Subgroups — C₆₇×#60983 #30740234

Order 17152.

1668 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3495	C₂	1	1	yes	maximal, characteristic
2	C₂×#541×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3261	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3258	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3242	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3236	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3232	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3223	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3209	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3196	C₂	1	1	yes	maximal, characteristic
12	C₆₇×#3195	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3190	C₂	1	1	yes	maximal, characteristic
14	C₆₇×#3189	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3178	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3177	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3127	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3120	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3117	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	#556×C₆₇	—	2	1	no	—
25	#554×C₆₇	—	2	1	no	—
26	#552×C₆₇	—	2	1	no	—
27	#552×C₆₇	—	2	1	no	—
28	#552×C₆₇	—	2	1	no	—
29	#552×C₆₇	—	2	1	no	—
30	#551×C₆₇	—	2	1	no	—
31	#551×C₆₇	—	2	1	no	—
32	#544×C₆₇	C₂²	1	1	yes	characteristic
33	#542×C₆₇	C₂²	1	1	yes	characteristic
34	#542×C₆₇	C₂²	1	1	yes	characteristic
35	#541×C₆₇	—	2	1	no	—
36	#541×C₆₇	—	2	1	no	—
37	#541×C₆₇	—	2	1	no	—
38	#541×C₆₇	—	2	1	no	—
39	#541×C₆₇	C₂²	1	2	yes	—
40	#541×C₆₇	C₂²	1	1	yes	characteristic
41	#541×C₆₇	C₂²	1	2	yes	—
42	#541×C₆₇	C₂²	1	2	yes	—
43	#541×C₆₇	C₂²	1	2	yes	—
44	#541×C₆₇	C₂²	1	1	yes	characteristic
45	#536×C₆₇	C₂²	1	1	yes	characteristic
46	#533×C₆₇	C₂²	1	1	yes	characteristic
47	#533×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
49	#529×C₆₇	C₂²	1	1	yes	characteristic
50	#529×C₆₇	C₂²	1	1	yes	characteristic
51	C₂×#126×C₆₇	—	2	1	no	—
52	C₂×#126×C₆₇	—	2	1	no	—
53	C₂×#125×C₆₇	—	2	1	no	—
54	C₂×#125×C₆₇	—	2	1	no	—
55	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
56	#525×C₆₇	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
60	#520×C₆₇	C₂²	1	1	yes	characteristic
61	#519×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
65	#501×C₆₇	C₂²	1	2	yes	complemented
66	#499×C₆₇	C₂²	1	2	yes	complemented
67	#497×C₆₇	C₂²	1	2	yes	complemented
68	#494×C₆₇	C₂²	1	2	yes	complemented
69	#491×C₆₇	C₂²	1	2	yes	complemented
70	#491×C₆₇	C₂²	1	2	yes	complemented
71	#488×C₆₇	C₂²	1	2	yes	complemented
72	#487×C₆₇	C₂²	1	2	yes	complemented
73	#485×C₆₇	C₂²	1	2	yes	—
74	#485×C₆₇	C₂²	1	2	yes	—
75	#484×C₆₇	C₂²	1	1	yes	characteristic
76	#484×C₆₇	C₂²	1	1	yes	characteristic
77	#484×C₆₇	C₂²	1	1	yes	characteristic
78	#484×C₆₇	C₂²	1	2	yes	—
79	#483×C₆₇	C₂²	1	1	yes	characteristic
80	#483×C₆₇	C₂²	1	1	yes	characteristic
81	#483×C₆₇	C₂²	1	1	yes	characteristic
82	#483×C₆₇	C₂²	1	2	yes	—
83	#481×C₆₇	C₂²	1	1	yes	characteristic
84	#480×C₆₇	C₂²	1	1	yes	characteristic
85	#479×C₆₇	C₂²	1	2	yes	complemented
86	#479×C₆₇	C₂²	1	2	yes	complemented
87	#479×C₆₇	C₂²	1	2	yes	complemented
88	#479×C₆₇	C₂²	1	2	yes	complemented
89	#479×C₆₇	C₂²	1	2	yes	complemented
90	#478×C₆₇	C₂²	1	2	yes	complemented
91	#477×C₆₇	C₂²	1	2	yes	complemented
92	#475×C₆₇	C₂²	1	2	yes	complemented
93	#470×C₆₇	C₂²	1	2	yes	—
94	#470×C₆₇	C₂²	1	2	yes	—
95	#470×C₆₇	C₂²	1	2	yes	—
96	#468×C₆₇	C₂²	1	2	yes	—
97	#467×C₆₇	C₂²	1	2	yes	—
98	#467×C₆₇	C₂²	1	2	yes	—
99	#467×C₆₇	C₂²	1	2	yes	—
100	#465×C₆₇	C₂²	1	2	yes	—
101	#464×C₆₇	C₂²	1	2	yes	complemented
102	#464×C₆₇	C₂²	1	2	yes	complemented
103	#462×C₆₇	C₂²	1	2	yes	complemented
104	#462×C₆₇	C₂²	1	2	yes	complemented
105	#462×C₆₇	C₂²	1	2	yes	complemented
106	#462×C₆₇	C₂²	1	2	yes	complemented
107	#462×C₆₇	C₂²	1	2	yes	complemented
108	#461×C₆₇	C₂²	1	2	yes	complemented
109	#452×C₆₇	C₂²	1	2	yes	—
110	#452×C₆₇	C₂²	1	2	yes	—
111	#451×C₆₇	C₂²	1	1	yes	characteristic
112	#451×C₆₇	C₂²	1	1	yes	characteristic
113	#451×C₆₇	C₂²	1	1	yes	characteristic
114	#451×C₆₇	C₂²	1	1	yes	characteristic
115	#451×C₆₇	C₂²	1	1	yes	characteristic
116	#451×C₆₇	C₂²	1	1	yes	characteristic
117	#451×C₆₇	C₂²	1	2	yes	—
118	#451×C₆₇	C₂²	1	2	yes	—
119	#448×C₆₇	C₂²	1	1	yes	characteristic
120	#448×C₆₇	C₂²	1	1	yes	characteristic
121	#441×C₆₇	C₂²	1	2	yes	complemented
122	#441×C₆₇	C₂²	1	2	yes	complemented
123	#441×C₆₇	C₂²	1	2	yes	complemented
124	#440×C₆₇	C₂²	1	2	yes	complemented
125	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
126	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
127	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
128	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
129	#433×C₆₇	C₂²	1	2	yes	—
130	#433×C₆₇	C₂²	1	2	yes	—
131	#432×C₆₇	C₂²	1	1	yes	characteristic
132	#432×C₆₇	C₂²	1	1	yes	characteristic
133	#431×C₆₇	C₂²	1	1	yes	characteristic
134	#431×C₆₇	C₂²	1	1	yes	characteristic
135	#424×C₆₇	C₂²	1	2	yes	—
136	#407×C₆₇	C₂²	1	1	yes	characteristic
137	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
138	#405×C₆₇	C₂²	1	2	yes	—
139	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
141	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₆₇	—	2	1	no	—
155	C₄⋊Q₈×C₆₇	—	2	1	no	—
156	C₄⋊Q₈×C₆₇	—	2	1	no	—
157	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	#126×C₆₇	—	2	1	no	—
164	#126×C₆₇	—	2	1	no	—
165	#126×C₆₇	—	2	2	no	—
166	#126×C₆₇	—	2	2	no	—
167	#126×C₆₇	—	2	2	no	—
168	#126×C₆₇	—	2	2	no	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#126×C₆₇	—	2	2	no	—
172	#126×C₆₇	—	2	2	no	—
173	#126×C₆₇	—	2	1	no	—
174	#126×C₆₇	—	2	1	no	—
175	#126×C₆₇	—	2	1	no	—
176	#126×C₆₇	—	2	1	no	—
177	#126×C₆₇	—	2	1	no	—
178	#126×C₆₇	—	2	1	no	—
179	#125×C₆₇	—	2	2	no	—
180	#125×C₆₇	—	2	2	no	—
181	#125×C₆₇	—	2	2	no	—
182	#125×C₆₇	—	2	2	no	—
183	#125×C₆₇	—	2	2	no	—
184	#125×C₆₇	—	2	2	no	—
185	#125×C₆₇	—	2	2	no	—
186	#125×C₆₇	—	2	2	no	—
187	#125×C₆₇	—	2	1	no	—
188	#125×C₆₇	—	2	1	no	—
189	#125×C₆₇	—	2	1	no	—
190	#125×C₆₇	—	2	1	no	—
191	#125×C₆₇	—	2	1	no	—
192	#125×C₆₇	—	2	1	no	—
193	#125×C₆₇	—	2	1	no	—
194	#125×C₆₇	—	2	1	no	—
195	#125×C₆₇	—	2	1	no	—
196	#125×C₆₇	C₂³	1	2	yes	—
197	#125×C₆₇	C₂³	1	1	yes	characteristic
198	#125×C₆₇	C₂³	1	2	yes	—
199	#125×C₆₇	C₂³	1	1	yes	characteristic
200	#124×C₆₇	—	2	1	no	—
201	#124×C₆₇	—	2	1	no	—
202	#124×C₆₇	C₂³	1	1	yes	characteristic
203	#124×C₆₇	C₂³	1	1	yes	characteristic
204	#123×C₆₇	—	2	1	no	—
205	#123×C₆₇	—	2	1	no	—
206	#123×C₆₇	—	2	1	no	—
207	#123×C₆₇	—	2	1	no	—
208	#123×C₆₇	—	2	1	no	—
209	#123×C₆₇	—	2	1	no	—
210	#123×C₆₇	—	2	1	no	—
211	C₂²⋊Q₈×C₆₇	—	2	1	no	—
212	C₂²⋊Q₈×C₆₇	—	2	1	no	—
213	C₂²⋊Q₈×C₆₇	—	2	1	no	—
214	C₂²⋊Q₈×C₆₇	—	2	1	no	—
215	C₂²⋊Q₈×C₆₇	—	2	1	no	—
216	C₂²⋊Q₈×C₆₇	—	2	1	no	—
217	C₂²⋊Q₈×C₆₇	—	2	1	no	—
218	C₂²⋊Q₈×C₆₇	—	2	1	no	—
219	C₂²⋊Q₈×C₆₇	—	2	1	no	—
220	C₂²⋊Q₈×C₆₇	—	2	1	no	—
221	C₂²⋊Q₈×C₆₇	—	2	1	no	—
222	C₂²⋊Q₈×C₆₇	—	2	1	no	—
223	C₂²⋊Q₈×C₆₇	—	2	1	no	—
224	C₂²⋊Q₈×C₆₇	—	2	1	no	—
225	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
229	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
230	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
231	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
232	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
233	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
234	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
235	#121×C₆₇	C₂³	1	1	yes	characteristic
236	#121×C₆₇	C₂³	1	1	yes	characteristic
237	#120×C₆₇	—	2	1	no	—
238	C₄×Q₈×C₆₇	—	2	1	no	—
239	C₄×Q₈×C₆₇	—	2	1	no	—
240	C₄×Q₈×C₆₇	—	2	1	no	—
241	C₄×Q₈×C₆₇	—	2	1	no	—
242	C₄×Q₈×C₆₇	—	2	1	no	—
243	C₄×Q₈×C₆₇	—	2	1	no	—
244	C₄×Q₈×C₆₇	—	2	1	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×Q₈×C₆₇	C₂³	1	2	yes	—
250	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
251	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
252	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
253	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
254	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
255	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₆₇	—	2	1	no	—
257	C₄×D₄×C₆₇	—	2	1	no	—
258	C₄×D₄×C₆₇	—	2	1	no	—
259	C₄×D₄×C₆₇	—	2	1	no	—
260	C₄×D₄×C₆₇	—	2	1	no	—
261	C₄×D₄×C₆₇	—	2	1	no	—
262	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
264	#117×C₆₇	—	2	1	no	—
265	#117×C₆₇	—	2	1	no	—
266	#117×C₆₇	—	2	1	no	—
267	#117×C₆₇	—	2	1	no	—
268	#117×C₆₇	—	2	1	no	—
269	#117×C₆₇	—	2	1	no	—
270	#117×C₆₇	—	2	1	no	—
271	#117×C₆₇	D₄	1	1	yes	characteristic
272	#117×C₆₇	D₄	1	1	yes	characteristic
273	#117×C₆₇	D₄	1	1	yes	characteristic
274	#117×C₆₇	D₄	1	1	yes	characteristic
275	#117×C₆₇	C₂³	1	1	yes	characteristic
276	#117×C₆₇	C₂³	1	1	yes	characteristic
277	#117×C₆₇	C₂³	1	1	yes	characteristic
278	#117×C₆₇	C₂³	1	1	yes	characteristic
279	#117×C₆₇	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
281	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
282	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
283	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
284	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
285	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
286	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
287	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
288	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
289	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
290	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
300	C₂×C₄²×C₆₇	—	2	1	no	—
301	C₂×C₄²×C₆₇	—	2	1	no	—
302	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
304	#107×C₆₇	C₂³	1	2	yes	—
305	#107×C₆₇	C₂³	1	2	yes	—
306	#107×C₆₇	C₂³	1	2	yes	—
307	#107×C₆₇	C₂³	1	2	yes	—
308	#106×C₆₇	C₂³	1	2	yes	—
309	#106×C₆₇	C₂³	1	2	yes	—
310	#106×C₆₇	C₂³	1	2	yes	—
311	#106×C₆₇	C₂³	1	2	yes	—
312	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
313	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
314	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
315	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
316	#103×C₆₇	C₂³	1	2	yes	—
317	#103×C₆₇	C₂³	1	2	yes	—
318	#103×C₆₇	C₂³	1	2	yes	—
319	#103×C₆₇	C₂³	1	2	yes	—
320	#103×C₆₇	C₂³	1	2	yes	—
321	#103×C₆₇	C₂³	1	2	yes	—
322	#103×C₆₇	C₂³	1	2	yes	—
323	#103×C₆₇	C₂³	1	2	yes	—
324	#103×C₆₇	C₂³	1	2	yes	—
325	#103×C₆₇	C₂³	1	2	yes	—
326	#103×C₆₇	C₂³	1	2	yes	—
327	#103×C₆₇	C₂³	1	2	yes	—
328	#103×C₆₇	C₂³	1	2	yes	—
329	#103×C₆₇	C₂³	1	2	yes	—
330	#102×C₆₇	C₂³	1	2	yes	—
331	#102×C₆₇	C₂³	1	2	yes	—
332	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
333	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
334	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
336	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
337	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
338	#97×C₆₇	C₂³	1	2	yes	—
339	#97×C₆₇	C₂³	1	2	yes	—
340	C₄×C₈×C₆₇	C₂³	1	2	yes	—
341	C₄×C₈×C₆₇	C₂³	1	2	yes	—
342	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
343	#41×C₆₇	—	4	2	no	—
344	C₂×Q₈×C₆₇	—	2	1	no	—
345	C₂×Q₈×C₆₇	—	2	1	no	—
346	C₂×Q₈×C₆₇	—	2	1	no	—
347	C₂×Q₈×C₆₇	—	2	1	no	—
348	C₂×Q₈×C₆₇	—	2	1	no	—
349	C₂×Q₈×C₆₇	—	4	2	no	—
350	C₂×Q₈×C₆₇	—	4	2	no	—
351	C₂×Q₈×C₆₇	—	4	2	no	—
352	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
354	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
356	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₆₇	—	2	1	no	—
358	C₂×D₄×C₆₇	—	2	1	no	—
359	C₂×D₄×C₆₇	—	2	1	no	—
360	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₆₇	—	2	1	no	—
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	1	no	—
364	C₂²×C₄×C₆₇	—	2	1	no	—
365	C₂²×C₄×C₆₇	—	2	1	no	—
366	C₂²×C₄×C₆₇	—	2	1	no	—
367	C₂²×C₄×C₆₇	—	2	1	no	—
368	C₂²×C₄×C₆₇	—	2	1	no	—
369	C₂²×C₄×C₆₇	—	2	1	no	—
370	C₂²×C₄×C₆₇	—	4	2	no	—
371	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
372	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
381	Q₁₆×C₆₇	—	4	2	no	—
382	Q₁₆×C₆₇	—	4	2	no	—
383	Q₁₆×C₆₇	—	4	2	no	—
384	Q₁₆×C₆₇	—	4	2	no	—
385	Q₁₆×C₆₇	—	4	2	no	—
386	Q₁₆×C₆₇	—	4	2	no	—
387	SD₁₆×C₆₇	—	4	2	no	—
388	SD₁₆×C₆₇	—	4	2	no	—
389	M₁₆×C₆₇	—	4	2	no	—
390	C₂×C₈×C₆₇	—	4	2	no	—
391	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
392	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
393	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
394	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
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	1	no	—
399	C₄⋊C₄×C₆₇	—	2	1	no	—
400	C₄⋊C₄×C₆₇	—	2	2	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	—	2	1	no	—
405	C₄⋊C₄×C₆₇	—	2	1	no	—
406	C₄⋊C₄×C₆₇	—	2	2	no	—
407	C₄⋊C₄×C₆₇	—	2	2	no	—
408	C₄⋊C₄×C₆₇	—	2	2	no	—
409	C₄⋊C₄×C₆₇	—	2	2	no	—
410	C₄⋊C₄×C₆₇	—	2	2	no	—
411	C₄⋊C₄×C₆₇	—	2	2	no	—
412	C₄⋊C₄×C₆₇	—	2	2	no	—
413	C₄⋊C₄×C₆₇	—	2	2	no	—
414	C₄⋊C₄×C₆₇	—	2	2	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	—	2	2	no	—
418	C₄⋊C₄×C₆₇	—	2	1	no	—
419	C₄⋊C₄×C₆₇	—	2	1	no	—
420	C₄⋊C₄×C₆₇	—	2	1	no	—
421	C₄⋊C₄×C₆₇	—	2	1	no	—
422	C₄⋊C₄×C₆₇	—	2	1	no	—
423	C₄⋊C₄×C₆₇	—	2	1	no	—
424	C₄⋊C₄×C₆₇	—	2	1	no	—
425	C₄⋊C₄×C₆₇	—	2	1	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	1	no	—
433	C₄⋊C₄×C₆₇	—	2	1	no	—
434	C₄⋊C₄×C₆₇	—	2	1	no	—
435	C₄⋊C₄×C₆₇	—	2	1	no	—
436	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
445	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
446	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₂²⋊C₄×C₆₇	—	2	1	no	—
451	C₂²⋊C₄×C₆₇	—	2	1	no	—
452	C₂²⋊C₄×C₆₇	—	2	1	no	—
453	C₂²⋊C₄×C₆₇	—	2	1	no	—
454	C₂²⋊C₄×C₆₇	—	2	2	no	—
455	C₂²⋊C₄×C₆₇	—	2	2	no	—
456	C₂²⋊C₄×C₆₇	—	2	2	no	—
457	C₂²⋊C₄×C₆₇	—	2	2	no	—
458	C₂²⋊C₄×C₆₇	—	2	1	no	—
459	C₂²⋊C₄×C₆₇	—	2	1	no	—
460	C₂²⋊C₄×C₆₇	—	2	1	no	—
461	C₂²⋊C₄×C₆₇	—	2	1	no	—
462	C₂²⋊C₄×C₆₇	—	2	1	no	—
463	C₂²⋊C₄×C₆₇	—	2	1	no	—
464	C₂²⋊C₄×C₆₇	—	2	1	no	—
465	C₂²⋊C₄×C₆₇	—	2	1	no	—
466	C₂²⋊C₄×C₆₇	—	2	1	no	—
467	C₂²⋊C₄×C₆₇	—	2	1	no	—
468	C₂²⋊C₄×C₆₇	—	2	1	no	—
469	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
470	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
471	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
472	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
473	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
474	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
475	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
476	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
477	C₄²×C₆₇	—	2	2	no	—
478	C₄²×C₆₇	—	2	2	no	—
479	C₄²×C₆₇	—	2	2	no	—
480	C₄²×C₆₇	—	2	2	no	—
481	C₄²×C₆₇	—	2	1	no	—
482	C₄²×C₆₇	—	2	1	no	—
483	C₄²×C₆₇	—	2	1	no	—
484	C₄²×C₆₇	—	2	1	no	—
485	C₄²×C₆₇	—	2	1	no	—
486	C₄²×C₆₇	—	2	1	no	—
487	C₄²×C₆₇	—	2	1	no	—
488	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
489	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
490	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
493	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
494	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
495	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₂³×C₆₇	—	2	2	no	—
497	C₂³×C₆₇	—	2	1	no	—
498	C₂³×C₆₇	—	4	1	no	—
499	C₂³×C₆₇	—	4	1	no	—
500	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
501	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
502	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
503	Q₈×C₆₇	—	2	2	no	—
504	Q₈×C₆₇	—	2	2	no	—
505	Q₈×C₆₇	—	2	2	no	—
506	Q₈×C₆₇	—	2	2	no	—
507	Q₈×C₆₇	—	2	2	no	—
508	Q₈×C₆₇	—	2	2	no	—
509	Q₈×C₆₇	—	2	2	no	—
510	Q₈×C₆₇	—	4	2	no	—
511	Q₈×C₆₇	—	4	2	no	—
512	Q₈×C₆₇	—	4	2	no	—
513	Q₈×C₆₇	—	8	1	no	—
514	Q₈×C₆₇	—	8	1	no	—
515	D₄×C₆₇	—	2	2	no	—
516	D₄×C₆₇	—	4	2	no	—
517	D₄×C₆₇	—	4	2	no	—
518	D₄×C₆₇	—	8	1	no	—
519	C₂×C₄×C₆₇	—	2	2	no	—
520	C₂×C₄×C₆₇	—	2	2	no	—
521	C₂×C₄×C₆₇	—	2	2	no	—
522	C₂×C₄×C₆₇	—	2	2	no	—
523	C₂×C₄×C₆₇	—	2	2	no	—
524	C₂×C₄×C₆₇	—	2	1	no	—
525	C₂×C₄×C₆₇	—	2	1	no	—
526	C₂×C₄×C₆₇	—	2	1	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	2	no	—
529	C₂×C₄×C₆₇	—	2	2	no	—
530	C₂×C₄×C₆₇	—	2	1	no	—
531	C₂×C₄×C₆₇	—	2	2	no	—
532	C₂×C₄×C₆₇	—	2	2	no	—
533	C₂×C₄×C₆₇	—	2	1	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	4	1	no	—
536	C₂×C₄×C₆₇	—	4	1	no	—
537	C₂×C₄×C₆₇	—	4	1	no	—
538	C₂×C₄×C₆₇	—	4	1	no	—
539	C₂×C₄×C₆₇	—	4	1	no	—
540	C₂×C₄×C₆₇	—	4	2	no	—
541	C₂×C₄×C₆₇	—	4	2	no	—
542	C₂×C₄×C₆₇	—	4	2	no	—
543	C₂×C₄×C₆₇	—	4	2	no	—
544	C₂×C₄×C₆₇	—	4	2	no	—
545	C₂×C₄×C₆₇	—	4	2	no	—
546	C₂×C₄×C₆₇	—	8	1	no	—
547	C₂×C₄×C₆₇	—	8	1	no	—
548	C₂×C₄×C₆₇	—	8	1	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	1	yes	characteristic
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	1	yes	characteristic
555	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
561	C₈×C₆₇	—	2	2	no	—
562	C₈×C₆₇	—	2	2	no	—
563	C₈×C₆₇	—	2	2	no	—
564	C₈×C₆₇	—	2	2	no	—
565	C₂²×C₆₇	—	2	1	no	—
566	C₂²×C₆₇	—	2	1	no	—
567	C₂²×C₆₇	—	2	1	no	—
568	C₂²×C₆₇	—	2	1	no	—
569	C₂²×C₆₇	—	2	1	no	—
570	C₂²×C₆₇	—	2	1	no	—
571	C₂²×C₆₇	—	2	1	no	—
572	C₂²×C₆₇	—	2	1	no	—
573	C₂²×C₆₇	—	4	1	no	—
574	C₂²×C₆₇	—	4	1	no	—
575	C₂²×C₆₇	—	4	1	no	—
576	C₂²×C₆₇	—	8	2	no	—
577	C₂²×C₆₇	#578	1	2	yes	—
578	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
579	C₄×C₆₇	—	2	1	no	—
580	C₄×C₆₇	—	2	1	no	—
581	C₄×C₆₇	—	2	1	no	—
582	C₄×C₆₇	—	2	1	no	—
583	C₄×C₆₇	—	2	1	no	—
584	C₄×C₆₇	—	2	1	no	—
585	C₄×C₆₇	—	2	1	no	—
586	C₄×C₆₇	—	2	1	no	—
587	C₄×C₆₇	—	2	1	no	—
588	C₄×C₆₇	—	2	1	no	—
589	C₄×C₆₇	—	2	1	no	—
590	C₄×C₆₇	—	4	2	no	—
591	C₄×C₆₇	—	4	1	no	—
592	C₄×C₆₇	—	4	1	no	—
593	C₄×C₆₇	—	4	1	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	—	4	2	no	—
599	C₄×C₆₇	—	4	2	no	—
600	C₄×C₆₇	—	4	1	no	—
601	C₄×C₆₇	#585	1	2	yes	—
602	#60983	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
603	C₂×C₆₇	—	2	2	no	—
604	C₂×C₆₇	—	4	1	no	—
605	C₂×C₆₇	—	4	1	no	—
606	C₂×C₆₇	—	8	1	no	—
607	C₂×C₆₇	#3449	1	1	yes	characteristic
608	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
609	C₂×C₆₇	#3586	1	1	yes	characteristic
610	#3495	C₂×C₆₇	1	1	yes	characteristic
611	C₂×#541	C₂×C₆₇	1	1	yes	characteristic, complemented
612	#3261	C₂×C₆₇	1	2	yes	complemented
613	#3258	C₂×C₆₇	1	2	yes	complemented
614	#3242	C₂×C₆₇	1	2	yes	complemented
615	#3236	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#3232	C₂×C₆₇	1	1	yes	characteristic, complemented
617	#3223	C₂×C₆₇	1	2	yes	complemented
618	#3218	C₂×C₆₇	1	1	yes	characteristic, complemented
619	#3209	C₂×C₆₇	1	1	yes	characteristic, complemented
620	#3196	C₂×C₆₇	1	1	yes	characteristic
621	#3195	C₂×C₆₇	1	1	yes	characteristic, complemented
622	#3190	C₂×C₆₇	1	1	yes	characteristic
623	#3189	C₂×C₆₇	1	1	yes	characteristic, complemented
624	#3178	C₂×C₆₇	1	2	yes	complemented
625	#3177	C₂×C₆₇	1	2	yes	complemented
626	#3127	C₂×C₆₇	1	2	yes	complemented
627	#3120	C₂×C₆₇	1	2	yes	complemented
628	#3117	C₂×C₆₇	1	1	yes	characteristic, complemented
629	#3113	C₂×C₆₇	1	1	yes	characteristic, complemented
630	#3108	C₂×C₆₇	1	1	yes	characteristic, complemented
631	#3104	C₂×C₆₇	1	1	yes	characteristic, complemented
632	#2924	C₂×C₆₇	1	1	yes	characteristic, complemented
633	C₆₇	#60983	1	1	yes	characteristic, direct product factor, Sylow
634	#556	—	2	1	no	—
635	#554	—	2	1	no	—
636	#552	—	2	1	no	—
637	#552	—	2	1	no	—
638	#552	—	2	1	no	—
639	#552	—	2	1	no	—
640	#551	—	2	1	no	—
641	#551	—	2	1	no	—
642	#544	C₂²×C₆₇	1	1	yes	characteristic
643	#542	C₂²×C₆₇	1	1	yes	characteristic
644	#542	C₂²×C₆₇	1	1	yes	characteristic
645	#541	—	2	1	no	—
646	#541	—	2	1	no	—
647	#541	—	2	1	no	—
648	#541	—	2	1	no	—
649	#541	C₂²×C₆₇	1	2	yes	—
650	#541	C₂²×C₆₇	1	1	yes	characteristic
651	#541	C₂²×C₆₇	1	2	yes	—
652	#541	C₂²×C₆₇	1	2	yes	—
653	#541	C₂²×C₆₇	1	2	yes	—
654	#541	C₂²×C₆₇	1	1	yes	characteristic
655	#536	C₂²×C₆₇	1	1	yes	characteristic
656	#533	C₂²×C₆₇	1	1	yes	characteristic
657	#533	C₂²×C₆₇	1	1	yes	characteristic
658	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
659	#529	C₂²×C₆₇	1	1	yes	characteristic
660	#529	C₂²×C₆₇	1	1	yes	characteristic
661	C₂×#126	—	2	1	no	—
662	C₂×#126	—	2	1	no	—
663	C₂×#125	—	2	1	no	—
664	C₂×#125	—	2	1	no	—
665	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
666	#525	C₂²×C₆₇	1	1	yes	characteristic
667	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
668	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
669	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
670	#520	C₂²×C₆₇	1	1	yes	characteristic
671	#519	C₂²×C₆₇	1	1	yes	characteristic
672	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
673	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
674	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
675	#501	C₂²×C₆₇	1	2	yes	complemented
676	#499	C₂²×C₆₇	1	2	yes	complemented
677	#497	C₂²×C₆₇	1	2	yes	complemented
678	#494	C₂²×C₆₇	1	2	yes	complemented
679	#491	C₂²×C₆₇	1	2	yes	complemented
680	#491	C₂²×C₆₇	1	2	yes	complemented
681	#488	C₂²×C₆₇	1	2	yes	complemented
682	#487	C₂²×C₆₇	1	2	yes	complemented
683	#485	C₂²×C₆₇	1	2	yes	—
684	#485	C₂²×C₆₇	1	2	yes	—
685	#484	C₂²×C₆₇	1	1	yes	characteristic
686	#484	C₂²×C₆₇	1	1	yes	characteristic
687	#484	C₂²×C₆₇	1	1	yes	characteristic
688	#484	C₂²×C₆₇	1	2	yes	—
689	#483	C₂²×C₆₇	1	1	yes	characteristic
690	#483	C₂²×C₆₇	1	1	yes	characteristic
691	#483	C₂²×C₆₇	1	1	yes	characteristic
692	#483	C₂²×C₆₇	1	2	yes	—
693	#481	C₂²×C₆₇	1	1	yes	characteristic
694	#480	C₂²×C₆₇	1	1	yes	characteristic
695	#479	C₂²×C₆₇	1	2	yes	complemented
696	#479	C₂²×C₆₇	1	2	yes	complemented
697	#479	C₂²×C₆₇	1	2	yes	complemented
698	#479	C₂²×C₆₇	1	2	yes	complemented
699	#479	C₂²×C₆₇	1	2	yes	complemented
700	#478	C₂²×C₆₇	1	2	yes	complemented
701	#477	C₂²×C₆₇	1	2	yes	complemented
702	#475	C₂²×C₆₇	1	2	yes	complemented
703	#470	C₂²×C₆₇	1	2	yes	—
704	#470	C₂²×C₆₇	1	2	yes	—
705	#470	C₂²×C₆₇	1	2	yes	—
706	#468	C₂²×C₆₇	1	2	yes	—
707	#467	C₂²×C₆₇	1	2	yes	—
708	#467	C₂²×C₆₇	1	2	yes	—
709	#467	C₂²×C₆₇	1	2	yes	—
710	#465	C₂²×C₆₇	1	2	yes	—
711	#464	C₂²×C₆₇	1	2	yes	complemented
712	#464	C₂²×C₆₇	1	2	yes	complemented
713	#462	C₂²×C₆₇	1	2	yes	complemented
714	#462	C₂²×C₆₇	1	2	yes	complemented
715	#462	C₂²×C₆₇	1	2	yes	complemented
716	#462	C₂²×C₆₇	1	2	yes	complemented
717	#462	C₂²×C₆₇	1	2	yes	complemented
718	#461	C₂²×C₆₇	1	2	yes	complemented
719	#452	C₂²×C₆₇	1	2	yes	—
720	#452	C₂²×C₆₇	1	2	yes	—
721	#451	C₂²×C₆₇	1	1	yes	characteristic
722	#451	C₂²×C₆₇	1	1	yes	characteristic
723	#451	C₂²×C₆₇	1	1	yes	characteristic
724	#451	C₂²×C₆₇	1	1	yes	characteristic
725	#451	C₂²×C₆₇	1	1	yes	characteristic
726	#451	C₂²×C₆₇	1	1	yes	characteristic
727	#451	C₂²×C₆₇	1	2	yes	—
728	#451	C₂²×C₆₇	1	2	yes	—
729	#448	C₂²×C₆₇	1	1	yes	characteristic
730	#448	C₂²×C₆₇	1	1	yes	characteristic
731	#441	C₂²×C₆₇	1	2	yes	complemented
732	#441	C₂²×C₆₇	1	2	yes	complemented
733	#441	C₂²×C₆₇	1	2	yes	complemented
734	#440	C₂²×C₆₇	1	2	yes	complemented
735	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
736	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
737	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
738	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
739	#433	C₂²×C₆₇	1	2	yes	—
740	#433	C₂²×C₆₇	1	2	yes	—
741	#432	C₂²×C₆₇	1	1	yes	characteristic
742	#432	C₂²×C₆₇	1	1	yes	characteristic
743	#431	C₂²×C₆₇	1	1	yes	characteristic
744	#431	C₂²×C₆₇	1	1	yes	characteristic
745	#424	C₂²×C₆₇	1	2	yes	—
746	#407	C₂²×C₆₇	1	1	yes	characteristic
747	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
748	#405	C₂²×C₆₇	1	2	yes	—
749	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
750	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
751	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
752	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
753	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
754	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
755	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
756	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
757	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
758	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
759	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
760	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
761	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
762	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
763	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
764	C₄⋊Q₈	—	2	1	no	—
765	C₄⋊Q₈	—	2	1	no	—
766	C₄⋊Q₈	—	2	1	no	—
767	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
768	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
769	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
770	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
771	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
772	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
773	#126	—	2	1	no	—
774	#126	—	2	1	no	—
775	#126	—	2	2	no	—
776	#126	—	2	2	no	—
777	#126	—	2	2	no	—
778	#126	—	2	2	no	—
779	#126	—	2	2	no	—
780	#126	—	2	2	no	—
781	#126	—	2	2	no	—
782	#126	—	2	2	no	—
783	#126	—	2	1	no	—
784	#126	—	2	1	no	—
785	#126	—	2	1	no	—
786	#126	—	2	1	no	—
787	#126	—	2	1	no	—
788	#126	—	2	1	no	—
789	#125	—	2	2	no	—
790	#125	—	2	2	no	—
791	#125	—	2	2	no	—
792	#125	—	2	2	no	—
793	#125	—	2	2	no	—
794	#125	—	2	2	no	—
795	#125	—	2	2	no	—
796	#125	—	2	2	no	—
797	#125	—	2	1	no	—
798	#125	—	2	1	no	—
799	#125	—	2	1	no	—
800	#125	—	2	1	no	—
801	#125	—	2	1	no	—
802	#125	—	2	1	no	—
803	#125	—	2	1	no	—
804	#125	—	2	1	no	—
805	#125	—	2	1	no	—
806	#125	C₂³×C₆₇	1	2	yes	—
807	#125	C₂³×C₆₇	1	2	yes	—
808	#125	C₂³×C₆₇	1	1	yes	characteristic
809	#125	C₂³×C₆₇	1	1	yes	characteristic
810	#124	—	2	1	no	—
811	#124	—	2	1	no	—
812	#124	C₂³×C₆₇	1	1	yes	characteristic
813	#124	C₂³×C₆₇	1	1	yes	characteristic
814	#123	—	2	1	no	—
815	#123	—	2	1	no	—
816	#123	—	2	1	no	—
817	#123	—	2	1	no	—
818	#123	—	2	1	no	—
819	#123	—	2	1	no	—
820	#123	—	2	1	no	—
821	C₂²⋊Q₈	—	2	1	no	—
822	C₂²⋊Q₈	—	2	1	no	—
823	C₂²⋊Q₈	—	2	1	no	—
824	C₂²⋊Q₈	—	2	1	no	—
825	C₂²⋊Q₈	—	2	1	no	—
826	C₂²⋊Q₈	—	2	1	no	—
827	C₂²⋊Q₈	—	2	1	no	—
828	C₂²⋊Q₈	—	2	1	no	—
829	C₂²⋊Q₈	—	2	1	no	—
830	C₂²⋊Q₈	—	2	1	no	—
831	C₂²⋊Q₈	—	2	1	no	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	—	2	1	no	—
834	C₂²⋊Q₈	—	2	1	no	—
835	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
836	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
837	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
838	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
839	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
840	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
841	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
842	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
843	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
844	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
845	#121	C₂³×C₆₇	1	1	yes	characteristic
846	#121	C₂³×C₆₇	1	1	yes	characteristic
847	#120	—	2	1	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	—	2	1	no	—
850	C₄×Q₈	—	2	1	no	—
851	C₄×Q₈	—	2	1	no	—
852	C₄×Q₈	—	2	1	no	—
853	C₄×Q₈	—	2	1	no	—
854	C₄×Q₈	—	2	1	no	—
855	C₄×Q₈	—	2	1	no	—
856	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
857	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
858	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
859	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
860	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
861	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
862	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
863	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
864	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
865	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
873	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
874	#117	—	2	1	no	—
875	#117	—	2	1	no	—
876	#117	—	2	1	no	—
877	#117	—	2	1	no	—
878	#117	—	2	1	no	—
879	#117	—	2	1	no	—
880	#117	—	2	1	no	—
881	#117	D₄×C₆₇	1	1	yes	characteristic
882	#117	D₄×C₆₇	1	1	yes	characteristic
883	#117	D₄×C₆₇	1	1	yes	characteristic
884	#117	D₄×C₆₇	1	1	yes	characteristic
885	#117	C₂³×C₆₇	1	1	yes	characteristic
886	#117	C₂³×C₆₇	1	1	yes	characteristic
887	#117	C₂³×C₆₇	1	1	yes	characteristic
888	#117	C₂³×C₆₇	1	1	yes	characteristic
889	#117	C₂³×C₆₇	1	1	yes	characteristic
890	C₂×C₄⋊C₄	—	2	1	no	—
891	C₂×C₄⋊C₄	—	2	1	no	—
892	C₂×C₄⋊C₄	—	2	1	no	—
893	C₂×C₄⋊C₄	—	2	1	no	—
894	C₂×C₄⋊C₄	—	2	1	no	—
895	C₂×C₄⋊C₄	—	2	1	no	—
896	C₂×C₄⋊C₄	—	2	1	no	—
897	C₂×C₄⋊C₄	—	2	1	no	—
898	C₂×C₄⋊C₄	—	2	1	no	—
899	C₂×C₄⋊C₄	—	2	1	no	—
900	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
901	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
902	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
903	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
904	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
905	C₂×C₂²⋊C₄	—	2	1	no	—
906	C₂×C₂²⋊C₄	—	2	1	no	—
907	C₂×C₂²⋊C₄	—	2	1	no	—
908	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
909	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
910	C₂×C₄²	—	2	1	no	—
911	C₂×C₄²	—	2	1	no	—
912	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
913	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
914	#107	C₂³×C₆₇	1	2	yes	—
915	#107	C₂³×C₆₇	1	2	yes	—
916	#107	C₂³×C₆₇	1	2	yes	—
917	#107	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	#106	C₂³×C₆₇	1	2	yes	—
922	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
923	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
924	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
925	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
926	#103	C₂³×C₆₇	1	2	yes	—
927	#103	C₂³×C₆₇	1	2	yes	—
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	2	yes	—
934	#103	C₂³×C₆₇	1	2	yes	—
935	#103	C₂³×C₆₇	1	2	yes	—
936	#103	C₂³×C₆₇	1	2	yes	—
937	#103	C₂³×C₆₇	1	2	yes	—
938	#103	C₂³×C₆₇	1	2	yes	—
939	#103	C₂³×C₆₇	1	2	yes	—
940	#102	C₂³×C₆₇	1	2	yes	—
941	#102	C₂³×C₆₇	1	2	yes	—
942	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
943	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
944	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
945	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
946	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
947	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
948	#97	C₂³×C₆₇	1	2	yes	—
949	#97	C₂³×C₆₇	1	2	yes	—
950	C₄×C₈	C₂³×C₆₇	1	2	yes	—
951	C₄×C₈	C₂³×C₆₇	1	2	yes	—
952	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
953	#41	—	4	2	no	—
954	C₂×Q₈	—	2	1	no	—
955	C₂×Q₈	—	2	1	no	—
956	C₂×Q₈	—	2	1	no	—
957	C₂×Q₈	—	2	1	no	—
958	C₂×Q₈	—	2	1	no	—
959	C₂×Q₈	—	4	2	no	—
960	C₂×Q₈	—	4	2	no	—
961	C₂×Q₈	—	4	2	no	—
962	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
963	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
964	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
965	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
966	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	1	no	—
969	C₂×D₄	—	2	1	no	—
970	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	2	1	no	—
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	1	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	4	2	no	—
981	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
982	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
983	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
984	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
985	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
986	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
987	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
988	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
989	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
990	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
991	Q₁₆	—	4	2	no	—
992	Q₁₆	—	4	2	no	—
993	Q₁₆	—	4	2	no	—
994	Q₁₆	—	4	2	no	—
995	Q₁₆	—	4	2	no	—
996	Q₁₆	—	4	2	no	—
997	SD₁₆	—	4	2	no	—
998	SD₁₆	—	4	2	no	—
999	M₁₆	—	4	2	no	—
1000	C₂×C₈	—	4	2	no	—
1001	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1002	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1003	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1004	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	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	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1047	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1048	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1049	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1050	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1051	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1052	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1053	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1054	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1055	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1056	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1057	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1058	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1059	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1080	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1081	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1082	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1083	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1084	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1085	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1086	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	2	no	—
1089	C₄²	—	2	2	no	—
1090	C₄²	—	2	2	no	—
1091	C₄²	—	2	1	no	—
1092	C₄²	—	2	1	no	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	1	no	—
1096	C₄²	—	2	1	no	—
1097	C₄²	—	2	1	no	—
1098	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1099	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1100	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1101	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1102	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1103	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1104	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1105	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1106	C₂³	—	2	2	no	—
1107	C₂³	—	2	1	no	—
1108	C₂³	—	4	1	no	—
1109	C₂³	—	4	1	no	—
1110	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1111	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1112	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1113	Q₈	—	2	2	no	—
1114	Q₈	—	2	2	no	—
1115	Q₈	—	2	2	no	—
1116	Q₈	—	2	2	no	—
1117	Q₈	—	2	2	no	—
1118	Q₈	—	2	2	no	—
1119	Q₈	—	2	2	no	—
1120	Q₈	—	4	2	no	—
1121	Q₈	—	4	2	no	—
1122	Q₈	—	4	2	no	—
1123	Q₈	—	8	1	no	—
1124	Q₈	—	8	1	no	—
1125	D₄	—	2	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	8	1	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	4	2	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	—	8	1	no	—
1159	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
1166	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1167	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1168	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1169	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1170	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1171	C₈	—	2	2	no	—
1172	C₈	—	2	2	no	—
1173	C₈	—	2	2	no	—
1174	C₈	—	2	2	no	—
1175	C₂²	—	2	1	no	—
1176	C₂²	—	2	1	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	8	2	no	—
1187	C₂²	#578×C₆₇	1	2	yes	—
1188	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1189	C₄	—	2	1	no	—
1190	C₄	—	2	1	no	—
1191	C₄	—	2	1	no	—
1192	C₄	—	2	1	no	—
1193	C₄	—	2	1	no	—
1194	C₄	—	2	1	no	—
1195	C₄	—	2	1	no	—
1196	C₄	—	2	1	no	—
1197	C₄	—	2	1	no	—
1198	C₄	—	2	1	no	—
1199	C₄	—	2	1	no	—
1200	C₄	—	4	2	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	2	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	2	no	—
1211	C₄	#585×C₆₇	1	2	yes	—
1212	C₂	—	2	2	no	—
1213	C₂	—	4	1	no	—
1214	C₂	—	4	1	no	—
1215	C₂	—	8	1	no	—
1216	C₂	C₆₇×#3449	1	1	yes	characteristic
1217	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
1218	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	#525×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#541×C₆₇	C₂	semidirect
3. C₆₇×#3261	C₂	semidirect
4. C₆₇×#3258	C₂	semidirect
5. C₆₇×#3242	C₂	semidirect
6. C₆₇×#3236	C₂	semidirect
7. C₆₇×#3232	C₂	semidirect
8. C₆₇×#3223	C₂	semidirect
9. C₆₇×#3218	C₂	semidirect
10. C₆₇×#3209	C₂	semidirect
12. C₆₇×#3195	C₂	semidirect
14. C₆₇×#3189	C₂	semidirect
15. C₆₇×#3178	C₂	semidirect
16. C₆₇×#3177	C₂	semidirect
17. C₆₇×#3127	C₂	semidirect
18. C₆₇×#3120	C₂	semidirect
19. C₆₇×#3117	C₂	semidirect
20. C₆₇×#3113	C₂	semidirect
21. C₆₇×#3108	C₂	semidirect
22. C₆₇×#3104	C₂	semidirect
23. C₆₇×#2924	C₂	semidirect
65. #501×C₆₇	C₂²	semidirect
66. #499×C₆₇	C₂²	semidirect
67. #497×C₆₇	C₂²	semidirect
68. #494×C₆₇	C₂²	semidirect
69. #491×C₆₇	C₂²	semidirect
70. #491×C₆₇	C₂²	semidirect
71. #488×C₆₇	C₂²	semidirect
72. #487×C₆₇	C₂²	semidirect
85. #479×C₆₇	C₂²	semidirect
86. #479×C₆₇	C₂²	semidirect
87. #479×C₆₇	C₂²	semidirect
88. #479×C₆₇	C₂²	semidirect
89. #479×C₆₇	C₂²	semidirect
90. #478×C₆₇	C₂²	semidirect
91. #477×C₆₇	C₂²	semidirect
92. #475×C₆₇	C₂²	semidirect
101. #464×C₆₇	C₂²	semidirect
102. #464×C₆₇	C₂²	semidirect
103. #462×C₆₇	C₂²	semidirect
104. #462×C₆₇	C₂²	semidirect
105. #462×C₆₇	C₂²	semidirect
106. #462×C₆₇	C₂²	semidirect
107. #462×C₆₇	C₂²	semidirect
108. #461×C₆₇	C₂²	semidirect
121. #441×C₆₇	C₂²	semidirect
122. #441×C₆₇	C₂²	semidirect
123. #441×C₆₇	C₂²	semidirect
124. #440×C₆₇	C₂²	semidirect
125. C₄×Q₁₆×C₆₇	C₂²	semidirect
126. C₄×Q₁₆×C₆₇	C₂²	semidirect
127. C₄×Q₁₆×C₆₇	C₂²	semidirect
128. C₄×SD₁₆×C₆₇	C₂²	semidirect
602. #60983	C₆₇	direct (N × H)
611. C₂×#541	C₂×C₆₇	semidirect
612. #3261	C₂×C₆₇	semidirect
613. #3258	C₂×C₆₇	semidirect
614. #3242	C₂×C₆₇	semidirect
615. #3236	C₂×C₆₇	semidirect
616. #3232	C₂×C₆₇	semidirect
617. #3223	C₂×C₆₇	semidirect
618. #3218	C₂×C₆₇	semidirect
619. #3209	C₂×C₆₇	semidirect
621. #3195	C₂×C₆₇	semidirect
623. #3189	C₂×C₆₇	semidirect
624. #3178	C₂×C₆₇	semidirect
625. #3177	C₂×C₆₇	semidirect
626. #3127	C₂×C₆₇	semidirect
627. #3120	C₂×C₆₇	semidirect
628. #3117	C₂×C₆₇	semidirect
629. #3113	C₂×C₆₇	semidirect
630. #3108	C₂×C₆₇	semidirect
631. #3104	C₂×C₆₇	semidirect
632. #2924	C₂×C₆₇	semidirect
633. C₆₇	#60983	direct (N × H)
675. #501	C₂²×C₆₇	semidirect
676. #499	C₂²×C₆₇	semidirect
677. #497	C₂²×C₆₇	semidirect
678. #494	C₂²×C₆₇	semidirect
679. #491	C₂²×C₆₇	semidirect
680. #491	C₂²×C₆₇	semidirect
681. #488	C₂²×C₆₇	semidirect
682. #487	C₂²×C₆₇	semidirect
695. #479	C₂²×C₆₇	semidirect
696. #479	C₂²×C₆₇	semidirect
697. #479	C₂²×C₆₇	semidirect
698. #479	C₂²×C₆₇	semidirect
699. #479	C₂²×C₆₇	semidirect
700. #478	C₂²×C₆₇	semidirect
701. #477	C₂²×C₆₇	semidirect
702. #475	C₂²×C₆₇	semidirect
711. #464	C₂²×C₆₇	semidirect
712. #464	C₂²×C₆₇	semidirect
713. #462	C₂²×C₆₇	semidirect
714. #462	C₂²×C₆₇	semidirect
715. #462	C₂²×C₆₇	semidirect
716. #462	C₂²×C₆₇	semidirect
717. #462	C₂²×C₆₇	semidirect
718. #461	C₂²×C₆₇	semidirect
731. #441	C₂²×C₆₇	semidirect
732. #441	C₂²×C₆₇	semidirect
733. #441	C₂²×C₆₇	semidirect
734. #440	C₂²×C₆₇	semidirect
735. C₄×Q₁₆	C₂²×C₆₇	semidirect
736. C₄×Q₁₆	C₂²×C₆₇	semidirect
737. C₄×Q₁₆	C₂²×C₆₇	semidirect
738. C₄×SD₁₆	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×#3495	2
C₂×#541×C₆₇	2
C₆₇×#3261	2
C₆₇×#3258	2
C₆₇×#3242	2
C₆₇×#3236	2
C₆₇×#3232	2
C₆₇×#3223	2
C₆₇×#3218	2
C₆₇×#3209	2
C₆₇×#3196	2
C₆₇×#3195	2
C₆₇×#3190	2
C₆₇×#3189	2
C₆₇×#3178	2
C₆₇×#3177	2
C₆₇×#3127	2
C₆₇×#3120	2
C₆₇×#3117	2
C₆₇×#3113	2
C₆₇×#3108	2
C₆₇×#3104	2
C₆₇×#2924	2
#60983	67

Subgroups — C67×#60983 #30740234

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60983 #30740234