Subgroups — C₆₇×#61539 #30740790

Order 17152.

1950 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×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3347	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3340	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3325	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3325	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3322	C₂	1	2	yes	maximal, complemented
13	D₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3264	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3179	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3122	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2948	C₂	1	2	yes	maximal, complemented
23	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
26	#559×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	#556×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#555×C₆₇	C₂²	1	1	yes	characteristic
29	#555×C₆₇	C₂²	1	2	yes	complemented
30	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#553×C₆₇	—	2	1	no	—
32	#553×C₆₇	C₂²	1	2	yes	complemented
33	#551×C₆₇	—	2	2	no	—
34	#550×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#548×C₆₇	—	2	1	no	—
37	#546×C₆₇	—	2	1	no	—
38	#546×C₆₇	—	2	2	no	—
39	#546×C₆₇	—	2	1	no	—
40	#546×C₆₇	C₂²	1	2	yes	complemented
41	D₄²×C₆₇	C₂²	1	1	yes	characteristic
42	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	D₄²×C₆₇	C₂²	1	2	yes	complemented
44	#542×C₆₇	C₂²	1	2	yes	complemented
45	#540×C₆₇	C₂²	1	2	yes	complemented
46	#538×C₆₇	—	2	2	no	—
47	#538×C₆₇	—	2	2	no	—
48	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#529×C₆₇	—	2	1	no	—
51	#529×C₆₇	C₂²	1	1	yes	characteristic
52	C₂×#124×C₆₇	—	2	1	no	—
53	#525×C₆₇	—	2	1	no	—
54	C₂×#121×C₆₇	—	2	1	no	—
55	#518×C₆₇	C₂²	1	2	yes	complemented
56	#518×C₆₇	C₂²	1	2	yes	complemented
57	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#501×C₆₇	C₂²	1	2	yes	complemented
60	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#496×C₆₇	C₂²	1	2	yes	complemented
62	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#488×C₆₇	C₂²	1	2	yes	complemented
64	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#486×C₆₇	C₂²	1	2	yes	complemented
66	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#485×C₆₇	C₂²	1	2	yes	complemented
68	#482×C₆₇	C₂²	1	2	yes	complemented
69	#482×C₆₇	C₂²	1	2	yes	complemented
70	#482×C₆₇	C₂²	1	2	yes	complemented
71	#482×C₆₇	C₂²	1	2	yes	complemented
72	#480×C₆₇	C₂²	1	2	yes	complemented
73	#478×C₆₇	C₂²	1	2	yes	complemented
74	#478×C₆₇	C₂²	1	2	yes	complemented
75	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#476×C₆₇	C₂²	1	2	yes	complemented
78	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#474×C₆₇	C₂²	1	2	yes	complemented
81	#469×C₆₇	C₂²	1	2	yes	complemented
82	#469×C₆₇	C₂²	1	2	yes	complemented
83	#469×C₆₇	C₂²	1	2	yes	complemented
84	#468×C₆₇	C₂²	1	2	yes	complemented
85	#466×C₆₇	C₂²	1	2	yes	complemented
86	#465×C₆₇	C₂²	1	2	yes	complemented
87	#463×C₆₇	C₂²	1	2	yes	complemented
88	#463×C₆₇	C₂²	1	2	yes	complemented
89	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#459×C₆₇	C₂²	1	1	yes	characteristic
91	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#459×C₆₇	C₂²	1	2	yes	complemented
94	#459×C₆₇	C₂²	1	2	yes	complemented
95	#450×C₆₇	C₂²	1	2	yes	complemented
96	#449×C₆₇	C₂²	1	2	yes	complemented
97	#447×C₆₇	C₂²	1	2	yes	—
98	#447×C₆₇	C₂²	1	2	yes	complemented
99	#447×C₆₇	C₂²	1	2	yes	complemented
100	#447×C₆₇	C₂²	1	2	yes	complemented
101	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#442×C₆₇	C₂²	1	2	yes	—
104	#442×C₆₇	C₂²	1	1	yes	characteristic
105	#442×C₆₇	C₂²	1	2	yes	complemented
106	#442×C₆₇	C₂²	1	2	yes	complemented
107	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#442×C₆₇	C₂²	1	2	yes	complemented
109	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
114	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
116	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
118	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
119	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
120	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
121	#436×C₆₇	C₂²	1	2	yes	complemented
122	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#433×C₆₇	C₂²	1	2	yes	complemented
126	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#427×C₆₇	C₂²	1	2	yes	complemented
129	#418×C₆₇	C₂²	1	2	yes	complemented
130	#418×C₆₇	C₂²	1	2	yes	complemented
131	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#405×C₆₇	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₆₇	—	2	1	no	—
136	C₂×#41×C₆₇	—	2	1	no	—
137	C₂×#41×C₆₇	—	2	1	no	—
138	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₆₇	—	2	1	no	—
140	C₂²×D₄×C₆₇	—	2	1	no	—
141	C₂²×D₄×C₆₇	—	2	2	no	—
142	C₂²×D₄×C₆₇	—	2	1	no	—
143	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
144	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
146	C₂³×C₄×C₆₇	—	2	1	no	—
147	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
148	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×D₈×C₆₇	—	2	8	no	—
152	C₂×D₈×C₆₇	C₂³	1	2	yes	—
153	C₂×D₈×C₆₇	C₂³	1	2	yes	—
154	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₆₇	C₂³	1	2	yes	—
156	C₂×D₈×C₆₇	C₂³	1	2	yes	—
157	C₂×D₈×C₆₇	C₂³	1	2	yes	—
158	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	#127×C₆₇	C₂³	1	1	yes	characteristic
167	#127×C₆₇	C₂³	1	2	yes	—
168	#127×C₆₇	C₂³	1	1	yes	characteristic
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#126×C₆₇	—	2	2	no	—
172	#126×C₆₇	D₄	1	2	yes	—
173	#125×C₆₇	D₄	1	1	yes	characteristic
174	#125×C₆₇	C₂³	1	2	yes	—
175	#124×C₆₇	—	2	1	no	—
176	#124×C₆₇	—	2	1	no	—
177	#124×C₆₇	—	2	2	no	—
178	#124×C₆₇	—	2	2	no	—
179	#124×C₆₇	—	2	2	no	—
180	#124×C₆₇	—	2	2	no	—
181	#124×C₆₇	—	2	1	no	—
182	#124×C₆₇	—	2	1	no	—
183	#124×C₆₇	D₄	1	1	yes	characteristic
184	#124×C₆₇	C₂³	1	2	yes	—
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	—	2	2	no	—
189	#123×C₆₇	—	2	2	no	—
190	#123×C₆₇	—	2	2	no	—
191	#123×C₆₇	D₄	1	2	yes	—
192	C₂²⋊Q₈×C₆₇	—	2	1	no	—
193	C₂²⋊Q₈×C₆₇	—	2	1	no	—
194	C₂²⋊Q₈×C₆₇	—	2	2	no	—
195	C₂²⋊Q₈×C₆₇	—	2	2	no	—
196	C₂²⋊Q₈×C₆₇	—	2	2	no	—
197	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
198	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
199	#121×C₆₇	—	2	2	no	—
200	#121×C₆₇	—	2	1	no	—
201	#121×C₆₇	—	2	2	no	—
202	#121×C₆₇	—	2	1	no	—
203	#121×C₆₇	—	2	1	no	—
204	#121×C₆₇	—	2	1	no	—
205	#121×C₆₇	—	2	1	no	—
206	#121×C₆₇	—	2	1	no	—
207	#121×C₆₇	—	2	2	no	—
208	#121×C₆₇	—	2	2	no	—
209	#121×C₆₇	—	2	2	no	—
210	#121×C₆₇	—	2	2	no	—
211	#121×C₆₇	—	2	2	no	—
212	#121×C₆₇	D₄	1	1	yes	characteristic
213	#121×C₆₇	C₂³	1	2	yes	—
214	#121×C₆₇	C₂³	1	2	yes	—
215	#121×C₆₇	C₂³	1	2	yes	—
216	#121×C₆₇	C₂³	1	2	yes	—
217	#121×C₆₇	C₂³	1	2	yes	—
218	#120×C₆₇	—	2	2	no	—
219	#120×C₆₇	—	2	2	no	—
220	#120×C₆₇	—	2	2	no	—
221	#120×C₆₇	—	2	2	no	—
222	#120×C₆₇	—	2	2	no	—
223	C₄×Q₈×C₆₇	—	2	1	no	—
224	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₆₇	—	2	1	no	—
228	C₄×D₄×C₆₇	—	2	1	no	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	—	2	2	no	—
231	C₄×D₄×C₆₇	—	2	2	no	—
232	C₄×D₄×C₆₇	—	2	2	no	—
233	C₄×D₄×C₆₇	—	2	1	no	—
234	C₄×D₄×C₆₇	—	2	2	no	—
235	C₄×D₄×C₆₇	—	2	1	no	—
236	C₄×D₄×C₆₇	—	2	1	no	—
237	C₄×D₄×C₆₇	—	2	1	no	—
238	C₄×D₄×C₆₇	—	2	1	no	—
239	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₆₇	C₂³	1	2	yes	—
243	C₄×D₄×C₆₇	C₂³	1	2	yes	—
244	C₄×D₄×C₆₇	C₂³	1	2	yes	—
245	C₄×D₄×C₆₇	C₂³	1	2	yes	—
246	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₆₇	C₂³	1	2	yes	—
250	C₄×D₄×C₆₇	C₂³	1	2	yes	—
251	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₆₇	C₂³	1	2	yes	—
253	#117×C₆₇	—	2	1	no	—
254	#117×C₆₇	—	2	2	no	—
255	#117×C₆₇	—	2	1	no	—
256	#117×C₆₇	C₂³	1	1	yes	characteristic
257	#117×C₆₇	C₂³	1	2	yes	—
258	#117×C₆₇	C₂³	1	2	yes	—
259	#117×C₆₇	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
268	C₂×C₄²×C₆₇	—	2	1	no	—
269	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
270	#107×C₆₇	C₂³	1	1	yes	characteristic
271	#107×C₆₇	C₂³	1	2	yes	—
272	#107×C₆₇	C₂³	1	2	yes	—
273	#107×C₆₇	C₂³	1	1	yes	characteristic
274	#107×C₆₇	C₂³	1	2	yes	—
275	#106×C₆₇	C₂³	1	2	yes	—
276	#106×C₆₇	C₂³	1	2	yes	—
277	#106×C₆₇	C₂³	1	2	yes	—
278	#106×C₆₇	C₂³	1	1	yes	characteristic
279	#106×C₆₇	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
284	#103×C₆₇	C₂³	1	2	yes	—
285	#103×C₆₇	C₂³	1	1	yes	characteristic
286	#103×C₆₇	C₂³	1	1	yes	characteristic
287	#102×C₆₇	C₂³	1	2	yes	—
288	#102×C₆₇	C₂³	1	2	yes	—
289	#102×C₆₇	C₂³	1	2	yes	—
290	#102×C₆₇	C₂³	1	2	yes	—
291	#102×C₆₇	C₂³	1	1	yes	characteristic
292	#102×C₆₇	C₂³	1	2	yes	—
293	#102×C₆₇	C₂³	1	2	yes	—
294	#102×C₆₇	C₂³	1	2	yes	—
295	#102×C₆₇	C₂³	1	2	yes	—
296	#102×C₆₇	C₂³	1	2	yes	—
297	#102×C₆₇	C₂³	1	2	yes	—
298	#102×C₆₇	C₂³	1	1	yes	characteristic
299	#102×C₆₇	C₂³	1	2	yes	—
300	#102×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	1	yes	characteristic
302	#102×C₆₇	C₂³	1	1	yes	characteristic
303	#102×C₆₇	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
307	#97×C₆₇	C₂³	1	2	yes	—
308	#97×C₆₇	C₂³	1	1	yes	characteristic
309	#97×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	2	yes	—
312	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₇	C₂³	1	2	yes	—
314	C₂⁴×C₆₇	—	2	1	no	—
315	C₂⁴×C₆₇	—	2	2	no	—
316	C₂⁴×C₆₇	—	2	2	no	—
317	#41×C₆₇	—	2	2	no	—
318	#41×C₆₇	—	4	1	no	—
319	#41×C₆₇	—	8	2	no	—
320	#41×C₆₇	—	8	2	no	—
321	#41×C₆₇	—	8	2	no	—
322	C₂×Q₈×C₆₇	—	2	1	no	—
323	C₂×Q₈×C₆₇	—	2	2	no	—
324	C₂×Q₈×C₆₇	—	2	1	no	—
325	C₂×Q₈×C₆₇	—	8	2	no	—
326	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₆₇	—	2	4	no	—
329	C₂×D₄×C₆₇	—	2	4	no	—
330	C₂×D₄×C₆₇	—	2	2	no	—
331	C₂×D₄×C₆₇	—	2	1	no	—
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	2	no	—
334	C₂×D₄×C₆₇	—	2	2	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	2	no	—
337	C₂×D₄×C₆₇	—	2	2	no	—
338	C₂×D₄×C₆₇	—	2	1	no	—
339	C₂×D₄×C₆₇	—	2	2	no	—
340	C₂×D₄×C₆₇	—	2	1	no	—
341	C₂×D₄×C₆₇	—	2	1	no	—
342	C₂×D₄×C₆₇	—	2	1	no	—
343	C₂×D₄×C₆₇	—	2	2	no	—
344	C₂×D₄×C₆₇	—	2	1	no	—
345	C₂×D₄×C₆₇	—	2	2	no	—
346	C₂×D₄×C₆₇	—	4	2	no	—
347	C₂×D₄×C₆₇	—	4	2	no	—
348	C₂×D₄×C₆₇	—	4	1	no	—
349	C₂×D₄×C₆₇	—	8	2	no	—
350	C₂×D₄×C₆₇	—	8	2	no	—
351	C₂×D₄×C₆₇	—	8	4	no	—
352	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
353	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
354	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
355	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
356	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₆₇	—	2	1	no	—
360	C₂²×C₄×C₆₇	—	2	1	no	—
361	C₂²×C₄×C₆₇	—	2	1	no	—
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	1	no	—
364	C₂²×C₄×C₆₇	—	2	1	no	—
365	C₂²×C₄×C₆₇	—	2	1	no	—
366	C₂²×C₄×C₆₇	—	2	2	no	—
367	C₂²×C₄×C₆₇	—	2	2	no	—
368	C₂²×C₄×C₆₇	—	2	2	no	—
369	C₂²×C₄×C₆₇	—	2	2	no	—
370	C₂²×C₄×C₆₇	—	2	2	no	—
371	C₂²×C₄×C₆₇	—	2	2	no	—
372	C₂²×C₄×C₆₇	—	2	1	no	—
373	C₂²×C₄×C₆₇	—	8	2	no	—
374	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
378	SD₁₆×C₆₇	—	2	2	no	—
379	SD₁₆×C₆₇	—	2	2	no	—
380	SD₁₆×C₆₇	—	4	2	no	—
381	D₈×C₆₇	—	2	4	no	—
382	D₈×C₆₇	—	2	4	no	—
383	D₈×C₆₇	—	2	2	no	—
384	D₈×C₆₇	—	2	4	no	—
385	D₈×C₆₇	—	4	2	no	—
386	D₈×C₆₇	—	4	2	no	—
387	D₈×C₆₇	#41	1	4	yes	complemented
388	M₁₆×C₆₇	—	2	2	no	—
389	M₁₆×C₆₇	—	4	1	no	—
390	M₁₆×C₆₇	—	4	2	no	—
391	C₂×C₈×C₆₇	—	2	4	no	—
392	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
395	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
397	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₆₇	—	2	1	no	—
399	C₄⋊C₄×C₆₇	—	2	2	no	—
400	C₄⋊C₄×C₆₇	—	2	1	no	—
401	C₄⋊C₄×C₆₇	—	2	1	no	—
402	C₄⋊C₄×C₆₇	—	2	1	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	2	2	no	—
405	C₄⋊C₄×C₆₇	—	2	1	no	—
406	C₄⋊C₄×C₆₇	—	2	2	no	—
407	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₂²⋊C₄×C₆₇	—	2	2	no	—
420	C₂²⋊C₄×C₆₇	—	2	2	no	—
421	C₂²⋊C₄×C₆₇	—	2	2	no	—
422	C₂²⋊C₄×C₆₇	—	2	1	no	—
423	C₂²⋊C₄×C₆₇	—	2	1	no	—
424	C₂²⋊C₄×C₆₇	—	2	1	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	1	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	1	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	1	no	—
433	C₂²⋊C₄×C₆₇	—	2	2	no	—
434	C₂²⋊C₄×C₆₇	—	2	2	no	—
435	C₂²⋊C₄×C₆₇	—	2	2	no	—
436	C₂²⋊C₄×C₆₇	—	2	1	no	—
437	C₂²⋊C₄×C₆₇	—	2	2	no	—
438	C₂²⋊C₄×C₆₇	—	2	2	no	—
439	C₂²⋊C₄×C₆₇	—	2	2	no	—
440	C₂²⋊C₄×C₆₇	—	2	2	no	—
441	C₂²⋊C₄×C₆₇	—	2	2	no	—
442	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
447	C₄²×C₆₇	—	2	1	no	—
448	C₄²×C₆₇	—	2	1	no	—
449	C₄²×C₆₇	—	2	1	no	—
450	C₄²×C₆₇	—	2	2	no	—
451	C₄²×C₆₇	—	2	2	no	—
452	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₄²×C₆₇	C₂⁴	1	2	yes	—
456	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
457	C₂³×C₆₇	—	2	1	no	—
458	C₂³×C₆₇	—	2	1	no	—
459	C₂³×C₆₇	—	2	2	no	—
460	C₂³×C₆₇	—	2	2	no	—
461	C₂³×C₆₇	—	2	1	no	—
462	C₂³×C₆₇	—	4	2	no	—
463	C₂³×C₆₇	—	4	4	no	—
464	C₂³×C₆₇	—	4	4	no	—
465	C₂³×C₆₇	—	4	2	no	—
466	C₂³×C₆₇	—	8	1	no	—
467	C₂³×C₆₇	—	8	2	no	—
468	C₂³×C₆₇	—	8	2	no	—
469	C₂³×C₆₇	—	8	2	no	—
470	C₂³×C₆₇	—	8	2	no	—
471	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
472	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
473	Q₈×C₆₇	—	2	2	no	—
474	Q₈×C₆₇	—	2	1	no	—
475	Q₈×C₆₇	—	2	1	no	—
476	Q₈×C₆₇	—	4	2	no	—
477	Q₈×C₆₇	—	8	2	no	—
478	Q₈×C₆₇	—	8	1	no	—
479	D₄×C₆₇	—	2	2	no	—
480	D₄×C₆₇	—	2	2	no	—
481	D₄×C₆₇	—	2	2	no	—
482	D₄×C₆₇	—	2	1	no	—
483	D₄×C₆₇	—	2	1	no	—
484	D₄×C₆₇	—	2	1	no	—
485	D₄×C₆₇	—	2	2	no	—
486	D₄×C₆₇	—	2	1	no	—
487	D₄×C₆₇	—	2	2	no	—
488	D₄×C₆₇	—	4	2	no	—
489	D₄×C₆₇	—	4	2	no	—
490	D₄×C₆₇	—	4	4	no	—
491	D₄×C₆₇	—	4	4	no	—
492	D₄×C₆₇	—	4	2	no	—
493	D₄×C₆₇	—	4	4	no	—
494	D₄×C₆₇	—	4	2	no	—
495	D₄×C₆₇	—	4	2	no	—
496	D₄×C₆₇	—	8	1	no	—
497	D₄×C₆₇	—	8	2	no	—
498	D₄×C₆₇	—	8	1	no	—
499	D₄×C₆₇	—	8	2	no	—
500	D₄×C₆₇	—	8	2	no	—
501	D₄×C₆₇	—	8	2	no	—
502	D₄×C₆₇	—	8	2	no	—
503	D₄×C₆₇	—	8	2	no	—
504	D₄×C₆₇	C₂×#41	1	2	yes	—
505	D₄×C₆₇	C₂×#41	1	2	yes	—
506	C₂×C₄×C₆₇	—	2	2	no	—
507	C₂×C₄×C₆₇	—	2	2	no	—
508	C₂×C₄×C₆₇	—	2	1	no	—
509	C₂×C₄×C₆₇	—	2	2	no	—
510	C₂×C₄×C₆₇	—	2	1	no	—
511	C₂×C₄×C₆₇	—	2	1	no	—
512	C₂×C₄×C₆₇	—	2	1	no	—
513	C₂×C₄×C₆₇	—	2	1	no	—
514	C₂×C₄×C₆₇	—	2	1	no	—
515	C₂×C₄×C₆₇	—	2	2	no	—
516	C₂×C₄×C₆₇	—	2	2	no	—
517	C₂×C₄×C₆₇	—	2	1	no	—
518	C₂×C₄×C₆₇	—	4	1	no	—
519	C₂×C₄×C₆₇	—	4	2	no	—
520	C₂×C₄×C₆₇	—	4	2	no	—
521	C₂×C₄×C₆₇	—	4	2	no	—
522	C₂×C₄×C₆₇	—	4	2	no	—
523	C₂×C₄×C₆₇	—	8	1	no	—
524	C₂×C₄×C₆₇	—	8	2	no	—
525	C₂×C₄×C₆₇	—	8	1	no	—
526	C₂×C₄×C₆₇	—	8	1	no	—
527	C₂×C₄×C₆₇	—	8	2	no	—
528	C₂×C₄×C₆₇	—	8	2	no	—
529	C₂×C₄×C₆₇	—	8	2	no	—
530	C₂×C₄×C₆₇	—	8	2	no	—
531	C₂×C₄×C₆₇	—	8	2	no	—
532	C₂×C₄×C₆₇	—	8	1	no	—
533	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
539	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
542	C₈×C₆₇	—	2	2	no	—
543	C₈×C₆₇	—	2	1	no	—
544	C₈×C₆₇	—	2	1	no	—
545	C₈×C₆₇	—	2	1	no	—
546	C₈×C₆₇	—	2	2	no	—
547	C₈×C₆₇	C₂×#41	1	2	yes	—
548	C₂²×C₆₇	—	2	1	no	—
549	C₂²×C₆₇	—	2	2	no	—
550	C₂²×C₆₇	—	2	1	no	—
551	C₂²×C₆₇	—	2	2	no	—
552	C₂²×C₆₇	—	2	2	no	—
553	C₂²×C₆₇	—	2	2	no	—
554	C₂²×C₆₇	—	2	1	no	—
555	C₂²×C₆₇	—	2	2	no	—
556	C₂²×C₆₇	—	4	1	no	—
557	C₂²×C₆₇	—	4	1	no	—
558	C₂²×C₆₇	—	4	1	no	—
559	C₂²×C₆₇	—	4	1	no	—
560	C₂²×C₆₇	—	4	2	no	—
561	C₂²×C₆₇	—	4	2	no	—
562	C₂²×C₆₇	—	4	1	no	—
563	C₂²×C₆₇	—	4	1	no	—
564	C₂²×C₆₇	—	4	2	no	—
565	C₂²×C₆₇	—	4	2	no	—
566	C₂²×C₆₇	—	4	1	no	—
567	C₂²×C₆₇	—	4	2	no	—
568	C₂²×C₆₇	—	4	2	no	—
569	C₂²×C₆₇	—	8	4	no	—
570	C₂²×C₆₇	—	16	4	no	—
571	C₂²×C₆₇	—	16	4	no	—
572	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
573	C₄×C₆₇	—	2	1	no	—
574	C₄×C₆₇	—	2	1	no	—
575	C₄×C₆₇	—	2	2	no	—
576	C₄×C₆₇	—	2	1	no	—
577	C₄×C₆₇	—	2	2	no	—
578	C₄×C₆₇	—	2	1	no	—
579	C₄×C₆₇	—	2	2	no	—
580	C₄×C₆₇	—	4	1	no	—
581	C₄×C₆₇	—	4	2	no	—
582	C₄×C₆₇	—	4	1	no	—
583	C₄×C₆₇	—	4	1	no	—
584	C₄×C₆₇	—	4	1	no	—
585	C₄×C₆₇	—	4	1	no	—
586	C₄×C₆₇	—	4	2	no	—
587	C₄×C₆₇	#576	1	2	yes	—
588	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
589	C₄×C₆₇	#585	1	1	yes	characteristic
590	#61539	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
591	C₂×C₆₇	—	4	1	no	—
592	C₂×C₆₇	—	4	2	no	—
593	C₂×C₆₇	—	4	2	no	—
594	C₂×C₆₇	—	4	2	no	—
595	C₂×C₆₇	—	8	1	no	—
596	C₂×C₆₇	—	8	2	no	—
597	C₂×C₆₇	—	8	2	no	—
598	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
599	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
600	C₂×C₆₇	#3585	1	1	yes	characteristic
601	#3519	C₂×C₆₇	1	1	yes	characteristic, complemented
602	#3514	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#3399	C₂×C₆₇	1	1	yes	characteristic, complemented
604	#3384	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#3361	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#3358	C₂×C₆₇	1	1	yes	characteristic, complemented
607	#3347	C₂×C₆₇	1	2	yes	complemented
608	#3340	C₂×C₆₇	1	1	yes	characteristic, complemented
609	#3325	C₂×C₆₇	1	1	yes	characteristic, complemented
610	#3325	C₂×C₆₇	1	2	yes	complemented
611	#3324	C₂×C₆₇	1	1	yes	characteristic, complemented
612	#3322	C₂×C₆₇	1	2	yes	complemented
613	D₄×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#3264	C₂×C₆₇	1	2	yes	complemented
615	#3184	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#3179	C₂×C₆₇	1	2	yes	complemented
617	#3122	C₂×C₆₇	1	2	yes	complemented
618	#3118	C₂×C₆₇	1	2	yes	complemented
619	#3106	C₂×C₆₇	1	1	yes	characteristic, complemented
620	#3100	C₂×C₆₇	1	1	yes	characteristic, complemented
621	#2969	C₂×C₆₇	1	1	yes	characteristic, complemented
622	#2948	C₂×C₆₇	1	2	yes	complemented
623	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
624	C₆₇	#61539	1	1	yes	characteristic, direct product factor, Sylow
625	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
626	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
627	#559	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	#556	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	#555	C₂²×C₆₇	1	1	yes	characteristic
630	#555	C₂²×C₆₇	1	2	yes	complemented
631	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
632	#553	—	2	1	no	—
633	#553	C₂²×C₆₇	1	2	yes	complemented
634	#551	—	2	2	no	—
635	#550	C₂²×C₆₇	1	1	yes	characteristic, complemented
636	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
637	#548	—	2	1	no	—
638	#546	—	2	1	no	—
639	#546	—	2	2	no	—
640	#546	—	2	1	no	—
641	#546	C₂²×C₆₇	1	2	yes	complemented
642	D₄²	C₂²×C₆₇	1	1	yes	characteristic
643	D₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
644	D₄²	C₂²×C₆₇	1	2	yes	complemented
645	#542	C₂²×C₆₇	1	2	yes	complemented
646	#540	C₂²×C₆₇	1	2	yes	complemented
647	#538	—	2	2	no	—
648	#538	—	2	2	no	—
649	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
650	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
651	#529	—	2	1	no	—
652	#529	C₂²×C₆₇	1	1	yes	characteristic
653	C₂×#124	—	2	1	no	—
654	#525	—	2	1	no	—
655	C₂×#121	—	2	1	no	—
656	#518	C₂²×C₆₇	1	2	yes	complemented
657	#518	C₂²×C₆₇	1	2	yes	complemented
658	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
659	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
660	#501	C₂²×C₆₇	1	2	yes	complemented
661	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
662	#496	C₂²×C₆₇	1	2	yes	complemented
663	#493	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	#488	C₂²×C₆₇	1	2	yes	complemented
665	#486	C₂²×C₆₇	1	2	yes	complemented
666	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
667	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
668	#485	C₂²×C₆₇	1	2	yes	complemented
669	#482	C₂²×C₆₇	1	2	yes	complemented
670	#482	C₂²×C₆₇	1	2	yes	complemented
671	#482	C₂²×C₆₇	1	2	yes	complemented
672	#482	C₂²×C₆₇	1	2	yes	complemented
673	#480	C₂²×C₆₇	1	2	yes	complemented
674	#478	C₂²×C₆₇	1	2	yes	complemented
675	#478	C₂²×C₆₇	1	2	yes	complemented
676	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
677	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
678	#476	C₂²×C₆₇	1	2	yes	complemented
679	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
680	#474	C₂²×C₆₇	1	2	yes	complemented
681	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
682	#469	C₂²×C₆₇	1	2	yes	complemented
683	#469	C₂²×C₆₇	1	2	yes	complemented
684	#469	C₂²×C₆₇	1	2	yes	complemented
685	#468	C₂²×C₆₇	1	2	yes	complemented
686	#466	C₂²×C₆₇	1	2	yes	complemented
687	#465	C₂²×C₆₇	1	2	yes	complemented
688	#463	C₂²×C₆₇	1	2	yes	complemented
689	#463	C₂²×C₆₇	1	2	yes	complemented
690	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
691	#459	C₂²×C₆₇	1	1	yes	characteristic
692	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
694	#459	C₂²×C₆₇	1	2	yes	complemented
695	#459	C₂²×C₆₇	1	2	yes	complemented
696	#450	C₂²×C₆₇	1	2	yes	complemented
697	#449	C₂²×C₆₇	1	2	yes	complemented
698	#447	C₂²×C₆₇	1	2	yes	—
699	#447	C₂²×C₆₇	1	2	yes	complemented
700	#447	C₂²×C₆₇	1	2	yes	complemented
701	#447	C₂²×C₆₇	1	2	yes	complemented
702	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
703	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
704	#442	C₂²×C₆₇	1	2	yes	—
705	#442	C₂²×C₆₇	1	1	yes	characteristic
706	#442	C₂²×C₆₇	1	2	yes	complemented
707	#442	C₂²×C₆₇	1	2	yes	complemented
708	#442	C₂²×C₆₇	1	1	yes	characteristic, complemented
709	#442	C₂²×C₆₇	1	2	yes	complemented
710	#440	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	#440	C₂²×C₆₇	1	1	yes	characteristic, complemented
712	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
713	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
714	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
715	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
716	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
717	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
718	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
719	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
720	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
721	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
722	#436	C₂²×C₆₇	1	2	yes	complemented
723	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
724	#435	C₂²×C₆₇	1	2	yes	complemented
725	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	#433	C₂²×C₆₇	1	2	yes	complemented
727	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
728	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
729	#427	C₂²×C₆₇	1	2	yes	complemented
730	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
731	#418	C₂²×C₆₇	1	2	yes	complemented
732	#418	C₂²×C₆₇	1	2	yes	complemented
733	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
734	#405	C₂²×C₆₇	1	2	yes	complemented
735	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
740	C₂²×Q₈	—	2	1	no	—
741	C₂²×D₄	—	2	1	no	—
742	C₂²×D₄	—	2	2	no	—
743	C₂²×D₄	—	2	1	no	—
744	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
745	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
746	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
747	C₂³×C₄	—	2	1	no	—
748	AGL(1,ℤ/8)	—	2	4	no	—
749	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
750	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
751	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
752	C₂×D₈	—	2	8	no	—
753	C₂×D₈	C₂³×C₆₇	1	2	yes	—
754	C₂×D₈	C₂³×C₆₇	1	2	yes	—
755	C₂×D₈	C₂³×C₆₇	1	2	yes	—
756	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
757	C₂×D₈	C₂³×C₆₇	1	2	yes	—
758	C₂×D₈	C₂³×C₆₇	1	2	yes	—
759	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
760	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
761	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
762	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
763	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
764	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
765	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
766	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
767	#127	C₂³×C₆₇	1	1	yes	characteristic
768	#127	C₂³×C₆₇	1	1	yes	characteristic
769	#127	C₂³×C₆₇	1	2	yes	—
770	#126	—	2	2	no	—
771	#126	—	2	2	no	—
772	#126	—	2	2	no	—
773	#126	D₄×C₆₇	1	2	yes	—
774	#125	D₄×C₆₇	1	1	yes	characteristic
775	#125	C₂³×C₆₇	1	2	yes	—
776	#124	—	2	1	no	—
777	#124	—	2	1	no	—
778	#124	—	2	2	no	—
779	#124	—	2	2	no	—
780	#124	—	2	2	no	—
781	#124	—	2	2	no	—
782	#124	—	2	1	no	—
783	#124	—	2	1	no	—
784	#124	D₄×C₆₇	1	1	yes	characteristic
785	#124	C₂³×C₆₇	1	2	yes	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	D₄×C₆₇	1	2	yes	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	1	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
799	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
800	#121	—	2	2	no	—
801	#121	—	2	1	no	—
802	#121	—	2	2	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	1	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	D₄×C₆₇	1	1	yes	characteristic
814	#121	C₂³×C₆₇	1	2	yes	—
815	#121	C₂³×C₆₇	1	2	yes	—
816	#121	C₂³×C₆₇	1	2	yes	—
817	#121	C₂³×C₆₇	1	2	yes	—
818	#121	C₂³×C₆₇	1	2	yes	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	C₄×Q₈	—	2	1	no	—
825	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
826	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
827	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₆₇	1	2	yes	—
847	C₄×D₄	C₂³×C₆₇	1	2	yes	—
848	C₄×D₄	C₂³×C₆₇	1	2	yes	—
849	C₄×D₄	C₂³×C₆₇	1	2	yes	—
850	C₄×D₄	C₂³×C₆₇	1	2	yes	—
851	C₄×D₄	C₂³×C₆₇	1	2	yes	—
852	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
853	C₄×D₄	C₂³×C₆₇	1	2	yes	—
854	#117	—	2	1	no	—
855	#117	—	2	2	no	—
856	#117	—	2	1	no	—
857	#117	C₂³×C₆₇	1	1	yes	characteristic
858	#117	C₂³×C₆₇	1	2	yes	—
859	#117	C₂³×C₆₇	1	2	yes	—
860	#117	C₂³×C₆₇	1	2	yes	—
861	C₂×C₄⋊C₄	—	2	1	no	—
862	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
863	C₂×C₂²⋊C₄	—	2	1	no	—
864	C₂×C₂²⋊C₄	—	2	2	no	—
865	C₂×C₂²⋊C₄	—	2	2	no	—
866	C₂×C₂²⋊C₄	—	2	2	no	—
867	C₂×C₂²⋊C₄	—	2	2	no	—
868	C₂×C₂²⋊C₄	—	2	2	no	—
869	C₂×C₄²	—	2	1	no	—
870	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
871	#107	C₂³×C₆₇	1	2	yes	—
872	#107	C₂³×C₆₇	1	2	yes	—
873	#107	C₂³×C₆₇	1	1	yes	characteristic
874	#107	C₂³×C₆₇	1	1	yes	characteristic
875	#107	C₂³×C₆₇	1	2	yes	—
876	#106	C₂³×C₆₇	1	1	yes	characteristic
877	#106	C₂³×C₆₇	1	2	yes	—
878	#106	C₂³×C₆₇	1	1	yes	characteristic
879	#106	C₂³×C₆₇	1	2	yes	—
880	#106	C₂³×C₆₇	1	2	yes	—
881	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
884	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
885	#103	C₂³×C₆₇	1	1	yes	characteristic
886	#103	C₂³×C₆₇	1	1	yes	characteristic
887	#103	C₂³×C₆₇	1	2	yes	—
888	#102	C₂³×C₆₇	1	1	yes	characteristic
889	#102	C₂³×C₆₇	1	1	yes	characteristic
890	#102	C₂³×C₆₇	1	1	yes	characteristic
891	#102	C₂³×C₆₇	1	1	yes	characteristic
892	#102	C₂³×C₆₇	1	1	yes	characteristic
893	#102	C₂³×C₆₇	1	2	yes	—
894	#102	C₂³×C₆₇	1	2	yes	—
895	#102	C₂³×C₆₇	1	2	yes	—
896	#102	C₂³×C₆₇	1	2	yes	—
897	#102	C₂³×C₆₇	1	2	yes	—
898	#102	C₂³×C₆₇	1	2	yes	—
899	#102	C₂³×C₆₇	1	1	yes	characteristic
900	#102	C₂³×C₆₇	1	2	yes	—
901	#102	C₂³×C₆₇	1	2	yes	—
902	#102	C₂³×C₆₇	1	2	yes	—
903	#102	C₂³×C₆₇	1	2	yes	—
904	#102	C₂³×C₆₇	1	2	yes	—
905	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
906	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
907	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
908	#97	C₂³×C₆₇	1	1	yes	characteristic
909	#97	C₂³×C₆₇	1	1	yes	characteristic
910	#97	C₂³×C₆₇	1	2	yes	—
911	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
912	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
913	C₄×C₈	C₂³×C₆₇	1	2	yes	—
914	C₄×C₈	C₂³×C₆₇	1	2	yes	—
915	C₂⁴	—	2	1	no	—
916	C₂⁴	—	2	2	no	—
917	C₂⁴	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	4	1	no	—
920	#41	—	8	2	no	—
921	#41	—	8	2	no	—
922	#41	—	8	2	no	—
923	C₂×Q₈	—	2	1	no	—
924	C₂×Q₈	—	2	2	no	—
925	C₂×Q₈	—	2	1	no	—
926	C₂×Q₈	—	8	2	no	—
927	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
928	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
929	C₂×D₄	—	2	4	no	—
930	C₂×D₄	—	2	4	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	4	2	no	—
948	C₂×D₄	—	4	2	no	—
949	C₂×D₄	—	4	1	no	—
950	C₂×D₄	—	8	2	no	—
951	C₂×D₄	—	8	2	no	—
952	C₂×D₄	—	8	4	no	—
953	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
954	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
955	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
956	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
957	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
958	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
959	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	8	2	no	—
975	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
976	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
977	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
979	SD₁₆	—	2	2	no	—
980	SD₁₆	—	2	2	no	—
981	SD₁₆	—	4	2	no	—
982	D₈	—	2	4	no	—
983	D₈	—	2	4	no	—
984	D₈	—	2	2	no	—
985	D₈	—	2	4	no	—
986	D₈	—	4	2	no	—
987	D₈	—	4	2	no	—
988	D₈	#41×C₆₇	1	4	yes	complemented
989	M₁₆	—	2	2	no	—
990	M₁₆	—	4	1	no	—
991	M₁₆	—	4	2	no	—
992	C₂×C₈	—	2	4	no	—
993	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
994	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
995	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
996	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
997	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
998	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1011	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1012	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1013	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1018	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1044	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1047	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	2	1	no	—
1051	C₄²	—	2	2	no	—
1052	C₄²	—	2	2	no	—
1053	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1054	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1056	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1057	C₄²	C₂⁴×C₆₇	1	2	yes	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	2	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	2	no	—
1063	C₂³	—	4	2	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	4	no	—
1066	C₂³	—	4	2	no	—
1067	C₂³	—	8	1	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	—	8	2	no	—
1071	C₂³	—	8	2	no	—
1072	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1073	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1074	Q₈	—	2	2	no	—
1075	Q₈	—	2	1	no	—
1076	Q₈	—	2	1	no	—
1077	Q₈	—	4	2	no	—
1078	Q₈	—	8	2	no	—
1079	Q₈	—	8	1	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	2	2	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	2	no	—
1087	D₄	—	2	1	no	—
1088	D₄	—	2	2	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	4	no	—
1092	D₄	—	4	4	no	—
1093	D₄	—	4	2	no	—
1094	D₄	—	4	4	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	8	2	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	1	no	—
1100	D₄	—	8	1	no	—
1101	D₄	—	8	2	no	—
1102	D₄	—	8	2	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	2	no	—
1105	D₄	C₂×#41×C₆₇	1	2	yes	—
1106	D₄	C₂×#41×C₆₇	1	2	yes	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	4	2	no	—
1123	C₂×C₄	—	4	2	no	—
1124	C₂×C₄	—	8	1	no	—
1125	C₂×C₄	—	8	1	no	—
1126	C₂×C₄	—	8	2	no	—
1127	C₂×C₄	—	8	2	no	—
1128	C₂×C₄	—	8	2	no	—
1129	C₂×C₄	—	8	2	no	—
1130	C₂×C₄	—	8	2	no	—
1131	C₂×C₄	—	8	1	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	1	no	—
1134	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1135	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1136	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1137	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1139	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1140	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1141	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1142	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1143	C₈	—	2	2	no	—
1144	C₈	—	2	1	no	—
1145	C₈	—	2	1	no	—
1146	C₈	—	2	1	no	—
1147	C₈	—	2	2	no	—
1148	C₈	C₂×#41×C₆₇	1	2	yes	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	1	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	8	4	no	—
1171	C₂²	—	16	4	no	—
1172	C₂²	—	16	4	no	—
1173	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1174	C₄	—	2	1	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	2	1	no	—
1177	C₄	—	2	1	no	—
1178	C₄	—	2	2	no	—
1179	C₄	—	2	1	no	—
1180	C₄	—	2	2	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	2	no	—
1187	C₄	—	4	1	no	—
1188	C₄	#576×C₆₇	1	2	yes	—
1189	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1190	C₄	#585×C₆₇	1	1	yes	characteristic
1191	C₂	—	4	1	no	—
1192	C₂	—	4	2	no	—
1193	C₂	—	4	2	no	—
1194	C₂	—	4	2	no	—
1195	C₂	—	8	1	no	—
1196	C₂	—	8	2	no	—
1197	C₂	—	8	2	no	—
1198	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1199	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
1200	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #529×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3519	C₂	semidirect
2. C₆₇×#3514	C₂	semidirect
3. C₆₇×#3399	C₂	semidirect
4. C₆₇×#3384	C₂	semidirect
5. C₆₇×#3361	C₂	semidirect
6. C₆₇×#3358	C₂	semidirect
7. C₆₇×#3347	C₂	semidirect
8. C₆₇×#3340	C₂	semidirect
9. C₆₇×#3325	C₂	semidirect
10. C₆₇×#3325	C₂	semidirect
11. C₆₇×#3324	C₂	semidirect
12. C₆₇×#3322	C₂	semidirect
13. D₄×D₈×C₆₇	C₂	semidirect
14. C₆₇×#3264	C₂	semidirect
15. C₆₇×#3184	C₂	semidirect
16. C₆₇×#3179	C₂	semidirect
17. C₆₇×#3122	C₂	semidirect
18. C₆₇×#3118	C₂	semidirect
19. C₆₇×#3106	C₂	semidirect
20. C₆₇×#3100	C₂	semidirect
21. C₆₇×#2969	C₂	semidirect
22. C₆₇×#2948	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
26. #559×C₆₇	C₂²	semidirect
27. #556×C₆₇	C₂²	semidirect
29. #555×C₆₇	C₂²	semidirect
30. #554×C₆₇	C₂²	semidirect
32. #553×C₆₇	C₂²	semidirect
34. #550×C₆₇	C₂²	semidirect
35. D₄×Q₈×C₆₇	C₂²	semidirect
40. #546×C₆₇	C₂²	semidirect
42. D₄²×C₆₇	C₂²	semidirect
43. D₄²×C₆₇	C₂²	semidirect
44. #542×C₆₇	C₂²	semidirect
45. #540×C₆₇	C₂²	semidirect
48. #532×C₆₇	C₂²	semidirect
49. #532×C₆₇	C₂²	semidirect
55. #518×C₆₇	C₂²	semidirect
56. #518×C₆₇	C₂²	semidirect
57. C₄×#41×C₆₇	C₂²	semidirect
58. C₂×C₄×D₄×C₆₇	C₂²	semidirect
59. #501×C₆₇	C₂²	semidirect
60. #498×C₆₇	C₂²	semidirect
61. #496×C₆₇	C₂²	semidirect
62. #493×C₆₇	C₂²	semidirect
63. #488×C₆₇	C₂²	semidirect
64. #486×C₆₇	C₂²	semidirect
65. #486×C₆₇	C₂²	semidirect
66. #486×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
68. #482×C₆₇	C₂²	semidirect
69. #482×C₆₇	C₂²	semidirect
70. #482×C₆₇	C₂²	semidirect
71. #482×C₆₇	C₂²	semidirect
72. #480×C₆₇	C₂²	semidirect
73. #478×C₆₇	C₂²	semidirect
74. #478×C₆₇	C₂²	semidirect
75. #477×C₆₇	C₂²	semidirect
76. #476×C₆₇	C₂²	semidirect
77. #476×C₆₇	C₂²	semidirect
78. #474×C₆₇	C₂²	semidirect
79. #474×C₆₇	C₂²	semidirect
80. #474×C₆₇	C₂²	semidirect
81. #469×C₆₇	C₂²	semidirect
82. #469×C₆₇	C₂²	semidirect
83. #469×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #466×C₆₇	C₂²	semidirect
86. #465×C₆₇	C₂²	semidirect
87. #463×C₆₇	C₂²	semidirect
88. #463×C₆₇	C₂²	semidirect
89. #460×C₆₇	C₂²	semidirect
91. #459×C₆₇	C₂²	semidirect
92. #459×C₆₇	C₂²	semidirect
93. #459×C₆₇	C₂²	semidirect
94. #459×C₆₇	C₂²	semidirect
95. #450×C₆₇	C₂²	semidirect
96. #449×C₆₇	C₂²	semidirect
98. #447×C₆₇	C₂²	semidirect
99. #447×C₆₇	C₂²	semidirect
100. #447×C₆₇	C₂²	semidirect
101. #446×C₆₇	C₂²	semidirect
102. C₈×Q₈×C₆₇	C₂²	semidirect
105. #442×C₆₇	C₂²	semidirect
106. #442×C₆₇	C₂²	semidirect
107. #442×C₆₇	C₂²	semidirect
108. #442×C₆₇	C₂²	semidirect
109. #440×C₆₇	C₂²	semidirect
110. #440×C₆₇	C₂²	semidirect
111. C₄×SD₁₆×C₆₇	C₂²	semidirect
112. C₄×SD₁₆×C₆₇	C₂²	semidirect
113. C₄×SD₁₆×C₆₇	C₂²	semidirect
115. C₄×D₈×C₆₇	C₂²	semidirect
116. C₄×D₈×C₆₇	C₂²	semidirect
117. C₄×D₈×C₆₇	C₂²	semidirect
118. C₄×D₈×C₆₇	C₂²	semidirect
119. C₄×D₈×C₆₇	C₂²	semidirect
120. C₄×D₈×C₆₇	C₂²	semidirect
121. #436×C₆₇	C₂²	semidirect
122. #436×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. C₈×D₄×C₆₇	C₂²	semidirect
125. #433×C₆₇	C₂²	semidirect
126. #431×C₆₇	C₂²	semidirect
127. #428×C₆₇	C₂²	semidirect
128. #427×C₆₇	C₂²	semidirect
129. #418×C₆₇	C₂²	semidirect
130. #418×C₆₇	C₂²	semidirect
131. #418×C₆₇	C₂²	semidirect
132. #417×C₆₇	C₂²	semidirect
133. #405×C₆₇	C₂²	semidirect
134. C₄×M₁₆×C₆₇	C₂²	semidirect
387. D₈×C₆₇	#41	semidirect
590. #61539	C₆₇	direct (N × H)
601. #3519	C₂×C₆₇	semidirect
602. #3514	C₂×C₆₇	semidirect
603. #3399	C₂×C₆₇	semidirect
604. #3384	C₂×C₆₇	semidirect
605. #3361	C₂×C₆₇	semidirect
606. #3358	C₂×C₆₇	semidirect
607. #3347	C₂×C₆₇	semidirect
608. #3340	C₂×C₆₇	semidirect
609. #3325	C₂×C₆₇	semidirect
610. #3325	C₂×C₆₇	semidirect
611. #3324	C₂×C₆₇	semidirect
612. #3322	C₂×C₆₇	semidirect
613. D₄×D₈	C₂×C₆₇	semidirect
614. #3264	C₂×C₆₇	semidirect
615. #3184	C₂×C₆₇	semidirect
616. #3179	C₂×C₆₇	semidirect
617. #3122	C₂×C₆₇	semidirect
618. #3118	C₂×C₆₇	semidirect
619. #3106	C₂×C₆₇	semidirect
620. #3100	C₂×C₆₇	semidirect
621. #2969	C₂×C₆₇	semidirect
622. #2948	C₂×C₆₇	semidirect
623. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
624. C₆₇	#61539	direct (N × H)
627. #559	C₂²×C₆₇	semidirect
628. #556	C₂²×C₆₇	semidirect
630. #555	C₂²×C₆₇	semidirect
631. #554	C₂²×C₆₇	semidirect
633. #553	C₂²×C₆₇	semidirect
635. #550	C₂²×C₆₇	semidirect
636. D₄×Q₈	C₂²×C₆₇	semidirect
641. #546	C₂²×C₆₇	semidirect
643. D₄²	C₂²×C₆₇	semidirect
644. D₄²	C₂²×C₆₇	semidirect
645. #542	C₂²×C₆₇	semidirect
646. #540	C₂²×C₆₇	semidirect
649. #532	C₂²×C₆₇	semidirect
650. #532	C₂²×C₆₇	semidirect
656. #518	C₂²×C₆₇	semidirect
657. #518	C₂²×C₆₇	semidirect
658. C₄×#41	C₂²×C₆₇	semidirect
659. C₂×C₄×D₄	C₂²×C₆₇	semidirect
660. #501	C₂²×C₆₇	semidirect
661. #498	C₂²×C₆₇	semidirect
662. #496	C₂²×C₆₇	semidirect
663. #493	C₂²×C₆₇	semidirect
664. #488	C₂²×C₆₇	semidirect
665. #486	C₂²×C₆₇	semidirect
666. #486	C₂²×C₆₇	semidirect
667. #486	C₂²×C₆₇	semidirect
668. #485	C₂²×C₆₇	semidirect
669. #482	C₂²×C₆₇	semidirect
670. #482	C₂²×C₆₇	semidirect
671. #482	C₂²×C₆₇	semidirect
672. #482	C₂²×C₆₇	semidirect
673. #480	C₂²×C₆₇	semidirect
674. #478	C₂²×C₆₇	semidirect
675. #478	C₂²×C₆₇	semidirect
676. #477	C₂²×C₆₇	semidirect
677. #476	C₂²×C₆₇	semidirect
678. #476	C₂²×C₆₇	semidirect
679. #474	C₂²×C₆₇	semidirect
680. #474	C₂²×C₆₇	semidirect
681. #474	C₂²×C₆₇	semidirect
682. #469	C₂²×C₆₇	semidirect
683. #469	C₂²×C₆₇	semidirect
684. #469	C₂²×C₆₇	semidirect
685. #468	C₂²×C₆₇	semidirect
686. #466	C₂²×C₆₇	semidirect
687. #465	C₂²×C₆₇	semidirect
688. #463	C₂²×C₆₇	semidirect
689. #463	C₂²×C₆₇	semidirect
690. #460	C₂²×C₆₇	semidirect
692. #459	C₂²×C₆₇	semidirect
693. #459	C₂²×C₆₇	semidirect
694. #459	C₂²×C₆₇	semidirect
695. #459	C₂²×C₆₇	semidirect
696. #450	C₂²×C₆₇	semidirect
697. #449	C₂²×C₆₇	semidirect
699. #447	C₂²×C₆₇	semidirect
700. #447	C₂²×C₆₇	semidirect
701. #447	C₂²×C₆₇	semidirect
702. #446	C₂²×C₆₇	semidirect
703. C₈×Q₈	C₂²×C₆₇	semidirect
706. #442	C₂²×C₆₇	semidirect
707. #442	C₂²×C₆₇	semidirect
708. #442	C₂²×C₆₇	semidirect
709. #442	C₂²×C₆₇	semidirect
710. #440	C₂²×C₆₇	semidirect
711. #440	C₂²×C₆₇	semidirect
712. C₄×SD₁₆	C₂²×C₆₇	semidirect
713. C₄×SD₁₆	C₂²×C₆₇	semidirect
714. C₄×SD₁₆	C₂²×C₆₇	semidirect
716. C₄×D₈	C₂²×C₆₇	semidirect
717. C₄×D₈	C₂²×C₆₇	semidirect
718. C₄×D₈	C₂²×C₆₇	semidirect
719. C₄×D₈	C₂²×C₆₇	semidirect
720. C₄×D₈	C₂²×C₆₇	semidirect
721. C₄×D₈	C₂²×C₆₇	semidirect
722. #436	C₂²×C₆₇	semidirect
723. #436	C₂²×C₆₇	semidirect
724. #435	C₂²×C₆₇	semidirect
725. C₈×D₄	C₂²×C₆₇	semidirect
726. #433	C₂²×C₆₇	semidirect
727. #431	C₂²×C₆₇	semidirect
728. #428	C₂²×C₆₇	semidirect
729. #427	C₂²×C₆₇	semidirect
730. #418	C₂²×C₆₇	semidirect
731. #418	C₂²×C₆₇	semidirect
732. #418	C₂²×C₆₇	semidirect
733. #417	C₂²×C₆₇	semidirect
734. #405	C₂²×C₆₇	semidirect
735. C₄×M₁₆	C₂²×C₆₇	semidirect
988. D₈	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3519	2
C₆₇×#3514	2
C₆₇×#3399	2
C₆₇×#3384	2
C₆₇×#3361	2
C₆₇×#3358	2
C₆₇×#3347	2
C₆₇×#3340	2
C₆₇×#3325	2
C₆₇×#3324	2
C₆₇×#3322	2
D₄×D₈×C₆₇	2
C₆₇×#3264	2
C₆₇×#3184	2
C₆₇×#3179	2
C₆₇×#3122	2
C₆₇×#3118	2
C₆₇×#3106	2
C₆₇×#3100	2
C₆₇×#2969	2
C₆₇×#2948	2
C₄×AGL(1,ℤ/8)×C₆₇	2
#61539	67

Subgroups — C67×#61539 #30740790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61539 #30740790