Subgroups — #31736463

Order 17152.

1818 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574008	C₂	1	2	yes	maximal, complemented
2	#22573167	C₂	1	2	yes	maximal, complemented
3	#22573163	C₂	1	2	yes	maximal, complemented
4	#22573111	C₂	1	2	yes	maximal, complemented
5	#22573103	C₂	1	2	yes	maximal, complemented
6	#22573077	C₂	1	1	yes	maximal, characteristic, complemented
7	#22573076	C₂	1	1	yes	maximal, characteristic, complemented
8	#22573076	C₂	1	1	yes	maximal, characteristic, complemented
9	#22573073	C₂	1	1	yes	maximal, characteristic, complemented
10	#22573073	C₂	1	1	yes	maximal, characteristic, complemented
11	D₈×Dic₁₃₄	C₂	1	1	yes	maximal, characteristic, complemented
12	#22573061	C₂	1	1	yes	maximal, characteristic, complemented
13	#22570746	C₂	1	1	yes	maximal, characteristic, complemented
14	#22570742	C₂	1	1	yes	maximal, characteristic, complemented
15	#22570722	C₂	1	1	yes	maximal, characteristic, complemented
16	#22570039	C₂	1	2	yes	maximal, complemented
17	#22570035	C₂	1	2	yes	maximal, complemented
18	#22570004	C₂	1	2	yes	maximal, complemented
19	#22569138	C₂	1	1	yes	maximal, characteristic, complemented
20	#22569056	C₂	1	1	yes	maximal, characteristic
21	#22569056	C₂	1	1	yes	maximal, characteristic
22	C₄×D₈×D₆₇	C₂	1	1	yes	maximal, characteristic
23	C₆₇×#3380	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₈×D₆₇	C₂²	1	1	yes	characteristic
25	#16864106	C₂²	1	2	yes	complemented
26	#16864105	C₂²	1	2	yes	complemented
27	#16864105	C₂²	1	2	yes	complemented
28	#16864102	C₂²	1	2	yes	complemented
29	#16864102	C₂²	1	2	yes	complemented
30	#16864101	—	2	2	no	—
31	#16864100	—	2	2	no	—
32	#16864100	—	2	2	no	—
33	D₄×Dic₁₃₄	C₂²	1	2	yes	complemented
34	#16864061	C₂²	1	2	yes	complemented
35	#16864059	—	2	2	no	—
36	#16864026	C₂²	1	2	yes	—
37	#16864023	C₂²	1	2	yes	—
38	#16864021	—	2	2	no	—
39	#16864021	—	2	2	no	—
40	#16863952	C₂²	1	2	yes	—
41	#16863950	C₂²	1	1	yes	characteristic
42	C₂×#14524021	—	2	2	no	—
43	C₂²⋊Q₈×D₆₇	—	2	2	no	—
44	#16863868	C₂²	1	2	yes	—
45	#16863868	C₂²	1	2	yes	—
46	C₄×D₄×D₆₇	C₂²	1	2	yes	—
47	#16863806	C₂²	1	2	yes	complemented
48	#16863804	C₂²	1	2	yes	complemented
49	#16863803	C₂²	1	2	yes	complemented
50	#16863802	C₂²	1	2	yes	complemented
51	#16863801	C₂²	1	1	yes	characteristic, complemented
52	#16863800	C₂²	1	1	yes	characteristic, complemented
53	#16863800	C₂²	1	1	yes	characteristic, complemented
54	#16863800	C₂²	1	1	yes	characteristic, complemented
55	#16863800	C₂²	1	1	yes	characteristic, complemented
56	#16863798	C₂²	1	1	yes	characteristic, complemented
57	#16863798	C₂²	1	1	yes	characteristic, complemented
58	#16863797	C₂²	1	1	yes	characteristic, complemented
59	#16863797	C₂²	1	1	yes	characteristic, complemented
60	#16863795	C₂²	1	2	yes	complemented
61	#16863793	C₂²	1	2	yes	complemented
62	#16863698	C₂²	1	2	yes	complemented
63	#16863698	C₂²	1	2	yes	complemented
64	#16863697	C₂²	1	2	yes	complemented
65	#16863697	C₂²	1	2	yes	complemented
66	#16863696	C₂²	1	2	yes	complemented
67	#16863696	C₂²	1	2	yes	complemented
68	#16863695	C₂²	1	2	yes	complemented
69	#16863695	C₂²	1	2	yes	complemented
70	#16863693	C₂²	1	2	yes	complemented
71	#16863693	C₂²	1	2	yes	complemented
72	#16863687	C₂²	1	2	yes	complemented
73	#16863685	C₂²	1	2	yes	complemented
74	#16863685	C₂²	1	2	yes	complemented
75	#16863684	C₂²	1	2	yes	complemented
76	#16863684	C₂²	1	2	yes	complemented
77	#16863676	C₂²	1	2	yes	complemented
78	#16863675	C₂²	1	2	yes	complemented
79	#16863675	C₂²	1	2	yes	complemented
80	#16863674	C₂²	1	2	yes	complemented
81	#16863674	C₂²	1	2	yes	complemented
82	#16863673	C₂²	1	2	yes	complemented
83	#16863527	C₂²	1	1	yes	characteristic, complemented
84	#16863525	C₂²	1	1	yes	characteristic, complemented
85	#16863525	C₂²	1	1	yes	characteristic, complemented
86	#16863523	C₂²	1	1	yes	characteristic, complemented
87	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
88	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
89	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
90	#16863506	C₂²	1	2	yes	—
91	#16863506	C₂²	1	2	yes	—
92	#16863505	C₂²	1	2	yes	—
93	#16863505	C₂²	1	2	yes	—
94	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
95	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
96	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
97	D₈×Dic₆₇	C₂²	1	1	yes	characteristic
98	D₈×Dic₆₇	C₂²	1	1	yes	characteristic
99	D₈×Dic₆₇	C₂²	1	1	yes	characteristic
100	#16863478	C₂²	1	1	yes	characteristic
101	#16863478	C₂²	1	1	yes	characteristic
102	#16863478	C₂²	1	1	yes	characteristic
103	C₄×#11761613	C₂²	1	2	yes	—
104	#16863476	C₂²	1	2	yes	—
105	#16863437	C₂²	1	2	yes	—
106	#16863435	C₂²	1	2	yes	—
107	#16863433	C₂²	1	1	yes	characteristic
108	#16863433	C₂²	1	1	yes	characteristic
109	#16863431	C₂²	1	2	yes	—
110	#107×D₆₇	C₂²	1	1	yes	characteristic
111	#16863421	C₂²	1	1	yes	characteristic
112	#16863421	C₂²	1	1	yes	characteristic
113	#16863418	C₂²	1	1	yes	characteristic
114	#16863399	C₂²	1	2	yes	—
115	#16863399	C₂²	1	2	yes	—
116	#102×D₆₇	C₂²	1	2	yes	—
117	#16863350	C₂²	1	1	yes	characteristic
118	#16863350	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
120	#554×C₆₇	C₂²	1	2	yes	complemented
121	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#499×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#499×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#478×C₆₇	C₂²	1	2	yes	complemented
125	#478×C₆₇	C₂²	1	2	yes	complemented
126	#476×C₆₇	C₂²	1	2	yes	complemented
127	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
131	C₂²×Dic₁₃₄	—	2	2	no	—
132	C₂×Q₈×D₆₇	—	2	2	no	—
133	C₂×D₄×D₆₇	C₂³	1	2	yes	—
134	C₂²×C₄×D₆₇	—	2	2	no	—
135	C₂×D₅₃₆	C₂³	1	1	yes	characteristic
136	C₂×#11761613	C₂³	1	2	yes	—
137	D₈×D₆₇	Q₈	1	8	yes	complemented
138	C₂×#11761611	C₂³	1	1	yes	characteristic
139	C₂×#11761611	C₂³	1	1	yes	characteristic
140	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
142	#14524043	C₂³	1	2	yes	—
143	#14524042	—	2	2	no	—
144	#14524042	D₄	1	1	yes	characteristic
145	#14524042	C₂³	1	2	yes	—
146	#14524042	C₂³	1	2	yes	—
147	#14524042	C₂³	1	2	yes	—
148	#14524042	C₂³	1	2	yes	—
149	#14524041	—	2	2	no	—
150	#14524041	D₄	1	1	yes	characteristic
151	#14524035	C₂³	1	2	yes	—
152	#14524035	C₂³	1	2	yes	—
153	#14524034	C₂³	1	2	yes	—
154	#14524034	C₂³	1	2	yes	—
155	#14524033	—	2	2	no	—
156	#14524033	—	2	2	no	—
157	#14524033	D₄	1	1	yes	characteristic
158	#14524033	D₄	1	1	yes	characteristic
159	#14524023	—	2	2	no	—
160	#14524023	—	2	2	no	—
161	#14524023	—	2	2	no	—
162	#14524023	D₄	1	1	yes	characteristic
163	#14524022	—	2	2	no	—
164	#14524022	—	2	2	no	—
165	#14524022	—	2	2	no	—
166	#14524021	—	2	2	no	—
167	#14524021	—	2	2	no	—
168	#14524021	—	2	2	no	—
169	#14524021	—	2	2	no	—
170	#14524021	—	2	2	no	—
171	#14524021	—	2	2	no	—
172	#14524021	—	2	2	no	—
173	#14524021	—	2	2	no	—
174	#14524021	—	2	2	no	—
175	#14524021	—	2	2	no	—
176	#14524021	—	2	2	no	—
177	#14524021	—	2	2	no	—
178	#14524021	D₄	1	1	yes	characteristic
179	#14524021	D₄	1	1	yes	characteristic
180	#14524020	—	2	2	no	—
181	#14524020	—	2	2	no	—
182	#14524020	—	2	2	no	—
183	#14524020	—	2	2	no	—
184	#14524020	—	2	2	no	—
185	#14524020	—	2	2	no	—
186	#14524019	—	2	2	no	—
187	#14524019	—	2	2	no	—
188	#14524019	—	2	2	no	—
189	#14524019	D₄	1	1	yes	characteristic
190	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
191	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
193	#14524008	—	2	2	no	—
194	#14524008	—	2	2	no	—
195	C₄×D₂₆₈	C₂³	1	2	yes	—
196	C₄×D₂₆₈	C₂³	1	2	yes	—
197	C₄×D₂₆₈	C₂³	1	2	yes	—
198	D₄×Dic₆₇	C₂³	1	2	yes	—
199	D₄×Dic₆₇	C₂³	1	2	yes	—
200	D₄×Dic₆₇	C₂³	1	2	yes	—
201	#14524005	C₂³	1	2	yes	—
202	#14524005	C₂³	1	2	yes	—
203	#14524005	C₂³	1	2	yes	—
204	C₄×C₂²⋊D₆₇	—	2	2	no	—
205	C₄×C₂²⋊D₆₇	—	2	2	no	—
206	C₄×C₂²⋊D₆₇	—	2	2	no	—
207	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
208	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
209	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
210	#14524001	C₂³	1	2	yes	—
211	#14524001	C₂³	1	2	yes	—
212	#14524000	C₂³	1	1	yes	characteristic
213	#14524000	C₂³	1	1	yes	characteristic
214	C₂×Dic₆₇⋊C₄	—	2	2	no	—
215	C₂×Dic₆₇⋊C₄	—	2	2	no	—
216	C₄⋊C₄×D₆₇	—	2	2	no	—
217	C₄⋊C₄×D₆₇	—	2	2	no	—
218	C₄⋊C₄×D₆₇	—	2	2	no	—
219	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
220	C₂×(C₂×D₆₇)⋊C₄	—	2	2	no	—
221	C₂×(C₂×D₆₇)⋊C₄	—	2	2	no	—
222	C₂²⋊C₄×D₆₇	—	2	2	no	—
223	C₂²⋊C₄×D₆₇	—	2	2	no	—
224	C₂²⋊C₄×D₆₇	—	2	2	no	—
225	C₄²×D₆₇	C₂³	1	1	yes	characteristic
226	#14523977	C₂³	1	1	yes	characteristic
227	#14523977	C₂³	1	1	yes	characteristic
228	#14523977	C₂³	1	1	yes	characteristic
229	#14523977	C₂³	1	2	yes	—
230	#14523976	C₂³	1	2	yes	—
231	#14523976	C₂³	1	2	yes	—
232	#14523976	C₂³	1	2	yes	—
233	#14523976	C₂³	1	2	yes	—
234	#14523976	C₂³	1	2	yes	—
235	#14523975	C₂³	1	2	yes	—
236	#14523975	C₂³	1	2	yes	—
237	#14523974	C₂³	1	2	yes	—
238	#14523974	C₂³	1	2	yes	—
239	#14523974	C₂³	1	2	yes	—
240	#14523974	C₂³	1	2	yes	—
241	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
242	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
243	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
244	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
245	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
246	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
247	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
248	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
249	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
250	#14523965	C₂³	1	2	yes	—
251	#14523965	C₂³	1	2	yes	—
252	#14523965	C₂³	1	2	yes	—
253	#14523964	C₂³	1	2	yes	—
254	#14523964	C₂³	1	2	yes	—
255	#14523964	C₂³	1	2	yes	—
256	#14523963	C₂³	1	2	yes	—
257	#14523963	C₂³	1	2	yes	—
258	#14523963	C₂³	1	2	yes	—
259	#14523954	C₂³	1	1	yes	characteristic
260	#14523954	C₂³	1	1	yes	characteristic
261	#14523953	C₂³	1	1	yes	characteristic
262	#14523953	C₂³	1	1	yes	characteristic
263	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
264	C₈×Dic₆₇	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	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
269	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
270	#125×C₆₇	C₂³	1	2	yes	—
271	#125×C₆₇	C₂³	1	2	yes	—
272	C₂²⋊Q₈×C₆₇	—	2	2	no	—
273	C₂²⋊Q₈×C₆₇	—	2	2	no	—
274	C₂²⋊Q₈×C₆₇	—	2	2	no	—
275	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₆₇	C₂³	1	2	yes	—
277	C₄×D₄×C₆₇	C₂³	1	2	yes	—
278	C₄×D₄×C₆₇	C₂³	1	2	yes	—
279	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
280	#107×C₆₇	C₂³	1	2	yes	—
281	#107×C₆₇	C₂³	1	1	yes	characteristic
282	#107×C₆₇	C₂³	1	1	yes	characteristic
283	#107×C₆₇	C₂³	1	1	yes	characteristic
284	#106×C₆₇	C₂³	1	2	yes	—
285	#106×C₆₇	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
289	#102×C₆₇	C₂³	1	2	yes	—
290	#102×C₆₇	C₂³	1	2	yes	—
291	#102×C₆₇	C₂³	1	2	yes	—
292	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
295	C₂³×D₆₇	—	2	2	no	—
296	C₂×Dic₁₃₄	—	2	2	no	—
297	C₂×Dic₁₃₄	—	2	2	no	—
298	C₂×Dic₁₃₄	—	2	2	no	—
299	C₂×Dic₁₃₄	—	2	2	no	—
300	C₂×Dic₁₃₄	—	2	2	no	—
301	C₂×Dic₁₃₄	—	8	4	no	—
302	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
303	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
304	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
305	Q₈×D₆₇	—	8	4	no	—
306	C₂×D₂₆₈	C₂⁴	1	2	yes	—
307	C₂×C₂²⋊D₆₇	—	2	2	no	—
308	D₄×D₆₇	—	2	4	no	—
309	D₄×D₆₇	C₂×Q₈	1	8	yes	complemented
310	C₂²×Dic₆₇	—	2	2	no	—
311	C₂²×Dic₆₇	—	2	2	no	—
312	C₂²×Dic₆₇	—	2	2	no	—
313	C₂×C₄×D₆₇	—	2	2	no	—
314	C₂×C₄×D₆₇	—	2	2	no	—
315	C₂×C₄×D₆₇	—	2	2	no	—
316	C₂×C₄×D₆₇	—	2	2	no	—
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	—	8	4	no	—
321	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
322	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
323	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
324	D₅₃₆	C₂×Q₈	1	4	yes	complemented
325	#11761613	C₂×Q₈	1	8	yes	complemented
326	#11761611	—	2	2	no	—
327	#11761611	—	2	2	no	—
328	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
329	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
330	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
331	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
332	C₈×D₆₇	—	2	2	no	—
333	C₈×D₆₇	C₂×Q₈	1	4	yes	complemented
334	C₄⋊Dic₆₇	—	2	2	no	—
335	C₄⋊Dic₆₇	—	2	2	no	—
336	C₄⋊Dic₆₇	—	2	2	no	—
337	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
338	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
339	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
340	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
341	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
342	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
343	Dic₆₇⋊C₄	—	2	2	no	—
344	Dic₆₇⋊C₄	—	2	2	no	—
345	Dic₆₇⋊C₄	—	2	2	no	—
346	Dic₆₇⋊C₄	—	2	2	no	—
347	Dic₆₇⋊C₄	—	2	2	no	—
348	Dic₆₇⋊C₄	—	2	2	no	—
349	Dic₆₇⋊C₄	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
355	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
356	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
357	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
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	(C₂×D₆₇)⋊C₄	—	2	2	no	—
368	(C₂×D₆₇)⋊C₄	—	2	2	no	—
369	(C₂×D₆₇)⋊C₄	—	2	2	no	—
370	(C₂×D₆₇)⋊C₄	—	2	2	no	—
371	(C₂×D₆₇)⋊C₄	—	2	2	no	—
372	(C₂×D₆₇)⋊C₄	—	2	2	no	—
373	(C₂×D₆₇)⋊C₄	—	2	2	no	—
374	(C₂×D₆₇)⋊C₄	—	2	2	no	—
375	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
376	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
377	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
378	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
379	C₄×Dic₆₇	—	2	2	no	—
380	C₄×Dic₆₇	—	2	2	no	—
381	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
382	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
383	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
384	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
385	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
386	C₂×Q₈×C₆₇	—	2	2	no	—
387	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
388	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
389	C₂²×C₄×C₆₇	—	2	2	no	—
390	C₂²×C₄×C₆₇	—	2	2	no	—
391	C₂²×C₄×C₆₇	—	2	2	no	—
392	D₈×C₆₇	C₂×Q₈	1	4	yes	complemented
393	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₆₇	—	2	2	no	—
398	C₄⋊C₄×C₆₇	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	2	no	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	2	no	—
402	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
408	C₂²⋊C₄×C₆₇	—	2	2	no	—
409	C₂²⋊C₄×C₆₇	—	2	2	no	—
410	C₂²⋊C₄×C₆₇	—	2	2	no	—
411	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
414	C₂³×C₆₇	—	2	2	no	—
415	C₂²×D₆₇	—	2	2	no	—
416	C₂²×D₆₇	—	2	8	no	—
417	C₂²×D₆₇	—	8	2	no	—
418	C₂²×D₆₇	—	8	2	no	—
419	C₂²×D₆₇	C₂²×D₄	1	1	yes	characteristic
420	Q₈×C₆₇	—	4	1	no	—
421	Q₈×C₆₇	—	8	2	no	—
422	D₄×C₆₇	—	2	2	no	—
423	D₄×C₆₇	C₂²×Q₈	1	4	yes	—
424	C₂×C₄×C₆₇	—	2	2	no	—
425	C₂×C₄×C₆₇	—	2	2	no	—
426	C₂×C₄×C₆₇	—	2	2	no	—
427	C₂×C₄×C₆₇	—	8	2	no	—
428	C₂×C₄×C₆₇	—	8	2	no	—
429	C₂×C₄×C₆₇	—	8	2	no	—
430	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
437	C₂²⋊D₆₇	—	2	8	no	—
438	C₂×Dic₆₇	—	2	2	no	—
439	C₂×Dic₆₇	—	2	2	no	—
440	C₂×Dic₆₇	—	2	2	no	—
441	C₂×Dic₆₇	—	4	4	no	—
442	C₂×Dic₆₇	—	8	2	no	—
443	C₂×Dic₆₇	—	8	2	no	—
444	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
445	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
446	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
447	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
448	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
449	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
450	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
451	D₂₆₈	—	2	2	no	—
452	D₂₆₈	C₂²×Q₈	1	4	yes	—
453	C₄×D₆₇	—	2	2	no	—
454	C₄×D₆₇	—	4	1	no	—
455	C₄×D₆₇	—	4	4	no	—
456	C₄×D₆₇	—	8	2	no	—
457	C₄×D₆₇	—	8	2	no	—
458	C₄×D₆₇	—	8	2	no	—
459	C₄×D₆₇	—	8	2	no	—
460	C₄×D₆₇	—	8	2	no	—
461	C₄×D₆₇	—	8	2	no	—
462	C₄×D₆₇	C₂²×Q₈	1	2	yes	—
463	C₄×D₆₇	2₋¹⁺⁴	1	2	yes	—
464	Dic₁₃₄	—	2	2	no	—
465	Dic₁₃₄	—	2	2	no	—
466	Dic₁₃₄	—	4	1	no	—
467	Dic₁₃₄	—	4	4	no	—
468	Dic₁₃₄	—	8	2	no	—
469	Dic₁₃₄	—	8	2	no	—
470	Dic₁₃₄	—	8	2	no	—
471	Dic₁₃₄	—	8	2	no	—
472	C₈×C₆₇	—	2	1	no	—
473	C₈×C₆₇	—	2	1	no	—
474	C₈×C₆₇	—	2	1	no	—
475	C₈×C₆₇	C₂²×Q₈	1	2	yes	—
476	C₆₇⋊C₈	—	2	1	no	—
477	C₆₇⋊C₈	—	2	1	no	—
478	C₆₇⋊C₈	—	2	1	no	—
479	C₆₇⋊C₈	C₂²×Q₈	1	2	yes	—
480	C₂²×C₆₇	—	2	4	no	—
481	C₂²×C₆₇	—	4	2	no	—
482	C₂²×C₆₇	—	4	2	no	—
483	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
484	C₂×D₆₇	—	2	1	no	—
485	C₂×D₆₇	—	2	1	no	—
486	C₂×D₆₇	—	2	4	no	—
487	C₂×D₆₇	—	4	2	no	—
488	C₂×D₆₇	—	4	2	no	—
489	C₂×D₆₇	—	8	8	no	—
490	C₂×D₆₇	D₄×Q₈	1	2	yes	—
491	C₄×C₆₇	—	2	1	no	—
492	C₄×C₆₇	—	2	1	no	—
493	C₄×C₆₇	—	2	1	no	—
494	C₄×C₆₇	—	2	1	no	—
495	C₄×C₆₇	—	2	1	no	—
496	C₄×C₆₇	—	2	1	no	—
497	C₄×C₆₇	—	4	2	no	—
498	C₄×C₆₇	—	4	2	no	—
499	C₄×C₆₇	—	4	2	no	—
500	C₄×C₆₇	C₂³×Q₈	1	1	yes	characteristic
501	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
502	Dic₆₇	—	2	1	no	—
503	Dic₆₇	—	2	1	no	—
504	Dic₆₇	—	2	1	no	—
505	Dic₆₇	—	2	1	no	—
506	Dic₆₇	—	2	1	no	—
507	Dic₆₇	—	4	2	no	—
508	Dic₆₇	—	4	2	no	—
509	Dic₆₇	—	4	2	no	—
510	Dic₆₇	D₄×Q₈	1	2	yes	—
511	Dic₆₇	#576	1	2	yes	—
512	#61370	—	67	1	no	maximal, Sylow
513	C₂×C₆₇	—	4	4	no	—
514	C₂×C₆₇	C₂×D₄×Q₈	1	1	yes	characteristic
515	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
516	C₂×C₆₇	#3584	1	1	yes	characteristic
517	D₆₇	—	2	2	no	—
518	D₆₇	—	4	4	no	—
519	#3501	—	67	2	no	—
520	#3389	—	67	2	no	—
521	#3389	—	67	2	no	—
522	#3384	—	67	2	no	—
523	#3384	—	67	2	no	—
524	#3380	—	67	1	no	—
525	#3380	—	67	1	no	—
526	#3380	—	67	1	no	—
527	#3380	—	67	1	no	—
528	#3380	—	67	1	no	—
529	#3380	D₆₇	1	1	yes	characteristic, complemented
530	Q₈×D₈	—	67	1	no	—
531	Q₈×D₈	—	67	1	no	—
532	#3164	—	67	1	no	—
533	#3164	—	67	1	no	—
534	#3160	—	67	1	no	—
535	#3081	—	67	2	no	—
536	#3081	—	67	2	no	—
537	#3077	—	67	2	no	—
538	#2960	—	67	1	no	—
539	#2948	—	67	1	no	—
540	#2948	—	67	1	no	—
541	C₂×C₄×D₈	—	67	1	no	—
542	C₆₇	#61370	1	1	yes	characteristic, complemented, Sylow
543	C₂²×D₈	—	67	1	no	—
544	#554	—	67	2	no	—
545	#554	—	67	2	no	—
546	#554	—	67	2	no	—
547	#554	—	67	2	no	—
548	#554	—	67	2	no	—
549	#554	—	134	2	no	—
550	#554	—	134	2	no	—
551	#554	—	134	2	no	—
552	#554	C₂×D₆₇	1	2	yes	complemented
553	D₄×Q₈	—	67	2	no	—
554	D₄×Q₈	—	67	2	no	—
555	D₄×Q₈	—	134	2	no	—
556	#544	—	67	2	no	—
557	#544	—	67	2	no	—
558	#543	—	134	2	no	—
559	#543	—	134	2	no	—
560	#533	—	67	1	no	—
561	#533	—	67	2	no	—
562	C₂×C₂²⋊Q₈	—	134	2	no	—
563	C₂×C₂²⋊Q₈	—	134	2	no	—
564	#518	—	67	2	no	—
565	#518	—	67	2	no	—
566	C₂×C₄×D₄	—	67	2	no	—
567	#501	—	67	2	no	—
568	#501	—	67	2	no	—
569	#501	—	67	2	no	—
570	#501	—	67	2	no	—
571	#500	—	67	1	no	—
572	#500	—	67	1	no	—
573	#500	—	67	1	no	—
574	#500	—	67	1	no	—
575	#500	—	67	1	no	—
576	#500	C₂×D₆₇	1	1	yes	characteristic, complemented
577	#499	—	67	2	no	—
578	#499	—	67	1	no	—
579	#499	—	67	1	no	—
580	#499	—	67	1	no	—
581	#499	—	67	1	no	—
582	#499	C₂×D₆₇	1	1	yes	characteristic, complemented
583	#499	C₂×D₆₇	1	1	yes	characteristic, complemented
584	#498	—	67	2	no	—
585	#478	—	67	2	no	—
586	#478	—	67	2	no	—
587	#478	—	67	2	no	—
588	#478	—	67	2	no	—
589	#478	—	67	2	no	—
590	#478	—	67	2	no	—
591	#478	—	67	2	no	—
592	#478	—	67	2	no	—
593	#478	—	67	2	no	—
594	#478	—	67	2	no	—
595	#478	C₂×D₆₇	1	2	yes	complemented
596	#478	C₂×D₆₇	1	2	yes	complemented
597	#476	—	67	2	no	—
598	#476	—	67	2	no	—
599	#476	—	67	2	no	—
600	#476	—	67	2	no	—
601	#476	—	67	2	no	—
602	#476	C₂×D₆₇	1	2	yes	complemented
603	#474	—	67	2	no	—
604	#474	—	67	2	no	—
605	#474	—	67	2	no	—
606	#474	—	67	2	no	—
607	#474	—	67	2	no	—
608	#474	—	67	2	no	—
609	#446	—	67	1	no	—
610	#446	—	67	1	no	—
611	#446	—	67	1	no	—
612	#446	—	67	1	no	—
613	C₈×Q₈	—	67	1	no	—
614	C₈×Q₈	—	67	1	no	—
615	C₈×Q₈	—	67	1	no	—
616	C₈×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
617	#442	—	67	2	no	—
618	#442	—	67	2	no	—
619	#442	—	67	2	no	—
620	#442	—	67	2	no	—
621	C₄×D₈	—	67	1	no	—
622	C₄×D₈	—	67	1	no	—
623	C₄×D₈	—	67	1	no	—
624	C₄×D₈	—	67	2	no	—
625	C₄×D₈	—	67	1	no	—
626	C₄×D₈	—	67	1	no	—
627	C₄×D₈	—	67	1	no	—
628	C₄×D₈	—	67	2	no	—
629	C₄×D₈	—	67	1	no	—
630	C₄×D₈	—	67	1	no	—
631	C₄×D₈	—	67	1	no	—
632	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
633	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
634	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
635	#428	—	67	2	no	—
636	#428	—	67	2	no	—
637	#427	—	67	1	no	—
638	#427	—	67	1	no	—
639	#427	—	67	2	no	—
640	C₂×#107	—	67	1	no	—
641	#424	—	67	1	no	—
642	#424	—	67	1	no	—
643	#423	—	67	1	no	—
644	#418	—	67	2	no	—
645	#418	—	67	2	no	—
646	C₂×#102	—	67	2	no	—
647	#405	—	67	1	no	—
648	#405	—	67	1	no	—
649	C₂×C₄×C₈	—	67	1	no	—
650	C₂²×Q₈	—	134	2	no	—
651	C₂²×Q₈	—	134	2	no	—
652	C₂²×D₄	—	67	2	no	—
653	C₂³×C₄	—	134	2	no	—
654	C₂×D₈	—	67	2	no	—
655	C₂×D₈	—	67	8	no	—
656	C₂×D₈	—	67	1	no	—
657	C₂×D₈	C₂²×D₆₇	1	1	yes	characteristic
658	C₂×M₁₆	—	67	1	no	—
659	C₂×M₁₆	—	67	1	no	—
660	C₂²×C₈	—	67	1	no	—
661	C₂²×C₈	—	67	1	no	—
662	C₄⋊Q₈	—	67	1	no	—
663	C₄⋊Q₈	—	67	1	no	—
664	C₄⋊Q₈	—	67	2	no	—
665	C₄⋊Q₈	—	67	2	no	—
666	C₄⋊Q₈	—	67	2	no	—
667	C₄⋊Q₈	—	67	2	no	—
668	C₄⋊Q₈	—	67	2	no	—
669	C₄⋊Q₈	—	134	2	no	—
670	C₄⋊Q₈	—	134	2	no	—
671	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
672	#125	—	67	1	no	—
673	#125	—	67	1	no	—
674	#125	—	67	2	no	—
675	#125	—	67	2	no	—
676	#125	—	67	2	no	—
677	#125	—	67	2	no	—
678	#125	—	134	2	no	—
679	#125	—	134	2	no	—
680	#125	C₂²×D₆₇	1	2	yes	—
681	#125	C₂²×D₆₇	1	2	yes	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	67	1	no	—
686	C₂²⋊Q₈	—	67	1	no	—
687	C₂²⋊Q₈	—	67	1	no	—
688	C₂²⋊Q₈	—	67	1	no	—
689	C₂²⋊Q₈	—	134	2	no	—
690	C₂²⋊Q₈	—	134	2	no	—
691	C₂²⋊Q₈	—	134	2	no	—
692	C₂²⋊Q₈	—	134	2	no	—
693	C₂²⋊Q₈	—	134	2	no	—
694	C₂²⋊Q₈	—	134	2	no	—
695	C₂²⋊Q₈	—	134	2	no	—
696	C₂²⋊Q₈	—	134	2	no	—
697	C₂²⋊Q₈	—	134	2	no	—
698	C₂²⋊Q₈	—	134	2	no	—
699	C₂²⋊Q₈	—	134	2	no	—
700	C₂²⋊Q₈	—	134	2	no	—
701	C₂²⋊Q₈	—	134	2	no	—
702	C₂²⋊Q₈	—	134	2	no	—
703	C₂²⋊Q₈	—	134	2	no	—
704	C₂²⋊Q₈	—	134	2	no	—
705	C₂²⋊Q₈	—	134	2	no	—
706	C₂²⋊Q₈	—	134	2	no	—
707	C₂²⋊Q₈	—	134	2	no	—
708	C₂²⋊Q₈	—	134	2	no	—
709	C₂²⋊Q₈	—	134	2	no	—
710	C₂²⋊Q₈	—	134	2	no	—
711	C₂²⋊Q₈	—	134	2	no	—
712	C₂²⋊Q₈	—	134	2	no	—
713	C₂²⋊Q₈	—	134	2	no	—
714	C₂²⋊Q₈	—	134	2	no	—
715	C₂²⋊Q₈	—	134	2	no	—
716	C₄×Q₈	—	67	1	no	—
717	C₄×Q₈	—	67	1	no	—
718	C₄×Q₈	—	67	1	no	—
719	C₄×Q₈	—	134	2	no	—
720	C₄×Q₈	—	134	2	no	—
721	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
722	C₄×D₄	—	67	2	no	—
723	C₄×D₄	—	67	2	no	—
724	C₄×D₄	—	67	2	no	—
725	C₄×D₄	—	67	2	no	—
726	C₄×D₄	—	67	2	no	—
727	C₄×D₄	—	67	2	no	—
728	C₄×D₄	—	67	2	no	—
729	C₄×D₄	—	67	2	no	—
730	C₄×D₄	—	67	2	no	—
731	C₄×D₄	—	134	2	no	—
732	C₄×D₄	—	134	2	no	—
733	C₄×D₄	—	134	2	no	—
734	C₄×D₄	—	134	2	no	—
735	C₄×D₄	—	134	2	no	—
736	C₄×D₄	—	134	2	no	—
737	C₄×D₄	C₂²×D₆₇	1	2	yes	—
738	C₄×D₄	C₂²×D₆₇	1	2	yes	—
739	C₄×D₄	C₂²×D₆₇	1	2	yes	—
740	#117	—	67	1	no	—
741	#117	—	67	1	no	—
742	#117	—	67	2	no	—
743	#117	—	67	2	no	—
744	C₂×C₄⋊C₄	—	2	2	no	—
745	C₂×C₄⋊C₄	—	67	2	no	—
746	C₂×C₄⋊C₄	—	134	2	no	—
747	C₂×C₄⋊C₄	—	134	2	no	—
748	C₂×C₄⋊C₄	—	134	2	no	—
749	C₂×C₄⋊C₄	—	134	2	no	—
750	C₂×C₄⋊C₄	—	134	2	no	—
751	C₂×C₂²⋊C₄	—	134	2	no	—
752	C₂×C₂²⋊C₄	—	134	2	no	—
753	C₂×C₂²⋊C₄	—	134	2	no	—
754	C₂×C₂²⋊C₄	—	134	2	no	—
755	C₂×C₂²⋊C₄	—	134	2	no	—
756	C₂×C₄²	—	67	1	no	—
757	#107	—	67	1	no	—
758	#107	—	67	1	no	—
759	#107	—	67	1	no	—
760	#107	—	67	2	no	—
761	#107	—	67	2	no	—
762	#107	—	67	2	no	—
763	#107	—	67	2	no	—
764	#107	—	67	2	no	—
765	#107	—	67	2	no	—
766	#107	C₂²×D₆₇	1	1	yes	characteristic
767	#107	C₂²×D₆₇	1	1	yes	characteristic
768	#107	C₂²×D₆₇	1	1	yes	characteristic
769	#107	C₂²×D₆₇	1	2	yes	—
770	#106	—	67	2	no	—
771	#106	—	67	2	no	—
772	#106	—	67	2	no	—
773	#106	—	67	2	no	—
774	#106	—	67	2	no	—
775	#106	—	67	2	no	—
776	#106	C₂²×D₆₇	1	2	yes	—
777	#106	C₂²×D₆₇	1	2	yes	—
778	C₄⋊C₈	—	67	1	no	—
779	C₄⋊C₈	—	67	1	no	—
780	C₄⋊C₈	—	67	1	no	—
781	C₄⋊C₈	—	67	1	no	—
782	C₄⋊C₈	—	67	1	no	—
783	C₄⋊C₈	—	67	1	no	—
784	C₄⋊C₈	—	67	1	no	—
785	C₄⋊C₈	—	67	1	no	—
786	C₄⋊C₈	—	67	1	no	—
787	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
788	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
789	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
790	#102	—	67	2	no	—
791	#102	—	67	2	no	—
792	#102	—	67	2	no	—
793	#102	—	67	2	no	—
794	#102	—	67	2	no	—
795	#102	—	67	2	no	—
796	#102	—	67	2	no	—
797	#102	—	67	2	no	—
798	#102	—	67	2	no	—
799	#102	C₂²×D₆₇	1	2	yes	—
800	#102	C₂²×D₆₇	1	2	yes	—
801	#102	C₂²×D₆₇	1	2	yes	—
802	#97	—	67	1	no	—
803	#97	—	67	1	no	—
804	#97	—	67	1	no	—
805	#97	—	67	1	no	—
806	C₄×C₈	—	67	1	no	—
807	C₄×C₈	—	67	1	no	—
808	C₄×C₈	—	67	1	no	—
809	C₄×C₈	—	67	1	no	—
810	C₄×C₈	—	67	1	no	—
811	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
812	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
813	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
814	C₂⁴	—	134	2	no	—
815	C₂×Q₈	—	2	2	no	—
816	C₂×Q₈	—	536	4	no	—
817	C₂×Q₈	—	536	4	no	—
818	C₂×Q₈	—	67	1	no	—
819	C₂×Q₈	—	67	1	no	—
820	C₂×Q₈	—	67	1	no	—
821	C₂×Q₈	—	134	2	no	—
822	C₂×Q₈	—	134	2	no	—
823	C₂×Q₈	—	134	2	no	—
824	C₂×Q₈	—	134	2	no	—
825	C₂×Q₈	—	134	2	no	—
826	C₂×Q₈	D₄×D₆₇	1	1	yes	characteristic
827	C₂×D₄	—	67	8	no	—
828	C₂×D₄	—	67	2	no	—
829	C₂×D₄	—	134	4	no	—
830	C₂×D₄	—	134	2	no	—
831	C₂×D₄	C₂³×D₆₇	1	2	yes	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	536	4	no	—
836	C₂²×C₄	—	67	1	no	—
837	C₂²×C₄	—	67	1	no	—
838	C₂²×C₄	—	67	1	no	—
839	C₂²×C₄	—	134	2	no	—
840	C₂²×C₄	—	134	2	no	—
841	C₂²×C₄	—	134	2	no	—
842	C₂²×C₄	—	134	2	no	—
843	C₂²×C₄	—	134	2	no	—
844	C₂²×C₄	—	134	2	no	—
845	C₂²×C₄	—	134	2	no	—
846	C₂²×C₄	—	134	2	no	—
847	C₂²×C₄	—	134	2	no	—
848	C₂²×C₄	—	134	2	no	—
849	D₈	—	67	8	no	—
850	D₈	—	67	4	no	—
851	D₈	Q₈×D₆₇	1	4	yes	complemented
852	M₁₆	—	134	2	no	—
853	M₁₆	—	134	2	no	—
854	C₂×C₈	—	67	1	no	—
855	C₂×C₈	—	67	4	no	—
856	C₂×C₈	—	67	1	no	—
857	C₂×C₈	—	67	1	no	—
858	C₂×C₈	—	67	1	no	—
859	C₂×C₈	—	134	2	no	—
860	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
861	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
862	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
863	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	67	1	no	—
870	C₄⋊C₄	—	67	1	no	—
871	C₄⋊C₄	—	67	1	no	—
872	C₄⋊C₄	—	67	1	no	—
873	C₄⋊C₄	—	67	1	no	—
874	C₄⋊C₄	—	67	1	no	—
875	C₄⋊C₄	—	67	1	no	—
876	C₄⋊C₄	—	67	1	no	—
877	C₄⋊C₄	—	67	1	no	—
878	C₄⋊C₄	—	67	1	no	—
879	C₄⋊C₄	—	67	1	no	—
880	C₄⋊C₄	—	67	1	no	—
881	C₄⋊C₄	—	67	1	no	—
882	C₄⋊C₄	—	67	2	no	—
883	C₄⋊C₄	—	67	2	no	—
884	C₄⋊C₄	—	67	2	no	—
885	C₄⋊C₄	—	134	2	no	—
886	C₄⋊C₄	—	134	2	no	—
887	C₄⋊C₄	—	134	2	no	—
888	C₄⋊C₄	—	134	2	no	—
889	C₄⋊C₄	—	134	2	no	—
890	C₄⋊C₄	—	134	2	no	—
891	C₄⋊C₄	—	134	2	no	—
892	C₄⋊C₄	—	134	2	no	—
893	C₄⋊C₄	—	134	2	no	—
894	C₄⋊C₄	—	134	2	no	—
895	C₄⋊C₄	—	134	2	no	—
896	C₄⋊C₄	—	134	2	no	—
897	C₄⋊C₄	—	134	2	no	—
898	C₄⋊C₄	—	134	2	no	—
899	C₄⋊C₄	D₄×D₆₇	1	1	yes	characteristic
900	C₄⋊C₄	D₄×D₆₇	1	1	yes	characteristic
901	C₄⋊C₄	D₄×D₆₇	1	1	yes	characteristic
902	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
903	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
904	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	67	1	no	—
909	C₂²⋊C₄	—	67	1	no	—
910	C₂²⋊C₄	—	67	1	no	—
911	C₂²⋊C₄	—	67	1	no	—
912	C₂²⋊C₄	—	134	2	no	—
913	C₂²⋊C₄	—	134	2	no	—
914	C₂²⋊C₄	—	134	2	no	—
915	C₂²⋊C₄	—	134	2	no	—
916	C₂²⋊C₄	—	134	2	no	—
917	C₂²⋊C₄	—	134	2	no	—
918	C₂²⋊C₄	—	134	2	no	—
919	C₂²⋊C₄	—	134	2	no	—
920	C₂²⋊C₄	—	134	2	no	—
921	C₂²⋊C₄	—	134	2	no	—
922	C₂²⋊C₄	—	134	2	no	—
923	C₄²	—	67	1	no	—
924	C₄²	—	67	1	no	—
925	C₄²	—	67	1	no	—
926	C₄²	—	67	1	no	—
927	C₄²	—	67	1	no	—
928	C₄²	—	134	2	no	—
929	C₄²	—	134	2	no	—
930	C₄²	C₂³×D₆₇	1	1	yes	characteristic
931	C₄²	C₂³×D₆₇	1	1	yes	characteristic
932	C₄²	C₂³×D₆₇	1	1	yes	characteristic
933	C₂³	—	2	2	no	—
934	C₂³	—	536	2	no	—
935	C₂³	—	536	2	no	—
936	C₂³	—	67	1	no	—
937	C₂³	—	134	8	no	—
938	C₂³	—	134	2	no	—
939	Q₈	—	4	1	no	—
940	Q₈	—	8	2	no	—
941	Q₈	—	268	1	no	—
942	Q₈	—	268	4	no	—
943	Q₈	—	536	2	no	—
944	Q₈	—	536	2	no	—
945	Q₈	—	536	2	no	—
946	Q₈	—	536	2	no	—
947	Q₈	—	134	2	no	—
948	Q₈	—	134	2	no	—
949	D₄	—	2	2	no	—
950	D₄	—	67	4	no	—
951	D₄	—	134	8	no	—
952	D₄	—	134	2	no	—
953	D₄	C₂×Q₈×D₆₇	1	4	yes	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	8	2	no	—
958	C₂×C₄	—	8	2	no	—
959	C₂×C₄	—	8	2	no	—
960	C₂×C₄	—	268	1	no	—
961	C₂×C₄	—	268	4	no	—
962	C₂×C₄	—	268	4	no	—
963	C₂×C₄	—	536	2	no	—
964	C₂×C₄	—	536	2	no	—
965	C₂×C₄	—	536	2	no	—
966	C₂×C₄	—	536	2	no	—
967	C₂×C₄	—	536	2	no	—
968	C₂×C₄	—	536	2	no	—
969	C₂×C₄	—	536	2	no	—
970	C₂×C₄	—	536	2	no	—
971	C₂×C₄	—	67	1	no	—
972	C₂×C₄	—	67	1	no	—
973	C₂×C₄	—	67	2	no	—
974	C₂×C₄	—	67	2	no	—
975	C₂×C₄	—	67	1	no	—
976	C₂×C₄	—	67	1	no	—
977	C₂×C₄	—	67	1	no	—
978	C₂×C₄	—	67	1	no	—
979	C₂×C₄	—	67	1	no	—
980	C₂×C₄	—	134	2	no	—
981	C₂×C₄	—	134	2	no	—
982	C₂×C₄	—	134	2	no	—
983	C₂×C₄	—	134	2	no	—
984	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
985	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
986	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
987	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
988	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
989	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
990	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
991	C₈	—	2	1	no	—
992	C₈	—	2	1	no	—
993	C₈	—	2	1	no	—
994	C₈	—	67	2	no	—
995	C₈	—	134	1	no	—
996	C₈	—	134	1	no	—
997	C₈	—	134	1	no	—
998	C₈	C₂×Q₈×D₆₇	1	2	yes	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	268	2	no	—
1003	C₂²	—	268	2	no	—
1004	C₂²	—	536	8	no	—
1005	C₂²	—	67	2	no	—
1006	C₂²	—	134	4	no	—
1007	C₂²	—	134	1	no	—
1008	C₂²	—	134	1	no	—
1009	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	268	2	no	—
1020	C₄	—	268	2	no	—
1021	C₄	—	268	2	no	—
1022	C₄	—	67	2	no	—
1023	C₄	—	67	2	no	—
1024	C₄	—	134	1	no	—
1025	C₄	—	134	1	no	—
1026	C₄	—	134	1	no	—
1027	C₄	—	134	1	no	—
1028	C₄	—	134	1	no	—
1029	C₄	C₂²×Q₈×D₆₇	1	1	yes	characteristic
1030	C₄	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
1031	C₂	—	4	4	no	—
1032	C₂	—	268	4	no	—
1033	C₂	—	134	2	no	—
1034	C₂	D₄×Q₈×D₆₇	1	1	yes	characteristic
1035	C₂	#576×D₆₇	1	1	yes	characteristic
1036	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×#3380	C₂
socle	C₂²×C₆₇	C₂³×D₄
prime radical	C₂×D₈×D₆₇	C₂²
hypercenter	#3380	D₆₇
hypocenter	C₆₇	#61370
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3380

Complements

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

N	H ≅ G/N	type
1. #22574008	C₂	semidirect
2. #22573167	C₂	semidirect
3. #22573163	C₂	semidirect
4. #22573111	C₂	semidirect
5. #22573103	C₂	semidirect
6. #22573077	C₂	semidirect
7. #22573076	C₂	semidirect
8. #22573076	C₂	semidirect
9. #22573073	C₂	semidirect
10. #22573073	C₂	semidirect
11. D₈×Dic₁₃₄	C₂	semidirect
12. #22573061	C₂	semidirect
13. #22570746	C₂	semidirect
14. #22570742	C₂	semidirect
15. #22570722	C₂	semidirect
16. #22570039	C₂	semidirect
17. #22570035	C₂	semidirect
18. #22570004	C₂	semidirect
19. #22569138	C₂	semidirect
23. C₆₇×#3380	C₂	semidirect
25. #16864106	C₂²	semidirect
26. #16864105	C₂²	semidirect
27. #16864105	C₂²	semidirect
28. #16864102	C₂²	semidirect
29. #16864102	C₂²	semidirect
33. D₄×Dic₁₃₄	C₂²	semidirect
34. #16864061	C₂²	semidirect
47. #16863806	C₂²	semidirect
48. #16863804	C₂²	semidirect
49. #16863803	C₂²	semidirect
50. #16863802	C₂²	semidirect
51. #16863801	C₂²	semidirect
52. #16863800	C₂²	semidirect
53. #16863800	C₂²	semidirect
54. #16863800	C₂²	semidirect
55. #16863800	C₂²	semidirect
56. #16863798	C₂²	semidirect
57. #16863798	C₂²	semidirect
58. #16863797	C₂²	semidirect
59. #16863797	C₂²	semidirect
60. #16863795	C₂²	semidirect
61. #16863793	C₂²	semidirect
62. #16863698	C₂²	semidirect
63. #16863698	C₂²	semidirect
64. #16863697	C₂²	semidirect
65. #16863697	C₂²	semidirect
66. #16863696	C₂²	semidirect
67. #16863696	C₂²	semidirect
68. #16863695	C₂²	semidirect
69. #16863695	C₂²	semidirect
70. #16863693	C₂²	semidirect
71. #16863693	C₂²	semidirect
72. #16863687	C₂²	semidirect
73. #16863685	C₂²	semidirect
74. #16863685	C₂²	semidirect
75. #16863684	C₂²	semidirect
76. #16863684	C₂²	semidirect
77. #16863676	C₂²	semidirect
78. #16863675	C₂²	semidirect
79. #16863675	C₂²	semidirect
80. #16863674	C₂²	semidirect
81. #16863674	C₂²	semidirect
82. #16863673	C₂²	semidirect
83. #16863527	C₂²	semidirect
84. #16863525	C₂²	semidirect
85. #16863525	C₂²	semidirect
86. #16863523	C₂²	semidirect
87. C₈×Dic₁₃₄	C₂²	semidirect
88. C₈×Dic₁₃₄	C₂²	semidirect
89. C₈×Dic₁₃₄	C₂²	semidirect
120. #554×C₆₇	C₂²	semidirect
121. #500×C₆₇	C₂²	semidirect
122. #499×C₆₇	C₂²	semidirect
123. #499×C₆₇	C₂²	semidirect
124. #478×C₆₇	C₂²	semidirect
125. #478×C₆₇	C₂²	semidirect
126. #476×C₆₇	C₂²	semidirect
127. C₈×Q₈×C₆₇	C₂²	semidirect
137. D₈×D₆₇	Q₈	semidirect
309. D₄×D₆₇	C₂×Q₈	semidirect
324. D₅₃₆	C₂×Q₈	semidirect
325. #11761613	C₂×Q₈	semidirect
333. C₈×D₆₇	C₂×Q₈	semidirect
392. D₈×C₆₇	C₂×Q₈	semidirect
529. #3380	D₆₇	semidirect
542. C₆₇	#61370	semidirect
552. #554	C₂×D₆₇	semidirect
576. #500	C₂×D₆₇	semidirect
582. #499	C₂×D₆₇	semidirect
583. #499	C₂×D₆₇	semidirect
595. #478	C₂×D₆₇	semidirect
596. #478	C₂×D₆₇	semidirect
602. #476	C₂×D₆₇	semidirect
616. C₈×Q₈	C₂×D₆₇	semidirect
851. D₈	Q₈×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574008	2
#22573167	2
#22573163	2
#22573111	2
#22573103	2
#22573077	2
#22573076	2
#22573073	2
D₈×Dic₁₃₄	2
#22573061	2
#22570746	2
#22570742	2
#22570722	2
#22570039	2
#22570035	2
#22570004	2
#22569138	2
#22569056	2
C₄×D₈×D₆₇	2
C₆₇×#3380	2
#61370	67