757	C₂	1	1	yes	maximal, characteristic, complemented
18	#22569746	C₂	1	1	yes	maximal, characteristic
19	#22569703	C₂	1	1	yes	maximal, characteristic, complemented
20	#22569149	C₂	1	1	yes	maximal, characteristic, complemented
21	#22569055	C₂	1	1	yes	maximal, characteristic, complemented
22	#22569044	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2943	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14524073	C₂²	1	1	yes	characteristic
25	C₂×#14524068	C₂²	1	1	yes	characteristic
26	#16864129	C₂²	1	2	yes	—
27	#16864129	C₂²	1	2	yes	—
28	Q₈×Dic₁₃₄	C₂²	1	2	yes	complemented
29	#16864125	C₂²	1	2	yes	complemented
30	#16864118	C₂²	1	2	yes	—
31	#16864118	C₂²	1	2	yes	—
32	#16864103	—	2	2	no	—
33	#16864103	C₂²	1	2	yes	complemented
34	#16864075	—	2	2	no	—
35	#16864075	—	2	2	no	—
36	D₄×Dic₁₃₄	—	2	2	no	—
37	D₄×Dic₁₃₄	C₂²	1	2	yes	complemented
38	#16864024	—	2	1	no	—
39	#16864024	—	2	1	no	—
40	#16864024	C₂²	1	1	yes	characteristic
41	#16864024	C₂²	1	1	yes	characteristic
42	#16864017	—	2	1	no	—
43	#16864017	—	2	1	no	—
44	#16863967	C₂²	1	1	yes	characteristic
45	#16863960	C₂²	1	1	yes	characteristic
46	#16863953	—	2	1	no	—
47	#16863953	C₂²	1	1	yes	characteristic
48	C₂×#14524043	—	2	1	no	—
49	C₂×#14524043	C₂²	1	1	yes	characteristic
50	#16863930	—	2	1	no	—
51	#16863930	—	2	1	no	—
52	C₂×#14524031	C₂²	1	1	yes	characteristic
53	#16863879	C₂²	1	1	yes	characteristic
54	#16863879	C₂²	1	1	yes	characteristic
55	#16863873	C₂²	1	1	yes	characteristic
56	#16863870	C₂²	1	1	yes	characteristic
57	#16863763	C₂²	1	2	yes	complemented
58	#16863759	C₂²	1	2	yes	—
59	#16863757	C₂²	1	2	yes	—
60	#16863756	C₂²	1	2	yes	—
61	#16863756	C₂²	1	2	yes	—
62	#16863756	C₂²	1	2	yes	—
63	#16863756	C₂²	1	2	yes	—
64	#16863754	C₂²	1	2	yes	complemented
65	#16863752	C₂²	1	2	yes	—
66	#16863749	C₂²	1	2	yes	complemented
67	#16863745	C₂²	1	2	yes	complemented
68	#16863741	C₂²	1	2	yes	—
69	#16863706	C₂²	1	2	yes	complemented
70	#16863702	C₂²	1	2	yes	complemented
71	#16863699	C₂²	1	2	yes	—
72	#16863695	C₂²	1	2	yes	—
73	#16863691	C₂²	1	2	yes	complemented
74	#16863690	C₂²	1	2	yes	complemented
75	#16863686	C₂²	1	2	yes	complemented
76	#16863685	C₂²	1	2	yes	—
77	#16863681	C₂²	1	2	yes	complemented
78	#16863680	C₂²	1	2	yes	complemented
79	#16863676	C₂²	1	2	yes	complemented
80	#16863675	C₂²	1	2	yes	—
81	#16863620	C₂²	1	2	yes	—
82	#16863618	C₂²	1	2	yes	—
83	#16863618	C₂²	1	2	yes	—
84	#16863616	C₂²	1	2	yes	complemented
85	#16863613	C₂²	1	2	yes	—
86	#16863611	C₂²	1	2	yes	—
87	#16863611	C₂²	1	2	yes	—
88	#16863609	C₂²	1	2	yes	complemented
89	#16863604	C₂²	1	2	yes	complemented
90	#16863599	C₂²	1	2	yes	complemented
91	#16863594	C₂²	1	2	yes	—
92	#16863589	C₂²	1	2	yes	—
93	#16863524	C₂²	1	2	yes	complemented
94	#16863524	C₂²	1	2	yes	complemented
95	#16863524	C₂²	1	2	yes	complemented
96	#16863524	C₂²	1	2	yes	complemented
97	#16863505	C₂²	1	2	yes	—
98	#16863500	C₂²	1	2	yes	complemented
99	#16863499	C₂²	1	2	yes	—
100	#16863493	C₂²	1	2	yes	complemented
101	#16863488	C₂²	1	2	yes	complemented
102	#16863487	C₂²	1	2	yes	complemented
103	#16863481	C₂²	1	2	yes	—
104	#16863476	C₂²	1	2	yes	—
105	#16863439	C₂²	1	1	yes	characteristic
106	#16863439	C₂²	1	1	yes	characteristic
107	#16863422	C₂²	1	1	yes	characteristic
108	#16863422	C₂²	1	1	yes	characteristic
109	#16863420	C₂²	1	1	yes	characteristic
110	#16863404	C₂²	1	1	yes	characteristic
111	#16863400	C₂²	1	1	yes	characteristic
112	#16863397	C₂²	1	1	yes	characteristic
113	#16863397	C₂²	1	1	yes	characteristic
114	C₂×#14523968	C₂²	1	1	yes	characteristic
115	C₂×#14523968	C₂²	1	1	yes	characteristic
116	C₂×#14523965	C₂²	1	1	yes	characteristic
117	C₂×#14523965	C₂²	1	1	yes	characteristic
118	#16863351	C₂²	1	1	yes	characteristic
119	#16863351	C₂²	1	1	yes	characteristic
120	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
122	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
123	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
126	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	#427×C₆₇	C₂²	1	1	yes	characteristic
132	#416×C₆₇	C₂²	1	1	yes	characteristic
133	#416×C₆₇	C₂²	1	1	yes	characteristic
134	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
135	C₂²×Dic₁₃₄	—	2	2	no	—
136	C₂²×Dic₁₃₄	—	2	1	no	—
137	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
138	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
139	#14524073	—	2	4	no	—
140	#14524068	—	2	4	no	—
141	C₂×#11761618	C₂³	1	2	yes	—
142	C₂×#11761616	C₂³	1	2	yes	—
143	C₂×#11761615	C₂³	1	2	yes	—
144	C₂×#11761613	C₂³	1	2	yes	—
145	C₂×#11761612	C₂³	1	1	yes	characteristic
146	C₂×#11761612	C₂³	1	1	yes	characteristic
147	#14524043	—	2	2	no	—
148	#14524043	—	2	1	no	—
149	#14524043	—	2	1	no	—
150	#14524043	—	2	2	no	—
151	#14524043	—	2	1	no	—
152	#14524043	—	2	1	no	—
153	#14524043	D₄	1	1	yes	characteristic
154	#14524043	D₄	1	1	yes	characteristic
155	#14524043	C₂³	1	2	yes	—
156	#14524043	C₂³	1	2	yes	—
157	#14524042	—	2	2	no	—
158	#14524042	—	2	2	no	—
159	#14524042	C₂³	1	2	yes	—
160	#14524042	C₂³	1	2	yes	—
161	#14524041	C₂³	1	2	yes	—
162	#14524039	C₂³	1	2	yes	—
163	#14524038	—	2	2	no	—
164	#14524038	—	2	2	no	—
165	#14524037	—	2	2	no	—
166	#14524037	—	2	2	no	—
167	#14524035	—	2	1	no	—
168	#14524035	—	2	1	no	—
169	#14524035	D₄	1	1	yes	characteristic
170	#14524035	D₄	1	1	yes	characteristic
171	#14524034	—	2	2	no	—
172	#14524034	—	2	2	no	—
173	#14524034	C₂³	1	2	yes	—
174	#14524034	C₂³	1	2	yes	—
175	#14524032	C₂³	1	2	yes	—
176	#14524031	—	2	1	no	—
177	#14524031	—	2	1	no	—
178	#14524031	C₂³	1	2	yes	—
179	#14524031	C₂³	1	2	yes	—
180	#14524030	C₂³	1	2	yes	—
181	#14524029	—	2	2	no	—
182	#14524029	—	2	2	no	—
183	#14524026	—	2	2	no	—
184	#14524026	—	2	2	no	—
185	#14524025	—	2	2	no	—
186	#14524025	—	2	2	no	—
187	#14524024	—	2	2	no	—
188	#14524022	—	2	2	no	—
189	#14524022	—	2	1	no	—
190	#14524022	—	2	1	no	—
191	#14524022	—	2	2	no	—
192	#14524022	D₄	1	2	yes	—
193	#14524022	D₄	1	2	yes	—
194	#14524021	—	2	2	no	—
195	#14524021	—	2	2	no	—
196	#14524020	—	2	2	no	—
197	#14524020	—	2	2	no	—
198	#14524020	—	2	2	no	—
199	#14524020	—	2	2	no	—
200	#14524020	—	2	2	no	—
201	#14524020	—	2	2	no	—
202	#14524017	—	2	1	no	—
203	#14524017	—	2	1	no	—
204	#14524011	—	2	2	no	—
205	Q₈×Dic₆₇	C₂³	1	2	yes	—
206	Q₈×Dic₆₇	C₂³	1	2	yes	—
207	C₄×Dic₁₃₄	—	2	2	no	—
208	C₄×Dic₁₃₄	—	2	1	no	—
209	C₄×Dic₁₃₄	—	2	1	no	—
210	C₄×Dic₁₃₄	—	2	2	no	—
211	C₄×Dic₁₃₄	C₂³	1	2	yes	—
212	C₄×Dic₁₃₄	C₂³	1	2	yes	—
213	#14524008	C₂³	1	2	yes	—
214	#14524008	C₂³	1	2	yes	—
215	C₄×D₂₆₈	—	2	1	no	—
216	C₄×D₂₆₈	—	2	1	no	—
217	D₄×Dic₆₇	—	2	2	no	—
218	D₄×Dic₆₇	—	2	2	no	—
219	D₄×Dic₆₇	C₂³	1	2	yes	—
220	D₄×Dic₆₇	C₂³	1	2	yes	—
221	#14524005	C₂³	1	2	yes	—
222	#14524005	C₂³	1	2	yes	—
223	C₄×C₂²⋊D₆₇	—	2	2	no	—
224	C₄×C₂²⋊D₆₇	—	2	2	no	—
225	#14524002	—	2	1	no	—
226	#14524002	—	2	1	no	—
227	#14524002	C₂³	1	1	yes	characteristic
228	#14524002	C₂³	1	1	yes	characteristic
229	#14524000	—	2	2	no	—
230	#14524000	—	2	2	no	—
231	#14523999	—	2	2	no	—
232	C₂×C₄⋊Dic₆₇	—	2	1	no	—
233	C₂×C₄⋊Dic₆₇	—	2	1	no	—
234	C₂×C₄⋊Dic₆₇	—	2	2	no	—
235	C₂×C₄⋊Dic₆₇	—	2	1	no	—
236	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
238	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
239	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
240	C₂²⋊C₄×D₆₇	—	2	2	no	—
241	#14523976	C₂³	1	2	yes	—
242	#14523976	C₂³	1	2	yes	—
243	#14523974	C₂³	1	2	yes	—
244	#14523974	C₂³	1	2	yes	—
245	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
246	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
247	Dic₆₇⋊C₈	C₂³	1	2	yes	—
248	Dic₆₇⋊C₈	C₂³	1	2	yes	—
249	Dic₆₇⋊C₈	C₂³	1	2	yes	—
250	Dic₆₇⋊C₈	C₂³	1	2	yes	—
251	#14523968	C₂³	1	2	yes	—
252	#14523968	C₂³	1	2	yes	—
253	#14523968	C₂³	1	2	yes	—
254	#14523968	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	#14523965	C₂³	1	2	yes	—
262	#14523965	C₂³	1	2	yes	—
263	#14523964	C₂³	1	2	yes	—
264	#14523964	C₂³	1	2	yes	—
265	#14523963	C₂³	1	2	yes	—
266	#14523963	C₂³	1	2	yes	—
267	#14523953	C₂³	1	2	yes	—
268	#14523953	C₂³	1	2	yes	—
269	C₈×Dic₆₇	C₂³	1	2	yes	—
270	C₈×Dic₆₇	C₂³	1	2	yes	—
271	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
272	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
273	#135×C₆₇	—	2	4	no	—
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×D₈×C₆₇	C₂³	1	1	yes	characteristic
278	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
279	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
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×D₄×C₆₇	—	2	1	no	—
285	C₄×D₄×C₆₇	—	2	1	no	—
286	C₄×D₄×C₆₇	—	2	1	no	—
287	C₄×D₄×C₆₇	—	2	1	no	—
288	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
292	#117×C₆₇	—	2	1	no	—
293	#117×C₆₇	—	2	1	no	—
294	#117×C₆₇	C₂³	1	1	yes	characteristic
295	#117×C₆₇	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₆₇	—	2	1	no	—
297	C₂×C₄²×C₆₇	—	2	1	no	—
298	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
299	#107×C₆₇	C₂³	1	1	yes	characteristic
300	#107×C₆₇	C₂³	1	1	yes	characteristic
301	#106×C₆₇	C₂³	1	1	yes	characteristic
302	#106×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	#102×C₆₇	C₂³	1	1	yes	characteristic
308	#102×C₆₇	C₂³	1	1	yes	characteristic
309	#102×C₆₇	C₂³	1	1	yes	characteristic
310	#102×C₆₇	C₂³	1	1	yes	characteristic
311	#97×C₆₇	C₂³	1	1	yes	characteristic
312	#97×C₆₇	C₂³	1	1	yes	characteristic
313	#97×C₆₇	C₂³	1	1	yes	characteristic
314	#97×C₆₇	C₂³	1	1	yes	characteristic
315	C₂³×D₆₇	—	2	1	no	—
316	C₂×Dic₁₃₄	—	2	2	no	—
317	C₂×Dic₁₃₄	—	2	2	no	—
318	C₂×Dic₁₃₄	—	2	1	no	—
319	C₂×Dic₁₃₄	—	2	2	no	—
320	C₂×Dic₁₃₄	—	2	2	no	—
321	C₂×Dic₁₃₄	—	2	2	no	—
322	C₂×Dic₁₃₄	—	2	2	no	—
323	C₂×Dic₁₃₄	—	8	4	no	—
324	C₂×Dic₁₃₄	—	8	2	no	—
325	C₂×Dic₁₃₄	C₂×D₄	1	2	yes	—
326	C₂×Dic₁₃₄	C₂×D₄	1	2	yes	—
327	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
328	C₂×D₂₆₈	—	2	2	no	—
329	C₂×D₂₆₈	—	2	2	no	—
330	C₂×D₂₆₈	—	2	1	no	—
331	C₂×D₂₆₈	C₂⁴	1	2	yes	—
332	C₂×C₂²⋊D₆₇	—	2	2	no	—
333	C₂×C₂²⋊D₆₇	—	2	2	no	—
334	C₂²×Dic₆₇	—	2	1	no	—
335	C₂²×Dic₆₇	—	2	1	no	—
336	C₂²×Dic₆₇	—	2	1	no	—
337	C₂²×Dic₆₇	—	2	2	no	—
338	C₂²×Dic₆₇	—	2	2	no	—
339	C₂×C₄×D₆₇	—	2	2	no	—
340	C₂×C₄×D₆₇	—	2	2	no	—
341	#11761618	—	2	4	no	—
342	#11761616	—	2	4	no	—
343	#11761615	—	2	4	no	—
344	#11761613	—	2	4	no	—
345	#11761612	—	2	2	no	—
346	#11761612	—	2	2	no	—
347	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
348	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
349	C₄⋊Dic₆₇	—	2	2	no	—
350	C₄⋊Dic₆₇	—	2	1	no	—
351	C₄⋊Dic₆₇	—	2	1	no	—
352	C₄⋊Dic₆₇	—	2	2	no	—
353	C₄⋊Dic₆₇	—	2	2	no	—
354	C₄⋊Dic₆₇	—	2	2	no	—
355	C₄⋊Dic₆₇	—	2	2	no	—
356	C₄⋊Dic₆₇	—	2	2	no	—
357	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
358	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
359	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
360	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
361	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
362	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
363	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
364	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
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	—	2	2	no	—
380	C₂²⋊Dic₆₇	—	2	2	no	—
381	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
382	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
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	C₄×Dic₆₇	—	2	2	no	—
392	C₄×Dic₆₇	—	2	2	no	—
393	C₄×Dic₆₇	—	2	2	no	—
394	C₄×Dic₆₇	—	2	2	no	—
395	C₄×Dic₆₇	C₂⁴	1	2	yes	—
396	C₄×Dic₆₇	C₂⁴	1	2	yes	—
397	#41×C₆₇	—	2	2	no	—
398	#41×C₆₇	—	2	2	no	—
399	#41×C₆₇	—	2	2	no	—
400	#41×C₆₇	#41	1	4	yes	—
401	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
402	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
403	C₂×D₄×C₆₇	—	2	1	no	—
404	C₂×D₄×C₆₇	—	2	1	no	—
405	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
406	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₆₇	—	2	1	no	—
408	C₂²×C₄×C₆₇	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
414	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
415	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
416	Q₁₆×C₆₇	—	2	2	no	—
417	SD₁₆×C₆₇	—	2	2	no	—
418	SD₁₆×C₆₇	—	2	2	no	—
419	D₈×C₆₇	—	2	2	no	—
420	C₂×C₈×C₆₇	—	2	2	no	—
421	C₂×C₈×C₆₇	—	2	2	no	—
422	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₆₇	—	2	1	no	—
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	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
432	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
433	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
434	C₂²⋊C₄×C₆₇	—	2	1	no	—
435	C₂²⋊C₄×C₆₇	—	2	1	no	—
436	C₂²⋊C₄×C₆₇	—	2	1	no	—
437	C₂²⋊C₄×C₆₇	—	2	1	no	—
438	C₂²⋊C₄×C₆₇	—	2	1	no	—
439	C₂²⋊C₄×C₆₇	—	2	1	no	—
440	C₄²×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	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₂³×C₆₇	—	2	1	no	—
451	C₂³×C₆₇	—	2	1	no	—
452	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
453	C₂²×D₆₇	—	2	2	no	—
454	C₂²×D₆₇	—	4	2	no	—
455	C₂²×D₆₇	—	8	1	no	—
456	C₂²×D₆₇	—	8	1	no	—
457	Q₈×C₆₇	—	2	1	no	—
458	Q₈×C₆₇	—	2	1	no	—
459	Q₈×C₆₇	—	2	1	no	—
460	Q₈×C₆₇	C₂×#41	1	2	yes	—
461	D₄×C₆₇	—	2	4	no	—
462	D₄×C₆₇	—	2	1	no	—
463	D₄×C₆₇	—	2	1	no	—
464	D₄×C₆₇	—	2	1	no	—
465	D₄×C₆₇	—	4	2	no	—
466	D₄×C₆₇	C₂×#41	1	2	yes	—
467	C₂×C₄×C₆₇	—	2	1	no	—
468	C₂×C₄×C₆₇	—	2	4	no	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	1	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	—	4	1	no	—
475	C₂×C₄×C₆₇	—	4	1	no	—
476	C₂×C₄×C₆₇	—	4	2	no	—
477	C₂×C₄×C₆₇	—	4	2	no	—
478	C₂×C₄×C₆₇	—	4	2	no	—
479	C₂×C₄×C₆₇	—	8	1	no	—
480	C₂×C₄×C₆₇	—	8	1	no	—
481	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
487	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
488	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
489	C₂²⋊D₆₇	—	8	2	no	—
490	C₂²⋊D₆₇	—	8	2	no	—
491	C₂×Dic₆₇	—	2	2	no	—
492	C₂×Dic₆₇	—	2	2	no	—
493	C₂×Dic₆₇	—	2	2	no	—
494	C₂×Dic₆₇	—	4	2	no	—
495	C₂×Dic₆₇	—	8	2	no	—
496	C₂×Dic₆₇	—	8	2	no	—
497	C₂×Dic₆₇	—	8	1	no	—
498	C₂×Dic₆₇	—	8	1	no	—
499	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
500	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
501	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
502	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
503	D₂₆₈	—	2	2	no	—
504	D₂₆₈	—	2	2	no	—
505	D₂₆₈	—	4	2	no	—
506	C₄×D₆₇	—	8	2	no	—
507	C₄×D₆₇	—	8	2	no	—
508	Dic₁₃₄	—	2	2	no	—
509	Dic₁₃₄	—	2	2	no	—
510	Dic₁₃₄	—	4	2	no	—
511	Dic₁₃₄	—	4	2	no	—
512	Dic₁₃₄	—	4	4	no	—
513	Dic₁₃₄	—	4	2	no	—
514	Dic₁₃₄	—	8	2	no	—
515	Dic₁₃₄	—	8	2	no	—
516	Dic₁₃₄	—	8	2	no	—
517	C₈×C₆₇	—	2	1	no	—
518	C₈×C₆₇	—	2	1	no	—
519	C₈×C₆₇	—	2	1	no	—
520	C₈×C₆₇	—	2	1	no	—
521	C₆₇⋊C₈	—	2	2	no	—
522	C₆₇⋊C₈	—	2	2	no	—
523	C₂²×C₆₇	—	2	1	no	—
524	C₂²×C₆₇	—	2	1	no	—
525	C₂²×C₆₇	—	2	2	no	—
526	C₂²×C₆₇	—	4	1	no	—
527	C₂²×C₆₇	—	4	1	no	—
528	C₂²×C₆₇	—	4	1	no	—
529	C₂²×C₆₇	—	4	1	no	—
530	C₂²×C₆₇	—	4	1	no	—
531	C₂²×C₆₇	#548	1	2	yes	—
532	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
533	C₂×D₆₇	—	4	2	no	—
534	C₂×D₆₇	—	4	2	no	—
535	C₂×D₆₇	—	4	2	no	—
536	C₂×D₆₇	—	16	2	no	—
537	C₄×C₆₇	—	2	1	no	—
538	C₄×C₆₇	—	2	1	no	—
539	C₄×C₆₇	—	2	1	no	—
540	C₄×C₆₇	—	2	1	no	—
541	C₄×C₆₇	—	2	2	no	—
542	C₄×C₆₇	—	4	1	no	—
543	C₄×C₆₇	—	4	1	no	—
544	C₄×C₆₇	—	4	1	no	—
545	C₄×C₆₇	—	4	1	no	—
546	C₄×C₆₇	—	4	1	no	—
547	C₄×C₆₇	#548	1	2	yes	—
548	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
549	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
550	Dic₆₇	—	2	2	no	—
551	Dic₆₇	—	2	2	no	—
552	Dic₆₇	—	2	2	no	—
553	Dic₆₇	—	2	2	no	—
554	Dic₆₇	—	4	2	no	—
555	Dic₆₇	—	4	2	no	—
556	Dic₆₇	—	4	2	no	—
557	#61336	—	67	1	no	maximal, Sylow
558	C₂×C₆₇	—	2	2	no	—
559	C₂×C₆₇	—	4	2	no	—
560	C₂×C₆₇	—	8	1	no	—
561	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
562	C₂×C₆₇	#3585	1	1	yes	characteristic
563	C₂×C₆₇	#3586	1	1	yes	characteristic
564	D₆₇	—	8	2	no	—
565	#3510	—	67	1	no	—
566	#3503	—	67	1	no	—
567	#3377	—	67	2	no	—
568	#3376	—	67	2	no	—
569	#3375	—	67	2	no	—
570	#3373	—	67	2	no	—
571	#3371	—	67	2	no	—
572	#3370	—	67	2	no	—
573	#3369	—	67	2	no	—
574	#3367	—	67	2	no	—
575	#3137	—	67	1	no	—
576	#3136	—	67	1	no	—
577	C₂×#489	—	67	1	no	—
578	#3082	—	67	1	no	—
579	#3081	—	67	1	no	—
580	#3079	—	67	1	no	—
581	#3046	—	67	1	no	—
582	#3045	—	67	1	no	—
583	#3040	—	67	1	no	—
584	#2961	—	67	1	no	—
585	#2947	—	67	1	no	—
586	#2946	—	67	1	no	—
587	#2943	D₆₇	1	1	yes	characteristic, complemented
588	C₆₇	#61336	1	1	yes	characteristic, complemented, Sylow
589	C₂×#137	—	67	1	no	—
590	C₂×AGL(1,ℤ/8)	—	67	1	no	—
591	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
592	#559	—	67	2	no	—
593	#559	—	67	2	no	—
594	Q₈²	—	67	2	no	—
595	#557	—	67	2	no	—
596	#556	—	67	2	no	—
597	#556	—	67	2	no	—
598	#554	—	67	2	no	—
599	#554	—	134	2	no	—
600	#551	—	134	2	no	—
601	#551	—	134	2	no	—
602	D₄×Q₈	—	67	2	no	—
603	D₄×Q₈	—	134	2	no	—
604	#544	—	67	1	no	—
605	#544	—	67	1	no	—
606	#544	—	134	1	no	—
607	#544	—	134	1	no	—
608	#542	—	134	1	no	—
609	#542	—	134	1	no	—
610	#536	—	67	1	no	—
611	#535	—	67	1	no	—
612	#533	—	67	1	no	—
613	#533	—	134	1	no	—
614	C₂×C₄⋊Q₈	—	67	1	no	—
615	C₂×C₄⋊Q₈	—	134	1	no	—
616	#529	—	134	1	no	—
617	#529	—	134	1	no	—
618	C₂×#124	—	67	1	no	—
619	#520	—	67	1	no	—
620	#520	—	67	1	no	—
621	#519	—	67	1	no	—
622	#518	—	67	1	no	—
623	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
624	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
625	#491	—	67	2	no	—
626	#490	—	67	2	no	—
627	#489	—	67	2	no	—
628	#489	—	67	2	no	—
629	#489	—	67	2	no	—
630	#489	—	67	2	no	—
631	#489	—	67	2	no	—
632	#489	—	67	2	no	—
633	#488	—	67	2	no	—
634	#488	—	67	2	no	—
635	#487	—	67	2	no	—
636	#486	—	67	2	no	—
637	#479	—	67	2	no	—
638	#479	—	67	2	no	—
639	#478	—	67	2	no	—
640	#478	—	67	2	no	—
641	#477	—	67	2	no	—
642	#477	—	67	2	no	—
643	#476	—	67	2	no	—
644	#476	—	67	2	no	—
645	#475	—	67	2	no	—
646	#475	—	67	2	no	—
647	#474	—	67	2	no	—
648	#474	—	67	2	no	—
649	#464	—	67	2	no	—
650	#464	—	67	2	no	—
651	#464	—	67	2	no	—
652	#464	—	67	2	no	—
653	#463	—	67	2	no	—
654	#463	—	67	2	no	—
655	#463	—	67	2	no	—
656	#463	—	67	2	no	—
657	#462	—	67	2	no	—
658	#461	—	67	2	no	—
659	#460	—	67	2	no	—
660	#459	—	67	2	no	—
661	#446	—	67	2	no	—
662	#446	—	67	2	no	—
663	#446	—	67	2	no	—
664	#446	—	67	2	no	—
665	#442	—	67	2	no	—
666	#442	C₂×D₆₇	1	1	yes	characteristic, complemented
667	#442	C₂×D₆₇	1	1	yes	characteristic, complemented
668	#441	—	67	2	no	—
669	#441	C₂×D₆₇	1	1	yes	characteristic, complemented
670	#441	C₂×D₆₇	1	1	yes	characteristic, complemented
671	#440	—	67	2	no	—
672	#440	—	67	2	no	—
673	#440	C₂×D₆₇	1	1	yes	characteristic, complemented
674	#440	C₂×D₆₇	1	1	yes	characteristic, complemented
675	#440	C₂×D₆₇	1	1	yes	characteristic, complemented
676	#440	C₂×D₆₇	1	1	yes	characteristic, complemented
677	C₄×Q₁₆	—	67	2	no	—
678	C₄×SD₁₆	—	67	2	no	—
679	C₄×SD₁₆	—	67	2	no	—
680	C₄×D₈	—	67	2	no	—
681	#428	—	67	1	no	—
682	#428	—	67	1	no	—
683	#427	C₂×D₆₇	1	1	yes	characteristic
684	#424	—	67	1	no	—
685	#424	—	67	1	no	—
686	#423	—	67	1	no	—
687	#419	—	67	1	no	—
688	#418	—	67	1	no	—
689	#417	—	67	1	no	—
690	#417	—	67	1	no	—
691	#416	C₂×D₆₇	1	1	yes	characteristic
692	#416	C₂×D₆₇	1	1	yes	characteristic
693	C₂×#103	—	67	1	no	—
694	C₂×#103	—	67	1	no	—
695	C₂×#102	—	67	1	no	—
696	C₂×#102	—	67	1	no	—
697	#405	—	67	1	no	—
698	#405	—	67	1	no	—
699	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
700	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
701	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
702	C₂²×Q₈	—	67	1	no	—
703	C₂²×Q₈	—	134	2	no	—
704	C₂²×Q₈	—	134	1	no	—
705	C₂²×D₄	—	67	1	no	—
706	#137	—	134	4	no	—
707	AGL(1,ℤ/8)	—	134	4	no	—
708	#135	—	2	4	no	—
709	C₂×Q₁₆	—	67	2	no	—
710	C₂×Q₁₆	C₂²×D₆₇	1	1	yes	characteristic
711	C₂×SD₁₆	—	67	2	no	—
712	C₂×SD₁₆	—	67	2	no	—
713	C₂×SD₁₆	C₂²×D₆₇	1	1	yes	characteristic
714	C₂×SD₁₆	C₂²×D₆₇	1	1	yes	characteristic
715	C₂×D₈	—	67	2	no	—
716	C₂×D₈	C₂²×D₆₇	1	1	yes	characteristic
717	C₂×M₁₆	—	67	1	no	—
718	C₂×M₁₆	—	67	1	no	—
719	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
720	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
721	C₄⋊Q₈	—	67	2	no	—
722	C₄⋊Q₈	—	67	2	no	—
723	C₄⋊Q₈	—	67	2	no	—
724	C₄⋊Q₈	—	67	1	no	—
725	C₄⋊Q₈	—	67	1	no	—
726	C₄⋊Q₈	—	67	2	no	—
727	C₄⋊Q₈	—	67	2	no	—
728	C₄⋊Q₈	—	134	1	no	—
729	C₄⋊Q₈	—	134	1	no	—
730	C₄⋊Q₈	—	134	2	no	—
731	C₄⋊Q₈	—	134	2	no	—
732	C₄⋊Q₈	—	134	2	no	—
733	C₄⋊Q₈	—	134	2	no	—
734	C₄⋊Q₈	—	134	1	no	—
735	C₄⋊Q₈	—	134	1	no	—
736	#127	—	67	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	2	no	—
743	#125	—	67	1	no	—
744	#125	—	67	1	no	—
745	#125	—	134	1	no	—
746	#125	—	134	1	no	—
747	#125	—	134	2	no	—
748	#125	—	134	2	no	—
749	#124	—	67	2	no	—
750	#124	—	67	2	no	—
751	#124	—	67	2	no	—
752	#124	—	67	2	no	—
753	#124	—	134	2	no	—
754	#124	—	134	2	no	—
755	#124	—	134	1	no	—
756	#124	—	134	1	no	—
757	#123	—	134	2	no	—
758	#123	—	134	2	no	—
759	#123	—	134	2	no	—
760	#123	—	134	2	no	—
761	#123	—	134	2	no	—
762	C₂²⋊Q₈	—	67	2	no	—
763	C₂²⋊Q₈	—	67	2	no	—
764	C₂²⋊Q₈	—	134	2	no	—
765	C₂²⋊Q₈	—	134	2	no	—
766	C₂²⋊Q₈	—	134	2	no	—
767	C₂²⋊Q₈	—	134	2	no	—
768	C₂²⋊Q₈	—	134	2	no	—
769	C₂²⋊Q₈	—	134	2	no	—
770	C₂²⋊Q₈	—	134	2	no	—
771	C₂²⋊Q₈	—	134	2	no	—
772	C₂²⋊Q₈	—	134	1	no	—
773	C₂²⋊Q₈	—	134	1	no	—
774	C₂²⋊Q₈	—	134	2	no	—
775	C₂²⋊Q₈	—	134	2	no	—
776	#121	—	134	1	no	—
777	#121	—	134	1	no	—
778	#120	—	134	2	no	—
779	C₄×Q₈	—	67	2	no	—
780	C₄×Q₈	—	67	2	no	—
781	C₄×Q₈	—	67	2	no	—
782	C₄×Q₈	—	67	2	no	—
783	C₄×Q₈	—	67	2	no	—
784	C₄×Q₈	—	67	2	no	—
785	C₄×Q₈	—	134	1	no	—
786	C₄×Q₈	—	134	1	no	—
787	C₄×Q₈	—	134	2	no	—
788	C₄×Q₈	—	134	2	no	—
789	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
790	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
791	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
792	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	67	2	no	—
798	C₄×D₄	—	67	2	no	—
799	C₄×D₄	—	67	2	no	—
800	C₄×D₄	—	67	2	no	—
801	C₄×D₄	—	134	1	no	—
802	C₄×D₄	—	134	1	no	—
803	C₄×D₄	—	134	2	no	—
804	C₄×D₄	—	134	2	no	—
805	C₄×D₄	—	134	2	no	—
806	C₄×D₄	—	134	2	no	—
807	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
808	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
809	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
810	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
811	#117	—	2	1	no	—
812	#117	—	2	1	no	—
813	#117	—	67	1	no	—
814	#117	—	67	1	no	—
815	#117	—	134	2	no	—
816	#117	—	134	2	no	—
817	#117	—	134	2	no	—
818	#117	—	134	1	no	—
819	#117	—	134	1	no	—
820	#117	C₂²×D₆₇	1	1	yes	characteristic
821	#117	C₂²×D₆₇	1	1	yes	characteristic
822	C₂×C₄⋊C₄	—	67	1	no	—
823	C₂×C₄⋊C₄	—	67	1	no	—
824	C₂×C₄⋊C₄	—	134	1	no	—
825	C₂×C₄⋊C₄	—	134	1	no	—
826	C₂×C₄⋊C₄	—	134	2	no	—
827	C₂×C₄⋊C₄	—	134	1	no	—
828	C₂×C₂²⋊C₄	—	134	2	no	—
829	C₂×C₂²⋊C₄	—	134	1	no	—
830	C₂×C₂²⋊C₄	—	134	1	no	—
831	C₂×C₄²	—	2	1	no	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
834	#107	—	67	2	no	—
835	#107	—	67	2	no	—
836	#107	C₂²×D₆₇	1	1	yes	characteristic
837	#107	C₂²×D₆₇	1	1	yes	characteristic
838	#106	—	67	2	no	—
839	#106	—	67	2	no	—
840	#106	C₂²×D₆₇	1	1	yes	characteristic
841	#106	C₂²×D₆₇	1	1	yes	characteristic
842	C₄⋊C₈	—	67	2	no	—
843	C₄⋊C₈	—	67	2	no	—
844	C₄⋊C₈	—	67	2	no	—
845	C₄⋊C₈	—	67	2	no	—
846	C₄⋊C₈	—	67	2	no	—
847	C₄⋊C₈	—	67	2	no	—
848	#103	—	67	2	no	—
849	#103	—	67	2	no	—
850	#103	—	67	2	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	C₂²×D₆₇	1	1	yes	characteristic
857	#103	C₂²×D₆₇	1	1	yes	characteristic
858	#103	C₂²×D₆₇	1	1	yes	characteristic
859	#103	C₂²×D₆₇	1	1	yes	characteristic
860	#102	—	67	2	no	—
861	#102	—	67	2	no	—
862	#102	—	67	2	no	—
863	#102	—	67	2	no	—
864	#102	—	67	2	no	—
865	#102	—	67	2	no	—
866	#102	—	67	2	no	—
867	#102	—	67	2	no	—
868	#102	C₂²×D₆₇	1	1	yes	characteristic
869	#102	C₂²×D₆₇	1	1	yes	characteristic
870	#102	C₂²×D₆₇	1	1	yes	characteristic
871	#102	C₂²×D₆₇	1	1	yes	characteristic
872	#97	—	67	2	no	—
873	#97	—	67	2	no	—
874	#97	C₂²×D₆₇	1	1	yes	characteristic
875	#97	C₂²×D₆₇	1	1	yes	characteristic
876	#97	C₂²×D₆₇	1	1	yes	characteristic
877	#97	C₂²×D₆₇	1	1	yes	characteristic
878	C₄×C₈	—	67	2	no	—
879	C₄×C₈	—	67	2	no	—
880	C₂⁴	—	134	1	no	—
881	#41	—	2	2	no	—
882	#41	—	2	2	no	—
883	#41	—	2	2	no	—
884	#41	#11761628	1	4	yes	—
885	C₂×Q₈	—	536	2	no	—
886	C₂×Q₈	—	536	4	no	—
887	C₂×Q₈	—	67	2	no	—
888	C₂×Q₈	—	67	2	no	—
889	C₂×Q₈	—	67	2	no	—
890	C₂×Q₈	—	134	2	no	—
891	C₂×Q₈	—	134	2	no	—
892	C₂×Q₈	—	134	2	no	—
893	C₂×Q₈	—	134	2	no	—
894	C₂×Q₈	—	134	1	no	—
895	C₂×Q₈	—	134	2	no	—
896	C₂×Q₈	—	134	2	no	—
897	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
898	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	67	2	no	—
902	C₂×D₄	—	134	2	no	—
903	C₂×D₄	—	134	2	no	—
904	C₂×D₄	—	134	1	no	—
905	C₂×D₄	—	134	2	no	—
906	C₂×D₄	—	134	2	no	—
907	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
908	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	134	2	no	—
916	C₂²×C₄	—	134	2	no	—
917	C₂²×C₄	—	134	1	no	—
918	C₂²×C₄	—	134	2	no	—
919	C₂²×C₄	—	134	2	no	—
920	C₂²×C₄	—	134	1	no	—
921	C₂²×C₄	—	134	1	no	—
922	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
923	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
924	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
925	Q₁₆	—	2	2	no	—
926	Q₁₆	—	134	4	no	—
927	SD₁₆	—	2	2	no	—
928	SD₁₆	—	2	2	no	—
929	SD₁₆	—	134	4	no	—
930	SD₁₆	—	134	4	no	—
931	D₈	—	2	2	no	—
932	D₈	—	134	4	no	—
933	M₁₆	—	134	2	no	—
934	M₁₆	—	134	2	no	—
935	C₂×C₈	—	2	2	no	—
936	C₂×C₈	—	2	2	no	—
937	C₂×C₈	—	67	2	no	—
938	C₂×C₈	—	67	2	no	—
939	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
940	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
941	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
942	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	67	1	no	—
948	C₄⋊C₄	—	67	1	no	—
949	C₄⋊C₄	—	67	2	no	—
950	C₄⋊C₄	—	67	1	no	—
951	C₄⋊C₄	—	67	1	no	—
952	C₄⋊C₄	—	67	2	no	—
953	C₄⋊C₄	—	67	2	no	—
954	C₄⋊C₄	—	67	2	no	—
955	C₄⋊C₄	—	67	2	no	—
956	C₄⋊C₄	—	67	2	no	—
957	C₄⋊C₄	—	67	2	no	—
958	C₄⋊C₄	—	67	2	no	—
959	C₄⋊C₄	—	134	2	no	—
960	C₄⋊C₄	—	134	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	1	no	—
972	C₄⋊C₄	—	134	1	no	—
973	C₄⋊C₄	—	134	2	no	—
974	C₄⋊C₄	—	134	2	no	—
975	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
976	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
977	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
978	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	67	2	no	—
986	C₂²⋊C₄	—	67	2	no	—
987	C₂²⋊C₄	—	134	2	no	—
988	C₂²⋊C₄	—	134	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	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	67	2	no	—
1006	C₄²	—	67	2	no	—
1007	C₄²	—	134	2	no	—
1008	C₄²	—	134	2	no	—
1009	C₄²	—	134	2	no	—
1010	C₄²	—	134	2	no	—
1011	C₄²	D₄×D₆₇	1	1	yes	characteristic
1012	C₄²	D₄×D₆₇	1	1	yes	characteristic
1013	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1014	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	268	2	no	—
1018	C₂³	—	536	1	no	—
1019	C₂³	—	536	1	no	—
1020	C₂³	—	134	2	no	—
1021	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1022	Q₈	—	2	1	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	268	4	no	—
1026	Q₈	—	268	2	no	—
1027	Q₈	—	268	2	no	—
1028	Q₈	—	268	2	no	—
1029	Q₈	—	536	2	no	—
1030	Q₈	—	536	2	no	—
1031	Q₈	—	536	2	no	—
1032	Q₈	—	134	2	no	—
1033	Q₈	—	134	2	no	—
1034	Q₈	C₂×#11761628	1	2	yes	—
1035	D₄	—	2	4	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	268	2	no	—
1041	D₄	—	536	2	no	—
1042	D₄	—	536	2	no	—
1043	D₄	—	134	2	no	—
1044	D₄	—	134	2	no	—
1045	D₄	C₂×#11761628	1	2	yes	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	4	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	4	1	no	—
1054	C₂×C₄	—	4	1	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	—	8	1	no	—
1060	C₂×C₄	—	268	2	no	—
1061	C₂×C₄	—	536	2	no	—
1062	C₂×C₄	—	536	2	no	—
1063	C₂×C₄	—	536	1	no	—
1064	C₂×C₄	—	536	1	no	—
1065	C₂×C₄	—	536	2	no	—
1066	C₂×C₄	—	536	2	no	—
1067	C₂×C₄	—	67	2	no	—
1068	C₂×C₄	—	67	2	no	—
1069	C₂×C₄	—	67	2	no	—
1070	C₂×C₄	—	67	2	no	—
1071	C₂×C₄	—	134	2	no	—
1072	C₂×C₄	—	134	2	no	—
1073	C₂×C₄	—	134	2	no	—
1074	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1075	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1076	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1077	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1078	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1079	C₂×C₄	C₂×#11761628	1	2	yes	—
1080	C₂×C₄	#14524090	1	2	yes	—
1081	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1082	C₈	—	2	1	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	1	no	—
1086	C₈	—	134	2	no	—
1087	C₈	—	134	2	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	268	2	no	—
1097	C₂²	—	268	2	no	—
1098	C₂²	—	268	2	no	—
1099	C₂²	—	1072	2	no	—
1100	C₂²	#16864055	1	2	yes	—
1101	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1102	C₄	—	2	2	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	268	2	no	—
1113	C₄	—	268	2	no	—
1114	C₄	—	268	2	no	—
1115	C₄	—	134	2	no	—
1116	C₄	—	134	2	no	—
1117	C₄	—	134	2	no	—
1118	C₄	—	134	2	no	—
1119	C₄	#16864055	1	2	yes	—
1120	C₄	C₂²×#11761628	1	1	yes	characteristic
1121	C₄	C₂×#14524090	1	1	yes	characteristic
1122	C₂	—	2	2	no	—
1123	C₂	—	4	2	no	—
1124	C₂	—	8	1	no	—
1125	C₂	—	536	2	no	—
1126	C₂	C₂×#16864055	1	1	yes	characteristic
1127	C₂	#22574986	1	1	yes	characteristic
1128	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	C₆₇×#2943	C₂
socle	C₂²×C₆₇	C₂³×D₄
prime radical	#22569746	C₂
hypercenter	#2943	D₆₇
hypocenter	C₆₇	#61336
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2943

Complements

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

N	H ≅ G/N	type
1. #22574105	C₂	semidirect
2. #22574028	C₂	semidirect
3. #22573056	C₂	semidirect
4. #22573041	C₂	semidirect
5. #22573024	C₂	semidirect
6. #22573002	C₂	semidirect
7. #22572982	C₂	semidirect
8. #22572967	C₂	semidirect
9. #22572950	C₂	semidirect
10. #22572928	C₂	semidirect
11. #22570578	C₂	semidirect
12. #22570567	C₂	semidirect
13. C₂×#16863756	C₂	semidirect
14. #22570054	C₂	semidirect
15. #22570043	C₂	semidirect
16. #22570024	C₂	semidirect
17. #22569757	C₂	semidirect
19. #22569703	C₂	semidirect
20. #22569149	C₂	semidirect
21. #22569055	C₂	semidirect
22. #22569044	C₂	semidirect
23. C₆₇×#2943	C₂	semidirect
28. Q₈×Dic₁₃₄	C₂²	semidirect
29. #16864125	C₂²	semidirect
33. #16864103	C₂²	semidirect
37. D₄×Dic₁₃₄	C₂²	semidirect
57. #16863763	C₂²	semidirect
64. #16863754	C₂²	semidirect
66. #16863749	C₂²	semidirect
67. #16863745	C₂²	semidirect
69. #16863706	C₂²	semidirect
70. #16863702	C₂²	semidirect
73. #16863691	C₂²	semidirect
74. #16863690	C₂²	semidirect
75. #16863686	C₂²	semidirect
77. #16863681	C₂²	semidirect
78. #16863680	C₂²	semidirect
79. #16863676	C₂²	semidirect
84. #16863616	C₂²	semidirect
88. #16863609	C₂²	semidirect
89. #16863604	C₂²	semidirect
90. #16863599	C₂²	semidirect
93. #16863524	C₂²	semidirect
94. #16863524	C₂²	semidirect
95. #16863524	C₂²	semidirect
96. #16863524	C₂²	semidirect
98. #16863500	C₂²	semidirect
100. #16863493	C₂²	semidirect
101. #16863488	C₂²	semidirect
102. #16863487	C₂²	semidirect
123. #442×C₆₇	C₂²	semidirect
124. #442×C₆₇	C₂²	semidirect
125. #441×C₆₇	C₂²	semidirect
126. #441×C₆₇	C₂²	semidirect
127. #440×C₆₇	C₂²	semidirect
128. #440×C₆₇	C₂²	semidirect
129. #440×C₆₇	C₂²	semidirect
130. #440×C₆₇	C₂²	semidirect
587. #2943	D₆₇	semidirect
588. C₆₇	#61336	semidirect
666. #442	C₂×D₆₇	semidirect
667. #442	C₂×D₆₇	semidirect
669. #441	C₂×D₆₇	semidirect
670. #441	C₂×D₆₇	semidirect
673. #440	C₂×D₆₇	semidirect
674. #440	C₂×D₆₇	semidirect
675. #440	C₂×D₆₇	semidirect
676. #440	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574105	2
#22574028	2
#22573056	2
#22573041	2
#22573024	2
#22573002	2
#22572982	2
#22572967	2
#22572950	2
#22572928	2
#22570578	2
#22570567	2
C₂×#16863756	2
#22570054	2
#22570043	2
#22570024	2
#22569757	2
#22569746	2
#22569703	2
#22569149	2
#22569055	2
#22569044	2
C₆₇×#2943	2
#61336	67