Subgroups — C₆₇×#61276 #30740527

Order 17152.

1824 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3354	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3351	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3350	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3347	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3347	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3343	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3340	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3339	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#482×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3081	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3055	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2946	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2913	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2911	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
27	#556×C₆₇	—	2	1	no	—
28	#556×C₆₇	C₂²	1	2	yes	complemented
29	#555×C₆₇	—	2	1	no	—
30	#555×C₆₇	C₂²	1	2	yes	—
31	#555×C₆₇	C₂²	1	2	yes	complemented
32	#553×C₆₇	—	2	1	no	—
33	#553×C₆₇	C₂²	1	2	yes	—
34	#553×C₆₇	C₂²	1	2	yes	—
35	#553×C₆₇	C₂²	1	2	yes	complemented
36	#552×C₆₇	—	2	1	no	—
37	#552×C₆₇	C₂²	1	2	yes	complemented
38	#551×C₆₇	—	2	2	no	—
39	#547×C₆₇	C₂²	1	2	yes	—
40	#546×C₆₇	—	2	2	no	—
41	#544×C₆₇	C₂²	1	1	yes	characteristic
42	#544×C₆₇	C₂²	1	1	yes	characteristic
43	#542×C₆₇	—	2	1	no	—
44	#540×C₆₇	—	2	1	no	—
45	#538×C₆₇	—	2	2	no	—
46	#537×C₆₇	C₂²	1	1	yes	characteristic
47	#535×C₆₇	C₂²	1	1	yes	characteristic
48	#532×C₆₇	—	2	1	no	—
49	#529×C₆₇	—	2	2	no	—
50	#529×C₆₇	—	2	1	no	—
51	#525×C₆₇	C₂²	1	1	yes	characteristic
52	#525×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
54	#520×C₆₇	C₂²	1	1	yes	characteristic
55	#520×C₆₇	C₂²	1	1	yes	characteristic
56	#520×C₆₇	C₂²	1	1	yes	characteristic
57	#518×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
60	#501×C₆₇	C₂²	1	2	yes	complemented
61	#501×C₆₇	C₂²	1	2	yes	complemented
62	#499×C₆₇	C₂²	1	2	yes	complemented
63	#498×C₆₇	C₂²	1	2	yes	complemented
64	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#485×C₆₇	C₂²	1	2	yes	complemented
66	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#483×C₆₇	C₂²	1	2	yes	complemented
69	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#482×C₆₇	C₂²	1	2	yes	—
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	1	yes	characteristic, complemented
75	#482×C₆₇	C₂²	1	2	yes	complemented
76	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#482×C₆₇	C₂²	1	2	yes	complemented
78	#482×C₆₇	C₂²	1	2	yes	complemented
79	#481×C₆₇	C₂²	1	2	yes	complemented
80	#481×C₆₇	C₂²	1	2	yes	complemented
81	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#480×C₆₇	C₂²	1	2	yes	complemented
83	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#479×C₆₇	C₂²	1	2	yes	complemented
85	#478×C₆₇	C₂²	1	2	yes	complemented
86	#478×C₆₇	C₂²	1	2	yes	complemented
87	#478×C₆₇	C₂²	1	2	yes	complemented
88	#477×C₆₇	C₂²	1	2	yes	complemented
89	#476×C₆₇	C₂²	1	2	yes	complemented
90	#474×C₆₇	C₂²	1	2	yes	complemented
91	#474×C₆₇	C₂²	1	2	yes	complemented
92	#469×C₆₇	C₂²	1	2	yes	—
93	#469×C₆₇	C₂²	1	2	yes	complemented
94	#468×C₆₇	C₂²	1	2	yes	—
95	#468×C₆₇	C₂²	1	2	yes	complemented
96	#466×C₆₇	C₂²	1	2	yes	—
97	#466×C₆₇	C₂²	1	2	yes	complemented
98	#465×C₆₇	C₂²	1	2	yes	—
99	#465×C₆₇	C₂²	1	2	yes	complemented
100	#442×C₆₇	C₂²	1	2	yes	complemented
101	#440×C₆₇	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
103	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
104	#436×C₆₇	C₂²	1	2	yes	complemented
105	#435×C₆₇	C₂²	1	2	yes	complemented
106	#435×C₆₇	C₂²	1	2	yes	complemented
107	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
108	#428×C₆₇	C₂²	1	1	yes	characteristic
109	#428×C₆₇	C₂²	1	1	yes	characteristic
110	#428×C₆₇	C₂²	1	1	yes	characteristic
111	#428×C₆₇	C₂²	1	1	yes	characteristic
112	#428×C₆₇	C₂²	1	1	yes	characteristic
113	#428×C₆₇	C₂²	1	2	yes	complemented
114	#428×C₆₇	C₂²	1	2	yes	complemented
115	#428×C₆₇	C₂²	1	2	yes	complemented
116	#428×C₆₇	C₂²	1	2	yes	complemented
117	#427×C₆₇	C₂²	1	1	yes	characteristic
118	#427×C₆₇	C₂²	1	1	yes	characteristic
119	#427×C₆₇	C₂²	1	2	yes	complemented
120	#427×C₆₇	C₂²	1	2	yes	complemented
121	#427×C₆₇	C₂²	1	2	yes	complemented
122	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
123	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
124	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
125	#424×C₆₇	C₂²	1	1	yes	characteristic
126	#418×C₆₇	C₂²	1	1	yes	characteristic
127	#417×C₆₇	C₂²	1	1	yes	characteristic
128	#416×C₆₇	C₂²	1	1	yes	characteristic
129	#416×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
131	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
134	#405×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₇	—	2	2	no	—
136	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₆₇	—	2	1	no	—
139	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
141	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
142	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
143	C₂×D₈×C₆₇	C₂³	1	2	yes	—
144	#131×C₆₇	—	2	4	no	—
145	C₂×M₁₆×C₆₇	—	2	4	no	—
146	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
151	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
152	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₆₇	—	2	1	no	—
155	C₄⋊Q₈×C₆₇	—	2	1	no	—
156	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
158	#127×C₆₇	—	2	1	no	—
159	#126×C₆₇	—	2	2	no	—
160	#126×C₆₇	—	2	2	no	—
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	#125×C₆₇	—	2	1	no	—
166	#125×C₆₇	—	2	2	no	—
167	#125×C₆₇	—	2	1	no	—
168	#125×C₆₇	C₂³	1	2	yes	—
169	#125×C₆₇	C₂³	1	2	yes	—
170	#124×C₆₇	—	2	1	no	—
171	#124×C₆₇	—	2	2	no	—
172	#124×C₆₇	—	2	2	no	—
173	#124×C₆₇	—	2	2	no	—
174	#124×C₆₇	—	2	2	no	—
175	#124×C₆₇	—	2	2	no	—
176	#123×C₆₇	—	2	2	no	—
177	#123×C₆₇	—	2	1	no	—
178	#123×C₆₇	—	2	2	no	—
179	#123×C₆₇	—	2	2	no	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	—	2	2	no	—
182	#123×C₆₇	—	2	2	no	—
183	#123×C₆₇	D₄	1	2	yes	—
184	C₂²⋊Q₈×C₆₇	—	2	1	no	—
185	C₂²⋊Q₈×C₆₇	—	2	2	no	—
186	C₂²⋊Q₈×C₆₇	—	2	2	no	—
187	C₂²⋊Q₈×C₆₇	—	2	2	no	—
188	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
189	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
190	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
191	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
192	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
193	#121×C₆₇	—	2	2	no	—
194	#121×C₆₇	—	2	2	no	—
195	#121×C₆₇	—	2	1	no	—
196	#121×C₆₇	—	2	2	no	—
197	#121×C₆₇	—	2	2	no	—
198	#121×C₆₇	—	2	2	no	—
199	#121×C₆₇	—	2	2	no	—
200	#121×C₆₇	—	2	1	no	—
201	#121×C₆₇	—	2	1	no	—
202	#121×C₆₇	D₄	1	1	yes	characteristic
203	#121×C₆₇	D₄	1	1	yes	characteristic
204	#121×C₆₇	C₂³	1	2	yes	—
205	#121×C₆₇	C₂³	1	2	yes	—
206	#121×C₆₇	C₂³	1	1	yes	characteristic
207	#121×C₆₇	C₂³	1	2	yes	—
208	#121×C₆₇	C₂³	1	2	yes	—
209	#121×C₆₇	C₂³	1	2	yes	—
210	#121×C₆₇	C₂³	1	1	yes	characteristic
211	#120×C₆₇	—	2	1	no	—
212	#120×C₆₇	—	2	2	no	—
213	#120×C₆₇	D₄	1	2	yes	—
214	C₄×Q₈×C₆₇	—	2	1	no	—
215	C₄×Q₈×C₆₇	—	2	1	no	—
216	C₄×Q₈×C₆₇	—	2	2	no	—
217	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
218	C₄×D₄×C₆₇	—	2	2	no	—
219	C₄×D₄×C₆₇	—	2	1	no	—
220	C₄×D₄×C₆₇	—	2	2	no	—
221	C₄×D₄×C₆₇	—	2	1	no	—
222	C₄×D₄×C₆₇	—	2	1	no	—
223	C₄×D₄×C₆₇	—	2	1	no	—
224	C₄×D₄×C₆₇	—	2	1	no	—
225	C₄×D₄×C₆₇	—	2	1	no	—
226	C₄×D₄×C₆₇	—	2	2	no	—
227	C₄×D₄×C₆₇	—	2	2	no	—
228	C₄×D₄×C₆₇	—	2	2	no	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	C₂³	1	2	yes	—
231	C₄×D₄×C₆₇	C₂³	1	2	yes	—
232	C₄×D₄×C₆₇	C₂³	1	2	yes	—
233	C₄×D₄×C₆₇	C₂³	1	2	yes	—
234	C₄×D₄×C₆₇	C₂³	1	2	yes	—
235	#117×C₆₇	—	2	1	no	—
236	#117×C₆₇	—	2	1	no	—
237	#117×C₆₇	—	2	1	no	—
238	#117×C₆₇	—	2	1	no	—
239	#117×C₆₇	—	2	1	no	—
240	#117×C₆₇	—	2	2	no	—
241	#117×C₆₇	—	2	2	no	—
242	#117×C₆₇	—	2	2	no	—
243	#117×C₆₇	C₂³	1	2	yes	—
244	#117×C₆₇	C₂³	1	2	yes	—
245	#117×C₆₇	C₂³	1	2	yes	—
246	#117×C₆₇	C₂³	1	1	yes	characteristic
247	#117×C₆₇	C₂³	1	1	yes	characteristic
248	#117×C₆₇	C₂³	1	2	yes	—
249	#117×C₆₇	C₂³	1	1	yes	characteristic
250	#117×C₆₇	C₂³	1	1	yes	characteristic
251	#117×C₆₇	C₂³	1	1	yes	characteristic
252	#117×C₆₇	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
254	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
262	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
265	C₂×C₄²×C₆₇	—	2	1	no	—
266	C₂×C₄²×C₆₇	—	2	1	no	—
267	#107×C₆₇	C₂³	1	2	yes	—
268	#107×C₆₇	C₂³	1	2	yes	—
269	#107×C₆₇	C₂³	1	1	yes	characteristic
270	#107×C₆₇	C₂³	1	2	yes	—
271	#107×C₆₇	C₂³	1	2	yes	—
272	#107×C₆₇	C₂³	1	2	yes	—
273	#107×C₆₇	C₂³	1	2	yes	—
274	#107×C₆₇	C₂³	1	1	yes	characteristic
275	#107×C₆₇	C₂³	1	1	yes	characteristic
276	#107×C₆₇	C₂³	1	1	yes	characteristic
277	#107×C₆₇	C₂³	1	2	yes	—
278	#106×C₆₇	C₂³	1	2	yes	—
279	#106×C₆₇	C₂³	1	2	yes	—
280	#106×C₆₇	C₂³	1	1	yes	characteristic
281	#106×C₆₇	C₂³	1	2	yes	—
282	#106×C₆₇	C₂³	1	1	yes	characteristic
283	#106×C₆₇	C₂³	1	2	yes	—
284	#106×C₆₇	C₂³	1	1	yes	characteristic
285	#106×C₆₇	C₂³	1	2	yes	—
286	#106×C₆₇	C₂³	1	1	yes	characteristic
287	#106×C₆₇	C₂³	1	2	yes	—
288	#106×C₆₇	C₂³	1	2	yes	—
289	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
290	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	1	yes	characteristic
293	#103×C₆₇	C₂³	1	1	yes	characteristic
294	#103×C₆₇	C₂³	1	1	yes	characteristic
295	#103×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
302	#102×C₆₇	C₂³	1	1	yes	characteristic
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	1	yes	characteristic
305	#102×C₆₇	C₂³	1	1	yes	characteristic
306	#102×C₆₇	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
313	#97×C₆₇	C₂³	1	2	yes	—
314	C₄×C₈×C₆₇	C₂³	1	2	yes	—
315	C₂⁴×C₆₇	—	2	1	no	—
316	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
317	#41×C₆₇	—	2	2	no	—
318	#41×C₆₇	—	2	2	no	—
319	#41×C₆₇	—	2	2	no	—
320	#41×C₆₇	—	2	2	no	—
321	#41×C₆₇	—	8	4	no	—
322	C₂×Q₈×C₆₇	—	2	2	no	—
323	C₂×Q₈×C₆₇	—	2	2	no	—
324	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₆₇	—	2	1	no	—
327	C₂×D₄×C₆₇	—	2	2	no	—
328	C₂×D₄×C₆₇	—	2	1	no	—
329	C₂×D₄×C₆₇	—	2	2	no	—
330	C₂×D₄×C₆₇	—	2	1	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	1	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	2	no	—
337	C₂×D₄×C₆₇	—	8	2	no	—
338	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₆₇	—	2	2	no	—
345	C₂²×C₄×C₆₇	—	2	2	no	—
346	C₂²×C₄×C₆₇	—	2	1	no	—
347	C₂²×C₄×C₆₇	—	2	1	no	—
348	C₂²×C₄×C₆₇	—	2	1	no	—
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	1	no	—
354	C₂²×C₄×C₆₇	—	2	2	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	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
364	SD₁₆×C₆₇	—	2	4	no	—
365	D₈×C₆₇	—	2	4	no	—
366	M₁₆×C₆₇	—	2	2	no	—
367	M₁₆×C₆₇	—	2	4	no	—
368	M₁₆×C₆₇	—	2	4	no	—
369	M₁₆×C₆₇	#41	1	4	yes	complemented
370	C₂×C₈×C₆₇	—	2	2	no	—
371	C₂×C₈×C₆₇	—	2	2	no	—
372	C₂×C₈×C₆₇	—	2	4	no	—
373	C₂×C₈×C₆₇	—	2	4	no	—
374	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
375	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
380	C₄⋊C₄×C₆₇	—	2	1	no	—
381	C₄⋊C₄×C₆₇	—	2	2	no	—
382	C₄⋊C₄×C₆₇	—	2	1	no	—
383	C₄⋊C₄×C₆₇	—	2	1	no	—
384	C₄⋊C₄×C₆₇	—	2	1	no	—
385	C₄⋊C₄×C₆₇	—	2	1	no	—
386	C₄⋊C₄×C₆₇	—	2	2	no	—
387	C₄⋊C₄×C₆₇	—	2	2	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	2	no	—
392	C₄⋊C₄×C₆₇	—	2	1	no	—
393	C₄⋊C₄×C₆₇	—	2	2	no	—
394	C₄⋊C₄×C₆₇	—	2	2	no	—
395	C₄⋊C₄×C₆₇	—	2	2	no	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂²⋊C₄×C₆₇	—	2	1	no	—
411	C₂²⋊C₄×C₆₇	—	2	1	no	—
412	C₂²⋊C₄×C₆₇	—	2	1	no	—
413	C₂²⋊C₄×C₆₇	—	2	1	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	1	no	—
422	C₂²⋊C₄×C₆₇	—	2	2	no	—
423	C₂²⋊C₄×C₆₇	—	2	2	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	—	2	1	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	1	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
437	C₄²×C₆₇	—	2	1	no	—
438	C₄²×C₆₇	—	2	2	no	—
439	C₄²×C₆₇	—	2	1	no	—
440	C₄²×C₆₇	—	2	1	no	—
441	C₄²×C₆₇	—	2	2	no	—
442	C₄²×C₆₇	—	2	1	no	—
443	C₄²×C₆₇	—	2	2	no	—
444	C₄²×C₆₇	—	2	2	no	—
445	C₄²×C₆₇	—	2	2	no	—
446	C₄²×C₆₇	—	2	1	no	—
447	C₄²×C₆₇	C₂⁴	1	2	yes	—
448	C₂³×C₆₇	—	2	2	no	—
449	C₂³×C₆₇	—	2	1	no	—
450	C₂³×C₆₇	—	2	2	no	—
451	C₂³×C₆₇	—	4	1	no	—
452	C₂³×C₆₇	—	4	1	no	—
453	C₂³×C₆₇	—	4	2	no	—
454	C₂³×C₆₇	—	8	1	no	—
455	C₂³×C₆₇	—	8	1	no	—
456	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
457	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
458	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
459	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
460	Q₈×C₆₇	—	2	2	no	—
461	Q₈×C₆₇	—	2	1	no	—
462	Q₈×C₆₇	—	2	1	no	—
463	Q₈×C₆₇	—	8	2	no	—
464	Q₈×C₆₇	—	8	2	no	—
465	D₄×C₆₇	—	2	4	no	—
466	D₄×C₆₇	—	2	2	no	—
467	D₄×C₆₇	—	2	1	no	—
468	D₄×C₆₇	—	2	2	no	—
469	D₄×C₆₇	—	2	2	no	—
470	D₄×C₆₇	—	2	1	no	—
471	D₄×C₆₇	—	4	2	no	—
472	D₄×C₆₇	—	4	2	no	—
473	D₄×C₆₇	—	4	4	no	—
474	D₄×C₆₇	—	4	2	no	—
475	D₄×C₆₇	—	4	2	no	—
476	D₄×C₆₇	—	8	2	no	—
477	D₄×C₆₇	—	8	2	no	—
478	D₄×C₆₇	—	8	1	no	—
479	D₄×C₆₇	—	8	1	no	—
480	D₄×C₆₇	—	8	2	no	—
481	D₄×C₆₇	—	8	2	no	—
482	C₂×C₄×C₆₇	—	2	2	no	—
483	C₂×C₄×C₆₇	—	2	2	no	—
484	C₂×C₄×C₆₇	—	2	2	no	—
485	C₂×C₄×C₆₇	—	2	1	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	1	no	—
488	C₂×C₄×C₆₇	—	2	1	no	—
489	C₂×C₄×C₆₇	—	2	1	no	—
490	C₂×C₄×C₆₇	—	2	2	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	2	2	no	—
493	C₂×C₄×C₆₇	—	2	1	no	—
494	C₂×C₄×C₆₇	—	2	1	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	2	no	—
497	C₂×C₄×C₆₇	—	2	1	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	1	no	—
500	C₂×C₄×C₆₇	—	2	2	no	—
501	C₂×C₄×C₆₇	—	4	2	no	—
502	C₂×C₄×C₆₇	—	4	2	no	—
503	C₂×C₄×C₆₇	—	8	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	1	no	—
508	C₂×C₄×C₆₇	—	8	1	no	—
509	C₂×C₄×C₆₇	—	8	2	no	—
510	C₂×C₄×C₆₇	—	8	1	no	—
511	C₂×C₄×C₆₇	—	8	2	no	—
512	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
519	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
520	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
521	C₈×C₆₇	—	2	1	no	—
522	C₈×C₆₇	—	2	1	no	—
523	C₈×C₆₇	—	2	2	no	—
524	C₈×C₆₇	—	2	1	no	—
525	C₈×C₆₇	—	2	1	no	—
526	C₈×C₆₇	C₂×#41	1	4	yes	—
527	C₂²×C₆₇	—	2	1	no	—
528	C₂²×C₆₇	—	2	1	no	—
529	C₂²×C₆₇	—	2	1	no	—
530	C₂²×C₆₇	—	2	1	no	—
531	C₂²×C₆₇	—	2	2	no	—
532	C₂²×C₆₇	—	2	1	no	—
533	C₂²×C₆₇	—	2	2	no	—
534	C₂²×C₆₇	—	2	1	no	—
535	C₂²×C₆₇	—	2	1	no	—
536	C₂²×C₆₇	—	2	1	no	—
537	C₂²×C₆₇	—	2	2	no	—
538	C₂²×C₆₇	—	4	2	no	—
539	C₂²×C₆₇	—	4	1	no	—
540	C₂²×C₆₇	—	4	1	no	—
541	C₂²×C₆₇	—	4	2	no	—
542	C₂²×C₆₇	—	4	1	no	—
543	C₂²×C₆₇	—	4	2	no	—
544	C₂²×C₆₇	—	8	2	no	—
545	C₂²×C₆₇	—	16	2	no	—
546	C₂²×C₆₇	#547	1	2	yes	—
547	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
548	C₄×C₆₇	—	2	2	no	—
549	C₄×C₆₇	—	2	2	no	—
550	C₄×C₆₇	—	2	1	no	—
551	C₄×C₆₇	—	2	1	no	—
552	C₄×C₆₇	—	2	2	no	—
553	C₄×C₆₇	—	4	1	no	—
554	C₄×C₆₇	—	4	1	no	—
555	C₄×C₆₇	—	4	2	no	—
556	C₄×C₆₇	—	4	1	no	—
557	C₄×C₆₇	—	4	1	no	—
558	C₄×C₆₇	—	4	1	no	—
559	C₄×C₆₇	—	4	2	no	—
560	C₄×C₆₇	—	4	2	no	—
561	C₄×C₆₇	—	4	1	no	—
562	C₄×C₆₇	—	4	1	no	—
563	C₄×C₆₇	#547	1	2	yes	—
564	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
565	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
566	#61276	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
567	C₂×C₆₇	—	2	2	no	—
568	C₂×C₆₇	—	4	2	no	—
569	C₂×C₆₇	—	4	1	no	—
570	C₂×C₆₇	—	4	1	no	—
571	C₂×C₆₇	—	8	1	no	—
572	C₂×C₆₇	—	8	2	no	—
573	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
574	C₂×C₆₇	#3584	1	1	yes	characteristic
575	C₂×C₆₇	#3585	1	1	yes	characteristic
576	#3494	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#3493	C₂×C₆₇	1	1	yes	characteristic, complemented
578	#3354	C₂×C₆₇	1	2	yes	complemented
579	#3351	C₂×C₆₇	1	2	yes	complemented
580	#3350	C₂×C₆₇	1	2	yes	complemented
581	#3347	C₂×C₆₇	1	2	yes	complemented
582	#3347	C₂×C₆₇	1	2	yes	complemented
583	#3343	C₂×C₆₇	1	2	yes	complemented
584	#3340	C₂×C₆₇	1	2	yes	complemented
585	#3339	C₂×C₆₇	1	2	yes	complemented
586	#3163	C₂×C₆₇	1	1	yes	characteristic, complemented
587	#3099	C₂×C₆₇	1	1	yes	characteristic, complemented
588	#3096	C₂×C₆₇	1	1	yes	characteristic, complemented
589	#3091	C₂×C₆₇	1	1	yes	characteristic, complemented
590	C₂×#482	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#3083	C₂×C₆₇	1	1	yes	characteristic, complemented
592	#3081	C₂×C₆₇	1	1	yes	characteristic, complemented
593	#3062	C₂×C₆₇	1	1	yes	characteristic, complemented
594	#3055	C₂×C₆₇	1	1	yes	characteristic, complemented
595	#2946	C₂×C₆₇	1	1	yes	characteristic, complemented
596	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
597	#2913	C₂×C₆₇	1	1	yes	characteristic, complemented
598	#2911	C₂×C₆₇	1	1	yes	characteristic, complemented
599	C₆₇	#61276	1	1	yes	characteristic, direct product factor, Sylow
600	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
601	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
602	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
603	#556	—	2	1	no	—
604	#556	C₂²×C₆₇	1	2	yes	complemented
605	#555	—	2	1	no	—
606	#555	C₂²×C₆₇	1	2	yes	—
607	#555	C₂²×C₆₇	1	2	yes	complemented
608	#553	—	2	1	no	—
609	#553	C₂²×C₆₇	1	2	yes	—
610	#553	C₂²×C₆₇	1	2	yes	—
611	#553	C₂²×C₆₇	1	2	yes	complemented
612	#552	—	2	1	no	—
613	#552	C₂²×C₆₇	1	2	yes	complemented
614	#551	—	2	2	no	—
615	#547	C₂²×C₆₇	1	2	yes	—
616	#546	—	2	2	no	—
617	#544	C₂²×C₆₇	1	1	yes	characteristic
618	#544	C₂²×C₆₇	1	1	yes	characteristic
619	#542	—	2	1	no	—
620	#540	—	2	1	no	—
621	#538	—	2	2	no	—
622	#537	C₂²×C₆₇	1	1	yes	characteristic
623	#535	C₂²×C₆₇	1	1	yes	characteristic
624	#532	—	2	1	no	—
625	#529	—	2	2	no	—
626	#529	—	2	1	no	—
627	#525	C₂²×C₆₇	1	1	yes	characteristic
628	#525	C₂²×C₆₇	1	1	yes	characteristic
629	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
630	#520	C₂²×C₆₇	1	1	yes	characteristic
631	#520	C₂²×C₆₇	1	1	yes	characteristic
632	#520	C₂²×C₆₇	1	1	yes	characteristic
633	#518	C₂²×C₆₇	1	1	yes	characteristic
634	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
635	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
636	#501	C₂²×C₆₇	1	2	yes	complemented
637	#501	C₂²×C₆₇	1	2	yes	complemented
638	#499	C₂²×C₆₇	1	2	yes	complemented
639	#498	C₂²×C₆₇	1	2	yes	complemented
640	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
641	#485	C₂²×C₆₇	1	2	yes	complemented
642	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
643	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
644	#483	C₂²×C₆₇	1	2	yes	complemented
645	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
646	#482	C₂²×C₆₇	1	2	yes	—
647	#482	C₂²×C₆₇	1	2	yes	—
648	#482	C₂²×C₆₇	1	2	yes	—
649	#482	C₂²×C₆₇	1	2	yes	—
650	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
651	#482	C₂²×C₆₇	1	2	yes	complemented
652	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
653	#482	C₂²×C₆₇	1	2	yes	complemented
654	#482	C₂²×C₆₇	1	2	yes	complemented
655	#481	C₂²×C₆₇	1	2	yes	complemented
656	#481	C₂²×C₆₇	1	2	yes	complemented
657	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
658	#480	C₂²×C₆₇	1	2	yes	complemented
659	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
660	#479	C₂²×C₆₇	1	2	yes	complemented
661	#478	C₂²×C₆₇	1	2	yes	complemented
662	#478	C₂²×C₆₇	1	2	yes	complemented
663	#478	C₂²×C₆₇	1	2	yes	complemented
664	#477	C₂²×C₆₇	1	2	yes	complemented
665	#476	C₂²×C₆₇	1	2	yes	complemented
666	#474	C₂²×C₆₇	1	2	yes	complemented
667	#474	C₂²×C₆₇	1	2	yes	complemented
668	#469	C₂²×C₆₇	1	2	yes	—
669	#469	C₂²×C₆₇	1	2	yes	complemented
670	#468	C₂²×C₆₇	1	2	yes	—
671	#468	C₂²×C₆₇	1	2	yes	complemented
672	#466	C₂²×C₆₇	1	2	yes	—
673	#466	C₂²×C₆₇	1	2	yes	complemented
674	#465	C₂²×C₆₇	1	2	yes	—
675	#465	C₂²×C₆₇	1	2	yes	complemented
676	#442	C₂²×C₆₇	1	2	yes	complemented
677	#440	C₂²×C₆₇	1	2	yes	complemented
678	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
679	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
680	#436	C₂²×C₆₇	1	2	yes	complemented
681	#435	C₂²×C₆₇	1	2	yes	complemented
682	#435	C₂²×C₆₇	1	2	yes	complemented
683	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
684	#428	C₂²×C₆₇	1	1	yes	characteristic
685	#428	C₂²×C₆₇	1	1	yes	characteristic
686	#428	C₂²×C₆₇	1	1	yes	characteristic
687	#428	C₂²×C₆₇	1	1	yes	characteristic
688	#428	C₂²×C₆₇	1	1	yes	characteristic
689	#428	C₂²×C₆₇	1	2	yes	complemented
690	#428	C₂²×C₆₇	1	2	yes	complemented
691	#428	C₂²×C₆₇	1	2	yes	complemented
692	#428	C₂²×C₆₇	1	2	yes	complemented
693	#427	C₂²×C₆₇	1	1	yes	characteristic
694	#427	C₂²×C₆₇	1	1	yes	characteristic
695	#427	C₂²×C₆₇	1	2	yes	complemented
696	#427	C₂²×C₆₇	1	2	yes	complemented
697	#427	C₂²×C₆₇	1	2	yes	complemented
698	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
699	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
700	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
701	#424	C₂²×C₆₇	1	1	yes	characteristic
702	#418	C₂²×C₆₇	1	1	yes	characteristic
703	#417	C₂²×C₆₇	1	1	yes	characteristic
704	#416	C₂²×C₆₇	1	1	yes	characteristic
705	#416	C₂²×C₆₇	1	1	yes	characteristic
706	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
707	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
708	#408	C₂²×C₆₇	1	1	yes	characteristic
709	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
710	#405	C₂²×C₆₇	1	1	yes	characteristic
711	C₂×#41	—	2	2	no	—
712	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
713	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
714	C₂²×D₄	—	2	1	no	—
715	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
716	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
717	AGL(1,ℤ/8)	—	2	4	no	—
718	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
719	C₂×D₈	C₂³×C₆₇	1	2	yes	—
720	#131	—	2	4	no	—
721	C₂×M₁₆	—	2	4	no	—
722	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
723	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
724	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
725	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
726	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
727	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
728	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
729	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
733	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
734	#127	—	2	1	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#125	—	2	1	no	—
742	#125	—	2	2	no	—
743	#125	—	2	1	no	—
744	#125	C₂³×C₆₇	1	2	yes	—
745	#125	C₂³×C₆₇	1	2	yes	—
746	#124	—	2	1	no	—
747	#124	—	2	2	no	—
748	#124	—	2	2	no	—
749	#124	—	2	2	no	—
750	#124	—	2	2	no	—
751	#124	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	1	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	D₄×C₆₇	1	2	yes	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
765	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
767	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
768	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	—	2	1	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	—	2	1	no	—
777	#121	—	2	1	no	—
778	#121	D₄×C₆₇	1	1	yes	characteristic
779	#121	D₄×C₆₇	1	1	yes	characteristic
780	#121	C₂³×C₆₇	1	2	yes	—
781	#121	C₂³×C₆₇	1	2	yes	—
782	#121	C₂³×C₆₇	1	1	yes	characteristic
783	#121	C₂³×C₆₇	1	1	yes	characteristic
784	#121	C₂³×C₆₇	1	2	yes	—
785	#121	C₂³×C₆₇	1	2	yes	—
786	#121	C₂³×C₆₇	1	2	yes	—
787	#120	—	2	1	no	—
788	#120	—	2	2	no	—
789	#120	D₄×C₆₇	1	2	yes	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	2	no	—
793	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	C₂³×C₆₇	1	2	yes	—
807	C₄×D₄	C₂³×C₆₇	1	2	yes	—
808	C₄×D₄	C₂³×C₆₇	1	2	yes	—
809	C₄×D₄	C₂³×C₆₇	1	2	yes	—
810	C₄×D₄	C₂³×C₆₇	1	2	yes	—
811	#117	—	2	1	no	—
812	#117	—	2	1	no	—
813	#117	—	2	1	no	—
814	#117	—	2	1	no	—
815	#117	—	2	1	no	—
816	#117	—	2	2	no	—
817	#117	—	2	2	no	—
818	#117	—	2	2	no	—
819	#117	C₂³×C₆₇	1	1	yes	characteristic
820	#117	C₂³×C₆₇	1	1	yes	characteristic
821	#117	C₂³×C₆₇	1	2	yes	—
822	#117	C₂³×C₆₇	1	1	yes	characteristic
823	#117	C₂³×C₆₇	1	2	yes	—
824	#117	C₂³×C₆₇	1	1	yes	characteristic
825	#117	C₂³×C₆₇	1	1	yes	characteristic
826	#117	C₂³×C₆₇	1	2	yes	—
827	#117	C₂³×C₆₇	1	2	yes	—
828	#117	C₂³×C₆₇	1	1	yes	characteristic
829	C₂×C₄⋊C₄	—	2	1	no	—
830	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
831	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
832	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
833	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
834	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
835	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
836	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
837	C₂×C₂²⋊C₄	—	2	1	no	—
838	C₂×C₂²⋊C₄	—	2	1	no	—
839	C₂×C₂²⋊C₄	—	2	1	no	—
840	C₂×C₂²⋊C₄	—	2	2	no	—
841	C₂×C₄²	—	2	1	no	—
842	C₂×C₄²	—	2	1	no	—
843	#107	C₂³×C₆₇	1	2	yes	—
844	#107	C₂³×C₆₇	1	2	yes	—
845	#107	C₂³×C₆₇	1	1	yes	characteristic
846	#107	C₂³×C₆₇	1	2	yes	—
847	#107	C₂³×C₆₇	1	2	yes	—
848	#107	C₂³×C₆₇	1	1	yes	characteristic
849	#107	C₂³×C₆₇	1	1	yes	characteristic
850	#107	C₂³×C₆₇	1	1	yes	characteristic
851	#107	C₂³×C₆₇	1	2	yes	—
852	#107	C₂³×C₆₇	1	2	yes	—
853	#107	C₂³×C₆₇	1	2	yes	—
854	#106	C₂³×C₆₇	1	2	yes	—
855	#106	C₂³×C₆₇	1	2	yes	—
856	#106	C₂³×C₆₇	1	1	yes	characteristic
857	#106	C₂³×C₆₇	1	1	yes	characteristic
858	#106	C₂³×C₆₇	1	1	yes	characteristic
859	#106	C₂³×C₆₇	1	1	yes	characteristic
860	#106	C₂³×C₆₇	1	2	yes	—
861	#106	C₂³×C₆₇	1	2	yes	—
862	#106	C₂³×C₆₇	1	2	yes	—
863	#106	C₂³×C₆₇	1	2	yes	—
864	#106	C₂³×C₆₇	1	2	yes	—
865	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
866	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
867	#103	C₂³×C₆₇	1	1	yes	characteristic
868	#103	C₂³×C₆₇	1	1	yes	characteristic
869	#103	C₂³×C₆₇	1	1	yes	characteristic
870	#103	C₂³×C₆₇	1	1	yes	characteristic
871	#103	C₂³×C₆₇	1	2	yes	—
872	#102	C₂³×C₆₇	1	2	yes	—
873	#102	C₂³×C₆₇	1	2	yes	—
874	#102	C₂³×C₆₇	1	2	yes	—
875	#102	C₂³×C₆₇	1	2	yes	—
876	#102	C₂³×C₆₇	1	1	yes	characteristic
877	#102	C₂³×C₆₇	1	1	yes	characteristic
878	#102	C₂³×C₆₇	1	1	yes	characteristic
879	#102	C₂³×C₆₇	1	1	yes	characteristic
880	#102	C₂³×C₆₇	1	2	yes	—
881	#102	C₂³×C₆₇	1	2	yes	—
882	#102	C₂³×C₆₇	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
884	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
885	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
886	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
889	#97	C₂³×C₆₇	1	2	yes	—
890	C₄×C₈	C₂³×C₆₇	1	2	yes	—
891	C₂⁴	—	2	1	no	—
892	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
893	#41	—	2	2	no	—
894	#41	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	2	2	no	—
897	#41	—	8	4	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	8	2	no	—
914	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
915	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
916	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
917	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
918	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
934	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
935	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
937	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
940	SD₁₆	—	2	4	no	—
941	D₈	—	2	4	no	—
942	M₁₆	—	2	2	no	—
943	M₁₆	—	2	4	no	—
944	M₁₆	—	2	4	no	—
945	M₁₆	#41×C₆₇	1	4	yes	complemented
946	C₂×C₈	—	2	2	no	—
947	C₂×C₈	—	2	2	no	—
948	C₂×C₈	—	2	4	no	—
949	C₂×C₈	—	2	4	no	—
950	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
953	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
954	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
955	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
974	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
975	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1011	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1012	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	C₂⁴×C₆₇	1	2	yes	—
1024	C₂³	—	2	2	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	2	no	—
1027	C₂³	—	4	1	no	—
1028	C₂³	—	4	1	no	—
1029	C₂³	—	4	2	no	—
1030	C₂³	—	8	1	no	—
1031	C₂³	—	8	1	no	—
1032	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1033	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1034	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1035	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1036	Q₈	—	2	2	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	8	2	no	—
1040	Q₈	—	8	2	no	—
1041	D₄	—	2	4	no	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	4	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	8	2	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	1	no	—
1057	D₄	—	8	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	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	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	1	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	1	no	—
1085	C₂×C₄	—	8	1	no	—
1086	C₂×C₄	—	8	1	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1092	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1093	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1094	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1095	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1096	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₈	—	2	1	no	—
1101	C₈	—	2	1	no	—
1102	C₈	C₂×#41×C₆₇	1	4	yes	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	1	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	2	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	8	2	no	—
1121	C₂²	—	16	2	no	—
1122	C₂²	#547×C₆₇	1	2	yes	—
1123	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1124	C₄	—	2	2	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	2	1	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	2	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	#547×C₆₇	1	2	yes	—
1140	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1141	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1142	C₂	—	2	2	no	—
1143	C₂	—	4	1	no	—
1144	C₂	—	4	1	no	—
1145	C₂	—	4	2	no	—
1146	C₂	—	8	2	no	—
1147	C₂	—	8	1	no	—
1148	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
1149	C₂	C₆₇×#3584	1	1	yes	characteristic
1150	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3494	C₂	semidirect
2. C₆₇×#3493	C₂	semidirect
3. C₆₇×#3354	C₂	semidirect
4. C₆₇×#3351	C₂	semidirect
5. C₆₇×#3350	C₂	semidirect
6. C₆₇×#3347	C₂	semidirect
7. C₆₇×#3347	C₂	semidirect
8. C₆₇×#3343	C₂	semidirect
9. C₆₇×#3340	C₂	semidirect
10. C₆₇×#3339	C₂	semidirect
11. C₆₇×#3163	C₂	semidirect
12. C₆₇×#3099	C₂	semidirect
13. C₆₇×#3096	C₂	semidirect
14. C₆₇×#3091	C₂	semidirect
15. C₂×#482×C₆₇	C₂	semidirect
16. C₆₇×#3083	C₂	semidirect
17. C₆₇×#3081	C₂	semidirect
18. C₆₇×#3062	C₂	semidirect
19. C₆₇×#3055	C₂	semidirect
20. C₆₇×#2946	C₂	semidirect
21. C₆₇×#2933	C₂	semidirect
22. C₆₇×#2913	C₂	semidirect
23. C₆₇×#2911	C₂	semidirect
28. #556×C₆₇	C₂²	semidirect
31. #555×C₆₇	C₂²	semidirect
35. #553×C₆₇	C₂²	semidirect
37. #552×C₆₇	C₂²	semidirect
60. #501×C₆₇	C₂²	semidirect
61. #501×C₆₇	C₂²	semidirect
62. #499×C₆₇	C₂²	semidirect
63. #498×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
74. #482×C₆₇	C₂²	semidirect
75. #482×C₆₇	C₂²	semidirect
76. #482×C₆₇	C₂²	semidirect
77. #482×C₆₇	C₂²	semidirect
78. #482×C₆₇	C₂²	semidirect
79. #481×C₆₇	C₂²	semidirect
80. #481×C₆₇	C₂²	semidirect
81. #481×C₆₇	C₂²	semidirect
82. #480×C₆₇	C₂²	semidirect
83. #480×C₆₇	C₂²	semidirect
84. #479×C₆₇	C₂²	semidirect
85. #478×C₆₇	C₂²	semidirect
86. #478×C₆₇	C₂²	semidirect
87. #478×C₆₇	C₂²	semidirect
88. #477×C₆₇	C₂²	semidirect
89. #476×C₆₇	C₂²	semidirect
90. #474×C₆₇	C₂²	semidirect
91. #474×C₆₇	C₂²	semidirect
93. #469×C₆₇	C₂²	semidirect
95. #468×C₆₇	C₂²	semidirect
97. #466×C₆₇	C₂²	semidirect
99. #465×C₆₇	C₂²	semidirect
100. #442×C₆₇	C₂²	semidirect
101. #440×C₆₇	C₂²	semidirect
102. C₄×SD₁₆×C₆₇	C₂²	semidirect
103. C₄×D₈×C₆₇	C₂²	semidirect
104. #436×C₆₇	C₂²	semidirect
105. #435×C₆₇	C₂²	semidirect
106. #435×C₆₇	C₂²	semidirect
107. C₈×D₄×C₆₇	C₂²	semidirect
113. #428×C₆₇	C₂²	semidirect
114. #428×C₆₇	C₂²	semidirect
115. #428×C₆₇	C₂²	semidirect
116. #428×C₆₇	C₂²	semidirect
119. #427×C₆₇	C₂²	semidirect
120. #427×C₆₇	C₂²	semidirect
121. #427×C₆₇	C₂²	semidirect
123. C₂×#107×C₆₇	C₂²	semidirect
369. M₁₆×C₆₇	#41	semidirect
566. #61276	C₆₇	direct (N × H)
576. #3494	C₂×C₆₇	semidirect
577. #3493	C₂×C₆₇	semidirect
578. #3354	C₂×C₆₇	semidirect
579. #3351	C₂×C₆₇	semidirect
580. #3350	C₂×C₆₇	semidirect
581. #3347	C₂×C₆₇	semidirect
582. #3347	C₂×C₆₇	semidirect
583. #3343	C₂×C₆₇	semidirect
584. #3340	C₂×C₆₇	semidirect
585. #3339	C₂×C₆₇	semidirect
586. #3163	C₂×C₆₇	semidirect
587. #3099	C₂×C₆₇	semidirect
588. #3096	C₂×C₆₇	semidirect
589. #3091	C₂×C₆₇	semidirect
590. C₂×#482	C₂×C₆₇	semidirect
591. #3083	C₂×C₆₇	semidirect
592. #3081	C₂×C₆₇	semidirect
593. #3062	C₂×C₆₇	semidirect
594. #3055	C₂×C₆₇	semidirect
595. #2946	C₂×C₆₇	semidirect
596. #2933	C₂×C₆₇	semidirect
597. #2913	C₂×C₆₇	semidirect
598. #2911	C₂×C₆₇	semidirect
599. C₆₇	#61276	direct (N × H)
604. #556	C₂²×C₆₇	semidirect
607. #555	C₂²×C₆₇	semidirect
611. #553	C₂²×C₆₇	semidirect
613. #552	C₂²×C₆₇	semidirect
636. #501	C₂²×C₆₇	semidirect
637. #501	C₂²×C₆₇	semidirect
638. #499	C₂²×C₆₇	semidirect
639. #498	C₂²×C₆₇	semidirect
640. #485	C₂²×C₆₇	semidirect
641. #485	C₂²×C₆₇	semidirect
642. #485	C₂²×C₆₇	semidirect
643. #484	C₂²×C₆₇	semidirect
644. #483	C₂²×C₆₇	semidirect
645. #483	C₂²×C₆₇	semidirect
650. #482	C₂²×C₆₇	semidirect
651. #482	C₂²×C₆₇	semidirect
652. #482	C₂²×C₆₇	semidirect
653. #482	C₂²×C₆₇	semidirect
654. #482	C₂²×C₆₇	semidirect
655. #481	C₂²×C₆₇	semidirect
656. #481	C₂²×C₆₇	semidirect
657. #481	C₂²×C₆₇	semidirect
658. #480	C₂²×C₆₇	semidirect
659. #480	C₂²×C₆₇	semidirect
660. #479	C₂²×C₆₇	semidirect
661. #478	C₂²×C₆₇	semidirect
662. #478	C₂²×C₆₇	semidirect
663. #478	C₂²×C₆₇	semidirect
664. #477	C₂²×C₆₇	semidirect
665. #476	C₂²×C₆₇	semidirect
666. #474	C₂²×C₆₇	semidirect
667. #474	C₂²×C₆₇	semidirect
669. #469	C₂²×C₆₇	semidirect
671. #468	C₂²×C₆₇	semidirect
673. #466	C₂²×C₆₇	semidirect
675. #465	C₂²×C₆₇	semidirect
676. #442	C₂²×C₆₇	semidirect
677. #440	C₂²×C₆₇	semidirect
678. C₄×SD₁₆	C₂²×C₆₇	semidirect
679. C₄×D₈	C₂²×C₆₇	semidirect
680. #436	C₂²×C₆₇	semidirect
681. #435	C₂²×C₆₇	semidirect
682. #435	C₂²×C₆₇	semidirect
683. C₈×D₄	C₂²×C₆₇	semidirect
689. #428	C₂²×C₆₇	semidirect
690. #428	C₂²×C₆₇	semidirect
691. #428	C₂²×C₆₇	semidirect
692. #428	C₂²×C₆₇	semidirect
695. #427	C₂²×C₆₇	semidirect
696. #427	C₂²×C₆₇	semidirect
697. #427	C₂²×C₆₇	semidirect
699. C₂×#107	C₂²×C₆₇	semidirect
945. M₁₆	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3494	2
C₆₇×#3493	2
C₆₇×#3354	2
C₆₇×#3351	2
C₆₇×#3350	2
C₆₇×#3347	2
C₆₇×#3343	2
C₆₇×#3340	2
C₆₇×#3339	2
C₆₇×#3163	2
C₆₇×#3099	2
C₆₇×#3096	2
C₆₇×#3091	2
C₂×#482×C₆₇	2
C₆₇×#3083	2
C₆₇×#3081	2
C₆₇×#3062	2
C₆₇×#3055	2
C₆₇×#2946	2
C₆₇×#2933	2
C₆₇×#2913	2
C₆₇×#2911	2
#61276	67

Subgroups — C67×#61276 #30740527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61276 #30740527