Subgroups — #31723501

Order 17152.

2054 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	#22574030	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#14524089	C₂	1	1	yes	maximal, characteristic
3	#22570069	C₂	1	1	yes	maximal, characteristic, complemented
4	#22570068	C₂	1	2	yes	maximal, complemented
5	#22570058	C₂	1	1	yes	maximal, characteristic, complemented
6	#22570057	C₂	1	2	yes	maximal, complemented
7	#22570043	C₂	1	1	yes	maximal, characteristic, complemented
8	#22570043	C₂	1	1	yes	maximal, characteristic, complemented
9	#22570035	C₂	1	2	yes	maximal, complemented
10	#22570033	C₂	1	2	yes	maximal, complemented
11	#22570031	C₂	1	1	yes	maximal, characteristic, complemented
12	#22570028	C₂	1	2	yes	maximal, complemented
13	#22570004	C₂	1	2	yes	maximal, complemented
14	#22570002	C₂	1	1	yes	maximal, characteristic, complemented
15	#22569996	C₂	1	2	yes	maximal, complemented
16	C₂×#16863697	C₂	1	1	yes	maximal, characteristic, complemented
17	#478×D₆₇	C₂	1	2	yes	maximal, complemented
18	#22568806	C₂	1	1	yes	maximal, characteristic, complemented
19	#22568801	C₂	1	1	yes	maximal, characteristic, complemented
20	#22568774	C₂	1	1	yes	maximal, characteristic, complemented
21	#22568731	C₂	1	1	yes	maximal, characteristic
22	#22568731	C₂	1	1	yes	maximal, characteristic
23	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14524089	C₂²	1	1	yes	characteristic
25	C₂×#14524049	C₂²	1	1	yes	characteristic
26	C₂×#14524049	C₂²	1	1	yes	characteristic
27	#16864124	—	2	1	no	—
28	#16864124	—	2	1	no	—
29	#16864106	—	2	1	no	—
30	#16864106	—	2	1	no	—
31	#16864100	—	2	2	no	—
32	#16864100	—	2	2	no	—
33	#16864024	C₂²	1	1	yes	characteristic, complemented
34	#16864024	C₂²	1	1	yes	characteristic, complemented
35	#16864023	C₂²	1	2	yes	complemented
36	#16864023	C₂²	1	2	yes	complemented
37	#16863952	C₂²	1	2	yes	complemented
38	C₂×#14524035	C₂²	1	1	yes	characteristic, complemented
39	#125×D₆₇	C₂²	1	2	yes	complemented
40	#16863879	C₂²	1	1	yes	characteristic
41	#16863878	C₂²	1	2	yes	—
42	#16863876	—	2	1	no	—
43	#16863876	C₂²	1	1	yes	characteristic
44	#16863876	C₂²	1	1	yes	characteristic
45	#16863876	C₂²	1	1	yes	characteristic
46	#16863870	—	2	1	no	—
47	#16863870	C₂²	1	1	yes	characteristic
48	#16863868	—	2	2	no	—
49	#16863868	C₂²	1	2	yes	—
50	C₄×#11761629	C₂²	1	2	yes	—
51	C₄×#11761628	—	2	1	no	—
52	C₄×#11761628	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₂₆₈	—	2	1	no	—
54	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
55	C₄×D₄×D₆₇	—	2	2	no	—
56	C₄×D₄×D₆₇	C₂²	1	2	yes	—
57	#16863705	C₂²	1	2	yes	complemented
58	#16863703	C₂²	1	2	yes	complemented
59	#16863703	C₂²	1	2	yes	complemented
60	#16863701	C₂²	1	2	yes	complemented
61	#16863699	C₂²	1	2	yes	complemented
62	#16863699	C₂²	1	2	yes	complemented
63	#16863698	C₂²	1	2	yes	complemented
64	#16863697	C₂²	1	2	yes	complemented
65	#16863697	C₂²	1	2	yes	complemented
66	#16863697	C₂²	1	2	yes	complemented
67	#16863697	C₂²	1	2	yes	complemented
68	#16863696	C₂²	1	2	yes	complemented
69	#16863696	C₂²	1	2	yes	complemented
70	#16863695	C₂²	1	2	yes	complemented
71	#16863695	C₂²	1	2	yes	complemented
72	#16863694	C₂²	1	2	yes	complemented
73	#16863693	C₂²	1	2	yes	complemented
74	#16863693	C₂²	1	2	yes	complemented
75	#16863689	C₂²	1	2	yes	complemented
76	#16863685	C₂²	1	2	yes	complemented
77	#16863685	C₂²	1	2	yes	complemented
78	#16863684	C₂²	1	2	yes	complemented
79	#16863683	C₂²	1	2	yes	complemented
80	#16863679	C₂²	1	2	yes	complemented
81	#16863675	C₂²	1	2	yes	complemented
82	#16863675	C₂²	1	2	yes	complemented
83	#16863674	C₂²	1	2	yes	complemented
84	#16863673	C₂²	1	2	yes	complemented
85	#16863439	C₂²	1	1	yes	characteristic, complemented
86	#16863439	C₂²	1	1	yes	characteristic, complemented
87	#16863439	C₂²	1	1	yes	characteristic, complemented
88	#16863439	C₂²	1	1	yes	characteristic, complemented
89	#16863437	C₂²	1	2	yes	complemented
90	#16863437	C₂²	1	2	yes	complemented
91	#16863435	C₂²	1	2	yes	complemented
92	#16863435	C₂²	1	2	yes	complemented
93	#16863433	C₂²	1	2	yes	complemented
94	#16863431	C₂²	1	2	yes	complemented
95	C₂×#14523977	C₂²	1	1	yes	characteristic, complemented
96	#107×D₆₇	C₂²	1	2	yes	complemented
97	C₂×#14523975	C₂²	1	1	yes	characteristic, complemented
98	#106×D₆₇	C₂²	1	2	yes	complemented
99	#16863422	C₂²	1	1	yes	characteristic, complemented
100	#16863422	C₂²	1	1	yes	characteristic, complemented
101	#16863421	C₂²	1	2	yes	complemented
102	#16863421	C₂²	1	2	yes	complemented
103	#16863420	C₂²	1	1	yes	characteristic, complemented
104	#16863418	C₂²	1	2	yes	complemented
105	C₄⋊C₈×D₆₇	C₂²	1	2	yes	complemented
106	#16863400	C₂²	1	1	yes	characteristic
107	#16863400	C₂²	1	1	yes	characteristic
108	#16863399	C₂²	1	2	yes	—
109	#16863399	C₂²	1	2	yes	—
110	#16863397	C₂²	1	1	yes	characteristic
111	#16863397	C₂²	1	1	yes	characteristic
112	#16863396	C₂²	1	2	yes	—
113	#16863396	C₂²	1	2	yes	—
114	#16863391	C₂²	1	2	yes	—
115	#16863391	C₂²	1	2	yes	—
116	C₂×#14523965	C₂²	1	1	yes	characteristic
117	C₂×#14523965	C₂²	1	1	yes	characteristic
118	#102×D₆₇	C₂²	1	2	yes	—
119	#102×D₆₇	C₂²	1	2	yes	—
120	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
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, complemented
131	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#416×C₆₇	C₂²	1	1	yes	characteristic
134	#416×C₆₇	C₂²	1	1	yes	characteristic
135	#14524089	—	2	4	no	—
136	#14524089	Q₈	1	8	yes	complemented
137	C₂×#11761629	C₂³	1	2	yes	—
138	C₂×#11761628	—	2	1	no	—
139	C₂×#11761628	C₂³	1	1	yes	characteristic
140	C₂²×D₂₆₈	—	2	1	no	—
141	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
142	C₂×D₄×D₆₇	—	2	2	no	—
143	C₂×D₄×D₆₇	C₂³	1	2	yes	—
144	C₂²×C₄×D₆₇	—	2	2	no	—
145	C₂²×C₄×D₆₇	—	2	1	no	—
146	#14524049	—	2	4	no	—
147	#14524049	—	2	4	no	—
148	C₂×#11761612	C₂³	1	1	yes	characteristic
149	C₂×#11761612	C₂³	1	1	yes	characteristic
150	C₂×#11761611	C₂³	1	2	yes	—
151	C₂×#11761611	C₂³	1	2	yes	—
152	C₂×C₈×D₆₇	C₂³	1	2	yes	—
153	C₂×C₈×D₆₇	C₂³	1	2	yes	—
154	#14524043	—	2	1	no	—
155	#14524043	—	2	1	no	—
156	#14524042	C₂³	1	2	yes	—
157	#14524042	C₂³	1	2	yes	—
158	#14524041	—	2	2	no	—
159	#14524041	—	2	2	no	—
160	#14524035	—	2	1	no	—
161	#14524035	—	2	1	no	—
162	#14524035	—	2	1	no	—
163	#14524035	—	2	1	no	—
164	#14524035	C₂³	1	2	yes	—
165	#14524035	C₂³	1	2	yes	—
166	#14524034	C₂³	1	2	yes	—
167	#14524034	C₂³	1	2	yes	—
168	#14524033	—	2	2	no	—
169	#14524033	—	2	2	no	—
170	#14524033	—	2	2	no	—
171	#14524033	—	2	2	no	—
172	#14524021	—	2	2	no	—
173	#14524021	—	2	2	no	—
174	#14524021	—	2	2	no	—
175	#14524021	—	2	2	no	—
176	#14524020	—	2	2	no	—
177	#14524020	—	2	2	no	—
178	#14524019	—	2	2	no	—
179	#14524019	—	2	2	no	—
180	Q₈×Dic₆₇	C₂³	1	2	yes	—
181	C₄×Dic₁₃₄	—	2	1	no	—
182	C₄×Dic₁₃₄	—	2	1	no	—
183	C₄×Dic₁₃₄	—	2	1	no	—
184	C₄×Dic₁₃₄	D₄	1	1	yes	characteristic
185	C₄×Dic₁₃₄	D₄	1	1	yes	characteristic
186	#14524008	—	2	2	no	—
187	#14524008	—	2	2	no	—
188	C₄×D₂₆₈	—	2	1	no	—
189	C₄×D₂₆₈	—	2	1	no	—
190	C₄×D₂₆₈	—	2	1	no	—
191	C₄×D₂₆₈	—	2	2	no	—
192	C₄×D₂₆₈	—	2	1	no	—
193	C₄×D₂₆₈	—	2	1	no	—
194	C₄×D₂₆₈	—	2	2	no	—
195	C₄×D₂₆₈	—	2	1	no	—
196	C₄×D₂₆₈	—	2	1	no	—
197	C₄×D₂₆₈	D₄	1	1	yes	characteristic
198	C₄×D₂₆₈	D₄	1	1	yes	characteristic
199	C₄×D₂₆₈	C₂³	1	2	yes	—
200	C₄×D₂₆₈	C₂³	1	2	yes	—
201	D₄×Dic₆₇	—	2	2	no	—
202	D₄×Dic₆₇	C₂³	1	2	yes	—
203	#14524005	—	2	2	no	—
204	#14524005	—	2	2	no	—
205	#14524005	C₂³	1	2	yes	—
206	#14524005	C₂³	1	2	yes	—
207	C₄×C₂²⋊D₆₇	—	2	2	no	—
208	C₄×C₂²⋊D₆₇	—	2	2	no	—
209	C₄×C₂²⋊D₆₇	D₄	1	2	yes	—
210	C₄×C₂²⋊D₆₇	D₄	1	2	yes	—
211	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
212	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
213	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
214	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
215	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
216	#14524002	—	2	1	no	—
217	#14524002	C₂³	1	1	yes	characteristic
218	#14524001	—	2	2	no	—
219	#14524001	C₂³	1	2	yes	—
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	—	2	1	no	—
225	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
228	C₂×Dic₆₇⋊C₄	—	2	1	no	—
229	C₂×Dic₆₇⋊C₄	—	2	1	no	—
230	C₄⋊C₄×D₆₇	—	2	2	no	—
231	C₄⋊C₄×D₆₇	—	2	2	no	—
232	C₄⋊C₄×D₆₇	—	2	2	no	—
233	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
234	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
235	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
236	C₂×(C₂×D₆₇)⋊C₄	—	2	2	no	—
237	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
238	C₂²⋊C₄×D₆₇	—	2	2	no	—
239	C₂²⋊C₄×D₆₇	—	2	2	no	—
240	C₂²⋊C₄×D₆₇	—	2	2	no	—
241	C₄²×D₆₇	—	2	2	no	—
242	C₄²×D₆₇	C₂³	1	2	yes	—
243	#14523977	C₂³	1	2	yes	—
244	#14523977	C₂³	1	2	yes	—
245	#14523976	C₂³	1	2	yes	—
246	#14523976	C₂³	1	2	yes	—
247	#14523976	C₂³	1	2	yes	—
248	#14523976	C₂³	1	2	yes	—
249	#14523975	C₂³	1	2	yes	—
250	#14523975	C₂³	1	2	yes	—
251	#14523974	C₂³	1	2	yes	—
252	#14523974	C₂³	1	2	yes	—
253	#14523974	C₂³	1	2	yes	—
254	#14523974	C₂³	1	2	yes	—
255	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
256	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
257	Dic₆₇⋊C₈	C₂³	1	2	yes	—
258	Dic₆₇⋊C₈	C₂³	1	2	yes	—
259	Dic₆₇⋊C₈	C₂³	1	2	yes	—
260	Dic₆₇⋊C₈	C₂³	1	2	yes	—
261	#14523967	C₂³	1	2	yes	—
262	#14523967	C₂³	1	2	yes	—
263	#14523965	C₂³	1	2	yes	—
264	#14523965	C₂³	1	2	yes	—
265	#14523965	C₂³	1	2	yes	—
266	#14523965	C₂³	1	2	yes	—
267	#14523964	C₂³	1	2	yes	—
268	#14523964	C₂³	1	2	yes	—
269	#14523963	C₂³	1	2	yes	—
270	#14523963	C₂³	1	2	yes	—
271	#14523963	C₂³	1	2	yes	—
272	#14523963	C₂³	1	2	yes	—
273	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
274	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
275	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
276	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
277	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
278	#125×C₆₇	C₂³	1	1	yes	characteristic
279	#125×C₆₇	C₂³	1	1	yes	characteristic
280	C₂²⋊Q₈×C₆₇	—	2	1	no	—
281	C₂²⋊Q₈×C₆₇	—	2	1	no	—
282	C₄×Q₈×C₆₇	—	2	1	no	—
283	C₄×Q₈×C₆₇	—	2	1	no	—
284	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₆₇	—	2	1	no	—
287	C₄×D₄×C₆₇	—	2	1	no	—
288	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
290	#117×C₆₇	—	2	1	no	—
291	#117×C₆₇	C₂³	1	1	yes	characteristic
292	#117×C₆₇	C₂³	1	1	yes	characteristic
293	#117×C₆₇	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₆₇	—	2	1	no	—
295	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
296	#107×C₆₇	C₂³	1	1	yes	characteristic
297	#107×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	#106×C₆₇	C₂³	1	1	yes	characteristic
303	#106×C₆₇	C₂³	1	1	yes	characteristic
304	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
305	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
306	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
307	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
308	#103×C₆₇	C₂³	1	1	yes	characteristic
309	#103×C₆₇	C₂³	1	1	yes	characteristic
310	#103×C₆₇	C₂³	1	1	yes	characteristic
311	#103×C₆₇	C₂³	1	1	yes	characteristic
312	#102×C₆₇	C₂³	1	1	yes	characteristic
313	#102×C₆₇	C₂³	1	1	yes	characteristic
314	#102×C₆₇	C₂³	1	1	yes	characteristic
315	#102×C₆₇	C₂³	1	1	yes	characteristic
316	C₂³×D₆₇	—	2	1	no	—
317	C₂³×D₆₇	—	2	2	no	—
318	#11761629	—	2	4	no	—
319	#11761629	C₂×Q₈	1	8	yes	—
320	#11761628	—	2	8	no	—
321	#11761628	C₂×Q₈	1	4	yes	—
322	#11761628	#41	1	4	yes	—
323	C₂×Dic₁₃₄	—	2	2	no	—
324	C₂×Dic₁₃₄	—	2	2	no	—
325	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
326	C₂×D₂₆₈	—	2	2	no	—
327	C₂×D₂₆₈	—	2	1	no	—
328	C₂×D₂₆₈	—	2	2	no	—
329	C₂×D₂₆₈	—	2	8	no	—
330	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
331	C₂×D₂₆₈	C₂×Q₈	1	4	yes	—
332	C₂×D₂₆₈	C₂⁴	1	2	yes	—
333	C₂×C₂²⋊D₆₇	—	2	2	no	—
334	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
335	D₄×D₆₇	—	2	16	no	—
336	D₄×D₆₇	—	2	4	no	—
337	D₄×D₆₇	C₂×Q₈	1	8	yes	—
338	C₂²×Dic₆₇	—	2	1	no	—
339	C₂²×Dic₆₇	—	2	1	no	—
340	C₂²×Dic₆₇	—	2	1	no	—
341	C₂²×Dic₆₇	—	2	2	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	—	2	2	no	—
347	C₂×C₄×D₆₇	—	2	2	no	—
348	C₂×C₄×D₆₇	—	2	2	no	—
349	C₂×C₄×D₆₇	—	2	2	no	—
350	C₂×C₄×D₆₇	—	8	4	no	—
351	C₂×C₄×D₆₇	—	8	2	no	—
352	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
353	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
354	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
355	#11761612	—	2	2	no	—
356	#11761612	—	2	2	no	—
357	#11761611	—	2	4	no	—
358	#11761611	—	2	4	no	—
359	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
360	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
361	C₈×D₆₇	—	2	4	no	—
362	C₈×D₆₇	—	2	4	no	—
363	C₄⋊Dic₆₇	—	2	1	no	—
364	C₄⋊Dic₆₇	—	2	1	no	—
365	C₄⋊Dic₆₇	—	2	1	no	—
366	C₄⋊Dic₆₇	—	2	2	no	—
367	C₄⋊Dic₆₇	—	2	2	no	—
368	C₄⋊Dic₆₇	—	2	2	no	—
369	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
370	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
371	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
372	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
373	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
374	Dic₆₇⋊C₄	—	2	2	no	—
375	Dic₆₇⋊C₄	—	2	2	no	—
376	Dic₆₇⋊C₄	—	2	2	no	—
377	Dic₆₇⋊C₄	—	2	2	no	—
378	Dic₆₇⋊C₄	—	2	2	no	—
379	Dic₆₇⋊C₄	—	2	2	no	—
380	Dic₆₇⋊C₄	—	2	2	no	—
381	Dic₆₇⋊C₄	—	2	2	no	—
382	Dic₆₇⋊C₄	—	2	2	no	—
383	Dic₆₇⋊C₄	—	2	2	no	—
384	Dic₆₇⋊C₄	—	2	2	no	—
385	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
386	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
387	C₂²⋊Dic₆₇	—	2	2	no	—
388	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
389	(C₂×D₆₇)⋊C₄	—	2	2	no	—
390	(C₂×D₆₇)⋊C₄	—	2	2	no	—
391	(C₂×D₆₇)⋊C₄	—	2	2	no	—
392	(C₂×D₆₇)⋊C₄	—	2	2	no	—
393	(C₂×D₆₇)⋊C₄	—	2	2	no	—
394	(C₂×D₆₇)⋊C₄	—	2	2	no	—
395	(C₂×D₆₇)⋊C₄	—	2	2	no	—
396	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
397	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
398	C₄×Dic₆₇	—	2	2	no	—
399	C₄×Dic₆₇	—	2	2	no	—
400	C₄×Dic₆₇	—	2	2	no	—
401	C₄×Dic₆₇	—	2	2	no	—
402	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
403	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
404	C₄×Dic₆₇	C₂⁴	1	2	yes	—
405	#41×C₆₇	—	2	2	no	—
406	#41×C₆₇	C₂×Q₈	1	4	yes	—
407	C₂×Q₈×C₆₇	—	2	1	no	—
408	C₂×Q₈×C₆₇	—	2	1	no	—
409	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂×D₄×C₆₇	—	2	1	no	—
411	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₆₇	—	2	2	no	—
419	C₂×C₈×C₆₇	—	2	2	no	—
420	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
421	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
423	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₆₇	—	2	1	no	—
425	C₄⋊C₄×C₆₇	—	2	1	no	—
426	C₄⋊C₄×C₆₇	—	2	1	no	—
427	C₄⋊C₄×C₆₇	—	2	1	no	—
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	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	C₂²⋊C₄×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	C₂²×D₄	1	1	yes	characteristic
454	C₂²×D₆₇	—	2	2	no	—
455	C₂²×D₆₇	—	2	4	no	—
456	C₂²×D₆₇	—	2	8	no	—
457	C₂²×D₆₇	—	8	2	no	—
458	C₂²×D₆₇	—	8	2	no	—
459	C₂²×D₆₇	—	8	1	no	—
460	C₂²×D₆₇	—	8	1	no	—
461	C₂²×D₆₇	C₂²×D₄	1	2	yes	—
462	Q₈×C₆₇	—	2	1	no	—
463	Q₈×C₆₇	—	8	1	no	—
464	Q₈×C₆₇	—	8	1	no	—
465	Q₈×C₆₇	C₂²×Q₈	1	2	yes	—
466	D₄×C₆₇	—	2	4	no	—
467	D₄×C₆₇	—	2	1	no	—
468	D₄×C₆₇	C₂²×Q₈	1	2	yes	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	4	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	—	2	1	no	—
477	C₂×C₄×C₆₇	—	4	1	no	—
478	C₂×C₄×C₆₇	—	4	1	no	—
479	C₂×C₄×C₆₇	—	4	2	no	—
480	C₂×C₄×C₆₇	—	8	1	no	—
481	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
487	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
488	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
489	C₂²⋊D₆₇	—	2	8	no	—
490	C₂²⋊D₆₇	C₂²⋊Q₈	1	8	yes	—
491	C₂×Dic₆₇	—	2	2	no	—
492	C₂×Dic₆₇	—	2	2	no	—
493	C₂×Dic₆₇	—	2	2	no	—
494	C₂×Dic₆₇	—	8	2	no	—
495	C₂×Dic₆₇	—	8	1	no	—
496	C₂×Dic₆₇	—	8	1	no	—
497	C₂×Dic₆₇	—	8	1	no	—
498	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
499	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
500	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
501	D₂₆₈	—	2	8	no	—
502	D₂₆₈	—	2	4	no	—
503	D₂₆₈	—	2	2	no	—
504	D₂₆₈	C₂²⋊Q₈	1	4	yes	—
505	D₂₆₈	C₂²×Q₈	1	4	yes	—
506	C₄×D₆₇	—	2	8	no	—
507	C₄×D₆₇	—	4	2	no	—
508	C₄×D₆₇	—	4	2	no	—
509	C₄×D₆₇	—	4	4	no	—
510	C₄×D₆₇	—	8	2	no	—
511	C₄×D₆₇	—	8	2	no	—
512	C₄×D₆₇	—	8	2	no	—
513	C₄×D₆₇	—	8	2	no	—
514	C₄×D₆₇	—	8	2	no	—
515	C₄×D₆₇	—	8	2	no	—
516	C₄×D₆₇	C₂²×Q₈	1	4	yes	—
517	C₄×D₆₇	C₂×#41	1	4	yes	—
518	Dic₁₃₄	—	8	2	no	—
519	Dic₁₃₄	—	8	2	no	—
520	Dic₁₃₄	C₂²⋊Q₈	1	4	yes	—
521	C₈×C₆₇	—	2	1	no	—
522	C₈×C₆₇	—	2	1	no	—
523	C₈×C₆₇	—	2	1	no	—
524	C₈×C₆₇	—	2	1	no	—
525	C₆₇⋊C₈	—	2	2	no	—
526	C₆₇⋊C₈	—	2	2	no	—
527	C₂²×C₆₇	—	2	1	no	—
528	C₂²×C₆₇	—	2	1	no	—
529	C₂²×C₆₇	—	2	2	no	—
530	C₂²×C₆₇	—	4	1	no	—
531	C₂²×C₆₇	—	4	1	no	—
532	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	2	yes	—
533	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
534	C₂×D₆₇	—	2	2	no	—
535	C₂×D₆₇	—	2	2	no	—
536	C₂×D₆₇	—	2	4	no	—
537	C₂×D₆₇	—	4	2	no	—
538	C₂×D₆₇	—	4	2	no	—
539	C₂×D₆₇	—	8	8	no	—
540	C₂×D₆₇	—	8	4	no	—
541	C₂×D₆₇	C₂×C₂²⋊Q₈	1	4	yes	—
542	C₄×C₆₇	—	2	1	no	—
543	C₄×C₆₇	—	2	1	no	—
544	C₄×C₆₇	—	2	1	no	—
545	C₄×C₆₇	—	2	1	no	—
546	C₄×C₆₇	—	2	2	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	—	4	1	no	—
553	C₄×C₆₇	C₂×C₂²⋊Q₈	1	2	yes	—
554	C₄×C₆₇	C₂³×Q₈	1	1	yes	characteristic
555	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
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	Dic₆₇	C₂×C₂²⋊Q₈	1	4	yes	—
562	#60496	—	67	1	no	maximal, Sylow
563	C₂×C₆₇	—	2	2	no	—
564	C₂×C₆₇	—	4	2	no	—
565	C₂×C₆₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
566	C₂×C₆₇	#3584	1	1	yes	characteristic
567	C₂×C₆₇	#3585	1	1	yes	characteristic
568	D₆₇	—	2	4	no	—
569	D₆₇	—	4	4	no	—
570	#3504	—	67	1	no	—
571	C₄×H(5,𝔽₂)	—	67	1	no	—
572	#3084	—	67	2	no	—
573	#3084	—	67	1	no	—
574	#3083	—	67	2	no	—
575	#3083	—	67	1	no	—
576	#3081	—	67	2	no	—
577	#3081	—	67	2	no	—
578	#3081	—	67	1	no	—
579	#3081	—	67	1	no	—
580	#3080	—	67	2	no	—
581	#3080	—	67	1	no	—
582	#3077	—	67	2	no	—
583	#3077	—	67	1	no	—
584	#3076	—	67	2	no	—
585	#3076	D₆₇	1	1	yes	characteristic, complemented
586	C₂×#478	—	67	2	no	—
587	C₂×#478	—	67	1	no	—
588	#2913	—	67	1	no	—
589	#2912	—	67	1	no	—
590	#2906	—	67	1	no	—
591	#2897	—	67	1	no	—
592	#2897	—	67	1	no	—
593	C₆₇	#60496	1	1	yes	characteristic, complemented, Sylow
594	C₂×H(5,𝔽₂)	—	67	1	no	—
595	C₂×#131	—	67	1	no	—
596	C₂×#131	—	67	1	no	—
597	#557	—	134	1	no	—
598	#557	—	134	1	no	—
599	#554	—	134	1	no	—
600	#554	—	134	1	no	—
601	#554	—	134	2	no	—
602	#554	—	134	2	no	—
603	#544	—	67	2	no	—
604	#544	—	67	2	no	—
605	#544	—	67	1	no	—
606	#544	—	67	1	no	—
607	#533	—	67	2	no	—
608	#533	C₂×D₆₇	1	1	yes	characteristic, complemented
609	C₂×#125	—	67	2	no	—
610	C₂×#125	—	67	1	no	—
611	#520	—	67	1	no	—
612	#520	—	67	1	no	—
613	#520	—	67	1	no	—
614	#520	—	67	1	no	—
615	#520	—	67	2	no	—
616	#520	—	134	1	no	—
617	#518	—	67	2	no	—
618	#518	—	67	1	no	—
619	#518	—	134	1	no	—
620	#518	—	134	2	no	—
621	C₄×#41	—	67	1	no	—
622	C₄×#41	—	67	2	no	—
623	C₄×#41	—	134	1	no	—
624	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
625	C₂×C₄×D₄	—	67	2	no	—
626	C₂×C₄×D₄	—	67	1	no	—
627	C₂×C₄×D₄	—	134	1	no	—
628	C₂×C₄×D₄	—	134	2	no	—
629	#479	—	67	2	no	—
630	#479	—	67	2	no	—
631	#479	—	67	2	no	—
632	#479	—	67	2	no	—
633	#479	C₂×D₆₇	1	1	yes	characteristic, complemented
634	#479	C₂×D₆₇	1	1	yes	characteristic, complemented
635	#478	—	67	2	no	—
636	#478	—	67	2	no	—
637	#478	—	67	2	no	—
638	#478	—	67	2	no	—
639	#478	—	67	2	no	—
640	#478	—	67	2	no	—
641	#478	—	67	2	no	—
642	#478	—	67	2	no	—
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	C₂×D₆₇	1	1	yes	characteristic, complemented
650	#478	C₂×D₆₇	1	1	yes	characteristic, complemented
651	#477	—	67	2	no	—
652	#477	C₂×D₆₇	1	1	yes	characteristic, complemented
653	#476	—	67	2	no	—
654	#476	—	67	2	no	—
655	#476	—	67	2	no	—
656	#476	—	67	2	no	—
657	#476	C₂×D₆₇	1	1	yes	characteristic, complemented
658	#475	—	67	2	no	—
659	#475	C₂×D₆₇	1	1	yes	characteristic, complemented
660	#474	—	67	2	no	—
661	#474	—	67	2	no	—
662	#474	—	67	2	no	—
663	#474	—	67	2	no	—
664	#474	C₂×D₆₇	1	1	yes	characteristic, complemented
665	#428	—	67	1	no	—
666	#428	—	67	1	no	—
667	#428	—	67	1	no	—
668	#428	—	67	1	no	—
669	#428	—	67	2	no	—
670	#428	—	67	2	no	—
671	#428	—	67	2	no	—
672	#428	—	67	2	no	—
673	#427	—	67	2	no	—
674	#427	—	67	2	no	—
675	#427	C₂×D₆₇	1	1	yes	characteristic, complemented
676	#427	C₂×D₆₇	1	1	yes	characteristic, complemented
677	C₂×#107	—	67	1	no	—
678	C₂×#107	—	67	2	no	—
679	C₂×#106	—	67	1	no	—
680	C₂×#106	—	67	2	no	—
681	#424	—	67	1	no	—
682	#424	—	67	1	no	—
683	#424	—	67	2	no	—
684	#424	—	67	2	no	—
685	#423	—	67	1	no	—
686	#423	—	67	2	no	—
687	C₂×C₄⋊C₈	—	67	2	no	—
688	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
689	#418	—	67	1	no	—
690	#418	—	67	1	no	—
691	#418	—	67	2	no	—
692	#418	—	67	2	no	—
693	#417	—	67	1	no	—
694	#417	—	67	1	no	—
695	#417	—	67	2	no	—
696	#417	—	67	2	no	—
697	#416	—	67	2	no	—
698	#416	—	67	2	no	—
699	#416	C₂×D₆₇	1	1	yes	characteristic
700	#416	C₂×D₆₇	1	1	yes	characteristic
701	C₂×#102	—	67	1	no	—
702	C₂×#102	—	67	1	no	—
703	C₂×#102	—	67	2	no	—
704	C₂×#102	—	67	2	no	—
705	H(5,𝔽₂)	—	67	8	no	—
706	H(5,𝔽₂)	—	134	4	no	—
707	C₂×#41	—	67	1	no	—
708	C₂×#41	—	67	2	no	—
709	C₂×#41	—	134	1	no	—
710	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
711	C₂²×D₄	—	67	2	no	—
712	C₂²×D₄	—	67	1	no	—
713	C₂²×D₄	—	134	1	no	—
714	C₂²×D₄	—	134	2	no	—
715	C₂³×C₄	—	134	2	no	—
716	C₂³×C₄	—	134	1	no	—
717	#131	—	134	4	no	—
718	#131	—	134	4	no	—
719	C₂×M₁₆	—	67	1	no	—
720	C₂×M₁₆	—	67	1	no	—
721	C₂×M₁₆	—	67	2	no	—
722	C₂×M₁₆	—	67	2	no	—
723	C₂²×C₈	—	67	2	no	—
724	C₂²×C₈	—	67	2	no	—
725	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
726	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
727	C₄⋊Q₈	—	67	2	no	—
728	C₄⋊Q₈	—	67	2	no	—
729	C₄⋊Q₈	—	134	1	no	—
730	C₄⋊Q₈	—	134	1	no	—
731	C₄⋊Q₈	—	134	2	no	—
732	C₄⋊Q₈	—	134	2	no	—
733	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
734	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
735	#125	—	67	2	no	—
736	#125	—	67	2	no	—
737	#125	—	67	2	no	—
738	#125	—	67	2	no	—
739	#125	—	134	1	no	—
740	#125	—	134	1	no	—
741	#125	—	134	2	no	—
742	#125	—	134	2	no	—
743	#125	—	134	2	no	—
744	#125	—	134	2	no	—
745	#125	—	134	1	no	—
746	#125	—	134	1	no	—
747	#125	C₂²×D₆₇	1	1	yes	characteristic
748	#125	C₂²×D₆₇	1	1	yes	characteristic
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	134	2	no	—
752	C₂²⋊Q₈	—	134	2	no	—
753	C₂²⋊Q₈	—	134	2	no	—
754	C₂²⋊Q₈	—	134	2	no	—
755	C₂²⋊Q₈	—	134	2	no	—
756	C₂²⋊Q₈	—	134	2	no	—
757	C₂²⋊Q₈	—	134	2	no	—
758	C₂²⋊Q₈	—	134	2	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	67	1	no	—
762	C₄×Q₈	—	67	1	no	—
763	C₄×Q₈	—	67	2	no	—
764	C₄×Q₈	—	134	1	no	—
765	C₄×Q₈	—	134	1	no	—
766	C₄×Q₈	—	134	1	no	—
767	C₄×Q₈	—	134	2	no	—
768	C₄×Q₈	—	134	2	no	—
769	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
770	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	67	2	no	—
774	C₄×D₄	—	67	2	no	—
775	C₄×D₄	—	67	2	no	—
776	C₄×D₄	—	67	2	no	—
777	C₄×D₄	—	67	2	no	—
778	C₄×D₄	—	67	1	no	—
779	C₄×D₄	—	67	1	no	—
780	C₄×D₄	—	67	2	no	—
781	C₄×D₄	—	67	2	no	—
782	C₄×D₄	—	134	2	no	—
783	C₄×D₄	—	134	1	no	—
784	C₄×D₄	—	134	1	no	—
785	C₄×D₄	—	134	2	no	—
786	C₄×D₄	—	134	1	no	—
787	C₄×D₄	—	134	1	no	—
788	C₄×D₄	—	134	1	no	—
789	C₄×D₄	—	134	2	no	—
790	C₄×D₄	—	134	2	no	—
791	C₄×D₄	—	134	2	no	—
792	C₄×D₄	—	134	2	no	—
793	C₄×D₄	—	134	2	no	—
794	C₄×D₄	—	134	2	no	—
795	C₄×D₄	—	134	2	no	—
796	C₄×D₄	—	134	2	no	—
797	C₄×D₄	—	134	2	no	—
798	C₄×D₄	—	134	2	no	—
799	C₄×D₄	—	134	1	no	—
800	C₄×D₄	—	134	1	no	—
801	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
802	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
803	#117	—	2	1	no	—
804	#117	—	67	1	no	—
805	#117	—	67	2	no	—
806	#117	—	67	2	no	—
807	#117	—	67	2	no	—
808	#117	—	67	2	no	—
809	#117	—	134	2	no	—
810	#117	—	134	2	no	—
811	#117	—	134	1	no	—
812	#117	C₂²×D₆₇	1	1	yes	characteristic
813	#117	C₂²×D₆₇	1	1	yes	characteristic
814	#117	C₂²×D₆₇	1	1	yes	characteristic
815	C₂×C₄⋊C₄	—	67	1	no	—
816	C₂×C₄⋊C₄	—	67	1	no	—
817	C₂×C₄⋊C₄	—	67	1	no	—
818	C₂×C₄⋊C₄	—	67	2	no	—
819	C₂×C₄⋊C₄	—	67	2	no	—
820	C₂×C₄⋊C₄	—	67	2	no	—
821	C₂×C₄⋊C₄	—	134	2	no	—
822	C₂×C₄⋊C₄	—	134	2	no	—
823	C₂×C₄⋊C₄	—	134	2	no	—
824	C₂×C₄⋊C₄	—	134	1	no	—
825	C₂×C₄⋊C₄	—	134	1	no	—
826	C₂×C₄⋊C₄	—	134	1	no	—
827	C₂×C₂²⋊C₄	—	134	2	no	—
828	C₂×C₂²⋊C₄	—	134	2	no	—
829	C₂×C₂²⋊C₄	—	134	2	no	—
830	C₂×C₂²⋊C₄	—	134	2	no	—
831	C₂×C₂²⋊C₄	—	134	1	no	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	—	67	2	no	—
834	C₂×C₄²	—	134	2	no	—
835	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
836	#107	—	67	2	no	—
837	#107	—	67	2	no	—
838	#107	—	67	2	no	—
839	#107	—	67	2	no	—
840	#107	—	67	2	no	—
841	#107	—	67	2	no	—
842	#107	C₂²×D₆₇	1	1	yes	characteristic
843	#107	C₂²×D₆₇	1	1	yes	characteristic
844	#107	C₂²×D₆₇	1	1	yes	characteristic
845	#107	C₂²×D₆₇	1	1	yes	characteristic
846	#106	—	67	2	no	—
847	#106	—	67	2	no	—
848	#106	—	67	2	no	—
849	#106	—	67	2	no	—
850	#106	—	67	2	no	—
851	#106	—	67	2	no	—
852	#106	C₂²×D₆₇	1	1	yes	characteristic
853	#106	C₂²×D₆₇	1	1	yes	characteristic
854	#106	C₂²×D₆₇	1	1	yes	characteristic
855	#106	C₂²×D₆₇	1	1	yes	characteristic
856	C₄⋊C₈	—	67	2	no	—
857	C₄⋊C₈	—	67	2	no	—
858	C₄⋊C₈	—	67	2	no	—
859	C₄⋊C₈	—	67	2	no	—
860	C₄⋊C₈	—	67	2	no	—
861	C₄⋊C₈	—	67	2	no	—
862	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
863	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
864	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
865	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
866	#103	—	67	2	no	—
867	#103	—	67	2	no	—
868	#103	C₂²×D₆₇	1	1	yes	characteristic
869	#103	C₂²×D₆₇	1	1	yes	characteristic
870	#103	C₂²×D₆₇	1	1	yes	characteristic
871	#103	C₂²×D₆₇	1	1	yes	characteristic
872	#102	—	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	#102	—	67	2	no	—
880	#102	—	67	2	no	—
881	#102	—	67	2	no	—
882	#102	C₂²×D₆₇	1	1	yes	characteristic
883	#102	C₂²×D₆₇	1	1	yes	characteristic
884	#102	C₂²×D₆₇	1	1	yes	characteristic
885	#102	C₂²×D₆₇	1	1	yes	characteristic
886	C₂⁴	—	134	2	no	—
887	C₂⁴	—	134	1	no	—
888	#41	—	2	2	no	—
889	#41	—	67	4	no	—
890	#41	—	67	4	no	—
891	#41	—	67	8	no	—
892	#41	—	134	8	no	—
893	#41	—	134	4	no	—
894	#41	Q₈×D₆₇	1	4	yes	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	67	1	no	—
898	C₂×Q₈	—	134	2	no	—
899	C₂×Q₈	—	134	2	no	—
900	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	67	2	no	—
903	C₂×D₄	—	67	8	no	—
904	C₂×D₄	—	67	1	no	—
905	C₂×D₄	—	67	4	no	—
906	C₂×D₄	—	67	2	no	—
907	C₂×D₄	—	134	8	no	—
908	C₂×D₄	—	134	2	no	—
909	C₂×D₄	—	134	4	no	—
910	C₂×D₄	—	134	2	no	—
911	C₂×D₄	—	134	16	no	—
912	C₂×D₄	—	134	1	no	—
913	C₂×D₄	—	134	2	no	—
914	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	536	2	no	—
919	C₂²×C₄	—	536	4	no	—
920	C₂²×C₄	—	67	2	no	—
921	C₂²×C₄	—	67	2	no	—
922	C₂²×C₄	—	67	2	no	—
923	C₂²×C₄	—	134	2	no	—
924	C₂²×C₄	—	134	2	no	—
925	C₂²×C₄	—	134	2	no	—
926	C₂²×C₄	—	134	2	no	—
927	C₂²×C₄	—	134	2	no	—
928	C₂²×C₄	—	134	2	no	—
929	C₂²×C₄	—	134	2	no	—
930	C₂²×C₄	—	134	2	no	—
931	C₂²×C₄	—	134	1	no	—
932	C₂²×C₄	—	134	1	no	—
933	C₂²×C₄	—	134	1	no	—
934	C₂²×C₄	—	134	2	no	—
935	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
936	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
937	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
938	M₁₆	—	134	4	no	—
939	M₁₆	—	134	4	no	—
940	M₁₆	—	134	2	no	—
941	M₁₆	—	134	2	no	—
942	C₂×C₈	—	2	2	no	—
943	C₂×C₈	—	2	2	no	—
944	C₂×C₈	—	67	2	no	—
945	C₂×C₈	—	67	2	no	—
946	C₂×C₈	—	134	4	no	—
947	C₂×C₈	—	134	4	no	—
948	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
949	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
950	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
951	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
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	—	2	1	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	2	no	—
974	C₄⋊C₄	—	134	2	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	—	134	1	no	—
980	C₄⋊C₄	—	134	2	no	—
981	C₄⋊C₄	—	134	2	no	—
982	C₄⋊C₄	—	134	2	no	—
983	C₄⋊C₄	—	134	2	no	—
984	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
986	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
988	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
989	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	67	2	no	—
996	C₂²⋊C₄	—	67	2	no	—
997	C₂²⋊C₄	—	67	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	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	67	2	no	—
1012	C₄²	—	67	2	no	—
1013	C₄²	—	67	2	no	—
1014	C₄²	—	134	2	no	—
1015	C₄²	—	134	2	no	—
1016	C₄²	—	134	2	no	—
1017	C₄²	—	134	2	no	—
1018	C₄²	D₄×D₆₇	1	1	yes	characteristic
1019	C₄²	D₄×D₆₇	1	1	yes	characteristic
1020	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1021	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1022	C₂³	—	2	1	no	—
1023	C₂³	—	536	1	no	—
1024	C₂³	—	536	1	no	—
1025	C₂³	—	536	2	no	—
1026	C₂³	—	536	2	no	—
1027	C₂³	—	67	2	no	—
1028	C₂³	—	134	8	no	—
1029	C₂³	—	134	2	no	—
1030	C₂³	—	134	4	no	—
1031	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1032	Q₈	—	2	1	no	—
1033	Q₈	—	8	1	no	—
1034	Q₈	—	8	1	no	—
1035	Q₈	—	536	2	no	—
1036	Q₈	—	536	2	no	—
1037	Q₈	—	67	4	no	—
1038	Q₈	C₂×Q₈×D₆₇	1	2	yes	—
1039	D₄	—	2	4	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	67	8	no	—
1042	D₄	—	67	4	no	—
1043	D₄	—	67	4	no	—
1044	D₄	—	134	8	no	—
1045	D₄	—	134	8	no	—
1046	D₄	—	134	4	no	—
1047	D₄	—	134	2	no	—
1048	D₄	C₂×Q₈×D₆₇	1	2	yes	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	4	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	—	4	1	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	268	4	no	—
1062	C₂×C₄	—	268	2	no	—
1063	C₂×C₄	—	268	2	no	—
1064	C₂×C₄	—	536	2	no	—
1065	C₂×C₄	—	536	2	no	—
1066	C₂×C₄	—	536	2	no	—
1067	C₂×C₄	—	536	2	no	—
1068	C₂×C₄	—	536	2	no	—
1069	C₂×C₄	—	536	2	no	—
1070	C₂×C₄	—	536	1	no	—
1071	C₂×C₄	—	536	1	no	—
1072	C₂×C₄	—	536	1	no	—
1073	C₂×C₄	—	536	2	no	—
1074	C₂×C₄	—	67	2	no	—
1075	C₂×C₄	—	67	4	no	—
1076	C₂×C₄	—	67	4	no	—
1077	C₂×C₄	—	67	2	no	—
1078	C₂×C₄	—	67	2	no	—
1079	C₂×C₄	—	134	8	no	—
1080	C₂×C₄	—	134	2	no	—
1081	C₂×C₄	—	134	2	no	—
1082	C₂×C₄	—	134	2	no	—
1083	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1084	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1085	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1086	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1087	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1088	C₂×C₄	C₂×Q₈×D₆₇	1	2	yes	—
1089	C₂×C₄	#41×D₆₇	1	2	yes	—
1090	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1091	C₈	—	2	1	no	—
1092	C₈	—	2	1	no	—
1093	C₈	—	2	1	no	—
1094	C₈	—	2	1	no	—
1095	C₈	—	134	2	no	—
1096	C₈	—	134	2	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	268	2	no	—
1103	C₂²	—	268	2	no	—
1104	C₂²	—	536	4	no	—
1105	C₂²	—	536	8	no	—
1106	C₂²	—	67	4	no	—
1107	C₂²	—	134	4	no	—
1108	C₂²	—	134	2	no	—
1109	C₂²	—	134	2	no	—
1110	C₂²	C₂²⋊Q₈×D₆₇	1	2	yes	—
1111	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1112	C₄	—	2	2	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	2	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	—	4	1	no	—
1123	C₄	—	268	2	no	—
1124	C₄	—	268	2	no	—
1125	C₄	—	268	2	no	—
1126	C₄	—	67	4	no	—
1127	C₄	—	134	2	no	—
1128	C₄	—	134	2	no	—
1129	C₄	C₂²⋊Q₈×D₆₇	1	2	yes	—
1130	C₄	C₂²×Q₈×D₆₇	1	1	yes	characteristic
1131	C₄	C₂×#41×D₆₇	1	1	yes	characteristic
1132	C₂	—	2	2	no	—
1133	C₂	—	4	2	no	—
1134	C₂	—	268	4	no	—
1135	C₂	—	134	4	no	—
1136	C₂	C₂×C₂²⋊Q₈×D₆₇	1	1	yes	characteristic
1137	C₂	#22574978	1	1	yes	characteristic
1138	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	C₂×#14524089	C₂²
hypercenter	#3076	D₆₇
hypocenter	C₆₇	#60496
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. #22570069	C₂	semidirect
4. #22570068	C₂	semidirect
5. #22570058	C₂	semidirect
6. #22570057	C₂	semidirect
7. #22570043	C₂	semidirect
8. #22570043	C₂	semidirect
9. #22570035	C₂	semidirect
10. #22570033	C₂	semidirect
11. #22570031	C₂	semidirect
12. #22570028	C₂	semidirect
13. #22570004	C₂	semidirect
14. #22570002	C₂	semidirect
15. #22569996	C₂	semidirect
16. C₂×#16863697	C₂	semidirect
17. #478×D₆₇	C₂	semidirect
18. #22568806	C₂	semidirect
19. #22568801	C₂	semidirect
20. #22568774	C₂	semidirect
23. C₆₇×#3076	C₂	semidirect
33. #16864024	C₂²	semidirect
34. #16864024	C₂²	semidirect
35. #16864023	C₂²	semidirect
36. #16864023	C₂²	semidirect
37. #16863952	C₂²	semidirect
38. C₂×#14524035	C₂²	semidirect
39. #125×D₆₇	C₂²	semidirect
57. #16863705	C₂²	semidirect
58. #16863703	C₂²	semidirect
59. #16863703	C₂²	semidirect
60. #16863701	C₂²	semidirect
61. #16863699	C₂²	semidirect
62. #16863699	C₂²	semidirect
63. #16863698	C₂²	semidirect
64. #16863697	C₂²	semidirect
65. #16863697	C₂²	semidirect
66. #16863697	C₂²	semidirect
67. #16863697	C₂²	semidirect
68. #16863696	C₂²	semidirect
69. #16863696	C₂²	semidirect
70. #16863695	C₂²	semidirect
71. #16863695	C₂²	semidirect
72. #16863694	C₂²	semidirect
73. #16863693	C₂²	semidirect
74. #16863693	C₂²	semidirect
75. #16863689	C₂²	semidirect
76. #16863685	C₂²	semidirect
77. #16863685	C₂²	semidirect
78. #16863684	C₂²	semidirect
79. #16863683	C₂²	semidirect
80. #16863679	C₂²	semidirect
81. #16863675	C₂²	semidirect
82. #16863675	C₂²	semidirect
83. #16863674	C₂²	semidirect
84. #16863673	C₂²	semidirect
85. #16863439	C₂²	semidirect
86. #16863439	C₂²	semidirect
87. #16863439	C₂²	semidirect
88. #16863439	C₂²	semidirect
89. #16863437	C₂²	semidirect
90. #16863437	C₂²	semidirect
91. #16863435	C₂²	semidirect
92. #16863435	C₂²	semidirect
93. #16863433	C₂²	semidirect
94. #16863431	C₂²	semidirect
95. C₂×#14523977	C₂²	semidirect
96. #107×D₆₇	C₂²	semidirect
97. C₂×#14523975	C₂²	semidirect
98. #106×D₆₇	C₂²	semidirect
99. #16863422	C₂²	semidirect
100. #16863422	C₂²	semidirect
101. #16863421	C₂²	semidirect
102. #16863421	C₂²	semidirect
103. #16863420	C₂²	semidirect
104. #16863418	C₂²	semidirect
105. C₄⋊C₈×D₆₇	C₂²	semidirect
120. #533×C₆₇	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
130. #427×C₆₇	C₂²	semidirect
131. #427×C₆₇	C₂²	semidirect
132. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
136. #14524089	Q₈	semidirect
585. #3076	D₆₇	semidirect
593. C₆₇	#60496	semidirect
608. #533	C₂×D₆₇	semidirect
633. #479	C₂×D₆₇	semidirect
634. #479	C₂×D₆₇	semidirect
649. #478	C₂×D₆₇	semidirect
650. #478	C₂×D₆₇	semidirect
652. #477	C₂×D₆₇	semidirect
657. #476	C₂×D₆₇	semidirect
659. #475	C₂×D₆₇	semidirect
664. #474	C₂×D₆₇	semidirect
675. #427	C₂×D₆₇	semidirect
676. #427	C₂×D₆₇	semidirect
688. C₂×C₄⋊C₈	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574030	2
C₄×#14524089	2
#22570069	2
#22570068	2
#22570058	2
#22570057	2
#22570043	2
#22570035	2
#22570033	2
#22570031	2
#22570028	2
#22570004	2
#22570002	2
#22569996	2
C₂×#16863697	2
#478×D₆₇	2
#22568806	2
#22568801	2
#22568774	2
#22568731	2
C₆₇×#3076	2
#60496	67