Subgroups — C₂×C₆₇×#3264 #30740273

Order 17152.

3366 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
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
1. C₂²×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
2. C₂³×D₈×C₆₇	C₂	semidirect
3. C₂×#546×C₆₇	C₂	semidirect
4. C₂×D₄²×C₆₇	C₂	semidirect
5. C₆₇×#3264	C₂	direct (N × H)
6. C₂×#496×C₆₇	C₂	semidirect
7. C₂×#469×C₆₇	C₂	semidirect
8. C₂×#465×C₆₇	C₂	semidirect
9. C₂×#463×C₆₇	C₂	semidirect
10. C₂×#459×C₆₇	C₂	semidirect
11. C₂×#449×C₆₇	C₂	semidirect
12. C₂×#450×C₆₇	C₂	semidirect
13. C₂×#447×C₆₇	C₂	semidirect
14. C₂×#447×C₆₇	C₂	semidirect
15. C₂×#442×C₆₇	C₂	semidirect
16. C₂×#435×C₆₇	C₂	semidirect
17. C₂²×#41×C₆₇	C₂²	semidirect
20. C₂³×D₄×C₆₇	C₂²	semidirect
21. C₂³×D₄×C₆₇	C₂²	semidirect
23. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
24. C₂²×SD₁₆×C₆₇	C₂²	semidirect
25. C₂²×SD₁₆×C₆₇	C₂²	semidirect
26. C₂²×SD₁₆×C₆₇	C₂²	semidirect
30. C₂²×D₈×C₆₇	C₂²	semidirect
31. C₂²×D₈×C₆₇	C₂²	semidirect
32. C₂²×D₈×C₆₇	C₂²	semidirect
33. C₂²×D₈×C₆₇	C₂²	semidirect
34. C₂²×D₈×C₆₇	C₂²	semidirect
35. C₂²×M₁₆×C₆₇	C₂²	semidirect
36. C₂³×C₈×C₆₇	C₂²	semidirect
38. #546×C₆₇	C₂²	semidirect
40. D₄²×C₆₇	C₂²	semidirect
41. C₂×#127×C₆₇	C₂²	semidirect
42. C₂×#124×C₆₇	C₂²	semidirect
44. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
48. C₂×#121×C₆₇	C₂²	semidirect
49. C₂×#121×C₆₇	C₂²	semidirect
54. C₂×C₄×D₄×C₆₇	C₂²	semidirect
55. C₂×C₄×D₄×C₆₇	C₂²	semidirect
57. #496×C₆₇	C₂²	semidirect
58. #469×C₆₇	C₂²	semidirect
59. #465×C₆₇	C₂²	semidirect
60. #463×C₆₇	C₂²	semidirect
61. #459×C₆₇	C₂²	semidirect
62. #450×C₆₇	C₂²	semidirect
63. #449×C₆₇	C₂²	semidirect
64. #447×C₆₇	C₂²	semidirect
65. #447×C₆₇	C₂²	semidirect
66. #442×C₆₇	C₂²	semidirect
67. #435×C₆₇	C₂²	semidirect
68. C₂×#106×C₆₇	C₂²	semidirect
69. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
70. C₂×#103×C₆₇	C₂²	semidirect
71. C₂×#102×C₆₇	C₂²	semidirect
72. C₂×#102×C₆₇	C₂²	semidirect
73. C₂×#102×C₆₇	C₂²	semidirect
74. C₂×#102×C₆₇	C₂²	semidirect
75. C₂×#102×C₆₇	C₂²	semidirect
76. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
77. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
78. C₂×#97×C₆₇	C₂²	semidirect
85. C₂×#41×C₆₇	C₂³	semidirect
114. C₂²×D₄×C₆₇	C₂³	semidirect
115. C₂²×D₄×C₆₇	C₂³	semidirect
125. C₂×SD₁₆×C₆₇	C₂³	semidirect
126. C₂×SD₁₆×C₆₇	C₂³	semidirect
127. C₂×SD₁₆×C₆₇	C₂³	semidirect
134. C₂×D₈×C₆₇	D₄	semidirect
137. C₂×D₈×C₆₇	C₂³	semidirect
138. C₂×D₈×C₆₇	C₂³	semidirect
139. C₂×D₈×C₆₇	C₂³	semidirect
140. C₂×D₈×C₆₇	C₂³	semidirect
142. C₂×M₁₆×C₆₇	C₂³	semidirect
148. C₂²×C₈×C₆₇	C₂³	semidirect
150. #127×C₆₇	C₂³	semidirect
152. #124×C₆₇	C₂³	semidirect
155. C₂²⋊Q₈×C₆₇	C₂³	semidirect
162. #121×C₆₇	C₂³	semidirect
163. #121×C₆₇	C₂³	semidirect
171. C₄×D₄×C₆₇	C₂³	semidirect
172. C₄×D₄×C₆₇	C₂³	semidirect
189. #106×C₆₇	C₂³	semidirect
190. C₄⋊C₈×C₆₇	C₂³	semidirect
191. #103×C₆₇	C₂³	semidirect
192. #102×C₆₇	C₂³	semidirect
193. #102×C₆₇	C₂³	semidirect
194. #102×C₆₇	C₂³	semidirect
195. #102×C₆₇	C₂³	semidirect
196. #102×C₆₇	C₂³	semidirect
197. C₂²⋊C₈×C₆₇	C₂³	semidirect
198. C₂²⋊C₈×C₆₇	C₂³	semidirect
199. #97×C₆₇	C₂³	semidirect
270. C₂×D₄×C₆₇	C₂×D₄	semidirect
306. D₈×C₆₇	C₂×D₄	semidirect
312. C₂×C₈×C₆₇	C₂×D₄	semidirect
372. C₂³×C₆₇	AGL(1,ℤ/8)	semidirect
403. D₄×C₆₇	C₂²×D₄	semidirect
434. C₈×C₆₇	C₂²×D₄	semidirect
467. C₂²×C₆₇	C₂×AGL(1,ℤ/8)	semidirect
480. C₂×#3264	C₆₇	direct (N × H)
488. C₂×C₆₇	#3264	direct (N × H)
492. C₂²×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
493. C₂³×D₈	C₂×C₆₇	semidirect
494. C₂×#546	C₂×C₆₇	semidirect
495. C₂×D₄²	C₂×C₆₇	semidirect
496. #3264	C₂×C₆₇	direct (N × H)
497. C₂×#496	C₂×C₆₇	semidirect
498. C₂×#469	C₂×C₆₇	semidirect
499. C₂×#465	C₂×C₆₇	semidirect
500. C₂×#463	C₂×C₆₇	semidirect
501. C₂×#459	C₂×C₆₇	semidirect
502. C₂×#449	C₂×C₆₇	semidirect
503. C₂×#450	C₂×C₆₇	semidirect
504. C₂×#447	C₂×C₆₇	semidirect
505. C₂×#447	C₂×C₆₇	semidirect
506. C₂×#442	C₂×C₆₇	semidirect
507. C₂×#435	C₂×C₆₇	semidirect
508. C₆₇	C₂×#3264	direct (N × H)
509. C₂²×#41	C₂²×C₆₇	semidirect
512. C₂³×D₄	C₂²×C₆₇	semidirect
513. C₂³×D₄	C₂²×C₆₇	semidirect
515. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
516. C₂²×SD₁₆	C₂²×C₆₇	semidirect
517. C₂²×SD₁₆	C₂²×C₆₇	semidirect
518. C₂²×SD₁₆	C₂²×C₆₇	semidirect
522. C₂²×D₈	C₂²×C₆₇	semidirect
523. C₂²×D₈	C₂²×C₆₇	semidirect
524. C₂²×D₈	C₂²×C₆₇	semidirect
525. C₂²×D₈	C₂²×C₆₇	semidirect
526. C₂²×D₈	C₂²×C₆₇	semidirect
527. C₂²×M₁₆	C₂²×C₆₇	semidirect
528. C₂³×C₈	C₂²×C₆₇	semidirect
530. #546	C₂²×C₆₇	semidirect
532. D₄²	C₂²×C₆₇	semidirect
533. C₂×#127	C₂²×C₆₇	semidirect
534. C₂×#124	C₂²×C₆₇	semidirect
536. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
540. C₂×#121	C₂²×C₆₇	semidirect
541. C₂×#121	C₂²×C₆₇	semidirect
546. C₂×C₄×D₄	C₂²×C₆₇	semidirect
547. C₂×C₄×D₄	C₂²×C₆₇	semidirect
549. #496	C₂²×C₆₇	semidirect
550. #469	C₂²×C₆₇	semidirect
551. #465	C₂²×C₆₇	semidirect
552. #463	C₂²×C₆₇	semidirect
553. #459	C₂²×C₆₇	semidirect
554. #450	C₂²×C₆₇	semidirect
555. #449	C₂²×C₆₇	semidirect
556. #447	C₂²×C₆₇	semidirect
557. #447	C₂²×C₆₇	semidirect
558. #442	C₂²×C₆₇	semidirect
559. #435	C₂²×C₆₇	semidirect
560. C₂×#106	C₂²×C₆₇	semidirect
561. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
562. C₂×#103	C₂²×C₆₇	semidirect
563. C₂×#102	C₂²×C₆₇	semidirect
564. C₂×#102	C₂²×C₆₇	semidirect
565. C₂×#102	C₂²×C₆₇	semidirect
566. C₂×#102	C₂²×C₆₇	semidirect
567. C₂×#102	C₂²×C₆₇	semidirect
568. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
569. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
570. C₂×#97	C₂²×C₆₇	semidirect
577. C₂×#41	C₂³×C₆₇	semidirect
606. C₂²×D₄	C₂³×C₆₇	semidirect
607. C₂²×D₄	C₂³×C₆₇	semidirect
617. C₂×SD₁₆	C₂³×C₆₇	semidirect
618. C₂×SD₁₆	C₂³×C₆₇	semidirect
619. C₂×SD₁₆	C₂³×C₆₇	semidirect
626. C₂×D₈	D₄×C₆₇	semidirect
629. C₂×D₈	C₂³×C₆₇	semidirect
630. C₂×D₈	C₂³×C₆₇	semidirect
631. C₂×D₈	C₂³×C₆₇	semidirect
632. C₂×D₈	C₂³×C₆₇	semidirect
634. C₂×M₁₆	C₂³×C₆₇	semidirect
640. C₂²×C₈	C₂³×C₆₇	semidirect
642. #127	C₂³×C₆₇	semidirect
644. #124	C₂³×C₆₇	semidirect
647. C₂²⋊Q₈	C₂³×C₆₇	semidirect
654. #121	C₂³×C₆₇	semidirect
655. #121	C₂³×C₆₇	semidirect
663. C₄×D₄	C₂³×C₆₇	semidirect
664. C₄×D₄	C₂³×C₆₇	semidirect
681. #106	C₂³×C₆₇	semidirect
682. C₄⋊C₈	C₂³×C₆₇	semidirect
683. #103	C₂³×C₆₇	semidirect
684. #102	C₂³×C₆₇	semidirect
685. #102	C₂³×C₆₇	semidirect
686. #102	C₂³×C₆₇	semidirect
687. #102	C₂³×C₆₇	semidirect
688. #102	C₂³×C₆₇	semidirect
689. C₂²⋊C₈	C₂³×C₆₇	semidirect
690. C₂²⋊C₈	C₂³×C₆₇	semidirect
691. #97	C₂³×C₆₇	semidirect
762. C₂×D₄	C₂×D₄×C₆₇	semidirect
798. D₈	C₂×D₄×C₆₇	semidirect
804. C₂×C₈	C₂×D₄×C₆₇	semidirect
864. C₂³	AGL(1,ℤ/8)×C₆₇	semidirect
895. D₄	C₂²×D₄×C₆₇	semidirect
926. C₈	C₂²×D₄×C₆₇	semidirect
959. C₂²	C₂×AGL(1,ℤ/8)×C₆₇	semidirect
979. C₂	C₆₇×#3264	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₆₇	2
C₂³×D₈×C₆₇	2
C₂×#546×C₆₇	2
C₂×D₄²×C₆₇	2
C₆₇×#3264	2
C₂×#496×C₆₇	2
C₂×#469×C₆₇	2
C₂×#465×C₆₇	2
C₂×#463×C₆₇	2
C₂×#459×C₆₇	2
C₂×#449×C₆₇	2
C₂×#450×C₆₇	2
C₂×#447×C₆₇	2
C₂×#442×C₆₇	2
C₂×#435×C₆₇	2
C₂×#3264	67

Subgroups — C2×C67×#3264 #30740273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3264 #30740273