Subgroups — #31749083

Order 17152.

1868 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574172	C₂	1	1	yes	maximal, characteristic, complemented
2	#22573804	C₂	1	1	yes	maximal, characteristic, complemented
3	#22573219	C₂	1	1	yes	maximal, characteristic, complemented
4	#22573203	C₂	1	1	yes	maximal, characteristic, complemented
5	#22572903	C₂	1	1	yes	maximal, characteristic, complemented
6	#22572892	C₂	1	1	yes	maximal, characteristic, complemented
7	#22572494	C₂	1	1	yes	maximal, characteristic, complemented
8	#22572465	C₂	1	2	yes	maximal, complemented
9	#22572442	C₂	1	1	yes	maximal, characteristic, complemented
10	#22572413	C₂	1	2	yes	maximal, complemented
11	#22571876	C₂	1	1	yes	maximal, characteristic, complemented
12	#22571866	C₂	1	2	yes	maximal, complemented
13	#22571843	C₂	1	2	yes	maximal, complemented
14	#22571830	C₂	1	1	yes	maximal, characteristic, complemented
15	#22571612	C₂	1	2	yes	maximal, complemented
16	#22571571	C₂	1	1	yes	maximal, characteristic, complemented
17	#22571178	C₂	1	2	yes	maximal, complemented
18	#22571144	C₂	1	1	yes	maximal, characteristic, complemented
19	#22570234	C₂	1	2	yes	maximal, complemented
20	#22569700	C₂	1	2	yes	maximal, complemented
21	#22569681	C₂	1	1	yes	maximal, characteristic, complemented
22	#22569338	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14524075	C₂²	1	2	yes	complemented
25	C₂×#14524074	C₂²	1	2	yes	complemented
26	C₂×#14524070	C₂²	1	2	yes	—
27	#16864131	—	2	1	no	—
28	#16864131	C₂²	1	1	yes	characteristic
29	#16864131	C₂²	1	1	yes	characteristic, complemented
30	#16864125	C₂²	1	1	yes	characteristic, complemented
31	#16864119	—	2	1	no	—
32	#16864119	C₂²	1	1	yes	characteristic
33	#16864116	C₂²	1	1	yes	characteristic
34	#16864111	—	2	1	no	—
35	#16864094	—	2	2	no	—
36	#16864094	C₂²	1	2	yes	complemented
37	#16864071	—	2	2	no	—
38	#16864068	C₂²	1	1	yes	characteristic
39	Q₈×D₂₆₈	C₂²	1	1	yes	characteristic
40	#16864057	C₂²	1	2	yes	complemented
41	#16864056	C₂²	1	2	yes	—
42	#16864043	C₂²	1	2	yes	—
43	#16864042	—	2	1	no	—
44	D₄×D₂₆₈	C₂²	1	1	yes	characteristic
45	#16864017	—	2	1	no	—
46	#16863982	—	2	2	no	—
47	#16863946	—	2	1	no	—
48	#16863946	C₂²	1	1	yes	characteristic
49	#16863946	C₂²	1	1	yes	characteristic, complemented
50	#16863933	—	2	2	no	—
51	#16863933	C₂²	1	2	yes	complemented
52	#16863931	C₂²	1	2	yes	—
53	#124×D₆₇	C₂²	1	2	yes	—
54	#16863870	—	2	1	no	—
55	C₄×#11761629	C₂²	1	2	yes	complemented
56	C₄×#11761628	—	2	1	no	—
57	C₄×#11761628	C₂²	1	1	yes	characteristic
58	#16863781	C₂²	1	2	yes	complemented
59	#16863777	C₂²	1	2	yes	—
60	#16863773	C₂²	1	1	yes	characteristic
61	#16863769	C₂²	1	1	yes	characteristic, complemented
62	#16863752	C₂²	1	2	yes	complemented
63	#16863749	C₂²	1	2	yes	—
64	#16863747	C₂²	1	1	yes	characteristic, complemented
65	#16863743	C₂²	1	1	yes	characteristic
66	#16863739	C₂²	1	2	yes	complemented
67	#16863722	C₂²	1	2	yes	—
68	#16863706	C₂²	1	2	yes	complemented
69	#16863699	C₂²	1	2	yes	complemented
70	#16863693	C₂²	1	2	yes	complemented
71	#16863681	C₂²	1	1	yes	characteristic, complemented
72	#16863676	C₂²	1	1	yes	characteristic
73	#16863653	C₂²	1	2	yes	complemented
74	#16863650	C₂²	1	2	yes	—
75	#16863647	C₂²	1	2	yes	—
76	#16863645	C₂²	1	2	yes	—
77	#16863644	C₂²	1	2	yes	complemented
78	#16863643	C₂²	1	2	yes	complemented
79	#16863621	C₂²	1	2	yes	complemented
80	#16863620	C₂²	1	2	yes	complemented
81	#16863618	C₂²	1	2	yes	complemented
82	#16863618	C₂²	1	2	yes	complemented
83	#16863616	C₂²	1	2	yes	—
84	#16863614	C₂²	1	2	yes	complemented
85	#16863614	C₂²	1	2	yes	complemented
86	#16863612	C₂²	1	2	yes	complemented
87	#16863612	C₂²	1	2	yes	complemented
88	#16863610	C₂²	1	2	yes	—
89	#16863608	C₂²	1	2	yes	—
90	#16863606	C₂²	1	1	yes	characteristic, complemented
91	#16863606	C₂²	1	1	yes	characteristic, complemented
92	#16863596	C₂²	1	1	yes	characteristic
93	#16863596	C₂²	1	1	yes	characteristic
94	#16863596	C₂²	1	1	yes	characteristic, complemented
95	#16863591	C₂²	1	1	yes	characteristic
96	#16863561	C₂²	1	2	yes	complemented
97	#16863550	C₂²	1	2	yes	complemented
98	#16863545	C₂²	1	2	yes	—
99	#16863544	C₂²	1	2	yes	—
100	#16863543	C₂²	1	2	yes	complemented
101	#16863543	C₂²	1	2	yes	complemented
102	#16863536	C₂²	1	2	yes	complemented
103	#16863531	C₂²	1	2	yes	—
104	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
105	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
106	#16863488	C₂²	1	2	yes	complemented
107	#16863483	C₂²	1	2	yes	complemented
108	#16863481	C₂²	1	2	yes	complemented
109	#16863478	C₂²	1	2	yes	complemented
110	#16863475	C₂²	1	1	yes	characteristic
111	#16863475	C₂²	1	1	yes	characteristic
112	#16863471	C₂²	1	2	yes	complemented
113	#16863471	C₂²	1	2	yes	complemented
114	#16863448	C₂²	1	2	yes	complemented
115	#16863420	C₂²	1	1	yes	characteristic, complemented
116	#16863418	C₂²	1	2	yes	complemented
117	#16863403	C₂²	1	2	yes	complemented
118	#16863399	C₂²	1	2	yes	—
119	#16863395	C₂²	1	2	yes	complemented
120	#529×C₆₇	C₂²	1	1	yes	characteristic
121	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#480×C₆₇	C₂²	1	1	yes	characteristic
124	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
126	#464×C₆₇	C₂²	1	1	yes	characteristic
127	#464×C₆₇	C₂²	1	1	yes	characteristic
128	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#448×C₆₇	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
133	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
134	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#11761629	C₂³	1	2	yes	—
136	C₂×#11761628	—	2	1	no	—
137	C₂×#11761628	D₄	1	1	yes	characteristic
138	C₂×#11761628	C₂³	1	2	yes	—
139	C₂×Q₈×D₆₇	C₂³	1	2	yes	—
140	C₂²×D₂₆₈	—	2	1	no	—
141	C₂×D₄×D₆₇	C₂³	1	2	yes	—
142	#14524075	—	4	4	no	—
143	#14524074	—	4	4	no	—
144	#14524070	—	4	4	no	—
145	C₂×#11761618	C₂³	1	2	yes	—
146	C₂×#11761618	C₂³	1	2	yes	—
147	C₂×#11761617	C₂³	1	2	yes	—
148	C₂×#11761617	C₂³	1	2	yes	—
149	C₂×#11761615	C₂³	1	2	yes	—
150	C₂×#11761615	C₂³	1	2	yes	—
151	C₂×#11761615	C₂³	1	2	yes	—
152	C₂×D₅₃₆	C₂³	1	2	yes	—
153	C₂×D₅₃₆	C₂³	1	2	yes	—
154	C₂×#11761613	C₂³	1	2	yes	—
155	C₂×#11761612	C₂³	1	2	yes	—
156	C₂×#11761611	C₂³	1	2	yes	—
157	C₂×#11761611	C₂³	1	2	yes	—
158	#14524043	—	2	1	no	—
159	#14524043	—	2	1	no	—
160	#14524043	C₂³	1	1	yes	characteristic
161	#14524043	C₂³	1	1	yes	characteristic
162	#14524040	—	2	1	no	—
163	#14524040	C₂³	1	1	yes	characteristic
164	#14524040	C₂³	1	1	yes	characteristic
165	#14524038	—	2	2	no	—
166	#14524038	—	2	2	no	—
167	#14524038	—	2	2	no	—
168	#14524038	—	2	2	no	—
169	#14524036	—	2	2	no	—
170	#14524034	—	2	2	no	—
171	#14524034	C₂³	1	2	yes	—
172	#14524032	—	2	2	no	—
173	#14524032	C₂³	1	2	yes	—
174	#14524032	C₂³	1	2	yes	—
175	#14524031	—	2	1	no	—
176	#14524031	—	2	1	no	—
177	#14524031	—	2	1	no	—
178	#14524031	—	2	1	no	—
179	#14524031	C₂³	1	2	yes	—
180	#14524030	C₂³	1	2	yes	—
181	#14524029	—	2	2	no	—
182	#14524029	—	2	2	no	—
183	#14524029	—	2	2	no	—
184	#14524028	—	2	2	no	—
185	#14524028	—	2	2	no	—
186	#14524028	—	2	2	no	—
187	#14524028	—	2	2	no	—
188	#14524028	—	2	2	no	—
189	#14524025	—	2	2	no	—
190	#14524023	—	2	2	no	—
191	#14524023	C₂³	1	2	yes	—
192	#14524022	—	2	1	no	—
193	#14524021	—	2	2	no	—
194	#14524019	—	2	2	no	—
195	#14524019	C₂³	1	2	yes	—
196	#14524018	—	2	2	no	—
197	#14524018	C₂³	1	2	yes	—
198	#14524018	C₂³	1	2	yes	—
199	#14524017	—	2	2	no	—
200	#14524017	—	2	2	no	—
201	#14524017	—	2	1	no	—
202	#14524017	—	2	1	no	—
203	#14524017	—	2	1	no	—
204	#14524017	—	2	1	no	—
205	#14524017	C₂³	1	2	yes	—
206	#14524016	—	2	2	no	—
207	#14524014	—	2	2	no	—
208	#14524013	—	2	2	no	—
209	#14524011	—	2	2	no	—
210	Q₈×Dic₆₇	C₂³	1	2	yes	—
211	C₄×Dic₁₃₄	—	2	1	no	—
212	C₄×Dic₁₃₄	—	2	1	no	—
213	C₄×Dic₁₃₄	D₄	1	1	yes	characteristic
214	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
215	#14524008	C₂³	1	2	yes	—
216	C₄×D₂₆₈	—	2	1	no	—
217	C₄×D₂₆₈	—	2	2	no	—
218	C₄×D₂₆₈	—	2	2	no	—
219	C₄×D₂₆₈	—	2	1	no	—
220	C₄×D₂₆₈	—	2	1	no	—
221	C₄×D₂₆₈	—	2	1	no	—
222	C₄×D₂₆₈	—	2	1	no	—
223	C₄×D₂₆₈	—	2	1	no	—
224	C₄×D₂₆₈	—	2	1	no	—
225	C₄×D₂₆₈	D₄	1	1	yes	characteristic
226	C₄×D₂₆₈	C₂³	1	2	yes	—
227	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
228	#14524005	—	2	2	no	—
229	#14524005	—	2	2	no	—
230	#14524005	—	2	2	no	—
231	#14524005	C₂³	1	2	yes	—
232	#14524005	C₂³	1	2	yes	—
233	C₄×C₂²⋊D₆₇	—	2	2	no	—
234	C₄×C₂²⋊D₆₇	—	2	2	no	—
235	C₄×C₂²⋊D₆₇	D₄	1	2	yes	—
236	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
237	#14524002	—	2	1	no	—
238	#14524002	D₄	1	1	yes	characteristic
239	#14524001	—	2	2	no	—
240	#14524001	—	2	2	no	—
241	#14524001	C₂³	1	2	yes	—
242	#14524000	—	2	2	no	—
243	#14524000	D₄	1	2	yes	—
244	C₂²⋊C₄×D₆₇	—	2	2	no	—
245	C₂²⋊C₄×D₆₇	—	2	2	no	—
246	C₂²⋊C₄×D₆₇	—	2	2	no	—
247	C₄²×D₆₇	—	2	2	no	—
248	C₄²×D₆₇	C₂³	1	2	yes	—
249	#14523976	C₂³	1	2	yes	—
250	#14523974	C₂³	1	2	yes	—
251	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
252	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
253	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
254	Dic₆₇⋊C₈	C₂³	1	2	yes	—
255	Dic₆₇⋊C₈	C₂³	1	2	yes	—
256	#14523968	C₂³	1	2	yes	—
257	#14523968	C₂³	1	2	yes	—
258	#14523967	C₂³	1	2	yes	—
259	#14523966	C₂³	1	2	yes	—
260	#14523966	C₂³	1	2	yes	—
261	#14523965	C₂³	1	2	yes	—
262	#14523965	C₂³	1	2	yes	—
263	#14523964	C₂³	1	2	yes	—
264	#14523963	C₂³	1	2	yes	—
265	#14523963	C₂³	1	2	yes	—
266	#14523963	C₂³	1	2	yes	—
267	#14523963	C₂³	1	2	yes	—
268	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
269	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
270	C₈×Dic₆₇	C₂³	1	2	yes	—
271	C₈×Dic₆₇	C₂³	1	2	yes	—
272	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
273	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
274	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
277	#126×C₆₇	—	2	1	no	—
278	#125×C₆₇	C₂³	1	1	yes	characteristic
279	#124×C₆₇	C₂³	1	1	yes	characteristic
280	#123×C₆₇	—	2	1	no	—
281	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
282	#121×C₆₇	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₆₇	—	2	1	no	—
284	C₄×Q₈×C₆₇	—	2	1	no	—
285	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
288	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₆₇	—	2	1	no	—
291	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
292	#117×C₆₇	—	2	1	no	—
293	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
294	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₆₇	—	2	1	no	—
296	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
297	#107×C₆₇	C₂³	1	1	yes	characteristic
298	#107×C₆₇	C₂³	1	1	yes	characteristic
299	#106×C₆₇	C₂³	1	1	yes	characteristic
300	#106×C₆₇	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
303	#103×C₆₇	C₂³	1	1	yes	characteristic
304	#103×C₆₇	C₂³	1	1	yes	characteristic
305	#103×C₆₇	C₂³	1	1	yes	characteristic
306	#103×C₆₇	C₂³	1	1	yes	characteristic
307	#103×C₆₇	C₂³	1	1	yes	characteristic
308	#103×C₆₇	C₂³	1	1	yes	characteristic
309	#102×C₆₇	C₂³	1	1	yes	characteristic
310	#102×C₆₇	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₂³×D₆₇	—	2	2	no	—
316	#11761629	—	2	4	no	—
317	#11761629	—	4	2	no	—
318	#11761628	—	4	2	no	—
319	#11761628	—	4	2	no	—
320	#11761628	—	4	2	no	—
321	#11761628	—	4	4	no	—
322	C₂×Dic₁₃₄	—	2	1	no	—
323	C₂×Dic₁₃₄	—	2	2	no	—
324	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
325	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
326	Q₈×D₆₇	—	4	2	no	—
327	Q₈×D₆₇	—	4	2	no	—
328	C₂×D₂₆₈	—	2	2	no	—
329	C₂×D₂₆₈	—	2	2	no	—
330	C₂×D₂₆₈	—	2	1	no	—
331	C₂×D₂₆₈	—	2	1	no	—
332	C₂×D₂₆₈	—	2	2	no	—
333	C₂×D₂₆₈	—	2	1	no	—
334	C₂×D₂₆₈	—	2	1	no	—
335	C₂×D₂₆₈	—	4	4	no	—
336	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
337	C₂×D₂₆₈	C₂⁴	1	2	yes	—
338	C₂×D₂₆₈	C₂⁴	1	2	yes	—
339	C₂×C₂²⋊D₆₇	—	2	2	no	—
340	C₂×C₂²⋊D₆₇	—	2	2	no	—
341	C₂×C₂²⋊D₆₇	—	2	2	no	—
342	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
343	D₄×D₆₇	—	4	2	no	—
344	D₄×D₆₇	—	4	2	no	—
345	C₂×C₄×D₆₇	—	2	2	no	—
346	C₂×C₄×D₆₇	—	2	2	no	—
347	C₂×C₄×D₆₇	—	2	2	no	—
348	C₂×C₄×D₆₇	—	2	2	no	—
349	C₂×C₄×D₆₇	—	2	2	no	—
350	C₂×C₄×D₆₇	—	2	2	no	—
351	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
352	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
353	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
354	#11761618	—	2	4	no	—
355	#11761618	—	4	2	no	—
356	#11761617	—	4	2	no	—
357	#11761617	—	4	2	no	—
358	#11761615	—	2	4	no	—
359	#11761615	—	4	2	no	—
360	#11761615	—	4	2	no	—
361	D₅₃₆	—	4	2	no	—
362	D₅₃₆	—	4	2	no	—
363	#11761613	—	4	2	no	—
364	#11761612	—	4	2	no	—
365	#11761611	—	4	2	no	—
366	#11761611	—	4	2	no	—
367	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
368	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
369	C₄⋊Dic₆₇	—	2	1	no	—
370	C₄⋊Dic₆₇	—	2	1	no	—
371	C₄⋊Dic₆₇	—	2	1	no	—
372	C₄⋊Dic₆₇	—	2	2	no	—
373	C₄⋊Dic₆₇	—	2	2	no	—
374	C₄⋊Dic₆₇	—	2	2	no	—
375	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
376	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
377	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
378	Dic₆₇⋊C₄	—	2	2	no	—
379	Dic₆₇⋊C₄	—	2	2	no	—
380	Dic₆₇⋊C₄	—	2	2	no	—
381	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
382	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
383	C₂²⋊Dic₆₇	—	2	2	no	—
384	C₂²⋊Dic₆₇	—	2	2	no	—
385	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
386	(C₂×D₆₇)⋊C₄	—	2	2	no	—
387	(C₂×D₆₇)⋊C₄	—	2	2	no	—
388	(C₂×D₆₇)⋊C₄	—	2	2	no	—
389	(C₂×D₆₇)⋊C₄	—	2	2	no	—
390	(C₂×D₆₇)⋊C₄	—	2	2	no	—
391	(C₂×D₆₇)⋊C₄	—	2	2	no	—
392	(C₂×D₆₇)⋊C₄	—	2	2	no	—
393	(C₂×D₆₇)⋊C₄	—	2	2	no	—
394	(C₂×D₆₇)⋊C₄	—	2	2	no	—
395	(C₂×D₆₇)⋊C₄	—	2	2	no	—
396	(C₂×D₆₇)⋊C₄	—	2	2	no	—
397	(C₂×D₆₇)⋊C₄	—	2	2	no	—
398	(C₂×D₆₇)⋊C₄	—	2	2	no	—
399	(C₂×D₆₇)⋊C₄	—	2	2	no	—
400	(C₂×D₆₇)⋊C₄	—	2	2	no	—
401	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
402	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
403	C₄×Dic₆₇	—	2	2	no	—
404	C₄×Dic₆₇	—	2	2	no	—
405	C₄×Dic₆₇	—	2	2	no	—
406	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
407	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
408	C₄×Dic₆₇	C₂⁴	1	2	yes	—
409	C₂×Q₈×C₆₇	—	2	1	no	—
410	C₂×Q₈×C₆₇	—	2	2	no	—
411	C₂×Q₈×C₆₇	—	4	1	no	—
412	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
414	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
415	C₂×D₄×C₆₇	—	2	1	no	—
416	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₆₇	—	2	1	no	—
418	C₂²×C₄×C₆₇	—	2	1	no	—
419	C₂²×C₄×C₆₇	—	2	1	no	—
420	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
421	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
422	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
423	Q₁₆×C₆₇	—	2	2	no	—
424	Q₁₆×C₆₇	—	4	1	no	—
425	SD₁₆×C₆₇	—	2	2	no	—
426	SD₁₆×C₆₇	—	4	1	no	—
427	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
428	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
429	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
430	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	—	2	1	no	—
433	C₄⋊C₄×C₆₇	—	2	1	no	—
434	C₄⋊C₄×C₆₇	—	2	1	no	—
435	C₄⋊C₄×C₆₇	—	2	1	no	—
436	C₄⋊C₄×C₆₇	—	2	1	no	—
437	C₄⋊C₄×C₆₇	—	2	1	no	—
438	C₄⋊C₄×C₆₇	—	2	1	no	—
439	C₄⋊C₄×C₆₇	—	2	1	no	—
440	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
442	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
443	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
444	C₂²⋊C₄×C₆₇	—	2	1	no	—
445	C₂²⋊C₄×C₆₇	—	2	1	no	—
446	C₂²⋊C₄×C₆₇	—	2	1	no	—
447	C₂²⋊C₄×C₆₇	—	2	1	no	—
448	C₂²⋊C₄×C₆₇	—	2	1	no	—
449	C₄²×C₆₇	—	2	1	no	—
450	C₄²×C₆₇	—	2	1	no	—
451	C₄²×C₆₇	—	2	1	no	—
452	C₄²×C₆₇	—	2	1	no	—
453	C₄²×C₆₇	—	2	1	no	—
454	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
457	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
458	C₂³×C₆₇	—	2	1	no	—
459	C₂³×C₆₇	C₂²×D₄	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	C₂²×D₄	1	2	yes	—
466	Q₈×C₆₇	—	2	1	no	—
467	Q₈×C₆₇	—	2	1	no	—
468	Q₈×C₆₇	—	2	1	no	—
469	Q₈×C₆₇	—	2	1	no	—
470	Q₈×C₆₇	—	2	1	no	—
471	Q₈×C₆₇	—	4	2	no	—
472	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
473	D₄×C₆₇	—	2	1	no	—
474	D₄×C₆₇	—	2	1	no	—
475	D₄×C₆₇	—	8	1	no	—
476	C₂×C₄×C₆₇	—	2	1	no	—
477	C₂×C₄×C₆₇	—	2	2	no	—
478	C₂×C₄×C₆₇	—	2	1	no	—
479	C₂×C₄×C₆₇	—	2	1	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	1	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	2	1	no	—
484	C₂×C₄×C₆₇	—	2	1	no	—
485	C₂×C₄×C₆₇	—	2	1	no	—
486	C₂×C₄×C₆₇	—	4	1	no	—
487	C₂×C₄×C₆₇	—	4	2	no	—
488	C₂×C₄×C₆₇	—	4	2	no	—
489	C₂×C₄×C₆₇	—	8	1	no	—
490	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
496	C₂²⋊D₆₇	—	4	2	no	—
497	C₂²⋊D₆₇	—	4	4	no	—
498	C₂²⋊D₆₇	—	8	2	no	—
499	C₂²⋊D₆₇	—	8	2	no	—
500	C₂×Dic₆₇	—	2	2	no	—
501	C₂×Dic₆₇	—	2	2	no	—
502	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
503	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
504	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
505	D₂₆₈	—	2	2	no	—
506	D₂₆₈	—	2	2	no	—
507	D₂₆₈	—	2	2	no	—
508	D₂₆₈	—	2	2	no	—
509	D₂₆₈	—	2	2	no	—
510	D₂₆₈	—	4	4	no	—
511	D₂₆₈	—	4	4	no	—
512	D₂₆₈	—	4	2	no	—
513	D₂₆₈	—	4	2	no	—
514	D₂₆₈	—	8	1	no	—
515	D₂₆₈	—	8	1	no	—
516	D₂₆₈	—	8	2	no	—
517	C₄×D₆₇	—	2	2	no	—
518	C₄×D₆₇	—	2	2	no	—
519	C₄×D₆₇	—	4	2	no	—
520	C₄×D₆₇	—	4	2	no	—
521	C₄×D₆₇	—	4	4	no	—
522	C₄×D₆₇	—	4	4	no	—
523	C₄×D₆₇	—	8	2	no	—
524	C₄×D₆₇	—	8	2	no	—
525	C₄×D₆₇	—	8	2	no	—
526	C₄×D₆₇	—	8	2	no	—
527	Dic₁₃₄	—	2	2	no	—
528	Dic₁₃₄	—	2	2	no	—
529	Dic₁₃₄	—	2	2	no	—
530	Dic₁₃₄	—	4	2	no	—
531	Dic₁₃₄	—	8	2	no	—
532	C₈×C₆₇	—	2	1	no	—
533	C₈×C₆₇	—	2	1	no	—
534	C₈×C₆₇	—	2	1	no	—
535	C₈×C₆₇	—	2	1	no	—
536	C₆₇⋊C₈	—	2	2	no	—
537	C₆₇⋊C₈	—	2	2	no	—
538	C₂²×C₆₇	—	2	1	no	—
539	C₂²×C₆₇	—	2	1	no	—
540	C₂²×C₆₇	—	2	1	no	—
541	C₂²×C₆₇	—	4	1	no	—
542	C₂²×C₆₇	—	4	1	no	—
543	C₂²×C₆₇	—	4	1	no	—
544	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
545	C₂×D₆₇	—	2	2	no	—
546	C₂×D₆₇	—	2	2	no	—
547	C₂×D₆₇	—	2	2	no	—
548	C₂×D₆₇	—	4	2	no	—
549	C₂×D₆₇	—	4	2	no	—
550	C₂×D₆₇	—	4	2	no	—
551	C₂×D₆₇	—	4	2	no	—
552	C₂×D₆₇	—	4	2	no	—
553	C₂×D₆₇	—	4	2	no	—
554	C₂×D₆₇	—	16	4	no	—
555	C₄×C₆₇	—	2	1	no	—
556	C₄×C₆₇	—	2	1	no	—
557	C₄×C₆₇	—	2	2	no	—
558	C₄×C₆₇	—	2	1	no	—
559	C₄×C₆₇	—	2	1	no	—
560	C₄×C₆₇	—	4	1	no	—
561	C₄×C₆₇	—	4	1	no	—
562	C₄×C₆₇	—	4	1	no	—
563	C₄×C₆₇	—	4	1	no	—
564	C₄×C₆₇	—	4	1	no	—
565	C₄×C₆₇	—	4	1	no	—
566	C₄×C₆₇	#575	1	2	yes	—
567	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
568	C₄×C₆₇	#585	1	1	yes	characteristic
569	Dic₆₇	—	2	2	no	—
570	Dic₆₇	—	2	2	no	—
571	Dic₆₇	—	2	2	no	—
572	Dic₆₇	—	4	2	no	—
573	Dic₆₇	—	4	2	no	—
574	#62006	—	67	1	no	maximal, Sylow
575	C₂×C₆₇	—	4	1	no	—
576	C₂×C₆₇	—	8	1	no	—
577	C₂×C₆₇	#3488	1	1	yes	characteristic
578	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
579	C₂×C₆₇	#3584	1	1	yes	characteristic
580	D₆₇	—	4	2	no	—
581	D₆₇	—	8	2	no	—
582	D₆₇	—	8	2	no	—
583	#3514	—	67	1	no	—
584	#3480	—	67	1	no	—
585	#3396	—	67	1	no	—
586	#3394	—	67	1	no	—
587	#3365	—	67	1	no	—
588	#3364	—	67	1	no	—
589	#3328	—	67	1	no	—
590	#3326	—	67	2	no	—
591	#3324	—	67	1	no	—
592	#3322	—	67	2	no	—
593	#3278	—	67	1	no	—
594	#3277	—	67	2	no	—
595	#3275	—	67	2	no	—
596	#3274	—	67	1	no	—
597	#3256	—	67	2	no	—
598	#3251	—	67	1	no	—
599	#3211	—	67	2	no	—
600	#3207	—	67	1	no	—
601	#3108	D₆₇	1	1	yes	characteristic, complemented
602	#3102	—	67	2	no	—
603	#3040	—	67	2	no	—
604	#3037	—	67	1	no	—
605	#2991	—	67	1	no	—
606	C₆₇	#62006	1	1	yes	characteristic, complemented, Sylow
607	C₂×#137	—	67	2	no	—
608	C₂×#137	—	67	2	no	—
609	C₂×AGL(1,ℤ/8)	—	67	2	no	—
610	#559	—	67	1	no	—
611	#559	—	67	1	no	—
612	#559	—	134	1	no	—
613	#557	—	67	1	no	—
614	#556	—	67	1	no	—
615	#556	—	67	1	no	—
616	#556	—	134	1	no	—
617	#555	—	134	1	no	—
618	#553	—	67	2	no	—
619	#553	—	134	2	no	—
620	#551	—	134	2	no	—
621	#550	—	67	1	no	—
622	D₄×Q₈	—	67	1	no	—
623	#548	—	67	2	no	—
624	#548	—	67	2	no	—
625	#546	—	67	2	no	—
626	#546	—	134	1	no	—
627	D₄²	—	67	1	no	—
628	#542	—	134	1	no	—
629	#538	—	134	2	no	—
630	#532	—	67	1	no	—
631	#532	—	67	1	no	—
632	#532	—	134	1	no	—
633	#529	—	67	2	no	—
634	#529	—	67	2	no	—
635	#529	—	134	2	no	—
636	#529	C₂×D₆₇	1	1	yes	characteristic
637	C₂×#124	—	67	2	no	—
638	#518	—	134	1	no	—
639	C₄×#41	—	67	1	no	—
640	C₄×#41	—	67	2	no	—
641	C₄×#41	—	134	1	no	—
642	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
643	#495	—	67	2	no	—
644	#495	—	67	2	no	—
645	#493	—	67	1	no	—
646	#492	—	67	1	no	—
647	#488	—	67	2	no	—
648	#488	—	67	2	no	—
649	#487	—	67	1	no	—
650	#486	—	67	1	no	—
651	#485	—	67	2	no	—
652	#483	C₂×D₆₇	1	1	yes	characteristic, complemented
653	#482	—	67	2	no	—
654	#480	C₂×D₆₇	1	1	yes	characteristic
655	#479	—	67	2	no	—
656	#479	C₂×D₆₇	1	1	yes	characteristic, complemented
657	#479	C₂×D₆₇	1	1	yes	characteristic, complemented
658	#478	—	67	2	no	—
659	#478	—	67	2	no	—
660	#475	—	67	1	no	—
661	#474	—	67	1	no	—
662	#470	—	67	2	no	—
663	#469	—	67	2	no	—
664	#469	—	67	2	no	—
665	#468	—	67	2	no	—
666	#468	—	67	2	no	—
667	#468	—	67	2	no	—
668	#464	—	67	2	no	—
669	#464	—	67	2	no	—
670	#464	—	67	2	no	—
671	#464	—	67	2	no	—
672	#464	—	67	2	no	—
673	#464	C₂×D₆₇	1	1	yes	characteristic
674	#464	C₂×D₆₇	1	1	yes	characteristic
675	#463	—	67	2	no	—
676	#463	—	67	2	no	—
677	#463	—	67	2	no	—
678	#463	—	67	2	no	—
679	#463	—	67	2	no	—
680	#463	—	67	2	no	—
681	#462	—	67	1	no	—
682	#462	—	67	1	no	—
683	#460	—	67	1	no	—
684	#460	—	67	1	no	—
685	#460	—	67	1	no	—
686	#459	—	67	1	no	—
687	#452	—	67	2	no	—
688	#451	—	67	2	no	—
689	#451	C₂×D₆₇	1	1	yes	characteristic, complemented
690	#450	—	67	2	no	—
691	#449	—	67	2	no	—
692	#449	—	67	2	no	—
693	#449	—	67	2	no	—
694	#448	—	67	2	no	—
695	#448	C₂×D₆₇	1	1	yes	characteristic
696	#447	—	67	2	no	—
697	C₈×Q₈	—	67	1	no	—
698	C₈×Q₈	—	67	1	no	—
699	C₄×Q₁₆	—	67	2	no	—
700	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
701	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
702	C₄×SD₁₆	—	67	2	no	—
703	C₄×SD₁₆	—	67	2	no	—
704	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic
705	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic
706	C₄×D₈	—	67	2	no	—
707	#436	—	67	2	no	—
708	#436	—	67	2	no	—
709	#436	—	67	1	no	—
710	#436	—	67	1	no	—
711	#431	—	67	2	no	—
712	#431	C₂×D₆₇	1	1	yes	characteristic, complemented
713	#423	—	67	1	no	—
714	#423	—	67	2	no	—
715	#419	—	67	2	no	—
716	#418	—	67	2	no	—
717	#417	—	67	2	no	—
718	C₂×#41	—	67	1	no	—
719	C₂×#41	—	67	2	no	—
720	C₂×#41	—	67	2	no	—
721	C₂×#41	—	134	1	no	—
722	C₂²×Q₈	—	67	2	no	—
723	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
724	C₂²×D₄	—	67	2	no	—
725	C₂²×D₄	—	134	1	no	—
726	#137	—	268	4	no	—
727	#137	—	268	4	no	—
728	AGL(1,ℤ/8)	—	268	4	no	—
729	C₂×Q₁₆	—	67	2	no	—
730	C₂×Q₁₆	—	67	2	no	—
731	C₂×Q₁₆	C₂²×D₆₇	1	1	yes	characteristic
732	C₂×Q₁₆	C₂²×D₆₇	1	1	yes	characteristic
733	C₂×SD₁₆	—	67	2	no	—
734	C₂×SD₁₆	—	67	2	no	—
735	C₂×SD₁₆	—	67	2	no	—
736	C₂×SD₁₆	—	67	2	no	—
737	C₂×SD₁₆	—	67	2	no	—
738	C₂×SD₁₆	C₂²×D₆₇	1	1	yes	characteristic
739	C₂×SD₁₆	C₂²×D₆₇	1	1	yes	characteristic
740	C₂×D₈	—	67	2	no	—
741	C₂×D₈	—	67	2	no	—
742	C₂×D₈	—	67	2	no	—
743	C₂×M₁₆	—	67	2	no	—
744	C₂×M₁₆	—	67	2	no	—
745	C₂×M₁₆	—	67	2	no	—
746	C₄⋊Q₈	—	67	1	no	—
747	C₄⋊Q₈	—	67	1	no	—
748	C₄⋊Q₈	—	134	1	no	—
749	C₄⋊Q₈	—	134	1	no	—
750	#127	—	67	1	no	—
751	#127	—	67	1	no	—
752	#127	—	134	1	no	—
753	#126	—	2	1	no	—
754	#126	—	134	2	no	—
755	#126	—	134	2	no	—
756	#126	—	134	2	no	—
757	#126	—	134	2	no	—
758	#126	—	134	2	no	—
759	#125	—	67	2	no	—
760	#125	—	134	2	no	—
761	#125	C₂²×D₆₇	1	1	yes	characteristic
762	#124	—	67	2	no	—
763	#124	—	67	2	no	—
764	#124	—	67	2	no	—
765	#124	—	67	2	no	—
766	#124	—	134	1	no	—
767	#124	—	134	1	no	—
768	#124	—	134	1	no	—
769	#124	—	134	2	no	—
770	#124	—	134	2	no	—
771	#124	—	134	2	no	—
772	#124	—	134	2	no	—
773	#124	—	134	1	no	—
774	#124	C₂²×D₆₇	1	1	yes	characteristic
775	#123	—	2	1	no	—
776	#123	—	134	2	no	—
777	#123	—	134	2	no	—
778	#123	—	134	2	no	—
779	#123	—	134	2	no	—
780	#123	—	134	2	no	—
781	#123	—	134	2	no	—
782	C₂²⋊Q₈	—	67	2	no	—
783	C₂²⋊Q₈	—	67	2	no	—
784	C₂²⋊Q₈	—	134	2	no	—
785	C₂²⋊Q₈	—	134	2	no	—
786	C₂²⋊Q₈	—	134	2	no	—
787	C₂²⋊Q₈	—	134	1	no	—
788	C₂²⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
789	#121	—	67	2	no	—
790	#121	—	67	2	no	—
791	#121	—	67	2	no	—
792	#121	—	134	2	no	—
793	#121	—	134	2	no	—
794	#121	—	134	2	no	—
795	#121	—	134	1	no	—
796	#121	—	134	2	no	—
797	#121	—	134	2	no	—
798	#121	—	134	1	no	—
799	#121	—	134	1	no	—
800	#121	—	134	1	no	—
801	#121	C₂²×D₆₇	1	1	yes	characteristic
802	#120	—	134	2	no	—
803	#120	—	134	2	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	67	1	no	—
807	C₄×Q₈	—	67	1	no	—
808	C₄×Q₈	—	67	2	no	—
809	C₄×Q₈	—	67	2	no	—
810	C₄×Q₈	—	134	1	no	—
811	C₄×Q₈	—	134	1	no	—
812	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
813	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
814	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
815	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
816	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	67	2	no	—
819	C₄×D₄	—	67	2	no	—
820	C₄×D₄	—	67	2	no	—
821	C₄×D₄	—	67	2	no	—
822	C₄×D₄	—	67	1	no	—
823	C₄×D₄	—	67	1	no	—
824	C₄×D₄	—	67	2	no	—
825	C₄×D₄	—	134	1	no	—
826	C₄×D₄	—	134	1	no	—
827	C₄×D₄	—	134	1	no	—
828	C₄×D₄	—	134	2	no	—
829	C₄×D₄	—	134	2	no	—
830	C₄×D₄	—	134	1	no	—
831	C₄×D₄	—	134	2	no	—
832	C₄×D₄	—	134	2	no	—
833	C₄×D₄	—	134	2	no	—
834	C₄×D₄	—	134	2	no	—
835	C₄×D₄	—	134	2	no	—
836	C₄×D₄	—	134	1	no	—
837	C₄×D₄	—	134	1	no	—
838	C₄×D₄	—	134	1	no	—
839	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
840	#117	—	2	1	no	—
841	#117	—	67	1	no	—
842	#117	—	67	2	no	—
843	#117	—	67	2	no	—
844	#117	—	134	2	no	—
845	#117	—	134	2	no	—
846	#117	—	134	2	no	—
847	#117	—	134	1	no	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
850	C₂×C₂²⋊C₄	—	134	2	no	—
851	C₂×C₂²⋊C₄	—	134	2	no	—
852	C₂×C₂²⋊C₄	—	134	2	no	—
853	C₂×C₄²	—	2	1	no	—
854	C₂×C₄²	—	67	2	no	—
855	C₂×C₄²	—	134	2	no	—
856	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
857	#107	—	67	2	no	—
858	#107	C₂²×D₆₇	1	1	yes	characteristic
859	#107	C₂²×D₆₇	1	1	yes	characteristic
860	#106	—	67	2	no	—
861	#106	C₂²×D₆₇	1	1	yes	characteristic
862	#106	C₂²×D₆₇	1	1	yes	characteristic
863	C₄⋊C₈	—	67	2	no	—
864	C₄⋊C₈	—	67	2	no	—
865	C₄⋊C₈	—	67	2	no	—
866	C₄⋊C₈	—	67	1	no	—
867	C₄⋊C₈	—	67	1	no	—
868	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
869	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
870	#103	—	67	2	no	—
871	#103	—	67	2	no	—
872	#103	—	67	2	no	—
873	#103	—	67	2	no	—
874	#103	—	67	2	no	—
875	#103	C₂²×D₆₇	1	1	yes	characteristic
876	#103	C₂²×D₆₇	1	1	yes	characteristic
877	#103	C₂²×D₆₇	1	1	yes	characteristic
878	#103	C₂²×D₆₇	1	1	yes	characteristic
879	#103	C₂²×D₆₇	1	1	yes	characteristic
880	#103	C₂²×D₆₇	1	1	yes	characteristic
881	#102	—	67	2	no	—
882	#102	—	67	2	no	—
883	#102	—	67	2	no	—
884	#102	—	67	2	no	—
885	#102	—	67	2	no	—
886	#102	—	67	2	no	—
887	#102	—	67	2	no	—
888	#102	C₂²×D₆₇	1	1	yes	characteristic
889	#102	C₂²×D₆₇	1	1	yes	characteristic
890	C₂²⋊C₈	—	67	2	no	—
891	C₂²⋊C₈	—	67	2	no	—
892	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
893	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
894	C₄×C₈	—	67	2	no	—
895	C₄×C₈	—	67	2	no	—
896	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
897	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
898	C₂⁴	—	134	2	no	—
899	#41	—	268	4	no	—
900	#41	—	268	2	no	—
901	#41	—	268	2	no	—
902	#41	—	268	2	no	—
903	#41	—	268	2	no	—
904	#41	—	134	4	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	4	1	no	—
908	C₂×Q₈	—	268	2	no	—
909	C₂×Q₈	—	268	2	no	—
910	C₂×Q₈	—	67	1	no	—
911	C₂×Q₈	—	67	2	no	—
912	C₂×Q₈	—	134	2	no	—
913	C₂×Q₈	—	134	1	no	—
914	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
915	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
916	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	268	4	no	—
919	C₂×D₄	—	268	2	no	—
920	C₂×D₄	—	268	2	no	—
921	C₂×D₄	—	67	2	no	—
922	C₂×D₄	—	67	1	no	—
923	C₂×D₄	—	67	2	no	—
924	C₂×D₄	—	67	2	no	—
925	C₂×D₄	—	134	2	no	—
926	C₂×D₄	—	134	2	no	—
927	C₂×D₄	—	134	2	no	—
928	C₂×D₄	—	134	2	no	—
929	C₂×D₄	—	134	2	no	—
930	C₂×D₄	—	134	2	no	—
931	C₂×D₄	—	134	1	no	—
932	C₂×D₄	—	134	1	no	—
933	C₂×D₄	—	134	1	no	—
934	C₂×D₄	—	134	1	no	—
935	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	67	2	no	—
940	C₂²×C₄	—	67	2	no	—
941	C₂²×C₄	—	67	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	D₄×D₆₇	1	1	yes	characteristic
949	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
950	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
951	Q₁₆	—	2	2	no	—
952	Q₁₆	—	4	1	no	—
953	Q₁₆	—	268	2	no	—
954	Q₁₆	—	134	4	no	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	4	1	no	—
957	SD₁₆	—	268	2	no	—
958	SD₁₆	—	268	2	no	—
959	SD₁₆	—	268	2	no	—
960	SD₁₆	—	268	2	no	—
961	SD₁₆	—	134	4	no	—
962	D₈	—	268	2	no	—
963	D₈	—	268	2	no	—
964	D₈	—	268	2	no	—
965	M₁₆	—	268	2	no	—
966	M₁₆	—	268	2	no	—
967	M₁₆	—	268	2	no	—
968	C₂×C₈	—	67	2	no	—
969	C₂×C₈	—	67	2	no	—
970	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
971	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
972	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
973	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	67	1	no	—
984	C₄⋊C₄	—	67	1	no	—
985	C₄⋊C₄	—	67	2	no	—
986	C₄⋊C₄	—	67	2	no	—
987	C₄⋊C₄	—	67	2	no	—
988	C₄⋊C₄	—	134	2	no	—
989	C₄⋊C₄	—	134	2	no	—
990	C₄⋊C₄	—	134	2	no	—
991	C₄⋊C₄	—	134	2	no	—
992	C₄⋊C₄	—	134	2	no	—
993	C₄⋊C₄	—	134	2	no	—
994	C₄⋊C₄	—	134	1	no	—
995	C₄⋊C₄	—	134	1	no	—
996	C₄⋊C₄	—	134	1	no	—
997	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
998	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
999	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1000	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	67	2	no	—
1007	C₂²⋊C₄	—	67	2	no	—
1008	C₂²⋊C₄	—	67	2	no	—
1009	C₂²⋊C₄	—	134	2	no	—
1010	C₂²⋊C₄	—	134	2	no	—
1011	C₂²⋊C₄	—	134	2	no	—
1012	C₂²⋊C₄	—	134	2	no	—
1013	C₂²⋊C₄	—	134	2	no	—
1014	C₂²⋊C₄	—	134	2	no	—
1015	C₂²⋊C₄	—	134	2	no	—
1016	C₂²⋊C₄	—	134	2	no	—
1017	C₂²⋊C₄	—	134	2	no	—
1018	C₂²⋊C₄	—	134	2	no	—
1019	C₂²⋊C₄	—	134	2	no	—
1020	C₂²⋊C₄	—	134	2	no	—
1021	C₂²⋊C₄	—	134	2	no	—
1022	C₂²⋊C₄	—	134	2	no	—
1023	C₂²⋊C₄	—	134	2	no	—
1024	C₂²⋊C₄	—	134	2	no	—
1025	C₂²⋊C₄	—	134	2	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	67	2	no	—
1032	C₄²	—	67	2	no	—
1033	C₄²	—	67	2	no	—
1034	C₄²	—	134	2	no	—
1035	C₄²	—	134	2	no	—
1036	C₄²	—	134	2	no	—
1037	C₄²	D₄×D₆₇	1	1	yes	characteristic
1038	C₄²	D₄×D₆₇	1	1	yes	characteristic
1039	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1040	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1041	C₂³	—	2	1	no	—
1042	C₂³	—	268	4	no	—
1043	C₂³	—	536	2	no	—
1044	C₂³	—	536	2	no	—
1045	C₂³	—	67	2	no	—
1046	C₂³	—	134	2	no	—
1047	C₂³	—	134	2	no	—
1048	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	4	2	no	—
1055	Q₈	—	268	2	no	—
1056	Q₈	—	536	2	no	—
1057	Q₈	—	134	2	no	—
1058	Q₈	—	134	2	no	—
1059	Q₈	—	134	2	no	—
1060	Q₈	#14524089	1	2	yes	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	8	1	no	—
1064	D₄	—	268	4	no	—
1065	D₄	—	268	4	no	—
1066	D₄	—	268	4	no	—
1067	D₄	—	268	2	no	—
1068	D₄	—	268	2	no	—
1069	D₄	—	268	2	no	—
1070	D₄	—	536	1	no	—
1071	D₄	—	536	1	no	—
1072	D₄	—	536	2	no	—
1073	D₄	—	536	2	no	—
1074	D₄	—	536	2	no	—
1075	D₄	—	134	2	no	—
1076	D₄	—	134	2	no	—
1077	D₄	—	134	2	no	—
1078	D₄	—	134	2	no	—
1079	D₄	—	134	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	—	268	4	no	—
1095	C₂×C₄	—	268	4	no	—
1096	C₂×C₄	—	268	2	no	—
1097	C₂×C₄	—	268	2	no	—
1098	C₂×C₄	—	536	2	no	—
1099	C₂×C₄	—	536	2	no	—
1100	C₂×C₄	—	536	2	no	—
1101	C₂×C₄	—	536	2	no	—
1102	C₂×C₄	—	67	2	no	—
1103	C₂×C₄	—	67	2	no	—
1104	C₂×C₄	—	67	2	no	—
1105	C₂×C₄	—	134	2	no	—
1106	C₂×C₄	—	134	2	no	—
1107	C₂×C₄	—	134	2	no	—
1108	C₂×C₄	—	134	2	no	—
1109	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1110	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1111	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1112	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1113	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1114	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	134	2	no	—
1120	C₈	—	134	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	268	2	no	—
1128	C₂²	—	268	2	no	—
1129	C₂²	—	268	2	no	—
1130	C₂²	—	268	2	no	—
1131	C₂²	—	268	2	no	—
1132	C₂²	—	268	2	no	—
1133	C₂²	—	1072	4	no	—
1134	C₂²	—	134	2	no	—
1135	C₂²	—	134	2	no	—
1136	C₂²	—	134	2	no	—
1137	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1138	C₄	—	2	1	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	2	1	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	268	2	no	—
1150	C₄	—	268	2	no	—
1151	C₄	—	134	2	no	—
1152	C₄	—	134	2	no	—
1153	C₄	—	134	2	no	—
1154	C₄	#16864195	1	2	yes	—
1155	C₄	C₂×#14524089	1	1	yes	characteristic
1156	C₄	#16864232	1	1	yes	characteristic
1157	C₂	—	4	1	no	—
1158	C₂	—	8	1	no	—
1159	C₂	—	268	2	no	—
1160	C₂	—	536	2	no	—
1161	C₂	—	536	2	no	—
1162	C₂	#22573870	1	1	yes	characteristic
1163	C₂	C₂×#16864195	1	1	yes	characteristic
1164	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×#3108	C₂
socle	C₂²×C₆₇	C₂³×D₄
hypercenter	#3108	D₆₇
hypocenter	C₆₇	#62006
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3108

Complements

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

N	H ≅ G/N	type
1. #22574172	C₂	semidirect
2. #22573804	C₂	semidirect
3. #22573219	C₂	semidirect
4. #22573203	C₂	semidirect
5. #22572903	C₂	semidirect
6. #22572892	C₂	semidirect
7. #22572494	C₂	semidirect
8. #22572465	C₂	semidirect
9. #22572442	C₂	semidirect
10. #22572413	C₂	semidirect
11. #22571876	C₂	semidirect
12. #22571866	C₂	semidirect
13. #22571843	C₂	semidirect
14. #22571830	C₂	semidirect
15. #22571612	C₂	semidirect
16. #22571571	C₂	semidirect
17. #22571178	C₂	semidirect
18. #22571144	C₂	semidirect
19. #22570234	C₂	semidirect
20. #22569700	C₂	semidirect
21. #22569681	C₂	semidirect
22. #22569338	C₂	semidirect
23. C₆₇×#3108	C₂	semidirect
24. C₂×#14524075	C₂²	semidirect
25. C₂×#14524074	C₂²	semidirect
29. #16864131	C₂²	semidirect
30. #16864125	C₂²	semidirect
36. #16864094	C₂²	semidirect
40. #16864057	C₂²	semidirect
49. #16863946	C₂²	semidirect
51. #16863933	C₂²	semidirect
55. C₄×#11761629	C₂²	semidirect
58. #16863781	C₂²	semidirect
61. #16863769	C₂²	semidirect
62. #16863752	C₂²	semidirect
64. #16863747	C₂²	semidirect
66. #16863739	C₂²	semidirect
68. #16863706	C₂²	semidirect
69. #16863699	C₂²	semidirect
70. #16863693	C₂²	semidirect
71. #16863681	C₂²	semidirect
73. #16863653	C₂²	semidirect
77. #16863644	C₂²	semidirect
78. #16863643	C₂²	semidirect
79. #16863621	C₂²	semidirect
80. #16863620	C₂²	semidirect
81. #16863618	C₂²	semidirect
82. #16863618	C₂²	semidirect
84. #16863614	C₂²	semidirect
85. #16863614	C₂²	semidirect
86. #16863612	C₂²	semidirect
87. #16863612	C₂²	semidirect
90. #16863606	C₂²	semidirect
91. #16863606	C₂²	semidirect
94. #16863596	C₂²	semidirect
96. #16863561	C₂²	semidirect
97. #16863550	C₂²	semidirect
100. #16863543	C₂²	semidirect
101. #16863543	C₂²	semidirect
102. #16863536	C₂²	semidirect
104. C₈×Dic₁₃₄	C₂²	semidirect
105. C₈×Dic₁₃₄	C₂²	semidirect
106. #16863488	C₂²	semidirect
107. #16863483	C₂²	semidirect
108. #16863481	C₂²	semidirect
109. #16863478	C₂²	semidirect
112. #16863471	C₂²	semidirect
113. #16863471	C₂²	semidirect
114. #16863448	C₂²	semidirect
115. #16863420	C₂²	semidirect
116. #16863418	C₂²	semidirect
117. #16863403	C₂²	semidirect
119. #16863395	C₂²	semidirect
121. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
122. #483×C₆₇	C₂²	semidirect
124. #479×C₆₇	C₂²	semidirect
125. #479×C₆₇	C₂²	semidirect
128. #451×C₆₇	C₂²	semidirect
130. C₄×Q₁₆×C₆₇	C₂²	semidirect
131. C₄×Q₁₆×C₆₇	C₂²	semidirect
134. #431×C₆₇	C₂²	semidirect
601. #3108	D₆₇	semidirect
606. C₆₇	#62006	semidirect
642. C₂×C₄×Q₈	C₂×D₆₇	semidirect
652. #483	C₂×D₆₇	semidirect
656. #479	C₂×D₆₇	semidirect
657. #479	C₂×D₆₇	semidirect
689. #451	C₂×D₆₇	semidirect
700. C₄×Q₁₆	C₂×D₆₇	semidirect
701. C₄×Q₁₆	C₂×D₆₇	semidirect
712. #431	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574172	2
#22573804	2
#22573219	2
#22573203	2
#22572903	2
#22572892	2
#22572494	2
#22572465	2
#22572442	2
#22572413	2
#22571876	2
#22571866	2
#22571843	2
#22571830	2
#22571612	2
#22571571	2
#22571178	2
#22571144	2
#22570234	2
#22569700	2
#22569681	2
#22569338	2
C₆₇×#3108	2
#62006	67