Subgroups — C₆₇×#61786 #30741037

Order 17152.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3546	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3353	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3351	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3342	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3337	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3323	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3304	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3296	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3201	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3200	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3099	C₂	1	2	yes	maximal, complemented
22	C₆₇×#3096	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	#560×C₆₇	—	2	2	no	—
25	#559×C₆₇	—	2	1	no	—
26	#557×C₆₇	—	2	1	no	—
27	#556×C₆₇	—	2	2	no	—
28	#556×C₆₇	C₂²	1	1	yes	characteristic
29	#556×C₆₇	C₂²	1	1	yes	characteristic
30	#556×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#554×C₆₇	C₂²	1	1	yes	characteristic
32	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#553×C₆₇	C₂²	1	2	yes	—
34	#552×C₆₇	C₂²	1	2	yes	complemented
35	#552×C₆₇	C₂²	1	2	yes	complemented
36	#550×C₆₇	—	2	1	no	—
37	#550×C₆₇	C₂²	1	1	yes	characteristic
38	#547×C₆₇	C₂²	1	1	yes	characteristic
39	#546×C₆₇	—	2	1	no	—
40	#546×C₆₇	C₂²	1	2	yes	—
41	D₄²×C₆₇	C₂²	1	1	yes	characteristic
42	#542×C₆₇	—	2	1	no	—
43	#539×C₆₇	—	2	2	no	—
44	#538×C₆₇	—	2	2	no	—
45	#537×C₆₇	C₂²	1	2	yes	—
46	#536×C₆₇	C₂²	1	2	yes	complemented
47	#535×C₆₇	—	2	1	no	—
48	#535×C₆₇	C₂²	1	2	yes	—
49	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#532×C₆₇	C₂²	1	1	yes	characteristic
51	#532×C₆₇	C₂²	1	1	yes	characteristic
52	#529×C₆₇	—	2	1	no	—
53	#529×C₆₇	—	2	1	no	—
54	#529×C₆₇	C₂²	1	1	yes	characteristic
55	#520×C₆₇	C₂²	1	2	yes	complemented
56	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#499×C₆₇	C₂²	1	2	yes	complemented
59	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#488×C₆₇	C₂²	1	2	yes	—
61	#486×C₆₇	C₂²	1	1	yes	characteristic
62	#486×C₆₇	C₂²	1	1	yes	characteristic
63	#485×C₆₇	C₂²	1	2	yes	complemented
64	#485×C₆₇	C₂²	1	2	yes	complemented
65	#485×C₆₇	C₂²	1	2	yes	complemented
66	#485×C₆₇	C₂²	1	2	yes	complemented
67	#484×C₆₇	C₂²	1	2	yes	complemented
68	#483×C₆₇	C₂²	1	2	yes	complemented
69	#483×C₆₇	C₂²	1	2	yes	complemented
70	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
71	#482×C₆₇	C₂²	1	2	yes	—
72	#482×C₆₇	C₂²	1	2	yes	—
73	#482×C₆₇	C₂²	1	2	yes	—
74	#482×C₆₇	C₂²	1	2	yes	complemented
75	#482×C₆₇	C₂²	1	2	yes	complemented
76	#482×C₆₇	C₂²	1	2	yes	complemented
77	#481×C₆₇	C₂²	1	2	yes	—
78	#481×C₆₇	C₂²	1	2	yes	—
79	#481×C₆₇	C₂²	1	2	yes	complemented
80	#480×C₆₇	C₂²	1	1	yes	characteristic
81	#480×C₆₇	C₂²	1	2	yes	complemented
82	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#478×C₆₇	C₂²	1	2	yes	complemented
85	#478×C₆₇	C₂²	1	2	yes	complemented
86	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#476×C₆₇	C₂²	1	1	yes	characteristic
88	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#474×C₆₇	C₂²	1	1	yes	characteristic
92	#470×C₆₇	C₂²	1	2	yes	complemented
93	#468×C₆₇	C₂²	1	2	yes	—
94	#468×C₆₇	C₂²	1	2	yes	—
95	#468×C₆₇	C₂²	1	2	yes	complemented
96	#467×C₆₇	C₂²	1	2	yes	complemented
97	#465×C₆₇	C₂²	1	2	yes	—
98	#465×C₆₇	C₂²	1	2	yes	—
99	#465×C₆₇	C₂²	1	2	yes	complemented
100	#464×C₆₇	C₂²	1	1	yes	characteristic
101	#464×C₆₇	C₂²	1	1	yes	characteristic
102	#460×C₆₇	C₂²	1	1	yes	characteristic
103	#460×C₆₇	C₂²	1	1	yes	characteristic
104	#452×C₆₇	C₂²	1	2	yes	complemented
105	#452×C₆₇	C₂²	1	2	yes	complemented
106	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#450×C₆₇	C₂²	1	2	yes	—
108	#450×C₆₇	C₂²	1	2	yes	—
109	#448×C₆₇	C₂²	1	1	yes	characteristic
110	#448×C₆₇	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
117	#436×C₆₇	C₂²	1	1	yes	characteristic
118	#436×C₆₇	C₂²	1	2	yes	complemented
119	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
122	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#428×C₆₇	C₂²	1	2	yes	complemented
126	#428×C₆₇	C₂²	1	2	yes	complemented
127	#427×C₆₇	C₂²	1	2	yes	complemented
128	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
129	#418×C₆₇	C₂²	1	2	yes	—
130	#417×C₆₇	C₂²	1	2	yes	complemented
131	#416×C₆₇	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₇	C₂²	1	2	yes	—
133	#408×C₆₇	C₂²	1	2	yes	complemented
134	#408×C₆₇	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₇	—	2	1	no	—
136	C₂×#41×C₆₇	—	2	1	no	—
137	C₂×#41×C₆₇	C₂³	1	2	yes	—
138	C₂×#41×C₆₇	C₂³	1	2	yes	—
139	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₆₇	—	2	1	no	—
141	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
151	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₆₇	—	2	2	no	—
153	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
154	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
157	#127×C₆₇	—	2	1	no	—
158	#127×C₆₇	—	2	2	no	—
159	#127×C₆₇	D₄	1	1	yes	characteristic
160	#127×C₆₇	C₂³	1	1	yes	characteristic
161	#126×C₆₇	—	2	2	no	—
162	#126×C₆₇	—	2	2	no	—
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	#125×C₆₇	—	2	1	no	—
169	#125×C₆₇	—	2	1	no	—
170	#125×C₆₇	—	2	2	no	—
171	#125×C₆₇	—	2	2	no	—
172	#125×C₆₇	C₂³	1	2	yes	—
173	#125×C₆₇	C₂³	1	1	yes	characteristic
174	#124×C₆₇	—	2	2	no	—
175	#124×C₆₇	—	2	1	no	—
176	#124×C₆₇	—	2	1	no	—
177	#124×C₆₇	—	2	1	no	—
178	#124×C₆₇	—	2	2	no	—
179	#124×C₆₇	—	2	1	no	—
180	#124×C₆₇	D₄	1	2	yes	—
181	#124×C₆₇	C₂³	1	1	yes	characteristic
182	#123×C₆₇	—	2	2	no	—
183	#123×C₆₇	—	2	2	no	—
184	#123×C₆₇	—	2	2	no	—
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	1	no	—
187	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	—	2	2	no	—
189	#123×C₆₇	—	2	2	no	—
190	C₂²⋊Q₈×C₆₇	—	2	2	no	—
191	C₂²⋊Q₈×C₆₇	—	2	1	no	—
192	C₂²⋊Q₈×C₆₇	—	2	1	no	—
193	C₂²⋊Q₈×C₆₇	—	2	1	no	—
194	C₂²⋊Q₈×C₆₇	—	2	2	no	—
195	C₂²⋊Q₈×C₆₇	—	2	2	no	—
196	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
199	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
202	#121×C₆₇	—	2	2	no	—
203	#121×C₆₇	—	2	2	no	—
204	#121×C₆₇	—	2	2	no	—
205	#121×C₆₇	—	2	2	no	—
206	#121×C₆₇	—	2	1	no	—
207	#121×C₆₇	—	2	1	no	—
208	#121×C₆₇	—	2	2	no	—
209	#121×C₆₇	—	2	2	no	—
210	#121×C₆₇	D₄	1	1	yes	characteristic
211	#121×C₆₇	D₄	1	1	yes	characteristic
212	#121×C₆₇	D₄	1	2	yes	—
213	#121×C₆₇	C₂³	1	1	yes	characteristic
214	#121×C₆₇	C₂³	1	2	yes	—
215	#121×C₆₇	C₂³	1	2	yes	—
216	#121×C₆₇	C₂³	1	2	yes	—
217	#121×C₆₇	C₂³	1	2	yes	—
218	#120×C₆₇	—	2	2	no	—
219	#120×C₆₇	—	2	2	no	—
220	#120×C₆₇	—	2	2	no	—
221	#120×C₆₇	—	2	2	no	—
222	C₄×Q₈×C₆₇	—	2	2	no	—
223	C₄×Q₈×C₆₇	—	2	1	no	—
224	C₄×Q₈×C₆₇	—	2	1	no	—
225	C₄×Q₈×C₆₇	—	2	1	no	—
226	C₄×Q₈×C₆₇	—	2	1	no	—
227	C₄×Q₈×C₆₇	—	2	1	no	—
228	C₄×Q₈×C₆₇	—	2	1	no	—
229	C₄×Q₈×C₆₇	—	2	1	no	—
230	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₆₇	—	2	2	no	—
236	C₄×D₄×C₆₇	—	2	2	no	—
237	C₄×D₄×C₆₇	—	2	2	no	—
238	C₄×D₄×C₆₇	—	2	1	no	—
239	C₄×D₄×C₆₇	—	2	1	no	—
240	C₄×D₄×C₆₇	—	2	1	no	—
241	C₄×D₄×C₆₇	—	2	1	no	—
242	C₄×D₄×C₆₇	—	2	2	no	—
243	C₄×D₄×C₆₇	—	2	1	no	—
244	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₇	C₂³	1	2	yes	—
246	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₇	C₂³	1	2	yes	—
248	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
249	#117×C₆₇	—	2	2	no	—
250	#117×C₆₇	—	2	2	no	—
251	#117×C₆₇	—	2	1	no	—
252	#117×C₆₇	C₂³	1	2	yes	—
253	#117×C₆₇	C₂³	1	2	yes	—
254	#117×C₆₇	C₂³	1	2	yes	—
255	#117×C₆₇	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
257	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
261	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
262	C₂×C₄²×C₆₇	—	2	1	no	—
263	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
264	#107×C₆₇	C₂³	1	2	yes	—
265	#107×C₆₇	C₂³	1	2	yes	—
266	#107×C₆₇	C₂³	1	2	yes	—
267	#107×C₆₇	C₂³	1	2	yes	—
268	#107×C₆₇	C₂³	1	1	yes	characteristic
269	#107×C₆₇	C₂³	1	1	yes	characteristic
270	#106×C₆₇	C₂³	1	2	yes	—
271	#106×C₆₇	C₂³	1	2	yes	—
272	#106×C₆₇	C₂³	1	2	yes	—
273	#106×C₆₇	C₂³	1	2	yes	—
274	#106×C₆₇	C₂³	1	2	yes	—
275	#106×C₆₇	C₂³	1	2	yes	—
276	#106×C₆₇	C₂³	1	1	yes	characteristic
277	#106×C₆₇	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	#103×C₆₇	C₂³	1	1	yes	characteristic
283	#103×C₆₇	C₂³	1	1	yes	characteristic
284	#103×C₆₇	C₂³	1	2	yes	—
285	#103×C₆₇	C₂³	1	2	yes	—
286	#103×C₆₇	C₂³	1	1	yes	characteristic
287	#103×C₆₇	C₂³	1	1	yes	characteristic
288	#103×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	1	yes	characteristic
291	#103×C₆₇	C₂³	1	1	yes	characteristic
292	#102×C₆₇	C₂³	1	2	yes	—
293	#102×C₆₇	C₂³	1	2	yes	—
294	#102×C₆₇	C₂³	1	2	yes	—
295	#102×C₆₇	C₂³	1	2	yes	—
296	#102×C₆₇	C₂³	1	2	yes	—
297	#102×C₆₇	C₂³	1	2	yes	—
298	#102×C₆₇	C₂³	1	2	yes	—
299	#102×C₆₇	C₂³	1	2	yes	—
300	#102×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	2	yes	—
312	C₂⁴×C₆₇	—	2	2	no	—
313	#41×C₆₇	—	4	2	no	—
314	#41×C₆₇	—	4	2	no	—
315	#41×C₆₇	—	4	2	no	—
316	#41×C₆₇	—	4	2	no	—
317	#41×C₆₇	—	8	2	no	—
318	#41×C₆₇	—	8	2	no	—
319	C₂×Q₈×C₆₇	—	2	1	no	—
320	C₂×Q₈×C₆₇	—	2	1	no	—
321	C₂×Q₈×C₆₇	—	2	1	no	—
322	C₂×Q₈×C₆₇	—	2	1	no	—
323	C₂×Q₈×C₆₇	—	4	1	no	—
324	C₂×Q₈×C₆₇	—	4	1	no	—
325	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₆₇	—	2	1	no	—
330	C₂×D₄×C₆₇	—	2	2	no	—
331	C₂×D₄×C₆₇	—	2	2	no	—
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	2	no	—
334	C₂×D₄×C₆₇	—	2	2	no	—
335	C₂×D₄×C₆₇	—	2	1	no	—
336	C₂×D₄×C₆₇	—	2	1	no	—
337	C₂×D₄×C₆₇	—	2	2	no	—
338	C₂×D₄×C₆₇	—	4	2	no	—
339	C₂×D₄×C₆₇	—	4	2	no	—
340	C₂×D₄×C₆₇	—	8	2	no	—
341	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₆₇	—	2	1	no	—
350	C₂²×C₄×C₆₇	—	2	1	no	—
351	C₂²×C₄×C₆₇	—	2	2	no	—
352	C₂²×C₄×C₆₇	—	2	2	no	—
353	C₂²×C₄×C₆₇	—	2	2	no	—
354	C₂²×C₄×C₆₇	—	2	1	no	—
355	C₂²×C₄×C₆₇	—	2	2	no	—
356	C₂²×C₄×C₆₇	—	2	2	no	—
357	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
362	Q₁₆×C₆₇	—	4	1	no	—
363	Q₁₆×C₆₇	—	4	1	no	—
364	SD₁₆×C₆₇	—	4	1	no	—
365	SD₁₆×C₆₇	—	4	2	no	—
366	SD₁₆×C₆₇	—	4	1	no	—
367	SD₁₆×C₆₇	—	4	2	no	—
368	M₁₆×C₆₇	—	4	2	no	—
369	M₁₆×C₆₇	—	4	2	no	—
370	C₂×C₈×C₆₇	—	4	2	no	—
371	C₂×C₈×C₆₇	—	4	2	no	—
372	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
375	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
377	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₆₇	—	2	1	no	—
379	C₄⋊C₄×C₆₇	—	2	1	no	—
380	C₄⋊C₄×C₆₇	—	2	1	no	—
381	C₄⋊C₄×C₆₇	—	2	1	no	—
382	C₄⋊C₄×C₆₇	—	2	1	no	—
383	C₄⋊C₄×C₆₇	—	2	2	no	—
384	C₄⋊C₄×C₆₇	—	2	2	no	—
385	C₄⋊C₄×C₆₇	—	2	2	no	—
386	C₄⋊C₄×C₆₇	—	2	2	no	—
387	C₄⋊C₄×C₆₇	—	2	1	no	—
388	C₄⋊C₄×C₆₇	—	2	1	no	—
389	C₄⋊C₄×C₆₇	—	2	2	no	—
390	C₄⋊C₄×C₆₇	—	2	2	no	—
391	C₄⋊C₄×C₆₇	—	2	1	no	—
392	C₄⋊C₄×C₆₇	—	2	1	no	—
393	C₄⋊C₄×C₆₇	—	2	1	no	—
394	C₄⋊C₄×C₆₇	—	2	2	no	—
395	C₄⋊C₄×C₆₇	—	2	2	no	—
396	C₄⋊C₄×C₆₇	—	2	1	no	—
397	C₄⋊C₄×C₆₇	—	2	2	no	—
398	C₄⋊C₄×C₆₇	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	1	no	—
400	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂²⋊C₄×C₆₇	—	2	2	no	—
411	C₂²⋊C₄×C₆₇	—	2	2	no	—
412	C₂²⋊C₄×C₆₇	—	2	2	no	—
413	C₂²⋊C₄×C₆₇	—	2	2	no	—
414	C₂²⋊C₄×C₆₇	—	2	2	no	—
415	C₂²⋊C₄×C₆₇	—	2	2	no	—
416	C₂²⋊C₄×C₆₇	—	2	2	no	—
417	C₂²⋊C₄×C₆₇	—	2	1	no	—
418	C₂²⋊C₄×C₆₇	—	2	2	no	—
419	C₂²⋊C₄×C₆₇	—	2	2	no	—
420	C₂²⋊C₄×C₆₇	—	2	1	no	—
421	C₂²⋊C₄×C₆₇	—	2	2	no	—
422	C₂²⋊C₄×C₆₇	—	2	1	no	—
423	C₂²⋊C₄×C₆₇	—	2	1	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	1	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
433	C₄²×C₆₇	—	2	1	no	—
434	C₄²×C₆₇	—	2	1	no	—
435	C₄²×C₆₇	—	2	1	no	—
436	C₄²×C₆₇	—	2	1	no	—
437	C₄²×C₆₇	—	2	2	no	—
438	C₄²×C₆₇	—	2	2	no	—
439	C₄²×C₆₇	—	2	1	no	—
440	C₄²×C₆₇	—	2	2	no	—
441	C₄²×C₆₇	—	2	2	no	—
442	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
445	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
446	C₂³×C₆₇	—	2	1	no	—
447	C₂³×C₆₇	—	2	2	no	—
448	C₂³×C₆₇	—	8	2	no	—
449	C₂³×C₆₇	—	8	2	no	—
450	C₂³×C₆₇	—	8	2	no	—
451	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
452	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
453	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
454	Q₈×C₆₇	—	2	1	no	—
455	Q₈×C₆₇	—	2	1	no	—
456	Q₈×C₆₇	—	2	1	no	—
457	Q₈×C₆₇	—	2	1	no	—
458	Q₈×C₆₇	—	2	1	no	—
459	Q₈×C₆₇	—	2	1	no	—
460	Q₈×C₆₇	—	4	2	no	—
461	Q₈×C₆₇	—	4	2	no	—
462	Q₈×C₆₇	—	4	2	no	—
463	Q₈×C₆₇	—	4	2	no	—
464	Q₈×C₆₇	—	8	1	no	—
465	D₄×C₆₇	—	2	2	no	—
466	D₄×C₆₇	—	2	2	no	—
467	D₄×C₆₇	—	2	1	no	—
468	D₄×C₆₇	—	2	1	no	—
469	D₄×C₆₇	—	2	2	no	—
470	D₄×C₆₇	—	2	2	no	—
471	D₄×C₆₇	—	4	2	no	—
472	D₄×C₆₇	—	4	2	no	—
473	D₄×C₆₇	—	4	2	no	—
474	D₄×C₆₇	—	4	2	no	—
475	D₄×C₆₇	—	4	2	no	—
476	D₄×C₆₇	—	8	1	no	—
477	D₄×C₆₇	—	8	2	no	—
478	D₄×C₆₇	—	8	1	no	—
479	D₄×C₆₇	—	8	2	no	—
480	D₄×C₆₇	—	8	2	no	—
481	D₄×C₆₇	—	8	2	no	—
482	D₄×C₆₇	—	8	2	no	—
483	D₄×C₆₇	—	8	2	no	—
484	C₂×C₄×C₆₇	—	2	2	no	—
485	C₂×C₄×C₆₇	—	2	2	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	2	1	no	—
490	C₂×C₄×C₆₇	—	2	1	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	2	1	no	—
493	C₂×C₄×C₆₇	—	2	2	no	—
494	C₂×C₄×C₆₇	—	2	1	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	1	no	—
498	C₂×C₄×C₆₇	—	2	2	no	—
499	C₂×C₄×C₆₇	—	2	2	no	—
500	C₂×C₄×C₆₇	—	2	1	no	—
501	C₂×C₄×C₆₇	—	4	1	no	—
502	C₂×C₄×C₆₇	—	4	2	no	—
503	C₂×C₄×C₆₇	—	4	2	no	—
504	C₂×C₄×C₆₇	—	8	2	no	—
505	C₂×C₄×C₆₇	—	8	2	no	—
506	C₂×C₄×C₆₇	—	8	1	no	—
507	C₂×C₄×C₆₇	—	8	2	no	—
508	C₂×C₄×C₆₇	—	8	2	no	—
509	C₂×C₄×C₆₇	—	8	2	no	—
510	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
518	C₈×C₆₇	—	2	1	no	—
519	C₈×C₆₇	—	2	2	no	—
520	C₈×C₆₇	—	2	1	no	—
521	C₈×C₆₇	—	2	2	no	—
522	C₈×C₆₇	—	2	1	no	—
523	C₈×C₆₇	—	2	1	no	—
524	C₂²×C₆₇	—	2	1	no	—
525	C₂²×C₆₇	—	2	2	no	—
526	C₂²×C₆₇	—	2	2	no	—
527	C₂²×C₆₇	—	2	1	no	—
528	C₂²×C₆₇	—	2	2	no	—
529	C₂²×C₆₇	—	2	2	no	—
530	C₂²×C₆₇	—	2	1	no	—
531	C₂²×C₆₇	—	2	2	no	—
532	C₂²×C₆₇	—	2	2	no	—
533	C₂²×C₆₇	—	4	2	no	—
534	C₂²×C₆₇	—	4	1	no	—
535	C₂²×C₆₇	—	4	2	no	—
536	C₂²×C₆₇	—	4	1	no	—
537	C₂²×C₆₇	—	4	1	no	—
538	C₂²×C₆₇	—	4	2	no	—
539	C₂²×C₆₇	—	16	4	no	—
540	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
541	C₄×C₆₇	—	2	1	no	—
542	C₄×C₆₇	—	2	1	no	—
543	C₄×C₆₇	—	2	2	no	—
544	C₄×C₆₇	—	2	1	no	—
545	C₄×C₆₇	—	2	2	no	—
546	C₄×C₆₇	—	2	1	no	—
547	C₄×C₆₇	—	4	1	no	—
548	C₄×C₆₇	—	4	1	no	—
549	C₄×C₆₇	—	4	2	no	—
550	C₄×C₆₇	—	4	1	no	—
551	C₄×C₆₇	—	4	1	no	—
552	C₄×C₆₇	—	4	1	no	—
553	C₄×C₆₇	—	4	1	no	—
554	C₄×C₆₇	—	4	1	no	—
555	C₄×C₆₇	—	4	2	no	—
556	C₄×C₆₇	—	4	2	no	—
557	C₄×C₆₇	#577	1	2	yes	—
558	C₄×C₆₇	#585	1	1	yes	characteristic
559	C₄×C₆₇	#585	1	1	yes	characteristic
560	#61786	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
561	C₂×C₆₇	—	4	1	no	—
562	C₂×C₆₇	—	4	2	no	—
563	C₂×C₆₇	—	4	2	no	—
564	C₂×C₆₇	—	8	2	no	—
565	C₂×C₆₇	—	8	1	no	—
566	C₂×C₆₇	#3485	1	1	yes	characteristic
567	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
568	C₂×C₆₇	#3584	1	1	yes	characteristic
569	#3546	C₂×C₆₇	1	1	yes	characteristic
570	#3507	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#3356	C₂×C₆₇	1	1	yes	characteristic, complemented
572	#3353	C₂×C₆₇	1	1	yes	characteristic, complemented
573	#3351	C₂×C₆₇	1	2	yes	complemented
574	#3342	C₂×C₆₇	1	1	yes	characteristic, complemented
575	#3337	C₂×C₆₇	1	2	yes	complemented
576	#3335	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#3333	C₂×C₆₇	1	1	yes	characteristic, complemented
578	#3324	C₂×C₆₇	1	1	yes	characteristic, complemented
579	#3323	C₂×C₆₇	1	2	yes	complemented
580	#3304	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#3296	C₂×C₆₇	1	2	yes	complemented
582	#3295	C₂×C₆₇	1	1	yes	characteristic, complemented
583	#3233	C₂×C₆₇	1	1	yes	characteristic, complemented
584	#3228	C₂×C₆₇	1	1	yes	characteristic, complemented
585	#3201	C₂×C₆₇	1	2	yes	complemented
586	#3200	C₂×C₆₇	1	2	yes	complemented
587	#3108	C₂×C₆₇	1	1	yes	characteristic, complemented
588	#3103	C₂×C₆₇	1	1	yes	characteristic, complemented
589	#3099	C₂×C₆₇	1	2	yes	complemented
590	#3096	C₂×C₆₇	1	2	yes	complemented
591	#2979	C₂×C₆₇	1	1	yes	characteristic, complemented
592	C₆₇	#61786	1	1	yes	characteristic, direct product factor, Sylow
593	#560	—	2	2	no	—
594	#559	—	2	1	no	—
595	#557	—	2	1	no	—
596	#556	—	2	2	no	—
597	#556	C₂²×C₆₇	1	1	yes	characteristic
598	#556	C₂²×C₆₇	1	1	yes	characteristic
599	#556	C₂²×C₆₇	1	1	yes	characteristic, complemented
600	#554	C₂²×C₆₇	1	1	yes	characteristic
601	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
602	#553	C₂²×C₆₇	1	2	yes	—
603	#552	C₂²×C₆₇	1	2	yes	complemented
604	#552	C₂²×C₆₇	1	2	yes	complemented
605	#550	—	2	1	no	—
606	#550	C₂²×C₆₇	1	1	yes	characteristic
607	#547	C₂²×C₆₇	1	1	yes	characteristic
608	#546	—	2	1	no	—
609	#546	C₂²×C₆₇	1	2	yes	—
610	D₄²	C₂²×C₆₇	1	1	yes	characteristic
611	#542	—	2	1	no	—
612	#539	—	2	2	no	—
613	#538	—	2	2	no	—
614	#537	C₂²×C₆₇	1	2	yes	—
615	#536	C₂²×C₆₇	1	2	yes	complemented
616	#535	—	2	1	no	—
617	#535	C₂²×C₆₇	1	2	yes	—
618	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
619	#532	C₂²×C₆₇	1	1	yes	characteristic
620	#532	C₂²×C₆₇	1	1	yes	characteristic
621	#529	—	2	1	no	—
622	#529	—	2	1	no	—
623	#529	C₂²×C₆₇	1	1	yes	characteristic
624	#520	C₂²×C₆₇	1	2	yes	complemented
625	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
626	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	#499	C₂²×C₆₇	1	2	yes	complemented
628	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	#488	C₂²×C₆₇	1	2	yes	—
630	#486	C₂²×C₆₇	1	1	yes	characteristic
631	#486	C₂²×C₆₇	1	1	yes	characteristic
632	#485	C₂²×C₆₇	1	2	yes	complemented
633	#485	C₂²×C₆₇	1	2	yes	complemented
634	#485	C₂²×C₆₇	1	2	yes	complemented
635	#485	C₂²×C₆₇	1	2	yes	complemented
636	#484	C₂²×C₆₇	1	2	yes	complemented
637	#483	C₂²×C₆₇	1	2	yes	complemented
638	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
639	#483	C₂²×C₆₇	1	2	yes	complemented
640	#482	C₂²×C₆₇	1	2	yes	—
641	#482	C₂²×C₆₇	1	2	yes	—
642	#482	C₂²×C₆₇	1	2	yes	—
643	#482	C₂²×C₆₇	1	2	yes	complemented
644	#482	C₂²×C₆₇	1	2	yes	complemented
645	#482	C₂²×C₆₇	1	2	yes	complemented
646	#481	C₂²×C₆₇	1	2	yes	—
647	#481	C₂²×C₆₇	1	2	yes	—
648	#481	C₂²×C₆₇	1	2	yes	complemented
649	#480	C₂²×C₆₇	1	1	yes	characteristic
650	#480	C₂²×C₆₇	1	2	yes	complemented
651	#479	C₂²×C₆₇	1	1	yes	characteristic, complemented
652	#479	C₂²×C₆₇	1	1	yes	characteristic, complemented
653	#478	C₂²×C₆₇	1	2	yes	complemented
654	#478	C₂²×C₆₇	1	2	yes	complemented
655	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
656	#476	C₂²×C₆₇	1	1	yes	characteristic
657	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
658	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
659	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
660	#474	C₂²×C₆₇	1	1	yes	characteristic
661	#470	C₂²×C₆₇	1	2	yes	complemented
662	#468	C₂²×C₆₇	1	2	yes	—
663	#468	C₂²×C₆₇	1	2	yes	—
664	#468	C₂²×C₆₇	1	2	yes	complemented
665	#467	C₂²×C₆₇	1	2	yes	complemented
666	#465	C₂²×C₆₇	1	2	yes	—
667	#465	C₂²×C₆₇	1	2	yes	—
668	#465	C₂²×C₆₇	1	2	yes	complemented
669	#464	C₂²×C₆₇	1	1	yes	characteristic
670	#464	C₂²×C₆₇	1	1	yes	characteristic
671	#460	C₂²×C₆₇	1	1	yes	characteristic
672	#460	C₂²×C₆₇	1	1	yes	characteristic
673	#452	C₂²×C₆₇	1	2	yes	complemented
674	#452	C₂²×C₆₇	1	2	yes	complemented
675	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
676	#450	C₂²×C₆₇	1	2	yes	—
677	#450	C₂²×C₆₇	1	2	yes	—
678	#448	C₂²×C₆₇	1	1	yes	characteristic
679	#448	C₂²×C₆₇	1	2	yes	complemented
680	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
681	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
682	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
683	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
684	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
685	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
686	#436	C₂²×C₆₇	1	1	yes	characteristic
687	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	#436	C₂²×C₆₇	1	2	yes	complemented
689	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
690	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
691	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
692	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
694	#428	C₂²×C₆₇	1	2	yes	complemented
695	#428	C₂²×C₆₇	1	2	yes	complemented
696	#427	C₂²×C₆₇	1	2	yes	complemented
697	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
698	#418	C₂²×C₆₇	1	2	yes	—
699	#417	C₂²×C₆₇	1	2	yes	complemented
700	#416	C₂²×C₆₇	1	2	yes	complemented
701	C₂×#102	C₂²×C₆₇	1	2	yes	—
702	#408	C₂²×C₆₇	1	2	yes	complemented
703	#408	C₂²×C₆₇	1	2	yes	complemented
704	C₂×#41	—	2	1	no	—
705	C₂×#41	—	2	1	no	—
706	C₂×#41	C₂³×C₆₇	1	2	yes	—
707	C₂×#41	C₂³×C₆₇	1	2	yes	—
708	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
709	C₂²×D₄	—	2	1	no	—
710	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
711	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
712	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
713	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
717	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
718	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
719	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
720	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
721	C₄⋊Q₈	—	2	2	no	—
722	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
726	#127	—	2	1	no	—
727	#127	—	2	2	no	—
728	#127	D₄×C₆₇	1	1	yes	characteristic
729	#127	C₂³×C₆₇	1	1	yes	characteristic
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	1	no	—
737	#125	—	2	1	no	—
738	#125	—	2	1	no	—
739	#125	—	2	2	no	—
740	#125	—	2	2	no	—
741	#125	C₂³×C₆₇	1	1	yes	characteristic
742	#125	C₂³×C₆₇	1	2	yes	—
743	#124	—	2	2	no	—
744	#124	—	2	1	no	—
745	#124	—	2	1	no	—
746	#124	—	2	1	no	—
747	#124	—	2	2	no	—
748	#124	—	2	1	no	—
749	#124	D₄×C₆₇	1	2	yes	—
750	#124	C₂³×C₆₇	1	1	yes	characteristic
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	1	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	1	no	—
776	#121	—	2	1	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	D₄×C₆₇	1	1	yes	characteristic
780	#121	D₄×C₆₇	1	1	yes	characteristic
781	#121	D₄×C₆₇	1	2	yes	—
782	#121	C₂³×C₆₇	1	1	yes	characteristic
783	#121	C₂³×C₆₇	1	2	yes	—
784	#121	C₂³×C₆₇	1	2	yes	—
785	#121	C₂³×C₆₇	1	2	yes	—
786	#121	C₂³×C₆₇	1	2	yes	—
787	#120	—	2	2	no	—
788	#120	—	2	2	no	—
789	#120	—	2	2	no	—
790	#120	—	2	2	no	—
791	C₄×Q₈	—	2	2	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₆₇	1	2	yes	—
815	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₆₇	1	2	yes	—
817	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
818	#117	—	2	2	no	—
819	#117	—	2	2	no	—
820	#117	—	2	1	no	—
821	#117	C₂³×C₆₇	1	2	yes	—
822	#117	C₂³×C₆₇	1	2	yes	—
823	#117	C₂³×C₆₇	1	2	yes	—
824	#117	C₂³×C₆₇	1	2	yes	—
825	C₂×C₄⋊C₄	—	2	1	no	—
826	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
827	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
828	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
829	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
830	C₂×C₂²⋊C₄	—	2	2	no	—
831	C₂×C₄²	—	2	1	no	—
832	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
833	#107	C₂³×C₆₇	1	1	yes	characteristic
834	#107	C₂³×C₆₇	1	2	yes	—
835	#107	C₂³×C₆₇	1	1	yes	characteristic
836	#107	C₂³×C₆₇	1	2	yes	—
837	#107	C₂³×C₆₇	1	2	yes	—
838	#107	C₂³×C₆₇	1	2	yes	—
839	#106	C₂³×C₆₇	1	1	yes	characteristic
840	#106	C₂³×C₆₇	1	2	yes	—
841	#106	C₂³×C₆₇	1	2	yes	—
842	#106	C₂³×C₆₇	1	2	yes	—
843	#106	C₂³×C₆₇	1	2	yes	—
844	#106	C₂³×C₆₇	1	1	yes	characteristic
845	#106	C₂³×C₆₇	1	2	yes	—
846	#106	C₂³×C₆₇	1	2	yes	—
847	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
849	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
850	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
851	#103	C₂³×C₆₇	1	1	yes	characteristic
852	#103	C₂³×C₆₇	1	2	yes	—
853	#103	C₂³×C₆₇	1	1	yes	characteristic
854	#103	C₂³×C₆₇	1	2	yes	—
855	#103	C₂³×C₆₇	1	1	yes	characteristic
856	#103	C₂³×C₆₇	1	1	yes	characteristic
857	#103	C₂³×C₆₇	1	2	yes	—
858	#103	C₂³×C₆₇	1	2	yes	—
859	#103	C₂³×C₆₇	1	1	yes	characteristic
860	#103	C₂³×C₆₇	1	1	yes	characteristic
861	#102	C₂³×C₆₇	1	1	yes	characteristic
862	#102	C₂³×C₆₇	1	2	yes	—
863	#102	C₂³×C₆₇	1	2	yes	—
864	#102	C₂³×C₆₇	1	2	yes	—
865	#102	C₂³×C₆₇	1	2	yes	—
866	#102	C₂³×C₆₇	1	2	yes	—
867	#102	C₂³×C₆₇	1	2	yes	—
868	#102	C₂³×C₆₇	1	1	yes	characteristic
869	#102	C₂³×C₆₇	1	2	yes	—
870	#102	C₂³×C₆₇	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
874	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
878	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
879	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
880	C₄×C₈	C₂³×C₆₇	1	2	yes	—
881	C₂⁴	—	2	2	no	—
882	#41	—	4	2	no	—
883	#41	—	4	2	no	—
884	#41	—	4	2	no	—
885	#41	—	4	2	no	—
886	#41	—	8	2	no	—
887	#41	—	8	2	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	1	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	4	1	no	—
893	C₂×Q₈	—	4	1	no	—
894	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
895	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
897	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	—	4	2	no	—
909	C₂×D₄	—	8	2	no	—
910	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
911	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
912	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
913	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
914	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
915	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
916	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
917	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
927	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
928	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
931	Q₁₆	—	4	1	no	—
932	Q₁₆	—	4	1	no	—
933	SD₁₆	—	4	1	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	1	no	—
936	SD₁₆	—	4	2	no	—
937	M₁₆	—	4	2	no	—
938	M₁₆	—	4	2	no	—
939	C₂×C₈	—	4	2	no	—
940	C₂×C₈	—	4	2	no	—
941	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
943	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
945	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
971	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
976	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1001	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1012	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	8	2	no	—
1018	C₂³	—	8	2	no	—
1019	C₂³	—	8	2	no	—
1020	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1021	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1022	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	1	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	4	2	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	4	2	no	—
1032	Q₈	—	4	2	no	—
1033	Q₈	—	8	1	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	2	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	1	no	—
1047	D₄	—	8	2	no	—
1048	D₄	—	8	2	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	8	2	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	1	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1082	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1086	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1087	C₈	—	2	1	no	—
1088	C₈	—	2	2	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	1	no	—
1091	C₈	—	2	2	no	—
1092	C₈	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	4	2	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	16	4	no	—
1109	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1110	C₄	—	2	1	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	1	no	—
1113	C₄	—	2	2	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	2	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	#577×C₆₇	1	2	yes	—
1127	C₄	#585×C₆₇	1	1	yes	characteristic
1128	C₄	#585×C₆₇	1	1	yes	characteristic
1129	C₂	—	4	2	no	—
1130	C₂	—	4	1	no	—
1131	C₂	—	4	2	no	—
1132	C₂	—	8	1	no	—
1133	C₂	—	8	2	no	—
1134	C₂	C₆₇×#3485	1	1	yes	characteristic
1135	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1136	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3546	C₂
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
2. C₆₇×#3507	C₂	semidirect
3. C₆₇×#3356	C₂	semidirect
4. C₆₇×#3353	C₂	semidirect
5. C₆₇×#3351	C₂	semidirect
6. C₆₇×#3342	C₂	semidirect
7. C₆₇×#3337	C₂	semidirect
8. C₆₇×#3335	C₂	semidirect
9. C₆₇×#3333	C₂	semidirect
10. C₆₇×#3324	C₂	semidirect
11. C₆₇×#3323	C₂	semidirect
12. C₆₇×#3304	C₂	semidirect
13. C₆₇×#3296	C₂	semidirect
14. C₆₇×#3295	C₂	semidirect
15. C₆₇×#3233	C₂	semidirect
16. C₆₇×#3228	C₂	semidirect
17. C₆₇×#3201	C₂	semidirect
18. C₆₇×#3200	C₂	semidirect
19. C₆₇×#3108	C₂	semidirect
20. C₆₇×#3103	C₂	semidirect
21. C₆₇×#3099	C₂	semidirect
22. C₆₇×#3096	C₂	semidirect
23. C₆₇×#2979	C₂	semidirect
30. #556×C₆₇	C₂²	semidirect
32. #554×C₆₇	C₂²	semidirect
34. #552×C₆₇	C₂²	semidirect
35. #552×C₆₇	C₂²	semidirect
46. #536×C₆₇	C₂²	semidirect
49. #533×C₆₇	C₂²	semidirect
55. #520×C₆₇	C₂²	semidirect
56. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
57. #500×C₆₇	C₂²	semidirect
58. #499×C₆₇	C₂²	semidirect
59. #498×C₆₇	C₂²	semidirect
63. #485×C₆₇	C₂²	semidirect
64. #485×C₆₇	C₂²	semidirect
65. #485×C₆₇	C₂²	semidirect
66. #485×C₆₇	C₂²	semidirect
67. #484×C₆₇	C₂²	semidirect
68. #483×C₆₇	C₂²	semidirect
69. #483×C₆₇	C₂²	semidirect
70. #483×C₆₇	C₂²	semidirect
74. #482×C₆₇	C₂²	semidirect
75. #482×C₆₇	C₂²	semidirect
76. #482×C₆₇	C₂²	semidirect
79. #481×C₆₇	C₂²	semidirect
81. #480×C₆₇	C₂²	semidirect
82. #479×C₆₇	C₂²	semidirect
83. #479×C₆₇	C₂²	semidirect
84. #478×C₆₇	C₂²	semidirect
85. #478×C₆₇	C₂²	semidirect
86. #477×C₆₇	C₂²	semidirect
88. #475×C₆₇	C₂²	semidirect
89. #475×C₆₇	C₂²	semidirect
90. #475×C₆₇	C₂²	semidirect
92. #470×C₆₇	C₂²	semidirect
95. #468×C₆₇	C₂²	semidirect
96. #467×C₆₇	C₂²	semidirect
99. #465×C₆₇	C₂²	semidirect
104. #452×C₆₇	C₂²	semidirect
105. #452×C₆₇	C₂²	semidirect
106. #451×C₆₇	C₂²	semidirect
110. #448×C₆₇	C₂²	semidirect
111. C₄×Q₁₆×C₆₇	C₂²	semidirect
112. C₄×Q₁₆×C₆₇	C₂²	semidirect
115. C₄×SD₁₆×C₆₇	C₂²	semidirect
116. C₄×SD₁₆×C₆₇	C₂²	semidirect
118. #436×C₆₇	C₂²	semidirect
119. #436×C₆₇	C₂²	semidirect
121. C₈×D₄×C₆₇	C₂²	semidirect
122. C₈×D₄×C₆₇	C₂²	semidirect
123. #431×C₆₇	C₂²	semidirect
124. #431×C₆₇	C₂²	semidirect
125. #428×C₆₇	C₂²	semidirect
126. #428×C₆₇	C₂²	semidirect
127. #427×C₆₇	C₂²	semidirect
128. C₂×#106×C₆₇	C₂²	semidirect
130. #417×C₆₇	C₂²	semidirect
131. #416×C₆₇	C₂²	semidirect
133. #408×C₆₇	C₂²	semidirect
134. #408×C₆₇	C₂²	semidirect
560. #61786	C₆₇	direct (N × H)
570. #3507	C₂×C₆₇	semidirect
571. #3356	C₂×C₆₇	semidirect
572. #3353	C₂×C₆₇	semidirect
573. #3351	C₂×C₆₇	semidirect
574. #3342	C₂×C₆₇	semidirect
575. #3337	C₂×C₆₇	semidirect
576. #3335	C₂×C₆₇	semidirect
577. #3333	C₂×C₆₇	semidirect
578. #3324	C₂×C₆₇	semidirect
579. #3323	C₂×C₆₇	semidirect
580. #3304	C₂×C₆₇	semidirect
581. #3296	C₂×C₆₇	semidirect
582. #3295	C₂×C₆₇	semidirect
583. #3233	C₂×C₆₇	semidirect
584. #3228	C₂×C₆₇	semidirect
585. #3201	C₂×C₆₇	semidirect
586. #3200	C₂×C₆₇	semidirect
587. #3108	C₂×C₆₇	semidirect
588. #3103	C₂×C₆₇	semidirect
589. #3099	C₂×C₆₇	semidirect
590. #3096	C₂×C₆₇	semidirect
591. #2979	C₂×C₆₇	semidirect
592. C₆₇	#61786	direct (N × H)
599. #556	C₂²×C₆₇	semidirect
601. #554	C₂²×C₆₇	semidirect
603. #552	C₂²×C₆₇	semidirect
604. #552	C₂²×C₆₇	semidirect
615. #536	C₂²×C₆₇	semidirect
618. #533	C₂²×C₆₇	semidirect
624. #520	C₂²×C₆₇	semidirect
625. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
626. #500	C₂²×C₆₇	semidirect
627. #499	C₂²×C₆₇	semidirect
628. #498	C₂²×C₆₇	semidirect
632. #485	C₂²×C₆₇	semidirect
633. #485	C₂²×C₆₇	semidirect
634. #485	C₂²×C₆₇	semidirect
635. #485	C₂²×C₆₇	semidirect
636. #484	C₂²×C₆₇	semidirect
637. #483	C₂²×C₆₇	semidirect
638. #483	C₂²×C₆₇	semidirect
639. #483	C₂²×C₆₇	semidirect
643. #482	C₂²×C₆₇	semidirect
644. #482	C₂²×C₆₇	semidirect
645. #482	C₂²×C₆₇	semidirect
648. #481	C₂²×C₆₇	semidirect
650. #480	C₂²×C₆₇	semidirect
651. #479	C₂²×C₆₇	semidirect
652. #479	C₂²×C₆₇	semidirect
653. #478	C₂²×C₆₇	semidirect
654. #478	C₂²×C₆₇	semidirect
655. #477	C₂²×C₆₇	semidirect
657. #475	C₂²×C₆₇	semidirect
658. #475	C₂²×C₆₇	semidirect
659. #475	C₂²×C₆₇	semidirect
661. #470	C₂²×C₆₇	semidirect
664. #468	C₂²×C₆₇	semidirect
665. #467	C₂²×C₆₇	semidirect
668. #465	C₂²×C₆₇	semidirect
673. #452	C₂²×C₆₇	semidirect
674. #452	C₂²×C₆₇	semidirect
675. #451	C₂²×C₆₇	semidirect
679. #448	C₂²×C₆₇	semidirect
680. C₄×Q₁₆	C₂²×C₆₇	semidirect
681. C₄×Q₁₆	C₂²×C₆₇	semidirect
684. C₄×SD₁₆	C₂²×C₆₇	semidirect
685. C₄×SD₁₆	C₂²×C₆₇	semidirect
687. #436	C₂²×C₆₇	semidirect
688. #436	C₂²×C₆₇	semidirect
690. C₈×D₄	C₂²×C₆₇	semidirect
691. C₈×D₄	C₂²×C₆₇	semidirect
692. #431	C₂²×C₆₇	semidirect
693. #431	C₂²×C₆₇	semidirect
694. #428	C₂²×C₆₇	semidirect
695. #428	C₂²×C₆₇	semidirect
696. #427	C₂²×C₆₇	semidirect
697. C₂×#106	C₂²×C₆₇	semidirect
699. #417	C₂²×C₆₇	semidirect
700. #416	C₂²×C₆₇	semidirect
702. #408	C₂²×C₆₇	semidirect
703. #408	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×#3546	2
C₆₇×#3507	2
C₆₇×#3356	2
C₆₇×#3353	2
C₆₇×#3351	2
C₆₇×#3342	2
C₆₇×#3337	2
C₆₇×#3335	2
C₆₇×#3333	2
C₆₇×#3324	2
C₆₇×#3323	2
C₆₇×#3304	2
C₆₇×#3296	2
C₆₇×#3295	2
C₆₇×#3233	2
C₆₇×#3228	2
C₆₇×#3201	2
C₆₇×#3200	2
C₆₇×#3108	2
C₆₇×#3103	2
C₆₇×#3099	2
C₆₇×#3096	2
C₆₇×#2979	2
#61786	67

Subgroups — C67×#61786 #30741037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61786 #30741037