Subgroups — C₆₇×#61554 #30740805

Order 17152.

1876 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3396	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3373	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3354	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3321	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3306	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3304	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3295	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3275	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3274	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3173	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3125	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2946	C₂	1	2	yes	maximal, complemented
23	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
26	#559×C₆₇	—	2	1	no	—
27	#559×C₆₇	C₂²	1	1	yes	characteristic
28	#559×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	Q₈²×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#556×C₆₇	C₂²	1	1	yes	characteristic
31	#555×C₆₇	C₂²	1	2	yes	—
32	#554×C₆₇	—	2	1	no	—
33	#554×C₆₇	C₂²	1	1	yes	characteristic
34	#551×C₆₇	—	2	2	no	—
35	#550×C₆₇	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	#548×C₆₇	—	2	1	no	—
38	#548×C₆₇	C₂²	1	2	yes	complemented
39	#547×C₆₇	—	2	2	no	—
40	#547×C₆₇	C₂²	1	2	yes	complemented
41	#546×C₆₇	—	2	1	no	—
42	#546×C₆₇	C₂²	1	2	yes	—
43	D₄²×C₆₇	C₂²	1	1	yes	characteristic
44	#542×C₆₇	—	2	2	no	—
45	#542×C₆₇	C₂²	1	2	yes	—
46	#542×C₆₇	C₂²	1	2	yes	complemented
47	#538×C₆₇	—	2	2	no	—
48	#532×C₆₇	—	2	1	no	—
49	#532×C₆₇	C₂²	1	1	yes	characteristic
50	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#529×C₆₇	—	2	1	no	—
52	#529×C₆₇	—	2	1	no	—
53	#529×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×#124×C₆₇	—	2	1	no	—
55	#520×C₆₇	C₂²	1	2	yes	complemented
56	#518×C₆₇	C₂²	1	2	yes	—
57	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#498×C₆₇	C₂²	1	2	yes	complemented
60	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#495×C₆₇	C₂²	1	2	yes	complemented
62	#493×C₆₇	C₂²	1	1	yes	characteristic
63	#489×C₆₇	C₂²	1	2	yes	complemented
64	#489×C₆₇	C₂²	1	2	yes	complemented
65	#486×C₆₇	C₂²	1	1	yes	characteristic
66	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#485×C₆₇	C₂²	1	2	yes	complemented
68	#483×C₆₇	C₂²	1	2	yes	complemented
69	#482×C₆₇	C₂²	1	2	yes	complemented
70	#482×C₆₇	C₂²	1	2	yes	complemented
71	#481×C₆₇	C₂²	1	2	yes	—
72	#481×C₆₇	C₂²	1	2	yes	complemented
73	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#476×C₆₇	C₂²	1	1	yes	characteristic
75	#476×C₆₇	C₂²	1	2	yes	—
76	#476×C₆₇	C₂²	1	2	yes	complemented
77	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#475×C₆₇	C₂²	1	2	yes	complemented
79	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#474×C₆₇	C₂²	1	2	yes	complemented
81	#470×C₆₇	C₂²	1	2	yes	complemented
82	#469×C₆₇	C₂²	1	2	yes	—
83	#469×C₆₇	C₂²	1	2	yes	complemented
84	#469×C₆₇	C₂²	1	2	yes	complemented
85	#465×C₆₇	C₂²	1	2	yes	—
86	#465×C₆₇	C₂²	1	2	yes	complemented
87	#464×C₆₇	C₂²	1	2	yes	complemented
88	#463×C₆₇	C₂²	1	2	yes	—
89	#463×C₆₇	C₂²	1	2	yes	complemented
90	#463×C₆₇	C₂²	1	2	yes	complemented
91	#460×C₆₇	C₂²	1	1	yes	characteristic
92	#460×C₆₇	C₂²	1	1	yes	characteristic
93	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#459×C₆₇	C₂²	1	1	yes	characteristic
95	#452×C₆₇	C₂²	1	2	yes	complemented
96	#450×C₆₇	C₂²	1	2	yes	—
97	#449×C₆₇	C₂²	1	2	yes	—
98	#449×C₆₇	C₂²	1	2	yes	—
99	#448×C₆₇	C₂²	1	2	yes	complemented
100	#447×C₆₇	C₂²	1	2	yes	—
101	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#442×C₆₇	C₂²	1	2	yes	—
104	#442×C₆₇	C₂²	1	2	yes	complemented
105	#442×C₆₇	C₂²	1	2	yes	complemented
106	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#440×C₆₇	C₂²	1	1	yes	characteristic
109	#440×C₆₇	C₂²	1	1	yes	characteristic
110	#440×C₆₇	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
119	C₄×D₈×C₆₇	C₂²	1	2	yes	—
120	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
121	#436×C₆₇	C₂²	1	1	yes	characteristic
122	#436×C₆₇	C₂²	1	2	yes	complemented
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
125	#433×C₆₇	C₂²	1	2	yes	complemented
126	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#428×C₆₇	C₂²	1	2	yes	complemented
129	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	#417×C₆₇	C₂²	1	1	yes	characteristic
131	#416×C₆₇	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₇	C₂²	1	2	yes	—
133	#405×C₆₇	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₆₇	—	2	2	no	—
136	C₂×#41×C₆₇	—	2	1	no	—
137	C₂×#41×C₆₇	—	2	1	no	—
138	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×#41×C₆₇	C₂³	1	2	yes	—
140	C₂²×Q₈×C₆₇	—	2	1	no	—
141	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₆₇	—	2	1	no	—
143	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
144	#137×C₆₇	—	2	4	no	—
145	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
146	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₆₇	C₂³	1	2	yes	—
154	C₂×D₈×C₆₇	C₂³	1	2	yes	—
155	C₂×D₈×C₆₇	C₂³	1	2	yes	—
156	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₇	—	2	1	no	—
161	C₄⋊Q₈×C₆₇	—	2	2	no	—
162	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	#127×C₆₇	—	2	1	no	—
167	#127×C₆₇	C₂³	1	1	yes	characteristic
168	#127×C₆₇	C₂³	1	1	yes	characteristic
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#126×C₆₇	—	2	2	no	—
172	#126×C₆₇	D₄	1	2	yes	—
173	#125×C₆₇	—	2	1	no	—
174	#125×C₆₇	D₄	1	1	yes	characteristic
175	#124×C₆₇	—	2	1	no	—
176	#124×C₆₇	—	2	1	no	—
177	#124×C₆₇	—	2	1	no	—
178	#124×C₆₇	—	2	2	no	—
179	#124×C₆₇	—	2	2	no	—
180	#124×C₆₇	—	2	2	no	—
181	#124×C₆₇	—	2	2	no	—
182	#124×C₆₇	—	2	2	no	—
183	#124×C₆₇	—	2	1	no	—
184	#124×C₆₇	—	2	1	no	—
185	#124×C₆₇	D₄	1	1	yes	characteristic
186	#124×C₆₇	C₂³	1	2	yes	—
187	#124×C₆₇	C₂³	1	2	yes	—
188	#123×C₆₇	—	2	2	no	—
189	#123×C₆₇	—	2	2	no	—
190	#123×C₆₇	—	2	2	no	—
191	#123×C₆₇	—	2	2	no	—
192	#123×C₆₇	—	2	2	no	—
193	#123×C₆₇	—	2	2	no	—
194	#123×C₆₇	—	2	2	no	—
195	#123×C₆₇	D₄	1	2	yes	—
196	C₂²⋊Q₈×C₆₇	—	2	1	no	—
197	C₂²⋊Q₈×C₆₇	—	2	2	no	—
198	C₂²⋊Q₈×C₆₇	—	2	2	no	—
199	C₂²⋊Q₈×C₆₇	—	2	2	no	—
200	C₂²⋊Q₈×C₆₇	—	2	2	no	—
201	C₂²⋊Q₈×C₆₇	—	2	2	no	—
202	C₂²⋊Q₈×C₆₇	—	2	2	no	—
203	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
204	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
205	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
206	#121×C₆₇	—	2	2	no	—
207	#121×C₆₇	—	2	2	no	—
208	#121×C₆₇	—	2	1	no	—
209	#121×C₆₇	—	2	1	no	—
210	#121×C₆₇	—	2	1	no	—
211	#121×C₆₇	—	2	2	no	—
212	#121×C₆₇	—	2	2	no	—
213	#121×C₆₇	D₄	1	1	yes	characteristic
214	#121×C₆₇	C₂³	1	2	yes	—
215	#121×C₆₇	C₂³	1	2	yes	—
216	#121×C₆₇	C₂³	1	2	yes	—
217	#121×C₆₇	C₂³	1	2	yes	—
218	#120×C₆₇	—	2	2	no	—
219	#120×C₆₇	—	2	2	no	—
220	C₄×Q₈×C₆₇	—	2	1	no	—
221	C₄×Q₈×C₆₇	—	2	1	no	—
222	C₄×Q₈×C₆₇	—	2	1	no	—
223	C₄×Q₈×C₆₇	—	2	1	no	—
224	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
228	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₆₇	—	2	1	no	—
233	C₄×D₄×C₆₇	—	2	1	no	—
234	C₄×D₄×C₆₇	—	2	1	no	—
235	C₄×D₄×C₆₇	—	2	2	no	—
236	C₄×D₄×C₆₇	—	2	2	no	—
237	C₄×D₄×C₆₇	—	2	1	no	—
238	C₄×D₄×C₆₇	—	2	1	no	—
239	C₄×D₄×C₆₇	—	2	1	no	—
240	C₄×D₄×C₆₇	—	2	2	no	—
241	C₄×D₄×C₆₇	—	2	2	no	—
242	C₄×D₄×C₆₇	—	2	2	no	—
243	C₄×D₄×C₆₇	—	2	1	no	—
244	C₄×D₄×C₆₇	—	2	1	no	—
245	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₇	C₂³	1	2	yes	—
247	C₄×D₄×C₆₇	C₂³	1	2	yes	—
248	C₄×D₄×C₆₇	C₂³	1	2	yes	—
249	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₆₇	C₂³	1	2	yes	—
251	C₄×D₄×C₆₇	C₂³	1	2	yes	—
252	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₆₇	C₂³	1	2	yes	—
254	#117×C₆₇	—	2	2	no	—
255	#117×C₆₇	—	2	2	no	—
256	#117×C₆₇	—	2	1	no	—
257	#117×C₆₇	C₂³	1	1	yes	characteristic
258	#117×C₆₇	C₂³	1	2	yes	—
259	#117×C₆₇	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
262	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
267	C₂×C₄²×C₆₇	—	2	1	no	—
268	C₂×C₄²×C₆₇	—	2	1	no	—
269	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
270	#107×C₆₇	C₂³	1	1	yes	characteristic
271	#107×C₆₇	C₂³	1	2	yes	—
272	#107×C₆₇	C₂³	1	1	yes	characteristic
273	#106×C₆₇	C₂³	1	2	yes	—
274	#106×C₆₇	C₂³	1	2	yes	—
275	#106×C₆₇	C₂³	1	1	yes	characteristic
276	#106×C₆₇	C₂³	1	2	yes	—
277	#106×C₆₇	C₂³	1	2	yes	—
278	#106×C₆₇	C₂³	1	2	yes	—
279	#106×C₆₇	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
284	#103×C₆₇	C₂³	1	2	yes	—
285	#103×C₆₇	C₂³	1	2	yes	—
286	#103×C₆₇	C₂³	1	1	yes	characteristic
287	#103×C₆₇	C₂³	1	2	yes	—
288	#103×C₆₇	C₂³	1	1	yes	characteristic
289	#103×C₆₇	C₂³	1	1	yes	characteristic
290	#103×C₆₇	C₂³	1	1	yes	characteristic
291	#103×C₆₇	C₂³	1	1	yes	characteristic
292	#103×C₆₇	C₂³	1	1	yes	characteristic
293	#102×C₆₇	C₂³	1	2	yes	—
294	#102×C₆₇	C₂³	1	2	yes	—
295	#102×C₆₇	C₂³	1	2	yes	—
296	#102×C₆₇	C₂³	1	2	yes	—
297	#102×C₆₇	C₂³	1	2	yes	—
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	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
307	#97×C₆₇	C₂³	1	2	yes	—
308	#97×C₆₇	C₂³	1	1	yes	characteristic
309	#97×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₇	C₂³	1	2	yes	—
313	C₄×C₈×C₆₇	C₂³	1	2	yes	—
314	C₂⁴×C₆₇	—	2	2	no	—
315	#41×C₆₇	—	2	4	no	—
316	#41×C₆₇	—	2	2	no	—
317	#41×C₆₇	—	4	2	no	—
318	#41×C₆₇	—	4	1	no	—
319	#41×C₆₇	—	8	2	no	—
320	#41×C₆₇	—	8	2	no	—
321	#41×C₆₇	—	8	4	no	—
322	C₂×Q₈×C₆₇	—	2	1	no	—
323	C₂×Q₈×C₆₇	—	2	1	no	—
324	C₂×Q₈×C₆₇	—	2	2	no	—
325	C₂×Q₈×C₆₇	—	2	2	no	—
326	C₂×Q₈×C₆₇	—	2	1	no	—
327	C₂×Q₈×C₆₇	—	2	2	no	—
328	C₂×Q₈×C₆₇	—	4	1	no	—
329	C₂×Q₈×C₆₇	—	8	2	no	—
330	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₆₇	—	2	4	no	—
335	C₂×D₄×C₆₇	—	2	1	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	—	2	2	no	—
340	C₂×D₄×C₆₇	—	2	2	no	—
341	C₂×D₄×C₆₇	—	2	1	no	—
342	C₂×D₄×C₆₇	—	2	2	no	—
343	C₂×D₄×C₆₇	—	2	1	no	—
344	C₂×D₄×C₆₇	—	2	1	no	—
345	C₂×D₄×C₆₇	—	2	1	no	—
346	C₂×D₄×C₆₇	—	4	2	no	—
347	C₂×D₄×C₆₇	—	8	2	no	—
348	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
349	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
351	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
352	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₆₇	—	2	1	no	—
354	C₂²×C₄×C₆₇	—	2	1	no	—
355	C₂²×C₄×C₆₇	—	2	2	no	—
356	C₂²×C₄×C₆₇	—	2	1	no	—
357	C₂²×C₄×C₆₇	—	2	1	no	—
358	C₂²×C₄×C₆₇	—	2	2	no	—
359	C₂²×C₄×C₆₇	—	2	1	no	—
360	C₂²×C₄×C₆₇	—	2	2	no	—
361	C₂²×C₄×C₆₇	—	2	2	no	—
362	C₂²×C₄×C₆₇	—	2	2	no	—
363	C₂²×C₄×C₆₇	—	2	2	no	—
364	C₂²×C₄×C₆₇	—	2	2	no	—
365	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
369	Q₁₆×C₆₇	—	2	2	no	—
370	Q₁₆×C₆₇	—	2	2	no	—
371	SD₁₆×C₆₇	—	2	4	no	—
372	SD₁₆×C₆₇	—	2	2	no	—
373	SD₁₆×C₆₇	—	4	2	no	—
374	SD₁₆×C₆₇	—	4	2	no	—
375	SD₁₆×C₆₇	#41	1	4	yes	complemented
376	D₈×C₆₇	—	2	4	no	—
377	D₈×C₆₇	—	2	4	no	—
378	D₈×C₆₇	—	4	2	no	—
379	M₁₆×C₆₇	—	2	4	no	—
380	M₁₆×C₆₇	—	2	2	no	—
381	M₁₆×C₆₇	—	4	1	no	—
382	C₂×C₈×C₆₇	—	4	2	no	—
383	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
386	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
387	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₆₇	—	2	1	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	—	2	1	no	—
396	C₄⋊C₄×C₆₇	—	2	1	no	—
397	C₄⋊C₄×C₆₇	—	2	1	no	—
398	C₄⋊C₄×C₆₇	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	1	no	—
400	C₄⋊C₄×C₆₇	—	2	1	no	—
401	C₄⋊C₄×C₆₇	—	2	2	no	—
402	C₄⋊C₄×C₆₇	—	2	2	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
416	C₂²⋊C₄×C₆₇	—	2	2	no	—
417	C₂²⋊C₄×C₆₇	—	2	2	no	—
418	C₂²⋊C₄×C₆₇	—	2	1	no	—
419	C₂²⋊C₄×C₆₇	—	2	2	no	—
420	C₂²⋊C₄×C₆₇	—	2	1	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	1	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	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	—	2	2	no	—
434	C₂²⋊C₄×C₆₇	—	2	2	no	—
435	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
440	C₄²×C₆₇	—	2	1	no	—
441	C₄²×C₆₇	—	2	1	no	—
442	C₄²×C₆₇	—	2	1	no	—
443	C₄²×C₆₇	—	2	1	no	—
444	C₄²×C₆₇	—	2	1	no	—
445	C₄²×C₆₇	—	2	1	no	—
446	C₄²×C₆₇	—	2	1	no	—
447	C₄²×C₆₇	—	2	2	no	—
448	C₄²×C₆₇	—	2	2	no	—
449	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₄²×C₆₇	C₂⁴	1	2	yes	—
453	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₂³×C₆₇	—	2	1	no	—
455	C₂³×C₆₇	—	2	2	no	—
456	C₂³×C₆₇	—	2	2	no	—
457	C₂³×C₆₇	—	4	4	no	—
458	C₂³×C₆₇	—	8	2	no	—
459	C₂³×C₆₇	—	8	2	no	—
460	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
461	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
462	Q₈×C₆₇	—	2	2	no	—
463	Q₈×C₆₇	—	2	1	no	—
464	Q₈×C₆₇	—	2	1	no	—
465	Q₈×C₆₇	—	2	1	no	—
466	Q₈×C₆₇	—	2	1	no	—
467	Q₈×C₆₇	—	2	1	no	—
468	Q₈×C₆₇	—	4	2	no	—
469	Q₈×C₆₇	—	4	2	no	—
470	Q₈×C₆₇	—	8	2	no	—
471	Q₈×C₆₇	—	8	1	no	—
472	Q₈×C₆₇	—	8	2	no	—
473	Q₈×C₆₇	C₂×#41	1	2	yes	—
474	D₄×C₆₇	—	2	2	no	—
475	D₄×C₆₇	—	2	2	no	—
476	D₄×C₆₇	—	2	2	no	—
477	D₄×C₆₇	—	2	1	no	—
478	D₄×C₆₇	—	2	2	no	—
479	D₄×C₆₇	—	2	2	no	—
480	D₄×C₆₇	—	4	2	no	—
481	D₄×C₆₇	—	4	4	no	—
482	D₄×C₆₇	—	4	4	no	—
483	D₄×C₆₇	—	4	2	no	—
484	D₄×C₆₇	—	4	4	no	—
485	D₄×C₆₇	—	4	2	no	—
486	D₄×C₆₇	—	4	2	no	—
487	D₄×C₆₇	—	8	1	no	—
488	D₄×C₆₇	—	8	1	no	—
489	D₄×C₆₇	—	8	2	no	—
490	D₄×C₆₇	—	8	2	no	—
491	D₄×C₆₇	—	8	2	no	—
492	D₄×C₆₇	C₂×#41	1	2	yes	—
493	C₂×C₄×C₆₇	—	2	1	no	—
494	C₂×C₄×C₆₇	—	2	2	no	—
495	C₂×C₄×C₆₇	—	2	2	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	2	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	1	no	—
500	C₂×C₄×C₆₇	—	2	1	no	—
501	C₂×C₄×C₆₇	—	2	1	no	—
502	C₂×C₄×C₆₇	—	2	1	no	—
503	C₂×C₄×C₆₇	—	2	1	no	—
504	C₂×C₄×C₆₇	—	2	1	no	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	2	no	—
507	C₂×C₄×C₆₇	—	4	1	no	—
508	C₂×C₄×C₆₇	—	4	4	no	—
509	C₂×C₄×C₆₇	—	4	2	no	—
510	C₂×C₄×C₆₇	—	4	2	no	—
511	C₂×C₄×C₆₇	—	4	2	no	—
512	C₂×C₄×C₆₇	—	4	2	no	—
513	C₂×C₄×C₆₇	—	8	1	no	—
514	C₂×C₄×C₆₇	—	8	2	no	—
515	C₂×C₄×C₆₇	—	8	2	no	—
516	C₂×C₄×C₆₇	—	8	2	no	—
517	C₂×C₄×C₆₇	—	8	2	no	—
518	C₂×C₄×C₆₇	—	8	2	no	—
519	C₂×C₄×C₆₇	—	8	2	no	—
520	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
529	C₈×C₆₇	—	2	2	no	—
530	C₈×C₆₇	—	2	1	no	—
531	C₈×C₆₇	—	2	1	no	—
532	C₈×C₆₇	—	2	2	no	—
533	C₈×C₆₇	—	2	1	no	—
534	C₈×C₆₇	C₂×#41	1	2	yes	—
535	C₂²×C₆₇	—	2	1	no	—
536	C₂²×C₆₇	—	2	2	no	—
537	C₂²×C₆₇	—	2	1	no	—
538	C₂²×C₆₇	—	2	2	no	—
539	C₂²×C₆₇	—	2	2	no	—
540	C₂²×C₆₇	—	2	1	no	—
541	C₂²×C₆₇	—	2	2	no	—
542	C₂²×C₆₇	—	4	1	no	—
543	C₂²×C₆₇	—	4	1	no	—
544	C₂²×C₆₇	—	4	2	no	—
545	C₂²×C₆₇	—	4	2	no	—
546	C₂²×C₆₇	—	4	2	no	—
547	C₂²×C₆₇	—	4	2	no	—
548	C₂²×C₆₇	—	4	2	no	—
549	C₂²×C₆₇	—	4	2	no	—
550	C₂²×C₆₇	—	16	4	no	—
551	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
552	C₄×C₆₇	—	2	1	no	—
553	C₄×C₆₇	—	2	1	no	—
554	C₄×C₆₇	—	2	2	no	—
555	C₄×C₆₇	—	2	2	no	—
556	C₄×C₆₇	—	2	1	no	—
557	C₄×C₆₇	—	2	2	no	—
558	C₄×C₆₇	—	2	1	no	—
559	C₄×C₆₇	—	2	2	no	—
560	C₄×C₆₇	—	4	1	no	—
561	C₄×C₆₇	—	4	1	no	—
562	C₄×C₆₇	—	4	1	no	—
563	C₄×C₆₇	—	4	2	no	—
564	C₄×C₆₇	—	4	1	no	—
565	C₄×C₆₇	—	4	1	no	—
566	C₄×C₆₇	—	4	1	no	—
567	C₄×C₆₇	—	4	2	no	—
568	C₄×C₆₇	#577	1	2	yes	—
569	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
570	C₄×C₆₇	#585	1	1	yes	characteristic
571	#61554	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
572	C₂×C₆₇	—	4	1	no	—
573	C₂×C₆₇	—	4	2	no	—
574	C₂×C₆₇	—	4	2	no	—
575	C₂×C₆₇	—	8	2	no	—
576	C₂×C₆₇	—	8	2	no	—
577	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
578	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
579	C₂×C₆₇	#3585	1	1	yes	characteristic
580	#3522	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#3514	C₂×C₆₇	1	1	yes	characteristic, complemented
582	#3396	C₂×C₆₇	1	1	yes	characteristic, complemented
583	Q₈×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
584	#3375	C₂×C₆₇	1	1	yes	characteristic, complemented
585	#3373	C₂×C₆₇	1	1	yes	characteristic, complemented
586	#3356	C₂×C₆₇	1	1	yes	characteristic, complemented
587	#3354	C₂×C₆₇	1	2	yes	complemented
588	#3321	C₂×C₆₇	1	2	yes	complemented
589	#3306	C₂×C₆₇	1	2	yes	complemented
590	#3304	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#3295	C₂×C₆₇	1	1	yes	characteristic, complemented
592	#3275	C₂×C₆₇	1	2	yes	complemented
593	#3274	C₂×C₆₇	1	1	yes	characteristic, complemented
594	#3184	C₂×C₆₇	1	1	yes	characteristic, complemented
595	#3173	C₂×C₆₇	1	2	yes	complemented
596	#3125	C₂×C₆₇	1	2	yes	complemented
597	#3118	C₂×C₆₇	1	2	yes	complemented
598	#3106	C₂×C₆₇	1	1	yes	characteristic, complemented
599	#3103	C₂×C₆₇	1	1	yes	characteristic, complemented
600	#2969	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#2946	C₂×C₆₇	1	2	yes	complemented
602	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
603	C₆₇	#61554	1	1	yes	characteristic, direct product factor, Sylow
604	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
605	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
606	#559	—	2	1	no	—
607	#559	C₂²×C₆₇	1	1	yes	characteristic
608	#559	C₂²×C₆₇	1	1	yes	characteristic, complemented
609	Q₈²	C₂²×C₆₇	1	1	yes	characteristic, complemented
610	#556	C₂²×C₆₇	1	1	yes	characteristic
611	#555	C₂²×C₆₇	1	2	yes	—
612	#554	—	2	1	no	—
613	#554	C₂²×C₆₇	1	1	yes	characteristic
614	#551	—	2	2	no	—
615	#550	C₂²×C₆₇	1	1	yes	characteristic
616	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
617	#548	—	2	1	no	—
618	#548	C₂²×C₆₇	1	2	yes	complemented
619	#547	—	2	2	no	—
620	#547	C₂²×C₆₇	1	2	yes	complemented
621	#546	—	2	1	no	—
622	#546	C₂²×C₆₇	1	2	yes	—
623	D₄²	C₂²×C₆₇	1	1	yes	characteristic
624	#542	—	2	2	no	—
625	#542	C₂²×C₆₇	1	2	yes	—
626	#542	C₂²×C₆₇	1	2	yes	complemented
627	#538	—	2	2	no	—
628	#532	—	2	1	no	—
629	#532	C₂²×C₆₇	1	1	yes	characteristic
630	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
631	#529	—	2	1	no	—
632	#529	—	2	1	no	—
633	#529	C₂²×C₆₇	1	1	yes	characteristic
634	C₂×#124	—	2	1	no	—
635	#520	C₂²×C₆₇	1	2	yes	complemented
636	#518	C₂²×C₆₇	1	2	yes	—
637	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
638	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
639	#498	C₂²×C₆₇	1	2	yes	complemented
640	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
641	#495	C₂²×C₆₇	1	2	yes	complemented
642	#493	C₂²×C₆₇	1	1	yes	characteristic
643	#489	C₂²×C₆₇	1	2	yes	complemented
644	#489	C₂²×C₆₇	1	2	yes	complemented
645	#486	C₂²×C₆₇	1	1	yes	characteristic
646	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
647	#485	C₂²×C₆₇	1	2	yes	complemented
648	#483	C₂²×C₆₇	1	2	yes	complemented
649	#482	C₂²×C₆₇	1	2	yes	complemented
650	#482	C₂²×C₆₇	1	2	yes	complemented
651	#481	C₂²×C₆₇	1	2	yes	—
652	#481	C₂²×C₆₇	1	2	yes	complemented
653	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	#476	C₂²×C₆₇	1	1	yes	characteristic
655	#476	C₂²×C₆₇	1	2	yes	—
656	#476	C₂²×C₆₇	1	2	yes	complemented
657	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
658	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
659	#475	C₂²×C₆₇	1	2	yes	complemented
660	#474	C₂²×C₆₇	1	2	yes	complemented
661	#470	C₂²×C₆₇	1	2	yes	complemented
662	#469	C₂²×C₆₇	1	2	yes	—
663	#469	C₂²×C₆₇	1	2	yes	complemented
664	#469	C₂²×C₆₇	1	2	yes	complemented
665	#465	C₂²×C₆₇	1	2	yes	—
666	#465	C₂²×C₆₇	1	2	yes	complemented
667	#464	C₂²×C₆₇	1	2	yes	complemented
668	#463	C₂²×C₆₇	1	2	yes	—
669	#463	C₂²×C₆₇	1	2	yes	complemented
670	#463	C₂²×C₆₇	1	2	yes	complemented
671	#460	C₂²×C₆₇	1	1	yes	characteristic
672	#460	C₂²×C₆₇	1	1	yes	characteristic
673	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
674	#459	C₂²×C₆₇	1	1	yes	characteristic
675	#452	C₂²×C₆₇	1	2	yes	complemented
676	#450	C₂²×C₆₇	1	2	yes	—
677	#449	C₂²×C₆₇	1	2	yes	—
678	#449	C₂²×C₆₇	1	2	yes	—
679	#448	C₂²×C₆₇	1	2	yes	complemented
680	#447	C₂²×C₆₇	1	2	yes	—
681	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
682	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
683	#442	C₂²×C₆₇	1	2	yes	—
684	#442	C₂²×C₆₇	1	2	yes	complemented
685	#442	C₂²×C₆₇	1	2	yes	complemented
686	#441	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	#441	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	#440	C₂²×C₆₇	1	1	yes	characteristic
689	#440	C₂²×C₆₇	1	1	yes	characteristic
690	#440	C₂²×C₆₇	1	2	yes	complemented
691	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
692	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
694	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
695	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
696	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
697	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
698	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
699	C₄×D₈	C₂²×C₆₇	1	2	yes	—
700	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
701	#436	C₂²×C₆₇	1	1	yes	characteristic
702	#436	C₂²×C₆₇	1	2	yes	complemented
703	#435	C₂²×C₆₇	1	2	yes	complemented
704	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
705	#433	C₂²×C₆₇	1	2	yes	complemented
706	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
707	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
708	#428	C₂²×C₆₇	1	2	yes	complemented
709	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	#417	C₂²×C₆₇	1	1	yes	characteristic
711	#416	C₂²×C₆₇	1	2	yes	complemented
712	C₂×#102	C₂²×C₆₇	1	2	yes	—
713	#405	C₂²×C₆₇	1	2	yes	complemented
714	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
715	C₂×#41	—	2	2	no	—
716	C₂×#41	—	2	1	no	—
717	C₂×#41	—	2	1	no	—
718	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
719	C₂×#41	C₂³×C₆₇	1	2	yes	—
720	C₂²×Q₈	—	2	1	no	—
721	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
722	C₂²×D₄	—	2	1	no	—
723	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
724	#137	—	2	4	no	—
725	AGL(1,ℤ/8)	—	2	8	no	—
726	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
727	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
733	C₂×D₈	C₂³×C₆₇	1	2	yes	—
734	C₂×D₈	C₂³×C₆₇	1	2	yes	—
735	C₂×D₈	C₂³×C₆₇	1	2	yes	—
736	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
737	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
739	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
740	C₄⋊Q₈	—	2	1	no	—
741	C₄⋊Q₈	—	2	2	no	—
742	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
743	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
744	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
745	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
746	#127	—	2	1	no	—
747	#127	C₂³×C₆₇	1	1	yes	characteristic
748	#127	C₂³×C₆₇	1	1	yes	characteristic
749	#126	—	2	2	no	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	D₄×C₆₇	1	2	yes	—
753	#125	—	2	1	no	—
754	#125	D₄×C₆₇	1	1	yes	characteristic
755	#124	—	2	1	no	—
756	#124	—	2	1	no	—
757	#124	—	2	1	no	—
758	#124	—	2	2	no	—
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	—	2	1	no	—
764	#124	—	2	1	no	—
765	#124	D₄×C₆₇	1	1	yes	characteristic
766	#124	C₂³×C₆₇	1	2	yes	—
767	#124	C₂³×C₆₇	1	2	yes	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	D₄×C₆₇	1	2	yes	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
785	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	1	no	—
789	#121	—	2	1	no	—
790	#121	—	2	1	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	D₄×C₆₇	1	1	yes	characteristic
794	#121	C₂³×C₆₇	1	2	yes	—
795	#121	C₂³×C₆₇	1	2	yes	—
796	#121	C₂³×C₆₇	1	2	yes	—
797	#121	C₂³×C₆₇	1	2	yes	—
798	#120	—	2	2	no	—
799	#120	—	2	2	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
811	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₆₇	1	2	yes	—
828	C₄×D₄	C₂³×C₆₇	1	2	yes	—
829	C₄×D₄	C₂³×C₆₇	1	2	yes	—
830	C₄×D₄	C₂³×C₆₇	1	2	yes	—
831	C₄×D₄	C₂³×C₆₇	1	2	yes	—
832	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₆₇	1	2	yes	—
834	#117	—	2	2	no	—
835	#117	—	2	2	no	—
836	#117	—	2	1	no	—
837	#117	C₂³×C₆₇	1	1	yes	characteristic
838	#117	C₂³×C₆₇	1	2	yes	—
839	#117	C₂³×C₆₇	1	2	yes	—
840	C₂×C₄⋊C₄	—	2	1	no	—
841	C₂×C₄⋊C₄	—	2	2	no	—
842	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₂²⋊C₄	—	2	2	no	—
846	C₂×C₂²⋊C₄	—	2	2	no	—
847	C₂×C₄²	—	2	1	no	—
848	C₂×C₄²	—	2	1	no	—
849	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
850	#107	C₂³×C₆₇	1	1	yes	characteristic
851	#107	C₂³×C₆₇	1	2	yes	—
852	#107	C₂³×C₆₇	1	1	yes	characteristic
853	#106	C₂³×C₆₇	1	1	yes	characteristic
854	#106	C₂³×C₆₇	1	1	yes	characteristic
855	#106	C₂³×C₆₇	1	2	yes	—
856	#106	C₂³×C₆₇	1	2	yes	—
857	#106	C₂³×C₆₇	1	2	yes	—
858	#106	C₂³×C₆₇	1	2	yes	—
859	#106	C₂³×C₆₇	1	2	yes	—
860	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
863	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
864	#103	C₂³×C₆₇	1	1	yes	characteristic
865	#103	C₂³×C₆₇	1	2	yes	—
866	#103	C₂³×C₆₇	1	1	yes	characteristic
867	#103	C₂³×C₆₇	1	1	yes	characteristic
868	#103	C₂³×C₆₇	1	1	yes	characteristic
869	#103	C₂³×C₆₇	1	1	yes	characteristic
870	#103	C₂³×C₆₇	1	1	yes	characteristic
871	#103	C₂³×C₆₇	1	2	yes	—
872	#103	C₂³×C₆₇	1	2	yes	—
873	#102	C₂³×C₆₇	1	1	yes	characteristic
874	#102	C₂³×C₆₇	1	2	yes	—
875	#102	C₂³×C₆₇	1	2	yes	—
876	#102	C₂³×C₆₇	1	2	yes	—
877	#102	C₂³×C₆₇	1	2	yes	—
878	#102	C₂³×C₆₇	1	2	yes	—
879	#102	C₂³×C₆₇	1	1	yes	characteristic
880	#102	C₂³×C₆₇	1	2	yes	—
881	#102	C₂³×C₆₇	1	2	yes	—
882	#102	C₂³×C₆₇	1	2	yes	—
883	#102	C₂³×C₆₇	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
887	#97	C₂³×C₆₇	1	1	yes	characteristic
888	#97	C₂³×C₆₇	1	1	yes	characteristic
889	#97	C₂³×C₆₇	1	2	yes	—
890	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₆₇	1	2	yes	—
893	C₄×C₈	C₂³×C₆₇	1	2	yes	—
894	C₂⁴	—	2	2	no	—
895	#41	—	2	4	no	—
896	#41	—	2	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	1	no	—
899	#41	—	8	2	no	—
900	#41	—	8	2	no	—
901	#41	—	8	4	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	2	no	—
908	C₂×Q₈	—	4	1	no	—
909	C₂×Q₈	—	8	2	no	—
910	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
914	C₂×D₄	—	2	4	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	4	2	no	—
927	C₂×D₄	—	8	2	no	—
928	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
929	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
930	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
931	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
932	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
949	Q₁₆	—	2	2	no	—
950	Q₁₆	—	2	2	no	—
951	SD₁₆	—	2	4	no	—
952	SD₁₆	—	2	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	#41×C₆₇	1	4	yes	complemented
956	D₈	—	2	4	no	—
957	D₈	—	2	4	no	—
958	D₈	—	4	2	no	—
959	M₁₆	—	2	4	no	—
960	M₁₆	—	2	2	no	—
961	M₁₆	—	4	1	no	—
962	C₂×C₈	—	4	2	no	—
963	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
964	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
967	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
985	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
986	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
987	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
988	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
989	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
994	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1018	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1019	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1030	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₆₇	1	2	yes	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	4	4	no	—
1038	C₂³	—	8	2	no	—
1039	C₂³	—	8	2	no	—
1040	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1041	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1042	Q₈	—	2	2	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	4	2	no	—
1049	Q₈	—	4	2	no	—
1050	Q₈	—	8	2	no	—
1051	Q₈	—	8	1	no	—
1052	Q₈	—	8	2	no	—
1053	Q₈	C₂×#41×C₆₇	1	2	yes	—
1054	D₄	—	2	2	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	4	4	no	—
1062	D₄	—	4	4	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	4	4	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	8	1	no	—
1068	D₄	—	8	1	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	C₂×#41×C₆₇	1	2	yes	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	4	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	1	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1107	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1108	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	2	no	—
1113	C₈	—	2	1	no	—
1114	C₈	C₂×#41×C₆₇	1	2	yes	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	16	4	no	—
1131	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	1	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	#577×C₆₇	1	2	yes	—
1149	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1150	C₄	#585×C₆₇	1	1	yes	characteristic
1151	C₂	—	4	2	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	2	no	—
1156	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1157	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1158	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 ◁ #529×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3522	C₂	semidirect
2. C₆₇×#3514	C₂	semidirect
3. C₆₇×#3396	C₂	semidirect
4. Q₈×SD₁₆×C₆₇	C₂	semidirect
5. C₆₇×#3375	C₂	semidirect
6. C₆₇×#3373	C₂	semidirect
7. C₆₇×#3356	C₂	semidirect
8. C₆₇×#3354	C₂	semidirect
9. C₆₇×#3321	C₂	semidirect
10. C₆₇×#3306	C₂	semidirect
11. C₆₇×#3304	C₂	semidirect
12. C₆₇×#3295	C₂	semidirect
13. C₆₇×#3275	C₂	semidirect
14. C₆₇×#3274	C₂	semidirect
15. C₆₇×#3184	C₂	semidirect
16. C₆₇×#3173	C₂	semidirect
17. C₆₇×#3125	C₂	semidirect
18. C₆₇×#3118	C₂	semidirect
19. C₆₇×#3106	C₂	semidirect
20. C₆₇×#3103	C₂	semidirect
21. C₆₇×#2969	C₂	semidirect
22. C₆₇×#2946	C₂	semidirect
23. C₄×#137×C₆₇	C₂	semidirect
28. #559×C₆₇	C₂²	semidirect
29. Q₈²×C₆₇	C₂²	semidirect
38. #548×C₆₇	C₂²	semidirect
40. #547×C₆₇	C₂²	semidirect
46. #542×C₆₇	C₂²	semidirect
50. #532×C₆₇	C₂²	semidirect
55. #520×C₆₇	C₂²	semidirect
58. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
59. #498×C₆₇	C₂²	semidirect
60. #498×C₆₇	C₂²	semidirect
61. #495×C₆₇	C₂²	semidirect
63. #489×C₆₇	C₂²	semidirect
64. #489×C₆₇	C₂²	semidirect
66. #486×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
68. #483×C₆₇	C₂²	semidirect
69. #482×C₆₇	C₂²	semidirect
70. #482×C₆₇	C₂²	semidirect
72. #481×C₆₇	C₂²	semidirect
73. #477×C₆₇	C₂²	semidirect
76. #476×C₆₇	C₂²	semidirect
77. #475×C₆₇	C₂²	semidirect
78. #475×C₆₇	C₂²	semidirect
79. #475×C₆₇	C₂²	semidirect
80. #474×C₆₇	C₂²	semidirect
81. #470×C₆₇	C₂²	semidirect
83. #469×C₆₇	C₂²	semidirect
84. #469×C₆₇	C₂²	semidirect
86. #465×C₆₇	C₂²	semidirect
87. #464×C₆₇	C₂²	semidirect
89. #463×C₆₇	C₂²	semidirect
90. #463×C₆₇	C₂²	semidirect
93. #460×C₆₇	C₂²	semidirect
95. #452×C₆₇	C₂²	semidirect
99. #448×C₆₇	C₂²	semidirect
101. #446×C₆₇	C₂²	semidirect
102. C₈×Q₈×C₆₇	C₂²	semidirect
104. #442×C₆₇	C₂²	semidirect
105. #442×C₆₇	C₂²	semidirect
106. #441×C₆₇	C₂²	semidirect
107. #441×C₆₇	C₂²	semidirect
110. #440×C₆₇	C₂²	semidirect
111. C₄×Q₁₆×C₆₇	C₂²	semidirect
112. C₄×Q₁₆×C₆₇	C₂²	semidirect
116. C₄×SD₁₆×C₆₇	C₂²	semidirect
117. C₄×SD₁₆×C₆₇	C₂²	semidirect
118. C₄×SD₁₆×C₆₇	C₂²	semidirect
120. C₄×D₈×C₆₇	C₂²	semidirect
122. #436×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
125. #433×C₆₇	C₂²	semidirect
126. #431×C₆₇	C₂²	semidirect
127. #428×C₆₇	C₂²	semidirect
128. #428×C₆₇	C₂²	semidirect
129. #419×C₆₇	C₂²	semidirect
131. #416×C₆₇	C₂²	semidirect
133. #405×C₆₇	C₂²	semidirect
134. C₄×M₁₆×C₆₇	C₂²	semidirect
375. SD₁₆×C₆₇	#41	semidirect
571. #61554	C₆₇	direct (N × H)
580. #3522	C₂×C₆₇	semidirect
581. #3514	C₂×C₆₇	semidirect
582. #3396	C₂×C₆₇	semidirect
583. Q₈×SD₁₆	C₂×C₆₇	semidirect
584. #3375	C₂×C₆₇	semidirect
585. #3373	C₂×C₆₇	semidirect
586. #3356	C₂×C₆₇	semidirect
587. #3354	C₂×C₆₇	semidirect
588. #3321	C₂×C₆₇	semidirect
589. #3306	C₂×C₆₇	semidirect
590. #3304	C₂×C₆₇	semidirect
591. #3295	C₂×C₆₇	semidirect
592. #3275	C₂×C₆₇	semidirect
593. #3274	C₂×C₆₇	semidirect
594. #3184	C₂×C₆₇	semidirect
595. #3173	C₂×C₆₇	semidirect
596. #3125	C₂×C₆₇	semidirect
597. #3118	C₂×C₆₇	semidirect
598. #3106	C₂×C₆₇	semidirect
599. #3103	C₂×C₆₇	semidirect
600. #2969	C₂×C₆₇	semidirect
601. #2946	C₂×C₆₇	semidirect
602. C₄×#137	C₂×C₆₇	semidirect
603. C₆₇	#61554	direct (N × H)
608. #559	C₂²×C₆₇	semidirect
609. Q₈²	C₂²×C₆₇	semidirect
618. #548	C₂²×C₆₇	semidirect
620. #547	C₂²×C₆₇	semidirect
626. #542	C₂²×C₆₇	semidirect
630. #532	C₂²×C₆₇	semidirect
635. #520	C₂²×C₆₇	semidirect
638. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
639. #498	C₂²×C₆₇	semidirect
640. #498	C₂²×C₆₇	semidirect
641. #495	C₂²×C₆₇	semidirect
643. #489	C₂²×C₆₇	semidirect
644. #489	C₂²×C₆₇	semidirect
646. #486	C₂²×C₆₇	semidirect
647. #485	C₂²×C₆₇	semidirect
648. #483	C₂²×C₆₇	semidirect
649. #482	C₂²×C₆₇	semidirect
650. #482	C₂²×C₆₇	semidirect
652. #481	C₂²×C₆₇	semidirect
653. #477	C₂²×C₆₇	semidirect
656. #476	C₂²×C₆₇	semidirect
657. #475	C₂²×C₆₇	semidirect
658. #475	C₂²×C₆₇	semidirect
659. #475	C₂²×C₆₇	semidirect
660. #474	C₂²×C₆₇	semidirect
661. #470	C₂²×C₆₇	semidirect
663. #469	C₂²×C₆₇	semidirect
664. #469	C₂²×C₆₇	semidirect
666. #465	C₂²×C₆₇	semidirect
667. #464	C₂²×C₆₇	semidirect
669. #463	C₂²×C₆₇	semidirect
670. #463	C₂²×C₆₇	semidirect
673. #460	C₂²×C₆₇	semidirect
675. #452	C₂²×C₆₇	semidirect
679. #448	C₂²×C₆₇	semidirect
681. #446	C₂²×C₆₇	semidirect
682. C₈×Q₈	C₂²×C₆₇	semidirect
684. #442	C₂²×C₆₇	semidirect
685. #442	C₂²×C₆₇	semidirect
686. #441	C₂²×C₆₇	semidirect
687. #441	C₂²×C₆₇	semidirect
690. #440	C₂²×C₆₇	semidirect
691. C₄×Q₁₆	C₂²×C₆₇	semidirect
692. C₄×Q₁₆	C₂²×C₆₇	semidirect
696. C₄×SD₁₆	C₂²×C₆₇	semidirect
697. C₄×SD₁₆	C₂²×C₆₇	semidirect
698. C₄×SD₁₆	C₂²×C₆₇	semidirect
700. C₄×D₈	C₂²×C₆₇	semidirect
702. #436	C₂²×C₆₇	semidirect
703. #435	C₂²×C₆₇	semidirect
705. #433	C₂²×C₆₇	semidirect
706. #431	C₂²×C₆₇	semidirect
707. #428	C₂²×C₆₇	semidirect
708. #428	C₂²×C₆₇	semidirect
709. #419	C₂²×C₆₇	semidirect
711. #416	C₂²×C₆₇	semidirect
713. #405	C₂²×C₆₇	semidirect
714. C₄×M₁₆	C₂²×C₆₇	semidirect
955. SD₁₆	#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×#3522	2
C₆₇×#3514	2
C₆₇×#3396	2
Q₈×SD₁₆×C₆₇	2
C₆₇×#3375	2
C₆₇×#3373	2
C₆₇×#3356	2
C₆₇×#3354	2
C₆₇×#3321	2
C₆₇×#3306	2
C₆₇×#3304	2
C₆₇×#3295	2
C₆₇×#3275	2
C₆₇×#3274	2
C₆₇×#3184	2
C₆₇×#3173	2
C₆₇×#3125	2
C₆₇×#3118	2
C₆₇×#3106	2
C₆₇×#3103	2
C₆₇×#2969	2
C₆₇×#2946	2
C₄×#137×C₆₇	2
#61554	67

Subgroups — C67×#61554 #30740805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61554 #30740805