Subgroups — #31728543

Order 17152.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574030	C₂	1	1	yes	maximal, characteristic, complemented
2	#22573625	C₂	1	1	yes	maximal, characteristic
3	#22571512	C₂	1	2	yes	maximal, complemented
4	#22571497	C₂	1	2	yes	maximal, complemented
5	#22571469	C₂	1	2	yes	maximal, complemented
6	#22571461	C₂	1	2	yes	maximal, complemented
7	#22571454	C₂	1	2	yes	maximal, complemented
8	#22571397	C₂	1	2	yes	maximal, complemented
9	#22571381	C₂	1	2	yes	maximal, complemented
10	#22571344	C₂	1	2	yes	maximal, complemented
11	#22570749	C₂	1	1	yes	maximal, characteristic, complemented
12	#22570741	C₂	1	1	yes	maximal, characteristic, complemented
13	#22570567	C₂	1	1	yes	maximal, characteristic, complemented
14	#22570567	C₂	1	1	yes	maximal, characteristic, complemented
15	#22570196	C₂	1	1	yes	maximal, characteristic, complemented
16	#22570185	C₂	1	1	yes	maximal, characteristic, complemented
17	#22570170	C₂	1	1	yes	maximal, characteristic, complemented
18	#22570170	C₂	1	1	yes	maximal, characteristic, complemented
19	#22570031	C₂	1	1	yes	maximal, characteristic, complemented
20	#22570002	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#16863697	C₂	1	1	yes	maximal, characteristic, complemented
22	#22568874	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
24	#16864124	—	2	1	no	—
25	#16864124	—	2	1	no	—
26	#16864106	—	2	1	no	—
27	#16864106	—	2	1	no	—
28	#16864100	—	2	2	no	—
29	#16864100	—	2	2	no	—
30	#16864024	C₂²	1	1	yes	characteristic
31	#16864024	C₂²	1	1	yes	characteristic
32	#16864024	C₂²	1	1	yes	characteristic
33	#16864023	C₂²	1	2	yes	complemented
34	#16864023	C₂²	1	2	yes	complemented
35	#16864018	C₂²	1	2	yes	—
36	#16864017	—	2	1	no	—
37	#16864001	—	2	1	no	—
38	#16863997	C₂²	1	2	yes	—
39	#16863979	—	2	2	no	—
40	#16863974	C₂²	1	1	yes	characteristic
41	#16863965	C₂²	1	1	yes	characteristic
42	#16863960	C₂²	1	1	yes	characteristic
43	#16863952	C₂²	1	2	yes	complemented
44	#16863946	—	2	1	no	—
45	#16863943	C₂²	1	2	yes	—
46	#16863933	C₂²	1	2	yes	—
47	#16863930	—	2	1	no	—
48	C₂×#14524035	C₂²	1	1	yes	characteristic
49	#125×D₆₇	C₂²	1	2	yes	complemented
50	#16863905	—	2	2	no	—
51	#16863876	C₂²	1	1	yes	characteristic
52	#16863876	C₂²	1	1	yes	characteristic
53	C₄×#11761628	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
55	#16863804	C₂²	1	2	yes	complemented
56	#16863804	C₂²	1	2	yes	complemented
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	#16863796	C₂²	1	2	yes	complemented
62	#16863793	C₂²	1	2	yes	complemented
63	#16863759	C₂²	1	2	yes	—
64	#16863759	C₂²	1	2	yes	—
65	#16863757	C₂²	1	2	yes	—
66	#16863757	C₂²	1	2	yes	—
67	#16863752	C₂²	1	2	yes	—
68	#16863752	C₂²	1	2	yes	—
69	#16863741	C₂²	1	2	yes	—
70	#16863741	C₂²	1	2	yes	—
71	#16863736	C₂²	1	2	yes	complemented
72	#16863735	C₂²	1	2	yes	complemented
73	#16863730	C₂²	1	2	yes	complemented
74	#16863725	C₂²	1	2	yes	complemented
75	#16863723	C₂²	1	2	yes	—
76	#16863723	C₂²	1	2	yes	—
77	#16863722	C₂²	1	2	yes	—
78	#16863722	C₂²	1	2	yes	—
79	#16863719	C₂²	1	2	yes	complemented
80	#16863718	C₂²	1	2	yes	complemented
81	#16863716	C₂²	1	2	yes	—
82	#16863716	C₂²	1	2	yes	—
83	#16863713	C₂²	1	2	yes	complemented
84	#16863711	C₂²	1	2	yes	—
85	#16863711	C₂²	1	2	yes	—
86	#16863708	C₂²	1	2	yes	complemented
87	#16863703	C₂²	1	2	yes	complemented
88	#16863703	C₂²	1	2	yes	complemented
89	#16863697	C₂²	1	2	yes	—
90	#16863697	C₂²	1	2	yes	—
91	#16863697	C₂²	1	2	yes	—
92	#16863697	C₂²	1	2	yes	—
93	#16863696	C₂²	1	2	yes	complemented
94	#16863696	C₂²	1	2	yes	complemented
95	#16863693	C₂²	1	2	yes	—
96	#16863693	C₂²	1	2	yes	—
97	#16863683	C₂²	1	2	yes	—
98	#16863673	C₂²	1	2	yes	—
99	#16863456	C₂²	1	2	yes	complemented
100	#16863456	C₂²	1	2	yes	complemented
101	#16863452	C₂²	1	2	yes	complemented
102	#16863448	C₂²	1	2	yes	complemented
103	#16863439	C₂²	1	1	yes	characteristic
104	#16863439	C₂²	1	1	yes	characteristic
105	#16863439	C₂²	1	1	yes	characteristic
106	#16863439	C₂²	1	1	yes	characteristic
107	C₂×#14523977	C₂²	1	1	yes	characteristic
108	C₂×#14523975	C₂²	1	1	yes	characteristic
109	#16863420	C₂²	1	1	yes	characteristic
110	#16863400	C₂²	1	1	yes	characteristic
111	#16863400	C₂²	1	1	yes	characteristic
112	#16863397	C₂²	1	1	yes	characteristic
113	#16863397	C₂²	1	1	yes	characteristic
114	C₂×#14523965	C₂²	1	1	yes	characteristic
115	C₂×#14523965	C₂²	1	1	yes	characteristic
116	#16863362	C₂²	1	1	yes	characteristic
117	#16863362	C₂²	1	1	yes	characteristic
118	#16863351	C₂²	1	1	yes	characteristic
119	#16863351	C₂²	1	1	yes	characteristic
120	#533×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
122	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#478×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#478×C₆₇	C₂²	1	1	yes	characteristic, complemented
126	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	#427×C₆₇	C₂²	1	1	yes	characteristic
131	#427×C₆₇	C₂²	1	1	yes	characteristic
132	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
133	#416×C₆₇	C₂²	1	1	yes	characteristic
134	#416×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#11761628	—	2	2	no	—
136	C₂×#11761628	C₂³	1	1	yes	characteristic
137	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
138	C₂²×C₄×D₆₇	—	2	1	no	—
139	C₂×#11761612	C₂³	1	1	yes	characteristic
140	C₂×#11761612	C₂³	1	1	yes	characteristic
141	#14524043	—	2	1	no	—
142	#14524043	—	2	1	no	—
143	#14524043	—	2	1	no	—
144	#14524042	C₂³	1	2	yes	—
145	#14524042	C₂³	1	2	yes	—
146	#14524042	C₂³	1	2	yes	—
147	#14524041	—	2	2	no	—
148	#14524041	—	2	2	no	—
149	#14524040	—	2	1	no	—
150	#14524039	C₂³	1	2	yes	—
151	#14524038	—	2	2	no	—
152	#14524037	—	2	2	no	—
153	#14524035	—	2	1	no	—
154	#14524035	—	2	1	no	—
155	#14524035	—	2	1	no	—
156	#14524035	—	2	1	no	—
157	#14524035	—	2	1	no	—
158	#14524035	C₂³	1	2	yes	—
159	#14524035	C₂³	1	2	yes	—
160	#14524034	C₂³	1	2	yes	—
161	#14524034	C₂³	1	2	yes	—
162	#14524034	C₂³	1	2	yes	—
163	#14524033	—	2	2	no	—
164	#14524033	—	2	2	no	—
165	#14524033	—	2	2	no	—
166	#14524033	—	2	2	no	—
167	#14524032	C₂³	1	2	yes	—
168	#14524031	—	2	1	no	—
169	#14524031	—	2	2	no	—
170	#14524029	—	2	2	no	—
171	#14524028	—	2	2	no	—
172	#14524028	—	2	2	no	—
173	#14524026	—	2	2	no	—
174	#14524025	—	2	2	no	—
175	#14524022	—	2	1	no	—
176	#14524021	—	2	2	no	—
177	#14524021	—	2	2	no	—
178	#14524021	—	2	2	no	—
179	#14524021	—	2	2	no	—
180	#14524021	—	2	2	no	—
181	#14524020	—	2	2	no	—
182	#14524020	—	2	2	no	—
183	#14524020	—	2	2	no	—
184	#14524019	—	2	2	no	—
185	#14524019	—	2	2	no	—
186	#14524019	C₂³	1	2	yes	—
187	#14524018	C₂³	1	2	yes	—
188	#14524018	C₂³	1	2	yes	—
189	#14524017	—	2	1	no	—
190	#14524017	—	2	1	no	—
191	#14524017	—	2	1	no	—
192	#14524017	—	2	2	no	—
193	#14524016	—	2	2	no	—
194	#14524016	—	2	2	no	—
195	#14524015	—	2	2	no	—
196	#14524014	C₂³	1	2	yes	—
197	#14524013	—	2	2	no	—
198	#14524011	—	2	2	no	—
199	C₄×Dic₁₃₄	—	2	1	no	—
200	C₄×Dic₁₃₄	—	2	1	no	—
201	C₄×Dic₁₃₄	D₄	1	1	yes	characteristic
202	C₄×Dic₁₃₄	D₄	1	1	yes	characteristic
203	#14524008	—	2	2	no	—
204	#14524008	—	2	2	no	—
205	C₄×D₂₆₈	—	2	1	no	—
206	C₄×D₂₆₈	—	2	1	no	—
207	C₄×D₂₆₈	—	2	2	no	—
208	C₄×D₂₆₈	—	2	1	no	—
209	C₄×D₂₆₈	—	2	1	no	—
210	C₄×D₂₆₈	D₄	1	1	yes	characteristic
211	C₄×D₂₆₈	D₄	1	1	yes	characteristic
212	C₄×D₂₆₈	C₂³	1	2	yes	—
213	C₄×D₂₆₈	C₂³	1	2	yes	—
214	C₄×C₂²⋊D₆₇	—	2	2	no	—
215	C₄×C₂²⋊D₆₇	D₄	1	2	yes	—
216	C₄×C₂²⋊D₆₇	D₄	1	2	yes	—
217	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
218	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
219	#14524002	C₂³	1	1	yes	characteristic
220	#14524001	C₂³	1	2	yes	—
221	#14524001	C₂³	1	2	yes	—
222	#14524000	—	2	2	no	—
223	#14524000	C₂³	1	2	yes	—
224	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
227	C₂×Dic₆₇⋊C₄	—	2	1	no	—
228	C₂×Dic₆₇⋊C₄	—	2	1	no	—
229	C₄⋊C₄×D₆₇	—	2	2	no	—
230	C₄⋊C₄×D₆₇	—	2	2	no	—
231	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
232	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
233	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
234	C₄²×D₆₇	C₂³	1	2	yes	—
235	#14523977	C₂³	1	2	yes	—
236	#14523977	C₂³	1	2	yes	—
237	#14523976	C₂³	1	2	yes	—
238	#14523976	C₂³	1	2	yes	—
239	#14523976	C₂³	1	2	yes	—
240	#14523976	C₂³	1	2	yes	—
241	#14523975	C₂³	1	2	yes	—
242	#14523975	C₂³	1	2	yes	—
243	#14523974	C₂³	1	2	yes	—
244	#14523974	C₂³	1	2	yes	—
245	#14523974	C₂³	1	2	yes	—
246	#14523974	C₂³	1	2	yes	—
247	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
248	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
249	#14523967	C₂³	1	2	yes	—
250	#14523967	C₂³	1	2	yes	—
251	#14523965	C₂³	1	2	yes	—
252	#14523965	C₂³	1	2	yes	—
253	#14523965	C₂³	1	2	yes	—
254	#14523965	C₂³	1	2	yes	—
255	#14523964	C₂³	1	2	yes	—
256	#14523964	C₂³	1	2	yes	—
257	#14523963	C₂³	1	2	yes	—
258	#14523963	C₂³	1	2	yes	—
259	#14523963	C₂³	1	2	yes	—
260	#14523963	C₂³	1	2	yes	—
261	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
262	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
263	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
264	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
265	#14523953	C₂³	1	2	yes	—
266	#14523953	C₂³	1	2	yes	—
267	C₈×Dic₆₇	C₂³	1	2	yes	—
268	C₈×Dic₆₇	C₂³	1	2	yes	—
269	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
270	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
272	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
273	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
274	#125×C₆₇	C₂³	1	1	yes	characteristic
275	#125×C₆₇	C₂³	1	1	yes	characteristic
276	C₂²⋊Q₈×C₆₇	—	2	1	no	—
277	C₂²⋊Q₈×C₆₇	—	2	1	no	—
278	C₄×Q₈×C₆₇	—	2	1	no	—
279	C₄×Q₈×C₆₇	—	2	1	no	—
280	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₄×D₄×C₆₇	—	2	1	no	—
283	C₄×D₄×C₆₇	—	2	1	no	—
284	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
285	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
286	#117×C₆₇	—	2	1	no	—
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	C₂×C₄²×C₆₇	—	2	1	no	—
291	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
292	#107×C₆₇	C₂³	1	1	yes	characteristic
293	#107×C₆₇	C₂³	1	1	yes	characteristic
294	#107×C₆₇	C₂³	1	1	yes	characteristic
295	#107×C₆₇	C₂³	1	1	yes	characteristic
296	#106×C₆₇	C₂³	1	1	yes	characteristic
297	#106×C₆₇	C₂³	1	1	yes	characteristic
298	#106×C₆₇	C₂³	1	1	yes	characteristic
299	#106×C₆₇	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×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	C₄⋊C₈×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	#102×C₆₇	C₂³	1	1	yes	characteristic
309	#102×C₆₇	C₂³	1	1	yes	characteristic
310	#102×C₆₇	C₂³	1	1	yes	characteristic
311	#102×C₆₇	C₂³	1	1	yes	characteristic
312	C₂³×D₆₇	—	2	1	no	—
313	#11761628	—	2	2	no	—
314	#11761628	—	2	2	no	—
315	#11761628	—	8	4	no	—
316	C₂×Dic₁₃₄	—	2	2	no	—
317	C₂×Dic₁₃₄	—	2	2	no	—
318	C₂×Dic₁₃₄	—	2	2	no	—
319	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
320	C₂×D₂₆₈	—	2	2	no	—
321	C₂×D₂₆₈	—	2	2	no	—
322	C₂×D₂₆₈	—	2	1	no	—
323	C₂×D₂₆₈	—	2	2	no	—
324	C₂×D₂₆₈	—	2	2	no	—
325	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
326	C₂×D₂₆₈	C₂⁴	1	2	yes	—
327	C₂×C₂²⋊D₆₇	—	2	2	no	—
328	C₂×C₂²⋊D₆₇	—	2	2	no	—
329	C₂×C₂²⋊D₆₇	—	2	2	no	—
330	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
331	C₂²×Dic₆₇	—	2	1	no	—
332	C₂²×Dic₆₇	—	2	1	no	—
333	C₂²×Dic₆₇	—	2	1	no	—
334	C₂×C₄×D₆₇	—	2	2	no	—
335	C₂×C₄×D₆₇	—	2	2	no	—
336	C₂×C₄×D₆₇	—	2	2	no	—
337	C₂×C₄×D₆₇	—	2	2	no	—
338	C₂×C₄×D₆₇	—	8	2	no	—
339	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
340	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
341	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
342	#11761612	—	2	2	no	—
343	#11761612	—	2	2	no	—
344	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
345	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
346	C₄⋊Dic₆₇	—	2	1	no	—
347	C₄⋊Dic₆₇	—	2	1	no	—
348	C₄⋊Dic₆₇	—	2	1	no	—
349	C₄⋊Dic₆₇	—	2	2	no	—
350	C₄⋊Dic₆₇	—	2	2	no	—
351	C₄⋊Dic₆₇	—	2	2	no	—
352	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
353	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
354	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
355	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
356	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
357	Dic₆₇⋊C₄	—	2	2	no	—
358	Dic₆₇⋊C₄	—	2	2	no	—
359	Dic₆₇⋊C₄	—	2	2	no	—
360	Dic₆₇⋊C₄	—	2	2	no	—
361	Dic₆₇⋊C₄	—	2	2	no	—
362	Dic₆₇⋊C₄	—	2	2	no	—
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	—	2	2	no	—
370	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
371	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
372	C₂²⋊Dic₆₇	—	2	2	no	—
373	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
374	(C₂×D₆₇)⋊C₄	—	2	2	no	—
375	(C₂×D₆₇)⋊C₄	—	2	2	no	—
376	(C₂×D₆₇)⋊C₄	—	2	2	no	—
377	(C₂×D₆₇)⋊C₄	—	2	2	no	—
378	(C₂×D₆₇)⋊C₄	—	2	2	no	—
379	(C₂×D₆₇)⋊C₄	—	2	2	no	—
380	(C₂×D₆₇)⋊C₄	—	2	2	no	—
381	(C₂×D₆₇)⋊C₄	—	2	2	no	—
382	(C₂×D₆₇)⋊C₄	—	2	2	no	—
383	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
384	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
385	C₄×Dic₆₇	—	2	2	no	—
386	C₄×Dic₆₇	—	2	2	no	—
387	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
388	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
389	C₄×Dic₆₇	C₂⁴	1	2	yes	—
390	#41×C₆₇	—	2	2	no	—
391	#41×C₆₇	—	2	2	no	—
392	C₂×Q₈×C₆₇	—	2	1	no	—
393	C₂×Q₈×C₆₇	—	2	1	no	—
394	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×D₄×C₆₇	—	2	1	no	—
396	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₆₇	—	2	1	no	—
398	C₂²×C₄×C₆₇	—	2	1	no	—
399	C₂²×C₄×C₆₇	—	2	1	no	—
400	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₆₇	—	2	2	no	—
404	C₂×C₈×C₆₇	—	2	2	no	—
405	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₇	—	2	1	no	—
410	C₄⋊C₄×C₆₇	—	2	1	no	—
411	C₄⋊C₄×C₆₇	—	2	1	no	—
412	C₄⋊C₄×C₆₇	—	2	1	no	—
413	C₄⋊C₄×C₆₇	—	2	1	no	—
414	C₄⋊C₄×C₆₇	—	2	1	no	—
415	C₄⋊C₄×C₆₇	—	2	1	no	—
416	C₄⋊C₄×C₆₇	—	2	1	no	—
417	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
423	C₂²⋊C₄×C₆₇	—	2	1	no	—
424	C₂²⋊C₄×C₆₇	—	2	1	no	—
425	C₂²⋊C₄×C₆₇	—	2	1	no	—
426	C₂²⋊C₄×C₆₇	—	2	1	no	—
427	C₂²⋊C₄×C₆₇	—	2	1	no	—
428	C₄²×C₆₇	—	2	1	no	—
429	C₄²×C₆₇	—	2	1	no	—
430	C₄²×C₆₇	—	2	1	no	—
431	C₄²×C₆₇	—	2	1	no	—
432	C₄²×C₆₇	—	2	1	no	—
433	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₂³×C₆₇	—	2	1	no	—
438	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
439	C₂²×D₆₇	—	2	2	no	—
440	C₂²×D₆₇	—	4	2	no	—
441	C₂²×D₆₇	—	8	1	no	—
442	C₂²×D₆₇	—	8	1	no	—
443	C₂²×D₆₇	C₂²×D₄	1	2	yes	—
444	Q₈×C₆₇	—	2	1	no	—
445	Q₈×C₆₇	—	2	1	no	—
446	Q₈×C₆₇	—	8	1	no	—
447	Q₈×C₆₇	—	8	1	no	—
448	D₄×C₆₇	—	2	1	no	—
449	D₄×C₆₇	—	2	1	no	—
450	D₄×C₆₇	—	4	2	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	2	1	no	—
453	C₂×C₄×C₆₇	—	2	1	no	—
454	C₂×C₄×C₆₇	—	2	1	no	—
455	C₂×C₄×C₆₇	—	2	1	no	—
456	C₂×C₄×C₆₇	—	2	1	no	—
457	C₂×C₄×C₆₇	—	2	1	no	—
458	C₂×C₄×C₆₇	—	4	1	no	—
459	C₂×C₄×C₆₇	—	4	1	no	—
460	C₂×C₄×C₆₇	—	4	2	no	—
461	C₂×C₄×C₆₇	—	4	2	no	—
462	C₂×C₄×C₆₇	—	8	1	no	—
463	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
469	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
470	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
471	C₂²⋊D₆₇	—	2	4	no	—
472	C₂²⋊D₆₇	—	8	2	no	—
473	C₂²⋊D₆₇	—	8	2	no	—
474	C₂²⋊D₆₇	—	8	2	no	—
475	C₂×Dic₆₇	—	2	2	no	—
476	C₂×Dic₆₇	—	2	2	no	—
477	C₂×Dic₆₇	—	2	2	no	—
478	C₂×Dic₆₇	—	8	1	no	—
479	C₂×Dic₆₇	—	8	1	no	—
480	C₂×Dic₆₇	—	8	1	no	—
481	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
482	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
483	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
484	D₂₆₈	—	2	2	no	—
485	D₂₆₈	—	2	2	no	—
486	D₂₆₈	—	2	2	no	—
487	D₂₆₈	—	4	2	no	—
488	D₂₆₈	—	8	2	no	—
489	D₂₆₈	—	8	2	no	—
490	C₄×D₆₇	—	2	2	no	—
491	C₄×D₆₇	—	2	2	no	—
492	C₄×D₆₇	—	4	2	no	—
493	C₄×D₆₇	—	4	2	no	—
494	C₄×D₆₇	—	4	4	no	—
495	C₄×D₆₇	—	8	2	no	—
496	C₄×D₆₇	—	8	2	no	—
497	C₄×D₆₇	—	8	2	no	—
498	Dic₁₃₄	—	2	2	no	—
499	Dic₁₃₄	—	8	2	no	—
500	Dic₁₃₄	—	8	2	no	—
501	Dic₁₃₄	—	8	2	no	—
502	C₈×C₆₇	—	2	1	no	—
503	C₈×C₆₇	—	2	1	no	—
504	C₈×C₆₇	—	2	1	no	—
505	C₈×C₆₇	—	2	1	no	—
506	C₆₇⋊C₈	—	2	2	no	—
507	C₆₇⋊C₈	—	2	2	no	—
508	C₂²×C₆₇	—	2	1	no	—
509	C₂²×C₆₇	—	2	1	no	—
510	C₂²×C₆₇	—	4	1	no	—
511	C₂²×C₆₇	—	4	1	no	—
512	C₂²×C₆₇	—	4	1	no	—
513	C₂²×C₆₇	#536	1	2	yes	—
514	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
515	C₂×D₆₇	—	2	2	no	—
516	C₂×D₆₇	—	2	2	no	—
517	C₂×D₆₇	—	2	2	no	—
518	C₂×D₆₇	—	4	2	no	—
519	C₂×D₆₇	—	4	2	no	—
520	C₂×D₆₇	—	4	2	no	—
521	C₂×D₆₇	—	8	4	no	—
522	C₄×C₆₇	—	2	1	no	—
523	C₄×C₆₇	—	2	1	no	—
524	C₄×C₆₇	—	2	1	no	—
525	C₄×C₆₇	—	2	1	no	—
526	C₄×C₆₇	—	4	1	no	—
527	C₄×C₆₇	—	4	1	no	—
528	C₄×C₆₇	—	4	1	no	—
529	C₄×C₆₇	—	4	1	no	—
530	C₄×C₆₇	—	4	1	no	—
531	C₄×C₆₇	—	4	1	no	—
532	C₄×C₆₇	—	4	1	no	—
533	C₄×C₆₇	#536	1	2	yes	—
534	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
535	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
536	Dic₆₇	—	2	2	no	—
537	Dic₆₇	—	2	2	no	—
538	Dic₆₇	—	2	2	no	—
539	Dic₆₇	—	4	2	no	—
540	Dic₆₇	—	4	2	no	—
541	Dic₆₇	—	4	2	no	—
542	#60890	—	67	1	no	maximal, Sylow
543	C₂×C₆₇	—	2	2	no	—
544	C₂×C₆₇	—	8	1	no	—
545	C₂×C₆₇	C₂×#536	1	1	yes	characteristic
546	C₂×C₆₇	#3584	1	1	yes	characteristic
547	C₂×C₆₇	#3585	1	1	yes	characteristic
548	D₆₇	—	4	2	no	—
549	D₆₇	—	8	2	no	—
550	#3504	—	67	1	no	—
551	#3460	—	67	1	no	—
552	#3244	—	67	2	no	—
553	#3243	—	67	2	no	—
554	#3241	—	67	2	no	—
555	#3241	—	67	2	no	—
556	#3240	—	67	2	no	—
557	#3234	—	67	2	no	—
558	#3232	—	67	2	no	—
559	#3228	—	67	2	no	—
560	#3164	—	67	1	no	—
561	#3163	—	67	1	no	—
562	#3136	—	67	1	no	—
563	#3136	—	67	1	no	—
564	#3099	—	67	1	no	—
565	#3098	—	67	1	no	—
566	#3096	—	67	1	no	—
567	#3096	—	67	1	no	—
568	#3080	—	67	1	no	—
569	#3077	—	67	1	no	—
570	#3076	D₆₇	1	1	yes	characteristic, complemented
571	C₂×#478	—	67	1	no	—
572	#2925	—	67	1	no	—
573	C₆₇	#60890	1	1	yes	characteristic, complemented, Sylow
574	#557	—	134	1	no	—
575	#557	—	134	1	no	—
576	#554	—	134	1	no	—
577	#554	—	134	1	no	—
578	#554	—	134	2	no	—
579	#554	—	134	2	no	—
580	#544	—	67	2	no	—
581	#544	—	67	2	no	—
582	#544	—	67	1	no	—
583	#544	—	67	1	no	—
584	#544	—	67	1	no	—
585	#542	—	67	2	no	—
586	#542	—	134	1	no	—
587	#540	—	67	2	no	—
588	#540	—	134	1	no	—
589	#538	—	134	2	no	—
590	#537	—	67	1	no	—
591	#535	—	67	1	no	—
592	#535	—	67	1	no	—
593	#533	—	67	2	no	—
594	#533	C₂×D₆₇	1	1	yes	characteristic
595	#532	—	67	2	no	—
596	#532	—	134	1	no	—
597	#529	—	67	2	no	—
598	#529	—	134	1	no	—
599	C₂×#125	—	67	2	no	—
600	C₂×#125	—	67	1	no	—
601	#525	—	134	2	no	—
602	#520	—	67	1	no	—
603	#520	—	67	1	no	—
604	C₄×#41	—	67	1	no	—
605	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
606	C₂×C₄×D₄	—	67	1	no	—
607	#501	—	67	2	no	—
608	#501	—	67	2	no	—
609	#501	—	67	2	no	—
610	#501	—	67	2	no	—
611	#500	—	67	2	no	—
612	#499	—	67	2	no	—
613	#499	—	67	2	no	—
614	#498	—	67	2	no	—
615	#490	—	67	2	no	—
616	#490	—	67	2	no	—
617	#489	—	67	2	no	—
618	#489	—	67	2	no	—
619	#488	—	67	2	no	—
620	#488	—	67	2	no	—
621	#486	—	67	2	no	—
622	#486	—	67	2	no	—
623	#485	—	67	2	no	—
624	#485	—	67	2	no	—
625	#484	—	67	2	no	—
626	#483	—	67	2	no	—
627	#482	—	67	2	no	—
628	#482	—	67	2	no	—
629	#482	—	67	2	no	—
630	#482	—	67	2	no	—
631	#482	—	67	2	no	—
632	#482	—	67	2	no	—
633	#481	—	67	2	no	—
634	#481	—	67	2	no	—
635	#481	—	67	2	no	—
636	#480	—	67	2	no	—
637	#480	—	67	2	no	—
638	#480	—	67	2	no	—
639	#479	—	67	2	no	—
640	#479	—	67	2	no	—
641	#479	C₂×D₆₇	1	1	yes	characteristic, complemented
642	#479	C₂×D₆₇	1	1	yes	characteristic, complemented
643	#478	—	67	2	no	—
644	#478	—	67	2	no	—
645	#478	—	67	2	no	—
646	#478	—	67	2	no	—
647	#478	—	67	2	no	—
648	#478	—	67	2	no	—
649	#478	—	67	2	no	—
650	#478	—	67	2	no	—
651	#478	C₂×D₆₇	1	1	yes	characteristic, complemented
652	#478	C₂×D₆₇	1	1	yes	characteristic, complemented
653	#477	C₂×D₆₇	1	1	yes	characteristic, complemented
654	#476	—	67	2	no	—
655	#476	C₂×D₆₇	1	1	yes	characteristic, complemented
656	#475	C₂×D₆₇	1	1	yes	characteristic, complemented
657	#474	—	67	2	no	—
658	#474	C₂×D₆₇	1	1	yes	characteristic, complemented
659	#433	—	67	2	no	—
660	#433	—	67	2	no	—
661	#432	—	67	2	no	—
662	#431	—	67	2	no	—
663	#428	—	67	1	no	—
664	#428	—	67	1	no	—
665	#428	—	67	1	no	—
666	#428	—	67	1	no	—
667	#427	C₂×D₆₇	1	1	yes	characteristic
668	#427	C₂×D₆₇	1	1	yes	characteristic
669	C₂×#107	—	67	1	no	—
670	C₂×#106	—	67	1	no	—
671	#423	—	67	1	no	—
672	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
673	#418	—	67	1	no	—
674	#418	—	67	1	no	—
675	#417	—	67	1	no	—
676	#417	—	67	1	no	—
677	#416	C₂×D₆₇	1	1	yes	characteristic
678	#416	C₂×D₆₇	1	1	yes	characteristic
679	C₂×#102	—	67	1	no	—
680	C₂×#102	—	67	1	no	—
681	#408	—	67	1	no	—
682	#408	—	67	1	no	—
683	#405	—	67	1	no	—
684	#405	—	67	1	no	—
685	C₂×#41	—	67	1	no	—
686	C₂×#41	—	134	2	no	—
687	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
688	C₂²×D₄	—	67	1	no	—
689	C₂³×C₄	—	134	1	no	—
690	C₂×M₁₆	—	67	1	no	—
691	C₂×M₁₆	—	67	1	no	—
692	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
693	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
694	C₄⋊Q₈	—	67	2	no	—
695	C₄⋊Q₈	—	67	2	no	—
696	C₄⋊Q₈	—	67	2	no	—
697	C₄⋊Q₈	—	134	1	no	—
698	C₄⋊Q₈	—	134	1	no	—
699	C₄⋊Q₈	—	134	1	no	—
700	C₄⋊Q₈	—	134	2	no	—
701	C₄⋊Q₈	—	134	2	no	—
702	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
703	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
704	#127	—	67	2	no	—
705	#127	—	134	1	no	—
706	#126	—	134	2	no	—
707	#126	—	134	2	no	—
708	#125	—	67	2	no	—
709	#125	—	67	2	no	—
710	#125	—	67	2	no	—
711	#125	—	67	2	no	—
712	#125	—	67	2	no	—
713	#125	—	134	1	no	—
714	#125	—	134	1	no	—
715	#125	—	134	1	no	—
716	#125	—	134	2	no	—
717	#125	—	134	2	no	—
718	#125	—	134	2	no	—
719	#125	—	134	2	no	—
720	#125	—	134	1	no	—
721	#125	—	134	1	no	—
722	#125	C₂²×D₆₇	1	1	yes	characteristic
723	#125	C₂²×D₆₇	1	1	yes	characteristic
724	#124	—	67	2	no	—
725	#124	—	134	2	no	—
726	#124	—	134	1	no	—
727	#124	—	134	2	no	—
728	#123	—	134	2	no	—
729	#123	—	134	2	no	—
730	#123	—	134	2	no	—
731	#123	—	134	2	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	1	no	—
734	C₂²⋊Q₈	—	67	2	no	—
735	C₂²⋊Q₈	—	134	2	no	—
736	C₂²⋊Q₈	—	134	2	no	—
737	C₂²⋊Q₈	—	134	2	no	—
738	C₂²⋊Q₈	—	134	2	no	—
739	C₂²⋊Q₈	—	134	2	no	—
740	C₂²⋊Q₈	—	134	2	no	—
741	C₂²⋊Q₈	—	134	2	no	—
742	C₂²⋊Q₈	—	134	2	no	—
743	C₂²⋊Q₈	—	134	2	no	—
744	C₂²⋊Q₈	—	134	2	no	—
745	C₂²⋊Q₈	—	134	1	no	—
746	#121	—	67	2	no	—
747	#121	—	67	2	no	—
748	#121	—	67	2	no	—
749	#121	—	134	2	no	—
750	#121	—	134	2	no	—
751	#121	—	134	2	no	—
752	#121	—	134	1	no	—
753	#121	—	134	1	no	—
754	#121	—	134	1	no	—
755	#121	—	134	2	no	—
756	#120	—	134	2	no	—
757	#120	—	134	2	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	67	1	no	—
761	C₄×Q₈	—	67	1	no	—
762	C₄×Q₈	—	134	1	no	—
763	C₄×Q₈	—	134	1	no	—
764	C₄×Q₈	—	134	2	no	—
765	C₄×Q₈	—	134	2	no	—
766	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
767	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
768	C₄×D₄	—	2	1	no	—
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	—	67	2	no	—
771	C₄×D₄	—	67	2	no	—
772	C₄×D₄	—	67	1	no	—
773	C₄×D₄	—	67	1	no	—
774	C₄×D₄	—	67	2	no	—
775	C₄×D₄	—	67	2	no	—
776	C₄×D₄	—	134	2	no	—
777	C₄×D₄	—	134	1	no	—
778	C₄×D₄	—	134	1	no	—
779	C₄×D₄	—	134	2	no	—
780	C₄×D₄	—	134	2	no	—
781	C₄×D₄	—	134	2	no	—
782	C₄×D₄	—	134	1	no	—
783	C₄×D₄	—	134	1	no	—
784	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
785	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
786	#117	—	2	1	no	—
787	#117	—	67	1	no	—
788	#117	—	67	2	no	—
789	#117	—	67	2	no	—
790	#117	—	67	2	no	—
791	#117	—	134	2	no	—
792	#117	C₂²×D₆₇	1	1	yes	characteristic
793	#117	C₂²×D₆₇	1	1	yes	characteristic
794	#117	C₂²×D₆₇	1	1	yes	characteristic
795	C₂×C₄⋊C₄	—	67	1	no	—
796	C₂×C₄⋊C₄	—	67	1	no	—
797	C₂×C₄⋊C₄	—	67	1	no	—
798	C₂×C₄⋊C₄	—	67	2	no	—
799	C₂×C₄⋊C₄	—	67	2	no	—
800	C₂×C₄⋊C₄	—	134	2	no	—
801	C₂×C₄⋊C₄	—	134	2	no	—
802	C₂×C₄⋊C₄	—	134	1	no	—
803	C₂×C₄⋊C₄	—	134	1	no	—
804	C₂×C₂²⋊C₄	—	134	1	no	—
805	C₂×C₄²	—	2	1	no	—
806	C₂×C₄²	—	67	2	no	—
807	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
808	#107	—	67	2	no	—
809	#107	—	67	2	no	—
810	#107	—	67	2	no	—
811	#107	—	67	2	no	—
812	#107	—	67	2	no	—
813	#107	—	67	2	no	—
814	#107	C₂²×D₆₇	1	1	yes	characteristic
815	#107	C₂²×D₆₇	1	1	yes	characteristic
816	#107	C₂²×D₆₇	1	1	yes	characteristic
817	#107	C₂²×D₆₇	1	1	yes	characteristic
818	#106	—	67	2	no	—
819	#106	—	67	2	no	—
820	#106	—	67	2	no	—
821	#106	—	67	2	no	—
822	#106	—	67	2	no	—
823	#106	—	67	2	no	—
824	#106	C₂²×D₆₇	1	1	yes	characteristic
825	#106	C₂²×D₆₇	1	1	yes	characteristic
826	#106	C₂²×D₆₇	1	1	yes	characteristic
827	#106	C₂²×D₆₇	1	1	yes	characteristic
828	C₄⋊C₈	—	67	2	no	—
829	C₄⋊C₈	—	67	2	no	—
830	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
831	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
832	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
833	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
834	#103	—	67	2	no	—
835	#103	—	67	2	no	—
836	#103	C₂²×D₆₇	1	1	yes	characteristic
837	#103	C₂²×D₆₇	1	1	yes	characteristic
838	#103	C₂²×D₆₇	1	1	yes	characteristic
839	#103	C₂²×D₆₇	1	1	yes	characteristic
840	#102	—	67	2	no	—
841	#102	—	67	2	no	—
842	#102	—	67	2	no	—
843	#102	—	67	2	no	—
844	#102	—	67	2	no	—
845	#102	—	67	2	no	—
846	#102	—	67	2	no	—
847	#102	—	67	2	no	—
848	#102	—	67	2	no	—
849	#102	—	67	2	no	—
850	#102	C₂²×D₆₇	1	1	yes	characteristic
851	#102	C₂²×D₆₇	1	1	yes	characteristic
852	#102	C₂²×D₆₇	1	1	yes	characteristic
853	#102	C₂²×D₆₇	1	1	yes	characteristic
854	C₂²⋊C₈	—	67	2	no	—
855	C₂²⋊C₈	—	67	2	no	—
856	C₂²⋊C₈	—	67	2	no	—
857	C₂²⋊C₈	—	67	2	no	—
858	#97	—	67	2	no	—
859	#97	—	67	2	no	—
860	C₄×C₈	—	67	2	no	—
861	C₄×C₈	—	67	2	no	—
862	C₂⁴	—	134	1	no	—
863	#41	—	2	2	no	—
864	#41	—	2	2	no	—
865	#41	—	536	4	no	—
866	#41	—	134	2	no	—
867	#41	—	134	2	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	67	1	no	—
871	C₂×Q₈	—	134	2	no	—
872	C₂×Q₈	—	134	2	no	—
873	C₂×Q₈	—	134	2	no	—
874	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	—	67	2	no	—
877	C₂×D₄	—	67	1	no	—
878	C₂×D₄	—	67	2	no	—
879	C₂×D₄	—	134	2	no	—
880	C₂×D₄	—	134	2	no	—
881	C₂×D₄	—	134	2	no	—
882	C₂×D₄	—	134	2	no	—
883	C₂×D₄	—	134	2	no	—
884	C₂×D₄	—	134	1	no	—
885	C₂×D₄	—	134	2	no	—
886	C₂×D₄	—	134	2	no	—
887	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	1	no	—
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	536	2	no	—
892	C₂²×C₄	—	67	2	no	—
893	C₂²×C₄	—	67	2	no	—
894	C₂²×C₄	—	67	2	no	—
895	C₂²×C₄	—	134	2	no	—
896	C₂²×C₄	—	134	2	no	—
897	C₂²×C₄	—	134	2	no	—
898	C₂²×C₄	—	134	1	no	—
899	C₂²×C₄	—	134	1	no	—
900	C₂²×C₄	—	134	1	no	—
901	C₂²×C₄	—	134	2	no	—
902	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
903	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
904	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
905	M₁₆	—	134	2	no	—
906	M₁₆	—	134	2	no	—
907	C₂×C₈	—	2	2	no	—
908	C₂×C₈	—	2	2	no	—
909	C₂×C₈	—	67	2	no	—
910	C₂×C₈	—	67	2	no	—
911	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
912	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
913	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
914	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	67	1	no	—
924	C₄⋊C₄	—	67	1	no	—
925	C₄⋊C₄	—	67	2	no	—
926	C₄⋊C₄	—	67	2	no	—
927	C₄⋊C₄	—	67	2	no	—
928	C₄⋊C₄	—	67	2	no	—
929	C₄⋊C₄	—	67	2	no	—
930	C₄⋊C₄	—	134	2	no	—
931	C₄⋊C₄	—	134	2	no	—
932	C₄⋊C₄	—	134	2	no	—
933	C₄⋊C₄	—	134	2	no	—
934	C₄⋊C₄	—	134	2	no	—
935	C₄⋊C₄	—	134	2	no	—
936	C₄⋊C₄	—	134	2	no	—
937	C₄⋊C₄	—	134	2	no	—
938	C₄⋊C₄	—	134	2	no	—
939	C₄⋊C₄	—	134	2	no	—
940	C₄⋊C₄	—	134	2	no	—
941	C₄⋊C₄	—	134	2	no	—
942	C₄⋊C₄	—	134	1	no	—
943	C₄⋊C₄	—	134	1	no	—
944	C₄⋊C₄	—	134	1	no	—
945	C₄⋊C₄	—	134	2	no	—
946	C₄⋊C₄	—	134	2	no	—
947	C₄⋊C₄	—	134	2	no	—
948	C₄⋊C₄	—	134	2	no	—
949	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
950	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
951	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
952	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
953	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
954	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	67	2	no	—
961	C₂²⋊C₄	—	67	2	no	—
962	C₂²⋊C₄	—	67	2	no	—
963	C₂²⋊C₄	—	134	2	no	—
964	C₂²⋊C₄	—	134	2	no	—
965	C₂²⋊C₄	—	134	2	no	—
966	C₂²⋊C₄	—	134	2	no	—
967	C₂²⋊C₄	—	134	2	no	—
968	C₂²⋊C₄	—	134	2	no	—
969	C₂²⋊C₄	—	134	2	no	—
970	C₂²⋊C₄	—	134	2	no	—
971	C₂²⋊C₄	—	134	2	no	—
972	C₂²⋊C₄	—	134	2	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	67	2	no	—
979	C₄²	—	67	2	no	—
980	C₄²	—	67	2	no	—
981	C₄²	—	134	2	no	—
982	C₄²	—	134	2	no	—
983	C₄²	D₄×D₆₇	1	1	yes	characteristic
984	C₄²	D₄×D₆₇	1	1	yes	characteristic
985	C₄²	C₂³×D₆₇	1	1	yes	characteristic
986	C₄²	C₂³×D₆₇	1	1	yes	characteristic
987	C₂³	—	2	1	no	—
988	C₂³	—	268	2	no	—
989	C₂³	—	536	1	no	—
990	C₂³	—	536	1	no	—
991	C₂³	—	67	2	no	—
992	C₂³	—	134	2	no	—
993	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
994	Q₈	—	2	1	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	8	1	no	—
997	Q₈	—	8	1	no	—
998	Q₈	—	536	2	no	—
999	Q₈	—	536	2	no	—
1000	Q₈	—	536	2	no	—
1001	Q₈	—	134	2	no	—
1002	D₄	—	2	1	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	4	2	no	—
1005	D₄	—	268	2	no	—
1006	D₄	—	536	2	no	—
1007	D₄	—	536	2	no	—
1008	D₄	—	536	2	no	—
1009	D₄	—	536	2	no	—
1010	D₄	—	536	2	no	—
1011	D₄	—	134	4	no	—
1012	D₄	—	134	2	no	—
1013	D₄	—	134	2	no	—
1014	D₄	—	134	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	4	1	no	—
1023	C₂×C₄	—	4	1	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	—	4	2	no	—
1026	C₂×C₄	—	8	1	no	—
1027	C₂×C₄	—	268	4	no	—
1028	C₂×C₄	—	268	2	no	—
1029	C₂×C₄	—	268	2	no	—
1030	C₂×C₄	—	536	2	no	—
1031	C₂×C₄	—	536	2	no	—
1032	C₂×C₄	—	536	2	no	—
1033	C₂×C₄	—	536	1	no	—
1034	C₂×C₄	—	536	1	no	—
1035	C₂×C₄	—	536	1	no	—
1036	C₂×C₄	—	67	2	no	—
1037	C₂×C₄	—	67	2	no	—
1038	C₂×C₄	—	67	2	no	—
1039	C₂×C₄	—	134	2	no	—
1040	C₂×C₄	—	134	2	no	—
1041	C₂×C₄	—	134	2	no	—
1042	C₂×C₄	—	134	2	no	—
1043	C₂×C₄	—	134	2	no	—
1044	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1045	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1046	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1047	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1048	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1049	C₂×C₄	#14524090	1	2	yes	—
1050	C₂×C₄	#14524091	1	2	yes	—
1051	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1052	C₈	—	2	1	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	1	no	—
1055	C₈	—	2	1	no	—
1056	C₈	—	134	2	no	—
1057	C₈	—	134	2	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	—	4	1	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	268	2	no	—
1064	C₂²	—	268	2	no	—
1065	C₂²	—	268	2	no	—
1066	C₂²	—	536	4	no	—
1067	C₂²	—	134	2	no	—
1068	C₂²	—	134	2	no	—
1069	C₂²	—	134	2	no	—
1070	C₂²	#16863969	1	2	yes	—
1071	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	1	no	—
1081	C₄	—	4	1	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	268	2	no	—
1084	C₄	—	268	2	no	—
1085	C₄	—	268	2	no	—
1086	C₄	—	134	2	no	—
1087	C₄	—	134	2	no	—
1088	C₄	—	134	2	no	—
1089	C₄	#16863969	1	2	yes	—
1090	C₄	C₂×#14524090	1	1	yes	characteristic
1091	C₄	C₂×#14524091	1	1	yes	characteristic
1092	C₂	—	2	2	no	—
1093	C₂	—	8	1	no	—
1094	C₂	—	268	2	no	—
1095	C₂	—	536	2	no	—
1096	C₂	C₂×#16863969	1	1	yes	characteristic
1097	C₂	#22574978	1	1	yes	characteristic
1098	C₂	#22574986	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×#3076	C₂
socle	C₂²×C₆₇	C₂³×D₄
prime radical	#22573625	C₂
hypercenter	#3076	D₆₇
hypocenter	C₆₇	#60890
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #22574030	C₂	semidirect
3. #22571512	C₂	semidirect
4. #22571497	C₂	semidirect
5. #22571469	C₂	semidirect
6. #22571461	C₂	semidirect
7. #22571454	C₂	semidirect
8. #22571397	C₂	semidirect
9. #22571381	C₂	semidirect
10. #22571344	C₂	semidirect
11. #22570749	C₂	semidirect
12. #22570741	C₂	semidirect
13. #22570567	C₂	semidirect
14. #22570567	C₂	semidirect
15. #22570196	C₂	semidirect
16. #22570185	C₂	semidirect
17. #22570170	C₂	semidirect
18. #22570170	C₂	semidirect
19. #22570031	C₂	semidirect
20. #22570002	C₂	semidirect
21. C₂×#16863697	C₂	semidirect
22. #22568874	C₂	semidirect
23. C₆₇×#3076	C₂	semidirect
33. #16864023	C₂²	semidirect
34. #16864023	C₂²	semidirect
43. #16863952	C₂²	semidirect
49. #125×D₆₇	C₂²	semidirect
55. #16863804	C₂²	semidirect
56. #16863804	C₂²	semidirect
57. #16863803	C₂²	semidirect
58. #16863803	C₂²	semidirect
59. #16863800	C₂²	semidirect
60. #16863797	C₂²	semidirect
61. #16863796	C₂²	semidirect
62. #16863793	C₂²	semidirect
71. #16863736	C₂²	semidirect
72. #16863735	C₂²	semidirect
73. #16863730	C₂²	semidirect
74. #16863725	C₂²	semidirect
79. #16863719	C₂²	semidirect
80. #16863718	C₂²	semidirect
83. #16863713	C₂²	semidirect
86. #16863708	C₂²	semidirect
87. #16863703	C₂²	semidirect
88. #16863703	C₂²	semidirect
93. #16863696	C₂²	semidirect
94. #16863696	C₂²	semidirect
99. #16863456	C₂²	semidirect
100. #16863456	C₂²	semidirect
101. #16863452	C₂²	semidirect
102. #16863448	C₂²	semidirect
122. #479×C₆₇	C₂²	semidirect
123. #479×C₆₇	C₂²	semidirect
124. #478×C₆₇	C₂²	semidirect
125. #478×C₆₇	C₂²	semidirect
126. #477×C₆₇	C₂²	semidirect
127. #476×C₆₇	C₂²	semidirect
128. #475×C₆₇	C₂²	semidirect
129. #474×C₆₇	C₂²	semidirect
570. #3076	D₆₇	semidirect
573. C₆₇	#60890	semidirect
641. #479	C₂×D₆₇	semidirect
642. #479	C₂×D₆₇	semidirect
651. #478	C₂×D₆₇	semidirect
652. #478	C₂×D₆₇	semidirect
653. #477	C₂×D₆₇	semidirect
655. #476	C₂×D₆₇	semidirect
656. #475	C₂×D₆₇	semidirect
658. #474	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574030	2
#22573625	2
#22571512	2
#22571497	2
#22571469	2
#22571461	2
#22571454	2
#22571397	2
#22571381	2
#22571344	2
#22570749	2
#22570741	2
#22570567	2
#22570196	2
#22570185	2
#22570170	2
#22570031	2
#22570002	2
C₂×#16863697	2
#22568874	2
C₆₇×#3076	2
#60890	67