Subgroups — C₆₇×#61622 #30740873

Order 17152.

2028 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3489	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3327	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3315	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3312	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3296	C₂	1	2	yes	maximal, complemented
7	D₄×Q₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3276	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3270	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3266	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3223	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3201	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3195	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3189	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3120	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3011	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#452×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2976	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
25	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
27	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
28	#563×C₆₇	—	2	2	no	—
29	#552×C₆₇	C₂²	1	2	yes	—
30	#552×C₆₇	C₂²	1	2	yes	complemented
31	#551×C₆₇	—	2	2	no	—
32	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
33	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
34	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
35	#548×C₆₇	C₂²	1	2	yes	—
36	#547×C₆₇	—	2	2	no	—
37	#547×C₆₇	C₂²	1	2	yes	—
38	#546×C₆₇	—	2	2	no	—
39	#546×C₆₇	C₂²	1	2	yes	—
40	#544×C₆₇	—	2	1	no	—
41	#544×C₆₇	—	2	1	no	—
42	#541×C₆₇	C₂²	1	2	yes	complemented
43	#539×C₆₇	—	2	1	no	—
44	#539×C₆₇	—	2	1	no	—
45	#537×C₆₇	—	2	1	no	—
46	#537×C₆₇	C₂²	1	1	yes	characteristic
47	#536×C₆₇	—	2	1	no	—
48	#536×C₆₇	C₂²	1	1	yes	characteristic
49	#536×C₆₇	C₂²	1	2	yes	complemented
50	#525×C₆₇	—	2	1	no	—
51	#525×C₆₇	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
53	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
56	#520×C₆₇	C₂²	1	1	yes	characteristic
57	#497×C₆₇	C₂²	1	2	yes	complemented
58	#494×C₆₇	C₂²	1	2	yes	complemented
59	#491×C₆₇	C₂²	1	2	yes	complemented
60	#488×C₆₇	C₂²	1	2	yes	complemented
61	#485×C₆₇	C₂²	1	2	yes	complemented
62	#484×C₆₇	C₂²	1	2	yes	complemented
63	#484×C₆₇	C₂²	1	2	yes	complemented
64	#483×C₆₇	C₂²	1	2	yes	—
65	#483×C₆₇	C₂²	1	2	yes	complemented
66	#482×C₆₇	C₂²	1	2	yes	complemented
67	#479×C₆₇	C₂²	1	2	yes	complemented
68	#478×C₆₇	C₂²	1	2	yes	complemented
69	#470×C₆₇	C₂²	1	2	yes	complemented
70	#470×C₆₇	C₂²	1	2	yes	complemented
71	#470×C₆₇	C₂²	1	2	yes	complemented
72	#468×C₆₇	C₂²	1	2	yes	complemented
73	#467×C₆₇	C₂²	1	2	yes	—
74	#467×C₆₇	C₂²	1	2	yes	—
75	#467×C₆₇	C₂²	1	2	yes	complemented
76	#465×C₆₇	C₂²	1	2	yes	complemented
77	#464×C₆₇	C₂²	1	2	yes	complemented
78	#464×C₆₇	C₂²	1	2	yes	complemented
79	#462×C₆₇	C₂²	1	2	yes	complemented
80	#462×C₆₇	C₂²	1	2	yes	complemented
81	#462×C₆₇	C₂²	1	2	yes	complemented
82	#461×C₆₇	C₂²	1	2	yes	complemented
83	#452×C₆₇	C₂²	1	2	yes	—
84	#452×C₆₇	C₂²	1	2	yes	—
85	#452×C₆₇	C₂²	1	2	yes	—
86	#452×C₆₇	C₂²	1	2	yes	—
87	#452×C₆₇	C₂²	1	2	yes	—
88	#452×C₆₇	C₂²	1	2	yes	—
89	#452×C₆₇	C₂²	1	2	yes	complemented
90	#452×C₆₇	C₂²	1	2	yes	complemented
91	#451×C₆₇	C₂²	1	2	yes	—
92	#451×C₆₇	C₂²	1	2	yes	—
93	#451×C₆₇	C₂²	1	2	yes	complemented
94	#451×C₆₇	C₂²	1	2	yes	complemented
95	#451×C₆₇	C₂²	1	2	yes	complemented
96	#451×C₆₇	C₂²	1	2	yes	complemented
97	#451×C₆₇	C₂²	1	2	yes	complemented
98	#451×C₆₇	C₂²	1	2	yes	complemented
99	#450×C₆₇	C₂²	1	2	yes	—
100	#448×C₆₇	C₂²	1	2	yes	complemented
101	#441×C₆₇	C₂²	1	2	yes	complemented
102	#440×C₆₇	C₂²	1	2	yes	complemented
103	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
105	#436×C₆₇	C₂²	1	2	yes	complemented
106	#435×C₆₇	C₂²	1	2	yes	—
107	#435×C₆₇	C₂²	1	2	yes	complemented
108	C₈×D₄×C₆₇	C₂²	1	2	yes	—
109	#433×C₆₇	C₂²	1	2	yes	complemented
110	#419×C₆₇	C₂²	1	2	yes	complemented
111	#417×C₆₇	C₂²	1	1	yes	characteristic
112	#417×C₆₇	C₂²	1	1	yes	characteristic
113	#416×C₆₇	C₂²	1	2	yes	complemented
114	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
115	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
116	#408×C₆₇	C₂²	1	2	yes	complemented
117	#407×C₆₇	C₂²	1	1	yes	characteristic
118	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
119	2₋¹⁺⁴×C₆₇	—	4	2	no	—
120	2₋¹⁺⁴×C₆₇	—	4	2	no	—
121	C₂×#41×C₆₇	—	2	1	no	—
122	C₂×#41×C₆₇	—	2	2	no	—
123	C₂×#41×C₆₇	—	2	1	no	—
124	C₂×#41×C₆₇	—	2	1	no	—
125	C₂×#41×C₆₇	—	4	2	no	—
126	C₂×#41×C₆₇	—	4	2	no	—
127	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×#41×C₆₇	C₂³	1	2	yes	—
131	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×Q₈×C₆₇	—	2	1	no	—
134	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
136	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
137	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₆₇	—	2	1	no	—
141	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₆₇	—	2	1	no	—
143	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
144	#137×C₆₇	—	4	2	no	—
145	#137×C₆₇	—	4	4	no	—
146	#137×C₆₇	—	4	2	no	—
147	C₂×Q₁₆×C₆₇	—	4	2	no	—
148	C₂×Q₁₆×C₆₇	—	4	4	no	—
149	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₆₇	—	4	2	no	—
158	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
163	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
166	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₆₇	—	2	2	no	—
169	C₄⋊Q₈×C₆₇	—	2	2	no	—
170	C₄⋊Q₈×C₆₇	—	2	2	no	—
171	C₄⋊Q₈×C₆₇	—	2	2	no	—
172	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
173	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
174	#126×C₆₇	—	2	2	no	—
175	#126×C₆₇	—	2	2	no	—
176	#126×C₆₇	—	2	2	no	—
177	#126×C₆₇	—	2	2	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	C₂³	1	2	yes	—
183	#124×C₆₇	—	2	2	no	—
184	#124×C₆₇	—	2	2	no	—
185	#124×C₆₇	C₂³	1	2	yes	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	—	2	2	no	—
189	#123×C₆₇	—	2	2	no	—
190	#123×C₆₇	—	2	2	no	—
191	#123×C₆₇	—	2	2	no	—
192	#123×C₆₇	—	2	2	no	—
193	#123×C₆₇	—	2	2	no	—
194	#123×C₆₇	D₄	1	2	yes	—
195	C₂²⋊Q₈×C₆₇	—	2	1	no	—
196	C₂²⋊Q₈×C₆₇	—	2	1	no	—
197	C₂²⋊Q₈×C₆₇	—	2	1	no	—
198	C₂²⋊Q₈×C₆₇	—	2	1	no	—
199	C₂²⋊Q₈×C₆₇	—	2	1	no	—
200	C₂²⋊Q₈×C₆₇	—	2	1	no	—
201	C₂²⋊Q₈×C₆₇	—	2	1	no	—
202	C₂²⋊Q₈×C₆₇	—	2	1	no	—
203	C₂²⋊Q₈×C₆₇	—	2	2	no	—
204	C₂²⋊Q₈×C₆₇	—	2	1	no	—
205	C₂²⋊Q₈×C₆₇	—	2	2	no	—
206	C₂²⋊Q₈×C₆₇	—	2	2	no	—
207	C₂²⋊Q₈×C₆₇	—	2	2	no	—
208	C₂²⋊Q₈×C₆₇	—	2	2	no	—
209	C₂²⋊Q₈×C₆₇	—	2	2	no	—
210	C₂²⋊Q₈×C₆₇	—	2	2	no	—
211	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
212	C₂²⋊Q₈×C₆₇	D₄	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	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
222	#121×C₆₇	—	2	1	no	—
223	#121×C₆₇	—	2	2	no	—
224	#121×C₆₇	—	2	2	no	—
225	#121×C₆₇	—	2	2	no	—
226	#121×C₆₇	—	2	2	no	—
227	#121×C₆₇	D₄	1	1	yes	characteristic
228	#121×C₆₇	D₄	1	1	yes	characteristic
229	#121×C₆₇	C₂³	1	2	yes	—
230	#120×C₆₇	—	2	2	no	—
231	#120×C₆₇	D₄	1	2	yes	—
232	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
233	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
234	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
235	C₄×D₄×C₆₇	—	2	2	no	—
236	C₄×D₄×C₆₇	—	2	2	no	—
237	C₄×D₄×C₆₇	—	2	2	no	—
238	C₄×D₄×C₆₇	—	2	2	no	—
239	C₄×D₄×C₆₇	—	2	2	no	—
240	C₄×D₄×C₆₇	C₂³	1	2	yes	—
241	C₄×D₄×C₆₇	C₂³	1	2	yes	—
242	C₄×D₄×C₆₇	C₂³	1	2	yes	—
243	#117×C₆₇	—	2	1	no	—
244	#117×C₆₇	—	2	2	no	—
245	#117×C₆₇	—	2	2	no	—
246	#117×C₆₇	C₂³	1	2	yes	—
247	#117×C₆₇	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
249	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
250	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
251	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
252	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
253	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
257	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
258	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
259	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
260	#107×C₆₇	C₂³	1	2	yes	—
261	#107×C₆₇	C₂³	1	2	yes	—
262	#106×C₆₇	C₂³	1	2	yes	—
263	#106×C₆₇	C₂³	1	2	yes	—
264	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
265	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
266	#103×C₆₇	C₂³	1	2	yes	—
267	#103×C₆₇	C₂³	1	2	yes	—
268	#103×C₆₇	C₂³	1	2	yes	—
269	#103×C₆₇	C₂³	1	2	yes	—
270	#103×C₆₇	C₂³	1	2	yes	—
271	#103×C₆₇	C₂³	1	2	yes	—
272	#103×C₆₇	C₂³	1	2	yes	—
273	#103×C₆₇	C₂³	1	2	yes	—
274	#103×C₆₇	C₂³	1	2	yes	—
275	#103×C₆₇	C₂³	1	2	yes	—
276	#103×C₆₇	C₂³	1	2	yes	—
277	#103×C₆₇	C₂³	1	2	yes	—
278	#102×C₆₇	C₂³	1	2	yes	—
279	#102×C₆₇	C₂³	1	2	yes	—
280	#102×C₆₇	C₂³	1	2	yes	—
281	#102×C₆₇	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
285	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
286	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
287	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
288	#97×C₆₇	C₂³	1	2	yes	—
289	C₄×C₈×C₆₇	C₂³	1	2	yes	—
290	C₂⁴×C₆₇	—	2	1	no	—
291	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
292	#41×C₆₇	—	2	2	no	—
293	#41×C₆₇	—	2	2	no	—
294	#41×C₆₇	—	2	2	no	—
295	#41×C₆₇	—	2	2	no	—
296	#41×C₆₇	—	2	4	no	—
297	#41×C₆₇	—	4	1	no	—
298	#41×C₆₇	—	4	1	no	—
299	#41×C₆₇	—	4	1	no	—
300	#41×C₆₇	—	4	1	no	—
301	#41×C₆₇	—	4	1	no	—
302	#41×C₆₇	—	4	1	no	—
303	#41×C₆₇	—	4	2	no	—
304	#41×C₆₇	—	4	4	no	—
305	#41×C₆₇	—	4	4	no	—
306	#41×C₆₇	—	4	4	no	—
307	#41×C₆₇	—	4	8	no	—
308	C₂×Q₈×C₆₇	—	2	1	no	—
309	C₂×Q₈×C₆₇	—	2	2	no	—
310	C₂×Q₈×C₆₇	—	2	1	no	—
311	C₂×Q₈×C₆₇	—	2	1	no	—
312	C₂×Q₈×C₆₇	—	2	1	no	—
313	C₂×Q₈×C₆₇	—	2	2	no	—
314	C₂×Q₈×C₆₇	—	2	2	no	—
315	C₂×Q₈×C₆₇	—	2	4	no	—
316	C₂×Q₈×C₆₇	—	4	1	no	—
317	C₂×Q₈×C₆₇	—	4	2	no	—
318	C₂×Q₈×C₆₇	—	4	1	no	—
319	C₂×Q₈×C₆₇	—	4	1	no	—
320	C₂×Q₈×C₆₇	—	4	4	no	—
321	C₂×Q₈×C₆₇	—	4	1	no	—
322	C₂×Q₈×C₆₇	—	4	1	no	—
323	C₂×Q₈×C₆₇	—	4	2	no	—
324	C₂×Q₈×C₆₇	—	4	1	no	—
325	C₂×Q₈×C₆₇	—	4	1	no	—
326	C₂×Q₈×C₆₇	—	4	2	no	—
327	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₆₇	—	2	1	no	—
334	C₂×D₄×C₆₇	—	2	2	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	1	no	—
337	C₂×D₄×C₆₇	—	2	1	no	—
338	C₂×D₄×C₆₇	—	2	1	no	—
339	C₂×D₄×C₆₇	—	2	2	no	—
340	C₂×D₄×C₆₇	—	2	1	no	—
341	C₂×D₄×C₆₇	—	4	1	no	—
342	C₂×D₄×C₆₇	—	4	4	no	—
343	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₆₇	—	2	1	no	—
350	C₂²×C₄×C₆₇	—	2	1	no	—
351	C₂²×C₄×C₆₇	—	2	1	no	—
352	C₂²×C₄×C₆₇	—	2	1	no	—
353	C₂²×C₄×C₆₇	—	2	2	no	—
354	C₂²×C₄×C₆₇	—	2	1	no	—
355	C₂²×C₄×C₆₇	—	2	1	no	—
356	C₂²×C₄×C₆₇	—	2	1	no	—
357	C₂²×C₄×C₆₇	—	2	1	no	—
358	C₂²×C₄×C₆₇	—	2	2	no	—
359	C₂²×C₄×C₆₇	—	2	2	no	—
360	C₂²×C₄×C₆₇	—	2	1	no	—
361	C₂²×C₄×C₆₇	—	2	1	no	—
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	2	no	—
364	C₂²×C₄×C₆₇	—	4	1	no	—
365	C₂²×C₄×C₆₇	—	4	1	no	—
366	C₂²×C₄×C₆₇	—	4	4	no	—
367	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
374	Q₁₆×C₆₇	—	2	4	no	—
375	Q₁₆×C₆₇	—	2	4	no	—
376	Q₁₆×C₆₇	—	4	2	no	—
377	Q₁₆×C₆₇	—	4	2	no	—
378	Q₁₆×C₆₇	—	4	2	no	—
379	Q₁₆×C₆₇	—	4	2	no	—
380	Q₁₆×C₆₇	—	4	2	no	—
381	Q₁₆×C₆₇	—	4	2	no	—
382	SD₁₆×C₆₇	—	2	4	no	—
383	SD₁₆×C₆₇	—	2	4	no	—
384	SD₁₆×C₆₇	—	4	2	no	—
385	SD₁₆×C₆₇	—	4	2	no	—
386	M₁₆×C₆₇	—	4	2	no	—
387	M₁₆×C₆₇	—	4	1	no	—
388	M₁₆×C₆₇	—	4	1	no	—
389	C₂×C₈×C₆₇	—	4	1	no	—
390	C₂×C₈×C₆₇	—	4	1	no	—
391	C₂×C₈×C₆₇	—	4	2	no	—
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	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	—	2	1	no	—
398	C₄⋊C₄×C₆₇	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	2	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	2	no	—
405	C₄⋊C₄×C₆₇	—	2	2	no	—
406	C₄⋊C₄×C₆₇	—	2	1	no	—
407	C₄⋊C₄×C₆₇	—	2	1	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	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	2	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	no	—
433	C₂²⋊C₄×C₆₇	—	2	2	no	—
434	C₂²⋊C₄×C₆₇	—	2	2	no	—
435	C₂²⋊C₄×C₆₇	—	2	2	no	—
436	C₂²⋊C₄×C₆₇	—	2	2	no	—
437	C₂²⋊C₄×C₆₇	—	2	2	no	—
438	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
443	C₄²×C₆₇	—	2	2	no	—
444	C₄²×C₆₇	—	2	2	no	—
445	C₄²×C₆₇	—	2	2	no	—
446	C₄²×C₆₇	—	2	2	no	—
447	C₄²×C₆₇	C₂⁴	1	2	yes	—
448	C₂³×C₆₇	—	2	1	no	—
449	C₂³×C₆₇	—	2	2	no	—
450	C₂³×C₆₇	—	2	1	no	—
451	C₂³×C₆₇	—	4	1	no	—
452	C₂³×C₆₇	—	4	1	no	—
453	C₂³×C₆₇	—	4	2	no	—
454	C₂³×C₆₇	—	4	2	no	—
455	C₂³×C₆₇	—	8	1	no	—
456	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
457	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
458	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
459	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
460	Q₈×C₆₇	—	2	1	no	—
461	Q₈×C₆₇	—	2	2	no	—
462	Q₈×C₆₇	—	2	2	no	—
463	Q₈×C₆₇	—	2	2	no	—
464	Q₈×C₆₇	—	2	2	no	—
465	Q₈×C₆₇	—	2	2	no	—
466	Q₈×C₆₇	—	2	1	no	—
467	Q₈×C₆₇	—	2	2	no	—
468	Q₈×C₆₇	—	2	1	no	—
469	Q₈×C₆₇	—	4	1	no	—
470	Q₈×C₆₇	—	4	4	no	—
471	Q₈×C₆₇	—	4	2	no	—
472	Q₈×C₆₇	—	4	2	no	—
473	Q₈×C₆₇	—	8	1	no	—
474	Q₈×C₆₇	—	8	1	no	—
475	Q₈×C₆₇	—	8	2	no	—
476	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
477	D₄×C₆₇	—	2	4	no	—
478	D₄×C₆₇	—	2	4	no	—
479	D₄×C₆₇	—	2	1	no	—
480	D₄×C₆₇	—	2	1	no	—
481	D₄×C₆₇	—	2	1	no	—
482	D₄×C₆₇	—	4	2	no	—
483	D₄×C₆₇	—	4	1	no	—
484	D₄×C₆₇	—	4	2	no	—
485	D₄×C₆₇	—	4	2	no	—
486	D₄×C₆₇	—	4	2	no	—
487	D₄×C₆₇	—	4	2	no	—
488	D₄×C₆₇	—	4	4	no	—
489	D₄×C₆₇	—	4	2	no	—
490	D₄×C₆₇	—	8	2	no	—
491	D₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
492	C₂×C₄×C₆₇	—	2	4	no	—
493	C₂×C₄×C₆₇	—	2	1	no	—
494	C₂×C₄×C₆₇	—	2	1	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	2	no	—
497	C₂×C₄×C₆₇	—	2	1	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	2	no	—
500	C₂×C₄×C₆₇	—	2	1	no	—
501	C₂×C₄×C₆₇	—	2	1	no	—
502	C₂×C₄×C₆₇	—	2	2	no	—
503	C₂×C₄×C₆₇	—	2	2	no	—
504	C₂×C₄×C₆₇	—	2	2	no	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	2	no	—
507	C₂×C₄×C₆₇	—	2	2	no	—
508	C₂×C₄×C₆₇	—	2	1	no	—
509	C₂×C₄×C₆₇	—	4	1	no	—
510	C₂×C₄×C₆₇	—	4	1	no	—
511	C₂×C₄×C₆₇	—	4	1	no	—
512	C₂×C₄×C₆₇	—	4	2	no	—
513	C₂×C₄×C₆₇	—	4	2	no	—
514	C₂×C₄×C₆₇	—	4	2	no	—
515	C₂×C₄×C₆₇	—	4	4	no	—
516	C₂×C₄×C₆₇	—	4	4	no	—
517	C₂×C₄×C₆₇	—	4	2	no	—
518	C₂×C₄×C₆₇	—	4	2	no	—
519	C₂×C₄×C₆₇	—	4	2	no	—
520	C₂×C₄×C₆₇	—	4	2	no	—
521	C₂×C₄×C₆₇	—	8	2	no	—
522	C₂×C₄×C₆₇	—	8	1	no	—
523	C₂×C₄×C₆₇	—	8	1	no	—
524	C₂×C₄×C₆₇	—	8	2	no	—
525	C₂×C₄×C₆₇	—	8	1	no	—
526	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
533	C₈×C₆₇	—	2	2	no	—
534	C₈×C₆₇	—	2	2	no	—
535	C₈×C₆₇	—	2	2	no	—
536	C₈×C₆₇	—	2	2	no	—
537	C₂²×C₆₇	—	2	1	no	—
538	C₂²×C₆₇	—	2	1	no	—
539	C₂²×C₆₇	—	2	1	no	—
540	C₂²×C₆₇	—	2	1	no	—
541	C₂²×C₆₇	—	2	2	no	—
542	C₂²×C₆₇	—	2	1	no	—
543	C₂²×C₆₇	—	2	2	no	—
544	C₂²×C₆₇	—	2	2	no	—
545	C₂²×C₆₇	—	2	1	no	—
546	C₂²×C₆₇	—	2	2	no	—
547	C₂²×C₆₇	—	2	1	no	—
548	C₂²×C₆₇	—	2	1	no	—
549	C₂²×C₆₇	—	4	1	no	—
550	C₂²×C₆₇	—	4	1	no	—
551	C₂²×C₆₇	—	4	1	no	—
552	C₂²×C₆₇	—	4	1	no	—
553	C₂²×C₆₇	—	4	1	no	—
554	C₂²×C₆₇	—	8	2	no	—
555	C₂²×C₆₇	—	8	4	no	—
556	C₂²×C₆₇	#578	1	2	yes	—
557	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
558	C₄×C₆₇	—	2	2	no	—
559	C₄×C₆₇	—	2	1	no	—
560	C₄×C₆₇	—	2	2	no	—
561	C₄×C₆₇	—	2	1	no	—
562	C₄×C₆₇	—	2	1	no	—
563	C₄×C₆₇	—	2	2	no	—
564	C₄×C₆₇	—	2	2	no	—
565	C₄×C₆₇	—	4	2	no	—
566	C₄×C₆₇	—	4	2	no	—
567	C₄×C₆₇	—	4	1	no	—
568	C₄×C₆₇	—	4	2	no	—
569	C₄×C₆₇	—	4	2	no	—
570	C₄×C₆₇	—	4	2	no	—
571	C₄×C₆₇	—	4	2	no	—
572	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
573	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
574	#61622	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
575	C₂×C₆₇	—	2	2	no	—
576	C₂×C₆₇	—	4	2	no	—
577	C₂×C₆₇	—	4	1	no	—
578	C₂×C₆₇	—	4	1	no	—
579	C₂×C₆₇	—	4	2	no	—
580	C₂×C₆₇	—	8	1	no	—
581	C₂×C₆₇	#3484	1	1	yes	characteristic
582	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
583	C₂×C₆₇	#3586	1	1	yes	characteristic
584	#3538	C₂×C₆₇	1	1	yes	characteristic, complemented
585	#3489	C₂×C₆₇	1	1	yes	characteristic
586	#3327	C₂×C₆₇	1	2	yes	complemented
587	#3315	C₂×C₆₇	1	2	yes	complemented
588	#3312	C₂×C₆₇	1	2	yes	complemented
589	#3296	C₂×C₆₇	1	2	yes	complemented
590	D₄×Q₁₆	C₂×C₆₇	1	2	yes	complemented
591	#3276	C₂×C₆₇	1	2	yes	complemented
592	#3270	C₂×C₆₇	1	2	yes	complemented
593	#3266	C₂×C₆₇	1	2	yes	complemented
594	#3223	C₂×C₆₇	1	2	yes	complemented
595	#3201	C₂×C₆₇	1	2	yes	complemented
596	#3195	C₂×C₆₇	1	1	yes	characteristic, complemented
597	#3189	C₂×C₆₇	1	1	yes	characteristic, complemented
598	#3120	C₂×C₆₇	1	2	yes	complemented
599	#3011	C₂×C₆₇	1	2	yes	complemented
600	#3007	C₂×C₆₇	1	1	yes	characteristic, complemented
601	C₂×#452	C₂×C₆₇	1	1	yes	characteristic, complemented
602	#2976	C₂×C₆₇	1	1	yes	characteristic, complemented
603	C₆₇	#61622	1	1	yes	characteristic, direct product factor, Sylow
604	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
605	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
606	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
607	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
608	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
609	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
610	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
611	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
612	#563	—	2	2	no	—
613	#552	C₂²×C₆₇	1	2	yes	—
614	#552	C₂²×C₆₇	1	2	yes	complemented
615	#551	—	2	2	no	—
616	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
617	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
618	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
619	#548	C₂²×C₆₇	1	2	yes	—
620	#547	—	2	2	no	—
621	#547	C₂²×C₆₇	1	2	yes	—
622	#546	—	2	2	no	—
623	#546	C₂²×C₆₇	1	2	yes	—
624	#544	—	2	1	no	—
625	#544	—	2	1	no	—
626	#541	C₂²×C₆₇	1	2	yes	complemented
627	#539	—	2	1	no	—
628	#539	—	2	1	no	—
629	#537	—	2	1	no	—
630	#537	C₂²×C₆₇	1	1	yes	characteristic
631	#536	—	2	1	no	—
632	#536	C₂²×C₆₇	1	1	yes	characteristic
633	#536	C₂²×C₆₇	1	2	yes	complemented
634	#525	—	2	1	no	—
635	#525	C₂²×C₆₇	1	1	yes	characteristic
636	C₂×C₂²⋊Q₈	—	2	1	no	—
637	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
638	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
639	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
640	#520	C₂²×C₆₇	1	1	yes	characteristic
641	#497	C₂²×C₆₇	1	2	yes	complemented
642	#494	C₂²×C₆₇	1	2	yes	complemented
643	#491	C₂²×C₆₇	1	2	yes	complemented
644	#488	C₂²×C₆₇	1	2	yes	complemented
645	#485	C₂²×C₆₇	1	2	yes	complemented
646	#484	C₂²×C₆₇	1	2	yes	complemented
647	#484	C₂²×C₆₇	1	2	yes	complemented
648	#483	C₂²×C₆₇	1	2	yes	—
649	#483	C₂²×C₆₇	1	2	yes	complemented
650	#482	C₂²×C₆₇	1	2	yes	complemented
651	#479	C₂²×C₆₇	1	2	yes	complemented
652	#478	C₂²×C₆₇	1	2	yes	complemented
653	#470	C₂²×C₆₇	1	2	yes	complemented
654	#470	C₂²×C₆₇	1	2	yes	complemented
655	#470	C₂²×C₆₇	1	2	yes	complemented
656	#468	C₂²×C₆₇	1	2	yes	complemented
657	#467	C₂²×C₆₇	1	2	yes	—
658	#467	C₂²×C₆₇	1	2	yes	—
659	#467	C₂²×C₆₇	1	2	yes	complemented
660	#465	C₂²×C₆₇	1	2	yes	complemented
661	#464	C₂²×C₆₇	1	2	yes	complemented
662	#464	C₂²×C₆₇	1	2	yes	complemented
663	#462	C₂²×C₆₇	1	2	yes	complemented
664	#462	C₂²×C₆₇	1	2	yes	complemented
665	#462	C₂²×C₆₇	1	2	yes	complemented
666	#461	C₂²×C₆₇	1	2	yes	complemented
667	#452	C₂²×C₆₇	1	2	yes	—
668	#452	C₂²×C₆₇	1	2	yes	—
669	#452	C₂²×C₆₇	1	2	yes	—
670	#452	C₂²×C₆₇	1	2	yes	—
671	#452	C₂²×C₆₇	1	2	yes	—
672	#452	C₂²×C₆₇	1	2	yes	—
673	#452	C₂²×C₆₇	1	2	yes	complemented
674	#452	C₂²×C₆₇	1	2	yes	complemented
675	#451	C₂²×C₆₇	1	2	yes	—
676	#451	C₂²×C₆₇	1	2	yes	—
677	#451	C₂²×C₆₇	1	2	yes	complemented
678	#451	C₂²×C₆₇	1	2	yes	complemented
679	#451	C₂²×C₆₇	1	2	yes	complemented
680	#451	C₂²×C₆₇	1	2	yes	complemented
681	#451	C₂²×C₆₇	1	2	yes	complemented
682	#451	C₂²×C₆₇	1	2	yes	complemented
683	#450	C₂²×C₆₇	1	2	yes	—
684	#448	C₂²×C₆₇	1	2	yes	complemented
685	#441	C₂²×C₆₇	1	2	yes	complemented
686	#440	C₂²×C₆₇	1	2	yes	complemented
687	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
688	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
689	#436	C₂²×C₆₇	1	2	yes	complemented
690	#435	C₂²×C₆₇	1	2	yes	—
691	#435	C₂²×C₆₇	1	2	yes	complemented
692	C₈×D₄	C₂²×C₆₇	1	2	yes	—
693	#433	C₂²×C₆₇	1	2	yes	complemented
694	#419	C₂²×C₆₇	1	2	yes	complemented
695	#417	C₂²×C₆₇	1	1	yes	characteristic
696	#417	C₂²×C₆₇	1	1	yes	characteristic
697	#416	C₂²×C₆₇	1	2	yes	complemented
698	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
699	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
700	#408	C₂²×C₆₇	1	2	yes	complemented
701	#407	C₂²×C₆₇	1	1	yes	characteristic
702	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
703	2₋¹⁺⁴	—	4	2	no	—
704	2₋¹⁺⁴	—	4	2	no	—
705	C₂×#41	—	2	1	no	—
706	C₂×#41	—	2	2	no	—
707	C₂×#41	—	2	1	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	—	4	2	no	—
710	C₂×#41	—	4	2	no	—
711	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
712	C₂×#41	C₂³×C₆₇	1	2	yes	—
713	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
714	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
715	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
716	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
717	C₂²×Q₈	—	2	1	no	—
718	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
719	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
720	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
721	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
722	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
723	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
724	C₂²×D₄	—	2	1	no	—
725	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
726	C₂³×C₄	—	2	1	no	—
727	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
728	#137	—	4	2	no	—
729	#137	—	4	4	no	—
730	#137	—	4	2	no	—
731	C₂×Q₁₆	—	4	2	no	—
732	C₂×Q₁₆	—	4	4	no	—
733	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
734	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
735	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
736	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
737	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
738	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
739	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
740	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
741	C₂×SD₁₆	—	4	2	no	—
742	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
746	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
747	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
748	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
749	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
750	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
751	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
752	C₄⋊Q₈	—	2	2	no	—
753	C₄⋊Q₈	—	2	2	no	—
754	C₄⋊Q₈	—	2	2	no	—
755	C₄⋊Q₈	—	2	2	no	—
756	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
757	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#126	—	2	2	no	—
762	#125	—	2	2	no	—
763	#125	—	2	2	no	—
764	#125	—	2	2	no	—
765	#125	—	2	2	no	—
766	#125	C₂³×C₆₇	1	2	yes	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	C₂³×C₆₇	1	2	yes	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	D₄×C₆₇	1	2	yes	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
796	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
797	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
798	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
799	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
803	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
804	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
805	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	D₄×C₆₇	1	1	yes	characteristic
812	#121	D₄×C₆₇	1	1	yes	characteristic
813	#121	C₂³×C₆₇	1	2	yes	—
814	#120	—	2	2	no	—
815	#120	D₄×C₆₇	1	2	yes	—
816	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
817	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
818	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	C₂³×C₆₇	1	2	yes	—
825	C₄×D₄	C₂³×C₆₇	1	2	yes	—
826	C₄×D₄	C₂³×C₆₇	1	2	yes	—
827	#117	—	2	1	no	—
828	#117	—	2	2	no	—
829	#117	—	2	2	no	—
830	#117	C₂³×C₆₇	1	2	yes	—
831	#117	C₂³×C₆₇	1	1	yes	characteristic
832	C₂×C₄⋊C₄	—	2	1	no	—
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	—	2	2	no	—
837	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
838	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
840	C₂×C₂²⋊C₄	—	2	1	no	—
841	C₂×C₂²⋊C₄	—	2	1	no	—
842	C₂×C₂²⋊C₄	—	2	1	no	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	#107	C₂³×C₆₇	1	2	yes	—
845	#107	C₂³×C₆₇	1	2	yes	—
846	#106	C₂³×C₆₇	1	2	yes	—
847	#106	C₂³×C₆₇	1	2	yes	—
848	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
849	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
850	#103	C₂³×C₆₇	1	2	yes	—
851	#103	C₂³×C₆₇	1	2	yes	—
852	#103	C₂³×C₆₇	1	2	yes	—
853	#103	C₂³×C₆₇	1	2	yes	—
854	#103	C₂³×C₆₇	1	2	yes	—
855	#103	C₂³×C₆₇	1	2	yes	—
856	#103	C₂³×C₆₇	1	2	yes	—
857	#103	C₂³×C₆₇	1	2	yes	—
858	#103	C₂³×C₆₇	1	2	yes	—
859	#103	C₂³×C₆₇	1	2	yes	—
860	#103	C₂³×C₆₇	1	2	yes	—
861	#103	C₂³×C₆₇	1	2	yes	—
862	#102	C₂³×C₆₇	1	2	yes	—
863	#102	C₂³×C₆₇	1	2	yes	—
864	#102	C₂³×C₆₇	1	2	yes	—
865	#102	C₂³×C₆₇	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
872	#97	C₂³×C₆₇	1	2	yes	—
873	C₄×C₈	C₂³×C₆₇	1	2	yes	—
874	C₂⁴	—	2	1	no	—
875	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
876	#41	—	2	2	no	—
877	#41	—	2	2	no	—
878	#41	—	2	2	no	—
879	#41	—	2	2	no	—
880	#41	—	2	4	no	—
881	#41	—	4	1	no	—
882	#41	—	4	1	no	—
883	#41	—	4	1	no	—
884	#41	—	4	1	no	—
885	#41	—	4	1	no	—
886	#41	—	4	1	no	—
887	#41	—	4	2	no	—
888	#41	—	4	4	no	—
889	#41	—	4	4	no	—
890	#41	—	4	4	no	—
891	#41	—	4	8	no	—
892	C₂×Q₈	—	2	1	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	2	2	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	4	no	—
900	C₂×Q₈	—	4	1	no	—
901	C₂×Q₈	—	4	2	no	—
902	C₂×Q₈	—	4	1	no	—
903	C₂×Q₈	—	4	1	no	—
904	C₂×Q₈	—	4	4	no	—
905	C₂×Q₈	—	4	1	no	—
906	C₂×Q₈	—	4	1	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	4	1	no	—
909	C₂×Q₈	—	4	1	no	—
910	C₂×Q₈	—	4	2	no	—
911	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
916	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	4	1	no	—
926	C₂×D₄	—	4	4	no	—
927	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
928	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
929	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
930	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
931	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
932	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	4	1	no	—
949	C₂²×C₄	—	4	1	no	—
950	C₂²×C₄	—	4	4	no	—
951	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
953	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
958	Q₁₆	—	2	4	no	—
959	Q₁₆	—	2	4	no	—
960	Q₁₆	—	4	2	no	—
961	Q₁₆	—	4	2	no	—
962	Q₁₆	—	4	2	no	—
963	Q₁₆	—	4	2	no	—
964	Q₁₆	—	4	2	no	—
965	Q₁₆	—	4	2	no	—
966	SD₁₆	—	2	4	no	—
967	SD₁₆	—	2	4	no	—
968	SD₁₆	—	4	2	no	—
969	SD₁₆	—	4	2	no	—
970	M₁₆	—	4	2	no	—
971	M₁₆	—	4	1	no	—
972	M₁₆	—	4	1	no	—
973	C₂×C₈	—	4	1	no	—
974	C₂×C₈	—	4	1	no	—
975	C₂×C₈	—	4	2	no	—
976	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
977	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
978	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
979	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1002	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1003	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1004	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1005	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1006	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1007	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	C₂⁴×C₆₇	1	2	yes	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	4	1	no	—
1036	C₂³	—	4	1	no	—
1037	C₂³	—	4	2	no	—
1038	C₂³	—	4	2	no	—
1039	C₂³	—	8	1	no	—
1040	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1041	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1042	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1043	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1044	Q₈	—	2	1	no	—
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	4	1	no	—
1054	Q₈	—	4	4	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	4	2	no	—
1057	Q₈	—	8	1	no	—
1058	Q₈	—	8	1	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1061	D₄	—	2	4	no	—
1062	D₄	—	2	4	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	4	1	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	4	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1076	C₂×C₄	—	2	4	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	4	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	1	no	—
1107	C₂×C₄	—	8	2	no	—
1108	C₂×C₄	—	8	1	no	—
1109	C₂×C₄	—	8	1	no	—
1110	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1115	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1116	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1117	C₈	—	2	2	no	—
1118	C₈	—	2	2	no	—
1119	C₈	—	2	2	no	—
1120	C₈	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	8	2	no	—
1139	C₂²	—	8	4	no	—
1140	C₂²	#578×C₆₇	1	2	yes	—
1141	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1142	C₄	—	2	2	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	4	2	no	—
1150	C₄	—	4	2	no	—
1151	C₄	—	4	2	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	2	no	—
1154	C₄	—	4	2	no	—
1155	C₄	—	4	2	no	—
1156	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1157	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1158	C₂	—	2	2	no	—
1159	C₂	—	4	1	no	—
1160	C₂	—	4	1	no	—
1161	C₂	—	4	2	no	—
1162	C₂	—	4	2	no	—
1163	C₂	—	8	1	no	—
1164	C₂	C₆₇×#3484	1	1	yes	characteristic
1165	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
1166	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×#3489	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3538	C₂	semidirect
3. C₆₇×#3327	C₂	semidirect
4. C₆₇×#3315	C₂	semidirect
5. C₆₇×#3312	C₂	semidirect
6. C₆₇×#3296	C₂	semidirect
7. D₄×Q₁₆×C₆₇	C₂	semidirect
8. C₆₇×#3276	C₂	semidirect
9. C₆₇×#3270	C₂	semidirect
10. C₆₇×#3266	C₂	semidirect
11. C₆₇×#3223	C₂	semidirect
12. C₆₇×#3201	C₂	semidirect
13. C₆₇×#3195	C₂	semidirect
14. C₆₇×#3189	C₂	semidirect
15. C₆₇×#3120	C₂	semidirect
16. C₆₇×#3011	C₂	semidirect
17. C₆₇×#3007	C₂	semidirect
18. C₂×#452×C₆₇	C₂	semidirect
19. C₆₇×#2976	C₂	semidirect
24. C₂×#137×C₆₇	C₂²	semidirect
26. C₂²×Q₁₆×C₆₇	C₂²	semidirect
30. #552×C₆₇	C₂²	semidirect
34. D₄×Q₈×C₆₇	C₂²	semidirect
42. #541×C₆₇	C₂²	semidirect
49. #536×C₆₇	C₂²	semidirect
57. #497×C₆₇	C₂²	semidirect
58. #494×C₆₇	C₂²	semidirect
59. #491×C₆₇	C₂²	semidirect
60. #488×C₆₇	C₂²	semidirect
61. #485×C₆₇	C₂²	semidirect
62. #484×C₆₇	C₂²	semidirect
63. #484×C₆₇	C₂²	semidirect
65. #483×C₆₇	C₂²	semidirect
66. #482×C₆₇	C₂²	semidirect
67. #479×C₆₇	C₂²	semidirect
68. #478×C₆₇	C₂²	semidirect
69. #470×C₆₇	C₂²	semidirect
70. #470×C₆₇	C₂²	semidirect
71. #470×C₆₇	C₂²	semidirect
72. #468×C₆₇	C₂²	semidirect
75. #467×C₆₇	C₂²	semidirect
76. #465×C₆₇	C₂²	semidirect
77. #464×C₆₇	C₂²	semidirect
78. #464×C₆₇	C₂²	semidirect
79. #462×C₆₇	C₂²	semidirect
80. #462×C₆₇	C₂²	semidirect
81. #462×C₆₇	C₂²	semidirect
82. #461×C₆₇	C₂²	semidirect
89. #452×C₆₇	C₂²	semidirect
90. #452×C₆₇	C₂²	semidirect
93. #451×C₆₇	C₂²	semidirect
94. #451×C₆₇	C₂²	semidirect
95. #451×C₆₇	C₂²	semidirect
96. #451×C₆₇	C₂²	semidirect
97. #451×C₆₇	C₂²	semidirect
98. #451×C₆₇	C₂²	semidirect
100. #448×C₆₇	C₂²	semidirect
101. #441×C₆₇	C₂²	semidirect
102. #440×C₆₇	C₂²	semidirect
103. C₄×Q₁₆×C₆₇	C₂²	semidirect
104. C₄×SD₁₆×C₆₇	C₂²	semidirect
105. #436×C₆₇	C₂²	semidirect
107. #435×C₆₇	C₂²	semidirect
109. #433×C₆₇	C₂²	semidirect
110. #419×C₆₇	C₂²	semidirect
113. #416×C₆₇	C₂²	semidirect
116. #408×C₆₇	C₂²	semidirect
574. #61622	C₆₇	direct (N × H)
584. #3538	C₂×C₆₇	semidirect
586. #3327	C₂×C₆₇	semidirect
587. #3315	C₂×C₆₇	semidirect
588. #3312	C₂×C₆₇	semidirect
589. #3296	C₂×C₆₇	semidirect
590. D₄×Q₁₆	C₂×C₆₇	semidirect
591. #3276	C₂×C₆₇	semidirect
592. #3270	C₂×C₆₇	semidirect
593. #3266	C₂×C₆₇	semidirect
594. #3223	C₂×C₆₇	semidirect
595. #3201	C₂×C₆₇	semidirect
596. #3195	C₂×C₆₇	semidirect
597. #3189	C₂×C₆₇	semidirect
598. #3120	C₂×C₆₇	semidirect
599. #3011	C₂×C₆₇	semidirect
600. #3007	C₂×C₆₇	semidirect
601. C₂×#452	C₂×C₆₇	semidirect
602. #2976	C₂×C₆₇	semidirect
603. C₆₇	#61622	direct (N × H)
608. C₂×#137	C₂²×C₆₇	semidirect
610. C₂²×Q₁₆	C₂²×C₆₇	semidirect
614. #552	C₂²×C₆₇	semidirect
618. D₄×Q₈	C₂²×C₆₇	semidirect
626. #541	C₂²×C₆₇	semidirect
633. #536	C₂²×C₆₇	semidirect
641. #497	C₂²×C₆₇	semidirect
642. #494	C₂²×C₆₇	semidirect
643. #491	C₂²×C₆₇	semidirect
644. #488	C₂²×C₆₇	semidirect
645. #485	C₂²×C₆₇	semidirect
646. #484	C₂²×C₆₇	semidirect
647. #484	C₂²×C₆₇	semidirect
649. #483	C₂²×C₆₇	semidirect
650. #482	C₂²×C₆₇	semidirect
651. #479	C₂²×C₆₇	semidirect
652. #478	C₂²×C₆₇	semidirect
653. #470	C₂²×C₆₇	semidirect
654. #470	C₂²×C₆₇	semidirect
655. #470	C₂²×C₆₇	semidirect
656. #468	C₂²×C₆₇	semidirect
659. #467	C₂²×C₆₇	semidirect
660. #465	C₂²×C₆₇	semidirect
661. #464	C₂²×C₆₇	semidirect
662. #464	C₂²×C₆₇	semidirect
663. #462	C₂²×C₆₇	semidirect
664. #462	C₂²×C₆₇	semidirect
665. #462	C₂²×C₆₇	semidirect
666. #461	C₂²×C₆₇	semidirect
673. #452	C₂²×C₆₇	semidirect
674. #452	C₂²×C₆₇	semidirect
677. #451	C₂²×C₆₇	semidirect
678. #451	C₂²×C₆₇	semidirect
679. #451	C₂²×C₆₇	semidirect
680. #451	C₂²×C₆₇	semidirect
681. #451	C₂²×C₆₇	semidirect
682. #451	C₂²×C₆₇	semidirect
684. #448	C₂²×C₆₇	semidirect
685. #441	C₂²×C₆₇	semidirect
686. #440	C₂²×C₆₇	semidirect
687. C₄×Q₁₆	C₂²×C₆₇	semidirect
688. C₄×SD₁₆	C₂²×C₆₇	semidirect
689. #436	C₂²×C₆₇	semidirect
691. #435	C₂²×C₆₇	semidirect
693. #433	C₂²×C₆₇	semidirect
694. #419	C₂²×C₆₇	semidirect
697. #416	C₂²×C₆₇	semidirect
700. #408	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3538	2
C₆₇×#3489	2
C₆₇×#3327	2
C₆₇×#3315	2
C₆₇×#3312	2
C₆₇×#3296	2
D₄×Q₁₆×C₆₇	2
C₆₇×#3276	2
C₆₇×#3270	2
C₆₇×#3266	2
C₆₇×#3223	2
C₆₇×#3201	2
C₆₇×#3195	2
C₆₇×#3189	2
C₆₇×#3120	2
C₆₇×#3011	2
C₆₇×#3007	2
C₂×#452×C₆₇	2
C₆₇×#2976	2
#61622	67

Subgroups — C67×#61622 #30740873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61622 #30740873