Subgroups — #31738220

Order 17152.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574143	C₂	1	2	yes	maximal, complemented
2	#22573218	C₂	1	1	yes	maximal, characteristic, complemented
3	#22573073	C₂	1	1	yes	maximal, characteristic, complemented
4	#22572968	C₂	1	2	yes	maximal, complemented
5	#22572610	C₂	1	1	yes	maximal, characteristic, complemented
6	#22572580	C₂	1	1	yes	maximal, characteristic, complemented
7	#22572553	C₂	1	1	yes	maximal, characteristic, complemented
8	#22572409	C₂	1	2	yes	maximal, complemented
9	#22572236	C₂	1	2	yes	maximal, complemented
10	#22572176	C₂	1	2	yes	maximal, complemented
11	#22571893	C₂	1	1	yes	maximal, characteristic, complemented
12	#22571891	C₂	1	1	yes	maximal, characteristic, complemented
13	#22571883	C₂	1	1	yes	maximal, characteristic, complemented
14	#22570855	C₂	1	1	yes	maximal, characteristic, complemented
15	#22570850	C₂	1	1	yes	maximal, characteristic, complemented
16	#22570414	C₂	1	2	yes	maximal, complemented
17	#22570399	C₂	1	2	yes	maximal, complemented
18	#22570343	C₂	1	2	yes	maximal, complemented
19	#22569184	C₂	1	1	yes	maximal, characteristic, complemented
20	#22569084	C₂	1	1	yes	maximal, characteristic, complemented
21	#22569056	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×D₅₃₆	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#3168	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14524066	C₂²	1	1	yes	characteristic
25	C₂²×D₅₃₆	C₂²	1	1	yes	characteristic
26	C₂×D₈×D₆₇	C₂²	1	1	yes	characteristic
27	#16864128	C₂²	1	2	yes	complemented
28	#16864102	C₂²	1	2	yes	complemented
29	#16864099	C₂²	1	2	yes	complemented
30	#16864090	—	2	2	no	—
31	#16864088	C₂²	1	2	yes	—
32	#16864075	—	2	2	no	—
33	#16864070	—	2	2	no	—
34	#16864046	C₂²	1	2	yes	complemented
35	#16864041	—	2	2	no	—
36	#16864039	C₂²	1	2	yes	complemented
37	#16864037	C₂²	1	2	yes	complemented
38	#16864030	C₂²	1	2	yes	—
39	#16864018	C₂²	1	2	yes	complemented
40	#16863997	C₂²	1	2	yes	complemented
41	#16863987	—	2	2	no	—
42	#16863985	—	2	2	no	—
43	#16863930	C₂²	1	1	yes	characteristic
44	#16863904	—	2	2	no	—
45	#123×D₆₇	—	2	2	no	—
46	#16863878	C₂²	1	2	yes	complemented
47	#16863868	C₂²	1	2	yes	complemented
48	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
49	#16863800	C₂²	1	1	yes	characteristic, complemented
50	#16863797	C₂²	1	1	yes	characteristic, complemented
51	#16863781	C₂²	1	1	yes	characteristic, complemented
52	#16863771	C₂²	1	1	yes	characteristic
53	#16863759	C₂²	1	2	yes	complemented
54	#16863757	C₂²	1	2	yes	complemented
55	#16863736	C₂²	1	2	yes	complemented
56	#16863724	C₂²	1	2	yes	complemented
57	#16863722	C₂²	1	2	yes	complemented
58	#16863716	C₂²	1	2	yes	complemented
59	#16863708	C₂²	1	2	yes	complemented
60	#16863707	C₂²	1	2	yes	complemented
61	#16863705	C₂²	1	2	yes	complemented
62	#16863695	C₂²	1	2	yes	complemented
63	#16863693	C₂²	1	2	yes	complemented
64	#16863693	C₂²	1	2	yes	complemented
65	#16863685	C₂²	1	2	yes	complemented
66	#16863674	C₂²	1	2	yes	complemented
67	#16863648	C₂²	1	2	yes	complemented
68	#16863645	C₂²	1	2	yes	complemented
69	#16863634	C₂²	1	1	yes	characteristic, complemented
70	#16863633	C₂²	1	1	yes	characteristic
71	#16863633	C₂²	1	1	yes	characteristic, complemented
72	#16863629	C₂²	1	1	yes	characteristic, complemented
73	#16863614	C₂²	1	2	yes	complemented
74	#16863613	C₂²	1	2	yes	complemented
75	#16863608	C₂²	1	2	yes	complemented
76	#16863608	C₂²	1	2	yes	complemented
77	#16863594	C₂²	1	2	yes	complemented
78	#16863590	C₂²	1	2	yes	—
79	#16863546	C₂²	1	2	yes	complemented
80	#16863545	C₂²	1	2	yes	complemented
81	#16863544	C₂²	1	2	yes	complemented
82	#16863540	C₂²	1	2	yes	complemented
83	#16863531	C₂²	1	2	yes	—
84	#16863529	C₂²	1	2	yes	—
85	#16863526	C₂²	1	1	yes	characteristic, complemented
86	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
87	#16863506	C₂²	1	2	yes	complemented
88	#16863506	C₂²	1	2	yes	complemented
89	#16863505	C₂²	1	2	yes	complemented
90	#16863499	C₂²	1	2	yes	complemented
91	#16863494	C₂²	1	2	yes	complemented
92	#16863494	C₂²	1	2	yes	complemented
93	Q₁₆×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
94	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
95	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
96	C₄×D₅₃₆	C₂²	1	1	yes	characteristic, complemented
97	C₄×D₅₃₆	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₅₃₆	C₂²	1	2	yes	complemented
99	C₄×D₅₃₆	C₂²	1	2	yes	complemented
100	D₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
101	#16863478	C₂²	1	1	yes	characteristic
102	#16863478	C₂²	1	1	yes	characteristic
103	#16863475	C₂²	1	1	yes	characteristic, complemented
104	#16863467	C₂²	1	1	yes	characteristic
105	#16863467	C₂²	1	1	yes	characteristic, complemented
106	C₈×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
107	C₈×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
108	C₈×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
109	#16863455	C₂²	1	1	yes	characteristic, complemented
110	#16863455	C₂²	1	1	yes	characteristic, complemented
111	#16863453	C₂²	1	1	yes	characteristic, complemented
112	#16863433	C₂²	1	1	yes	characteristic, complemented
113	C₂×#14523977	C₂²	1	1	yes	characteristic, complemented
114	#107×D₆₇	C₂²	1	1	yes	characteristic, complemented
115	#16863399	C₂²	1	2	yes	complemented
116	#16863396	C₂²	1	2	yes	complemented
117	C₂×#14523965	C₂²	1	2	yes	complemented
118	#16863350	C₂²	1	1	yes	characteristic, complemented
119	#16863350	C₂²	1	1	yes	characteristic, complemented
120	#529×C₆₇	C₂²	1	2	yes	complemented
121	#499×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#495×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#488×C₆₇	C₂²	1	2	yes	complemented
124	#467×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#466×C₆₇	C₂²	1	1	yes	characteristic
126	#465×C₆₇	C₂²	1	2	yes	complemented
127	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
129	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	C₂×#11761629	C₂³	1	2	yes	—
132	C₂×#11761627	—	2	2	no	—
133	C₂²×D₂₆₈	C₂³	1	2	yes	—
134	C₂×D₄×D₆₇	—	2	2	no	—
135	C₂×D₄×D₆₇	C₂³	1	2	yes	—
136	C₂²×C₄×D₆₇	—	2	2	no	—
137	#14524066	—	2	4	no	—
138	C₂×#11761615	C₂³	1	2	yes	—
139	C₂×#11761615	C₂³	1	2	yes	—
140	C₂×D₅₃₆	—	2	4	no	—
141	C₂×D₅₃₆	C₂³	1	1	yes	characteristic
142	C₂×D₅₃₆	C₂³	1	2	yes	—
143	C₂×D₅₃₆	C₂³	1	1	yes	characteristic
144	C₂×#11761613	C₂³	1	2	yes	—
145	C₂×#11761613	C₂³	1	2	yes	—
146	D₈×D₆₇	—	2	4	no	—
147	C₂×#11761611	C₂³	1	1	yes	characteristic
148	C₂×#11761611	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
151	#14524042	C₂³	1	2	yes	—
152	#14524039	C₂³	1	2	yes	—
153	#14524038	—	2	2	no	—
154	#14524038	—	2	2	no	—
155	#14524037	—	2	2	no	—
156	#14524037	D₄	1	1	yes	characteristic
157	#14524037	D₄	1	1	yes	characteristic
158	#14524035	D₄	1	1	yes	characteristic
159	#14524034	—	2	2	no	—
160	#14524034	C₂³	1	2	yes	—
161	#14524032	C₂³	1	2	yes	—
162	#14524031	—	2	2	no	—
163	#14524031	D₄	1	1	yes	characteristic
164	#14524029	—	2	2	no	—
165	#14524028	—	2	2	no	—
166	#14524028	—	2	2	no	—
167	#14524028	—	2	2	no	—
168	#14524027	—	2	2	no	—
169	#14524027	—	2	2	no	—
170	#14524026	—	2	2	no	—
171	#14524026	D₄	1	1	yes	characteristic
172	#14524026	D₄	1	1	yes	characteristic
173	#14524025	—	2	2	no	—
174	#14524025	—	2	2	no	—
175	#14524025	—	2	2	no	—
176	#14524025	—	2	2	no	—
177	#14524024	—	2	2	no	—
178	#14524023	—	2	2	no	—
179	#14524022	D₄	1	1	yes	characteristic
180	#14524021	—	2	2	no	—
181	#14524021	—	2	2	no	—
182	#14524021	—	2	2	no	—
183	#14524020	—	2	2	no	—
184	#14524019	C₂³	1	2	yes	—
185	#14524018	—	2	2	no	—
186	#14524018	—	2	2	no	—
187	#14524018	C₂³	1	2	yes	—
188	#14524018	C₂³	1	2	yes	—
189	#14524017	—	2	2	no	—
190	#14524017	D₄	1	1	yes	characteristic
191	#14524016	—	2	2	no	—
192	#14524016	—	2	2	no	—
193	#14524016	—	2	2	no	—
194	#14524014	C₂³	1	2	yes	—
195	#14524013	—	2	2	no	—
196	#14524013	—	2	2	no	—
197	#14524013	—	2	2	no	—
198	#14524011	—	2	2	no	—
199	Q₈×Dic₆₇	C₂³	1	2	yes	—
200	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
201	C₄×D₂₆₈	—	2	2	no	—
202	C₄×D₂₆₈	—	2	2	no	—
203	C₄×D₂₆₈	—	2	2	no	—
204	C₄×D₂₆₈	C₂³	1	2	yes	—
205	C₄×D₂₆₈	C₂³	1	2	yes	—
206	C₄×D₂₆₈	C₂³	1	2	yes	—
207	C₄×D₂₆₈	C₂³	1	2	yes	—
208	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
209	D₄×Dic₆₇	C₂³	1	2	yes	—
210	#14524005	—	2	2	no	—
211	#14524005	—	2	2	no	—
212	#14524005	C₂³	1	2	yes	—
213	#14524005	C₂³	1	2	yes	—
214	C₄×C₂²⋊D₆₇	—	2	2	no	—
215	C₄×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
216	C₄×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
217	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
218	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
219	#14524001	C₂³	1	2	yes	—
220	#14524000	—	2	2	no	—
221	#14524000	C₂³	1	1	yes	characteristic
222	#14524000	C₂³	1	1	yes	characteristic
223	#14523999	—	2	2	no	—
224	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
225	C₄⋊C₄×D₆₇	—	2	2	no	—
226	C₄⋊C₄×D₆₇	—	2	2	no	—
227	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
228	C₂×(C₂×D₆₇)⋊C₄	—	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	#14523977	C₂³	1	1	yes	characteristic
234	#14523977	C₂³	1	1	yes	characteristic
235	#14523977	C₂³	1	2	yes	—
236	#14523976	C₂³	1	2	yes	—
237	#14523976	C₂³	1	2	yes	—
238	#14523974	C₂³	1	2	yes	—
239	#14523974	C₂³	1	2	yes	—
240	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
241	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
242	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
243	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
244	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
245	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
246	#14523967	C₂³	1	2	yes	—
247	#14523967	C₂³	1	2	yes	—
248	#14523965	C₂³	1	2	yes	—
249	#14523965	C₂³	1	2	yes	—
250	#14523965	C₂³	1	2	yes	—
251	#14523965	C₂³	1	2	yes	—
252	#14523964	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	#14523963	C₂³	1	2	yes	—
258	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
259	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
260	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
261	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
262	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
263	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
264	#14523954	C₂³	1	1	yes	characteristic
265	#14523954	C₂³	1	1	yes	characteristic
266	#14523953	C₂³	1	1	yes	characteristic
267	#14523953	C₂³	1	1	yes	characteristic
268	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
269	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
270	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
271	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
272	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
273	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
274	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
275	#126×C₆₇	—	2	2	no	—
276	#125×C₆₇	C₂³	1	2	yes	—
277	#124×C₆₇	C₂³	1	2	yes	—
278	#123×C₆₇	—	2	2	no	—
279	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
280	#121×C₆₇	C₂³	1	2	yes	—
281	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
282	C₄×D₄×C₆₇	—	2	2	no	—
283	C₄×D₄×C₆₇	C₂³	1	2	yes	—
284	#117×C₆₇	—	2	2	no	—
285	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
286	#107×C₆₇	C₂³	1	1	yes	characteristic
287	#107×C₆₇	C₂³	1	1	yes	characteristic
288	#106×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	2	yes	—
291	#102×C₆₇	C₂³	1	2	yes	—
292	#102×C₆₇	C₂³	1	2	yes	—
293	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
297	C₂³×D₆₇	—	2	2	no	—
298	C₂³×D₆₇	—	2	2	no	—
299	#11761629	—	2	4	no	—
300	#11761629	—	4	2	no	—
301	#11761627	—	8	4	no	—
302	C₂×Dic₁₃₄	—	2	2	no	—
303	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
304	C₂×D₂₆₈	—	2	4	no	—
305	C₂×D₂₆₈	—	2	2	no	—
306	C₂×D₂₆₈	—	2	2	no	—
307	C₂×D₂₆₈	—	2	2	no	—
308	C₂×D₂₆₈	—	2	2	no	—
309	C₂×D₂₆₈	—	4	2	no	—
310	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
311	C₂×D₂₆₈	C₂⁴	1	2	yes	—
312	C₂×D₂₆₈	C₂⁴	1	2	yes	—
313	C₂×C₂²⋊D₆₇	—	2	2	no	—
314	C₂×C₂²⋊D₆₇	—	2	2	no	—
315	C₂×C₂²⋊D₆₇	—	2	2	no	—
316	C₂×C₂²⋊D₆₇	—	2	2	no	—
317	C₂×C₂²⋊D₆₇	C₂×D₄	1	1	yes	characteristic
318	C₂×C₂²⋊D₆₇	C₂×D₄	1	1	yes	characteristic
319	D₄×D₆₇	—	2	4	no	—
320	D₄×D₆₇	—	4	2	no	—
321	D₄×D₆₇	—	8	4	no	—
322	C₂²×Dic₆₇	—	2	2	no	—
323	C₂²×Dic₆₇	—	2	2	no	—
324	C₂×C₄×D₆₇	—	2	2	no	—
325	C₂×C₄×D₆₇	—	2	2	no	—
326	C₂×C₄×D₆₇	—	2	2	no	—
327	C₂×C₄×D₆₇	—	2	2	no	—
328	C₂×C₄×D₆₇	—	2	2	no	—
329	C₂×C₄×D₆₇	—	2	2	no	—
330	C₂×C₄×D₆₇	—	2	2	no	—
331	C₂×C₄×D₆₇	—	2	2	no	—
332	C₂×C₄×D₆₇	—	8	4	no	—
333	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
334	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
335	#11761615	—	2	4	no	—
336	#11761615	—	4	2	no	—
337	D₅₃₆	—	2	4	no	—
338	D₅₃₆	—	2	2	no	—
339	D₅₃₆	#41	1	4	yes	complemented
340	#11761613	—	2	4	no	—
341	#11761613	—	4	2	no	—
342	#11761611	—	4	1	no	—
343	#11761611	—	4	1	no	—
344	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
345	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
346	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
347	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
348	C₈×D₆₇	—	2	2	no	—
349	C₈×D₆₇	—	2	2	no	—
350	C₄⋊Dic₆₇	—	2	2	no	—
351	C₄⋊Dic₆₇	—	2	2	no	—
352	C₄⋊Dic₆₇	—	2	2	no	—
353	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
354	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
355	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
356	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
357	Dic₆₇⋊C₄	—	2	2	no	—
358	Dic₆₇⋊C₄	—	2	2	no	—
359	Dic₆₇⋊C₄	—	2	2	no	—
360	Dic₆₇⋊C₄	—	2	2	no	—
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	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
365	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
366	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
367	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
368	Dic₆₇⋊C₄	C₂×D₄	1	1	yes	characteristic
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	(C₂×D₆₇)⋊C₄	—	2	2	no	—
374	(C₂×D₆₇)⋊C₄	—	2	2	no	—
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	—	2	2	no	—
383	(C₂×D₆₇)⋊C₄	—	2	2	no	—
384	(C₂×D₆₇)⋊C₄	—	2	2	no	—
385	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
386	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
387	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
388	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
389	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
390	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
391	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
392	(C₂×D₆₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
393	C₄×Dic₆₇	—	2	2	no	—
394	C₄×Dic₆₇	—	2	2	no	—
395	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
396	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
397	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
398	C₂×D₄×C₆₇	—	2	2	no	—
399	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
400	C₂²×C₄×C₆₇	—	2	2	no	—
401	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	Q₁₆×C₆₇	—	2	2	no	—
405	SD₁₆×C₆₇	—	4	2	no	—
406	D₈×C₆₇	—	2	2	no	—
407	C₂×C₈×C₆₇	—	2	2	no	—
408	C₂×C₈×C₆₇	—	4	1	no	—
409	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₆₇	—	2	2	no	—
414	C₄⋊C₄×C₆₇	—	2	2	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
418	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
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	—	2	2	no	—
423	C₂²⋊C₄×C₆₇	—	2	2	no	—
424	C₄²×C₆₇	—	2	2	no	—
425	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
426	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
427	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
428	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
429	C₂³×C₆₇	—	2	2	no	—
430	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
431	C₂²×D₆₇	—	2	2	no	—
432	C₂²×D₆₇	—	2	2	no	—
433	C₂²×D₆₇	—	4	4	no	—
434	C₂²×D₆₇	—	4	4	no	—
435	C₂²×D₆₇	—	4	4	no	—
436	C₂²×D₆₇	—	8	2	no	—
437	C₂²×D₆₇	—	8	2	no	—
438	C₂²×D₆₇	—	8	2	no	—
439	C₂²×D₆₇	C₂²×D₄	1	1	yes	characteristic
440	C₂²×D₆₇	C₂²×D₄	1	1	yes	characteristic
441	Q₈×C₆₇	—	2	2	no	—
442	Q₈×C₆₇	—	2	2	no	—
443	D₄×C₆₇	—	2	2	no	—
444	D₄×C₆₇	—	2	2	no	—
445	D₄×C₆₇	—	4	4	no	—
446	C₂×C₄×C₆₇	—	2	2	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	2	no	—
450	C₂×C₄×C₆₇	—	2	2	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	4	1	no	—
453	C₂×C₄×C₆₇	—	8	2	no	—
454	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
460	C₂²⋊D₆₇	—	2	2	no	—
461	C₂²⋊D₆₇	—	2	2	no	—
462	C₂²⋊D₆₇	—	4	4	no	—
463	C₂²⋊D₆₇	—	8	2	no	—
464	C₂²⋊D₆₇	—	8	2	no	—
465	C₂²⋊D₆₇	—	8	2	no	—
466	C₂×Dic₆₇	—	2	2	no	—
467	C₂×Dic₆₇	—	2	2	no	—
468	C₂×Dic₆₇	—	4	4	no	—
469	C₂×Dic₆₇	—	8	2	no	—
470	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
471	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
473	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
474	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
476	D₂₆₈	—	2	2	no	—
477	D₂₆₈	—	2	2	no	—
478	D₂₆₈	—	2	2	no	—
479	D₂₆₈	—	4	1	no	—
480	D₂₆₈	—	4	4	no	—
481	D₂₆₈	—	4	4	no	—
482	D₂₆₈	—	8	2	no	—
483	D₂₆₈	—	8	2	no	—
484	D₂₆₈	C₂×#41	1	4	yes	—
485	C₄×D₆₇	—	2	1	no	—
486	C₄×D₆₇	—	2	1	no	—
487	C₄×D₆₇	—	2	1	no	—
488	C₄×D₆₇	—	2	1	no	—
489	C₄×D₆₇	—	4	4	no	—
490	C₄×D₆₇	—	8	2	no	—
491	C₄×D₆₇	—	8	2	no	—
492	C₄×D₆₇	—	8	2	no	—
493	C₄×D₆₇	—	8	2	no	—
494	C₄×D₆₇	—	8	2	no	—
495	C₄×D₆₇	—	8	2	no	—
496	C₄×D₆₇	—	8	2	no	—
497	Dic₁₃₄	—	4	1	no	—
498	Dic₁₃₄	—	8	2	no	—
499	C₈×C₆₇	—	2	1	no	—
500	C₈×C₆₇	—	2	1	no	—
501	C₈×C₆₇	—	2	1	no	—
502	C₈×C₆₇	C₂×#41	1	2	yes	—
503	C₆₇⋊C₈	—	2	1	no	—
504	C₆₇⋊C₈	—	2	1	no	—
505	C₆₇⋊C₈	—	2	1	no	—
506	C₆₇⋊C₈	—	2	1	no	—
507	C₂²×C₆₇	—	2	1	no	—
508	C₂²×C₆₇	—	2	1	no	—
509	C₂²×C₆₇	—	4	2	no	—
510	C₂²×C₆₇	—	4	2	no	—
511	C₂²×C₆₇	—	4	2	no	—
512	C₂²×C₆₇	#576	1	2	yes	—
513	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
514	C₂×D₆₇	—	2	1	no	—
515	C₂×D₆₇	—	2	1	no	—
516	C₂×D₆₇	—	2	1	no	—
517	C₂×D₆₇	—	2	1	no	—
518	C₂×D₆₇	—	2	4	no	—
519	C₂×D₆₇	—	2	1	no	—
520	C₂×D₆₇	—	2	1	no	—
521	C₂×D₆₇	—	4	2	no	—
522	C₂×D₆₇	—	4	2	no	—
523	C₂×D₆₇	—	4	2	no	—
524	C₂×D₆₇	—	4	2	no	—
525	C₂×D₆₇	—	4	2	no	—
526	C₂×D₆₇	—	8	8	no	—
527	C₂×D₆₇	—	16	4	no	—
528	C₄×C₆₇	—	2	1	no	—
529	C₄×C₆₇	—	2	1	no	—
530	C₄×C₆₇	—	2	1	no	—
531	C₄×C₆₇	—	2	1	no	—
532	C₄×C₆₇	—	2	1	no	—
533	C₄×C₆₇	—	4	2	no	—
534	C₄×C₆₇	—	4	2	no	—
535	C₄×C₆₇	—	4	2	no	—
536	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
537	C₄×C₆₇	#585	1	1	yes	characteristic
538	Dic₆₇	—	2	1	no	—
539	Dic₆₇	—	2	1	no	—
540	Dic₆₇	—	2	1	no	—
541	Dic₆₇	—	2	1	no	—
542	Dic₆₇	—	2	1	no	—
543	Dic₆₇	—	2	1	no	—
544	Dic₆₇	—	4	2	no	—
545	Dic₆₇	—	4	2	no	—
546	#61471	—	67	1	no	maximal, Sylow
547	C₂×C₆₇	—	2	2	no	—
548	C₂×C₆₇	—	8	2	no	—
549	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
550	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
551	C₂×C₆₇	#3584	1	1	yes	characteristic
552	D₆₇	—	4	1	no	—
553	D₆₇	—	4	1	no	—
554	D₆₇	—	4	4	no	—
555	D₆₇	—	8	2	no	—
556	#3513	—	67	2	no	—
557	#3396	—	67	1	no	—
558	#3380	—	67	1	no	—
559	#3370	—	67	2	no	—
560	#3339	—	67	1	no	—
561	#3336	—	67	1	no	—
562	#3334	—	67	1	no	—
563	#3322	—	67	2	no	—
564	#3310	—	67	2	no	—
565	#3306	—	67	2	no	—
566	#3280	—	67	1	no	—
567	#3280	—	67	1	no	—
568	D₄×D₈	—	67	1	no	—
569	#3176	—	67	1	no	—
570	#3175	—	67	1	no	—
571	#3168	D₆₇	1	1	yes	characteristic, complemented
572	#3119	—	67	2	no	—
573	#3118	—	67	2	no	—
574	#3114	—	67	2	no	—
575	#2966	—	67	1	no	—
576	#2951	—	67	1	no	—
577	#2948	—	67	1	no	—
578	C₂×C₄×D₈	—	67	1	no	—
579	C₆₇	#61471	1	1	yes	characteristic, complemented, Sylow
580	C₂×#135	—	67	1	no	—
581	C₂²×D₈	—	67	1	no	—
582	C₂²×D₈	—	67	1	no	—
583	#559	—	67	2	no	—
584	#554	—	67	2	no	—
585	#553	—	67	2	no	—
586	#553	—	134	2	no	—
587	#552	—	67	2	no	—
588	#551	—	134	2	no	—
589	#551	—	134	2	no	—
590	#547	—	67	2	no	—
591	#546	—	67	2	no	—
592	#546	—	67	2	no	—
593	#546	—	134	2	no	—
594	D₄²	—	67	2	no	—
595	#542	—	67	2	no	—
596	#540	—	67	2	no	—
597	#539	—	134	2	no	—
598	#538	—	134	2	no	—
599	#529	—	67	1	no	—
600	#529	C₂×D₆₇	1	2	yes	complemented
601	#525	—	134	2	no	—
602	C₂×#123	—	134	2	no	—
603	#520	—	67	2	no	—
604	#518	—	67	2	no	—
605	C₂×C₄×D₄	—	67	2	no	—
606	#500	—	67	1	no	—
607	#499	—	67	1	no	—
608	#499	C₂×D₆₇	1	1	yes	characteristic, complemented
609	#495	—	67	1	no	—
610	#495	C₂×D₆₇	1	1	yes	characteristic, complemented
611	#493	—	67	1	no	—
612	#490	—	67	2	no	—
613	#489	—	67	2	no	—
614	#488	C₂×D₆₇	1	2	yes	complemented
615	#485	—	67	2	no	—
616	#483	—	67	2	no	—
617	#482	—	67	2	no	—
618	#481	—	67	2	no	—
619	#480	—	67	2	no	—
620	#480	—	67	2	no	—
621	#479	—	67	2	no	—
622	#478	—	67	2	no	—
623	#478	—	67	2	no	—
624	#478	—	67	2	no	—
625	#476	—	67	2	no	—
626	#474	—	67	2	no	—
627	#469	—	67	2	no	—
628	#468	—	67	2	no	—
629	#467	—	67	1	no	—
630	#467	C₂×D₆₇	1	1	yes	characteristic, complemented
631	#466	—	67	1	no	—
632	#466	—	67	1	no	—
633	#466	—	67	1	no	—
634	#466	C₂×D₆₇	1	1	yes	characteristic
635	#465	C₂×D₆₇	1	2	yes	complemented
636	#463	—	67	2	no	—
637	#463	—	67	2	no	—
638	#463	—	67	2	no	—
639	#463	—	67	2	no	—
640	#460	—	67	2	no	—
641	#459	—	67	2	no	—
642	#450	—	67	2	no	—
643	#450	—	67	2	no	—
644	#449	—	67	2	no	—
645	#449	—	67	2	no	—
646	#447	—	67	2	no	—
647	#447	—	67	2	no	—
648	#446	—	67	1	no	—
649	C₈×Q₈	—	67	1	no	—
650	#442	—	67	2	no	—
651	#442	—	67	2	no	—
652	#442	—	67	2	no	—
653	#440	—	67	2	no	—
654	#440	—	67	2	no	—
655	#440	—	67	2	no	—
656	C₄×Q₁₆	—	67	1	no	—
657	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
658	C₄×SD₁₆	C₂×D₆₇	1	2	yes	complemented
659	C₄×D₈	—	67	1	no	—
660	C₄×D₈	—	67	1	no	—
661	C₄×D₈	—	67	1	no	—
662	C₄×D₈	—	67	1	no	—
663	C₄×D₈	—	67	2	no	—
664	C₄×D₈	—	67	2	no	—
665	C₄×D₈	—	67	1	no	—
666	C₄×D₈	—	67	1	no	—
667	C₄×D₈	—	67	1	no	—
668	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic, complemented
669	#436	—	67	1	no	—
670	#435	—	67	1	no	—
671	#435	—	67	1	no	—
672	C₈×D₄	—	67	1	no	—
673	C₈×D₄	—	67	1	no	—
674	C₈×D₄	—	67	1	no	—
675	#433	—	67	1	no	—
676	#433	—	67	1	no	—
677	#432	—	67	1	no	—
678	#427	—	67	1	no	—
679	C₂×#107	—	67	1	no	—
680	C₂×#107	—	67	1	no	—
681	#418	—	67	2	no	—
682	#417	—	67	2	no	—
683	C₂×#102	—	67	2	no	—
684	#405	—	67	1	no	—
685	#405	—	67	1	no	—
686	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
687	C₂×#41	—	67	2	no	—
688	C₂×#41	—	134	2	no	—
689	C₂²×D₄	—	67	2	no	—
690	C₂²×D₄	—	67	2	no	—
691	C₂²×D₄	—	134	2	no	—
692	C₂³×C₄	—	134	2	no	—
693	#135	—	134	4	no	—
694	C₂×Q₁₆	C₂²×D₆₇	1	1	yes	characteristic
695	C₂×SD₁₆	—	67	2	no	—
696	C₂×SD₁₆	—	67	2	no	—
697	C₂×SD₁₆	C₂²×D₆₇	1	2	yes	—
698	C₂×D₈	—	67	2	no	—
699	C₂×D₈	—	67	2	no	—
700	C₂×D₈	—	67	1	no	—
701	C₂×D₈	—	67	2	no	—
702	C₂×D₈	—	67	1	no	—
703	C₂×D₈	—	134	4	no	—
704	C₂×D₈	—	134	4	no	—
705	C₂×D₈	C₂²×D₆₇	1	1	yes	characteristic
706	C₂×M₁₆	—	67	1	no	—
707	C₂×M₁₆	—	67	1	no	—
708	C₂²×C₈	—	67	1	no	—
709	C₂²×C₈	—	67	1	no	—
710	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
711	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
712	C₄⋊Q₈	—	67	2	no	—
713	#127	—	67	2	no	—
714	#126	—	2	2	no	—
715	#126	—	67	1	no	—
716	#126	—	67	1	no	—
717	#126	—	134	2	no	—
718	#126	—	134	2	no	—
719	#126	—	134	2	no	—
720	#125	—	67	2	no	—
721	#125	—	67	1	no	—
722	#125	—	134	2	no	—
723	#125	C₂²×D₆₇	1	2	yes	—
724	#124	—	67	2	no	—
725	#124	—	67	1	no	—
726	#124	—	134	2	no	—
727	#124	—	134	2	no	—
728	#124	C₂²×D₆₇	1	2	yes	—
729	#123	—	2	2	no	—
730	#123	—	67	1	no	—
731	#123	—	67	1	no	—
732	#123	—	134	2	no	—
733	#123	—	134	2	no	—
734	#123	—	134	2	no	—
735	#123	—	134	2	no	—
736	#123	—	134	2	no	—
737	#123	—	134	2	no	—
738	#123	—	134	2	no	—
739	#123	—	134	2	no	—
740	#123	—	134	2	no	—
741	#123	—	134	2	no	—
742	#123	—	134	2	no	—
743	C₂²⋊Q₈	—	67	1	no	—
744	C₂²⋊Q₈	—	67	2	no	—
745	C₂²⋊Q₈	—	134	2	no	—
746	C₂²⋊Q₈	—	134	2	no	—
747	C₂²⋊Q₈	—	134	2	no	—
748	C₂²⋊Q₈	—	134	2	no	—
749	C₂²⋊Q₈	—	134	2	no	—
750	C₂²⋊Q₈	C₂²×D₆₇	1	2	yes	—
751	#121	—	67	1	no	—
752	#121	—	67	2	no	—
753	#121	—	67	2	no	—
754	#121	—	67	2	no	—
755	#121	—	134	2	no	—
756	#121	—	134	2	no	—
757	#121	—	134	2	no	—
758	#121	—	134	2	no	—
759	#121	—	134	2	no	—
760	#121	—	134	2	no	—
761	#121	C₂²×D₆₇	1	2	yes	—
762	#120	—	134	2	no	—
763	#120	—	134	2	no	—
764	#120	—	134	2	no	—
765	#120	—	134	2	no	—
766	C₄×Q₈	—	67	1	no	—
767	C₄×Q₈	—	67	2	no	—
768	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	67	1	no	—
771	C₄×D₄	—	67	1	no	—
772	C₄×D₄	—	67	2	no	—
773	C₄×D₄	—	67	2	no	—
774	C₄×D₄	—	67	2	no	—
775	C₄×D₄	—	67	1	no	—
776	C₄×D₄	—	67	2	no	—
777	C₄×D₄	—	67	2	no	—
778	C₄×D₄	—	67	2	no	—
779	C₄×D₄	—	67	2	no	—
780	C₄×D₄	—	134	2	no	—
781	C₄×D₄	—	134	2	no	—
782	C₄×D₄	—	134	2	no	—
783	C₄×D₄	—	134	2	no	—
784	C₄×D₄	—	134	2	no	—
785	C₄×D₄	—	134	2	no	—
786	C₄×D₄	—	134	2	no	—
787	C₄×D₄	—	134	2	no	—
788	C₄×D₄	C₂²×D₆₇	1	2	yes	—
789	#117	—	2	2	no	—
790	#117	—	67	1	no	—
791	#117	—	67	1	no	—
792	#117	—	67	2	no	—
793	#117	—	134	2	no	—
794	#117	—	134	2	no	—
795	C₂×C₄⋊C₄	—	67	2	no	—
796	C₂×C₄⋊C₄	—	67	2	no	—
797	C₂×C₄⋊C₄	—	134	2	no	—
798	C₂×C₄⋊C₄	—	134	2	no	—
799	C₂×C₂²⋊C₄	—	134	2	no	—
800	C₂×C₂²⋊C₄	—	134	2	no	—
801	C₂×C₂²⋊C₄	—	134	2	no	—
802	C₂×C₂²⋊C₄	—	134	2	no	—
803	C₂×C₂²⋊C₄	—	134	2	no	—
804	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
805	#107	—	67	1	no	—
806	#107	—	67	1	no	—
807	#107	—	67	2	no	—
808	#107	—	67	2	no	—
809	#107	—	67	2	no	—
810	#107	C₂²×D₆₇	1	1	yes	characteristic
811	#107	C₂²×D₆₇	1	1	yes	characteristic
812	#106	—	67	2	no	—
813	#106	—	67	2	no	—
814	#106	C₂²×D₆₇	1	2	yes	—
815	C₄⋊C₈	—	67	1	no	—
816	C₄⋊C₈	—	67	1	no	—
817	C₄⋊C₈	—	67	1	no	—
818	C₄⋊C₈	—	67	1	no	—
819	C₄⋊C₈	—	67	1	no	—
820	C₄⋊C₈	—	67	1	no	—
821	#103	—	67	2	no	—
822	#103	—	67	2	no	—
823	#103	C₂²×D₆₇	1	2	yes	—
824	#103	C₂²×D₆₇	1	2	yes	—
825	#102	—	67	2	no	—
826	#102	—	67	2	no	—
827	#102	—	67	2	no	—
828	#102	—	67	2	no	—
829	#102	—	67	2	no	—
830	#102	—	67	2	no	—
831	#102	—	67	2	no	—
832	#102	—	67	2	no	—
833	#102	—	67	2	no	—
834	#102	—	67	2	no	—
835	#102	C₂²×D₆₇	1	2	yes	—
836	#102	C₂²×D₆₇	1	2	yes	—
837	C₂²⋊C₈	—	67	1	no	—
838	C₂²⋊C₈	—	67	1	no	—
839	C₂²⋊C₈	—	67	1	no	—
840	C₂²⋊C₈	—	67	1	no	—
841	C₂²⋊C₈	—	67	1	no	—
842	C₂²⋊C₈	—	67	1	no	—
843	#97	—	67	1	no	—
844	#97	—	67	1	no	—
845	#97	—	67	1	no	—
846	#97	—	67	1	no	—
847	C₄×C₈	—	67	1	no	—
848	C₄×C₈	—	67	1	no	—
849	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
850	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
851	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
852	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
853	C₂⁴	—	134	2	no	—
854	C₂⁴	—	134	2	no	—
855	#41	—	268	2	no	—
856	#41	—	536	4	no	—
857	#41	—	134	4	no	—
858	C₂×Q₈	—	67	1	no	—
859	C₂×Q₈	—	134	2	no	—
860	C₂×Q₈	C₂³×D₆₇	1	2	yes	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	268	2	no	—
863	C₂×D₄	—	268	2	no	—
864	C₂×D₄	—	536	4	no	—
865	C₂×D₄	—	67	1	no	—
866	C₂×D₄	—	67	1	no	—
867	C₂×D₄	—	67	1	no	—
868	C₂×D₄	—	67	2	no	—
869	C₂×D₄	—	67	2	no	—
870	C₂×D₄	—	134	2	no	—
871	C₂×D₄	—	134	4	no	—
872	C₂×D₄	—	134	2	no	—
873	C₂×D₄	—	134	2	no	—
874	C₂×D₄	—	134	2	no	—
875	C₂×D₄	—	134	2	no	—
876	C₂×D₄	—	134	2	no	—
877	C₂×D₄	—	134	4	no	—
878	C₂×D₄	—	134	2	no	—
879	C₂×D₄	—	134	2	no	—
880	C₂×D₄	C₂³×D₆₇	1	2	yes	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	536	4	no	—
883	C₂²×C₄	—	67	1	no	—
884	C₂²×C₄	—	67	1	no	—
885	C₂²×C₄	—	134	2	no	—
886	C₂²×C₄	—	134	2	no	—
887	C₂²×C₄	—	134	2	no	—
888	C₂²×C₄	—	134	2	no	—
889	C₂²×C₄	—	134	2	no	—
890	C₂²×C₄	—	134	2	no	—
891	C₂²×C₄	—	134	2	no	—
892	C₂²×C₄	—	134	2	no	—
893	C₂²×C₄	—	134	2	no	—
894	C₂²×C₄	—	134	2	no	—
895	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
896	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
897	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
898	Q₁₆	—	2	2	no	—
899	SD₁₆	—	4	2	no	—
900	SD₁₆	—	268	2	no	—
901	SD₁₆	—	134	4	no	—
902	D₈	—	2	2	no	—
903	D₈	—	268	2	no	—
904	D₈	—	67	4	no	—
905	D₈	—	134	4	no	—
906	D₈	—	134	4	no	—
907	D₈	—	134	2	no	—
908	M₁₆	—	268	1	no	—
909	M₁₆	—	268	1	no	—
910	C₂×C₈	—	2	2	no	—
911	C₂×C₈	—	4	1	no	—
912	C₂×C₈	—	67	1	no	—
913	C₂×C₈	—	67	1	no	—
914	C₂×C₈	—	67	1	no	—
915	C₂×C₈	—	67	1	no	—
916	C₂×C₈	—	134	2	no	—
917	C₂×C₈	—	134	2	no	—
918	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
919	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
920	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
921	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	67	1	no	—
927	C₄⋊C₄	—	67	1	no	—
928	C₄⋊C₄	—	67	1	no	—
929	C₄⋊C₄	—	67	1	no	—
930	C₄⋊C₄	—	67	1	no	—
931	C₄⋊C₄	—	67	1	no	—
932	C₄⋊C₄	—	67	1	no	—
933	C₄⋊C₄	—	67	1	no	—
934	C₄⋊C₄	—	67	1	no	—
935	C₄⋊C₄	—	67	1	no	—
936	C₄⋊C₄	—	67	2	no	—
937	C₄⋊C₄	—	67	2	no	—
938	C₄⋊C₄	—	134	2	no	—
939	C₄⋊C₄	—	134	2	no	—
940	C₄⋊C₄	—	134	2	no	—
941	C₄⋊C₄	—	134	2	no	—
942	C₄⋊C₄	—	134	2	no	—
943	C₄⋊C₄	—	134	2	no	—
944	C₄⋊C₄	—	134	2	no	—
945	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
946	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	67	1	no	—
953	C₂²⋊C₄	—	67	1	no	—
954	C₂²⋊C₄	—	67	1	no	—
955	C₂²⋊C₄	—	67	1	no	—
956	C₂²⋊C₄	—	67	1	no	—
957	C₂²⋊C₄	—	67	1	no	—
958	C₂²⋊C₄	—	67	1	no	—
959	C₂²⋊C₄	—	67	1	no	—
960	C₂²⋊C₄	—	67	1	no	—
961	C₂²⋊C₄	—	67	1	no	—
962	C₂²⋊C₄	—	134	2	no	—
963	C₂²⋊C₄	—	134	2	no	—
964	C₂²⋊C₄	—	134	2	no	—
965	C₂²⋊C₄	—	134	2	no	—
966	C₂²⋊C₄	—	134	2	no	—
967	C₂²⋊C₄	—	134	2	no	—
968	C₂²⋊C₄	—	134	2	no	—
969	C₂²⋊C₄	—	134	2	no	—
970	C₂²⋊C₄	—	134	2	no	—
971	C₂²⋊C₄	—	134	2	no	—
972	C₂²⋊C₄	—	134	2	no	—
973	C₂²⋊C₄	—	134	2	no	—
974	C₂²⋊C₄	—	134	2	no	—
975	C₂²⋊C₄	—	134	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	67	1	no	—
978	C₄²	—	67	1	no	—
979	C₄²	—	134	2	no	—
980	C₄²	—	134	2	no	—
981	C₄²	D₄×D₆₇	1	1	yes	characteristic
982	C₄²	D₄×D₆₇	1	1	yes	characteristic
983	C₄²	C₂³×D₆₇	1	1	yes	characteristic
984	C₄²	C₂³×D₆₇	1	1	yes	characteristic
985	C₂³	—	2	2	no	—
986	C₂³	—	268	4	no	—
987	C₂³	—	268	4	no	—
988	C₂³	—	268	4	no	—
989	C₂³	—	536	2	no	—
990	C₂³	—	536	2	no	—
991	C₂³	—	536	2	no	—
992	C₂³	—	67	1	no	—
993	C₂³	—	67	1	no	—
994	C₂³	—	134	2	no	—
995	C₂³	—	134	2	no	—
996	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
997	Q₈	—	2	2	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	268	1	no	—
1000	Q₈	—	536	2	no	—
1001	D₄	—	2	2	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	4	4	no	—
1004	D₄	—	268	4	no	—
1005	D₄	—	268	1	no	—
1006	D₄	—	268	4	no	—
1007	D₄	—	268	4	no	—
1008	D₄	—	536	2	no	—
1009	D₄	—	536	2	no	—
1010	D₄	—	536	2	no	—
1011	D₄	—	536	2	no	—
1012	D₄	—	536	2	no	—
1013	D₄	—	67	4	no	—
1014	D₄	—	134	2	no	—
1015	D₄	—	134	2	no	—
1016	D₄	—	134	2	no	—
1017	D₄	—	134	2	no	—
1018	D₄	—	134	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	4	1	no	—
1026	C₂×C₄	—	8	2	no	—
1027	C₂×C₄	—	268	4	no	—
1028	C₂×C₄	—	268	4	no	—
1029	C₂×C₄	—	536	2	no	—
1030	C₂×C₄	—	536	2	no	—
1031	C₂×C₄	—	536	2	no	—
1032	C₂×C₄	—	536	2	no	—
1033	C₂×C₄	—	536	2	no	—
1034	C₂×C₄	—	536	2	no	—
1035	C₂×C₄	—	536	2	no	—
1036	C₂×C₄	—	536	2	no	—
1037	C₂×C₄	—	67	1	no	—
1038	C₂×C₄	—	67	1	no	—
1039	C₂×C₄	—	67	1	no	—
1040	C₂×C₄	—	67	1	no	—
1041	C₂×C₄	—	67	1	no	—
1042	C₂×C₄	—	67	1	no	—
1043	C₂×C₄	—	134	2	no	—
1044	C₂×C₄	—	134	2	no	—
1045	C₂×C₄	—	134	1	no	—
1046	C₂×C₄	—	134	1	no	—
1047	C₂×C₄	—	134	1	no	—
1048	C₂×C₄	—	134	1	no	—
1049	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1050	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1051	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1052	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1053	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1054	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1055	C₈	—	2	1	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	134	1	no	—
1059	C₈	—	134	1	no	—
1060	C₈	—	134	1	no	—
1061	C₈	—	134	1	no	—
1062	C₈	#41×D₆₇	1	2	yes	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	268	2	no	—
1069	C₂²	—	268	2	no	—
1070	C₂²	—	268	2	no	—
1071	C₂²	—	268	2	no	—
1072	C₂²	—	268	2	no	—
1073	C₂²	—	536	8	no	—
1074	C₂²	—	1072	4	no	—
1075	C₂²	—	134	1	no	—
1076	C₂²	—	134	1	no	—
1077	C₂²	—	134	4	no	—
1078	C₂²	—	134	1	no	—
1079	C₂²	—	134	1	no	—
1080	C₂²	—	134	1	no	—
1081	C₂²	—	134	1	no	—
1082	C₂²	#16864198	1	2	yes	—
1083	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	268	2	no	—
1093	C₄	—	268	2	no	—
1094	C₄	—	134	1	no	—
1095	C₄	—	134	1	no	—
1096	C₄	—	134	1	no	—
1097	C₄	—	134	1	no	—
1098	C₄	—	134	1	no	—
1099	C₄	—	134	1	no	—
1100	C₄	C₂×#41×D₆₇	1	1	yes	characteristic
1101	C₄	#16864232	1	1	yes	characteristic
1102	C₂	—	2	2	no	—
1103	C₂	—	8	2	no	—
1104	C₂	—	268	4	no	—
1105	C₂	—	268	1	no	—
1106	C₂	—	268	1	no	—
1107	C₂	—	536	2	no	—
1108	C₂	#22573695	1	1	yes	characteristic
1109	C₂	C₂×#16864198	1	1	yes	characteristic
1110	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×#3168	C₂
socle	C₂²×C₆₇	C₂³×D₄
hypercenter	#3168	D₆₇
hypocenter	C₆₇	#61471
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3168

Complements

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

N	H ≅ G/N	type
1. #22574143	C₂	semidirect
2. #22573218	C₂	semidirect
3. #22573073	C₂	semidirect
4. #22572968	C₂	semidirect
5. #22572610	C₂	semidirect
6. #22572580	C₂	semidirect
7. #22572553	C₂	semidirect
8. #22572409	C₂	semidirect
9. #22572236	C₂	semidirect
10. #22572176	C₂	semidirect
11. #22571893	C₂	semidirect
12. #22571891	C₂	semidirect
13. #22571883	C₂	semidirect
14. #22570855	C₂	semidirect
15. #22570850	C₂	semidirect
16. #22570414	C₂	semidirect
17. #22570399	C₂	semidirect
18. #22570343	C₂	semidirect
19. #22569184	C₂	semidirect
20. #22569084	C₂	semidirect
21. #22569056	C₂	semidirect
22. C₂×C₄×D₅₃₆	C₂	semidirect
23. C₆₇×#3168	C₂	semidirect
27. #16864128	C₂²	semidirect
28. #16864102	C₂²	semidirect
29. #16864099	C₂²	semidirect
34. #16864046	C₂²	semidirect
36. #16864039	C₂²	semidirect
37. #16864037	C₂²	semidirect
39. #16864018	C₂²	semidirect
40. #16863997	C₂²	semidirect
46. #16863878	C₂²	semidirect
47. #16863868	C₂²	semidirect
48. C₂×C₄×D₂₆₈	C₂²	semidirect
49. #16863800	C₂²	semidirect
50. #16863797	C₂²	semidirect
51. #16863781	C₂²	semidirect
53. #16863759	C₂²	semidirect
54. #16863757	C₂²	semidirect
55. #16863736	C₂²	semidirect
56. #16863724	C₂²	semidirect
57. #16863722	C₂²	semidirect
58. #16863716	C₂²	semidirect
59. #16863708	C₂²	semidirect
60. #16863707	C₂²	semidirect
61. #16863705	C₂²	semidirect
62. #16863695	C₂²	semidirect
63. #16863693	C₂²	semidirect
64. #16863693	C₂²	semidirect
65. #16863685	C₂²	semidirect
66. #16863674	C₂²	semidirect
67. #16863648	C₂²	semidirect
68. #16863645	C₂²	semidirect
69. #16863634	C₂²	semidirect
71. #16863633	C₂²	semidirect
72. #16863629	C₂²	semidirect
73. #16863614	C₂²	semidirect
74. #16863613	C₂²	semidirect
75. #16863608	C₂²	semidirect
76. #16863608	C₂²	semidirect
77. #16863594	C₂²	semidirect
79. #16863546	C₂²	semidirect
80. #16863545	C₂²	semidirect
81. #16863544	C₂²	semidirect
82. #16863540	C₂²	semidirect
85. #16863526	C₂²	semidirect
86. C₈×Dic₁₃₄	C₂²	semidirect
87. #16863506	C₂²	semidirect
88. #16863506	C₂²	semidirect
89. #16863505	C₂²	semidirect
90. #16863499	C₂²	semidirect
91. #16863494	C₂²	semidirect
92. #16863494	C₂²	semidirect
93. Q₁₆×Dic₆₇	C₂²	semidirect
96. C₄×D₅₃₆	C₂²	semidirect
97. C₄×D₅₃₆	C₂²	semidirect
98. C₄×D₅₃₆	C₂²	semidirect
99. C₄×D₅₃₆	C₂²	semidirect
100. D₈×Dic₆₇	C₂²	semidirect
103. #16863475	C₂²	semidirect
105. #16863467	C₂²	semidirect
106. C₈×D₂₆₈	C₂²	semidirect
108. C₈×C₂²⋊D₆₇	C₂²	semidirect
109. #16863455	C₂²	semidirect
110. #16863455	C₂²	semidirect
111. #16863453	C₂²	semidirect
112. #16863433	C₂²	semidirect
113. C₂×#14523977	C₂²	semidirect
114. #107×D₆₇	C₂²	semidirect
115. #16863399	C₂²	semidirect
116. #16863396	C₂²	semidirect
117. C₂×#14523965	C₂²	semidirect
118. #16863350	C₂²	semidirect
119. #16863350	C₂²	semidirect
120. #529×C₆₇	C₂²	semidirect
121. #499×C₆₇	C₂²	semidirect
122. #495×C₆₇	C₂²	semidirect
123. #488×C₆₇	C₂²	semidirect
124. #467×C₆₇	C₂²	semidirect
126. #465×C₆₇	C₂²	semidirect
127. C₄×Q₁₆×C₆₇	C₂²	semidirect
128. C₄×SD₁₆×C₆₇	C₂²	semidirect
129. C₄×D₈×C₆₇	C₂²	semidirect
130. C₂×C₄×C₈×C₆₇	C₂²	semidirect
339. D₅₃₆	#41	semidirect
571. #3168	D₆₇	semidirect
579. C₆₇	#61471	semidirect
600. #529	C₂×D₆₇	semidirect
608. #499	C₂×D₆₇	semidirect
610. #495	C₂×D₆₇	semidirect
614. #488	C₂×D₆₇	semidirect
630. #467	C₂×D₆₇	semidirect
635. #465	C₂×D₆₇	semidirect
657. C₄×Q₁₆	C₂×D₆₇	semidirect
658. C₄×SD₁₆	C₂×D₆₇	semidirect
668. C₄×D₈	C₂×D₆₇	semidirect
686. C₂×C₄×C₈	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574143	2
#22573218	2
#22573073	2
#22572968	2
#22572610	2
#22572580	2
#22572553	2
#22572409	2
#22572236	2
#22572176	2
#22571893	2
#22571891	2
#22571883	2
#22570855	2
#22570850	2
#22570414	2
#22570399	2
#22570343	2
#22569184	2
#22569084	2
#22569056	2
C₂×C₄×D₅₃₆	2
C₆₇×#3168	2
#61471	67