Subgroups — C₆₇×#61021 #30740272

Order 17152.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3258	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3257	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3239	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3238	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3236	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3234	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3219	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3219	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3214	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3204	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3203	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3181	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3180	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3172	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3171	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3125	C₂	1	2	yes	maximal, complemented
20	C₆₇×#3124	C₂	1	2	yes	maximal, complemented
21	C₆₇×#3120	C₂	1	2	yes	maximal, complemented
22	C₆₇×#3119	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
24	#556×C₆₇	—	2	1	no	—
25	#555×C₆₇	—	2	1	no	—
26	#554×C₆₇	—	2	1	no	—
27	#553×C₆₇	—	2	1	no	—
28	#553×C₆₇	—	2	1	no	—
29	#553×C₆₇	—	2	1	no	—
30	#553×C₆₇	—	2	1	no	—
31	#553×C₆₇	—	2	1	no	—
32	#553×C₆₇	—	2	1	no	—
33	#553×C₆₇	—	2	1	no	—
34	#553×C₆₇	—	2	1	no	—
35	#552×C₆₇	—	2	1	no	—
36	#552×C₆₇	—	2	1	no	—
37	#548×C₆₇	—	2	1	no	—
38	#548×C₆₇	—	2	1	no	—
39	#547×C₆₇	—	2	1	no	—
40	#542×C₆₇	C₂²	1	2	yes	—
41	#542×C₆₇	C₂²	1	2	yes	—
42	#541×C₆₇	C₂²	1	1	yes	characteristic
43	#541×C₆₇	C₂²	1	1	yes	characteristic
44	#540×C₆₇	C₂²	1	1	yes	characteristic
45	#540×C₆₇	C₂²	1	1	yes	characteristic
46	#537×C₆₇	C₂²	1	1	yes	characteristic
47	#537×C₆₇	C₂²	1	2	yes	—
48	#537×C₆₇	C₂²	1	1	yes	characteristic
49	#533×C₆₇	C₂²	1	1	yes	characteristic
50	#533×C₆₇	C₂²	1	1	yes	characteristic
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×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
56	#529×C₆₇	C₂²	1	1	yes	characteristic
57	#529×C₆₇	C₂²	1	1	yes	characteristic
58	#529×C₆₇	C₂²	1	1	yes	characteristic
59	#529×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
61	#520×C₆₇	C₂²	1	2	yes	—
62	#520×C₆₇	C₂²	1	1	yes	characteristic
63	#520×C₆₇	C₂²	1	1	yes	characteristic
64	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
65	#501×C₆₇	C₂²	1	1	yes	characteristic
66	#501×C₆₇	C₂²	1	1	yes	characteristic
67	#501×C₆₇	C₂²	1	1	yes	characteristic
68	#501×C₆₇	C₂²	1	1	yes	characteristic
69	#497×C₆₇	C₂²	1	1	yes	characteristic
70	#497×C₆₇	C₂²	1	1	yes	characteristic
71	#496×C₆₇	C₂²	1	1	yes	characteristic
72	#496×C₆₇	C₂²	1	1	yes	characteristic
73	#491×C₆₇	C₂²	1	1	yes	characteristic
74	#491×C₆₇	C₂²	1	1	yes	characteristic
75	#490×C₆₇	C₂²	1	1	yes	characteristic
76	#490×C₆₇	C₂²	1	1	yes	characteristic
77	#489×C₆₇	C₂²	1	1	yes	characteristic
78	#489×C₆₇	C₂²	1	1	yes	characteristic
79	#489×C₆₇	C₂²	1	1	yes	characteristic
80	#489×C₆₇	C₂²	1	1	yes	characteristic
81	#484×C₆₇	C₂²	1	2	yes	—
82	#484×C₆₇	C₂²	1	2	yes	—
83	#483×C₆₇	C₂²	1	2	yes	—
84	#483×C₆₇	C₂²	1	2	yes	—
85	#481×C₆₇	C₂²	1	2	yes	—
86	#481×C₆₇	C₂²	1	2	yes	—
87	#480×C₆₇	C₂²	1	2	yes	—
88	#480×C₆₇	C₂²	1	2	yes	—
89	#479×C₆₇	C₂²	1	2	yes	—
90	#479×C₆₇	C₂²	1	2	yes	—
91	#478×C₆₇	C₂²	1	2	yes	—
92	#478×C₆₇	C₂²	1	2	yes	—
93	#477×C₆₇	C₂²	1	2	yes	—
94	#476×C₆₇	C₂²	1	2	yes	—
95	#475×C₆₇	C₂²	1	2	yes	—
96	#474×C₆₇	C₂²	1	2	yes	—
97	#470×C₆₇	C₂²	1	2	yes	—
98	#469×C₆₇	C₂²	1	2	yes	—
99	#468×C₆₇	C₂²	1	2	yes	—
100	#468×C₆₇	C₂²	1	2	yes	—
101	#467×C₆₇	C₂²	1	2	yes	—
102	#466×C₆₇	C₂²	1	2	yes	—
103	#465×C₆₇	C₂²	1	2	yes	—
104	#465×C₆₇	C₂²	1	2	yes	—
105	#464×C₆₇	C₂²	1	2	yes	—
106	#464×C₆₇	C₂²	1	2	yes	—
107	#463×C₆₇	C₂²	1	2	yes	—
108	#463×C₆₇	C₂²	1	2	yes	—
109	#462×C₆₇	C₂²	1	2	yes	—
110	#461×C₆₇	C₂²	1	2	yes	—
111	#460×C₆₇	C₂²	1	2	yes	—
112	#459×C₆₇	C₂²	1	2	yes	—
113	#452×C₆₇	C₂²	1	2	yes	—
114	#452×C₆₇	C₂²	1	2	yes	—
115	#452×C₆₇	C₂²	1	2	yes	—
116	#452×C₆₇	C₂²	1	2	yes	—
117	#449×C₆₇	C₂²	1	2	yes	—
118	#449×C₆₇	C₂²	1	2	yes	—
119	#449×C₆₇	C₂²	1	2	yes	—
120	#449×C₆₇	C₂²	1	2	yes	—
121	#442×C₆₇	C₂²	1	2	yes	—
122	#441×C₆₇	C₂²	1	2	yes	—
123	#440×C₆₇	C₂²	1	2	yes	—
124	#440×C₆₇	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
126	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
128	C₄×D₈×C₆₇	C₂²	1	2	yes	—
129	#433×C₆₇	C₂²	1	2	yes	—
130	#433×C₆₇	C₂²	1	2	yes	—
131	#432×C₆₇	C₂²	1	1	yes	characteristic
132	#432×C₆₇	C₂²	1	1	yes	characteristic
133	#432×C₆₇	C₂²	1	1	yes	characteristic
134	#432×C₆₇	C₂²	1	1	yes	characteristic
135	#424×C₆₇	C₂²	1	2	yes	—
136	#408×C₆₇	C₂²	1	2	yes	—
137	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
138	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
139	C₂×#41×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	C₂³	1	2	yes	—
142	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₆₇	—	2	1	no	—
146	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×SD₁₆×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×D₈×C₆₇	C₂³	1	2	yes	—
153	C₂×D₈×C₆₇	C₂³	1	2	yes	—
154	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₆₇	—	2	1	no	—
157	C₄⋊Q₈×C₆₇	—	2	1	no	—
158	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	#127×C₆₇	C₂³	1	1	yes	characteristic
164	#127×C₆₇	C₂³	1	1	yes	characteristic
165	#126×C₆₇	—	2	2	no	—
166	#126×C₆₇	—	2	2	no	—
167	#126×C₆₇	—	2	1	no	—
168	#126×C₆₇	—	2	1	no	—
169	#126×C₆₇	—	2	1	no	—
170	#126×C₆₇	—	2	1	no	—
171	#126×C₆₇	—	2	1	no	—
172	#126×C₆₇	—	2	1	no	—
173	#126×C₆₇	—	2	1	no	—
174	#126×C₆₇	—	2	1	no	—
175	#125×C₆₇	—	2	1	no	—
176	#125×C₆₇	—	2	1	no	—
177	#125×C₆₇	—	2	1	no	—
178	#125×C₆₇	—	2	1	no	—
179	#125×C₆₇	—	2	1	no	—
180	#125×C₆₇	—	2	1	no	—
181	#125×C₆₇	—	2	1	no	—
182	#125×C₆₇	—	2	1	no	—
183	#125×C₆₇	C₂³	1	1	yes	characteristic
184	#125×C₆₇	C₂³	1	1	yes	characteristic
185	#125×C₆₇	C₂³	1	1	yes	characteristic
186	#125×C₆₇	C₂³	1	1	yes	characteristic
187	#124×C₆₇	—	2	2	no	—
188	#124×C₆₇	—	2	2	no	—
189	#124×C₆₇	—	2	1	no	—
190	#124×C₆₇	—	2	1	no	—
191	#124×C₆₇	C₂³	1	2	yes	—
192	#124×C₆₇	C₂³	1	1	yes	characteristic
193	#124×C₆₇	C₂³	1	1	yes	characteristic
194	#123×C₆₇	—	2	1	no	—
195	#123×C₆₇	—	2	1	no	—
196	#123×C₆₇	—	2	1	no	—
197	#123×C₆₇	—	2	1	no	—
198	#123×C₆₇	—	2	1	no	—
199	#123×C₆₇	—	2	1	no	—
200	#123×C₆₇	—	2	1	no	—
201	#123×C₆₇	—	2	1	no	—
202	#123×C₆₇	—	2	2	no	—
203	#123×C₆₇	—	2	2	no	—
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	1	no	—
208	C₂²⋊Q₈×C₆₇	—	2	1	no	—
209	C₂²⋊Q₈×C₆₇	—	2	2	no	—
210	C₂²⋊Q₈×C₆₇	—	2	2	no	—
211	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
214	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
215	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
217	#121×C₆₇	—	2	2	no	—
218	#121×C₆₇	—	2	2	no	—
219	#121×C₆₇	—	2	2	no	—
220	#121×C₆₇	—	2	1	no	—
221	#121×C₆₇	—	2	1	no	—
222	#121×C₆₇	—	2	1	no	—
223	#121×C₆₇	—	2	1	no	—
224	#121×C₆₇	—	2	1	no	—
225	#121×C₆₇	—	2	1	no	—
226	#121×C₆₇	—	2	1	no	—
227	#121×C₆₇	—	2	1	no	—
228	#121×C₆₇	—	2	1	no	—
229	#121×C₆₇	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
237	#121×C₆₇	C₂³	1	2	yes	—
238	#121×C₆₇	C₂³	1	1	yes	characteristic
239	#121×C₆₇	C₂³	1	1	yes	characteristic
240	#121×C₆₇	C₂³	1	2	yes	—
241	#121×C₆₇	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₆₇	—	2	1	no	—
243	C₄×Q₈×C₆₇	—	2	1	no	—
244	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
245	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
246	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
247	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
252	C₄×D₄×C₆₇	—	2	1	no	—
253	C₄×D₄×C₆₇	—	2	1	no	—
254	C₄×D₄×C₆₇	—	2	1	no	—
255	C₄×D₄×C₆₇	—	2	1	no	—
256	C₄×D₄×C₆₇	—	2	2	no	—
257	C₄×D₄×C₆₇	—	2	2	no	—
258	C₄×D₄×C₆₇	—	2	1	no	—
259	C₄×D₄×C₆₇	—	2	1	no	—
260	C₄×D₄×C₆₇	—	2	1	no	—
261	C₄×D₄×C₆₇	—	2	1	no	—
262	C₄×D₄×C₆₇	—	2	1	no	—
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	1	no	—
268	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
269	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
270	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
271	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
272	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
273	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
274	C₄×D₄×C₆₇	C₂³	1	2	yes	—
275	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
277	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
278	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₆₇	C₂³	1	2	yes	—
280	#117×C₆₇	—	2	1	no	—
281	#117×C₆₇	—	2	1	no	—
282	#117×C₆₇	—	2	1	no	—
283	#117×C₆₇	—	2	1	no	—
284	#117×C₆₇	—	2	2	no	—
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	C₂³	1	1	yes	characteristic
290	#117×C₆₇	C₂³	1	1	yes	characteristic
291	#117×C₆₇	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
293	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
294	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
295	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
296	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
297	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
298	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
300	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
313	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
314	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
315	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
316	#103×C₆₇	C₂³	1	2	yes	—
317	#103×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	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
333	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
334	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
335	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
336	#97×C₆₇	C₂³	1	1	yes	characteristic
337	#97×C₆₇	C₂³	1	1	yes	characteristic
338	#97×C₆₇	C₂³	1	1	yes	characteristic
339	#97×C₆₇	C₂³	1	1	yes	characteristic
340	#97×C₆₇	C₂³	1	2	yes	—
341	C₄×C₈×C₆₇	C₂³	1	2	yes	—
342	#41×C₆₇	—	4	2	no	—
343	#41×C₆₇	—	4	2	no	—
344	#41×C₆₇	—	4	2	no	—
345	#41×C₆₇	—	4	2	no	—
346	#41×C₆₇	—	4	2	no	—
347	#41×C₆₇	—	8	2	no	—
348	#41×C₆₇	—	8	2	no	—
349	C₂×Q₈×C₆₇	—	2	1	no	—
350	C₂×Q₈×C₆₇	—	2	1	no	—
351	C₂×Q₈×C₆₇	—	2	2	no	—
352	C₂×Q₈×C₆₇	—	8	2	no	—
353	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
354	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₆₇	—	2	2	no	—
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	1	no	—
362	C₂×D₄×C₆₇	—	2	1	no	—
363	C₂×D₄×C₆₇	—	2	1	no	—
364	C₂×D₄×C₆₇	—	2	2	no	—
365	C₂×D₄×C₆₇	—	2	2	no	—
366	C₂×D₄×C₆₇	—	2	1	no	—
367	C₂×D₄×C₆₇	—	2	1	no	—
368	C₂×D₄×C₆₇	—	2	1	no	—
369	C₂×D₄×C₆₇	—	2	1	no	—
370	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
372	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
374	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
382	C₂²×C₄×C₆₇	—	2	1	no	—
383	C₂²×C₄×C₆₇	—	2	1	no	—
384	C₂²×C₄×C₆₇	—	2	1	no	—
385	C₂²×C₄×C₆₇	—	2	1	no	—
386	C₂²×C₄×C₆₇	—	2	2	no	—
387	C₂²×C₄×C₆₇	—	2	2	no	—
388	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
397	Q₁₆×C₆₇	—	4	2	no	—
398	Q₁₆×C₆₇	—	4	2	no	—
399	SD₁₆×C₆₇	—	4	2	no	—
400	SD₁₆×C₆₇	—	4	2	no	—
401	SD₁₆×C₆₇	—	4	2	no	—
402	SD₁₆×C₆₇	—	4	2	no	—
403	D₈×C₆₇	—	4	2	no	—
404	D₈×C₆₇	—	4	2	no	—
405	M₁₆×C₆₇	—	4	2	no	—
406	C₂×C₈×C₆₇	—	4	2	no	—
407	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
408	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
409	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
410	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₆₇	—	2	1	no	—
412	C₄⋊C₄×C₆₇	—	2	1	no	—
413	C₄⋊C₄×C₆₇	—	2	2	no	—
414	C₄⋊C₄×C₆₇	—	2	1	no	—
415	C₄⋊C₄×C₆₇	—	2	1	no	—
416	C₄⋊C₄×C₆₇	—	2	1	no	—
417	C₄⋊C₄×C₆₇	—	2	1	no	—
418	C₄⋊C₄×C₆₇	—	2	1	no	—
419	C₄⋊C₄×C₆₇	—	2	1	no	—
420	C₄⋊C₄×C₆₇	—	2	2	no	—
421	C₄⋊C₄×C₆₇	—	2	2	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	2	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	1	no	—
438	C₄⋊C₄×C₆₇	—	2	1	no	—
439	C₄⋊C₄×C₆₇	—	2	2	no	—
440	C₄⋊C₄×C₆₇	—	2	2	no	—
441	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
450	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
451	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
453	C₂²⋊C₄×C₆₇	—	2	2	no	—
454	C₂²⋊C₄×C₆₇	—	2	2	no	—
455	C₂²⋊C₄×C₆₇	—	2	1	no	—
456	C₂²⋊C₄×C₆₇	—	2	1	no	—
457	C₂²⋊C₄×C₆₇	—	2	1	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	1	no	—
468	C₂²⋊C₄×C₆₇	—	2	1	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	2	no	—
474	C₂²⋊C₄×C₆₇	—	2	2	no	—
475	C₂²⋊C₄×C₆₇	—	2	2	no	—
476	C₂²⋊C₄×C₆₇	—	2	2	no	—
477	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
483	C₄²×C₆₇	—	2	1	no	—
484	C₄²×C₆₇	—	2	1	no	—
485	C₄²×C₆₇	—	2	1	no	—
486	C₄²×C₆₇	—	2	1	no	—
487	C₄²×C₆₇	—	2	2	no	—
488	C₄²×C₆₇	—	2	2	no	—
489	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
490	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
497	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
498	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
499	C₂³×C₆₇	—	2	2	no	—
500	C₂³×C₆₇	—	2	1	no	—
501	C₂³×C₆₇	—	2	1	no	—
502	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
503	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
504	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
505	Q₈×C₆₇	—	2	2	no	—
506	Q₈×C₆₇	—	2	2	no	—
507	Q₈×C₆₇	—	2	2	no	—
508	Q₈×C₆₇	—	2	2	no	—
509	Q₈×C₆₇	—	4	1	no	—
510	Q₈×C₆₇	—	4	2	no	—
511	Q₈×C₆₇	—	4	2	no	—
512	Q₈×C₆₇	—	8	2	no	—
513	D₄×C₆₇	—	2	2	no	—
514	D₄×C₆₇	—	2	2	no	—
515	D₄×C₆₇	—	2	2	no	—
516	D₄×C₆₇	—	2	2	no	—
517	D₄×C₆₇	—	4	1	no	—
518	D₄×C₆₇	—	4	1	no	—
519	D₄×C₆₇	—	4	1	no	—
520	D₄×C₆₇	—	4	2	no	—
521	D₄×C₆₇	—	4	2	no	—
522	D₄×C₆₇	—	4	4	no	—
523	D₄×C₆₇	—	4	2	no	—
524	D₄×C₆₇	—	4	2	no	—
525	D₄×C₆₇	—	8	1	no	—
526	D₄×C₆₇	—	8	1	no	—
527	D₄×C₆₇	—	8	1	no	—
528	D₄×C₆₇	—	8	1	no	—
529	D₄×C₆₇	—	8	1	no	—
530	D₄×C₆₇	—	8	1	no	—
531	D₄×C₆₇	—	8	2	no	—
532	D₄×C₆₇	—	8	2	no	—
533	C₂×C₄×C₆₇	—	2	2	no	—
534	C₂×C₄×C₆₇	—	2	2	no	—
535	C₂×C₄×C₆₇	—	2	2	no	—
536	C₂×C₄×C₆₇	—	2	1	no	—
537	C₂×C₄×C₆₇	—	2	1	no	—
538	C₂×C₄×C₆₇	—	2	2	no	—
539	C₂×C₄×C₆₇	—	2	1	no	—
540	C₂×C₄×C₆₇	—	2	1	no	—
541	C₂×C₄×C₆₇	—	2	1	no	—
542	C₂×C₄×C₆₇	—	2	1	no	—
543	C₂×C₄×C₆₇	—	2	2	no	—
544	C₂×C₄×C₆₇	—	2	2	no	—
545	C₂×C₄×C₆₇	—	4	1	no	—
546	C₂×C₄×C₆₇	—	4	1	no	—
547	C₂×C₄×C₆₇	—	4	1	no	—
548	C₂×C₄×C₆₇	—	4	1	no	—
549	C₂×C₄×C₆₇	—	4	1	no	—
550	C₂×C₄×C₆₇	—	4	1	no	—
551	C₂×C₄×C₆₇	—	4	4	no	—
552	C₂×C₄×C₆₇	—	4	2	no	—
553	C₂×C₄×C₆₇	—	4	2	no	—
554	C₂×C₄×C₆₇	—	8	1	no	—
555	C₂×C₄×C₆₇	—	8	1	no	—
556	C₂×C₄×C₆₇	—	8	1	no	—
557	C₂×C₄×C₆₇	—	8	1	no	—
558	C₂×C₄×C₆₇	—	8	2	no	—
559	C₂×C₄×C₆₇	—	8	2	no	—
560	C₂×C₄×C₆₇	—	8	1	no	—
561	C₂×C₄×C₆₇	—	8	1	no	—
562	C₂×C₄×C₆₇	—	8	2	no	—
563	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
575	C₈×C₆₇	—	2	2	no	—
576	C₈×C₆₇	—	2	2	no	—
577	C₈×C₆₇	—	2	2	no	—
578	C₈×C₆₇	—	2	2	no	—
579	C₂²×C₆₇	—	2	1	no	—
580	C₂²×C₆₇	—	2	1	no	—
581	C₂²×C₆₇	—	2	1	no	—
582	C₂²×C₆₇	—	2	1	no	—
583	C₂²×C₆₇	—	2	1	no	—
584	C₂²×C₆₇	—	2	1	no	—
585	C₂²×C₆₇	—	2	1	no	—
586	C₂²×C₆₇	—	2	1	no	—
587	C₂²×C₆₇	—	2	1	no	—
588	C₂²×C₆₇	—	4	2	no	—
589	C₂²×C₆₇	—	4	1	no	—
590	C₂²×C₆₇	—	4	1	no	—
591	C₂²×C₆₇	—	4	1	no	—
592	C₂²×C₆₇	—	4	2	no	—
593	C₂²×C₆₇	—	4	1	no	—
594	C₂²×C₆₇	—	4	2	no	—
595	C₂²×C₆₇	—	4	1	no	—
596	C₂²×C₆₇	—	4	1	no	—
597	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
598	C₄×C₆₇	—	2	1	no	—
599	C₄×C₆₇	—	2	1	no	—
600	C₄×C₆₇	—	2	1	no	—
601	C₄×C₆₇	—	2	1	no	—
602	C₄×C₆₇	—	2	1	no	—
603	C₄×C₆₇	—	2	1	no	—
604	C₄×C₆₇	—	2	1	no	—
605	C₄×C₆₇	—	2	1	no	—
606	C₄×C₆₇	—	2	1	no	—
607	C₄×C₆₇	—	2	1	no	—
608	C₄×C₆₇	—	2	1	no	—
609	C₄×C₆₇	—	4	1	no	—
610	C₄×C₆₇	—	4	1	no	—
611	C₄×C₆₇	—	4	2	no	—
612	C₄×C₆₇	—	4	2	no	—
613	C₄×C₆₇	—	4	1	no	—
614	C₄×C₆₇	—	4	1	no	—
615	C₄×C₆₇	—	4	2	no	—
616	C₄×C₆₇	—	4	1	no	—
617	C₄×C₆₇	—	4	1	no	—
618	C₄×C₆₇	#585	1	2	yes	—
619	#61021	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
620	C₂×C₆₇	—	4	1	no	—
621	C₂×C₆₇	—	4	1	no	—
622	C₂×C₆₇	—	4	1	no	—
623	C₂×C₆₇	—	8	2	no	—
624	C₂×C₆₇	—	8	1	no	—
625	C₂×C₆₇	—	8	1	no	—
626	C₂×C₆₇	#3449	1	1	yes	characteristic
627	C₂×C₆₇	#3585	1	1	yes	characteristic
628	C₂×C₆₇	#3586	1	1	yes	characteristic
629	#3512	C₂×C₆₇	1	1	yes	characteristic, complemented
630	#3511	C₂×C₆₇	1	1	yes	characteristic, complemented
631	#3258	C₂×C₆₇	1	2	yes	complemented
632	#3257	C₂×C₆₇	1	2	yes	complemented
633	#3239	C₂×C₆₇	1	1	yes	characteristic, complemented
634	#3238	C₂×C₆₇	1	1	yes	characteristic, complemented
635	#3236	C₂×C₆₇	1	1	yes	characteristic, complemented
636	#3234	C₂×C₆₇	1	1	yes	characteristic, complemented
637	#3219	C₂×C₆₇	1	1	yes	characteristic, complemented
638	#3219	C₂×C₆₇	1	1	yes	characteristic, complemented
639	#3216	C₂×C₆₇	1	1	yes	characteristic, complemented
640	#3214	C₂×C₆₇	1	1	yes	characteristic, complemented
641	#3204	C₂×C₆₇	1	2	yes	complemented
642	#3203	C₂×C₆₇	1	2	yes	complemented
643	#3181	C₂×C₆₇	1	1	yes	characteristic, complemented
644	#3180	C₂×C₆₇	1	1	yes	characteristic, complemented
645	#3172	C₂×C₆₇	1	1	yes	characteristic, complemented
646	#3171	C₂×C₆₇	1	1	yes	characteristic, complemented
647	#3125	C₂×C₆₇	1	2	yes	complemented
648	#3124	C₂×C₆₇	1	2	yes	complemented
649	#3120	C₂×C₆₇	1	2	yes	complemented
650	#3119	C₂×C₆₇	1	2	yes	complemented
651	#2923	C₂×C₆₇	1	1	yes	characteristic, complemented
652	C₆₇	#61021	1	1	yes	characteristic, direct product factor, Sylow
653	#556	—	2	1	no	—
654	#555	—	2	1	no	—
655	#554	—	2	1	no	—
656	#553	—	2	1	no	—
657	#553	—	2	1	no	—
658	#553	—	2	1	no	—
659	#553	—	2	1	no	—
660	#553	—	2	1	no	—
661	#553	—	2	1	no	—
662	#553	—	2	1	no	—
663	#553	—	2	1	no	—
664	#552	—	2	1	no	—
665	#552	—	2	1	no	—
666	#548	—	2	1	no	—
667	#548	—	2	1	no	—
668	#547	—	2	1	no	—
669	#542	C₂²×C₆₇	1	2	yes	—
670	#542	C₂²×C₆₇	1	2	yes	—
671	#541	C₂²×C₆₇	1	1	yes	characteristic
672	#541	C₂²×C₆₇	1	1	yes	characteristic
673	#540	C₂²×C₆₇	1	1	yes	characteristic
674	#540	C₂²×C₆₇	1	1	yes	characteristic
675	#537	C₂²×C₆₇	1	1	yes	characteristic
676	#537	C₂²×C₆₇	1	2	yes	—
677	#537	C₂²×C₆₇	1	1	yes	characteristic
678	#533	C₂²×C₆₇	1	1	yes	characteristic
679	#533	C₂²×C₆₇	1	1	yes	characteristic
680	#532	C₂²×C₆₇	1	1	yes	characteristic
681	#532	C₂²×C₆₇	1	1	yes	characteristic
682	#532	C₂²×C₆₇	1	1	yes	characteristic
683	#532	C₂²×C₆₇	1	1	yes	characteristic
684	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
685	#529	C₂²×C₆₇	1	1	yes	characteristic
686	#529	C₂²×C₆₇	1	1	yes	characteristic
687	#529	C₂²×C₆₇	1	1	yes	characteristic
688	#529	C₂²×C₆₇	1	1	yes	characteristic
689	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
690	#520	C₂²×C₆₇	1	2	yes	—
691	#520	C₂²×C₆₇	1	1	yes	characteristic
692	#520	C₂²×C₆₇	1	1	yes	characteristic
693	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
694	#501	C₂²×C₆₇	1	1	yes	characteristic
695	#501	C₂²×C₆₇	1	1	yes	characteristic
696	#501	C₂²×C₆₇	1	1	yes	characteristic
697	#501	C₂²×C₆₇	1	1	yes	characteristic
698	#497	C₂²×C₆₇	1	1	yes	characteristic
699	#497	C₂²×C₆₇	1	1	yes	characteristic
700	#496	C₂²×C₆₇	1	1	yes	characteristic
701	#496	C₂²×C₆₇	1	1	yes	characteristic
702	#491	C₂²×C₆₇	1	1	yes	characteristic
703	#491	C₂²×C₆₇	1	1	yes	characteristic
704	#490	C₂²×C₆₇	1	1	yes	characteristic
705	#490	C₂²×C₆₇	1	1	yes	characteristic
706	#489	C₂²×C₆₇	1	1	yes	characteristic
707	#489	C₂²×C₆₇	1	1	yes	characteristic
708	#489	C₂²×C₆₇	1	1	yes	characteristic
709	#489	C₂²×C₆₇	1	1	yes	characteristic
710	#484	C₂²×C₆₇	1	2	yes	—
711	#484	C₂²×C₆₇	1	2	yes	—
712	#483	C₂²×C₆₇	1	2	yes	—
713	#483	C₂²×C₆₇	1	2	yes	—
714	#481	C₂²×C₆₇	1	2	yes	—
715	#481	C₂²×C₆₇	1	2	yes	—
716	#480	C₂²×C₆₇	1	2	yes	—
717	#480	C₂²×C₆₇	1	2	yes	—
718	#479	C₂²×C₆₇	1	2	yes	—
719	#479	C₂²×C₆₇	1	2	yes	—
720	#478	C₂²×C₆₇	1	2	yes	—
721	#478	C₂²×C₆₇	1	2	yes	—
722	#477	C₂²×C₆₇	1	2	yes	—
723	#476	C₂²×C₆₇	1	2	yes	—
724	#475	C₂²×C₆₇	1	2	yes	—
725	#474	C₂²×C₆₇	1	2	yes	—
726	#470	C₂²×C₆₇	1	2	yes	—
727	#469	C₂²×C₆₇	1	2	yes	—
728	#468	C₂²×C₆₇	1	2	yes	—
729	#468	C₂²×C₆₇	1	2	yes	—
730	#467	C₂²×C₆₇	1	2	yes	—
731	#466	C₂²×C₆₇	1	2	yes	—
732	#465	C₂²×C₆₇	1	2	yes	—
733	#465	C₂²×C₆₇	1	2	yes	—
734	#464	C₂²×C₆₇	1	2	yes	—
735	#464	C₂²×C₆₇	1	2	yes	—
736	#463	C₂²×C₆₇	1	2	yes	—
737	#463	C₂²×C₆₇	1	2	yes	—
738	#462	C₂²×C₆₇	1	2	yes	—
739	#461	C₂²×C₆₇	1	2	yes	—
740	#460	C₂²×C₆₇	1	2	yes	—
741	#459	C₂²×C₆₇	1	2	yes	—
742	#452	C₂²×C₆₇	1	2	yes	—
743	#452	C₂²×C₆₇	1	2	yes	—
744	#452	C₂²×C₆₇	1	2	yes	—
745	#452	C₂²×C₆₇	1	2	yes	—
746	#449	C₂²×C₆₇	1	2	yes	—
747	#449	C₂²×C₆₇	1	2	yes	—
748	#449	C₂²×C₆₇	1	2	yes	—
749	#449	C₂²×C₆₇	1	2	yes	—
750	#442	C₂²×C₆₇	1	2	yes	—
751	#441	C₂²×C₆₇	1	2	yes	—
752	#440	C₂²×C₆₇	1	2	yes	—
753	#440	C₂²×C₆₇	1	2	yes	—
754	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
755	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
756	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
757	C₄×D₈	C₂²×C₆₇	1	2	yes	—
758	#433	C₂²×C₆₇	1	2	yes	—
759	#433	C₂²×C₆₇	1	2	yes	—
760	#432	C₂²×C₆₇	1	1	yes	characteristic
761	#432	C₂²×C₆₇	1	1	yes	characteristic
762	#432	C₂²×C₆₇	1	1	yes	characteristic
763	#432	C₂²×C₆₇	1	1	yes	characteristic
764	#424	C₂²×C₆₇	1	2	yes	—
765	#408	C₂²×C₆₇	1	2	yes	—
766	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
767	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
768	C₂×#41	—	2	1	no	—
769	C₂×#41	—	2	1	no	—
770	C₂×#41	C₂³×C₆₇	1	2	yes	—
771	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
772	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
773	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
774	C₂²×Q₈	—	2	1	no	—
775	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
776	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
781	C₂×D₈	C₂³×C₆₇	1	2	yes	—
782	C₂×D₈	C₂³×C₆₇	1	2	yes	—
783	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
784	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
785	C₄⋊Q₈	—	2	1	no	—
786	C₄⋊Q₈	—	2	1	no	—
787	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
788	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
789	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
790	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
791	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
792	#127	C₂³×C₆₇	1	1	yes	characteristic
793	#127	C₂³×C₆₇	1	1	yes	characteristic
794	#126	—	2	2	no	—
795	#126	—	2	2	no	—
796	#126	—	2	1	no	—
797	#126	—	2	1	no	—
798	#126	—	2	1	no	—
799	#126	—	2	1	no	—
800	#126	—	2	1	no	—
801	#126	—	2	1	no	—
802	#126	—	2	1	no	—
803	#126	—	2	1	no	—
804	#125	—	2	1	no	—
805	#125	—	2	1	no	—
806	#125	—	2	1	no	—
807	#125	—	2	1	no	—
808	#125	—	2	1	no	—
809	#125	—	2	1	no	—
810	#125	—	2	1	no	—
811	#125	—	2	1	no	—
812	#125	C₂³×C₆₇	1	1	yes	characteristic
813	#125	C₂³×C₆₇	1	1	yes	characteristic
814	#125	C₂³×C₆₇	1	1	yes	characteristic
815	#125	C₂³×C₆₇	1	1	yes	characteristic
816	#124	—	2	2	no	—
817	#124	—	2	2	no	—
818	#124	—	2	1	no	—
819	#124	—	2	1	no	—
820	#124	C₂³×C₆₇	1	1	yes	characteristic
821	#124	C₂³×C₆₇	1	1	yes	characteristic
822	#124	C₂³×C₆₇	1	2	yes	—
823	#123	—	2	1	no	—
824	#123	—	2	1	no	—
825	#123	—	2	1	no	—
826	#123	—	2	1	no	—
827	#123	—	2	1	no	—
828	#123	—	2	1	no	—
829	#123	—	2	1	no	—
830	#123	—	2	1	no	—
831	#123	—	2	2	no	—
832	#123	—	2	2	no	—
833	C₂²⋊Q₈	—	2	1	no	—
834	C₂²⋊Q₈	—	2	1	no	—
835	C₂²⋊Q₈	—	2	2	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	—	2	2	no	—
839	C₂²⋊Q₈	—	2	2	no	—
840	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
841	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
842	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
843	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
844	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
845	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
846	#121	—	2	2	no	—
847	#121	—	2	2	no	—
848	#121	—	2	2	no	—
849	#121	—	2	1	no	—
850	#121	—	2	1	no	—
851	#121	—	2	1	no	—
852	#121	—	2	1	no	—
853	#121	—	2	1	no	—
854	#121	—	2	1	no	—
855	#121	—	2	1	no	—
856	#121	—	2	1	no	—
857	#121	—	2	1	no	—
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	1	no	—
862	#121	—	2	1	no	—
863	#121	—	2	1	no	—
864	#121	—	2	1	no	—
865	#121	C₂³×C₆₇	1	1	yes	characteristic
866	#121	C₂³×C₆₇	1	1	yes	characteristic
867	#121	C₂³×C₆₇	1	1	yes	characteristic
868	#121	C₂³×C₆₇	1	1	yes	characteristic
869	#121	C₂³×C₆₇	1	2	yes	—
870	#121	C₂³×C₆₇	1	2	yes	—
871	C₄×Q₈	—	2	1	no	—
872	C₄×Q₈	—	2	1	no	—
873	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
874	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
875	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
876	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
877	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
878	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
879	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
880	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	2	no	—
886	C₄×D₄	—	2	2	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	1	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
898	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
899	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
900	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
901	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
902	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
903	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
904	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
905	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
906	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
907	C₄×D₄	C₂³×C₆₇	1	2	yes	—
908	C₄×D₄	C₂³×C₆₇	1	2	yes	—
909	#117	—	2	1	no	—
910	#117	—	2	1	no	—
911	#117	—	2	1	no	—
912	#117	—	2	1	no	—
913	#117	—	2	2	no	—
914	#117	—	2	1	no	—
915	#117	—	2	1	no	—
916	#117	—	2	1	no	—
917	#117	—	2	1	no	—
918	#117	C₂³×C₆₇	1	1	yes	characteristic
919	#117	C₂³×C₆₇	1	1	yes	characteristic
920	#117	C₂³×C₆₇	1	1	yes	characteristic
921	C₂×C₄⋊C₄	—	2	1	no	—
922	C₂×C₄⋊C₄	—	2	1	no	—
923	C₂×C₄⋊C₄	—	2	1	no	—
924	C₂×C₄⋊C₄	—	2	2	no	—
925	C₂×C₄⋊C₄	—	2	1	no	—
926	C₂×C₄⋊C₄	—	2	1	no	—
927	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
928	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
929	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
930	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
931	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
932	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
933	#107	C₂³×C₆₇	1	2	yes	—
934	#107	C₂³×C₆₇	1	2	yes	—
935	#107	C₂³×C₆₇	1	2	yes	—
936	#107	C₂³×C₆₇	1	2	yes	—
937	#106	C₂³×C₆₇	1	2	yes	—
938	#106	C₂³×C₆₇	1	2	yes	—
939	#106	C₂³×C₆₇	1	2	yes	—
940	#106	C₂³×C₆₇	1	2	yes	—
941	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
942	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
943	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
944	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
945	#103	C₂³×C₆₇	1	2	yes	—
946	#103	C₂³×C₆₇	1	2	yes	—
947	#103	C₂³×C₆₇	1	2	yes	—
948	#103	C₂³×C₆₇	1	2	yes	—
949	#103	C₂³×C₆₇	1	2	yes	—
950	#103	C₂³×C₆₇	1	2	yes	—
951	#103	C₂³×C₆₇	1	2	yes	—
952	#103	C₂³×C₆₇	1	2	yes	—
953	#102	C₂³×C₆₇	1	2	yes	—
954	#102	C₂³×C₆₇	1	2	yes	—
955	#102	C₂³×C₆₇	1	2	yes	—
956	#102	C₂³×C₆₇	1	2	yes	—
957	#102	C₂³×C₆₇	1	2	yes	—
958	#102	C₂³×C₆₇	1	2	yes	—
959	#102	C₂³×C₆₇	1	2	yes	—
960	#102	C₂³×C₆₇	1	2	yes	—
961	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
962	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
963	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
964	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
965	#97	C₂³×C₆₇	1	1	yes	characteristic
966	#97	C₂³×C₆₇	1	1	yes	characteristic
967	#97	C₂³×C₆₇	1	2	yes	—
968	#97	C₂³×C₆₇	1	1	yes	characteristic
969	#97	C₂³×C₆₇	1	1	yes	characteristic
970	C₄×C₈	C₂³×C₆₇	1	2	yes	—
971	#41	—	4	2	no	—
972	#41	—	4	2	no	—
973	#41	—	4	2	no	—
974	#41	—	4	2	no	—
975	#41	—	4	2	no	—
976	#41	—	8	2	no	—
977	#41	—	8	2	no	—
978	C₂×Q₈	—	2	1	no	—
979	C₂×Q₈	—	2	1	no	—
980	C₂×Q₈	—	2	2	no	—
981	C₂×Q₈	—	8	2	no	—
982	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
983	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
984	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
985	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1000	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1001	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1002	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1003	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1004	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	2	2	no	—
1016	C₂²×C₄	—	2	2	no	—
1017	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1018	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1019	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1020	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1021	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1022	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1023	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1024	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1025	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1026	Q₁₆	—	4	2	no	—
1027	Q₁₆	—	4	2	no	—
1028	SD₁₆	—	4	2	no	—
1029	SD₁₆	—	4	2	no	—
1030	SD₁₆	—	4	2	no	—
1031	SD₁₆	—	4	2	no	—
1032	D₈	—	4	2	no	—
1033	D₈	—	4	2	no	—
1034	M₁₆	—	4	2	no	—
1035	C₂×C₈	—	4	2	no	—
1036	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1037	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1038	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1039	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	2	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1071	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1072	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1073	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1074	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1075	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1076	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1077	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1078	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1079	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1080	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1081	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1107	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1108	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1109	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1110	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1111	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	—	2	1	no	—
1116	C₄²	—	2	2	no	—
1117	C₄²	—	2	2	no	—
1118	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1119	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1120	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1121	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1122	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1123	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1124	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1125	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1126	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1127	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1128	C₂³	—	2	2	no	—
1129	C₂³	—	2	1	no	—
1130	C₂³	—	2	1	no	—
1131	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1132	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1133	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1134	Q₈	—	2	2	no	—
1135	Q₈	—	2	2	no	—
1136	Q₈	—	2	2	no	—
1137	Q₈	—	2	2	no	—
1138	Q₈	—	4	1	no	—
1139	Q₈	—	4	2	no	—
1140	Q₈	—	4	2	no	—
1141	Q₈	—	8	2	no	—
1142	D₄	—	2	2	no	—
1143	D₄	—	2	2	no	—
1144	D₄	—	2	2	no	—
1145	D₄	—	2	2	no	—
1146	D₄	—	4	1	no	—
1147	D₄	—	4	1	no	—
1148	D₄	—	4	1	no	—
1149	D₄	—	4	2	no	—
1150	D₄	—	4	2	no	—
1151	D₄	—	4	4	no	—
1152	D₄	—	4	2	no	—
1153	D₄	—	4	2	no	—
1154	D₄	—	8	1	no	—
1155	D₄	—	8	1	no	—
1156	D₄	—	8	2	no	—
1157	D₄	—	8	2	no	—
1158	D₄	—	8	1	no	—
1159	D₄	—	8	1	no	—
1160	D₄	—	8	1	no	—
1161	D₄	—	8	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	1	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	4	no	—
1181	C₂×C₄	—	4	2	no	—
1182	C₂×C₄	—	4	2	no	—
1183	C₂×C₄	—	8	2	no	—
1184	C₂×C₄	—	8	2	no	—
1185	C₂×C₄	—	8	1	no	—
1186	C₂×C₄	—	8	1	no	—
1187	C₂×C₄	—	8	1	no	—
1188	C₂×C₄	—	8	1	no	—
1189	C₂×C₄	—	8	2	no	—
1190	C₂×C₄	—	8	1	no	—
1191	C₂×C₄	—	8	1	no	—
1192	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1193	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1194	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1195	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1196	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1197	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1198	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1199	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1200	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1201	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1202	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1203	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1204	C₈	—	2	2	no	—
1205	C₈	—	2	2	no	—
1206	C₈	—	2	2	no	—
1207	C₈	—	2	2	no	—
1208	C₂²	—	2	1	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	1	no	—
1212	C₂²	—	2	1	no	—
1213	C₂²	—	2	1	no	—
1214	C₂²	—	2	1	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	2	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	2	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1227	C₄	—	2	1	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	2	1	no	—
1231	C₄	—	2	1	no	—
1232	C₄	—	2	1	no	—
1233	C₄	—	2	1	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	1	no	—
1236	C₄	—	2	1	no	—
1237	C₄	—	2	1	no	—
1238	C₄	—	4	2	no	—
1239	C₄	—	4	2	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	2	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	#585×C₆₇	1	2	yes	—
1248	C₂	—	4	1	no	—
1249	C₂	—	4	1	no	—
1250	C₂	—	4	1	no	—
1251	C₂	—	8	2	no	—
1252	C₂	—	8	1	no	—
1253	C₂	—	8	1	no	—
1254	C₂	C₆₇×#3449	1	1	yes	characteristic
1255	C₂	C₆₇×#3585	1	1	yes	characteristic
1256	C₂	C₆₇×#3586	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×#3512	C₂	semidirect
2. C₆₇×#3511	C₂	semidirect
3. C₆₇×#3258	C₂	semidirect
4. C₆₇×#3257	C₂	semidirect
5. C₆₇×#3239	C₂	semidirect
6. C₆₇×#3238	C₂	semidirect
7. C₆₇×#3236	C₂	semidirect
8. C₆₇×#3234	C₂	semidirect
9. C₆₇×#3219	C₂	semidirect
10. C₆₇×#3219	C₂	semidirect
11. C₆₇×#3216	C₂	semidirect
12. C₆₇×#3214	C₂	semidirect
13. C₆₇×#3204	C₂	semidirect
14. C₆₇×#3203	C₂	semidirect
15. C₆₇×#3181	C₂	semidirect
16. C₆₇×#3180	C₂	semidirect
17. C₆₇×#3172	C₂	semidirect
18. C₆₇×#3171	C₂	semidirect
19. C₆₇×#3125	C₂	semidirect
20. C₆₇×#3124	C₂	semidirect
21. C₆₇×#3120	C₂	semidirect
22. C₆₇×#3119	C₂	semidirect
23. C₆₇×#2923	C₂	semidirect
619. #61021	C₆₇	direct (N × H)
629. #3512	C₂×C₆₇	semidirect
630. #3511	C₂×C₆₇	semidirect
631. #3258	C₂×C₆₇	semidirect
632. #3257	C₂×C₆₇	semidirect
633. #3239	C₂×C₆₇	semidirect
634. #3238	C₂×C₆₇	semidirect
635. #3236	C₂×C₆₇	semidirect
636. #3234	C₂×C₆₇	semidirect
637. #3219	C₂×C₆₇	semidirect
638. #3219	C₂×C₆₇	semidirect
639. #3216	C₂×C₆₇	semidirect
640. #3214	C₂×C₆₇	semidirect
641. #3204	C₂×C₆₇	semidirect
642. #3203	C₂×C₆₇	semidirect
643. #3181	C₂×C₆₇	semidirect
644. #3180	C₂×C₆₇	semidirect
645. #3172	C₂×C₆₇	semidirect
646. #3171	C₂×C₆₇	semidirect
647. #3125	C₂×C₆₇	semidirect
648. #3124	C₂×C₆₇	semidirect
649. #3120	C₂×C₆₇	semidirect
650. #3119	C₂×C₆₇	semidirect
651. #2923	C₂×C₆₇	semidirect
652. C₆₇	#61021	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3512	2
C₆₇×#3511	2
C₆₇×#3258	2
C₆₇×#3257	2
C₆₇×#3239	2
C₆₇×#3238	2
C₆₇×#3236	2
C₆₇×#3234	2
C₆₇×#3219	2
C₆₇×#3216	2
C₆₇×#3214	2
C₆₇×#3204	2
C₆₇×#3203	2
C₆₇×#3181	2
C₆₇×#3180	2
C₆₇×#3172	2
C₆₇×#3171	2
C₆₇×#3125	2
C₆₇×#3124	2
C₆₇×#3120	2
C₆₇×#3119	2
C₆₇×#2923	2
#61021	67

Subgroups — C67×#61021 #30740272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61021 #30740272