Subgroups — C₆₇×#22421 #30701672

Order 17152.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#548×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#435×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#103×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1983	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1959	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1894	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1874	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#1788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#1787	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#1763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
20	#548×C₆₇	—	2	4	no	—
21	#548×C₆₇	C₄	1	8	yes	complemented
22	C₂×#124×C₆₇	—	2	1	no	—
23	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#121×C₆₇	—	2	1	no	—
27	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₇	—	2	1	no	—
30	C₂×C₄×D₄×C₆₇	—	2	1	no	—
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	#435×C₆₇	—	2	4	no	—
35	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
36	#417×C₆₇	—	2	4	no	—
37	C₂×#103×C₆₇	—	2	4	no	—
38	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
52	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
53	#389×C₆₇	—	2	1	no	—
54	#385×C₆₇	—	2	1	no	—
55	#385×C₆₇	—	2	1	no	—
56	#384×C₆₇	C₂²	1	1	yes	characteristic
57	#380×C₆₇	C₂²	1	1	yes	characteristic
58	#380×C₆₇	C₂²	1	1	yes	characteristic
59	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
60	#340×C₆₇	C₂²	1	1	yes	characteristic
61	#340×C₆₇	C₂²	1	1	yes	characteristic
62	#340×C₆₇	C₂²	1	1	yes	characteristic
63	#340×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×#41×C₆₇	—	2	2	no	—
65	C₂×#41×C₆₇	—	2	2	no	—
66	C₂×#41×C₆₇	—	2	2	no	—
67	C₂×#41×C₆₇	—	4	1	no	—
68	C₂×#41×C₆₇	—	4	1	no	—
69	C₂×#41×C₆₇	C₂×C₄	1	4	yes	complemented
70	C₂²×Q₈×C₆₇	—	2	1	no	—
71	C₂²×Q₈×C₆₇	—	2	2	no	—
72	C₂²×Q₈×C₆₇	—	2	2	no	—
73	C₂²×Q₈×C₆₇	—	2	2	no	—
74	C₂²×Q₈×C₆₇	—	4	1	no	—
75	C₂²×Q₈×C₆₇	—	4	1	no	—
76	C₂²×Q₈×C₆₇	C₂×C₄	1	4	yes	complemented
77	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₆₇	—	2	1	no	—
80	C₂²×D₄×C₆₇	—	2	1	no	—
81	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₆₇	—	2	1	no	—
84	C₂³×C₄×C₆₇	—	2	1	no	—
85	C₂³×C₄×C₆₇	—	2	1	no	—
86	C₂³×C₄×C₆₇	—	2	1	no	—
87	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂×M₁₆×C₆₇	—	2	2	no	—
90	C₂×M₁₆×C₆₇	—	2	2	no	—
91	C₂×M₁₆×C₆₇	—	4	1	no	—
92	C₂²×C₈×C₆₇	—	2	2	no	—
93	C₂²×C₈×C₆₇	—	2	2	no	—
94	C₂²×C₈×C₆₇	—	4	1	no	—
95	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
99	#124×C₆₇	—	2	8	no	—
100	#124×C₆₇	—	2	2	no	—
101	#124×C₆₇	C₂×C₄	1	4	yes	complemented
102	C₂²⋊Q₈×C₆₇	—	2	2	no	—
103	C₂²⋊Q₈×C₆₇	—	2	8	no	—
104	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	complemented
105	#121×C₆₇	—	2	8	no	—
106	#121×C₆₇	—	2	2	no	—
107	#121×C₆₇	C₂×C₄	1	4	yes	complemented
108	C₄×Q₈×C₆₇	—	2	2	no	—
109	C₄×Q₈×C₆₇	C₂×C₄	1	4	yes	complemented
110	C₄×D₄×C₆₇	—	2	8	no	—
111	C₄×D₄×C₆₇	—	4	4	no	—
112	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
113	C₄×D₄×C₆₇	D₄	1	4	yes	—
114	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
115	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
116	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
117	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
118	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
119	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
120	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
121	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
122	C₂×C₄⋊C₄×C₆₇	—	4	1	no	—
123	C₂×C₄⋊C₄×C₆₇	—	4	1	no	—
124	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
138	C₂×C₄²×C₆₇	—	2	1	no	—
139	C₂×C₄²×C₆₇	—	2	1	no	—
140	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
141	C₄⋊C₈×C₆₇	—	2	2	no	—
142	#103×C₆₇	—	2	2	no	—
143	#103×C₆₇	—	2	2	no	—
144	#103×C₆₇	—	2	2	no	—
145	#103×C₆₇	—	2	2	no	—
146	#103×C₆₇	—	2	2	no	—
147	#103×C₆₇	—	4	1	no	—
148	#103×C₆₇	—	4	1	no	—
149	#103×C₆₇	D₄	1	4	yes	complemented
150	#102×C₆₇	—	2	2	no	—
151	#102×C₆₇	—	2	2	no	—
152	#102×C₆₇	—	4	1	no	—
153	#102×C₆₇	—	4	1	no	—
154	C₂²⋊C₈×C₆₇	—	2	2	no	—
155	C₂²⋊C₈×C₆₇	—	2	2	no	—
156	#97×C₆₇	—	2	2	no	—
157	#95×C₆₇	—	2	1	no	—
158	#95×C₆₇	—	2	1	no	—
159	#95×C₆₇	—	2	1	no	—
160	C₂⁴×C₆₇	—	2	1	no	—
161	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
162	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
163	#41×C₆₇	—	2	8	no	—
164	#41×C₆₇	—	4	4	no	—
165	#41×C₆₇	—	4	4	no	—
166	#41×C₆₇	—	4	4	no	—
167	C₂×Q₈×C₆₇	—	2	4	no	—
168	C₂×Q₈×C₆₇	—	2	1	no	—
169	C₂×Q₈×C₆₇	—	2	1	no	—
170	C₂×Q₈×C₆₇	—	2	1	no	—
171	C₂×Q₈×C₆₇	—	2	1	no	—
172	C₂×Q₈×C₆₇	—	2	8	no	—
173	C₂×Q₈×C₆₇	—	2	1	no	—
174	C₂×Q₈×C₆₇	—	2	1	no	—
175	C₂×Q₈×C₆₇	—	2	1	no	—
176	C₂×Q₈×C₆₇	—	2	1	no	—
177	C₂×Q₈×C₆₇	—	4	2	no	—
178	C₂×Q₈×C₆₇	—	4	2	no	—
179	C₂×Q₈×C₆₇	—	4	4	no	—
180	C₂×Q₈×C₆₇	—	4	4	no	—
181	C₂×Q₈×C₆₇	—	4	4	no	—
182	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
183	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
184	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
185	C₂×Q₈×C₆₇	#41	1	2	yes	—
186	C₂×D₄×C₆₇	—	2	2	no	—
187	C₂×D₄×C₆₇	—	2	2	no	—
188	C₂×D₄×C₆₇	—	2	4	no	—
189	C₂×D₄×C₆₇	—	2	4	no	—
190	C₂×D₄×C₆₇	—	2	1	no	—
191	C₂×D₄×C₆₇	—	2	1	no	—
192	C₂×D₄×C₆₇	—	2	1	no	—
193	C₂×D₄×C₆₇	—	2	1	no	—
194	C₂×D₄×C₆₇	—	2	1	no	—
195	C₂×D₄×C₆₇	—	4	2	no	—
196	C₂×D₄×C₆₇	—	4	2	no	—
197	C₂×D₄×C₆₇	—	4	2	no	—
198	C₂×D₄×C₆₇	—	4	2	no	—
199	C₂×D₄×C₆₇	C₂²⋊C₄	1	4	yes	—
200	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
201	C₂²×C₄×C₆₇	—	2	1	no	—
202	C₂²×C₄×C₆₇	—	2	1	no	—
203	C₂²×C₄×C₆₇	—	2	1	no	—
204	C₂²×C₄×C₆₇	—	2	1	no	—
205	C₂²×C₄×C₆₇	—	2	1	no	—
206	C₂²×C₄×C₆₇	—	2	1	no	—
207	C₂²×C₄×C₆₇	—	2	1	no	—
208	C₂²×C₄×C₆₇	—	2	1	no	—
209	C₂²×C₄×C₆₇	—	2	1	no	—
210	C₂²×C₄×C₆₇	—	2	4	no	—
211	C₂²×C₄×C₆₇	—	2	1	no	—
212	C₂²×C₄×C₆₇	—	2	1	no	—
213	C₂²×C₄×C₆₇	—	2	1	no	—
214	C₂²×C₄×C₆₇	—	2	4	no	—
215	C₂²×C₄×C₆₇	—	2	1	no	—
216	C₂²×C₄×C₆₇	—	2	1	no	—
217	C₂²×C₄×C₆₇	—	2	1	no	—
218	C₂²×C₄×C₆₇	—	4	2	no	—
219	C₂²×C₄×C₆₇	—	4	2	no	—
220	C₂²×C₄×C₆₇	—	4	2	no	—
221	C₂²×C₄×C₆₇	—	4	2	no	—
222	C₂²×C₄×C₆₇	—	4	2	no	—
223	C₂²×C₄×C₆₇	—	4	2	no	—
224	C₂²×C₄×C₆₇	—	4	2	no	—
225	C₂²×C₄×C₆₇	—	4	2	no	—
226	C₂²×C₄×C₆₇	—	8	1	no	—
227	C₂²×C₄×C₆₇	—	8	1	no	—
228	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
229	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
230	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
237	M₁₆×C₆₇	—	4	4	no	—
238	C₂×C₈×C₆₇	—	2	1	no	—
239	C₂×C₈×C₆₇	—	2	1	no	—
240	C₂×C₈×C₆₇	—	2	1	no	—
241	C₂×C₈×C₆₇	—	2	1	no	—
242	C₂×C₈×C₆₇	—	2	1	no	—
243	C₂×C₈×C₆₇	—	2	1	no	—
244	C₂×C₈×C₆₇	—	2	1	no	—
245	C₂×C₈×C₆₇	—	2	1	no	—
246	C₂×C₈×C₆₇	—	2	1	no	—
247	C₂×C₈×C₆₇	—	2	1	no	—
248	C₂×C₈×C₆₇	—	2	1	no	—
249	C₂×C₈×C₆₇	—	4	4	no	—
250	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
251	C₄⋊C₄×C₆₇	—	2	4	no	—
252	C₄⋊C₄×C₆₇	—	2	4	no	—
253	C₄⋊C₄×C₆₇	—	2	1	no	—
254	C₄⋊C₄×C₆₇	—	2	1	no	—
255	C₄⋊C₄×C₆₇	—	2	1	no	—
256	C₄⋊C₄×C₆₇	—	2	1	no	—
257	C₄⋊C₄×C₆₇	—	2	1	no	—
258	C₄⋊C₄×C₆₇	—	2	1	no	—
259	C₄⋊C₄×C₆₇	—	2	1	no	—
260	C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₄⋊C₄×C₆₇	—	4	2	no	—
262	C₄⋊C₄×C₆₇	—	4	2	no	—
263	C₄⋊C₄×C₆₇	—	4	2	no	—
264	C₄⋊C₄×C₆₇	—	8	1	no	—
265	C₄⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
266	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
267	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
268	C₂²⋊C₄×C₆₇	—	2	4	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	4	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	4	2	no	—
273	C₂²⋊C₄×C₆₇	—	4	2	no	—
274	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
275	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
276	C₄²×C₆₇	—	2	4	no	—
277	C₄²×C₆₇	—	4	2	no	—
278	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
279	C₄²×C₆₇	C₂×D₄	1	2	yes	—
280	C₂³×C₆₇	—	2	1	no	—
281	C₂³×C₆₇	—	2	1	no	—
282	C₂³×C₆₇	—	2	1	no	—
283	C₂³×C₆₇	—	2	1	no	—
284	C₂³×C₆₇	—	2	1	no	—
285	C₂³×C₆₇	—	2	1	no	—
286	C₂³×C₆₇	—	2	1	no	—
287	C₂³×C₆₇	—	2	1	no	—
288	C₂³×C₆₇	—	2	1	no	—
289	C₂³×C₆₇	—	2	1	no	—
290	C₂³×C₆₇	—	2	2	no	—
291	C₂³×C₆₇	—	4	1	no	—
292	C₂³×C₆₇	—	4	1	no	—
293	C₂³×C₆₇	—	4	1	no	—
294	C₂³×C₆₇	—	4	1	no	—
295	C₂³×C₆₇	—	4	1	no	—
296	C₂³×C₆₇	—	4	1	no	—
297	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
298	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
299	C₂³×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
300	C₂³×C₆₇	#137	1	2	yes	—
301	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₆₇	—	2	2	no	—
303	Q₈×C₆₇	—	2	2	no	—
304	Q₈×C₆₇	—	2	2	no	—
305	Q₈×C₆₇	—	2	2	no	—
306	Q₈×C₆₇	—	2	2	no	—
307	Q₈×C₆₇	—	4	8	no	—
308	Q₈×C₆₇	—	4	1	no	—
309	Q₈×C₆₇	—	4	1	no	—
310	Q₈×C₆₇	C₄×D₄	1	4	yes	complemented
311	D₄×C₆₇	—	2	8	no	—
312	D₄×C₆₇	—	2	2	no	—
313	D₄×C₆₇	—	2	2	no	—
314	D₄×C₆₇	—	4	8	no	—
315	D₄×C₆₇	—	4	8	no	—
316	D₄×C₆₇	—	4	1	no	—
317	D₄×C₆₇	—	4	1	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	1	no	—
320	C₂×C₄×C₆₇	—	2	1	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	1	no	—
323	C₂×C₄×C₆₇	—	2	1	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	1	no	—
326	C₂×C₄×C₆₇	—	2	1	no	—
327	C₂×C₄×C₆₇	—	2	1	no	—
328	C₂×C₄×C₆₇	—	2	1	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	4	8	no	—
341	C₂×C₄×C₆₇	—	4	8	no	—
342	C₂×C₄×C₆₇	—	4	1	no	—
343	C₂×C₄×C₆₇	—	4	1	no	—
344	C₂×C₄×C₆₇	—	4	1	no	—
345	C₂×C₄×C₆₇	—	4	1	no	—
346	C₂×C₄×C₆₇	—	4	1	no	—
347	C₂×C₄×C₆₇	—	4	1	no	—
348	C₂×C₄×C₆₇	—	4	1	no	—
349	C₂×C₄×C₆₇	—	4	1	no	—
350	C₂×C₄×C₆₇	—	4	1	no	—
351	C₂×C₄×C₆₇	—	4	1	no	—
352	C₂×C₄×C₆₇	—	4	1	no	—
353	C₂×C₄×C₆₇	—	4	1	no	—
354	C₂×C₄×C₆₇	—	4	1	no	—
355	C₂×C₄×C₆₇	—	4	1	no	—
356	C₂×C₄×C₆₇	—	4	1	no	—
357	C₂×C₄×C₆₇	—	8	4	no	—
358	C₂×C₄×C₆₇	—	8	4	no	—
359	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
360	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
361	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
362	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
363	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
364	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
367	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
368	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
369	C₈×C₆₇	—	2	2	no	—
370	C₈×C₆₇	—	4	1	no	—
371	C₈×C₆₇	—	4	1	no	—
372	C₈×C₆₇	—	4	1	no	—
373	C₂²×C₆₇	—	2	2	no	—
374	C₂²×C₆₇	—	2	2	no	—
375	C₂²×C₆₇	—	2	2	no	—
376	C₂²×C₆₇	—	2	2	no	—
377	C₂²×C₆₇	—	2	2	no	—
378	C₂²×C₆₇	—	2	2	no	—
379	C₂²×C₆₇	—	2	2	no	—
380	C₂²×C₆₇	—	2	2	no	—
381	C₂²×C₆₇	—	2	2	no	—
382	C₂²×C₆₇	—	4	1	no	—
383	C₂²×C₆₇	—	4	1	no	—
384	C₂²×C₆₇	—	4	1	no	—
385	C₂²×C₆₇	—	4	1	no	—
386	C₂²×C₆₇	—	4	2	no	—
387	C₂²×C₆₇	—	4	2	no	—
388	C₂²×C₆₇	—	4	2	no	—
389	C₂²×C₆₇	—	8	1	no	—
390	C₂²×C₆₇	—	8	1	no	—
391	C₂²×C₆₇	—	8	1	no	—
392	C₂²×C₆₇	—	8	1	no	—
393	C₂²×C₆₇	#417	1	4	yes	complemented
394	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
395	C₂²×C₆₇	D₄²	1	1	yes	characteristic
396	C₂²×C₆₇	#546	1	1	yes	characteristic
397	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
398	C₂²×C₆₇	C₂×#137	1	1	yes	characteristic
399	C₂²×C₆₇	#577	1	1	yes	characteristic
400	C₂²×C₆₇	#578	1	1	yes	characteristic
401	C₄×C₆₇	—	2	2	no	—
402	C₄×C₆₇	—	2	2	no	—
403	C₄×C₆₇	—	2	4	no	—
404	C₄×C₆₇	—	2	2	no	—
405	C₄×C₆₇	—	2	2	no	—
406	C₄×C₆₇	—	4	2	no	—
407	C₄×C₆₇	—	4	2	no	—
408	C₄×C₆₇	—	4	2	no	—
409	C₄×C₆₇	—	8	1	no	—
410	C₄×C₆₇	—	8	1	no	—
411	C₄×C₆₇	—	8	1	no	—
412	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
413	C₄×C₆₇	#518	1	1	yes	characteristic
414	C₄×C₆₇	D₄²	1	1	yes	characteristic
415	C₄×C₆₇	#546	1	1	yes	characteristic
416	#22421	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
417	C₂×C₆₇	—	2	4	no	—
418	C₂×C₆₇	—	4	2	no	—
419	C₂×C₆₇	—	8	2	no	—
420	C₂×C₆₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
421	C₂×C₆₇	C₂×#417	1	1	yes	characteristic
422	C₂×C₆₇	#2898	1	1	yes	characteristic
423	C₂×C₆₇	#3265	1	1	yes	characteristic
424	C₂×C₆₇	#3270	1	1	yes	characteristic
425	C₂×C₆₇	#3308	1	1	yes	characteristic
426	C₂×C₆₇	#3316	1	1	yes	characteristic
427	C₂×#548	C₂×C₆₇	1	1	yes	characteristic
428	C₂×#435	C₂×C₆₇	1	1	yes	characteristic, complemented
429	C₂×#417	C₂×C₆₇	1	1	yes	characteristic, complemented
430	C₂²×#103	C₂×C₆₇	1	1	yes	characteristic, complemented
431	D₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
432	#1983	C₂×C₆₇	1	1	yes	characteristic, complemented
433	#1959	C₂×C₆₇	1	1	yes	characteristic, complemented
434	#1894	C₂×C₆₇	1	1	yes	characteristic, complemented
435	#1893	C₂×C₆₇	1	1	yes	characteristic, complemented
436	#1874	C₂×C₆₇	1	1	yes	characteristic, complemented
437	#1872	C₂×C₆₇	1	1	yes	characteristic, complemented
438	#1803	C₂×C₆₇	1	1	yes	characteristic, complemented
439	#1788	C₂×C₆₇	1	1	yes	characteristic, complemented
440	#1787	C₂×C₆₇	1	1	yes	characteristic, complemented
441	#1763	C₂×C₆₇	1	1	yes	characteristic, complemented
442	C₆₇	#22421	1	1	yes	characteristic, direct product factor, Sylow
443	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
444	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
445	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
446	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
447	#548	—	2	4	no	—
448	#548	C₄×C₆₇	1	8	yes	complemented
449	C₂×#124	—	2	1	no	—
450	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
451	C₂×C₂²⋊Q₈	—	2	1	no	—
452	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
453	C₂×#121	—	2	1	no	—
454	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
455	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
456	C₂×C₄×D₄	—	2	1	no	—
457	C₂×C₄×D₄	—	2	1	no	—
458	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
459	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
460	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
461	#435	—	2	4	no	—
462	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
463	#417	—	2	4	no	—
464	C₂×#103	—	2	4	no	—
465	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
466	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
467	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
468	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
469	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
470	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
471	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
472	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
473	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
474	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
475	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
476	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
477	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
478	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
479	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
480	#389	—	2	1	no	—
481	#385	—	2	1	no	—
482	#385	—	2	1	no	—
483	#384	C₂²×C₆₇	1	1	yes	characteristic
484	#380	C₂²×C₆₇	1	1	yes	characteristic
485	#380	C₂²×C₆₇	1	1	yes	characteristic
486	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
487	#340	C₂²×C₆₇	1	1	yes	characteristic
488	#340	C₂²×C₆₇	1	1	yes	characteristic
489	#340	C₂²×C₆₇	1	1	yes	characteristic
490	#340	C₂²×C₆₇	1	1	yes	characteristic
491	C₂×#41	—	2	2	no	—
492	C₂×#41	—	2	2	no	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	4	1	no	—
495	C₂×#41	—	4	1	no	—
496	C₂×#41	C₂×C₄×C₆₇	1	4	yes	complemented
497	C₂²×Q₈	—	2	1	no	—
498	C₂²×Q₈	—	2	2	no	—
499	C₂²×Q₈	—	2	2	no	—
500	C₂²×Q₈	—	2	2	no	—
501	C₂²×Q₈	—	4	1	no	—
502	C₂²×Q₈	—	4	1	no	—
503	C₂²×Q₈	C₂×C₄×C₆₇	1	4	yes	complemented
504	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
505	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
509	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	—	2	1	no	—
512	C₂³×C₄	—	2	1	no	—
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
516	C₂×M₁₆	—	2	2	no	—
517	C₂×M₁₆	—	2	2	no	—
518	C₂×M₁₆	—	4	1	no	—
519	C₂²×C₈	—	2	2	no	—
520	C₂²×C₈	—	2	2	no	—
521	C₂²×C₈	—	4	1	no	—
522	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
523	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
524	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
525	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
526	#124	—	2	8	no	—
527	#124	—	2	2	no	—
528	#124	C₂×C₄×C₆₇	1	4	yes	complemented
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	8	no	—
531	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	complemented
532	#121	—	2	8	no	—
533	#121	—	2	2	no	—
534	#121	C₂×C₄×C₆₇	1	4	yes	complemented
535	C₄×Q₈	—	2	2	no	—
536	C₄×Q₈	C₂×C₄×C₆₇	1	4	yes	complemented
537	C₄×D₄	—	2	8	no	—
538	C₄×D₄	—	4	4	no	—
539	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
540	C₄×D₄	D₄×C₆₇	1	4	yes	—
541	C₂×C₄⋊C₄	—	2	1	no	—
542	C₂×C₄⋊C₄	—	2	1	no	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	—	2	2	no	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	—	2	1	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	—	4	1	no	—
550	C₂×C₄⋊C₄	—	4	1	no	—
551	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	—	2	1	no	—
561	C₂×C₂²⋊C₄	—	2	1	no	—
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
564	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
565	C₂×C₄²	—	2	1	no	—
566	C₂×C₄²	—	2	1	no	—
567	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
568	C₄⋊C₈	—	2	2	no	—
569	#103	—	2	2	no	—
570	#103	—	2	2	no	—
571	#103	—	2	2	no	—
572	#103	—	2	2	no	—
573	#103	—	2	2	no	—
574	#103	—	4	1	no	—
575	#103	—	4	1	no	—
576	#103	D₄×C₆₇	1	4	yes	complemented
577	#102	—	2	2	no	—
578	#102	—	2	2	no	—
579	#102	—	4	1	no	—
580	#102	—	4	1	no	—
581	C₂²⋊C₈	—	2	2	no	—
582	C₂²⋊C₈	—	2	2	no	—
583	#97	—	2	2	no	—
584	#95	—	2	1	no	—
585	#95	—	2	1	no	—
586	#95	—	2	1	no	—
587	C₂⁴	—	2	1	no	—
588	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
589	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
590	#41	—	2	8	no	—
591	#41	—	4	4	no	—
592	#41	—	4	4	no	—
593	#41	—	4	4	no	—
594	C₂×Q₈	—	2	4	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	8	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	4	2	no	—
605	C₂×Q₈	—	4	2	no	—
606	C₂×Q₈	—	4	4	no	—
607	C₂×Q₈	—	4	4	no	—
608	C₂×Q₈	—	4	4	no	—
609	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
610	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
611	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
612	C₂×Q₈	#41×C₆₇	1	2	yes	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	4	2	no	—
623	C₂×D₄	—	4	2	no	—
624	C₂×D₄	—	4	2	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	C₂²⋊C₄×C₆₇	1	4	yes	—
627	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	4	2	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	8	1	no	—
654	C₂²×C₄	—	8	1	no	—
655	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
656	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
657	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
662	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
664	M₁₆	—	4	4	no	—
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₂×C₈	—	2	1	no	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	4	4	no	—
677	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	8	1	no	—
692	C₄⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
693	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
694	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	4	2	no	—
700	C₂²⋊C₄	—	4	2	no	—
701	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
702	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
703	C₄²	—	2	4	no	—
704	C₄²	—	4	2	no	—
705	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
706	C₄²	C₂×D₄×C₆₇	1	2	yes	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	4	1	no	—
719	C₂³	—	4	1	no	—
720	C₂³	—	4	1	no	—
721	C₂³	—	4	1	no	—
722	C₂³	—	4	1	no	—
723	C₂³	—	4	1	no	—
724	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
725	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
726	C₂³	AGL(1,ℤ/8)×C₆₇	1	2	yes	—
727	C₂³	#137×C₆₇	1	2	yes	—
728	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
729	Q₈	—	2	2	no	—
730	Q₈	—	2	2	no	—
731	Q₈	—	2	2	no	—
732	Q₈	—	2	2	no	—
733	Q₈	—	2	2	no	—
734	Q₈	—	4	8	no	—
735	Q₈	—	4	1	no	—
736	Q₈	—	4	1	no	—
737	Q₈	C₄×D₄×C₆₇	1	4	yes	complemented
738	D₄	—	2	8	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	4	8	no	—
742	D₄	—	4	8	no	—
743	D₄	—	4	1	no	—
744	D₄	—	4	1	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	4	8	no	—
768	C₂×C₄	—	4	8	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	8	4	no	—
785	C₂×C₄	—	8	4	no	—
786	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
787	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
788	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
789	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
790	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
793	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
794	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
795	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
796	C₈	—	2	2	no	—
797	C₈	—	4	1	no	—
798	C₈	—	4	1	no	—
799	C₈	—	4	1	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	8	1	no	—
817	C₂²	—	8	1	no	—
818	C₂²	—	8	1	no	—
819	C₂²	—	8	1	no	—
820	C₂²	#417×C₆₇	1	4	yes	complemented
821	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
822	C₂²	D₄²×C₆₇	1	1	yes	characteristic
823	C₂²	#546×C₆₇	1	1	yes	characteristic
824	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
825	C₂²	C₂×#137×C₆₇	1	1	yes	characteristic
826	C₂²	#577×C₆₇	1	1	yes	characteristic
827	C₂²	#578×C₆₇	1	1	yes	characteristic
828	C₄	—	2	2	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	4	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	8	1	no	—
837	C₄	—	8	1	no	—
838	C₄	—	8	1	no	—
839	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
840	C₄	#518×C₆₇	1	1	yes	characteristic
841	C₄	D₄²×C₆₇	1	1	yes	characteristic
842	C₄	#546×C₆₇	1	1	yes	characteristic
843	C₂	—	2	4	no	—
844	C₂	—	4	2	no	—
845	C₂	—	8	2	no	—
846	C₂	D₄×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
847	C₂	C₂×#417×C₆₇	1	1	yes	characteristic
848	C₂	C₆₇×#2898	1	1	yes	characteristic
849	C₂	C₆₇×#3265	1	1	yes	characteristic
850	C₂	C₆₇×#3270	1	1	yes	characteristic
851	C₂	C₆₇×#3308	1	1	yes	characteristic
852	C₂	C₆₇×#3316	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂×#548×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#435×C₆₇	C₂	semidirect
3. C₂×#417×C₆₇	C₂	semidirect
4. C₂²×#103×C₆₇	C₂	semidirect
5. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
6. C₆₇×#1983	C₂	semidirect
7. C₆₇×#1959	C₂	semidirect
8. C₆₇×#1894	C₂	semidirect
9. C₆₇×#1893	C₂	semidirect
10. C₆₇×#1874	C₂	semidirect
11. C₆₇×#1872	C₂	semidirect
12. C₆₇×#1803	C₂	semidirect
13. C₆₇×#1788	C₂	semidirect
14. C₆₇×#1787	C₂	semidirect
15. C₆₇×#1763	C₂	semidirect
21. #548×C₆₇	C₄	semidirect
69. C₂×#41×C₆₇	C₂×C₄	semidirect
76. C₂²×Q₈×C₆₇	C₂×C₄	semidirect
101. #124×C₆₇	C₂×C₄	semidirect
104. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
107. #121×C₆₇	C₂×C₄	semidirect
109. C₄×Q₈×C₆₇	C₂×C₄	semidirect
149. #103×C₆₇	D₄	semidirect
310. Q₈×C₆₇	C₄×D₄	semidirect
393. C₂²×C₆₇	#417	semidirect
416. #22421	C₆₇	direct (N × H)
428. C₂×#435	C₂×C₆₇	semidirect
429. C₂×#417	C₂×C₆₇	semidirect
430. C₂²×#103	C₂×C₆₇	semidirect
431. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
432. #1983	C₂×C₆₇	semidirect
433. #1959	C₂×C₆₇	semidirect
434. #1894	C₂×C₆₇	semidirect
435. #1893	C₂×C₆₇	semidirect
436. #1874	C₂×C₆₇	semidirect
437. #1872	C₂×C₆₇	semidirect
438. #1803	C₂×C₆₇	semidirect
439. #1788	C₂×C₆₇	semidirect
440. #1787	C₂×C₆₇	semidirect
441. #1763	C₂×C₆₇	semidirect
442. C₆₇	#22421	direct (N × H)
448. #548	C₄×C₆₇	semidirect
496. C₂×#41	C₂×C₄×C₆₇	semidirect
503. C₂²×Q₈	C₂×C₄×C₆₇	semidirect
528. #124	C₂×C₄×C₆₇	semidirect
531. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
534. #121	C₂×C₄×C₆₇	semidirect
536. C₄×Q₈	C₂×C₄×C₆₇	semidirect
576. #103	D₄×C₆₇	semidirect
737. Q₈	C₄×D₄×C₆₇	semidirect
820. C₂²	#417×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#548×C₆₇	2
C₂×#435×C₆₇	2
C₂×#417×C₆₇	2
C₂²×#103×C₆₇	2
D₄×C₄⋊C₄×C₆₇	2
C₆₇×#1983	2
C₆₇×#1959	2
C₆₇×#1894	2
C₆₇×#1893	2
C₆₇×#1874	2
C₆₇×#1872	2
C₆₇×#1803	2
C₆₇×#1788	2
C₆₇×#1787	2
C₆₇×#1763	2
#22421	67

Subgroups — C67×#22421 #30701672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#22421 #30701672