Subgroups — #31720738

Order 17152.

2136 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569285	C₂	1	2	yes	maximal, complemented
2	#22569280	C₂	1	2	yes	maximal, complemented
3	#22569271	C₂	1	2	yes	maximal, complemented
4	#22569265	C₂	1	2	yes	maximal, complemented
5	#22569257	C₂	1	2	yes	maximal, complemented
6	#22569257	C₂	1	2	yes	maximal, complemented
7	#22569244	C₂	1	2	yes	maximal, complemented
8	#22569238	C₂	1	2	yes	maximal, complemented
9	#22568953	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×#11761612	C₂	1	1	yes	maximal, characteristic, complemented
11	#22568936	C₂	1	1	yes	maximal, characteristic, complemented
12	#22568936	C₂	1	1	yes	maximal, characteristic, complemented
13	#22568927	C₂	1	1	yes	maximal, characteristic, complemented
14	#22568913	C₂	1	1	yes	maximal, characteristic, complemented
15	#22568904	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16863468	C₂	1	1	yes	maximal, characteristic, complemented
17	#22568875	C₂	1	1	yes	maximal, characteristic, complemented
18	#22568860	C₂	1	1	yes	maximal, characteristic, complemented
19	#22568658	C₂	1	1	yes	maximal, characteristic, complemented
20	#22568658	C₂	1	1	yes	maximal, characteristic, complemented
21	#22568654	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16863363	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic
24	C₂×#14524050	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14524050	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14524050	C₂²	1	1	yes	characteristic, complemented
27	C₂×#14524050	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#11761612	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#11761612	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#11761612	C₂²	1	1	yes	characteristic, complemented
31	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	#16863474	C₂²	1	2	yes	complemented
33	#16863474	C₂²	1	2	yes	complemented
34	#16863474	C₂²	1	2	yes	complemented
35	#16863474	C₂²	1	2	yes	complemented
36	#16863474	C₂²	1	2	yes	complemented
37	#16863474	C₂²	1	2	yes	complemented
38	#16863468	C₂²	1	1	yes	characteristic
39	#16863468	C₂²	1	2	yes	—
40	#16863468	C₂²	1	1	yes	characteristic
41	#16863468	C₂²	1	2	yes	complemented
42	#16863468	C₂²	1	2	yes	complemented
43	#16863468	C₂²	1	2	yes	complemented
44	#16863468	C₂²	1	2	yes	complemented
45	#16863468	C₂²	1	2	yes	complemented
46	#16863468	C₂²	1	2	yes	complemented
47	#16863468	C₂²	1	2	yes	complemented
48	#16863468	C₂²	1	2	yes	complemented
49	#16863468	C₂²	1	1	yes	characteristic, complemented
50	#16863468	C₂²	1	1	yes	characteristic, complemented
51	#16863468	C₂²	1	2	yes	complemented
52	#16863468	C₂²	1	2	yes	complemented
53	#16863468	C₂²	1	2	yes	complemented
54	#16863468	C₂²	1	1	yes	characteristic, complemented
55	#16863468	C₂²	1	2	yes	complemented
56	#16863468	C₂²	1	2	yes	complemented
57	#16863468	C₂²	1	1	yes	characteristic, complemented
58	#16863468	C₂²	1	2	yes	complemented
59	#16863468	C₂²	1	1	yes	characteristic, complemented
60	#16863468	C₂²	1	2	yes	complemented
61	#16863468	C₂²	1	1	yes	characteristic, complemented
62	D₄×C₆₇⋊C₈	C₂²	1	2	yes	complemented
63	D₄×C₆₇⋊C₈	C₂²	1	2	yes	complemented
64	D₄×C₆₇⋊C₈	C₂²	1	2	yes	complemented
65	D₄×C₆₇⋊C₈	C₂²	1	2	yes	complemented
66	D₄×C₆₇⋊C₈	C₂²	1	2	yes	complemented
67	D₄×C₆₇⋊C₈	C₂²	1	2	yes	complemented
68	#16863457	C₂²	1	2	yes	complemented
69	#16863457	C₂²	1	2	yes	complemented
70	#16863457	C₂²	1	2	yes	complemented
71	#16863457	C₂²	1	2	yes	complemented
72	#16863453	C₂²	1	2	yes	complemented
73	#16863453	C₂²	1	2	yes	complemented
74	#16863453	C₂²	1	2	yes	complemented
75	#16863449	C₂²	1	2	yes	complemented
76	#16863423	C₂²	1	1	yes	characteristic, complemented
77	#16863423	C₂²	1	1	yes	characteristic, complemented
78	#16863420	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
80	#16863363	C₂²	1	1	yes	characteristic
81	#16863363	C₂²	1	1	yes	characteristic
82	#16863363	C₂²	1	1	yes	characteristic
83	#16863363	C₂²	1	1	yes	characteristic
84	#16863363	C₂²	1	2	yes	complemented
85	#16863363	C₂²	1	2	yes	complemented
86	#16863363	C₂²	1	2	yes	complemented
87	#16863363	C₂²	1	2	yes	complemented
88	#16863363	C₂²	1	2	yes	complemented
89	#16863363	C₂²	1	2	yes	complemented
90	#16863363	C₂²	1	2	yes	complemented
91	#16863363	C₂²	1	2	yes	complemented
92	#16863363	C₂²	1	1	yes	characteristic, complemented
93	#16863363	C₂²	1	1	yes	characteristic, complemented
94	#16863363	C₂²	1	1	yes	characteristic, complemented
95	#16863363	C₂²	1	1	yes	characteristic, complemented
96	#16863360	C₂²	1	2	yes	complemented
97	#16863360	C₂²	1	2	yes	complemented
98	#16863360	C₂²	1	2	yes	complemented
99	#16863360	C₂²	1	2	yes	complemented
100	#16863360	C₂²	1	1	yes	characteristic, complemented
101	#16863360	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	2	yes	complemented
103	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	2	yes	complemented
104	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	2	yes	complemented
105	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
108	#16863352	C₂²	1	1	yes	characteristic, complemented
109	#16863352	C₂²	1	1	yes	characteristic, complemented
110	C₄×#11761612	C₂²	1	1	yes	characteristic, complemented
111	C₂×#14523954	C₂²	1	1	yes	characteristic, complemented
112	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
113	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
114	#550×C₆₇	C₄	1	1	yes	characteristic
115	D₄×Q₈×C₆₇	C₄	1	1	yes	characteristic
116	#548×C₆₇	C₄	1	1	yes	characteristic
117	#548×C₆₇	C₄	1	1	yes	characteristic
118	#547×C₆₇	C₄	1	2	yes	—
119	#547×C₆₇	C₄	1	1	yes	characteristic
120	#546×C₆₇	C₄	1	2	yes	—
121	#546×C₆₇	C₄	1	2	yes	—
122	#546×C₆₇	C₄	1	1	yes	characteristic
123	#546×C₆₇	C₄	1	1	yes	characteristic
124	D₄²×C₆₇	C₄	1	1	yes	characteristic
125	D₄²×C₆₇	C₄	1	2	yes	—
126	#532×C₆₇	C₂²	1	2	yes	—
127	#532×C₆₇	C₂²	1	1	yes	characteristic
128	#525×C₆₇	C₂²	1	2	yes	—
129	#525×C₆₇	C₂²	1	2	yes	—
130	#525×C₆₇	C₂²	1	1	yes	characteristic
131	#525×C₆₇	C₂²	1	1	yes	characteristic
132	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
133	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
134	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
135	#14524050	—	4	2	no	—
136	#14524050	—	4	2	no	—
137	#14524050	—	4	2	no	—
138	#14524050	—	4	2	no	—
139	C₂×#11761612	—	4	2	no	—
140	C₂×#11761612	—	4	2	no	—
141	C₂×#11761612	—	4	2	no	—
142	C₂×#11761612	C₂³	1	1	yes	characteristic
143	C₂×#11761612	C₂³	1	1	yes	characteristic
144	C₂×#11761612	C₂³	1	1	yes	characteristic
145	C₂×#11761612	C₂³	1	1	yes	characteristic
146	C₂×#11761612	C₂³	1	1	yes	characteristic
147	C₂×#11761612	C₂³	1	1	yes	characteristic
148	C₂×#11761612	C₂³	1	2	yes	—
149	C₂×#11761612	C₂³	1	2	yes	—
150	C₂×#11761612	C₂³	1	2	yes	—
151	C₂×#11761612	C₂³	1	2	yes	—
152	C₂×#11761612	C₂³	1	2	yes	—
153	C₂×#11761612	C₂³	1	1	yes	characteristic
154	C₂×#11761612	C₂³	1	1	yes	characteristic
155	C₂×#11761612	C₂³	1	2	yes	—
156	C₂²×C₆₇⋊C₈	—	4	2	no	—
157	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
158	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
159	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
160	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
161	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
162	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
163	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
164	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
165	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
166	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
167	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
168	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
169	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
170	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
171	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
172	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
173	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
174	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
175	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
176	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
177	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
178	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
179	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
180	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
181	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
182	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
183	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
184	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
185	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
186	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
187	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
188	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
189	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
190	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
191	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
192	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
193	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
194	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
195	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
196	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
197	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
198	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
199	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
200	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
201	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
202	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
203	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
204	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
205	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
206	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
207	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
208	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
209	#14523954	C₂³	1	1	yes	characteristic
210	#14523954	C₂³	1	1	yes	characteristic
211	#14523954	C₂³	1	1	yes	characteristic
212	#14523954	C₂³	1	1	yes	characteristic
213	#14523954	C₂³	1	2	yes	—
214	#14523954	C₂³	1	2	yes	—
215	#14523954	C₂³	1	2	yes	—
216	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
217	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
218	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
219	C₂×#41×C₆₇	—	4	2	no	—
220	C₂×#41×C₆₇	—	4	2	no	—
221	C₂×#41×C₆₇	—	4	2	no	—
222	C₂×#41×C₆₇	—	4	2	no	—
223	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
224	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
225	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
226	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
227	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
228	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
229	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×#41×C₆₇	C₂³	1	2	yes	—
233	C₂×#41×C₆₇	C₂³	1	2	yes	—
234	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
235	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
236	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
237	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
238	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
239	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
240	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
241	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
242	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
243	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
244	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
245	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
246	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
247	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
248	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
249	#127×C₆₇	C₂×C₄	1	2	yes	—
250	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
251	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
252	#124×C₆₇	C₂×C₄	1	2	yes	—
253	#124×C₆₇	C₂×C₄	1	2	yes	—
254	#123×C₆₇	C₂×C₄	1	2	yes	—
255	#123×C₆₇	C₂×C₄	1	2	yes	—
256	#123×C₆₇	C₂×C₄	1	2	yes	—
257	#123×C₆₇	C₂×C₄	1	2	yes	—
258	#123×C₆₇	C₂×C₄	1	2	yes	—
259	#123×C₆₇	C₂×C₄	1	2	yes	—
260	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
261	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
262	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
263	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
264	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
265	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
266	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
267	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
268	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
269	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
270	#121×C₆₇	C₂×C₄	1	2	yes	—
271	#121×C₆₇	C₂×C₄	1	2	yes	—
272	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
273	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
274	#121×C₆₇	C₂×C₄	1	2	yes	—
275	#121×C₆₇	C₂×C₄	1	2	yes	—
276	#121×C₆₇	C₂×C₄	1	2	yes	—
277	#121×C₆₇	C₂×C₄	1	2	yes	—
278	#121×C₆₇	C₂×C₄	1	2	yes	—
279	#121×C₆₇	C₂×C₄	1	2	yes	—
280	#121×C₆₇	C₂×C₄	1	2	yes	—
281	#121×C₆₇	C₂×C₄	1	2	yes	—
282	#120×C₆₇	C₂×C₄	1	2	yes	—
283	#120×C₆₇	C₂×C₄	1	2	yes	—
284	#120×C₆₇	C₂×C₄	1	2	yes	—
285	#120×C₆₇	C₂×C₄	1	2	yes	—
286	#120×C₆₇	C₂×C₄	1	2	yes	—
287	#120×C₆₇	C₂×C₄	1	2	yes	—
288	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
289	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
290	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
291	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
292	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
293	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
294	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
295	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
296	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
297	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
298	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
299	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
300	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
301	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
302	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
303	C₄×D₄×C₆₇	C₂³	1	2	yes	—
304	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
305	C₄×D₄×C₆₇	C₂³	1	2	yes	—
306	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
307	C₄×D₄×C₆₇	C₂³	1	2	yes	—
308	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
309	C₄×D₄×C₆₇	C₂³	1	2	yes	—
310	C₄×D₄×C₆₇	C₂³	1	2	yes	—
311	C₄×D₄×C₆₇	C₂³	1	2	yes	—
312	#117×C₆₇	C₂³	1	1	yes	characteristic
313	#117×C₆₇	C₂³	1	2	yes	—
314	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
315	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
316	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
317	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
318	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
319	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
320	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
321	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
322	#11761612	—	2	2	no	—
323	#11761612	—	2	2	no	—
324	#11761612	—	2	2	no	—
325	#11761612	—	2	2	no	—
326	#11761612	—	4	1	no	—
327	#11761612	—	4	1	no	—
328	#11761612	—	4	1	no	—
329	#11761612	—	4	1	no	—
330	#11761612	—	4	2	no	—
331	#11761612	—	4	2	no	—
332	#11761612	—	4	2	no	—
333	#11761612	—	4	2	no	—
334	#11761612	—	4	2	no	—
335	#11761612	—	4	2	no	—
336	C₂×C₆₇⋊C₈	—	2	2	no	—
337	C₂×C₆₇⋊C₈	—	2	2	no	—
338	C₂×C₆₇⋊C₈	—	2	2	no	—
339	C₂×C₆₇⋊C₈	—	2	2	no	—
340	C₂×C₆₇⋊C₈	—	4	1	no	—
341	C₂×C₆₇⋊C₈	—	4	1	no	—
342	C₂×C₆₇⋊C₈	—	4	1	no	—
343	C₂×C₆₇⋊C₈	—	4	1	no	—
344	C₂×C₆₇⋊C₈	—	4	2	no	—
345	C₂×C₆₇⋊C₈	—	4	2	no	—
346	C₂×C₆₇⋊C₈	—	4	2	no	—
347	C₂×C₆₇⋊C₈	—	4	2	no	—
348	C₂×C₆₇⋊C₈	—	4	2	no	—
349	C₂×C₆₇⋊C₈	—	4	2	no	—
350	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
351	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
352	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
353	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
354	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
355	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
356	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
357	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
358	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
360	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
361	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
362	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
363	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
364	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
365	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
366	#41×C₆₇	—	2	2	no	—
367	#41×C₆₇	—	2	2	no	—
368	#41×C₆₇	—	2	2	no	—
369	#41×C₆₇	—	2	2	no	—
370	#41×C₆₇	—	2	2	no	—
371	#41×C₆₇	—	2	2	no	—
372	#41×C₆₇	—	4	2	no	—
373	#41×C₆₇	—	4	2	no	—
374	#41×C₆₇	—	4	2	no	—
375	#41×C₆₇	—	4	2	no	—
376	#41×C₆₇	—	4	4	no	—
377	#41×C₆₇	—	4	4	no	—
378	#41×C₆₇	—	4	2	no	—
379	#41×C₆₇	—	4	2	no	—
380	#41×C₆₇	—	4	2	no	—
381	#41×C₆₇	—	4	2	no	—
382	C₂×Q₈×C₆₇	—	4	2	no	—
383	C₂×Q₈×C₆₇	—	4	2	no	—
384	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
385	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
386	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
387	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
388	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
389	C₂×D₄×C₆₇	—	4	2	no	—
390	C₂×D₄×C₆₇	—	4	2	no	—
391	C₂×D₄×C₆₇	—	4	2	no	—
392	C₂×D₄×C₆₇	—	4	4	no	—
393	C₂×D₄×C₆₇	—	4	4	no	—
394	C₂×D₄×C₆₇	—	4	4	no	—
395	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
396	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
397	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
398	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
399	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
400	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
401	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
402	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
403	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
404	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
405	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
406	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
407	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
408	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
409	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
410	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
411	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
412	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
413	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
414	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
415	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
416	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
417	C₂²×C₄×C₆₇	—	2	2	no	—
418	C₂²×C₄×C₆₇	—	2	2	no	—
419	C₂²×C₄×C₆₇	—	2	2	no	—
420	C₂²×C₄×C₆₇	—	2	2	no	—
421	C₂²×C₄×C₆₇	—	4	2	no	—
422	C₂²×C₄×C₆₇	—	4	2	no	—
423	C₂²×C₄×C₆₇	—	4	2	no	—
424	C₂²×C₄×C₆₇	—	4	2	no	—
425	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
426	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
427	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
428	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
429	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
430	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
431	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
432	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
433	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
434	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
435	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
436	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
437	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
438	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
439	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
440	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
441	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
442	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
443	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
446	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
447	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
448	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
451	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
452	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
453	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
454	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
455	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
456	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
457	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
458	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
459	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
460	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
461	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
462	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
463	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
464	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
465	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
466	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
467	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
468	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
469	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
470	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
471	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
472	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
473	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
474	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
475	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
476	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
477	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
478	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
479	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
480	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
481	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
482	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
483	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
484	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
485	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
486	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
487	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
488	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
489	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
490	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
491	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
492	C₄²×C₆₇	C₂⁴	1	2	yes	—
493	C₂³×C₆₇	—	2	2	no	—
494	C₂³×C₆₇	—	2	2	no	—
495	C₂³×C₆₇	—	2	2	no	—
496	C₂³×C₆₇	—	2	4	no	—
497	C₂³×C₆₇	—	4	1	no	—
498	C₂³×C₆₇	—	4	2	no	—
499	C₂³×C₆₇	—	4	2	no	—
500	C₂³×C₆₇	—	4	1	no	—
501	C₂³×C₆₇	—	4	2	no	—
502	C₂³×C₆₇	—	4	1	no	—
503	C₂³×C₆₇	—	4	2	no	—
504	C₂³×C₆₇	—	4	2	no	—
505	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
506	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
507	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
508	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
509	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
510	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
511	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
512	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
513	Q₈×C₆₇	—	2	2	no	—
514	Q₈×C₆₇	—	2	2	no	—
515	Q₈×C₆₇	—	2	2	no	—
516	Q₈×C₆₇	—	4	2	no	—
517	Q₈×C₆₇	—	4	2	no	—
518	D₄×C₆₇	—	2	4	no	—
519	D₄×C₆₇	—	2	4	no	—
520	D₄×C₆₇	—	2	4	no	—
521	D₄×C₆₇	—	2	2	no	—
522	D₄×C₆₇	—	2	2	no	—
523	D₄×C₆₇	—	2	4	no	—
524	D₄×C₆₇	—	2	2	no	—
525	D₄×C₆₇	—	2	2	no	—
526	D₄×C₆₇	—	2	2	no	—
527	D₄×C₆₇	—	4	1	no	—
528	D₄×C₆₇	—	4	2	no	—
529	D₄×C₆₇	—	4	1	no	—
530	D₄×C₆₇	—	4	2	no	—
531	D₄×C₆₇	—	4	2	no	—
532	D₄×C₆₇	—	4	2	no	—
533	D₄×C₆₇	—	4	2	no	—
534	D₄×C₆₇	—	4	2	no	—
535	D₄×C₆₇	—	4	2	no	—
536	D₄×C₆₇	—	4	2	no	—
537	D₄×C₆₇	—	4	2	no	—
538	D₄×C₆₇	—	4	2	no	—
539	D₄×C₆₇	—	4	2	no	—
540	C₂×C₄×C₆₇	—	2	2	no	—
541	C₂×C₄×C₆₇	—	2	2	no	—
542	C₂×C₄×C₆₇	—	2	2	no	—
543	C₂×C₄×C₆₇	—	2	2	no	—
544	C₂×C₄×C₆₇	—	2	2	no	—
545	C₂×C₄×C₆₇	—	2	2	no	—
546	C₂×C₄×C₆₇	—	2	1	no	—
547	C₂×C₄×C₆₇	—	2	1	no	—
548	C₂×C₄×C₆₇	—	2	1	no	—
549	C₂×C₄×C₆₇	—	2	1	no	—
550	C₂×C₄×C₆₇	—	2	1	no	—
551	C₂×C₄×C₆₇	—	2	1	no	—
552	C₂×C₄×C₆₇	—	2	1	no	—
553	C₂×C₄×C₆₇	—	2	1	no	—
554	C₂×C₄×C₆₇	—	2	2	no	—
555	C₂×C₄×C₆₇	—	2	2	no	—
556	C₂×C₄×C₆₇	—	2	2	no	—
557	C₂×C₄×C₆₇	—	2	2	no	—
558	C₂×C₄×C₆₇	—	2	2	no	—
559	C₂×C₄×C₆₇	—	2	2	no	—
560	C₂×C₄×C₆₇	—	4	2	no	—
561	C₂×C₄×C₆₇	—	4	2	no	—
562	C₂×C₄×C₆₇	—	4	2	no	—
563	C₂×C₄×C₆₇	—	4	2	no	—
564	C₂×C₄×C₆₇	—	4	2	no	—
565	C₂×C₄×C₆₇	—	4	2	no	—
566	C₂×C₄×C₆₇	—	4	1	no	—
567	C₂×C₄×C₆₇	—	4	2	no	—
568	C₂×C₄×C₆₇	—	4	1	no	—
569	C₂×C₄×C₆₇	—	4	2	no	—
570	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
571	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
572	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
573	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
574	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
575	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
577	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
578	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
579	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
580	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
581	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
582	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
583	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
584	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
585	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
586	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
587	C₆₇⋊C₈	—	2	1	no	—
588	C₆₇⋊C₈	—	2	1	no	—
589	C₆₇⋊C₈	—	2	1	no	—
590	C₆₇⋊C₈	—	2	1	no	—
591	C₆₇⋊C₈	—	2	1	no	—
592	C₆₇⋊C₈	—	2	1	no	—
593	C₆₇⋊C₈	—	2	1	no	—
594	C₆₇⋊C₈	—	2	1	no	—
595	C₆₇⋊C₈	—	2	2	no	—
596	C₆₇⋊C₈	—	2	2	no	—
597	C₆₇⋊C₈	—	2	2	no	—
598	C₆₇⋊C₈	—	2	2	no	—
599	C₂²×C₆₇	—	2	1	no	—
600	C₂²×C₆₇	—	2	1	no	—
601	C₂²×C₆₇	—	2	1	no	—
602	C₂²×C₆₇	—	2	1	no	—
603	C₂²×C₆₇	—	2	1	no	—
604	C₂²×C₆₇	—	2	1	no	—
605	C₂²×C₆₇	—	2	1	no	—
606	C₂²×C₆₇	—	2	2	no	—
607	C₂²×C₆₇	—	2	2	no	—
608	C₂²×C₆₇	—	2	2	no	—
609	C₂²×C₆₇	—	2	2	no	—
610	C₂²×C₆₇	—	2	1	no	—
611	C₂²×C₆₇	—	2	1	no	—
612	C₂²×C₆₇	—	2	2	no	—
613	C₂²×C₆₇	—	2	1	no	—
614	C₂²×C₆₇	—	2	2	no	—
615	C₂²×C₆₇	—	2	2	no	—
616	C₂²×C₆₇	—	2	1	no	—
617	C₂²×C₆₇	—	2	1	no	—
618	C₂²×C₆₇	—	2	2	no	—
619	C₂²×C₆₇	—	2	2	no	—
620	C₂²×C₆₇	—	2	1	no	—
621	C₂²×C₆₇	—	4	4	no	—
622	C₂²×C₆₇	—	8	4	no	—
623	C₂²×C₆₇	—	8	2	no	—
624	C₂²×C₆₇	—	8	4	no	—
625	C₂²×C₆₇	#518	1	2	yes	—
626	C₂²×C₆₇	#568	1	2	yes	—
627	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
628	C₄×C₆₇	—	2	1	no	—
629	C₄×C₆₇	—	2	1	no	—
630	C₄×C₆₇	—	2	1	no	—
631	C₄×C₆₇	—	2	1	no	—
632	C₄×C₆₇	—	2	2	no	—
633	C₄×C₆₇	—	2	2	no	—
634	C₄×C₆₇	—	2	2	no	—
635	C₄×C₆₇	—	2	1	no	—
636	C₄×C₆₇	—	2	1	no	—
637	C₄×C₆₇	—	2	2	no	—
638	C₄×C₆₇	—	2	1	no	—
639	C₄×C₆₇	—	2	1	no	—
640	C₄×C₆₇	—	2	2	no	—
641	C₄×C₆₇	#518	1	2	yes	—
642	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
643	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
644	#60240	—	67	1	no	maximal, Sylow
645	C₂×C₆₇	—	2	2	no	—
646	C₂×C₆₇	—	2	2	no	—
647	C₂×C₆₇	—	4	1	no	—
648	C₂×C₆₇	—	4	1	no	—
649	C₂×C₆₇	—	4	2	no	—
650	C₂×C₆₇	—	4	2	no	—
651	C₂×C₆₇	—	4	2	no	—
652	C₂×C₆₇	—	4	1	no	—
653	C₂×C₆₇	C₂×#518	1	1	yes	characteristic
654	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
655	C₂×C₆₇	#3573	1	1	yes	characteristic
656	D₄×#41	D₆₇	1	1	yes	characteristic
657	#2981	—	67	2	no	—
658	#2980	—	67	2	no	—
659	#2978	—	67	2	no	—
660	#2977	—	67	2	no	—
661	#2976	—	67	2	no	—
662	#2976	—	67	2	no	—
663	#2974	—	67	2	no	—
664	#2973	—	67	2	no	—
665	#2935	—	67	1	no	—
666	D₄×M₁₆	—	67	1	no	—
667	#2933	—	67	1	no	—
668	#2933	—	67	1	no	—
669	#2932	—	67	1	no	—
670	#2930	—	67	1	no	—
671	#2929	—	67	1	no	—
672	C₂×#435	—	67	1	no	—
673	#2925	—	67	1	no	—
674	#2923	—	67	1	no	—
675	#2880	—	67	1	no	—
676	#2880	—	67	1	no	—
677	#2879	—	67	1	no	—
678	C₂×#408	—	67	1	no	—
679	C₆₇	#60240	1	1	yes	characteristic, complemented, Sylow
680	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
681	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
682	C₂×#131	—	67	1	no	—
683	C₂×#131	—	67	1	no	—
684	C₂×#131	—	67	1	no	—
685	C₂×#131	—	67	1	no	—
686	C₂²×M₁₆	—	67	1	no	—
687	C₂²×M₁₆	—	67	1	no	—
688	C₂²×M₁₆	—	67	1	no	—
689	C₂³×C₈	—	67	1	no	—
690	#550	Dic₆₇	1	1	yes	characteristic
691	D₄×Q₈	Dic₆₇	1	1	yes	characteristic
692	#548	Dic₆₇	1	1	yes	characteristic
693	#548	Dic₆₇	1	1	yes	characteristic
694	#547	Dic₆₇	1	2	yes	—
695	#547	Dic₆₇	1	1	yes	characteristic
696	#546	Dic₆₇	1	2	yes	—
697	#546	Dic₆₇	1	2	yes	—
698	#546	Dic₆₇	1	1	yes	characteristic
699	#546	Dic₆₇	1	1	yes	characteristic
700	D₄²	Dic₆₇	1	1	yes	characteristic
701	D₄²	Dic₆₇	1	2	yes	—
702	#532	C₂×D₆₇	1	1	yes	characteristic
703	#532	C₂×D₆₇	1	2	yes	—
704	#525	C₂×D₆₇	1	1	yes	characteristic
705	#525	C₂×D₆₇	1	1	yes	characteristic
706	#525	C₂×D₆₇	1	2	yes	—
707	#525	C₂×D₆₇	1	2	yes	—
708	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
709	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
710	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	—
711	#436	—	67	2	no	—
712	#436	—	67	2	no	—
713	#436	—	67	2	no	—
714	#436	—	67	2	no	—
715	#436	—	67	2	no	—
716	#436	—	67	2	no	—
717	#435	—	67	1	no	—
718	#435	—	67	1	no	—
719	#435	—	67	1	no	—
720	#435	—	67	1	no	—
721	#435	—	67	1	no	—
722	#435	—	67	1	no	—
723	#435	—	67	1	no	—
724	#435	—	67	1	no	—
725	#435	—	67	2	no	—
726	#435	—	67	2	no	—
727	#435	—	67	2	no	—
728	#435	—	67	2	no	—
729	#435	—	67	2	no	—
730	#435	—	67	2	no	—
731	#435	—	67	2	no	—
732	#435	—	67	2	no	—
733	#435	—	67	2	no	—
734	#435	—	67	2	no	—
735	#435	—	67	2	no	—
736	#435	—	67	2	no	—
737	#435	—	67	2	no	—
738	#435	—	67	2	no	—
739	#435	—	67	2	no	—
740	#435	—	67	2	no	—
741	C₈×D₄	—	67	2	no	—
742	C₈×D₄	—	67	2	no	—
743	C₈×D₄	—	67	2	no	—
744	C₈×D₄	—	67	2	no	—
745	C₈×D₄	—	67	2	no	—
746	C₈×D₄	—	67	2	no	—
747	#433	—	67	2	no	—
748	#433	—	67	2	no	—
749	#433	—	67	2	no	—
750	#433	—	67	2	no	—
751	#432	—	67	2	no	—
752	#432	—	67	2	no	—
753	#432	—	67	2	no	—
754	#431	—	67	2	no	—
755	#424	—	67	1	no	—
756	#424	—	67	1	no	—
757	#423	—	67	1	no	—
758	C₂×C₄⋊C₈	—	67	1	no	—
759	#408	—	67	1	no	—
760	#408	—	67	1	no	—
761	#408	—	67	1	no	—
762	#408	—	67	1	no	—
763	#408	—	67	2	no	—
764	#408	—	67	2	no	—
765	#408	—	67	1	no	—
766	#408	—	67	1	no	—
767	#408	—	67	1	no	—
768	#408	—	67	2	no	—
769	#408	—	67	2	no	—
770	#408	—	67	1	no	—
771	#408	—	67	2	no	—
772	#408	—	67	2	no	—
773	#408	—	67	2	no	—
774	#408	—	67	2	no	—
775	#407	—	67	2	no	—
776	#407	—	67	2	no	—
777	#407	—	67	1	no	—
778	#407	—	67	1	no	—
779	#407	—	67	2	no	—
780	#407	—	67	2	no	—
781	C₂×C₂²⋊C₈	—	67	2	no	—
782	C₂×C₂²⋊C₈	—	67	2	no	—
783	C₂×C₂²⋊C₈	—	67	1	no	—
784	C₂×C₂²⋊C₈	—	67	1	no	—
785	C₂×C₂²⋊C₈	—	67	2	no	—
786	C₂×C₂²⋊C₈	—	67	2	no	—
787	#405	—	67	1	no	—
788	#405	—	67	1	no	—
789	C₄×M₁₆	—	67	1	no	—
790	C₂×#97	—	67	1	no	—
791	C₂×#41	—	4	2	no	—
792	C₂×#41	—	4	2	no	—
793	C₂×#41	—	4	2	no	—
794	C₂×#41	—	4	2	no	—
795	C₂×#41	C₂×Dic₆₇	1	2	yes	—
796	C₂×#41	C₂×Dic₆₇	1	2	yes	—
797	C₂×#41	C₂×Dic₆₇	1	1	yes	characteristic
798	C₂×#41	C₂×Dic₆₇	1	1	yes	characteristic
799	C₂×#41	C₂×Dic₆₇	1	1	yes	characteristic
800	C₂×#41	C₂×Dic₆₇	1	1	yes	characteristic
801	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
802	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
803	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
804	C₂×#41	C₂²×D₆₇	1	2	yes	—
805	C₂×#41	C₂²×D₆₇	1	2	yes	—
806	C₂²×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
807	C₂²×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
808	C₂²×D₄	C₂×Dic₆₇	1	1	yes	characteristic
809	C₂²×D₄	C₂×Dic₆₇	1	2	yes	—
810	C₂²×D₄	C₂×Dic₆₇	1	1	yes	characteristic
811	C₂²×D₄	C₂×Dic₆₇	1	1	yes	characteristic
812	C₂²×D₄	C₂×Dic₆₇	1	2	yes	—
813	C₂²×D₄	C₂×Dic₆₇	1	2	yes	—
814	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
815	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
816	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
817	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
818	#131	—	268	2	no	—
819	#131	—	268	2	no	—
820	#131	—	268	2	no	—
821	#131	—	268	2	no	—
822	C₂×M₁₆	—	268	2	no	—
823	C₂×M₁₆	—	268	2	no	—
824	C₂×M₁₆	—	268	2	no	—
825	C₂×M₁₆	—	67	1	no	—
826	C₂×M₁₆	—	67	1	no	—
827	C₂×M₁₆	—	67	2	no	—
828	C₂×M₁₆	—	67	1	no	—
829	C₂×M₁₆	—	67	1	no	—
830	C₂×M₁₆	—	67	2	no	—
831	C₂×M₁₆	—	67	2	no	—
832	C₂×M₁₆	—	67	2	no	—
833	C₂×M₁₆	—	67	2	no	—
834	C₂×M₁₆	—	67	2	no	—
835	C₂×M₁₆	—	67	1	no	—
836	C₂×M₁₆	—	67	1	no	—
837	C₂×M₁₆	—	67	1	no	—
838	C₂×M₁₆	—	67	1	no	—
839	C₂²×C₈	—	268	2	no	—
840	C₂²×C₈	—	67	1	no	—
841	C₂²×C₈	—	67	1	no	—
842	C₂²×C₈	—	67	1	no	—
843	C₂²×C₈	—	67	1	no	—
844	C₂²×C₈	—	67	2	no	—
845	C₂²×C₈	—	67	2	no	—
846	C₂²×C₈	—	67	2	no	—
847	C₂²×C₈	—	67	2	no	—
848	C₂²×C₈	—	67	2	no	—
849	C₂²×C₈	—	67	2	no	—
850	C₂²×C₈	—	67	1	no	—
851	C₂²×C₈	—	67	1	no	—
852	C₂²×C₈	—	67	1	no	—
853	C₂²×C₈	—	67	1	no	—
854	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
855	C₄⋊Q₈	C₂×Dic₆₇	1	2	yes	—
856	#127	C₂×Dic₆₇	1	1	yes	characteristic
857	#127	C₂×Dic₆₇	1	2	yes	—
858	#124	C₂×Dic₆₇	1	1	yes	characteristic
859	#124	C₂×Dic₆₇	1	1	yes	characteristic
860	#124	C₂×Dic₆₇	1	2	yes	—
861	#124	C₂×Dic₆₇	1	2	yes	—
862	#123	C₂×Dic₆₇	1	2	yes	—
863	#123	C₂×Dic₆₇	1	2	yes	—
864	#123	C₂×Dic₆₇	1	2	yes	—
865	#123	C₂×Dic₆₇	1	2	yes	—
866	#123	C₂×Dic₆₇	1	2	yes	—
867	#123	C₂×Dic₆₇	1	2	yes	—
868	C₂²⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
869	C₂²⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
870	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
871	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
872	C₂²⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
873	C₂²⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
874	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
875	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
876	#121	C₂×Dic₆₇	1	1	yes	characteristic
877	#121	C₂×Dic₆₇	1	1	yes	characteristic
878	#121	C₂×Dic₆₇	1	2	yes	—
879	#121	C₂×Dic₆₇	1	2	yes	—
880	#121	C₂×Dic₆₇	1	1	yes	characteristic
881	#121	C₂×Dic₆₇	1	1	yes	characteristic
882	#121	C₂×Dic₆₇	1	2	yes	—
883	#121	C₂×Dic₆₇	1	2	yes	—
884	#121	C₂×Dic₆₇	1	2	yes	—
885	#121	C₂×Dic₆₇	1	2	yes	—
886	#121	C₂×Dic₆₇	1	2	yes	—
887	#121	C₂×Dic₆₇	1	2	yes	—
888	#121	C₂×Dic₆₇	1	2	yes	—
889	#121	C₂×Dic₆₇	1	2	yes	—
890	#120	C₂×Dic₆₇	1	2	yes	—
891	#120	C₂×Dic₆₇	1	2	yes	—
892	#120	C₂×Dic₆₇	1	2	yes	—
893	#120	C₂×Dic₆₇	1	2	yes	—
894	#120	C₂×Dic₆₇	1	2	yes	—
895	#120	C₂×Dic₆₇	1	2	yes	—
896	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
897	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
898	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
899	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
900	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
901	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
902	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
903	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
904	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
905	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
906	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
907	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
908	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
909	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
910	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
911	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
912	C₄×D₄	C₂²×D₆₇	1	2	yes	—
913	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
914	C₄×D₄	C₂²×D₆₇	1	2	yes	—
915	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
916	C₄×D₄	C₂²×D₆₇	1	2	yes	—
917	C₄×D₄	C₂²×D₆₇	1	2	yes	—
918	C₄×D₄	C₂²×D₆₇	1	2	yes	—
919	C₄×D₄	C₂²×D₆₇	1	2	yes	—
920	#117	C₂²×D₆₇	1	1	yes	characteristic
921	#117	C₂²×D₆₇	1	2	yes	—
922	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
923	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
924	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
925	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
926	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	2	yes	—
927	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	2	yes	—
928	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
929	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
930	C₄⋊C₈	—	67	1	no	—
931	C₄⋊C₈	—	67	1	no	—
932	C₄⋊C₈	—	67	1	no	—
933	C₄⋊C₈	—	67	1	no	—
934	C₄⋊C₈	—	67	2	no	—
935	C₄⋊C₈	—	67	2	no	—
936	C₄⋊C₈	—	67	2	no	—
937	C₄⋊C₈	—	67	2	no	—
938	C₄⋊C₈	—	67	2	no	—
939	C₄⋊C₈	—	67	2	no	—
940	C₂²⋊C₈	—	67	1	no	—
941	C₂²⋊C₈	—	67	1	no	—
942	C₂²⋊C₈	—	67	2	no	—
943	C₂²⋊C₈	—	67	1	no	—
944	C₂²⋊C₈	—	67	2	no	—
945	C₂²⋊C₈	—	67	1	no	—
946	C₂²⋊C₈	—	67	2	no	—
947	C₂²⋊C₈	—	67	2	no	—
948	C₂²⋊C₈	—	67	2	no	—
949	C₂²⋊C₈	—	67	2	no	—
950	C₂²⋊C₈	—	67	2	no	—
951	C₂²⋊C₈	—	67	2	no	—
952	C₂²⋊C₈	—	67	2	no	—
953	C₂²⋊C₈	—	67	1	no	—
954	C₂²⋊C₈	—	67	2	no	—
955	C₂²⋊C₈	—	67	1	no	—
956	C₂²⋊C₈	—	67	1	no	—
957	C₂²⋊C₈	—	67	2	no	—
958	C₂²⋊C₈	—	67	2	no	—
959	C₂²⋊C₈	—	67	2	no	—
960	C₂²⋊C₈	—	67	1	no	—
961	C₂²⋊C₈	—	67	2	no	—
962	C₂²⋊C₈	—	67	2	no	—
963	C₂²⋊C₈	—	67	2	no	—
964	C₂²⋊C₈	—	67	2	no	—
965	C₂²⋊C₈	—	67	2	no	—
966	C₂²⋊C₈	—	67	2	no	—
967	C₂²⋊C₈	—	67	2	no	—
968	#97	—	67	1	no	—
969	#97	—	67	1	no	—
970	#97	—	67	1	no	—
971	#97	—	67	1	no	—
972	#97	—	67	2	no	—
973	#97	—	67	2	no	—
974	#97	—	67	2	no	—
975	C₄×C₈	—	67	2	no	—
976	C₄×C₈	—	67	2	no	—
977	C₄×C₈	—	67	2	no	—
978	C₂⁴	C₂²×Dic₆₇	1	1	yes	characteristic
979	C₂⁴	C₂²×Dic₆₇	1	1	yes	characteristic
980	C₂⁴	C₂²×Dic₆₇	1	2	yes	—
981	C₂⁴	C₂²×Dic₆₇	1	2	yes	—
982	#41	—	2	2	no	—
983	#41	—	2	2	no	—
984	#41	—	2	2	no	—
985	#41	—	2	2	no	—
986	#41	—	2	2	no	—
987	#41	—	2	2	no	—
988	#41	—	4	2	no	—
989	#41	—	4	2	no	—
990	#41	—	4	2	no	—
991	#41	—	4	2	no	—
992	#41	—	4	4	no	—
993	#41	—	4	4	no	—
994	#41	—	4	2	no	—
995	#41	—	4	2	no	—
996	#41	—	4	2	no	—
997	#41	—	4	2	no	—
998	C₂×Q₈	—	4	2	no	—
999	C₂×Q₈	—	4	2	no	—
1000	C₂×Q₈	C₂²×Dic₆₇	1	1	yes	characteristic
1001	C₂×Q₈	C₂²×Dic₆₇	1	1	yes	characteristic
1002	C₂×Q₈	C₂²×Dic₆₇	1	1	yes	characteristic
1003	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
1004	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
1005	C₂×D₄	—	4	2	no	—
1006	C₂×D₄	—	4	2	no	—
1007	C₂×D₄	—	4	4	no	—
1008	C₂×D₄	—	4	4	no	—
1009	C₂×D₄	—	4	2	no	—
1010	C₂×D₄	—	4	4	no	—
1011	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
1012	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1013	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
1014	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
1015	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1016	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1017	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1018	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
1019	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
1020	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
1021	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1022	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
1023	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1024	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1025	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1026	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1027	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1028	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1029	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1030	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1031	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1032	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
1033	C₂²×C₄	—	2	2	no	—
1034	C₂²×C₄	—	2	2	no	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	4	2	no	—
1038	C₂²×C₄	—	4	2	no	—
1039	C₂²×C₄	—	4	2	no	—
1040	C₂²×C₄	—	4	2	no	—
1041	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1042	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1043	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1044	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1045	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1046	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1047	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
1048	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1049	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
1050	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1051	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
1052	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
1053	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
1054	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
1055	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
1056	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
1057	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1058	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1059	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1060	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1061	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1062	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1063	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1064	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1065	M₁₆	—	268	1	no	—
1066	M₁₆	—	268	1	no	—
1067	M₁₆	—	268	1	no	—
1068	M₁₆	—	268	1	no	—
1069	M₁₆	—	268	2	no	—
1070	M₁₆	—	268	2	no	—
1071	M₁₆	—	268	2	no	—
1072	M₁₆	—	268	2	no	—
1073	M₁₆	—	268	2	no	—
1074	M₁₆	—	268	2	no	—
1075	M₁₆	—	134	2	no	—
1076	M₁₆	—	134	2	no	—
1077	M₁₆	—	134	2	no	—
1078	M₁₆	—	134	2	no	—
1079	C₂×C₈	—	268	1	no	—
1080	C₂×C₈	—	268	1	no	—
1081	C₂×C₈	—	268	1	no	—
1082	C₂×C₈	—	268	1	no	—
1083	C₂×C₈	—	268	2	no	—
1084	C₂×C₈	—	268	2	no	—
1085	C₂×C₈	—	268	2	no	—
1086	C₂×C₈	—	268	2	no	—
1087	C₂×C₈	—	268	2	no	—
1088	C₂×C₈	—	268	2	no	—
1089	C₂×C₈	—	67	1	no	—
1090	C₂×C₈	—	67	1	no	—
1091	C₂×C₈	—	67	2	no	—
1092	C₂×C₈	—	67	2	no	—
1093	C₂×C₈	—	67	2	no	—
1094	C₂×C₈	—	67	2	no	—
1095	C₂×C₈	—	67	1	no	—
1096	C₂×C₈	—	67	1	no	—
1097	C₂×C₈	—	67	1	no	—
1098	C₂×C₈	—	67	1	no	—
1099	C₂×C₈	—	67	1	no	—
1100	C₂×C₈	—	67	1	no	—
1101	C₂×C₈	—	134	2	no	—
1102	C₂×C₈	—	134	2	no	—
1103	C₂×C₈	—	134	2	no	—
1104	C₂×C₈	—	134	2	no	—
1105	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1106	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1107	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1108	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1109	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1110	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1111	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1112	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1113	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1114	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1115	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1116	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1117	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1118	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1119	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1120	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1122	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1123	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1124	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1125	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1126	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1127	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1128	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1129	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1130	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1131	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1132	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1133	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1134	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1135	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1136	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1137	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1138	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1139	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1140	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1141	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1142	C₄²	C₂²×Dic₆₇	1	2	yes	—
1143	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
1144	C₄²	C₂²×Dic₆₇	1	2	yes	—
1145	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
1146	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1147	C₄²	C₂³×D₆₇	1	2	yes	—
1148	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1149	C₂³	—	2	2	no	—
1150	C₂³	—	2	2	no	—
1151	C₂³	—	2	2	no	—
1152	C₂³	—	2	4	no	—
1153	C₂³	—	4	1	no	—
1154	C₂³	—	4	2	no	—
1155	C₂³	—	4	2	no	—
1156	C₂³	—	4	1	no	—
1157	C₂³	—	4	2	no	—
1158	C₂³	—	4	1	no	—
1159	C₂³	—	4	2	no	—
1160	C₂³	—	4	2	no	—
1161	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
1162	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
1163	C₂³	C₂³×Dic₆₇	1	2	yes	—
1164	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
1165	C₂³	C₂³×Dic₆₇	1	2	yes	—
1166	C₂³	C₂³×Dic₆₇	1	2	yes	—
1167	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
1168	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
1169	Q₈	—	2	2	no	—
1170	Q₈	—	2	2	no	—
1171	Q₈	—	2	2	no	—
1172	Q₈	—	4	2	no	—
1173	Q₈	—	4	2	no	—
1174	D₄	—	2	4	no	—
1175	D₄	—	2	4	no	—
1176	D₄	—	2	4	no	—
1177	D₄	—	2	2	no	—
1178	D₄	—	2	2	no	—
1179	D₄	—	2	4	no	—
1180	D₄	—	2	2	no	—
1181	D₄	—	2	2	no	—
1182	D₄	—	2	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	4	2	no	—
1187	D₄	—	4	2	no	—
1188	D₄	—	4	2	no	—
1189	D₄	—	4	1	no	—
1190	D₄	—	4	2	no	—
1191	D₄	—	4	1	no	—
1192	D₄	—	4	2	no	—
1193	D₄	—	4	2	no	—
1194	D₄	—	4	2	no	—
1195	D₄	—	4	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	2	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	2	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	4	2	no	—
1221	C₂×C₄	—	4	2	no	—
1222	C₂×C₄	—	4	1	no	—
1223	C₂×C₄	—	4	2	no	—
1224	C₂×C₄	—	4	1	no	—
1225	C₂×C₄	—	4	2	no	—
1226	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1227	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1228	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1229	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1230	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1231	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1232	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1233	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1234	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1235	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1236	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1237	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1238	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1239	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1240	C₂×C₄	#14524088	1	2	yes	—
1241	C₂×C₄	#14524088	1	2	yes	—
1242	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1243	C₈	—	134	1	no	—
1244	C₈	—	134	1	no	—
1245	C₈	—	134	1	no	—
1246	C₈	—	134	1	no	—
1247	C₈	—	134	1	no	—
1248	C₈	—	134	1	no	—
1249	C₈	—	134	1	no	—
1250	C₈	—	134	2	no	—
1251	C₈	—	134	2	no	—
1252	C₈	—	134	2	no	—
1253	C₈	—	134	2	no	—
1254	C₈	—	134	1	no	—
1255	C₂²	—	2	1	no	—
1256	C₂²	—	2	1	no	—
1257	C₂²	—	2	1	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	2	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	2	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	2	no	—
1265	C₂²	—	2	2	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	2	no	—
1269	C₂²	—	2	2	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	2	no	—
1275	C₂²	—	2	2	no	—
1276	C₂²	—	2	2	no	—
1277	C₂²	—	4	4	no	—
1278	C₂²	—	8	4	no	—
1279	C₂²	—	8	2	no	—
1280	C₂²	—	8	4	no	—
1281	C₂²	#16863871	1	2	yes	—
1282	C₂²	#16864163	1	2	yes	—
1283	C₂²	C₂⁴×Dic₆₇	1	1	yes	characteristic
1284	C₄	—	2	1	no	—
1285	C₄	—	2	1	no	—
1286	C₄	—	2	2	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	2	no	—
1290	C₄	—	2	1	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	1	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	2	no	—
1296	C₄	—	2	2	no	—
1297	C₄	#16863871	1	2	yes	—
1298	C₄	C₂×#14524088	1	1	yes	characteristic
1299	C₄	C₂×#14524088	1	1	yes	characteristic
1300	C₂	—	2	2	no	—
1301	C₂	—	2	2	no	—
1302	C₂	—	4	1	no	—
1303	C₂	—	4	1	no	—
1304	C₂	—	4	2	no	—
1305	C₂	—	4	1	no	—
1306	C₂	—	4	2	no	—
1307	C₂	—	4	2	no	—
1308	C₂	C₂×#16863871	1	1	yes	characteristic
1309	C₂	C₂×#16864163	1	1	yes	characteristic
1310	C₂	#22574921	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁴×C₄
Fitting, prime radical	D₄×#41×C₆₇	C₂
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	D₄×#41	D₆₇
hypocenter	C₆₇	#60240
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ D₄×#41

Complements

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

N	H ≅ G/N	type
1. #22569285	C₂	semidirect
2. #22569280	C₂	semidirect
3. #22569271	C₂	semidirect
4. #22569265	C₂	semidirect
5. #22569257	C₂	semidirect
6. #22569257	C₂	semidirect
7. #22569244	C₂	semidirect
8. #22569238	C₂	semidirect
9. #22568953	C₂	semidirect
10. D₄×#11761612	C₂	semidirect
11. #22568936	C₂	semidirect
12. #22568936	C₂	semidirect
13. #22568927	C₂	semidirect
14. #22568913	C₂	semidirect
15. #22568904	C₂	semidirect
16. C₂×#16863468	C₂	semidirect
17. #22568875	C₂	semidirect
18. #22568860	C₂	semidirect
19. #22568658	C₂	semidirect
20. #22568658	C₂	semidirect
21. #22568654	C₂	semidirect
22. C₂×#16863363	C₂	semidirect
24. C₂×#14524050	C₂²	semidirect
25. C₂×#14524050	C₂²	semidirect
26. C₂×#14524050	C₂²	semidirect
27. C₂×#14524050	C₂²	semidirect
28. C₂²×#11761612	C₂²	semidirect
29. C₂²×#11761612	C₂²	semidirect
30. C₂²×#11761612	C₂²	semidirect
31. C₂³×C₆₇⋊C₈	C₂²	semidirect
32. #16863474	C₂²	semidirect
33. #16863474	C₂²	semidirect
34. #16863474	C₂²	semidirect
35. #16863474	C₂²	semidirect
36. #16863474	C₂²	semidirect
37. #16863474	C₂²	semidirect
41. #16863468	C₂²	semidirect
42. #16863468	C₂²	semidirect
43. #16863468	C₂²	semidirect
44. #16863468	C₂²	semidirect
45. #16863468	C₂²	semidirect
46. #16863468	C₂²	semidirect
47. #16863468	C₂²	semidirect
48. #16863468	C₂²	semidirect
49. #16863468	C₂²	semidirect
50. #16863468	C₂²	semidirect
51. #16863468	C₂²	semidirect
52. #16863468	C₂²	semidirect
53. #16863468	C₂²	semidirect
54. #16863468	C₂²	semidirect
55. #16863468	C₂²	semidirect
56. #16863468	C₂²	semidirect
57. #16863468	C₂²	semidirect
58. #16863468	C₂²	semidirect
59. #16863468	C₂²	semidirect
60. #16863468	C₂²	semidirect
61. #16863468	C₂²	semidirect
62. D₄×C₆₇⋊C₈	C₂²	semidirect
63. D₄×C₆₇⋊C₈	C₂²	semidirect
64. D₄×C₆₇⋊C₈	C₂²	semidirect
65. D₄×C₆₇⋊C₈	C₂²	semidirect
66. D₄×C₆₇⋊C₈	C₂²	semidirect
67. D₄×C₆₇⋊C₈	C₂²	semidirect
68. #16863457	C₂²	semidirect
69. #16863457	C₂²	semidirect
70. #16863457	C₂²	semidirect
71. #16863457	C₂²	semidirect
72. #16863453	C₂²	semidirect
73. #16863453	C₂²	semidirect
74. #16863453	C₂²	semidirect
75. #16863449	C₂²	semidirect
76. #16863423	C₂²	semidirect
77. #16863423	C₂²	semidirect
78. #16863420	C₂²	semidirect
79. C₂×C₄⋊(C₆₇⋊C₈)	C₂²	semidirect
84. #16863363	C₂²	semidirect
85. #16863363	C₂²	semidirect
86. #16863363	C₂²	semidirect
87. #16863363	C₂²	semidirect
88. #16863363	C₂²	semidirect
89. #16863363	C₂²	semidirect
90. #16863363	C₂²	semidirect
91. #16863363	C₂²	semidirect
92. #16863363	C₂²	semidirect
93. #16863363	C₂²	semidirect
94. #16863363	C₂²	semidirect
95. #16863363	C₂²	semidirect
96. #16863360	C₂²	semidirect
97. #16863360	C₂²	semidirect
98. #16863360	C₂²	semidirect
99. #16863360	C₂²	semidirect
100. #16863360	C₂²	semidirect
101. #16863360	C₂²	semidirect
102. C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	semidirect
103. C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	semidirect
104. C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	semidirect
105. C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	semidirect
106. C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	semidirect
107. C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	semidirect
108. #16863352	C₂²	semidirect
109. #16863352	C₂²	semidirect
110. C₄×#11761612	C₂²	semidirect
111. C₂×#14523954	C₂²	semidirect
679. C₆₇	#60240	semidirect

Maximal subgroups

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

subgroup	index
#22569285	2
#22569280	2
#22569271	2
#22569265	2
#22569257	2
#22569244	2
#22569238	2
#22568953	2
D₄×#11761612	2
#22568936	2
#22568927	2
#22568913	2
#22568904	2
C₂×#16863468	2
#22568875	2
#22568860	2
#22568658	2
#22568654	2
C₂×#16863363	2
D₄×#41×C₆₇	2
#60240	67