Subgroups — C₆₇×#60982 #30740233

Order 17152.

1728 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×#3494	C₂	1	1	yes	maximal, characteristic
2	C₂×#541×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3260	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×#3234	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3232	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3222	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3196	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3193	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3190	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3187	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3178	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3174	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3123	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×#3112	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#3103	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	#555×C₆₇	—	2	1	no	—
25	#553×C₆₇	—	2	1	no	—
26	#553×C₆₇	—	2	1	no	—
27	#551×C₆₇	—	2	1	no	—
28	#551×C₆₇	—	2	1	no	—
29	#547×C₆₇	—	2	1	no	—
30	#546×C₆₇	—	2	1	no	—
31	#546×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	2	yes	—
41	#541×C₆₇	C₂²	1	2	yes	complemented
42	#541×C₆₇	C₂²	1	2	yes	complemented
43	#540×C₆₇	C₂²	1	1	yes	characteristic
44	#540×C₆₇	C₂²	1	1	yes	characteristic
45	#535×C₆₇	C₂²	1	1	yes	characteristic
46	#532×C₆₇	C₂²	1	1	yes	characteristic
47	#532×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
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, complemented
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×#121×C₆₇	C₂²	1	1	yes	characteristic
60	#520×C₆₇	C₂²	1	1	yes	characteristic
61	#518×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
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	#492×C₆₇	C₂²	1	2	yes	complemented
69	#491×C₆₇	C₂²	1	2	yes	complemented
70	#490×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	2	yes	—
76	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#483×C₆₇	C₂²	1	2	yes	—
78	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	#481×C₆₇	C₂²	1	1	yes	characteristic
80	#481×C₆₇	C₂²	1	1	yes	characteristic
81	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#480×C₆₇	C₂²	1	1	yes	characteristic
83	#480×C₆₇	C₂²	1	1	yes	characteristic
84	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
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	#478×C₆₇	C₂²	1	2	yes	complemented
89	#478×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	complemented
94	#468×C₆₇	C₂²	1	2	yes	—
95	#468×C₆₇	C₂²	1	2	yes	—
96	#468×C₆₇	C₂²	1	2	yes	complemented
97	#467×C₆₇	C₂²	1	2	yes	complemented
98	#465×C₆₇	C₂²	1	2	yes	—
99	#465×C₆₇	C₂²	1	2	yes	—
100	#465×C₆₇	C₂²	1	2	yes	complemented
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	#461×C₆₇	C₂²	1	2	yes	complemented
105	#461×C₆₇	C₂²	1	2	yes	complemented
106	#461×C₆₇	C₂²	1	2	yes	complemented
107	#460×C₆₇	C₂²	1	2	yes	complemented
108	#460×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, complemented
112	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#450×C₆₇	C₂²	1	2	yes	—
114	#450×C₆₇	C₂²	1	2	yes	—
115	#448×C₆₇	C₂²	1	1	yes	characteristic
116	#448×C₆₇	C₂²	1	1	yes	characteristic
117	#448×C₆₇	C₂²	1	1	yes	characteristic
118	#448×C₆₇	C₂²	1	1	yes	characteristic
119	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#441×C₆₇	C₂²	1	2	yes	complemented
122	#440×C₆₇	C₂²	1	2	yes	complemented
123	#440×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×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
127	C₄×SD₁₆×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, complemented
132	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	#424×C₆₇	C₂²	1	2	yes	complemented
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	complemented
139	C₂×#41×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₆₇	—	2	1	no	—
145	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₆₇	—	2	1	no	—
158	C₄⋊Q₈×C₆₇	—	2	1	no	—
159	C₄⋊Q₈×C₆₇	—	2	1	no	—
160	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	#127×C₆₇	C₂³	1	1	yes	characteristic
165	#127×C₆₇	C₂³	1	1	yes	characteristic
166	#126×C₆₇	—	2	1	no	—
167	#126×C₆₇	—	2	1	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	2	no	—
174	#126×C₆₇	—	2	2	no	—
175	#126×C₆₇	—	2	2	no	—
176	#126×C₆₇	—	2	1	no	—
177	#126×C₆₇	—	2	1	no	—
178	#125×C₆₇	—	2	2	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	1	no	—
187	#125×C₆₇	—	2	1	no	—
188	#125×C₆₇	—	2	1	no	—
189	#125×C₆₇	C₂³	1	2	yes	—
190	#125×C₆₇	C₂³	1	1	yes	characteristic
191	#125×C₆₇	C₂³	1	2	yes	—
192	#125×C₆₇	C₂³	1	1	yes	characteristic
193	#124×C₆₇	—	2	1	no	—
194	#124×C₆₇	—	2	1	no	—
195	#124×C₆₇	—	2	1	no	—
196	#124×C₆₇	—	2	1	no	—
197	#124×C₆₇	C₂³	1	1	yes	characteristic
198	#124×C₆₇	C₂³	1	1	yes	characteristic
199	#123×C₆₇	—	2	1	no	—
200	#123×C₆₇	—	2	1	no	—
201	#123×C₆₇	—	2	1	no	—
202	#123×C₆₇	—	2	1	no	—
203	#123×C₆₇	—	2	1	no	—
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	C₂²⋊Q₈×C₆₇	—	2	1	no	—
209	C₂²⋊Q₈×C₆₇	—	2	1	no	—
210	C₂²⋊Q₈×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	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	1	yes	characteristic
222	#121×C₆₇	—	2	1	no	—
223	#121×C₆₇	—	2	1	no	—
224	#121×C₆₇	—	2	1	no	—
225	#121×C₆₇	—	2	1	no	—
226	#121×C₆₇	—	2	1	no	—
227	#121×C₆₇	—	2	1	no	—
228	#121×C₆₇	—	2	1	no	—
229	#121×C₆₇	—	2	1	no	—
230	#121×C₆₇	—	2	1	no	—
231	#121×C₆₇	—	2	1	no	—
232	#121×C₆₇	C₂³	1	1	yes	characteristic
233	#121×C₆₇	C₂³	1	1	yes	characteristic
234	#121×C₆₇	C₂³	1	1	yes	characteristic
235	#121×C₆₇	C₂³	1	1	yes	characteristic
236	#121×C₆₇	C₂³	1	1	yes	characteristic
237	#121×C₆₇	C₂³	1	1	yes	characteristic
238	#120×C₆₇	—	2	1	no	—
239	#120×C₆₇	—	2	1	no	—
240	#120×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	C₂³	1	2	yes	—
246	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
247	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
249	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
250	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₆₇	—	2	1	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	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	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
266	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
267	#117×C₆₇	—	2	1	no	—
268	#117×C₆₇	—	2	1	no	—
269	#117×C₆₇	—	2	1	no	—
270	#117×C₆₇	D₄	1	1	yes	characteristic
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	C₂³	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	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
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	D₄	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
294	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
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	#102×C₆₇	C₂³	1	2	yes	—
327	#102×C₆₇	C₂³	1	2	yes	—
328	#102×C₆₇	C₂³	1	2	yes	—
329	#102×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	—	2	1	no	—
343	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
344	#41×C₆₇	—	4	2	no	—
345	#41×C₆₇	—	8	2	no	—
346	#41×C₆₇	—	8	2	no	—
347	C₂×Q₈×C₆₇	—	2	1	no	—
348	C₂×Q₈×C₆₇	—	2	1	no	—
349	C₂×Q₈×C₆₇	—	2	1	no	—
350	C₂×Q₈×C₆₇	—	2	1	no	—
351	C₂×Q₈×C₆₇	—	4	2	no	—
352	C₂×Q₈×C₆₇	—	4	2	no	—
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×D₄×C₆₇	—	2	1	no	—
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	—	2	1	no	—
361	C₂×D₄×C₆₇	—	2	1	no	—
362	C₂×D₄×C₆₇	—	2	1	no	—
363	C₂×D₄×C₆₇	—	2	1	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	1	no	—
368	C₂×D₄×C₆₇	—	4	2	no	—
369	C₂×D₄×C₆₇	—	8	2	no	—
370	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₆₇	—	2	1	no	—
374	C₂²×C₄×C₆₇	—	2	1	no	—
375	C₂²×C₄×C₆₇	—	2	1	no	—
376	C₂²×C₄×C₆₇	—	2	1	no	—
377	C₂²×C₄×C₆₇	—	2	1	no	—
378	C₂²×C₄×C₆₇	—	2	1	no	—
379	C₂²×C₄×C₆₇	—	2	1	no	—
380	C₂²×C₄×C₆₇	—	2	1	no	—
381	C₂²×C₄×C₆₇	—	2	1	no	—
382	C₂²×C₄×C₆₇	—	2	1	no	—
383	C₂²×C₄×C₆₇	—	2	1	no	—
384	C₂²×C₄×C₆₇	—	2	1	no	—
385	C₂²×C₄×C₆₇	—	4	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	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
396	Q₁₆×C₆₇	—	4	2	no	—
397	Q₁₆×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	SD₁₆×C₆₇	—	4	2	no	—
404	M₁₆×C₆₇	—	4	2	no	—
405	C₂×C₈×C₆₇	—	4	2	no	—
406	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
407	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
408	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
409	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₆₇	—	2	1	no	—
411	C₄⋊C₄×C₆₇	—	2	1	no	—
412	C₄⋊C₄×C₆₇	—	2	1	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	2	no	—
419	C₄⋊C₄×C₆₇	—	2	2	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	2	no	—
427	C₄⋊C₄×C₆₇	—	2	2	no	—
428	C₄⋊C₄×C₆₇	—	2	2	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	—	2	1	no	—
437	C₄⋊C₄×C₆₇	—	2	1	no	—
438	C₄⋊C₄×C₆₇	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
448	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
449	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
470	C₂²⋊C₄×C₆₇	—	2	1	no	—
471	C₂²⋊C₄×C₆₇	—	2	1	no	—
472	C₂²⋊C₄×C₆₇	—	2	1	no	—
473	C₂²⋊C₄×C₆₇	—	2	1	no	—
474	C₂²⋊C₄×C₆₇	—	2	1	no	—
475	C₂²⋊C₄×C₆₇	—	2	1	no	—
476	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
484	C₄²×C₆₇	—	2	2	no	—
485	C₄²×C₆₇	—	2	2	no	—
486	C₄²×C₆₇	—	2	2	no	—
487	C₄²×C₆₇	—	2	2	no	—
488	C₄²×C₆₇	—	2	1	no	—
489	C₄²×C₆₇	—	2	1	no	—
490	C₄²×C₆₇	—	2	1	no	—
491	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
497	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
498	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
499	C₂³×C₆₇	—	2	2	no	—
500	C₂³×C₆₇	—	2	1	no	—
501	C₂³×C₆₇	—	2	1	no	—
502	C₂³×C₆₇	—	2	1	no	—
503	C₂³×C₆₇	—	4	1	no	—
504	C₂³×C₆₇	—	4	1	no	—
505	C₂³×C₆₇	—	4	2	no	—
506	C₂³×C₆₇	—	8	1	no	—
507	C₂³×C₆₇	—	8	1	no	—
508	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
509	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
511	Q₈×C₆₇	—	2	2	no	—
512	Q₈×C₆₇	—	2	2	no	—
513	Q₈×C₆₇	—	2	2	no	—
514	Q₈×C₆₇	—	2	2	no	—
515	Q₈×C₆₇	—	2	2	no	—
516	Q₈×C₆₇	—	4	2	no	—
517	Q₈×C₆₇	—	4	2	no	—
518	Q₈×C₆₇	—	8	1	no	—
519	Q₈×C₆₇	—	8	1	no	—
520	D₄×C₆₇	—	2	2	no	—
521	D₄×C₆₇	—	2	2	no	—
522	D₄×C₆₇	—	2	2	no	—
523	D₄×C₆₇	—	4	2	no	—
524	D₄×C₆₇	—	4	2	no	—
525	D₄×C₆₇	—	4	2	no	—
526	D₄×C₆₇	—	4	2	no	—
527	D₄×C₆₇	—	4	2	no	—
528	D₄×C₆₇	—	8	1	no	—
529	D₄×C₆₇	—	8	1	no	—
530	D₄×C₆₇	—	8	1	no	—
531	D₄×C₆₇	—	8	1	no	—
532	D₄×C₆₇	—	8	1	no	—
533	D₄×C₆₇	—	8	1	no	—
534	D₄×C₆₇	—	8	1	no	—
535	C₂×C₄×C₆₇	—	2	2	no	—
536	C₂×C₄×C₆₇	—	2	2	no	—
537	C₂×C₄×C₆₇	—	2	2	no	—
538	C₂×C₄×C₆₇	—	2	2	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	2	no	—
543	C₂×C₄×C₆₇	—	2	2	no	—
544	C₂×C₄×C₆₇	—	2	2	no	—
545	C₂×C₄×C₆₇	—	2	1	no	—
546	C₂×C₄×C₆₇	—	2	1	no	—
547	C₂×C₄×C₆₇	—	2	1	no	—
548	C₂×C₄×C₆₇	—	2	1	no	—
549	C₂×C₄×C₆₇	—	4	1	no	—
550	C₂×C₄×C₆₇	—	4	1	no	—
551	C₂×C₄×C₆₇	—	4	1	no	—
552	C₂×C₄×C₆₇	—	4	1	no	—
553	C₂×C₄×C₆₇	—	4	1	no	—
554	C₂×C₄×C₆₇	—	4	2	no	—
555	C₂×C₄×C₆₇	—	4	2	no	—
556	C₂×C₄×C₆₇	—	4	2	no	—
557	C₂×C₄×C₆₇	—	4	2	no	—
558	C₂×C₄×C₆₇	—	4	2	no	—
559	C₂×C₄×C₆₇	—	8	1	no	—
560	C₂×C₄×C₆₇	—	8	1	no	—
561	C₂×C₄×C₆₇	—	8	1	no	—
562	C₂×C₄×C₆₇	—	8	1	no	—
563	C₂×C₄×C₆₇	—	8	1	no	—
564	C₂×C₄×C₆₇	—	8	1	no	—
565	C₂×C₄×C₆₇	—	8	1	no	—
566	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
578	C₈×C₆₇	—	2	2	no	—
579	C₈×C₆₇	—	2	2	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	1	no	—
588	C₂²×C₆₇	—	2	1	no	—
589	C₂²×C₆₇	—	2	1	no	—
590	C₂²×C₆₇	—	4	1	no	—
591	C₂²×C₆₇	—	4	1	no	—
592	C₂²×C₆₇	—	4	1	no	—
593	C₂²×C₆₇	—	4	1	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	—	8	2	no	—
600	C₂²×C₆₇	—	16	2	no	—
601	C₂²×C₆₇	#577	1	2	yes	—
602	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
603	C₄×C₆₇	—	2	1	no	—
604	C₄×C₆₇	—	2	1	no	—
605	C₄×C₆₇	—	2	1	no	—
606	C₄×C₆₇	—	2	1	no	—
607	C₄×C₆₇	—	2	1	no	—
608	C₄×C₆₇	—	2	1	no	—
609	C₄×C₆₇	—	2	1	no	—
610	C₄×C₆₇	—	2	1	no	—
611	C₄×C₆₇	—	2	1	no	—
612	C₄×C₆₇	—	2	1	no	—
613	C₄×C₆₇	—	2	1	no	—
614	C₄×C₆₇	—	4	2	no	—
615	C₄×C₆₇	—	4	1	no	—
616	C₄×C₆₇	—	4	1	no	—
617	C₄×C₆₇	—	4	2	no	—
618	C₄×C₆₇	—	4	2	no	—
619	C₄×C₆₇	—	4	2	no	—
620	C₄×C₆₇	—	4	1	no	—
621	C₄×C₆₇	—	4	1	no	—
622	C₄×C₆₇	—	4	1	no	—
623	C₄×C₆₇	#585	1	2	yes	—
624	#60982	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
625	C₂×C₆₇	—	2	2	no	—
626	C₂×C₆₇	—	4	1	no	—
627	C₂×C₆₇	—	4	1	no	—
628	C₂×C₆₇	—	8	1	no	—
629	C₂×C₆₇	—	8	1	no	—
630	C₂×C₆₇	—	8	1	no	—
631	C₂×C₆₇	#3449	1	1	yes	characteristic
632	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
633	C₂×C₆₇	#3586	1	1	yes	characteristic
634	#3494	C₂×C₆₇	1	1	yes	characteristic
635	C₂×#541	C₂×C₆₇	1	1	yes	characteristic, complemented
636	#3260	C₂×C₆₇	1	2	yes	complemented
637	#3258	C₂×C₆₇	1	2	yes	complemented
638	#3242	C₂×C₆₇	1	2	yes	complemented
639	#3234	C₂×C₆₇	1	1	yes	characteristic, complemented
640	#3232	C₂×C₆₇	1	1	yes	characteristic, complemented
641	#3222	C₂×C₆₇	1	2	yes	complemented
642	#3218	C₂×C₆₇	1	1	yes	characteristic, complemented
643	#3206	C₂×C₆₇	1	1	yes	characteristic, complemented
644	#3196	C₂×C₆₇	1	1	yes	characteristic, complemented
645	#3193	C₂×C₆₇	1	1	yes	characteristic, complemented
646	#3190	C₂×C₆₇	1	1	yes	characteristic, complemented
647	#3187	C₂×C₆₇	1	1	yes	characteristic, complemented
648	#3178	C₂×C₆₇	1	2	yes	complemented
649	#3174	C₂×C₆₇	1	2	yes	complemented
650	#3123	C₂×C₆₇	1	2	yes	complemented
651	#3120	C₂×C₆₇	1	2	yes	complemented
652	#3117	C₂×C₆₇	1	1	yes	characteristic, complemented
653	#3112	C₂×C₆₇	1	1	yes	characteristic, complemented
654	#3108	C₂×C₆₇	1	1	yes	characteristic, complemented
655	#3103	C₂×C₆₇	1	1	yes	characteristic, complemented
656	#2924	C₂×C₆₇	1	1	yes	characteristic, complemented
657	C₆₇	#60982	1	1	yes	characteristic, direct product factor, Sylow
658	#555	—	2	1	no	—
659	#553	—	2	1	no	—
660	#553	—	2	1	no	—
661	#551	—	2	1	no	—
662	#551	—	2	1	no	—
663	#547	—	2	1	no	—
664	#546	—	2	1	no	—
665	#546	—	2	1	no	—
666	#544	C₂²×C₆₇	1	1	yes	characteristic
667	#542	C₂²×C₆₇	1	1	yes	characteristic
668	#542	C₂²×C₆₇	1	1	yes	characteristic
669	#541	—	2	1	no	—
670	#541	—	2	1	no	—
671	#541	—	2	1	no	—
672	#541	—	2	1	no	—
673	#541	C₂²×C₆₇	1	2	yes	—
674	#541	C₂²×C₆₇	1	2	yes	—
675	#541	C₂²×C₆₇	1	2	yes	complemented
676	#541	C₂²×C₆₇	1	2	yes	complemented
677	#540	C₂²×C₆₇	1	1	yes	characteristic
678	#540	C₂²×C₆₇	1	1	yes	characteristic
679	#535	C₂²×C₆₇	1	1	yes	characteristic
680	#532	C₂²×C₆₇	1	1	yes	characteristic
681	#532	C₂²×C₆₇	1	1	yes	characteristic
682	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
683	#529	C₂²×C₆₇	1	1	yes	characteristic
684	#529	C₂²×C₆₇	1	1	yes	characteristic
685	C₂×#126	—	2	1	no	—
686	C₂×#126	—	2	1	no	—
687	C₂×#125	—	2	1	no	—
688	C₂×#125	—	2	1	no	—
689	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	#525	C₂²×C₆₇	1	1	yes	characteristic
691	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
692	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
693	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
694	#520	C₂²×C₆₇	1	1	yes	characteristic
695	#518	C₂²×C₆₇	1	1	yes	characteristic
696	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
697	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
698	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
699	#501	C₂²×C₆₇	1	2	yes	complemented
700	#499	C₂²×C₆₇	1	2	yes	complemented
701	#497	C₂²×C₆₇	1	2	yes	complemented
702	#492	C₂²×C₆₇	1	2	yes	complemented
703	#491	C₂²×C₆₇	1	2	yes	complemented
704	#490	C₂²×C₆₇	1	2	yes	complemented
705	#488	C₂²×C₆₇	1	2	yes	complemented
706	#487	C₂²×C₆₇	1	2	yes	complemented
707	#485	C₂²×C₆₇	1	2	yes	—
708	#485	C₂²×C₆₇	1	2	yes	—
709	#484	C₂²×C₆₇	1	2	yes	—
710	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	#483	C₂²×C₆₇	1	2	yes	—
712	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
713	#481	C₂²×C₆₇	1	1	yes	characteristic
714	#481	C₂²×C₆₇	1	1	yes	characteristic
715	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
716	#480	C₂²×C₆₇	1	1	yes	characteristic
717	#480	C₂²×C₆₇	1	1	yes	characteristic
718	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
719	#479	C₂²×C₆₇	1	2	yes	complemented
720	#479	C₂²×C₆₇	1	2	yes	complemented
721	#479	C₂²×C₆₇	1	2	yes	complemented
722	#478	C₂²×C₆₇	1	2	yes	complemented
723	#478	C₂²×C₆₇	1	2	yes	complemented
724	#478	C₂²×C₆₇	1	2	yes	complemented
725	#477	C₂²×C₆₇	1	2	yes	complemented
726	#475	C₂²×C₆₇	1	2	yes	complemented
727	#470	C₂²×C₆₇	1	2	yes	complemented
728	#468	C₂²×C₆₇	1	2	yes	—
729	#468	C₂²×C₆₇	1	2	yes	—
730	#468	C₂²×C₆₇	1	2	yes	complemented
731	#467	C₂²×C₆₇	1	2	yes	complemented
732	#465	C₂²×C₆₇	1	2	yes	—
733	#465	C₂²×C₆₇	1	2	yes	—
734	#465	C₂²×C₆₇	1	2	yes	complemented
735	#464	C₂²×C₆₇	1	2	yes	complemented
736	#464	C₂²×C₆₇	1	2	yes	complemented
737	#462	C₂²×C₆₇	1	2	yes	complemented
738	#461	C₂²×C₆₇	1	2	yes	complemented
739	#461	C₂²×C₆₇	1	2	yes	complemented
740	#461	C₂²×C₆₇	1	2	yes	complemented
741	#460	C₂²×C₆₇	1	2	yes	complemented
742	#460	C₂²×C₆₇	1	2	yes	complemented
743	#452	C₂²×C₆₇	1	2	yes	—
744	#452	C₂²×C₆₇	1	2	yes	—
745	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
746	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
747	#450	C₂²×C₆₇	1	2	yes	—
748	#450	C₂²×C₆₇	1	2	yes	—
749	#448	C₂²×C₆₇	1	1	yes	characteristic
750	#448	C₂²×C₆₇	1	1	yes	characteristic
751	#448	C₂²×C₆₇	1	1	yes	characteristic
752	#448	C₂²×C₆₇	1	1	yes	characteristic
753	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
754	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
755	#441	C₂²×C₆₇	1	2	yes	complemented
756	#440	C₂²×C₆₇	1	2	yes	complemented
757	#440	C₂²×C₆₇	1	2	yes	complemented
758	#440	C₂²×C₆₇	1	2	yes	complemented
759	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
760	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
761	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
762	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
763	#433	C₂²×C₆₇	1	2	yes	—
764	#433	C₂²×C₆₇	1	2	yes	—
765	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
766	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
767	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
768	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
769	#424	C₂²×C₆₇	1	2	yes	complemented
770	#407	C₂²×C₆₇	1	1	yes	characteristic
771	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
772	#405	C₂²×C₆₇	1	2	yes	complemented
773	C₂×#41	—	2	1	no	—
774	C₂×#41	—	2	1	no	—
775	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
776	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
777	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
778	C₂²×D₄	—	2	1	no	—
779	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
780	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
781	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
782	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
783	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
785	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
786	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
787	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
788	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
789	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
790	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
791	C₄⋊Q₈	—	2	1	no	—
792	C₄⋊Q₈	—	2	1	no	—
793	C₄⋊Q₈	—	2	1	no	—
794	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
795	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
796	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
797	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
798	#127	C₂³×C₆₇	1	1	yes	characteristic
799	#127	C₂³×C₆₇	1	1	yes	characteristic
800	#126	—	2	1	no	—
801	#126	—	2	1	no	—
802	#126	—	2	2	no	—
803	#126	—	2	2	no	—
804	#126	—	2	2	no	—
805	#126	—	2	2	no	—
806	#126	—	2	2	no	—
807	#126	—	2	2	no	—
808	#126	—	2	2	no	—
809	#126	—	2	2	no	—
810	#126	—	2	1	no	—
811	#126	—	2	1	no	—
812	#125	—	2	2	no	—
813	#125	—	2	2	no	—
814	#125	—	2	2	no	—
815	#125	—	2	2	no	—
816	#125	—	2	2	no	—
817	#125	—	2	2	no	—
818	#125	—	2	2	no	—
819	#125	—	2	2	no	—
820	#125	—	2	1	no	—
821	#125	—	2	1	no	—
822	#125	—	2	1	no	—
823	#125	C₂³×C₆₇	1	2	yes	—
824	#125	C₂³×C₆₇	1	2	yes	—
825	#125	C₂³×C₆₇	1	1	yes	characteristic
826	#125	C₂³×C₆₇	1	1	yes	characteristic
827	#124	—	2	1	no	—
828	#124	—	2	1	no	—
829	#124	—	2	1	no	—
830	#124	—	2	1	no	—
831	#124	C₂³×C₆₇	1	1	yes	characteristic
832	#124	C₂³×C₆₇	1	1	yes	characteristic
833	#123	—	2	1	no	—
834	#123	—	2	1	no	—
835	#123	—	2	1	no	—
836	#123	—	2	1	no	—
837	#123	—	2	1	no	—
838	#123	—	2	1	no	—
839	#123	—	2	1	no	—
840	#123	—	2	1	no	—
841	#123	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	—	2	1	no	—
847	C₂²⋊Q₈	—	2	1	no	—
848	C₂²⋊Q₈	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
851	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
852	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
853	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
854	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
855	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
856	#121	—	2	1	no	—
857	#121	—	2	1	no	—
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	1	no	—
862	#121	—	2	1	no	—
863	#121	—	2	1	no	—
864	#121	—	2	1	no	—
865	#121	—	2	1	no	—
866	#121	C₂³×C₆₇	1	1	yes	characteristic
867	#121	C₂³×C₆₇	1	1	yes	characteristic
868	#121	C₂³×C₆₇	1	1	yes	characteristic
869	#121	C₂³×C₆₇	1	1	yes	characteristic
870	#121	C₂³×C₆₇	1	1	yes	characteristic
871	#121	C₂³×C₆₇	1	1	yes	characteristic
872	#120	—	2	1	no	—
873	#120	—	2	1	no	—
874	#120	—	2	1	no	—
875	C₄×Q₈	—	2	1	no	—
876	C₄×Q₈	—	2	1	no	—
877	C₄×Q₈	—	2	1	no	—
878	C₄×Q₈	—	2	1	no	—
879	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
880	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
881	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
882	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
883	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
884	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	1	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
896	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
897	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
898	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
899	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
900	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
901	#117	—	2	1	no	—
902	#117	—	2	1	no	—
903	#117	—	2	1	no	—
904	#117	D₄×C₆₇	1	1	yes	characteristic
905	#117	D₄×C₆₇	1	1	yes	characteristic
906	#117	D₄×C₆₇	1	1	yes	characteristic
907	#117	D₄×C₆₇	1	1	yes	characteristic
908	#117	C₂³×C₆₇	1	1	yes	characteristic
909	#117	C₂³×C₆₇	1	1	yes	characteristic
910	#117	C₂³×C₆₇	1	1	yes	characteristic
911	#117	C₂³×C₆₇	1	1	yes	characteristic
912	#117	C₂³×C₆₇	1	1	yes	characteristic
913	C₂×C₄⋊C₄	—	2	1	no	—
914	C₂×C₄⋊C₄	—	2	1	no	—
915	C₂×C₄⋊C₄	—	2	1	no	—
916	C₂×C₄⋊C₄	—	2	1	no	—
917	C₂×C₄⋊C₄	—	2	1	no	—
918	C₂×C₄⋊C₄	—	2	1	no	—
919	C₂×C₄⋊C₄	—	2	1	no	—
920	C₂×C₄⋊C₄	—	2	1	no	—
921	C₂×C₄⋊C₄	—	2	1	no	—
922	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
923	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
924	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
925	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
926	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
927	C₂×C₂²⋊C₄	—	2	1	no	—
928	C₂×C₂²⋊C₄	—	2	1	no	—
929	C₂×C₂²⋊C₄	—	2	1	no	—
930	C₂×C₂²⋊C₄	—	2	1	no	—
931	C₂×C₂²⋊C₄	—	2	1	no	—
932	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
933	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
934	C₂×C₄²	—	2	1	no	—
935	C₂×C₄²	—	2	1	no	—
936	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
937	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
938	#107	C₂³×C₆₇	1	2	yes	—
939	#107	C₂³×C₆₇	1	2	yes	—
940	#107	C₂³×C₆₇	1	2	yes	—
941	#107	C₂³×C₆₇	1	2	yes	—
942	#106	C₂³×C₆₇	1	2	yes	—
943	#106	C₂³×C₆₇	1	2	yes	—
944	#106	C₂³×C₆₇	1	2	yes	—
945	#106	C₂³×C₆₇	1	2	yes	—
946	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
947	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
948	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
949	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
950	#103	C₂³×C₆₇	1	2	yes	—
951	#103	C₂³×C₆₇	1	2	yes	—
952	#103	C₂³×C₆₇	1	2	yes	—
953	#103	C₂³×C₆₇	1	2	yes	—
954	#103	C₂³×C₆₇	1	2	yes	—
955	#103	C₂³×C₆₇	1	2	yes	—
956	#103	C₂³×C₆₇	1	2	yes	—
957	#103	C₂³×C₆₇	1	2	yes	—
958	#103	C₂³×C₆₇	1	2	yes	—
959	#103	C₂³×C₆₇	1	2	yes	—
960	#102	C₂³×C₆₇	1	2	yes	—
961	#102	C₂³×C₆₇	1	2	yes	—
962	#102	C₂³×C₆₇	1	2	yes	—
963	#102	C₂³×C₆₇	1	2	yes	—
964	#102	C₂³×C₆₇	1	2	yes	—
965	#102	C₂³×C₆₇	1	2	yes	—
966	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
967	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
968	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
969	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
970	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
971	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
972	#97	C₂³×C₆₇	1	2	yes	—
973	#97	C₂³×C₆₇	1	2	yes	—
974	C₄×C₈	C₂³×C₆₇	1	2	yes	—
975	C₄×C₈	C₂³×C₆₇	1	2	yes	—
976	C₂⁴	—	2	1	no	—
977	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
978	#41	—	4	2	no	—
979	#41	—	8	2	no	—
980	#41	—	8	2	no	—
981	C₂×Q₈	—	2	1	no	—
982	C₂×Q₈	—	2	1	no	—
983	C₂×Q₈	—	2	1	no	—
984	C₂×Q₈	—	2	1	no	—
985	C₂×Q₈	—	4	2	no	—
986	C₂×Q₈	—	4	2	no	—
987	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
988	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
989	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	4	2	no	—
1003	C₂×D₄	—	8	2	no	—
1004	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1005	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1006	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	2	1	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	1	no	—
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	4	2	no	—
1020	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1021	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1022	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1023	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1024	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1025	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1026	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1027	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1028	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1029	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1030	Q₁₆	—	4	2	no	—
1031	Q₁₆	—	4	2	no	—
1032	SD₁₆	—	4	2	no	—
1033	SD₁₆	—	4	2	no	—
1034	SD₁₆	—	4	2	no	—
1035	SD₁₆	—	4	2	no	—
1036	SD₁₆	—	4	2	no	—
1037	SD₁₆	—	4	2	no	—
1038	M₁₆	—	4	2	no	—
1039	C₂×C₈	—	4	2	no	—
1040	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1041	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1042	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1043	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1074	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1075	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1076	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1077	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1078	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1079	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1080	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1081	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1082	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1083	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1084	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1085	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1086	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1111	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1112	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1113	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1114	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1115	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1116	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1117	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1118	C₄²	—	2	2	no	—
1119	C₄²	—	2	2	no	—
1120	C₄²	—	2	2	no	—
1121	C₄²	—	2	2	no	—
1122	C₄²	—	2	1	no	—
1123	C₄²	—	2	1	no	—
1124	C₄²	—	2	1	no	—
1125	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1126	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1127	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1128	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1129	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1130	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1131	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1132	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1133	C₂³	—	2	2	no	—
1134	C₂³	—	2	1	no	—
1135	C₂³	—	2	1	no	—
1136	C₂³	—	2	1	no	—
1137	C₂³	—	4	1	no	—
1138	C₂³	—	4	1	no	—
1139	C₂³	—	4	2	no	—
1140	C₂³	—	8	1	no	—
1141	C₂³	—	8	1	no	—
1142	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1143	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1144	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1145	Q₈	—	2	2	no	—
1146	Q₈	—	2	2	no	—
1147	Q₈	—	2	2	no	—
1148	Q₈	—	2	2	no	—
1149	Q₈	—	2	2	no	—
1150	Q₈	—	4	2	no	—
1151	Q₈	—	4	2	no	—
1152	Q₈	—	8	1	no	—
1153	Q₈	—	8	1	no	—
1154	D₄	—	2	2	no	—
1155	D₄	—	2	2	no	—
1156	D₄	—	2	2	no	—
1157	D₄	—	4	2	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	8	1	no	—
1163	D₄	—	8	1	no	—
1164	D₄	—	8	1	no	—
1165	D₄	—	8	1	no	—
1166	D₄	—	8	1	no	—
1167	D₄	—	8	1	no	—
1168	D₄	—	8	1	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	2	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	2	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	4	1	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	4	2	no	—
1191	C₂×C₄	—	4	2	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	8	1	no	—
1194	C₂×C₄	—	8	1	no	—
1195	C₂×C₄	—	8	1	no	—
1196	C₂×C₄	—	8	1	no	—
1197	C₂×C₄	—	8	1	no	—
1198	C₂×C₄	—	8	1	no	—
1199	C₂×C₄	—	8	1	no	—
1200	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1201	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1202	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1203	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
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	C₂²×D₄×C₆₇	1	1	yes	characteristic
1208	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1209	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1210	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1211	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1212	C₈	—	2	2	no	—
1213	C₈	—	2	2	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	1	no	—
1222	C₂²	—	2	1	no	—
1223	C₂²	—	2	1	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	1	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	—	8	2	no	—
1234	C₂²	—	16	2	no	—
1235	C₂²	#577×C₆₇	1	2	yes	—
1236	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1237	C₄	—	2	1	no	—
1238	C₄	—	2	1	no	—
1239	C₄	—	2	1	no	—
1240	C₄	—	2	1	no	—
1241	C₄	—	2	1	no	—
1242	C₄	—	2	1	no	—
1243	C₄	—	2	1	no	—
1244	C₄	—	2	1	no	—
1245	C₄	—	2	1	no	—
1246	C₄	—	2	1	no	—
1247	C₄	—	2	1	no	—
1248	C₄	—	4	2	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	2	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	2	no	—
1256	C₄	—	4	2	no	—
1257	C₄	#585×C₆₇	1	2	yes	—
1258	C₂	—	2	2	no	—
1259	C₂	—	4	1	no	—
1260	C₂	—	4	1	no	—
1261	C₂	—	8	1	no	—
1262	C₂	—	8	1	no	—
1263	C₂	—	8	1	no	—
1264	C₂	C₆₇×#3449	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
prime radical	C₆₇×#3494	C₂
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×#3260	C₂	semidirect
4. C₆₇×#3258	C₂	semidirect
5. C₆₇×#3242	C₂	semidirect
6. C₆₇×#3234	C₂	semidirect
7. C₆₇×#3232	C₂	semidirect
8. C₆₇×#3222	C₂	semidirect
9. C₆₇×#3218	C₂	semidirect
10. C₆₇×#3206	C₂	semidirect
11. C₆₇×#3196	C₂	semidirect
12. C₆₇×#3193	C₂	semidirect
13. C₆₇×#3190	C₂	semidirect
14. C₆₇×#3187	C₂	semidirect
15. C₆₇×#3178	C₂	semidirect
16. C₆₇×#3174	C₂	semidirect
17. C₆₇×#3123	C₂	semidirect
18. C₆₇×#3120	C₂	semidirect
19. C₆₇×#3117	C₂	semidirect
20. C₆₇×#3112	C₂	semidirect
21. C₆₇×#3108	C₂	semidirect
22. C₆₇×#3103	C₂	semidirect
23. C₆₇×#2924	C₂	semidirect
41. #541×C₆₇	C₂²	semidirect
42. #541×C₆₇	C₂²	semidirect
48. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
55. C₂×#125×C₆₇	C₂²	semidirect
62. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
63. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
65. #501×C₆₇	C₂²	semidirect
66. #499×C₆₇	C₂²	semidirect
67. #497×C₆₇	C₂²	semidirect
68. #492×C₆₇	C₂²	semidirect
69. #491×C₆₇	C₂²	semidirect
70. #490×C₆₇	C₂²	semidirect
71. #488×C₆₇	C₂²	semidirect
72. #487×C₆₇	C₂²	semidirect
76. #484×C₆₇	C₂²	semidirect
78. #483×C₆₇	C₂²	semidirect
81. #481×C₆₇	C₂²	semidirect
84. #480×C₆₇	C₂²	semidirect
85. #479×C₆₇	C₂²	semidirect
86. #479×C₆₇	C₂²	semidirect
87. #479×C₆₇	C₂²	semidirect
88. #478×C₆₇	C₂²	semidirect
89. #478×C₆₇	C₂²	semidirect
90. #478×C₆₇	C₂²	semidirect
91. #477×C₆₇	C₂²	semidirect
92. #475×C₆₇	C₂²	semidirect
93. #470×C₆₇	C₂²	semidirect
96. #468×C₆₇	C₂²	semidirect
97. #467×C₆₇	C₂²	semidirect
100. #465×C₆₇	C₂²	semidirect
101. #464×C₆₇	C₂²	semidirect
102. #464×C₆₇	C₂²	semidirect
103. #462×C₆₇	C₂²	semidirect
104. #461×C₆₇	C₂²	semidirect
105. #461×C₆₇	C₂²	semidirect
106. #461×C₆₇	C₂²	semidirect
107. #460×C₆₇	C₂²	semidirect
108. #460×C₆₇	C₂²	semidirect
111. #451×C₆₇	C₂²	semidirect
112. #451×C₆₇	C₂²	semidirect
119. #448×C₆₇	C₂²	semidirect
120. #448×C₆₇	C₂²	semidirect
121. #441×C₆₇	C₂²	semidirect
122. #440×C₆₇	C₂²	semidirect
123. #440×C₆₇	C₂²	semidirect
124. #440×C₆₇	C₂²	semidirect
125. C₄×Q₁₆×C₆₇	C₂²	semidirect
126. C₄×SD₁₆×C₆₇	C₂²	semidirect
127. C₄×SD₁₆×C₆₇	C₂²	semidirect
128. C₄×SD₁₆×C₆₇	C₂²	semidirect
131. #432×C₆₇	C₂²	semidirect
132. #432×C₆₇	C₂²	semidirect
133. #431×C₆₇	C₂²	semidirect
134. #431×C₆₇	C₂²	semidirect
135. #424×C₆₇	C₂²	semidirect
138. #405×C₆₇	C₂²	semidirect
624. #60982	C₆₇	direct (N × H)
635. C₂×#541	C₂×C₆₇	semidirect
636. #3260	C₂×C₆₇	semidirect
637. #3258	C₂×C₆₇	semidirect
638. #3242	C₂×C₆₇	semidirect
639. #3234	C₂×C₆₇	semidirect
640. #3232	C₂×C₆₇	semidirect
641. #3222	C₂×C₆₇	semidirect
642. #3218	C₂×C₆₇	semidirect
643. #3206	C₂×C₆₇	semidirect
644. #3196	C₂×C₆₇	semidirect
645. #3193	C₂×C₆₇	semidirect
646. #3190	C₂×C₆₇	semidirect
647. #3187	C₂×C₆₇	semidirect
648. #3178	C₂×C₆₇	semidirect
649. #3174	C₂×C₆₇	semidirect
650. #3123	C₂×C₆₇	semidirect
651. #3120	C₂×C₆₇	semidirect
652. #3117	C₂×C₆₇	semidirect
653. #3112	C₂×C₆₇	semidirect
654. #3108	C₂×C₆₇	semidirect
655. #3103	C₂×C₆₇	semidirect
656. #2924	C₂×C₆₇	semidirect
657. C₆₇	#60982	direct (N × H)
675. #541	C₂²×C₆₇	semidirect
676. #541	C₂²×C₆₇	semidirect
682. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
689. C₂×#125	C₂²×C₆₇	semidirect
696. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
697. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
699. #501	C₂²×C₆₇	semidirect
700. #499	C₂²×C₆₇	semidirect
701. #497	C₂²×C₆₇	semidirect
702. #492	C₂²×C₆₇	semidirect
703. #491	C₂²×C₆₇	semidirect
704. #490	C₂²×C₆₇	semidirect
705. #488	C₂²×C₆₇	semidirect
706. #487	C₂²×C₆₇	semidirect
710. #484	C₂²×C₆₇	semidirect
712. #483	C₂²×C₆₇	semidirect
715. #481	C₂²×C₆₇	semidirect
718. #480	C₂²×C₆₇	semidirect
719. #479	C₂²×C₆₇	semidirect
720. #479	C₂²×C₆₇	semidirect
721. #479	C₂²×C₆₇	semidirect
722. #478	C₂²×C₆₇	semidirect
723. #478	C₂²×C₆₇	semidirect
724. #478	C₂²×C₆₇	semidirect
725. #477	C₂²×C₆₇	semidirect
726. #475	C₂²×C₆₇	semidirect
727. #470	C₂²×C₆₇	semidirect
730. #468	C₂²×C₆₇	semidirect
731. #467	C₂²×C₆₇	semidirect
734. #465	C₂²×C₆₇	semidirect
735. #464	C₂²×C₆₇	semidirect
736. #464	C₂²×C₆₇	semidirect
737. #462	C₂²×C₆₇	semidirect
738. #461	C₂²×C₆₇	semidirect
739. #461	C₂²×C₆₇	semidirect
740. #461	C₂²×C₆₇	semidirect
741. #460	C₂²×C₆₇	semidirect
742. #460	C₂²×C₆₇	semidirect
745. #451	C₂²×C₆₇	semidirect
746. #451	C₂²×C₆₇	semidirect
753. #448	C₂²×C₆₇	semidirect
754. #448	C₂²×C₆₇	semidirect
755. #441	C₂²×C₆₇	semidirect
756. #440	C₂²×C₆₇	semidirect
757. #440	C₂²×C₆₇	semidirect
758. #440	C₂²×C₆₇	semidirect
759. C₄×Q₁₆	C₂²×C₆₇	semidirect
760. C₄×SD₁₆	C₂²×C₆₇	semidirect
761. C₄×SD₁₆	C₂²×C₆₇	semidirect
762. C₄×SD₁₆	C₂²×C₆₇	semidirect
765. #432	C₂²×C₆₇	semidirect
766. #432	C₂²×C₆₇	semidirect
767. #431	C₂²×C₆₇	semidirect
768. #431	C₂²×C₆₇	semidirect
769. #424	C₂²×C₆₇	semidirect
772. #405	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×#3494	2
C₂×#541×C₆₇	2
C₆₇×#3260	2
C₆₇×#3258	2
C₆₇×#3242	2
C₆₇×#3234	2
C₆₇×#3232	2
C₆₇×#3222	2
C₆₇×#3218	2
C₆₇×#3206	2
C₆₇×#3196	2
C₆₇×#3193	2
C₆₇×#3190	2
C₆₇×#3187	2
C₆₇×#3178	2
C₆₇×#3174	2
C₆₇×#3123	2
C₆₇×#3120	2
C₆₇×#3117	2
C₆₇×#3112	2
C₆₇×#3108	2
C₆₇×#3103	2
C₆₇×#2924	2
#60982	67

Subgroups — C67×#60982 #30740233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60982 #30740233