Subgroups — C₆₇×#61571 #30740822

Order 17152.

2578 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3318	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3310	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3265	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3264	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3217	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3194	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3187	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3186	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3114	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3003	C₂	1	2	yes	maximal, complemented
13	C₂×#450×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#447×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₆₇	—	2	1	no	—
17	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
20	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
21	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
22	#553×C₆₇	—	2	2	no	—
23	#553×C₆₇	C₂²	1	2	yes	complemented
24	#552×C₆₇	C₂²	1	2	yes	complemented
25	#551×C₆₇	—	2	2	no	—
26	#548×C₆₇	C₂²	1	2	yes	complemented
27	#546×C₆₇	C₂²	1	2	yes	complemented
28	D₄²×C₆₇	—	2	2	no	—
29	D₄²×C₆₇	—	2	2	no	—
30	D₄²×C₆₇	C₂²	1	4	yes	—
31	D₄²×C₆₇	C₂²	1	4	yes	complemented
32	#539×C₆₇	—	2	1	no	—
33	#538×C₆₇	—	2	1	no	—
34	#534×C₆₇	—	2	1	no	—
35	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#529×C₆₇	C₂²	1	2	yes	complemented
37	#525×C₆₇	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×#121×C₆₇	—	2	1	no	—
40	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#120×C₆₇	—	2	1	no	—
44	C₂×#120×C₆₇	—	2	1	no	—
45	#518×C₆₇	—	2	1	no	—
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#496×C₆₇	C₂²	1	4	yes	complemented
49	#490×C₆₇	C₂²	1	4	yes	complemented
50	#483×C₆₇	C₂²	1	2	yes	complemented
51	#482×C₆₇	C₂²	1	4	yes	complemented
52	#481×C₆₇	C₂²	1	2	yes	complemented
53	#480×C₆₇	C₂²	1	2	yes	complemented
54	#480×C₆₇	C₂²	1	2	yes	complemented
55	#478×C₆₇	C₂²	1	4	yes	complemented
56	#469×C₆₇	C₂²	1	4	yes	complemented
57	#468×C₆₇	C₂²	1	4	yes	complemented
58	#466×C₆₇	C₂²	1	4	yes	complemented
59	#465×C₆₇	C₂²	1	4	yes	complemented
60	#463×C₆₇	C₂²	1	4	yes	complemented
61	#460×C₆₇	C₂²	1	4	yes	complemented
62	#459×C₆₇	C₂²	1	4	yes	complemented
63	#450×C₆₇	C₂²	1	2	yes	complemented
64	#450×C₆₇	C₂²	1	4	yes	complemented
65	#450×C₆₇	C₂²	1	4	yes	complemented
66	#450×C₆₇	C₂²	1	2	yes	complemented
67	#450×C₆₇	C₂²	1	2	yes	complemented
68	#449×C₆₇	C₂²	1	4	yes	complemented
69	#448×C₆₇	C₂²	1	2	yes	complemented
70	#447×C₆₇	C₂²	1	2	yes	—
71	#447×C₆₇	C₂²	1	4	yes	complemented
72	#447×C₆₇	C₂²	1	4	yes	complemented
73	#447×C₆₇	C₂²	1	2	yes	complemented
74	#447×C₆₇	C₂²	1	2	yes	complemented
75	#447×C₆₇	C₂²	1	2	yes	complemented
76	#442×C₆₇	C₂²	1	4	yes	complemented
77	#440×C₆₇	C₂²	1	4	yes	complemented
78	#435×C₆₇	C₂²	1	4	yes	complemented
79	#435×C₆₇	C₂²	1	4	yes	complemented
80	#432×C₆₇	C₂²	1	2	yes	complemented
81	#418×C₆₇	C₂²	1	4	yes	complemented
82	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
83	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
84	#407×C₆₇	C₂²	1	2	yes	complemented
85	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	C₂⁵×C₆₇	—	2	1	no	—
88	C₂⁵×C₆₇	—	2	1	no	—
89	C₂×#41×C₆₇	C₂³	1	2	yes	complemented
90	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
91	C₂²×D₄×C₆₇	—	2	1	no	—
92	C₂²×D₄×C₆₇	—	2	1	no	—
93	C₂²×D₄×C₆₇	—	2	1	no	—
94	C₂²×D₄×C₆₇	—	2	4	no	—
95	C₂²×D₄×C₆₇	—	2	4	no	—
96	C₂²×D₄×C₆₇	—	2	1	no	—
97	C₂²×D₄×C₆₇	—	2	1	no	—
98	C₂²×D₄×C₆₇	—	2	1	no	—
99	C₂²×D₄×C₆₇	—	2	1	no	—
100	C₂²×D₄×C₆₇	—	2	1	no	—
101	C₂²×D₄×C₆₇	—	2	2	no	—
102	C₂²×D₄×C₆₇	—	2	1	no	—
103	C₂²×D₄×C₆₇	—	4	4	no	—
104	C₂²×D₄×C₆₇	—	4	4	no	—
105	C₂²×D₄×C₆₇	—	4	8	no	—
106	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
107	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
114	C₂³×C₄×C₆₇	—	2	1	no	—
115	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
117	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
118	C₂×SD₁₆×C₆₇	—	4	4	no	—
119	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
120	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
121	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
122	C₂×D₈×C₆₇	—	4	4	no	—
123	C₂×D₈×C₆₇	C₂³	1	4	yes	—
124	C₂×D₈×C₆₇	C₂³	1	4	yes	complemented
125	C₂×D₈×C₆₇	C₂³	1	4	yes	complemented
126	C₂×M₁₆×C₆₇	C₂³	1	4	yes	complemented
127	C₂²×C₈×C₆₇	C₂³	1	2	yes	complemented
128	C₂²×C₈×C₆₇	C₂³	1	2	yes	complemented
129	#127×C₆₇	—	2	2	no	—
130	#127×C₆₇	C₂³	1	4	yes	—
131	#126×C₆₇	—	2	2	no	—
132	#126×C₆₇	—	2	2	no	—
133	#126×C₆₇	—	2	2	no	—
134	#125×C₆₇	—	2	2	no	—
135	#125×C₆₇	C₂³	1	2	yes	complemented
136	#124×C₆₇	—	2	2	no	—
137	#124×C₆₇	C₂³	1	2	yes	complemented
138	#123×C₆₇	—	2	2	no	—
139	#123×C₆₇	—	2	2	no	—
140	#123×C₆₇	—	2	2	no	—
141	#123×C₆₇	—	2	2	no	—
142	#123×C₆₇	—	2	2	no	—
143	C₂²⋊Q₈×C₆₇	—	2	1	no	—
144	C₂²⋊Q₈×C₆₇	—	2	1	no	—
145	C₂²⋊Q₈×C₆₇	—	2	2	no	—
146	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
147	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
148	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
149	#121×C₆₇	—	2	2	no	—
150	#121×C₆₇	—	2	2	no	—
151	#121×C₆₇	—	2	1	no	—
152	#121×C₆₇	—	2	1	no	—
153	#121×C₆₇	—	2	1	no	—
154	#121×C₆₇	—	2	2	no	—
155	#121×C₆₇	—	2	1	no	—
156	#121×C₆₇	—	2	4	no	—
157	#121×C₆₇	—	2	4	no	—
158	#121×C₆₇	—	2	2	no	—
159	#121×C₆₇	C₂³	1	2	yes	—
160	#121×C₆₇	C₂³	1	4	yes	—
161	#121×C₆₇	C₂³	1	2	yes	—
162	#121×C₆₇	C₂³	1	2	yes	—
163	#121×C₆₇	C₂³	1	2	yes	complemented
164	#121×C₆₇	C₂³	1	2	yes	complemented
165	#120×C₆₇	—	2	2	no	—
166	#120×C₆₇	—	2	2	no	—
167	#120×C₆₇	—	2	4	no	—
168	#120×C₆₇	—	2	4	no	—
169	#120×C₆₇	—	2	4	no	—
170	#120×C₆₇	—	2	4	no	—
171	C₄×Q₈×C₆₇	C₂³	1	2	yes	complemented
172	C₄×D₄×C₆₇	—	2	2	no	—
173	C₄×D₄×C₆₇	—	2	2	no	—
174	C₄×D₄×C₆₇	—	2	2	no	—
175	C₄×D₄×C₆₇	—	2	2	no	—
176	C₄×D₄×C₆₇	—	2	2	no	—
177	C₄×D₄×C₆₇	—	2	2	no	—
178	C₄×D₄×C₆₇	D₄	1	2	yes	—
179	C₄×D₄×C₆₇	D₄	1	2	yes	—
180	C₄×D₄×C₆₇	C₂³	1	4	yes	—
181	C₄×D₄×C₆₇	C₂³	1	2	yes	—
182	C₄×D₄×C₆₇	C₂³	1	2	yes	—
183	C₄×D₄×C₆₇	C₂³	1	2	yes	complemented
184	#117×C₆₇	—	2	2	no	—
185	#117×C₆₇	—	2	2	no	—
186	#117×C₆₇	C₂³	1	2	yes	complemented
187	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
188	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
192	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
196	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
197	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
200	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
201	#107×C₆₇	C₂³	1	4	yes	complemented
202	#106×C₆₇	C₂³	1	4	yes	complemented
203	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
204	#103×C₆₇	C₂³	1	4	yes	complemented
205	#102×C₆₇	C₂³	1	4	yes	—
206	#102×C₆₇	C₂³	1	4	yes	—
207	#102×C₆₇	C₂³	1	4	yes	complemented
208	#102×C₆₇	C₂³	1	4	yes	complemented
209	#102×C₆₇	C₂³	1	4	yes	complemented
210	#102×C₆₇	C₂³	1	4	yes	complemented
211	#102×C₆₇	C₂³	1	4	yes	complemented
212	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
213	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
214	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	complemented
215	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	complemented
216	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	complemented
217	#97×C₆₇	C₂³	1	4	yes	complemented
218	C₂⁴×C₆₇	—	2	1	no	—
219	C₂⁴×C₆₇	—	2	1	no	—
220	C₂⁴×C₆₇	—	2	1	no	—
221	C₂⁴×C₆₇	—	2	4	no	—
222	C₂⁴×C₆₇	—	2	2	no	—
223	C₂⁴×C₆₇	—	2	2	no	—
224	C₂⁴×C₆₇	—	2	1	no	—
225	C₂⁴×C₆₇	—	4	4	no	—
226	C₂⁴×C₆₇	—	4	4	no	—
227	C₂⁴×C₆₇	—	4	4	no	—
228	C₂⁴×C₆₇	—	4	4	no	—
229	C₂⁴×C₆₇	—	8	2	no	—
230	C₂⁴×C₆₇	—	8	2	no	—
231	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
232	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
233	#41×C₆₇	—	4	4	no	—
234	C₂×Q₈×C₆₇	—	2	1	no	—
235	C₂×Q₈×C₆₇	—	4	2	no	—
236	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
237	C₂×D₄×C₆₇	—	2	4	no	—
238	C₂×D₄×C₆₇	—	2	4	no	—
239	C₂×D₄×C₆₇	—	2	4	no	—
240	C₂×D₄×C₆₇	—	2	4	no	—
241	C₂×D₄×C₆₇	—	2	8	no	—
242	C₂×D₄×C₆₇	—	2	2	no	—
243	C₂×D₄×C₆₇	—	2	2	no	—
244	C₂×D₄×C₆₇	—	2	4	no	—
245	C₂×D₄×C₆₇	—	2	2	no	—
246	C₂×D₄×C₆₇	—	2	2	no	—
247	C₂×D₄×C₆₇	—	2	2	no	—
248	C₂×D₄×C₆₇	—	2	2	no	—
249	C₂×D₄×C₆₇	—	2	1	no	—
250	C₂×D₄×C₆₇	—	2	4	no	—
251	C₂×D₄×C₆₇	—	2	2	no	—
252	C₂×D₄×C₆₇	—	2	2	no	—
253	C₂×D₄×C₆₇	—	2	1	no	—
254	C₂×D₄×C₆₇	—	2	1	no	—
255	C₂×D₄×C₆₇	—	2	4	no	—
256	C₂×D₄×C₆₇	—	2	4	no	—
257	C₂×D₄×C₆₇	—	2	1	no	—
258	C₂×D₄×C₆₇	—	4	2	no	—
259	C₂×D₄×C₆₇	—	4	2	no	—
260	C₂×D₄×C₆₇	—	4	4	no	—
261	C₂×D₄×C₆₇	—	4	2	no	—
262	C₂×D₄×C₆₇	—	4	2	no	—
263	C₂×D₄×C₆₇	—	4	2	no	—
264	C₂×D₄×C₆₇	—	4	4	no	—
265	C₂×D₄×C₆₇	—	4	4	no	—
266	C₂×D₄×C₆₇	—	4	4	no	—
267	C₂×D₄×C₆₇	—	4	8	no	—
268	C₂×D₄×C₆₇	—	4	16	no	—
269	C₂×D₄×C₆₇	—	4	16	no	—
270	C₂×D₄×C₆₇	—	4	4	no	—
271	C₂×D₄×C₆₇	—	4	4	no	—
272	C₂×D₄×C₆₇	—	4	4	no	—
273	C₂×D₄×C₆₇	—	4	4	no	—
274	C₂×D₄×C₆₇	—	4	4	no	—
275	C₂×D₄×C₆₇	—	8	2	no	—
276	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
277	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
278	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
279	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
280	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
281	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₆₇	—	2	1	no	—
283	C₂²×C₄×C₆₇	—	2	1	no	—
284	C₂²×C₄×C₆₇	—	2	1	no	—
285	C₂²×C₄×C₆₇	—	2	1	no	—
286	C₂²×C₄×C₆₇	—	2	4	no	—
287	C₂²×C₄×C₆₇	—	2	2	no	—
288	C₂²×C₄×C₆₇	—	2	2	no	—
289	C₂²×C₄×C₆₇	—	4	2	no	—
290	C₂²×C₄×C₆₇	—	4	2	no	—
291	C₂²×C₄×C₆₇	—	4	4	no	—
292	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
303	SD₁₆×C₆₇	—	2	8	no	—
304	SD₁₆×C₆₇	—	4	4	no	—
305	SD₁₆×C₆₇	—	4	4	no	—
306	D₈×C₆₇	—	2	8	no	—
307	D₈×C₆₇	—	4	4	no	—
308	D₈×C₆₇	—	4	4	no	—
309	M₁₆×C₆₇	—	4	4	no	—
310	C₂×C₈×C₆₇	—	4	2	no	—
311	C₂×C₈×C₆₇	—	4	2	no	—
312	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
313	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
314	C₄⋊C₄×C₆₇	—	2	2	no	—
315	C₄⋊C₄×C₆₇	—	2	2	no	—
316	C₄⋊C₄×C₆₇	—	2	1	no	—
317	C₄⋊C₄×C₆₇	—	2	1	no	—
318	C₄⋊C₄×C₆₇	—	2	1	no	—
319	C₄⋊C₄×C₆₇	—	2	2	no	—
320	C₄⋊C₄×C₆₇	—	2	2	no	—
321	C₄⋊C₄×C₆₇	—	2	2	no	—
322	C₄⋊C₄×C₆₇	—	2	2	no	—
323	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
324	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
325	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
326	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
327	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
328	C₂²⋊C₄×C₆₇	—	2	2	no	—
329	C₂²⋊C₄×C₆₇	—	2	2	no	—
330	C₂²⋊C₄×C₆₇	—	2	2	no	—
331	C₂²⋊C₄×C₆₇	—	2	2	no	—
332	C₂²⋊C₄×C₆₇	—	2	2	no	—
333	C₂²⋊C₄×C₆₇	—	2	2	no	—
334	C₂²⋊C₄×C₆₇	—	2	2	no	—
335	C₂²⋊C₄×C₆₇	—	2	4	no	—
336	C₂²⋊C₄×C₆₇	—	2	4	no	—
337	C₂²⋊C₄×C₆₇	—	2	2	no	—
338	C₂²⋊C₄×C₆₇	—	2	2	no	—
339	C₂²⋊C₄×C₆₇	—	2	2	no	—
340	C₂²⋊C₄×C₆₇	—	2	2	no	—
341	C₂²⋊C₄×C₆₇	—	2	2	no	—
342	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
343	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
344	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
345	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
346	C₄²×C₆₇	—	2	2	no	—
347	C₄²×C₆₇	—	2	2	no	—
348	C₄²×C₆₇	C₂×D₄	1	2	yes	—
349	C₄²×C₆₇	C₂⁴	1	2	yes	—
350	C₂³×C₆₇	—	2	4	no	—
351	C₂³×C₆₇	—	2	2	no	—
352	C₂³×C₆₇	—	2	2	no	—
353	C₂³×C₆₇	—	2	2	no	—
354	C₂³×C₆₇	—	2	2	no	—
355	C₂³×C₆₇	—	2	2	no	—
356	C₂³×C₆₇	—	4	1	no	—
357	C₂³×C₆₇	—	4	1	no	—
358	C₂³×C₆₇	—	4	1	no	—
359	C₂³×C₆₇	—	4	1	no	—
360	C₂³×C₆₇	—	4	4	no	—
361	C₂³×C₆₇	—	4	4	no	—
362	C₂³×C₆₇	—	4	8	no	—
363	C₂³×C₆₇	—	4	2	no	—
364	C₂³×C₆₇	—	4	2	no	—
365	C₂³×C₆₇	—	4	2	no	—
366	C₂³×C₆₇	—	4	8	no	—
367	C₂³×C₆₇	—	4	2	no	—
368	C₂³×C₆₇	—	4	2	no	—
369	C₂³×C₆₇	—	4	2	no	—
370	C₂³×C₆₇	—	4	4	no	—
371	C₂³×C₆₇	—	4	4	no	—
372	C₂³×C₆₇	—	4	2	no	—
373	C₂³×C₆₇	—	4	2	no	—
374	C₂³×C₆₇	—	4	2	no	—
375	C₂³×C₆₇	—	8	2	no	—
376	C₂³×C₆₇	—	8	2	no	—
377	C₂³×C₆₇	—	8	4	no	—
378	C₂³×C₆₇	—	8	1	no	—
379	C₂³×C₆₇	—	8	1	no	—
380	C₂³×C₆₇	—	8	16	no	—
381	C₂³×C₆₇	—	8	16	no	—
382	C₂³×C₆₇	AGL(1,ℤ/8)	1	4	yes	complemented
383	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
384	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
385	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
386	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
387	Q₈×C₆₇	—	2	4	no	—
388	Q₈×C₆₇	—	8	1	no	—
389	D₄×C₆₇	—	2	4	no	—
390	D₄×C₆₇	—	2	4	no	—
391	D₄×C₆₇	—	2	4	no	—
392	D₄×C₆₇	—	2	2	no	—
393	D₄×C₆₇	—	2	4	no	—
394	D₄×C₆₇	—	2	2	no	—
395	D₄×C₆₇	—	2	4	no	—
396	D₄×C₆₇	—	2	2	no	—
397	D₄×C₆₇	—	4	8	no	—
398	D₄×C₆₇	—	4	4	no	—
399	D₄×C₆₇	—	4	4	no	—
400	D₄×C₆₇	—	4	2	no	—
401	D₄×C₆₇	—	4	2	no	—
402	D₄×C₆₇	—	4	8	no	—
403	D₄×C₆₇	—	4	8	no	—
404	D₄×C₆₇	—	4	4	no	—
405	D₄×C₆₇	—	4	4	no	—
406	D₄×C₆₇	—	4	4	no	—
407	D₄×C₆₇	—	4	4	no	—
408	D₄×C₆₇	—	8	1	no	—
409	D₄×C₆₇	—	8	4	no	—
410	D₄×C₆₇	—	8	2	no	—
411	D₄×C₆₇	—	8	2	no	—
412	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
413	C₂×C₄×C₆₇	—	2	2	no	—
414	C₂×C₄×C₆₇	—	2	2	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	4	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	2	2	no	—
419	C₂×C₄×C₆₇	—	2	2	no	—
420	C₂×C₄×C₆₇	—	2	2	no	—
421	C₂×C₄×C₆₇	—	2	2	no	—
422	C₂×C₄×C₆₇	—	4	2	no	—
423	C₂×C₄×C₆₇	—	4	1	no	—
424	C₂×C₄×C₆₇	—	4	1	no	—
425	C₂×C₄×C₆₇	—	4	1	no	—
426	C₂×C₄×C₆₇	—	4	1	no	—
427	C₂×C₄×C₆₇	—	4	1	no	—
428	C₂×C₄×C₆₇	—	4	8	no	—
429	C₂×C₄×C₆₇	—	4	2	no	—
430	C₂×C₄×C₆₇	—	4	2	no	—
431	C₂×C₄×C₆₇	—	8	2	no	—
432	C₂×C₄×C₆₇	—	8	2	no	—
433	C₂×C₄×C₆₇	—	8	1	no	—
434	C₂×C₄×C₆₇	—	8	1	no	—
435	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
442	C₈×C₆₇	—	2	4	no	—
443	C₈×C₆₇	—	2	4	no	—
444	C₂²×C₆₇	—	2	1	no	—
445	C₂²×C₆₇	—	2	1	no	—
446	C₂²×C₆₇	—	2	1	no	—
447	C₂²×C₆₇	—	2	1	no	—
448	C₂²×C₆₇	—	2	1	no	—
449	C₂²×C₆₇	—	2	1	no	—
450	C₂²×C₆₇	—	2	2	no	—
451	C₂²×C₆₇	—	2	2	no	—
452	C₂²×C₆₇	—	2	4	no	—
453	C₂²×C₆₇	—	2	2	no	—
454	C₂²×C₆₇	—	4	4	no	—
455	C₂²×C₆₇	—	4	4	no	—
456	C₂²×C₆₇	—	4	8	no	—
457	C₂²×C₆₇	—	4	2	no	—
458	C₂²×C₆₇	—	4	2	no	—
459	C₂²×C₆₇	—	4	2	no	—
460	C₂²×C₆₇	—	4	2	no	—
461	C₂²×C₆₇	—	4	2	no	—
462	C₂²×C₆₇	—	4	2	no	—
463	C₂²×C₆₇	—	4	2	no	—
464	C₂²×C₆₇	—	4	2	no	—
465	C₂²×C₆₇	—	4	2	no	—
466	C₂²×C₆₇	—	4	2	no	—
467	C₂²×C₆₇	—	4	2	no	—
468	C₂²×C₆₇	—	8	8	no	—
469	C₂²×C₆₇	—	8	8	no	—
470	C₂²×C₆₇	—	8	4	no	—
471	C₂²×C₆₇	—	8	4	no	—
472	C₂²×C₆₇	—	8	16	no	—
473	C₂²×C₆₇	—	16	2	no	—
474	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
475	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
476	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
477	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
478	C₄×C₆₇	—	2	2	no	—
479	C₄×C₆₇	—	2	1	no	—
480	C₄×C₆₇	—	2	2	no	—
481	C₄×C₆₇	—	2	1	no	—
482	C₄×C₆₇	—	2	1	no	—
483	C₄×C₆₇	—	2	2	no	—
484	C₄×C₆₇	—	4	2	no	—
485	C₄×C₆₇	—	4	2	no	—
486	C₄×C₆₇	—	4	2	no	—
487	C₄×C₆₇	—	4	2	no	—
488	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
489	#61571	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
490	C₂×C₆₇	—	2	2	no	—
491	C₂×C₆₇	—	2	2	no	—
492	C₂×C₆₇	—	2	2	no	—
493	C₂×C₆₇	—	4	2	no	—
494	C₂×C₆₇	—	4	4	no	—
495	C₂×C₆₇	—	8	2	no	—
496	C₂×C₆₇	—	8	2	no	—
497	C₂×C₆₇	—	8	2	no	—
498	C₂×C₆₇	#3484	1	1	yes	characteristic
499	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
500	C₂×C₆₇	#3585	1	1	yes	characteristic
501	#3505	C₂×C₆₇	1	1	yes	characteristic, complemented
502	C₂×D₄²	C₂×C₆₇	1	1	yes	characteristic, complemented
503	#3318	C₂×C₆₇	1	4	yes	complemented
504	#3310	C₂×C₆₇	1	4	yes	complemented
505	#3265	C₂×C₆₇	1	4	yes	complemented
506	#3264	C₂×C₆₇	1	4	yes	complemented
507	#3217	C₂×C₆₇	1	2	yes	complemented
508	#3194	C₂×C₆₇	1	2	yes	complemented
509	#3187	C₂×C₆₇	1	1	yes	characteristic, complemented
510	#3186	C₂×C₆₇	1	1	yes	characteristic, complemented
511	#3114	C₂×C₆₇	1	2	yes	complemented
512	#3003	C₂×C₆₇	1	2	yes	complemented
513	C₂×#450	C₂×C₆₇	1	1	yes	characteristic, complemented
514	C₂×#447	C₂×C₆₇	1	1	yes	characteristic, complemented
515	#2973	C₂×C₆₇	1	1	yes	characteristic, complemented
516	C₆₇	#61571	1	1	yes	characteristic, direct product factor, Sylow
517	C₂³×D₄	—	2	1	no	—
518	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
519	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
520	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
521	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
522	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
523	#553	—	2	2	no	—
524	#553	C₂²×C₆₇	1	2	yes	complemented
525	#552	C₂²×C₆₇	1	2	yes	complemented
526	#551	—	2	2	no	—
527	#548	C₂²×C₆₇	1	2	yes	complemented
528	#546	C₂²×C₆₇	1	2	yes	complemented
529	D₄²	—	2	2	no	—
530	D₄²	—	2	2	no	—
531	D₄²	C₂²×C₆₇	1	4	yes	—
532	D₄²	C₂²×C₆₇	1	4	yes	complemented
533	#539	—	2	1	no	—
534	#538	—	2	1	no	—
535	#534	—	2	1	no	—
536	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic, complemented
537	#529	C₂²×C₆₇	1	2	yes	complemented
538	#525	C₂²×C₆₇	1	2	yes	complemented
539	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
540	C₂×#121	—	2	1	no	—
541	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
542	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
543	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
544	C₂×#120	—	2	1	no	—
545	C₂×#120	—	2	1	no	—
546	#518	—	2	1	no	—
547	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
548	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
549	#496	C₂²×C₆₇	1	4	yes	complemented
550	#490	C₂²×C₆₇	1	4	yes	complemented
551	#483	C₂²×C₆₇	1	2	yes	complemented
552	#482	C₂²×C₆₇	1	4	yes	complemented
553	#481	C₂²×C₆₇	1	2	yes	complemented
554	#480	C₂²×C₆₇	1	2	yes	complemented
555	#480	C₂²×C₆₇	1	2	yes	complemented
556	#478	C₂²×C₆₇	1	4	yes	complemented
557	#469	C₂²×C₆₇	1	4	yes	complemented
558	#468	C₂²×C₆₇	1	4	yes	complemented
559	#466	C₂²×C₆₇	1	4	yes	complemented
560	#465	C₂²×C₆₇	1	4	yes	complemented
561	#463	C₂²×C₆₇	1	4	yes	complemented
562	#460	C₂²×C₆₇	1	4	yes	complemented
563	#459	C₂²×C₆₇	1	4	yes	complemented
564	#450	C₂²×C₆₇	1	2	yes	complemented
565	#450	C₂²×C₆₇	1	2	yes	complemented
566	#450	C₂²×C₆₇	1	2	yes	complemented
567	#450	C₂²×C₆₇	1	4	yes	complemented
568	#450	C₂²×C₆₇	1	4	yes	complemented
569	#449	C₂²×C₆₇	1	4	yes	complemented
570	#448	C₂²×C₆₇	1	2	yes	complemented
571	#447	C₂²×C₆₇	1	2	yes	—
572	#447	C₂²×C₆₇	1	2	yes	complemented
573	#447	C₂²×C₆₇	1	2	yes	complemented
574	#447	C₂²×C₆₇	1	4	yes	complemented
575	#447	C₂²×C₆₇	1	4	yes	complemented
576	#447	C₂²×C₆₇	1	2	yes	complemented
577	#442	C₂²×C₆₇	1	4	yes	complemented
578	#440	C₂²×C₆₇	1	4	yes	complemented
579	#435	C₂²×C₆₇	1	4	yes	complemented
580	#435	C₂²×C₆₇	1	4	yes	complemented
581	#432	C₂²×C₆₇	1	2	yes	complemented
582	#418	C₂²×C₆₇	1	4	yes	complemented
583	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
584	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
585	#407	C₂²×C₆₇	1	2	yes	complemented
586	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
587	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
588	C₂⁵	—	2	1	no	—
589	C₂⁵	—	2	1	no	—
590	C₂×#41	C₂³×C₆₇	1	2	yes	complemented
591	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
592	C₂²×D₄	—	2	1	no	—
593	C₂²×D₄	—	2	1	no	—
594	C₂²×D₄	—	2	1	no	—
595	C₂²×D₄	—	2	4	no	—
596	C₂²×D₄	—	2	4	no	—
597	C₂²×D₄	—	2	1	no	—
598	C₂²×D₄	—	2	1	no	—
599	C₂²×D₄	—	2	1	no	—
600	C₂²×D₄	—	2	1	no	—
601	C₂²×D₄	—	2	1	no	—
602	C₂²×D₄	—	2	2	no	—
603	C₂²×D₄	—	2	1	no	—
604	C₂²×D₄	—	4	4	no	—
605	C₂²×D₄	—	4	4	no	—
606	C₂²×D₄	—	4	8	no	—
607	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
608	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
609	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
610	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
611	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
612	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
613	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
615	C₂³×C₄	—	2	1	no	—
616	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
618	AGL(1,ℤ/8)	—	4	8	no	—
619	C₂×SD₁₆	—	4	4	no	—
620	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
621	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
622	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
623	C₂×D₈	—	4	4	no	—
624	C₂×D₈	C₂³×C₆₇	1	4	yes	—
625	C₂×D₈	C₂³×C₆₇	1	4	yes	complemented
626	C₂×D₈	C₂³×C₆₇	1	4	yes	complemented
627	C₂×M₁₆	C₂³×C₆₇	1	4	yes	complemented
628	C₂²×C₈	C₂³×C₆₇	1	2	yes	complemented
629	C₂²×C₈	C₂³×C₆₇	1	2	yes	complemented
630	#127	—	2	2	no	—
631	#127	C₂³×C₆₇	1	4	yes	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	C₂³×C₆₇	1	2	yes	complemented
637	#124	—	2	2	no	—
638	#124	C₂³×C₆₇	1	2	yes	complemented
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	#123	—	2	2	no	—
643	#123	—	2	2	no	—
644	C₂²⋊Q₈	—	2	1	no	—
645	C₂²⋊Q₈	—	2	1	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
648	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
649	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	—	2	1	no	—
653	#121	—	2	1	no	—
654	#121	—	2	1	no	—
655	#121	—	2	2	no	—
656	#121	—	2	1	no	—
657	#121	—	2	4	no	—
658	#121	—	2	4	no	—
659	#121	—	2	2	no	—
660	#121	C₂³×C₆₇	1	2	yes	—
661	#121	C₂³×C₆₇	1	2	yes	—
662	#121	C₂³×C₆₇	1	2	yes	—
663	#121	C₂³×C₆₇	1	4	yes	—
664	#121	C₂³×C₆₇	1	2	yes	complemented
665	#121	C₂³×C₆₇	1	2	yes	complemented
666	#120	—	2	2	no	—
667	#120	—	2	2	no	—
668	#120	—	2	4	no	—
669	#120	—	2	4	no	—
670	#120	—	2	4	no	—
671	#120	—	2	4	no	—
672	C₄×Q₈	C₂³×C₆₇	1	2	yes	complemented
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	D₄×C₆₇	1	2	yes	—
680	C₄×D₄	D₄×C₆₇	1	2	yes	—
681	C₄×D₄	C₂³×C₆₇	1	4	yes	—
682	C₄×D₄	C₂³×C₆₇	1	2	yes	—
683	C₄×D₄	C₂³×C₆₇	1	2	yes	—
684	C₄×D₄	C₂³×C₆₇	1	2	yes	complemented
685	#117	—	2	2	no	—
686	#117	—	2	2	no	—
687	#117	C₂³×C₆₇	1	2	yes	complemented
688	C₂×C₄⋊C₄	—	2	1	no	—
689	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
692	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
693	C₂×C₂²⋊C₄	—	2	1	no	—
694	C₂×C₂²⋊C₄	—	2	1	no	—
695	C₂×C₂²⋊C₄	—	2	1	no	—
696	C₂×C₂²⋊C₄	—	2	1	no	—
697	C₂×C₂²⋊C₄	—	2	1	no	—
698	C₂×C₂²⋊C₄	—	2	2	no	—
699	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
702	#107	C₂³×C₆₇	1	4	yes	complemented
703	#106	C₂³×C₆₇	1	4	yes	complemented
704	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
705	#103	C₂³×C₆₇	1	4	yes	complemented
706	#102	C₂³×C₆₇	1	4	yes	—
707	#102	C₂³×C₆₇	1	4	yes	—
708	#102	C₂³×C₆₇	1	4	yes	complemented
709	#102	C₂³×C₆₇	1	4	yes	complemented
710	#102	C₂³×C₆₇	1	4	yes	complemented
711	#102	C₂³×C₆₇	1	4	yes	complemented
712	#102	C₂³×C₆₇	1	4	yes	complemented
713	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
714	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
715	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	complemented
716	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	complemented
717	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
718	#97	C₂³×C₆₇	1	4	yes	complemented
719	C₂⁴	—	2	1	no	—
720	C₂⁴	—	2	1	no	—
721	C₂⁴	—	2	1	no	—
722	C₂⁴	—	2	4	no	—
723	C₂⁴	—	2	2	no	—
724	C₂⁴	—	2	2	no	—
725	C₂⁴	—	2	1	no	—
726	C₂⁴	—	4	4	no	—
727	C₂⁴	—	4	4	no	—
728	C₂⁴	—	4	4	no	—
729	C₂⁴	—	4	4	no	—
730	C₂⁴	—	8	2	no	—
731	C₂⁴	—	8	2	no	—
732	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
733	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
734	#41	—	4	4	no	—
735	C₂×Q₈	—	2	1	no	—
736	C₂×Q₈	—	4	2	no	—
737	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	8	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	1	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	1	no	—
755	C₂×D₄	—	2	1	no	—
756	C₂×D₄	—	2	4	no	—
757	C₂×D₄	—	2	4	no	—
758	C₂×D₄	—	2	1	no	—
759	C₂×D₄	—	4	2	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂×D₄	—	4	4	no	—
762	C₂×D₄	—	4	2	no	—
763	C₂×D₄	—	4	2	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	4	4	no	—
766	C₂×D₄	—	4	4	no	—
767	C₂×D₄	—	4	4	no	—
768	C₂×D₄	—	4	8	no	—
769	C₂×D₄	—	4	16	no	—
770	C₂×D₄	—	4	16	no	—
771	C₂×D₄	—	4	4	no	—
772	C₂×D₄	—	4	4	no	—
773	C₂×D₄	—	4	4	no	—
774	C₂×D₄	—	4	4	no	—
775	C₂×D₄	—	4	4	no	—
776	C₂×D₄	—	8	2	no	—
777	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
778	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
779	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
780	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
781	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
782	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
783	C₂²×C₄	—	2	1	no	—
784	C₂²×C₄	—	2	1	no	—
785	C₂²×C₄	—	2	1	no	—
786	C₂²×C₄	—	2	1	no	—
787	C₂²×C₄	—	2	4	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	4	2	no	—
791	C₂²×C₄	—	4	2	no	—
792	C₂²×C₄	—	4	4	no	—
793	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
794	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
796	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
798	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
799	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
804	SD₁₆	—	2	8	no	—
805	SD₁₆	—	4	4	no	—
806	SD₁₆	—	4	4	no	—
807	D₈	—	2	8	no	—
808	D₈	—	4	4	no	—
809	D₈	—	4	4	no	—
810	M₁₆	—	4	4	no	—
811	C₂×C₈	—	4	2	no	—
812	C₂×C₈	—	4	2	no	—
813	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
814	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	1	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
825	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
828	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	4	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
844	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
845	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
846	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	C₂×D₄×C₆₇	1	2	yes	—
850	C₄²	C₂⁴×C₆₇	1	2	yes	—
851	C₂³	—	2	4	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	4	1	no	—
858	C₂³	—	4	1	no	—
859	C₂³	—	4	1	no	—
860	C₂³	—	4	1	no	—
861	C₂³	—	4	4	no	—
862	C₂³	—	4	4	no	—
863	C₂³	—	4	8	no	—
864	C₂³	—	4	2	no	—
865	C₂³	—	4	2	no	—
866	C₂³	—	4	2	no	—
867	C₂³	—	4	8	no	—
868	C₂³	—	4	2	no	—
869	C₂³	—	4	2	no	—
870	C₂³	—	4	2	no	—
871	C₂³	—	4	4	no	—
872	C₂³	—	4	4	no	—
873	C₂³	—	4	2	no	—
874	C₂³	—	4	2	no	—
875	C₂³	—	4	2	no	—
876	C₂³	—	8	2	no	—
877	C₂³	—	8	2	no	—
878	C₂³	—	8	4	no	—
879	C₂³	—	8	1	no	—
880	C₂³	—	8	1	no	—
881	C₂³	—	8	16	no	—
882	C₂³	—	8	16	no	—
883	C₂³	AGL(1,ℤ/8)×C₆₇	1	4	yes	complemented
884	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
885	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
886	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
887	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
888	Q₈	—	2	4	no	—
889	Q₈	—	8	1	no	—
890	D₄	—	2	4	no	—
891	D₄	—	2	4	no	—
892	D₄	—	2	4	no	—
893	D₄	—	2	2	no	—
894	D₄	—	2	4	no	—
895	D₄	—	2	2	no	—
896	D₄	—	2	4	no	—
897	D₄	—	2	2	no	—
898	D₄	—	4	8	no	—
899	D₄	—	4	4	no	—
900	D₄	—	4	4	no	—
901	D₄	—	4	8	no	—
902	D₄	—	4	2	no	—
903	D₄	—	4	2	no	—
904	D₄	—	4	8	no	—
905	D₄	—	4	4	no	—
906	D₄	—	4	4	no	—
907	D₄	—	4	4	no	—
908	D₄	—	4	4	no	—
909	D₄	—	8	1	no	—
910	D₄	—	8	4	no	—
911	D₄	—	8	2	no	—
912	D₄	—	8	2	no	—
913	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	4	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	4	2	no	—
924	C₂×C₄	—	4	1	no	—
925	C₂×C₄	—	4	1	no	—
926	C₂×C₄	—	4	1	no	—
927	C₂×C₄	—	4	1	no	—
928	C₂×C₄	—	4	1	no	—
929	C₂×C₄	—	4	8	no	—
930	C₂×C₄	—	4	2	no	—
931	C₂×C₄	—	4	2	no	—
932	C₂×C₄	—	8	2	no	—
933	C₂×C₄	—	8	2	no	—
934	C₂×C₄	—	8	1	no	—
935	C₂×C₄	—	8	1	no	—
936	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
937	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
938	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
939	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
940	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
941	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
942	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
943	C₈	—	2	4	no	—
944	C₈	—	2	4	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	2	1	no	—
949	C₂²	—	2	1	no	—
950	C₂²	—	2	1	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	4	no	—
955	C₂²	—	4	4	no	—
956	C₂²	—	4	4	no	—
957	C₂²	—	4	8	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	8	8	no	—
970	C₂²	—	8	8	no	—
971	C₂²	—	8	4	no	—
972	C₂²	—	8	4	no	—
973	C₂²	—	8	16	no	—
974	C₂²	—	16	2	no	—
975	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
976	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
977	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
978	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
979	C₄	—	2	2	no	—
980	C₄	—	2	2	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	2	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
990	C₂	—	2	2	no	—
991	C₂	—	2	2	no	—
992	C₂	—	2	2	no	—
993	C₂	—	4	2	no	—
994	C₂	—	4	4	no	—
995	C₂	—	8	2	no	—
996	C₂	—	8	2	no	—
997	C₂	—	8	2	no	—
998	C₂	C₆₇×#3484	1	1	yes	characteristic
999	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
1000	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 ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3505	C₂	semidirect
2. C₂×D₄²×C₆₇	C₂	semidirect
3. C₆₇×#3318	C₂	semidirect
4. C₆₇×#3310	C₂	semidirect
5. C₆₇×#3265	C₂	semidirect
6. C₆₇×#3264	C₂	semidirect
7. C₆₇×#3217	C₂	semidirect
8. C₆₇×#3194	C₂	semidirect
9. C₆₇×#3187	C₂	semidirect
10. C₆₇×#3186	C₂	semidirect
11. C₆₇×#3114	C₂	semidirect
12. C₆₇×#3003	C₂	semidirect
13. C₂×#450×C₆₇	C₂	semidirect
14. C₂×#447×C₆₇	C₂	semidirect
15. C₆₇×#2973	C₂	semidirect
18. C₂³×D₄×C₆₇	C₂²	semidirect
19. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
20. C₂²×SD₁₆×C₆₇	C₂²	semidirect
21. C₂²×D₈×C₆₇	C₂²	semidirect
23. #553×C₆₇	C₂²	semidirect
24. #552×C₆₇	C₂²	semidirect
26. #548×C₆₇	C₂²	semidirect
27. #546×C₆₇	C₂²	semidirect
31. D₄²×C₆₇	C₂²	semidirect
35. C₂×#127×C₆₇	C₂²	semidirect
36. #529×C₆₇	C₂²	semidirect
37. #525×C₆₇	C₂²	semidirect
38. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
41. C₂×#121×C₆₇	C₂²	semidirect
42. C₂×#121×C₆₇	C₂²	semidirect
47. C₂×C₄×D₄×C₆₇	C₂²	semidirect
48. #496×C₆₇	C₂²	semidirect
49. #490×C₆₇	C₂²	semidirect
50. #483×C₆₇	C₂²	semidirect
51. #482×C₆₇	C₂²	semidirect
52. #481×C₆₇	C₂²	semidirect
53. #480×C₆₇	C₂²	semidirect
54. #480×C₆₇	C₂²	semidirect
55. #478×C₆₇	C₂²	semidirect
56. #469×C₆₇	C₂²	semidirect
57. #468×C₆₇	C₂²	semidirect
58. #466×C₆₇	C₂²	semidirect
59. #465×C₆₇	C₂²	semidirect
60. #463×C₆₇	C₂²	semidirect
61. #460×C₆₇	C₂²	semidirect
62. #459×C₆₇	C₂²	semidirect
63. #450×C₆₇	C₂²	semidirect
64. #450×C₆₇	C₂²	semidirect
65. #450×C₆₇	C₂²	semidirect
66. #450×C₆₇	C₂²	semidirect
67. #450×C₆₇	C₂²	semidirect
68. #449×C₆₇	C₂²	semidirect
69. #448×C₆₇	C₂²	semidirect
71. #447×C₆₇	C₂²	semidirect
72. #447×C₆₇	C₂²	semidirect
73. #447×C₆₇	C₂²	semidirect
74. #447×C₆₇	C₂²	semidirect
75. #447×C₆₇	C₂²	semidirect
76. #442×C₆₇	C₂²	semidirect
77. #440×C₆₇	C₂²	semidirect
78. #435×C₆₇	C₂²	semidirect
79. #435×C₆₇	C₂²	semidirect
80. #432×C₆₇	C₂²	semidirect
81. #418×C₆₇	C₂²	semidirect
82. C₂×#102×C₆₇	C₂²	semidirect
83. C₂×#102×C₆₇	C₂²	semidirect
84. #407×C₆₇	C₂²	semidirect
85. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
86. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
89. C₂×#41×C₆₇	C₂³	semidirect
90. C₂²×Q₈×C₆₇	C₂³	semidirect
113. C₂²×D₄×C₆₇	C₂³	semidirect
120. C₂×SD₁₆×C₆₇	C₂³	semidirect
121. C₂×SD₁₆×C₆₇	C₂³	semidirect
124. C₂×D₈×C₆₇	C₂³	semidirect
125. C₂×D₈×C₆₇	C₂³	semidirect
126. C₂×M₁₆×C₆₇	C₂³	semidirect
127. C₂²×C₈×C₆₇	C₂³	semidirect
128. C₂²×C₈×C₆₇	C₂³	semidirect
135. #125×C₆₇	C₂³	semidirect
137. #124×C₆₇	C₂³	semidirect
147. C₂²⋊Q₈×C₆₇	C₂³	semidirect
148. C₂²⋊Q₈×C₆₇	C₂³	semidirect
163. #121×C₆₇	C₂³	semidirect
164. #121×C₆₇	C₂³	semidirect
171. C₄×Q₈×C₆₇	C₂³	semidirect
183. C₄×D₄×C₆₇	C₂³	semidirect
186. #117×C₆₇	C₂³	semidirect
190. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
191. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
201. #107×C₆₇	C₂³	semidirect
202. #106×C₆₇	C₂³	semidirect
203. C₄⋊C₈×C₆₇	C₂³	semidirect
204. #103×C₆₇	C₂³	semidirect
207. #102×C₆₇	C₂³	semidirect
208. #102×C₆₇	C₂³	semidirect
209. #102×C₆₇	C₂³	semidirect
210. #102×C₆₇	C₂³	semidirect
211. #102×C₆₇	C₂³	semidirect
214. C₂²⋊C₈×C₆₇	C₂³	semidirect
215. C₂²⋊C₈×C₆₇	C₂³	semidirect
216. C₂²⋊C₈×C₆₇	C₂³	semidirect
217. #97×C₆₇	C₂³	semidirect
382. C₂³×C₆₇	AGL(1,ℤ/8)	semidirect
489. #61571	C₆₇	direct (N × H)
501. #3505	C₂×C₆₇	semidirect
502. C₂×D₄²	C₂×C₆₇	semidirect
503. #3318	C₂×C₆₇	semidirect
504. #3310	C₂×C₆₇	semidirect
505. #3265	C₂×C₆₇	semidirect
506. #3264	C₂×C₆₇	semidirect
507. #3217	C₂×C₆₇	semidirect
508. #3194	C₂×C₆₇	semidirect
509. #3187	C₂×C₆₇	semidirect
510. #3186	C₂×C₆₇	semidirect
511. #3114	C₂×C₆₇	semidirect
512. #3003	C₂×C₆₇	semidirect
513. C₂×#450	C₂×C₆₇	semidirect
514. C₂×#447	C₂×C₆₇	semidirect
515. #2973	C₂×C₆₇	semidirect
516. C₆₇	#61571	direct (N × H)
519. C₂³×D₄	C₂²×C₆₇	semidirect
520. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
521. C₂²×SD₁₆	C₂²×C₆₇	semidirect
522. C₂²×D₈	C₂²×C₆₇	semidirect
524. #553	C₂²×C₆₇	semidirect
525. #552	C₂²×C₆₇	semidirect
527. #548	C₂²×C₆₇	semidirect
528. #546	C₂²×C₆₇	semidirect
532. D₄²	C₂²×C₆₇	semidirect
536. C₂×#127	C₂²×C₆₇	semidirect
537. #529	C₂²×C₆₇	semidirect
538. #525	C₂²×C₆₇	semidirect
539. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
542. C₂×#121	C₂²×C₆₇	semidirect
543. C₂×#121	C₂²×C₆₇	semidirect
548. C₂×C₄×D₄	C₂²×C₆₇	semidirect
549. #496	C₂²×C₆₇	semidirect
550. #490	C₂²×C₆₇	semidirect
551. #483	C₂²×C₆₇	semidirect
552. #482	C₂²×C₆₇	semidirect
553. #481	C₂²×C₆₇	semidirect
554. #480	C₂²×C₆₇	semidirect
555. #480	C₂²×C₆₇	semidirect
556. #478	C₂²×C₆₇	semidirect
557. #469	C₂²×C₆₇	semidirect
558. #468	C₂²×C₆₇	semidirect
559. #466	C₂²×C₆₇	semidirect
560. #465	C₂²×C₆₇	semidirect
561. #463	C₂²×C₆₇	semidirect
562. #460	C₂²×C₆₇	semidirect
563. #459	C₂²×C₆₇	semidirect
564. #450	C₂²×C₆₇	semidirect
565. #450	C₂²×C₆₇	semidirect
566. #450	C₂²×C₆₇	semidirect
567. #450	C₂²×C₆₇	semidirect
568. #450	C₂²×C₆₇	semidirect
569. #449	C₂²×C₆₇	semidirect
570. #448	C₂²×C₆₇	semidirect
572. #447	C₂²×C₆₇	semidirect
573. #447	C₂²×C₆₇	semidirect
574. #447	C₂²×C₆₇	semidirect
575. #447	C₂²×C₆₇	semidirect
576. #447	C₂²×C₆₇	semidirect
577. #442	C₂²×C₆₇	semidirect
578. #440	C₂²×C₆₇	semidirect
579. #435	C₂²×C₆₇	semidirect
580. #435	C₂²×C₆₇	semidirect
581. #432	C₂²×C₆₇	semidirect
582. #418	C₂²×C₆₇	semidirect
583. C₂×#102	C₂²×C₆₇	semidirect
584. C₂×#102	C₂²×C₆₇	semidirect
585. #407	C₂²×C₆₇	semidirect
586. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
587. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
590. C₂×#41	C₂³×C₆₇	semidirect
591. C₂²×Q₈	C₂³×C₆₇	semidirect
614. C₂²×D₄	C₂³×C₆₇	semidirect
621. C₂×SD₁₆	C₂³×C₆₇	semidirect
622. C₂×SD₁₆	C₂³×C₆₇	semidirect
625. C₂×D₈	C₂³×C₆₇	semidirect
626. C₂×D₈	C₂³×C₆₇	semidirect
627. C₂×M₁₆	C₂³×C₆₇	semidirect
628. C₂²×C₈	C₂³×C₆₇	semidirect
629. C₂²×C₈	C₂³×C₆₇	semidirect
636. #125	C₂³×C₆₇	semidirect
638. #124	C₂³×C₆₇	semidirect
648. C₂²⋊Q₈	C₂³×C₆₇	semidirect
649. C₂²⋊Q₈	C₂³×C₆₇	semidirect
664. #121	C₂³×C₆₇	semidirect
665. #121	C₂³×C₆₇	semidirect
672. C₄×Q₈	C₂³×C₆₇	semidirect
684. C₄×D₄	C₂³×C₆₇	semidirect
687. #117	C₂³×C₆₇	semidirect
691. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
692. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
702. #107	C₂³×C₆₇	semidirect
703. #106	C₂³×C₆₇	semidirect
704. C₄⋊C₈	C₂³×C₆₇	semidirect
705. #103	C₂³×C₆₇	semidirect
708. #102	C₂³×C₆₇	semidirect
709. #102	C₂³×C₆₇	semidirect
710. #102	C₂³×C₆₇	semidirect
711. #102	C₂³×C₆₇	semidirect
712. #102	C₂³×C₆₇	semidirect
715. C₂²⋊C₈	C₂³×C₆₇	semidirect
716. C₂²⋊C₈	C₂³×C₆₇	semidirect
717. C₂²⋊C₈	C₂³×C₆₇	semidirect
718. #97	C₂³×C₆₇	semidirect
883. C₂³	AGL(1,ℤ/8)×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3505	2
C₂×D₄²×C₆₇	2
C₆₇×#3318	2
C₆₇×#3310	2
C₆₇×#3265	2
C₆₇×#3264	2
C₆₇×#3217	2
C₆₇×#3194	2
C₆₇×#3187	2
C₆₇×#3186	2
C₆₇×#3114	2
C₆₇×#3003	2
C₂×#450×C₆₇	2
C₂×#447×C₆₇	2
C₆₇×#2973	2
#61571	67

Subgroups — C67×#61571 #30740822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61571 #30740822