Subgroups — C₆₇×#61692 #30740943

Order 17152.

2078 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3330	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3320	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3307	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3302	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3298	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3284	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3267	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3266	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3218	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3201	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3200	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
22	C₆₇×#3010	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2981	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	complemented
25	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
27	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
29	#560×C₆₇	—	2	2	no	—
30	#556×C₆₇	C₂²	1	1	yes	characteristic
31	#553×C₆₇	C₂²	1	2	yes	—
32	#550×C₆₇	—	2	1	no	—
33	#550×C₆₇	C₂²	1	1	yes	characteristic
34	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
36	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	#547×C₆₇	—	2	1	no	—
38	#547×C₆₇	—	2	1	no	—
39	#547×C₆₇	—	2	2	no	—
40	#547×C₆₇	C₂²	1	1	yes	characteristic
41	#547×C₆₇	C₂²	1	1	yes	characteristic
42	#547×C₆₇	C₂²	1	2	yes	complemented
43	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	#546×C₆₇	—	2	1	no	—
45	#546×C₆₇	C₂²	1	2	yes	—
46	D₄²×C₆₇	C₂²	1	1	yes	characteristic
47	#542×C₆₇	—	2	1	no	—
48	#538×C₆₇	—	2	2	no	—
49	#537×C₆₇	C₂²	1	2	yes	—
50	#536×C₆₇	—	2	2	no	—
51	#536×C₆₇	C₂²	1	2	yes	complemented
52	#535×C₆₇	—	2	1	no	—
53	#535×C₆₇	C₂²	1	2	yes	—
54	#532×C₆₇	—	2	1	no	—
55	#532×C₆₇	C₂²	1	1	yes	characteristic
56	#532×C₆₇	C₂²	1	1	yes	characteristic
57	C₂×C₄⋊Q₈×C₆₇	—	2	1	no	—
58	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#529×C₆₇	C₂²	1	1	yes	characteristic
60	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#497×C₆₇	C₂²	1	2	yes	—
62	#492×C₆₇	C₂²	1	1	yes	characteristic
63	#492×C₆₇	C₂²	1	1	yes	characteristic
64	#491×C₆₇	C₂²	1	2	yes	complemented
65	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#485×C₆₇	C₂²	1	2	yes	complemented
68	#485×C₆₇	C₂²	1	2	yes	complemented
69	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#484×C₆₇	C₂²	1	2	yes	complemented
71	#483×C₆₇	C₂²	1	2	yes	complemented
72	#482×C₆₇	C₂²	1	1	yes	characteristic
73	#482×C₆₇	C₂²	1	2	yes	complemented
74	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#478×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#470×C₆₇	C₂²	1	2	yes	complemented
79	#468×C₆₇	C₂²	1	2	yes	—
80	#468×C₆₇	C₂²	1	2	yes	—
81	#468×C₆₇	C₂²	1	2	yes	complemented
82	#467×C₆₇	C₂²	1	2	yes	complemented
83	#465×C₆₇	C₂²	1	2	yes	—
84	#465×C₆₇	C₂²	1	2	yes	—
85	#465×C₆₇	C₂²	1	2	yes	complemented
86	#464×C₆₇	C₂²	1	1	yes	characteristic
87	#463×C₆₇	C₂²	1	1	yes	characteristic
88	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#461×C₆₇	C₂²	1	1	yes	characteristic
91	#461×C₆₇	C₂²	1	1	yes	characteristic
92	#461×C₆₇	C₂²	1	2	yes	complemented
93	#461×C₆₇	C₂²	1	2	yes	complemented
94	#460×C₆₇	C₂²	1	1	yes	characteristic
95	#459×C₆₇	C₂²	1	1	yes	characteristic
96	#452×C₆₇	C₂²	1	2	yes	complemented
97	#452×C₆₇	C₂²	1	2	yes	complemented
98	#452×C₆₇	C₂²	1	2	yes	complemented
99	#452×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#451×C₆₇	C₂²	1	2	yes	complemented
101	#451×C₆₇	C₂²	1	2	yes	complemented
102	#450×C₆₇	C₂²	1	2	yes	—
103	#450×C₆₇	C₂²	1	2	yes	—
104	#449×C₆₇	C₂²	1	1	yes	characteristic
105	#449×C₆₇	C₂²	1	2	yes	—
106	#449×C₆₇	C₂²	1	2	yes	—
107	#449×C₆₇	C₂²	1	2	yes	complemented
108	#449×C₆₇	C₂²	1	2	yes	complemented
109	#448×C₆₇	C₂²	1	2	yes	—
110	#448×C₆₇	C₂²	1	2	yes	—
111	#448×C₆₇	C₂²	1	2	yes	—
112	#448×C₆₇	C₂²	1	2	yes	complemented
113	#448×C₆₇	C₂²	1	2	yes	complemented
114	#448×C₆₇	C₂²	1	2	yes	complemented
115	#442×C₆₇	C₂²	1	2	yes	complemented
116	#440×C₆₇	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
121	#436×C₆₇	C₂²	1	1	yes	characteristic
122	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	#435×C₆₇	C₂²	1	2	yes	complemented
125	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
126	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#419×C₆₇	C₂²	1	2	yes	complemented
130	#417×C₆₇	C₂²	1	2	yes	complemented
131	#416×C₆₇	C₂²	1	2	yes	complemented
132	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
133	#408×C₆₇	C₂²	1	2	yes	complemented
134	#408×C₆₇	C₂²	1	2	yes	complemented
135	2₋¹⁺⁴×C₆₇	—	4	4	no	—
136	2₋¹⁺⁴×C₆₇	—	4	4	no	—
137	C₂×#41×C₆₇	—	2	2	no	—
138	C₂×#41×C₆₇	—	2	2	no	—
139	C₂×#41×C₆₇	—	2	2	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	—	2	1	no	—
142	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×#41×C₆₇	C₂³	1	2	yes	—
144	C₂×#41×C₆₇	C₂³	1	2	yes	—
145	C₂×#41×C₆₇	C₂³	1	2	yes	—
146	C₂×#41×C₆₇	C₂³	1	2	yes	—
147	C₂²×Q₈×C₆₇	—	2	2	no	—
148	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
149	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
150	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
151	C₂²×D₄×C₆₇	—	2	1	no	—
152	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
153	#137×C₆₇	—	4	4	no	—
154	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
155	#135×C₆₇	—	4	4	no	—
156	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₆₇	—	4	4	no	—
160	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
169	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×D₈×C₆₇	C₂³	1	2	yes	—
171	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
172	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
173	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
174	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
175	C₄⋊Q₈×C₆₇	—	2	2	no	—
176	C₄⋊Q₈×C₆₇	—	2	1	no	—
177	C₄⋊Q₈×C₆₇	—	2	1	no	—
178	C₄⋊Q₈×C₆₇	—	2	2	no	—
179	C₄⋊Q₈×C₆₇	—	2	1	no	—
180	C₄⋊Q₈×C₆₇	—	2	1	no	—
181	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
182	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
183	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
184	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
185	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
186	#127×C₆₇	—	2	1	no	—
187	#127×C₆₇	—	2	2	no	—
188	#127×C₆₇	D₄	1	1	yes	characteristic
189	#127×C₆₇	C₂³	1	1	yes	characteristic
190	#126×C₆₇	—	2	2	no	—
191	#126×C₆₇	—	2	2	no	—
192	#126×C₆₇	—	2	1	no	—
193	#125×C₆₇	C₂³	1	1	yes	characteristic
194	#124×C₆₇	—	2	2	no	—
195	#124×C₆₇	—	2	2	no	—
196	#124×C₆₇	—	2	1	no	—
197	#124×C₆₇	—	2	1	no	—
198	#124×C₆₇	D₄	1	2	yes	—
199	#124×C₆₇	C₂³	1	1	yes	characteristic
200	#123×C₆₇	—	2	2	no	—
201	#123×C₆₇	—	2	2	no	—
202	#123×C₆₇	—	2	1	no	—
203	#123×C₆₇	—	2	2	no	—
204	#123×C₆₇	—	2	2	no	—
205	#123×C₆₇	—	2	2	no	—
206	#123×C₆₇	—	2	2	no	—
207	#123×C₆₇	—	2	2	no	—
208	#123×C₆₇	—	2	2	no	—
209	#123×C₆₇	—	2	2	no	—
210	C₂²⋊Q₈×C₆₇	—	2	2	no	—
211	C₂²⋊Q₈×C₆₇	—	2	1	no	—
212	C₂²⋊Q₈×C₆₇	—	2	2	no	—
213	C₂²⋊Q₈×C₆₇	—	2	2	no	—
214	C₂²⋊Q₈×C₆₇	—	2	2	no	—
215	C₂²⋊Q₈×C₆₇	—	2	2	no	—
216	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
219	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
222	#121×C₆₇	—	2	1	no	—
223	#121×C₆₇	—	2	1	no	—
224	#121×C₆₇	—	2	2	no	—
225	#121×C₆₇	—	2	2	no	—
226	#121×C₆₇	—	2	2	no	—
227	#121×C₆₇	—	2	2	no	—
228	#121×C₆₇	—	2	2	no	—
229	#121×C₆₇	—	2	1	no	—
230	#121×C₆₇	—	2	1	no	—
231	#121×C₆₇	—	2	2	no	—
232	#121×C₆₇	—	2	2	no	—
233	#121×C₆₇	D₄	1	1	yes	characteristic
234	#121×C₆₇	D₄	1	1	yes	characteristic
235	#121×C₆₇	D₄	1	2	yes	—
236	#121×C₆₇	C₂³	1	1	yes	characteristic
237	#121×C₆₇	C₂³	1	2	yes	—
238	#121×C₆₇	C₂³	1	2	yes	—
239	#121×C₆₇	C₂³	1	2	yes	—
240	#121×C₆₇	C₂³	1	2	yes	—
241	#120×C₆₇	—	2	2	no	—
242	#120×C₆₇	—	2	2	no	—
243	#120×C₆₇	—	2	2	no	—
244	#120×C₆₇	—	2	2	no	—
245	C₄×Q₈×C₆₇	—	2	1	no	—
246	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₆₇	—	2	1	no	—
250	C₄×D₄×C₆₇	—	2	1	no	—
251	C₄×D₄×C₆₇	—	2	2	no	—
252	C₄×D₄×C₆₇	—	2	1	no	—
253	C₄×D₄×C₆₇	—	2	1	no	—
254	C₄×D₄×C₆₇	—	2	1	no	—
255	C₄×D₄×C₆₇	—	2	1	no	—
256	C₄×D₄×C₆₇	—	2	2	no	—
257	C₄×D₄×C₆₇	—	2	1	no	—
258	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₆₇	C₂³	1	2	yes	—
261	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₆₇	C₂³	1	2	yes	—
264	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
265	#117×C₆₇	—	2	1	no	—
266	#117×C₆₇	—	2	1	no	—
267	#117×C₆₇	C₂³	1	1	yes	characteristic
268	#117×C₆₇	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
272	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
274	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
275	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
276	C₂×C₄²×C₆₇	—	2	1	no	—
277	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
278	#107×C₆₇	C₂³	1	2	yes	—
279	#107×C₆₇	C₂³	1	1	yes	characteristic
280	#107×C₆₇	C₂³	1	1	yes	characteristic
281	#106×C₆₇	C₂³	1	1	yes	characteristic
282	#106×C₆₇	C₂³	1	2	yes	—
283	#106×C₆₇	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
288	#103×C₆₇	C₂³	1	1	yes	characteristic
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	1	yes	characteristic
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	2	yes	—
297	#103×C₆₇	C₂³	1	2	yes	—
298	#103×C₆₇	C₂³	1	2	yes	—
299	#103×C₆₇	C₂³	1	1	yes	characteristic
300	#103×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	1	yes	characteristic
302	#102×C₆₇	C₂³	1	1	yes	characteristic
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	1	yes	characteristic
305	#102×C₆₇	C₂³	1	1	yes	characteristic
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
315	#97×C₆₇	C₂³	1	2	yes	—
316	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
318	C₂⁴×C₆₇	—	2	2	no	—
319	#41×C₆₇	—	2	2	no	—
320	#41×C₆₇	—	2	2	no	—
321	#41×C₆₇	—	2	4	no	—
322	#41×C₆₇	—	2	4	no	—
323	#41×C₆₇	—	4	2	no	—
324	#41×C₆₇	—	4	2	no	—
325	#41×C₆₇	—	4	2	no	—
326	#41×C₆₇	—	4	2	no	—
327	#41×C₆₇	—	4	8	no	—
328	#41×C₆₇	—	4	2	no	—
329	#41×C₆₇	—	4	2	no	—
330	#41×C₆₇	—	4	8	no	—
331	#41×C₆₇	—	4	8	no	—
332	#41×C₆₇	—	8	2	no	—
333	#41×C₆₇	—	8	2	no	—
334	C₂×Q₈×C₆₇	—	2	1	no	—
335	C₂×Q₈×C₆₇	—	2	2	no	—
336	C₂×Q₈×C₆₇	—	2	2	no	—
337	C₂×Q₈×C₆₇	—	2	2	no	—
338	C₂×Q₈×C₆₇	—	2	4	no	—
339	C₂×Q₈×C₆₇	—	2	4	no	—
340	C₂×Q₈×C₆₇	—	4	2	no	—
341	C₂×Q₈×C₆₇	—	4	2	no	—
342	C₂×Q₈×C₆₇	—	4	2	no	—
343	C₂×Q₈×C₆₇	—	4	2	no	—
344	C₂×Q₈×C₆₇	—	4	8	no	—
345	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
346	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
347	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
348	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₆₇	—	2	1	no	—
351	C₂×D₄×C₆₇	—	2	2	no	—
352	C₂×D₄×C₆₇	—	2	2	no	—
353	C₂×D₄×C₆₇	—	2	1	no	—
354	C₂×D₄×C₆₇	—	2	2	no	—
355	C₂×D₄×C₆₇	—	2	2	no	—
356	C₂×D₄×C₆₇	—	2	2	no	—
357	C₂×D₄×C₆₇	—	2	2	no	—
358	C₂×D₄×C₆₇	—	2	2	no	—
359	C₂×D₄×C₆₇	—	2	1	no	—
360	C₂×D₄×C₆₇	—	2	1	no	—
361	C₂×D₄×C₆₇	—	2	2	no	—
362	C₂×D₄×C₆₇	—	4	2	no	—
363	C₂×D₄×C₆₇	—	4	2	no	—
364	C₂×D₄×C₆₇	—	8	2	no	—
365	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
373	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₆₇	—	2	1	no	—
375	C₂²×C₄×C₆₇	—	2	2	no	—
376	C₂²×C₄×C₆₇	—	2	2	no	—
377	C₂²×C₄×C₆₇	—	2	2	no	—
378	C₂²×C₄×C₆₇	—	2	2	no	—
379	C₂²×C₄×C₆₇	—	2	1	no	—
380	C₂²×C₄×C₆₇	—	2	1	no	—
381	C₂²×C₄×C₆₇	—	2	2	no	—
382	C₂²×C₄×C₆₇	—	2	2	no	—
383	C₂²×C₄×C₆₇	—	2	1	no	—
384	C₂²×C₄×C₆₇	—	2	2	no	—
385	C₂²×C₄×C₆₇	—	2	2	no	—
386	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
390	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
391	Q₁₆×C₆₇	—	2	2	no	—
392	Q₁₆×C₆₇	—	4	2	no	—
393	Q₁₆×C₆₇	—	4	2	no	—
394	SD₁₆×C₆₇	—	2	2	no	—
395	SD₁₆×C₆₇	—	2	4	no	—
396	SD₁₆×C₆₇	—	2	2	no	—
397	SD₁₆×C₆₇	—	4	2	no	—
398	SD₁₆×C₆₇	—	4	2	no	—
399	SD₁₆×C₆₇	—	4	2	no	—
400	SD₁₆×C₆₇	—	4	2	no	—
401	SD₁₆×C₆₇	—	4	2	no	—
402	SD₁₆×C₆₇	—	4	2	no	—
403	D₈×C₆₇	—	2	4	no	—
404	D₈×C₆₇	—	2	2	no	—
405	M₁₆×C₆₇	—	4	2	no	—
406	M₁₆×C₆₇	—	4	2	no	—
407	C₂×C₈×C₆₇	—	4	2	no	—
408	C₂×C₈×C₆₇	—	4	2	no	—
409	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
410	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
414	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	—	2	1	no	—
417	C₄⋊C₄×C₆₇	—	2	1	no	—
418	C₄⋊C₄×C₆₇	—	2	1	no	—
419	C₄⋊C₄×C₆₇	—	2	1	no	—
420	C₄⋊C₄×C₆₇	—	2	2	no	—
421	C₄⋊C₄×C₆₇	—	2	2	no	—
422	C₄⋊C₄×C₆₇	—	2	2	no	—
423	C₄⋊C₄×C₆₇	—	2	2	no	—
424	C₄⋊C₄×C₆₇	—	2	2	no	—
425	C₄⋊C₄×C₆₇	—	2	2	no	—
426	C₄⋊C₄×C₆₇	—	2	1	no	—
427	C₄⋊C₄×C₆₇	—	2	1	no	—
428	C₄⋊C₄×C₆₇	—	2	1	no	—
429	C₄⋊C₄×C₆₇	—	2	1	no	—
430	C₄⋊C₄×C₆₇	—	2	1	no	—
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	—	2	2	no	—
433	C₄⋊C₄×C₆₇	—	2	1	no	—
434	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
437	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
441	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
442	C₂²⋊C₄×C₆₇	—	2	2	no	—
443	C₂²⋊C₄×C₆₇	—	2	1	no	—
444	C₂²⋊C₄×C₆₇	—	2	2	no	—
445	C₂²⋊C₄×C₆₇	—	2	1	no	—
446	C₂²⋊C₄×C₆₇	—	2	2	no	—
447	C₂²⋊C₄×C₆₇	—	2	2	no	—
448	C₂²⋊C₄×C₆₇	—	2	2	no	—
449	C₂²⋊C₄×C₆₇	—	2	2	no	—
450	C₂²⋊C₄×C₆₇	—	2	1	no	—
451	C₂²⋊C₄×C₆₇	—	2	2	no	—
452	C₂²⋊C₄×C₆₇	—	2	1	no	—
453	C₂²⋊C₄×C₆₇	—	2	1	no	—
454	C₂²⋊C₄×C₆₇	—	2	1	no	—
455	C₂²⋊C₄×C₆₇	—	2	1	no	—
456	C₂²⋊C₄×C₆₇	—	2	2	no	—
457	C₂²⋊C₄×C₆₇	—	2	2	no	—
458	C₂²⋊C₄×C₆₇	—	2	2	no	—
459	C₂²⋊C₄×C₆₇	—	2	1	no	—
460	C₂²⋊C₄×C₆₇	—	2	2	no	—
461	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
465	C₄²×C₆₇	—	2	1	no	—
466	C₄²×C₆₇	—	2	1	no	—
467	C₄²×C₆₇	—	2	1	no	—
468	C₄²×C₆₇	—	2	1	no	—
469	C₄²×C₆₇	—	2	2	no	—
470	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
473	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
474	C₂³×C₆₇	—	2	1	no	—
475	C₂³×C₆₇	—	2	1	no	—
476	C₂³×C₆₇	—	2	2	no	—
477	C₂³×C₆₇	—	8	2	no	—
478	C₂³×C₆₇	—	8	2	no	—
479	C₂³×C₆₇	—	8	2	no	—
480	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
481	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
482	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
483	Q₈×C₆₇	—	2	1	no	—
484	Q₈×C₆₇	—	2	1	no	—
485	Q₈×C₆₇	—	2	2	no	—
486	Q₈×C₆₇	—	2	2	no	—
487	Q₈×C₆₇	—	2	2	no	—
488	Q₈×C₆₇	—	2	2	no	—
489	Q₈×C₆₇	—	2	1	no	—
490	Q₈×C₆₇	—	4	2	no	—
491	Q₈×C₆₇	—	4	4	no	—
492	Q₈×C₆₇	—	4	4	no	—
493	Q₈×C₆₇	—	4	4	no	—
494	Q₈×C₆₇	—	4	2	no	—
495	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
496	D₄×C₆₇	—	2	4	no	—
497	D₄×C₆₇	—	2	2	no	—
498	D₄×C₆₇	—	2	2	no	—
499	D₄×C₆₇	—	2	1	no	—
500	D₄×C₆₇	—	2	1	no	—
501	D₄×C₆₇	—	2	2	no	—
502	D₄×C₆₇	—	2	1	no	—
503	D₄×C₆₇	—	2	2	no	—
504	D₄×C₆₇	—	4	2	no	—
505	D₄×C₆₇	—	4	2	no	—
506	D₄×C₆₇	—	4	2	no	—
507	D₄×C₆₇	—	4	2	no	—
508	D₄×C₆₇	—	4	4	no	—
509	D₄×C₆₇	—	4	4	no	—
510	D₄×C₆₇	—	4	2	no	—
511	D₄×C₆₇	—	8	1	no	—
512	D₄×C₆₇	—	8	2	no	—
513	D₄×C₆₇	—	8	1	no	—
514	D₄×C₆₇	—	8	2	no	—
515	D₄×C₆₇	—	8	2	no	—
516	D₄×C₆₇	—	8	2	no	—
517	D₄×C₆₇	—	8	2	no	—
518	D₄×C₆₇	—	8	2	no	—
519	D₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
520	C₂×C₄×C₆₇	—	2	4	no	—
521	C₂×C₄×C₆₇	—	2	1	no	—
522	C₂×C₄×C₆₇	—	2	2	no	—
523	C₂×C₄×C₆₇	—	2	2	no	—
524	C₂×C₄×C₆₇	—	2	2	no	—
525	C₂×C₄×C₆₇	—	2	2	no	—
526	C₂×C₄×C₆₇	—	2	2	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	1	no	—
529	C₂×C₄×C₆₇	—	2	1	no	—
530	C₂×C₄×C₆₇	—	2	1	no	—
531	C₂×C₄×C₆₇	—	2	1	no	—
532	C₂×C₄×C₆₇	—	2	1	no	—
533	C₂×C₄×C₆₇	—	2	2	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	2	2	no	—
536	C₂×C₄×C₆₇	—	2	2	no	—
537	C₂×C₄×C₆₇	—	4	1	no	—
538	C₂×C₄×C₆₇	—	4	4	no	—
539	C₂×C₄×C₆₇	—	4	4	no	—
540	C₂×C₄×C₆₇	—	4	4	no	—
541	C₂×C₄×C₆₇	—	4	4	no	—
542	C₂×C₄×C₆₇	—	4	2	no	—
543	C₂×C₄×C₆₇	—	4	4	no	—
544	C₂×C₄×C₆₇	—	4	2	no	—
545	C₂×C₄×C₆₇	—	4	2	no	—
546	C₂×C₄×C₆₇	—	8	2	no	—
547	C₂×C₄×C₆₇	—	8	2	no	—
548	C₂×C₄×C₆₇	—	8	2	no	—
549	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
552	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
557	C₈×C₆₇	—	2	1	no	—
558	C₈×C₆₇	—	2	1	no	—
559	C₈×C₆₇	—	2	2	no	—
560	C₈×C₆₇	—	2	2	no	—
561	C₈×C₆₇	—	2	1	no	—
562	C₈×C₆₇	—	2	1	no	—
563	C₂²×C₆₇	—	2	1	no	—
564	C₂²×C₆₇	—	2	2	no	—
565	C₂²×C₆₇	—	2	2	no	—
566	C₂²×C₆₇	—	2	1	no	—
567	C₂²×C₆₇	—	2	2	no	—
568	C₂²×C₆₇	—	2	2	no	—
569	C₂²×C₆₇	—	2	2	no	—
570	C₂²×C₆₇	—	2	1	no	—
571	C₂²×C₆₇	—	2	2	no	—
572	C₂²×C₆₇	—	2	2	no	—
573	C₂²×C₆₇	—	4	1	no	—
574	C₂²×C₆₇	—	4	1	no	—
575	C₂²×C₆₇	—	4	2	no	—
576	C₂²×C₆₇	—	4	1	no	—
577	C₂²×C₆₇	—	4	2	no	—
578	C₂²×C₆₇	—	4	1	no	—
579	C₂²×C₆₇	—	4	1	no	—
580	C₂²×C₆₇	—	4	2	no	—
581	C₂²×C₆₇	—	16	4	no	—
582	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
583	C₄×C₆₇	—	2	1	no	—
584	C₄×C₆₇	—	2	1	no	—
585	C₄×C₆₇	—	2	1	no	—
586	C₄×C₆₇	—	2	2	no	—
587	C₄×C₆₇	—	2	2	no	—
588	C₄×C₆₇	—	2	2	no	—
589	C₄×C₆₇	—	2	1	no	—
590	C₄×C₆₇	—	4	1	no	—
591	C₄×C₆₇	—	4	1	no	—
592	C₄×C₆₇	—	4	2	no	—
593	C₄×C₆₇	—	4	2	no	—
594	C₄×C₆₇	—	4	1	no	—
595	C₄×C₆₇	—	4	1	no	—
596	C₄×C₆₇	—	4	1	no	—
597	C₄×C₆₇	—	4	2	no	—
598	C₄×C₆₇	#577	1	2	yes	—
599	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
600	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
601	#61692	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
602	C₂×C₆₇	—	4	1	no	—
603	C₂×C₆₇	—	4	2	no	—
604	C₂×C₆₇	—	4	2	no	—
605	C₂×C₆₇	—	4	2	no	—
606	C₂×C₆₇	—	8	2	no	—
607	C₂×C₆₇	—	8	1	no	—
608	C₂×C₆₇	#3484	1	1	yes	characteristic
609	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
610	C₂×C₆₇	#3586	1	1	yes	characteristic
611	#3546	C₂×C₆₇	1	1	yes	characteristic, complemented
612	#3499	C₂×C₆₇	1	1	yes	characteristic, complemented
613	#3330	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#3328	C₂×C₆₇	1	1	yes	characteristic, complemented
615	#3320	C₂×C₆₇	1	2	yes	complemented
616	#3307	C₂×C₆₇	1	2	yes	complemented
617	#3302	C₂×C₆₇	1	1	yes	characteristic, complemented
618	#3298	C₂×C₆₇	1	1	yes	characteristic, complemented
619	#3284	C₂×C₆₇	1	1	yes	characteristic, complemented
620	D₄×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
621	#3278	C₂×C₆₇	1	1	yes	characteristic, complemented
622	#3272	C₂×C₆₇	1	1	yes	characteristic, complemented
623	#3267	C₂×C₆₇	1	2	yes	complemented
624	#3266	C₂×C₆₇	1	2	yes	complemented
625	#3218	C₂×C₆₇	1	1	yes	characteristic, complemented
626	#3206	C₂×C₆₇	1	1	yes	characteristic, complemented
627	#3201	C₂×C₆₇	1	2	yes	complemented
628	#3200	C₂×C₆₇	1	2	yes	complemented
629	#3115	C₂×C₆₇	1	1	yes	characteristic, complemented
630	#3102	C₂×C₆₇	1	1	yes	characteristic, complemented
631	#3013	C₂×C₆₇	1	2	yes	complemented
632	#3010	C₂×C₆₇	1	2	yes	complemented
633	#2981	C₂×C₆₇	1	1	yes	characteristic, complemented
634	C₆₇	#61692	1	1	yes	characteristic, direct product factor, Sylow
635	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	complemented
636	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
637	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
638	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
639	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
640	#560	—	2	2	no	—
641	#556	C₂²×C₆₇	1	1	yes	characteristic
642	#553	C₂²×C₆₇	1	2	yes	—
643	#550	—	2	1	no	—
644	#550	C₂²×C₆₇	1	1	yes	characteristic
645	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
646	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
647	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
648	#547	—	2	1	no	—
649	#547	—	2	1	no	—
650	#547	—	2	2	no	—
651	#547	C₂²×C₆₇	1	1	yes	characteristic
652	#547	C₂²×C₆₇	1	1	yes	characteristic
653	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	#547	C₂²×C₆₇	1	2	yes	complemented
655	#546	—	2	1	no	—
656	#546	C₂²×C₆₇	1	2	yes	—
657	D₄²	C₂²×C₆₇	1	1	yes	characteristic
658	#542	—	2	1	no	—
659	#538	—	2	2	no	—
660	#537	C₂²×C₆₇	1	2	yes	—
661	#536	—	2	2	no	—
662	#536	C₂²×C₆₇	1	2	yes	complemented
663	#535	—	2	1	no	—
664	#535	C₂²×C₆₇	1	2	yes	—
665	#532	—	2	1	no	—
666	#532	C₂²×C₆₇	1	1	yes	characteristic
667	#532	C₂²×C₆₇	1	1	yes	characteristic
668	C₂×C₄⋊Q₈	—	2	1	no	—
669	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
670	#529	C₂²×C₆₇	1	1	yes	characteristic
671	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
672	#497	C₂²×C₆₇	1	2	yes	—
673	#492	C₂²×C₆₇	1	1	yes	characteristic
674	#492	C₂²×C₆₇	1	1	yes	characteristic
675	#491	C₂²×C₆₇	1	2	yes	complemented
676	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
677	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
678	#485	C₂²×C₆₇	1	2	yes	complemented
679	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
680	#485	C₂²×C₆₇	1	2	yes	complemented
681	#484	C₂²×C₆₇	1	2	yes	complemented
682	#483	C₂²×C₆₇	1	2	yes	complemented
683	#482	C₂²×C₆₇	1	1	yes	characteristic
684	#482	C₂²×C₆₇	1	2	yes	complemented
685	#479	C₂²×C₆₇	1	1	yes	characteristic, complemented
686	#478	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
689	#470	C₂²×C₆₇	1	2	yes	complemented
690	#468	C₂²×C₆₇	1	2	yes	—
691	#468	C₂²×C₆₇	1	2	yes	—
692	#468	C₂²×C₆₇	1	2	yes	complemented
693	#467	C₂²×C₆₇	1	2	yes	complemented
694	#465	C₂²×C₆₇	1	2	yes	—
695	#465	C₂²×C₆₇	1	2	yes	—
696	#465	C₂²×C₆₇	1	2	yes	complemented
697	#464	C₂²×C₆₇	1	1	yes	characteristic
698	#463	C₂²×C₆₇	1	1	yes	characteristic
699	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
700	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
701	#461	C₂²×C₆₇	1	1	yes	characteristic
702	#461	C₂²×C₆₇	1	1	yes	characteristic
703	#461	C₂²×C₆₇	1	2	yes	complemented
704	#461	C₂²×C₆₇	1	2	yes	complemented
705	#460	C₂²×C₆₇	1	1	yes	characteristic
706	#459	C₂²×C₆₇	1	1	yes	characteristic
707	#452	C₂²×C₆₇	1	1	yes	characteristic, complemented
708	#452	C₂²×C₆₇	1	2	yes	complemented
709	#452	C₂²×C₆₇	1	2	yes	complemented
710	#452	C₂²×C₆₇	1	2	yes	complemented
711	#451	C₂²×C₆₇	1	2	yes	complemented
712	#451	C₂²×C₆₇	1	2	yes	complemented
713	#450	C₂²×C₆₇	1	2	yes	—
714	#450	C₂²×C₆₇	1	2	yes	—
715	#449	C₂²×C₆₇	1	2	yes	—
716	#449	C₂²×C₆₇	1	1	yes	characteristic
717	#449	C₂²×C₆₇	1	2	yes	—
718	#449	C₂²×C₆₇	1	2	yes	complemented
719	#449	C₂²×C₆₇	1	2	yes	complemented
720	#448	C₂²×C₆₇	1	2	yes	—
721	#448	C₂²×C₆₇	1	2	yes	—
722	#448	C₂²×C₆₇	1	2	yes	—
723	#448	C₂²×C₆₇	1	2	yes	complemented
724	#448	C₂²×C₆₇	1	2	yes	complemented
725	#448	C₂²×C₆₇	1	2	yes	complemented
726	#442	C₂²×C₆₇	1	2	yes	complemented
727	#440	C₂²×C₆₇	1	2	yes	complemented
728	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
729	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
730	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
731	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
732	#436	C₂²×C₆₇	1	1	yes	characteristic
733	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
734	#435	C₂²×C₆₇	1	2	yes	complemented
735	#435	C₂²×C₆₇	1	2	yes	complemented
736	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
737	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
738	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
739	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
740	#419	C₂²×C₆₇	1	2	yes	complemented
741	#417	C₂²×C₆₇	1	2	yes	complemented
742	#416	C₂²×C₆₇	1	2	yes	complemented
743	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
744	#408	C₂²×C₆₇	1	2	yes	complemented
745	#408	C₂²×C₆₇	1	2	yes	complemented
746	2₋¹⁺⁴	—	4	4	no	—
747	2₋¹⁺⁴	—	4	4	no	—
748	C₂×#41	—	2	2	no	—
749	C₂×#41	—	2	2	no	—
750	C₂×#41	—	2	2	no	—
751	C₂×#41	—	2	1	no	—
752	C₂×#41	—	2	1	no	—
753	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
754	C₂×#41	C₂³×C₆₇	1	2	yes	—
755	C₂×#41	C₂³×C₆₇	1	2	yes	—
756	C₂×#41	C₂³×C₆₇	1	2	yes	—
757	C₂×#41	C₂³×C₆₇	1	2	yes	—
758	C₂²×Q₈	—	2	2	no	—
759	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
760	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
761	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
762	C₂²×D₄	—	2	1	no	—
763	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
764	#137	—	4	4	no	—
765	AGL(1,ℤ/8)	—	4	4	no	—
766	#135	—	4	4	no	—
767	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
768	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
769	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
770	C₂×SD₁₆	—	4	4	no	—
771	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
772	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
773	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
774	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
780	C₂×D₈	C₂³×C₆₇	1	2	yes	—
781	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
782	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
783	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
784	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
785	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
786	C₄⋊Q₈	—	2	2	no	—
787	C₄⋊Q₈	—	2	1	no	—
788	C₄⋊Q₈	—	2	1	no	—
789	C₄⋊Q₈	—	2	2	no	—
790	C₄⋊Q₈	—	2	1	no	—
791	C₄⋊Q₈	—	2	1	no	—
792	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
793	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
794	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
795	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
796	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
797	#127	—	2	1	no	—
798	#127	—	2	2	no	—
799	#127	D₄×C₆₇	1	1	yes	characteristic
800	#127	C₂³×C₆₇	1	1	yes	characteristic
801	#126	—	2	2	no	—
802	#126	—	2	2	no	—
803	#126	—	2	1	no	—
804	#125	C₂³×C₆₇	1	1	yes	characteristic
805	#124	—	2	2	no	—
806	#124	—	2	2	no	—
807	#124	—	2	1	no	—
808	#124	—	2	1	no	—
809	#124	D₄×C₆₇	1	2	yes	—
810	#124	C₂³×C₆₇	1	1	yes	characteristic
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	1	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	—	2	1	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	—	2	2	no	—
825	C₂²⋊Q₈	—	2	2	no	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
828	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
829	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
830	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
831	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
832	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
833	#121	—	2	1	no	—
834	#121	—	2	1	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	1	no	—
841	#121	—	2	1	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	D₄×C₆₇	1	1	yes	characteristic
845	#121	D₄×C₆₇	1	1	yes	characteristic
846	#121	D₄×C₆₇	1	2	yes	—
847	#121	C₂³×C₆₇	1	1	yes	characteristic
848	#121	C₂³×C₆₇	1	2	yes	—
849	#121	C₂³×C₆₇	1	2	yes	—
850	#121	C₂³×C₆₇	1	2	yes	—
851	#121	C₂³×C₆₇	1	2	yes	—
852	#120	—	2	2	no	—
853	#120	—	2	2	no	—
854	#120	—	2	2	no	—
855	#120	—	2	2	no	—
856	C₄×Q₈	—	2	1	no	—
857	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
858	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
859	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
870	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
871	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
872	C₄×D₄	C₂³×C₆₇	1	2	yes	—
873	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
874	C₄×D₄	C₂³×C₆₇	1	2	yes	—
875	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
876	#117	—	2	1	no	—
877	#117	—	2	1	no	—
878	#117	C₂³×C₆₇	1	1	yes	characteristic
879	#117	C₂³×C₆₇	1	2	yes	—
880	C₂×C₄⋊C₄	—	2	1	no	—
881	C₂×C₄⋊C₄	—	2	1	no	—
882	C₂×C₄⋊C₄	—	2	1	no	—
883	C₂×C₄⋊C₄	—	2	1	no	—
884	C₂×C₄⋊C₄	—	2	2	no	—
885	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
886	C₂×C₂²⋊C₄	—	2	2	no	—
887	C₂×C₄²	—	2	1	no	—
888	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
889	#107	C₂³×C₆₇	1	1	yes	characteristic
890	#107	C₂³×C₆₇	1	1	yes	characteristic
891	#107	C₂³×C₆₇	1	2	yes	—
892	#106	C₂³×C₆₇	1	1	yes	characteristic
893	#106	C₂³×C₆₇	1	1	yes	characteristic
894	#106	C₂³×C₆₇	1	2	yes	—
895	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
896	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
897	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
898	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
899	#103	C₂³×C₆₇	1	1	yes	characteristic
900	#103	C₂³×C₆₇	1	2	yes	—
901	#103	C₂³×C₆₇	1	2	yes	—
902	#103	C₂³×C₆₇	1	2	yes	—
903	#103	C₂³×C₆₇	1	2	yes	—
904	#103	C₂³×C₆₇	1	2	yes	—
905	#103	C₂³×C₆₇	1	2	yes	—
906	#103	C₂³×C₆₇	1	2	yes	—
907	#103	C₂³×C₆₇	1	1	yes	characteristic
908	#103	C₂³×C₆₇	1	2	yes	—
909	#103	C₂³×C₆₇	1	2	yes	—
910	#103	C₂³×C₆₇	1	1	yes	characteristic
911	#103	C₂³×C₆₇	1	1	yes	characteristic
912	#102	C₂³×C₆₇	1	1	yes	characteristic
913	#102	C₂³×C₆₇	1	2	yes	—
914	#102	C₂³×C₆₇	1	1	yes	characteristic
915	#102	C₂³×C₆₇	1	1	yes	characteristic
916	#102	C₂³×C₆₇	1	1	yes	characteristic
917	#102	C₂³×C₆₇	1	2	yes	—
918	#102	C₂³×C₆₇	1	2	yes	—
919	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
920	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
921	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
922	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
923	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
924	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
925	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
926	#97	C₂³×C₆₇	1	2	yes	—
927	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
928	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
929	C₂⁴	—	2	2	no	—
930	#41	—	2	2	no	—
931	#41	—	2	2	no	—
932	#41	—	2	4	no	—
933	#41	—	2	4	no	—
934	#41	—	4	2	no	—
935	#41	—	4	2	no	—
936	#41	—	4	2	no	—
937	#41	—	4	2	no	—
938	#41	—	4	8	no	—
939	#41	—	4	2	no	—
940	#41	—	4	2	no	—
941	#41	—	4	8	no	—
942	#41	—	4	8	no	—
943	#41	—	8	2	no	—
944	#41	—	8	2	no	—
945	C₂×Q₈	—	2	1	no	—
946	C₂×Q₈	—	2	2	no	—
947	C₂×Q₈	—	2	2	no	—
948	C₂×Q₈	—	2	2	no	—
949	C₂×Q₈	—	2	4	no	—
950	C₂×Q₈	—	2	4	no	—
951	C₂×Q₈	—	4	2	no	—
952	C₂×Q₈	—	4	2	no	—
953	C₂×Q₈	—	4	2	no	—
954	C₂×Q₈	—	4	2	no	—
955	C₂×Q₈	—	4	8	no	—
956	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
957	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
958	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
959	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
960	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	1	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	4	2	no	—
974	C₂×D₄	—	4	2	no	—
975	C₂×D₄	—	8	2	no	—
976	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
977	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
978	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
979	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
980	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
981	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
982	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
983	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
984	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
985	C₂²×C₄	—	2	1	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	1	no	—
991	C₂²×C₄	—	2	1	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
998	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1000	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1001	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1002	Q₁₆	—	2	2	no	—
1003	Q₁₆	—	4	2	no	—
1004	Q₁₆	—	4	2	no	—
1005	SD₁₆	—	2	2	no	—
1006	SD₁₆	—	2	4	no	—
1007	SD₁₆	—	2	2	no	—
1008	SD₁₆	—	4	2	no	—
1009	SD₁₆	—	4	2	no	—
1010	SD₁₆	—	4	2	no	—
1011	SD₁₆	—	4	2	no	—
1012	SD₁₆	—	4	2	no	—
1013	SD₁₆	—	4	2	no	—
1014	D₈	—	2	4	no	—
1015	D₈	—	2	2	no	—
1016	M₁₆	—	4	2	no	—
1017	M₁₆	—	4	2	no	—
1018	C₂×C₈	—	4	2	no	—
1019	C₂×C₈	—	4	2	no	—
1020	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1021	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1022	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1023	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1024	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1025	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1046	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1047	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1048	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1051	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1052	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1073	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1074	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1076	C₄²	—	2	1	no	—
1077	C₄²	—	2	1	no	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	2	no	—
1081	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1082	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1083	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1084	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1085	C₂³	—	2	1	no	—
1086	C₂³	—	2	1	no	—
1087	C₂³	—	2	2	no	—
1088	C₂³	—	8	2	no	—
1089	C₂³	—	8	2	no	—
1090	C₂³	—	8	2	no	—
1091	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1092	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1093	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1094	Q₈	—	2	1	no	—
1095	Q₈	—	2	1	no	—
1096	Q₈	—	2	2	no	—
1097	Q₈	—	2	2	no	—
1098	Q₈	—	2	2	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	1	no	—
1101	Q₈	—	4	2	no	—
1102	Q₈	—	4	4	no	—
1103	Q₈	—	4	4	no	—
1104	Q₈	—	4	4	no	—
1105	Q₈	—	4	2	no	—
1106	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1107	D₄	—	2	4	no	—
1108	D₄	—	2	2	no	—
1109	D₄	—	2	2	no	—
1110	D₄	—	2	1	no	—
1111	D₄	—	2	1	no	—
1112	D₄	—	2	2	no	—
1113	D₄	—	2	1	no	—
1114	D₄	—	2	2	no	—
1115	D₄	—	4	2	no	—
1116	D₄	—	4	2	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	4	2	no	—
1119	D₄	—	4	4	no	—
1120	D₄	—	4	4	no	—
1121	D₄	—	4	2	no	—
1122	D₄	—	8	2	no	—
1123	D₄	—	8	1	no	—
1124	D₄	—	8	2	no	—
1125	D₄	—	8	2	no	—
1126	D₄	—	8	2	no	—
1127	D₄	—	8	2	no	—
1128	D₄	—	8	1	no	—
1129	D₄	—	8	2	no	—
1130	D₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1131	C₂×C₄	—	2	4	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	4	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	4	4	no	—
1155	C₂×C₄	—	4	2	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	8	2	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1161	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1162	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1166	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1167	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1168	C₈	—	2	1	no	—
1169	C₈	—	2	1	no	—
1170	C₈	—	2	2	no	—
1171	C₈	—	2	2	no	—
1172	C₈	—	2	1	no	—
1173	C₈	—	2	1	no	—
1174	C₂²	—	2	1	no	—
1175	C₂²	—	2	2	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	2	2	no	—
1179	C₂²	—	2	2	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	2	no	—
1188	C₂²	—	4	2	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	2	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	16	4	no	—
1193	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1194	C₄	—	2	1	no	—
1195	C₄	—	2	1	no	—
1196	C₄	—	2	1	no	—
1197	C₄	—	2	1	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	2	2	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	2	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	2	no	—
1208	C₄	—	4	1	no	—
1209	C₄	#577×C₆₇	1	2	yes	—
1210	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1211	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1212	C₂	—	4	2	no	—
1213	C₂	—	4	1	no	—
1214	C₂	—	4	2	no	—
1215	C₂	—	4	2	no	—
1216	C₂	—	8	1	no	—
1217	C₂	—	8	2	no	—
1218	C₂	C₆₇×#3484	1	1	yes	characteristic
1219	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1220	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 ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3546	C₂	semidirect
2. C₆₇×#3499	C₂	semidirect
3. C₆₇×#3330	C₂	semidirect
4. C₆₇×#3328	C₂	semidirect
5. C₆₇×#3320	C₂	semidirect
6. C₆₇×#3307	C₂	semidirect
7. C₆₇×#3302	C₂	semidirect
8. C₆₇×#3298	C₂	semidirect
9. C₆₇×#3284	C₂	semidirect
10. D₄×SD₁₆×C₆₇	C₂	semidirect
11. C₆₇×#3278	C₂	semidirect
12. C₆₇×#3272	C₂	semidirect
13. C₆₇×#3267	C₂	semidirect
14. C₆₇×#3266	C₂	semidirect
15. C₆₇×#3218	C₂	semidirect
16. C₆₇×#3206	C₂	semidirect
17. C₆₇×#3201	C₂	semidirect
18. C₆₇×#3200	C₂	semidirect
19. C₆₇×#3115	C₂	semidirect
20. C₆₇×#3102	C₂	semidirect
21. C₆₇×#3013	C₂	semidirect
22. C₆₇×#3010	C₂	semidirect
23. C₆₇×#2981	C₂	semidirect
24. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
25. C₂×#137×C₆₇	C₂²	semidirect
27. C₂×#135×C₆₇	C₂²	semidirect
35. D₄×Q₈×C₆₇	C₂²	semidirect
36. D₄×Q₈×C₆₇	C₂²	semidirect
42. #547×C₆₇	C₂²	semidirect
43. #547×C₆₇	C₂²	semidirect
51. #536×C₆₇	C₂²	semidirect
58. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
60. C₄×#41×C₆₇	C₂²	semidirect
64. #491×C₆₇	C₂²	semidirect
65. #487×C₆₇	C₂²	semidirect
66. #487×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
68. #485×C₆₇	C₂²	semidirect
69. #485×C₆₇	C₂²	semidirect
70. #484×C₆₇	C₂²	semidirect
71. #483×C₆₇	C₂²	semidirect
73. #482×C₆₇	C₂²	semidirect
74. #479×C₆₇	C₂²	semidirect
75. #478×C₆₇	C₂²	semidirect
76. #475×C₆₇	C₂²	semidirect
77. #474×C₆₇	C₂²	semidirect
78. #470×C₆₇	C₂²	semidirect
81. #468×C₆₇	C₂²	semidirect
82. #467×C₆₇	C₂²	semidirect
85. #465×C₆₇	C₂²	semidirect
88. #462×C₆₇	C₂²	semidirect
89. #462×C₆₇	C₂²	semidirect
92. #461×C₆₇	C₂²	semidirect
93. #461×C₆₇	C₂²	semidirect
96. #452×C₆₇	C₂²	semidirect
97. #452×C₆₇	C₂²	semidirect
98. #452×C₆₇	C₂²	semidirect
99. #452×C₆₇	C₂²	semidirect
100. #451×C₆₇	C₂²	semidirect
101. #451×C₆₇	C₂²	semidirect
107. #449×C₆₇	C₂²	semidirect
108. #449×C₆₇	C₂²	semidirect
112. #448×C₆₇	C₂²	semidirect
113. #448×C₆₇	C₂²	semidirect
114. #448×C₆₇	C₂²	semidirect
115. #442×C₆₇	C₂²	semidirect
116. #440×C₆₇	C₂²	semidirect
117. C₄×Q₁₆×C₆₇	C₂²	semidirect
119. C₄×SD₁₆×C₆₇	C₂²	semidirect
122. #436×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. #435×C₆₇	C₂²	semidirect
126. C₈×D₄×C₆₇	C₂²	semidirect
127. #432×C₆₇	C₂²	semidirect
128. #431×C₆₇	C₂²	semidirect
129. #419×C₆₇	C₂²	semidirect
130. #417×C₆₇	C₂²	semidirect
131. #416×C₆₇	C₂²	semidirect
132. C₂×#103×C₆₇	C₂²	semidirect
133. #408×C₆₇	C₂²	semidirect
134. #408×C₆₇	C₂²	semidirect
601. #61692	C₆₇	direct (N × H)
611. #3546	C₂×C₆₇	semidirect
612. #3499	C₂×C₆₇	semidirect
613. #3330	C₂×C₆₇	semidirect
614. #3328	C₂×C₆₇	semidirect
615. #3320	C₂×C₆₇	semidirect
616. #3307	C₂×C₆₇	semidirect
617. #3302	C₂×C₆₇	semidirect
618. #3298	C₂×C₆₇	semidirect
619. #3284	C₂×C₆₇	semidirect
620. D₄×SD₁₆	C₂×C₆₇	semidirect
621. #3278	C₂×C₆₇	semidirect
622. #3272	C₂×C₆₇	semidirect
623. #3267	C₂×C₆₇	semidirect
624. #3266	C₂×C₆₇	semidirect
625. #3218	C₂×C₆₇	semidirect
626. #3206	C₂×C₆₇	semidirect
627. #3201	C₂×C₆₇	semidirect
628. #3200	C₂×C₆₇	semidirect
629. #3115	C₂×C₆₇	semidirect
630. #3102	C₂×C₆₇	semidirect
631. #3013	C₂×C₆₇	semidirect
632. #3010	C₂×C₆₇	semidirect
633. #2981	C₂×C₆₇	semidirect
634. C₆₇	#61692	direct (N × H)
635. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
636. C₂×#137	C₂²×C₆₇	semidirect
638. C₂×#135	C₂²×C₆₇	semidirect
646. D₄×Q₈	C₂²×C₆₇	semidirect
647. D₄×Q₈	C₂²×C₆₇	semidirect
653. #547	C₂²×C₆₇	semidirect
654. #547	C₂²×C₆₇	semidirect
662. #536	C₂²×C₆₇	semidirect
669. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
671. C₄×#41	C₂²×C₆₇	semidirect
675. #491	C₂²×C₆₇	semidirect
676. #487	C₂²×C₆₇	semidirect
677. #487	C₂²×C₆₇	semidirect
678. #485	C₂²×C₆₇	semidirect
679. #485	C₂²×C₆₇	semidirect
680. #485	C₂²×C₆₇	semidirect
681. #484	C₂²×C₆₇	semidirect
682. #483	C₂²×C₆₇	semidirect
684. #482	C₂²×C₆₇	semidirect
685. #479	C₂²×C₆₇	semidirect
686. #478	C₂²×C₆₇	semidirect
687. #475	C₂²×C₆₇	semidirect
688. #474	C₂²×C₆₇	semidirect
689. #470	C₂²×C₆₇	semidirect
692. #468	C₂²×C₆₇	semidirect
693. #467	C₂²×C₆₇	semidirect
696. #465	C₂²×C₆₇	semidirect
699. #462	C₂²×C₆₇	semidirect
700. #462	C₂²×C₆₇	semidirect
703. #461	C₂²×C₆₇	semidirect
704. #461	C₂²×C₆₇	semidirect
707. #452	C₂²×C₆₇	semidirect
708. #452	C₂²×C₆₇	semidirect
709. #452	C₂²×C₆₇	semidirect
710. #452	C₂²×C₆₇	semidirect
711. #451	C₂²×C₆₇	semidirect
712. #451	C₂²×C₆₇	semidirect
718. #449	C₂²×C₆₇	semidirect
719. #449	C₂²×C₆₇	semidirect
723. #448	C₂²×C₆₇	semidirect
724. #448	C₂²×C₆₇	semidirect
725. #448	C₂²×C₆₇	semidirect
726. #442	C₂²×C₆₇	semidirect
727. #440	C₂²×C₆₇	semidirect
728. C₄×Q₁₆	C₂²×C₆₇	semidirect
730. C₄×SD₁₆	C₂²×C₆₇	semidirect
733. #436	C₂²×C₆₇	semidirect
734. #435	C₂²×C₆₇	semidirect
735. #435	C₂²×C₆₇	semidirect
737. C₈×D₄	C₂²×C₆₇	semidirect
738. #432	C₂²×C₆₇	semidirect
739. #431	C₂²×C₆₇	semidirect
740. #419	C₂²×C₆₇	semidirect
741. #417	C₂²×C₆₇	semidirect
742. #416	C₂²×C₆₇	semidirect
743. C₂×#103	C₂²×C₆₇	semidirect
744. #408	C₂²×C₆₇	semidirect
745. #408	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×#3546	2
C₆₇×#3499	2
C₆₇×#3330	2
C₆₇×#3328	2
C₆₇×#3320	2
C₆₇×#3307	2
C₆₇×#3302	2
C₆₇×#3298	2
C₆₇×#3284	2
D₄×SD₁₆×C₆₇	2
C₆₇×#3278	2
C₆₇×#3272	2
C₆₇×#3267	2
C₆₇×#3266	2
C₆₇×#3218	2
C₆₇×#3206	2
C₆₇×#3201	2
C₆₇×#3200	2
C₆₇×#3115	2
C₆₇×#3102	2
C₆₇×#3013	2
C₆₇×#3010	2
C₆₇×#2981	2
#61692	67

Subgroups — C67×#61692 #30740943

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61692 #30740943