Subgroups — #31738283

Order 17152.

1834 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574226	C₂	1	1	yes	maximal, characteristic, complemented
2	#22574170	C₂	1	1	yes	maximal, characteristic, complemented
3	#22573203	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₁₆×Dic₁₃₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#22573021	C₂	1	1	yes	maximal, characteristic, complemented
6	#22572925	C₂	1	1	yes	maximal, characteristic, complemented
7	#22572624	C₂	1	1	yes	maximal, characteristic, complemented
8	#22572618	C₂	1	2	yes	maximal, complemented
9	#22572494	C₂	1	1	yes	maximal, characteristic, complemented
10	#22572453	C₂	1	1	yes	maximal, characteristic, complemented
11	#22572391	C₂	1	2	yes	maximal, complemented
12	#22572241	C₂	1	2	yes	maximal, complemented
13	#22571910	C₂	1	2	yes	maximal, complemented
14	SD₁₆×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
15	#22570822	C₂	1	2	yes	maximal, complemented
16	#22570768	C₂	1	1	yes	maximal, characteristic, complemented
17	#22570444	C₂	1	2	yes	maximal, complemented
18	#22570389	C₂	1	2	yes	maximal, complemented
19	#22570371	C₂	1	1	yes	maximal, characteristic, complemented
20	#22570360	C₂	1	1	yes	maximal, characteristic, complemented
21	#22569184	C₂	1	1	yes	maximal, characteristic, complemented
22	#22569063	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×SD₁₆×D₆₇	C₂²	1	2	yes	—
25	#16864131	C₂²	1	1	yes	characteristic
26	Q₈×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
27	#16864119	C₂²	1	1	yes	characteristic
28	#16864116	—	2	1	no	—
29	#16864116	C₂²	1	1	yes	characteristic, complemented
30	#16864114	—	2	2	no	—
31	#16864114	C₂²	1	2	yes	complemented
32	#16864111	—	2	1	no	—
33	#16864111	C₂²	1	1	yes	characteristic
34	#16864109	C₂²	1	2	yes	—
35	#16864070	—	2	2	no	—
36	Q₈×D₂₆₈	C₂²	1	1	yes	characteristic
37	D₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
38	#16864055	—	2	1	no	—
39	#16864053	C₂²	1	2	yes	complemented
40	#16864042	—	2	1	no	—
41	#16864034	C₂²	1	2	yes	—
42	D₄×D₂₆₈	C₂²	1	1	yes	characteristic
43	#16864018	C₂²	1	2	yes	—
44	#16864011	—	2	2	no	—
45	#16864011	C₂²	1	2	yes	complemented
46	#16863979	—	2	2	no	—
47	#16863953	—	2	1	no	—
48	#16863953	C₂²	1	1	yes	characteristic, complemented
49	#16863946	C₂²	1	1	yes	characteristic
50	#16863930	—	2	1	no	—
51	#16863930	—	2	1	no	—
52	#16863930	C₂²	1	1	yes	characteristic
53	C₂×#14524031	—	2	1	no	—
54	#16863872	C₂²	1	2	yes	complemented
55	#16863868	C₂²	1	2	yes	—
56	#16863794	C₂²	1	1	yes	characteristic, complemented
57	#16863793	C₂²	1	2	yes	complemented
58	#16863777	C₂²	1	2	yes	complemented
59	#16863769	C₂²	1	1	yes	characteristic
60	#16863757	C₂²	1	2	yes	complemented
61	#16863754	C₂²	1	2	yes	complemented
62	#16863747	C₂²	1	1	yes	characteristic, complemented
63	#16863743	C₂²	1	1	yes	characteristic
64	#16863739	C₂²	1	2	yes	complemented
65	#16863737	C₂²	1	2	yes	complemented
66	#16863735	C₂²	1	2	yes	complemented
67	#16863723	C₂²	1	2	yes	—
68	#16863720	C₂²	1	2	yes	complemented
69	#16863719	C₂²	1	2	yes	complemented
70	#16863691	C₂²	1	1	yes	characteristic, complemented
71	#16863690	C₂²	1	2	yes	complemented
72	#16863686	C₂²	1	1	yes	characteristic
73	#16863684	C₂²	1	2	yes	—
74	#16863681	C₂²	1	1	yes	characteristic, complemented
75	#16863679	C₂²	1	2	yes	complemented
76	#16863676	C₂²	1	1	yes	characteristic, complemented
77	#16863675	C₂²	1	2	yes	complemented
78	#16863653	C₂²	1	2	yes	complemented
79	#16863648	C₂²	1	2	yes	—
80	#16863626	C₂²	1	2	yes	—
81	#16863625	C₂²	1	2	yes	complemented
82	#16863625	C₂²	1	2	yes	complemented
83	#16863622	C₂²	1	2	yes	complemented
84	#16863621	C₂²	1	2	yes	complemented
85	#16863620	C₂²	1	2	yes	complemented
86	#16863610	C₂²	1	2	yes	complemented
87	#16863609	C₂²	1	2	yes	—
88	#16863606	C₂²	1	1	yes	characteristic, complemented
89	#16863601	C₂²	1	1	yes	characteristic
90	#16863596	C₂²	1	1	yes	characteristic
91	#16863591	C₂²	1	1	yes	characteristic
92	#16863558	C₂²	1	2	yes	—
93	#16863550	C₂²	1	2	yes	complemented
94	#16863548	C₂²	1	2	yes	—
95	#16863541	C₂²	1	2	yes	complemented
96	#16863536	C₂²	1	2	yes	—
97	#16863528	C₂²	1	2	yes	—
98	#16863526	C₂²	1	1	yes	characteristic, complemented
99	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
100	#16863506	C₂²	1	2	yes	complemented
101	#16863501	C₂²	1	2	yes	complemented
102	#16863499	C₂²	1	2	yes	complemented
103	#16863496	C₂²	1	2	yes	—
104	#16863494	C₂²	1	2	yes	complemented
105	#16863493	C₂²	1	2	yes	—
106	C₄×#11761617	C₂²	1	2	yes	complemented
107	C₄×#11761617	C₂²	1	2	yes	complemented
108	SD₁₆×Dic₆₇	C₂²	1	2	yes	—
109	#16863483	C₂²	1	2	yes	complemented
110	#16863475	C₂²	1	1	yes	characteristic
111	#16863467	C₂²	1	2	yes	complemented
112	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
113	C₈×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
114	#16863455	C₂²	1	2	yes	complemented
115	#16863453	C₂²	1	1	yes	characteristic, complemented
116	#16863431	C₂²	1	2	yes	complemented
117	#16863403	C₂²	1	2	yes	complemented
118	#16863399	C₂²	1	2	yes	—
119	#16863350	C₂²	1	2	yes	complemented
120	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
122	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
131	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	#416×C₆₇	C₂²	1	1	yes	characteristic
133	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#11761628	—	2	1	no	—
136	C₂²×Dic₁₃₄	—	2	1	no	—
137	C₂×Q₈×D₆₇	C₂³	1	2	yes	—
138	C₂²×D₂₆₈	—	2	1	no	—
139	C₂×D₄×D₆₇	C₂³	1	2	yes	—
140	C₂×#11761618	C₂³	1	2	yes	—
141	C₂×#11761617	C₂³	1	2	yes	—
142	C₂×#11761617	C₂³	1	2	yes	—
143	C₂×#11761616	C₂³	1	2	yes	—
144	C₂×#11761615	C₂³	1	2	yes	—
145	SD₁₆×D₆₇	—	2	8	no	—
146	C₂×#11761613	C₂³	1	2	yes	—
147	C₂×#11761611	C₂³	1	2	yes	—
148	C₂×C₈×D₆₇	C₂³	1	2	yes	—
149	#14524043	—	2	1	no	—
150	#14524043	—	2	1	no	—
151	#14524043	C₂³	1	1	yes	characteristic
152	#14524043	C₂³	1	1	yes	characteristic
153	#14524043	C₂³	1	1	yes	characteristic
154	#14524042	—	2	2	no	—
155	#14524042	C₂³	1	2	yes	—
156	#14524042	C₂³	1	2	yes	—
157	#14524040	C₂³	1	1	yes	characteristic
158	#14524038	—	2	2	no	—
159	#14524037	—	2	2	no	—
160	#14524037	—	2	2	no	—
161	#14524037	D₄	1	2	yes	—
162	#14524036	—	2	2	no	—
163	#14524036	—	2	2	no	—
164	#14524036	—	2	2	no	—
165	#14524035	—	2	1	no	—
166	#14524035	D₄	1	1	yes	characteristic
167	#14524032	C₂³	1	2	yes	—
168	#14524031	—	2	1	no	—
169	#14524031	—	2	1	no	—
170	#14524031	—	2	2	no	—
171	#14524031	—	2	2	no	—
172	#14524031	—	2	1	no	—
173	#14524031	D₄	1	1	yes	characteristic
174	#14524030	—	2	2	no	—
175	#14524030	C₂³	1	2	yes	—
176	#14524029	—	2	2	no	—
177	#14524029	—	2	2	no	—
178	#14524029	—	2	2	no	—
179	#14524029	—	2	2	no	—
180	#14524028	—	2	2	no	—
181	#14524028	—	2	2	no	—
182	#14524026	—	2	2	no	—
183	#14524026	—	2	2	no	—
184	#14524026	D₄	1	2	yes	—
185	#14524023	—	2	2	no	—
186	#14524023	C₂³	1	2	yes	—
187	#14524022	—	2	1	no	—
188	#14524022	—	2	1	no	—
189	#14524022	—	2	2	no	—
190	#14524022	—	2	2	no	—
191	#14524022	—	2	1	no	—
192	#14524022	D₄	1	1	yes	characteristic
193	#14524022	C₂³	1	2	yes	—
194	#14524021	—	2	2	no	—
195	#14524020	—	2	2	no	—
196	#14524019	C₂³	1	2	yes	—
197	#14524018	C₂³	1	2	yes	—
198	#14524017	—	2	1	no	—
199	#14524017	—	2	1	no	—
200	#14524017	—	2	1	no	—
201	#14524017	D₄	1	1	yes	characteristic
202	#14524017	C₂³	1	2	yes	—
203	#14524016	—	2	2	no	—
204	#14524015	—	2	2	no	—
205	#14524014	—	2	2	no	—
206	#14524014	C₂³	1	2	yes	—
207	#14524013	—	2	2	no	—
208	#14524011	—	2	2	no	—
209	Q₈×Dic₆₇	C₂³	1	2	yes	—
210	C₄×Dic₁₃₄	—	2	1	no	—
211	C₄×Dic₁₃₄	—	2	1	no	—
212	C₄×Dic₁₃₄	—	2	2	no	—
213	C₄×Dic₁₃₄	—	2	2	no	—
214	C₄×Dic₁₃₄	—	2	1	no	—
215	C₄×Dic₁₃₄	C₂³	1	2	yes	—
216	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
217	#14524008	—	2	2	no	—
218	#14524008	C₂³	1	2	yes	—
219	C₄×D₂₆₈	—	2	1	no	—
220	C₄×D₂₆₈	—	2	1	no	—
221	C₄×D₂₆₈	—	2	1	no	—
222	C₄×D₂₆₈	C₂³	1	2	yes	—
223	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
224	D₄×Dic₆₇	C₂³	1	2	yes	—
225	#14524005	C₂³	1	2	yes	—
226	C₄×C₂²⋊D₆₇	—	2	2	no	—
227	C₄×C₂²⋊D₆₇	—	2	2	no	—
228	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
229	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
230	#14524002	—	2	1	no	—
231	#14524002	—	2	1	no	—
232	#14524002	—	2	1	no	—
233	#14524001	—	2	2	no	—
234	#14524001	C₂³	1	2	yes	—
235	#14524001	C₂³	1	2	yes	—
236	#14524000	—	2	2	no	—
237	#14524000	—	2	2	no	—
238	#14524000	C₂³	1	2	yes	—
239	C₂×(C₂×D₆₇)⋊C₄	—	2	2	no	—
240	C₂×(C₂×D₆₇)⋊C₄	—	2	2	no	—
241	C₂²⋊C₄×D₆₇	—	2	2	no	—
242	#14523976	C₂³	1	2	yes	—
243	#14523976	C₂³	1	2	yes	—
244	#14523975	C₂³	1	2	yes	—
245	#14523975	C₂³	1	2	yes	—
246	#14523974	C₂³	1	2	yes	—
247	#14523974	C₂³	1	2	yes	—
248	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
249	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
250	Dic₆₇⋊C₈	C₂³	1	2	yes	—
251	Dic₆₇⋊C₈	C₂³	1	2	yes	—
252	#14523968	C₂³	1	2	yes	—
253	#14523968	C₂³	1	2	yes	—
254	#14523967	C₂³	1	2	yes	—
255	#14523967	C₂³	1	2	yes	—
256	#14523966	C₂³	1	2	yes	—
257	#14523966	C₂³	1	2	yes	—
258	#14523965	C₂³	1	2	yes	—
259	#14523965	C₂³	1	2	yes	—
260	#14523964	C₂³	1	2	yes	—
261	#14523964	C₂³	1	2	yes	—
262	#14523963	C₂³	1	2	yes	—
263	#14523963	C₂³	1	2	yes	—
264	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
265	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
267	#14523954	C₂³	1	2	yes	—
268	#14523953	C₂³	1	2	yes	—
269	C₈×Dic₆₇	C₂³	1	2	yes	—
270	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
271	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
272	#135×C₆₇	—	2	4	no	—
273	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
274	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
276	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
277	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
278	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
279	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₆₇	—	2	1	no	—
284	C₄×D₄×C₆₇	—	2	1	no	—
285	C₄×D₄×C₆₇	—	2	1	no	—
286	C₄×D₄×C₆₇	—	2	1	no	—
287	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
291	#117×C₆₇	—	2	1	no	—
292	#117×C₆₇	—	2	1	no	—
293	#117×C₆₇	C₂³	1	1	yes	characteristic
294	#117×C₆₇	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₆₇	—	2	1	no	—
296	C₂×C₄²×C₆₇	—	2	1	no	—
297	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
298	#107×C₆₇	C₂³	1	1	yes	characteristic
299	#107×C₆₇	C₂³	1	1	yes	characteristic
300	#106×C₆₇	C₂³	1	1	yes	characteristic
301	#106×C₆₇	C₂³	1	1	yes	characteristic
302	#103×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	#102×C₆₇	C₂³	1	1	yes	characteristic
307	#102×C₆₇	C₂³	1	1	yes	characteristic
308	#102×C₆₇	C₂³	1	1	yes	characteristic
309	#102×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₂³×D₆₇	—	2	2	no	—
315	#11761628	—	8	2	no	—
316	C₂×Dic₁₃₄	—	2	1	no	—
317	C₂×Dic₁₃₄	—	2	2	no	—
318	C₂×Dic₁₃₄	—	2	1	no	—
319	C₂×Dic₁₃₄	—	2	2	no	—
320	C₂×Dic₁₃₄	—	2	2	no	—
321	C₂×Dic₁₃₄	—	8	2	no	—
322	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
323	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
324	Q₈×D₆₇	—	2	4	no	—
325	Q₈×D₆₇	—	4	2	no	—
326	C₂×D₂₆₈	—	2	1	no	—
327	C₂×D₂₆₈	—	2	2	no	—
328	C₂×D₂₆₈	—	2	1	no	—
329	C₂×D₂₆₈	—	8	2	no	—
330	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
331	C₂×D₂₆₈	C₂⁴	1	2	yes	—
332	C₂×C₂²⋊D₆₇	—	2	2	no	—
333	C₂×C₂²⋊D₆₇	—	2	2	no	—
334	C₂×C₂²⋊D₆₇	—	2	2	no	—
335	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
336	D₄×D₆₇	—	2	4	no	—
337	D₄×D₆₇	—	4	2	no	—
338	C₂²×Dic₆₇	—	2	2	no	—
339	C₂×C₄×D₆₇	—	2	2	no	—
340	C₂×C₄×D₆₇	—	2	2	no	—
341	C₂×C₄×D₆₇	—	2	2	no	—
342	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
343	#11761618	—	4	2	no	—
344	#11761617	—	2	4	no	—
345	#11761617	—	4	2	no	—
346	#11761616	—	2	4	no	—
347	#11761615	—	2	4	no	—
348	#11761613	—	4	2	no	—
349	#11761611	—	4	2	no	—
350	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
351	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
352	C₈×D₆₇	—	2	4	no	—
353	C₄⋊Dic₆₇	—	2	1	no	—
354	C₄⋊Dic₆₇	—	2	1	no	—
355	C₄⋊Dic₆₇	—	2	1	no	—
356	C₄⋊Dic₆₇	—	2	1	no	—
357	C₄⋊Dic₆₇	—	2	2	no	—
358	C₄⋊Dic₆₇	—	2	2	no	—
359	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
360	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
361	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
362	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
363	Dic₆₇⋊C₄	—	2	2	no	—
364	Dic₆₇⋊C₄	—	2	2	no	—
365	Dic₆₇⋊C₄	—	2	2	no	—
366	Dic₆₇⋊C₄	—	2	2	no	—
367	Dic₆₇⋊C₄	—	2	2	no	—
368	Dic₆₇⋊C₄	—	2	2	no	—
369	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
370	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
371	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
372	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
373	C₂²⋊Dic₆₇	—	2	2	no	—
374	C₂²⋊Dic₆₇	—	2	2	no	—
375	C₂²⋊Dic₆₇	—	2	2	no	—
376	C₂²⋊Dic₆₇	—	2	2	no	—
377	C₂²⋊Dic₆₇	—	2	2	no	—
378	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
386	(C₂×D₆₇)⋊C₄	—	2	2	no	—
387	(C₂×D₆₇)⋊C₄	—	2	2	no	—
388	(C₂×D₆₇)⋊C₄	—	2	2	no	—
389	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
390	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
391	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
392	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
393	C₄×Dic₆₇	—	2	2	no	—
394	C₄×Dic₆₇	—	2	2	no	—
395	C₄×Dic₆₇	—	2	2	no	—
396	C₄×Dic₆₇	—	2	2	no	—
397	C₄×Dic₆₇	—	2	2	no	—
398	C₄×Dic₆₇	C₂⁴	1	2	yes	—
399	#41×C₆₇	—	2	2	no	—
400	#41×C₆₇	—	2	2	no	—
401	#41×C₆₇	—	4	1	no	—
402	#41×C₆₇	—	4	1	no	—
403	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₂×D₄×C₆₇	—	2	1	no	—
406	C₂×D₄×C₆₇	—	2	1	no	—
407	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₆₇	—	2	1	no	—
410	C₂²×C₄×C₆₇	—	2	1	no	—
411	C₂²×C₄×C₆₇	—	2	1	no	—
412	C₂²×C₄×C₆₇	—	2	1	no	—
413	C₂²×C₄×C₆₇	—	2	1	no	—
414	C₂²×C₄×C₆₇	—	2	1	no	—
415	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
416	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
417	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
418	Q₁₆×C₆₇	—	2	2	no	—
419	SD₁₆×C₆₇	—	2	2	no	—
420	SD₁₆×C₆₇	#41	1	4	yes	complemented
421	D₈×C₆₇	—	2	2	no	—
422	C₂×C₈×C₆₇	—	2	2	no	—
423	C₂×C₈×C₆₇	—	4	1	no	—
424	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
427	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₆₇	—	2	1	no	—
429	C₄⋊C₄×C₆₇	—	2	1	no	—
430	C₄⋊C₄×C₆₇	—	2	1	no	—
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
433	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
434	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₂²⋊C₄×C₆₇	—	2	1	no	—
437	C₂²⋊C₄×C₆₇	—	2	1	no	—
438	C₂²⋊C₄×C₆₇	—	2	1	no	—
439	C₂²⋊C₄×C₆₇	—	2	1	no	—
440	C₂²⋊C₄×C₆₇	—	2	1	no	—
441	C₂²⋊C₄×C₆₇	—	2	1	no	—
442	C₄²×C₆₇	—	2	1	no	—
443	C₄²×C₆₇	—	2	1	no	—
444	C₄²×C₆₇	—	2	1	no	—
445	C₄²×C₆₇	—	2	1	no	—
446	C₄²×C₆₇	—	2	1	no	—
447	C₄²×C₆₇	—	2	1	no	—
448	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
451	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₂³×C₆₇	—	2	1	no	—
453	C₂³×C₆₇	—	2	1	no	—
454	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
455	C₂²×D₆₇	—	2	2	no	—
456	C₂²×D₆₇	—	4	4	no	—
457	C₂²×D₆₇	—	8	2	no	—
458	C₂²×D₆₇	—	8	2	no	—
459	C₂²×D₆₇	C₂²×D₄	1	2	yes	—
460	Q₈×C₆₇	—	2	1	no	—
461	Q₈×C₆₇	—	2	1	no	—
462	Q₈×C₆₇	—	2	1	no	—
463	Q₈×C₆₇	C₂×#41	1	2	yes	—
464	D₄×C₆₇	—	2	1	no	—
465	D₄×C₆₇	—	2	1	no	—
466	D₄×C₆₇	—	2	1	no	—
467	D₄×C₆₇	—	4	2	no	—
468	D₄×C₆₇	—	4	2	no	—
469	D₄×C₆₇	C₂×#41	1	2	yes	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	2	no	—
472	C₂×C₄×C₆₇	—	2	1	no	—
473	C₂×C₄×C₆₇	—	2	1	no	—
474	C₂×C₄×C₆₇	—	2	1	no	—
475	C₂×C₄×C₆₇	—	2	1	no	—
476	C₂×C₄×C₆₇	—	2	1	no	—
477	C₂×C₄×C₆₇	—	2	1	no	—
478	C₂×C₄×C₆₇	—	2	1	no	—
479	C₂×C₄×C₆₇	—	4	1	no	—
480	C₂×C₄×C₆₇	—	4	2	no	—
481	C₂×C₄×C₆₇	—	4	2	no	—
482	C₂×C₄×C₆₇	—	4	2	no	—
483	C₂×C₄×C₆₇	—	4	2	no	—
484	C₂×C₄×C₆₇	—	8	1	no	—
485	C₂×C₄×C₆₇	—	8	1	no	—
486	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
492	C₂²⋊D₆₇	—	4	2	no	—
493	C₂²⋊D₆₇	—	4	4	no	—
494	C₂²⋊D₆₇	—	8	2	no	—
495	C₂²⋊D₆₇	—	8	2	no	—
496	C₂×Dic₆₇	—	2	2	no	—
497	C₂×Dic₆₇	—	2	2	no	—
498	C₂×Dic₆₇	—	2	2	no	—
499	C₂×Dic₆₇	—	8	2	no	—
500	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
501	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
502	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
503	D₂₆₈	—	2	2	no	—
504	D₂₆₈	—	2	2	no	—
505	D₂₆₈	—	2	2	no	—
506	D₂₆₈	—	4	2	no	—
507	D₂₆₈	—	8	1	no	—
508	D₂₆₈	—	8	2	no	—
509	C₄×D₆₇	—	2	2	no	—
510	C₄×D₆₇	—	2	2	no	—
511	C₄×D₆₇	—	4	4	no	—
512	C₄×D₆₇	—	8	2	no	—
513	C₄×D₆₇	—	8	2	no	—
514	Dic₁₃₄	—	2	2	no	—
515	Dic₁₃₄	—	2	2	no	—
516	Dic₁₃₄	—	2	2	no	—
517	Dic₁₃₄	—	4	4	no	—
518	Dic₁₃₄	—	4	2	no	—
519	Dic₁₃₄	—	8	2	no	—
520	Dic₁₃₄	—	8	2	no	—
521	Dic₁₃₄	—	8	1	no	—
522	C₈×C₆₇	—	2	1	no	—
523	C₈×C₆₇	—	2	1	no	—
524	C₈×C₆₇	—	2	1	no	—
525	C₈×C₆₇	C₂×#41	1	2	yes	—
526	C₆₇⋊C₈	—	2	2	no	—
527	C₆₇⋊C₈	—	2	2	no	—
528	C₂²×C₆₇	—	2	1	no	—
529	C₂²×C₆₇	—	2	2	no	—
530	C₂²×C₆₇	—	2	1	no	—
531	C₂²×C₆₇	—	2	1	no	—
532	C₂²×C₆₇	—	4	1	no	—
533	C₂²×C₆₇	—	4	1	no	—
534	C₂²×C₆₇	—	4	1	no	—
535	C₂²×C₆₇	—	4	1	no	—
536	C₂²×C₆₇	—	4	1	no	—
537	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
538	C₂×D₆₇	—	2	2	no	—
539	C₂×D₆₇	—	2	2	no	—
540	C₂×D₆₇	—	2	2	no	—
541	C₂×D₆₇	—	4	2	no	—
542	C₂×D₆₇	—	4	2	no	—
543	C₂×D₆₇	—	4	2	no	—
544	C₂×D₆₇	—	16	4	no	—
545	C₄×C₆₇	—	2	1	no	—
546	C₄×C₆₇	—	2	1	no	—
547	C₄×C₆₇	—	2	2	no	—
548	C₄×C₆₇	—	2	1	no	—
549	C₄×C₆₇	—	2	1	no	—
550	C₄×C₆₇	—	4	1	no	—
551	C₄×C₆₇	—	4	1	no	—
552	C₄×C₆₇	—	4	1	no	—
553	C₄×C₆₇	—	4	1	no	—
554	C₄×C₆₇	—	4	1	no	—
555	C₄×C₆₇	#577	1	2	yes	—
556	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
557	C₄×C₆₇	#585	1	1	yes	characteristic
558	Dic₆₇	—	2	2	no	—
559	Dic₆₇	—	2	2	no	—
560	Dic₆₇	—	2	2	no	—
561	Dic₆₇	—	4	2	no	—
562	Dic₆₇	—	4	2	no	—
563	Dic₆₇	—	4	2	no	—
564	#61474	—	67	1	no	maximal, Sylow
565	C₂×C₆₇	—	4	2	no	—
566	C₂×C₆₇	—	4	1	no	—
567	C₂×C₆₇	—	8	1	no	—
568	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
569	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
570	C₂×C₆₇	#3584	1	1	yes	characteristic
571	D₆₇	—	4	2	no	—
572	D₆₇	—	8	2	no	—
573	#3518	—	67	1	no	—
574	#3514	—	67	1	no	—
575	#3394	—	67	1	no	—
576	Q₈×SD₁₆	—	67	1	no	—
577	#3375	—	67	1	no	—
578	#3367	—	67	1	no	—
579	#3340	—	67	1	no	—
580	#3340	—	67	2	no	—
581	#3328	—	67	1	no	—
582	#3325	—	67	1	no	—
583	#3321	—	67	2	no	—
584	#3311	—	67	2	no	—
585	#3282	—	67	2	no	—
586	D₄×SD₁₆	—	67	1	no	—
587	#3173	—	67	2	no	—
588	#3167	—	67	1	no	—
589	#3121	—	67	2	no	—
590	#3118	—	67	2	no	—
591	#3116	—	67	1	no	—
592	#3115	—	67	1	no	—
593	#2966	—	67	1	no	—
594	#2949	—	67	2	no	—
595	C₄×#135	D₆₇	1	1	yes	characteristic, complemented
596	C₆₇	#61474	1	1	yes	characteristic, complemented, Sylow
597	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
598	C₂²×SD₁₆	—	67	2	no	—
599	#559	—	67	1	no	—
600	Q₈²	—	67	1	no	—
601	#556	—	67	1	no	—
602	#556	—	67	2	no	—
603	#556	—	67	1	no	—
604	#556	—	134	2	no	—
605	#556	—	134	1	no	—
606	#555	—	67	1	no	—
607	#555	—	67	2	no	—
608	#555	—	134	1	no	—
609	#551	—	134	2	no	—
610	D₄×Q₈	—	67	1	no	—
611	D₄×Q₈	—	67	1	no	—
612	#548	—	67	2	no	—
613	#548	—	134	1	no	—
614	#546	—	67	2	no	—
615	#546	—	134	1	no	—
616	D₄²	—	67	1	no	—
617	#542	—	67	2	no	—
618	#542	—	67	2	no	—
619	#542	—	134	2	no	—
620	#538	—	134	2	no	—
621	#533	—	67	1	no	—
622	#533	—	134	1	no	—
623	#532	—	67	1	no	—
624	#529	—	67	1	no	—
625	#529	—	134	1	no	—
626	#529	—	134	1	no	—
627	C₂×#124	—	134	1	no	—
628	#519	—	67	2	no	—
629	#518	—	67	2	no	—
630	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
631	C₄×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
632	#498	—	67	2	no	—
633	#498	—	67	1	no	—
634	#495	—	67	2	no	—
635	#492	—	67	1	no	—
636	#489	—	67	2	no	—
637	#489	—	67	2	no	—
638	#487	—	67	1	no	—
639	#486	—	67	1	no	—
640	#485	—	67	2	no	—
641	#485	—	67	2	no	—
642	#485	—	67	2	no	—
643	#482	—	67	2	no	—
644	#482	—	67	2	no	—
645	#482	—	67	2	no	—
646	#477	—	67	1	no	—
647	#477	—	67	2	no	—
648	#476	—	67	1	no	—
649	#476	—	67	2	no	—
650	#475	—	67	1	no	—
651	#475	—	67	2	no	—
652	#474	—	67	1	no	—
653	#474	—	67	2	no	—
654	#470	—	67	2	no	—
655	#469	—	67	2	no	—
656	#465	—	67	2	no	—
657	#465	—	67	2	no	—
658	#465	—	67	2	no	—
659	#465	—	67	2	no	—
660	#464	—	67	2	no	—
661	#464	—	67	2	no	—
662	#463	—	67	2	no	—
663	#463	—	67	2	no	—
664	#462	—	67	1	no	—
665	#461	—	67	1	no	—
666	#460	—	67	1	no	—
667	#459	—	67	1	no	—
668	#452	—	67	2	no	—
669	#451	—	67	2	no	—
670	#450	—	67	2	no	—
671	#449	—	67	2	no	—
672	#448	—	67	2	no	—
673	#447	—	67	2	no	—
674	#446	—	67	1	no	—
675	C₈×Q₈	—	67	1	no	—
676	#442	—	67	2	no	—
677	#441	—	67	2	no	—
678	#440	—	67	2	no	—
679	#440	—	67	2	no	—
680	#440	—	67	2	no	—
681	#440	—	67	2	no	—
682	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
683	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
684	C₄×SD₁₆	—	67	2	no	—
685	C₄×SD₁₆	—	67	2	no	—
686	C₄×SD₁₆	—	67	2	no	—
687	C₄×SD₁₆	—	67	2	no	—
688	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic
689	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic
690	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
691	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
692	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
693	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
694	#436	—	67	1	no	—
695	#435	—	67	2	no	—
696	C₈×D₄	—	67	2	no	—
697	C₈×D₄	—	67	1	no	—
698	#433	—	67	2	no	—
699	#432	—	67	1	no	—
700	#427	—	67	2	no	—
701	#427	C₂×D₆₇	1	1	yes	characteristic, complemented
702	#419	—	67	2	no	—
703	#418	—	67	2	no	—
704	#416	C₂×D₆₇	1	1	yes	characteristic
705	#416	C₂×D₆₇	1	1	yes	characteristic, complemented
706	#405	—	67	2	no	—
707	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
708	C₂×#41	—	134	1	no	—
709	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
710	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
711	C₂²×Q₈	—	67	2	no	—
712	C₂²×Q₈	—	134	1	no	—
713	C₂²×D₄	—	67	2	no	—
714	C₂²×D₄	—	134	1	no	—
715	#135	—	2	4	no	—
716	C₂×Q₁₆	—	67	2	no	—
717	C₂×Q₁₆	C₂²×D₆₇	1	1	yes	characteristic
718	C₂×SD₁₆	—	67	2	no	—
719	C₂×SD₁₆	—	67	2	no	—
720	C₂×SD₁₆	—	67	2	no	—
721	C₂×SD₁₆	—	67	2	no	—
722	C₂×SD₁₆	—	134	8	no	—
723	C₂×SD₁₆	C₂²×D₆₇	1	1	yes	characteristic
724	C₂×SD₁₆	C₂²×D₆₇	1	1	yes	characteristic
725	C₂×D₈	—	67	2	no	—
726	C₂×D₈	C₂²×D₆₇	1	1	yes	characteristic
727	C₂×M₁₆	—	67	2	no	—
728	C₂²×C₈	—	67	2	no	—
729	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
730	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
731	C₄⋊Q₈	—	67	2	no	—
732	C₄⋊Q₈	—	67	2	no	—
733	C₄⋊Q₈	—	67	1	no	—
734	C₄⋊Q₈	—	67	1	no	—
735	C₄⋊Q₈	—	67	1	no	—
736	C₄⋊Q₈	—	134	1	no	—
737	C₄⋊Q₈	—	134	1	no	—
738	C₄⋊Q₈	—	134	2	no	—
739	#127	—	67	1	no	—
740	#126	—	67	2	no	—
741	#126	—	134	2	no	—
742	#126	—	134	2	no	—
743	#126	—	134	2	no	—
744	#126	—	134	2	no	—
745	#126	—	134	2	no	—
746	#126	—	134	2	no	—
747	#125	—	67	1	no	—
748	#125	—	134	1	no	—
749	#124	—	67	2	no	—
750	#124	—	67	2	no	—
751	#124	—	67	1	no	—
752	#124	—	134	2	no	—
753	#124	—	134	2	no	—
754	#124	—	134	1	no	—
755	#124	—	134	1	no	—
756	#124	—	134	2	no	—
757	#124	—	134	2	no	—
758	#124	—	134	2	no	—
759	#124	—	134	2	no	—
760	#124	—	134	2	no	—
761	#124	—	134	1	no	—
762	#123	—	67	2	no	—
763	#123	—	134	2	no	—
764	#123	—	134	2	no	—
765	#123	—	134	2	no	—
766	#123	—	134	2	no	—
767	C₂²⋊Q₈	—	67	1	no	—
768	C₂²⋊Q₈	—	67	2	no	—
769	C₂²⋊Q₈	—	67	2	no	—
770	C₂²⋊Q₈	—	67	2	no	—
771	C₂²⋊Q₈	—	134	2	no	—
772	C₂²⋊Q₈	—	134	2	no	—
773	C₂²⋊Q₈	—	134	2	no	—
774	C₂²⋊Q₈	—	134	1	no	—
775	C₂²⋊Q₈	—	134	2	no	—
776	C₂²⋊Q₈	—	134	2	no	—
777	C₂²⋊Q₈	—	134	1	no	—
778	C₂²⋊Q₈	—	134	1	no	—
779	#121	—	67	1	no	—
780	#121	—	67	2	no	—
781	#121	—	67	2	no	—
782	#121	—	67	2	no	—
783	#121	—	134	2	no	—
784	#121	—	134	2	no	—
785	#121	—	134	1	no	—
786	#121	—	134	1	no	—
787	#121	—	134	2	no	—
788	#121	—	134	1	no	—
789	#120	—	134	2	no	—
790	#120	—	134	2	no	—
791	C₄×Q₈	—	67	1	no	—
792	C₄×Q₈	—	67	2	no	—
793	C₄×Q₈	—	67	2	no	—
794	C₄×Q₈	—	67	2	no	—
795	C₄×Q₈	—	134	2	no	—
796	C₄×Q₈	—	134	1	no	—
797	C₄×Q₈	—	134	2	no	—
798	C₄×Q₈	—	134	1	no	—
799	C₄×Q₈	—	134	2	no	—
800	C₄×Q₈	—	134	1	no	—
801	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
802	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
803	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
804	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	67	2	no	—
810	C₄×D₄	—	67	2	no	—
811	C₄×D₄	—	67	2	no	—
812	C₄×D₄	—	67	1	no	—
813	C₄×D₄	—	67	2	no	—
814	C₄×D₄	—	134	1	no	—
815	C₄×D₄	—	134	1	no	—
816	C₄×D₄	—	134	2	no	—
817	C₄×D₄	—	134	2	no	—
818	C₄×D₄	—	134	2	no	—
819	C₄×D₄	—	134	1	no	—
820	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
821	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
822	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
823	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
824	#117	—	2	1	no	—
825	#117	—	2	1	no	—
826	#117	—	67	2	no	—
827	#117	—	67	2	no	—
828	#117	—	67	2	no	—
829	#117	—	134	2	no	—
830	#117	—	134	2	no	—
831	#117	—	134	2	no	—
832	#117	—	134	1	no	—
833	#117	—	134	1	no	—
834	#117	—	134	1	no	—
835	#117	C₂²×D₆₇	1	1	yes	characteristic
836	#117	C₂²×D₆₇	1	1	yes	characteristic
837	C₂×C₂²⋊C₄	—	134	2	no	—
838	C₂×C₂²⋊C₄	—	134	2	no	—
839	C₂×C₂²⋊C₄	—	134	2	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	—	2	1	no	—
842	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
843	#107	—	67	2	no	—
844	#107	—	67	2	no	—
845	#107	C₂²×D₆₇	1	1	yes	characteristic
846	#107	C₂²×D₆₇	1	1	yes	characteristic
847	#106	—	67	2	no	—
848	#106	—	67	2	no	—
849	#106	—	67	2	no	—
850	#106	—	67	2	no	—
851	#106	C₂²×D₆₇	1	1	yes	characteristic
852	#106	C₂²×D₆₇	1	1	yes	characteristic
853	C₄⋊C₈	—	67	2	no	—
854	C₄⋊C₈	—	67	2	no	—
855	C₄⋊C₈	—	67	1	no	—
856	C₄⋊C₈	—	67	1	no	—
857	#103	—	67	2	no	—
858	#103	—	67	2	no	—
859	#103	—	67	2	no	—
860	#103	—	67	2	no	—
861	#103	—	67	2	no	—
862	#103	—	67	2	no	—
863	#103	C₂²×D₆₇	1	1	yes	characteristic
864	#103	C₂²×D₆₇	1	1	yes	characteristic
865	#103	C₂²×D₆₇	1	1	yes	characteristic
866	#103	C₂²×D₆₇	1	1	yes	characteristic
867	#102	—	67	2	no	—
868	#102	—	67	2	no	—
869	#102	—	67	2	no	—
870	#102	—	67	2	no	—
871	#102	—	67	2	no	—
872	#102	—	67	2	no	—
873	#102	C₂²×D₆₇	1	1	yes	characteristic
874	#102	C₂²×D₆₇	1	1	yes	characteristic
875	#102	C₂²×D₆₇	1	1	yes	characteristic
876	#102	C₂²×D₆₇	1	1	yes	characteristic
877	C₂²⋊C₈	—	67	2	no	—
878	C₂²⋊C₈	—	67	2	no	—
879	C₂²⋊C₈	—	67	2	no	—
880	#97	—	67	2	no	—
881	#97	—	67	2	no	—
882	C₄×C₈	—	67	2	no	—
883	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
884	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
885	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
886	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
887	C₂⁴	—	134	2	no	—
888	#41	—	2	2	no	—
889	#41	—	2	2	no	—
890	#41	—	4	1	no	—
891	#41	—	4	1	no	—
892	#41	—	536	2	no	—
893	C₂×Q₈	—	268	2	no	—
894	C₂×Q₈	—	536	2	no	—
895	C₂×Q₈	—	67	1	no	—
896	C₂×Q₈	—	67	2	no	—
897	C₂×Q₈	—	134	2	no	—
898	C₂×Q₈	—	134	2	no	—
899	C₂×Q₈	—	134	2	no	—
900	C₂×Q₈	—	134	4	no	—
901	C₂×Q₈	—	134	1	no	—
902	C₂×Q₈	—	134	1	no	—
903	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
904	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	268	2	no	—
908	C₂×D₄	—	536	2	no	—
909	C₂×D₄	—	67	2	no	—
910	C₂×D₄	—	67	1	no	—
911	C₂×D₄	—	67	2	no	—
912	C₂×D₄	—	134	2	no	—
913	C₂×D₄	—	134	2	no	—
914	C₂×D₄	—	134	4	no	—
915	C₂×D₄	—	134	2	no	—
916	C₂×D₄	—	134	2	no	—
917	C₂×D₄	—	134	1	no	—
918	C₂×D₄	—	134	1	no	—
919	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
920	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	67	2	no	—
928	C₂²×C₄	—	134	2	no	—
929	C₂²×C₄	—	134	2	no	—
930	C₂²×C₄	—	134	2	no	—
931	C₂²×C₄	—	134	2	no	—
932	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
933	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
934	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
935	Q₁₆	—	2	2	no	—
936	Q₁₆	—	268	2	no	—
937	SD₁₆	—	2	2	no	—
938	SD₁₆	—	268	2	no	—
939	SD₁₆	—	134	4	no	—
940	SD₁₆	—	134	4	no	—
941	SD₁₆	—	134	4	no	—
942	SD₁₆	#11761628	1	4	yes	complemented
943	D₈	—	2	2	no	—
944	D₈	—	268	2	no	—
945	M₁₆	—	268	2	no	—
946	C₂×C₈	—	2	2	no	—
947	C₂×C₈	—	4	1	no	—
948	C₂×C₈	—	67	2	no	—
949	C₂×C₈	—	67	2	no	—
950	C₂×C₈	—	134	4	no	—
951	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
952	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
953	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
954	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	67	2	no	—
960	C₄⋊C₄	—	67	2	no	—
961	C₄⋊C₄	—	67	1	no	—
962	C₄⋊C₄	—	67	2	no	—
963	C₄⋊C₄	—	67	1	no	—
964	C₄⋊C₄	—	67	2	no	—
965	C₄⋊C₄	—	67	2	no	—
966	C₄⋊C₄	—	67	2	no	—
967	C₄⋊C₄	—	134	2	no	—
968	C₄⋊C₄	—	134	2	no	—
969	C₄⋊C₄	—	134	2	no	—
970	C₄⋊C₄	—	134	2	no	—
971	C₄⋊C₄	—	134	2	no	—
972	C₄⋊C₄	—	134	2	no	—
973	C₄⋊C₄	—	134	1	no	—
974	C₄⋊C₄	—	134	1	no	—
975	C₄⋊C₄	—	134	2	no	—
976	C₄⋊C₄	—	134	2	no	—
977	C₄⋊C₄	—	134	1	no	—
978	C₄⋊C₄	—	134	1	no	—
979	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
980	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
981	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
982	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	67	2	no	—
990	C₂²⋊C₄	—	67	2	no	—
991	C₂²⋊C₄	—	67	2	no	—
992	C₂²⋊C₄	—	67	2	no	—
993	C₂²⋊C₄	—	67	2	no	—
994	C₂²⋊C₄	—	134	2	no	—
995	C₂²⋊C₄	—	134	2	no	—
996	C₂²⋊C₄	—	134	2	no	—
997	C₂²⋊C₄	—	134	2	no	—
998	C₂²⋊C₄	—	134	2	no	—
999	C₂²⋊C₄	—	134	2	no	—
1000	C₂²⋊C₄	—	134	2	no	—
1001	C₂²⋊C₄	—	134	2	no	—
1002	C₂²⋊C₄	—	134	2	no	—
1003	C₂²⋊C₄	—	134	2	no	—
1004	C₂²⋊C₄	—	134	2	no	—
1005	C₂²⋊C₄	—	134	2	no	—
1006	C₂²⋊C₄	—	134	2	no	—
1007	C₂²⋊C₄	—	134	2	no	—
1008	C₂²⋊C₄	—	134	2	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	67	2	no	—
1016	C₄²	—	134	2	no	—
1017	C₄²	—	134	2	no	—
1018	C₄²	—	134	2	no	—
1019	C₄²	—	134	2	no	—
1020	C₄²	—	134	2	no	—
1021	C₄²	D₄×D₆₇	1	1	yes	characteristic
1022	C₄²	D₄×D₆₇	1	1	yes	characteristic
1023	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1024	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	268	4	no	—
1028	C₂³	—	536	2	no	—
1029	C₂³	—	536	2	no	—
1030	C₂³	—	67	2	no	—
1031	C₂³	—	134	2	no	—
1032	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	268	4	no	—
1037	Q₈	—	268	2	no	—
1038	Q₈	—	536	1	no	—
1039	Q₈	—	536	2	no	—
1040	Q₈	—	536	2	no	—
1041	Q₈	—	134	2	no	—
1042	Q₈	—	134	2	no	—
1043	Q₈	—	134	2	no	—
1044	Q₈	C₂×#11761628	1	2	yes	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	268	4	no	—
1051	D₄	—	268	2	no	—
1052	D₄	—	268	2	no	—
1053	D₄	—	536	1	no	—
1054	D₄	—	536	2	no	—
1055	D₄	—	536	2	no	—
1056	D₄	—	536	2	no	—
1057	D₄	—	134	2	no	—
1058	D₄	—	134	2	no	—
1059	D₄	—	134	2	no	—
1060	D₄	C₂×#11761628	1	2	yes	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	8	1	no	—
1076	C₂×C₄	—	8	1	no	—
1077	C₂×C₄	—	268	4	no	—
1078	C₂×C₄	—	536	2	no	—
1079	C₂×C₄	—	536	2	no	—
1080	C₂×C₄	—	536	2	no	—
1081	C₂×C₄	—	67	2	no	—
1082	C₂×C₄	—	67	2	no	—
1083	C₂×C₄	—	67	2	no	—
1084	C₂×C₄	—	134	2	no	—
1085	C₂×C₄	—	134	2	no	—
1086	C₂×C₄	—	134	2	no	—
1087	C₂×C₄	—	134	2	no	—
1088	C₂×C₄	—	134	2	no	—
1089	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1090	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1091	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1092	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1093	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1094	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1095	C₈	—	2	1	no	—
1096	C₈	—	2	1	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	134	2	no	—
1099	C₈	—	134	2	no	—
1100	C₈	C₂×#11761628	1	2	yes	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	268	2	no	—
1111	C₂²	—	268	2	no	—
1112	C₂²	—	268	2	no	—
1113	C₂²	—	1072	4	no	—
1114	C₂²	—	134	2	no	—
1115	C₂²	—	134	2	no	—
1116	C₂²	—	134	2	no	—
1117	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	268	2	no	—
1129	C₄	—	268	2	no	—
1130	C₄	—	268	2	no	—
1131	C₄	—	134	2	no	—
1132	C₄	—	134	2	no	—
1133	C₄	—	134	2	no	—
1134	C₄	#16864203	1	2	yes	—
1135	C₄	C₂²×#11761628	1	1	yes	characteristic
1136	C₄	#16864232	1	1	yes	characteristic
1137	C₂	—	4	1	no	—
1138	C₂	—	4	2	no	—
1139	C₂	—	8	1	no	—
1140	C₂	—	268	2	no	—
1141	C₂	—	536	2	no	—
1142	C₂	D₄×#11761628	1	1	yes	characteristic
1143	C₂	C₂×#16864203	1	1	yes	characteristic
1144	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	C₄×#135×C₆₇	C₂
socle	C₂²×C₆₇	C₂³×D₄
hypercenter	C₄×#135	D₆₇
hypocenter	C₆₇	#61474
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #22574226	C₂	semidirect
2. #22574170	C₂	semidirect
3. #22573203	C₂	semidirect
4. SD₁₆×Dic₁₃₄	C₂	semidirect
5. #22573021	C₂	semidirect
6. #22572925	C₂	semidirect
7. #22572624	C₂	semidirect
8. #22572618	C₂	semidirect
9. #22572494	C₂	semidirect
10. #22572453	C₂	semidirect
11. #22572391	C₂	semidirect
12. #22572241	C₂	semidirect
13. #22571910	C₂	semidirect
14. SD₁₆×D₂₆₈	C₂	semidirect
15. #22570822	C₂	semidirect
16. #22570768	C₂	semidirect
17. #22570444	C₂	semidirect
18. #22570389	C₂	semidirect
19. #22570371	C₂	semidirect
20. #22570360	C₂	semidirect
21. #22569184	C₂	semidirect
22. #22569063	C₂	semidirect
23. C₄×#135×C₆₇	C₂	semidirect
26. Q₈×Dic₁₃₄	C₂²	semidirect
29. #16864116	C₂²	semidirect
31. #16864114	C₂²	semidirect
39. #16864053	C₂²	semidirect
45. #16864011	C₂²	semidirect
48. #16863953	C₂²	semidirect
54. #16863872	C₂²	semidirect
56. #16863794	C₂²	semidirect
57. #16863793	C₂²	semidirect
58. #16863777	C₂²	semidirect
60. #16863757	C₂²	semidirect
61. #16863754	C₂²	semidirect
62. #16863747	C₂²	semidirect
64. #16863739	C₂²	semidirect
65. #16863737	C₂²	semidirect
66. #16863735	C₂²	semidirect
68. #16863720	C₂²	semidirect
69. #16863719	C₂²	semidirect
70. #16863691	C₂²	semidirect
71. #16863690	C₂²	semidirect
74. #16863681	C₂²	semidirect
75. #16863679	C₂²	semidirect
76. #16863676	C₂²	semidirect
77. #16863675	C₂²	semidirect
78. #16863653	C₂²	semidirect
81. #16863625	C₂²	semidirect
82. #16863625	C₂²	semidirect
83. #16863622	C₂²	semidirect
84. #16863621	C₂²	semidirect
85. #16863620	C₂²	semidirect
86. #16863610	C₂²	semidirect
88. #16863606	C₂²	semidirect
93. #16863550	C₂²	semidirect
95. #16863541	C₂²	semidirect
98. #16863526	C₂²	semidirect
99. C₈×Dic₁₃₄	C₂²	semidirect
100. #16863506	C₂²	semidirect
101. #16863501	C₂²	semidirect
102. #16863499	C₂²	semidirect
104. #16863494	C₂²	semidirect
106. C₄×#11761617	C₂²	semidirect
107. C₄×#11761617	C₂²	semidirect
109. #16863483	C₂²	semidirect
111. #16863467	C₂²	semidirect
113. C₈×C₂²⋊D₆₇	C₂²	semidirect
114. #16863455	C₂²	semidirect
115. #16863453	C₂²	semidirect
116. #16863431	C₂²	semidirect
117. #16863403	C₂²	semidirect
119. #16863350	C₂²	semidirect
122. C₄×#41×C₆₇	C₂²	semidirect
123. C₄×Q₁₆×C₆₇	C₂²	semidirect
124. C₄×Q₁₆×C₆₇	C₂²	semidirect
127. C₄×SD₁₆×C₆₇	C₂²	semidirect
128. C₄×SD₁₆×C₆₇	C₂²	semidirect
131. #427×C₆₇	C₂²	semidirect
133. #416×C₆₇	C₂²	semidirect
134. C₂×C₄×C₈×C₆₇	C₂²	semidirect
420. SD₁₆×C₆₇	#41	semidirect
595. C₄×#135	D₆₇	semidirect
596. C₆₇	#61474	semidirect
631. C₄×#41	C₂×D₆₇	semidirect
682. C₄×Q₁₆	C₂×D₆₇	semidirect
683. C₄×Q₁₆	C₂×D₆₇	semidirect
690. C₄×SD₁₆	C₂×D₆₇	semidirect
691. C₄×SD₁₆	C₂×D₆₇	semidirect
701. #427	C₂×D₆₇	semidirect
705. #416	C₂×D₆₇	semidirect
707. C₂×C₄×C₈	C₂×D₆₇	semidirect
942. SD₁₆	#11761628	semidirect

Maximal subgroups

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

subgroup	index
#22574226	2
#22574170	2
#22573203	2
SD₁₆×Dic₁₃₄	2
#22573021	2
#22572925	2
#22572624	2
#22572618	2
#22572494	2
#22572453	2
#22572391	2
#22572241	2
#22571910	2
SD₁₆×D₂₆₈	2
#22570822	2
#22570768	2
#22570444	2
#22570389	2
#22570371	2
#22570360	2
#22569184	2
#22569063	2
C₄×#135×C₆₇	2
#61474	67