Subgroups — C₆₇×#60588 #30739839

Order 17152.

2134 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3125	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3119	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3117	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3109	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3105	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3103	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3092	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#481×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3084	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3045	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2952	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2946	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
20	C₂×#135×C₆₇	C₂²	1	2	yes	—
21	#555×C₆₇	—	2	1	no	—
22	#553×C₆₇	—	2	1	no	—
23	#553×C₆₇	—	2	1	no	—
24	#551×C₆₇	—	2	2	no	—
25	#547×C₆₇	—	2	1	no	—
26	#546×C₆₇	—	2	2	no	—
27	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#542×C₆₇	C₂²	1	2	yes	complemented
29	#540×C₆₇	C₂²	1	2	yes	complemented
30	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#532×C₆₇	C₂²	1	2	yes	—
32	#529×C₆₇	C₂²	1	2	yes	—
33	#525×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
35	#520×C₆₇	—	2	1	no	—
36	#520×C₆₇	—	2	1	no	—
37	#520×C₆₇	—	2	2	no	—
38	#520×C₆₇	C₂²	1	2	yes	—
39	#520×C₆₇	C₂²	1	2	yes	—
40	#520×C₆₇	C₂²	1	4	yes	complemented
41	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#518×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
44	C₂×C₄×D₄×C₆₇	—	2	2	no	—
45	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
46	C₂×#117×C₆₇	—	2	1	no	—
47	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
49	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
50	#484×C₆₇	C₂²	1	2	yes	complemented
51	#483×C₆₇	C₂²	1	2	yes	complemented
52	#481×C₆₇	C₂²	1	2	yes	—
53	#481×C₆₇	C₂²	1	2	yes	—
54	#481×C₆₇	C₂²	1	4	yes	complemented
55	#481×C₆₇	C₂²	1	2	yes	complemented
56	#480×C₆₇	C₂²	1	2	yes	complemented
57	#479×C₆₇	C₂²	1	4	yes	complemented
58	#478×C₆₇	C₂²	1	4	yes	complemented
59	#476×C₆₇	C₂²	1	4	yes	complemented
60	#475×C₆₇	C₂²	1	4	yes	complemented
61	#464×C₆₇	C₂²	1	4	yes	complemented
62	#463×C₆₇	C₂²	1	4	yes	complemented
63	#460×C₆₇	C₂²	1	4	yes	complemented
64	#459×C₆₇	C₂²	1	4	yes	complemented
65	#452×C₆₇	C₂²	1	2	yes	complemented
66	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#449×C₆₇	C₂²	1	4	yes	—
69	#449×C₆₇	C₂²	1	2	yes	complemented
70	#448×C₆₇	C₂²	1	2	yes	—
71	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#447×C₆₇	C₂²	1	2	yes	—
73	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#442×C₆₇	C₂²	1	4	yes	complemented
75	#442×C₆₇	C₂²	1	4	yes	complemented
76	#441×C₆₇	C₂²	1	4	yes	complemented
77	#440×C₆₇	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
81	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
82	#433×C₆₇	C₂²	1	4	yes	complemented
83	#432×C₆₇	C₂²	1	2	yes	complemented
84	#431×C₆₇	C₂²	1	2	yes	complemented
85	#428×C₆₇	C₂²	1	2	yes	complemented
86	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
87	#424×C₆₇	C₂²	1	2	yes	complemented
88	#417×C₆₇	C₂²	1	2	yes	—
89	#417×C₆₇	C₂²	1	2	yes	complemented
90	#416×C₆₇	C₂²	1	2	yes	—
91	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
92	#407×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
94	#405×C₆₇	C₂²	1	2	yes	complemented
95	C₂×#41×C₆₇	—	2	8	no	—
96	C₂×#41×C₆₇	—	2	1	no	—
97	C₂×#41×C₆₇	—	2	1	no	—
98	C₂×#41×C₆₇	—	2	2	no	—
99	C₂×#41×C₆₇	C₂³	1	2	yes	—
100	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
101	C₂×#41×C₆₇	C₂³	1	2	yes	—
102	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₆₇	—	2	1	no	—
104	C₂²×D₄×C₆₇	—	2	1	no	—
105	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₆₇	—	2	1	no	—
108	C₂³×C₄×C₆₇	—	2	1	no	—
109	C₂³×C₄×C₆₇	—	2	2	no	—
110	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
111	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
112	#135×C₆₇	—	2	8	no	—
113	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
117	C₂×D₈×C₆₇	C₂³	1	4	yes	—
118	C₂×D₈×C₆₇	C₂³	1	2	yes	—
119	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
120	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₆₇	—	2	1	no	—
122	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
123	#127×C₆₇	C₂³	1	2	yes	—
124	#126×C₆₇	—	2	2	no	—
125	#126×C₆₇	—	2	2	no	—
126	#125×C₆₇	—	2	1	no	—
127	#125×C₆₇	C₂³	1	2	yes	—
128	#124×C₆₇	—	2	2	no	—
129	#124×C₆₇	—	2	2	no	—
130	#124×C₆₇	C₂³	1	2	yes	—
131	#123×C₆₇	—	2	1	no	—
132	#123×C₆₇	—	2	2	no	—
133	#123×C₆₇	—	2	2	no	—
134	#123×C₆₇	—	2	2	no	—
135	#123×C₆₇	—	2	2	no	—
136	C₂²⋊Q₈×C₆₇	—	2	2	no	—
137	C₂²⋊Q₈×C₆₇	—	2	2	no	—
138	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
140	#121×C₆₇	—	2	1	no	—
141	#121×C₆₇	—	2	1	no	—
142	#121×C₆₇	—	2	2	no	—
143	#121×C₆₇	—	2	1	no	—
144	#121×C₆₇	—	2	1	no	—
145	#121×C₆₇	—	2	2	no	—
146	#121×C₆₇	—	2	2	no	—
147	#121×C₆₇	C₂³	1	2	yes	—
148	#121×C₆₇	C₂³	1	1	yes	characteristic
149	#121×C₆₇	C₂³	1	2	yes	—
150	#121×C₆₇	C₂³	1	1	yes	characteristic
151	#120×C₆₇	—	2	1	no	—
152	#120×C₆₇	—	2	2	no	—
153	C₄×Q₈×C₆₇	—	2	2	no	—
154	C₄×Q₈×C₆₇	—	2	2	no	—
155	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
156	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
157	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄×D₄×C₆₇	—	2	1	no	—
159	C₄×D₄×C₆₇	—	2	1	no	—
160	C₄×D₄×C₆₇	—	2	2	no	—
161	C₄×D₄×C₆₇	—	2	1	no	—
162	C₄×D₄×C₆₇	—	2	1	no	—
163	C₄×D₄×C₆₇	—	2	4	no	—
164	C₄×D₄×C₆₇	—	2	4	no	—
165	C₄×D₄×C₆₇	—	2	4	no	—
166	C₄×D₄×C₆₇	—	2	4	no	—
167	C₄×D₄×C₆₇	—	2	2	no	—
168	C₄×D₄×C₆₇	—	2	2	no	—
169	C₄×D₄×C₆₇	—	2	2	no	—
170	C₄×D₄×C₆₇	—	2	2	no	—
171	C₄×D₄×C₆₇	C₂³	1	4	yes	—
172	C₄×D₄×C₆₇	C₂³	1	4	yes	—
173	C₄×D₄×C₆₇	C₂³	1	2	yes	—
174	C₄×D₄×C₆₇	C₂³	1	2	yes	—
175	C₄×D₄×C₆₇	C₂³	1	2	yes	—
176	#117×C₆₇	—	2	2	no	—
177	#117×C₆₇	—	2	2	no	—
178	#117×C₆₇	—	2	4	no	—
179	#117×C₆₇	—	2	1	no	—
180	#117×C₆₇	—	2	2	no	—
181	#117×C₆₇	D₄	1	2	yes	—
182	#117×C₆₇	D₄	1	1	yes	characteristic
183	#117×C₆₇	D₄	1	1	yes	characteristic
184	#117×C₆₇	C₂³	1	1	yes	characteristic
185	#117×C₆₇	C₂³	1	1	yes	characteristic
186	#117×C₆₇	C₂³	1	1	yes	characteristic
187	#117×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
189	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
190	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
191	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
192	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
193	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
194	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
195	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
196	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
203	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
204	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
206	C₂×C₄²×C₆₇	—	2	2	no	—
207	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
208	#107×C₆₇	C₂³	1	4	yes	—
209	#106×C₆₇	C₂³	1	4	yes	—
210	#106×C₆₇	C₂³	1	4	yes	—
211	#106×C₆₇	C₂³	1	4	yes	—
212	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
213	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
214	#103×C₆₇	C₂³	1	4	yes	—
215	#103×C₆₇	C₂³	1	2	yes	—
216	#103×C₆₇	C₂³	1	2	yes	—
217	#103×C₆₇	C₂³	1	4	yes	—
218	#102×C₆₇	C₂³	1	4	yes	—
219	#102×C₆₇	C₂³	1	2	yes	—
220	#102×C₆₇	C₂³	1	2	yes	—
221	#102×C₆₇	C₂³	1	4	yes	—
222	#102×C₆₇	C₂³	1	4	yes	—
223	#102×C₆₇	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
225	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
228	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
229	#97×C₆₇	C₂³	1	4	yes	—
230	C₄×C₈×C₆₇	C₂³	1	4	yes	—
231	C₂⁴×C₆₇	—	2	1	no	—
232	C₂⁴×C₆₇	—	2	1	no	—
233	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
234	#41×C₆₇	—	2	8	no	—
235	#41×C₆₇	—	2	8	no	—
236	#41×C₆₇	—	2	4	no	—
237	#41×C₆₇	—	2	4	no	—
238	#41×C₆₇	—	2	4	no	—
239	#41×C₆₇	—	2	4	no	—
240	#41×C₆₇	—	8	4	no	—
241	#41×C₆₇	#41	1	8	yes	complemented
242	C₂×Q₈×C₆₇	—	2	4	no	—
243	C₂×Q₈×C₆₇	—	2	1	no	—
244	C₂×Q₈×C₆₇	—	2	2	no	—
245	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
247	C₂×D₄×C₆₇	—	2	8	no	—
248	C₂×D₄×C₆₇	—	2	2	no	—
249	C₂×D₄×C₆₇	—	2	2	no	—
250	C₂×D₄×C₆₇	—	2	4	no	—
251	C₂×D₄×C₆₇	—	2	1	no	—
252	C₂×D₄×C₆₇	—	2	1	no	—
253	C₂×D₄×C₆₇	—	2	2	no	—
254	C₂×D₄×C₆₇	—	2	1	no	—
255	C₂×D₄×C₆₇	—	2	2	no	—
256	C₂×D₄×C₆₇	—	2	1	no	—
257	C₂×D₄×C₆₇	—	2	1	no	—
258	C₂×D₄×C₆₇	—	2	2	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂×D₄×C₆₇	—	2	4	no	—
261	C₂×D₄×C₆₇	—	8	2	no	—
262	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₆₇	—	2	8	no	—
266	C₂²×C₄×C₆₇	—	2	1	no	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	2	no	—
269	C₂²×C₄×C₆₇	—	2	4	no	—
270	C₂²×C₄×C₆₇	—	2	2	no	—
271	C₂²×C₄×C₆₇	—	2	1	no	—
272	C₂²×C₄×C₆₇	—	2	2	no	—
273	C₂²×C₄×C₆₇	—	2	2	no	—
274	C₂²×C₄×C₆₇	—	2	1	no	—
275	C₂²×C₄×C₆₇	—	2	2	no	—
276	C₂²×C₄×C₆₇	—	2	2	no	—
277	C₂²×C₄×C₆₇	—	2	4	no	—
278	C₂²×C₄×C₆₇	—	2	4	no	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	8	4	no	—
281	C₂²×C₄×C₆₇	—	8	2	no	—
282	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
290	Q₁₆×C₆₇	—	2	4	no	—
291	SD₁₆×C₆₇	—	2	4	no	—
292	SD₁₆×C₆₇	—	2	8	no	—
293	SD₁₆×C₆₇	—	2	4	no	—
294	D₈×C₆₇	—	2	4	no	—
295	D₈×C₆₇	—	2	8	no	—
296	M₁₆×C₆₇	—	2	4	no	—
297	C₂×C₈×C₆₇	—	2	4	no	—
298	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
299	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
300	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
301	C₄⋊C₄×C₆₇	—	2	2	no	—
302	C₄⋊C₄×C₆₇	—	2	2	no	—
303	C₄⋊C₄×C₆₇	—	2	4	no	—
304	C₄⋊C₄×C₆₇	—	2	4	no	—
305	C₄⋊C₄×C₆₇	—	2	2	no	—
306	C₄⋊C₄×C₆₇	—	2	1	no	—
307	C₄⋊C₄×C₆₇	—	2	2	no	—
308	C₄⋊C₄×C₆₇	—	2	1	no	—
309	C₄⋊C₄×C₆₇	—	2	2	no	—
310	C₄⋊C₄×C₆₇	—	2	2	no	—
311	C₄⋊C₄×C₆₇	—	2	2	no	—
312	C₄⋊C₄×C₆₇	—	2	1	no	—
313	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
314	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
315	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
316	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
317	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
318	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
319	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
320	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₂²⋊C₄×C₆₇	—	2	1	no	—
324	C₂²⋊C₄×C₆₇	—	2	1	no	—
325	C₂²⋊C₄×C₆₇	—	2	1	no	—
326	C₂²⋊C₄×C₆₇	—	2	4	no	—
327	C₂²⋊C₄×C₆₇	—	2	4	no	—
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	1	no	—
335	C₂²⋊C₄×C₆₇	—	2	2	no	—
336	C₂²⋊C₄×C₆₇	—	2	1	no	—
337	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
338	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
339	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
340	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
341	C₄²×C₆₇	—	2	4	no	—
342	C₄²×C₆₇	—	2	4	no	—
343	C₄²×C₆₇	—	2	2	no	—
344	C₄²×C₆₇	—	2	1	no	—
345	C₄²×C₆₇	C₂×D₄	1	2	yes	—
346	C₄²×C₆₇	C₂×D₄	1	2	yes	—
347	C₄²×C₆₇	C₂⁴	1	2	yes	—
348	C₄²×C₆₇	C₂⁴	1	2	yes	—
349	C₂³×C₆₇	—	2	4	no	—
350	C₂³×C₆₇	—	2	2	no	—
351	C₂³×C₆₇	—	2	2	no	—
352	C₂³×C₆₇	—	2	2	no	—
353	C₂³×C₆₇	—	2	2	no	—
354	C₂³×C₆₇	—	2	1	no	—
355	C₂³×C₆₇	—	4	1	no	—
356	C₂³×C₆₇	—	4	2	no	—
357	C₂³×C₆₇	—	4	2	no	—
358	C₂³×C₆₇	—	4	2	no	—
359	C₂³×C₆₇	—	8	1	no	—
360	C₂³×C₆₇	—	8	1	no	—
361	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
362	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
363	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
364	Q₈×C₆₇	—	2	4	no	—
365	Q₈×C₆₇	—	2	2	no	—
366	Q₈×C₆₇	—	2	2	no	—
367	Q₈×C₆₇	—	8	2	no	—
368	Q₈×C₆₇	C₂×#41	1	4	yes	—
369	D₄×C₆₇	—	2	8	no	—
370	D₄×C₆₇	—	2	4	no	—
371	D₄×C₆₇	—	2	8	no	—
372	D₄×C₆₇	—	2	2	no	—
373	D₄×C₆₇	—	2	4	no	—
374	D₄×C₆₇	—	2	2	no	—
375	D₄×C₆₇	—	4	2	no	—
376	D₄×C₆₇	—	4	4	no	—
377	D₄×C₆₇	—	4	2	no	—
378	D₄×C₆₇	—	4	2	no	—
379	D₄×C₆₇	—	8	2	no	—
380	D₄×C₆₇	—	8	2	no	—
381	D₄×C₆₇	—	8	1	no	—
382	D₄×C₆₇	—	8	2	no	—
383	D₄×C₆₇	C₂×#41	1	4	yes	—
384	C₂×C₄×C₆₇	—	2	4	no	—
385	C₂×C₄×C₆₇	—	2	8	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	4	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	8	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	1	no	—
395	C₂×C₄×C₆₇	—	2	4	no	—
396	C₂×C₄×C₆₇	—	2	1	no	—
397	C₂×C₄×C₆₇	—	2	1	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	4	2	no	—
400	C₂×C₄×C₆₇	—	4	4	no	—
401	C₂×C₄×C₆₇	—	4	2	no	—
402	C₂×C₄×C₆₇	—	8	2	no	—
403	C₂×C₄×C₆₇	—	8	4	no	—
404	C₂×C₄×C₆₇	—	8	4	no	—
405	C₂×C₄×C₆₇	—	8	2	no	—
406	C₂×C₄×C₆₇	—	8	2	no	—
407	C₂×C₄×C₆₇	—	8	2	no	—
408	C₂×C₄×C₆₇	—	8	2	no	—
409	C₂×C₄×C₆₇	—	8	1	no	—
410	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
418	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
419	C₈×C₆₇	—	2	2	no	—
420	C₈×C₆₇	—	2	2	no	—
421	C₈×C₆₇	—	2	4	no	—
422	C₂²×C₆₇	—	2	1	no	—
423	C₂²×C₆₇	—	2	1	no	—
424	C₂²×C₆₇	—	2	1	no	—
425	C₂²×C₆₇	—	2	1	no	—
426	C₂²×C₆₇	—	2	1	no	—
427	C₂²×C₆₇	—	2	1	no	—
428	C₂²×C₆₇	—	2	4	no	—
429	C₂²×C₆₇	—	2	1	no	—
430	C₂²×C₆₇	—	4	4	no	—
431	C₂²×C₆₇	—	4	8	no	—
432	C₂²×C₆₇	—	4	2	no	—
433	C₂²×C₆₇	—	4	2	no	—
434	C₂²×C₆₇	—	4	2	no	—
435	C₂²×C₆₇	—	4	1	no	—
436	C₂²×C₆₇	—	4	1	no	—
437	C₂²×C₆₇	—	4	2	no	—
438	C₂²×C₆₇	—	4	1	no	—
439	C₂²×C₆₇	—	4	2	no	—
440	C₂²×C₆₇	—	16	2	no	—
441	C₂²×C₆₇	#525	1	2	yes	—
442	C₂²×C₆₇	#577	1	2	yes	—
443	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
444	C₄×C₆₇	—	2	2	no	—
445	C₄×C₆₇	—	2	2	no	—
446	C₄×C₆₇	—	2	1	no	—
447	C₄×C₆₇	—	2	4	no	—
448	C₄×C₆₇	—	2	1	no	—
449	C₄×C₆₇	—	2	2	no	—
450	C₄×C₆₇	—	2	2	no	—
451	C₄×C₆₇	—	4	4	no	—
452	C₄×C₆₇	—	4	1	no	—
453	C₄×C₆₇	—	4	1	no	—
454	C₄×C₆₇	—	4	2	no	—
455	C₄×C₆₇	—	4	1	no	—
456	C₄×C₆₇	#525	1	2	yes	—
457	C₄×C₆₇	C₂²×#41	1	2	yes	—
458	#60588	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
459	C₂×C₆₇	—	2	2	no	—
460	C₂×C₆₇	—	2	2	no	—
461	C₂×C₆₇	—	4	1	no	—
462	C₂×C₆₇	—	4	4	no	—
463	C₂×C₆₇	—	8	1	no	—
464	C₂×C₆₇	—	8	2	no	—
465	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
466	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
467	C₂×C₆₇	#3585	1	1	yes	characteristic
468	#3494	C₂×C₆₇	1	1	yes	characteristic, complemented
469	C₂×#520	C₂×C₆₇	1	1	yes	characteristic, complemented
470	#3125	C₂×C₆₇	1	4	yes	complemented
471	#3119	C₂×C₆₇	1	4	yes	complemented
472	#3117	C₂×C₆₇	1	2	yes	complemented
473	#3109	C₂×C₆₇	1	2	yes	complemented
474	#3105	C₂×C₆₇	1	2	yes	complemented
475	#3103	C₂×C₆₇	1	2	yes	complemented
476	#3092	C₂×C₆₇	1	1	yes	characteristic, complemented
477	C₂×#481	C₂×C₆₇	1	1	yes	characteristic, complemented
478	#3084	C₂×C₆₇	1	2	yes	complemented
479	#3045	C₂×C₆₇	1	2	yes	complemented
480	#3006	C₂×C₆₇	1	1	yes	characteristic, complemented
481	#3002	C₂×C₆₇	1	1	yes	characteristic, complemented
482	#2952	C₂×C₆₇	1	2	yes	complemented
483	#2946	C₂×C₆₇	1	2	yes	complemented
484	#2924	C₂×C₆₇	1	1	yes	characteristic, complemented
485	C₆₇	#60588	1	1	yes	characteristic, direct product factor, Sylow
486	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
487	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
488	C₂×#135	C₂²×C₆₇	1	2	yes	—
489	#555	—	2	1	no	—
490	#553	—	2	1	no	—
491	#553	—	2	1	no	—
492	#551	—	2	2	no	—
493	#547	—	2	1	no	—
494	#546	—	2	2	no	—
495	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
496	#542	C₂²×C₆₇	1	2	yes	complemented
497	#540	C₂²×C₆₇	1	2	yes	complemented
498	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
499	#532	C₂²×C₆₇	1	2	yes	—
500	#529	C₂²×C₆₇	1	2	yes	—
501	#525	C₂²×C₆₇	1	1	yes	characteristic
502	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
503	#520	—	2	1	no	—
504	#520	—	2	1	no	—
505	#520	—	2	2	no	—
506	#520	C₂²×C₆₇	1	2	yes	—
507	#520	C₂²×C₆₇	1	2	yes	—
508	#520	C₂²×C₆₇	1	4	yes	complemented
509	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
510	#518	C₂²×C₆₇	1	1	yes	characteristic, complemented
511	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
512	C₂×C₄×D₄	—	2	2	no	—
513	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
514	C₂×#117	—	2	1	no	—
515	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
516	C₂²×C₄⋊C₄	—	2	1	no	—
517	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
518	#484	C₂²×C₆₇	1	2	yes	complemented
519	#483	C₂²×C₆₇	1	2	yes	complemented
520	#481	C₂²×C₆₇	1	2	yes	—
521	#481	C₂²×C₆₇	1	2	yes	—
522	#481	C₂²×C₆₇	1	4	yes	complemented
523	#481	C₂²×C₆₇	1	2	yes	complemented
524	#480	C₂²×C₆₇	1	2	yes	complemented
525	#479	C₂²×C₆₇	1	4	yes	complemented
526	#478	C₂²×C₆₇	1	4	yes	complemented
527	#476	C₂²×C₆₇	1	4	yes	complemented
528	#475	C₂²×C₆₇	1	4	yes	complemented
529	#464	C₂²×C₆₇	1	4	yes	complemented
530	#463	C₂²×C₆₇	1	4	yes	complemented
531	#460	C₂²×C₆₇	1	4	yes	complemented
532	#459	C₂²×C₆₇	1	4	yes	complemented
533	#452	C₂²×C₆₇	1	2	yes	complemented
534	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
535	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
536	#449	C₂²×C₆₇	1	4	yes	—
537	#449	C₂²×C₆₇	1	2	yes	complemented
538	#448	C₂²×C₆₇	1	2	yes	—
539	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
540	#447	C₂²×C₆₇	1	2	yes	—
541	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
542	#442	C₂²×C₆₇	1	4	yes	complemented
543	#442	C₂²×C₆₇	1	4	yes	complemented
544	#441	C₂²×C₆₇	1	4	yes	complemented
545	#440	C₂²×C₆₇	1	4	yes	complemented
546	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
547	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
548	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
549	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
550	#433	C₂²×C₆₇	1	4	yes	complemented
551	#432	C₂²×C₆₇	1	2	yes	complemented
552	#431	C₂²×C₆₇	1	2	yes	complemented
553	#428	C₂²×C₆₇	1	2	yes	complemented
554	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
555	#424	C₂²×C₆₇	1	2	yes	complemented
556	#417	C₂²×C₆₇	1	2	yes	—
557	#417	C₂²×C₆₇	1	2	yes	complemented
558	#416	C₂²×C₆₇	1	2	yes	—
559	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
560	#407	C₂²×C₆₇	1	1	yes	characteristic
561	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
562	#405	C₂²×C₆₇	1	2	yes	complemented
563	C₂×#41	—	2	8	no	—
564	C₂×#41	—	2	1	no	—
565	C₂×#41	—	2	1	no	—
566	C₂×#41	—	2	2	no	—
567	C₂×#41	C₂³×C₆₇	1	2	yes	—
568	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
569	C₂×#41	C₂³×C₆₇	1	2	yes	—
570	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
571	C₂²×D₄	—	2	1	no	—
572	C₂²×D₄	—	2	1	no	—
573	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
574	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
575	C₂³×C₄	—	2	1	no	—
576	C₂³×C₄	—	2	1	no	—
577	C₂³×C₄	—	2	2	no	—
578	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
579	AGL(1,ℤ/8)	—	2	8	no	—
580	#135	—	2	8	no	—
581	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
582	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
583	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
584	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
585	C₂×D₈	C₂³×C₆₇	1	2	yes	—
586	C₂×D₈	C₂³×C₆₇	1	4	yes	—
587	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
588	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
589	C₄⋊Q₈	—	2	1	no	—
590	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
591	#127	C₂³×C₆₇	1	2	yes	—
592	#126	—	2	2	no	—
593	#126	—	2	2	no	—
594	#125	—	2	1	no	—
595	#125	C₂³×C₆₇	1	2	yes	—
596	#124	—	2	2	no	—
597	#124	—	2	2	no	—
598	#124	C₂³×C₆₇	1	2	yes	—
599	#123	—	2	1	no	—
600	#123	—	2	2	no	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	#123	—	2	2	no	—
604	C₂²⋊Q₈	—	2	2	no	—
605	C₂²⋊Q₈	—	2	2	no	—
606	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
607	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
608	#121	—	2	1	no	—
609	#121	—	2	1	no	—
610	#121	—	2	2	no	—
611	#121	—	2	1	no	—
612	#121	—	2	1	no	—
613	#121	—	2	2	no	—
614	#121	—	2	2	no	—
615	#121	C₂³×C₆₇	1	2	yes	—
616	#121	C₂³×C₆₇	1	2	yes	—
617	#121	C₂³×C₆₇	1	1	yes	characteristic
618	#121	C₂³×C₆₇	1	1	yes	characteristic
619	#120	—	2	1	no	—
620	#120	—	2	2	no	—
621	C₄×Q₈	—	2	2	no	—
622	C₄×Q₈	—	2	2	no	—
623	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
624	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
625	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	4	no	—
632	C₄×D₄	—	2	4	no	—
633	C₄×D₄	—	2	4	no	—
634	C₄×D₄	—	2	4	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	C₂³×C₆₇	1	4	yes	—
640	C₄×D₄	C₂³×C₆₇	1	4	yes	—
641	C₄×D₄	C₂³×C₆₇	1	2	yes	—
642	C₄×D₄	C₂³×C₆₇	1	2	yes	—
643	C₄×D₄	C₂³×C₆₇	1	2	yes	—
644	#117	—	2	2	no	—
645	#117	—	2	2	no	—
646	#117	—	2	4	no	—
647	#117	—	2	1	no	—
648	#117	—	2	2	no	—
649	#117	D₄×C₆₇	1	2	yes	—
650	#117	D₄×C₆₇	1	1	yes	characteristic
651	#117	D₄×C₆₇	1	1	yes	characteristic
652	#117	C₂³×C₆₇	1	1	yes	characteristic
653	#117	C₂³×C₆₇	1	1	yes	characteristic
654	#117	C₂³×C₆₇	1	1	yes	characteristic
655	#117	C₂³×C₆₇	1	2	yes	—
656	C₂×C₄⋊C₄	—	2	1	no	—
657	C₂×C₄⋊C₄	—	2	2	no	—
658	C₂×C₄⋊C₄	—	2	1	no	—
659	C₂×C₄⋊C₄	—	2	1	no	—
660	C₂×C₄⋊C₄	—	2	2	no	—
661	C₂×C₄⋊C₄	—	2	2	no	—
662	C₂×C₄⋊C₄	—	2	4	no	—
663	C₂×C₄⋊C₄	—	2	1	no	—
664	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
665	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	—	2	2	no	—
671	C₂×C₂²⋊C₄	—	2	1	no	—
672	C₂×C₂²⋊C₄	—	2	2	no	—
673	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
674	C₂×C₄²	—	2	2	no	—
675	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
676	#107	C₂³×C₆₇	1	4	yes	—
677	#106	C₂³×C₆₇	1	4	yes	—
678	#106	C₂³×C₆₇	1	4	yes	—
679	#106	C₂³×C₆₇	1	4	yes	—
680	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
681	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
682	#103	C₂³×C₆₇	1	2	yes	—
683	#103	C₂³×C₆₇	1	2	yes	—
684	#103	C₂³×C₆₇	1	4	yes	—
685	#103	C₂³×C₆₇	1	4	yes	—
686	#102	C₂³×C₆₇	1	4	yes	—
687	#102	C₂³×C₆₇	1	4	yes	—
688	#102	C₂³×C₆₇	1	2	yes	—
689	#102	C₂³×C₆₇	1	2	yes	—
690	#102	C₂³×C₆₇	1	4	yes	—
691	#102	C₂³×C₆₇	1	4	yes	—
692	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
693	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
694	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
695	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
696	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
697	#97	C₂³×C₆₇	1	4	yes	—
698	C₄×C₈	C₂³×C₆₇	1	4	yes	—
699	C₂⁴	—	2	1	no	—
700	C₂⁴	—	2	1	no	—
701	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
702	#41	—	2	8	no	—
703	#41	—	2	8	no	—
704	#41	—	2	4	no	—
705	#41	—	2	4	no	—
706	#41	—	2	4	no	—
707	#41	—	2	4	no	—
708	#41	—	8	4	no	—
709	#41	#41×C₆₇	1	8	yes	complemented
710	C₂×Q₈	—	2	4	no	—
711	C₂×Q₈	—	2	1	no	—
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
714	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
715	C₂×D₄	—	2	8	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	1	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	8	2	no	—
730	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
731	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
732	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
733	C₂²×C₄	—	2	8	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	8	4	no	—
749	C₂²×C₄	—	8	2	no	—
750	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
751	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
752	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
753	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
754	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
758	Q₁₆	—	2	4	no	—
759	SD₁₆	—	2	4	no	—
760	SD₁₆	—	2	8	no	—
761	SD₁₆	—	2	4	no	—
762	D₈	—	2	4	no	—
763	D₈	—	2	8	no	—
764	M₁₆	—	2	4	no	—
765	C₂×C₈	—	2	4	no	—
766	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
767	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
768	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
782	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
783	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
784	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
785	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
786	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
787	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
788	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
789	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
790	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	1	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	1	no	—
805	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
806	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
807	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
808	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
809	C₄²	—	2	4	no	—
810	C₄²	—	2	4	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	1	no	—
813	C₄²	C₂×D₄×C₆₇	1	2	yes	—
814	C₄²	C₂×D₄×C₆₇	1	2	yes	—
815	C₄²	C₂⁴×C₆₇	1	2	yes	—
816	C₄²	C₂⁴×C₆₇	1	2	yes	—
817	C₂³	—	2	4	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	4	1	no	—
824	C₂³	—	4	2	no	—
825	C₂³	—	4	2	no	—
826	C₂³	—	4	2	no	—
827	C₂³	—	8	1	no	—
828	C₂³	—	8	1	no	—
829	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
830	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
831	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
832	Q₈	—	2	4	no	—
833	Q₈	—	2	2	no	—
834	Q₈	—	2	2	no	—
835	Q₈	—	8	2	no	—
836	Q₈	C₂×#41×C₆₇	1	4	yes	—
837	D₄	—	2	8	no	—
838	D₄	—	2	4	no	—
839	D₄	—	2	8	no	—
840	D₄	—	2	2	no	—
841	D₄	—	2	4	no	—
842	D₄	—	2	2	no	—
843	D₄	—	4	2	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	2	no	—
846	D₄	—	4	2	no	—
847	D₄	—	8	2	no	—
848	D₄	—	8	2	no	—
849	D₄	—	8	2	no	—
850	D₄	—	8	1	no	—
851	D₄	C₂×#41×C₆₇	1	4	yes	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	8	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	8	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	4	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	4	2	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	8	4	no	—
871	C₂×C₄	—	8	4	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	—	8	2	no	—
874	C₂×C₄	—	8	2	no	—
875	C₂×C₄	—	8	2	no	—
876	C₂×C₄	—	8	2	no	—
877	C₂×C₄	—	8	1	no	—
878	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
879	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
880	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
881	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
882	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
883	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
884	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
885	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
886	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
887	C₈	—	2	2	no	—
888	C₈	—	2	2	no	—
889	C₈	—	2	4	no	—
890	C₂²	—	2	1	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	2	1	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	4	4	no	—
899	C₂²	—	4	8	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	16	2	no	—
909	C₂²	#525×C₆₇	1	2	yes	—
910	C₂²	#577×C₆₇	1	2	yes	—
911	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	4	no	—
918	C₄	—	2	1	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	4	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	1	no	—
924	C₄	#525×C₆₇	1	2	yes	—
925	C₄	C₂²×#41×C₆₇	1	2	yes	—
926	C₂	—	2	2	no	—
927	C₂	—	2	2	no	—
928	C₂	—	4	1	no	—
929	C₂	—	4	4	no	—
930	C₂	—	8	2	no	—
931	C₂	—	8	1	no	—
932	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
933	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
934	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×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3494	C₂	semidirect
2. C₂×#520×C₆₇	C₂	semidirect
3. C₆₇×#3125	C₂	semidirect
4. C₆₇×#3119	C₂	semidirect
5. C₆₇×#3117	C₂	semidirect
6. C₆₇×#3109	C₂	semidirect
7. C₆₇×#3105	C₂	semidirect
8. C₆₇×#3103	C₂	semidirect
9. C₆₇×#3092	C₂	semidirect
10. C₂×#481×C₆₇	C₂	semidirect
11. C₆₇×#3084	C₂	semidirect
12. C₆₇×#3045	C₂	semidirect
13. C₆₇×#3006	C₂	semidirect
14. C₆₇×#3002	C₂	semidirect
15. C₆₇×#2952	C₂	semidirect
16. C₆₇×#2946	C₂	semidirect
17. C₆₇×#2924	C₂	semidirect
27. #544×C₆₇	C₂²	semidirect
28. #542×C₆₇	C₂²	semidirect
29. #540×C₆₇	C₂²	semidirect
30. #535×C₆₇	C₂²	semidirect
40. #520×C₆₇	C₂²	semidirect
41. #520×C₆₇	C₂²	semidirect
42. #518×C₆₇	C₂²	semidirect
43. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
45. C₂×C₄×D₄×C₆₇	C₂²	semidirect
50. #484×C₆₇	C₂²	semidirect
51. #483×C₆₇	C₂²	semidirect
54. #481×C₆₇	C₂²	semidirect
55. #481×C₆₇	C₂²	semidirect
56. #480×C₆₇	C₂²	semidirect
57. #479×C₆₇	C₂²	semidirect
58. #478×C₆₇	C₂²	semidirect
59. #476×C₆₇	C₂²	semidirect
60. #475×C₆₇	C₂²	semidirect
61. #464×C₆₇	C₂²	semidirect
62. #463×C₆₇	C₂²	semidirect
63. #460×C₆₇	C₂²	semidirect
64. #459×C₆₇	C₂²	semidirect
65. #452×C₆₇	C₂²	semidirect
66. #451×C₆₇	C₂²	semidirect
67. #450×C₆₇	C₂²	semidirect
69. #449×C₆₇	C₂²	semidirect
71. #448×C₆₇	C₂²	semidirect
73. #447×C₆₇	C₂²	semidirect
74. #442×C₆₇	C₂²	semidirect
75. #442×C₆₇	C₂²	semidirect
76. #441×C₆₇	C₂²	semidirect
77. #440×C₆₇	C₂²	semidirect
78. C₄×SD₁₆×C₆₇	C₂²	semidirect
79. C₄×SD₁₆×C₆₇	C₂²	semidirect
80. C₄×SD₁₆×C₆₇	C₂²	semidirect
81. C₄×D₈×C₆₇	C₂²	semidirect
82. #433×C₆₇	C₂²	semidirect
83. #432×C₆₇	C₂²	semidirect
84. #431×C₆₇	C₂²	semidirect
85. #428×C₆₇	C₂²	semidirect
86. C₂×#106×C₆₇	C₂²	semidirect
87. #424×C₆₇	C₂²	semidirect
89. #417×C₆₇	C₂²	semidirect
91. C₂×#102×C₆₇	C₂²	semidirect
94. #405×C₆₇	C₂²	semidirect
241. #41×C₆₇	#41	semidirect
458. #60588	C₆₇	direct (N × H)
468. #3494	C₂×C₆₇	semidirect
469. C₂×#520	C₂×C₆₇	semidirect
470. #3125	C₂×C₆₇	semidirect
471. #3119	C₂×C₆₇	semidirect
472. #3117	C₂×C₆₇	semidirect
473. #3109	C₂×C₆₇	semidirect
474. #3105	C₂×C₆₇	semidirect
475. #3103	C₂×C₆₇	semidirect
476. #3092	C₂×C₆₇	semidirect
477. C₂×#481	C₂×C₆₇	semidirect
478. #3084	C₂×C₆₇	semidirect
479. #3045	C₂×C₆₇	semidirect
480. #3006	C₂×C₆₇	semidirect
481. #3002	C₂×C₆₇	semidirect
482. #2952	C₂×C₆₇	semidirect
483. #2946	C₂×C₆₇	semidirect
484. #2924	C₂×C₆₇	semidirect
485. C₆₇	#60588	direct (N × H)
495. #544	C₂²×C₆₇	semidirect
496. #542	C₂²×C₆₇	semidirect
497. #540	C₂²×C₆₇	semidirect
498. #535	C₂²×C₆₇	semidirect
508. #520	C₂²×C₆₇	semidirect
509. #520	C₂²×C₆₇	semidirect
510. #518	C₂²×C₆₇	semidirect
511. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
513. C₂×C₄×D₄	C₂²×C₆₇	semidirect
518. #484	C₂²×C₆₇	semidirect
519. #483	C₂²×C₆₇	semidirect
522. #481	C₂²×C₆₇	semidirect
523. #481	C₂²×C₆₇	semidirect
524. #480	C₂²×C₆₇	semidirect
525. #479	C₂²×C₆₇	semidirect
526. #478	C₂²×C₆₇	semidirect
527. #476	C₂²×C₆₇	semidirect
528. #475	C₂²×C₆₇	semidirect
529. #464	C₂²×C₆₇	semidirect
530. #463	C₂²×C₆₇	semidirect
531. #460	C₂²×C₆₇	semidirect
532. #459	C₂²×C₆₇	semidirect
533. #452	C₂²×C₆₇	semidirect
534. #451	C₂²×C₆₇	semidirect
535. #450	C₂²×C₆₇	semidirect
537. #449	C₂²×C₆₇	semidirect
539. #448	C₂²×C₆₇	semidirect
541. #447	C₂²×C₆₇	semidirect
542. #442	C₂²×C₆₇	semidirect
543. #442	C₂²×C₆₇	semidirect
544. #441	C₂²×C₆₇	semidirect
545. #440	C₂²×C₆₇	semidirect
546. C₄×SD₁₆	C₂²×C₆₇	semidirect
547. C₄×SD₁₆	C₂²×C₆₇	semidirect
548. C₄×SD₁₆	C₂²×C₆₇	semidirect
549. C₄×D₈	C₂²×C₆₇	semidirect
550. #433	C₂²×C₆₇	semidirect
551. #432	C₂²×C₆₇	semidirect
552. #431	C₂²×C₆₇	semidirect
553. #428	C₂²×C₆₇	semidirect
554. C₂×#106	C₂²×C₆₇	semidirect
555. #424	C₂²×C₆₇	semidirect
557. #417	C₂²×C₆₇	semidirect
559. C₂×#102	C₂²×C₆₇	semidirect
562. #405	C₂²×C₆₇	semidirect
709. #41	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3494	2
C₂×#520×C₆₇	2
C₆₇×#3125	2
C₆₇×#3119	2
C₆₇×#3117	2
C₆₇×#3109	2
C₆₇×#3105	2
C₆₇×#3103	2
C₆₇×#3092	2
C₂×#481×C₆₇	2
C₆₇×#3084	2
C₆₇×#3045	2
C₆₇×#3006	2
C₆₇×#3002	2
C₆₇×#2952	2
C₆₇×#2946	2
C₆₇×#2924	2
#60588	67

Subgroups — C67×#60588 #30739839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60588 #30739839