Subgroups — C₆₇×#61193 #30740444

Order 17152.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3489	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3331	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3326	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3316	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3312	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3307	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3306	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3298	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3296	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#483×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3060	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2952	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#417×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
31	#554×C₆₇	—	2	1	no	—
32	#554×C₆₇	C₂²	1	2	yes	complemented
33	#553×C₆₇	—	2	1	no	—
34	#553×C₆₇	C₂²	1	2	yes	complemented
35	#552×C₆₇	—	2	1	no	—
36	#552×C₆₇	C₂²	1	2	yes	—
37	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
38	#548×C₆₇	C₂²	1	2	yes	—
39	#547×C₆₇	—	2	2	no	—
40	#547×C₆₇	—	2	1	no	—
41	#547×C₆₇	C₂²	1	2	yes	—
42	#547×C₆₇	C₂²	1	2	yes	—
43	#546×C₆₇	—	2	2	no	—
44	#546×C₆₇	C₂²	1	2	yes	—
45	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#539×C₆₇	—	2	2	no	—
47	#537×C₆₇	—	2	1	no	—
48	#537×C₆₇	C₂²	1	1	yes	characteristic
49	#537×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#536×C₆₇	—	2	1	no	—
51	#536×C₆₇	C₂²	1	1	yes	characteristic
52	#525×C₆₇	—	2	1	no	—
53	#525×C₆₇	—	2	2	no	—
54	#525×C₆₇	C₂²	1	1	yes	characteristic
55	#525×C₆₇	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
57	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
58	#520×C₆₇	C₂²	1	1	yes	characteristic
59	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
62	#491×C₆₇	C₂²	1	2	yes	complemented
63	#489×C₆₇	C₂²	1	2	yes	complemented
64	#488×C₆₇	C₂²	1	2	yes	complemented
65	#487×C₆₇	C₂²	1	2	yes	complemented
66	#485×C₆₇	C₂²	1	2	yes	complemented
67	#483×C₆₇	C₂²	1	2	yes	—
68	#483×C₆₇	C₂²	1	2	yes	—
69	#483×C₆₇	C₂²	1	2	yes	complemented
70	#483×C₆₇	C₂²	1	2	yes	complemented
71	#483×C₆₇	C₂²	1	2	yes	complemented
72	#482×C₆₇	C₂²	1	2	yes	complemented
73	#481×C₆₇	C₂²	1	2	yes	complemented
74	#479×C₆₇	C₂²	1	2	yes	complemented
75	#478×C₆₇	C₂²	1	2	yes	complemented
76	#476×C₆₇	C₂²	1	2	yes	complemented
77	#475×C₆₇	C₂²	1	2	yes	complemented
78	#470×C₆₇	C₂²	1	2	yes	complemented
79	#470×C₆₇	C₂²	1	2	yes	complemented
80	#469×C₆₇	C₂²	1	2	yes	complemented
81	#468×C₆₇	C₂²	1	2	yes	complemented
82	#467×C₆₇	C₂²	1	2	yes	—
83	#465×C₆₇	C₂²	1	2	yes	—
84	#465×C₆₇	C₂²	1	2	yes	complemented
85	#465×C₆₇	C₂²	1	2	yes	complemented
86	#464×C₆₇	C₂²	1	2	yes	complemented
87	#463×C₆₇	C₂²	1	2	yes	complemented
88	#462×C₆₇	C₂²	1	2	yes	complemented
89	#461×C₆₇	C₂²	1	2	yes	complemented
90	#452×C₆₇	C₂²	1	1	yes	characteristic
91	#452×C₆₇	C₂²	1	1	yes	characteristic
92	#452×C₆₇	C₂²	1	2	yes	complemented
93	#451×C₆₇	C₂²	1	1	yes	characteristic
94	#451×C₆₇	C₂²	1	2	yes	complemented
95	#450×C₆₇	C₂²	1	1	yes	characteristic
96	#449×C₆₇	C₂²	1	1	yes	characteristic
97	#449×C₆₇	C₂²	1	1	yes	characteristic
98	#449×C₆₇	C₂²	1	2	yes	complemented
99	#448×C₆₇	C₂²	1	1	yes	characteristic
100	#448×C₆₇	C₂²	1	2	yes	complemented
101	#447×C₆₇	C₂²	1	1	yes	characteristic
102	#442×C₆₇	C₂²	1	2	yes	complemented
103	#441×C₆₇	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
106	#436×C₆₇	C₂²	1	2	yes	complemented
107	#435×C₆₇	C₂²	1	2	yes	—
108	#435×C₆₇	C₂²	1	2	yes	complemented
109	C₈×D₄×C₆₇	C₂²	1	2	yes	—
110	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	#419×C₆₇	C₂²	1	2	yes	complemented
116	#417×C₆₇	C₂²	1	1	yes	characteristic
117	#417×C₆₇	C₂²	1	1	yes	characteristic
118	#417×C₆₇	C₂²	1	2	yes	—
119	#417×C₆₇	C₂²	1	1	yes	characteristic
120	#417×C₆₇	C₂²	1	2	yes	—
121	#417×C₆₇	C₂²	1	1	yes	characteristic
122	#417×C₆₇	C₂²	1	2	yes	complemented
123	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#416×C₆₇	C₂²	1	1	yes	characteristic
125	#416×C₆₇	C₂²	1	1	yes	characteristic
126	#416×C₆₇	C₂²	1	2	yes	complemented
127	C₂×#103×C₆₇	C₂²	1	2	yes	—
128	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
130	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	C₂×#102×C₆₇	C₂²	1	2	yes	—
132	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
134	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	2₋¹⁺⁴×C₆₇	—	2	4	no	—
136	2₋¹⁺⁴×C₆₇	—	4	2	no	—
137	C₂×#41×C₆₇	—	2	1	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	—	2	4	no	—
143	C₂×#41×C₆₇	—	4	2	no	—
144	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×#41×C₆₇	C₂³	1	2	yes	—
149	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₆₇	—	2	1	no	—
152	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
155	C₂²×D₄×C₆₇	—	2	1	no	—
156	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₆₇	—	2	1	no	—
158	C₂³×C₄×C₆₇	—	2	1	no	—
159	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
160	#137×C₆₇	—	4	2	no	—
161	#135×C₆₇	—	2	4	no	—
162	#135×C₆₇	—	4	2	no	—
163	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
170	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
173	#131×C₆₇	—	4	2	no	—
174	C₂×M₁₆×C₆₇	—	4	2	no	—
175	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
178	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
179	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
181	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
182	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
183	C₄⋊Q₈×C₆₇	—	2	2	no	—
184	C₄⋊Q₈×C₆₇	—	2	1	no	—
185	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
186	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
187	#126×C₆₇	—	2	2	no	—
188	#126×C₆₇	—	2	2	no	—
189	#125×C₆₇	—	2	2	no	—
190	#125×C₆₇	—	2	2	no	—
191	#125×C₆₇	—	2	1	no	—
192	#125×C₆₇	C₂³	1	2	yes	—
193	#124×C₆₇	—	2	2	no	—
194	#124×C₆₇	C₂³	1	2	yes	—
195	#123×C₆₇	—	2	2	no	—
196	#123×C₆₇	—	2	1	no	—
197	#123×C₆₇	—	2	2	no	—
198	#123×C₆₇	—	2	2	no	—
199	#123×C₆₇	—	2	2	no	—
200	#123×C₆₇	—	2	2	no	—
201	#123×C₆₇	—	2	2	no	—
202	#123×C₆₇	—	2	2	no	—
203	#123×C₆₇	—	2	2	no	—
204	#123×C₆₇	D₄	1	2	yes	—
205	C₂²⋊Q₈×C₆₇	—	2	1	no	—
206	C₂²⋊Q₈×C₆₇	—	2	1	no	—
207	C₂²⋊Q₈×C₆₇	—	2	1	no	—
208	C₂²⋊Q₈×C₆₇	—	2	1	no	—
209	C₂²⋊Q₈×C₆₇	—	2	1	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	—	2	2	no	—
217	C₂²⋊Q₈×C₆₇	—	2	2	no	—
218	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
219	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
220	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
221	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
223	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
225	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
226	#121×C₆₇	—	2	1	no	—
227	#121×C₆₇	—	2	2	no	—
228	#121×C₆₇	—	2	2	no	—
229	#121×C₆₇	—	2	2	no	—
230	#121×C₆₇	—	2	2	no	—
231	#121×C₆₇	—	2	2	no	—
232	#121×C₆₇	—	2	1	no	—
233	#121×C₆₇	—	2	2	no	—
234	#121×C₆₇	D₄	1	1	yes	characteristic
235	#121×C₆₇	D₄	1	1	yes	characteristic
236	#121×C₆₇	C₂³	1	1	yes	characteristic
237	#121×C₆₇	C₂³	1	2	yes	—
238	#121×C₆₇	C₂³	1	1	yes	characteristic
239	#121×C₆₇	C₂³	1	2	yes	—
240	#120×C₆₇	—	2	1	no	—
241	#120×C₆₇	—	2	2	no	—
242	#120×C₆₇	D₄	1	2	yes	—
243	C₄×Q₈×C₆₇	—	2	1	no	—
244	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
245	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
246	C₄×D₄×C₆₇	—	2	2	no	—
247	C₄×D₄×C₆₇	—	2	1	no	—
248	C₄×D₄×C₆₇	—	2	2	no	—
249	C₄×D₄×C₆₇	—	2	2	no	—
250	C₄×D₄×C₆₇	—	2	1	no	—
251	C₄×D₄×C₆₇	—	2	1	no	—
252	C₄×D₄×C₆₇	—	2	2	no	—
253	C₄×D₄×C₆₇	—	2	2	no	—
254	C₄×D₄×C₆₇	—	2	2	no	—
255	C₄×D₄×C₆₇	—	2	2	no	—
256	C₄×D₄×C₆₇	C₂³	1	2	yes	—
257	C₄×D₄×C₆₇	C₂³	1	2	yes	—
258	C₄×D₄×C₆₇	C₂³	1	2	yes	—
259	C₄×D₄×C₆₇	C₂³	1	2	yes	—
260	#117×C₆₇	—	2	1	no	—
261	#117×C₆₇	—	2	1	no	—
262	#117×C₆₇	—	2	2	no	—
263	#117×C₆₇	C₂³	1	2	yes	—
264	#117×C₆₇	C₂³	1	1	yes	characteristic
265	#117×C₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
267	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
268	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
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	2	no	—
273	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
274	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
275	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
276	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
278	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
280	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
281	#107×C₆₇	C₂³	1	2	yes	—
282	#106×C₆₇	C₂³	1	2	yes	—
283	#106×C₆₇	C₂³	1	2	yes	—
284	#106×C₆₇	C₂³	1	2	yes	—
285	#106×C₆₇	C₂³	1	2	yes	—
286	#106×C₆₇	C₂³	1	2	yes	—
287	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
288	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	1	yes	characteristic
290	#103×C₆₇	C₂³	1	1	yes	characteristic
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
300	#103×C₆₇	C₂³	1	2	yes	—
301	#103×C₆₇	C₂³	1	2	yes	—
302	#103×C₆₇	C₂³	1	2	yes	—
303	#103×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	1	yes	characteristic
308	#102×C₆₇	C₂³	1	1	yes	characteristic
309	#102×C₆₇	C₂³	1	2	yes	—
310	#102×C₆₇	C₂³	1	2	yes	—
311	#102×C₆₇	C₂³	1	2	yes	—
312	#102×C₆₇	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
315	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
319	#97×C₆₇	C₂³	1	2	yes	—
320	C₄×C₈×C₆₇	C₂³	1	2	yes	—
321	C₂⁴×C₆₇	—	2	1	no	—
322	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
323	#41×C₆₇	—	2	2	no	—
324	#41×C₆₇	—	2	2	no	—
325	#41×C₆₇	—	2	2	no	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	—	2	2	no	—
328	#41×C₆₇	—	2	4	no	—
329	#41×C₆₇	—	2	2	no	—
330	#41×C₆₇	—	2	2	no	—
331	#41×C₆₇	—	2	2	no	—
332	#41×C₆₇	—	2	2	no	—
333	#41×C₆₇	—	4	4	no	—
334	#41×C₆₇	—	4	1	no	—
335	#41×C₆₇	—	4	1	no	—
336	#41×C₆₇	—	4	2	no	—
337	#41×C₆₇	—	4	4	no	—
338	#41×C₆₇	—	4	4	no	—
339	#41×C₆₇	—	4	8	no	—
340	#41×C₆₇	—	8	4	no	—
341	#41×C₆₇	#41	1	4	yes	complemented
342	C₂×Q₈×C₆₇	—	2	1	no	—
343	C₂×Q₈×C₆₇	—	2	2	no	—
344	C₂×Q₈×C₆₇	—	2	1	no	—
345	C₂×Q₈×C₆₇	—	2	2	no	—
346	C₂×Q₈×C₆₇	—	2	2	no	—
347	C₂×Q₈×C₆₇	—	2	4	no	—
348	C₂×Q₈×C₆₇	—	2	2	no	—
349	C₂×Q₈×C₆₇	—	2	2	no	—
350	C₂×Q₈×C₆₇	—	4	1	no	—
351	C₂×Q₈×C₆₇	—	4	2	no	—
352	C₂×Q₈×C₆₇	—	4	4	no	—
353	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
354	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₆₇	—	2	1	no	—
359	C₂×D₄×C₆₇	—	2	2	no	—
360	C₂×D₄×C₆₇	—	2	1	no	—
361	C₂×D₄×C₆₇	—	2	1	no	—
362	C₂×D₄×C₆₇	—	2	1	no	—
363	C₂×D₄×C₆₇	—	2	2	no	—
364	C₂×D₄×C₆₇	—	2	1	no	—
365	C₂×D₄×C₆₇	—	2	1	no	—
366	C₂×D₄×C₆₇	—	2	1	no	—
367	C₂×D₄×C₆₇	—	2	2	no	—
368	C₂×D₄×C₆₇	—	2	2	no	—
369	C₂×D₄×C₆₇	—	2	1	no	—
370	C₂×D₄×C₆₇	—	4	1	no	—
371	C₂×D₄×C₆₇	—	4	4	no	—
372	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
373	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
374	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
376	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
378	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₆₇	—	2	1	no	—
380	C₂²×C₄×C₆₇	—	2	2	no	—
381	C₂²×C₄×C₆₇	—	2	2	no	—
382	C₂²×C₄×C₆₇	—	2	1	no	—
383	C₂²×C₄×C₆₇	—	2	2	no	—
384	C₂²×C₄×C₆₇	—	2	2	no	—
385	C₂²×C₄×C₆₇	—	2	1	no	—
386	C₂²×C₄×C₆₇	—	2	1	no	—
387	C₂²×C₄×C₆₇	—	2	1	no	—
388	C₂²×C₄×C₆₇	—	2	2	no	—
389	C₂²×C₄×C₆₇	—	2	1	no	—
390	C₂²×C₄×C₆₇	—	2	2	no	—
391	C₂²×C₄×C₆₇	—	2	2	no	—
392	C₂²×C₄×C₆₇	—	2	1	no	—
393	C₂²×C₄×C₆₇	—	2	1	no	—
394	C₂²×C₄×C₆₇	—	2	1	no	—
395	C₂²×C₄×C₆₇	—	2	1	no	—
396	C₂²×C₄×C₆₇	—	2	2	no	—
397	C₂²×C₄×C₆₇	—	2	2	no	—
398	C₂²×C₄×C₆₇	—	4	4	no	—
399	C₂²×C₄×C₆₇	—	8	2	no	—
400	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
407	Q₁₆×C₆₇	—	2	2	no	—
408	Q₁₆×C₆₇	—	4	1	no	—
409	Q₁₆×C₆₇	—	4	2	no	—
410	SD₁₆×C₆₇	—	2	2	no	—
411	SD₁₆×C₆₇	—	2	2	no	—
412	SD₁₆×C₆₇	—	4	1	no	—
413	SD₁₆×C₆₇	—	4	1	no	—
414	SD₁₆×C₆₇	—	4	2	no	—
415	D₈×C₆₇	—	2	2	no	—
416	D₈×C₆₇	—	4	1	no	—
417	M₁₆×C₆₇	—	2	2	no	—
418	M₁₆×C₆₇	—	2	2	no	—
419	M₁₆×C₆₇	—	4	2	no	—
420	M₁₆×C₆₇	—	4	2	no	—
421	C₂×C₈×C₆₇	—	2	2	no	—
422	C₂×C₈×C₆₇	—	2	2	no	—
423	C₂×C₈×C₆₇	—	4	2	no	—
424	C₂×C₈×C₆₇	—	4	2	no	—
425	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
426	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
427	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
428	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
429	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
430	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	—	2	1	no	—
433	C₄⋊C₄×C₆₇	—	2	2	no	—
434	C₄⋊C₄×C₆₇	—	2	2	no	—
435	C₄⋊C₄×C₆₇	—	2	2	no	—
436	C₄⋊C₄×C₆₇	—	2	1	no	—
437	C₄⋊C₄×C₆₇	—	2	2	no	—
438	C₄⋊C₄×C₆₇	—	2	2	no	—
439	C₄⋊C₄×C₆₇	—	2	2	no	—
440	C₄⋊C₄×C₆₇	—	2	2	no	—
441	C₄⋊C₄×C₆₇	—	2	2	no	—
442	C₄⋊C₄×C₆₇	—	2	2	no	—
443	C₄⋊C₄×C₆₇	—	2	2	no	—
444	C₄⋊C₄×C₆₇	—	2	2	no	—
445	C₄⋊C₄×C₆₇	—	2	1	no	—
446	C₄⋊C₄×C₆₇	—	2	2	no	—
447	C₄⋊C₄×C₆₇	—	2	2	no	—
448	C₄⋊C₄×C₆₇	—	2	2	no	—
449	C₄⋊C₄×C₆₇	—	2	1	no	—
450	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
452	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
453	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
454	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
455	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
456	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
458	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
459	C₂²⋊C₄×C₆₇	—	2	2	no	—
460	C₂²⋊C₄×C₆₇	—	2	2	no	—
461	C₂²⋊C₄×C₆₇	—	2	1	no	—
462	C₂²⋊C₄×C₆₇	—	2	1	no	—
463	C₂²⋊C₄×C₆₇	—	2	2	no	—
464	C₂²⋊C₄×C₆₇	—	2	1	no	—
465	C₂²⋊C₄×C₆₇	—	2	2	no	—
466	C₂²⋊C₄×C₆₇	—	2	2	no	—
467	C₂²⋊C₄×C₆₇	—	2	2	no	—
468	C₂²⋊C₄×C₆₇	—	2	2	no	—
469	C₂²⋊C₄×C₆₇	—	2	2	no	—
470	C₂²⋊C₄×C₆₇	—	2	2	no	—
471	C₂²⋊C₄×C₆₇	—	2	2	no	—
472	C₂²⋊C₄×C₆₇	—	2	2	no	—
473	C₂²⋊C₄×C₆₇	—	2	1	no	—
474	C₂²⋊C₄×C₆₇	—	2	1	no	—
475	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
476	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
477	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
478	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
479	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
480	C₄²×C₆₇	—	2	2	no	—
481	C₄²×C₆₇	—	2	2	no	—
482	C₄²×C₆₇	—	2	2	no	—
483	C₄²×C₆₇	—	2	1	no	—
484	C₄²×C₆₇	C₂⁴	1	2	yes	—
485	C₂³×C₆₇	—	2	2	no	—
486	C₂³×C₆₇	—	2	2	no	—
487	C₂³×C₆₇	—	2	1	no	—
488	C₂³×C₆₇	—	2	1	no	—
489	C₂³×C₆₇	—	2	1	no	—
490	C₂³×C₆₇	—	4	1	no	—
491	C₂³×C₆₇	—	4	2	no	—
492	C₂³×C₆₇	—	4	2	no	—
493	C₂³×C₆₇	—	8	1	no	—
494	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
495	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
496	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
497	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
498	Q₈×C₆₇	—	2	2	no	—
499	Q₈×C₆₇	—	2	1	no	—
500	Q₈×C₆₇	—	2	1	no	—
501	Q₈×C₆₇	—	2	2	no	—
502	Q₈×C₆₇	—	2	1	no	—
503	Q₈×C₆₇	—	2	1	no	—
504	Q₈×C₆₇	—	2	2	no	—
505	Q₈×C₆₇	—	2	1	no	—
506	Q₈×C₆₇	—	4	4	no	—
507	Q₈×C₆₇	—	4	2	no	—
508	Q₈×C₆₇	—	4	2	no	—
509	Q₈×C₆₇	—	8	2	no	—
510	Q₈×C₆₇	C₂×#41	1	2	yes	—
511	D₄×C₆₇	—	2	4	no	—
512	D₄×C₆₇	—	2	4	no	—
513	D₄×C₆₇	—	2	4	no	—
514	D₄×C₆₇	—	2	2	no	—
515	D₄×C₆₇	—	2	1	no	—
516	D₄×C₆₇	—	2	1	no	—
517	D₄×C₆₇	—	2	1	no	—
518	D₄×C₆₇	—	2	1	no	—
519	D₄×C₆₇	—	2	1	no	—
520	D₄×C₆₇	—	4	2	no	—
521	D₄×C₆₇	—	4	2	no	—
522	D₄×C₆₇	—	4	2	no	—
523	D₄×C₆₇	—	4	2	no	—
524	D₄×C₆₇	—	4	4	no	—
525	D₄×C₆₇	—	4	2	no	—
526	D₄×C₆₇	—	4	2	no	—
527	D₄×C₆₇	—	4	2	no	—
528	D₄×C₆₇	—	4	2	no	—
529	D₄×C₆₇	—	8	2	no	—
530	D₄×C₆₇	—	8	2	no	—
531	D₄×C₆₇	C₂×#41	1	2	yes	—
532	C₂×C₄×C₆₇	—	2	2	no	—
533	C₂×C₄×C₆₇	—	2	1	no	—
534	C₂×C₄×C₆₇	—	2	2	no	—
535	C₂×C₄×C₆₇	—	2	2	no	—
536	C₂×C₄×C₆₇	—	2	4	no	—
537	C₂×C₄×C₆₇	—	2	1	no	—
538	C₂×C₄×C₆₇	—	2	1	no	—
539	C₂×C₄×C₆₇	—	2	2	no	—
540	C₂×C₄×C₆₇	—	2	1	no	—
541	C₂×C₄×C₆₇	—	2	2	no	—
542	C₂×C₄×C₆₇	—	2	1	no	—
543	C₂×C₄×C₆₇	—	2	1	no	—
544	C₂×C₄×C₆₇	—	2	1	no	—
545	C₂×C₄×C₆₇	—	2	2	no	—
546	C₂×C₄×C₆₇	—	2	2	no	—
547	C₂×C₄×C₆₇	—	2	1	no	—
548	C₂×C₄×C₆₇	—	2	2	no	—
549	C₂×C₄×C₆₇	—	2	2	no	—
550	C₂×C₄×C₆₇	—	2	1	no	—
551	C₂×C₄×C₆₇	—	4	2	no	—
552	C₂×C₄×C₆₇	—	4	2	no	—
553	C₂×C₄×C₆₇	—	4	2	no	—
554	C₂×C₄×C₆₇	—	4	4	no	—
555	C₂×C₄×C₆₇	—	4	4	no	—
556	C₂×C₄×C₆₇	—	4	2	no	—
557	C₂×C₄×C₆₇	—	4	4	no	—
558	C₂×C₄×C₆₇	—	4	2	no	—
559	C₂×C₄×C₆₇	—	4	2	no	—
560	C₂×C₄×C₆₇	—	8	2	no	—
561	C₂×C₄×C₆₇	—	8	2	no	—
562	C₂×C₄×C₆₇	—	8	1	no	—
563	C₂×C₄×C₆₇	—	8	1	no	—
564	C₂×C₄×C₆₇	—	8	2	no	—
565	C₂×C₄×C₆₇	—	8	1	no	—
566	C₂×C₄×C₆₇	—	8	2	no	—
567	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
568	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
569	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
570	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
574	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
575	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
576	C₈×C₆₇	—	2	1	no	—
577	C₈×C₆₇	—	2	1	no	—
578	C₈×C₆₇	—	2	1	no	—
579	C₈×C₆₇	—	2	1	no	—
580	C₈×C₆₇	—	2	2	no	—
581	C₈×C₆₇	—	2	2	no	—
582	C₂²×C₆₇	—	2	1	no	—
583	C₂²×C₆₇	—	2	1	no	—
584	C₂²×C₆₇	—	2	1	no	—
585	C₂²×C₆₇	—	2	1	no	—
586	C₂²×C₆₇	—	2	1	no	—
587	C₂²×C₆₇	—	2	2	no	—
588	C₂²×C₆₇	—	2	1	no	—
589	C₂²×C₆₇	—	2	2	no	—
590	C₂²×C₆₇	—	2	2	no	—
591	C₂²×C₆₇	—	2	1	no	—
592	C₂²×C₆₇	—	2	2	no	—
593	C₂²×C₆₇	—	4	4	no	—
594	C₂²×C₆₇	—	4	1	no	—
595	C₂²×C₆₇	—	4	1	no	—
596	C₂²×C₆₇	—	4	1	no	—
597	C₂²×C₆₇	—	4	1	no	—
598	C₂²×C₆₇	—	4	1	no	—
599	C₂²×C₆₇	—	4	1	no	—
600	C₂²×C₆₇	—	4	1	no	—
601	C₂²×C₆₇	—	4	1	no	—
602	C₂²×C₆₇	—	8	4	no	—
603	C₂²×C₆₇	#546	1	2	yes	—
604	C₂²×C₆₇	#577	1	2	yes	—
605	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
606	C₄×C₆₇	—	2	2	no	—
607	C₄×C₆₇	—	2	1	no	—
608	C₄×C₆₇	—	2	1	no	—
609	C₄×C₆₇	—	2	2	no	—
610	C₄×C₆₇	—	2	2	no	—
611	C₄×C₆₇	—	2	2	no	—
612	C₄×C₆₇	—	4	2	no	—
613	C₄×C₆₇	—	4	1	no	—
614	C₄×C₆₇	—	4	1	no	—
615	C₄×C₆₇	—	4	2	no	—
616	C₄×C₆₇	—	4	1	no	—
617	C₄×C₆₇	—	4	2	no	—
618	C₄×C₆₇	—	4	2	no	—
619	C₄×C₆₇	—	4	1	no	—
620	C₄×C₆₇	#546	1	2	yes	—
621	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
622	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
623	#61193	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
624	C₂×C₆₇	—	2	2	no	—
625	C₂×C₆₇	—	2	2	no	—
626	C₂×C₆₇	—	4	2	no	—
627	C₂×C₆₇	—	4	1	no	—
628	C₂×C₆₇	—	4	2	no	—
629	C₂×C₆₇	—	8	1	no	—
630	C₂×C₆₇	—	8	1	no	—
631	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
632	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
633	C₂×C₆₇	#3586	1	1	yes	characteristic
634	#3492	C₂×C₆₇	1	1	yes	characteristic, complemented
635	#3489	C₂×C₆₇	1	1	yes	characteristic, complemented
636	#3331	C₂×C₆₇	1	2	yes	complemented
637	#3326	C₂×C₆₇	1	2	yes	complemented
638	#3316	C₂×C₆₇	1	2	yes	complemented
639	#3312	C₂×C₆₇	1	2	yes	complemented
640	#3307	C₂×C₆₇	1	2	yes	complemented
641	#3306	C₂×C₆₇	1	2	yes	complemented
642	#3298	C₂×C₆₇	1	2	yes	complemented
643	#3296	C₂×C₆₇	1	2	yes	complemented
644	#3137	C₂×C₆₇	1	1	yes	characteristic, complemented
645	#3099	C₂×C₆₇	1	1	yes	characteristic, complemented
646	C₂×#483	C₂×C₆₇	1	1	yes	characteristic, complemented
647	#3084	C₂×C₆₇	1	1	yes	characteristic, complemented
648	#3060	C₂×C₆₇	1	1	yes	characteristic, complemented
649	#3056	C₂×C₆₇	1	1	yes	characteristic, complemented
650	#3046	C₂×C₆₇	1	1	yes	characteristic, complemented
651	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
652	#3002	C₂×C₆₇	1	1	yes	characteristic, complemented
653	#2952	C₂×C₆₇	1	1	yes	characteristic, complemented
654	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
655	#2898	C₂×C₆₇	1	1	yes	characteristic, complemented
656	C₂×#417	C₂×C₆₇	1	1	yes	characteristic, complemented
657	C₆₇	#61193	1	1	yes	characteristic, direct product factor, Sylow
658	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
659	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
660	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
661	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
662	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
663	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
665	#554	—	2	1	no	—
666	#554	C₂²×C₆₇	1	2	yes	complemented
667	#553	—	2	1	no	—
668	#553	C₂²×C₆₇	1	2	yes	complemented
669	#552	—	2	1	no	—
670	#552	C₂²×C₆₇	1	2	yes	—
671	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
672	#548	C₂²×C₆₇	1	2	yes	—
673	#547	—	2	2	no	—
674	#547	—	2	1	no	—
675	#547	C₂²×C₆₇	1	2	yes	—
676	#547	C₂²×C₆₇	1	2	yes	—
677	#546	—	2	2	no	—
678	#546	C₂²×C₆₇	1	2	yes	—
679	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
680	#539	—	2	2	no	—
681	#537	—	2	1	no	—
682	#537	C₂²×C₆₇	1	1	yes	characteristic
683	#537	C₂²×C₆₇	1	1	yes	characteristic, complemented
684	#536	—	2	1	no	—
685	#536	C₂²×C₆₇	1	1	yes	characteristic
686	#525	—	2	1	no	—
687	#525	—	2	2	no	—
688	#525	C₂²×C₆₇	1	1	yes	characteristic
689	#525	C₂²×C₆₇	1	1	yes	characteristic
690	C₂×C₂²⋊Q₈	—	2	1	no	—
691	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
692	#520	C₂²×C₆₇	1	1	yes	characteristic
693	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
694	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
695	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
696	#491	C₂²×C₆₇	1	2	yes	complemented
697	#489	C₂²×C₆₇	1	2	yes	complemented
698	#488	C₂²×C₆₇	1	2	yes	complemented
699	#487	C₂²×C₆₇	1	2	yes	complemented
700	#485	C₂²×C₆₇	1	2	yes	complemented
701	#483	C₂²×C₆₇	1	2	yes	—
702	#483	C₂²×C₆₇	1	2	yes	—
703	#483	C₂²×C₆₇	1	2	yes	complemented
704	#483	C₂²×C₆₇	1	2	yes	complemented
705	#483	C₂²×C₆₇	1	2	yes	complemented
706	#482	C₂²×C₆₇	1	2	yes	complemented
707	#481	C₂²×C₆₇	1	2	yes	complemented
708	#479	C₂²×C₆₇	1	2	yes	complemented
709	#478	C₂²×C₆₇	1	2	yes	complemented
710	#476	C₂²×C₆₇	1	2	yes	complemented
711	#475	C₂²×C₆₇	1	2	yes	complemented
712	#470	C₂²×C₆₇	1	2	yes	complemented
713	#470	C₂²×C₆₇	1	2	yes	complemented
714	#469	C₂²×C₆₇	1	2	yes	complemented
715	#468	C₂²×C₆₇	1	2	yes	complemented
716	#467	C₂²×C₆₇	1	2	yes	—
717	#465	C₂²×C₆₇	1	2	yes	—
718	#465	C₂²×C₆₇	1	2	yes	complemented
719	#465	C₂²×C₆₇	1	2	yes	complemented
720	#464	C₂²×C₆₇	1	2	yes	complemented
721	#463	C₂²×C₆₇	1	2	yes	complemented
722	#462	C₂²×C₆₇	1	2	yes	complemented
723	#461	C₂²×C₆₇	1	2	yes	complemented
724	#452	C₂²×C₆₇	1	1	yes	characteristic
725	#452	C₂²×C₆₇	1	1	yes	characteristic
726	#452	C₂²×C₆₇	1	2	yes	complemented
727	#451	C₂²×C₆₇	1	1	yes	characteristic
728	#451	C₂²×C₆₇	1	2	yes	complemented
729	#450	C₂²×C₆₇	1	1	yes	characteristic
730	#449	C₂²×C₆₇	1	1	yes	characteristic
731	#449	C₂²×C₆₇	1	1	yes	characteristic
732	#449	C₂²×C₆₇	1	2	yes	complemented
733	#448	C₂²×C₆₇	1	1	yes	characteristic
734	#448	C₂²×C₆₇	1	2	yes	complemented
735	#447	C₂²×C₆₇	1	1	yes	characteristic
736	#442	C₂²×C₆₇	1	2	yes	complemented
737	#441	C₂²×C₆₇	1	2	yes	complemented
738	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
739	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
740	#436	C₂²×C₆₇	1	2	yes	complemented
741	#435	C₂²×C₆₇	1	2	yes	—
742	#435	C₂²×C₆₇	1	2	yes	complemented
743	C₈×D₄	C₂²×C₆₇	1	2	yes	—
744	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
745	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
746	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
747	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
748	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
749	#419	C₂²×C₆₇	1	2	yes	complemented
750	#417	C₂²×C₆₇	1	2	yes	—
751	#417	C₂²×C₆₇	1	1	yes	characteristic
752	#417	C₂²×C₆₇	1	1	yes	characteristic
753	#417	C₂²×C₆₇	1	1	yes	characteristic
754	#417	C₂²×C₆₇	1	1	yes	characteristic
755	#417	C₂²×C₆₇	1	2	yes	—
756	#417	C₂²×C₆₇	1	2	yes	complemented
757	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
758	#416	C₂²×C₆₇	1	1	yes	characteristic
759	#416	C₂²×C₆₇	1	1	yes	characteristic
760	#416	C₂²×C₆₇	1	2	yes	complemented
761	C₂×#103	C₂²×C₆₇	1	2	yes	—
762	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
763	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
764	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
765	C₂×#102	C₂²×C₆₇	1	2	yes	—
766	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
767	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
768	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
769	2₋¹⁺⁴	—	2	4	no	—
770	2₋¹⁺⁴	—	4	2	no	—
771	C₂×#41	—	2	1	no	—
772	C₂×#41	—	2	2	no	—
773	C₂×#41	—	2	2	no	—
774	C₂×#41	—	2	1	no	—
775	C₂×#41	—	2	1	no	—
776	C₂×#41	—	2	4	no	—
777	C₂×#41	—	4	2	no	—
778	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
779	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
780	C₂×#41	C₂³×C₆₇	1	2	yes	—
781	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
782	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
783	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
784	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
785	C₂²×Q₈	—	2	1	no	—
786	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
787	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
788	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
789	C₂²×D₄	—	2	1	no	—
790	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
791	C₂³×C₄	—	2	1	no	—
792	C₂³×C₄	—	2	1	no	—
793	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
794	#137	—	4	2	no	—
795	#135	—	2	4	no	—
796	#135	—	4	2	no	—
797	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
798	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
799	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
800	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
801	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
802	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
803	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
804	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
805	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
806	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
807	#131	—	4	2	no	—
808	C₂×M₁₆	—	4	2	no	—
809	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
810	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
811	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
812	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
813	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
814	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
815	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
816	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
817	C₄⋊Q₈	—	2	2	no	—
818	C₄⋊Q₈	—	2	1	no	—
819	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
820	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
821	#126	—	2	2	no	—
822	#126	—	2	2	no	—
823	#125	—	2	2	no	—
824	#125	—	2	2	no	—
825	#125	—	2	1	no	—
826	#125	C₂³×C₆₇	1	2	yes	—
827	#124	—	2	2	no	—
828	#124	C₂³×C₆₇	1	2	yes	—
829	#123	—	2	2	no	—
830	#123	—	2	1	no	—
831	#123	—	2	2	no	—
832	#123	—	2	2	no	—
833	#123	—	2	2	no	—
834	#123	—	2	2	no	—
835	#123	—	2	2	no	—
836	#123	—	2	2	no	—
837	#123	—	2	2	no	—
838	#123	D₄×C₆₇	1	2	yes	—
839	C₂²⋊Q₈	—	2	1	no	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	no	—
844	C₂²⋊Q₈	—	2	2	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	—	2	2	no	—
847	C₂²⋊Q₈	—	2	2	no	—
848	C₂²⋊Q₈	—	2	2	no	—
849	C₂²⋊Q₈	—	2	2	no	—
850	C₂²⋊Q₈	—	2	2	no	—
851	C₂²⋊Q₈	—	2	2	no	—
852	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
853	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
854	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
855	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
856	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
857	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
858	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
859	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
860	#121	—	2	1	no	—
861	#121	—	2	2	no	—
862	#121	—	2	2	no	—
863	#121	—	2	2	no	—
864	#121	—	2	2	no	—
865	#121	—	2	2	no	—
866	#121	—	2	1	no	—
867	#121	—	2	2	no	—
868	#121	D₄×C₆₇	1	1	yes	characteristic
869	#121	D₄×C₆₇	1	1	yes	characteristic
870	#121	C₂³×C₆₇	1	1	yes	characteristic
871	#121	C₂³×C₆₇	1	1	yes	characteristic
872	#121	C₂³×C₆₇	1	2	yes	—
873	#121	C₂³×C₆₇	1	2	yes	—
874	#120	—	2	1	no	—
875	#120	—	2	2	no	—
876	#120	D₄×C₆₇	1	2	yes	—
877	C₄×Q₈	—	2	1	no	—
878	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
879	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
880	C₄×D₄	—	2	2	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	2	no	—
883	C₄×D₄	—	2	2	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	2	no	—
887	C₄×D₄	—	2	2	no	—
888	C₄×D₄	—	2	2	no	—
889	C₄×D₄	—	2	2	no	—
890	C₄×D₄	C₂³×C₆₇	1	2	yes	—
891	C₄×D₄	C₂³×C₆₇	1	2	yes	—
892	C₄×D₄	C₂³×C₆₇	1	2	yes	—
893	C₄×D₄	C₂³×C₆₇	1	2	yes	—
894	#117	—	2	1	no	—
895	#117	—	2	1	no	—
896	#117	—	2	2	no	—
897	#117	C₂³×C₆₇	1	1	yes	characteristic
898	#117	C₂³×C₆₇	1	2	yes	—
899	#117	C₂³×C₆₇	1	1	yes	characteristic
900	C₂×C₄⋊C₄	—	2	1	no	—
901	C₂×C₄⋊C₄	—	2	1	no	—
902	C₂×C₄⋊C₄	—	2	1	no	—
903	C₂×C₄⋊C₄	—	2	1	no	—
904	C₂×C₄⋊C₄	—	2	1	no	—
905	C₂×C₄⋊C₄	—	2	1	no	—
906	C₂×C₄⋊C₄	—	2	2	no	—
907	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
908	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
909	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
910	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
911	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
912	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
913	C₂×C₂²⋊C₄	—	2	1	no	—
914	C₂×C₂²⋊C₄	—	2	2	no	—
915	#107	C₂³×C₆₇	1	2	yes	—
916	#106	C₂³×C₆₇	1	2	yes	—
917	#106	C₂³×C₆₇	1	2	yes	—
918	#106	C₂³×C₆₇	1	2	yes	—
919	#106	C₂³×C₆₇	1	2	yes	—
920	#106	C₂³×C₆₇	1	2	yes	—
921	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
922	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
923	#103	C₂³×C₆₇	1	2	yes	—
924	#103	C₂³×C₆₇	1	2	yes	—
925	#103	C₂³×C₆₇	1	2	yes	—
926	#103	C₂³×C₆₇	1	2	yes	—
927	#103	C₂³×C₆₇	1	1	yes	characteristic
928	#103	C₂³×C₆₇	1	2	yes	—
929	#103	C₂³×C₆₇	1	2	yes	—
930	#103	C₂³×C₆₇	1	2	yes	—
931	#103	C₂³×C₆₇	1	2	yes	—
932	#103	C₂³×C₆₇	1	2	yes	—
933	#103	C₂³×C₆₇	1	1	yes	characteristic
934	#103	C₂³×C₆₇	1	1	yes	characteristic
935	#103	C₂³×C₆₇	1	1	yes	characteristic
936	#103	C₂³×C₆₇	1	2	yes	—
937	#103	C₂³×C₆₇	1	2	yes	—
938	#102	C₂³×C₆₇	1	2	yes	—
939	#102	C₂³×C₆₇	1	2	yes	—
940	#102	C₂³×C₆₇	1	2	yes	—
941	#102	C₂³×C₆₇	1	2	yes	—
942	#102	C₂³×C₆₇	1	1	yes	characteristic
943	#102	C₂³×C₆₇	1	1	yes	characteristic
944	#102	C₂³×C₆₇	1	1	yes	characteristic
945	#102	C₂³×C₆₇	1	1	yes	characteristic
946	#102	C₂³×C₆₇	1	2	yes	—
947	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
948	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
949	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
950	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
951	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
952	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
953	#97	C₂³×C₆₇	1	2	yes	—
954	C₄×C₈	C₂³×C₆₇	1	2	yes	—
955	C₂⁴	—	2	1	no	—
956	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
957	#41	—	2	2	no	—
958	#41	—	2	2	no	—
959	#41	—	2	2	no	—
960	#41	—	2	2	no	—
961	#41	—	2	2	no	—
962	#41	—	2	4	no	—
963	#41	—	2	2	no	—
964	#41	—	2	2	no	—
965	#41	—	2	2	no	—
966	#41	—	2	2	no	—
967	#41	—	4	4	no	—
968	#41	—	4	1	no	—
969	#41	—	4	1	no	—
970	#41	—	4	2	no	—
971	#41	—	4	4	no	—
972	#41	—	4	4	no	—
973	#41	—	4	8	no	—
974	#41	—	8	4	no	—
975	#41	#41×C₆₇	1	4	yes	complemented
976	C₂×Q₈	—	2	1	no	—
977	C₂×Q₈	—	2	2	no	—
978	C₂×Q₈	—	2	1	no	—
979	C₂×Q₈	—	2	2	no	—
980	C₂×Q₈	—	2	2	no	—
981	C₂×Q₈	—	2	4	no	—
982	C₂×Q₈	—	2	2	no	—
983	C₂×Q₈	—	2	2	no	—
984	C₂×Q₈	—	4	1	no	—
985	C₂×Q₈	—	4	2	no	—
986	C₂×Q₈	—	4	4	no	—
987	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
988	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
989	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
990	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
991	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	4	1	no	—
1005	C₂×D₄	—	4	4	no	—
1006	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1007	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1008	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1009	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1010	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1011	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1012	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	2	no	—
1015	C₂²×C₄	—	2	2	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	2	no	—
1018	C₂²×C₄	—	2	2	no	—
1019	C₂²×C₄	—	2	1	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	2	no	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	2	no	—
1025	C₂²×C₄	—	2	2	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	1	no	—
1029	C₂²×C₄	—	2	1	no	—
1030	C₂²×C₄	—	2	2	no	—
1031	C₂²×C₄	—	2	2	no	—
1032	C₂²×C₄	—	4	4	no	—
1033	C₂²×C₄	—	8	2	no	—
1034	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1035	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1036	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1037	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1038	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1039	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1040	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1041	Q₁₆	—	2	2	no	—
1042	Q₁₆	—	4	1	no	—
1043	Q₁₆	—	4	2	no	—
1044	SD₁₆	—	2	2	no	—
1045	SD₁₆	—	2	2	no	—
1046	SD₁₆	—	4	1	no	—
1047	SD₁₆	—	4	1	no	—
1048	SD₁₆	—	4	2	no	—
1049	D₈	—	2	2	no	—
1050	D₈	—	4	1	no	—
1051	M₁₆	—	2	2	no	—
1052	M₁₆	—	2	2	no	—
1053	M₁₆	—	4	2	no	—
1054	M₁₆	—	4	2	no	—
1055	C₂×C₈	—	2	2	no	—
1056	C₂×C₈	—	2	2	no	—
1057	C₂×C₈	—	4	2	no	—
1058	C₂×C₈	—	4	2	no	—
1059	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1060	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1061	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1062	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1063	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1064	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	2	no	—
1068	C₄⋊C₄	—	2	2	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	2	no	—
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	2	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	2	no	—
1081	C₄⋊C₄	—	2	2	no	—
1082	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1085	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1086	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1087	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1088	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1089	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1090	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1091	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1092	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1110	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1111	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1112	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1113	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1114	C₄²	—	2	2	no	—
1115	C₄²	—	2	2	no	—
1116	C₄²	—	2	2	no	—
1117	C₄²	—	2	1	no	—
1118	C₄²	C₂⁴×C₆₇	1	2	yes	—
1119	C₂³	—	2	2	no	—
1120	C₂³	—	2	2	no	—
1121	C₂³	—	2	1	no	—
1122	C₂³	—	2	1	no	—
1123	C₂³	—	2	1	no	—
1124	C₂³	—	4	1	no	—
1125	C₂³	—	4	2	no	—
1126	C₂³	—	4	2	no	—
1127	C₂³	—	8	1	no	—
1128	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1129	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1130	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1131	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1132	Q₈	—	2	2	no	—
1133	Q₈	—	2	1	no	—
1134	Q₈	—	2	1	no	—
1135	Q₈	—	2	2	no	—
1136	Q₈	—	2	1	no	—
1137	Q₈	—	2	1	no	—
1138	Q₈	—	2	2	no	—
1139	Q₈	—	2	1	no	—
1140	Q₈	—	4	4	no	—
1141	Q₈	—	4	2	no	—
1142	Q₈	—	4	2	no	—
1143	Q₈	—	8	2	no	—
1144	Q₈	C₂×#41×C₆₇	1	2	yes	—
1145	D₄	—	2	4	no	—
1146	D₄	—	2	4	no	—
1147	D₄	—	2	4	no	—
1148	D₄	—	2	2	no	—
1149	D₄	—	2	1	no	—
1150	D₄	—	2	1	no	—
1151	D₄	—	2	1	no	—
1152	D₄	—	2	1	no	—
1153	D₄	—	2	1	no	—
1154	D₄	—	4	2	no	—
1155	D₄	—	4	2	no	—
1156	D₄	—	4	2	no	—
1157	D₄	—	4	2	no	—
1158	D₄	—	4	4	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	4	2	no	—
1163	D₄	—	8	2	no	—
1164	D₄	—	8	2	no	—
1165	D₄	C₂×#41×C₆₇	1	2	yes	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	4	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	2	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	4	2	no	—
1186	C₂×C₄	—	4	2	no	—
1187	C₂×C₄	—	4	2	no	—
1188	C₂×C₄	—	4	4	no	—
1189	C₂×C₄	—	4	4	no	—
1190	C₂×C₄	—	4	2	no	—
1191	C₂×C₄	—	4	4	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	4	2	no	—
1194	C₂×C₄	—	8	2	no	—
1195	C₂×C₄	—	8	2	no	—
1196	C₂×C₄	—	8	1	no	—
1197	C₂×C₄	—	8	2	no	—
1198	C₂×C₄	—	8	1	no	—
1199	C₂×C₄	—	8	2	no	—
1200	C₂×C₄	—	8	1	no	—
1201	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1202	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1203	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1204	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1205	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1207	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1208	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1209	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1210	C₈	—	2	1	no	—
1211	C₈	—	2	1	no	—
1212	C₈	—	2	1	no	—
1213	C₈	—	2	1	no	—
1214	C₈	—	2	2	no	—
1215	C₈	—	2	2	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	1	no	—
1221	C₂²	—	2	2	no	—
1222	C₂²	—	2	1	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	1	no	—
1225	C₂²	—	2	2	no	—
1226	C₂²	—	2	2	no	—
1227	C₂²	—	4	4	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	4	1	no	—
1233	C₂²	—	4	1	no	—
1234	C₂²	—	4	1	no	—
1235	C₂²	—	4	1	no	—
1236	C₂²	—	8	4	no	—
1237	C₂²	#546×C₆₇	1	2	yes	—
1238	C₂²	#577×C₆₇	1	2	yes	—
1239	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1240	C₄	—	2	2	no	—
1241	C₄	—	2	2	no	—
1242	C₄	—	2	1	no	—
1243	C₄	—	2	1	no	—
1244	C₄	—	2	2	no	—
1245	C₄	—	2	2	no	—
1246	C₄	—	4	2	no	—
1247	C₄	—	4	2	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	2	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	2	no	—
1253	C₄	—	4	1	no	—
1254	C₄	#546×C₆₇	1	2	yes	—
1255	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1256	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1257	C₂	—	2	2	no	—
1258	C₂	—	2	2	no	—
1259	C₂	—	4	1	no	—
1260	C₂	—	4	2	no	—
1261	C₂	—	4	2	no	—
1262	C₂	—	8	1	no	—
1263	C₂	—	8	1	no	—
1264	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1265	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1266	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 ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3492	C₂	semidirect
2. C₆₇×#3489	C₂	semidirect
3. C₆₇×#3331	C₂	semidirect
4. C₆₇×#3326	C₂	semidirect
5. C₆₇×#3316	C₂	semidirect
6. C₆₇×#3312	C₂	semidirect
7. C₆₇×#3307	C₂	semidirect
8. C₆₇×#3306	C₂	semidirect
9. C₆₇×#3298	C₂	semidirect
10. C₆₇×#3296	C₂	semidirect
11. C₆₇×#3137	C₂	semidirect
12. C₆₇×#3099	C₂	semidirect
13. C₂×#483×C₆₇	C₂	semidirect
14. C₆₇×#3084	C₂	semidirect
15. C₆₇×#3060	C₂	semidirect
16. C₆₇×#3056	C₂	semidirect
17. C₆₇×#3046	C₂	semidirect
18. C₆₇×#3013	C₂	semidirect
19. C₆₇×#3002	C₂	semidirect
20. C₆₇×#2952	C₂	semidirect
21. C₆₇×#2933	C₂	semidirect
22. C₆₇×#2898	C₂	semidirect
23. C₂×#417×C₆₇	C₂	semidirect
26. C₂×#137×C₆₇	C₂²	semidirect
29. C₂×#131×C₆₇	C₂²	semidirect
32. #554×C₆₇	C₂²	semidirect
34. #553×C₆₇	C₂²	semidirect
45. #544×C₆₇	C₂²	semidirect
49. #537×C₆₇	C₂²	semidirect
59. #520×C₆₇	C₂²	semidirect
60. #520×C₆₇	C₂²	semidirect
62. #491×C₆₇	C₂²	semidirect
63. #489×C₆₇	C₂²	semidirect
64. #488×C₆₇	C₂²	semidirect
65. #487×C₆₇	C₂²	semidirect
66. #485×C₆₇	C₂²	semidirect
69. #483×C₆₇	C₂²	semidirect
70. #483×C₆₇	C₂²	semidirect
71. #483×C₆₇	C₂²	semidirect
72. #482×C₆₇	C₂²	semidirect
73. #481×C₆₇	C₂²	semidirect
74. #479×C₆₇	C₂²	semidirect
75. #478×C₆₇	C₂²	semidirect
76. #476×C₆₇	C₂²	semidirect
77. #475×C₆₇	C₂²	semidirect
78. #470×C₆₇	C₂²	semidirect
79. #470×C₆₇	C₂²	semidirect
80. #469×C₆₇	C₂²	semidirect
81. #468×C₆₇	C₂²	semidirect
84. #465×C₆₇	C₂²	semidirect
85. #465×C₆₇	C₂²	semidirect
86. #464×C₆₇	C₂²	semidirect
87. #463×C₆₇	C₂²	semidirect
88. #462×C₆₇	C₂²	semidirect
89. #461×C₆₇	C₂²	semidirect
92. #452×C₆₇	C₂²	semidirect
94. #451×C₆₇	C₂²	semidirect
98. #449×C₆₇	C₂²	semidirect
100. #448×C₆₇	C₂²	semidirect
102. #442×C₆₇	C₂²	semidirect
103. #441×C₆₇	C₂²	semidirect
104. C₄×SD₁₆×C₆₇	C₂²	semidirect
105. C₄×SD₁₆×C₆₇	C₂²	semidirect
106. #436×C₆₇	C₂²	semidirect
108. #435×C₆₇	C₂²	semidirect
110. #428×C₆₇	C₂²	semidirect
111. C₂×#106×C₆₇	C₂²	semidirect
112. C₂×#106×C₆₇	C₂²	semidirect
113. #424×C₆₇	C₂²	semidirect
114. #419×C₆₇	C₂²	semidirect
115. #419×C₆₇	C₂²	semidirect
122. #417×C₆₇	C₂²	semidirect
123. #417×C₆₇	C₂²	semidirect
126. #416×C₆₇	C₂²	semidirect
128. C₂×#103×C₆₇	C₂²	semidirect
129. C₂×#103×C₆₇	C₂²	semidirect
130. C₂×#103×C₆₇	C₂²	semidirect
132. #408×C₆₇	C₂²	semidirect
134. #405×C₆₇	C₂²	semidirect
341. #41×C₆₇	#41	semidirect
623. #61193	C₆₇	direct (N × H)
634. #3492	C₂×C₆₇	semidirect
635. #3489	C₂×C₆₇	semidirect
636. #3331	C₂×C₆₇	semidirect
637. #3326	C₂×C₆₇	semidirect
638. #3316	C₂×C₆₇	semidirect
639. #3312	C₂×C₆₇	semidirect
640. #3307	C₂×C₆₇	semidirect
641. #3306	C₂×C₆₇	semidirect
642. #3298	C₂×C₆₇	semidirect
643. #3296	C₂×C₆₇	semidirect
644. #3137	C₂×C₆₇	semidirect
645. #3099	C₂×C₆₇	semidirect
646. C₂×#483	C₂×C₆₇	semidirect
647. #3084	C₂×C₆₇	semidirect
648. #3060	C₂×C₆₇	semidirect
649. #3056	C₂×C₆₇	semidirect
650. #3046	C₂×C₆₇	semidirect
651. #3013	C₂×C₆₇	semidirect
652. #3002	C₂×C₆₇	semidirect
653. #2952	C₂×C₆₇	semidirect
654. #2933	C₂×C₆₇	semidirect
655. #2898	C₂×C₆₇	semidirect
656. C₂×#417	C₂×C₆₇	semidirect
657. C₆₇	#61193	direct (N × H)
660. C₂×#137	C₂²×C₆₇	semidirect
663. C₂×#131	C₂²×C₆₇	semidirect
666. #554	C₂²×C₆₇	semidirect
668. #553	C₂²×C₆₇	semidirect
679. #544	C₂²×C₆₇	semidirect
683. #537	C₂²×C₆₇	semidirect
693. #520	C₂²×C₆₇	semidirect
694. #520	C₂²×C₆₇	semidirect
696. #491	C₂²×C₆₇	semidirect
697. #489	C₂²×C₆₇	semidirect
698. #488	C₂²×C₆₇	semidirect
699. #487	C₂²×C₆₇	semidirect
700. #485	C₂²×C₆₇	semidirect
703. #483	C₂²×C₆₇	semidirect
704. #483	C₂²×C₆₇	semidirect
705. #483	C₂²×C₆₇	semidirect
706. #482	C₂²×C₆₇	semidirect
707. #481	C₂²×C₆₇	semidirect
708. #479	C₂²×C₆₇	semidirect
709. #478	C₂²×C₆₇	semidirect
710. #476	C₂²×C₆₇	semidirect
711. #475	C₂²×C₆₇	semidirect
712. #470	C₂²×C₆₇	semidirect
713. #470	C₂²×C₆₇	semidirect
714. #469	C₂²×C₆₇	semidirect
715. #468	C₂²×C₆₇	semidirect
718. #465	C₂²×C₆₇	semidirect
719. #465	C₂²×C₆₇	semidirect
720. #464	C₂²×C₆₇	semidirect
721. #463	C₂²×C₆₇	semidirect
722. #462	C₂²×C₆₇	semidirect
723. #461	C₂²×C₆₇	semidirect
726. #452	C₂²×C₆₇	semidirect
728. #451	C₂²×C₆₇	semidirect
732. #449	C₂²×C₆₇	semidirect
734. #448	C₂²×C₆₇	semidirect
736. #442	C₂²×C₆₇	semidirect
737. #441	C₂²×C₆₇	semidirect
738. C₄×SD₁₆	C₂²×C₆₇	semidirect
739. C₄×SD₁₆	C₂²×C₆₇	semidirect
740. #436	C₂²×C₆₇	semidirect
742. #435	C₂²×C₆₇	semidirect
744. #428	C₂²×C₆₇	semidirect
745. C₂×#106	C₂²×C₆₇	semidirect
746. C₂×#106	C₂²×C₆₇	semidirect
747. #424	C₂²×C₆₇	semidirect
748. #419	C₂²×C₆₇	semidirect
749. #419	C₂²×C₆₇	semidirect
756. #417	C₂²×C₆₇	semidirect
757. #417	C₂²×C₆₇	semidirect
760. #416	C₂²×C₆₇	semidirect
762. C₂×#103	C₂²×C₆₇	semidirect
763. C₂×#103	C₂²×C₆₇	semidirect
764. C₂×#103	C₂²×C₆₇	semidirect
766. #408	C₂²×C₆₇	semidirect
768. #405	C₂²×C₆₇	semidirect
975. #41	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3492	2
C₆₇×#3489	2
C₆₇×#3331	2
C₆₇×#3326	2
C₆₇×#3316	2
C₆₇×#3312	2
C₆₇×#3307	2
C₆₇×#3306	2
C₆₇×#3298	2
C₆₇×#3296	2
C₆₇×#3137	2
C₆₇×#3099	2
C₂×#483×C₆₇	2
C₆₇×#3084	2
C₆₇×#3060	2
C₆₇×#3056	2
C₆₇×#3046	2
C₆₇×#3013	2
C₆₇×#3002	2
C₆₇×#2952	2
C₆₇×#2933	2
C₆₇×#2898	2
C₂×#417×C₆₇	2
#61193	67

Subgroups — C67×#61193 #30740444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61193 #30740444