Subgroups — C₆₇×#61204 #30740455

Order 17152.

2032 conjugacy classes of subgroups.

The subgroup lattice has 1226 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×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3327	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3326	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3320	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3317	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3312	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3309	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3301	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3300	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#479×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3061	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3060	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
31	#553×C₆₇	—	2	2	no	—
32	#553×C₆₇	—	2	2	no	—
33	#553×C₆₇	C₂²	1	2	yes	—
34	#553×C₆₇	C₂²	1	2	yes	—
35	#552×C₆₇	C₂²	1	2	yes	—
36	#552×C₆₇	C₂²	1	2	yes	—
37	#550×C₆₇	—	2	1	no	—
38	#550×C₆₇	C₂²	1	2	yes	—
39	D₄×Q₈×C₆₇	—	2	1	no	—
40	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
41	#548×C₆₇	—	2	1	no	—
42	#548×C₆₇	—	2	1	no	—
43	#548×C₆₇	C₂²	1	2	yes	—
44	#548×C₆₇	C₂²	1	2	yes	—
45	#541×C₆₇	—	2	1	no	—
46	#540×C₆₇	—	2	1	no	—
47	#537×C₆₇	—	2	2	no	—
48	#537×C₆₇	C₂²	1	1	yes	characteristic
49	#537×C₆₇	C₂²	1	1	yes	characteristic
50	#537×C₆₇	C₂²	1	1	yes	characteristic
51	#537×C₆₇	C₂²	1	1	yes	characteristic
52	#532×C₆₇	—	2	2	no	—
53	#532×C₆₇	C₂²	1	1	yes	characteristic
54	#532×C₆₇	C₂²	1	1	yes	characteristic
55	#529×C₆₇	—	2	1	no	—
56	#529×C₆₇	—	2	1	no	—
57	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
58	#520×C₆₇	C₂²	1	1	yes	characteristic
59	#520×C₆₇	C₂²	1	1	yes	characteristic
60	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
62	#491×C₆₇	C₂²	1	2	yes	—
63	#490×C₆₇	C₂²	1	2	yes	—
64	#488×C₆₇	C₂²	1	2	yes	—
65	#488×C₆₇	C₂²	1	2	yes	—
66	#485×C₆₇	C₂²	1	2	yes	—
67	#485×C₆₇	C₂²	1	2	yes	—
68	#484×C₆₇	C₂²	1	2	yes	—
69	#483×C₆₇	C₂²	1	2	yes	—
70	#482×C₆₇	C₂²	1	2	yes	—
71	#482×C₆₇	C₂²	1	2	yes	—
72	#481×C₆₇	C₂²	1	2	yes	—
73	#480×C₆₇	C₂²	1	2	yes	—
74	#479×C₆₇	C₂²	1	2	yes	—
75	#479×C₆₇	C₂²	1	2	yes	—
76	#479×C₆₇	C₂²	1	2	yes	—
77	#479×C₆₇	C₂²	1	2	yes	—
78	#470×C₆₇	C₂²	1	2	yes	—
79	#469×C₆₇	C₂²	1	2	yes	—
80	#468×C₆₇	C₂²	1	2	yes	—
81	#468×C₆₇	C₂²	1	2	yes	—
82	#467×C₆₇	C₂²	1	2	yes	—
83	#466×C₆₇	C₂²	1	2	yes	—
84	#465×C₆₇	C₂²	1	2	yes	—
85	#465×C₆₇	C₂²	1	2	yes	—
86	#464×C₆₇	C₂²	1	1	yes	characteristic
87	#464×C₆₇	C₂²	1	1	yes	characteristic
88	#463×C₆₇	C₂²	1	1	yes	characteristic
89	#463×C₆₇	C₂²	1	1	yes	characteristic
90	#462×C₆₇	C₂²	1	1	yes	characteristic
91	#461×C₆₇	C₂²	1	1	yes	characteristic
92	#460×C₆₇	C₂²	1	1	yes	characteristic
93	#459×C₆₇	C₂²	1	1	yes	characteristic
94	#452×C₆₇	C₂²	1	2	yes	—
95	#452×C₆₇	C₂²	1	2	yes	—
96	#451×C₆₇	C₂²	1	2	yes	—
97	#451×C₆₇	C₂²	1	2	yes	—
98	#449×C₆₇	C₂²	1	2	yes	—
99	#449×C₆₇	C₂²	1	2	yes	—
100	#448×C₆₇	C₂²	1	2	yes	—
101	#448×C₆₇	C₂²	1	2	yes	—
102	#441×C₆₇	C₂²	1	2	yes	—
103	#440×C₆₇	C₂²	1	2	yes	—
104	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
105	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
106	#436×C₆₇	C₂²	1	2	yes	—
107	#435×C₆₇	C₂²	1	2	yes	—
108	#435×C₆₇	C₂²	1	2	yes	—
109	C₈×D₄×C₆₇	C₂²	1	2	yes	—
110	#428×C₆₇	C₂²	1	1	yes	characteristic
111	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
112	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
113	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
114	#419×C₆₇	C₂²	1	2	yes	—
115	#419×C₆₇	C₂²	1	2	yes	—
116	#419×C₆₇	C₂²	1	1	yes	characteristic
117	#417×C₆₇	C₂²	1	1	yes	characteristic
118	#417×C₆₇	C₂²	1	1	yes	characteristic
119	#417×C₆₇	C₂²	1	2	yes	—
120	#417×C₆₇	C₂²	1	1	yes	characteristic
121	#417×C₆₇	C₂²	1	1	yes	characteristic
122	#417×C₆₇	C₂²	1	1	yes	characteristic
123	#417×C₆₇	C₂²	1	2	yes	—
124	#416×C₆₇	C₂²	1	1	yes	characteristic
125	#416×C₆₇	C₂²	1	1	yes	characteristic
126	#416×C₆₇	C₂²	1	2	yes	—
127	#416×C₆₇	C₂²	1	2	yes	—
128	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
129	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×#103×C₆₇	C₂²	1	2	yes	—
131	C₂×#103×C₆₇	C₂²	1	2	yes	—
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	#408×C₆₇	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
135	2₋¹⁺⁴×C₆₇	—	2	4	no	—
136	2₋¹⁺⁴×C₆₇	—	2	4	no	—
137	2₋¹⁺⁴×C₆₇	—	4	2	no	—
138	2₋¹⁺⁴×C₆₇	—	4	2	no	—
139	C₂×#41×C₆₇	—	2	2	no	—
140	C₂×#41×C₆₇	—	2	2	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	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×#41×C₆₇	C₂³	1	2	yes	—
147	C₂×#41×C₆₇	C₂³	1	2	yes	—
148	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₆₇	—	2	1	no	—
151	C₂²×Q₈×C₆₇	—	2	1	no	—
152	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
153	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
154	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
155	#137×C₆₇	—	2	4	no	—
156	#135×C₆₇	—	4	2	no	—
157	#135×C₆₇	—	4	2	no	—
158	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
168	#131×C₆₇	—	4	2	no	—
169	#131×C₆₇	—	4	2	no	—
170	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
173	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
174	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
177	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
178	C₄⋊Q₈×C₆₇	—	2	2	no	—
179	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
180	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
181	#127×C₆₇	—	2	2	no	—
182	#127×C₆₇	D₄	1	1	yes	characteristic
183	#127×C₆₇	C₂³	1	1	yes	characteristic
184	#126×C₆₇	—	2	2	no	—
185	#126×C₆₇	—	2	2	no	—
186	#126×C₆₇	—	2	2	no	—
187	#126×C₆₇	—	2	2	no	—
188	#125×C₆₇	—	2	2	no	—
189	#125×C₆₇	—	2	2	no	—
190	#125×C₆₇	—	2	1	no	—
191	#125×C₆₇	—	2	1	no	—
192	#125×C₆₇	C₂³	1	2	yes	—
193	#125×C₆₇	C₂³	1	2	yes	—
194	#124×C₆₇	—	2	2	no	—
195	#124×C₆₇	—	2	2	no	—
196	#124×C₆₇	D₄	1	1	yes	characteristic
197	#124×C₆₇	D₄	1	1	yes	characteristic
198	#124×C₆₇	C₂³	1	1	yes	characteristic
199	#124×C₆₇	C₂³	1	1	yes	characteristic
200	#123×C₆₇	—	2	2	no	—
201	#123×C₆₇	—	2	2	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	1	no	—
207	C₂²⋊Q₈×C₆₇	—	2	1	no	—
208	C₂²⋊Q₈×C₆₇	—	2	2	no	—
209	C₂²⋊Q₈×C₆₇	—	2	2	no	—
210	C₂²⋊Q₈×C₆₇	—	2	2	no	—
211	C₂²⋊Q₈×C₆₇	—	2	2	no	—
212	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
215	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
216	#121×C₆₇	—	2	1	no	—
217	#121×C₆₇	—	2	1	no	—
218	#121×C₆₇	—	2	2	no	—
219	#121×C₆₇	—	2	2	no	—
220	#121×C₆₇	—	2	2	no	—
221	#121×C₆₇	—	2	2	no	—
222	#121×C₆₇	—	2	1	no	—
223	#121×C₆₇	—	2	1	no	—
224	#121×C₆₇	—	2	2	no	—
225	#121×C₆₇	—	2	2	no	—
226	#121×C₆₇	—	2	2	no	—
227	#121×C₆₇	—	2	2	no	—
228	#121×C₆₇	—	2	1	no	—
229	#121×C₆₇	—	2	1	no	—
230	#121×C₆₇	—	2	2	no	—
231	#121×C₆₇	—	2	2	no	—
232	#121×C₆₇	D₄	1	2	yes	—
233	#121×C₆₇	D₄	1	2	yes	—
234	#121×C₆₇	C₂³	1	2	yes	—
235	#121×C₆₇	C₂³	1	2	yes	—
236	#121×C₆₇	C₂³	1	2	yes	—
237	#121×C₆₇	C₂³	1	2	yes	—
238	C₄×Q₈×C₆₇	—	2	1	no	—
239	C₄×Q₈×C₆₇	—	2	1	no	—
240	C₄×Q₈×C₆₇	—	2	1	no	—
241	C₄×Q₈×C₆₇	—	2	1	no	—
242	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
245	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
246	C₄×D₄×C₆₇	—	2	1	no	—
247	C₄×D₄×C₆₇	—	2	1	no	—
248	C₄×D₄×C₆₇	—	2	2	no	—
249	C₄×D₄×C₆₇	—	2	2	no	—
250	C₄×D₄×C₆₇	—	2	2	no	—
251	C₄×D₄×C₆₇	—	2	1	no	—
252	C₄×D₄×C₆₇	—	2	1	no	—
253	C₄×D₄×C₆₇	—	2	2	no	—
254	C₄×D₄×C₆₇	—	2	2	no	—
255	C₄×D₄×C₆₇	—	2	2	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	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₆₇	C₂³	1	2	yes	—
263	C₄×D₄×C₆₇	C₂³	1	2	yes	—
264	#117×C₆₇	—	2	2	no	—
265	#117×C₆₇	—	2	2	no	—
266	#117×C₆₇	—	2	1	no	—
267	#117×C₆₇	C₂³	1	2	yes	—
268	#117×C₆₇	C₂³	1	2	yes	—
269	#117×C₆₇	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
272	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
274	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
275	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
278	C₂×C₄²×C₆₇	—	2	1	no	—
279	C₂×C₄²×C₆₇	—	2	1	no	—
280	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
281	#107×C₆₇	C₂³	1	2	yes	—
282	#107×C₆₇	C₂³	1	2	yes	—
283	#107×C₆₇	C₂³	1	2	yes	—
284	#106×C₆₇	C₂³	1	2	yes	—
285	#106×C₆₇	C₂³	1	2	yes	—
286	#106×C₆₇	C₂³	1	2	yes	—
287	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	2	yes	—
297	#103×C₆₇	C₂³	1	1	yes	characteristic
298	#103×C₆₇	C₂³	1	1	yes	characteristic
299	#103×C₆₇	C₂³	1	1	yes	characteristic
300	#103×C₆₇	C₂³	1	1	yes	characteristic
301	#103×C₆₇	C₂³	1	2	yes	—
302	#103×C₆₇	C₂³	1	2	yes	—
303	#103×C₆₇	C₂³	1	2	yes	—
304	#103×C₆₇	C₂³	1	2	yes	—
305	#103×C₆₇	C₂³	1	2	yes	—
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	2	yes	—
308	#102×C₆₇	C₂³	1	1	yes	characteristic
309	#102×C₆₇	C₂³	1	1	yes	characteristic
310	#102×C₆₇	C₂³	1	1	yes	characteristic
311	#102×C₆₇	C₂³	1	1	yes	characteristic
312	#102×C₆₇	C₂³	1	2	yes	—
313	#102×C₆₇	C₂³	1	2	yes	—
314	#102×C₆₇	C₂³	1	2	yes	—
315	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
316	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
319	#97×C₆₇	C₂³	1	2	yes	—
320	C₄×C₈×C₆₇	C₂³	1	2	yes	—
321	#41×C₆₇	—	2	2	no	—
322	#41×C₆₇	—	2	2	no	—
323	#41×C₆₇	—	2	2	no	—
324	#41×C₆₇	—	2	2	no	—
325	#41×C₆₇	—	2	4	no	—
326	#41×C₆₇	—	2	4	no	—
327	#41×C₆₇	—	2	2	no	—
328	#41×C₆₇	—	2	2	no	—
329	#41×C₆₇	—	2	2	no	—
330	#41×C₆₇	—	2	2	no	—
331	#41×C₆₇	—	2	2	no	—
332	#41×C₆₇	—	2	2	no	—
333	#41×C₆₇	—	4	2	no	—
334	#41×C₆₇	—	4	2	no	—
335	#41×C₆₇	—	4	8	no	—
336	#41×C₆₇	—	4	8	no	—
337	#41×C₆₇	—	4	4	no	—
338	#41×C₆₇	—	4	4	no	—
339	C₂×Q₈×C₆₇	—	2	1	no	—
340	C₂×Q₈×C₆₇	—	2	2	no	—
341	C₂×Q₈×C₆₇	—	2	2	no	—
342	C₂×Q₈×C₆₇	—	2	2	no	—
343	C₂×Q₈×C₆₇	—	2	4	no	—
344	C₂×Q₈×C₆₇	—	2	4	no	—
345	C₂×Q₈×C₆₇	—	4	2	no	—
346	C₂×Q₈×C₆₇	—	4	2	no	—
347	C₂×Q₈×C₆₇	—	4	4	no	—
348	C₂×Q₈×C₆₇	—	4	4	no	—
349	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
350	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
351	C₂×Q₈×C₆₇	#41	1	4	yes	—
352	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
354	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
356	C₂×D₄×C₆₇	—	2	1	no	—
357	C₂×D₄×C₆₇	—	2	1	no	—
358	C₂×D₄×C₆₇	—	2	1	no	—
359	C₂×D₄×C₆₇	—	2	2	no	—
360	C₂×D₄×C₆₇	—	2	2	no	—
361	C₂×D₄×C₆₇	—	2	2	no	—
362	C₂×D₄×C₆₇	—	2	2	no	—
363	C₂×D₄×C₆₇	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
373	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	no	—
378	C₂²×C₄×C₆₇	—	2	2	no	—
379	C₂²×C₄×C₆₇	—	2	1	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	2	no	—
384	C₂²×C₄×C₆₇	—	2	1	no	—
385	C₂²×C₄×C₆₇	—	2	2	no	—
386	C₂²×C₄×C₆₇	—	2	2	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	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
394	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
395	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
396	Q₁₆×C₆₇	—	2	4	no	—
397	Q₁₆×C₆₇	—	4	1	no	—
398	Q₁₆×C₆₇	—	4	1	no	—
399	SD₁₆×C₆₇	—	2	4	no	—
400	SD₁₆×C₆₇	—	4	1	no	—
401	SD₁₆×C₆₇	—	4	1	no	—
402	SD₁₆×C₆₇	—	4	1	no	—
403	SD₁₆×C₆₇	—	4	1	no	—
404	D₈×C₆₇	—	4	1	no	—
405	D₈×C₆₇	—	4	1	no	—
406	M₁₆×C₆₇	—	2	2	no	—
407	M₁₆×C₆₇	—	2	2	no	—
408	M₁₆×C₆₇	—	4	2	no	—
409	M₁₆×C₆₇	—	4	2	no	—
410	C₂×C₈×C₆₇	—	2	2	no	—
411	C₂×C₈×C₆₇	—	2	2	no	—
412	C₂×C₈×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	1	yes	characteristic
417	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₆₇	—	2	2	no	—
421	C₄⋊C₄×C₆₇	—	2	2	no	—
422	C₄⋊C₄×C₆₇	—	2	2	no	—
423	C₄⋊C₄×C₆₇	—	2	2	no	—
424	C₄⋊C₄×C₆₇	—	2	2	no	—
425	C₄⋊C₄×C₆₇	—	2	2	no	—
426	C₄⋊C₄×C₆₇	—	2	1	no	—
427	C₄⋊C₄×C₆₇	—	2	1	no	—
428	C₄⋊C₄×C₆₇	—	2	2	no	—
429	C₄⋊C₄×C₆₇	—	2	2	no	—
430	C₄⋊C₄×C₆₇	—	2	1	no	—
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	—	2	1	no	—
433	C₄⋊C₄×C₆₇	—	2	2	no	—
434	C₄⋊C₄×C₆₇	—	2	2	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	C₂×D₄	1	2	yes	—
440	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
441	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
442	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
443	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
445	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
446	C₂²⋊C₄×C₆₇	—	2	2	no	—
447	C₂²⋊C₄×C₆₇	—	2	2	no	—
448	C₂²⋊C₄×C₆₇	—	2	1	no	—
449	C₂²⋊C₄×C₆₇	—	2	2	no	—
450	C₂²⋊C₄×C₆₇	—	2	2	no	—
451	C₂²⋊C₄×C₆₇	—	2	2	no	—
452	C₂²⋊C₄×C₆₇	—	2	2	no	—
453	C₂²⋊C₄×C₆₇	—	2	1	no	—
454	C₂²⋊C₄×C₆₇	—	2	1	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	2	no	—
460	C₂²⋊C₄×C₆₇	—	2	2	no	—
461	C₂²⋊C₄×C₆₇	—	2	2	no	—
462	C₂²⋊C₄×C₆₇	—	2	2	no	—
463	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
467	C₄²×C₆₇	—	2	1	no	—
468	C₄²×C₆₇	—	2	1	no	—
469	C₄²×C₆₇	—	2	1	no	—
470	C₄²×C₆₇	—	2	2	no	—
471	C₄²×C₆₇	—	2	2	no	—
472	C₄²×C₆₇	—	2	2	no	—
473	C₄²×C₆₇	—	2	2	no	—
474	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
475	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
476	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
477	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
478	C₂³×C₆₇	—	2	1	no	—
479	C₂³×C₆₇	—	2	1	no	—
480	C₂³×C₆₇	—	2	1	no	—
481	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
482	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
483	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
484	Q₈×C₆₇	—	2	4	no	—
485	Q₈×C₆₇	—	2	2	no	—
486	Q₈×C₆₇	—	2	2	no	—
487	Q₈×C₆₇	—	2	2	no	—
488	Q₈×C₆₇	—	2	1	no	—
489	Q₈×C₆₇	—	2	1	no	—
490	Q₈×C₆₇	—	2	1	no	—
491	Q₈×C₆₇	—	2	1	no	—
492	Q₈×C₆₇	—	2	1	no	—
493	Q₈×C₆₇	—	2	1	no	—
494	Q₈×C₆₇	—	4	4	no	—
495	Q₈×C₆₇	—	4	4	no	—
496	Q₈×C₆₇	C₂×#41	1	4	yes	—
497	D₄×C₆₇	—	2	4	no	—
498	D₄×C₆₇	—	2	4	no	—
499	D₄×C₆₇	—	2	2	no	—
500	D₄×C₆₇	—	2	2	no	—
501	D₄×C₆₇	—	2	1	no	—
502	D₄×C₆₇	—	2	1	no	—
503	D₄×C₆₇	—	2	1	no	—
504	D₄×C₆₇	—	2	1	no	—
505	D₄×C₆₇	—	2	1	no	—
506	D₄×C₆₇	—	2	1	no	—
507	D₄×C₆₇	—	4	2	no	—
508	D₄×C₆₇	—	4	2	no	—
509	D₄×C₆₇	—	4	4	no	—
510	D₄×C₆₇	—	4	4	no	—
511	D₄×C₆₇	—	4	2	no	—
512	D₄×C₆₇	—	4	2	no	—
513	D₄×C₆₇	—	4	2	no	—
514	D₄×C₆₇	—	4	2	no	—
515	D₄×C₆₇	—	8	1	no	—
516	D₄×C₆₇	—	8	2	no	—
517	D₄×C₆₇	—	8	2	no	—
518	D₄×C₆₇	—	8	2	no	—
519	D₄×C₆₇	—	8	2	no	—
520	C₂×C₄×C₆₇	—	2	4	no	—
521	C₂×C₄×C₆₇	—	2	2	no	—
522	C₂×C₄×C₆₇	—	2	2	no	—
523	C₂×C₄×C₆₇	—	2	2	no	—
524	C₂×C₄×C₆₇	—	2	2	no	—
525	C₂×C₄×C₆₇	—	2	2	no	—
526	C₂×C₄×C₆₇	—	2	1	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	1	no	—
529	C₂×C₄×C₆₇	—	2	2	no	—
530	C₂×C₄×C₆₇	—	2	2	no	—
531	C₂×C₄×C₆₇	—	2	2	no	—
532	C₂×C₄×C₆₇	—	2	1	no	—
533	C₂×C₄×C₆₇	—	2	1	no	—
534	C₂×C₄×C₆₇	—	4	1	no	—
535	C₂×C₄×C₆₇	—	4	1	no	—
536	C₂×C₄×C₆₇	—	4	4	no	—
537	C₂×C₄×C₆₇	—	4	4	no	—
538	C₂×C₄×C₆₇	—	4	4	no	—
539	C₂×C₄×C₆₇	—	4	4	no	—
540	C₂×C₄×C₆₇	—	4	2	no	—
541	C₂×C₄×C₆₇	—	4	2	no	—
542	C₂×C₄×C₆₇	—	4	2	no	—
543	C₂×C₄×C₆₇	—	8	1	no	—
544	C₂×C₄×C₆₇	—	8	1	no	—
545	C₂×C₄×C₆₇	—	8	2	no	—
546	C₂×C₄×C₆₇	—	8	1	no	—
547	C₂×C₄×C₆₇	—	8	1	no	—
548	C₂×C₄×C₆₇	—	8	2	no	—
549	C₂×C₄×C₆₇	—	8	1	no	—
550	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
554	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
558	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
559	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
560	C₈×C₆₇	—	2	2	no	—
561	C₈×C₆₇	—	2	1	no	—
562	C₈×C₆₇	—	2	1	no	—
563	C₈×C₆₇	—	2	1	no	—
564	C₈×C₆₇	—	2	1	no	—
565	C₈×C₆₇	—	2	2	no	—
566	C₂²×C₆₇	—	2	1	no	—
567	C₂²×C₆₇	—	2	1	no	—
568	C₂²×C₆₇	—	2	2	no	—
569	C₂²×C₆₇	—	2	2	no	—
570	C₂²×C₆₇	—	2	2	no	—
571	C₂²×C₆₇	—	2	2	no	—
572	C₂²×C₆₇	—	2	2	no	—
573	C₂²×C₆₇	—	2	2	no	—
574	C₂²×C₆₇	—	4	1	no	—
575	C₂²×C₆₇	—	4	1	no	—
576	C₂²×C₆₇	—	4	1	no	—
577	C₂²×C₆₇	—	4	1	no	—
578	C₂²×C₆₇	—	4	1	no	—
579	C₂²×C₆₇	—	4	1	no	—
580	C₂²×C₆₇	—	4	1	no	—
581	C₂²×C₆₇	—	4	1	no	—
582	C₂²×C₆₇	—	4	1	no	—
583	C₂²×C₆₇	#546	1	2	yes	—
584	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
585	C₄×C₆₇	—	2	1	no	—
586	C₄×C₆₇	—	2	1	no	—
587	C₄×C₆₇	—	2	1	no	—
588	C₄×C₆₇	—	2	1	no	—
589	C₄×C₆₇	—	2	4	no	—
590	C₄×C₆₇	—	2	2	no	—
591	C₄×C₆₇	—	2	2	no	—
592	C₄×C₆₇	—	4	1	no	—
593	C₄×C₆₇	—	4	2	no	—
594	C₄×C₆₇	—	4	2	no	—
595	C₄×C₆₇	—	4	1	no	—
596	C₄×C₆₇	—	4	2	no	—
597	C₄×C₆₇	—	4	1	no	—
598	C₄×C₆₇	—	4	1	no	—
599	C₄×C₆₇	—	4	1	no	—
600	C₄×C₆₇	#546	1	2	yes	—
601	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
602	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
603	#61204	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
604	C₂×C₆₇	—	2	2	no	—
605	C₂×C₆₇	—	4	2	no	—
606	C₂×C₆₇	—	4	2	no	—
607	C₂×C₆₇	—	8	1	no	—
608	C₂×C₆₇	—	8	1	no	—
609	C₂×C₆₇	—	8	1	no	—
610	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
611	C₂×C₆₇	#3584	1	1	yes	characteristic
612	C₂×C₆₇	#3586	1	1	yes	characteristic
613	#3512	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#3497	C₂×C₆₇	1	1	yes	characteristic, complemented
615	#3327	C₂×C₆₇	1	2	yes	complemented
616	#3326	C₂×C₆₇	1	2	yes	complemented
617	#3320	C₂×C₆₇	1	2	yes	complemented
618	#3317	C₂×C₆₇	1	2	yes	complemented
619	#3312	C₂×C₆₇	1	2	yes	complemented
620	#3309	C₂×C₆₇	1	2	yes	complemented
621	#3301	C₂×C₆₇	1	2	yes	complemented
622	#3300	C₂×C₆₇	1	2	yes	complemented
623	#3142	C₂×C₆₇	1	1	yes	characteristic, complemented
624	#3099	C₂×C₆₇	1	1	yes	characteristic, complemented
625	#3098	C₂×C₆₇	1	1	yes	characteristic, complemented
626	C₂×#479	C₂×C₆₇	1	1	yes	characteristic, complemented
627	#3061	C₂×C₆₇	1	1	yes	characteristic, complemented
628	#3060	C₂×C₆₇	1	1	yes	characteristic, complemented
629	#3035	C₂×C₆₇	1	1	yes	characteristic, complemented
630	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
631	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
632	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
633	#2935	C₂×C₆₇	1	1	yes	characteristic, complemented
634	#2898	C₂×C₆₇	1	1	yes	characteristic, complemented
635	#2898	C₂×C₆₇	1	1	yes	characteristic, complemented
636	C₆₇	#61204	1	1	yes	characteristic, direct product factor, Sylow
637	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
638	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
639	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
640	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
641	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
642	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
643	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
644	#553	—	2	2	no	—
645	#553	—	2	2	no	—
646	#553	C₂²×C₆₇	1	2	yes	—
647	#553	C₂²×C₆₇	1	2	yes	—
648	#552	C₂²×C₆₇	1	2	yes	—
649	#552	C₂²×C₆₇	1	2	yes	—
650	#550	—	2	1	no	—
651	#550	C₂²×C₆₇	1	2	yes	—
652	D₄×Q₈	—	2	1	no	—
653	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
654	#548	—	2	1	no	—
655	#548	—	2	1	no	—
656	#548	C₂²×C₆₇	1	2	yes	—
657	#548	C₂²×C₆₇	1	2	yes	—
658	#541	—	2	1	no	—
659	#540	—	2	1	no	—
660	#537	—	2	2	no	—
661	#537	C₂²×C₆₇	1	1	yes	characteristic
662	#537	C₂²×C₆₇	1	1	yes	characteristic
663	#537	C₂²×C₆₇	1	1	yes	characteristic
664	#537	C₂²×C₆₇	1	1	yes	characteristic
665	#532	—	2	2	no	—
666	#532	C₂²×C₆₇	1	1	yes	characteristic
667	#532	C₂²×C₆₇	1	1	yes	characteristic
668	#529	—	2	1	no	—
669	#529	—	2	1	no	—
670	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
671	#520	C₂²×C₆₇	1	1	yes	characteristic
672	#520	C₂²×C₆₇	1	1	yes	characteristic
673	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
674	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
675	#491	C₂²×C₆₇	1	2	yes	—
676	#490	C₂²×C₆₇	1	2	yes	—
677	#488	C₂²×C₆₇	1	2	yes	—
678	#488	C₂²×C₆₇	1	2	yes	—
679	#485	C₂²×C₆₇	1	2	yes	—
680	#485	C₂²×C₆₇	1	2	yes	—
681	#484	C₂²×C₆₇	1	2	yes	—
682	#483	C₂²×C₆₇	1	2	yes	—
683	#482	C₂²×C₆₇	1	2	yes	—
684	#482	C₂²×C₆₇	1	2	yes	—
685	#481	C₂²×C₆₇	1	2	yes	—
686	#480	C₂²×C₆₇	1	2	yes	—
687	#479	C₂²×C₆₇	1	2	yes	—
688	#479	C₂²×C₆₇	1	2	yes	—
689	#479	C₂²×C₆₇	1	2	yes	—
690	#479	C₂²×C₆₇	1	2	yes	—
691	#470	C₂²×C₆₇	1	2	yes	—
692	#469	C₂²×C₆₇	1	2	yes	—
693	#468	C₂²×C₆₇	1	2	yes	—
694	#468	C₂²×C₆₇	1	2	yes	—
695	#467	C₂²×C₆₇	1	2	yes	—
696	#466	C₂²×C₆₇	1	2	yes	—
697	#465	C₂²×C₆₇	1	2	yes	—
698	#465	C₂²×C₆₇	1	2	yes	—
699	#464	C₂²×C₆₇	1	1	yes	characteristic
700	#464	C₂²×C₆₇	1	1	yes	characteristic
701	#463	C₂²×C₆₇	1	1	yes	characteristic
702	#463	C₂²×C₆₇	1	1	yes	characteristic
703	#462	C₂²×C₆₇	1	1	yes	characteristic
704	#461	C₂²×C₆₇	1	1	yes	characteristic
705	#460	C₂²×C₆₇	1	1	yes	characteristic
706	#459	C₂²×C₆₇	1	1	yes	characteristic
707	#452	C₂²×C₆₇	1	2	yes	—
708	#452	C₂²×C₆₇	1	2	yes	—
709	#451	C₂²×C₆₇	1	2	yes	—
710	#451	C₂²×C₆₇	1	2	yes	—
711	#449	C₂²×C₆₇	1	2	yes	—
712	#449	C₂²×C₆₇	1	2	yes	—
713	#448	C₂²×C₆₇	1	2	yes	—
714	#448	C₂²×C₆₇	1	2	yes	—
715	#441	C₂²×C₆₇	1	2	yes	—
716	#440	C₂²×C₆₇	1	2	yes	—
717	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
718	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
719	#436	C₂²×C₆₇	1	2	yes	—
720	#435	C₂²×C₆₇	1	2	yes	—
721	#435	C₂²×C₆₇	1	2	yes	—
722	C₈×D₄	C₂²×C₆₇	1	2	yes	—
723	#428	C₂²×C₆₇	1	1	yes	characteristic
724	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
725	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
726	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
727	#419	C₂²×C₆₇	1	1	yes	characteristic
728	#419	C₂²×C₆₇	1	2	yes	—
729	#419	C₂²×C₆₇	1	2	yes	—
730	#417	C₂²×C₆₇	1	1	yes	characteristic
731	#417	C₂²×C₆₇	1	1	yes	characteristic
732	#417	C₂²×C₆₇	1	1	yes	characteristic
733	#417	C₂²×C₆₇	1	1	yes	characteristic
734	#417	C₂²×C₆₇	1	2	yes	—
735	#417	C₂²×C₆₇	1	2	yes	—
736	#417	C₂²×C₆₇	1	1	yes	characteristic
737	#416	C₂²×C₆₇	1	1	yes	characteristic
738	#416	C₂²×C₆₇	1	1	yes	characteristic
739	#416	C₂²×C₆₇	1	2	yes	—
740	#416	C₂²×C₆₇	1	2	yes	—
741	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
742	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
743	C₂×#103	C₂²×C₆₇	1	2	yes	—
744	C₂×#103	C₂²×C₆₇	1	2	yes	—
745	#408	C₂²×C₆₇	1	1	yes	characteristic
746	#408	C₂²×C₆₇	1	1	yes	characteristic
747	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
748	2₋¹⁺⁴	—	2	4	no	—
749	2₋¹⁺⁴	—	2	4	no	—
750	2₋¹⁺⁴	—	4	2	no	—
751	2₋¹⁺⁴	—	4	2	no	—
752	C₂×#41	—	2	2	no	—
753	C₂×#41	—	2	2	no	—
754	C₂×#41	—	2	1	no	—
755	C₂×#41	—	2	1	no	—
756	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
757	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
758	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
759	C₂×#41	C₂³×C₆₇	1	2	yes	—
760	C₂×#41	C₂³×C₆₇	1	2	yes	—
761	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
762	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
763	C₂²×Q₈	—	2	1	no	—
764	C₂²×Q₈	—	2	1	no	—
765	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
766	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
767	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
768	#137	—	2	4	no	—
769	#135	—	4	2	no	—
770	#135	—	4	2	no	—
771	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
772	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
773	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
774	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
776	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
777	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
778	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
779	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
780	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
781	#131	—	4	2	no	—
782	#131	—	4	2	no	—
783	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
784	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
785	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
786	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
787	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
788	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
789	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
790	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
791	C₄⋊Q₈	—	2	2	no	—
792	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
793	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
794	#127	—	2	2	no	—
795	#127	D₄×C₆₇	1	1	yes	characteristic
796	#127	C₂³×C₆₇	1	1	yes	characteristic
797	#126	—	2	2	no	—
798	#126	—	2	2	no	—
799	#126	—	2	2	no	—
800	#126	—	2	2	no	—
801	#125	—	2	2	no	—
802	#125	—	2	2	no	—
803	#125	—	2	1	no	—
804	#125	—	2	1	no	—
805	#125	C₂³×C₆₇	1	2	yes	—
806	#125	C₂³×C₆₇	1	2	yes	—
807	#124	—	2	2	no	—
808	#124	—	2	2	no	—
809	#124	D₄×C₆₇	1	1	yes	characteristic
810	#124	D₄×C₆₇	1	1	yes	characteristic
811	#124	C₂³×C₆₇	1	1	yes	characteristic
812	#124	C₂³×C₆₇	1	1	yes	characteristic
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	C₂²⋊Q₈	—	2	1	no	—
818	C₂²⋊Q₈	—	2	1	no	—
819	C₂²⋊Q₈	—	2	1	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	—	2	2	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	—	2	2	no	—
825	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
827	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
828	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	2	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	1	no	—
836	#121	—	2	1	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	—	2	1	no	—
842	#121	—	2	1	no	—
843	#121	—	2	2	no	—
844	#121	—	2	2	no	—
845	#121	D₄×C₆₇	1	2	yes	—
846	#121	D₄×C₆₇	1	2	yes	—
847	#121	C₂³×C₆₇	1	2	yes	—
848	#121	C₂³×C₆₇	1	2	yes	—
849	#121	C₂³×C₆₇	1	2	yes	—
850	#121	C₂³×C₆₇	1	2	yes	—
851	C₄×Q₈	—	2	1	no	—
852	C₄×Q₈	—	2	1	no	—
853	C₄×Q₈	—	2	1	no	—
854	C₄×Q₈	—	2	1	no	—
855	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
856	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
857	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
858	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	2	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	2	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
874	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
875	C₄×D₄	C₂³×C₆₇	1	2	yes	—
876	C₄×D₄	C₂³×C₆₇	1	2	yes	—
877	#117	—	2	2	no	—
878	#117	—	2	2	no	—
879	#117	—	2	1	no	—
880	#117	C₂³×C₆₇	1	1	yes	characteristic
881	#117	C₂³×C₆₇	1	2	yes	—
882	#117	C₂³×C₆₇	1	2	yes	—
883	C₂×C₄⋊C₄	—	2	1	no	—
884	C₂×C₄⋊C₄	—	2	1	no	—
885	C₂×C₄⋊C₄	—	2	1	no	—
886	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
888	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
889	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
890	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
891	C₂×C₄²	—	2	1	no	—
892	C₂×C₄²	—	2	1	no	—
893	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
894	#107	C₂³×C₆₇	1	2	yes	—
895	#107	C₂³×C₆₇	1	2	yes	—
896	#107	C₂³×C₆₇	1	2	yes	—
897	#106	C₂³×C₆₇	1	2	yes	—
898	#106	C₂³×C₆₇	1	2	yes	—
899	#106	C₂³×C₆₇	1	2	yes	—
900	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
901	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
902	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
903	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
904	#103	C₂³×C₆₇	1	2	yes	—
905	#103	C₂³×C₆₇	1	2	yes	—
906	#103	C₂³×C₆₇	1	1	yes	characteristic
907	#103	C₂³×C₆₇	1	1	yes	characteristic
908	#103	C₂³×C₆₇	1	2	yes	—
909	#103	C₂³×C₆₇	1	2	yes	—
910	#103	C₂³×C₆₇	1	2	yes	—
911	#103	C₂³×C₆₇	1	2	yes	—
912	#103	C₂³×C₆₇	1	2	yes	—
913	#103	C₂³×C₆₇	1	2	yes	—
914	#103	C₂³×C₆₇	1	1	yes	characteristic
915	#103	C₂³×C₆₇	1	1	yes	characteristic
916	#103	C₂³×C₆₇	1	2	yes	—
917	#103	C₂³×C₆₇	1	2	yes	—
918	#103	C₂³×C₆₇	1	2	yes	—
919	#102	C₂³×C₆₇	1	1	yes	characteristic
920	#102	C₂³×C₆₇	1	1	yes	characteristic
921	#102	C₂³×C₆₇	1	1	yes	characteristic
922	#102	C₂³×C₆₇	1	1	yes	characteristic
923	#102	C₂³×C₆₇	1	2	yes	—
924	#102	C₂³×C₆₇	1	2	yes	—
925	#102	C₂³×C₆₇	1	2	yes	—
926	#102	C₂³×C₆₇	1	2	yes	—
927	#102	C₂³×C₆₇	1	2	yes	—
928	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
930	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
931	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
932	#97	C₂³×C₆₇	1	2	yes	—
933	C₄×C₈	C₂³×C₆₇	1	2	yes	—
934	#41	—	2	2	no	—
935	#41	—	2	2	no	—
936	#41	—	2	2	no	—
937	#41	—	2	2	no	—
938	#41	—	2	4	no	—
939	#41	—	2	4	no	—
940	#41	—	2	2	no	—
941	#41	—	2	2	no	—
942	#41	—	2	2	no	—
943	#41	—	2	2	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	8	no	—
949	#41	—	4	8	no	—
950	#41	—	4	4	no	—
951	#41	—	4	4	no	—
952	C₂×Q₈	—	2	1	no	—
953	C₂×Q₈	—	2	2	no	—
954	C₂×Q₈	—	2	2	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	—	2	4	no	—
957	C₂×Q₈	—	2	4	no	—
958	C₂×Q₈	—	4	2	no	—
959	C₂×Q₈	—	4	2	no	—
960	C₂×Q₈	—	4	4	no	—
961	C₂×Q₈	—	4	4	no	—
962	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
963	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
964	C₂×Q₈	#41×C₆₇	1	4	yes	—
965	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
966	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
967	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
968	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
969	C₂×D₄	—	2	1	no	—
970	C₂×D₄	—	2	1	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
981	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
982	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
983	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
984	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
985	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
986	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
987	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
988	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1005	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1006	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1007	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1008	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1009	Q₁₆	—	2	4	no	—
1010	Q₁₆	—	4	1	no	—
1011	Q₁₆	—	4	1	no	—
1012	SD₁₆	—	2	4	no	—
1013	SD₁₆	—	4	1	no	—
1014	SD₁₆	—	4	1	no	—
1015	SD₁₆	—	4	1	no	—
1016	SD₁₆	—	4	1	no	—
1017	D₈	—	4	1	no	—
1018	D₈	—	4	1	no	—
1019	M₁₆	—	2	2	no	—
1020	M₁₆	—	2	2	no	—
1021	M₁₆	—	4	2	no	—
1022	M₁₆	—	4	2	no	—
1023	C₂×C₈	—	2	2	no	—
1024	C₂×C₈	—	2	2	no	—
1025	C₂×C₈	—	4	2	no	—
1026	C₂×C₈	—	4	2	no	—
1027	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1028	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1029	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1030	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1031	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1032	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	2	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	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1053	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1054	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1055	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1056	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1057	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1058	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1078	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1079	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1080	C₄²	—	2	1	no	—
1081	C₄²	—	2	1	no	—
1082	C₄²	—	2	1	no	—
1083	C₄²	—	2	2	no	—
1084	C₄²	—	2	2	no	—
1085	C₄²	—	2	2	no	—
1086	C₄²	—	2	2	no	—
1087	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1088	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1089	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1090	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	1	no	—
1093	C₂³	—	2	1	no	—
1094	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1095	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1096	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1097	Q₈	—	2	4	no	—
1098	Q₈	—	2	2	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	2	no	—
1101	Q₈	—	2	1	no	—
1102	Q₈	—	2	1	no	—
1103	Q₈	—	2	1	no	—
1104	Q₈	—	2	1	no	—
1105	Q₈	—	2	1	no	—
1106	Q₈	—	2	1	no	—
1107	Q₈	—	4	4	no	—
1108	Q₈	—	4	4	no	—
1109	Q₈	C₂×#41×C₆₇	1	4	yes	—
1110	D₄	—	2	4	no	—
1111	D₄	—	2	4	no	—
1112	D₄	—	2	2	no	—
1113	D₄	—	2	2	no	—
1114	D₄	—	2	1	no	—
1115	D₄	—	2	1	no	—
1116	D₄	—	2	1	no	—
1117	D₄	—	2	1	no	—
1118	D₄	—	2	1	no	—
1119	D₄	—	2	1	no	—
1120	D₄	—	4	2	no	—
1121	D₄	—	4	2	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	8	1	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	2	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	C₂×C₄	—	2	4	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	4	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	4	2	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	1	no	—
1160	C₂×C₄	—	8	1	no	—
1161	C₂×C₄	—	8	2	no	—
1162	C₂×C₄	—	8	1	no	—
1163	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1166	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1167	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1168	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1169	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1170	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1171	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1172	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1173	C₈	—	2	2	no	—
1174	C₈	—	2	1	no	—
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	1	no	—
1178	C₈	—	2	2	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	#546×C₆₇	1	2	yes	—
1197	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1198	C₄	—	2	1	no	—
1199	C₄	—	2	1	no	—
1200	C₄	—	2	1	no	—
1201	C₄	—	2	1	no	—
1202	C₄	—	2	4	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	2	2	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	2	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	#546×C₆₇	1	2	yes	—
1214	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1215	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1216	C₂	—	2	2	no	—
1217	C₂	—	4	2	no	—
1218	C₂	—	4	2	no	—
1219	C₂	—	8	1	no	—
1220	C₂	—	8	1	no	—
1221	C₂	—	8	1	no	—
1222	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1223	C₂	C₆₇×#3584	1	1	yes	characteristic
1224	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 ◁ #532×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×#3497	C₂	semidirect
3. C₆₇×#3327	C₂	semidirect
4. C₆₇×#3326	C₂	semidirect
5. C₆₇×#3320	C₂	semidirect
6. C₆₇×#3317	C₂	semidirect
7. C₆₇×#3312	C₂	semidirect
8. C₆₇×#3309	C₂	semidirect
9. C₆₇×#3301	C₂	semidirect
10. C₆₇×#3300	C₂	semidirect
11. C₆₇×#3142	C₂	semidirect
12. C₆₇×#3099	C₂	semidirect
13. C₆₇×#3098	C₂	semidirect
14. C₂×#479×C₆₇	C₂	semidirect
15. C₆₇×#3061	C₂	semidirect
16. C₆₇×#3060	C₂	semidirect
17. C₆₇×#3035	C₂	semidirect
18. C₆₇×#3013	C₂	semidirect
19. C₆₇×#3013	C₂	semidirect
20. C₄×#137×C₆₇	C₂	semidirect
21. C₆₇×#2935	C₂	semidirect
22. C₆₇×#2898	C₂	semidirect
23. C₆₇×#2898	C₂	semidirect
603. #61204	C₆₇	direct (N × H)
613. #3512	C₂×C₆₇	semidirect
614. #3497	C₂×C₆₇	semidirect
615. #3327	C₂×C₆₇	semidirect
616. #3326	C₂×C₆₇	semidirect
617. #3320	C₂×C₆₇	semidirect
618. #3317	C₂×C₆₇	semidirect
619. #3312	C₂×C₆₇	semidirect
620. #3309	C₂×C₆₇	semidirect
621. #3301	C₂×C₆₇	semidirect
622. #3300	C₂×C₆₇	semidirect
623. #3142	C₂×C₆₇	semidirect
624. #3099	C₂×C₆₇	semidirect
625. #3098	C₂×C₆₇	semidirect
626. C₂×#479	C₂×C₆₇	semidirect
627. #3061	C₂×C₆₇	semidirect
628. #3060	C₂×C₆₇	semidirect
629. #3035	C₂×C₆₇	semidirect
630. #3013	C₂×C₆₇	semidirect
631. #3013	C₂×C₆₇	semidirect
632. C₄×#137	C₂×C₆₇	semidirect
633. #2935	C₂×C₆₇	semidirect
634. #2898	C₂×C₆₇	semidirect
635. #2898	C₂×C₆₇	semidirect
636. C₆₇	#61204	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×#3497	2
C₆₇×#3327	2
C₆₇×#3326	2
C₆₇×#3320	2
C₆₇×#3317	2
C₆₇×#3312	2
C₆₇×#3309	2
C₆₇×#3301	2
C₆₇×#3300	2
C₆₇×#3142	2
C₆₇×#3099	2
C₆₇×#3098	2
C₂×#479×C₆₇	2
C₆₇×#3061	2
C₆₇×#3060	2
C₆₇×#3035	2
C₆₇×#3013	2
C₄×#137×C₆₇	2
C₆₇×#2935	2
C₆₇×#2898	2
#61204	67

Subgroups — C67×#61204 #30740455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61204 #30740455