Subgroups — C₆₇×#61589 #30740840

Order 17152.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3332	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3328	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3327	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3324	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3323	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3278	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3277	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3276	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3276	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3275	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3197	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3196	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3007	C₂	1	2	yes	maximal, complemented
22	C₆₇×#3005	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	2	yes	—
25	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
26	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
27	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
28	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
29	#556×C₆₇	C₂²	1	1	yes	characteristic
30	#554×C₆₇	—	2	1	no	—
31	#552×C₆₇	C₂²	1	2	yes	complemented
32	#551×C₆₇	—	2	2	no	—
33	#550×C₆₇	C₂²	1	1	yes	characteristic
34	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#548×C₆₇	C₂²	1	2	yes	—
37	#548×C₆₇	C₂²	1	2	yes	complemented
38	#547×C₆₇	—	2	1	no	—
39	#547×C₆₇	C₂²	1	1	yes	characteristic
40	#547×C₆₇	C₂²	1	1	yes	characteristic
41	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#546×C₆₇	—	2	1	no	—
43	#546×C₆₇	—	2	2	no	—
44	#546×C₆₇	C₂²	1	2	yes	—
45	D₄²×C₆₇	—	2	1	no	—
46	D₄²×C₆₇	C₂²	1	1	yes	characteristic
47	#542×C₆₇	—	2	1	no	—
48	#539×C₆₇	—	2	2	no	—
49	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#532×C₆₇	—	2	1	no	—
51	#532×C₆₇	C₂²	1	1	yes	characteristic
52	#529×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#525×C₆₇	—	2	2	no	—
54	#525×C₆₇	C₂²	1	2	yes	—
55	#525×C₆₇	C₂²	1	2	yes	complemented
56	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
57	#520×C₆₇	—	2	1	no	—
58	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₆₇	—	2	1	no	—
60	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
61	#495×C₆₇	C₂²	1	2	yes	complemented
62	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#488×C₆₇	C₂²	1	2	yes	complemented
65	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#485×C₆₇	C₂²	1	2	yes	complemented
68	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#485×C₆₇	C₂²	1	2	yes	complemented
70	#484×C₆₇	C₂²	1	2	yes	complemented
71	#482×C₆₇	C₂²	1	2	yes	complemented
72	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#481×C₆₇	C₂²	1	2	yes	complemented
74	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#478×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#470×C₆₇	C₂²	1	2	yes	complemented
79	#470×C₆₇	C₂²	1	2	yes	complemented
80	#470×C₆₇	C₂²	1	2	yes	complemented
81	#469×C₆₇	C₂²	1	2	yes	complemented
82	#468×C₆₇	C₂²	1	2	yes	complemented
83	#468×C₆₇	C₂²	1	2	yes	complemented
84	#468×C₆₇	C₂²	1	2	yes	complemented
85	#468×C₆₇	C₂²	1	2	yes	complemented
86	#464×C₆₇	C₂²	1	2	yes	complemented
87	#464×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#464×C₆₇	C₂²	1	2	yes	complemented
89	#463×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#452×C₆₇	C₂²	1	1	yes	characteristic
97	#452×C₆₇	C₂²	1	2	yes	—
98	#452×C₆₇	C₂²	1	2	yes	complemented
99	#452×C₆₇	C₂²	1	2	yes	complemented
100	#452×C₆₇	C₂²	1	2	yes	complemented
101	#452×C₆₇	C₂²	1	2	yes	complemented
102	#452×C₆₇	C₂²	1	2	yes	complemented
103	#452×C₆₇	C₂²	1	2	yes	complemented
104	#451×C₆₇	C₂²	1	2	yes	complemented
105	#451×C₆₇	C₂²	1	2	yes	complemented
106	#451×C₆₇	C₂²	1	2	yes	complemented
107	#450×C₆₇	C₂²	1	2	yes	complemented
108	#450×C₆₇	C₂²	1	2	yes	complemented
109	#449×C₆₇	C₂²	1	1	yes	characteristic
110	#449×C₆₇	C₂²	1	2	yes	complemented
111	#449×C₆₇	C₂²	1	2	yes	complemented
112	#449×C₆₇	C₂²	1	2	yes	complemented
113	#449×C₆₇	C₂²	1	2	yes	complemented
114	#448×C₆₇	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
116	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#436×C₆₇	C₂²	1	1	yes	characteristic
122	#436×C₆₇	C₂²	1	1	yes	characteristic
123	#436×C₆₇	C₂²	1	2	yes	complemented
124	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#436×C₆₇	C₂²	1	2	yes	complemented
126	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#419×C₆₇	C₂²	1	2	yes	complemented
130	#418×C₆₇	C₂²	1	2	yes	complemented
131	#417×C₆₇	C₂²	1	2	yes	complemented
132	#417×C₆₇	C₂²	1	2	yes	complemented
133	#407×C₆₇	C₂²	1	2	yes	complemented
134	#407×C₆₇	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₇	—	2	1	no	—
136	C₂×#41×C₆₇	—	2	2	no	—
137	C₂×#41×C₆₇	—	2	2	no	—
138	C₂×#41×C₆₇	—	4	4	no	—
139	C₂×#41×C₆₇	—	4	4	no	—
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	2	yes	—
142	C₂×#41×C₆₇	C₂³	1	2	yes	—
143	C₂×#41×C₆₇	C₂³	1	2	yes	—
144	C₂×#41×C₆₇	C₂³	1	2	yes	—
145	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
146	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
147	C₂²×D₄×C₆₇	—	2	2	no	—
148	C₂²×D₄×C₆₇	—	2	1	no	—
149	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
150	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
151	C₂³×C₄×C₆₇	—	2	2	no	—
152	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
153	#137×C₆₇	—	4	4	no	—
154	#137×C₆₇	—	4	4	no	—
155	#137×C₆₇	—	4	4	no	—
156	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
157	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
169	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×D₈×C₆₇	C₂³	1	2	yes	—
171	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
172	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
173	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
174	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
175	C₄⋊Q₈×C₆₇	—	2	1	no	—
176	C₄⋊Q₈×C₆₇	—	2	1	no	—
177	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
178	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
180	#127×C₆₇	—	2	1	no	—
181	#127×C₆₇	C₂³	1	1	yes	characteristic
182	#126×C₆₇	—	2	2	no	—
183	#126×C₆₇	—	2	2	no	—
184	#126×C₆₇	—	2	1	no	—
185	#125×C₆₇	—	2	2	no	—
186	#125×C₆₇	—	2	1	no	—
187	#125×C₆₇	C₂³	1	1	yes	characteristic
188	#124×C₆₇	—	2	1	no	—
189	#124×C₆₇	—	2	2	no	—
190	#124×C₆₇	—	2	2	no	—
191	#124×C₆₇	C₂³	1	1	yes	characteristic
192	#124×C₆₇	C₂³	1	2	yes	—
193	#123×C₆₇	—	2	2	no	—
194	#123×C₆₇	—	2	2	no	—
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	C₂²⋊Q₈×C₆₇	—	2	2	no	—
202	C₂²⋊Q₈×C₆₇	—	2	2	no	—
203	C₂²⋊Q₈×C₆₇	—	2	1	no	—
204	C₂²⋊Q₈×C₆₇	—	2	2	no	—
205	C₂²⋊Q₈×C₆₇	—	2	2	no	—
206	C₂²⋊Q₈×C₆₇	—	2	1	no	—
207	C₂²⋊Q₈×C₆₇	—	2	2	no	—
208	C₂²⋊Q₈×C₆₇	—	2	2	no	—
209	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
215	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
216	#121×C₆₇	—	2	2	no	—
217	#121×C₆₇	—	2	1	no	—
218	#121×C₆₇	—	2	2	no	—
219	#121×C₆₇	—	2	1	no	—
220	#121×C₆₇	—	2	1	no	—
221	#121×C₆₇	—	2	1	no	—
222	#121×C₆₇	—	2	1	no	—
223	#121×C₆₇	—	2	2	no	—
224	#121×C₆₇	—	2	2	no	—
225	#121×C₆₇	C₂³	1	2	yes	—
226	#121×C₆₇	C₂³	1	1	yes	characteristic
227	#121×C₆₇	C₂³	1	2	yes	—
228	#121×C₆₇	C₂³	1	2	yes	—
229	#120×C₆₇	—	2	2	no	—
230	#120×C₆₇	—	2	2	no	—
231	#120×C₆₇	—	2	2	no	—
232	#120×C₆₇	—	2	2	no	—
233	C₄×Q₈×C₆₇	—	2	1	no	—
234	C₄×Q₈×C₆₇	—	2	1	no	—
235	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
238	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₆₇	—	2	1	no	—
240	C₄×D₄×C₆₇	—	2	1	no	—
241	C₄×D₄×C₆₇	—	2	2	no	—
242	C₄×D₄×C₆₇	—	2	1	no	—
243	C₄×D₄×C₆₇	—	2	1	no	—
244	C₄×D₄×C₆₇	—	2	2	no	—
245	C₄×D₄×C₆₇	—	2	2	no	—
246	C₄×D₄×C₆₇	—	2	2	no	—
247	C₄×D₄×C₆₇	—	2	1	no	—
248	C₄×D₄×C₆₇	—	2	1	no	—
249	C₄×D₄×C₆₇	—	2	2	no	—
250	C₄×D₄×C₆₇	—	2	2	no	—
251	C₄×D₄×C₆₇	—	2	1	no	—
252	C₄×D₄×C₆₇	—	2	1	no	—
253	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
254	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
255	C₄×D₄×C₆₇	D₄	1	2	yes	—
256	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₆₇	C₂³	1	2	yes	—
261	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
262	#117×C₆₇	—	2	1	no	—
263	#117×C₆₇	—	2	2	no	—
264	#117×C₆₇	—	2	1	no	—
265	#117×C₆₇	—	2	1	no	—
266	#117×C₆₇	C₂³	1	1	yes	characteristic
267	#117×C₆₇	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
269	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
273	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
276	C₂×C₄²×C₆₇	—	2	1	no	—
277	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
278	#107×C₆₇	C₂³	1	2	yes	—
279	#107×C₆₇	C₂³	1	1	yes	characteristic
280	#107×C₆₇	C₂³	1	1	yes	characteristic
281	#106×C₆₇	C₂³	1	2	yes	—
282	#106×C₆₇	C₂³	1	1	yes	characteristic
283	#106×C₆₇	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
288	#103×C₆₇	C₂³	1	1	yes	characteristic
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	1	yes	characteristic
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	1	yes	characteristic
296	#103×C₆₇	C₂³	1	1	yes	characteristic
297	#103×C₆₇	C₂³	1	2	yes	—
298	#103×C₆₇	C₂³	1	2	yes	—
299	#102×C₆₇	C₂³	1	1	yes	characteristic
300	#102×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	1	yes	characteristic
305	#102×C₆₇	C₂³	1	2	yes	—
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₆₇	C₂³	1	2	yes	—
318	C₂⁴×C₆₇	—	2	2	no	—
319	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
320	#41×C₆₇	—	2	2	no	—
321	#41×C₆₇	—	2	2	no	—
322	#41×C₆₇	—	2	4	no	—
323	#41×C₆₇	—	2	4	no	—
324	#41×C₆₇	—	4	2	no	—
325	#41×C₆₇	—	4	2	no	—
326	#41×C₆₇	—	4	2	no	—
327	#41×C₆₇	—	4	2	no	—
328	#41×C₆₇	—	4	8	no	—
329	#41×C₆₇	—	4	2	no	—
330	#41×C₆₇	—	4	2	no	—
331	#41×C₆₇	—	4	4	no	—
332	#41×C₆₇	—	4	8	no	—
333	C₂×Q₈×C₆₇	—	2	1	no	—
334	C₂×Q₈×C₆₇	—	2	2	no	—
335	C₂×Q₈×C₆₇	—	2	2	no	—
336	C₂×Q₈×C₆₇	—	2	4	no	—
337	C₂×Q₈×C₆₇	—	4	2	no	—
338	C₂×Q₈×C₆₇	—	4	2	no	—
339	C₂×Q₈×C₆₇	—	4	2	no	—
340	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
341	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
342	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
343	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₆₇	—	2	1	no	—
345	C₂×D₄×C₆₇	—	2	4	no	—
346	C₂×D₄×C₆₇	—	2	1	no	—
347	C₂×D₄×C₆₇	—	2	2	no	—
348	C₂×D₄×C₆₇	—	2	2	no	—
349	C₂×D₄×C₆₇	—	2	2	no	—
350	C₂×D₄×C₆₇	—	2	2	no	—
351	C₂×D₄×C₆₇	—	2	2	no	—
352	C₂×D₄×C₆₇	—	2	2	no	—
353	C₂×D₄×C₆₇	—	2	2	no	—
354	C₂×D₄×C₆₇	—	2	1	no	—
355	C₂×D₄×C₆₇	—	2	2	no	—
356	C₂×D₄×C₆₇	—	2	1	no	—
357	C₂×D₄×C₆₇	—	4	2	no	—
358	C₂×D₄×C₆₇	—	4	2	no	—
359	C₂×D₄×C₆₇	—	4	4	no	—
360	C₂×D₄×C₆₇	—	4	8	no	—
361	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
362	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
364	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
365	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
366	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₆₇	—	2	1	no	—
368	C₂²×C₄×C₆₇	—	2	2	no	—
369	C₂²×C₄×C₆₇	—	2	2	no	—
370	C₂²×C₄×C₆₇	—	2	2	no	—
371	C₂²×C₄×C₆₇	—	2	1	no	—
372	C₂²×C₄×C₆₇	—	2	2	no	—
373	C₂²×C₄×C₆₇	—	2	1	no	—
374	C₂²×C₄×C₆₇	—	2	2	no	—
375	C₂²×C₄×C₆₇	—	2	2	no	—
376	C₂²×C₄×C₆₇	—	2	1	no	—
377	C₂²×C₄×C₆₇	—	2	2	no	—
378	C₂²×C₄×C₆₇	—	4	2	no	—
379	C₂²×C₄×C₆₇	—	4	2	no	—
380	C₂²×C₄×C₆₇	—	4	8	no	—
381	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
384	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
385	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
386	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
388	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
389	Q₁₆×C₆₇	—	2	2	no	—
390	Q₁₆×C₆₇	—	2	4	no	—
391	Q₁₆×C₆₇	—	4	2	no	—
392	Q₁₆×C₆₇	—	4	2	no	—
393	Q₁₆×C₆₇	—	4	2	no	—
394	SD₁₆×C₆₇	—	2	2	no	—
395	SD₁₆×C₆₇	—	2	4	no	—
396	SD₁₆×C₆₇	—	2	2	no	—
397	SD₁₆×C₆₇	—	4	2	no	—
398	SD₁₆×C₆₇	—	4	2	no	—
399	SD₁₆×C₆₇	—	4	2	no	—
400	SD₁₆×C₆₇	—	4	2	no	—
401	D₈×C₆₇	—	2	2	no	—
402	D₈×C₆₇	—	4	2	no	—
403	M₁₆×C₆₇	—	4	2	no	—
404	M₁₆×C₆₇	—	4	2	no	—
405	M₁₆×C₆₇	—	4	2	no	—
406	M₁₆×C₆₇	—	4	2	no	—
407	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
411	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
412	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₆₇	—	2	1	no	—
414	C₄⋊C₄×C₆₇	—	2	2	no	—
415	C₄⋊C₄×C₆₇	—	2	1	no	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	—	2	1	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	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	2	no	—
428	C₄⋊C₄×C₆₇	—	2	2	no	—
429	C₄⋊C₄×C₆₇	—	2	1	no	—
430	C₄⋊C₄×C₆₇	—	2	2	no	—
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
433	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
435	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
437	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄×C₆₇	—	2	1	no	—
441	C₂²⋊C₄×C₆₇	—	2	2	no	—
442	C₂²⋊C₄×C₆₇	—	2	2	no	—
443	C₂²⋊C₄×C₆₇	—	2	2	no	—
444	C₂²⋊C₄×C₆₇	—	2	2	no	—
445	C₂²⋊C₄×C₆₇	—	2	2	no	—
446	C₂²⋊C₄×C₆₇	—	2	1	no	—
447	C₂²⋊C₄×C₆₇	—	2	2	no	—
448	C₂²⋊C₄×C₆₇	—	2	2	no	—
449	C₂²⋊C₄×C₆₇	—	2	2	no	—
450	C₂²⋊C₄×C₆₇	—	2	2	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	1	no	—
455	C₂²⋊C₄×C₆₇	—	2	2	no	—
456	C₂²⋊C₄×C₆₇	—	2	2	no	—
457	C₂²⋊C₄×C₆₇	—	2	1	no	—
458	C₂²⋊C₄×C₆₇	—	2	2	no	—
459	C₂²⋊C₄×C₆₇	—	2	1	no	—
460	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
464	C₄²×C₆₇	—	2	1	no	—
465	C₄²×C₆₇	—	2	1	no	—
466	C₄²×C₆₇	—	2	1	no	—
467	C₄²×C₆₇	—	2	2	no	—
468	C₄²×C₆₇	—	2	2	no	—
469	C₄²×C₆₇	—	2	1	no	—
470	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
473	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
474	C₂³×C₆₇	—	2	1	no	—
475	C₂³×C₆₇	—	2	1	no	—
476	C₂³×C₆₇	—	2	2	no	—
477	C₂³×C₆₇	—	4	2	no	—
478	C₂³×C₆₇	—	4	2	no	—
479	C₂³×C₆₇	—	4	2	no	—
480	C₂³×C₆₇	—	4	4	no	—
481	C₂³×C₆₇	—	4	4	no	—
482	C₂³×C₆₇	—	8	2	no	—
483	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
484	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
485	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
486	Q₈×C₆₇	—	2	1	no	—
487	Q₈×C₆₇	—	2	2	no	—
488	Q₈×C₆₇	—	2	1	no	—
489	Q₈×C₆₇	—	2	1	no	—
490	Q₈×C₆₇	—	2	2	no	—
491	Q₈×C₆₇	—	2	2	no	—
492	Q₈×C₆₇	—	2	2	no	—
493	Q₈×C₆₇	—	4	4	no	—
494	Q₈×C₆₇	—	4	2	no	—
495	Q₈×C₆₇	—	8	2	no	—
496	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
497	D₄×C₆₇	—	2	4	no	—
498	D₄×C₆₇	—	2	2	no	—
499	D₄×C₆₇	—	2	2	no	—
500	D₄×C₆₇	—	2	1	no	—
501	D₄×C₆₇	—	2	1	no	—
502	D₄×C₆₇	—	2	2	no	—
503	D₄×C₆₇	—	2	1	no	—
504	D₄×C₆₇	—	2	2	no	—
505	D₄×C₆₇	—	4	2	no	—
506	D₄×C₆₇	—	4	4	no	—
507	D₄×C₆₇	—	4	4	no	—
508	D₄×C₆₇	—	4	4	no	—
509	D₄×C₆₇	—	4	2	no	—
510	D₄×C₆₇	—	4	4	no	—
511	D₄×C₆₇	—	4	4	no	—
512	D₄×C₆₇	—	4	4	no	—
513	D₄×C₆₇	—	4	2	no	—
514	D₄×C₆₇	—	8	1	no	—
515	D₄×C₆₇	—	8	2	no	—
516	D₄×C₆₇	—	8	2	no	—
517	D₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
518	C₂×C₄×C₆₇	—	2	4	no	—
519	C₂×C₄×C₆₇	—	2	1	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	2	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	1	no	—
529	C₂×C₄×C₆₇	—	2	1	no	—
530	C₂×C₄×C₆₇	—	2	2	no	—
531	C₂×C₄×C₆₇	—	2	1	no	—
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	—	4	2	no	—
536	C₂×C₄×C₆₇	—	4	2	no	—
537	C₂×C₄×C₆₇	—	4	2	no	—
538	C₂×C₄×C₆₇	—	4	1	no	—
539	C₂×C₄×C₆₇	—	4	4	no	—
540	C₂×C₄×C₆₇	—	4	4	no	—
541	C₂×C₄×C₆₇	—	4	4	no	—
542	C₂×C₄×C₆₇	—	4	4	no	—
543	C₂×C₄×C₆₇	—	4	4	no	—
544	C₂×C₄×C₆₇	—	4	2	no	—
545	C₂×C₄×C₆₇	—	4	2	no	—
546	C₂×C₄×C₆₇	—	8	1	no	—
547	C₂×C₄×C₆₇	—	8	2	no	—
548	C₂×C₄×C₆₇	—	8	2	no	—
549	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
552	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
557	C₈×C₆₇	—	2	1	no	—
558	C₈×C₆₇	—	2	2	no	—
559	C₈×C₆₇	—	2	1	no	—
560	C₈×C₆₇	—	2	1	no	—
561	C₈×C₆₇	—	2	1	no	—
562	C₈×C₆₇	—	2	2	no	—
563	C₂²×C₆₇	—	2	1	no	—
564	C₂²×C₆₇	—	2	2	no	—
565	C₂²×C₆₇	—	2	2	no	—
566	C₂²×C₆₇	—	2	2	no	—
567	C₂²×C₆₇	—	2	1	no	—
568	C₂²×C₆₇	—	2	2	no	—
569	C₂²×C₆₇	—	2	2	no	—
570	C₂²×C₆₇	—	2	1	no	—
571	C₂²×C₆₇	—	2	2	no	—
572	C₂²×C₆₇	—	2	2	no	—
573	C₂²×C₆₇	—	4	1	no	—
574	C₂²×C₆₇	—	4	1	no	—
575	C₂²×C₆₇	—	4	1	no	—
576	C₂²×C₆₇	—	4	2	no	—
577	C₂²×C₆₇	—	4	2	no	—
578	C₂²×C₆₇	—	4	1	no	—
579	C₂²×C₆₇	—	4	1	no	—
580	C₂²×C₆₇	—	4	2	no	—
581	C₂²×C₆₇	—	8	4	no	—
582	C₂²×C₆₇	—	8	8	no	—
583	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
584	C₄×C₆₇	—	2	1	no	—
585	C₄×C₆₇	—	2	1	no	—
586	C₄×C₆₇	—	2	1	no	—
587	C₄×C₆₇	—	2	2	no	—
588	C₄×C₆₇	—	2	2	no	—
589	C₄×C₆₇	—	2	2	no	—
590	C₄×C₆₇	—	2	1	no	—
591	C₄×C₆₇	—	4	1	no	—
592	C₄×C₆₇	—	4	1	no	—
593	C₄×C₆₇	—	4	2	no	—
594	C₄×C₆₇	—	4	2	no	—
595	C₄×C₆₇	—	4	1	no	—
596	C₄×C₆₇	—	4	1	no	—
597	C₄×C₆₇	—	4	1	no	—
598	C₄×C₆₇	—	4	2	no	—
599	C₄×C₆₇	#575	1	2	yes	—
600	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
601	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
602	#61589	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
603	C₂×C₆₇	—	4	2	no	—
604	C₂×C₆₇	—	4	1	no	—
605	C₂×C₆₇	—	4	2	no	—
606	C₂×C₆₇	—	4	2	no	—
607	C₂×C₆₇	—	8	1	no	—
608	C₂×C₆₇	—	8	2	no	—
609	C₂×C₆₇	#3484	1	1	yes	characteristic
610	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
611	C₂×C₆₇	#3586	1	1	yes	characteristic
612	#3520	C₂×C₆₇	1	1	yes	characteristic, complemented
613	D₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#3332	C₂×C₆₇	1	1	yes	characteristic, complemented
615	#3330	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#3328	C₂×C₆₇	1	1	yes	characteristic, complemented
617	#3327	C₂×C₆₇	1	2	yes	complemented
618	#3324	C₂×C₆₇	1	1	yes	characteristic, complemented
619	#3323	C₂×C₆₇	1	2	yes	complemented
620	#3278	C₂×C₆₇	1	1	yes	characteristic, complemented
621	#3277	C₂×C₆₇	1	2	yes	complemented
622	#3276	C₂×C₆₇	1	1	yes	characteristic, complemented
623	#3276	C₂×C₆₇	1	1	yes	characteristic, complemented
624	#3275	C₂×C₆₇	1	2	yes	complemented
625	#3272	C₂×C₆₇	1	1	yes	characteristic, complemented
626	#3212	C₂×C₆₇	1	1	yes	characteristic, complemented
627	#3210	C₂×C₆₇	1	1	yes	characteristic, complemented
628	#3197	C₂×C₆₇	1	2	yes	complemented
629	#3196	C₂×C₆₇	1	2	yes	complemented
630	#3107	C₂×C₆₇	1	1	yes	characteristic, complemented
631	#3102	C₂×C₆₇	1	1	yes	characteristic, complemented
632	#3007	C₂×C₆₇	1	2	yes	complemented
633	#3005	C₂×C₆₇	1	2	yes	complemented
634	#2975	C₂×C₆₇	1	1	yes	characteristic, complemented
635	C₆₇	#61589	1	1	yes	characteristic, direct product factor, Sylow
636	C₂²×#41	C₂²×C₆₇	1	2	yes	—
637	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
638	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
639	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
640	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
641	#556	C₂²×C₆₇	1	1	yes	characteristic
642	#554	—	2	1	no	—
643	#552	C₂²×C₆₇	1	2	yes	complemented
644	#551	—	2	2	no	—
645	#550	C₂²×C₆₇	1	1	yes	characteristic
646	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
647	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
648	#548	C₂²×C₆₇	1	2	yes	—
649	#548	C₂²×C₆₇	1	2	yes	complemented
650	#547	—	2	1	no	—
651	#547	C₂²×C₆₇	1	1	yes	characteristic
652	#547	C₂²×C₆₇	1	1	yes	characteristic
653	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	#546	—	2	1	no	—
655	#546	—	2	2	no	—
656	#546	C₂²×C₆₇	1	2	yes	—
657	D₄²	—	2	1	no	—
658	D₄²	C₂²×C₆₇	1	1	yes	characteristic
659	#542	—	2	1	no	—
660	#539	—	2	2	no	—
661	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
662	#532	—	2	1	no	—
663	#532	C₂²×C₆₇	1	1	yes	characteristic
664	#529	C₂²×C₆₇	1	1	yes	characteristic, complemented
665	#525	—	2	2	no	—
666	#525	C₂²×C₆₇	1	2	yes	—
667	#525	C₂²×C₆₇	1	2	yes	complemented
668	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
669	#520	—	2	1	no	—
670	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
671	C₂×C₄×D₄	—	2	1	no	—
672	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
673	#495	C₂²×C₆₇	1	2	yes	complemented
674	#494	C₂²×C₆₇	1	1	yes	characteristic, complemented
675	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
676	#488	C₂²×C₆₇	1	2	yes	complemented
677	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
678	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
679	#485	C₂²×C₆₇	1	2	yes	complemented
680	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
681	#485	C₂²×C₆₇	1	2	yes	complemented
682	#484	C₂²×C₆₇	1	2	yes	complemented
683	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
684	#482	C₂²×C₆₇	1	2	yes	complemented
685	#481	C₂²×C₆₇	1	2	yes	complemented
686	#479	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	#478	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
689	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	#470	C₂²×C₆₇	1	2	yes	complemented
691	#470	C₂²×C₆₇	1	2	yes	complemented
692	#470	C₂²×C₆₇	1	2	yes	complemented
693	#469	C₂²×C₆₇	1	2	yes	complemented
694	#468	C₂²×C₆₇	1	2	yes	complemented
695	#468	C₂²×C₆₇	1	2	yes	complemented
696	#468	C₂²×C₆₇	1	2	yes	complemented
697	#468	C₂²×C₆₇	1	2	yes	complemented
698	#464	C₂²×C₆₇	1	1	yes	characteristic, complemented
699	#464	C₂²×C₆₇	1	2	yes	complemented
700	#464	C₂²×C₆₇	1	2	yes	complemented
701	#463	C₂²×C₆₇	1	1	yes	characteristic, complemented
702	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
703	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
704	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
705	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
706	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
707	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
708	#452	C₂²×C₆₇	1	1	yes	characteristic
709	#452	C₂²×C₆₇	1	2	yes	—
710	#452	C₂²×C₆₇	1	2	yes	complemented
711	#452	C₂²×C₆₇	1	2	yes	complemented
712	#452	C₂²×C₆₇	1	2	yes	complemented
713	#452	C₂²×C₆₇	1	2	yes	complemented
714	#452	C₂²×C₆₇	1	2	yes	complemented
715	#452	C₂²×C₆₇	1	2	yes	complemented
716	#451	C₂²×C₆₇	1	2	yes	complemented
717	#451	C₂²×C₆₇	1	2	yes	complemented
718	#451	C₂²×C₆₇	1	2	yes	complemented
719	#450	C₂²×C₆₇	1	2	yes	complemented
720	#450	C₂²×C₆₇	1	2	yes	complemented
721	#449	C₂²×C₆₇	1	1	yes	characteristic
722	#449	C₂²×C₆₇	1	2	yes	complemented
723	#449	C₂²×C₆₇	1	2	yes	complemented
724	#449	C₂²×C₆₇	1	2	yes	complemented
725	#449	C₂²×C₆₇	1	2	yes	complemented
726	#448	C₂²×C₆₇	1	2	yes	complemented
727	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
728	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
729	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
730	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
731	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
732	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
733	#436	C₂²×C₆₇	1	1	yes	characteristic
734	#436	C₂²×C₆₇	1	1	yes	characteristic
735	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
736	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
737	#436	C₂²×C₆₇	1	2	yes	complemented
738	#436	C₂²×C₆₇	1	2	yes	complemented
739	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
740	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
741	#419	C₂²×C₆₇	1	2	yes	complemented
742	#418	C₂²×C₆₇	1	2	yes	complemented
743	#417	C₂²×C₆₇	1	2	yes	complemented
744	#417	C₂²×C₆₇	1	2	yes	complemented
745	#407	C₂²×C₆₇	1	2	yes	complemented
746	#407	C₂²×C₆₇	1	2	yes	complemented
747	C₂×#41	—	2	1	no	—
748	C₂×#41	—	2	2	no	—
749	C₂×#41	—	2	2	no	—
750	C₂×#41	—	4	4	no	—
751	C₂×#41	—	4	4	no	—
752	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
753	C₂×#41	C₂³×C₆₇	1	2	yes	—
754	C₂×#41	C₂³×C₆₇	1	2	yes	—
755	C₂×#41	C₂³×C₆₇	1	2	yes	—
756	C₂×#41	C₂³×C₆₇	1	2	yes	—
757	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
758	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
759	C₂²×D₄	—	2	2	no	—
760	C₂²×D₄	—	2	1	no	—
761	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
762	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
763	C₂³×C₄	—	2	2	no	—
764	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
765	#137	—	4	4	no	—
766	#137	—	4	4	no	—
767	#137	—	4	4	no	—
768	AGL(1,ℤ/8)	—	4	4	no	—
769	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
770	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
771	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
772	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
773	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
776	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
777	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
781	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
782	C₂×D₈	C₂³×C₆₇	1	2	yes	—
783	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
784	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
785	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
786	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
787	C₄⋊Q₈	—	2	1	no	—
788	C₄⋊Q₈	—	2	1	no	—
789	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
790	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
791	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
792	#127	—	2	1	no	—
793	#127	C₂³×C₆₇	1	1	yes	characteristic
794	#126	—	2	2	no	—
795	#126	—	2	2	no	—
796	#126	—	2	1	no	—
797	#125	—	2	2	no	—
798	#125	—	2	1	no	—
799	#125	C₂³×C₆₇	1	1	yes	characteristic
800	#124	—	2	1	no	—
801	#124	—	2	2	no	—
802	#124	—	2	2	no	—
803	#124	C₂³×C₆₇	1	1	yes	characteristic
804	#124	C₂³×C₆₇	1	2	yes	—
805	#123	—	2	2	no	—
806	#123	—	2	2	no	—
807	#123	—	2	2	no	—
808	#123	—	2	1	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	C₂²⋊Q₈	—	2	2	no	—
814	C₂²⋊Q₈	—	2	2	no	—
815	C₂²⋊Q₈	—	2	1	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	—	2	1	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	—	2	2	no	—
821	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
822	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
823	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
824	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
827	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
828	#121	—	2	2	no	—
829	#121	—	2	1	no	—
830	#121	—	2	2	no	—
831	#121	—	2	1	no	—
832	#121	—	2	1	no	—
833	#121	—	2	1	no	—
834	#121	—	2	1	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	C₂³×C₆₇	1	2	yes	—
838	#121	C₂³×C₆₇	1	2	yes	—
839	#121	C₂³×C₆₇	1	1	yes	characteristic
840	#121	C₂³×C₆₇	1	2	yes	—
841	#120	—	2	2	no	—
842	#120	—	2	2	no	—
843	#120	—	2	2	no	—
844	#120	—	2	2	no	—
845	C₄×Q₈	—	2	1	no	—
846	C₄×Q₈	—	2	1	no	—
847	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
848	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
849	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
850	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	2	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
866	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
867	C₄×D₄	D₄×C₆₇	1	2	yes	—
868	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
869	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
870	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
871	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
872	C₄×D₄	C₂³×C₆₇	1	2	yes	—
873	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
874	#117	—	2	1	no	—
875	#117	—	2	2	no	—
876	#117	—	2	1	no	—
877	#117	—	2	1	no	—
878	#117	C₂³×C₆₇	1	1	yes	characteristic
879	#117	C₂³×C₆₇	1	2	yes	—
880	C₂×C₄⋊C₄	—	2	2	no	—
881	C₂×C₄⋊C₄	—	2	1	no	—
882	C₂×C₄⋊C₄	—	2	1	no	—
883	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
885	C₂×C₂²⋊C₄	—	2	2	no	—
886	C₂×C₂²⋊C₄	—	2	2	no	—
887	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
888	C₂×C₄²	—	2	1	no	—
889	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
890	#107	C₂³×C₆₇	1	1	yes	characteristic
891	#107	C₂³×C₆₇	1	2	yes	—
892	#107	C₂³×C₆₇	1	1	yes	characteristic
893	#106	C₂³×C₆₇	1	2	yes	—
894	#106	C₂³×C₆₇	1	1	yes	characteristic
895	#106	C₂³×C₆₇	1	1	yes	characteristic
896	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
897	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
898	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
899	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
900	#103	C₂³×C₆₇	1	1	yes	characteristic
901	#103	C₂³×C₆₇	1	2	yes	—
902	#103	C₂³×C₆₇	1	2	yes	—
903	#103	C₂³×C₆₇	1	2	yes	—
904	#103	C₂³×C₆₇	1	1	yes	characteristic
905	#103	C₂³×C₆₇	1	2	yes	—
906	#103	C₂³×C₆₇	1	2	yes	—
907	#103	C₂³×C₆₇	1	2	yes	—
908	#103	C₂³×C₆₇	1	1	yes	characteristic
909	#103	C₂³×C₆₇	1	1	yes	characteristic
910	#103	C₂³×C₆₇	1	2	yes	—
911	#102	C₂³×C₆₇	1	1	yes	characteristic
912	#102	C₂³×C₆₇	1	2	yes	—
913	#102	C₂³×C₆₇	1	2	yes	—
914	#102	C₂³×C₆₇	1	2	yes	—
915	#102	C₂³×C₆₇	1	1	yes	characteristic
916	#102	C₂³×C₆₇	1	2	yes	—
917	#102	C₂³×C₆₇	1	2	yes	—
918	#102	C₂³×C₆₇	1	1	yes	characteristic
919	#102	C₂³×C₆₇	1	1	yes	characteristic
920	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
921	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
922	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
923	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
924	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
925	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
926	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
927	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
928	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
929	C₄×C₈	C₂³×C₆₇	1	2	yes	—
930	C₂⁴	—	2	2	no	—
931	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
932	#41	—	2	2	no	—
933	#41	—	2	2	no	—
934	#41	—	2	4	no	—
935	#41	—	2	4	no	—
936	#41	—	4	2	no	—
937	#41	—	4	2	no	—
938	#41	—	4	2	no	—
939	#41	—	4	2	no	—
940	#41	—	4	8	no	—
941	#41	—	4	2	no	—
942	#41	—	4	2	no	—
943	#41	—	4	8	no	—
944	#41	—	4	4	no	—
945	C₂×Q₈	—	2	1	no	—
946	C₂×Q₈	—	2	2	no	—
947	C₂×Q₈	—	2	2	no	—
948	C₂×Q₈	—	2	4	no	—
949	C₂×Q₈	—	4	2	no	—
950	C₂×Q₈	—	4	2	no	—
951	C₂×Q₈	—	4	2	no	—
952	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
953	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
954	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
955	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
956	C₂×D₄	—	2	1	no	—
957	C₂×D₄	—	2	4	no	—
958	C₂×D₄	—	2	1	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	1	no	—
969	C₂×D₄	—	4	2	no	—
970	C₂×D₄	—	4	2	no	—
971	C₂×D₄	—	4	8	no	—
972	C₂×D₄	—	4	4	no	—
973	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
974	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
975	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
976	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
977	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
978	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	4	2	no	—
991	C₂²×C₄	—	4	2	no	—
992	C₂²×C₄	—	4	8	no	—
993	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
994	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
995	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
996	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
997	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
998	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1000	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1001	Q₁₆	—	2	2	no	—
1002	Q₁₆	—	2	4	no	—
1003	Q₁₆	—	4	2	no	—
1004	Q₁₆	—	4	2	no	—
1005	Q₁₆	—	4	2	no	—
1006	SD₁₆	—	2	2	no	—
1007	SD₁₆	—	2	4	no	—
1008	SD₁₆	—	2	2	no	—
1009	SD₁₆	—	4	2	no	—
1010	SD₁₆	—	4	2	no	—
1011	SD₁₆	—	4	2	no	—
1012	SD₁₆	—	4	2	no	—
1013	D₈	—	2	2	no	—
1014	D₈	—	4	2	no	—
1015	M₁₆	—	4	2	no	—
1016	M₁₆	—	4	2	no	—
1017	M₁₆	—	4	2	no	—
1018	M₁₆	—	4	2	no	—
1019	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1020	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1021	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1022	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1023	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1024	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1025	C₄⋊C₄	—	2	1	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	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	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1045	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1046	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1047	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1048	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1049	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1051	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1073	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1074	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1076	C₄²	—	2	1	no	—
1077	C₄²	—	2	1	no	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	2	no	—
1080	C₄²	—	2	2	no	—
1081	C₄²	—	2	1	no	—
1082	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1083	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1084	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1085	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1086	C₂³	—	2	1	no	—
1087	C₂³	—	2	1	no	—
1088	C₂³	—	2	2	no	—
1089	C₂³	—	4	2	no	—
1090	C₂³	—	4	2	no	—
1091	C₂³	—	4	2	no	—
1092	C₂³	—	4	4	no	—
1093	C₂³	—	4	4	no	—
1094	C₂³	—	8	2	no	—
1095	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1096	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1097	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1098	Q₈	—	2	1	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	1	no	—
1101	Q₈	—	2	1	no	—
1102	Q₈	—	2	2	no	—
1103	Q₈	—	2	2	no	—
1104	Q₈	—	2	2	no	—
1105	Q₈	—	4	4	no	—
1106	Q₈	—	4	2	no	—
1107	Q₈	—	8	2	no	—
1108	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1109	D₄	—	2	4	no	—
1110	D₄	—	2	2	no	—
1111	D₄	—	2	2	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	2	1	no	—
1114	D₄	—	2	2	no	—
1115	D₄	—	2	1	no	—
1116	D₄	—	2	2	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	4	4	no	—
1119	D₄	—	4	4	no	—
1120	D₄	—	4	4	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	8	1	no	—
1127	D₄	—	8	2	no	—
1128	D₄	—	8	2	no	—
1129	D₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1130	C₂×C₄	—	2	4	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	4	2	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	2	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	4	no	—
1153	C₂×C₄	—	4	4	no	—
1154	C₂×C₄	—	4	4	no	—
1155	C₂×C₄	—	4	4	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	4	2	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	1	no	—
1160	C₂×C₄	—	8	2	no	—
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	2	yes	—
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	2	yes	—
1167	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1168	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1169	C₈	—	2	1	no	—
1170	C₈	—	2	2	no	—
1171	C₈	—	2	1	no	—
1172	C₈	—	2	1	no	—
1173	C₈	—	2	1	no	—
1174	C₈	—	2	2	no	—
1175	C₂²	—	2	1	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	2	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	2	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	2	no	—
1191	C₂²	—	4	2	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	8	4	no	—
1194	C₂²	—	8	8	no	—
1195	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1196	C₄	—	2	1	no	—
1197	C₄	—	2	1	no	—
1198	C₄	—	2	1	no	—
1199	C₄	—	2	1	no	—
1200	C₄	—	2	2	no	—
1201	C₄	—	2	2	no	—
1202	C₄	—	2	2	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	2	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	2	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	#575×C₆₇	1	2	yes	—
1212	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1213	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1214	C₂	—	4	2	no	—
1215	C₂	—	4	1	no	—
1216	C₂	—	4	2	no	—
1217	C₂	—	4	2	no	—
1218	C₂	—	8	2	no	—
1219	C₂	—	8	1	no	—
1220	C₂	C₆₇×#3484	1	1	yes	characteristic
1221	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
1222	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 ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3520	C₂	semidirect
2. D₄×#41×C₆₇	C₂	semidirect
3. C₆₇×#3332	C₂	semidirect
4. C₆₇×#3330	C₂	semidirect
5. C₆₇×#3328	C₂	semidirect
6. C₆₇×#3327	C₂	semidirect
7. C₆₇×#3324	C₂	semidirect
8. C₆₇×#3323	C₂	semidirect
9. C₆₇×#3278	C₂	semidirect
10. C₆₇×#3277	C₂	semidirect
11. C₆₇×#3276	C₂	semidirect
12. C₆₇×#3276	C₂	semidirect
13. C₆₇×#3275	C₂	semidirect
14. C₆₇×#3272	C₂	semidirect
15. C₆₇×#3212	C₂	semidirect
16. C₆₇×#3210	C₂	semidirect
17. C₆₇×#3197	C₂	semidirect
18. C₆₇×#3196	C₂	semidirect
19. C₆₇×#3107	C₂	semidirect
20. C₆₇×#3102	C₂	semidirect
21. C₆₇×#3007	C₂	semidirect
22. C₆₇×#3005	C₂	semidirect
23. C₆₇×#2975	C₂	semidirect
25. C₂×#137×C₆₇	C₂²	semidirect
26. C₂×#137×C₆₇	C₂²	semidirect
27. C₂×#137×C₆₇	C₂²	semidirect
28. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
31. #552×C₆₇	C₂²	semidirect
35. D₄×Q₈×C₆₇	C₂²	semidirect
37. #548×C₆₇	C₂²	semidirect
41. #547×C₆₇	C₂²	semidirect
49. #533×C₆₇	C₂²	semidirect
52. #529×C₆₇	C₂²	semidirect
55. #525×C₆₇	C₂²	semidirect
56. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
61. #495×C₆₇	C₂²	semidirect
62. #494×C₆₇	C₂²	semidirect
63. #492×C₆₇	C₂²	semidirect
64. #488×C₆₇	C₂²	semidirect
65. #487×C₆₇	C₂²	semidirect
66. #486×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
68. #485×C₆₇	C₂²	semidirect
69. #485×C₆₇	C₂²	semidirect
70. #484×C₆₇	C₂²	semidirect
71. #482×C₆₇	C₂²	semidirect
72. #482×C₆₇	C₂²	semidirect
73. #481×C₆₇	C₂²	semidirect
74. #479×C₆₇	C₂²	semidirect
75. #478×C₆₇	C₂²	semidirect
76. #475×C₆₇	C₂²	semidirect
77. #474×C₆₇	C₂²	semidirect
78. #470×C₆₇	C₂²	semidirect
79. #470×C₆₇	C₂²	semidirect
80. #470×C₆₇	C₂²	semidirect
81. #469×C₆₇	C₂²	semidirect
82. #468×C₆₇	C₂²	semidirect
83. #468×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #468×C₆₇	C₂²	semidirect
86. #464×C₆₇	C₂²	semidirect
87. #464×C₆₇	C₂²	semidirect
88. #464×C₆₇	C₂²	semidirect
89. #463×C₆₇	C₂²	semidirect
90. #462×C₆₇	C₂²	semidirect
91. #462×C₆₇	C₂²	semidirect
92. #461×C₆₇	C₂²	semidirect
93. #461×C₆₇	C₂²	semidirect
94. #460×C₆₇	C₂²	semidirect
95. #459×C₆₇	C₂²	semidirect
98. #452×C₆₇	C₂²	semidirect
99. #452×C₆₇	C₂²	semidirect
100. #452×C₆₇	C₂²	semidirect
101. #452×C₆₇	C₂²	semidirect
102. #452×C₆₇	C₂²	semidirect
103. #452×C₆₇	C₂²	semidirect
104. #451×C₆₇	C₂²	semidirect
105. #451×C₆₇	C₂²	semidirect
106. #451×C₆₇	C₂²	semidirect
107. #450×C₆₇	C₂²	semidirect
108. #450×C₆₇	C₂²	semidirect
110. #449×C₆₇	C₂²	semidirect
111. #449×C₆₇	C₂²	semidirect
112. #449×C₆₇	C₂²	semidirect
113. #449×C₆₇	C₂²	semidirect
114. #448×C₆₇	C₂²	semidirect
115. C₄×Q₁₆×C₆₇	C₂²	semidirect
116. C₄×Q₁₆×C₆₇	C₂²	semidirect
117. C₄×SD₁₆×C₆₇	C₂²	semidirect
118. C₄×SD₁₆×C₆₇	C₂²	semidirect
119. C₄×SD₁₆×C₆₇	C₂²	semidirect
120. C₄×D₈×C₆₇	C₂²	semidirect
123. #436×C₆₇	C₂²	semidirect
124. #436×C₆₇	C₂²	semidirect
125. #436×C₆₇	C₂²	semidirect
126. #436×C₆₇	C₂²	semidirect
127. #431×C₆₇	C₂²	semidirect
128. #431×C₆₇	C₂²	semidirect
129. #419×C₆₇	C₂²	semidirect
130. #418×C₆₇	C₂²	semidirect
131. #417×C₆₇	C₂²	semidirect
132. #417×C₆₇	C₂²	semidirect
133. #407×C₆₇	C₂²	semidirect
134. #407×C₆₇	C₂²	semidirect
602. #61589	C₆₇	direct (N × H)
612. #3520	C₂×C₆₇	semidirect
613. D₄×#41	C₂×C₆₇	semidirect
614. #3332	C₂×C₆₇	semidirect
615. #3330	C₂×C₆₇	semidirect
616. #3328	C₂×C₆₇	semidirect
617. #3327	C₂×C₆₇	semidirect
618. #3324	C₂×C₆₇	semidirect
619. #3323	C₂×C₆₇	semidirect
620. #3278	C₂×C₆₇	semidirect
621. #3277	C₂×C₆₇	semidirect
622. #3276	C₂×C₆₇	semidirect
623. #3276	C₂×C₆₇	semidirect
624. #3275	C₂×C₆₇	semidirect
625. #3272	C₂×C₆₇	semidirect
626. #3212	C₂×C₆₇	semidirect
627. #3210	C₂×C₆₇	semidirect
628. #3197	C₂×C₆₇	semidirect
629. #3196	C₂×C₆₇	semidirect
630. #3107	C₂×C₆₇	semidirect
631. #3102	C₂×C₆₇	semidirect
632. #3007	C₂×C₆₇	semidirect
633. #3005	C₂×C₆₇	semidirect
634. #2975	C₂×C₆₇	semidirect
635. C₆₇	#61589	direct (N × H)
637. C₂×#137	C₂²×C₆₇	semidirect
638. C₂×#137	C₂²×C₆₇	semidirect
639. C₂×#137	C₂²×C₆₇	semidirect
640. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
643. #552	C₂²×C₆₇	semidirect
647. D₄×Q₈	C₂²×C₆₇	semidirect
649. #548	C₂²×C₆₇	semidirect
653. #547	C₂²×C₆₇	semidirect
661. #533	C₂²×C₆₇	semidirect
664. #529	C₂²×C₆₇	semidirect
667. #525	C₂²×C₆₇	semidirect
668. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
673. #495	C₂²×C₆₇	semidirect
674. #494	C₂²×C₆₇	semidirect
675. #492	C₂²×C₆₇	semidirect
676. #488	C₂²×C₆₇	semidirect
677. #487	C₂²×C₆₇	semidirect
678. #486	C₂²×C₆₇	semidirect
679. #485	C₂²×C₆₇	semidirect
680. #485	C₂²×C₆₇	semidirect
681. #485	C₂²×C₆₇	semidirect
682. #484	C₂²×C₆₇	semidirect
683. #482	C₂²×C₆₇	semidirect
684. #482	C₂²×C₆₇	semidirect
685. #481	C₂²×C₆₇	semidirect
686. #479	C₂²×C₆₇	semidirect
687. #478	C₂²×C₆₇	semidirect
688. #475	C₂²×C₆₇	semidirect
689. #474	C₂²×C₆₇	semidirect
690. #470	C₂²×C₆₇	semidirect
691. #470	C₂²×C₆₇	semidirect
692. #470	C₂²×C₆₇	semidirect
693. #469	C₂²×C₆₇	semidirect
694. #468	C₂²×C₆₇	semidirect
695. #468	C₂²×C₆₇	semidirect
696. #468	C₂²×C₆₇	semidirect
697. #468	C₂²×C₆₇	semidirect
698. #464	C₂²×C₆₇	semidirect
699. #464	C₂²×C₆₇	semidirect
700. #464	C₂²×C₆₇	semidirect
701. #463	C₂²×C₆₇	semidirect
702. #462	C₂²×C₆₇	semidirect
703. #462	C₂²×C₆₇	semidirect
704. #461	C₂²×C₆₇	semidirect
705. #461	C₂²×C₆₇	semidirect
706. #460	C₂²×C₆₇	semidirect
707. #459	C₂²×C₆₇	semidirect
710. #452	C₂²×C₆₇	semidirect
711. #452	C₂²×C₆₇	semidirect
712. #452	C₂²×C₆₇	semidirect
713. #452	C₂²×C₆₇	semidirect
714. #452	C₂²×C₆₇	semidirect
715. #452	C₂²×C₆₇	semidirect
716. #451	C₂²×C₆₇	semidirect
717. #451	C₂²×C₆₇	semidirect
718. #451	C₂²×C₆₇	semidirect
719. #450	C₂²×C₆₇	semidirect
720. #450	C₂²×C₆₇	semidirect
722. #449	C₂²×C₆₇	semidirect
723. #449	C₂²×C₆₇	semidirect
724. #449	C₂²×C₆₇	semidirect
725. #449	C₂²×C₆₇	semidirect
726. #448	C₂²×C₆₇	semidirect
727. C₄×Q₁₆	C₂²×C₆₇	semidirect
728. C₄×Q₁₆	C₂²×C₆₇	semidirect
729. C₄×SD₁₆	C₂²×C₆₇	semidirect
730. C₄×SD₁₆	C₂²×C₆₇	semidirect
731. C₄×SD₁₆	C₂²×C₆₇	semidirect
732. C₄×D₈	C₂²×C₆₇	semidirect
735. #436	C₂²×C₆₇	semidirect
736. #436	C₂²×C₆₇	semidirect
737. #436	C₂²×C₆₇	semidirect
738. #436	C₂²×C₆₇	semidirect
739. #431	C₂²×C₆₇	semidirect
740. #431	C₂²×C₆₇	semidirect
741. #419	C₂²×C₆₇	semidirect
742. #418	C₂²×C₆₇	semidirect
743. #417	C₂²×C₆₇	semidirect
744. #417	C₂²×C₆₇	semidirect
745. #407	C₂²×C₆₇	semidirect
746. #407	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×#3520	2
D₄×#41×C₆₇	2
C₆₇×#3332	2
C₆₇×#3330	2
C₆₇×#3328	2
C₆₇×#3327	2
C₆₇×#3324	2
C₆₇×#3323	2
C₆₇×#3278	2
C₆₇×#3277	2
C₆₇×#3276	2
C₆₇×#3275	2
C₆₇×#3272	2
C₆₇×#3212	2
C₆₇×#3210	2
C₆₇×#3197	2
C₆₇×#3196	2
C₆₇×#3107	2
C₆₇×#3102	2
C₆₇×#3007	2
C₆₇×#3005	2
C₆₇×#2975	2
#61589	67

Subgroups — C67×#61589 #30740840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61589 #30740840