Subgroups — C₆₇×#61583 #30740834

Order 17152.

2118 conjugacy classes of subgroups.

The subgroup lattice has 924 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×#548×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3327	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3326	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3277	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3275	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3211	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3195	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3194	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3193	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3108	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3004	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
18	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
19	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
20	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
21	#553×C₆₇	—	2	2	no	—
22	#553×C₆₇	C₂²	1	2	yes	complemented
23	#552×C₆₇	C₂²	1	2	yes	complemented
24	#551×C₆₇	—	2	2	no	—
25	#548×C₆₇	—	2	2	no	—
26	#548×C₆₇	—	2	2	no	—
27	#548×C₆₇	C₂²	1	4	yes	—
28	#548×C₆₇	C₂²	1	2	yes	complemented
29	#548×C₆₇	C₂²	1	4	yes	complemented
30	#546×C₆₇	C₂²	1	2	yes	complemented
31	#539×C₆₇	—	2	1	no	—
32	#538×C₆₇	—	2	1	no	—
33	#534×C₆₇	—	2	1	no	—
34	#529×C₆₇	C₂²	1	2	yes	—
35	C₂×#124×C₆₇	—	2	1	no	—
36	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	#525×C₆₇	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
39	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#121×C₆₇	—	2	1	no	—
42	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	#518×C₆₇	—	2	1	no	—
45	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₆₇	—	2	1	no	—
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
48	#495×C₆₇	C₂²	1	4	yes	complemented
49	#488×C₆₇	C₂²	1	4	yes	complemented
50	#484×C₆₇	C₂²	1	2	yes	complemented
51	#483×C₆₇	C₂²	1	2	yes	complemented
52	#483×C₆₇	C₂²	1	2	yes	complemented
53	#482×C₆₇	C₂²	1	4	yes	complemented
54	#480×C₆₇	C₂²	1	2	yes	—
55	#479×C₆₇	C₂²	1	4	yes	complemented
56	#470×C₆₇	C₂²	1	4	yes	complemented
57	#469×C₆₇	C₂²	1	4	yes	complemented
58	#468×C₆₇	C₂²	1	4	yes	complemented
59	#468×C₆₇	C₂²	1	4	yes	complemented
60	#464×C₆₇	C₂²	1	4	yes	complemented
61	#464×C₆₇	C₂²	1	4	yes	complemented
62	#463×C₆₇	C₂²	1	4	yes	complemented
63	#452×C₆₇	C₂²	1	4	yes	complemented
64	#451×C₆₇	C₂²	1	2	yes	complemented
65	#451×C₆₇	C₂²	1	4	yes	complemented
66	#451×C₆₇	C₂²	1	2	yes	complemented
67	#451×C₆₇	C₂²	1	2	yes	complemented
68	#450×C₆₇	C₂²	1	2	yes	complemented
69	#450×C₆₇	C₂²	1	2	yes	complemented
70	#449×C₆₇	C₂²	1	4	yes	complemented
71	#449×C₆₇	C₂²	1	4	yes	complemented
72	#448×C₆₇	C₂²	1	2	yes	—
73	#448×C₆₇	C₂²	1	2	yes	—
74	#448×C₆₇	C₂²	1	4	yes	complemented
75	#447×C₆₇	C₂²	1	2	yes	—
76	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	complemented
77	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
78	#436×C₆₇	C₂²	1	4	yes	complemented
79	#436×C₆₇	C₂²	1	4	yes	complemented
80	#431×C₆₇	C₂²	1	2	yes	complemented
81	#419×C₆₇	C₂²	1	4	yes	complemented
82	#417×C₆₇	C₂²	1	2	yes	complemented
83	#417×C₆₇	C₂²	1	2	yes	complemented
84	#407×C₆₇	C₂²	1	1	yes	characteristic
85	#407×C₆₇	C₂²	1	1	yes	characteristic
86	#407×C₆₇	C₂²	1	2	yes	complemented
87	C₂×#41×C₆₇	—	2	1	no	—
88	C₂×#41×C₆₇	—	2	1	no	—
89	C₂×#41×C₆₇	—	4	4	no	—
90	C₂×#41×C₆₇	C₂³	1	2	yes	—
91	C₂×#41×C₆₇	C₂³	1	2	yes	—
92	C₂×#41×C₆₇	C₂³	1	2	yes	—
93	C₂²×Q₈×C₆₇	—	2	1	no	—
94	C₂²×Q₈×C₆₇	—	2	2	no	—
95	C₂²×Q₈×C₆₇	—	4	4	no	—
96	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
98	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₆₇	—	2	1	no	—
101	C₂²×D₄×C₆₇	—	2	1	no	—
102	C₂²×D₄×C₆₇	—	2	1	no	—
103	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
104	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₆₇	—	2	1	no	—
107	C₂³×C₄×C₆₇	—	2	1	no	—
108	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
110	#137×C₆₇	—	4	8	no	—
111	#137×C₆₇	—	4	4	no	—
112	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
113	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
114	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
118	C₂×D₈×C₆₇	C₂³	1	4	yes	—
119	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
120	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
121	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
122	#126×C₆₇	—	2	2	no	—
123	#126×C₆₇	—	2	2	no	—
124	#126×C₆₇	—	2	2	no	—
125	#125×C₆₇	—	2	2	no	—
126	#125×C₆₇	C₂³	1	2	yes	—
127	#124×C₆₇	—	2	4	no	—
128	#124×C₆₇	—	2	4	no	—
129	#124×C₆₇	—	2	2	no	—
130	#124×C₆₇	—	2	2	no	—
131	#124×C₆₇	C₂³	1	4	yes	—
132	#124×C₆₇	C₂³	1	2	yes	—
133	#123×C₆₇	—	2	2	no	—
134	#123×C₆₇	—	2	2	no	—
135	#123×C₆₇	—	2	2	no	—
136	#123×C₆₇	—	2	2	no	—
137	#123×C₆₇	—	2	2	no	—
138	C₂²⋊Q₈×C₆₇	—	2	1	no	—
139	C₂²⋊Q₈×C₆₇	—	2	1	no	—
140	C₂²⋊Q₈×C₆₇	—	2	1	no	—
141	C₂²⋊Q₈×C₆₇	—	2	1	no	—
142	C₂²⋊Q₈×C₆₇	—	2	4	no	—
143	C₂²⋊Q₈×C₆₇	—	2	4	no	—
144	C₂²⋊Q₈×C₆₇	—	2	2	no	—
145	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
146	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
147	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
148	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
149	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
150	#121×C₆₇	—	2	4	no	—
151	#121×C₆₇	—	2	4	no	—
152	#121×C₆₇	—	2	2	no	—
153	#121×C₆₇	—	2	2	no	—
154	#121×C₆₇	—	2	1	no	—
155	#121×C₆₇	—	2	1	no	—
156	#121×C₆₇	—	2	2	no	—
157	#121×C₆₇	—	2	2	no	—
158	#121×C₆₇	C₂³	1	2	yes	—
159	#121×C₆₇	C₂³	1	2	yes	—
160	#121×C₆₇	C₂³	1	2	yes	—
161	#121×C₆₇	C₂³	1	4	yes	—
162	#120×C₆₇	—	2	2	no	—
163	#120×C₆₇	—	2	2	no	—
164	C₄×Q₈×C₆₇	—	2	2	no	—
165	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
166	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
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	4	no	—
171	C₄×D₄×C₆₇	—	2	4	no	—
172	C₄×D₄×C₆₇	—	2	2	no	—
173	C₄×D₄×C₆₇	—	2	2	no	—
174	C₄×D₄×C₆₇	D₄	1	2	yes	—
175	C₄×D₄×C₆₇	D₄	1	2	yes	—
176	C₄×D₄×C₆₇	C₂³	1	2	yes	—
177	C₄×D₄×C₆₇	C₂³	1	2	yes	—
178	C₄×D₄×C₆₇	C₂³	1	2	yes	—
179	#117×C₆₇	—	2	2	no	—
180	#117×C₆₇	—	2	2	no	—
181	#117×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
183	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
184	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
185	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
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	2	no	—
196	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₆₇	—	2	1	no	—
199	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
200	#107×C₆₇	C₂³	1	4	yes	—
201	#106×C₆₇	C₂³	1	4	yes	—
202	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
203	#103×C₆₇	C₂³	1	4	yes	—
204	#103×C₆₇	C₂³	1	4	yes	—
205	#103×C₆₇	C₂³	1	4	yes	—
206	#103×C₆₇	C₂³	1	4	yes	—
207	#103×C₆₇	C₂³	1	4	yes	—
208	#102×C₆₇	C₂³	1	4	yes	—
209	#102×C₆₇	C₂³	1	4	yes	—
210	#102×C₆₇	C₂³	1	4	yes	—
211	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
213	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
214	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
215	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
216	C₄×C₈×C₆₇	C₂³	1	4	yes	—
217	C₂⁴×C₆₇	—	2	1	no	—
218	C₂⁴×C₆₇	—	2	1	no	—
219	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
220	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
221	#41×C₆₇	—	2	4	no	—
222	#41×C₆₇	—	2	4	no	—
223	#41×C₆₇	—	4	2	no	—
224	#41×C₆₇	—	4	2	no	—
225	#41×C₆₇	—	4	4	no	—
226	#41×C₆₇	—	4	4	no	—
227	#41×C₆₇	—	4	4	no	—
228	C₂×Q₈×C₆₇	—	2	4	no	—
229	C₂×Q₈×C₆₇	—	2	1	no	—
230	C₂×Q₈×C₆₇	—	2	4	no	—
231	C₂×Q₈×C₆₇	—	2	1	no	—
232	C₂×Q₈×C₆₇	—	2	1	no	—
233	C₂×Q₈×C₆₇	—	2	8	no	—
234	C₂×Q₈×C₆₇	—	4	4	no	—
235	C₂×Q₈×C₆₇	—	4	2	no	—
236	C₂×Q₈×C₆₇	—	4	4	no	—
237	C₂×Q₈×C₆₇	—	4	2	no	—
238	C₂×Q₈×C₆₇	—	4	8	no	—
239	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
240	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
242	C₂×D₄×C₆₇	—	2	2	no	—
243	C₂×D₄×C₆₇	—	2	4	no	—
244	C₂×D₄×C₆₇	—	2	2	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	1	no	—
251	C₂×D₄×C₆₇	—	4	2	no	—
252	C₂×D₄×C₆₇	—	4	2	no	—
253	C₂×D₄×C₆₇	—	4	2	no	—
254	C₂×D₄×C₆₇	—	4	4	no	—
255	C₂×D₄×C₆₇	—	4	4	no	—
256	C₂×D₄×C₆₇	—	4	4	no	—
257	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	—	2	1	no	—
262	C₂²×C₄×C₆₇	—	2	1	no	—
263	C₂²×C₄×C₆₇	—	2	1	no	—
264	C₂²×C₄×C₆₇	—	2	1	no	—
265	C₂²×C₄×C₆₇	—	2	4	no	—
266	C₂²×C₄×C₆₇	—	2	1	no	—
267	C₂²×C₄×C₆₇	—	2	1	no	—
268	C₂²×C₄×C₆₇	—	2	2	no	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	2	2	no	—
271	C₂²×C₄×C₆₇	—	2	2	no	—
272	C₂²×C₄×C₆₇	—	4	2	no	—
273	C₂²×C₄×C₆₇	—	4	2	no	—
274	C₂²×C₄×C₆₇	—	4	4	no	—
275	C₂²×C₄×C₆₇	—	4	4	no	—
276	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
287	Q₁₆×C₆₇	—	2	8	no	—
288	Q₁₆×C₆₇	—	4	4	no	—
289	SD₁₆×C₆₇	—	2	8	no	—
290	SD₁₆×C₆₇	—	4	4	no	—
291	SD₁₆×C₆₇	—	4	4	no	—
292	D₈×C₆₇	—	4	4	no	—
293	M₁₆×C₆₇	—	4	2	no	—
294	M₁₆×C₆₇	—	4	4	no	—
295	M₁₆×C₆₇	—	4	2	no	—
296	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
297	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
298	C₄⋊C₄×C₆₇	—	2	2	no	—
299	C₄⋊C₄×C₆₇	—	2	2	no	—
300	C₄⋊C₄×C₆₇	—	2	2	no	—
301	C₄⋊C₄×C₆₇	—	2	4	no	—
302	C₄⋊C₄×C₆₇	—	2	2	no	—
303	C₄⋊C₄×C₆₇	—	2	1	no	—
304	C₄⋊C₄×C₆₇	—	2	1	no	—
305	C₄⋊C₄×C₆₇	—	2	1	no	—
306	C₄⋊C₄×C₆₇	—	2	2	no	—
307	C₄⋊C₄×C₆₇	—	2	2	no	—
308	C₄⋊C₄×C₆₇	—	2	2	no	—
309	C₄⋊C₄×C₆₇	—	2	2	no	—
310	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
315	C₂²⋊C₄×C₆₇	—	2	2	no	—
316	C₂²⋊C₄×C₆₇	—	2	2	no	—
317	C₂²⋊C₄×C₆₇	—	2	2	no	—
318	C₂²⋊C₄×C₆₇	—	2	2	no	—
319	C₂²⋊C₄×C₆₇	—	2	2	no	—
320	C₂²⋊C₄×C₆₇	—	2	2	no	—
321	C₂²⋊C₄×C₆₇	—	2	2	no	—
322	C₂²⋊C₄×C₆₇	—	2	2	no	—
323	C₂²⋊C₄×C₆₇	—	2	2	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	2	no	—
328	C₂²⋊C₄×C₆₇	—	2	2	no	—
329	C₂²⋊C₄×C₆₇	—	2	2	no	—
330	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
333	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
334	C₄²×C₆₇	—	2	4	no	—
335	C₄²×C₆₇	—	2	2	no	—
336	C₄²×C₆₇	—	2	2	no	—
337	C₄²×C₆₇	C₂×D₄	1	2	yes	—
338	C₄²×C₆₇	C₂⁴	1	2	yes	—
339	C₂³×C₆₇	—	2	2	no	—
340	C₂³×C₆₇	—	2	2	no	—
341	C₂³×C₆₇	—	2	2	no	—
342	C₂³×C₆₇	—	2	2	no	—
343	C₂³×C₆₇	—	4	1	no	—
344	C₂³×C₆₇	—	4	1	no	—
345	C₂³×C₆₇	—	4	1	no	—
346	C₂³×C₆₇	—	4	1	no	—
347	C₂³×C₆₇	—	4	2	no	—
348	C₂³×C₆₇	—	4	2	no	—
349	C₂³×C₆₇	—	4	2	no	—
350	C₂³×C₆₇	—	4	2	no	—
351	C₂³×C₆₇	—	8	1	no	—
352	C₂³×C₆₇	—	8	1	no	—
353	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
354	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
355	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
356	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₆₇	—	2	4	no	—
358	Q₈×C₆₇	—	2	2	no	—
359	Q₈×C₆₇	—	2	4	no	—
360	Q₈×C₆₇	—	2	4	no	—
361	Q₈×C₆₇	—	4	8	no	—
362	Q₈×C₆₇	—	4	2	no	—
363	Q₈×C₆₇	—	8	1	no	—
364	Q₈×C₆₇	H(5,𝔽₂)	1	4	yes	—
365	D₄×C₆₇	—	2	2	no	—
366	D₄×C₆₇	—	2	4	no	—
367	D₄×C₆₇	—	2	2	no	—
368	D₄×C₆₇	—	4	2	no	—
369	D₄×C₆₇	—	4	2	no	—
370	D₄×C₆₇	—	4	4	no	—
371	D₄×C₆₇	—	4	4	no	—
372	D₄×C₆₇	—	4	2	no	—
373	D₄×C₆₇	—	4	4	no	—
374	D₄×C₆₇	—	4	8	no	—
375	D₄×C₆₇	—	4	4	no	—
376	D₄×C₆₇	—	8	1	no	—
377	D₄×C₆₇	—	8	2	no	—
378	D₄×C₆₇	—	8	2	no	—
379	C₂×C₄×C₆₇	—	2	4	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	4	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	4	1	no	—
392	C₂×C₄×C₆₇	—	4	2	no	—
393	C₂×C₄×C₆₇	—	4	1	no	—
394	C₂×C₄×C₆₇	—	4	1	no	—
395	C₂×C₄×C₆₇	—	4	1	no	—
396	C₂×C₄×C₆₇	—	4	1	no	—
397	C₂×C₄×C₆₇	—	4	4	no	—
398	C₂×C₄×C₆₇	—	4	4	no	—
399	C₂×C₄×C₆₇	—	4	8	no	—
400	C₂×C₄×C₆₇	—	4	2	no	—
401	C₂×C₄×C₆₇	—	4	2	no	—
402	C₂×C₄×C₆₇	—	4	2	no	—
403	C₂×C₄×C₆₇	—	8	2	no	—
404	C₂×C₄×C₆₇	—	8	2	no	—
405	C₂×C₄×C₆₇	—	8	1	no	—
406	C₂×C₄×C₆₇	—	8	1	no	—
407	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
414	C₈×C₆₇	—	2	4	no	—
415	C₈×C₆₇	—	2	4	no	—
416	C₂²×C₆₇	—	2	1	no	—
417	C₂²×C₆₇	—	2	1	no	—
418	C₂²×C₆₇	—	2	1	no	—
419	C₂²×C₆₇	—	2	2	no	—
420	C₂²×C₆₇	—	2	1	no	—
421	C₂²×C₆₇	—	2	2	no	—
422	C₂²×C₆₇	—	2	1	no	—
423	C₂²×C₆₇	—	2	1	no	—
424	C₂²×C₆₇	—	2	1	no	—
425	C₂²×C₆₇	—	2	2	no	—
426	C₂²×C₆₇	—	2	1	no	—
427	C₂²×C₆₇	—	4	4	no	—
428	C₂²×C₆₇	—	4	2	no	—
429	C₂²×C₆₇	—	4	2	no	—
430	C₂²×C₆₇	—	4	2	no	—
431	C₂²×C₆₇	—	4	2	no	—
432	C₂²×C₆₇	—	4	2	no	—
433	C₂²×C₆₇	—	4	2	no	—
434	C₂²×C₆₇	—	8	2	no	—
435	C₂²×C₆₇	—	8	4	no	—
436	C₂²×C₆₇	—	16	2	no	—
437	C₂²×C₆₇	#575	1	2	yes	—
438	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₆₇	—	2	2	no	—
440	C₄×C₆₇	—	2	4	no	—
441	C₄×C₆₇	—	2	1	no	—
442	C₄×C₆₇	—	2	1	no	—
443	C₄×C₆₇	—	2	1	no	—
444	C₄×C₆₇	—	2	2	no	—
445	C₄×C₆₇	—	2	2	no	—
446	C₄×C₆₇	—	4	2	no	—
447	C₄×C₆₇	—	4	2	no	—
448	C₄×C₆₇	—	4	2	no	—
449	C₄×C₆₇	—	4	2	no	—
450	C₄×C₆₇	—	4	2	no	—
451	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
452	#61583	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂×C₆₇	—	2	2	no	—
454	C₂×C₆₇	—	4	2	no	—
455	C₂×C₆₇	—	4	1	no	—
456	C₂×C₆₇	—	4	1	no	—
457	C₂×C₆₇	—	8	2	no	—
458	C₂×C₆₇	—	8	2	no	—
459	C₂×C₆₇	#3484	1	1	yes	characteristic
460	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
461	C₂×C₆₇	#3586	1	1	yes	characteristic
462	#3505	C₂×C₆₇	1	1	yes	characteristic, complemented
463	C₂×#548	C₂×C₆₇	1	1	yes	characteristic, complemented
464	#3327	C₂×C₆₇	1	4	yes	complemented
465	#3326	C₂×C₆₇	1	4	yes	complemented
466	#3277	C₂×C₆₇	1	4	yes	complemented
467	#3275	C₂×C₆₇	1	4	yes	complemented
468	#3211	C₂×C₆₇	1	2	yes	complemented
469	#3195	C₂×C₆₇	1	1	yes	characteristic, complemented
470	#3194	C₂×C₆₇	1	2	yes	complemented
471	#3193	C₂×C₆₇	1	1	yes	characteristic, complemented
472	#3108	C₂×C₆₇	1	2	yes	complemented
473	#3007	C₂×C₆₇	1	1	yes	characteristic, complemented
474	#3006	C₂×C₆₇	1	1	yes	characteristic, complemented
475	#3004	C₂×C₆₇	1	2	yes	complemented
476	#2975	C₂×C₆₇	1	1	yes	characteristic, complemented
477	C₆₇	#61583	1	1	yes	characteristic, direct product factor, Sylow
478	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
479	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
480	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
481	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
482	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
483	#553	—	2	2	no	—
484	#553	C₂²×C₆₇	1	2	yes	complemented
485	#552	C₂²×C₆₇	1	2	yes	complemented
486	#551	—	2	2	no	—
487	#548	—	2	2	no	—
488	#548	—	2	2	no	—
489	#548	C₂²×C₆₇	1	4	yes	—
490	#548	C₂²×C₆₇	1	4	yes	complemented
491	#548	C₂²×C₆₇	1	2	yes	complemented
492	#546	C₂²×C₆₇	1	2	yes	complemented
493	#539	—	2	1	no	—
494	#538	—	2	1	no	—
495	#534	—	2	1	no	—
496	#529	C₂²×C₆₇	1	2	yes	—
497	C₂×#124	—	2	1	no	—
498	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
499	#525	C₂²×C₆₇	1	2	yes	—
500	C₂×C₂²⋊Q₈	—	2	1	no	—
501	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
502	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
503	C₂×#121	—	2	1	no	—
504	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
505	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
506	#518	—	2	1	no	—
507	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
508	C₂×C₄×D₄	—	2	1	no	—
509	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
510	#495	C₂²×C₆₇	1	4	yes	complemented
511	#488	C₂²×C₆₇	1	4	yes	complemented
512	#484	C₂²×C₆₇	1	2	yes	complemented
513	#483	C₂²×C₆₇	1	2	yes	complemented
514	#483	C₂²×C₆₇	1	2	yes	complemented
515	#482	C₂²×C₆₇	1	4	yes	complemented
516	#480	C₂²×C₆₇	1	2	yes	—
517	#479	C₂²×C₆₇	1	4	yes	complemented
518	#470	C₂²×C₆₇	1	4	yes	complemented
519	#469	C₂²×C₆₇	1	4	yes	complemented
520	#468	C₂²×C₆₇	1	4	yes	complemented
521	#468	C₂²×C₆₇	1	4	yes	complemented
522	#464	C₂²×C₆₇	1	4	yes	complemented
523	#464	C₂²×C₆₇	1	4	yes	complemented
524	#463	C₂²×C₆₇	1	4	yes	complemented
525	#452	C₂²×C₆₇	1	4	yes	complemented
526	#451	C₂²×C₆₇	1	2	yes	complemented
527	#451	C₂²×C₆₇	1	2	yes	complemented
528	#451	C₂²×C₆₇	1	2	yes	complemented
529	#451	C₂²×C₆₇	1	4	yes	complemented
530	#450	C₂²×C₆₇	1	2	yes	complemented
531	#450	C₂²×C₆₇	1	2	yes	complemented
532	#449	C₂²×C₆₇	1	4	yes	complemented
533	#449	C₂²×C₆₇	1	4	yes	complemented
534	#448	C₂²×C₆₇	1	2	yes	—
535	#448	C₂²×C₆₇	1	2	yes	—
536	#448	C₂²×C₆₇	1	4	yes	complemented
537	#447	C₂²×C₆₇	1	2	yes	—
538	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	complemented
539	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
540	#436	C₂²×C₆₇	1	4	yes	complemented
541	#436	C₂²×C₆₇	1	4	yes	complemented
542	#431	C₂²×C₆₇	1	2	yes	complemented
543	#419	C₂²×C₆₇	1	4	yes	complemented
544	#417	C₂²×C₆₇	1	2	yes	complemented
545	#417	C₂²×C₆₇	1	2	yes	complemented
546	#407	C₂²×C₆₇	1	1	yes	characteristic
547	#407	C₂²×C₆₇	1	1	yes	characteristic
548	#407	C₂²×C₆₇	1	2	yes	complemented
549	C₂×#41	—	2	1	no	—
550	C₂×#41	—	2	1	no	—
551	C₂×#41	—	4	4	no	—
552	C₂×#41	C₂³×C₆₇	1	2	yes	—
553	C₂×#41	C₂³×C₆₇	1	2	yes	—
554	C₂×#41	C₂³×C₆₇	1	2	yes	—
555	C₂²×Q₈	—	2	1	no	—
556	C₂²×Q₈	—	2	2	no	—
557	C₂²×Q₈	—	4	4	no	—
558	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
559	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
560	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
561	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
562	C₂²×D₄	—	2	1	no	—
563	C₂²×D₄	—	2	1	no	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
568	C₂³×C₄	—	2	1	no	—
569	C₂³×C₄	—	2	1	no	—
570	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
572	#137	—	4	8	no	—
573	#137	—	4	4	no	—
574	AGL(1,ℤ/8)	—	4	4	no	—
575	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
576	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
577	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
578	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
579	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
580	C₂×D₈	C₂³×C₆₇	1	4	yes	—
581	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
582	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
583	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
584	#126	—	2	2	no	—
585	#126	—	2	2	no	—
586	#126	—	2	2	no	—
587	#125	—	2	2	no	—
588	#125	C₂³×C₆₇	1	2	yes	—
589	#124	—	2	4	no	—
590	#124	—	2	4	no	—
591	#124	—	2	2	no	—
592	#124	—	2	2	no	—
593	#124	C₂³×C₆₇	1	4	yes	—
594	#124	C₂³×C₆₇	1	2	yes	—
595	#123	—	2	2	no	—
596	#123	—	2	2	no	—
597	#123	—	2	2	no	—
598	#123	—	2	2	no	—
599	#123	—	2	2	no	—
600	C₂²⋊Q₈	—	2	1	no	—
601	C₂²⋊Q₈	—	2	1	no	—
602	C₂²⋊Q₈	—	2	1	no	—
603	C₂²⋊Q₈	—	2	1	no	—
604	C₂²⋊Q₈	—	2	4	no	—
605	C₂²⋊Q₈	—	2	4	no	—
606	C₂²⋊Q₈	—	2	2	no	—
607	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
608	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
609	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
610	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
611	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
612	#121	—	2	4	no	—
613	#121	—	2	4	no	—
614	#121	—	2	2	no	—
615	#121	—	2	2	no	—
616	#121	—	2	1	no	—
617	#121	—	2	1	no	—
618	#121	—	2	2	no	—
619	#121	—	2	2	no	—
620	#121	C₂³×C₆₇	1	2	yes	—
621	#121	C₂³×C₆₇	1	2	yes	—
622	#121	C₂³×C₆₇	1	4	yes	—
623	#121	C₂³×C₆₇	1	2	yes	—
624	#120	—	2	2	no	—
625	#120	—	2	2	no	—
626	C₄×Q₈	—	2	2	no	—
627	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
628	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	4	no	—
633	C₄×D₄	—	2	4	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	D₄×C₆₇	1	2	yes	—
637	C₄×D₄	D₄×C₆₇	1	2	yes	—
638	C₄×D₄	C₂³×C₆₇	1	2	yes	—
639	C₄×D₄	C₂³×C₆₇	1	2	yes	—
640	C₄×D₄	C₂³×C₆₇	1	2	yes	—
641	#117	—	2	2	no	—
642	#117	—	2	2	no	—
643	#117	C₂³×C₆₇	1	2	yes	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	2	no	—
658	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
662	#107	C₂³×C₆₇	1	4	yes	—
663	#106	C₂³×C₆₇	1	4	yes	—
664	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
665	#103	C₂³×C₆₇	1	4	yes	—
666	#103	C₂³×C₆₇	1	4	yes	—
667	#103	C₂³×C₆₇	1	4	yes	—
668	#103	C₂³×C₆₇	1	4	yes	—
669	#103	C₂³×C₆₇	1	4	yes	—
670	#102	C₂³×C₆₇	1	4	yes	—
671	#102	C₂³×C₆₇	1	4	yes	—
672	#102	C₂³×C₆₇	1	4	yes	—
673	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
674	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
675	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
676	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
678	C₄×C₈	C₂³×C₆₇	1	4	yes	—
679	C₂⁴	—	2	1	no	—
680	C₂⁴	—	2	1	no	—
681	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
682	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
683	#41	—	2	4	no	—
684	#41	—	2	4	no	—
685	#41	—	4	2	no	—
686	#41	—	4	2	no	—
687	#41	—	4	4	no	—
688	#41	—	4	4	no	—
689	#41	—	4	4	no	—
690	C₂×Q₈	—	2	4	no	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	2	4	no	—
693	C₂×Q₈	—	2	1	no	—
694	C₂×Q₈	—	2	1	no	—
695	C₂×Q₈	—	2	8	no	—
696	C₂×Q₈	—	4	4	no	—
697	C₂×Q₈	—	4	2	no	—
698	C₂×Q₈	—	4	4	no	—
699	C₂×Q₈	—	4	2	no	—
700	C₂×Q₈	—	4	8	no	—
701	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
702	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
703	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	4	2	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	4	no	—
717	C₂×D₄	—	4	4	no	—
718	C₂×D₄	—	4	4	no	—
719	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
720	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
721	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
722	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	—	4	4	no	—
737	C₂²×C₄	—	4	4	no	—
738	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
739	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
740	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
741	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
742	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
749	Q₁₆	—	2	8	no	—
750	Q₁₆	—	4	4	no	—
751	SD₁₆	—	2	8	no	—
752	SD₁₆	—	4	4	no	—
753	SD₁₆	—	4	4	no	—
754	D₈	—	4	4	no	—
755	M₁₆	—	4	2	no	—
756	M₁₆	—	4	4	no	—
757	M₁₆	—	4	2	no	—
758	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
759	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
773	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
774	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
775	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
776	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
793	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
794	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
795	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
796	C₄²	—	2	4	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	C₂×D₄×C₆₇	1	2	yes	—
800	C₄²	C₂⁴×C₆₇	1	2	yes	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	2	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	8	1	no	—
814	C₂³	—	8	1	no	—
815	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
816	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
817	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
818	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
819	Q₈	—	2	4	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	2	4	no	—
822	Q₈	—	2	4	no	—
823	Q₈	—	4	8	no	—
824	Q₈	—	4	2	no	—
825	Q₈	—	8	1	no	—
826	Q₈	H(5,𝔽₂)×C₆₇	1	4	yes	—
827	D₄	—	2	2	no	—
828	D₄	—	2	4	no	—
829	D₄	—	2	2	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	2	no	—
832	D₄	—	4	4	no	—
833	D₄	—	4	4	no	—
834	D₄	—	4	2	no	—
835	D₄	—	4	4	no	—
836	D₄	—	4	8	no	—
837	D₄	—	4	4	no	—
838	D₄	—	8	1	no	—
839	D₄	—	8	2	no	—
840	D₄	—	8	2	no	—
841	C₂×C₄	—	2	4	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	4	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	2	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	4	8	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	—	8	1	no	—
868	C₂×C₄	—	8	1	no	—
869	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
875	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
876	C₈	—	2	4	no	—
877	C₈	—	2	4	no	—
878	C₂²	—	2	1	no	—
879	C₂²	—	2	1	no	—
880	C₂²	—	2	1	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	1	no	—
888	C₂²	—	2	1	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	8	2	no	—
897	C₂²	—	8	4	no	—
898	C₂²	—	16	2	no	—
899	C₂²	#575×C₆₇	1	2	yes	—
900	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	1	no	—
906	C₄	—	2	1	no	—
907	C₄	—	2	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
914	C₂	—	2	2	no	—
915	C₂	—	4	2	no	—
916	C₂	—	4	1	no	—
917	C₂	—	4	1	no	—
918	C₂	—	8	2	no	—
919	C₂	—	8	2	no	—
920	C₂	C₆₇×#3484	1	1	yes	characteristic
921	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
922	C₂	C₆₇×#3586	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×#548×C₆₇	C₂	semidirect
3. C₆₇×#3327	C₂	semidirect
4. C₆₇×#3326	C₂	semidirect
5. C₆₇×#3277	C₂	semidirect
6. C₆₇×#3275	C₂	semidirect
7. C₆₇×#3211	C₂	semidirect
8. C₆₇×#3195	C₂	semidirect
9. C₆₇×#3194	C₂	semidirect
10. C₆₇×#3193	C₂	semidirect
11. C₆₇×#3108	C₂	semidirect
12. C₆₇×#3007	C₂	semidirect
13. C₆₇×#3006	C₂	semidirect
14. C₆₇×#3004	C₂	semidirect
15. C₆₇×#2975	C₂	semidirect
17. C₂³×Q₈×C₆₇	C₂²	semidirect
18. C₂×#137×C₆₇	C₂²	semidirect
19. C₂×#137×C₆₇	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
22. #553×C₆₇	C₂²	semidirect
23. #552×C₆₇	C₂²	semidirect
28. #548×C₆₇	C₂²	semidirect
29. #548×C₆₇	C₂²	semidirect
30. #546×C₆₇	C₂²	semidirect
36. C₂×#124×C₆₇	C₂²	semidirect
43. C₂×#121×C₆₇	C₂²	semidirect
45. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
48. #495×C₆₇	C₂²	semidirect
49. #488×C₆₇	C₂²	semidirect
50. #484×C₆₇	C₂²	semidirect
51. #483×C₆₇	C₂²	semidirect
52. #483×C₆₇	C₂²	semidirect
53. #482×C₆₇	C₂²	semidirect
55. #479×C₆₇	C₂²	semidirect
56. #470×C₆₇	C₂²	semidirect
57. #469×C₆₇	C₂²	semidirect
58. #468×C₆₇	C₂²	semidirect
59. #468×C₆₇	C₂²	semidirect
60. #464×C₆₇	C₂²	semidirect
61. #464×C₆₇	C₂²	semidirect
62. #463×C₆₇	C₂²	semidirect
63. #452×C₆₇	C₂²	semidirect
64. #451×C₆₇	C₂²	semidirect
65. #451×C₆₇	C₂²	semidirect
66. #451×C₆₇	C₂²	semidirect
67. #451×C₆₇	C₂²	semidirect
68. #450×C₆₇	C₂²	semidirect
69. #450×C₆₇	C₂²	semidirect
70. #449×C₆₇	C₂²	semidirect
71. #449×C₆₇	C₂²	semidirect
74. #448×C₆₇	C₂²	semidirect
76. C₄×Q₁₆×C₆₇	C₂²	semidirect
77. C₄×SD₁₆×C₆₇	C₂²	semidirect
78. #436×C₆₇	C₂²	semidirect
79. #436×C₆₇	C₂²	semidirect
80. #431×C₆₇	C₂²	semidirect
81. #419×C₆₇	C₂²	semidirect
82. #417×C₆₇	C₂²	semidirect
83. #417×C₆₇	C₂²	semidirect
86. #407×C₆₇	C₂²	semidirect
452. #61583	C₆₇	direct (N × H)
462. #3505	C₂×C₆₇	semidirect
463. C₂×#548	C₂×C₆₇	semidirect
464. #3327	C₂×C₆₇	semidirect
465. #3326	C₂×C₆₇	semidirect
466. #3277	C₂×C₆₇	semidirect
467. #3275	C₂×C₆₇	semidirect
468. #3211	C₂×C₆₇	semidirect
469. #3195	C₂×C₆₇	semidirect
470. #3194	C₂×C₆₇	semidirect
471. #3193	C₂×C₆₇	semidirect
472. #3108	C₂×C₆₇	semidirect
473. #3007	C₂×C₆₇	semidirect
474. #3006	C₂×C₆₇	semidirect
475. #3004	C₂×C₆₇	semidirect
476. #2975	C₂×C₆₇	semidirect
477. C₆₇	#61583	direct (N × H)
479. C₂³×Q₈	C₂²×C₆₇	semidirect
480. C₂×#137	C₂²×C₆₇	semidirect
481. C₂×#137	C₂²×C₆₇	semidirect
482. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
484. #553	C₂²×C₆₇	semidirect
485. #552	C₂²×C₆₇	semidirect
490. #548	C₂²×C₆₇	semidirect
491. #548	C₂²×C₆₇	semidirect
492. #546	C₂²×C₆₇	semidirect
498. C₂×#124	C₂²×C₆₇	semidirect
505. C₂×#121	C₂²×C₆₇	semidirect
507. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
510. #495	C₂²×C₆₇	semidirect
511. #488	C₂²×C₆₇	semidirect
512. #484	C₂²×C₆₇	semidirect
513. #483	C₂²×C₆₇	semidirect
514. #483	C₂²×C₆₇	semidirect
515. #482	C₂²×C₆₇	semidirect
517. #479	C₂²×C₆₇	semidirect
518. #470	C₂²×C₆₇	semidirect
519. #469	C₂²×C₆₇	semidirect
520. #468	C₂²×C₆₇	semidirect
521. #468	C₂²×C₆₇	semidirect
522. #464	C₂²×C₆₇	semidirect
523. #464	C₂²×C₆₇	semidirect
524. #463	C₂²×C₆₇	semidirect
525. #452	C₂²×C₆₇	semidirect
526. #451	C₂²×C₆₇	semidirect
527. #451	C₂²×C₆₇	semidirect
528. #451	C₂²×C₆₇	semidirect
529. #451	C₂²×C₆₇	semidirect
530. #450	C₂²×C₆₇	semidirect
531. #450	C₂²×C₆₇	semidirect
532. #449	C₂²×C₆₇	semidirect
533. #449	C₂²×C₆₇	semidirect
536. #448	C₂²×C₆₇	semidirect
538. C₄×Q₁₆	C₂²×C₆₇	semidirect
539. C₄×SD₁₆	C₂²×C₆₇	semidirect
540. #436	C₂²×C₆₇	semidirect
541. #436	C₂²×C₆₇	semidirect
542. #431	C₂²×C₆₇	semidirect
543. #419	C₂²×C₆₇	semidirect
544. #417	C₂²×C₆₇	semidirect
545. #417	C₂²×C₆₇	semidirect
548. #407	C₂²×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×#548×C₆₇	2
C₆₇×#3327	2
C₆₇×#3326	2
C₆₇×#3277	2
C₆₇×#3275	2
C₆₇×#3211	2
C₆₇×#3195	2
C₆₇×#3194	2
C₆₇×#3193	2
C₆₇×#3108	2
C₆₇×#3007	2
C₆₇×#3006	2
C₆₇×#3004	2
C₆₇×#2975	2
#61583	67

Subgroups — C67×#61583 #30740834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61583 #30740834