Subgroups — C₆₇×#61186 #30740437

Order 17152.

2022 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3486	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3328	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3327	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3316	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3313	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3312	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3312	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3300	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3299	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3059	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#451×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2950	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#419×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
31	#556×C₆₇	C₂²	1	2	yes	—
32	#554×C₆₇	C₂²	1	2	yes	—
33	#552×C₆₇	—	2	2	no	—
34	#552×C₆₇	C₂²	1	2	yes	—
35	#552×C₆₇	C₂²	1	2	yes	—
36	#551×C₆₇	—	2	2	no	—
37	D₄×Q₈×C₆₇	—	2	1	no	—
38	D₄×Q₈×C₆₇	—	2	1	no	—
39	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
40	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
41	#548×C₆₇	—	2	1	no	—
42	#548×C₆₇	—	2	1	no	—
43	#548×C₆₇	C₂²	1	2	yes	—
44	#548×C₆₇	C₂²	1	2	yes	—
45	#544×C₆₇	C₂²	1	1	yes	characteristic
46	#542×C₆₇	—	2	1	no	—
47	#541×C₆₇	—	2	1	no	—
48	#536×C₆₇	—	2	2	no	—
49	#536×C₆₇	C₂²	1	1	yes	characteristic
50	#536×C₆₇	C₂²	1	1	yes	characteristic
51	#536×C₆₇	C₂²	1	1	yes	characteristic
52	#533×C₆₇	—	2	1	no	—
53	#529×C₆₇	—	2	1	no	—
54	#525×C₆₇	—	2	2	no	—
55	#525×C₆₇	C₂²	1	1	yes	characteristic
56	#525×C₆₇	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
58	#520×C₆₇	C₂²	1	1	yes	characteristic
59	#519×C₆₇	C₂²	1	1	yes	characteristic
60	#519×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
62	#491×C₆₇	C₂²	1	2	yes	complemented
63	#489×C₆₇	C₂²	1	2	yes	complemented
64	#488×C₆₇	C₂²	1	2	yes	complemented
65	#487×C₆₇	C₂²	1	2	yes	complemented
66	#485×C₆₇	C₂²	1	1	yes	characteristic
67	#485×C₆₇	C₂²	1	1	yes	characteristic
68	#485×C₆₇	C₂²	1	2	yes	complemented
69	#485×C₆₇	C₂²	1	2	yes	complemented
70	#484×C₆₇	C₂²	1	1	yes	characteristic
71	#484×C₆₇	C₂²	1	2	yes	complemented
72	#483×C₆₇	C₂²	1	1	yes	characteristic
73	#483×C₆₇	C₂²	1	2	yes	complemented
74	#482×C₆₇	C₂²	1	1	yes	characteristic
75	#482×C₆₇	C₂²	1	1	yes	characteristic
76	#481×C₆₇	C₂²	1	1	yes	characteristic
77	#480×C₆₇	C₂²	1	1	yes	characteristic
78	#479×C₆₇	C₂²	1	2	yes	complemented
79	#479×C₆₇	C₂²	1	2	yes	complemented
80	#477×C₆₇	C₂²	1	2	yes	complemented
81	#475×C₆₇	C₂²	1	2	yes	complemented
82	#470×C₆₇	C₂²	1	2	yes	—
83	#470×C₆₇	C₂²	1	2	yes	complemented
84	#470×C₆₇	C₂²	1	2	yes	complemented
85	#468×C₆₇	C₂²	1	2	yes	—
86	#467×C₆₇	C₂²	1	2	yes	—
87	#467×C₆₇	C₂²	1	2	yes	complemented
88	#467×C₆₇	C₂²	1	2	yes	complemented
89	#465×C₆₇	C₂²	1	2	yes	—
90	#464×C₆₇	C₂²	1	2	yes	complemented
91	#464×C₆₇	C₂²	1	2	yes	complemented
92	#462×C₆₇	C₂²	1	2	yes	complemented
93	#462×C₆₇	C₂²	1	2	yes	complemented
94	#452×C₆₇	C₂²	1	2	yes	complemented
95	#452×C₆₇	C₂²	1	2	yes	complemented
96	#451×C₆₇	C₂²	1	2	yes	—
97	#451×C₆₇	C₂²	1	2	yes	—
98	#451×C₆₇	C₂²	1	2	yes	—
99	#451×C₆₇	C₂²	1	2	yes	—
100	#451×C₆₇	C₂²	1	2	yes	complemented
101	#451×C₆₇	C₂²	1	2	yes	complemented
102	#441×C₆₇	C₂²	1	2	yes	complemented
103	#441×C₆₇	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
106	#436×C₆₇	C₂²	1	2	yes	—
107	#435×C₆₇	C₂²	1	2	yes	—
108	#435×C₆₇	C₂²	1	2	yes	—
109	C₈×D₄×C₆₇	C₂²	1	2	yes	—
110	#428×C₆₇	C₂²	1	1	yes	characteristic
111	#427×C₆₇	C₂²	1	1	yes	characteristic
112	#427×C₆₇	C₂²	1	1	yes	characteristic
113	#424×C₆₇	C₂²	1	1	yes	characteristic
114	#419×C₆₇	C₂²	1	1	yes	characteristic
115	#419×C₆₇	C₂²	1	1	yes	characteristic
116	#419×C₆₇	C₂²	1	1	yes	characteristic
117	#419×C₆₇	C₂²	1	2	yes	—
118	#419×C₆₇	C₂²	1	2	yes	—
119	#419×C₆₇	C₂²	1	1	yes	characteristic
120	#419×C₆₇	C₂²	1	1	yes	characteristic
121	#419×C₆₇	C₂²	1	2	yes	complemented
122	#417×C₆₇	C₂²	1	1	yes	characteristic
123	#417×C₆₇	C₂²	1	2	yes	complemented
124	#416×C₆₇	C₂²	1	1	yes	characteristic
125	#416×C₆₇	C₂²	1	1	yes	characteristic
126	#416×C₆₇	C₂²	1	2	yes	complemented
127	C₂×#103×C₆₇	C₂²	1	2	yes	—
128	C₂×#103×C₆₇	C₂²	1	2	yes	—
129	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
131	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
134	#405×C₆₇	C₂²	1	1	yes	characteristic
135	2₋¹⁺⁴×C₆₇	—	2	4	no	—
136	2₋¹⁺⁴×C₆₇	—	4	2	no	—
137	C₂×#41×C₆₇	—	2	2	no	—
138	C₂×#41×C₆₇	—	2	1	no	—
139	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×#41×C₆₇	C₂³	1	2	yes	—
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₆₇	—	2	1	no	—
143	C₂²×Q₈×C₆₇	—	2	1	no	—
144	C₂²×Q₈×C₆₇	—	2	1	no	—
145	C₂²×Q₈×C₆₇	—	2	1	no	—
146	C₂²×Q₈×C₆₇	—	2	4	no	—
147	C₂²×Q₈×C₆₇	—	4	2	no	—
148	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
151	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
152	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
153	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₆₇	—	2	1	no	—
155	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
156	#137×C₆₇	—	4	2	no	—
157	C₂×Q₁₆×C₆₇	—	2	4	no	—
158	C₂×Q₁₆×C₆₇	—	4	2	no	—
159	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
163	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
165	#131×C₆₇	—	4	2	no	—
166	C₂×M₁₆×C₆₇	—	4	2	no	—
167	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
170	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
171	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
172	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
174	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
175	C₄⋊Q₈×C₆₇	—	2	1	no	—
176	C₄⋊Q₈×C₆₇	—	2	1	no	—
177	C₄⋊Q₈×C₆₇	—	2	1	no	—
178	C₄⋊Q₈×C₆₇	—	2	2	no	—
179	C₄⋊Q₈×C₆₇	—	2	2	no	—
180	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
181	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
182	#126×C₆₇	—	2	2	no	—
183	#126×C₆₇	—	2	2	no	—
184	#126×C₆₇	—	2	2	no	—
185	#126×C₆₇	—	2	2	no	—
186	#125×C₆₇	—	2	1	no	—
187	#125×C₆₇	—	2	2	no	—
188	#125×C₆₇	—	2	2	no	—
189	#125×C₆₇	—	2	2	no	—
190	#125×C₆₇	C₂³	1	2	yes	—
191	#124×C₆₇	—	2	1	no	—
192	#124×C₆₇	—	2	1	no	—
193	#124×C₆₇	—	2	2	no	—
194	#124×C₆₇	—	2	2	no	—
195	#124×C₆₇	—	2	2	no	—
196	#124×C₆₇	C₂³	1	2	yes	—
197	#123×C₆₇	—	2	2	no	—
198	#123×C₆₇	—	2	2	no	—
199	#123×C₆₇	—	2	2	no	—
200	#123×C₆₇	—	2	2	no	—
201	#123×C₆₇	—	2	1	no	—
202	#123×C₆₇	—	2	2	no	—
203	#123×C₆₇	D₄	1	2	yes	—
204	C₂²⋊Q₈×C₆₇	—	2	1	no	—
205	C₂²⋊Q₈×C₆₇	—	2	1	no	—
206	C₂²⋊Q₈×C₆₇	—	2	2	no	—
207	C₂²⋊Q₈×C₆₇	—	2	2	no	—
208	C₂²⋊Q₈×C₆₇	—	2	1	no	—
209	C₂²⋊Q₈×C₆₇	—	2	1	no	—
210	C₂²⋊Q₈×C₆₇	—	2	2	no	—
211	C₂²⋊Q₈×C₆₇	—	2	2	no	—
212	C₂²⋊Q₈×C₆₇	—	2	2	no	—
213	C₂²⋊Q₈×C₆₇	—	2	2	no	—
214	C₂²⋊Q₈×C₆₇	—	2	2	no	—
215	C₂²⋊Q₈×C₆₇	—	2	2	no	—
216	C₂²⋊Q₈×C₆₇	—	2	2	no	—
217	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
218	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
219	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
223	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
224	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
225	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
226	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
227	#121×C₆₇	—	2	2	no	—
228	#121×C₆₇	—	2	2	no	—
229	#121×C₆₇	D₄	1	1	yes	characteristic
230	#121×C₆₇	D₄	1	1	yes	characteristic
231	#121×C₆₇	C₂³	1	1	yes	characteristic
232	#121×C₆₇	C₂³	1	1	yes	characteristic
233	#120×C₆₇	—	2	1	no	—
234	#120×C₆₇	D₄	1	2	yes	—
235	C₄×Q₈×C₆₇	—	2	1	no	—
236	C₄×Q₈×C₆₇	—	2	1	no	—
237	C₄×Q₈×C₆₇	—	2	1	no	—
238	C₄×Q₈×C₆₇	—	2	1	no	—
239	C₄×Q₈×C₆₇	—	2	1	no	—
240	C₄×Q₈×C₆₇	—	2	2	no	—
241	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
242	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
243	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
244	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
245	C₄×D₄×C₆₇	—	2	1	no	—
246	C₄×D₄×C₆₇	—	2	2	no	—
247	C₄×D₄×C₆₇	—	2	2	no	—
248	C₄×D₄×C₆₇	—	2	2	no	—
249	C₄×D₄×C₆₇	—	2	2	no	—
250	C₄×D₄×C₆₇	—	2	1	no	—
251	C₄×D₄×C₆₇	—	2	1	no	—
252	C₄×D₄×C₆₇	—	2	2	no	—
253	C₄×D₄×C₆₇	—	2	2	no	—
254	C₄×D₄×C₆₇	C₂³	1	2	yes	—
255	C₄×D₄×C₆₇	C₂³	1	2	yes	—
256	#117×C₆₇	—	2	1	no	—
257	#117×C₆₇	—	2	1	no	—
258	#117×C₆₇	—	2	2	no	—
259	#117×C₆₇	—	2	2	no	—
260	#117×C₆₇	—	2	2	no	—
261	#117×C₆₇	—	2	2	no	—
262	#117×C₆₇	C₂³	1	1	yes	characteristic
263	#117×C₆₇	C₂³	1	1	yes	characteristic
264	#117×C₆₇	C₂³	1	2	yes	—
265	#117×C₆₇	C₂³	1	1	yes	characteristic
266	#117×C₆₇	C₂³	1	1	yes	characteristic
267	#117×C₆₇	C₂³	1	1	yes	characteristic
268	#117×C₆₇	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
273	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
275	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
276	C₂×C₄²×C₆₇	—	2	1	no	—
277	#107×C₆₇	C₂³	1	2	yes	—
278	#107×C₆₇	C₂³	1	1	yes	characteristic
279	#107×C₆₇	C₂³	1	1	yes	characteristic
280	#107×C₆₇	C₂³	1	1	yes	characteristic
281	#107×C₆₇	C₂³	1	1	yes	characteristic
282	#106×C₆₇	C₂³	1	2	yes	—
283	#106×C₆₇	C₂³	1	1	yes	characteristic
284	#106×C₆₇	C₂³	1	1	yes	characteristic
285	#106×C₆₇	C₂³	1	1	yes	characteristic
286	#106×C₆₇	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
288	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	1	yes	characteristic
294	#103×C₆₇	C₂³	1	1	yes	characteristic
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	2	yes	—
297	#103×C₆₇	C₂³	1	1	yes	characteristic
298	#103×C₆₇	C₂³	1	1	yes	characteristic
299	#103×C₆₇	C₂³	1	2	yes	—
300	#103×C₆₇	C₂³	1	2	yes	—
301	#103×C₆₇	C₂³	1	2	yes	—
302	#103×C₆₇	C₂³	1	2	yes	—
303	#103×C₆₇	C₂³	1	2	yes	—
304	#103×C₆₇	C₂³	1	2	yes	—
305	#103×C₆₇	C₂³	1	2	yes	—
306	#103×C₆₇	C₂³	1	2	yes	—
307	#103×C₆₇	C₂³	1	2	yes	—
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	#102×C₆₇	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
319	#97×C₆₇	C₂³	1	2	yes	—
320	C₄×C₈×C₆₇	C₂³	1	2	yes	—
321	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
322	#41×C₆₇	—	2	2	no	—
323	#41×C₆₇	—	2	2	no	—
324	#41×C₆₇	—	2	4	no	—
325	#41×C₆₇	—	2	2	no	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	—	4	2	no	—
328	#41×C₆₇	—	4	8	no	—
329	#41×C₆₇	—	4	4	no	—
330	C₂×Q₈×C₆₇	—	2	1	no	—
331	C₂×Q₈×C₆₇	—	2	1	no	—
332	C₂×Q₈×C₆₇	—	2	2	no	—
333	C₂×Q₈×C₆₇	—	2	2	no	—
334	C₂×Q₈×C₆₇	—	2	1	no	—
335	C₂×Q₈×C₆₇	—	2	2	no	—
336	C₂×Q₈×C₆₇	—	2	2	no	—
337	C₂×Q₈×C₆₇	—	2	2	no	—
338	C₂×Q₈×C₆₇	—	2	4	no	—
339	C₂×Q₈×C₆₇	—	2	4	no	—
340	C₂×Q₈×C₆₇	—	2	4	no	—
341	C₂×Q₈×C₆₇	—	2	2	no	—
342	C₂×Q₈×C₆₇	—	2	2	no	—
343	C₂×Q₈×C₆₇	—	2	2	no	—
344	C₂×Q₈×C₆₇	—	2	2	no	—
345	C₂×Q₈×C₆₇	—	4	4	no	—
346	C₂×Q₈×C₆₇	—	4	2	no	—
347	C₂×Q₈×C₆₇	—	4	2	no	—
348	C₂×Q₈×C₆₇	—	4	2	no	—
349	C₂×Q₈×C₆₇	—	4	4	no	—
350	C₂×Q₈×C₆₇	—	4	4	no	—
351	C₂×Q₈×C₆₇	—	4	4	no	—
352	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
353	C₂×Q₈×C₆₇	#41	1	4	yes	—
354	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
357	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
358	C₂×D₄×C₆₇	—	2	1	no	—
359	C₂×D₄×C₆₇	—	2	1	no	—
360	C₂×D₄×C₆₇	—	2	1	no	—
361	C₂×D₄×C₆₇	—	2	2	no	—
362	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
363	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
364	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
365	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
366	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₆₇	—	2	1	no	—
368	C₂²×C₄×C₆₇	—	2	2	no	—
369	C₂²×C₄×C₆₇	—	2	2	no	—
370	C₂²×C₄×C₆₇	—	2	1	no	—
371	C₂²×C₄×C₆₇	—	2	1	no	—
372	C₂²×C₄×C₆₇	—	2	2	no	—
373	C₂²×C₄×C₆₇	—	2	2	no	—
374	C₂²×C₄×C₆₇	—	2	2	no	—
375	C₂²×C₄×C₆₇	—	2	1	no	—
376	C₂²×C₄×C₆₇	—	2	1	no	—
377	C₂²×C₄×C₆₇	—	2	1	no	—
378	C₂²×C₄×C₆₇	—	2	2	no	—
379	C₂²×C₄×C₆₇	—	2	2	no	—
380	C₂²×C₄×C₆₇	—	2	1	no	—
381	C₂²×C₄×C₆₇	—	4	4	no	—
382	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
389	Q₁₆×C₆₇	—	2	4	no	—
390	Q₁₆×C₆₇	—	2	4	no	—
391	Q₁₆×C₆₇	—	4	2	no	—
392	Q₁₆×C₆₇	—	4	2	no	—
393	Q₁₆×C₆₇	—	4	2	no	—
394	SD₁₆×C₆₇	—	4	2	no	—
395	M₁₆×C₆₇	—	2	2	no	—
396	M₁₆×C₆₇	—	2	2	no	—
397	M₁₆×C₆₇	—	4	2	no	—
398	M₁₆×C₆₇	—	4	2	no	—
399	C₂×C₈×C₆₇	—	2	2	no	—
400	C₂×C₈×C₆₇	—	2	2	no	—
401	C₂×C₈×C₆₇	—	4	2	no	—
402	C₂×C₈×C₆₇	—	4	2	no	—
403	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
404	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
409	C₄⋊C₄×C₆₇	—	2	2	no	—
410	C₄⋊C₄×C₆₇	—	2	2	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	2	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	—	2	2	no	—
418	C₄⋊C₄×C₆₇	—	2	2	no	—
419	C₄⋊C₄×C₆₇	—	2	2	no	—
420	C₄⋊C₄×C₆₇	—	2	2	no	—
421	C₄⋊C₄×C₆₇	—	2	2	no	—
422	C₄⋊C₄×C₆₇	—	2	2	no	—
423	C₄⋊C₄×C₆₇	—	2	2	no	—
424	C₄⋊C₄×C₆₇	—	2	2	no	—
425	C₄⋊C₄×C₆₇	—	2	2	no	—
426	C₄⋊C₄×C₆₇	—	2	1	no	—
427	C₄⋊C₄×C₆₇	—	2	1	no	—
428	C₄⋊C₄×C₆₇	—	2	2	no	—
429	C₄⋊C₄×C₆₇	—	2	2	no	—
430	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
431	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
432	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
434	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
436	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
441	C₂²⋊C₄×C₆₇	—	2	1	no	—
442	C₂²⋊C₄×C₆₇	—	2	1	no	—
443	C₂²⋊C₄×C₆₇	—	2	1	no	—
444	C₂²⋊C₄×C₆₇	—	2	1	no	—
445	C₂²⋊C₄×C₆₇	—	2	2	no	—
446	C₂²⋊C₄×C₆₇	—	2	2	no	—
447	C₂²⋊C₄×C₆₇	—	2	1	no	—
448	C₂²⋊C₄×C₆₇	—	2	2	no	—
449	C₂²⋊C₄×C₆₇	—	2	2	no	—
450	C₂²⋊C₄×C₆₇	—	2	1	no	—
451	C₂²⋊C₄×C₆₇	—	2	1	no	—
452	C₂²⋊C₄×C₆₇	—	2	2	no	—
453	C₂²⋊C₄×C₆₇	—	2	2	no	—
454	C₂²⋊C₄×C₆₇	—	2	2	no	—
455	C₂²⋊C₄×C₆₇	—	2	2	no	—
456	C₂²⋊C₄×C₆₇	—	2	2	no	—
457	C₂²⋊C₄×C₆₇	—	2	1	no	—
458	C₂²⋊C₄×C₆₇	—	2	1	no	—
459	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
460	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
464	C₄²×C₆₇	—	2	1	no	—
465	C₄²×C₆₇	—	2	1	no	—
466	C₄²×C₆₇	—	2	1	no	—
467	C₄²×C₆₇	—	2	1	no	—
468	C₄²×C₆₇	—	2	2	no	—
469	C₄²×C₆₇	—	2	2	no	—
470	C₄²×C₆₇	—	2	2	no	—
471	C₄²×C₆₇	—	2	2	no	—
472	C₄²×C₆₇	—	2	2	no	—
473	C₄²×C₆₇	—	2	1	no	—
474	C₄²×C₆₇	C₂⁴	1	2	yes	—
475	C₂³×C₆₇	—	2	2	no	—
476	C₂³×C₆₇	—	2	2	no	—
477	C₂³×C₆₇	—	2	1	no	—
478	C₂³×C₆₇	—	4	1	no	—
479	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
480	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
481	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
482	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
483	Q₈×C₆₇	—	2	4	no	—
484	Q₈×C₆₇	—	2	2	no	—
485	Q₈×C₆₇	—	2	2	no	—
486	Q₈×C₆₇	—	2	2	no	—
487	Q₈×C₆₇	—	2	2	no	—
488	Q₈×C₆₇	—	2	1	no	—
489	Q₈×C₆₇	—	2	2	no	—
490	Q₈×C₆₇	—	2	2	no	—
491	Q₈×C₆₇	—	2	1	no	—
492	Q₈×C₆₇	—	4	4	no	—
493	Q₈×C₆₇	—	4	4	no	—
494	Q₈×C₆₇	—	4	4	no	—
495	Q₈×C₆₇	—	4	2	no	—
496	Q₈×C₆₇	—	4	2	no	—
497	Q₈×C₆₇	—	8	2	no	—
498	Q₈×C₆₇	C₂×#41	1	4	yes	—
499	D₄×C₆₇	—	2	4	no	—
500	D₄×C₆₇	—	2	4	no	—
501	D₄×C₆₇	—	2	2	no	—
502	D₄×C₆₇	—	2	1	no	—
503	D₄×C₆₇	—	2	1	no	—
504	D₄×C₆₇	—	4	2	no	—
505	D₄×C₆₇	—	4	4	no	—
506	D₄×C₆₇	—	4	2	no	—
507	D₄×C₆₇	—	4	2	no	—
508	D₄×C₆₇	—	4	2	no	—
509	C₂×C₄×C₆₇	—	2	2	no	—
510	C₂×C₄×C₆₇	—	2	4	no	—
511	C₂×C₄×C₆₇	—	2	2	no	—
512	C₂×C₄×C₆₇	—	2	2	no	—
513	C₂×C₄×C₆₇	—	2	2	no	—
514	C₂×C₄×C₆₇	—	2	1	no	—
515	C₂×C₄×C₆₇	—	2	1	no	—
516	C₂×C₄×C₆₇	—	2	2	no	—
517	C₂×C₄×C₆₇	—	2	1	no	—
518	C₂×C₄×C₆₇	—	2	2	no	—
519	C₂×C₄×C₆₇	—	2	1	no	—
520	C₂×C₄×C₆₇	—	2	1	no	—
521	C₂×C₄×C₆₇	—	2	1	no	—
522	C₂×C₄×C₆₇	—	2	1	no	—
523	C₂×C₄×C₆₇	—	2	1	no	—
524	C₂×C₄×C₆₇	—	2	1	no	—
525	C₂×C₄×C₆₇	—	2	2	no	—
526	C₂×C₄×C₆₇	—	2	1	no	—
527	C₂×C₄×C₆₇	—	2	2	no	—
528	C₂×C₄×C₆₇	—	2	2	no	—
529	C₂×C₄×C₆₇	—	2	1	no	—
530	C₂×C₄×C₆₇	—	4	4	no	—
531	C₂×C₄×C₆₇	—	4	4	no	—
532	C₂×C₄×C₆₇	—	4	4	no	—
533	C₂×C₄×C₆₇	—	4	4	no	—
534	C₂×C₄×C₆₇	—	4	2	no	—
535	C₂×C₄×C₆₇	—	4	2	no	—
536	C₂×C₄×C₆₇	—	4	2	no	—
537	C₂×C₄×C₆₇	—	4	2	no	—
538	C₂×C₄×C₆₇	—	8	2	no	—
539	C₂×C₄×C₆₇	—	8	1	no	—
540	C₂×C₄×C₆₇	—	8	1	no	—
541	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
542	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
545	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
548	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
549	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
550	C₈×C₆₇	—	2	1	no	—
551	C₈×C₆₇	—	2	1	no	—
552	C₈×C₆₇	—	2	1	no	—
553	C₈×C₆₇	—	2	1	no	—
554	C₈×C₆₇	—	2	2	no	—
555	C₈×C₆₇	—	2	2	no	—
556	C₂²×C₆₇	—	2	1	no	—
557	C₂²×C₆₇	—	2	1	no	—
558	C₂²×C₆₇	—	2	1	no	—
559	C₂²×C₆₇	—	2	1	no	—
560	C₂²×C₆₇	—	2	2	no	—
561	C₂²×C₆₇	—	2	1	no	—
562	C₂²×C₆₇	—	2	1	no	—
563	C₂²×C₆₇	—	2	2	no	—
564	C₂²×C₆₇	—	2	2	no	—
565	C₂²×C₆₇	—	2	1	no	—
566	C₂²×C₆₇	—	4	4	no	—
567	C₂²×C₆₇	—	4	1	no	—
568	C₂²×C₆₇	—	4	1	no	—
569	C₂²×C₆₇	—	4	1	no	—
570	C₂²×C₆₇	#546	1	2	yes	—
571	C₂²×C₆₇	#578	1	2	yes	—
572	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
573	C₄×C₆₇	—	2	2	no	—
574	C₄×C₆₇	—	2	1	no	—
575	C₄×C₆₇	—	2	1	no	—
576	C₄×C₆₇	—	2	4	no	—
577	C₄×C₆₇	—	2	2	no	—
578	C₄×C₆₇	—	2	2	no	—
579	C₄×C₆₇	—	4	1	no	—
580	C₄×C₆₇	—	4	2	no	—
581	C₄×C₆₇	—	4	1	no	—
582	C₄×C₆₇	—	4	1	no	—
583	C₄×C₆₇	—	4	1	no	—
584	C₄×C₆₇	—	4	2	no	—
585	C₄×C₆₇	—	4	2	no	—
586	C₄×C₆₇	—	4	1	no	—
587	C₄×C₆₇	—	4	1	no	—
588	C₄×C₆₇	—	4	1	no	—
589	C₄×C₆₇	#546	1	2	yes	—
590	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
591	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
592	#61186	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
593	C₂×C₆₇	—	2	2	no	—
594	C₂×C₆₇	—	2	2	no	—
595	C₂×C₆₇	—	4	2	no	—
596	C₂×C₆₇	—	4	1	no	—
597	C₂×C₆₇	—	8	1	no	—
598	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
599	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
600	C₂×C₆₇	#3586	1	1	yes	characteristic
601	#3495	C₂×C₆₇	1	1	yes	characteristic, complemented
602	#3486	C₂×C₆₇	1	1	yes	characteristic
603	#3328	C₂×C₆₇	1	2	yes	complemented
604	#3327	C₂×C₆₇	1	2	yes	complemented
605	#3316	C₂×C₆₇	1	2	yes	complemented
606	#3313	C₂×C₆₇	1	2	yes	complemented
607	#3312	C₂×C₆₇	1	2	yes	complemented
608	#3312	C₂×C₆₇	1	2	yes	complemented
609	#3300	C₂×C₆₇	1	2	yes	complemented
610	#3299	C₂×C₆₇	1	2	yes	complemented
611	#3137	C₂×C₆₇	1	1	yes	characteristic, complemented
612	#3097	C₂×C₆₇	1	1	yes	characteristic, complemented
613	#3091	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#3082	C₂×C₆₇	1	1	yes	characteristic, complemented
615	#3059	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#3056	C₂×C₆₇	1	1	yes	characteristic, complemented
617	#3044	C₂×C₆₇	1	1	yes	characteristic, complemented
618	#3011	C₂×C₆₇	1	1	yes	characteristic, complemented
619	C₂×#451	C₂×C₆₇	1	1	yes	characteristic, complemented
620	#2950	C₂×C₆₇	1	1	yes	characteristic, complemented
621	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
622	#2898	C₂×C₆₇	1	1	yes	characteristic, complemented
623	C₂×#419	C₂×C₆₇	1	1	yes	characteristic, complemented
624	C₆₇	#61186	1	1	yes	characteristic, direct product factor, Sylow
625	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
626	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
627	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
628	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
629	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
630	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
631	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
632	#556	C₂²×C₆₇	1	2	yes	—
633	#554	C₂²×C₆₇	1	2	yes	—
634	#552	—	2	2	no	—
635	#552	C₂²×C₆₇	1	2	yes	—
636	#552	C₂²×C₆₇	1	2	yes	—
637	#551	—	2	2	no	—
638	D₄×Q₈	—	2	1	no	—
639	D₄×Q₈	—	2	1	no	—
640	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
641	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
642	#548	—	2	1	no	—
643	#548	—	2	1	no	—
644	#548	C₂²×C₆₇	1	2	yes	—
645	#548	C₂²×C₆₇	1	2	yes	—
646	#544	C₂²×C₆₇	1	1	yes	characteristic
647	#542	—	2	1	no	—
648	#541	—	2	1	no	—
649	#536	—	2	2	no	—
650	#536	C₂²×C₆₇	1	1	yes	characteristic
651	#536	C₂²×C₆₇	1	1	yes	characteristic
652	#536	C₂²×C₆₇	1	1	yes	characteristic
653	#533	—	2	1	no	—
654	#529	—	2	1	no	—
655	#525	—	2	2	no	—
656	#525	C₂²×C₆₇	1	1	yes	characteristic
657	#525	C₂²×C₆₇	1	1	yes	characteristic
658	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
659	#520	C₂²×C₆₇	1	1	yes	characteristic
660	#519	C₂²×C₆₇	1	1	yes	characteristic
661	#519	C₂²×C₆₇	1	1	yes	characteristic
662	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
663	#491	C₂²×C₆₇	1	2	yes	complemented
664	#489	C₂²×C₆₇	1	2	yes	complemented
665	#488	C₂²×C₆₇	1	2	yes	complemented
666	#487	C₂²×C₆₇	1	2	yes	complemented
667	#485	C₂²×C₆₇	1	1	yes	characteristic
668	#485	C₂²×C₆₇	1	1	yes	characteristic
669	#485	C₂²×C₆₇	1	2	yes	complemented
670	#485	C₂²×C₆₇	1	2	yes	complemented
671	#484	C₂²×C₆₇	1	1	yes	characteristic
672	#484	C₂²×C₆₇	1	2	yes	complemented
673	#483	C₂²×C₆₇	1	1	yes	characteristic
674	#483	C₂²×C₆₇	1	2	yes	complemented
675	#482	C₂²×C₆₇	1	1	yes	characteristic
676	#482	C₂²×C₆₇	1	1	yes	characteristic
677	#481	C₂²×C₆₇	1	1	yes	characteristic
678	#480	C₂²×C₆₇	1	1	yes	characteristic
679	#479	C₂²×C₆₇	1	2	yes	complemented
680	#479	C₂²×C₆₇	1	2	yes	complemented
681	#477	C₂²×C₆₇	1	2	yes	complemented
682	#475	C₂²×C₆₇	1	2	yes	complemented
683	#470	C₂²×C₆₇	1	2	yes	—
684	#470	C₂²×C₆₇	1	2	yes	complemented
685	#470	C₂²×C₆₇	1	2	yes	complemented
686	#468	C₂²×C₆₇	1	2	yes	—
687	#467	C₂²×C₆₇	1	2	yes	—
688	#467	C₂²×C₆₇	1	2	yes	complemented
689	#467	C₂²×C₆₇	1	2	yes	complemented
690	#465	C₂²×C₆₇	1	2	yes	—
691	#464	C₂²×C₆₇	1	2	yes	complemented
692	#464	C₂²×C₆₇	1	2	yes	complemented
693	#462	C₂²×C₆₇	1	2	yes	complemented
694	#462	C₂²×C₆₇	1	2	yes	complemented
695	#452	C₂²×C₆₇	1	2	yes	complemented
696	#452	C₂²×C₆₇	1	2	yes	complemented
697	#451	C₂²×C₆₇	1	2	yes	—
698	#451	C₂²×C₆₇	1	2	yes	—
699	#451	C₂²×C₆₇	1	2	yes	—
700	#451	C₂²×C₆₇	1	2	yes	—
701	#451	C₂²×C₆₇	1	2	yes	complemented
702	#451	C₂²×C₆₇	1	2	yes	complemented
703	#441	C₂²×C₆₇	1	2	yes	complemented
704	#441	C₂²×C₆₇	1	2	yes	complemented
705	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
706	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
707	#436	C₂²×C₆₇	1	2	yes	—
708	#435	C₂²×C₆₇	1	2	yes	—
709	#435	C₂²×C₆₇	1	2	yes	—
710	C₈×D₄	C₂²×C₆₇	1	2	yes	—
711	#428	C₂²×C₆₇	1	1	yes	characteristic
712	#427	C₂²×C₆₇	1	1	yes	characteristic
713	#427	C₂²×C₆₇	1	1	yes	characteristic
714	#424	C₂²×C₆₇	1	1	yes	characteristic
715	#419	C₂²×C₆₇	1	2	yes	—
716	#419	C₂²×C₆₇	1	1	yes	characteristic
717	#419	C₂²×C₆₇	1	1	yes	characteristic
718	#419	C₂²×C₆₇	1	1	yes	characteristic
719	#419	C₂²×C₆₇	1	1	yes	characteristic
720	#419	C₂²×C₆₇	1	2	yes	—
721	#419	C₂²×C₆₇	1	1	yes	characteristic
722	#419	C₂²×C₆₇	1	2	yes	complemented
723	#417	C₂²×C₆₇	1	1	yes	characteristic
724	#417	C₂²×C₆₇	1	2	yes	complemented
725	#416	C₂²×C₆₇	1	1	yes	characteristic
726	#416	C₂²×C₆₇	1	1	yes	characteristic
727	#416	C₂²×C₆₇	1	2	yes	complemented
728	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
729	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
730	C₂×#103	C₂²×C₆₇	1	2	yes	—
731	C₂×#103	C₂²×C₆₇	1	2	yes	—
732	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
733	#408	C₂²×C₆₇	1	1	yes	characteristic
734	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
735	#405	C₂²×C₆₇	1	1	yes	characteristic
736	2₋¹⁺⁴	—	2	4	no	—
737	2₋¹⁺⁴	—	4	2	no	—
738	C₂×#41	—	2	2	no	—
739	C₂×#41	—	2	1	no	—
740	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×#41	C₂³×C₆₇	1	2	yes	—
742	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
743	C₂²×Q₈	—	2	1	no	—
744	C₂²×Q₈	—	2	1	no	—
745	C₂²×Q₈	—	2	1	no	—
746	C₂²×Q₈	—	2	1	no	—
747	C₂²×Q₈	—	2	4	no	—
748	C₂²×Q₈	—	4	2	no	—
749	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
750	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
751	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
752	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
753	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
754	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
755	C₂³×C₄	—	2	1	no	—
756	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
757	#137	—	4	2	no	—
758	C₂×Q₁₆	—	2	4	no	—
759	C₂×Q₁₆	—	4	2	no	—
760	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
761	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
762	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
763	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
764	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
765	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
766	#131	—	4	2	no	—
767	C₂×M₁₆	—	4	2	no	—
768	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
769	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
770	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
771	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
772	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
773	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
774	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
775	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
776	C₄⋊Q₈	—	2	1	no	—
777	C₄⋊Q₈	—	2	1	no	—
778	C₄⋊Q₈	—	2	1	no	—
779	C₄⋊Q₈	—	2	2	no	—
780	C₄⋊Q₈	—	2	2	no	—
781	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
782	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
783	#126	—	2	2	no	—
784	#126	—	2	2	no	—
785	#126	—	2	2	no	—
786	#126	—	2	2	no	—
787	#125	—	2	1	no	—
788	#125	—	2	2	no	—
789	#125	—	2	2	no	—
790	#125	—	2	2	no	—
791	#125	C₂³×C₆₇	1	2	yes	—
792	#124	—	2	1	no	—
793	#124	—	2	1	no	—
794	#124	—	2	2	no	—
795	#124	—	2	2	no	—
796	#124	—	2	2	no	—
797	#124	C₂³×C₆₇	1	2	yes	—
798	#123	—	2	2	no	—
799	#123	—	2	2	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	#123	—	2	1	no	—
803	#123	—	2	2	no	—
804	#123	D₄×C₆₇	1	2	yes	—
805	C₂²⋊Q₈	—	2	1	no	—
806	C₂²⋊Q₈	—	2	1	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	—	2	1	no	—
810	C₂²⋊Q₈	—	2	1	no	—
811	C₂²⋊Q₈	—	2	2	no	—
812	C₂²⋊Q₈	—	2	2	no	—
813	C₂²⋊Q₈	—	2	2	no	—
814	C₂²⋊Q₈	—	2	2	no	—
815	C₂²⋊Q₈	—	2	2	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
819	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
820	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
821	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
822	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
823	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
824	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
827	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
828	#121	—	2	2	no	—
829	#121	—	2	2	no	—
830	#121	D₄×C₆₇	1	1	yes	characteristic
831	#121	D₄×C₆₇	1	1	yes	characteristic
832	#121	C₂³×C₆₇	1	1	yes	characteristic
833	#121	C₂³×C₆₇	1	1	yes	characteristic
834	#120	—	2	1	no	—
835	#120	D₄×C₆₇	1	2	yes	—
836	C₄×Q₈	—	2	1	no	—
837	C₄×Q₈	—	2	1	no	—
838	C₄×Q₈	—	2	1	no	—
839	C₄×Q₈	—	2	1	no	—
840	C₄×Q₈	—	2	1	no	—
841	C₄×Q₈	—	2	2	no	—
842	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
843	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
844	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
845	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	2	no	—
848	C₄×D₄	—	2	2	no	—
849	C₄×D₄	—	2	2	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	2	no	—
854	C₄×D₄	—	2	2	no	—
855	C₄×D₄	C₂³×C₆₇	1	2	yes	—
856	C₄×D₄	C₂³×C₆₇	1	2	yes	—
857	#117	—	2	1	no	—
858	#117	—	2	1	no	—
859	#117	—	2	2	no	—
860	#117	—	2	2	no	—
861	#117	—	2	2	no	—
862	#117	—	2	2	no	—
863	#117	C₂³×C₆₇	1	1	yes	characteristic
864	#117	C₂³×C₆₇	1	1	yes	characteristic
865	#117	C₂³×C₆₇	1	1	yes	characteristic
866	#117	C₂³×C₆₇	1	1	yes	characteristic
867	#117	C₂³×C₆₇	1	1	yes	characteristic
868	#117	C₂³×C₆₇	1	2	yes	—
869	#117	C₂³×C₆₇	1	1	yes	characteristic
870	C₂×C₄⋊C₄	—	2	1	no	—
871	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
872	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
873	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
874	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
875	C₂×C₂²⋊C₄	—	2	1	no	—
876	C₂×C₂²⋊C₄	—	2	1	no	—
877	C₂×C₄²	—	2	1	no	—
878	#107	C₂³×C₆₇	1	1	yes	characteristic
879	#107	C₂³×C₆₇	1	1	yes	characteristic
880	#107	C₂³×C₆₇	1	1	yes	characteristic
881	#107	C₂³×C₆₇	1	1	yes	characteristic
882	#107	C₂³×C₆₇	1	2	yes	—
883	#106	C₂³×C₆₇	1	1	yes	characteristic
884	#106	C₂³×C₆₇	1	1	yes	characteristic
885	#106	C₂³×C₆₇	1	1	yes	characteristic
886	#106	C₂³×C₆₇	1	1	yes	characteristic
887	#106	C₂³×C₆₇	1	2	yes	—
888	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
889	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
890	#103	C₂³×C₆₇	1	2	yes	—
891	#103	C₂³×C₆₇	1	2	yes	—
892	#103	C₂³×C₆₇	1	2	yes	—
893	#103	C₂³×C₆₇	1	2	yes	—
894	#103	C₂³×C₆₇	1	2	yes	—
895	#103	C₂³×C₆₇	1	2	yes	—
896	#103	C₂³×C₆₇	1	2	yes	—
897	#103	C₂³×C₆₇	1	2	yes	—
898	#103	C₂³×C₆₇	1	2	yes	—
899	#103	C₂³×C₆₇	1	2	yes	—
900	#103	C₂³×C₆₇	1	2	yes	—
901	#103	C₂³×C₆₇	1	2	yes	—
902	#103	C₂³×C₆₇	1	1	yes	characteristic
903	#103	C₂³×C₆₇	1	2	yes	—
904	#103	C₂³×C₆₇	1	1	yes	characteristic
905	#103	C₂³×C₆₇	1	1	yes	characteristic
906	#103	C₂³×C₆₇	1	1	yes	characteristic
907	#103	C₂³×C₆₇	1	2	yes	—
908	#103	C₂³×C₆₇	1	2	yes	—
909	#102	C₂³×C₆₇	1	1	yes	characteristic
910	#102	C₂³×C₆₇	1	1	yes	characteristic
911	#102	C₂³×C₆₇	1	1	yes	characteristic
912	#102	C₂³×C₆₇	1	1	yes	characteristic
913	#102	C₂³×C₆₇	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
915	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
916	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
917	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
918	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
919	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
920	#97	C₂³×C₆₇	1	2	yes	—
921	C₄×C₈	C₂³×C₆₇	1	2	yes	—
922	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
923	#41	—	2	2	no	—
924	#41	—	2	2	no	—
925	#41	—	2	4	no	—
926	#41	—	2	2	no	—
927	#41	—	2	2	no	—
928	#41	—	4	2	no	—
929	#41	—	4	8	no	—
930	#41	—	4	4	no	—
931	C₂×Q₈	—	2	1	no	—
932	C₂×Q₈	—	2	1	no	—
933	C₂×Q₈	—	2	2	no	—
934	C₂×Q₈	—	2	2	no	—
935	C₂×Q₈	—	2	1	no	—
936	C₂×Q₈	—	2	2	no	—
937	C₂×Q₈	—	2	2	no	—
938	C₂×Q₈	—	2	2	no	—
939	C₂×Q₈	—	2	4	no	—
940	C₂×Q₈	—	2	4	no	—
941	C₂×Q₈	—	2	4	no	—
942	C₂×Q₈	—	2	2	no	—
943	C₂×Q₈	—	2	2	no	—
944	C₂×Q₈	—	2	2	no	—
945	C₂×Q₈	—	2	2	no	—
946	C₂×Q₈	—	4	4	no	—
947	C₂×Q₈	—	4	2	no	—
948	C₂×Q₈	—	4	2	no	—
949	C₂×Q₈	—	4	2	no	—
950	C₂×Q₈	—	4	4	no	—
951	C₂×Q₈	—	4	4	no	—
952	C₂×Q₈	—	4	4	no	—
953	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
954	C₂×Q₈	#41×C₆₇	1	4	yes	—
955	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
956	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
957	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
958	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
964	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
965	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
966	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
967	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	1	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	1	no	—
982	C₂²×C₄	—	4	4	no	—
983	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
984	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
985	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
986	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
987	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
988	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
989	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
990	Q₁₆	—	2	4	no	—
991	Q₁₆	—	2	4	no	—
992	Q₁₆	—	4	2	no	—
993	Q₁₆	—	4	2	no	—
994	Q₁₆	—	4	2	no	—
995	SD₁₆	—	4	2	no	—
996	M₁₆	—	2	2	no	—
997	M₁₆	—	2	2	no	—
998	M₁₆	—	4	2	no	—
999	M₁₆	—	4	2	no	—
1000	C₂×C₈	—	2	2	no	—
1001	C₂×C₈	—	2	2	no	—
1002	C₂×C₈	—	4	2	no	—
1003	C₂×C₈	—	4	2	no	—
1004	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1005	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1006	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1007	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1008	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1009	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1032	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1033	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1034	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1035	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1036	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1037	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1038	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1039	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1040	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1041	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1061	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1062	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1063	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1064	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1065	C₄²	—	2	1	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	—	2	2	no	—
1070	C₄²	—	2	2	no	—
1071	C₄²	—	2	2	no	—
1072	C₄²	—	2	2	no	—
1073	C₄²	—	2	2	no	—
1074	C₄²	—	2	1	no	—
1075	C₄²	C₂⁴×C₆₇	1	2	yes	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	2	2	no	—
1078	C₂³	—	2	1	no	—
1079	C₂³	—	4	1	no	—
1080	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1081	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1082	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1083	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1084	Q₈	—	2	4	no	—
1085	Q₈	—	2	2	no	—
1086	Q₈	—	2	2	no	—
1087	Q₈	—	2	2	no	—
1088	Q₈	—	2	2	no	—
1089	Q₈	—	2	1	no	—
1090	Q₈	—	2	2	no	—
1091	Q₈	—	2	2	no	—
1092	Q₈	—	2	1	no	—
1093	Q₈	—	4	4	no	—
1094	Q₈	—	4	4	no	—
1095	Q₈	—	4	4	no	—
1096	Q₈	—	4	2	no	—
1097	Q₈	—	4	2	no	—
1098	Q₈	—	8	2	no	—
1099	Q₈	C₂×#41×C₆₇	1	4	yes	—
1100	D₄	—	2	4	no	—
1101	D₄	—	2	4	no	—
1102	D₄	—	2	2	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	4	2	no	—
1106	D₄	—	4	4	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	2	no	—
1109	D₄	—	4	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	4	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	4	4	no	—
1135	C₂×C₄	—	4	2	no	—
1136	C₂×C₄	—	4	2	no	—
1137	C₂×C₄	—	4	2	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	8	2	no	—
1140	C₂×C₄	—	8	1	no	—
1141	C₂×C₄	—	8	1	no	—
1142	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1143	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1144	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1145	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1146	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1147	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1148	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1149	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1150	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1151	C₈	—	2	1	no	—
1152	C₈	—	2	1	no	—
1153	C₈	—	2	1	no	—
1154	C₈	—	2	1	no	—
1155	C₈	—	2	2	no	—
1156	C₈	—	2	2	no	—
1157	C₂²	—	2	1	no	—
1158	C₂²	—	2	1	no	—
1159	C₂²	—	2	1	no	—
1160	C₂²	—	2	1	no	—
1161	C₂²	—	2	2	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	1	no	—
1165	C₂²	—	2	1	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	4	4	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	#546×C₆₇	1	2	yes	—
1172	C₂²	#578×C₆₇	1	2	yes	—
1173	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1174	C₄	—	2	2	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	2	1	no	—
1177	C₄	—	2	1	no	—
1178	C₄	—	2	4	no	—
1179	C₄	—	2	2	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	2	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	2	no	—
1189	C₄	—	4	2	no	—
1190	C₄	#546×C₆₇	1	2	yes	—
1191	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1192	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1193	C₂	—	2	2	no	—
1194	C₂	—	2	2	no	—
1195	C₂	—	4	1	no	—
1196	C₂	—	4	2	no	—
1197	C₂	—	8	1	no	—
1198	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1199	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
1200	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3486	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3495	C₂	semidirect
3. C₆₇×#3328	C₂	semidirect
4. C₆₇×#3327	C₂	semidirect
5. C₆₇×#3316	C₂	semidirect
6. C₆₇×#3313	C₂	semidirect
7. C₆₇×#3312	C₂	semidirect
8. C₆₇×#3312	C₂	semidirect
9. C₆₇×#3300	C₂	semidirect
10. C₆₇×#3299	C₂	semidirect
11. C₆₇×#3137	C₂	semidirect
12. C₆₇×#3097	C₂	semidirect
13. C₆₇×#3091	C₂	semidirect
14. C₆₇×#3082	C₂	semidirect
15. C₆₇×#3059	C₂	semidirect
16. C₆₇×#3056	C₂	semidirect
17. C₆₇×#3044	C₂	semidirect
18. C₆₇×#3011	C₂	semidirect
19. C₂×#451×C₆₇	C₂	semidirect
20. C₆₇×#2950	C₂	semidirect
21. C₆₇×#2933	C₂	semidirect
22. C₆₇×#2898	C₂	semidirect
23. C₂×#419×C₆₇	C₂	semidirect
62. #491×C₆₇	C₂²	semidirect
63. #489×C₆₇	C₂²	semidirect
64. #488×C₆₇	C₂²	semidirect
65. #487×C₆₇	C₂²	semidirect
68. #485×C₆₇	C₂²	semidirect
69. #485×C₆₇	C₂²	semidirect
71. #484×C₆₇	C₂²	semidirect
73. #483×C₆₇	C₂²	semidirect
78. #479×C₆₇	C₂²	semidirect
79. #479×C₆₇	C₂²	semidirect
80. #477×C₆₇	C₂²	semidirect
81. #475×C₆₇	C₂²	semidirect
83. #470×C₆₇	C₂²	semidirect
84. #470×C₆₇	C₂²	semidirect
87. #467×C₆₇	C₂²	semidirect
88. #467×C₆₇	C₂²	semidirect
90. #464×C₆₇	C₂²	semidirect
91. #464×C₆₇	C₂²	semidirect
92. #462×C₆₇	C₂²	semidirect
93. #462×C₆₇	C₂²	semidirect
94. #452×C₆₇	C₂²	semidirect
95. #452×C₆₇	C₂²	semidirect
100. #451×C₆₇	C₂²	semidirect
101. #451×C₆₇	C₂²	semidirect
102. #441×C₆₇	C₂²	semidirect
103. #441×C₆₇	C₂²	semidirect
104. C₄×Q₁₆×C₆₇	C₂²	semidirect
105. C₄×Q₁₆×C₆₇	C₂²	semidirect
121. #419×C₆₇	C₂²	semidirect
123. #417×C₆₇	C₂²	semidirect
126. #416×C₆₇	C₂²	semidirect
131. C₂×#103×C₆₇	C₂²	semidirect
592. #61186	C₆₇	direct (N × H)
601. #3495	C₂×C₆₇	semidirect
603. #3328	C₂×C₆₇	semidirect
604. #3327	C₂×C₆₇	semidirect
605. #3316	C₂×C₆₇	semidirect
606. #3313	C₂×C₆₇	semidirect
607. #3312	C₂×C₆₇	semidirect
608. #3312	C₂×C₆₇	semidirect
609. #3300	C₂×C₆₇	semidirect
610. #3299	C₂×C₆₇	semidirect
611. #3137	C₂×C₆₇	semidirect
612. #3097	C₂×C₆₇	semidirect
613. #3091	C₂×C₆₇	semidirect
614. #3082	C₂×C₆₇	semidirect
615. #3059	C₂×C₆₇	semidirect
616. #3056	C₂×C₆₇	semidirect
617. #3044	C₂×C₆₇	semidirect
618. #3011	C₂×C₆₇	semidirect
619. C₂×#451	C₂×C₆₇	semidirect
620. #2950	C₂×C₆₇	semidirect
621. #2933	C₂×C₆₇	semidirect
622. #2898	C₂×C₆₇	semidirect
623. C₂×#419	C₂×C₆₇	semidirect
624. C₆₇	#61186	direct (N × H)
663. #491	C₂²×C₆₇	semidirect
664. #489	C₂²×C₆₇	semidirect
665. #488	C₂²×C₆₇	semidirect
666. #487	C₂²×C₆₇	semidirect
669. #485	C₂²×C₆₇	semidirect
670. #485	C₂²×C₆₇	semidirect
672. #484	C₂²×C₆₇	semidirect
674. #483	C₂²×C₆₇	semidirect
679. #479	C₂²×C₆₇	semidirect
680. #479	C₂²×C₆₇	semidirect
681. #477	C₂²×C₆₇	semidirect
682. #475	C₂²×C₆₇	semidirect
684. #470	C₂²×C₆₇	semidirect
685. #470	C₂²×C₆₇	semidirect
688. #467	C₂²×C₆₇	semidirect
689. #467	C₂²×C₆₇	semidirect
691. #464	C₂²×C₆₇	semidirect
692. #464	C₂²×C₆₇	semidirect
693. #462	C₂²×C₆₇	semidirect
694. #462	C₂²×C₆₇	semidirect
695. #452	C₂²×C₆₇	semidirect
696. #452	C₂²×C₆₇	semidirect
701. #451	C₂²×C₆₇	semidirect
702. #451	C₂²×C₆₇	semidirect
703. #441	C₂²×C₆₇	semidirect
704. #441	C₂²×C₆₇	semidirect
705. C₄×Q₁₆	C₂²×C₆₇	semidirect
706. C₄×Q₁₆	C₂²×C₆₇	semidirect
722. #419	C₂²×C₆₇	semidirect
724. #417	C₂²×C₆₇	semidirect
727. #416	C₂²×C₆₇	semidirect
732. C₂×#103	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3495	2
C₆₇×#3486	2
C₆₇×#3328	2
C₆₇×#3327	2
C₆₇×#3316	2
C₆₇×#3313	2
C₆₇×#3312	2
C₆₇×#3300	2
C₆₇×#3299	2
C₆₇×#3137	2
C₆₇×#3097	2
C₆₇×#3091	2
C₆₇×#3082	2
C₆₇×#3059	2
C₆₇×#3056	2
C₆₇×#3044	2
C₆₇×#3011	2
C₂×#451×C₆₇	2
C₆₇×#2950	2
C₆₇×#2933	2
C₆₇×#2898	2
C₂×#419×C₆₇	2
#61186	67

Subgroups — C67×#61186 #30740437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61186 #30740437