Subgroups — #31738557

Order 17152.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574272	C₂	1	2	yes	maximal, complemented
2	#22573195	C₂	1	1	yes	maximal, characteristic, complemented
3	#22573073	C₂	1	1	yes	maximal, characteristic, complemented
4	#22573039	C₂	1	2	yes	maximal, complemented
5	#22572637	C₂	1	1	yes	maximal, characteristic, complemented
6	#22572573	C₂	1	1	yes	maximal, characteristic, complemented
7	#22572428	C₂	1	2	yes	maximal, complemented
8	#22572243	C₂	1	2	yes	maximal, complemented
9	#22572179	C₂	1	2	yes	maximal, complemented
10	#22571931	C₂	1	1	yes	maximal, characteristic, complemented
11	#22571897	C₂	1	1	yes	maximal, characteristic, complemented
12	#22571897	C₂	1	1	yes	maximal, characteristic, complemented
13	#22570869	C₂	1	1	yes	maximal, characteristic, complemented
14	#22570841	C₂	1	1	yes	maximal, characteristic, complemented
15	#22570774	C₂	1	1	yes	maximal, characteristic, complemented
16	#22570489	C₂	1	2	yes	maximal, complemented
17	#22570463	C₂	1	2	yes	maximal, complemented
18	#22570313	C₂	1	2	yes	maximal, complemented
19	#22569177	C₂	1	1	yes	maximal, characteristic, complemented
20	#22569083	C₂	1	1	yes	maximal, characteristic, complemented
21	#22569056	C₂	1	1	yes	maximal, characteristic, complemented
22	#22568980	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#3339	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14524065	C₂²	1	1	yes	characteristic
25	C₂×#14524065	C₂²	1	1	yes	characteristic
26	C₂×D₈×D₆₇	C₂²	1	1	yes	characteristic
27	#16864116	C₂²	1	2	yes	complemented
28	#16864114	C₂²	1	2	yes	—
29	#16864102	C₂²	1	2	yes	complemented
30	#16864093	—	2	2	no	—
31	#16864082	—	2	2	no	—
32	#16864081	C₂²	1	2	yes	—
33	#16864075	—	2	2	no	—
34	#16864069	—	2	2	no	—
35	#16864051	C₂²	1	2	yes	complemented
36	#16864043	C₂²	1	2	yes	—
37	#16864043	C₂²	1	2	yes	—
38	#16864013	C₂²	1	2	yes	complemented
39	#16864009	C₂²	1	2	yes	—
40	#16863989	—	2	2	no	—
41	#16863978	—	2	2	no	—
42	#16863928	—	2	2	no	—
43	#16863927	C₂²	1	2	yes	complemented
44	#16863926	C₂²	1	1	yes	characteristic
45	#126×D₆₇	—	2	2	no	—
46	#16863877	C₂²	1	2	yes	complemented
47	#16863868	C₂²	1	2	yes	—
48	#16863864	C₂²	1	2	yes	complemented
49	#16863800	C₂²	1	1	yes	characteristic, complemented
50	#16863797	C₂²	1	1	yes	characteristic, complemented
51	#16863779	C₂²	1	1	yes	characteristic
52	#16863779	C₂²	1	1	yes	characteristic
53	#16863776	C₂²	1	1	yes	characteristic, complemented
54	#16863766	C₂²	1	2	yes	complemented
55	#16863754	C₂²	1	2	yes	complemented
56	#16863749	C₂²	1	2	yes	complemented
57	#16863740	C₂²	1	2	yes	—
58	#16863739	C₂²	1	2	yes	—
59	#16863737	C₂²	1	2	yes	complemented
60	#16863726	C₂²	1	2	yes	complemented
61	#16863702	C₂²	1	2	yes	complemented
62	#16863695	C₂²	1	2	yes	complemented
63	#16863693	C₂²	1	2	yes	complemented
64	#16863685	C₂²	1	2	yes	complemented
65	#16863680	C₂²	1	2	yes	complemented
66	#16863655	C₂²	1	2	yes	—
67	#16863640	C₂²	1	2	yes	complemented
68	#16863638	C₂²	1	1	yes	characteristic
69	#16863638	C₂²	1	1	yes	characteristic
70	#16863637	C₂²	1	1	yes	characteristic, complemented
71	#16863637	C₂²	1	1	yes	characteristic, complemented
72	#16863623	C₂²	1	2	yes	complemented
73	#16863617	C₂²	1	2	yes	complemented
74	#16863617	C₂²	1	2	yes	complemented
75	#16863610	C₂²	1	2	yes	—
76	#16863610	C₂²	1	2	yes	—
77	#16863602	C₂²	1	2	yes	complemented
78	#16863601	C₂²	1	2	yes	complemented
79	#16863560	C₂²	1	2	yes	complemented
80	#16863560	C₂²	1	2	yes	complemented
81	#16863548	C₂²	1	2	yes	—
82	#16863548	C₂²	1	2	yes	—
83	#16863539	C₂²	1	2	yes	—
84	#16863539	C₂²	1	2	yes	—
85	#16863525	C₂²	1	1	yes	characteristic, complemented
86	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
87	#16863506	C₂²	1	2	yes	—
88	#16863505	C₂²	1	2	yes	—
89	#16863502	C₂²	1	2	yes	complemented
90	#16863495	C₂²	1	2	yes	complemented
91	#16863495	C₂²	1	2	yes	complemented
92	#16863493	C₂²	1	2	yes	complemented
93	#16863490	C₂²	1	1	yes	characteristic, complemented
94	#16863490	C₂²	1	1	yes	characteristic, complemented
95	#16863490	C₂²	1	1	yes	characteristic, complemented
96	#16863490	C₂²	1	1	yes	characteristic, complemented
97	#16863487	C₂²	1	2	yes	complemented
98	#16863483	C₂²	1	2	yes	complemented
99	#16863483	C₂²	1	2	yes	complemented
100	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
101	D₈×Dic₆₇	C₂²	1	1	yes	characteristic
102	#16863478	C₂²	1	1	yes	characteristic
103	#16863478	C₂²	1	1	yes	characteristic
104	#16863478	C₂²	1	1	yes	characteristic
105	#16863471	C₂²	1	1	yes	characteristic
106	#16863468	C₂²	1	1	yes	characteristic, complemented
107	#16863464	C₂²	1	1	yes	characteristic
108	C₈×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
109	C₈×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
110	#16863456	C₂²	1	1	yes	characteristic
111	#16863454	C₂²	1	1	yes	characteristic, complemented
112	#16863450	C₂²	1	1	yes	characteristic, complemented
113	#16863433	C₂²	1	1	yes	characteristic
114	#16863399	C₂²	1	2	yes	—
115	#16863395	C₂²	1	2	yes	complemented
116	#16863390	C₂²	1	2	yes	complemented
117	#16863351	C₂²	1	1	yes	characteristic, complemented
118	#16863350	C₂²	1	1	yes	characteristic
119	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
120	#553×C₆₇	C₂²	1	2	yes	complemented
121	#499×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#482×C₆₇	C₂²	1	2	yes	complemented
123	#481×C₆₇	C₂²	1	2	yes	complemented
124	#478×C₆₇	C₂²	1	2	yes	complemented
125	#466×C₆₇	C₂²	1	1	yes	characteristic
126	#466×C₆₇	C₂²	1	1	yes	characteristic
127	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
128	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	C₂×#11761628	C₂³	1	2	yes	—
132	C₂×#11761628	C₂³	1	2	yes	—
133	C₂×D₄×D₆₇	C₂³	1	2	yes	—
134	#14524065	—	2	4	no	—
135	#14524065	—	2	4	no	—
136	C₂×Dic₂₆₈	C₂³	1	1	yes	characteristic
137	C₂×Dic₂₆₈	C₂³	1	1	yes	characteristic
138	C₂×Dic₂₆₈	C₂³	1	2	yes	—
139	C₂×#11761617	C₂³	1	2	yes	—
140	C₂×#11761617	C₂³	1	2	yes	—
141	C₂×#11761616	C₂³	1	2	yes	—
142	C₂×#11761616	C₂³	1	2	yes	—
143	C₂×D₅₃₆	C₂³	1	1	yes	characteristic
144	C₂×#11761613	C₂³	1	2	yes	—
145	D₈×D₆₇	—	2	4	no	—
146	C₂×#11761612	C₂³	1	1	yes	characteristic
147	C₂×#11761611	C₂³	1	1	yes	characteristic
148	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
150	#14524043	C₂³	1	2	yes	—
151	#14524042	C₂³	1	2	yes	—
152	#14524038	—	2	2	no	—
153	#14524038	—	2	2	no	—
154	#14524038	—	2	2	no	—
155	#14524038	D₄	1	1	yes	characteristic
156	#14524037	—	2	2	no	—
157	#14524036	—	2	2	no	—
158	#14524036	—	2	2	no	—
159	#14524036	—	2	2	no	—
160	#14524036	—	2	2	no	—
161	#14524036	—	2	2	no	—
162	#14524036	D₄	1	1	yes	characteristic
163	#14524034	—	2	2	no	—
164	#14524034	—	2	2	no	—
165	#14524034	C₂³	1	2	yes	—
166	#14524033	—	2	2	no	—
167	#14524033	D₄	1	1	yes	characteristic
168	#14524030	—	2	2	no	—
169	#14524030	C₂³	1	2	yes	—
170	#14524030	C₂³	1	2	yes	—
171	#14524029	—	2	2	no	—
172	#14524029	D₄	1	1	yes	characteristic
173	#14524027	D₄	1	1	yes	characteristic
174	#14524026	—	2	2	no	—
175	#14524025	—	2	2	no	—
176	#14524025	—	2	2	no	—
177	#14524025	—	2	2	no	—
178	#14524025	—	2	2	no	—
179	#14524024	—	2	2	no	—
180	#14524024	—	2	2	no	—
181	#14524024	D₄	1	1	yes	characteristic
182	#14524023	—	2	2	no	—
183	#14524023	C₂³	1	2	yes	—
184	#14524023	C₂³	1	2	yes	—
185	#14524022	—	2	2	no	—
186	#14524022	C₂³	1	2	yes	—
187	#14524022	C₂³	1	2	yes	—
188	#14524021	—	2	2	no	—
189	#14524021	—	2	2	no	—
190	#14524020	—	2	2	no	—
191	#14524020	D₄	1	1	yes	characteristic
192	#14524015	D₄	1	1	yes	characteristic
193	#14524014	—	2	2	no	—
194	#14524014	—	2	2	no	—
195	#14524014	—	2	2	no	—
196	#14524011	—	2	2	no	—
197	#14524011	—	2	2	no	—
198	C₄×Dic₁₃₄	—	2	2	no	—
199	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
200	#14524008	C₂³	1	2	yes	—
201	#14524008	C₂³	1	2	yes	—
202	#14524008	C₂³	1	2	yes	—
203	#14524008	C₂³	1	2	yes	—
204	C₄×D₂₆₈	C₂³	1	2	yes	—
205	D₄×Dic₆₇	—	2	2	no	—
206	D₄×Dic₆₇	C₂³	1	2	yes	—
207	#14524005	C₂³	1	2	yes	—
208	#14524005	C₂³	1	2	yes	—
209	#14524005	C₂³	1	2	yes	—
210	C₄×C₂²⋊D₆₇	—	2	2	no	—
211	C₄×C₂²⋊D₆₇	—	2	2	no	—
212	C₄×C₂²⋊D₆₇	—	2	2	no	—
213	C₄×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
214	C₄×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
215	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
216	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
217	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
218	#14524002	—	2	2	no	—
219	#14524002	—	2	2	no	—
220	#14524002	C₂³	1	1	yes	characteristic
221	#14524001	—	2	2	no	—
222	#14524001	C₂³	1	2	yes	—
223	#14524000	—	2	2	no	—
224	#14524000	C₂³	1	1	yes	characteristic
225	#14523999	—	2	2	no	—
226	C₄⋊C₄×D₆₇	—	2	2	no	—
227	C₄⋊C₄×D₆₇	—	2	2	no	—
228	C₄⋊C₄×D₆₇	—	2	2	no	—
229	C₂×(C₂×D₆₇)⋊C₄	—	2	2	no	—
230	C₂²⋊C₄×D₆₇	—	2	2	no	—
231	C₂²⋊C₄×D₆₇	—	2	2	no	—
232	C₂²⋊C₄×D₆₇	—	2	2	no	—
233	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
234	C₄²×D₆₇	—	2	2	no	—
235	#14523977	C₂³	1	1	yes	characteristic
236	#14523976	C₂³	1	2	yes	—
237	#14523974	C₂³	1	2	yes	—
238	#14523974	C₂³	1	2	yes	—
239	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
240	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
241	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
242	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
243	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
244	#14523968	C₂³	1	2	yes	—
245	#14523968	C₂³	1	2	yes	—
246	#14523966	C₂³	1	2	yes	—
247	#14523966	C₂³	1	2	yes	—
248	#14523966	C₂³	1	2	yes	—
249	#14523966	C₂³	1	2	yes	—
250	#14523966	C₂³	1	2	yes	—
251	#14523966	C₂³	1	2	yes	—
252	#14523965	C₂³	1	2	yes	—
253	#14523964	C₂³	1	2	yes	—
254	#14523963	C₂³	1	2	yes	—
255	#14523963	C₂³	1	2	yes	—
256	#14523963	C₂³	1	2	yes	—
257	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
258	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
259	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
260	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
261	#14523954	C₂³	1	1	yes	characteristic
262	#14523953	C₂³	1	1	yes	characteristic
263	#14523953	C₂³	1	1	yes	characteristic
264	#14523953	C₂³	1	1	yes	characteristic
265	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
266	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
267	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
268	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
269	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
270	C₂×D₈×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	#126×C₆₇	—	2	2	no	—
274	#125×C₆₇	C₂³	1	2	yes	—
275	#123×C₆₇	—	2	2	no	—
276	#121×C₆₇	—	2	2	no	—
277	#121×C₆₇	C₂³	1	2	yes	—
278	#121×C₆₇	C₂³	1	2	yes	—
279	C₄×D₄×C₆₇	—	2	2	no	—
280	C₄×D₄×C₆₇	C₂³	1	2	yes	—
281	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
282	#117×C₆₇	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
284	#107×C₆₇	C₂³	1	1	yes	characteristic
285	#107×C₆₇	C₂³	1	1	yes	characteristic
286	#107×C₆₇	C₂³	1	1	yes	characteristic
287	#107×C₆₇	C₂³	1	2	yes	—
288	#106×C₆₇	C₂³	1	2	yes	—
289	#106×C₆₇	C₂³	1	2	yes	—
290	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
291	#102×C₆₇	C₂³	1	2	yes	—
292	#102×C₆₇	C₂³	1	2	yes	—
293	#102×C₆₇	C₂³	1	2	yes	—
294	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
295	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
297	C₂³×D₆₇	—	2	2	no	—
298	#11761628	—	2	4	no	—
299	#11761628	—	2	4	no	—
300	#11761628	—	4	2	no	—
301	#11761628	—	4	2	no	—
302	C₂×Dic₁₃₄	—	2	2	no	—
303	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
304	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
305	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
306	C₂×D₂₆₈	C₂⁴	1	2	yes	—
307	C₂×C₂²⋊D₆₇	—	2	2	no	—
308	C₂×C₂²⋊D₆₇	—	2	2	no	—
309	C₂×C₂²⋊D₆₇	—	2	2	no	—
310	C₂×C₂²⋊D₆₇	C₂×D₄	1	1	yes	characteristic
311	C₂×C₂²⋊D₆₇	C₂×D₄	1	1	yes	characteristic
312	D₄×D₆₇	—	2	4	no	—
313	D₄×D₆₇	—	4	2	no	—
314	C₂²×Dic₆₇	—	2	2	no	—
315	C₂²×Dic₆₇	C₂×D₄	1	1	yes	characteristic
316	C₂²×Dic₆₇	C₂×D₄	1	1	yes	characteristic
317	C₂×C₄×D₆₇	—	2	2	no	—
318	C₂×C₄×D₆₇	—	2	2	no	—
319	C₂×C₄×D₆₇	—	2	2	no	—
320	C₂×C₄×D₆₇	—	2	2	no	—
321	C₂×C₄×D₆₇	—	2	2	no	—
322	C₂×C₄×D₆₇	—	2	2	no	—
323	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
324	Dic₂₆₈	—	2	2	no	—
325	Dic₂₆₈	—	2	2	no	—
326	Dic₂₆₈	—	4	2	no	—
327	#11761617	—	2	4	no	—
328	#11761617	—	2	4	no	—
329	#11761616	—	4	2	no	—
330	#11761616	—	4	2	no	—
331	D₅₃₆	#41	1	4	yes	—
332	#11761613	—	2	4	no	—
333	#11761612	—	4	1	no	—
334	#11761611	—	4	1	no	—
335	C₂×C₆₇⋊C₈	—	4	1	no	—
336	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
337	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
338	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
339	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
340	C₈×D₆₇	—	2	2	no	—
341	C₄⋊Dic₆₇	—	2	2	no	—
342	C₄⋊Dic₆₇	—	2	2	no	—
343	C₄⋊Dic₆₇	—	2	2	no	—
344	C₄⋊Dic₆₇	—	2	2	no	—
345	C₄⋊Dic₆₇	—	2	2	no	—
346	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
347	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
348	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
349	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
350	Dic₆₇⋊C₄	—	2	2	no	—
351	Dic₆₇⋊C₄	—	2	2	no	—
352	Dic₆₇⋊C₄	—	2	2	no	—
353	Dic₆₇⋊C₄	—	2	2	no	—
354	Dic₆₇⋊C₄	—	2	2	no	—
355	Dic₆₇⋊C₄	—	2	2	no	—
356	Dic₆₇⋊C₄	—	2	2	no	—
357	Dic₆₇⋊C₄	—	2	2	no	—
358	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
359	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
360	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
361	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
362	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
363	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
364	C₂²⋊Dic₆₇	—	2	2	no	—
365	C₂²⋊Dic₆₇	—	2	2	no	—
366	C₂²⋊Dic₆₇	—	2	2	no	—
367	C₂²⋊Dic₆₇	—	2	2	no	—
368	C₂²⋊Dic₆₇	—	2	2	no	—
369	C₂²⋊Dic₆₇	—	2	2	no	—
370	C₂²⋊Dic₆₇	—	2	2	no	—
371	C₂²⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
372	C₂²⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
373	C₂²⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
374	C₂²⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
375	(C₂×D₆₇)⋊C₄	—	2	2	no	—
376	(C₂×D₆₇)⋊C₄	—	2	2	no	—
377	(C₂×D₆₇)⋊C₄	—	2	2	no	—
378	(C₂×D₆₇)⋊C₄	—	2	2	no	—
379	(C₂×D₆₇)⋊C₄	—	2	2	no	—
380	(C₂×D₆₇)⋊C₄	—	2	2	no	—
381	(C₂×D₆₇)⋊C₄	—	2	2	no	—
382	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
383	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
384	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
385	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
386	C₄×Dic₆₇	—	2	2	no	—
387	C₄×Dic₆₇	—	2	2	no	—
388	C₄×Dic₆₇	—	2	2	no	—
389	C₄×Dic₆₇	—	2	2	no	—
390	C₄×Dic₆₇	—	2	2	no	—
391	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
392	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
393	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
394	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
395	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×D₄×C₆₇	—	2	2	no	—
397	C₂×D₄×C₆₇	—	2	2	no	—
398	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
399	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
400	C₂²×C₄×C₆₇	—	2	2	no	—
401	C₂²×C₄×C₆₇	—	2	2	no	—
402	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	D₈×C₆₇	—	2	2	no	—
405	C₂×C₈×C₆₇	—	2	2	no	—
406	C₂×C₈×C₆₇	—	2	2	no	—
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	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₆₇	—	2	2	no	—
412	C₄⋊C₄×C₆₇	—	2	2	no	—
413	C₄⋊C₄×C₆₇	—	2	2	no	—
414	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
418	C₂²⋊C₄×C₆₇	—	2	2	no	—
419	C₂²⋊C₄×C₆₇	—	2	2	no	—
420	C₂²⋊C₄×C₆₇	—	2	2	no	—
421	C₂²⋊C₄×C₆₇	—	2	2	no	—
422	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
423	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
424	C₄²×C₆₇	—	2	2	no	—
425	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₂³×C₆₇	—	2	2	no	—
427	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
428	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
429	C₂²×D₆₇	—	2	2	no	—
430	C₂²×D₆₇	—	4	4	no	—
431	C₂²×D₆₇	—	8	2	no	—
432	C₂²×D₆₇	—	8	2	no	—
433	C₂²×D₆₇	C₂²×D₄	1	1	yes	characteristic
434	D₄×C₆₇	—	2	2	no	—
435	D₄×C₆₇	—	2	2	no	—
436	D₄×C₆₇	—	4	1	no	—
437	D₄×C₆₇	—	8	2	no	—
438	D₄×C₆₇	—	8	2	no	—
439	C₂×C₄×C₆₇	—	2	1	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	2	no	—
446	C₂×C₄×C₆₇	—	8	2	no	—
447	C₂×C₄×C₆₇	—	8	2	no	—
448	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
453	C₂²⋊D₆₇	—	4	1	no	—
454	C₂²⋊D₆₇	—	4	1	no	—
455	C₂²⋊D₆₇	—	4	4	no	—
456	C₂²⋊D₆₇	—	4	4	no	—
457	C₂²⋊D₆₇	—	4	4	no	—
458	C₂×Dic₆₇	—	2	2	no	—
459	C₂×Dic₆₇	—	2	2	no	—
460	C₂×Dic₆₇	—	2	2	no	—
461	C₂×Dic₆₇	—	4	1	no	—
462	C₂×Dic₆₇	—	4	1	no	—
463	C₂×Dic₆₇	—	8	2	no	—
464	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
465	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
466	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
467	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
469	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
470	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
471	D₂₆₈	—	2	2	no	—
472	D₂₆₈	C₂×#41	1	4	yes	—
473	C₄×D₆₇	—	2	1	no	—
474	C₄×D₆₇	—	2	1	no	—
475	C₄×D₆₇	—	4	4	no	—
476	C₄×D₆₇	—	4	4	no	—
477	C₄×D₆₇	—	8	2	no	—
478	C₄×D₆₇	—	8	2	no	—
479	C₄×D₆₇	—	8	2	no	—
480	C₄×D₆₇	—	8	2	no	—
481	Dic₁₃₄	—	2	2	no	—
482	Dic₁₃₄	—	2	2	no	—
483	Dic₁₃₄	—	2	2	no	—
484	Dic₁₃₄	—	2	2	no	—
485	Dic₁₃₄	—	4	1	no	—
486	Dic₁₃₄	—	8	2	no	—
487	C₈×C₆₇	—	2	1	no	—
488	C₈×C₆₇	—	2	1	no	—
489	C₈×C₆₇	—	2	1	no	—
490	C₈×C₆₇	C₂×#41	1	2	yes	—
491	C₆₇⋊C₈	—	2	1	no	—
492	C₆₇⋊C₈	—	2	1	no	—
493	C₆₇⋊C₈	—	2	1	no	—
494	C₆₇⋊C₈	—	2	1	no	—
495	C₂²×C₆₇	—	2	1	no	—
496	C₂²×C₆₇	—	2	1	no	—
497	C₂²×C₆₇	—	2	1	no	—
498	C₂²×C₆₇	—	2	1	no	—
499	C₂²×C₆₇	—	2	1	no	—
500	C₂²×C₆₇	—	2	1	no	—
501	C₂²×C₆₇	—	4	2	no	—
502	C₂²×C₆₇	—	4	2	no	—
503	C₂²×C₆₇	—	4	2	no	—
504	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
505	C₂×D₆₇	—	2	1	no	—
506	C₂×D₆₇	—	2	1	no	—
507	C₂×D₆₇	—	2	1	no	—
508	C₂×D₆₇	—	2	4	no	—
509	C₂×D₆₇	—	4	2	no	—
510	C₂×D₆₇	—	4	2	no	—
511	C₂×D₆₇	—	16	4	no	—
512	C₄×C₆₇	—	2	1	no	—
513	C₄×C₆₇	—	2	1	no	—
514	C₄×C₆₇	—	2	1	no	—
515	C₄×C₆₇	—	2	1	no	—
516	C₄×C₆₇	—	4	2	no	—
517	C₄×C₆₇	—	4	2	no	—
518	C₄×C₆₇	—	4	2	no	—
519	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
520	C₄×C₆₇	#585	1	1	yes	characteristic
521	Dic₆₇	—	2	1	no	—
522	Dic₆₇	—	2	1	no	—
523	Dic₆₇	—	2	1	no	—
524	Dic₆₇	—	2	1	no	—
525	Dic₆₇	—	2	1	no	—
526	Dic₆₇	—	2	1	no	—
527	Dic₆₇	—	2	1	no	—
528	Dic₆₇	—	4	2	no	—
529	Dic₆₇	—	4	2	no	—
530	Dic₆₇	—	4	2	no	—
531	#61487	—	67	1	no	maximal, Sylow
532	C₂×C₆₇	—	4	1	no	—
533	C₂×C₆₇	—	4	1	no	—
534	C₂×C₆₇	—	8	2	no	—
535	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
536	C₂×C₆₇	#3584	1	1	yes	characteristic
537	C₂×C₆₇	#3584	1	1	yes	characteristic
538	D₆₇	—	4	1	no	—
539	D₆₇	—	4	4	no	—
540	#3521	—	67	2	no	—
541	#3393	—	67	1	no	—
542	#3380	—	67	1	no	—
543	#3376	—	67	2	no	—
544	#3342	—	67	1	no	—
545	#3339	D₆₇	1	1	yes	characteristic, complemented
546	#3336	—	67	1	no	—
547	#3323	—	67	2	no	—
548	#3311	—	67	2	no	—
549	#3307	—	67	2	no	—
550	#3283	—	67	1	no	—
551	#3280	—	67	1	no	—
552	#3280	—	67	1	no	—
553	#3177	—	67	1	no	—
554	#3175	—	67	1	no	—
555	#3168	—	67	1	no	—
556	#3125	—	67	2	no	—
557	#3123	—	67	2	no	—
558	#3111	—	67	2	no	—
559	#2966	—	67	1	no	—
560	#2951	—	67	1	no	—
561	#2948	—	67	1	no	—
562	C₄×#135	—	67	1	no	—
563	C₆₇	#61487	1	1	yes	characteristic, complemented, Sylow
564	C₂×#135	—	67	1	no	—
565	C₂×#135	—	67	1	no	—
566	C₂²×D₈	—	67	1	no	—
567	#556	—	67	2	no	—
568	#556	—	67	2	no	—
569	#554	—	67	2	no	—
570	#553	—	134	2	no	—
571	#553	C₂×D₆₇	1	2	yes	complemented
572	#552	—	67	2	no	—
573	#552	—	134	2	no	—
574	#551	—	134	2	no	—
575	#551	—	134	2	no	—
576	#547	—	67	2	no	—
577	#546	—	67	2	no	—
578	#546	—	67	2	no	—
579	#542	—	67	2	no	—
580	#541	—	67	2	no	—
581	#539	—	134	2	no	—
582	#538	—	134	2	no	—
583	#529	—	67	1	no	—
584	#529	—	67	2	no	—
585	#529	—	134	2	no	—
586	C₂×#126	—	134	2	no	—
587	#520	—	67	2	no	—
588	#518	—	67	2	no	—
589	C₄×#41	—	67	2	no	—
590	#500	—	67	1	no	—
591	#499	—	67	1	no	—
592	#499	C₂×D₆₇	1	1	yes	characteristic, complemented
593	#495	—	67	1	no	—
594	#495	—	67	1	no	—
595	#494	—	67	1	no	—
596	#491	—	67	2	no	—
597	#489	—	67	2	no	—
598	#488	—	67	2	no	—
599	#485	—	67	2	no	—
600	#485	—	67	2	no	—
601	#485	—	67	2	no	—
602	#483	—	67	2	no	—
603	#482	C₂×D₆₇	1	2	yes	complemented
604	#481	C₂×D₆₇	1	2	yes	complemented
605	#479	—	67	2	no	—
606	#478	—	67	2	no	—
607	#478	—	67	2	no	—
608	#478	C₂×D₆₇	1	2	yes	complemented
609	#476	—	67	2	no	—
610	#475	—	67	2	no	—
611	#470	—	67	2	no	—
612	#468	—	67	2	no	—
613	#467	—	67	1	no	—
614	#467	—	67	1	no	—
615	#467	—	67	1	no	—
616	#467	—	67	1	no	—
617	#466	C₂×D₆₇	1	1	yes	characteristic
618	#466	C₂×D₆₇	1	1	yes	characteristic
619	#465	—	67	2	no	—
620	#464	—	67	2	no	—
621	#464	—	67	2	no	—
622	#463	—	67	2	no	—
623	#463	—	67	2	no	—
624	#461	—	67	2	no	—
625	#461	—	67	2	no	—
626	#452	—	67	2	no	—
627	#452	—	67	2	no	—
628	#450	—	67	2	no	—
629	#450	—	67	2	no	—
630	#449	—	67	2	no	—
631	#449	—	67	2	no	—
632	#446	—	67	1	no	—
633	C₈×Q₈	—	67	1	no	—
634	#442	—	67	2	no	—
635	#442	—	67	2	no	—
636	#441	—	67	2	no	—
637	#440	—	67	2	no	—
638	#440	—	67	2	no	—
639	#440	—	67	2	no	—
640	C₄×Q₁₆	—	67	1	no	—
641	C₄×Q₁₆	—	67	1	no	—
642	C₄×Q₁₆	—	67	1	no	—
643	C₄×Q₁₆	—	67	1	no	—
644	C₄×SD₁₆	—	67	2	no	—
645	C₄×SD₁₆	—	67	2	no	—
646	C₄×SD₁₆	—	67	2	no	—
647	C₄×D₈	—	67	1	no	—
648	C₄×D₈	—	67	1	no	—
649	C₄×D₈	—	67	1	no	—
650	C₄×D₈	—	67	1	no	—
651	C₄×D₈	—	67	1	no	—
652	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
653	#436	—	67	1	no	—
654	#435	—	67	1	no	—
655	#435	—	67	1	no	—
656	C₈×D₄	—	67	1	no	—
657	C₈×D₄	—	67	1	no	—
658	C₈×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
659	#433	—	67	1	no	—
660	#433	—	67	1	no	—
661	#432	—	67	1	no	—
662	#427	—	67	1	no	—
663	#427	C₂×D₆₇	1	1	yes	characteristic, complemented
664	C₂×#107	C₂×D₆₇	1	1	yes	characteristic, complemented
665	#418	—	67	2	no	—
666	#417	—	67	2	no	—
667	#416	—	67	2	no	—
668	#405	—	67	1	no	—
669	#405	—	67	1	no	—
670	C₂×C₄×C₈	—	67	1	no	—
671	C₂×#41	—	67	2	no	—
672	C₂×#41	—	67	2	no	—
673	C₂²×D₄	—	67	2	no	—
674	#135	—	134	4	no	—
675	#135	—	134	4	no	—
676	C₂×Q₁₆	—	67	2	no	—
677	C₂×Q₁₆	—	67	1	no	—
678	C₂×Q₁₆	—	67	1	no	—
679	C₂×SD₁₆	—	67	2	no	—
680	C₂×SD₁₆	—	67	2	no	—
681	C₂×SD₁₆	—	67	2	no	—
682	C₂×SD₁₆	—	67	2	no	—
683	C₂×D₈	—	67	2	no	—
684	C₂×D₈	—	67	1	no	—
685	C₂×D₈	—	134	4	no	—
686	C₂×D₈	C₂²×D₆₇	1	1	yes	characteristic
687	C₂×M₁₆	—	67	1	no	—
688	C₂×M₁₆	—	67	1	no	—
689	C₂²×C₈	—	67	1	no	—
690	C₂²×C₈	—	67	1	no	—
691	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
692	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
693	C₄⋊Q₈	—	67	2	no	—
694	C₄⋊Q₈	—	67	2	no	—
695	#126	—	2	2	no	—
696	#126	—	67	1	no	—
697	#126	—	67	1	no	—
698	#126	—	134	2	no	—
699	#126	—	134	2	no	—
700	#126	—	134	2	no	—
701	#126	—	134	2	no	—
702	#126	—	134	2	no	—
703	#126	—	134	2	no	—
704	#126	—	134	2	no	—
705	#126	—	134	2	no	—
706	#126	—	134	2	no	—
707	#125	—	67	1	no	—
708	#125	—	67	2	no	—
709	#125	—	134	2	no	—
710	#125	—	134	2	no	—
711	#125	—	134	2	no	—
712	#125	C₂²×D₆₇	1	2	yes	—
713	#124	—	67	1	no	—
714	#124	—	67	2	no	—
715	#124	—	67	2	no	—
716	#124	—	134	2	no	—
717	#124	—	134	2	no	—
718	#123	—	2	2	no	—
719	#123	—	67	1	no	—
720	#123	—	67	1	no	—
721	#123	—	134	2	no	—
722	#123	—	134	2	no	—
723	#123	—	134	2	no	—
724	#123	—	134	2	no	—
725	#123	—	134	2	no	—
726	#123	—	134	2	no	—
727	#123	—	134	2	no	—
728	C₂²⋊Q₈	—	67	1	no	—
729	C₂²⋊Q₈	—	67	2	no	—
730	C₂²⋊Q₈	—	67	2	no	—
731	C₂²⋊Q₈	—	67	2	no	—
732	C₂²⋊Q₈	—	67	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	#121	—	2	2	no	—
739	#121	—	67	1	no	—
740	#121	—	134	2	no	—
741	#121	—	134	2	no	—
742	#121	—	134	2	no	—
743	#121	C₂²×D₆₇	1	2	yes	—
744	#121	C₂²×D₆₇	1	2	yes	—
745	#120	—	134	2	no	—
746	#120	—	134	2	no	—
747	C₄×Q₈	—	67	1	no	—
748	C₄×Q₈	—	67	2	no	—
749	C₄×Q₈	—	67	2	no	—
750	C₄×Q₈	—	67	2	no	—
751	C₄×Q₈	—	67	2	no	—
752	C₄×Q₈	—	134	2	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	67	1	no	—
755	C₄×D₄	—	67	1	no	—
756	C₄×D₄	—	67	2	no	—
757	C₄×D₄	—	67	2	no	—
758	C₄×D₄	—	67	2	no	—
759	C₄×D₄	—	67	2	no	—
760	C₄×D₄	—	67	2	no	—
761	C₄×D₄	—	134	2	no	—
762	C₄×D₄	—	134	2	no	—
763	C₄×D₄	—	134	2	no	—
764	C₄×D₄	—	134	2	no	—
765	C₄×D₄	—	134	2	no	—
766	C₄×D₄	—	134	2	no	—
767	C₄×D₄	—	134	2	no	—
768	C₄×D₄	C₂²×D₆₇	1	2	yes	—
769	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
770	#117	—	67	1	no	—
771	#117	—	67	1	no	—
772	#117	—	67	2	no	—
773	#117	—	134	2	no	—
774	#117	—	134	2	no	—
775	#117	—	134	2	no	—
776	#117	—	134	2	no	—
777	#117	—	134	2	no	—
778	#117	C₂²×D₆₇	1	2	yes	—
779	C₂×C₄⋊C₄	—	134	2	no	—
780	C₂×C₄⋊C₄	—	134	2	no	—
781	C₂×C₄⋊C₄	—	134	2	no	—
782	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
783	C₂×C₂²⋊C₄	—	134	2	no	—
784	C₂×C₂²⋊C₄	—	134	2	no	—
785	C₂×C₂²⋊C₄	—	134	2	no	—
786	C₂×C₂²⋊C₄	—	134	2	no	—
787	C₂×C₄²	—	67	1	no	—
788	C₂×C₄²	—	134	2	no	—
789	#107	—	67	1	no	—
790	#107	—	67	2	no	—
791	#107	C₂²×D₆₇	1	1	yes	characteristic
792	#107	C₂²×D₆₇	1	1	yes	characteristic
793	#107	C₂²×D₆₇	1	2	yes	—
794	#107	C₂²×D₆₇	1	1	yes	characteristic
795	#106	—	67	2	no	—
796	#106	—	67	2	no	—
797	#106	C₂²×D₆₇	1	2	yes	—
798	#106	C₂²×D₆₇	1	2	yes	—
799	C₄⋊C₈	—	67	1	no	—
800	C₄⋊C₈	—	67	1	no	—
801	C₄⋊C₈	—	67	1	no	—
802	C₄⋊C₈	—	67	1	no	—
803	C₄⋊C₈	—	67	1	no	—
804	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
805	#103	—	67	2	no	—
806	#103	—	67	2	no	—
807	#103	—	67	2	no	—
808	#103	—	67	2	no	—
809	#103	—	67	2	no	—
810	#103	—	67	2	no	—
811	#103	—	67	2	no	—
812	#103	—	67	2	no	—
813	#102	—	67	2	no	—
814	#102	—	67	2	no	—
815	#102	—	67	2	no	—
816	#102	—	67	2	no	—
817	#102	—	67	2	no	—
818	#102	C₂²×D₆₇	1	2	yes	—
819	#102	C₂²×D₆₇	1	2	yes	—
820	#102	C₂²×D₆₇	1	2	yes	—
821	C₂²⋊C₈	—	67	1	no	—
822	C₂²⋊C₈	—	67	1	no	—
823	C₂²⋊C₈	—	67	1	no	—
824	C₂²⋊C₈	—	67	1	no	—
825	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
826	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
827	#97	—	67	1	no	—
828	#97	—	67	1	no	—
829	#97	—	67	1	no	—
830	#97	—	67	1	no	—
831	C₄×C₈	—	67	1	no	—
832	C₄×C₈	—	67	1	no	—
833	C₄×C₈	—	67	1	no	—
834	C₄×C₈	—	67	1	no	—
835	C₄×C₈	—	67	1	no	—
836	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
837	C₂⁴	—	134	2	no	—
838	#41	—	268	2	no	—
839	#41	—	268	2	no	—
840	#41	—	134	4	no	—
841	#41	—	134	4	no	—
842	C₂×Q₈	—	67	1	no	—
843	C₂×Q₈	—	67	2	no	—
844	C₂×Q₈	—	67	2	no	—
845	C₂×Q₈	—	134	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	268	2	no	—
849	C₂×D₄	—	67	1	no	—
850	C₂×D₄	—	67	1	no	—
851	C₂×D₄	—	67	2	no	—
852	C₂×D₄	—	134	2	no	—
853	C₂×D₄	—	134	4	no	—
854	C₂×D₄	—	134	2	no	—
855	C₂×D₄	—	134	2	no	—
856	C₂×D₄	D₄×D₆₇	1	1	yes	characteristic
857	C₂×D₄	C₂³×D₆₇	1	2	yes	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	67	1	no	—
861	C₂²×C₄	—	67	1	no	—
862	C₂²×C₄	—	67	1	no	—
863	C₂²×C₄	—	134	2	no	—
864	C₂²×C₄	—	134	2	no	—
865	C₂²×C₄	—	134	2	no	—
866	C₂²×C₄	—	134	2	no	—
867	C₂²×C₄	—	134	2	no	—
868	C₂²×C₄	—	134	2	no	—
869	C₂²×C₄	—	134	2	no	—
870	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
871	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
872	Q₁₆	—	268	2	no	—
873	Q₁₆	—	134	2	no	—
874	Q₁₆	—	134	2	no	—
875	SD₁₆	—	268	2	no	—
876	SD₁₆	—	268	2	no	—
877	SD₁₆	—	134	4	no	—
878	SD₁₆	—	134	4	no	—
879	D₈	—	2	2	no	—
880	D₈	—	67	4	no	—
881	D₈	—	134	4	no	—
882	M₁₆	—	268	1	no	—
883	M₁₆	—	268	1	no	—
884	C₂×C₈	—	2	2	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	—	268	1	no	—
887	C₂×C₈	—	67	1	no	—
888	C₂×C₈	—	67	1	no	—
889	C₂×C₈	—	67	1	no	—
890	C₂×C₈	—	67	1	no	—
891	C₂×C₈	—	134	2	no	—
892	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
893	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
894	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
895	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	67	1	no	—
900	C₄⋊C₄	—	67	1	no	—
901	C₄⋊C₄	—	67	1	no	—
902	C₄⋊C₄	—	67	1	no	—
903	C₄⋊C₄	—	67	1	no	—
904	C₄⋊C₄	—	67	1	no	—
905	C₄⋊C₄	—	67	1	no	—
906	C₄⋊C₄	—	67	1	no	—
907	C₄⋊C₄	—	67	1	no	—
908	C₄⋊C₄	—	67	2	no	—
909	C₄⋊C₄	—	134	2	no	—
910	C₄⋊C₄	—	134	2	no	—
911	C₄⋊C₄	—	134	2	no	—
912	C₄⋊C₄	—	134	2	no	—
913	C₄⋊C₄	—	134	2	no	—
914	C₄⋊C₄	—	134	2	no	—
915	C₄⋊C₄	—	134	2	no	—
916	C₄⋊C₄	—	134	2	no	—
917	C₄⋊C₄	—	134	2	no	—
918	C₄⋊C₄	—	134	2	no	—
919	C₄⋊C₄	—	134	2	no	—
920	C₄⋊C₄	—	134	2	no	—
921	C₄⋊C₄	—	134	2	no	—
922	C₄⋊C₄	D₄×D₆₇	1	1	yes	characteristic
923	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
924	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
925	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	67	1	no	—
931	C₂²⋊C₄	—	67	1	no	—
932	C₂²⋊C₄	—	67	1	no	—
933	C₂²⋊C₄	—	67	1	no	—
934	C₂²⋊C₄	—	67	1	no	—
935	C₂²⋊C₄	—	67	1	no	—
936	C₂²⋊C₄	—	67	1	no	—
937	C₂²⋊C₄	—	67	1	no	—
938	C₂²⋊C₄	—	134	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	—	134	2	no	—
947	C₂²⋊C₄	—	134	2	no	—
948	C₂²⋊C₄	—	134	2	no	—
949	C₂²⋊C₄	—	134	2	no	—
950	C₂²⋊C₄	—	134	2	no	—
951	C₂²⋊C₄	—	134	2	no	—
952	C₂²⋊C₄	D₄×D₆₇	1	1	yes	characteristic
953	C₂²⋊C₄	D₄×D₆₇	1	1	yes	characteristic
954	C₄²	—	2	2	no	—
955	C₄²	—	67	1	no	—
956	C₄²	—	67	1	no	—
957	C₄²	—	67	1	no	—
958	C₄²	—	67	1	no	—
959	C₄²	—	67	1	no	—
960	C₄²	—	134	2	no	—
961	C₄²	—	134	2	no	—
962	C₄²	—	134	2	no	—
963	C₄²	—	134	2	no	—
964	C₄²	—	134	2	no	—
965	C₄²	C₂³×D₆₇	1	1	yes	characteristic
966	C₂³	—	2	2	no	—
967	C₂³	—	268	4	no	—
968	C₂³	—	536	2	no	—
969	C₂³	—	536	2	no	—
970	C₂³	—	67	1	no	—
971	C₂³	—	134	2	no	—
972	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
973	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
974	Q₈	—	268	1	no	—
975	Q₈	—	536	2	no	—
976	Q₈	—	134	2	no	—
977	Q₈	—	134	2	no	—
978	Q₈	—	134	2	no	—
979	Q₈	—	134	2	no	—
980	D₄	—	2	2	no	—
981	D₄	—	2	2	no	—
982	D₄	—	4	1	no	—
983	D₄	—	8	2	no	—
984	D₄	—	8	2	no	—
985	D₄	—	268	4	no	—
986	D₄	—	268	4	no	—
987	D₄	—	268	1	no	—
988	D₄	—	268	1	no	—
989	D₄	—	268	4	no	—
990	D₄	—	67	4	no	—
991	D₄	—	134	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	8	2	no	—
1000	C₂×C₄	—	8	2	no	—
1001	C₂×C₄	—	268	4	no	—
1002	C₂×C₄	—	268	4	no	—
1003	C₂×C₄	—	268	1	no	—
1004	C₂×C₄	—	268	1	no	—
1005	C₂×C₄	—	536	2	no	—
1006	C₂×C₄	—	536	2	no	—
1007	C₂×C₄	—	536	2	no	—
1008	C₂×C₄	—	536	2	no	—
1009	C₂×C₄	—	536	2	no	—
1010	C₂×C₄	—	67	1	no	—
1011	C₂×C₄	—	67	1	no	—
1012	C₂×C₄	—	67	1	no	—
1013	C₂×C₄	—	67	1	no	—
1014	C₂×C₄	—	67	1	no	—
1015	C₂×C₄	—	67	1	no	—
1016	C₂×C₄	—	67	1	no	—
1017	C₂×C₄	—	134	2	no	—
1018	C₂×C₄	—	134	2	no	—
1019	C₂×C₄	—	134	2	no	—
1020	C₂×C₄	—	134	1	no	—
1021	C₂×C₄	—	134	1	no	—
1022	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1023	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1024	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1025	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1026	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1027	C₈	—	2	1	no	—
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	134	1	no	—
1031	C₈	—	134	1	no	—
1032	C₈	—	134	1	no	—
1033	C₈	—	134	1	no	—
1034	C₈	#41×D₆₇	1	2	yes	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	4	2	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	268	2	no	—
1045	C₂²	—	268	2	no	—
1046	C₂²	—	1072	4	no	—
1047	C₂²	—	134	4	no	—
1048	C₂²	—	134	1	no	—
1049	C₂²	—	134	1	no	—
1050	C₂²	—	134	1	no	—
1051	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	4	2	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	268	2	no	—
1060	C₄	—	268	2	no	—
1061	C₄	—	268	2	no	—
1062	C₄	—	134	1	no	—
1063	C₄	—	134	1	no	—
1064	C₄	—	134	1	no	—
1065	C₄	—	134	1	no	—
1066	C₄	—	134	1	no	—
1067	C₄	—	134	1	no	—
1068	C₄	—	134	1	no	—
1069	C₄	C₂×#41×D₆₇	1	1	yes	characteristic
1070	C₄	#16864233	1	1	yes	characteristic
1071	C₂	—	4	1	no	—
1072	C₂	—	4	1	no	—
1073	C₂	—	8	2	no	—
1074	C₂	—	268	4	no	—
1075	C₂	—	268	1	no	—
1076	C₂	#22573696	1	1	yes	characteristic
1077	C₂	#22574977	1	1	yes	characteristic
1078	C₂	#22574978	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×#3339	C₂
socle	C₂²×C₆₇	C₂³×D₄
hypercenter	#3339	D₆₇
hypocenter	C₆₇	#61487
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3339

Complements

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

N	H ≅ G/N	type
1. #22574272	C₂	semidirect
2. #22573195	C₂	semidirect
3. #22573073	C₂	semidirect
4. #22573039	C₂	semidirect
5. #22572637	C₂	semidirect
6. #22572573	C₂	semidirect
7. #22572428	C₂	semidirect
8. #22572243	C₂	semidirect
9. #22572179	C₂	semidirect
10. #22571931	C₂	semidirect
11. #22571897	C₂	semidirect
12. #22571897	C₂	semidirect
13. #22570869	C₂	semidirect
14. #22570841	C₂	semidirect
15. #22570774	C₂	semidirect
16. #22570489	C₂	semidirect
17. #22570463	C₂	semidirect
18. #22570313	C₂	semidirect
19. #22569177	C₂	semidirect
20. #22569083	C₂	semidirect
21. #22569056	C₂	semidirect
22. #22568980	C₂	semidirect
23. C₆₇×#3339	C₂	semidirect
27. #16864116	C₂²	semidirect
29. #16864102	C₂²	semidirect
35. #16864051	C₂²	semidirect
38. #16864013	C₂²	semidirect
43. #16863927	C₂²	semidirect
46. #16863877	C₂²	semidirect
48. #16863864	C₂²	semidirect
49. #16863800	C₂²	semidirect
50. #16863797	C₂²	semidirect
53. #16863776	C₂²	semidirect
54. #16863766	C₂²	semidirect
55. #16863754	C₂²	semidirect
56. #16863749	C₂²	semidirect
59. #16863737	C₂²	semidirect
60. #16863726	C₂²	semidirect
61. #16863702	C₂²	semidirect
62. #16863695	C₂²	semidirect
63. #16863693	C₂²	semidirect
64. #16863685	C₂²	semidirect
65. #16863680	C₂²	semidirect
67. #16863640	C₂²	semidirect
70. #16863637	C₂²	semidirect
71. #16863637	C₂²	semidirect
72. #16863623	C₂²	semidirect
73. #16863617	C₂²	semidirect
74. #16863617	C₂²	semidirect
77. #16863602	C₂²	semidirect
78. #16863601	C₂²	semidirect
79. #16863560	C₂²	semidirect
80. #16863560	C₂²	semidirect
85. #16863525	C₂²	semidirect
86. C₈×Dic₁₃₄	C₂²	semidirect
89. #16863502	C₂²	semidirect
90. #16863495	C₂²	semidirect
91. #16863495	C₂²	semidirect
92. #16863493	C₂²	semidirect
93. #16863490	C₂²	semidirect
94. #16863490	C₂²	semidirect
95. #16863490	C₂²	semidirect
96. #16863490	C₂²	semidirect
97. #16863487	C₂²	semidirect
98. #16863483	C₂²	semidirect
99. #16863483	C₂²	semidirect
106. #16863468	C₂²	semidirect
111. #16863454	C₂²	semidirect
112. #16863450	C₂²	semidirect
115. #16863395	C₂²	semidirect
116. #16863390	C₂²	semidirect
117. #16863351	C₂²	semidirect
119. C₂×C₈×Dic₆₇	C₂²	semidirect
120. #553×C₆₇	C₂²	semidirect
121. #499×C₆₇	C₂²	semidirect
122. #482×C₆₇	C₂²	semidirect
123. #481×C₆₇	C₂²	semidirect
124. #478×C₆₇	C₂²	semidirect
128. C₈×D₄×C₆₇	C₂²	semidirect
129. #427×C₆₇	C₂²	semidirect
130. C₂×#107×C₆₇	C₂²	semidirect
545. #3339	D₆₇	semidirect
563. C₆₇	#61487	semidirect
571. #553	C₂×D₆₇	semidirect
592. #499	C₂×D₆₇	semidirect
603. #482	C₂×D₆₇	semidirect
604. #481	C₂×D₆₇	semidirect
608. #478	C₂×D₆₇	semidirect
658. C₈×D₄	C₂×D₆₇	semidirect
663. #427	C₂×D₆₇	semidirect
664. C₂×#107	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574272	2
#22573195	2
#22573073	2
#22573039	2
#22572637	2
#22572573	2
#22572428	2
#22572243	2
#22572179	2
#22571931	2
#22571897	2
#22570869	2
#22570841	2
#22570774	2
#22570489	2
#22570463	2
#22570313	2
#22569177	2
#22569083	2
#22569056	2
#22568980	2
C₆₇×#3339	2
#61487	67