Subgroups — #31734903

Order 17152.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573961	C₂	1	1	yes	maximal, characteristic, complemented
2	#22573944	C₂	1	1	yes	maximal, characteristic
3	#22572831	C₂	1	2	yes	maximal, complemented
4	#22572789	C₂	1	2	yes	maximal, complemented
5	#22572770	C₂	1	2	yes	maximal, complemented
6	#22572765	C₂	1	2	yes	maximal, complemented
7	#22572755	C₂	1	2	yes	maximal, complemented
8	#22572725	C₂	1	2	yes	maximal, complemented
9	#22572695	C₂	1	2	yes	maximal, complemented
10	#22572650	C₂	1	2	yes	maximal, complemented
11	#22570749	C₂	1	1	yes	maximal, characteristic, complemented
12	#22570181	C₂	1	1	yes	maximal, characteristic, complemented
13	#22570170	C₂	1	1	yes	maximal, characteristic, complemented
14	#22570157	C₂	1	1	yes	maximal, characteristic, complemented
15	#22570149	C₂	1	1	yes	maximal, characteristic, complemented
16	#22570054	C₂	1	1	yes	maximal, characteristic, complemented
17	#22570043	C₂	1	1	yes	maximal, characteristic, complemented
18	#22569849	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#16863642	C₂	1	1	yes	maximal, characteristic, complemented
20	#22569067	C₂	1	1	yes	maximal, characteristic, complemented
21	#22568912	C₂	1	1	yes	maximal, characteristic, complemented
22	#22568806	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2911	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#11761617	C₂²	1	1	yes	characteristic
25	C₂×#14524049	C₂²	1	1	yes	characteristic
26	#16864114	C₂²	1	2	yes	complemented
27	#16864109	C₂²	1	2	yes	—
28	#16864101	C₂²	1	2	yes	complemented
29	#16864094	C₂²	1	2	yes	—
30	#16864090	C₂²	1	2	yes	—
31	#16864085	C₂²	1	2	yes	complemented
32	#16864081	C₂²	1	2	yes	complemented
33	#16864079	—	2	2	no	—
34	#16864072	—	2	2	no	—
35	#16864070	—	2	2	no	—
36	#16864047	C₂²	1	2	yes	—
37	#16864036	—	2	2	no	—
38	#16864024	C₂²	1	1	yes	characteristic
39	#16864024	C₂²	1	1	yes	characteristic
40	#16864017	—	2	1	no	—
41	#16864017	—	2	1	no	—
42	#16864008	—	2	1	no	—
43	#16864001	—	2	1	no	—
44	#16863972	C₂²	1	1	yes	characteristic
45	#16863965	C₂²	1	1	yes	characteristic
46	#16863953	—	2	1	no	—
47	#16863946	—	2	1	no	—
48	#16863930	—	2	1	no	—
49	#16863930	—	2	1	no	—
50	#16863907	C₂²	1	1	yes	characteristic
51	C₂×#14524022	C₂²	1	1	yes	characteristic
52	C₂×#14524017	C₂²	1	1	yes	characteristic
53	#16863876	C₂²	1	1	yes	characteristic
54	#16863876	C₂²	1	1	yes	characteristic
55	#16863873	C₂²	1	1	yes	characteristic
56	#16863870	C₂²	1	1	yes	characteristic
57	#16863803	C₂²	1	2	yes	complemented
58	#16863803	C₂²	1	2	yes	complemented
59	#16863800	C₂²	1	2	yes	complemented
60	#16863797	C₂²	1	2	yes	complemented
61	#16863740	C₂²	1	2	yes	complemented
62	#16863739	C₂²	1	2	yes	complemented
63	#16863737	C₂²	1	2	yes	complemented
64	#16863737	C₂²	1	2	yes	complemented
65	#16863733	C₂²	1	2	yes	complemented
66	#16863731	C₂²	1	2	yes	complemented
67	#16863728	C₂²	1	2	yes	complemented
68	#16863726	C₂²	1	2	yes	complemented
69	#16863723	C₂²	1	2	yes	complemented
70	#16863722	C₂²	1	2	yes	complemented
71	#16863720	C₂²	1	2	yes	—
72	#16863720	C₂²	1	2	yes	—
73	#16863716	C₂²	1	2	yes	complemented
74	#16863714	C₂²	1	2	yes	—
75	#16863711	C₂²	1	2	yes	complemented
76	#16863709	C₂²	1	2	yes	—
77	#16863706	C₂²	1	2	yes	complemented
78	#16863702	C₂²	1	2	yes	complemented
79	#16863699	C₂²	1	2	yes	complemented
80	#16863695	C₂²	1	2	yes	complemented
81	#16863690	C₂²	1	2	yes	complemented
82	#16863685	C₂²	1	2	yes	complemented
83	#16863680	C₂²	1	2	yes	complemented
84	#16863675	C₂²	1	2	yes	complemented
85	#16863643	C₂²	1	2	yes	complemented
86	#16863643	C₂²	1	2	yes	complemented
87	#16863642	C₂²	1	2	yes	—
88	#16863642	C₂²	1	2	yes	—
89	#16863642	C₂²	1	2	yes	—
90	#16863642	C₂²	1	2	yes	—
91	#16863626	C₂²	1	2	yes	complemented
92	#16863626	C₂²	1	2	yes	complemented
93	#16863495	C₂²	1	2	yes	complemented
94	#16863495	C₂²	1	2	yes	complemented
95	#16863483	C₂²	1	2	yes	complemented
96	#16863483	C₂²	1	2	yes	complemented
97	#16863472	C₂²	1	2	yes	complemented
98	#16863472	C₂²	1	2	yes	complemented
99	#16863465	C₂²	1	2	yes	complemented
100	#16863465	C₂²	1	2	yes	complemented
101	#16863439	C₂²	1	1	yes	characteristic
102	#16863439	C₂²	1	1	yes	characteristic
103	#16863439	C₂²	1	1	yes	characteristic
104	#16863439	C₂²	1	1	yes	characteristic
105	#16863435	C₂²	1	2	yes	complemented
106	#16863435	C₂²	1	2	yes	complemented
107	#16863433	C₂²	1	2	yes	complemented
108	C₂×#14523977	C₂²	1	1	yes	characteristic
109	#107×D₆₇	C₂²	1	2	yes	complemented
110	#16863422	C₂²	1	1	yes	characteristic
111	#16863404	C₂²	1	1	yes	characteristic
112	#16863404	C₂²	1	1	yes	characteristic
113	#16863400	C₂²	1	1	yes	characteristic
114	#16863400	C₂²	1	1	yes	characteristic
115	C₂×#14523968	C₂²	1	1	yes	characteristic
116	C₂×#14523965	C₂²	1	1	yes	characteristic
117	#16863362	C₂²	1	1	yes	characteristic
118	#16863360	C₂²	1	1	yes	characteristic
119	#16863351	C₂²	1	1	yes	characteristic
120	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
121	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
123	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
126	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	#427×C₆₇	C₂²	1	1	yes	characteristic
132	#427×C₆₇	C₂²	1	1	yes	characteristic
133	#427×C₆₇	C₂²	1	1	yes	characteristic
134	#427×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#11761628	—	2	2	no	—
136	C₂×#11761628	C₂³	1	1	yes	characteristic
137	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
138	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
139	C₂²×C₂²⋊D₆₇	—	2	1	no	—
140	C₂×#11761617	—	2	4	no	—
141	C₂×#11761617	C₂³	1	2	yes	—
142	C₂×#11761617	C₂³	1	2	yes	—
143	#14524049	—	2	4	no	—
144	C₂×#11761612	C₂³	1	1	yes	characteristic
145	C₂×#11761612	C₂³	1	1	yes	characteristic
146	C₂×#11761611	C₂³	1	2	yes	—
147	C₂×C₈×D₆₇	C₂³	1	2	yes	—
148	#14524043	—	2	1	no	—
149	#14524043	—	2	1	no	—
150	#14524043	—	2	1	no	—
151	#14524042	C₂³	1	2	yes	—
152	#14524042	C₂³	1	2	yes	—
153	#14524040	—	2	1	no	—
154	#14524038	—	2	2	no	—
155	#14524038	—	2	2	no	—
156	#14524037	—	2	2	no	—
157	#14524037	—	2	2	no	—
158	#14524036	—	2	2	no	—
159	#14524036	—	2	2	no	—
160	#14524035	—	2	1	no	—
161	#14524035	—	2	1	no	—
162	#14524035	—	2	2	no	—
163	#14524034	C₂³	1	2	yes	—
164	#14524034	C₂³	1	2	yes	—
165	#14524033	—	2	2	no	—
166	#14524033	—	2	2	no	—
167	#14524031	—	2	1	no	—
168	#14524031	—	2	1	no	—
169	#14524031	—	2	2	no	—
170	#14524029	—	2	2	no	—
171	#14524029	—	2	2	no	—
172	#14524028	—	2	2	no	—
173	#14524028	—	2	2	no	—
174	#14524027	—	2	2	no	—
175	#14524026	—	2	2	no	—
176	#14524026	—	2	2	no	—
177	#14524026	D₄	1	2	yes	—
178	#14524025	—	2	2	no	—
179	#14524025	—	2	2	no	—
180	#14524023	C₂³	1	2	yes	—
181	#14524023	C₂³	1	2	yes	—
182	#14524022	—	2	2	no	—
183	#14524022	—	2	1	no	—
184	#14524022	—	2	1	no	—
185	#14524022	D₄	1	1	yes	characteristic
186	#14524022	D₄	1	1	yes	characteristic
187	#14524022	C₂³	1	2	yes	—
188	#14524022	C₂³	1	2	yes	—
189	#14524021	—	2	2	no	—
190	#14524021	—	2	2	no	—
191	#14524020	—	2	2	no	—
192	#14524020	—	2	2	no	—
193	#14524018	C₂³	1	2	yes	—
194	#14524018	C₂³	1	2	yes	—
195	#14524017	—	2	2	no	—
196	#14524017	—	2	1	no	—
197	#14524017	—	2	1	no	—
198	#14524017	D₄	1	1	yes	characteristic
199	#14524017	D₄	1	1	yes	characteristic
200	#14524017	C₂³	1	2	yes	—
201	#14524017	C₂³	1	2	yes	—
202	#14524016	—	2	2	no	—
203	#14524016	—	2	2	no	—
204	#14524013	—	2	2	no	—
205	#14524012	D₄	1	2	yes	—
206	C₄×Dic₁₃₄	—	2	1	no	—
207	C₄×Dic₁₃₄	—	2	1	no	—
208	C₄×Dic₁₃₄	—	2	1	no	—
209	C₄×Dic₁₃₄	—	2	1	no	—
210	C₄×Dic₁₃₄	—	2	2	no	—
211	#14524008	C₂³	1	2	yes	—
212	#14524008	C₂³	1	2	yes	—
213	C₄×D₂₆₈	—	2	1	no	—
214	C₄×D₂₆₈	—	2	1	no	—
215	C₄×D₂₆₈	—	2	1	no	—
216	C₄×D₂₆₈	—	2	1	no	—
217	C₄×D₂₆₈	—	2	2	no	—
218	#14524005	C₂³	1	2	yes	—
219	#14524005	C₂³	1	2	yes	—
220	C₄×C₂²⋊D₆₇	—	2	2	no	—
221	C₄×C₂²⋊D₆₇	—	2	2	no	—
222	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
223	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
224	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
225	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
226	#14524002	—	2	2	no	—
227	#14524002	C₂³	1	1	yes	characteristic
228	#14524001	C₂³	1	2	yes	—
229	#14524001	C₂³	1	2	yes	—
230	#14524000	—	2	2	no	—
231	#14524000	—	2	2	no	—
232	#14523999	—	2	2	no	—
233	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
235	C₂×Dic₆₇⋊C₄	—	2	1	no	—
236	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
237	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
238	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
239	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
240	C₂²⋊C₄×D₆₇	—	2	2	no	—
241	#14523977	C₂³	1	2	yes	—
242	#14523977	C₂³	1	2	yes	—
243	#14523976	C₂³	1	2	yes	—
244	#14523976	C₂³	1	2	yes	—
245	#14523976	C₂³	1	2	yes	—
246	#14523976	C₂³	1	2	yes	—
247	#14523974	C₂³	1	2	yes	—
248	#14523974	C₂³	1	2	yes	—
249	#14523974	C₂³	1	2	yes	—
250	#14523974	C₂³	1	2	yes	—
251	Dic₆₇⋊C₈	C₂³	1	2	yes	—
252	Dic₆₇⋊C₈	C₂³	1	2	yes	—
253	#14523968	C₂³	1	2	yes	—
254	#14523968	C₂³	1	2	yes	—
255	#14523966	C₂³	1	2	yes	—
256	#14523966	C₂³	1	2	yes	—
257	#14523966	C₂³	1	2	yes	—
258	#14523966	C₂³	1	2	yes	—
259	#14523965	C₂³	1	2	yes	—
260	#14523965	C₂³	1	2	yes	—
261	#14523963	C₂³	1	2	yes	—
262	#14523963	C₂³	1	2	yes	—
263	#14523963	C₂³	1	2	yes	—
264	#14523963	C₂³	1	2	yes	—
265	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
266	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
267	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
268	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
269	#14523953	C₂³	1	2	yes	—
270	C₈×Dic₆₇	C₂³	1	2	yes	—
271	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
272	C₂×M₁₆×C₆₇	—	2	4	no	—
273	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
274	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
275	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
276	C₂×M₁₆×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	#117×C₆₇	—	2	1	no	—
280	#117×C₆₇	—	2	1	no	—
281	#117×C₆₇	—	2	1	no	—
282	#117×C₆₇	—	2	1	no	—
283	#117×C₆₇	C₂³	1	1	yes	characteristic
284	#117×C₆₇	C₂³	1	1	yes	characteristic
285	#117×C₆₇	C₂³	1	1	yes	characteristic
286	#117×C₆₇	C₂³	1	1	yes	characteristic
287	#117×C₆₇	C₂³	1	1	yes	characteristic
288	#117×C₆₇	C₂³	1	1	yes	characteristic
289	#117×C₆₇	C₂³	1	1	yes	characteristic
290	#117×C₆₇	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
297	C₂×C₄²×C₆₇	—	2	1	no	—
298	C₂×C₄²×C₆₇	—	2	1	no	—
299	#107×C₆₇	C₂³	1	1	yes	characteristic
300	#107×C₆₇	C₂³	1	1	yes	characteristic
301	#107×C₆₇	C₂³	1	1	yes	characteristic
302	#107×C₆₇	C₂³	1	1	yes	characteristic
303	#107×C₆₇	C₂³	1	1	yes	characteristic
304	#107×C₆₇	C₂³	1	1	yes	characteristic
305	#107×C₆₇	C₂³	1	1	yes	characteristic
306	#107×C₆₇	C₂³	1	1	yes	characteristic
307	#106×C₆₇	C₂³	1	1	yes	characteristic
308	#106×C₆₇	C₂³	1	1	yes	characteristic
309	#106×C₆₇	C₂³	1	1	yes	characteristic
310	#106×C₆₇	C₂³	1	1	yes	characteristic
311	#106×C₆₇	C₂³	1	1	yes	characteristic
312	#106×C₆₇	C₂³	1	1	yes	characteristic
313	#106×C₆₇	C₂³	1	1	yes	characteristic
314	#106×C₆₇	C₂³	1	1	yes	characteristic
315	C₂³×D₆₇	—	2	1	no	—
316	#11761628	—	2	2	no	—
317	#11761628	—	2	2	no	—
318	#11761628	—	8	4	no	—
319	C₂×Dic₁₃₄	—	2	2	no	—
320	C₂×Dic₁₃₄	—	2	2	no	—
321	C₂×Dic₁₃₄	—	2	1	no	—
322	C₂×Dic₁₃₄	—	2	2	no	—
323	C₂×Dic₁₃₄	—	2	2	no	—
324	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
325	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
326	C₂×D₂₆₈	—	2	2	no	—
327	C₂×D₂₆₈	—	2	2	no	—
328	C₂×D₂₆₈	—	2	1	no	—
329	C₂×D₂₆₈	—	2	2	no	—
330	C₂×D₂₆₈	—	2	2	no	—
331	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
332	C₂×D₂₆₈	C₂⁴	1	2	yes	—
333	C₂×C₂²⋊D₆₇	—	2	2	no	—
334	C₂×C₂²⋊D₆₇	—	2	2	no	—
335	C₂×C₂²⋊D₆₇	—	8	2	no	—
336	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
337	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
338	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
339	C₂²×Dic₆₇	—	2	1	no	—
340	C₂²×Dic₆₇	—	2	1	no	—
341	C₂²×Dic₆₇	—	2	1	no	—
342	C₂×C₄×D₆₇	—	2	2	no	—
343	C₂×C₄×D₆₇	—	2	2	no	—
344	C₂×C₄×D₆₇	—	2	2	no	—
345	C₂×C₄×D₆₇	—	2	2	no	—
346	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
347	#11761617	—	2	4	no	—
348	#11761617	—	2	4	no	—
349	#11761612	—	2	2	no	—
350	#11761612	—	2	2	no	—
351	#11761611	—	2	4	no	—
352	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
353	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
354	C₈×D₆₇	—	2	4	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	—	2	2	no	—
360	C₄⋊Dic₆₇	—	2	2	no	—
361	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
362	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
363	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
364	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
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	—	2	2	no	—
370	Dic₆₇⋊C₄	—	2	2	no	—
371	Dic₆₇⋊C₄	—	2	2	no	—
372	Dic₆₇⋊C₄	—	2	2	no	—
373	Dic₆₇⋊C₄	—	2	2	no	—
374	Dic₆₇⋊C₄	—	2	2	no	—
375	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
376	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
377	C₂²⋊Dic₆₇	—	2	2	no	—
378	C₂²⋊Dic₆₇	—	2	2	no	—
379	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
380	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
381	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
390	(C₂×D₆₇)⋊C₄	—	2	2	no	—
391	(C₂×D₆₇)⋊C₄	—	2	2	no	—
392	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
393	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
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	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₆₇	—	2	2	no	—
401	C₂²×C₄×C₆₇	—	2	2	no	—
402	C₂²×C₄×C₆₇	—	2	1	no	—
403	C₂²×C₄×C₆₇	—	2	1	no	—
404	C₂²×C₄×C₆₇	—	2	1	no	—
405	C₂²×C₄×C₆₇	—	2	1	no	—
406	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
407	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
412	M₁₆×C₆₇	—	2	2	no	—
413	M₁₆×C₆₇	—	2	2	no	—
414	M₁₆×C₆₇	—	2	2	no	—
415	M₁₆×C₆₇	—	2	2	no	—
416	C₂×C₈×C₆₇	—	2	2	no	—
417	C₂×C₈×C₆₇	#41	1	4	yes	complemented
418	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
421	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₆₇	—	2	1	no	—
423	C₄⋊C₄×C₆₇	—	2	1	no	—
424	C₄⋊C₄×C₆₇	—	2	1	no	—
425	C₄⋊C₄×C₆₇	—	2	1	no	—
426	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
429	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
430	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
432	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
433	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
434	C₂²⋊C₄×C₆₇	—	2	1	no	—
435	C₂²⋊C₄×C₆₇	—	2	1	no	—
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	—	2	1	no	—
449	C₄²×C₆₇	—	2	1	no	—
450	C₂³×C₆₇	—	2	2	no	—
451	C₂³×C₆₇	—	4	1	no	—
452	C₂³×C₆₇	—	4	1	no	—
453	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
454	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
455	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
456	C₂²×D₆₇	—	2	2	no	—
457	C₂²×D₆₇	—	4	2	no	—
458	C₂²×D₆₇	—	8	1	no	—
459	C₂²×D₆₇	—	8	1	no	—
460	C₂²×D₆₇	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₆₇	—	2	2	no	—
462	C₂×C₄×C₆₇	—	2	2	no	—
463	C₂×C₄×C₆₇	—	2	2	no	—
464	C₂×C₄×C₆₇	—	2	1	no	—
465	C₂×C₄×C₆₇	—	2	1	no	—
466	C₂×C₄×C₆₇	—	2	1	no	—
467	C₂×C₄×C₆₇	—	2	1	no	—
468	C₂×C₄×C₆₇	—	2	1	no	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	1	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	—	4	2	no	—
477	C₂×C₄×C₆₇	—	4	2	no	—
478	C₂×C₄×C₆₇	—	8	1	no	—
479	C₂×C₄×C₆₇	—	8	1	no	—
480	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
484	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
485	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
486	C₂²⋊D₆₇	—	2	4	no	—
487	C₂²⋊D₆₇	—	4	2	no	—
488	C₂²⋊D₆₇	—	4	2	no	—
489	C₂²⋊D₆₇	—	4	4	no	—
490	C₂²⋊D₆₇	—	8	2	no	—
491	C₂×Dic₆₇	—	2	2	no	—
492	C₂×Dic₆₇	—	2	2	no	—
493	C₂×Dic₆₇	—	2	2	no	—
494	C₂×Dic₆₇	—	4	2	no	—
495	C₂×Dic₆₇	—	8	1	no	—
496	C₂×Dic₆₇	—	8	1	no	—
497	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
498	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
499	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
500	D₂₆₈	—	2	2	no	—
501	D₂₆₈	—	2	2	no	—
502	D₂₆₈	—	2	2	no	—
503	D₂₆₈	—	4	2	no	—
504	D₂₆₈	—	8	2	no	—
505	D₂₆₈	—	8	2	no	—
506	C₄×D₆₇	—	2	2	no	—
507	C₄×D₆₇	—	2	2	no	—
508	C₄×D₆₇	—	8	2	no	—
509	C₄×D₆₇	—	8	2	no	—
510	C₄×D₆₇	—	8	2	no	—
511	C₄×D₆₇	—	8	2	no	—
512	Dic₁₃₄	—	2	2	no	—
513	Dic₁₃₄	—	2	2	no	—
514	Dic₁₃₄	—	2	2	no	—
515	Dic₁₃₄	—	4	2	no	—
516	Dic₁₃₄	—	8	2	no	—
517	Dic₁₃₄	—	8	2	no	—
518	C₈×C₆₇	—	2	1	no	—
519	C₈×C₆₇	—	2	1	no	—
520	C₈×C₆₇	C₂×#41	1	2	yes	—
521	C₈×C₆₇	C₂×#41	1	2	yes	—
522	C₆₇⋊C₈	—	2	2	no	—
523	C₆₇⋊C₈	—	2	2	no	—
524	C₂²×C₆₇	—	2	1	no	—
525	C₂²×C₆₇	—	2	1	no	—
526	C₂²×C₆₇	—	2	1	no	—
527	C₂²×C₆₇	—	2	1	no	—
528	C₂²×C₆₇	—	2	1	no	—
529	C₂²×C₆₇	—	2	1	no	—
530	C₂²×C₆₇	—	2	1	no	—
531	C₂²×C₆₇	—	2	1	no	—
532	C₂²×C₆₇	—	8	2	no	—
533	C₂²×C₆₇	#547	1	2	yes	—
534	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
535	C₂×D₆₇	—	2	2	no	—
536	C₂×D₆₇	—	2	2	no	—
537	C₂×D₆₇	—	2	2	no	—
538	C₂×D₆₇	—	4	2	no	—
539	C₂×D₆₇	—	4	2	no	—
540	C₂×D₆₇	—	4	2	no	—
541	C₂×D₆₇	—	16	2	no	—
542	C₄×C₆₇	—	2	1	no	—
543	C₄×C₆₇	—	2	1	no	—
544	C₄×C₆₇	—	4	1	no	—
545	C₄×C₆₇	—	4	1	no	—
546	C₄×C₆₇	—	4	1	no	—
547	C₄×C₆₇	—	4	1	no	—
548	C₄×C₆₇	—	4	1	no	—
549	C₄×C₆₇	—	4	1	no	—
550	C₄×C₆₇	—	4	1	no	—
551	C₄×C₆₇	—	4	1	no	—
552	C₄×C₆₇	#547	1	2	yes	—
553	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
554	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
555	Dic₆₇	—	2	2	no	—
556	Dic₆₇	—	2	2	no	—
557	Dic₆₇	—	2	2	no	—
558	Dic₆₇	—	4	2	no	—
559	Dic₆₇	—	4	2	no	—
560	Dic₆₇	—	4	2	no	—
561	#61268	—	67	1	no	maximal, Sylow
562	C₂×C₆₇	—	2	2	no	—
563	C₂×C₆₇	—	4	1	no	—
564	C₂×C₆₇	—	4	1	no	—
565	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
566	C₂×C₆₇	#3585	1	1	yes	characteristic
567	C₂×C₆₇	#3586	1	1	yes	characteristic
568	D₆₇	—	4	2	no	—
569	D₆₇	—	8	2	no	—
570	#3495	—	67	1	no	—
571	#3494	—	67	1	no	—
572	#3357	—	67	2	no	—
573	#3353	—	67	2	no	—
574	#3351	—	67	2	no	—
575	#3351	—	67	2	no	—
576	#3350	—	67	2	no	—
577	#3348	—	67	2	no	—
578	#3346	—	67	2	no	—
579	#3343	—	67	2	no	—
580	#3164	—	67	1	no	—
581	#3097	—	67	1	no	—
582	#3096	—	67	1	no	—
583	#3095	—	67	1	no	—
584	#3094	—	67	1	no	—
585	#3082	—	67	1	no	—
586	#3081	—	67	1	no	—
587	#3057	—	67	1	no	—
588	C₂×#468	—	67	1	no	—
589	#2949	—	67	1	no	—
590	#2930	—	67	1	no	—
591	#2913	—	67	1	no	—
592	#2911	D₆₇	1	1	yes	characteristic, complemented
593	C₆₇	#61268	1	1	yes	characteristic, complemented, Sylow
594	C₂²×SD₁₆	—	67	1	no	—
595	C₂×#131	—	67	1	no	—
596	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
597	#556	—	67	2	no	—
598	#555	—	67	2	no	—
599	#554	—	67	2	no	—
600	#553	—	67	2	no	—
601	#553	—	67	2	no	—
602	#552	—	67	2	no	—
603	#552	—	67	2	no	—
604	#552	—	134	2	no	—
605	#551	—	134	2	no	—
606	#551	—	134	2	no	—
607	#547	—	67	2	no	—
608	#546	—	134	2	no	—
609	#544	—	67	1	no	—
610	#544	—	67	1	no	—
611	#542	—	134	1	no	—
612	#542	—	134	1	no	—
613	#541	—	134	1	no	—
614	#540	—	134	1	no	—
615	#536	—	67	1	no	—
616	#535	—	67	1	no	—
617	#533	—	134	1	no	—
618	#532	—	134	1	no	—
619	#529	—	134	1	no	—
620	#529	—	134	1	no	—
621	#525	—	67	1	no	—
622	C₂×C₂²⋊Q₈	—	67	1	no	—
623	C₂×#121	—	67	1	no	—
624	#520	—	67	1	no	—
625	#520	—	67	1	no	—
626	#519	—	67	1	no	—
627	#518	—	67	1	no	—
628	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
629	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
630	#501	—	67	2	no	—
631	#501	—	67	2	no	—
632	#500	—	67	2	no	—
633	#499	—	67	2	no	—
634	#485	—	67	2	no	—
635	#485	—	67	2	no	—
636	#485	—	67	2	no	—
637	#485	—	67	2	no	—
638	#484	—	67	2	no	—
639	#484	—	67	2	no	—
640	#483	—	67	2	no	—
641	#483	—	67	2	no	—
642	#482	—	67	2	no	—
643	#482	—	67	2	no	—
644	#482	—	67	2	no	—
645	#482	—	67	2	no	—
646	#481	—	67	2	no	—
647	#481	—	67	2	no	—
648	#480	—	67	2	no	—
649	#480	—	67	2	no	—
650	#479	—	67	2	no	—
651	#479	—	67	2	no	—
652	#478	—	67	2	no	—
653	#478	—	67	2	no	—
654	#477	—	67	2	no	—
655	#476	—	67	2	no	—
656	#475	—	67	2	no	—
657	#474	—	67	2	no	—
658	#468	—	67	2	no	—
659	#468	—	67	2	no	—
660	#468	—	67	2	no	—
661	#468	—	67	2	no	—
662	#468	—	67	2	no	—
663	#468	—	67	2	no	—
664	#465	—	67	2	no	—
665	#465	—	67	2	no	—
666	#440	—	67	2	no	—
667	#440	—	67	2	no	—
668	C₄×SD₁₆	—	67	2	no	—
669	C₄×SD₁₆	—	67	2	no	—
670	#436	—	67	2	no	—
671	#436	—	67	2	no	—
672	#435	—	67	2	no	—
673	#435	—	67	2	no	—
674	#428	—	67	1	no	—
675	#428	—	67	1	no	—
676	#428	—	67	1	no	—
677	#428	—	67	1	no	—
678	#428	—	67	2	no	—
679	#428	—	67	2	no	—
680	#428	C₂×D₆₇	1	1	yes	characteristic, complemented
681	#428	C₂×D₆₇	1	1	yes	characteristic, complemented
682	#428	C₂×D₆₇	1	1	yes	characteristic, complemented
683	#428	C₂×D₆₇	1	1	yes	characteristic, complemented
684	#428	C₂×D₆₇	1	1	yes	characteristic, complemented
685	#428	C₂×D₆₇	1	1	yes	characteristic, complemented
686	#428	C₂×D₆₇	1	1	yes	characteristic, complemented
687	#428	C₂×D₆₇	1	1	yes	characteristic, complemented
688	#427	—	67	2	no	—
689	#427	C₂×D₆₇	1	1	yes	characteristic
690	#427	C₂×D₆₇	1	1	yes	characteristic
691	#427	C₂×D₆₇	1	1	yes	characteristic
692	#427	C₂×D₆₇	1	1	yes	characteristic
693	C₂×#107	—	67	1	no	—
694	C₂×#107	—	67	2	no	—
695	#424	—	67	1	no	—
696	#419	—	67	1	no	—
697	#419	—	67	1	no	—
698	#418	—	67	1	no	—
699	#418	—	67	1	no	—
700	C₂×#103	—	67	1	no	—
701	C₂×#102	—	67	1	no	—
702	#408	—	67	1	no	—
703	#407	—	67	1	no	—
704	#405	—	67	1	no	—
705	C₂×#41	—	67	1	no	—
706	C₂×#41	—	134	2	no	—
707	C₂²×Q₈	—	67	1	no	—
708	C₂²×D₄	—	67	1	no	—
709	C₂²×D₄	—	134	1	no	—
710	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
711	C₂×SD₁₆	—	67	2	no	—
712	C₂×SD₁₆	—	67	2	no	—
713	C₂×SD₁₆	—	134	4	no	—
714	#131	—	134	4	no	—
715	C₂×M₁₆	—	2	4	no	—
716	C₂×M₁₆	—	67	1	no	—
717	C₂×M₁₆	—	67	1	no	—
718	C₂×M₁₆	—	67	2	no	—
719	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
720	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
721	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
722	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
723	C₂²×C₈	—	67	2	no	—
724	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
725	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
726	C₄⋊Q₈	—	67	2	no	—
727	C₄⋊Q₈	—	67	2	no	—
728	C₄⋊Q₈	—	134	1	no	—
729	C₄⋊Q₈	—	134	1	no	—
730	C₄⋊Q₈	—	134	1	no	—
731	#127	—	134	1	no	—
732	#126	—	134	2	no	—
733	#126	—	134	2	no	—
734	#126	—	134	2	no	—
735	#126	—	134	2	no	—
736	#126	—	134	2	no	—
737	#126	—	134	2	no	—
738	#125	—	67	2	no	—
739	#125	—	67	2	no	—
740	#125	—	134	1	no	—
741	#125	—	134	1	no	—
742	#125	—	134	2	no	—
743	#125	—	134	2	no	—
744	#125	—	134	2	no	—
745	#124	—	134	2	no	—
746	#124	—	134	1	no	—
747	#124	—	134	1	no	—
748	#124	—	134	2	no	—
749	#124	—	134	2	no	—
750	#123	—	67	2	no	—
751	#123	—	134	2	no	—
752	#123	—	134	2	no	—
753	#123	—	134	2	no	—
754	#123	—	134	2	no	—
755	#123	—	134	2	no	—
756	#123	—	134	2	no	—
757	#123	—	134	2	no	—
758	C₂²⋊Q₈	—	67	1	no	—
759	C₂²⋊Q₈	—	67	1	no	—
760	C₂²⋊Q₈	—	67	2	no	—
761	C₂²⋊Q₈	—	67	2	no	—
762	C₂²⋊Q₈	—	67	2	no	—
763	C₂²⋊Q₈	—	67	2	no	—
764	C₂²⋊Q₈	—	134	2	no	—
765	C₂²⋊Q₈	—	134	2	no	—
766	C₂²⋊Q₈	—	134	2	no	—
767	C₂²⋊Q₈	—	134	2	no	—
768	C₂²⋊Q₈	—	134	2	no	—
769	C₂²⋊Q₈	—	134	1	no	—
770	C₂²⋊Q₈	—	134	1	no	—
771	#121	—	67	1	no	—
772	#121	—	67	1	no	—
773	#121	—	67	2	no	—
774	#121	—	67	2	no	—
775	#121	—	67	2	no	—
776	#121	—	67	2	no	—
777	#121	—	134	2	no	—
778	#121	—	134	2	no	—
779	#121	—	134	2	no	—
780	#121	—	134	1	no	—
781	#121	—	134	1	no	—
782	#120	—	67	2	no	—
783	#120	—	134	2	no	—
784	C₄×Q₈	—	67	2	no	—
785	C₄×Q₈	—	67	2	no	—
786	C₄×Q₈	—	134	1	no	—
787	C₄×Q₈	—	134	1	no	—
788	C₄×Q₈	—	134	2	no	—
789	C₄×Q₈	—	134	1	no	—
790	C₄×Q₈	—	134	1	no	—
791	C₄×D₄	—	67	2	no	—
792	C₄×D₄	—	67	2	no	—
793	C₄×D₄	—	67	2	no	—
794	C₄×D₄	—	67	2	no	—
795	C₄×D₄	—	134	2	no	—
796	C₄×D₄	—	134	1	no	—
797	C₄×D₄	—	134	1	no	—
798	C₄×D₄	—	134	1	no	—
799	C₄×D₄	—	134	1	no	—
800	C₄×D₄	—	134	2	no	—
801	C₄×D₄	—	134	2	no	—
802	C₄×D₄	—	134	2	no	—
803	C₄×D₄	—	134	2	no	—
804	#117	—	2	1	no	—
805	#117	—	2	1	no	—
806	#117	—	2	1	no	—
807	#117	—	2	1	no	—
808	#117	—	67	1	no	—
809	#117	—	67	2	no	—
810	#117	—	67	2	no	—
811	#117	—	134	2	no	—
812	#117	—	134	2	no	—
813	#117	—	134	2	no	—
814	#117	—	134	2	no	—
815	#117	C₂²×D₆₇	1	1	yes	characteristic
816	#117	C₂²×D₆₇	1	1	yes	characteristic
817	#117	C₂²×D₆₇	1	1	yes	characteristic
818	#117	C₂²×D₆₇	1	1	yes	characteristic
819	#117	C₂²×D₆₇	1	1	yes	characteristic
820	#117	C₂²×D₆₇	1	1	yes	characteristic
821	#117	C₂²×D₆₇	1	1	yes	characteristic
822	#117	C₂²×D₆₇	1	1	yes	characteristic
823	C₂×C₄⋊C₄	—	67	1	no	—
824	C₂×C₄⋊C₄	—	67	1	no	—
825	C₂×C₄⋊C₄	—	67	2	no	—
826	C₂×C₄⋊C₄	—	67	2	no	—
827	C₂×C₄⋊C₄	—	134	1	no	—
828	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
829	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
830	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
831	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
832	C₂×C₂²⋊C₄	—	2	1	no	—
833	C₂×C₂²⋊C₄	—	2	1	no	—
834	C₂×C₂²⋊C₄	—	134	2	no	—
835	C₂×C₂²⋊C₄	—	134	1	no	—
836	C₂×C₂²⋊C₄	—	134	1	no	—
837	C₂×C₄²	—	2	1	no	—
838	C₂×C₄²	—	2	1	no	—
839	#107	—	67	2	no	—
840	#107	—	67	2	no	—
841	#107	—	67	2	no	—
842	#107	—	67	2	no	—
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	#107	C₂²×D₆₇	1	1	yes	characteristic
848	#107	C₂²×D₆₇	1	1	yes	characteristic
849	#107	C₂²×D₆₇	1	1	yes	characteristic
850	#107	C₂²×D₆₇	1	1	yes	characteristic
851	#107	C₂²×D₆₇	1	1	yes	characteristic
852	#107	C₂²×D₆₇	1	1	yes	characteristic
853	#106	—	67	2	no	—
854	#106	—	67	2	no	—
855	#106	—	67	2	no	—
856	#106	—	67	2	no	—
857	#106	C₂²×D₆₇	1	1	yes	characteristic
858	#106	C₂²×D₆₇	1	1	yes	characteristic
859	#106	C₂²×D₆₇	1	1	yes	characteristic
860	#106	C₂²×D₆₇	1	1	yes	characteristic
861	#106	C₂²×D₆₇	1	1	yes	characteristic
862	#106	C₂²×D₆₇	1	1	yes	characteristic
863	#106	C₂²×D₆₇	1	1	yes	characteristic
864	#106	C₂²×D₆₇	1	1	yes	characteristic
865	C₄⋊C₈	—	67	2	no	—
866	C₄⋊C₈	—	67	2	no	—
867	#103	—	67	2	no	—
868	#103	—	67	2	no	—
869	#103	—	67	2	no	—
870	#103	—	67	2	no	—
871	#103	—	67	2	no	—
872	#103	—	67	2	no	—
873	#102	—	67	2	no	—
874	#102	—	67	2	no	—
875	#102	—	67	2	no	—
876	#102	—	67	2	no	—
877	#102	—	67	2	no	—
878	#102	—	67	2	no	—
879	C₂²⋊C₈	—	67	2	no	—
880	C₂²⋊C₈	—	67	2	no	—
881	C₂²⋊C₈	—	67	2	no	—
882	C₂²⋊C₈	—	67	2	no	—
883	#97	—	67	2	no	—
884	C₄×C₈	—	67	2	no	—
885	C₂⁴	—	134	1	no	—
886	C₂⁴	D₄×D₆₇	1	1	yes	characteristic
887	#41	—	536	4	no	—
888	#41	—	134	2	no	—
889	#41	—	134	2	no	—
890	C₂×Q₈	—	67	1	no	—
891	C₂×Q₈	—	67	2	no	—
892	C₂×Q₈	—	134	2	no	—
893	C₂×Q₈	—	134	2	no	—
894	C₂×Q₈	—	134	2	no	—
895	C₂×Q₈	—	134	2	no	—
896	C₂×Q₈	—	134	1	no	—
897	C₂×D₄	—	536	2	no	—
898	C₂×D₄	—	67	2	no	—
899	C₂×D₄	—	67	2	no	—
900	C₂×D₄	—	67	2	no	—
901	C₂×D₄	—	67	1	no	—
902	C₂×D₄	—	67	2	no	—
903	C₂×D₄	—	134	2	no	—
904	C₂×D₄	—	134	2	no	—
905	C₂×D₄	—	134	2	no	—
906	C₂×D₄	—	134	2	no	—
907	C₂×D₄	—	134	1	no	—
908	C₂×D₄	—	134	2	no	—
909	C₂×D₄	—	134	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	67	2	no	—
917	C₂²×C₄	—	134	2	no	—
918	C₂²×C₄	—	134	2	no	—
919	C₂²×C₄	—	134	2	no	—
920	C₂²×C₄	—	134	2	no	—
921	C₂²×C₄	—	134	1	no	—
922	C₂²×C₄	—	134	1	no	—
923	C₂²×C₄	—	134	1	no	—
924	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
925	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
926	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
927	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
928	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
929	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
930	SD₁₆	—	134	4	no	—
931	SD₁₆	—	134	4	no	—
932	M₁₆	—	2	2	no	—
933	M₁₆	—	2	2	no	—
934	M₁₆	—	2	2	no	—
935	M₁₆	—	2	2	no	—
936	M₁₆	—	134	2	no	—
937	M₁₆	—	134	2	no	—
938	M₁₆	—	134	4	no	—
939	C₂×C₈	—	2	2	no	—
940	C₂×C₈	—	67	2	no	—
941	C₂×C₈	—	67	2	no	—
942	C₂×C₈	—	134	4	no	—
943	C₂×C₈	#11761628	1	4	yes	complemented
944	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
945	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
946	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
947	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	67	1	no	—
953	C₄⋊C₄	—	67	1	no	—
954	C₄⋊C₄	—	67	2	no	—
955	C₄⋊C₄	—	67	2	no	—
956	C₄⋊C₄	—	67	2	no	—
957	C₄⋊C₄	—	67	2	no	—
958	C₄⋊C₄	—	134	2	no	—
959	C₄⋊C₄	—	134	2	no	—
960	C₄⋊C₄	—	134	2	no	—
961	C₄⋊C₄	—	134	2	no	—
962	C₄⋊C₄	—	134	2	no	—
963	C₄⋊C₄	—	134	2	no	—
964	C₄⋊C₄	—	134	2	no	—
965	C₄⋊C₄	—	134	2	no	—
966	C₄⋊C₄	—	134	2	no	—
967	C₄⋊C₄	—	134	2	no	—
968	C₄⋊C₄	—	134	2	no	—
969	C₄⋊C₄	—	134	2	no	—
970	C₄⋊C₄	—	134	1	no	—
971	C₄⋊C₄	—	134	1	no	—
972	C₄⋊C₄	—	134	2	no	—
973	C₄⋊C₄	—	134	2	no	—
974	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
975	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
976	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
977	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
978	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	1	no	—
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	—	2	1	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	—	67	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	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	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	C₂³	—	2	2	no	—
1021	C₂³	—	4	1	no	—
1022	C₂³	—	4	1	no	—
1023	C₂³	—	268	2	no	—
1024	C₂³	—	536	1	no	—
1025	C₂³	—	536	1	no	—
1026	C₂³	—	67	2	no	—
1027	C₂³	—	134	2	no	—
1028	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1029	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1030	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1031	Q₈	—	268	2	no	—
1032	Q₈	—	536	2	no	—
1033	Q₈	—	536	2	no	—
1034	Q₈	—	134	2	no	—
1035	Q₈	—	134	2	no	—
1036	Q₈	—	134	2	no	—
1037	D₄	—	268	4	no	—
1038	D₄	—	268	2	no	—
1039	D₄	—	268	2	no	—
1040	D₄	—	268	2	no	—
1041	D₄	—	536	2	no	—
1042	D₄	—	536	2	no	—
1043	D₄	—	536	2	no	—
1044	D₄	—	134	4	no	—
1045	D₄	—	134	2	no	—
1046	D₄	—	134	2	no	—
1047	D₄	—	134	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	4	2	no	—
1064	C₂×C₄	—	4	2	no	—
1065	C₂×C₄	—	8	1	no	—
1066	C₂×C₄	—	8	1	no	—
1067	C₂×C₄	—	268	2	no	—
1068	C₂×C₄	—	536	2	no	—
1069	C₂×C₄	—	536	2	no	—
1070	C₂×C₄	—	536	2	no	—
1071	C₂×C₄	—	536	2	no	—
1072	C₂×C₄	—	536	1	no	—
1073	C₂×C₄	—	536	1	no	—
1074	C₂×C₄	—	67	2	no	—
1075	C₂×C₄	—	67	2	no	—
1076	C₂×C₄	—	67	2	no	—
1077	C₂×C₄	—	134	2	no	—
1078	C₂×C₄	—	134	2	no	—
1079	C₂×C₄	—	134	2	no	—
1080	C₂×C₄	—	134	2	no	—
1081	C₂×C₄	—	134	2	no	—
1082	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1083	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1084	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1085	C₂×C₄	C₂×#11761628	1	2	yes	—
1086	C₂×C₄	#14524091	1	2	yes	—
1087	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	134	2	no	—
1091	C₈	—	134	2	no	—
1092	C₈	C₂×#11761628	1	2	yes	—
1093	C₈	C₂×#11761628	1	2	yes	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	8	2	no	—
1103	C₂²	—	268	2	no	—
1104	C₂²	—	268	2	no	—
1105	C₂²	—	268	2	no	—
1106	C₂²	—	1072	2	no	—
1107	C₂²	—	134	2	no	—
1108	C₂²	—	134	2	no	—
1109	C₂²	—	134	2	no	—
1110	C₂²	#16864047	1	2	yes	—
1111	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1112	C₄	—	2	1	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	268	2	no	—
1123	C₄	—	268	2	no	—
1124	C₄	—	268	2	no	—
1125	C₄	—	134	2	no	—
1126	C₄	—	134	2	no	—
1127	C₄	—	134	2	no	—
1128	C₄	#16864047	1	2	yes	—
1129	C₄	C₂²×#11761628	1	1	yes	characteristic
1130	C₄	C₂×#14524091	1	1	yes	characteristic
1131	C₂	—	2	2	no	—
1132	C₂	—	4	1	no	—
1133	C₂	—	4	1	no	—
1134	C₂	—	268	2	no	—
1135	C₂	—	536	2	no	—
1136	C₂	C₂×#16864047	1	1	yes	characteristic
1137	C₂	#22574986	1	1	yes	characteristic
1138	C₂	#22574993	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×#2911	C₂
socle	C₂²×C₆₇	C₂³×D₄
prime radical	#22573944	C₂
hypercenter	#2911	D₆₇
hypocenter	C₆₇	#61268
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2911

Complements

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

N	H ≅ G/N	type
1. #22573961	C₂	semidirect
3. #22572831	C₂	semidirect
4. #22572789	C₂	semidirect
5. #22572770	C₂	semidirect
6. #22572765	C₂	semidirect
7. #22572755	C₂	semidirect
8. #22572725	C₂	semidirect
9. #22572695	C₂	semidirect
10. #22572650	C₂	semidirect
11. #22570749	C₂	semidirect
12. #22570181	C₂	semidirect
13. #22570170	C₂	semidirect
14. #22570157	C₂	semidirect
15. #22570149	C₂	semidirect
16. #22570054	C₂	semidirect
17. #22570043	C₂	semidirect
18. #22569849	C₂	semidirect
19. C₂×#16863642	C₂	semidirect
20. #22569067	C₂	semidirect
21. #22568912	C₂	semidirect
22. #22568806	C₂	semidirect
23. C₆₇×#2911	C₂	semidirect
26. #16864114	C₂²	semidirect
28. #16864101	C₂²	semidirect
31. #16864085	C₂²	semidirect
32. #16864081	C₂²	semidirect
57. #16863803	C₂²	semidirect
58. #16863803	C₂²	semidirect
59. #16863800	C₂²	semidirect
60. #16863797	C₂²	semidirect
61. #16863740	C₂²	semidirect
62. #16863739	C₂²	semidirect
63. #16863737	C₂²	semidirect
64. #16863737	C₂²	semidirect
65. #16863733	C₂²	semidirect
66. #16863731	C₂²	semidirect
67. #16863728	C₂²	semidirect
68. #16863726	C₂²	semidirect
69. #16863723	C₂²	semidirect
70. #16863722	C₂²	semidirect
73. #16863716	C₂²	semidirect
75. #16863711	C₂²	semidirect
77. #16863706	C₂²	semidirect
78. #16863702	C₂²	semidirect
79. #16863699	C₂²	semidirect
80. #16863695	C₂²	semidirect
81. #16863690	C₂²	semidirect
82. #16863685	C₂²	semidirect
83. #16863680	C₂²	semidirect
84. #16863675	C₂²	semidirect
85. #16863643	C₂²	semidirect
86. #16863643	C₂²	semidirect
91. #16863626	C₂²	semidirect
92. #16863626	C₂²	semidirect
93. #16863495	C₂²	semidirect
94. #16863495	C₂²	semidirect
95. #16863483	C₂²	semidirect
96. #16863483	C₂²	semidirect
97. #16863472	C₂²	semidirect
98. #16863472	C₂²	semidirect
99. #16863465	C₂²	semidirect
100. #16863465	C₂²	semidirect
105. #16863435	C₂²	semidirect
106. #16863435	C₂²	semidirect
107. #16863433	C₂²	semidirect
109. #107×D₆₇	C₂²	semidirect
123. #428×C₆₇	C₂²	semidirect
124. #428×C₆₇	C₂²	semidirect
125. #428×C₆₇	C₂²	semidirect
126. #428×C₆₇	C₂²	semidirect
127. #428×C₆₇	C₂²	semidirect
128. #428×C₆₇	C₂²	semidirect
129. #428×C₆₇	C₂²	semidirect
130. #428×C₆₇	C₂²	semidirect
417. C₂×C₈×C₆₇	#41	semidirect
592. #2911	D₆₇	semidirect
593. C₆₇	#61268	semidirect
680. #428	C₂×D₆₇	semidirect
681. #428	C₂×D₆₇	semidirect
682. #428	C₂×D₆₇	semidirect
683. #428	C₂×D₆₇	semidirect
684. #428	C₂×D₆₇	semidirect
685. #428	C₂×D₆₇	semidirect
686. #428	C₂×D₆₇	semidirect
687. #428	C₂×D₆₇	semidirect
943. C₂×C₈	#11761628	semidirect

Maximal subgroups

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

subgroup	index
#22573961	2
#22573944	2
#22572831	2
#22572789	2
#22572770	2
#22572765	2
#22572755	2
#22572725	2
#22572695	2
#22572650	2
#22570749	2
#22570181	2
#22570170	2
#22570157	2
#22570149	2
#22570054	2
#22570043	2
#22569849	2
C₂×#16863642	2
#22569067	2
#22568912	2
#22568806	2
C₆₇×#2911	2
#61268	67