Subgroups — C₆₇×#60993 #30740244

Order 17152.

1718 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3511	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×#3252	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3249	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3247	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3243	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3238	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3225	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3212	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3203	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3201	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3178	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3175	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3124	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3120	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3116	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×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2925	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	#548×C₆₇	—	2	1	no	—
30	#548×C₆₇	—	2	1	no	—
31	#547×C₆₇	—	2	1	no	—
32	#544×C₆₇	C₂²	1	1	yes	characteristic
33	#542×C₆₇	—	2	1	no	—
34	#542×C₆₇	C₂²	1	1	yes	characteristic
35	#542×C₆₇	C₂²	1	1	yes	characteristic
36	#542×C₆₇	C₂²	1	2	yes	—
37	#542×C₆₇	C₂²	1	2	yes	—
38	#541×C₆₇	—	2	1	no	—
39	#541×C₆₇	C₂²	1	1	yes	characteristic
40	#541×C₆₇	C₂²	1	1	yes	characteristic
41	#539×C₆₇	—	2	1	no	—
42	#539×C₆₇	—	2	1	no	—
43	#537×C₆₇	C₂²	1	2	yes	—
44	#537×C₆₇	C₂²	1	1	yes	characteristic
45	#536×C₆₇	C₂²	1	1	yes	characteristic
46	#536×C₆₇	C₂²	1	1	yes	characteristic
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
51	#533×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	—	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
61	#520×C₆₇	C₂²	1	2	yes	—
62	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
63	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
65	#501×C₆₇	C₂²	1	2	yes	—
66	#500×C₆₇	C₂²	1	2	yes	—
67	#497×C₆₇	C₂²	1	2	yes	—
68	#495×C₆₇	C₂²	1	2	yes	—
69	#489×C₆₇	C₂²	1	2	yes	—
70	#489×C₆₇	C₂²	1	2	yes	—
71	#488×C₆₇	C₂²	1	2	yes	—
72	#487×C₆₇	C₂²	1	2	yes	—
73	#485×C₆₇	C₂²	1	2	yes	—
74	#484×C₆₇	C₂²	1	2	yes	—
75	#484×C₆₇	C₂²	1	2	yes	—
76	#484×C₆₇	C₂²	1	2	yes	—
77	#483×C₆₇	C₂²	1	2	yes	—
78	#482×C₆₇	C₂²	1	2	yes	—
79	#480×C₆₇	C₂²	1	2	yes	—
80	#480×C₆₇	C₂²	1	2	yes	—
81	#479×C₆₇	C₂²	1	2	yes	—
82	#478×C₆₇	C₂²	1	2	yes	—
83	#477×C₆₇	C₂²	1	1	yes	characteristic
84	#477×C₆₇	C₂²	1	1	yes	characteristic
85	#477×C₆₇	C₂²	1	1	yes	characteristic
86	#477×C₆₇	C₂²	1	1	yes	characteristic
87	#477×C₆₇	C₂²	1	1	yes	characteristic
88	#477×C₆₇	C₂²	1	1	yes	characteristic
89	#477×C₆₇	C₂²	1	2	yes	—
90	#476×C₆₇	C₂²	1	1	yes	characteristic
91	#476×C₆₇	C₂²	1	1	yes	characteristic
92	#474×C₆₇	C₂²	1	2	yes	—
93	#470×C₆₇	C₂²	1	2	yes	—
94	#468×C₆₇	C₂²	1	2	yes	—
95	#468×C₆₇	C₂²	1	2	yes	—
96	#468×C₆₇	C₂²	1	2	yes	—
97	#467×C₆₇	C₂²	1	2	yes	—
98	#467×C₆₇	C₂²	1	2	yes	—
99	#466×C₆₇	C₂²	1	2	yes	—
100	#465×C₆₇	C₂²	1	2	yes	—
101	#464×C₆₇	C₂²	1	2	yes	—
102	#463×C₆₇	C₂²	1	2	yes	—
103	#462×C₆₇	C₂²	1	1	yes	characteristic
104	#462×C₆₇	C₂²	1	1	yes	characteristic
105	#462×C₆₇	C₂²	1	1	yes	characteristic
106	#462×C₆₇	C₂²	1	2	yes	—
107	#461×C₆₇	C₂²	1	1	yes	characteristic
108	#461×C₆₇	C₂²	1	2	yes	—
109	#460×C₆₇	C₂²	1	1	yes	characteristic
110	#460×C₆₇	C₂²	1	1	yes	characteristic
111	#460×C₆₇	C₂²	1	1	yes	characteristic
112	#459×C₆₇	C₂²	1	1	yes	characteristic
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	#451×C₆₇	C₂²	1	2	yes	—
118	#449×C₆₇	C₂²	1	2	yes	—
119	#449×C₆₇	C₂²	1	2	yes	—
120	#448×C₆₇	C₂²	1	2	yes	—
121	#441×C₆₇	C₂²	1	2	yes	—
122	#440×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×Q₁₆×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	#431×C₆₇	C₂²	1	1	yes	characteristic
134	#431×C₆₇	C₂²	1	1	yes	characteristic
135	#423×C₆₇	C₂²	1	1	yes	characteristic
136	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
137	#408×C₆₇	C₂²	1	2	yes	—
138	#405×C₆₇	C₂²	1	2	yes	—
139	C₂×#41×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×#41×C₆₇	C₂³	1	2	yes	—
143	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₆₇	—	2	1	no	—
145	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×Q₁₆×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×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	—	2	1	no	—
159	C₄⋊Q₈×C₆₇	—	2	1	no	—
160	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
167	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
168	#127×C₆₇	C₂³	1	1	yes	characteristic
169	#126×C₆₇	—	2	1	no	—
170	#126×C₆₇	—	2	1	no	—
171	#126×C₆₇	—	2	2	no	—
172	#126×C₆₇	—	2	2	no	—
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	#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	—	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	1	yes	characteristic
190	#124×C₆₇	—	2	1	no	—
191	#124×C₆₇	—	2	1	no	—
192	#124×C₆₇	—	2	1	no	—
193	#124×C₆₇	—	2	2	no	—
194	#124×C₆₇	—	2	2	no	—
195	#124×C₆₇	—	2	1	no	—
196	#124×C₆₇	—	2	1	no	—
197	#124×C₆₇	C₂³	1	1	yes	characteristic
198	#124×C₆₇	C₂³	1	2	yes	—
199	#124×C₆₇	C₂³	1	1	yes	characteristic
200	#123×C₆₇	—	2	1	no	—
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	1	no	—
206	#123×C₆₇	—	2	1	no	—
207	#123×C₆₇	—	2	1	no	—
208	#123×C₆₇	—	2	2	no	—
209	#123×C₆₇	—	2	2	no	—
210	C₂²⋊Q₈×C₆₇	—	2	1	no	—
211	C₂²⋊Q₈×C₆₇	—	2	2	no	—
212	C₂²⋊Q₈×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	2	no	—
221	C₂²⋊Q₈×C₆₇	—	2	2	no	—
222	C₂²⋊Q₈×C₆₇	—	2	1	no	—
223	C₂²⋊Q₈×C₆₇	—	2	1	no	—
224	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
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	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
231	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
232	#121×C₆₇	—	2	1	no	—
233	#121×C₆₇	—	2	1	no	—
234	#121×C₆₇	—	2	1	no	—
235	#121×C₆₇	—	2	2	no	—
236	#121×C₆₇	—	2	2	no	—
237	#121×C₆₇	—	2	2	no	—
238	#121×C₆₇	—	2	1	no	—
239	#121×C₆₇	—	2	1	no	—
240	#121×C₆₇	—	2	1	no	—
241	#121×C₆₇	—	2	1	no	—
242	#121×C₆₇	C₂³	1	2	yes	—
243	#121×C₆₇	C₂³	1	1	yes	characteristic
244	#121×C₆₇	C₂³	1	2	yes	—
245	#121×C₆₇	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₆₇	—	2	1	no	—
247	C₄×Q₈×C₆₇	—	2	1	no	—
248	C₄×Q₈×C₆₇	—	2	1	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	D₄	1	1	yes	characteristic
253	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
254	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
255	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
256	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
257	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
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	2	no	—
267	C₄×D₄×C₆₇	—	2	2	no	—
268	C₄×D₄×C₆₇	—	2	1	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	D₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₆₇	C₂³	1	2	yes	—
280	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
281	C₄×D₄×C₆₇	C₂³	1	2	yes	—
282	#117×C₆₇	—	2	1	no	—
283	#117×C₆₇	—	2	1	no	—
284	#117×C₆₇	—	2	1	no	—
285	#117×C₆₇	—	2	1	no	—
286	#117×C₆₇	—	2	2	no	—
287	#117×C₆₇	—	2	1	no	—
288	#117×C₆₇	—	2	1	no	—
289	#117×C₆₇	—	2	1	no	—
290	#117×C₆₇	C₂³	1	1	yes	characteristic
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	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
295	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
296	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
297	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	#107×C₆₇	C₂³	1	2	yes	—
309	#107×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	#103×C₆₇	C₂³	1	2	yes	—
325	#103×C₆₇	C₂³	1	2	yes	—
326	#103×C₆₇	C₂³	1	2	yes	—
327	#103×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	#41×C₆₇	—	4	1	no	—
343	#41×C₆₇	—	4	1	no	—
344	#41×C₆₇	—	4	1	no	—
345	#41×C₆₇	—	4	1	no	—
346	#41×C₆₇	—	4	2	no	—
347	#41×C₆₇	—	4	2	no	—
348	#41×C₆₇	—	8	2	no	—
349	#41×C₆₇	—	8	2	no	—
350	C₂×Q₈×C₆₇	—	2	1	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	2	no	—
356	C₂×Q₈×C₆₇	—	4	1	no	—
357	C₂×Q₈×C₆₇	—	4	1	no	—
358	C₂×Q₈×C₆₇	—	8	2	no	—
359	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
360	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
361	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
362	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
363	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
364	C₂×D₄×C₆₇	—	2	2	no	—
365	C₂×D₄×C₆₇	—	2	1	no	—
366	C₂×D₄×C₆₇	—	2	1	no	—
367	C₂×D₄×C₆₇	—	2	1	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	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
377	C₂²×C₄×C₆₇	—	2	1	no	—
378	C₂²×C₄×C₆₇	—	2	1	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	2	no	—
383	C₂²×C₄×C₆₇	—	2	1	no	—
384	C₂²×C₄×C₆₇	—	2	2	no	—
385	C₂²×C₄×C₆₇	—	2	2	no	—
386	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
395	Q₁₆×C₆₇	—	4	2	no	—
396	Q₁₆×C₆₇	—	4	2	no	—
397	Q₁₆×C₆₇	—	4	2	no	—
398	SD₁₆×C₆₇	—	4	2	no	—
399	SD₁₆×C₆₇	—	4	2	no	—
400	SD₁₆×C₆₇	—	4	2	no	—
401	SD₁₆×C₆₇	—	4	2	no	—
402	D₈×C₆₇	—	4	2	no	—
403	M₁₆×C₆₇	—	4	2	no	—
404	C₂×C₈×C₆₇	—	4	2	no	—
405	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
406	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
407	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
408	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₆₇	—	2	2	no	—
410	C₄⋊C₄×C₆₇	—	2	1	no	—
411	C₄⋊C₄×C₆₇	—	2	1	no	—
412	C₄⋊C₄×C₆₇	—	2	2	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	2	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	2	no	—
435	C₄⋊C₄×C₆₇	—	2	2	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	1	no	—
440	C₄⋊C₄×C₆₇	—	2	1	no	—
441	C₄⋊C₄×C₆₇	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
453	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
454	C₂²⋊C₄×C₆₇	—	2	2	no	—
455	C₂²⋊C₄×C₆₇	—	2	2	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	2	no	—
464	C₂²⋊C₄×C₆₇	—	2	2	no	—
465	C₂²⋊C₄×C₆₇	—	2	1	no	—
466	C₂²⋊C₄×C₆₇	—	2	1	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	2	no	—
472	C₂²⋊C₄×C₆₇	—	2	2	no	—
473	C₂²⋊C₄×C₆₇	—	2	2	no	—
474	C₂²⋊C₄×C₆₇	—	2	2	no	—
475	C₂²⋊C₄×C₆₇	—	2	1	no	—
476	C₂²⋊C₄×C₆₇	—	2	1	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	1	no	—
488	C₄²×C₆₇	—	2	1	no	—
489	C₄²×C₆₇	—	2	1	no	—
490	C₄²×C₆₇	—	2	2	no	—
491	C₄²×C₆₇	—	2	2	no	—
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	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	C₂⁴	1	1	yes	characteristic
499	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
500	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
501	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
502	C₂³×C₆₇	—	2	1	no	—
503	C₂³×C₆₇	—	2	2	no	—
504	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
505	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
506	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
507	Q₈×C₆₇	—	2	1	no	—
508	Q₈×C₆₇	—	2	1	no	—
509	Q₈×C₆₇	—	2	1	no	—
510	Q₈×C₆₇	—	2	2	no	—
511	Q₈×C₆₇	—	2	1	no	—
512	Q₈×C₆₇	—	2	1	no	—
513	Q₈×C₆₇	—	2	2	no	—
514	Q₈×C₆₇	—	2	1	no	—
515	Q₈×C₆₇	—	4	1	no	—
516	Q₈×C₆₇	—	4	2	no	—
517	Q₈×C₆₇	—	4	2	no	—
518	Q₈×C₆₇	—	4	2	no	—
519	Q₈×C₆₇	—	8	1	no	—
520	Q₈×C₆₇	—	8	1	no	—
521	Q₈×C₆₇	—	8	2	no	—
522	D₄×C₆₇	—	2	1	no	—
523	D₄×C₆₇	—	2	2	no	—
524	D₄×C₆₇	—	2	1	no	—
525	D₄×C₆₇	—	2	2	no	—
526	D₄×C₆₇	—	4	1	no	—
527	D₄×C₆₇	—	4	1	no	—
528	D₄×C₆₇	—	4	1	no	—
529	D₄×C₆₇	—	4	2	no	—
530	D₄×C₆₇	—	4	2	no	—
531	D₄×C₆₇	—	4	4	no	—
532	D₄×C₆₇	—	4	2	no	—
533	D₄×C₆₇	—	8	1	no	—
534	D₄×C₆₇	—	8	1	no	—
535	D₄×C₆₇	—	8	2	no	—
536	D₄×C₆₇	—	8	2	no	—
537	C₂×C₄×C₆₇	—	2	2	no	—
538	C₂×C₄×C₆₇	—	2	2	no	—
539	C₂×C₄×C₆₇	—	2	2	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	1	no	—
544	C₂×C₄×C₆₇	—	2	1	no	—
545	C₂×C₄×C₆₇	—	2	1	no	—
546	C₂×C₄×C₆₇	—	2	1	no	—
547	C₂×C₄×C₆₇	—	2	2	no	—
548	C₂×C₄×C₆₇	—	2	1	no	—
549	C₂×C₄×C₆₇	—	2	1	no	—
550	C₂×C₄×C₆₇	—	2	1	no	—
551	C₂×C₄×C₆₇	—	2	1	no	—
552	C₂×C₄×C₆₇	—	2	1	no	—
553	C₂×C₄×C₆₇	—	2	1	no	—
554	C₂×C₄×C₆₇	—	2	2	no	—
555	C₂×C₄×C₆₇	—	2	2	no	—
556	C₂×C₄×C₆₇	—	4	1	no	—
557	C₂×C₄×C₆₇	—	4	1	no	—
558	C₂×C₄×C₆₇	—	4	1	no	—
559	C₂×C₄×C₆₇	—	4	4	no	—
560	C₂×C₄×C₆₇	—	4	2	no	—
561	C₂×C₄×C₆₇	—	4	2	no	—
562	C₂×C₄×C₆₇	—	4	2	no	—
563	C₂×C₄×C₆₇	—	8	1	no	—
564	C₂×C₄×C₆₇	—	8	2	no	—
565	C₂×C₄×C₆₇	—	8	2	no	—
566	C₂×C₄×C₆₇	—	8	1	no	—
567	C₂×C₄×C₆₇	—	8	2	no	—
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	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
580	C₈×C₆₇	—	2	2	no	—
581	C₈×C₆₇	—	2	2	no	—
582	C₈×C₆₇	—	2	2	no	—
583	C₈×C₆₇	—	2	2	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	—	2	1	no	—
589	C₂²×C₆₇	—	2	1	no	—
590	C₂²×C₆₇	—	2	1	no	—
591	C₂²×C₆₇	—	2	1	no	—
592	C₂²×C₆₇	—	2	1	no	—
593	C₂²×C₆₇	—	4	2	no	—
594	C₂²×C₆₇	—	4	1	no	—
595	C₂²×C₆₇	—	4	1	no	—
596	C₂²×C₆₇	—	4	2	no	—
597	C₂²×C₆₇	—	4	1	no	—
598	C₂²×C₆₇	—	4	2	no	—
599	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
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	—	2	1	no	—
610	C₄×C₆₇	—	4	2	no	—
611	C₄×C₆₇	—	4	2	no	—
612	C₄×C₆₇	—	4	1	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	—	4	1	no	—
619	C₄×C₆₇	—	4	1	no	—
620	C₄×C₆₇	#578	1	2	yes	—
621	C₄×C₆₇	#585	1	1	yes	characteristic
622	C₄×C₆₇	#585	1	1	yes	characteristic
623	#60993	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
624	C₂×C₆₇	—	4	1	no	—
625	C₂×C₆₇	—	4	1	no	—
626	C₂×C₆₇	—	4	1	no	—
627	C₂×C₆₇	—	8	2	no	—
628	C₂×C₆₇	—	8	1	no	—
629	C₂×C₆₇	#3449	1	1	yes	characteristic
630	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
631	C₂×C₆₇	#3585	1	1	yes	characteristic
632	#3511	C₂×C₆₇	1	1	yes	characteristic, complemented
633	#3461	C₂×C₆₇	1	1	yes	characteristic, complemented
634	#3254	C₂×C₆₇	1	1	yes	characteristic, complemented
635	#3252	C₂×C₆₇	1	1	yes	characteristic, complemented
636	#3249	C₂×C₆₇	1	1	yes	characteristic, complemented
637	#3247	C₂×C₆₇	1	1	yes	characteristic, complemented
638	#3243	C₂×C₆₇	1	2	yes	complemented
639	#3238	C₂×C₆₇	1	1	yes	characteristic, complemented
640	#3230	C₂×C₆₇	1	1	yes	characteristic, complemented
641	#3225	C₂×C₆₇	1	2	yes	complemented
642	#3216	C₂×C₆₇	1	1	yes	characteristic, complemented
643	#3212	C₂×C₆₇	1	1	yes	characteristic, complemented
644	#3203	C₂×C₆₇	1	2	yes	complemented
645	#3201	C₂×C₆₇	1	2	yes	complemented
646	#3178	C₂×C₆₇	1	2	yes	complemented
647	#3175	C₂×C₆₇	1	2	yes	complemented
648	#3124	C₂×C₆₇	1	2	yes	complemented
649	#3120	C₂×C₆₇	1	2	yes	complemented
650	#3116	C₂×C₆₇	1	1	yes	characteristic, complemented
651	#3112	C₂×C₆₇	1	1	yes	characteristic, complemented
652	#3106	C₂×C₆₇	1	1	yes	characteristic, complemented
653	#3104	C₂×C₆₇	1	1	yes	characteristic, complemented
654	#2925	C₂×C₆₇	1	1	yes	characteristic, complemented
655	C₆₇	#60993	1	1	yes	characteristic, direct product factor, Sylow
656	#556	—	2	1	no	—
657	#555	—	2	1	no	—
658	#554	—	2	1	no	—
659	#553	—	2	1	no	—
660	#553	—	2	1	no	—
661	#548	—	2	1	no	—
662	#548	—	2	1	no	—
663	#547	—	2	1	no	—
664	#544	C₂²×C₆₇	1	1	yes	characteristic
665	#542	—	2	1	no	—
666	#542	C₂²×C₆₇	1	1	yes	characteristic
667	#542	C₂²×C₆₇	1	1	yes	characteristic
668	#542	C₂²×C₆₇	1	2	yes	—
669	#542	C₂²×C₆₇	1	2	yes	—
670	#541	—	2	1	no	—
671	#541	C₂²×C₆₇	1	1	yes	characteristic
672	#541	C₂²×C₆₇	1	1	yes	characteristic
673	#539	—	2	1	no	—
674	#539	—	2	1	no	—
675	#537	C₂²×C₆₇	1	2	yes	—
676	#537	C₂²×C₆₇	1	1	yes	characteristic
677	#536	C₂²×C₆₇	1	1	yes	characteristic
678	#536	C₂²×C₆₇	1	1	yes	characteristic
679	#533	—	2	1	no	—
680	#533	C₂²×C₆₇	1	1	yes	characteristic
681	#533	C₂²×C₆₇	1	1	yes	characteristic
682	#533	C₂²×C₆₇	1	1	yes	characteristic
683	#533	C₂²×C₆₇	1	1	yes	characteristic
684	#532	C₂²×C₆₇	1	1	yes	characteristic
685	#532	C₂²×C₆₇	1	1	yes	characteristic
686	#532	C₂²×C₆₇	1	1	yes	characteristic
687	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
688	#529	—	2	1	no	—
689	#529	—	2	1	no	—
690	#529	—	2	1	no	—
691	#529	C₂²×C₆₇	1	1	yes	characteristic
692	#529	C₂²×C₆₇	1	1	yes	characteristic
693	#520	C₂²×C₆₇	1	2	yes	—
694	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
695	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
696	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
697	#501	C₂²×C₆₇	1	2	yes	—
698	#500	C₂²×C₆₇	1	2	yes	—
699	#497	C₂²×C₆₇	1	2	yes	—
700	#495	C₂²×C₆₇	1	2	yes	—
701	#489	C₂²×C₆₇	1	2	yes	—
702	#489	C₂²×C₆₇	1	2	yes	—
703	#488	C₂²×C₆₇	1	2	yes	—
704	#487	C₂²×C₆₇	1	2	yes	—
705	#485	C₂²×C₆₇	1	2	yes	—
706	#484	C₂²×C₆₇	1	2	yes	—
707	#484	C₂²×C₆₇	1	2	yes	—
708	#484	C₂²×C₆₇	1	2	yes	—
709	#483	C₂²×C₆₇	1	2	yes	—
710	#482	C₂²×C₆₇	1	2	yes	—
711	#480	C₂²×C₆₇	1	2	yes	—
712	#480	C₂²×C₆₇	1	2	yes	—
713	#479	C₂²×C₆₇	1	2	yes	—
714	#478	C₂²×C₆₇	1	2	yes	—
715	#477	C₂²×C₆₇	1	1	yes	characteristic
716	#477	C₂²×C₆₇	1	1	yes	characteristic
717	#477	C₂²×C₆₇	1	1	yes	characteristic
718	#477	C₂²×C₆₇	1	1	yes	characteristic
719	#477	C₂²×C₆₇	1	1	yes	characteristic
720	#477	C₂²×C₆₇	1	1	yes	characteristic
721	#477	C₂²×C₆₇	1	2	yes	—
722	#476	C₂²×C₆₇	1	1	yes	characteristic
723	#476	C₂²×C₆₇	1	1	yes	characteristic
724	#474	C₂²×C₆₇	1	2	yes	—
725	#470	C₂²×C₆₇	1	2	yes	—
726	#468	C₂²×C₆₇	1	2	yes	—
727	#468	C₂²×C₆₇	1	2	yes	—
728	#468	C₂²×C₆₇	1	2	yes	—
729	#467	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	#464	C₂²×C₆₇	1	2	yes	—
734	#463	C₂²×C₆₇	1	2	yes	—
735	#462	C₂²×C₆₇	1	1	yes	characteristic
736	#462	C₂²×C₆₇	1	1	yes	characteristic
737	#462	C₂²×C₆₇	1	1	yes	characteristic
738	#462	C₂²×C₆₇	1	2	yes	—
739	#461	C₂²×C₆₇	1	1	yes	characteristic
740	#461	C₂²×C₆₇	1	2	yes	—
741	#460	C₂²×C₆₇	1	1	yes	characteristic
742	#460	C₂²×C₆₇	1	1	yes	characteristic
743	#460	C₂²×C₆₇	1	1	yes	characteristic
744	#459	C₂²×C₆₇	1	1	yes	characteristic
745	#452	C₂²×C₆₇	1	2	yes	—
746	#452	C₂²×C₆₇	1	2	yes	—
747	#452	C₂²×C₆₇	1	2	yes	—
748	#452	C₂²×C₆₇	1	2	yes	—
749	#451	C₂²×C₆₇	1	2	yes	—
750	#449	C₂²×C₆₇	1	2	yes	—
751	#449	C₂²×C₆₇	1	2	yes	—
752	#448	C₂²×C₆₇	1	2	yes	—
753	#441	C₂²×C₆₇	1	2	yes	—
754	#440	C₂²×C₆₇	1	2	yes	—
755	#440	C₂²×C₆₇	1	2	yes	—
756	#440	C₂²×C₆₇	1	2	yes	—
757	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
758	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
759	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
760	C₄×D₈	C₂²×C₆₇	1	2	yes	—
761	#433	C₂²×C₆₇	1	2	yes	—
762	#433	C₂²×C₆₇	1	2	yes	—
763	#432	C₂²×C₆₇	1	1	yes	characteristic
764	#432	C₂²×C₆₇	1	1	yes	characteristic
765	#431	C₂²×C₆₇	1	1	yes	characteristic
766	#431	C₂²×C₆₇	1	1	yes	characteristic
767	#423	C₂²×C₆₇	1	1	yes	characteristic
768	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
769	#408	C₂²×C₆₇	1	2	yes	—
770	#405	C₂²×C₆₇	1	2	yes	—
771	C₂×#41	—	2	1	no	—
772	C₂×#41	—	2	1	no	—
773	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
774	C₂×#41	C₂³×C₆₇	1	2	yes	—
775	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
776	C₂²×Q₈	—	2	1	no	—
777	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
778	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
779	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
780	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
781	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
782	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
783	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
785	C₂×D₈	C₂³×C₆₇	1	2	yes	—
786	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
787	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
788	C₄⋊Q₈	—	2	1	no	—
789	C₄⋊Q₈	—	2	1	no	—
790	C₄⋊Q₈	—	2	1	no	—
791	C₄⋊Q₈	—	2	1	no	—
792	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
793	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
794	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
795	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
796	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
797	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
798	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
799	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
800	#127	C₂³×C₆₇	1	1	yes	characteristic
801	#126	—	2	1	no	—
802	#126	—	2	1	no	—
803	#126	—	2	2	no	—
804	#126	—	2	2	no	—
805	#126	—	2	1	no	—
806	#126	—	2	1	no	—
807	#126	—	2	1	no	—
808	#126	—	2	1	no	—
809	#126	—	2	1	no	—
810	#126	—	2	1	no	—
811	#125	—	2	1	no	—
812	#125	—	2	1	no	—
813	#125	—	2	1	no	—
814	#125	—	2	1	no	—
815	#125	—	2	1	no	—
816	#125	—	2	1	no	—
817	#125	—	2	1	no	—
818	#125	—	2	1	no	—
819	#125	—	2	1	no	—
820	#125	C₂³×C₆₇	1	1	yes	characteristic
821	#125	C₂³×C₆₇	1	1	yes	characteristic
822	#124	—	2	1	no	—
823	#124	—	2	1	no	—
824	#124	—	2	1	no	—
825	#124	—	2	2	no	—
826	#124	—	2	2	no	—
827	#124	—	2	1	no	—
828	#124	—	2	1	no	—
829	#124	C₂³×C₆₇	1	1	yes	characteristic
830	#124	C₂³×C₆₇	1	1	yes	characteristic
831	#124	C₂³×C₆₇	1	2	yes	—
832	#123	—	2	1	no	—
833	#123	—	2	1	no	—
834	#123	—	2	1	no	—
835	#123	—	2	1	no	—
836	#123	—	2	1	no	—
837	#123	—	2	1	no	—
838	#123	—	2	1	no	—
839	#123	—	2	1	no	—
840	#123	—	2	2	no	—
841	#123	—	2	2	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	2	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	—	2	1	no	—
847	C₂²⋊Q₈	—	2	1	no	—
848	C₂²⋊Q₈	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	—	2	1	no	—
851	C₂²⋊Q₈	—	2	1	no	—
852	C₂²⋊Q₈	—	2	2	no	—
853	C₂²⋊Q₈	—	2	2	no	—
854	C₂²⋊Q₈	—	2	1	no	—
855	C₂²⋊Q₈	—	2	1	no	—
856	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
857	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
858	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
859	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
860	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
861	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
862	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
863	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
864	#121	—	2	1	no	—
865	#121	—	2	1	no	—
866	#121	—	2	1	no	—
867	#121	—	2	2	no	—
868	#121	—	2	2	no	—
869	#121	—	2	2	no	—
870	#121	—	2	1	no	—
871	#121	—	2	1	no	—
872	#121	—	2	1	no	—
873	#121	—	2	1	no	—
874	#121	C₂³×C₆₇	1	1	yes	characteristic
875	#121	C₂³×C₆₇	1	1	yes	characteristic
876	#121	C₂³×C₆₇	1	2	yes	—
877	#121	C₂³×C₆₇	1	2	yes	—
878	C₄×Q₈	—	2	1	no	—
879	C₄×Q₈	—	2	1	no	—
880	C₄×Q₈	—	2	1	no	—
881	C₄×Q₈	—	2	1	no	—
882	C₄×Q₈	—	2	1	no	—
883	C₄×Q₈	—	2	1	no	—
884	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
885	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
886	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
887	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
888	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
889	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
890	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
891	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
892	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
893	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	2	no	—
899	C₄×D₄	—	2	2	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	1	no	—
903	C₄×D₄	—	2	1	no	—
904	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
905	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
906	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
907	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
908	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
909	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
910	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
911	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
912	C₄×D₄	C₂³×C₆₇	1	2	yes	—
913	C₄×D₄	C₂³×C₆₇	1	2	yes	—
914	#117	—	2	1	no	—
915	#117	—	2	1	no	—
916	#117	—	2	1	no	—
917	#117	—	2	1	no	—
918	#117	—	2	2	no	—
919	#117	—	2	1	no	—
920	#117	—	2	1	no	—
921	#117	—	2	1	no	—
922	#117	C₂³×C₆₇	1	1	yes	characteristic
923	#117	C₂³×C₆₇	1	1	yes	characteristic
924	#117	C₂³×C₆₇	1	1	yes	characteristic
925	#117	C₂³×C₆₇	1	1	yes	characteristic
926	C₂×C₄⋊C₄	—	2	1	no	—
927	C₂×C₄⋊C₄	—	2	1	no	—
928	C₂×C₄⋊C₄	—	2	2	no	—
929	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
930	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
931	C₂×C₄²	—	2	1	no	—
932	C₂×C₄²	—	2	1	no	—
933	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
934	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
935	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
936	#107	C₂³×C₆₇	1	2	yes	—
937	#107	C₂³×C₆₇	1	2	yes	—
938	#107	C₂³×C₆₇	1	2	yes	—
939	#107	C₂³×C₆₇	1	2	yes	—
940	#107	C₂³×C₆₇	1	2	yes	—
941	#107	C₂³×C₆₇	1	2	yes	—
942	#106	C₂³×C₆₇	1	2	yes	—
943	#106	C₂³×C₆₇	1	2	yes	—
944	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
945	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
946	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
947	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
948	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
949	C₄⋊C₈	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	#103	C₂³×C₆₇	1	2	yes	—
954	#103	C₂³×C₆₇	1	2	yes	—
955	#103	C₂³×C₆₇	1	2	yes	—
956	#103	C₂³×C₆₇	1	2	yes	—
957	#103	C₂³×C₆₇	1	2	yes	—
958	#103	C₂³×C₆₇	1	2	yes	—
959	#103	C₂³×C₆₇	1	2	yes	—
960	#102	C₂³×C₆₇	1	2	yes	—
961	#102	C₂³×C₆₇	1	2	yes	—
962	#102	C₂³×C₆₇	1	2	yes	—
963	#102	C₂³×C₆₇	1	2	yes	—
964	#102	C₂³×C₆₇	1	2	yes	—
965	#102	C₂³×C₆₇	1	2	yes	—
966	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
967	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
968	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
969	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
970	#97	C₂³×C₆₇	1	2	yes	—
971	#97	C₂³×C₆₇	1	2	yes	—
972	C₄×C₈	C₂³×C₆₇	1	2	yes	—
973	C₄×C₈	C₂³×C₆₇	1	2	yes	—
974	#41	—	4	1	no	—
975	#41	—	4	1	no	—
976	#41	—	4	1	no	—
977	#41	—	4	1	no	—
978	#41	—	4	2	no	—
979	#41	—	4	2	no	—
980	#41	—	8	2	no	—
981	#41	—	8	2	no	—
982	C₂×Q₈	—	2	1	no	—
983	C₂×Q₈	—	2	1	no	—
984	C₂×Q₈	—	2	1	no	—
985	C₂×Q₈	—	2	1	no	—
986	C₂×Q₈	—	2	1	no	—
987	C₂×Q₈	—	2	2	no	—
988	C₂×Q₈	—	4	1	no	—
989	C₂×Q₈	—	4	1	no	—
990	C₂×Q₈	—	8	2	no	—
991	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
992	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
993	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
994	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
995	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1005	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1006	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1007	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1008	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	2	no	—
1015	C₂²×C₄	—	2	1	no	—
1016	C₂²×C₄	—	2	2	no	—
1017	C₂²×C₄	—	2	2	no	—
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	C₂×D₄×C₆₇	1	1	yes	characteristic
1024	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1025	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1026	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1027	Q₁₆	—	4	2	no	—
1028	Q₁₆	—	4	2	no	—
1029	Q₁₆	—	4	2	no	—
1030	SD₁₆	—	4	2	no	—
1031	SD₁₆	—	4	2	no	—
1032	SD₁₆	—	4	2	no	—
1033	SD₁₆	—	4	2	no	—
1034	D₈	—	4	2	no	—
1035	M₁₆	—	4	2	no	—
1036	C₂×C₈	—	4	2	no	—
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	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	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	1	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	2	no	—
1067	C₄⋊C₄	—	2	2	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	C₂×D₄×C₆₇	1	1	yes	characteristic
1075	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1076	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1077	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1078	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1079	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1080	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1081	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1082	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1083	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1084	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1085	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	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	1	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	2	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	1	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1113	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1114	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1115	C₄²	—	2	1	no	—
1116	C₄²	—	2	1	no	—
1117	C₄²	—	2	1	no	—
1118	C₄²	—	2	1	no	—
1119	C₄²	—	2	1	no	—
1120	C₄²	—	2	1	no	—
1121	C₄²	—	2	1	no	—
1122	C₄²	—	2	2	no	—
1123	C₄²	—	2	2	no	—
1124	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1125	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1126	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1127	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1128	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1129	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1130	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1131	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1132	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1133	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1134	C₂³	—	2	1	no	—
1135	C₂³	—	2	2	no	—
1136	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1137	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1138	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1139	Q₈	—	2	1	no	—
1140	Q₈	—	2	1	no	—
1141	Q₈	—	2	1	no	—
1142	Q₈	—	2	2	no	—
1143	Q₈	—	2	1	no	—
1144	Q₈	—	2	1	no	—
1145	Q₈	—	2	2	no	—
1146	Q₈	—	2	1	no	—
1147	Q₈	—	4	1	no	—
1148	Q₈	—	4	2	no	—
1149	Q₈	—	4	2	no	—
1150	Q₈	—	4	2	no	—
1151	Q₈	—	8	2	no	—
1152	Q₈	—	8	1	no	—
1153	Q₈	—	8	1	no	—
1154	D₄	—	2	1	no	—
1155	D₄	—	2	2	no	—
1156	D₄	—	2	1	no	—
1157	D₄	—	2	2	no	—
1158	D₄	—	4	1	no	—
1159	D₄	—	4	1	no	—
1160	D₄	—	4	1	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	4	2	no	—
1163	D₄	—	4	4	no	—
1164	D₄	—	4	2	no	—
1165	D₄	—	8	2	no	—
1166	D₄	—	8	2	no	—
1167	D₄	—	8	1	no	—
1168	D₄	—	8	1	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	2	no	—
1187	C₂×C₄	—	2	2	no	—
1188	C₂×C₄	—	4	1	no	—
1189	C₂×C₄	—	4	1	no	—
1190	C₂×C₄	—	4	1	no	—
1191	C₂×C₄	—	4	4	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	4	2	no	—
1194	C₂×C₄	—	4	2	no	—
1195	C₂×C₄	—	8	2	no	—
1196	C₂×C₄	—	8	2	no	—
1197	C₂×C₄	—	8	1	no	—
1198	C₂×C₄	—	8	2	no	—
1199	C₂×C₄	—	8	1	no	—
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	C₂²×D₄×C₆₇	1	1	yes	characteristic
1204	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1205	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1207	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1208	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1209	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1210	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1211	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1212	C₈	—	2	2	no	—
1213	C₈	—	2	2	no	—
1214	C₈	—	2	2	no	—
1215	C₈	—	2	2	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	1	no	—
1221	C₂²	—	2	1	no	—
1222	C₂²	—	2	1	no	—
1223	C₂²	—	2	1	no	—
1224	C₂²	—	2	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	2	no	—
1227	C₂²	—	4	2	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	2	no	—
1231	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
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	—	2	1	no	—
1239	C₄	—	2	1	no	—
1240	C₄	—	2	1	no	—
1241	C₄	—	2	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	2	no	—
1244	C₄	—	4	2	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	2	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	#578×C₆₇	1	2	yes	—
1253	C₄	#585×C₆₇	1	1	yes	characteristic
1254	C₄	#585×C₆₇	1	1	yes	characteristic
1255	C₂	—	4	1	no	—
1256	C₂	—	4	1	no	—
1257	C₂	—	4	1	no	—
1258	C₂	—	8	1	no	—
1259	C₂	—	8	2	no	—
1260	C₂	C₆₇×#3449	1	1	yes	characteristic
1261	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
1262	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×#3511	C₂	semidirect
2. C₆₇×#3461	C₂	semidirect
3. C₆₇×#3254	C₂	semidirect
4. C₆₇×#3252	C₂	semidirect
5. C₆₇×#3249	C₂	semidirect
6. C₆₇×#3247	C₂	semidirect
7. C₆₇×#3243	C₂	semidirect
8. C₆₇×#3238	C₂	semidirect
9. C₆₇×#3230	C₂	semidirect
10. C₆₇×#3225	C₂	semidirect
11. C₆₇×#3216	C₂	semidirect
12. C₆₇×#3212	C₂	semidirect
13. C₆₇×#3203	C₂	semidirect
14. C₆₇×#3201	C₂	semidirect
15. C₆₇×#3178	C₂	semidirect
16. C₆₇×#3175	C₂	semidirect
17. C₆₇×#3124	C₂	semidirect
18. C₆₇×#3120	C₂	semidirect
19. C₆₇×#3116	C₂	semidirect
20. C₆₇×#3112	C₂	semidirect
21. C₆₇×#3106	C₂	semidirect
22. C₆₇×#3104	C₂	semidirect
23. C₆₇×#2925	C₂	semidirect
623. #60993	C₆₇	direct (N × H)
632. #3511	C₂×C₆₇	semidirect
633. #3461	C₂×C₆₇	semidirect
634. #3254	C₂×C₆₇	semidirect
635. #3252	C₂×C₆₇	semidirect
636. #3249	C₂×C₆₇	semidirect
637. #3247	C₂×C₆₇	semidirect
638. #3243	C₂×C₆₇	semidirect
639. #3238	C₂×C₆₇	semidirect
640. #3230	C₂×C₆₇	semidirect
641. #3225	C₂×C₆₇	semidirect
642. #3216	C₂×C₆₇	semidirect
643. #3212	C₂×C₆₇	semidirect
644. #3203	C₂×C₆₇	semidirect
645. #3201	C₂×C₆₇	semidirect
646. #3178	C₂×C₆₇	semidirect
647. #3175	C₂×C₆₇	semidirect
648. #3124	C₂×C₆₇	semidirect
649. #3120	C₂×C₆₇	semidirect
650. #3116	C₂×C₆₇	semidirect
651. #3112	C₂×C₆₇	semidirect
652. #3106	C₂×C₆₇	semidirect
653. #3104	C₂×C₆₇	semidirect
654. #2925	C₂×C₆₇	semidirect
655. C₆₇	#60993	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×#3511	2
C₆₇×#3461	2
C₆₇×#3254	2
C₆₇×#3252	2
C₆₇×#3249	2
C₆₇×#3247	2
C₆₇×#3243	2
C₆₇×#3238	2
C₆₇×#3230	2
C₆₇×#3225	2
C₆₇×#3216	2
C₆₇×#3212	2
C₆₇×#3203	2
C₆₇×#3201	2
C₆₇×#3178	2
C₆₇×#3175	2
C₆₇×#3124	2
C₆₇×#3120	2
C₆₇×#3116	2
C₆₇×#3112	2
C₆₇×#3106	2
C₆₇×#3104	2
C₆₇×#2925	2
#60993	67

Subgroups — C67×#60993 #30740244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60993 #30740244