Subgroups — C₆₇×#60994 #30740245

Order 17152.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3254	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3251	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3247	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3246	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3241	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3237	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3233	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3221	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3217	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3200	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3198	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3179	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3174	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3123	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#3103	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	#559×C₆₇	—	2	1	no	—
25	#559×C₆₇	—	2	1	no	—
26	#550×C₆₇	—	2	1	no	—
27	#550×C₆₇	—	2	1	no	—
28	#546×C₆₇	—	2	1	no	—
29	#546×C₆₇	—	2	1	no	—
30	#546×C₆₇	—	2	1	no	—
31	#546×C₆₇	—	2	1	no	—
32	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#542×C₆₇	—	2	1	no	—
34	#542×C₆₇	C₂²	1	1	yes	characteristic
35	#542×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#541×C₆₇	—	2	1	no	—
37	#541×C₆₇	C₂²	1	1	yes	characteristic
38	#541×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#540×C₆₇	C₂²	1	2	yes	—
40	#540×C₆₇	C₂²	1	2	yes	—
41	#539×C₆₇	—	2	1	no	—
42	#539×C₆₇	—	2	1	no	—
43	#537×C₆₇	C₂²	1	1	yes	characteristic
44	#536×C₆₇	C₂²	1	1	yes	characteristic
45	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#535×C₆₇	C₂²	1	2	yes	—
47	#533×C₆₇	—	2	1	no	—
48	#533×C₆₇	C₂²	1	1	yes	characteristic
49	#533×C₆₇	C₂²	1	1	yes	characteristic
50	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#532×C₆₇	C₂²	1	1	yes	characteristic
52	#532×C₆₇	C₂²	1	1	yes	characteristic
53	#532×C₆₇	C₂²	1	1	yes	characteristic
54	#532×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
56	#529×C₆₇	—	2	1	no	—
57	#529×C₆₇	—	2	1	no	—
58	#529×C₆₇	—	2	1	no	—
59	#529×C₆₇	C₂²	1	1	yes	characteristic
60	#529×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#518×C₆₇	C₂²	1	2	yes	—
62	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
63	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#501×C₆₇	C₂²	1	2	yes	complemented
66	#499×C₆₇	C₂²	1	2	yes	complemented
67	#496×C₆₇	C₂²	1	2	yes	—
68	#492×C₆₇	C₂²	1	2	yes	—
69	#491×C₆₇	C₂²	1	2	yes	complemented
70	#490×C₆₇	C₂²	1	2	yes	—
71	#488×C₆₇	C₂²	1	2	yes	complemented
72	#486×C₆₇	C₂²	1	2	yes	—
73	#485×C₆₇	C₂²	1	2	yes	—
74	#485×C₆₇	C₂²	1	2	yes	—
75	#485×C₆₇	C₂²	1	2	yes	—
76	#482×C₆₇	C₂²	1	2	yes	—
77	#482×C₆₇	C₂²	1	2	yes	complemented
78	#482×C₆₇	C₂²	1	2	yes	complemented
79	#481×C₆₇	C₂²	1	2	yes	complemented
80	#480×C₆₇	C₂²	1	2	yes	complemented
81	#478×C₆₇	C₂²	1	2	yes	complemented
82	#478×C₆₇	C₂²	1	2	yes	complemented
83	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#476×C₆₇	C₂²	1	2	yes	complemented
88	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#474×C₆₇	C₂²	1	2	yes	complemented
93	#469×C₆₇	C₂²	1	2	yes	complemented
94	#468×C₆₇	C₂²	1	2	yes	complemented
95	#468×C₆₇	C₂²	1	2	yes	complemented
96	#468×C₆₇	C₂²	1	2	yes	complemented
97	#466×C₆₇	C₂²	1	2	yes	complemented
98	#465×C₆₇	C₂²	1	2	yes	complemented
99	#465×C₆₇	C₂²	1	2	yes	complemented
100	#465×C₆₇	C₂²	1	2	yes	complemented
101	#463×C₆₇	C₂²	1	2	yes	complemented
102	#463×C₆₇	C₂²	1	2	yes	complemented
103	#461×C₆₇	C₂²	1	2	yes	complemented
104	#461×C₆₇	C₂²	1	2	yes	complemented
105	#460×C₆₇	C₂²	1	1	yes	characteristic
106	#460×C₆₇	C₂²	1	1	yes	characteristic
107	#460×C₆₇	C₂²	1	1	yes	characteristic
108	#460×C₆₇	C₂²	1	1	yes	characteristic
109	#460×C₆₇	C₂²	1	1	yes	characteristic
110	#460×C₆₇	C₂²	1	1	yes	characteristic
111	#459×C₆₇	C₂²	1	1	yes	characteristic
112	#459×C₆₇	C₂²	1	1	yes	characteristic
113	#450×C₆₇	C₂²	1	2	yes	—
114	#450×C₆₇	C₂²	1	2	yes	—
115	#450×C₆₇	C₂²	1	2	yes	—
116	#449×C₆₇	C₂²	1	2	yes	complemented
117	#449×C₆₇	C₂²	1	2	yes	complemented
118	#448×C₆₇	C₂²	1	2	yes	complemented
119	#448×C₆₇	C₂²	1	2	yes	complemented
120	#447×C₆₇	C₂²	1	2	yes	—
121	#442×C₆₇	C₂²	1	2	yes	complemented
122	#440×C₆₇	C₂²	1	2	yes	complemented
123	#440×C₆₇	C₂²	1	2	yes	complemented
124	#440×C₆₇	C₂²	1	2	yes	complemented
125	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
126	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
127	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
128	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
129	#433×C₆₇	C₂²	1	2	yes	—
130	#433×C₆₇	C₂²	1	2	yes	complemented
131	#432×C₆₇	C₂²	1	1	yes	characteristic
132	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#431×C₆₇	C₂²	1	1	yes	characteristic
134	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	#408×C₆₇	C₂²	1	2	yes	—
138	#405×C₆₇	C₂²	1	2	yes	complemented
139	C₂×#41×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	—	2	1	no	—
142	C₂×#41×C₆₇	—	2	1	no	—
143	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₆₇	—	2	1	no	—
147	C₂²×D₄×C₆₇	—	2	1	no	—
148	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×D₈×C₆₇	C₂³	1	2	yes	—
156	C₂×D₈×C₆₇	C₂³	1	2	yes	—
157	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₆₇	—	2	1	no	—
160	C₄⋊Q₈×C₆₇	—	2	1	no	—
161	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
167	#127×C₆₇	—	2	2	no	—
168	#127×C₆₇	—	2	1	no	—
169	#127×C₆₇	—	2	1	no	—
170	#127×C₆₇	C₂³	1	1	yes	characteristic
171	#127×C₆₇	C₂³	1	1	yes	characteristic
172	#127×C₆₇	C₂³	1	2	yes	—
173	#126×C₆₇	—	2	1	no	—
174	#126×C₆₇	—	2	1	no	—
175	#126×C₆₇	—	2	1	no	—
176	#126×C₆₇	—	2	1	no	—
177	#126×C₆₇	—	2	1	no	—
178	#126×C₆₇	—	2	1	no	—
179	#126×C₆₇	—	2	1	no	—
180	#126×C₆₇	—	2	1	no	—
181	#125×C₆₇	—	2	1	no	—
182	#125×C₆₇	—	2	1	no	—
183	#125×C₆₇	—	2	1	no	—
184	#125×C₆₇	—	2	1	no	—
185	#125×C₆₇	—	2	1	no	—
186	#125×C₆₇	—	2	1	no	—
187	#125×C₆₇	—	2	1	no	—
188	#125×C₆₇	C₂³	1	1	yes	characteristic
189	#125×C₆₇	C₂³	1	2	yes	—
190	#125×C₆₇	C₂³	1	1	yes	characteristic
191	#124×C₆₇	—	2	2	no	—
192	#124×C₆₇	—	2	1	no	—
193	#124×C₆₇	—	2	1	no	—
194	#124×C₆₇	—	2	1	no	—
195	#124×C₆₇	—	2	1	no	—
196	#124×C₆₇	—	2	1	no	—
197	#124×C₆₇	—	2	1	no	—
198	#124×C₆₇	—	2	1	no	—
199	#124×C₆₇	C₂³	1	1	yes	characteristic
200	#124×C₆₇	C₂³	1	1	yes	characteristic
201	#123×C₆₇	—	2	1	no	—
202	#123×C₆₇	—	2	1	no	—
203	#123×C₆₇	—	2	1	no	—
204	#123×C₆₇	—	2	1	no	—
205	#123×C₆₇	—	2	2	no	—
206	#123×C₆₇	—	2	2	no	—
207	#123×C₆₇	—	2	2	no	—
208	#123×C₆₇	—	2	2	no	—
209	#123×C₆₇	—	2	1	no	—
210	#123×C₆₇	—	2	1	no	—
211	#123×C₆₇	—	2	1	no	—
212	#123×C₆₇	—	2	1	no	—
213	C₂²⋊Q₈×C₆₇	—	2	1	no	—
214	C₂²⋊Q₈×C₆₇	—	2	1	no	—
215	C₂²⋊Q₈×C₆₇	—	2	1	no	—
216	C₂²⋊Q₈×C₆₇	—	2	1	no	—
217	C₂²⋊Q₈×C₆₇	—	2	1	no	—
218	C₂²⋊Q₈×C₆₇	—	2	1	no	—
219	C₂²⋊Q₈×C₆₇	—	2	1	no	—
220	C₂²⋊Q₈×C₆₇	—	2	1	no	—
221	C₂²⋊Q₈×C₆₇	—	2	1	no	—
222	C₂²⋊Q₈×C₆₇	—	2	1	no	—
223	C₂²⋊Q₈×C₆₇	—	2	1	no	—
224	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
229	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
230	#121×C₆₇	—	2	1	no	—
231	#121×C₆₇	—	2	1	no	—
232	#121×C₆₇	—	2	1	no	—
233	#121×C₆₇	—	2	1	no	—
234	#121×C₆₇	—	2	1	no	—
235	#121×C₆₇	—	2	1	no	—
236	#121×C₆₇	—	2	1	no	—
237	#121×C₆₇	—	2	2	no	—
238	#121×C₆₇	—	2	2	no	—
239	#121×C₆₇	—	2	2	no	—
240	#121×C₆₇	—	2	2	no	—
241	#121×C₆₇	C₂³	1	2	yes	—
242	#121×C₆₇	C₂³	1	2	yes	—
243	#121×C₆₇	C₂³	1	2	yes	—
244	#121×C₆₇	C₂³	1	2	yes	—
245	#121×C₆₇	C₂³	1	1	yes	characteristic
246	#121×C₆₇	C₂³	1	1	yes	characteristic
247	#120×C₆₇	—	2	2	no	—
248	#120×C₆₇	—	2	2	no	—
249	C₄×Q₈×C₆₇	—	2	1	no	—
250	C₄×Q₈×C₆₇	—	2	1	no	—
251	C₄×Q₈×C₆₇	—	2	1	no	—
252	C₄×Q₈×C₆₇	—	2	1	no	—
253	C₄×Q₈×C₆₇	—	2	1	no	—
254	C₄×Q₈×C₆₇	—	2	1	no	—
255	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
256	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
257	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
258	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
259	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
260	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
261	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
262	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₆₇	—	2	1	no	—
264	C₄×D₄×C₆₇	—	2	1	no	—
265	C₄×D₄×C₆₇	—	2	1	no	—
266	C₄×D₄×C₆₇	—	2	1	no	—
267	C₄×D₄×C₆₇	—	2	2	no	—
268	C₄×D₄×C₆₇	—	2	2	no	—
269	C₄×D₄×C₆₇	—	2	1	no	—
270	C₄×D₄×C₆₇	—	2	1	no	—
271	C₄×D₄×C₆₇	—	2	1	no	—
272	C₄×D₄×C₆₇	—	2	1	no	—
273	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
274	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
275	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
276	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
277	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
278	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
279	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₆₇	C₂³	1	2	yes	—
281	C₄×D₄×C₆₇	C₂³	1	2	yes	—
282	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₆₇	C₂³	1	2	yes	—
284	C₄×D₄×C₆₇	C₂³	1	2	yes	—
285	#117×C₆₇	—	2	1	no	—
286	#117×C₆₇	—	2	1	no	—
287	#117×C₆₇	—	2	1	no	—
288	#117×C₆₇	—	2	1	no	—
289	#117×C₆₇	—	2	1	no	—
290	#117×C₆₇	C₂³	1	2	yes	—
291	#117×C₆₇	C₂³	1	1	yes	characteristic
292	#117×C₆₇	C₂³	1	1	yes	characteristic
293	#117×C₆₇	C₂³	1	1	yes	characteristic
294	#117×C₆₇	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
296	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
298	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
299	C₂×C₄²×C₆₇	—	2	1	no	—
300	C₂×C₄²×C₆₇	—	2	1	no	—
301	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
304	#107×C₆₇	C₂³	1	2	yes	—
305	#107×C₆₇	C₂³	1	2	yes	—
306	#107×C₆₇	C₂³	1	2	yes	—
307	#107×C₆₇	C₂³	1	2	yes	—
308	#106×C₆₇	C₂³	1	2	yes	—
309	#106×C₆₇	C₂³	1	2	yes	—
310	#106×C₆₇	C₂³	1	2	yes	—
311	#106×C₆₇	C₂³	1	2	yes	—
312	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
317	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
318	#103×C₆₇	C₂³	1	2	yes	—
319	#103×C₆₇	C₂³	1	2	yes	—
320	#103×C₆₇	C₂³	1	2	yes	—
321	#103×C₆₇	C₂³	1	2	yes	—
322	#103×C₆₇	C₂³	1	2	yes	—
323	#103×C₆₇	C₂³	1	2	yes	—
324	#102×C₆₇	C₂³	1	2	yes	—
325	#102×C₆₇	C₂³	1	2	yes	—
326	#102×C₆₇	C₂³	1	2	yes	—
327	#102×C₆₇	C₂³	1	2	yes	—
328	#102×C₆₇	C₂³	1	2	yes	—
329	#102×C₆₇	C₂³	1	2	yes	—
330	#102×C₆₇	C₂³	1	2	yes	—
331	#102×C₆₇	C₂³	1	2	yes	—
332	#102×C₆₇	C₂³	1	2	yes	—
333	#102×C₆₇	C₂³	1	2	yes	—
334	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
335	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
336	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
337	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
338	#97×C₆₇	C₂³	1	2	yes	—
339	#97×C₆₇	C₂³	1	2	yes	—
340	C₄×C₈×C₆₇	C₂³	1	2	yes	—
341	C₄×C₈×C₆₇	C₂³	1	2	yes	—
342	C₂⁴×C₆₇	—	2	2	no	—
343	#41×C₆₇	—	4	1	no	—
344	#41×C₆₇	—	4	1	no	—
345	#41×C₆₇	—	4	1	no	—
346	#41×C₆₇	—	4	1	no	—
347	#41×C₆₇	—	8	2	no	—
348	#41×C₆₇	—	8	2	no	—
349	#41×C₆₇	—	8	2	no	—
350	#41×C₆₇	—	8	2	no	—
351	C₂×Q₈×C₆₇	—	2	1	no	—
352	C₂×Q₈×C₆₇	—	2	1	no	—
353	C₂×Q₈×C₆₇	—	2	1	no	—
354	C₂×Q₈×C₆₇	—	2	1	no	—
355	C₂×Q₈×C₆₇	—	2	1	no	—
356	C₂×Q₈×C₆₇	—	4	1	no	—
357	C₂×Q₈×C₆₇	—	4	1	no	—
358	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
359	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
360	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
361	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₆₇	—	2	1	no	—
363	C₂×D₄×C₆₇	—	2	1	no	—
364	C₂×D₄×C₆₇	—	2	1	no	—
365	C₂×D₄×C₆₇	—	2	2	no	—
366	C₂×D₄×C₆₇	—	2	2	no	—
367	C₂×D₄×C₆₇	—	2	2	no	—
368	C₂×D₄×C₆₇	—	2	2	no	—
369	C₂×D₄×C₆₇	—	2	2	no	—
370	C₂×D₄×C₆₇	—	2	1	no	—
371	C₂×D₄×C₆₇	—	2	1	no	—
372	C₂×D₄×C₆₇	—	2	1	no	—
373	C₂×D₄×C₆₇	—	2	1	no	—
374	C₂×D₄×C₆₇	—	2	2	no	—
375	C₂×D₄×C₆₇	—	2	2	no	—
376	C₂×D₄×C₆₇	—	4	2	no	—
377	C₂×D₄×C₆₇	—	4	2	no	—
378	C₂×D₄×C₆₇	—	8	2	no	—
379	C₂×D₄×C₆₇	—	8	2	no	—
380	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
381	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
382	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
385	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
386	C₂²×C₄×C₆₇	—	2	1	no	—
387	C₂²×C₄×C₆₇	—	2	1	no	—
388	C₂²×C₄×C₆₇	—	2	1	no	—
389	C₂²×C₄×C₆₇	—	2	1	no	—
390	C₂²×C₄×C₆₇	—	2	1	no	—
391	C₂²×C₄×C₆₇	—	2	2	no	—
392	C₂²×C₄×C₆₇	—	2	2	no	—
393	C₂²×C₄×C₆₇	—	2	2	no	—
394	C₂²×C₄×C₆₇	—	2	2	no	—
395	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	SD₁₆×C₆₇	—	4	2	no	—
405	SD₁₆×C₆₇	—	4	2	no	—
406	SD₁₆×C₆₇	—	4	2	no	—
407	SD₁₆×C₆₇	—	4	2	no	—
408	SD₁₆×C₆₇	—	4	2	no	—
409	SD₁₆×C₆₇	—	4	2	no	—
410	D₈×C₆₇	—	4	2	no	—
411	D₈×C₆₇	—	4	2	no	—
412	M₁₆×C₆₇	—	4	2	no	—
413	C₂×C₈×C₆₇	—	4	2	no	—
414	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
415	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
416	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
417	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
418	C₄⋊C₄×C₆₇	—	2	1	no	—
419	C₄⋊C₄×C₆₇	—	2	1	no	—
420	C₄⋊C₄×C₆₇	—	2	1	no	—
421	C₄⋊C₄×C₆₇	—	2	1	no	—
422	C₄⋊C₄×C₆₇	—	2	1	no	—
423	C₄⋊C₄×C₆₇	—	2	1	no	—
424	C₄⋊C₄×C₆₇	—	2	1	no	—
425	C₄⋊C₄×C₆₇	—	2	1	no	—
426	C₄⋊C₄×C₆₇	—	2	1	no	—
427	C₄⋊C₄×C₆₇	—	2	1	no	—
428	C₄⋊C₄×C₆₇	—	2	1	no	—
429	C₄⋊C₄×C₆₇	—	2	1	no	—
430	C₄⋊C₄×C₆₇	—	2	1	no	—
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	—	2	1	no	—
433	C₄⋊C₄×C₆₇	—	2	1	no	—
434	C₄⋊C₄×C₆₇	—	2	1	no	—
435	C₄⋊C₄×C₆₇	—	2	1	no	—
436	C₄⋊C₄×C₆₇	—	2	1	no	—
437	C₄⋊C₄×C₆₇	—	2	2	no	—
438	C₄⋊C₄×C₆₇	—	2	2	no	—
439	C₄⋊C₄×C₆₇	—	2	1	no	—
440	C₄⋊C₄×C₆₇	—	2	1	no	—
441	C₄⋊C₄×C₆₇	—	2	1	no	—
442	C₄⋊C₄×C₆₇	—	2	1	no	—
443	C₄⋊C₄×C₆₇	—	2	1	no	—
444	C₄⋊C₄×C₆₇	—	2	1	no	—
445	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
456	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
457	C₂²⋊C₄×C₆₇	—	2	2	no	—
458	C₂²⋊C₄×C₆₇	—	2	1	no	—
459	C₂²⋊C₄×C₆₇	—	2	1	no	—
460	C₂²⋊C₄×C₆₇	—	2	1	no	—
461	C₂²⋊C₄×C₆₇	—	2	1	no	—
462	C₂²⋊C₄×C₆₇	—	2	1	no	—
463	C₂²⋊C₄×C₆₇	—	2	1	no	—
464	C₂²⋊C₄×C₆₇	—	2	1	no	—
465	C₂²⋊C₄×C₆₇	—	2	2	no	—
466	C₂²⋊C₄×C₆₇	—	2	2	no	—
467	C₂²⋊C₄×C₆₇	—	2	2	no	—
468	C₂²⋊C₄×C₆₇	—	2	2	no	—
469	C₂²⋊C₄×C₆₇	—	2	1	no	—
470	C₂²⋊C₄×C₆₇	—	2	1	no	—
471	C₂²⋊C₄×C₆₇	—	2	1	no	—
472	C₂²⋊C₄×C₆₇	—	2	1	no	—
473	C₂²⋊C₄×C₆₇	—	2	1	no	—
474	C₂²⋊C₄×C₆₇	—	2	1	no	—
475	C₂²⋊C₄×C₆₇	—	2	2	no	—
476	C₂²⋊C₄×C₆₇	—	2	2	no	—
477	C₂²⋊C₄×C₆₇	—	2	2	no	—
478	C₂²⋊C₄×C₆₇	—	2	2	no	—
479	C₂²⋊C₄×C₆₇	—	2	1	no	—
480	C₂²⋊C₄×C₆₇	—	2	1	no	—
481	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
486	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
487	C₄²×C₆₇	—	2	1	no	—
488	C₄²×C₆₇	—	2	1	no	—
489	C₄²×C₆₇	—	2	1	no	—
490	C₄²×C₆₇	—	2	1	no	—
491	C₄²×C₆₇	—	2	1	no	—
492	C₄²×C₆₇	—	2	1	no	—
493	C₄²×C₆₇	—	2	1	no	—
494	C₄²×C₆₇	—	2	2	no	—
495	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
497	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
498	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
499	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
500	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
501	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
502	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
503	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
504	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
505	C₂³×C₆₇	—	2	1	no	—
506	C₂³×C₆₇	—	2	2	no	—
507	C₂³×C₆₇	—	2	2	no	—
508	C₂³×C₆₇	—	4	4	no	—
509	C₂³×C₆₇	—	8	2	no	—
510	C₂³×C₆₇	—	8	2	no	—
511	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
512	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
513	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
514	Q₈×C₆₇	—	2	1	no	—
515	Q₈×C₆₇	—	2	1	no	—
516	Q₈×C₆₇	—	2	1	no	—
517	Q₈×C₆₇	—	2	1	no	—
518	Q₈×C₆₇	—	2	1	no	—
519	Q₈×C₆₇	—	2	1	no	—
520	Q₈×C₆₇	—	4	1	no	—
521	Q₈×C₆₇	—	4	2	no	—
522	Q₈×C₆₇	—	4	2	no	—
523	Q₈×C₆₇	—	4	2	no	—
524	Q₈×C₆₇	—	8	1	no	—
525	Q₈×C₆₇	—	8	1	no	—
526	D₄×C₆₇	—	2	1	no	—
527	D₄×C₆₇	—	2	1	no	—
528	D₄×C₆₇	—	2	2	no	—
529	D₄×C₆₇	—	2	2	no	—
530	D₄×C₆₇	—	2	2	no	—
531	D₄×C₆₇	—	2	2	no	—
532	D₄×C₆₇	—	4	1	no	—
533	D₄×C₆₇	—	4	1	no	—
534	D₄×C₆₇	—	4	1	no	—
535	D₄×C₆₇	—	4	4	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	D₄×C₆₇	—	4	2	no	—
541	D₄×C₆₇	—	8	2	no	—
542	D₄×C₆₇	—	8	2	no	—
543	D₄×C₆₇	—	8	1	no	—
544	D₄×C₆₇	—	8	1	no	—
545	D₄×C₆₇	—	8	2	no	—
546	D₄×C₆₇	—	8	2	no	—
547	D₄×C₆₇	—	8	2	no	—
548	D₄×C₆₇	—	8	2	no	—
549	C₂×C₄×C₆₇	—	2	2	no	—
550	C₂×C₄×C₆₇	—	2	2	no	—
551	C₂×C₄×C₆₇	—	2	2	no	—
552	C₂×C₄×C₆₇	—	2	1	no	—
553	C₂×C₄×C₆₇	—	2	1	no	—
554	C₂×C₄×C₆₇	—	2	1	no	—
555	C₂×C₄×C₆₇	—	2	1	no	—
556	C₂×C₄×C₆₇	—	2	1	no	—
557	C₂×C₄×C₆₇	—	2	1	no	—
558	C₂×C₄×C₆₇	—	2	1	no	—
559	C₂×C₄×C₆₇	—	2	1	no	—
560	C₂×C₄×C₆₇	—	2	1	no	—
561	C₂×C₄×C₆₇	—	2	1	no	—
562	C₂×C₄×C₆₇	—	2	1	no	—
563	C₂×C₄×C₆₇	—	2	1	no	—
564	C₂×C₄×C₆₇	—	2	1	no	—
565	C₂×C₄×C₆₇	—	2	2	no	—
566	C₂×C₄×C₆₇	—	2	2	no	—
567	C₂×C₄×C₆₇	—	4	1	no	—
568	C₂×C₄×C₆₇	—	4	1	no	—
569	C₂×C₄×C₆₇	—	4	1	no	—
570	C₂×C₄×C₆₇	—	4	2	no	—
571	C₂×C₄×C₆₇	—	4	2	no	—
572	C₂×C₄×C₆₇	—	4	2	no	—
573	C₂×C₄×C₆₇	—	8	1	no	—
574	C₂×C₄×C₆₇	—	8	2	no	—
575	C₂×C₄×C₆₇	—	8	2	no	—
576	C₂×C₄×C₆₇	—	8	2	no	—
577	C₂×C₄×C₆₇	—	8	2	no	—
578	C₂×C₄×C₆₇	—	8	1	no	—
579	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
591	C₈×C₆₇	—	2	2	no	—
592	C₈×C₆₇	—	2	2	no	—
593	C₈×C₆₇	—	2	2	no	—
594	C₈×C₆₇	—	2	2	no	—
595	C₂²×C₆₇	—	2	1	no	—
596	C₂²×C₆₇	—	2	1	no	—
597	C₂²×C₆₇	—	2	1	no	—
598	C₂²×C₆₇	—	2	1	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	—	4	2	no	—
605	C₂²×C₆₇	—	4	2	no	—
606	C₂²×C₆₇	—	4	1	no	—
607	C₂²×C₆₇	—	4	1	no	—
608	C₂²×C₆₇	—	4	2	no	—
609	C₂²×C₆₇	—	4	2	no	—
610	C₂²×C₆₇	—	4	1	no	—
611	C₂²×C₆₇	—	4	2	no	—
612	C₂²×C₆₇	—	4	2	no	—
613	C₂²×C₆₇	—	16	4	no	—
614	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
615	C₄×C₆₇	—	2	1	no	—
616	C₄×C₆₇	—	2	1	no	—
617	C₄×C₆₇	—	2	1	no	—
618	C₄×C₆₇	—	2	1	no	—
619	C₄×C₆₇	—	2	1	no	—
620	C₄×C₆₇	—	2	1	no	—
621	C₄×C₆₇	—	2	1	no	—
622	C₄×C₆₇	—	2	1	no	—
623	C₄×C₆₇	—	2	1	no	—
624	C₄×C₆₇	—	2	1	no	—
625	C₄×C₆₇	—	4	2	no	—
626	C₄×C₆₇	—	4	1	no	—
627	C₄×C₆₇	—	4	1	no	—
628	C₄×C₆₇	—	4	1	no	—
629	C₄×C₆₇	—	4	1	no	—
630	C₄×C₆₇	—	4	1	no	—
631	C₄×C₆₇	—	4	1	no	—
632	C₄×C₆₇	—	4	1	no	—
633	C₄×C₆₇	—	4	2	no	—
634	C₄×C₆₇	#577	1	2	yes	—
635	C₄×C₆₇	#585	1	1	yes	characteristic
636	C₄×C₆₇	#585	1	1	yes	characteristic
637	#60994	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
638	C₂×C₆₇	—	4	1	no	—
639	C₂×C₆₇	—	4	1	no	—
640	C₂×C₆₇	—	4	1	no	—
641	C₂×C₆₇	—	8	1	no	—
642	C₂×C₆₇	—	8	2	no	—
643	C₂×C₆₇	—	8	2	no	—
644	C₂×C₆₇	#3449	1	1	yes	characteristic
645	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
646	C₂×C₆₇	#3585	1	1	yes	characteristic
647	#3508	C₂×C₆₇	1	1	yes	characteristic, complemented
648	#3461	C₂×C₆₇	1	1	yes	characteristic, complemented
649	#3254	C₂×C₆₇	1	1	yes	characteristic, complemented
650	#3251	C₂×C₆₇	1	1	yes	characteristic, complemented
651	#3247	C₂×C₆₇	1	1	yes	characteristic, complemented
652	#3246	C₂×C₆₇	1	1	yes	characteristic, complemented
653	#3241	C₂×C₆₇	1	2	yes	complemented
654	#3237	C₂×C₆₇	1	1	yes	characteristic, complemented
655	#3233	C₂×C₆₇	1	1	yes	characteristic, complemented
656	#3221	C₂×C₆₇	1	2	yes	complemented
657	#3217	C₂×C₆₇	1	1	yes	characteristic, complemented
658	#3208	C₂×C₆₇	1	1	yes	characteristic, complemented
659	#3200	C₂×C₆₇	1	2	yes	complemented
660	#3198	C₂×C₆₇	1	2	yes	complemented
661	#3179	C₂×C₆₇	1	2	yes	complemented
662	#3174	C₂×C₆₇	1	2	yes	complemented
663	#3123	C₂×C₆₇	1	2	yes	complemented
664	#3118	C₂×C₆₇	1	2	yes	complemented
665	#3115	C₂×C₆₇	1	1	yes	characteristic, complemented
666	#3112	C₂×C₆₇	1	1	yes	characteristic, complemented
667	#3106	C₂×C₆₇	1	1	yes	characteristic, complemented
668	#3103	C₂×C₆₇	1	1	yes	characteristic, complemented
669	#2925	C₂×C₆₇	1	1	yes	characteristic, complemented
670	C₆₇	#60994	1	1	yes	characteristic, direct product factor, Sylow
671	#559	—	2	1	no	—
672	#559	—	2	1	no	—
673	#550	—	2	1	no	—
674	#550	—	2	1	no	—
675	#546	—	2	1	no	—
676	#546	—	2	1	no	—
677	#546	—	2	1	no	—
678	#546	—	2	1	no	—
679	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
680	#542	—	2	1	no	—
681	#542	C₂²×C₆₇	1	1	yes	characteristic
682	#542	C₂²×C₆₇	1	1	yes	characteristic, complemented
683	#541	—	2	1	no	—
684	#541	C₂²×C₆₇	1	1	yes	characteristic
685	#541	C₂²×C₆₇	1	1	yes	characteristic, complemented
686	#540	C₂²×C₆₇	1	2	yes	—
687	#540	C₂²×C₆₇	1	2	yes	—
688	#539	—	2	1	no	—
689	#539	—	2	1	no	—
690	#537	C₂²×C₆₇	1	1	yes	characteristic
691	#536	C₂²×C₆₇	1	1	yes	characteristic
692	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	#535	C₂²×C₆₇	1	2	yes	—
694	#533	—	2	1	no	—
695	#533	C₂²×C₆₇	1	1	yes	characteristic
696	#533	C₂²×C₆₇	1	1	yes	characteristic
697	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
698	#532	C₂²×C₆₇	1	1	yes	characteristic
699	#532	C₂²×C₆₇	1	1	yes	characteristic
700	#532	C₂²×C₆₇	1	1	yes	characteristic
701	#532	C₂²×C₆₇	1	1	yes	characteristic
702	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
703	#529	—	2	1	no	—
704	#529	—	2	1	no	—
705	#529	—	2	1	no	—
706	#529	C₂²×C₆₇	1	1	yes	characteristic
707	#529	C₂²×C₆₇	1	1	yes	characteristic, complemented
708	#518	C₂²×C₆₇	1	2	yes	—
709	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
710	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
712	#501	C₂²×C₆₇	1	2	yes	complemented
713	#499	C₂²×C₆₇	1	2	yes	complemented
714	#496	C₂²×C₆₇	1	2	yes	—
715	#492	C₂²×C₆₇	1	2	yes	—
716	#491	C₂²×C₆₇	1	2	yes	complemented
717	#490	C₂²×C₆₇	1	2	yes	—
718	#488	C₂²×C₆₇	1	2	yes	complemented
719	#486	C₂²×C₆₇	1	2	yes	—
720	#485	C₂²×C₆₇	1	2	yes	—
721	#485	C₂²×C₆₇	1	2	yes	—
722	#485	C₂²×C₆₇	1	2	yes	—
723	#482	C₂²×C₆₇	1	2	yes	—
724	#482	C₂²×C₆₇	1	2	yes	complemented
725	#482	C₂²×C₆₇	1	2	yes	complemented
726	#481	C₂²×C₆₇	1	2	yes	complemented
727	#480	C₂²×C₆₇	1	2	yes	complemented
728	#478	C₂²×C₆₇	1	2	yes	complemented
729	#478	C₂²×C₆₇	1	2	yes	complemented
730	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
731	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
732	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
733	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
734	#476	C₂²×C₆₇	1	2	yes	complemented
735	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
736	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
737	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
738	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
739	#474	C₂²×C₆₇	1	2	yes	complemented
740	#469	C₂²×C₆₇	1	2	yes	complemented
741	#468	C₂²×C₆₇	1	2	yes	complemented
742	#468	C₂²×C₆₇	1	2	yes	complemented
743	#468	C₂²×C₆₇	1	2	yes	complemented
744	#466	C₂²×C₆₇	1	2	yes	complemented
745	#465	C₂²×C₆₇	1	2	yes	complemented
746	#465	C₂²×C₆₇	1	2	yes	complemented
747	#465	C₂²×C₆₇	1	2	yes	complemented
748	#463	C₂²×C₆₇	1	2	yes	complemented
749	#463	C₂²×C₆₇	1	2	yes	complemented
750	#461	C₂²×C₆₇	1	2	yes	complemented
751	#461	C₂²×C₆₇	1	2	yes	complemented
752	#460	C₂²×C₆₇	1	1	yes	characteristic
753	#460	C₂²×C₆₇	1	1	yes	characteristic
754	#460	C₂²×C₆₇	1	1	yes	characteristic
755	#460	C₂²×C₆₇	1	1	yes	characteristic
756	#460	C₂²×C₆₇	1	1	yes	characteristic
757	#460	C₂²×C₆₇	1	1	yes	characteristic
758	#459	C₂²×C₆₇	1	1	yes	characteristic
759	#459	C₂²×C₆₇	1	1	yes	characteristic
760	#450	C₂²×C₆₇	1	2	yes	—
761	#450	C₂²×C₆₇	1	2	yes	—
762	#450	C₂²×C₆₇	1	2	yes	—
763	#449	C₂²×C₆₇	1	2	yes	complemented
764	#449	C₂²×C₆₇	1	2	yes	complemented
765	#448	C₂²×C₆₇	1	2	yes	complemented
766	#448	C₂²×C₆₇	1	2	yes	complemented
767	#447	C₂²×C₆₇	1	2	yes	—
768	#442	C₂²×C₆₇	1	2	yes	complemented
769	#440	C₂²×C₆₇	1	2	yes	complemented
770	#440	C₂²×C₆₇	1	2	yes	complemented
771	#440	C₂²×C₆₇	1	2	yes	complemented
772	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
773	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
774	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
775	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
776	#433	C₂²×C₆₇	1	2	yes	—
777	#433	C₂²×C₆₇	1	2	yes	complemented
778	#432	C₂²×C₆₇	1	1	yes	characteristic
779	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
780	#431	C₂²×C₆₇	1	1	yes	characteristic
781	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
782	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
783	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
784	#408	C₂²×C₆₇	1	2	yes	—
785	#405	C₂²×C₆₇	1	2	yes	complemented
786	C₂×#41	—	2	1	no	—
787	C₂×#41	—	2	1	no	—
788	C₂×#41	—	2	1	no	—
789	C₂×#41	—	2	1	no	—
790	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
791	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
792	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
793	C₂²×D₄	—	2	1	no	—
794	C₂²×D₄	—	2	1	no	—
795	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
796	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
797	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
798	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
799	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
800	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
801	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
802	C₂×D₈	C₂³×C₆₇	1	2	yes	—
803	C₂×D₈	C₂³×C₆₇	1	2	yes	—
804	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
805	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
806	C₄⋊Q₈	—	2	1	no	—
807	C₄⋊Q₈	—	2	1	no	—
808	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
809	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
810	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
811	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
812	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
813	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
814	#127	—	2	2	no	—
815	#127	—	2	1	no	—
816	#127	—	2	1	no	—
817	#127	C₂³×C₆₇	1	1	yes	characteristic
818	#127	C₂³×C₆₇	1	1	yes	characteristic
819	#127	C₂³×C₆₇	1	2	yes	—
820	#126	—	2	1	no	—
821	#126	—	2	1	no	—
822	#126	—	2	1	no	—
823	#126	—	2	1	no	—
824	#126	—	2	1	no	—
825	#126	—	2	1	no	—
826	#126	—	2	1	no	—
827	#126	—	2	1	no	—
828	#125	—	2	1	no	—
829	#125	—	2	1	no	—
830	#125	—	2	1	no	—
831	#125	—	2	1	no	—
832	#125	—	2	1	no	—
833	#125	—	2	1	no	—
834	#125	—	2	1	no	—
835	#125	C₂³×C₆₇	1	1	yes	characteristic
836	#125	C₂³×C₆₇	1	1	yes	characteristic
837	#125	C₂³×C₆₇	1	2	yes	—
838	#124	—	2	2	no	—
839	#124	—	2	1	no	—
840	#124	—	2	1	no	—
841	#124	—	2	1	no	—
842	#124	—	2	1	no	—
843	#124	—	2	1	no	—
844	#124	—	2	1	no	—
845	#124	—	2	1	no	—
846	#124	C₂³×C₆₇	1	1	yes	characteristic
847	#124	C₂³×C₆₇	1	1	yes	characteristic
848	#123	—	2	1	no	—
849	#123	—	2	1	no	—
850	#123	—	2	1	no	—
851	#123	—	2	1	no	—
852	#123	—	2	2	no	—
853	#123	—	2	2	no	—
854	#123	—	2	2	no	—
855	#123	—	2	2	no	—
856	#123	—	2	1	no	—
857	#123	—	2	1	no	—
858	#123	—	2	1	no	—
859	#123	—	2	1	no	—
860	C₂²⋊Q₈	—	2	1	no	—
861	C₂²⋊Q₈	—	2	1	no	—
862	C₂²⋊Q₈	—	2	1	no	—
863	C₂²⋊Q₈	—	2	1	no	—
864	C₂²⋊Q₈	—	2	1	no	—
865	C₂²⋊Q₈	—	2	1	no	—
866	C₂²⋊Q₈	—	2	1	no	—
867	C₂²⋊Q₈	—	2	1	no	—
868	C₂²⋊Q₈	—	2	1	no	—
869	C₂²⋊Q₈	—	2	1	no	—
870	C₂²⋊Q₈	—	2	1	no	—
871	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
872	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
873	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
874	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
875	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
876	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
877	#121	—	2	1	no	—
878	#121	—	2	1	no	—
879	#121	—	2	1	no	—
880	#121	—	2	1	no	—
881	#121	—	2	1	no	—
882	#121	—	2	1	no	—
883	#121	—	2	1	no	—
884	#121	—	2	2	no	—
885	#121	—	2	2	no	—
886	#121	—	2	2	no	—
887	#121	—	2	2	no	—
888	#121	C₂³×C₆₇	1	1	yes	characteristic
889	#121	C₂³×C₆₇	1	1	yes	characteristic
890	#121	C₂³×C₆₇	1	2	yes	—
891	#121	C₂³×C₆₇	1	2	yes	—
892	#121	C₂³×C₆₇	1	2	yes	—
893	#121	C₂³×C₆₇	1	2	yes	—
894	#120	—	2	2	no	—
895	#120	—	2	2	no	—
896	C₄×Q₈	—	2	1	no	—
897	C₄×Q₈	—	2	1	no	—
898	C₄×Q₈	—	2	1	no	—
899	C₄×Q₈	—	2	1	no	—
900	C₄×Q₈	—	2	1	no	—
901	C₄×Q₈	—	2	1	no	—
902	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
903	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
904	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
905	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
906	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
907	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
908	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
909	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
910	C₄×D₄	—	2	1	no	—
911	C₄×D₄	—	2	1	no	—
912	C₄×D₄	—	2	1	no	—
913	C₄×D₄	—	2	1	no	—
914	C₄×D₄	—	2	2	no	—
915	C₄×D₄	—	2	2	no	—
916	C₄×D₄	—	2	1	no	—
917	C₄×D₄	—	2	1	no	—
918	C₄×D₄	—	2	1	no	—
919	C₄×D₄	—	2	1	no	—
920	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
921	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
922	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
923	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
924	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
925	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
926	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
927	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
928	C₄×D₄	C₂³×C₆₇	1	2	yes	—
929	C₄×D₄	C₂³×C₆₇	1	2	yes	—
930	C₄×D₄	C₂³×C₆₇	1	2	yes	—
931	C₄×D₄	C₂³×C₆₇	1	2	yes	—
932	#117	—	2	1	no	—
933	#117	—	2	1	no	—
934	#117	—	2	1	no	—
935	#117	—	2	1	no	—
936	#117	—	2	1	no	—
937	#117	C₂³×C₆₇	1	1	yes	characteristic
938	#117	C₂³×C₆₇	1	2	yes	—
939	#117	C₂³×C₆₇	1	1	yes	characteristic
940	#117	C₂³×C₆₇	1	1	yes	characteristic
941	#117	C₂³×C₆₇	1	1	yes	characteristic
942	C₂×C₄⋊C₄	—	2	1	no	—
943	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
944	C₂×C₂²⋊C₄	—	2	2	no	—
945	C₂×C₂²⋊C₄	—	2	2	no	—
946	C₂×C₄²	—	2	1	no	—
947	C₂×C₄²	—	2	1	no	—
948	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
949	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
950	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
951	#107	C₂³×C₆₇	1	2	yes	—
952	#107	C₂³×C₆₇	1	2	yes	—
953	#107	C₂³×C₆₇	1	2	yes	—
954	#107	C₂³×C₆₇	1	2	yes	—
955	#106	C₂³×C₆₇	1	2	yes	—
956	#106	C₂³×C₆₇	1	2	yes	—
957	#106	C₂³×C₆₇	1	2	yes	—
958	#106	C₂³×C₆₇	1	2	yes	—
959	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
960	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
961	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
962	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
963	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
964	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
965	#103	C₂³×C₆₇	1	2	yes	—
966	#103	C₂³×C₆₇	1	2	yes	—
967	#103	C₂³×C₆₇	1	2	yes	—
968	#103	C₂³×C₆₇	1	2	yes	—
969	#103	C₂³×C₆₇	1	2	yes	—
970	#103	C₂³×C₆₇	1	2	yes	—
971	#102	C₂³×C₆₇	1	2	yes	—
972	#102	C₂³×C₆₇	1	2	yes	—
973	#102	C₂³×C₆₇	1	2	yes	—
974	#102	C₂³×C₆₇	1	2	yes	—
975	#102	C₂³×C₆₇	1	2	yes	—
976	#102	C₂³×C₆₇	1	2	yes	—
977	#102	C₂³×C₆₇	1	2	yes	—
978	#102	C₂³×C₆₇	1	2	yes	—
979	#102	C₂³×C₆₇	1	2	yes	—
980	#102	C₂³×C₆₇	1	2	yes	—
981	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
982	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
983	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
984	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
985	#97	C₂³×C₆₇	1	2	yes	—
986	#97	C₂³×C₆₇	1	2	yes	—
987	C₄×C₈	C₂³×C₆₇	1	2	yes	—
988	C₄×C₈	C₂³×C₆₇	1	2	yes	—
989	C₂⁴	—	2	2	no	—
990	#41	—	4	1	no	—
991	#41	—	4	1	no	—
992	#41	—	4	1	no	—
993	#41	—	4	1	no	—
994	#41	—	8	2	no	—
995	#41	—	8	2	no	—
996	#41	—	8	2	no	—
997	#41	—	8	2	no	—
998	C₂×Q₈	—	2	1	no	—
999	C₂×Q₈	—	2	1	no	—
1000	C₂×Q₈	—	2	1	no	—
1001	C₂×Q₈	—	2	1	no	—
1002	C₂×Q₈	—	2	1	no	—
1003	C₂×Q₈	—	4	1	no	—
1004	C₂×Q₈	—	4	1	no	—
1005	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1006	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1007	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1008	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	1	no	—
1018	C₂×D₄	—	2	1	no	—
1019	C₂×D₄	—	2	1	no	—
1020	C₂×D₄	—	2	1	no	—
1021	C₂×D₄	—	2	2	no	—
1022	C₂×D₄	—	2	2	no	—
1023	C₂×D₄	—	4	2	no	—
1024	C₂×D₄	—	4	2	no	—
1025	C₂×D₄	—	8	2	no	—
1026	C₂×D₄	—	8	2	no	—
1027	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1028	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1029	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1030	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1031	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1032	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1033	C₂²×C₄	—	2	1	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	1	no	—
1036	C₂²×C₄	—	2	1	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	C₂×D₄×C₆₇	1	1	yes	characteristic
1043	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1044	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1045	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1046	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1047	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1048	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1049	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1050	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1051	SD₁₆	—	4	2	no	—
1052	SD₁₆	—	4	2	no	—
1053	SD₁₆	—	4	2	no	—
1054	SD₁₆	—	4	2	no	—
1055	SD₁₆	—	4	2	no	—
1056	SD₁₆	—	4	2	no	—
1057	D₈	—	4	2	no	—
1058	D₈	—	4	2	no	—
1059	M₁₆	—	4	2	no	—
1060	C₂×C₈	—	4	2	no	—
1061	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1062	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1063	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1064	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	1	no	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1093	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1094	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1095	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1096	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1097	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1098	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1099	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1100	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1101	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1102	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1103	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	—	2	1	no	—
1121	C₂²⋊C₄	—	2	1	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	2	no	—
1125	C₂²⋊C₄	—	2	2	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1129	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1130	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1131	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1132	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1133	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1134	C₄²	—	2	1	no	—
1135	C₄²	—	2	1	no	—
1136	C₄²	—	2	1	no	—
1137	C₄²	—	2	1	no	—
1138	C₄²	—	2	1	no	—
1139	C₄²	—	2	1	no	—
1140	C₄²	—	2	1	no	—
1141	C₄²	—	2	2	no	—
1142	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1143	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1144	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1145	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1146	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1147	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1148	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1149	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1150	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1151	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1152	C₂³	—	2	1	no	—
1153	C₂³	—	2	2	no	—
1154	C₂³	—	2	2	no	—
1155	C₂³	—	4	4	no	—
1156	C₂³	—	8	2	no	—
1157	C₂³	—	8	2	no	—
1158	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1159	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1160	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1161	Q₈	—	2	1	no	—
1162	Q₈	—	2	1	no	—
1163	Q₈	—	2	1	no	—
1164	Q₈	—	2	1	no	—
1165	Q₈	—	2	1	no	—
1166	Q₈	—	2	1	no	—
1167	Q₈	—	4	1	no	—
1168	Q₈	—	4	2	no	—
1169	Q₈	—	4	2	no	—
1170	Q₈	—	4	2	no	—
1171	Q₈	—	8	1	no	—
1172	Q₈	—	8	1	no	—
1173	D₄	—	2	1	no	—
1174	D₄	—	2	1	no	—
1175	D₄	—	2	2	no	—
1176	D₄	—	2	2	no	—
1177	D₄	—	2	2	no	—
1178	D₄	—	2	2	no	—
1179	D₄	—	4	1	no	—
1180	D₄	—	4	1	no	—
1181	D₄	—	4	1	no	—
1182	D₄	—	4	4	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	—	8	2	no	—
1189	D₄	—	8	2	no	—
1190	D₄	—	8	2	no	—
1191	D₄	—	8	2	no	—
1192	D₄	—	8	2	no	—
1193	D₄	—	8	2	no	—
1194	D₄	—	8	1	no	—
1195	D₄	—	8	1	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	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	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	2	2	no	—
1214	C₂×C₄	—	4	1	no	—
1215	C₂×C₄	—	4	1	no	—
1216	C₂×C₄	—	4	1	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	8	2	no	—
1221	C₂×C₄	—	8	2	no	—
1222	C₂×C₄	—	8	2	no	—
1223	C₂×C₄	—	8	2	no	—
1224	C₂×C₄	—	8	1	no	—
1225	C₂×C₄	—	8	1	no	—
1226	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1227	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1228	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1229	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1230	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1231	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1232	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1233	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1234	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1235	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1236	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1237	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1238	C₈	—	2	2	no	—
1239	C₈	—	2	2	no	—
1240	C₈	—	2	2	no	—
1241	C₈	—	2	2	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	1	no	—
1247	C₂²	—	2	1	no	—
1248	C₂²	—	2	1	no	—
1249	C₂²	—	2	1	no	—
1250	C₂²	—	2	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	4	2	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	4	2	no	—
1256	C₂²	—	4	1	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	2	no	—
1259	C₂²	—	4	2	no	—
1260	C₂²	—	16	4	no	—
1261	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1262	C₄	—	2	1	no	—
1263	C₄	—	2	1	no	—
1264	C₄	—	2	1	no	—
1265	C₄	—	2	1	no	—
1266	C₄	—	2	1	no	—
1267	C₄	—	2	1	no	—
1268	C₄	—	2	1	no	—
1269	C₄	—	2	1	no	—
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	2	no	—
1274	C₄	—	4	2	no	—
1275	C₄	—	4	1	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	1	no	—
1279	C₄	—	4	1	no	—
1280	C₄	—	4	1	no	—
1281	C₄	#577×C₆₇	1	2	yes	—
1282	C₄	#585×C₆₇	1	1	yes	characteristic
1283	C₄	#585×C₆₇	1	1	yes	characteristic
1284	C₂	—	4	1	no	—
1285	C₂	—	4	1	no	—
1286	C₂	—	4	1	no	—
1287	C₂	—	8	2	no	—
1288	C₂	—	8	2	no	—
1289	C₂	—	8	1	no	—
1290	C₂	C₆₇×#3449	1	1	yes	characteristic
1291	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1292	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 ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3508	C₂	semidirect
2. C₆₇×#3461	C₂	semidirect
3. C₆₇×#3254	C₂	semidirect
4. C₆₇×#3251	C₂	semidirect
5. C₆₇×#3247	C₂	semidirect
6. C₆₇×#3246	C₂	semidirect
7. C₆₇×#3241	C₂	semidirect
8. C₆₇×#3237	C₂	semidirect
9. C₆₇×#3233	C₂	semidirect
10. C₆₇×#3221	C₂	semidirect
11. C₆₇×#3217	C₂	semidirect
12. C₆₇×#3208	C₂	semidirect
13. C₆₇×#3200	C₂	semidirect
14. C₆₇×#3198	C₂	semidirect
15. C₆₇×#3179	C₂	semidirect
16. C₆₇×#3174	C₂	semidirect
17. C₆₇×#3123	C₂	semidirect
18. C₆₇×#3118	C₂	semidirect
19. C₆₇×#3115	C₂	semidirect
20. C₆₇×#3112	C₂	semidirect
21. C₆₇×#3106	C₂	semidirect
22. C₆₇×#3103	C₂	semidirect
23. C₆₇×#2925	C₂	semidirect
32. #544×C₆₇	C₂²	semidirect
35. #542×C₆₇	C₂²	semidirect
38. #541×C₆₇	C₂²	semidirect
45. #536×C₆₇	C₂²	semidirect
50. #533×C₆₇	C₂²	semidirect
60. #529×C₆₇	C₂²	semidirect
63. C₄×#41×C₆₇	C₂²	semidirect
64. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
65. #501×C₆₇	C₂²	semidirect
66. #499×C₆₇	C₂²	semidirect
69. #491×C₆₇	C₂²	semidirect
71. #488×C₆₇	C₂²	semidirect
77. #482×C₆₇	C₂²	semidirect
78. #482×C₆₇	C₂²	semidirect
79. #481×C₆₇	C₂²	semidirect
80. #480×C₆₇	C₂²	semidirect
81. #478×C₆₇	C₂²	semidirect
82. #478×C₆₇	C₂²	semidirect
83. #477×C₆₇	C₂²	semidirect
84. #477×C₆₇	C₂²	semidirect
85. #477×C₆₇	C₂²	semidirect
86. #476×C₆₇	C₂²	semidirect
87. #476×C₆₇	C₂²	semidirect
88. #475×C₆₇	C₂²	semidirect
89. #475×C₆₇	C₂²	semidirect
90. #475×C₆₇	C₂²	semidirect
91. #474×C₆₇	C₂²	semidirect
92. #474×C₆₇	C₂²	semidirect
93. #469×C₆₇	C₂²	semidirect
94. #468×C₆₇	C₂²	semidirect
95. #468×C₆₇	C₂²	semidirect
96. #468×C₆₇	C₂²	semidirect
97. #466×C₆₇	C₂²	semidirect
98. #465×C₆₇	C₂²	semidirect
99. #465×C₆₇	C₂²	semidirect
100. #465×C₆₇	C₂²	semidirect
101. #463×C₆₇	C₂²	semidirect
102. #463×C₆₇	C₂²	semidirect
103. #461×C₆₇	C₂²	semidirect
104. #461×C₆₇	C₂²	semidirect
116. #449×C₆₇	C₂²	semidirect
117. #449×C₆₇	C₂²	semidirect
118. #448×C₆₇	C₂²	semidirect
119. #448×C₆₇	C₂²	semidirect
121. #442×C₆₇	C₂²	semidirect
122. #440×C₆₇	C₂²	semidirect
123. #440×C₆₇	C₂²	semidirect
124. #440×C₆₇	C₂²	semidirect
125. C₄×SD₁₆×C₆₇	C₂²	semidirect
126. C₄×SD₁₆×C₆₇	C₂²	semidirect
127. C₄×SD₁₆×C₆₇	C₂²	semidirect
128. C₄×D₈×C₆₇	C₂²	semidirect
130. #433×C₆₇	C₂²	semidirect
132. #432×C₆₇	C₂²	semidirect
134. #431×C₆₇	C₂²	semidirect
135. #423×C₆₇	C₂²	semidirect
136. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
138. #405×C₆₇	C₂²	semidirect
637. #60994	C₆₇	direct (N × H)
647. #3508	C₂×C₆₇	semidirect
648. #3461	C₂×C₆₇	semidirect
649. #3254	C₂×C₆₇	semidirect
650. #3251	C₂×C₆₇	semidirect
651. #3247	C₂×C₆₇	semidirect
652. #3246	C₂×C₆₇	semidirect
653. #3241	C₂×C₆₇	semidirect
654. #3237	C₂×C₆₇	semidirect
655. #3233	C₂×C₆₇	semidirect
656. #3221	C₂×C₆₇	semidirect
657. #3217	C₂×C₆₇	semidirect
658. #3208	C₂×C₆₇	semidirect
659. #3200	C₂×C₆₇	semidirect
660. #3198	C₂×C₆₇	semidirect
661. #3179	C₂×C₆₇	semidirect
662. #3174	C₂×C₆₇	semidirect
663. #3123	C₂×C₆₇	semidirect
664. #3118	C₂×C₆₇	semidirect
665. #3115	C₂×C₆₇	semidirect
666. #3112	C₂×C₆₇	semidirect
667. #3106	C₂×C₆₇	semidirect
668. #3103	C₂×C₆₇	semidirect
669. #2925	C₂×C₆₇	semidirect
670. C₆₇	#60994	direct (N × H)
679. #544	C₂²×C₆₇	semidirect
682. #542	C₂²×C₆₇	semidirect
685. #541	C₂²×C₆₇	semidirect
692. #536	C₂²×C₆₇	semidirect
697. #533	C₂²×C₆₇	semidirect
707. #529	C₂²×C₆₇	semidirect
710. C₄×#41	C₂²×C₆₇	semidirect
711. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
712. #501	C₂²×C₆₇	semidirect
713. #499	C₂²×C₆₇	semidirect
716. #491	C₂²×C₆₇	semidirect
718. #488	C₂²×C₆₇	semidirect
724. #482	C₂²×C₆₇	semidirect
725. #482	C₂²×C₆₇	semidirect
726. #481	C₂²×C₆₇	semidirect
727. #480	C₂²×C₆₇	semidirect
728. #478	C₂²×C₆₇	semidirect
729. #478	C₂²×C₆₇	semidirect
730. #477	C₂²×C₆₇	semidirect
731. #477	C₂²×C₆₇	semidirect
732. #477	C₂²×C₆₇	semidirect
733. #476	C₂²×C₆₇	semidirect
734. #476	C₂²×C₆₇	semidirect
735. #475	C₂²×C₆₇	semidirect
736. #475	C₂²×C₆₇	semidirect
737. #475	C₂²×C₆₇	semidirect
738. #474	C₂²×C₆₇	semidirect
739. #474	C₂²×C₆₇	semidirect
740. #469	C₂²×C₆₇	semidirect
741. #468	C₂²×C₆₇	semidirect
742. #468	C₂²×C₆₇	semidirect
743. #468	C₂²×C₆₇	semidirect
744. #466	C₂²×C₆₇	semidirect
745. #465	C₂²×C₆₇	semidirect
746. #465	C₂²×C₆₇	semidirect
747. #465	C₂²×C₆₇	semidirect
748. #463	C₂²×C₆₇	semidirect
749. #463	C₂²×C₆₇	semidirect
750. #461	C₂²×C₆₇	semidirect
751. #461	C₂²×C₆₇	semidirect
763. #449	C₂²×C₆₇	semidirect
764. #449	C₂²×C₆₇	semidirect
765. #448	C₂²×C₆₇	semidirect
766. #448	C₂²×C₆₇	semidirect
768. #442	C₂²×C₆₇	semidirect
769. #440	C₂²×C₆₇	semidirect
770. #440	C₂²×C₆₇	semidirect
771. #440	C₂²×C₆₇	semidirect
772. C₄×SD₁₆	C₂²×C₆₇	semidirect
773. C₄×SD₁₆	C₂²×C₆₇	semidirect
774. C₄×SD₁₆	C₂²×C₆₇	semidirect
775. C₄×D₈	C₂²×C₆₇	semidirect
777. #433	C₂²×C₆₇	semidirect
779. #432	C₂²×C₆₇	semidirect
781. #431	C₂²×C₆₇	semidirect
782. #423	C₂²×C₆₇	semidirect
783. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
785. #405	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×#3508	2
C₆₇×#3461	2
C₆₇×#3254	2
C₆₇×#3251	2
C₆₇×#3247	2
C₆₇×#3246	2
C₆₇×#3241	2
C₆₇×#3237	2
C₆₇×#3233	2
C₆₇×#3221	2
C₆₇×#3217	2
C₆₇×#3208	2
C₆₇×#3200	2
C₆₇×#3198	2
C₆₇×#3179	2
C₆₇×#3174	2
C₆₇×#3123	2
C₆₇×#3118	2
C₆₇×#3115	2
C₆₇×#3112	2
C₆₇×#3106	2
C₆₇×#3103	2
C₆₇×#2925	2
#60994	67

Subgroups — C67×#60994 #30740245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60994 #30740245