Subgroups — C₆₇×#61736 #30740987

Order 17152.

1822 conjugacy classes of subgroups.

The subgroup lattice has 1296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#553×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3351	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3350	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3345	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3337	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3326	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3320	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3307	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3301	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3236	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3232	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3194	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3193	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3188	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3187	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3101	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3095	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3092	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#483×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	#556×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	#554×C₆₇	—	2	1	no	—
26	#553×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	C₂²	1	2	yes	—
31	#553×C₆₇	C₂²	1	2	yes	—
32	#553×C₆₇	C₂²	1	2	yes	—
33	#553×C₆₇	C₂²	1	2	yes	—
34	#552×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	#552×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#551×C₆₇	—	2	1	no	—
37	#551×C₆₇	—	2	1	no	—
38	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#548×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#548×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#546×C₆₇	—	2	1	no	—
44	#542×C₆₇	—	2	1	no	—
45	#539×C₆₇	—	2	1	no	—
46	#539×C₆₇	—	2	1	no	—
47	#533×C₆₇	C₂²	1	1	yes	characteristic
48	#529×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×#126×C₆₇	—	2	1	no	—
50	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
51	#525×C₆₇	C₂²	1	1	yes	characteristic
52	#525×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×#123×C₆₇	—	2	1	no	—
54	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
56	C₂×#121×C₆₇	—	2	1	no	—
57	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
59	#520×C₆₇	—	2	1	no	—
60	C₂×C₄×D₄×C₆₇	—	2	1	no	—
61	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
64	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
65	#501×C₆₇	C₂²	1	2	yes	complemented
66	#499×C₆₇	C₂²	1	2	yes	complemented
67	#491×C₆₇	C₂²	1	2	yes	complemented
68	#488×C₆₇	C₂²	1	2	yes	complemented
69	#485×C₆₇	C₂²	1	2	yes	complemented
70	#485×C₆₇	C₂²	1	2	yes	complemented
71	#485×C₆₇	C₂²	1	2	yes	complemented
72	#484×C₆₇	C₂²	1	1	yes	characteristic
73	#484×C₆₇	C₂²	1	1	yes	characteristic
74	#484×C₆₇	C₂²	1	1	yes	characteristic
75	#484×C₆₇	C₂²	1	2	yes	complemented
76	#483×C₆₇	C₂²	1	1	yes	characteristic
77	#483×C₆₇	C₂²	1	1	yes	characteristic
78	#483×C₆₇	C₂²	1	1	yes	characteristic
79	#483×C₆₇	C₂²	1	1	yes	characteristic
80	#483×C₆₇	C₂²	1	1	yes	characteristic
81	#483×C₆₇	C₂²	1	1	yes	characteristic
82	#483×C₆₇	C₂²	1	2	yes	complemented
83	#483×C₆₇	C₂²	1	2	yes	complemented
84	#482×C₆₇	C₂²	1	2	yes	complemented
85	#482×C₆₇	C₂²	1	2	yes	complemented
86	#482×C₆₇	C₂²	1	2	yes	complemented
87	#481×C₆₇	C₂²	1	1	yes	characteristic
88	#481×C₆₇	C₂²	1	2	yes	complemented
89	#481×C₆₇	C₂²	1	2	yes	complemented
90	#480×C₆₇	C₂²	1	1	yes	characteristic
91	#480×C₆₇	C₂²	1	1	yes	characteristic
92	#480×C₆₇	C₂²	1	2	yes	complemented
93	#479×C₆₇	C₂²	1	2	yes	complemented
94	#479×C₆₇	C₂²	1	2	yes	complemented
95	#479×C₆₇	C₂²	1	2	yes	complemented
96	#478×C₆₇	C₂²	1	2	yes	complemented
97	#478×C₆₇	C₂²	1	2	yes	complemented
98	#476×C₆₇	C₂²	1	2	yes	complemented
99	#469×C₆₇	C₂²	1	2	yes	complemented
100	#468×C₆₇	C₂²	1	2	yes	complemented
101	#468×C₆₇	C₂²	1	2	yes	complemented
102	#468×C₆₇	C₂²	1	2	yes	complemented
103	#466×C₆₇	C₂²	1	2	yes	complemented
104	#465×C₆₇	C₂²	1	2	yes	complemented
105	#465×C₆₇	C₂²	1	2	yes	complemented
106	#465×C₆₇	C₂²	1	2	yes	complemented
107	#463×C₆₇	C₂²	1	2	yes	complemented
108	#461×C₆₇	C₂²	1	2	yes	complemented
109	#450×C₆₇	C₂²	1	1	yes	characteristic
110	#450×C₆₇	C₂²	1	1	yes	characteristic
111	#450×C₆₇	C₂²	1	1	yes	characteristic
112	#449×C₆₇	C₂²	1	2	yes	complemented
113	#449×C₆₇	C₂²	1	2	yes	complemented
114	#448×C₆₇	C₂²	1	2	yes	complemented
115	#448×C₆₇	C₂²	1	2	yes	complemented
116	#447×C₆₇	C₂²	1	1	yes	characteristic
117	#442×C₆₇	C₂²	1	2	yes	complemented
118	#440×C₆₇	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
121	#436×C₆₇	C₂²	1	2	yes	complemented
122	#435×C₆₇	C₂²	1	2	yes	complemented
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
125	#432×C₆₇	C₂²	1	1	yes	characteristic
126	#431×C₆₇	C₂²	1	1	yes	characteristic
127	#428×C₆₇	C₂²	1	2	yes	complemented
128	#428×C₆₇	C₂²	1	2	yes	complemented
129	#427×C₆₇	C₂²	1	2	yes	complemented
130	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
131	#419×C₆₇	C₂²	1	2	yes	complemented
132	#417×C₆₇	C₂²	1	2	yes	complemented
133	#416×C₆₇	C₂²	1	2	yes	complemented
134	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
135	#407×C₆₇	C₂²	1	1	yes	characteristic
136	#407×C₆₇	C₂²	1	1	yes	characteristic
137	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
138	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
139	C₂×#41×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₆₇	—	2	1	no	—
145	C₂²×D₄×C₆₇	—	2	1	no	—
146	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
147	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₆₇	—	2	1	no	—
149	C₂³×C₄×C₆₇	—	2	1	no	—
150	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×D₈×C₆₇	C₂³	1	2	yes	—
156	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
159	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₇	—	2	1	no	—
161	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	#126×C₆₇	—	2	2	no	—
164	#126×C₆₇	—	2	2	no	—
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	#125×C₆₇	—	2	1	no	—
173	#125×C₆₇	—	2	1	no	—
174	#125×C₆₇	—	2	1	no	—
175	#125×C₆₇	—	2	1	no	—
176	#125×C₆₇	—	2	1	no	—
177	#125×C₆₇	C₂³	1	1	yes	characteristic
178	#125×C₆₇	C₂³	1	2	yes	—
179	#125×C₆₇	C₂³	1	2	yes	—
180	#124×C₆₇	—	2	1	no	—
181	#124×C₆₇	—	2	1	no	—
182	#124×C₆₇	—	2	1	no	—
183	#124×C₆₇	C₂³	1	1	yes	characteristic
184	#123×C₆₇	—	2	1	no	—
185	#123×C₆₇	—	2	1	no	—
186	#123×C₆₇	—	2	1	no	—
187	#123×C₆₇	—	2	1	no	—
188	#123×C₆₇	—	2	1	no	—
189	#123×C₆₇	—	2	2	no	—
190	#123×C₆₇	—	2	2	no	—
191	#123×C₆₇	—	2	2	no	—
192	#123×C₆₇	—	2	2	no	—
193	#123×C₆₇	—	2	1	no	—
194	#123×C₆₇	—	2	1	no	—
195	#123×C₆₇	—	2	1	no	—
196	#123×C₆₇	—	2	1	no	—
197	C₂²⋊Q₈×C₆₇	—	2	1	no	—
198	C₂²⋊Q₈×C₆₇	—	2	1	no	—
199	C₂²⋊Q₈×C₆₇	—	2	1	no	—
200	C₂²⋊Q₈×C₆₇	—	2	1	no	—
201	C₂²⋊Q₈×C₆₇	—	2	1	no	—
202	C₂²⋊Q₈×C₆₇	—	2	1	no	—
203	C₂²⋊Q₈×C₆₇	—	2	1	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	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
209	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
210	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
211	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
214	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
215	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
216	#121×C₆₇	—	2	2	no	—
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	C₂³	1	2	yes	—
228	#121×C₆₇	C₂³	1	2	yes	—
229	#121×C₆₇	C₂³	1	2	yes	—
230	#121×C₆₇	C₂³	1	2	yes	—
231	#121×C₆₇	C₂³	1	1	yes	characteristic
232	#121×C₆₇	C₂³	1	1	yes	characteristic
233	#121×C₆₇	C₂³	1	1	yes	characteristic
234	#120×C₆₇	—	2	1	no	—
235	#120×C₆₇	—	2	1	no	—
236	C₄×Q₈×C₆₇	—	2	1	no	—
237	C₄×Q₈×C₆₇	—	2	1	no	—
238	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₇	—	2	1	no	—
242	C₄×D₄×C₆₇	—	2	1	no	—
243	C₄×D₄×C₆₇	—	2	1	no	—
244	C₄×D₄×C₆₇	—	2	1	no	—
245	C₄×D₄×C₆₇	—	2	1	no	—
246	C₄×D₄×C₆₇	—	2	1	no	—
247	C₄×D₄×C₆₇	—	2	2	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	1	no	—
254	C₄×D₄×C₆₇	—	2	1	no	—
255	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
256	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
257	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
258	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
259	C₄×D₄×C₆₇	C₂³	1	2	yes	—
260	C₄×D₄×C₆₇	C₂³	1	2	yes	—
261	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
266	#117×C₆₇	—	2	1	no	—
267	#117×C₆₇	—	2	1	no	—
268	#117×C₆₇	—	2	1	no	—
269	#117×C₆₇	—	2	1	no	—
270	#117×C₆₇	—	2	1	no	—
271	#117×C₆₇	—	2	1	no	—
272	#117×C₆₇	C₂³	1	1	yes	characteristic
273	#117×C₆₇	C₂³	1	1	yes	characteristic
274	#117×C₆₇	C₂³	1	2	yes	—
275	#117×C₆₇	C₂³	1	2	yes	—
276	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
277	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
278	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
279	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
280	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
281	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
282	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
283	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
284	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
291	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
292	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
293	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
294	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
300	C₂×C₄²×C₆₇	—	2	1	no	—
301	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
302	#107×C₆₇	C₂³	1	2	yes	—
303	#107×C₆₇	C₂³	1	2	yes	—
304	#107×C₆₇	C₂³	1	2	yes	—
305	#107×C₆₇	C₂³	1	2	yes	—
306	#107×C₆₇	C₂³	1	2	yes	—
307	#106×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	#106×C₆₇	C₂³	1	2	yes	—
313	#106×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	#103×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	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
337	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
338	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
339	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
340	#97×C₆₇	C₂³	1	2	yes	—
341	C₄×C₈×C₆₇	C₂³	1	2	yes	—
342	C₂⁴×C₆₇	—	2	1	no	—
343	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
344	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
345	#41×C₆₇	—	4	2	no	—
346	#41×C₆₇	—	4	2	no	—
347	#41×C₆₇	—	4	4	no	—
348	C₂×Q₈×C₆₇	—	2	1	no	—
349	C₂×Q₈×C₆₇	—	2	1	no	—
350	C₂×Q₈×C₆₇	—	2	1	no	—
351	C₂×Q₈×C₆₇	—	4	2	no	—
352	C₂×Q₈×C₆₇	—	4	2	no	—
353	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
354	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
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	1	no	—
362	C₂×D₄×C₆₇	—	2	1	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	—	4	2	no	—
367	C₂×D₄×C₆₇	—	4	2	no	—
368	C₂×D₄×C₆₇	—	4	4	no	—
369	C₂×D₄×C₆₇	—	8	2	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	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
376	C₂²×C₄×C₆₇	—	2	1	no	—
377	C₂²×C₄×C₆₇	—	2	1	no	—
378	C₂²×C₄×C₆₇	—	2	1	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	1	no	—
383	C₂²×C₄×C₆₇	—	2	2	no	—
384	C₂²×C₄×C₆₇	—	2	2	no	—
385	C₂²×C₄×C₆₇	—	2	1	no	—
386	C₂²×C₄×C₆₇	—	2	1	no	—
387	C₂²×C₄×C₆₇	—	2	1	no	—
388	C₂²×C₄×C₆₇	—	2	2	no	—
389	C₂²×C₄×C₆₇	—	2	2	no	—
390	C₂²×C₄×C₆₇	—	4	2	no	—
391	C₂²×C₄×C₆₇	—	4	2	no	—
392	C₂²×C₄×C₆₇	—	8	2	no	—
393	C₂²×C₄×C₆₇	—	8	2	no	—
394	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
407	SD₁₆×C₆₇	—	4	2	no	—
408	SD₁₆×C₆₇	—	4	2	no	—
409	SD₁₆×C₆₇	—	4	2	no	—
410	D₈×C₆₇	—	4	2	no	—
411	M₁₆×C₆₇	—	4	2	no	—
412	M₁₆×C₆₇	—	4	2	no	—
413	C₂×C₈×C₆₇	—	4	2	no	—
414	C₂×C₈×C₆₇	—	4	2	no	—
415	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
416	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
417	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
418	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
419	C₄⋊C₄×C₆₇	—	2	1	no	—
420	C₄⋊C₄×C₆₇	—	2	1	no	—
421	C₄⋊C₄×C₆₇	—	2	2	no	—
422	C₄⋊C₄×C₆₇	—	2	2	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	2	no	—
427	C₄⋊C₄×C₆₇	—	2	2	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	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	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	—	2	1	no	—
443	C₄⋊C₄×C₆₇	—	2	1	no	—
444	C₄⋊C₄×C₆₇	—	2	1	no	—
445	C₄⋊C₄×C₆₇	—	2	1	no	—
446	C₄⋊C₄×C₆₇	—	2	1	no	—
447	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
456	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
457	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
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	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	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	2	no	—
476	C₂²⋊C₄×C₆₇	—	2	2	no	—
477	C₂²⋊C₄×C₆₇	—	2	1	no	—
478	C₂²⋊C₄×C₆₇	—	2	1	no	—
479	C₂²⋊C₄×C₆₇	—	2	1	no	—
480	C₂²⋊C₄×C₆₇	—	2	1	no	—
481	C₂²⋊C₄×C₆₇	—	2	1	no	—
482	C₂²⋊C₄×C₆₇	—	2	1	no	—
483	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
486	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
487	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
488	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
489	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
490	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₆₇	—	2	2	no	—
492	C₄²×C₆₇	—	2	2	no	—
493	C₄²×C₆₇	—	2	1	no	—
494	C₄²×C₆₇	—	2	1	no	—
495	C₄²×C₆₇	—	2	1	no	—
496	C₄²×C₆₇	—	2	1	no	—
497	C₄²×C₆₇	—	2	1	no	—
498	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
499	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
500	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
501	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
502	C₂³×C₆₇	—	2	2	no	—
503	C₂³×C₆₇	—	2	2	no	—
504	C₂³×C₆₇	—	2	2	no	—
505	C₂³×C₆₇	—	2	1	no	—
506	C₂³×C₆₇	—	2	2	no	—
507	C₂³×C₆₇	—	4	1	no	—
508	C₂³×C₆₇	—	4	1	no	—
509	C₂³×C₆₇	—	4	1	no	—
510	C₂³×C₆₇	—	4	2	no	—
511	C₂³×C₆₇	—	4	2	no	—
512	C₂³×C₆₇	—	4	2	no	—
513	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
514	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
515	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
516	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
517	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
518	Q₈×C₆₇	—	2	2	no	—
519	Q₈×C₆₇	—	2	2	no	—
520	Q₈×C₆₇	—	2	2	no	—
521	Q₈×C₆₇	—	4	2	no	—
522	Q₈×C₆₇	—	8	1	no	—
523	Q₈×C₆₇	—	8	1	no	—
524	D₄×C₆₇	—	2	2	no	—
525	D₄×C₆₇	—	2	2	no	—
526	D₄×C₆₇	—	2	2	no	—
527	D₄×C₆₇	—	2	2	no	—
528	D₄×C₆₇	—	2	2	no	—
529	D₄×C₆₇	—	4	1	no	—
530	D₄×C₆₇	—	4	1	no	—
531	D₄×C₆₇	—	4	2	no	—
532	D₄×C₆₇	—	4	4	no	—
533	D₄×C₆₇	—	4	2	no	—
534	D₄×C₆₇	—	4	4	no	—
535	D₄×C₆₇	—	4	2	no	—
536	D₄×C₆₇	—	4	2	no	—
537	D₄×C₆₇	—	8	2	no	—
538	D₄×C₆₇	—	8	2	no	—
539	D₄×C₆₇	—	8	1	no	—
540	D₄×C₆₇	—	8	1	no	—
541	C₂×C₄×C₆₇	—	2	2	no	—
542	C₂×C₄×C₆₇	—	2	2	no	—
543	C₂×C₄×C₆₇	—	2	2	no	—
544	C₂×C₄×C₆₇	—	2	2	no	—
545	C₂×C₄×C₆₇	—	2	2	no	—
546	C₂×C₄×C₆₇	—	2	2	no	—
547	C₂×C₄×C₆₇	—	2	1	no	—
548	C₂×C₄×C₆₇	—	2	2	no	—
549	C₂×C₄×C₆₇	—	2	1	no	—
550	C₂×C₄×C₆₇	—	2	1	no	—
551	C₂×C₄×C₆₇	—	2	2	no	—
552	C₂×C₄×C₆₇	—	2	1	no	—
553	C₂×C₄×C₆₇	—	2	1	no	—
554	C₂×C₄×C₆₇	—	2	1	no	—
555	C₂×C₄×C₆₇	—	2	1	no	—
556	C₂×C₄×C₆₇	—	2	2	no	—
557	C₂×C₄×C₆₇	—	4	1	no	—
558	C₂×C₄×C₆₇	—	4	1	no	—
559	C₂×C₄×C₆₇	—	4	1	no	—
560	C₂×C₄×C₆₇	—	4	1	no	—
561	C₂×C₄×C₆₇	—	4	1	no	—
562	C₂×C₄×C₆₇	—	4	1	no	—
563	C₂×C₄×C₆₇	—	4	1	no	—
564	C₂×C₄×C₆₇	—	4	2	no	—
565	C₂×C₄×C₆₇	—	4	2	no	—
566	C₂×C₄×C₆₇	—	4	2	no	—
567	C₂×C₄×C₆₇	—	4	2	no	—
568	C₂×C₄×C₆₇	—	4	2	no	—
569	C₂×C₄×C₆₇	—	4	2	no	—
570	C₂×C₄×C₆₇	—	8	2	no	—
571	C₂×C₄×C₆₇	—	8	2	no	—
572	C₂×C₄×C₆₇	—	8	1	no	—
573	C₂×C₄×C₆₇	—	8	1	no	—
574	C₂×C₄×C₆₇	—	8	2	no	—
575	C₂×C₄×C₆₇	—	8	2	no	—
576	C₂×C₄×C₆₇	—	8	1	no	—
577	C₂×C₄×C₆₇	—	8	1	no	—
578	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
588	C₈×C₆₇	—	2	2	no	—
589	C₈×C₆₇	—	2	2	no	—
590	C₈×C₆₇	—	2	2	no	—
591	C₈×C₆₇	—	2	2	no	—
592	C₂²×C₆₇	—	2	1	no	—
593	C₂²×C₆₇	—	2	1	no	—
594	C₂²×C₆₇	—	2	1	no	—
595	C₂²×C₆₇	—	2	1	no	—
596	C₂²×C₆₇	—	2	1	no	—
597	C₂²×C₆₇	—	2	1	no	—
598	C₂²×C₆₇	—	2	1	no	—
599	C₂²×C₆₇	—	2	1	no	—
600	C₂²×C₆₇	—	2	1	no	—
601	C₂²×C₆₇	—	2	1	no	—
602	C₂²×C₆₇	—	2	1	no	—
603	C₂²×C₆₇	—	2	1	no	—
604	C₂²×C₆₇	—	2	1	no	—
605	C₂²×C₆₇	—	4	4	no	—
606	C₂²×C₆₇	—	4	1	no	—
607	C₂²×C₆₇	—	4	2	no	—
608	C₂²×C₆₇	—	4	1	no	—
609	C₂²×C₆₇	—	4	2	no	—
610	C₂²×C₆₇	—	4	2	no	—
611	C₂²×C₆₇	—	4	1	no	—
612	C₂²×C₆₇	—	8	2	no	—
613	C₂²×C₆₇	—	8	4	no	—
614	C₂²×C₆₇	#575	1	2	yes	—
615	C₂²×C₆₇	#577	1	2	yes	—
616	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
617	C₄×C₆₇	—	2	1	no	—
618	C₄×C₆₇	—	2	1	no	—
619	C₄×C₆₇	—	2	1	no	—
620	C₄×C₆₇	—	2	1	no	—
621	C₄×C₆₇	—	2	1	no	—
622	C₄×C₆₇	—	2	1	no	—
623	C₄×C₆₇	—	2	1	no	—
624	C₄×C₆₇	—	2	1	no	—
625	C₄×C₆₇	—	2	1	no	—
626	C₄×C₆₇	—	4	1	no	—
627	C₄×C₆₇	—	4	1	no	—
628	C₄×C₆₇	—	4	1	no	—
629	C₄×C₆₇	—	4	1	no	—
630	C₄×C₆₇	—	4	2	no	—
631	C₄×C₆₇	—	4	1	no	—
632	C₄×C₆₇	—	4	1	no	—
633	C₄×C₆₇	—	4	2	no	—
634	C₄×C₆₇	—	4	2	no	—
635	C₄×C₆₇	—	4	1	no	—
636	C₄×C₆₇	#585	1	2	yes	—
637	#61736	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
638	C₂×C₆₇	—	2	2	no	—
639	C₂×C₆₇	—	2	2	no	—
640	C₂×C₆₇	—	4	1	no	—
641	C₂×C₆₇	—	4	1	no	—
642	C₂×C₆₇	—	4	1	no	—
643	C₂×C₆₇	—	8	1	no	—
644	C₂×C₆₇	—	8	2	no	—
645	C₂×C₆₇	#3485	1	1	yes	characteristic
646	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
647	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
648	#3520	C₂×C₆₇	1	1	yes	characteristic, complemented
649	C₂×#553	C₂×C₆₇	1	1	yes	characteristic, complemented
650	#3351	C₂×C₆₇	1	2	yes	complemented
651	#3350	C₂×C₆₇	1	2	yes	complemented
652	#3345	C₂×C₆₇	1	2	yes	complemented
653	#3337	C₂×C₆₇	1	2	yes	complemented
654	#3326	C₂×C₆₇	1	2	yes	complemented
655	#3320	C₂×C₆₇	1	2	yes	complemented
656	#3307	C₂×C₆₇	1	2	yes	complemented
657	#3301	C₂×C₆₇	1	2	yes	complemented
658	#3236	C₂×C₆₇	1	1	yes	characteristic, complemented
659	#3232	C₂×C₆₇	1	1	yes	characteristic, complemented
660	#3194	C₂×C₆₇	1	1	yes	characteristic, complemented
661	#3193	C₂×C₆₇	1	1	yes	characteristic, complemented
662	#3188	C₂×C₆₇	1	1	yes	characteristic, complemented
663	#3187	C₂×C₆₇	1	1	yes	characteristic, complemented
664	#3114	C₂×C₆₇	1	1	yes	characteristic, complemented
665	#3101	C₂×C₆₇	1	1	yes	characteristic, complemented
666	#3095	C₂×C₆₇	1	1	yes	characteristic, complemented
667	#3092	C₂×C₆₇	1	1	yes	characteristic, complemented
668	#3091	C₂×C₆₇	1	1	yes	characteristic, complemented
669	C₂×#483	C₂×C₆₇	1	1	yes	characteristic, complemented
670	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
671	C₆₇	#61736	1	1	yes	characteristic, direct product factor, Sylow
672	#556	C₂²×C₆₇	1	1	yes	characteristic, complemented
673	#554	—	2	1	no	—
674	#553	—	2	1	no	—
675	#553	—	2	1	no	—
676	#553	—	2	1	no	—
677	#553	—	2	1	no	—
678	#553	C₂²×C₆₇	1	2	yes	—
679	#553	C₂²×C₆₇	1	2	yes	—
680	#553	C₂²×C₆₇	1	2	yes	—
681	#553	C₂²×C₆₇	1	2	yes	—
682	#552	C₂²×C₆₇	1	1	yes	characteristic, complemented
683	#552	C₂²×C₆₇	1	1	yes	characteristic, complemented
684	#551	—	2	1	no	—
685	#551	—	2	1	no	—
686	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	#548	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	#548	C₂²×C₆₇	1	1	yes	characteristic, complemented
689	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
691	#546	—	2	1	no	—
692	#542	—	2	1	no	—
693	#539	—	2	1	no	—
694	#539	—	2	1	no	—
695	#533	C₂²×C₆₇	1	1	yes	characteristic
696	#529	C₂²×C₆₇	1	1	yes	characteristic
697	C₂×#126	—	2	1	no	—
698	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
699	#525	C₂²×C₆₇	1	1	yes	characteristic
700	#525	C₂²×C₆₇	1	1	yes	characteristic
701	C₂×#123	—	2	1	no	—
702	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
703	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
704	C₂×#121	—	2	1	no	—
705	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
706	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
707	#520	—	2	1	no	—
708	C₂×C₄×D₄	—	2	1	no	—
709	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
710	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
711	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
712	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
713	#501	C₂²×C₆₇	1	2	yes	complemented
714	#499	C₂²×C₆₇	1	2	yes	complemented
715	#491	C₂²×C₆₇	1	2	yes	complemented
716	#488	C₂²×C₆₇	1	2	yes	complemented
717	#485	C₂²×C₆₇	1	2	yes	complemented
718	#485	C₂²×C₆₇	1	2	yes	complemented
719	#485	C₂²×C₆₇	1	2	yes	complemented
720	#484	C₂²×C₆₇	1	1	yes	characteristic
721	#484	C₂²×C₆₇	1	1	yes	characteristic
722	#484	C₂²×C₆₇	1	1	yes	characteristic
723	#484	C₂²×C₆₇	1	2	yes	complemented
724	#483	C₂²×C₆₇	1	1	yes	characteristic
725	#483	C₂²×C₆₇	1	1	yes	characteristic
726	#483	C₂²×C₆₇	1	1	yes	characteristic
727	#483	C₂²×C₆₇	1	1	yes	characteristic
728	#483	C₂²×C₆₇	1	1	yes	characteristic
729	#483	C₂²×C₆₇	1	1	yes	characteristic
730	#483	C₂²×C₆₇	1	2	yes	complemented
731	#483	C₂²×C₆₇	1	2	yes	complemented
732	#482	C₂²×C₆₇	1	2	yes	complemented
733	#482	C₂²×C₆₇	1	2	yes	complemented
734	#482	C₂²×C₆₇	1	2	yes	complemented
735	#481	C₂²×C₆₇	1	1	yes	characteristic
736	#481	C₂²×C₆₇	1	2	yes	complemented
737	#481	C₂²×C₆₇	1	2	yes	complemented
738	#480	C₂²×C₆₇	1	1	yes	characteristic
739	#480	C₂²×C₆₇	1	1	yes	characteristic
740	#480	C₂²×C₆₇	1	2	yes	complemented
741	#479	C₂²×C₆₇	1	2	yes	complemented
742	#479	C₂²×C₆₇	1	2	yes	complemented
743	#479	C₂²×C₆₇	1	2	yes	complemented
744	#478	C₂²×C₆₇	1	2	yes	complemented
745	#478	C₂²×C₆₇	1	2	yes	complemented
746	#476	C₂²×C₆₇	1	2	yes	complemented
747	#469	C₂²×C₆₇	1	2	yes	complemented
748	#468	C₂²×C₆₇	1	2	yes	complemented
749	#468	C₂²×C₆₇	1	2	yes	complemented
750	#468	C₂²×C₆₇	1	2	yes	complemented
751	#466	C₂²×C₆₇	1	2	yes	complemented
752	#465	C₂²×C₆₇	1	2	yes	complemented
753	#465	C₂²×C₆₇	1	2	yes	complemented
754	#465	C₂²×C₆₇	1	2	yes	complemented
755	#463	C₂²×C₆₇	1	2	yes	complemented
756	#461	C₂²×C₆₇	1	2	yes	complemented
757	#450	C₂²×C₆₇	1	1	yes	characteristic
758	#450	C₂²×C₆₇	1	1	yes	characteristic
759	#450	C₂²×C₆₇	1	1	yes	characteristic
760	#449	C₂²×C₆₇	1	2	yes	complemented
761	#449	C₂²×C₆₇	1	2	yes	complemented
762	#448	C₂²×C₆₇	1	2	yes	complemented
763	#448	C₂²×C₆₇	1	2	yes	complemented
764	#447	C₂²×C₆₇	1	1	yes	characteristic
765	#442	C₂²×C₆₇	1	2	yes	complemented
766	#440	C₂²×C₆₇	1	2	yes	complemented
767	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
768	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
769	#436	C₂²×C₆₇	1	2	yes	complemented
770	#435	C₂²×C₆₇	1	2	yes	complemented
771	#435	C₂²×C₆₇	1	2	yes	complemented
772	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
773	#432	C₂²×C₆₇	1	1	yes	characteristic
774	#431	C₂²×C₆₇	1	1	yes	characteristic
775	#428	C₂²×C₆₇	1	2	yes	complemented
776	#428	C₂²×C₆₇	1	2	yes	complemented
777	#427	C₂²×C₆₇	1	2	yes	complemented
778	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
779	#419	C₂²×C₆₇	1	2	yes	complemented
780	#417	C₂²×C₆₇	1	2	yes	complemented
781	#416	C₂²×C₆₇	1	2	yes	complemented
782	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
783	#407	C₂²×C₆₇	1	1	yes	characteristic
784	#407	C₂²×C₆₇	1	1	yes	characteristic
785	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
786	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
787	C₂×#41	—	2	1	no	—
788	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
789	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
790	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
791	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
792	C₂²×D₄	—	2	1	no	—
793	C₂²×D₄	—	2	1	no	—
794	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
795	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
796	C₂³×C₄	—	2	1	no	—
797	C₂³×C₄	—	2	1	no	—
798	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
799	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
800	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
801	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
802	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
803	C₂×D₈	C₂³×C₆₇	1	2	yes	—
804	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
805	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
806	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
807	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
808	C₄⋊Q₈	—	2	1	no	—
809	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
810	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
811	#126	—	2	2	no	—
812	#126	—	2	2	no	—
813	#126	—	2	2	no	—
814	#126	—	2	2	no	—
815	#126	—	2	1	no	—
816	#126	—	2	1	no	—
817	#126	—	2	1	no	—
818	#126	—	2	1	no	—
819	#126	—	2	1	no	—
820	#125	—	2	1	no	—
821	#125	—	2	1	no	—
822	#125	—	2	1	no	—
823	#125	—	2	1	no	—
824	#125	—	2	1	no	—
825	#125	C₂³×C₆₇	1	2	yes	—
826	#125	C₂³×C₆₇	1	2	yes	—
827	#125	C₂³×C₆₇	1	1	yes	characteristic
828	#124	—	2	1	no	—
829	#124	—	2	1	no	—
830	#124	—	2	1	no	—
831	#124	C₂³×C₆₇	1	1	yes	characteristic
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	2	no	—
838	#123	—	2	2	no	—
839	#123	—	2	2	no	—
840	#123	—	2	2	no	—
841	#123	—	2	1	no	—
842	#123	—	2	1	no	—
843	#123	—	2	1	no	—
844	#123	—	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	1	no	—
853	C₂²⋊Q₈	—	2	1	no	—
854	C₂²⋊Q₈	—	2	1	no	—
855	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
863	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
864	#121	—	2	2	no	—
865	#121	—	2	2	no	—
866	#121	—	2	2	no	—
867	#121	—	2	2	no	—
868	#121	—	2	1	no	—
869	#121	—	2	1	no	—
870	#121	—	2	1	no	—
871	#121	—	2	1	no	—
872	#121	—	2	1	no	—
873	#121	—	2	1	no	—
874	#121	—	2	1	no	—
875	#121	C₂³×C₆₇	1	2	yes	—
876	#121	C₂³×C₆₇	1	2	yes	—
877	#121	C₂³×C₆₇	1	2	yes	—
878	#121	C₂³×C₆₇	1	2	yes	—
879	#121	C₂³×C₆₇	1	1	yes	characteristic
880	#121	C₂³×C₆₇	1	1	yes	characteristic
881	#121	C₂³×C₆₇	1	1	yes	characteristic
882	#120	—	2	1	no	—
883	#120	—	2	1	no	—
884	C₄×Q₈	—	2	1	no	—
885	C₄×Q₈	—	2	1	no	—
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×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	2	no	—
896	C₄×D₄	—	2	2	no	—
897	C₄×D₄	—	2	2	no	—
898	C₄×D₄	—	2	2	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	1	no	—
903	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
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	C₂³×C₆₇	1	2	yes	—
908	C₄×D₄	C₂³×C₆₇	1	2	yes	—
909	C₄×D₄	C₂³×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	1	yes	characteristic
913	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
914	#117	—	2	1	no	—
915	#117	—	2	1	no	—
916	#117	—	2	1	no	—
917	#117	—	2	1	no	—
918	#117	—	2	1	no	—
919	#117	—	2	1	no	—
920	#117	C₂³×C₆₇	1	2	yes	—
921	#117	C₂³×C₆₇	1	2	yes	—
922	#117	C₂³×C₆₇	1	1	yes	characteristic
923	#117	C₂³×C₆₇	1	1	yes	characteristic
924	C₂×C₄⋊C₄	—	2	1	no	—
925	C₂×C₄⋊C₄	—	2	1	no	—
926	C₂×C₄⋊C₄	—	2	1	no	—
927	C₂×C₄⋊C₄	—	2	1	no	—
928	C₂×C₄⋊C₄	—	2	1	no	—
929	C₂×C₄⋊C₄	—	2	1	no	—
930	C₂×C₄⋊C₄	—	2	1	no	—
931	C₂×C₄⋊C₄	—	2	1	no	—
932	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
934	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
935	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
936	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
937	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
938	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
939	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
940	C₂×C₂²⋊C₄	—	2	1	no	—
941	C₂×C₂²⋊C₄	—	2	1	no	—
942	C₂×C₂²⋊C₄	—	2	1	no	—
943	C₂×C₂²⋊C₄	—	2	1	no	—
944	C₂×C₂²⋊C₄	—	2	1	no	—
945	C₂×C₂²⋊C₄	—	2	1	no	—
946	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
947	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
948	C₂×C₄²	—	2	1	no	—
949	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
950	#107	C₂³×C₆₇	1	2	yes	—
951	#107	C₂³×C₆₇	1	2	yes	—
952	#107	C₂³×C₆₇	1	2	yes	—
953	#107	C₂³×C₆₇	1	2	yes	—
954	#107	C₂³×C₆₇	1	2	yes	—
955	#106	C₂³×C₆₇	1	2	yes	—
956	#106	C₂³×C₆₇	1	2	yes	—
957	#106	C₂³×C₆₇	1	2	yes	—
958	#106	C₂³×C₆₇	1	2	yes	—
959	#106	C₂³×C₆₇	1	2	yes	—
960	#106	C₂³×C₆₇	1	2	yes	—
961	#106	C₂³×C₆₇	1	2	yes	—
962	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
963	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
964	#103	C₂³×C₆₇	1	2	yes	—
965	#103	C₂³×C₆₇	1	2	yes	—
966	#103	C₂³×C₆₇	1	2	yes	—
967	#103	C₂³×C₆₇	1	2	yes	—
968	#103	C₂³×C₆₇	1	2	yes	—
969	#103	C₂³×C₆₇	1	2	yes	—
970	#103	C₂³×C₆₇	1	2	yes	—
971	#103	C₂³×C₆₇	1	2	yes	—
972	#103	C₂³×C₆₇	1	2	yes	—
973	#102	C₂³×C₆₇	1	2	yes	—
974	#102	C₂³×C₆₇	1	2	yes	—
975	#102	C₂³×C₆₇	1	2	yes	—
976	#102	C₂³×C₆₇	1	2	yes	—
977	#102	C₂³×C₆₇	1	2	yes	—
978	#102	C₂³×C₆₇	1	2	yes	—
979	#102	C₂³×C₆₇	1	2	yes	—
980	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
981	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
982	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
983	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
984	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
985	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
986	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
987	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
988	#97	C₂³×C₆₇	1	2	yes	—
989	C₄×C₈	C₂³×C₆₇	1	2	yes	—
990	C₂⁴	—	2	1	no	—
991	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
992	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
993	#41	—	4	2	no	—
994	#41	—	4	2	no	—
995	#41	—	4	4	no	—
996	C₂×Q₈	—	2	1	no	—
997	C₂×Q₈	—	2	1	no	—
998	C₂×Q₈	—	2	1	no	—
999	C₂×Q₈	—	4	2	no	—
1000	C₂×Q₈	—	4	2	no	—
1001	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1002	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1003	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	1	no	—
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	2	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	2	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	4	2	no	—
1015	C₂×D₄	—	4	2	no	—
1016	C₂×D₄	—	4	4	no	—
1017	C₂×D₄	—	8	2	no	—
1018	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1019	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1020	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1021	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1022	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1023	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	1	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	1	no	—
1029	C₂²×C₄	—	2	1	no	—
1030	C₂²×C₄	—	2	1	no	—
1031	C₂²×C₄	—	2	2	no	—
1032	C₂²×C₄	—	2	2	no	—
1033	C₂²×C₄	—	2	1	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	1	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	4	2	no	—
1039	C₂²×C₄	—	4	2	no	—
1040	C₂²×C₄	—	8	2	no	—
1041	C₂²×C₄	—	8	2	no	—
1042	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1043	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1044	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1045	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1046	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1047	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1048	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1049	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1050	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1051	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1052	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1053	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1054	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1055	SD₁₆	—	4	2	no	—
1056	SD₁₆	—	4	2	no	—
1057	SD₁₆	—	4	2	no	—
1058	D₈	—	4	2	no	—
1059	M₁₆	—	4	2	no	—
1060	M₁₆	—	4	2	no	—
1061	C₂×C₈	—	4	2	no	—
1062	C₂×C₈	—	4	2	no	—
1063	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1064	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1065	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1066	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	1	no	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	2	no	—
1082	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	1	no	—
1085	C₄⋊C₄	—	2	1	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1096	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1097	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1098	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1099	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1100	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1101	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1102	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1103	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1104	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1105	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	2	no	—
1125	C₂²⋊C₄	—	2	1	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	1	no	—
1129	C₂²⋊C₄	—	2	1	no	—
1130	C₂²⋊C₄	—	2	1	no	—
1131	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1132	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1133	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1134	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1135	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1136	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1137	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1138	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1139	C₄²	—	2	2	no	—
1140	C₄²	—	2	2	no	—
1141	C₄²	—	2	1	no	—
1142	C₄²	—	2	1	no	—
1143	C₄²	—	2	1	no	—
1144	C₄²	—	2	1	no	—
1145	C₄²	—	2	1	no	—
1146	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1147	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1148	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1149	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1150	C₂³	—	2	2	no	—
1151	C₂³	—	2	2	no	—
1152	C₂³	—	2	2	no	—
1153	C₂³	—	2	1	no	—
1154	C₂³	—	2	2	no	—
1155	C₂³	—	4	1	no	—
1156	C₂³	—	4	1	no	—
1157	C₂³	—	4	1	no	—
1158	C₂³	—	4	2	no	—
1159	C₂³	—	4	2	no	—
1160	C₂³	—	4	2	no	—
1161	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1162	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1163	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1164	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1165	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1166	Q₈	—	2	2	no	—
1167	Q₈	—	2	2	no	—
1168	Q₈	—	2	2	no	—
1169	Q₈	—	4	2	no	—
1170	Q₈	—	8	1	no	—
1171	Q₈	—	8	1	no	—
1172	D₄	—	2	2	no	—
1173	D₄	—	2	2	no	—
1174	D₄	—	2	2	no	—
1175	D₄	—	2	2	no	—
1176	D₄	—	2	2	no	—
1177	D₄	—	4	1	no	—
1178	D₄	—	4	1	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	4	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	4	4	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	8	2	no	—
1186	D₄	—	8	2	no	—
1187	D₄	—	8	1	no	—
1188	D₄	—	8	1	no	—
1189	C₂×C₄	—	2	2	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	4	1	no	—
1206	C₂×C₄	—	4	1	no	—
1207	C₂×C₄	—	4	1	no	—
1208	C₂×C₄	—	4	1	no	—
1209	C₂×C₄	—	4	1	no	—
1210	C₂×C₄	—	4	1	no	—
1211	C₂×C₄	—	4	1	no	—
1212	C₂×C₄	—	4	2	no	—
1213	C₂×C₄	—	4	2	no	—
1214	C₂×C₄	—	4	2	no	—
1215	C₂×C₄	—	4	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	8	2	no	—
1219	C₂×C₄	—	8	2	no	—
1220	C₂×C₄	—	8	1	no	—
1221	C₂×C₄	—	8	1	no	—
1222	C₂×C₄	—	8	2	no	—
1223	C₂×C₄	—	8	2	no	—
1224	C₂×C₄	—	8	1	no	—
1225	C₂×C₄	—	8	1	no	—
1226	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1227	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1228	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1229	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1230	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1231	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1232	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1233	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1234	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1235	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1236	C₈	—	2	2	no	—
1237	C₈	—	2	2	no	—
1238	C₈	—	2	2	no	—
1239	C₈	—	2	2	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	1	no	—
1247	C₂²	—	2	1	no	—
1248	C₂²	—	2	1	no	—
1249	C₂²	—	2	1	no	—
1250	C₂²	—	2	1	no	—
1251	C₂²	—	2	1	no	—
1252	C₂²	—	2	1	no	—
1253	C₂²	—	4	4	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	2	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	4	2	no	—
1260	C₂²	—	8	2	no	—
1261	C₂²	—	8	4	no	—
1262	C₂²	#575×C₆₇	1	2	yes	—
1263	C₂²	#577×C₆₇	1	2	yes	—
1264	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1265	C₄	—	2	1	no	—
1266	C₄	—	2	1	no	—
1267	C₄	—	2	1	no	—
1268	C₄	—	2	1	no	—
1269	C₄	—	2	1	no	—
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	2	1	no	—
1273	C₄	—	2	1	no	—
1274	C₄	—	4	1	no	—
1275	C₄	—	4	2	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	2	no	—
1279	C₄	—	4	2	no	—
1280	C₄	—	4	1	no	—
1281	C₄	—	4	1	no	—
1282	C₄	—	4	1	no	—
1283	C₄	—	4	1	no	—
1284	C₄	#585×C₆₇	1	2	yes	—
1285	C₂	—	2	2	no	—
1286	C₂	—	2	2	no	—
1287	C₂	—	4	1	no	—
1288	C₂	—	4	1	no	—
1289	C₂	—	4	1	no	—
1290	C₂	—	8	2	no	—
1291	C₂	—	8	1	no	—
1292	C₂	C₆₇×#3485	1	1	yes	characteristic
1293	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
1294	C₂	C₂×#577×C₆₇	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 ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3520	C₂	semidirect
2. C₂×#553×C₆₇	C₂	semidirect
3. C₆₇×#3351	C₂	semidirect
4. C₆₇×#3350	C₂	semidirect
5. C₆₇×#3345	C₂	semidirect
6. C₆₇×#3337	C₂	semidirect
7. C₆₇×#3326	C₂	semidirect
8. C₆₇×#3320	C₂	semidirect
9. C₆₇×#3307	C₂	semidirect
10. C₆₇×#3301	C₂	semidirect
11. C₆₇×#3236	C₂	semidirect
12. C₆₇×#3232	C₂	semidirect
13. C₆₇×#3194	C₂	semidirect
14. C₆₇×#3193	C₂	semidirect
15. C₆₇×#3188	C₂	semidirect
16. C₆₇×#3187	C₂	semidirect
17. C₆₇×#3114	C₂	semidirect
18. C₆₇×#3101	C₂	semidirect
19. C₆₇×#3095	C₂	semidirect
20. C₆₇×#3092	C₂	semidirect
21. C₆₇×#3091	C₂	semidirect
22. C₂×#483×C₆₇	C₂	semidirect
23. C₆₇×#2974	C₂	semidirect
24. #556×C₆₇	C₂²	semidirect
34. #552×C₆₇	C₂²	semidirect
35. #552×C₆₇	C₂²	semidirect
38. D₄×Q₈×C₆₇	C₂²	semidirect
39. #548×C₆₇	C₂²	semidirect
40. #548×C₆₇	C₂²	semidirect
41. #547×C₆₇	C₂²	semidirect
42. #547×C₆₇	C₂²	semidirect
65. #501×C₆₇	C₂²	semidirect
66. #499×C₆₇	C₂²	semidirect
67. #491×C₆₇	C₂²	semidirect
68. #488×C₆₇	C₂²	semidirect
69. #485×C₆₇	C₂²	semidirect
70. #485×C₆₇	C₂²	semidirect
71. #485×C₆₇	C₂²	semidirect
75. #484×C₆₇	C₂²	semidirect
82. #483×C₆₇	C₂²	semidirect
83. #483×C₆₇	C₂²	semidirect
84. #482×C₆₇	C₂²	semidirect
85. #482×C₆₇	C₂²	semidirect
86. #482×C₆₇	C₂²	semidirect
88. #481×C₆₇	C₂²	semidirect
89. #481×C₆₇	C₂²	semidirect
92. #480×C₆₇	C₂²	semidirect
93. #479×C₆₇	C₂²	semidirect
94. #479×C₆₇	C₂²	semidirect
95. #479×C₆₇	C₂²	semidirect
96. #478×C₆₇	C₂²	semidirect
97. #478×C₆₇	C₂²	semidirect
98. #476×C₆₇	C₂²	semidirect
99. #469×C₆₇	C₂²	semidirect
100. #468×C₆₇	C₂²	semidirect
101. #468×C₆₇	C₂²	semidirect
102. #468×C₆₇	C₂²	semidirect
103. #466×C₆₇	C₂²	semidirect
104. #465×C₆₇	C₂²	semidirect
105. #465×C₆₇	C₂²	semidirect
106. #465×C₆₇	C₂²	semidirect
107. #463×C₆₇	C₂²	semidirect
108. #461×C₆₇	C₂²	semidirect
112. #449×C₆₇	C₂²	semidirect
113. #449×C₆₇	C₂²	semidirect
114. #448×C₆₇	C₂²	semidirect
115. #448×C₆₇	C₂²	semidirect
117. #442×C₆₇	C₂²	semidirect
118. #440×C₆₇	C₂²	semidirect
119. C₄×SD₁₆×C₆₇	C₂²	semidirect
120. C₄×SD₁₆×C₆₇	C₂²	semidirect
121. #436×C₆₇	C₂²	semidirect
122. #435×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. C₈×D₄×C₆₇	C₂²	semidirect
127. #428×C₆₇	C₂²	semidirect
128. #428×C₆₇	C₂²	semidirect
129. #427×C₆₇	C₂²	semidirect
130. C₂×#106×C₆₇	C₂²	semidirect
131. #419×C₆₇	C₂²	semidirect
132. #417×C₆₇	C₂²	semidirect
133. #416×C₆₇	C₂²	semidirect
134. C₂×#103×C₆₇	C₂²	semidirect
637. #61736	C₆₇	direct (N × H)
648. #3520	C₂×C₆₇	semidirect
649. C₂×#553	C₂×C₆₇	semidirect
650. #3351	C₂×C₆₇	semidirect
651. #3350	C₂×C₆₇	semidirect
652. #3345	C₂×C₆₇	semidirect
653. #3337	C₂×C₆₇	semidirect
654. #3326	C₂×C₆₇	semidirect
655. #3320	C₂×C₆₇	semidirect
656. #3307	C₂×C₆₇	semidirect
657. #3301	C₂×C₆₇	semidirect
658. #3236	C₂×C₆₇	semidirect
659. #3232	C₂×C₆₇	semidirect
660. #3194	C₂×C₆₇	semidirect
661. #3193	C₂×C₆₇	semidirect
662. #3188	C₂×C₆₇	semidirect
663. #3187	C₂×C₆₇	semidirect
664. #3114	C₂×C₆₇	semidirect
665. #3101	C₂×C₆₇	semidirect
666. #3095	C₂×C₆₇	semidirect
667. #3092	C₂×C₆₇	semidirect
668. #3091	C₂×C₆₇	semidirect
669. C₂×#483	C₂×C₆₇	semidirect
670. #2974	C₂×C₆₇	semidirect
671. C₆₇	#61736	direct (N × H)
672. #556	C₂²×C₆₇	semidirect
682. #552	C₂²×C₆₇	semidirect
683. #552	C₂²×C₆₇	semidirect
686. D₄×Q₈	C₂²×C₆₇	semidirect
687. #548	C₂²×C₆₇	semidirect
688. #548	C₂²×C₆₇	semidirect
689. #547	C₂²×C₆₇	semidirect
690. #547	C₂²×C₆₇	semidirect
713. #501	C₂²×C₆₇	semidirect
714. #499	C₂²×C₆₇	semidirect
715. #491	C₂²×C₆₇	semidirect
716. #488	C₂²×C₆₇	semidirect
717. #485	C₂²×C₆₇	semidirect
718. #485	C₂²×C₆₇	semidirect
719. #485	C₂²×C₆₇	semidirect
723. #484	C₂²×C₆₇	semidirect
730. #483	C₂²×C₆₇	semidirect
731. #483	C₂²×C₆₇	semidirect
732. #482	C₂²×C₆₇	semidirect
733. #482	C₂²×C₆₇	semidirect
734. #482	C₂²×C₆₇	semidirect
736. #481	C₂²×C₆₇	semidirect
737. #481	C₂²×C₆₇	semidirect
740. #480	C₂²×C₆₇	semidirect
741. #479	C₂²×C₆₇	semidirect
742. #479	C₂²×C₆₇	semidirect
743. #479	C₂²×C₆₇	semidirect
744. #478	C₂²×C₆₇	semidirect
745. #478	C₂²×C₆₇	semidirect
746. #476	C₂²×C₆₇	semidirect
747. #469	C₂²×C₆₇	semidirect
748. #468	C₂²×C₆₇	semidirect
749. #468	C₂²×C₆₇	semidirect
750. #468	C₂²×C₆₇	semidirect
751. #466	C₂²×C₆₇	semidirect
752. #465	C₂²×C₆₇	semidirect
753. #465	C₂²×C₆₇	semidirect
754. #465	C₂²×C₆₇	semidirect
755. #463	C₂²×C₆₇	semidirect
756. #461	C₂²×C₆₇	semidirect
760. #449	C₂²×C₆₇	semidirect
761. #449	C₂²×C₆₇	semidirect
762. #448	C₂²×C₆₇	semidirect
763. #448	C₂²×C₆₇	semidirect
765. #442	C₂²×C₆₇	semidirect
766. #440	C₂²×C₆₇	semidirect
767. C₄×SD₁₆	C₂²×C₆₇	semidirect
768. C₄×SD₁₆	C₂²×C₆₇	semidirect
769. #436	C₂²×C₆₇	semidirect
770. #435	C₂²×C₆₇	semidirect
771. #435	C₂²×C₆₇	semidirect
772. C₈×D₄	C₂²×C₆₇	semidirect
775. #428	C₂²×C₆₇	semidirect
776. #428	C₂²×C₆₇	semidirect
777. #427	C₂²×C₆₇	semidirect
778. C₂×#106	C₂²×C₆₇	semidirect
779. #419	C₂²×C₆₇	semidirect
780. #417	C₂²×C₆₇	semidirect
781. #416	C₂²×C₆₇	semidirect
782. C₂×#103	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3520	2
C₂×#553×C₆₇	2
C₆₇×#3351	2
C₆₇×#3350	2
C₆₇×#3345	2
C₆₇×#3337	2
C₆₇×#3326	2
C₆₇×#3320	2
C₆₇×#3307	2
C₆₇×#3301	2
C₆₇×#3236	2
C₆₇×#3232	2
C₆₇×#3194	2
C₆₇×#3193	2
C₆₇×#3188	2
C₆₇×#3187	2
C₆₇×#3114	2
C₆₇×#3101	2
C₆₇×#3095	2
C₆₇×#3092	2
C₆₇×#3091	2
C₂×#483×C₆₇	2
C₆₇×#2974	2
#61736	67

Subgroups — C67×#61736 #30740987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61736 #30740987