Subgroups — C₆₇×#61343 #30740594

Order 17152.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3376	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3376	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3373	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3370	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3370	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3367	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3361	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3360	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3136	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3081	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3042	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3041	C₂	1	1	yes	maximal, characteristic
19	C₂×#463×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2949	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2948	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
27	#559×C₆₇	C₂²	1	2	yes	complemented
28	#559×C₆₇	C₂²	1	2	yes	complemented
29	#556×C₆₇	C₂²	1	2	yes	complemented
30	#556×C₆₇	C₂²	1	2	yes	complemented
31	#554×C₆₇	—	2	1	no	—
32	#554×C₆₇	—	2	1	no	—
33	#554×C₆₇	—	2	1	no	—
34	#554×C₆₇	C₂²	1	2	yes	complemented
35	#554×C₆₇	C₂²	1	2	yes	complemented
36	#554×C₆₇	C₂²	1	2	yes	complemented
37	#551×C₆₇	—	2	2	no	—
38	#551×C₆₇	—	2	2	no	—
39	D₄×Q₈×C₆₇	—	2	1	no	—
40	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
41	#544×C₆₇	C₂²	1	1	yes	characteristic
42	#544×C₆₇	C₂²	1	1	yes	characteristic
43	#543×C₆₇	—	2	2	no	—
44	#542×C₆₇	—	2	1	no	—
45	#542×C₆₇	—	2	1	no	—
46	#536×C₆₇	C₂²	1	1	yes	characteristic
47	#535×C₆₇	C₂²	1	1	yes	characteristic
48	#533×C₆₇	C₂²	1	1	yes	characteristic
49	#533×C₆₇	C₂²	1	1	yes	characteristic
50	#529×C₆₇	—	2	1	no	—
51	#529×C₆₇	—	2	1	no	—
52	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
54	#519×C₆₇	C₂²	1	1	yes	characteristic
55	#518×C₆₇	C₂²	1	1	yes	characteristic
56	#518×C₆₇	C₂²	1	1	yes	characteristic
57	#518×C₆₇	C₂²	1	1	yes	characteristic
58	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
60	#491×C₆₇	C₂²	1	2	yes	complemented
61	#490×C₆₇	C₂²	1	2	yes	complemented
62	#489×C₆₇	C₂²	1	2	yes	complemented
63	#489×C₆₇	C₂²	1	2	yes	complemented
64	#489×C₆₇	C₂²	1	2	yes	complemented
65	#489×C₆₇	C₂²	1	2	yes	complemented
66	#488×C₆₇	C₂²	1	2	yes	complemented
67	#488×C₆₇	C₂²	1	2	yes	complemented
68	#488×C₆₇	C₂²	1	2	yes	complemented
69	#488×C₆₇	C₂²	1	2	yes	complemented
70	#487×C₆₇	C₂²	1	2	yes	complemented
71	#486×C₆₇	C₂²	1	2	yes	complemented
72	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#479×C₆₇	C₂²	1	2	yes	complemented
75	#479×C₆₇	C₂²	1	2	yes	complemented
76	#478×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#478×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#478×C₆₇	C₂²	1	2	yes	complemented
79	#478×C₆₇	C₂²	1	2	yes	complemented
80	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#477×C₆₇	C₂²	1	2	yes	complemented
82	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	#476×C₆₇	C₂²	1	2	yes	complemented
84	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#475×C₆₇	C₂²	1	2	yes	complemented
86	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#474×C₆₇	C₂²	1	2	yes	complemented
88	#463×C₆₇	C₂²	1	2	yes	—
89	#463×C₆₇	C₂²	1	2	yes	—
90	#463×C₆₇	C₂²	1	2	yes	—
91	#463×C₆₇	C₂²	1	2	yes	—
92	#463×C₆₇	C₂²	1	2	yes	—
93	#463×C₆₇	C₂²	1	2	yes	—
94	#463×C₆₇	C₂²	1	2	yes	complemented
95	#463×C₆₇	C₂²	1	2	yes	complemented
96	#461×C₆₇	C₂²	1	2	yes	complemented
97	#461×C₆₇	C₂²	1	2	yes	complemented
98	#459×C₆₇	C₂²	1	2	yes	—
99	#459×C₆₇	C₂²	1	2	yes	—
100	#446×C₆₇	C₂²	1	2	yes	complemented
101	#446×C₆₇	C₂²	1	2	yes	complemented
102	#446×C₆₇	C₂²	1	2	yes	complemented
103	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
104	#442×C₆₇	C₂²	1	2	yes	—
105	#442×C₆₇	C₂²	1	2	yes	—
106	#442×C₆₇	C₂²	1	2	yes	complemented
107	#440×C₆₇	C₂²	1	2	yes	complemented
108	#440×C₆₇	C₂²	1	2	yes	complemented
109	#440×C₆₇	C₂²	1	2	yes	complemented
110	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
112	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
113	C₄×D₈×C₆₇	C₂²	1	2	yes	—
114	C₄×D₈×C₆₇	C₂²	1	2	yes	—
115	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
116	#428×C₆₇	C₂²	1	1	yes	characteristic
117	#427×C₆₇	C₂²	1	1	yes	characteristic
118	#427×C₆₇	C₂²	1	1	yes	characteristic
119	#424×C₆₇	C₂²	1	1	yes	characteristic
120	#424×C₆₇	C₂²	1	1	yes	characteristic
121	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
122	#419×C₆₇	C₂²	1	1	yes	characteristic
123	#419×C₆₇	C₂²	1	1	yes	characteristic
124	#418×C₆₇	C₂²	1	1	yes	characteristic
125	#418×C₆₇	C₂²	1	1	yes	characteristic
126	#418×C₆₇	C₂²	1	1	yes	characteristic
127	#417×C₆₇	C₂²	1	1	yes	characteristic
128	#416×C₆₇	C₂²	1	1	yes	characteristic
129	#416×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
131	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
132	#405×C₆₇	C₂²	1	1	yes	characteristic
133	#405×C₆₇	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₆₇	—	2	2	no	—
137	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	—	2	1	no	—
141	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
142	C₂×SD₁₆×C₆₇	—	2	4	no	—
143	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×D₈×C₆₇	—	2	4	no	—
147	C₂×D₈×C₆₇	C₂³	1	2	yes	—
148	C₂×D₈×C₆₇	C₂³	1	2	yes	—
149	C₂×D₈×C₆₇	C₂³	1	2	yes	—
150	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₆₇	—	2	1	no	—
155	C₄⋊Q₈×C₆₇	—	2	1	no	—
156	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
157	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	#127×C₆₇	C₂³	1	2	yes	—
164	#126×C₆₇	—	2	2	no	—
165	#126×C₆₇	—	2	2	no	—
166	#126×C₆₇	—	2	2	no	—
167	#126×C₆₇	—	2	2	no	—
168	#125×C₆₇	—	2	1	no	—
169	#125×C₆₇	—	2	1	no	—
170	#125×C₆₇	D₄	1	1	yes	characteristic
171	#125×C₆₇	D₄	1	1	yes	characteristic
172	#125×C₆₇	C₂³	1	2	yes	—
173	#125×C₆₇	C₂³	1	1	yes	characteristic
174	#125×C₆₇	C₂³	1	1	yes	characteristic
175	#125×C₆₇	C₂³	1	2	yes	—
176	#124×C₆₇	—	2	2	no	—
177	#124×C₆₇	—	2	2	no	—
178	#124×C₆₇	—	2	1	no	—
179	#124×C₆₇	—	2	1	no	—
180	#124×C₆₇	C₂³	1	2	yes	—
181	#124×C₆₇	C₂³	1	2	yes	—
182	#124×C₆₇	C₂³	1	2	yes	—
183	#124×C₆₇	C₂³	1	2	yes	—
184	#123×C₆₇	—	2	2	no	—
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	—	2	2	no	—
189	C₂²⋊Q₈×C₆₇	—	2	2	no	—
190	C₂²⋊Q₈×C₆₇	—	2	2	no	—
191	C₂²⋊Q₈×C₆₇	—	2	2	no	—
192	C₂²⋊Q₈×C₆₇	—	2	2	no	—
193	C₂²⋊Q₈×C₆₇	—	2	2	no	—
194	C₂²⋊Q₈×C₆₇	—	2	1	no	—
195	C₂²⋊Q₈×C₆₇	—	2	1	no	—
196	C₂²⋊Q₈×C₆₇	—	2	2	no	—
197	C₂²⋊Q₈×C₆₇	—	2	2	no	—
198	C₂²⋊Q₈×C₆₇	—	2	2	no	—
199	C₂²⋊Q₈×C₆₇	—	2	1	no	—
200	C₂²⋊Q₈×C₆₇	—	2	1	no	—
201	C₂²⋊Q₈×C₆₇	—	2	2	no	—
202	C₂²⋊Q₈×C₆₇	—	2	2	no	—
203	C₂²⋊Q₈×C₆₇	—	2	2	no	—
204	C₂²⋊Q₈×C₆₇	—	2	2	no	—
205	C₂²⋊Q₈×C₆₇	—	2	2	no	—
206	C₂²⋊Q₈×C₆₇	—	2	2	no	—
207	C₂²⋊Q₈×C₆₇	—	2	2	no	—
208	C₂²⋊Q₈×C₆₇	—	2	2	no	—
209	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
210	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
211	#121×C₆₇	—	2	1	no	—
212	#121×C₆₇	—	2	1	no	—
213	#120×C₆₇	—	2	2	no	—
214	C₄×Q₈×C₆₇	—	2	1	no	—
215	C₄×Q₈×C₆₇	—	2	1	no	—
216	C₄×Q₈×C₆₇	—	2	1	no	—
217	C₄×Q₈×C₆₇	—	2	1	no	—
218	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
220	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
221	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
223	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
224	C₄×D₄×C₆₇	—	2	1	no	—
225	C₄×D₄×C₆₇	—	2	1	no	—
226	C₄×D₄×C₆₇	—	2	1	no	—
227	C₄×D₄×C₆₇	—	2	1	no	—
228	C₄×D₄×C₆₇	—	2	1	no	—
229	C₄×D₄×C₆₇	—	2	1	no	—
230	C₄×D₄×C₆₇	—	2	1	no	—
231	C₄×D₄×C₆₇	—	2	1	no	—
232	C₄×D₄×C₆₇	—	2	2	no	—
233	C₄×D₄×C₆₇	—	2	2	no	—
234	C₄×D₄×C₆₇	—	2	1	no	—
235	C₄×D₄×C₆₇	—	2	1	no	—
236	C₄×D₄×C₆₇	C₂³	1	2	yes	—
237	C₄×D₄×C₆₇	C₂³	1	2	yes	—
238	C₄×D₄×C₆₇	C₂³	1	2	yes	—
239	C₄×D₄×C₆₇	C₂³	1	2	yes	—
240	C₄×D₄×C₆₇	C₂³	1	2	yes	—
241	C₄×D₄×C₆₇	C₂³	1	2	yes	—
242	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₇	C₂³	1	2	yes	—
244	C₄×D₄×C₆₇	C₂³	1	2	yes	—
245	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
246	#117×C₆₇	—	2	2	no	—
247	#117×C₆₇	—	2	2	no	—
248	#117×C₆₇	—	2	2	no	—
249	#117×C₆₇	—	2	1	no	—
250	#117×C₆₇	C₂³	1	1	yes	characteristic
251	#117×C₆₇	C₂³	1	1	yes	characteristic
252	#117×C₆₇	C₂³	1	1	yes	characteristic
253	#117×C₆₇	C₂³	1	1	yes	characteristic
254	#117×C₆₇	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
256	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
257	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
258	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
260	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
261	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
262	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
263	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
265	C₂×C₄²×C₆₇	—	2	1	no	—
266	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
267	#107×C₆₇	C₂³	1	1	yes	characteristic
268	#107×C₆₇	C₂³	1	2	yes	—
269	#107×C₆₇	C₂³	1	1	yes	characteristic
270	#107×C₆₇	C₂³	1	1	yes	characteristic
271	#107×C₆₇	C₂³	1	1	yes	characteristic
272	#106×C₆₇	C₂³	1	1	yes	characteristic
273	#106×C₆₇	C₂³	1	2	yes	—
274	#106×C₆₇	C₂³	1	1	yes	characteristic
275	#106×C₆₇	C₂³	1	1	yes	characteristic
276	#106×C₆₇	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
278	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
279	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
285	#103×C₆₇	C₂³	1	1	yes	characteristic
286	#103×C₆₇	C₂³	1	1	yes	characteristic
287	#103×C₆₇	C₂³	1	2	yes	—
288	#103×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	1	yes	characteristic
291	#103×C₆₇	C₂³	1	1	yes	characteristic
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	2	yes	—
296	#102×C₆₇	C₂³	1	1	yes	characteristic
297	#102×C₆₇	C₂³	1	1	yes	characteristic
298	#102×C₆₇	C₂³	1	2	yes	—
299	#102×C₆₇	C₂³	1	2	yes	—
300	#102×C₆₇	C₂³	1	2	yes	—
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	1	yes	characteristic
303	#102×C₆₇	C₂³	1	1	yes	characteristic
304	#102×C₆₇	C₂³	1	2	yes	—
305	#102×C₆₇	C₂³	1	2	yes	—
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	2	yes	—
308	#102×C₆₇	C₂³	1	2	yes	—
309	#97×C₆₇	C₂³	1	2	yes	—
310	#97×C₆₇	C₂³	1	2	yes	—
311	#97×C₆₇	C₂³	1	2	yes	—
312	C₄×C₈×C₆₇	C₂³	1	2	yes	—
313	C₄×C₈×C₆₇	C₂³	1	2	yes	—
314	C₄×C₈×C₆₇	C₂³	1	2	yes	—
315	C₂⁴×C₆₇	—	2	1	no	—
316	C₂⁴×C₆₇	—	2	1	no	—
317	#41×C₆₇	—	2	2	no	—
318	#41×C₆₇	—	2	2	no	—
319	C₂×Q₈×C₆₇	—	2	1	no	—
320	C₂×Q₈×C₆₇	—	2	1	no	—
321	C₂×Q₈×C₆₇	—	2	1	no	—
322	C₂×Q₈×C₆₇	—	2	2	no	—
323	C₂×Q₈×C₆₇	—	2	2	no	—
324	C₂×Q₈×C₆₇	—	2	2	no	—
325	C₂×Q₈×C₆₇	—	2	2	no	—
326	C₂×Q₈×C₆₇	—	8	4	no	—
327	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
328	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
329	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₆₇	—	2	1	no	—
332	C₂×D₄×C₆₇	—	2	1	no	—
333	C₂×D₄×C₆₇	—	2	1	no	—
334	C₂×D₄×C₆₇	—	2	2	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	2	no	—
337	C₂×D₄×C₆₇	—	2	2	no	—
338	C₂×D₄×C₆₇	—	2	2	no	—
339	C₂×D₄×C₆₇	#41	1	4	yes	—
340	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
341	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₆₇	—	2	1	no	—
344	C₂²×C₄×C₆₇	—	2	1	no	—
345	C₂²×C₄×C₆₇	—	2	1	no	—
346	C₂²×C₄×C₆₇	—	2	2	no	—
347	C₂²×C₄×C₆₇	—	2	1	no	—
348	C₂²×C₄×C₆₇	—	2	1	no	—
349	C₂²×C₄×C₆₇	—	2	2	no	—
350	C₂²×C₄×C₆₇	—	2	2	no	—
351	C₂²×C₄×C₆₇	—	2	2	no	—
352	C₂²×C₄×C₆₇	—	2	2	no	—
353	C₂²×C₄×C₆₇	—	2	2	no	—
354	C₂²×C₄×C₆₇	—	2	2	no	—
355	C₂²×C₄×C₆₇	—	2	2	no	—
356	C₂²×C₄×C₆₇	—	8	2	no	—
357	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
360	SD₁₆×C₆₇	—	2	4	no	—
361	SD₁₆×C₆₇	—	2	4	no	—
362	SD₁₆×C₆₇	—	2	4	no	—
363	D₈×C₆₇	—	2	4	no	—
364	D₈×C₆₇	—	2	4	no	—
365	D₈×C₆₇	—	2	4	no	—
366	M₁₆×C₆₇	—	2	2	no	—
367	M₁₆×C₆₇	—	2	2	no	—
368	C₂×C₈×C₆₇	—	2	2	no	—
369	C₂×C₈×C₆₇	—	2	2	no	—
370	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
371	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
374	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₆₇	—	2	1	no	—
377	C₄⋊C₄×C₆₇	—	2	1	no	—
378	C₄⋊C₄×C₆₇	—	2	1	no	—
379	C₄⋊C₄×C₆₇	—	2	2	no	—
380	C₄⋊C₄×C₆₇	—	2	2	no	—
381	C₄⋊C₄×C₆₇	—	2	2	no	—
382	C₄⋊C₄×C₆₇	—	2	2	no	—
383	C₄⋊C₄×C₆₇	—	2	2	no	—
384	C₄⋊C₄×C₆₇	—	2	2	no	—
385	C₄⋊C₄×C₆₇	—	2	1	no	—
386	C₄⋊C₄×C₆₇	—	2	1	no	—
387	C₄⋊C₄×C₆₇	—	2	1	no	—
388	C₄⋊C₄×C₆₇	—	2	2	no	—
389	C₄⋊C₄×C₆₇	—	2	2	no	—
390	C₄⋊C₄×C₆₇	—	2	2	no	—
391	C₄⋊C₄×C₆₇	—	2	2	no	—
392	C₄⋊C₄×C₆₇	—	2	1	no	—
393	C₄⋊C₄×C₆₇	—	2	1	no	—
394	C₄⋊C₄×C₆₇	—	2	1	no	—
395	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₆₇	—	2	1	no	—
413	C₂²⋊C₄×C₆₇	—	2	1	no	—
414	C₂²⋊C₄×C₆₇	—	2	1	no	—
415	C₂²⋊C₄×C₆₇	—	2	2	no	—
416	C₂²⋊C₄×C₆₇	—	2	2	no	—
417	C₂²⋊C₄×C₆₇	—	2	2	no	—
418	C₂²⋊C₄×C₆₇	—	2	2	no	—
419	C₂²⋊C₄×C₆₇	—	2	2	no	—
420	C₂²⋊C₄×C₆₇	—	2	2	no	—
421	C₂²⋊C₄×C₆₇	—	2	2	no	—
422	C₂²⋊C₄×C₆₇	—	2	2	no	—
423	C₂²⋊C₄×C₆₇	—	2	2	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	1	no	—
428	C₂²⋊C₄×C₆₇	—	2	1	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	2	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	no	—
433	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
435	C₄²×C₆₇	—	2	1	no	—
436	C₄²×C₆₇	—	2	1	no	—
437	C₄²×C₆₇	—	2	1	no	—
438	C₄²×C₆₇	—	2	2	no	—
439	C₄²×C₆₇	—	2	2	no	—
440	C₄²×C₆₇	—	2	1	no	—
441	C₄²×C₆₇	—	2	1	no	—
442	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
445	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
446	C₄²×C₆₇	C₂⁴	1	2	yes	—
447	C₄²×C₆₇	C₂⁴	1	2	yes	—
448	C₂³×C₆₇	—	2	2	no	—
449	C₂³×C₆₇	—	2	4	no	—
450	C₂³×C₆₇	—	2	2	no	—
451	C₂³×C₆₇	—	2	1	no	—
452	C₂³×C₆₇	—	4	2	no	—
453	C₂³×C₆₇	—	8	1	no	—
454	C₂³×C₆₇	—	8	1	no	—
455	C₂³×C₆₇	—	8	1	no	—
456	C₂³×C₆₇	—	8	1	no	—
457	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
458	Q₈×C₆₇	—	2	2	no	—
459	Q₈×C₆₇	—	2	1	no	—
460	Q₈×C₆₇	—	2	2	no	—
461	Q₈×C₆₇	—	2	1	no	—
462	Q₈×C₆₇	—	4	2	no	—
463	Q₈×C₆₇	—	4	2	no	—
464	Q₈×C₆₇	—	4	2	no	—
465	Q₈×C₆₇	—	4	2	no	—
466	Q₈×C₆₇	—	8	1	no	—
467	Q₈×C₆₇	—	8	2	no	—
468	Q₈×C₆₇	—	8	2	no	—
469	D₄×C₆₇	—	2	4	no	—
470	D₄×C₆₇	—	2	2	no	—
471	D₄×C₆₇	—	2	1	no	—
472	D₄×C₆₇	—	2	2	no	—
473	D₄×C₆₇	—	2	2	no	—
474	D₄×C₆₇	—	2	1	no	—
475	D₄×C₆₇	—	4	2	no	—
476	D₄×C₆₇	—	4	2	no	—
477	D₄×C₆₇	—	8	2	no	—
478	D₄×C₆₇	—	8	2	no	—
479	D₄×C₆₇	C₂×#41	1	4	yes	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	1	no	—
482	C₂×C₄×C₆₇	—	2	2	no	—
483	C₂×C₄×C₆₇	—	2	1	no	—
484	C₂×C₄×C₆₇	—	2	1	no	—
485	C₂×C₄×C₆₇	—	2	1	no	—
486	C₂×C₄×C₆₇	—	2	1	no	—
487	C₂×C₄×C₆₇	—	2	1	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	4	1	no	—
490	C₂×C₄×C₆₇	—	4	1	no	—
491	C₂×C₄×C₆₇	—	4	4	no	—
492	C₂×C₄×C₆₇	—	4	2	no	—
493	C₂×C₄×C₆₇	—	4	2	no	—
494	C₂×C₄×C₆₇	—	8	1	no	—
495	C₂×C₄×C₆₇	—	8	2	no	—
496	C₂×C₄×C₆₇	—	8	2	no	—
497	C₂×C₄×C₆₇	—	8	2	no	—
498	C₂×C₄×C₆₇	—	8	1	no	—
499	C₂×C₄×C₆₇	—	8	2	no	—
500	C₂×C₄×C₆₇	—	8	2	no	—
501	C₂×C₄×C₆₇	—	8	2	no	—
502	C₂×C₄×C₆₇	—	8	2	no	—
503	C₂×C₄×C₆₇	—	8	1	no	—
504	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
514	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
515	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
516	C₈×C₆₇	—	2	1	no	—
517	C₈×C₆₇	—	2	1	no	—
518	C₈×C₆₇	—	2	1	no	—
519	C₈×C₆₇	—	2	1	no	—
520	C₈×C₆₇	—	2	2	no	—
521	C₈×C₆₇	—	2	2	no	—
522	C₂²×C₆₇	—	2	1	no	—
523	C₂²×C₆₇	—	2	1	no	—
524	C₂²×C₆₇	—	2	4	no	—
525	C₂²×C₆₇	—	4	2	no	—
526	C₂²×C₆₇	—	4	2	no	—
527	C₂²×C₆₇	—	4	1	no	—
528	C₂²×C₆₇	—	4	2	no	—
529	C₂²×C₆₇	—	4	1	no	—
530	C₂²×C₆₇	—	4	2	no	—
531	C₂²×C₆₇	—	4	1	no	—
532	C₂²×C₆₇	—	4	2	no	—
533	C₂²×C₆₇	—	8	4	no	—
534	C₂²×C₆₇	—	16	2	no	—
535	C₂²×C₆₇	#548	1	2	yes	—
536	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
537	C₄×C₆₇	—	2	1	no	—
538	C₄×C₆₇	—	2	1	no	—
539	C₄×C₆₇	—	2	2	no	—
540	C₄×C₆₇	—	2	2	no	—
541	C₄×C₆₇	—	2	1	no	—
542	C₄×C₆₇	—	2	1	no	—
543	C₄×C₆₇	—	2	2	no	—
544	C₄×C₆₇	—	2	2	no	—
545	C₄×C₆₇	—	4	1	no	—
546	C₄×C₆₇	—	4	1	no	—
547	C₄×C₆₇	—	4	1	no	—
548	C₄×C₆₇	—	4	2	no	—
549	C₄×C₆₇	—	4	1	no	—
550	C₄×C₆₇	—	4	1	no	—
551	C₄×C₆₇	—	4	1	no	—
552	C₄×C₆₇	—	4	1	no	—
553	C₄×C₆₇	—	4	2	no	—
554	C₄×C₆₇	#548	1	2	yes	—
555	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
556	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
557	#61343	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
558	C₂×C₆₇	—	2	2	no	—
559	C₂×C₆₇	—	4	4	no	—
560	C₂×C₆₇	—	8	1	no	—
561	C₂×C₆₇	—	8	2	no	—
562	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
563	C₂×C₆₇	#3584	1	1	yes	characteristic
564	C₂×C₆₇	#3585	1	1	yes	characteristic
565	#3510	C₂×C₆₇	1	1	yes	characteristic, complemented
566	#3501	C₂×C₆₇	1	1	yes	characteristic, complemented
567	#3376	C₂×C₆₇	1	2	yes	complemented
568	#3376	C₂×C₆₇	1	2	yes	complemented
569	#3373	C₂×C₆₇	1	2	yes	complemented
570	#3370	C₂×C₆₇	1	2	yes	complemented
571	#3370	C₂×C₆₇	1	2	yes	complemented
572	#3367	C₂×C₆₇	1	2	yes	complemented
573	#3361	C₂×C₆₇	1	2	yes	complemented
574	#3360	C₂×C₆₇	1	2	yes	complemented
575	#3140	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#3137	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#3136	C₂×C₆₇	1	1	yes	characteristic, complemented
578	#3082	C₂×C₆₇	1	1	yes	characteristic, complemented
579	#3081	C₂×C₆₇	1	1	yes	characteristic, complemented
580	#3076	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#3042	C₂×C₆₇	1	1	yes	characteristic, complemented
582	#3041	C₂×C₆₇	1	1	yes	characteristic
583	C₂×#463	C₂×C₆₇	1	1	yes	characteristic, complemented
584	#2962	C₂×C₆₇	1	1	yes	characteristic, complemented
585	#2949	C₂×C₆₇	1	1	yes	characteristic, complemented
586	#2948	C₂×C₆₇	1	1	yes	characteristic, complemented
587	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
588	C₆₇	#61343	1	1	yes	characteristic, direct product factor, Sylow
589	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
590	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
591	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
592	#559	C₂²×C₆₇	1	2	yes	complemented
593	#559	C₂²×C₆₇	1	2	yes	complemented
594	#556	C₂²×C₆₇	1	2	yes	complemented
595	#556	C₂²×C₆₇	1	2	yes	complemented
596	#554	—	2	1	no	—
597	#554	—	2	1	no	—
598	#554	—	2	1	no	—
599	#554	C₂²×C₆₇	1	2	yes	complemented
600	#554	C₂²×C₆₇	1	2	yes	complemented
601	#554	C₂²×C₆₇	1	2	yes	complemented
602	#551	—	2	2	no	—
603	#551	—	2	2	no	—
604	D₄×Q₈	—	2	1	no	—
605	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
606	#544	C₂²×C₆₇	1	1	yes	characteristic
607	#544	C₂²×C₆₇	1	1	yes	characteristic
608	#543	—	2	2	no	—
609	#542	—	2	1	no	—
610	#542	—	2	1	no	—
611	#536	C₂²×C₆₇	1	1	yes	characteristic
612	#535	C₂²×C₆₇	1	1	yes	characteristic
613	#533	C₂²×C₆₇	1	1	yes	characteristic
614	#533	C₂²×C₆₇	1	1	yes	characteristic
615	#529	—	2	1	no	—
616	#529	—	2	1	no	—
617	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
618	C₂×C₂²⋊Q₈	—	2	2	no	—
619	#519	C₂²×C₆₇	1	1	yes	characteristic
620	#518	C₂²×C₆₇	1	1	yes	characteristic
621	#518	C₂²×C₆₇	1	1	yes	characteristic
622	#518	C₂²×C₆₇	1	1	yes	characteristic
623	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
624	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
625	#491	C₂²×C₆₇	1	2	yes	complemented
626	#490	C₂²×C₆₇	1	2	yes	complemented
627	#489	C₂²×C₆₇	1	2	yes	complemented
628	#489	C₂²×C₆₇	1	2	yes	complemented
629	#489	C₂²×C₆₇	1	2	yes	complemented
630	#489	C₂²×C₆₇	1	2	yes	complemented
631	#488	C₂²×C₆₇	1	2	yes	complemented
632	#488	C₂²×C₆₇	1	2	yes	complemented
633	#488	C₂²×C₆₇	1	2	yes	complemented
634	#488	C₂²×C₆₇	1	2	yes	complemented
635	#487	C₂²×C₆₇	1	2	yes	complemented
636	#486	C₂²×C₆₇	1	2	yes	complemented
637	#479	C₂²×C₆₇	1	1	yes	characteristic, complemented
638	#479	C₂²×C₆₇	1	1	yes	characteristic, complemented
639	#479	C₂²×C₆₇	1	2	yes	complemented
640	#479	C₂²×C₆₇	1	2	yes	complemented
641	#478	C₂²×C₆₇	1	1	yes	characteristic, complemented
642	#478	C₂²×C₆₇	1	1	yes	characteristic, complemented
643	#478	C₂²×C₆₇	1	2	yes	complemented
644	#478	C₂²×C₆₇	1	2	yes	complemented
645	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
646	#477	C₂²×C₆₇	1	2	yes	complemented
647	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
648	#476	C₂²×C₆₇	1	2	yes	complemented
649	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
650	#475	C₂²×C₆₇	1	2	yes	complemented
651	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
652	#474	C₂²×C₆₇	1	2	yes	complemented
653	#463	C₂²×C₆₇	1	2	yes	—
654	#463	C₂²×C₆₇	1	2	yes	—
655	#463	C₂²×C₆₇	1	2	yes	—
656	#463	C₂²×C₆₇	1	2	yes	—
657	#463	C₂²×C₆₇	1	2	yes	—
658	#463	C₂²×C₆₇	1	2	yes	—
659	#463	C₂²×C₆₇	1	2	yes	complemented
660	#463	C₂²×C₆₇	1	2	yes	complemented
661	#461	C₂²×C₆₇	1	2	yes	complemented
662	#461	C₂²×C₆₇	1	2	yes	complemented
663	#459	C₂²×C₆₇	1	2	yes	—
664	#459	C₂²×C₆₇	1	2	yes	—
665	#446	C₂²×C₆₇	1	2	yes	complemented
666	#446	C₂²×C₆₇	1	2	yes	complemented
667	#446	C₂²×C₆₇	1	2	yes	complemented
668	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
669	#442	C₂²×C₆₇	1	2	yes	—
670	#442	C₂²×C₆₇	1	2	yes	—
671	#442	C₂²×C₆₇	1	2	yes	complemented
672	#440	C₂²×C₆₇	1	2	yes	complemented
673	#440	C₂²×C₆₇	1	2	yes	complemented
674	#440	C₂²×C₆₇	1	2	yes	complemented
675	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
676	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
677	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
678	C₄×D₈	C₂²×C₆₇	1	2	yes	—
679	C₄×D₈	C₂²×C₆₇	1	2	yes	—
680	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
681	#428	C₂²×C₆₇	1	1	yes	characteristic
682	#427	C₂²×C₆₇	1	1	yes	characteristic
683	#427	C₂²×C₆₇	1	1	yes	characteristic
684	#424	C₂²×C₆₇	1	1	yes	characteristic
685	#424	C₂²×C₆₇	1	1	yes	characteristic
686	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
687	#419	C₂²×C₆₇	1	1	yes	characteristic
688	#419	C₂²×C₆₇	1	1	yes	characteristic
689	#418	C₂²×C₆₇	1	1	yes	characteristic
690	#418	C₂²×C₆₇	1	1	yes	characteristic
691	#418	C₂²×C₆₇	1	1	yes	characteristic
692	#417	C₂²×C₆₇	1	1	yes	characteristic
693	#416	C₂²×C₆₇	1	1	yes	characteristic
694	#416	C₂²×C₆₇	1	1	yes	characteristic
695	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
696	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
697	#405	C₂²×C₆₇	1	1	yes	characteristic
698	#405	C₂²×C₆₇	1	1	yes	characteristic
699	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
700	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
701	C₂²×Q₈	—	2	2	no	—
702	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
703	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
704	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
705	C₂³×C₄	—	2	1	no	—
706	AGL(1,ℤ/8)	—	2	4	no	—
707	C₂×SD₁₆	—	2	4	no	—
708	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
709	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
711	C₂×D₈	—	2	4	no	—
712	C₂×D₈	C₂³×C₆₇	1	2	yes	—
713	C₂×D₈	C₂³×C₆₇	1	2	yes	—
714	C₂×D₈	C₂³×C₆₇	1	2	yes	—
715	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
716	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
717	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
718	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
719	C₄⋊Q₈	—	2	1	no	—
720	C₄⋊Q₈	—	2	1	no	—
721	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
722	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
724	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
727	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
728	#127	C₂³×C₆₇	1	2	yes	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#125	—	2	1	no	—
734	#125	—	2	1	no	—
735	#125	D₄×C₆₇	1	1	yes	characteristic
736	#125	D₄×C₆₇	1	1	yes	characteristic
737	#125	C₂³×C₆₇	1	1	yes	characteristic
738	#125	C₂³×C₆₇	1	1	yes	characteristic
739	#125	C₂³×C₆₇	1	2	yes	—
740	#125	C₂³×C₆₇	1	2	yes	—
741	#124	—	2	2	no	—
742	#124	—	2	2	no	—
743	#124	—	2	1	no	—
744	#124	—	2	1	no	—
745	#124	C₂³×C₆₇	1	2	yes	—
746	#124	C₂³×C₆₇	1	2	yes	—
747	#124	C₂³×C₆₇	1	2	yes	—
748	#124	C₂³×C₆₇	1	2	yes	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
775	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
776	#121	—	2	1	no	—
777	#121	—	2	1	no	—
778	#120	—	2	2	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
786	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
787	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
788	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	C₂³×C₆₇	1	2	yes	—
802	C₄×D₄	C₂³×C₆₇	1	2	yes	—
803	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₆₇	1	2	yes	—
806	C₄×D₄	C₂³×C₆₇	1	2	yes	—
807	C₄×D₄	C₂³×C₆₇	1	2	yes	—
808	C₄×D₄	C₂³×C₆₇	1	2	yes	—
809	C₄×D₄	C₂³×C₆₇	1	2	yes	—
810	C₄×D₄	C₂³×C₆₇	1	2	yes	—
811	#117	—	2	2	no	—
812	#117	—	2	2	no	—
813	#117	—	2	2	no	—
814	#117	—	2	1	no	—
815	#117	C₂³×C₆₇	1	1	yes	characteristic
816	#117	C₂³×C₆₇	1	1	yes	characteristic
817	#117	C₂³×C₆₇	1	1	yes	characteristic
818	#117	C₂³×C₆₇	1	1	yes	characteristic
819	#117	C₂³×C₆₇	1	1	yes	characteristic
820	C₂×C₄⋊C₄	—	2	2	no	—
821	C₂×C₄⋊C₄	—	2	2	no	—
822	C₂×C₄⋊C₄	—	2	2	no	—
823	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
824	C₂×C₂²⋊C₄	—	2	1	no	—
825	C₂×C₂²⋊C₄	—	2	1	no	—
826	C₂×C₂²⋊C₄	—	2	1	no	—
827	C₂×C₂²⋊C₄	—	2	2	no	—
828	C₂×C₂²⋊C₄	—	2	2	no	—
829	C₂×C₂²⋊C₄	—	2	2	no	—
830	C₂×C₄²	—	2	1	no	—
831	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
832	#107	C₂³×C₆₇	1	1	yes	characteristic
833	#107	C₂³×C₆₇	1	1	yes	characteristic
834	#107	C₂³×C₆₇	1	1	yes	characteristic
835	#107	C₂³×C₆₇	1	1	yes	characteristic
836	#107	C₂³×C₆₇	1	2	yes	—
837	#106	C₂³×C₆₇	1	1	yes	characteristic
838	#106	C₂³×C₆₇	1	1	yes	characteristic
839	#106	C₂³×C₆₇	1	1	yes	characteristic
840	#106	C₂³×C₆₇	1	1	yes	characteristic
841	#106	C₂³×C₆₇	1	2	yes	—
842	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
847	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
848	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
849	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
850	#103	C₂³×C₆₇	1	2	yes	—
851	#103	C₂³×C₆₇	1	2	yes	—
852	#103	C₂³×C₆₇	1	1	yes	characteristic
853	#103	C₂³×C₆₇	1	1	yes	characteristic
854	#103	C₂³×C₆₇	1	1	yes	characteristic
855	#103	C₂³×C₆₇	1	1	yes	characteristic
856	#103	C₂³×C₆₇	1	2	yes	—
857	#103	C₂³×C₆₇	1	2	yes	—
858	#103	C₂³×C₆₇	1	2	yes	—
859	#103	C₂³×C₆₇	1	2	yes	—
860	#103	C₂³×C₆₇	1	2	yes	—
861	#102	C₂³×C₆₇	1	2	yes	—
862	#102	C₂³×C₆₇	1	2	yes	—
863	#102	C₂³×C₆₇	1	1	yes	characteristic
864	#102	C₂³×C₆₇	1	1	yes	characteristic
865	#102	C₂³×C₆₇	1	1	yes	characteristic
866	#102	C₂³×C₆₇	1	1	yes	characteristic
867	#102	C₂³×C₆₇	1	2	yes	—
868	#102	C₂³×C₆₇	1	2	yes	—
869	#102	C₂³×C₆₇	1	2	yes	—
870	#102	C₂³×C₆₇	1	2	yes	—
871	#102	C₂³×C₆₇	1	2	yes	—
872	#102	C₂³×C₆₇	1	2	yes	—
873	#102	C₂³×C₆₇	1	2	yes	—
874	#97	C₂³×C₆₇	1	2	yes	—
875	#97	C₂³×C₆₇	1	2	yes	—
876	#97	C₂³×C₆₇	1	2	yes	—
877	C₄×C₈	C₂³×C₆₇	1	2	yes	—
878	C₄×C₈	C₂³×C₆₇	1	2	yes	—
879	C₄×C₈	C₂³×C₆₇	1	2	yes	—
880	C₂⁴	—	2	1	no	—
881	C₂⁴	—	2	1	no	—
882	#41	—	2	2	no	—
883	#41	—	2	2	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	2	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	2	no	—
891	C₂×Q₈	—	8	4	no	—
892	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
893	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
894	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
895	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	#41×C₆₇	1	4	yes	—
905	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
906	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
907	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	8	2	no	—
922	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
923	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
925	SD₁₆	—	2	4	no	—
926	SD₁₆	—	2	4	no	—
927	SD₁₆	—	2	4	no	—
928	D₈	—	2	4	no	—
929	D₈	—	2	4	no	—
930	D₈	—	2	4	no	—
931	M₁₆	—	2	2	no	—
932	M₁₆	—	2	2	no	—
933	C₂×C₈	—	2	2	no	—
934	C₂×C₈	—	2	2	no	—
935	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
936	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
939	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
962	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
963	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
964	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
965	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
966	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
967	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1008	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1010	C₄²	C₂⁴×C₆₇	1	2	yes	—
1011	C₄²	C₂⁴×C₆₇	1	2	yes	—
1012	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1013	C₂³	—	2	2	no	—
1014	C₂³	—	2	4	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	4	2	no	—
1018	C₂³	—	8	1	no	—
1019	C₂³	—	8	1	no	—
1020	C₂³	—	8	1	no	—
1021	C₂³	—	8	1	no	—
1022	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	4	2	no	—
1029	Q₈	—	4	2	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	8	2	no	—
1032	Q₈	—	8	2	no	—
1033	Q₈	—	8	1	no	—
1034	D₄	—	2	4	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	8	2	no	—
1043	D₄	—	8	2	no	—
1044	D₄	C₂×#41×C₆₇	1	4	yes	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	4	1	no	—
1055	C₂×C₄	—	4	1	no	—
1056	C₂×C₄	—	4	4	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	1	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	—	8	1	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	—	8	1	no	—
1069	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1077	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1078	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1079	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1080	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1081	C₈	—	2	1	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	2	no	—
1086	C₈	—	2	2	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	4	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	8	4	no	—
1099	C₂²	—	16	2	no	—
1100	C₂²	#548×C₆₇	1	2	yes	—
1101	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	#548×C₆₇	1	2	yes	—
1120	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1121	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1122	C₂	—	2	2	no	—
1123	C₂	—	4	4	no	—
1124	C₂	—	8	2	no	—
1125	C₂	—	8	1	no	—
1126	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
1127	C₂	C₆₇×#3584	1	1	yes	characteristic
1128	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3041	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #533×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3510	C₂	semidirect
2. C₆₇×#3501	C₂	semidirect
3. C₆₇×#3376	C₂	semidirect
4. C₆₇×#3376	C₂	semidirect
5. C₆₇×#3373	C₂	semidirect
6. C₆₇×#3370	C₂	semidirect
7. C₆₇×#3370	C₂	semidirect
8. C₆₇×#3367	C₂	semidirect
9. C₆₇×#3361	C₂	semidirect
10. C₆₇×#3360	C₂	semidirect
11. C₆₇×#3140	C₂	semidirect
12. C₆₇×#3137	C₂	semidirect
13. C₆₇×#3136	C₂	semidirect
14. C₆₇×#3082	C₂	semidirect
15. C₆₇×#3081	C₂	semidirect
16. C₆₇×#3076	C₂	semidirect
17. C₆₇×#3042	C₂	semidirect
19. C₂×#463×C₆₇	C₂	semidirect
20. C₆₇×#2962	C₂	semidirect
21. C₆₇×#2949	C₂	semidirect
22. C₆₇×#2948	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
27. #559×C₆₇	C₂²	semidirect
28. #559×C₆₇	C₂²	semidirect
29. #556×C₆₇	C₂²	semidirect
30. #556×C₆₇	C₂²	semidirect
34. #554×C₆₇	C₂²	semidirect
35. #554×C₆₇	C₂²	semidirect
36. #554×C₆₇	C₂²	semidirect
40. D₄×Q₈×C₆₇	C₂²	semidirect
60. #491×C₆₇	C₂²	semidirect
61. #490×C₆₇	C₂²	semidirect
62. #489×C₆₇	C₂²	semidirect
63. #489×C₆₇	C₂²	semidirect
64. #489×C₆₇	C₂²	semidirect
65. #489×C₆₇	C₂²	semidirect
66. #488×C₆₇	C₂²	semidirect
67. #488×C₆₇	C₂²	semidirect
68. #488×C₆₇	C₂²	semidirect
69. #488×C₆₇	C₂²	semidirect
70. #487×C₆₇	C₂²	semidirect
71. #486×C₆₇	C₂²	semidirect
72. #479×C₆₇	C₂²	semidirect
73. #479×C₆₇	C₂²	semidirect
74. #479×C₆₇	C₂²	semidirect
75. #479×C₆₇	C₂²	semidirect
76. #478×C₆₇	C₂²	semidirect
77. #478×C₆₇	C₂²	semidirect
78. #478×C₆₇	C₂²	semidirect
79. #478×C₆₇	C₂²	semidirect
80. #477×C₆₇	C₂²	semidirect
81. #477×C₆₇	C₂²	semidirect
82. #476×C₆₇	C₂²	semidirect
83. #476×C₆₇	C₂²	semidirect
84. #475×C₆₇	C₂²	semidirect
85. #475×C₆₇	C₂²	semidirect
86. #474×C₆₇	C₂²	semidirect
87. #474×C₆₇	C₂²	semidirect
94. #463×C₆₇	C₂²	semidirect
95. #463×C₆₇	C₂²	semidirect
96. #461×C₆₇	C₂²	semidirect
97. #461×C₆₇	C₂²	semidirect
100. #446×C₆₇	C₂²	semidirect
101. #446×C₆₇	C₂²	semidirect
102. #446×C₆₇	C₂²	semidirect
103. C₈×Q₈×C₆₇	C₂²	semidirect
106. #442×C₆₇	C₂²	semidirect
107. #440×C₆₇	C₂²	semidirect
108. #440×C₆₇	C₂²	semidirect
109. #440×C₆₇	C₂²	semidirect
110. C₄×SD₁₆×C₆₇	C₂²	semidirect
111. C₄×SD₁₆×C₆₇	C₂²	semidirect
112. C₄×SD₁₆×C₆₇	C₂²	semidirect
115. C₄×D₈×C₆₇	C₂²	semidirect
557. #61343	C₆₇	direct (N × H)
565. #3510	C₂×C₆₇	semidirect
566. #3501	C₂×C₆₇	semidirect
567. #3376	C₂×C₆₇	semidirect
568. #3376	C₂×C₆₇	semidirect
569. #3373	C₂×C₆₇	semidirect
570. #3370	C₂×C₆₇	semidirect
571. #3370	C₂×C₆₇	semidirect
572. #3367	C₂×C₆₇	semidirect
573. #3361	C₂×C₆₇	semidirect
574. #3360	C₂×C₆₇	semidirect
575. #3140	C₂×C₆₇	semidirect
576. #3137	C₂×C₆₇	semidirect
577. #3136	C₂×C₆₇	semidirect
578. #3082	C₂×C₆₇	semidirect
579. #3081	C₂×C₆₇	semidirect
580. #3076	C₂×C₆₇	semidirect
581. #3042	C₂×C₆₇	semidirect
583. C₂×#463	C₂×C₆₇	semidirect
584. #2962	C₂×C₆₇	semidirect
585. #2949	C₂×C₆₇	semidirect
586. #2948	C₂×C₆₇	semidirect
587. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
588. C₆₇	#61343	direct (N × H)
592. #559	C₂²×C₆₇	semidirect
593. #559	C₂²×C₆₇	semidirect
594. #556	C₂²×C₆₇	semidirect
595. #556	C₂²×C₆₇	semidirect
599. #554	C₂²×C₆₇	semidirect
600. #554	C₂²×C₆₇	semidirect
601. #554	C₂²×C₆₇	semidirect
605. D₄×Q₈	C₂²×C₆₇	semidirect
625. #491	C₂²×C₆₇	semidirect
626. #490	C₂²×C₆₇	semidirect
627. #489	C₂²×C₆₇	semidirect
628. #489	C₂²×C₆₇	semidirect
629. #489	C₂²×C₆₇	semidirect
630. #489	C₂²×C₆₇	semidirect
631. #488	C₂²×C₆₇	semidirect
632. #488	C₂²×C₆₇	semidirect
633. #488	C₂²×C₆₇	semidirect
634. #488	C₂²×C₆₇	semidirect
635. #487	C₂²×C₆₇	semidirect
636. #486	C₂²×C₆₇	semidirect
637. #479	C₂²×C₆₇	semidirect
638. #479	C₂²×C₆₇	semidirect
639. #479	C₂²×C₆₇	semidirect
640. #479	C₂²×C₆₇	semidirect
641. #478	C₂²×C₆₇	semidirect
642. #478	C₂²×C₆₇	semidirect
643. #478	C₂²×C₆₇	semidirect
644. #478	C₂²×C₆₇	semidirect
645. #477	C₂²×C₆₇	semidirect
646. #477	C₂²×C₆₇	semidirect
647. #476	C₂²×C₆₇	semidirect
648. #476	C₂²×C₆₇	semidirect
649. #475	C₂²×C₆₇	semidirect
650. #475	C₂²×C₆₇	semidirect
651. #474	C₂²×C₆₇	semidirect
652. #474	C₂²×C₆₇	semidirect
659. #463	C₂²×C₆₇	semidirect
660. #463	C₂²×C₆₇	semidirect
661. #461	C₂²×C₆₇	semidirect
662. #461	C₂²×C₆₇	semidirect
665. #446	C₂²×C₆₇	semidirect
666. #446	C₂²×C₆₇	semidirect
667. #446	C₂²×C₆₇	semidirect
668. C₈×Q₈	C₂²×C₆₇	semidirect
671. #442	C₂²×C₆₇	semidirect
672. #440	C₂²×C₆₇	semidirect
673. #440	C₂²×C₆₇	semidirect
674. #440	C₂²×C₆₇	semidirect
675. C₄×SD₁₆	C₂²×C₆₇	semidirect
676. C₄×SD₁₆	C₂²×C₆₇	semidirect
677. C₄×SD₁₆	C₂²×C₆₇	semidirect
680. C₄×D₈	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×#3510	2
C₆₇×#3501	2
C₆₇×#3376	2
C₆₇×#3373	2
C₆₇×#3370	2
C₆₇×#3367	2
C₆₇×#3361	2
C₆₇×#3360	2
C₆₇×#3140	2
C₆₇×#3137	2
C₆₇×#3136	2
C₆₇×#3082	2
C₆₇×#3081	2
C₆₇×#3076	2
C₆₇×#3042	2
C₆₇×#3041	2
C₂×#463×C₆₇	2
C₆₇×#2962	2
C₆₇×#2949	2
C₆₇×#2948	2
C₄×AGL(1,ℤ/8)×C₆₇	2
#61343	67

Subgroups — C67×#61343 #30740594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61343 #30740594