Subgroups — C₆₇×#61742 #30740993

Order 17152.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3475	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3356	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3346	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3344	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3329	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3320	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3312	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3299	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3298	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3237	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3231	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3196	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3190	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3095	C₂	1	2	yes	maximal, complemented
22	C₂×#485×C₆₇	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	#556×C₆₇	C₂²	1	1	yes	characteristic
25	#555×C₆₇	C₂²	1	1	yes	characteristic
26	#554×C₆₇	—	2	1	no	—
27	#554×C₆₇	—	2	2	no	—
28	#554×C₆₇	—	2	1	no	—
29	#554×C₆₇	C₂²	1	1	yes	characteristic
30	#554×C₆₇	C₂²	1	1	yes	characteristic
31	#554×C₆₇	C₂²	1	2	yes	—
32	#554×C₆₇	C₂²	1	1	yes	characteristic
33	#553×C₆₇	C₂²	1	2	yes	—
34	#552×C₆₇	—	2	1	no	—
35	#552×C₆₇	C₂²	1	2	yes	—
36	#551×C₆₇	—	2	2	no	—
37	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
39	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
40	#547×C₆₇	C₂²	1	1	yes	characteristic
41	#546×C₆₇	—	2	1	no	—
42	#544×C₆₇	—	2	1	no	—
43	#543×C₆₇	—	2	2	no	—
44	#533×C₆₇	C₂²	1	1	yes	characteristic
45	#533×C₆₇	C₂²	1	1	yes	characteristic
46	#533×C₆₇	C₂²	1	1	yes	characteristic
47	#529×C₆₇	—	2	2	no	—
48	#529×C₆₇	—	2	1	no	—
49	#525×C₆₇	C₂²	1	2	yes	—
50	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
51	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
52	#518×C₆₇	—	2	1	no	—
53	C₄×#41×C₆₇	—	2	1	no	—
54	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
56	C₂×#117×C₆₇	C₂²	1	2	yes	—
57	#501×C₆₇	C₂²	1	2	yes	complemented
58	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#491×C₆₇	C₂²	1	2	yes	complemented
61	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#485×C₆₇	C₂²	1	1	yes	characteristic
64	#485×C₆₇	C₂²	1	2	yes	—
65	#485×C₆₇	C₂²	1	2	yes	—
66	#485×C₆₇	C₂²	1	2	yes	—
67	#485×C₆₇	C₂²	1	1	yes	characteristic
68	#485×C₆₇	C₂²	1	2	yes	—
69	#485×C₆₇	C₂²	1	2	yes	—
70	#485×C₆₇	C₂²	1	2	yes	complemented
71	#485×C₆₇	C₂²	1	2	yes	complemented
72	#485×C₆₇	C₂²	1	2	yes	complemented
73	#485×C₆₇	C₂²	1	2	yes	complemented
74	#484×C₆₇	C₂²	1	2	yes	complemented
75	#484×C₆₇	C₂²	1	2	yes	complemented
76	#484×C₆₇	C₂²	1	2	yes	complemented
77	#483×C₆₇	C₂²	1	2	yes	complemented
78	#483×C₆₇	C₂²	1	2	yes	complemented
79	#483×C₆₇	C₂²	1	2	yes	complemented
80	#481×C₆₇	C₂²	1	2	yes	complemented
81	#480×C₆₇	C₂²	1	2	yes	complemented
82	#479×C₆₇	C₂²	1	2	yes	complemented
83	#479×C₆₇	C₂²	1	2	yes	complemented
84	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#470×C₆₇	C₂²	1	2	yes	complemented
93	#470×C₆₇	C₂²	1	2	yes	complemented
94	#468×C₆₇	C₂²	1	2	yes	complemented
95	#468×C₆₇	C₂²	1	2	yes	complemented
96	#467×C₆₇	C₂²	1	2	yes	complemented
97	#467×C₆₇	C₂²	1	2	yes	complemented
98	#465×C₆₇	C₂²	1	2	yes	complemented
99	#465×C₆₇	C₂²	1	2	yes	complemented
100	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	#452×C₆₇	C₂²	1	1	yes	characteristic
105	#452×C₆₇	C₂²	1	1	yes	characteristic
106	#452×C₆₇	C₂²	1	2	yes	—
107	#451×C₆₇	C₂²	1	2	yes	complemented
108	#451×C₆₇	C₂²	1	2	yes	complemented
109	#448×C₆₇	C₂²	1	2	yes	complemented
110	#448×C₆₇	C₂²	1	2	yes	complemented
111	#441×C₆₇	C₂²	1	2	yes	complemented
112	#440×C₆₇	C₂²	1	2	yes	complemented
113	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#436×C₆₇	C₂²	1	1	yes	characteristic
118	#436×C₆₇	C₂²	1	1	yes	characteristic
119	#435×C₆₇	C₂²	1	2	yes	—
120	#435×C₆₇	C₂²	1	2	yes	—
121	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
123	#432×C₆₇	C₂²	1	1	yes	characteristic
124	#431×C₆₇	C₂²	1	1	yes	characteristic
125	#428×C₆₇	C₂²	1	2	yes	complemented
126	#428×C₆₇	C₂²	1	2	yes	complemented
127	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
128	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
129	#419×C₆₇	C₂²	1	2	yes	complemented
130	#419×C₆₇	C₂²	1	2	yes	complemented
131	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
132	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
133	#407×C₆₇	C₂²	1	2	yes	—
134	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
135	C₂×#41×C₆₇	—	2	1	no	—
136	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
138	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
150	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
151	C₄⋊Q₈×C₆₇	—	2	1	no	—
152	C₄⋊Q₈×C₆₇	—	2	1	no	—
153	C₄⋊Q₈×C₆₇	—	2	2	no	—
154	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
160	#126×C₆₇	—	2	2	no	—
161	#126×C₆₇	—	2	2	no	—
162	#126×C₆₇	—	2	2	no	—
163	#125×C₆₇	—	2	2	no	—
164	#125×C₆₇	—	2	1	no	—
165	#125×C₆₇	—	2	1	no	—
166	#125×C₆₇	—	2	1	no	—
167	#125×C₆₇	—	2	2	no	—
168	#125×C₆₇	—	2	1	no	—
169	#125×C₆₇	—	2	1	no	—
170	#125×C₆₇	C₂³	1	2	yes	—
171	#124×C₆₇	—	2	1	no	—
172	#124×C₆₇	—	2	2	no	—
173	#123×C₆₇	—	2	2	no	—
174	#123×C₆₇	—	2	2	no	—
175	#123×C₆₇	—	2	2	no	—
176	#123×C₆₇	—	2	2	no	—
177	C₂²⋊Q₈×C₆₇	—	2	2	no	—
178	C₂²⋊Q₈×C₆₇	—	2	2	no	—
179	C₂²⋊Q₈×C₆₇	—	2	2	no	—
180	C₂²⋊Q₈×C₆₇	—	2	2	no	—
181	C₂²⋊Q₈×C₆₇	—	2	1	no	—
182	C₂²⋊Q₈×C₆₇	—	2	1	no	—
183	C₂²⋊Q₈×C₆₇	—	2	1	no	—
184	C₂²⋊Q₈×C₆₇	—	2	1	no	—
185	C₂²⋊Q₈×C₆₇	—	2	1	no	—
186	C₂²⋊Q₈×C₆₇	—	2	2	no	—
187	C₂²⋊Q₈×C₆₇	—	2	2	no	—
188	C₂²⋊Q₈×C₆₇	—	2	2	no	—
189	C₂²⋊Q₈×C₆₇	—	2	2	no	—
190	C₂²⋊Q₈×C₆₇	—	2	2	no	—
191	C₂²⋊Q₈×C₆₇	—	2	2	no	—
192	C₂²⋊Q₈×C₆₇	—	2	2	no	—
193	C₂²⋊Q₈×C₆₇	—	2	2	no	—
194	C₂²⋊Q₈×C₆₇	—	2	2	no	—
195	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
198	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
199	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
203	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
204	#121×C₆₇	—	2	2	no	—
205	#121×C₆₇	—	2	1	no	—
206	#121×C₆₇	C₂³	1	2	yes	—
207	#121×C₆₇	C₂³	1	2	yes	—
208	#120×C₆₇	—	2	2	no	—
209	C₄×Q₈×C₆₇	—	2	1	no	—
210	C₄×Q₈×C₆₇	—	2	1	no	—
211	C₄×Q₈×C₆₇	—	2	1	no	—
212	C₄×Q₈×C₆₇	—	2	1	no	—
213	C₄×Q₈×C₆₇	—	2	1	no	—
214	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
219	C₄×D₄×C₆₇	—	2	1	no	—
220	C₄×D₄×C₆₇	—	2	2	no	—
221	C₄×D₄×C₆₇	—	2	1	no	—
222	C₄×D₄×C₆₇	—	2	1	no	—
223	C₄×D₄×C₆₇	—	2	2	no	—
224	C₄×D₄×C₆₇	—	2	1	no	—
225	C₄×D₄×C₆₇	—	2	1	no	—
226	C₄×D₄×C₆₇	—	2	2	no	—
227	C₄×D₄×C₆₇	—	2	1	no	—
228	C₄×D₄×C₆₇	—	2	1	no	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	—	2	2	no	—
231	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
232	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
233	C₄×D₄×C₆₇	D₄	1	2	yes	—
234	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₆₇	C₂³	1	2	yes	—
238	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
239	#117×C₆₇	—	2	2	no	—
240	#117×C₆₇	—	2	2	no	—
241	#117×C₆₇	—	2	1	no	—
242	#117×C₆₇	—	2	1	no	—
243	#117×C₆₇	—	2	1	no	—
244	#117×C₆₇	—	2	2	no	—
245	#117×C₆₇	—	2	1	no	—
246	#117×C₆₇	C₂³	1	1	yes	characteristic
247	#117×C₆₇	C₂³	1	2	yes	—
248	#117×C₆₇	C₂³	1	2	yes	—
249	#117×C₆₇	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
251	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
252	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
257	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
258	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
261	C₂×C₄²×C₆₇	—	2	2	no	—
262	C₂×C₄²×C₆₇	—	2	1	no	—
263	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
264	#107×C₆₇	C₂³	1	2	yes	—
265	#107×C₆₇	C₂³	1	2	yes	—
266	#107×C₆₇	C₂³	1	2	yes	—
267	#107×C₆₇	C₂³	1	2	yes	—
268	#107×C₆₇	C₂³	1	1	yes	characteristic
269	#107×C₆₇	C₂³	1	1	yes	characteristic
270	#107×C₆₇	C₂³	1	2	yes	—
271	#106×C₆₇	C₂³	1	2	yes	—
272	#106×C₆₇	C₂³	1	2	yes	—
273	#106×C₆₇	C₂³	1	2	yes	—
274	#106×C₆₇	C₂³	1	2	yes	—
275	#106×C₆₇	C₂³	1	1	yes	characteristic
276	#106×C₆₇	C₂³	1	1	yes	characteristic
277	#106×C₆₇	C₂³	1	2	yes	—
278	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	#103×C₆₇	C₂³	1	2	yes	—
283	#103×C₆₇	C₂³	1	2	yes	—
284	#103×C₆₇	C₂³	1	2	yes	—
285	#103×C₆₇	C₂³	1	2	yes	—
286	#103×C₆₇	C₂³	1	2	yes	—
287	#103×C₆₇	C₂³	1	2	yes	—
288	#103×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
299	#102×C₆₇	C₂³	1	1	yes	characteristic
300	#102×C₆₇	C₂³	1	2	yes	—
301	#102×C₆₇	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
303	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
309	#97×C₆₇	C₂³	1	2	yes	—
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
312	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
313	#41×C₆₇	—	4	1	no	—
314	#41×C₆₇	—	4	1	no	—
315	#41×C₆₇	—	4	4	no	—
316	C₂×Q₈×C₆₇	—	2	1	no	—
317	C₂×Q₈×C₆₇	—	2	1	no	—
318	C₂×Q₈×C₆₇	—	2	1	no	—
319	C₂×Q₈×C₆₇	—	2	1	no	—
320	C₂×Q₈×C₆₇	—	2	2	no	—
321	C₂×Q₈×C₆₇	—	2	2	no	—
322	C₂×Q₈×C₆₇	—	4	2	no	—
323	C₂×Q₈×C₆₇	—	4	2	no	—
324	C₂×Q₈×C₆₇	—	4	2	no	—
325	C₂×Q₈×C₆₇	—	4	2	no	—
326	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₆₇	—	2	4	no	—
331	C₂×D₄×C₆₇	—	2	1	no	—
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	2	no	—
334	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₆₇	—	2	2	no	—
339	C₂²×C₄×C₆₇	—	2	2	no	—
340	C₂²×C₄×C₆₇	—	2	2	no	—
341	C₂²×C₄×C₆₇	—	2	2	no	—
342	C₂²×C₄×C₆₇	—	2	2	no	—
343	C₂²×C₄×C₆₇	—	2	2	no	—
344	C₂²×C₄×C₆₇	—	2	1	no	—
345	C₂²×C₄×C₆₇	—	2	1	no	—
346	C₂²×C₄×C₆₇	—	2	1	no	—
347	C₂²×C₄×C₆₇	—	4	2	no	—
348	C₂²×C₄×C₆₇	—	4	2	no	—
349	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
351	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
353	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
354	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
357	Q₁₆×C₆₇	—	4	1	no	—
358	Q₁₆×C₆₇	—	4	2	no	—
359	Q₁₆×C₆₇	—	4	1	no	—
360	SD₁₆×C₆₇	—	4	1	no	—
361	SD₁₆×C₆₇	—	4	2	no	—
362	SD₁₆×C₆₇	—	4	1	no	—
363	M₁₆×C₆₇	—	4	2	no	—
364	M₁₆×C₆₇	—	4	2	no	—
365	C₂×C₈×C₆₇	—	4	2	no	—
366	C₂×C₈×C₆₇	—	4	2	no	—
367	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
368	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
372	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₆₇	—	2	1	no	—
374	C₄⋊C₄×C₆₇	—	2	2	no	—
375	C₄⋊C₄×C₆₇	—	2	1	no	—
376	C₄⋊C₄×C₆₇	—	2	2	no	—
377	C₄⋊C₄×C₆₇	—	2	2	no	—
378	C₄⋊C₄×C₆₇	—	2	2	no	—
379	C₄⋊C₄×C₆₇	—	2	2	no	—
380	C₄⋊C₄×C₆₇	—	2	2	no	—
381	C₄⋊C₄×C₆₇	—	2	2	no	—
382	C₄⋊C₄×C₆₇	—	2	2	no	—
383	C₄⋊C₄×C₆₇	—	2	2	no	—
384	C₄⋊C₄×C₆₇	—	2	1	no	—
385	C₄⋊C₄×C₆₇	—	2	1	no	—
386	C₄⋊C₄×C₆₇	—	2	1	no	—
387	C₄⋊C₄×C₆₇	—	2	1	no	—
388	C₄⋊C₄×C₆₇	—	2	1	no	—
389	C₄⋊C₄×C₆₇	—	2	2	no	—
390	C₄⋊C₄×C₆₇	—	2	2	no	—
391	C₄⋊C₄×C₆₇	—	2	1	no	—
392	C₄⋊C₄×C₆₇	—	2	1	no	—
393	C₄⋊C₄×C₆₇	—	2	2	no	—
394	C₄⋊C₄×C₆₇	—	2	2	no	—
395	C₄⋊C₄×C₆₇	—	2	1	no	—
396	C₄⋊C₄×C₆₇	—	2	1	no	—
397	C₄⋊C₄×C₆₇	—	2	1	no	—
398	C₄⋊C₄×C₆₇	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	1	no	—
400	C₄⋊C₄×C₆₇	—	2	1	no	—
401	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
411	C₂²⋊C₄×C₆₇	—	2	1	no	—
412	C₂²⋊C₄×C₆₇	—	2	1	no	—
413	C₂²⋊C₄×C₆₇	—	2	2	no	—
414	C₂²⋊C₄×C₆₇	—	2	1	no	—
415	C₂²⋊C₄×C₆₇	—	2	2	no	—
416	C₂²⋊C₄×C₆₇	—	2	2	no	—
417	C₂²⋊C₄×C₆₇	—	2	2	no	—
418	C₂²⋊C₄×C₆₇	—	2	2	no	—
419	C₂²⋊C₄×C₆₇	—	2	2	no	—
420	C₂²⋊C₄×C₆₇	—	2	2	no	—
421	C₂²⋊C₄×C₆₇	—	2	2	no	—
422	C₂²⋊C₄×C₆₇	—	2	2	no	—
423	C₂²⋊C₄×C₆₇	—	2	2	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	1	no	—
426	C₂²⋊C₄×C₆₇	—	2	1	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
432	C₄²×C₆₇	—	2	1	no	—
433	C₄²×C₆₇	—	2	2	no	—
434	C₄²×C₆₇	—	2	1	no	—
435	C₄²×C₆₇	—	2	2	no	—
436	C₄²×C₆₇	—	2	2	no	—
437	C₄²×C₆₇	—	2	1	no	—
438	C₄²×C₆₇	—	2	2	no	—
439	C₄²×C₆₇	—	2	1	no	—
440	C₄²×C₆₇	—	2	1	no	—
441	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
444	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
445	C₂³×C₆₇	—	2	4	no	—
446	C₂³×C₆₇	—	2	1	no	—
447	C₂³×C₆₇	—	4	2	no	—
448	C₂³×C₆₇	—	4	2	no	—
449	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
450	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
451	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
452	Q₈×C₆₇	—	2	1	no	—
453	Q₈×C₆₇	—	2	1	no	—
454	Q₈×C₆₇	—	2	2	no	—
455	Q₈×C₆₇	—	2	1	no	—
456	Q₈×C₆₇	—	2	1	no	—
457	Q₈×C₆₇	—	2	2	no	—
458	Q₈×C₆₇	—	2	1	no	—
459	Q₈×C₆₇	—	2	1	no	—
460	Q₈×C₆₇	—	4	2	no	—
461	Q₈×C₆₇	—	8	1	no	—
462	Q₈×C₆₇	—	8	1	no	—
463	Q₈×C₆₇	—	8	1	no	—
464	Q₈×C₆₇	—	8	2	no	—
465	Q₈×C₆₇	—	8	2	no	—
466	D₄×C₆₇	—	2	4	no	—
467	D₄×C₆₇	—	2	2	no	—
468	D₄×C₆₇	—	2	1	no	—
469	D₄×C₆₇	—	2	1	no	—
470	D₄×C₆₇	—	4	2	no	—
471	D₄×C₆₇	—	4	4	no	—
472	D₄×C₆₇	—	8	2	no	—
473	D₄×C₆₇	#137	1	4	yes	—
474	C₂×C₄×C₆₇	—	2	2	no	—
475	C₂×C₄×C₆₇	—	2	2	no	—
476	C₂×C₄×C₆₇	—	2	2	no	—
477	C₂×C₄×C₆₇	—	2	2	no	—
478	C₂×C₄×C₆₇	—	2	2	no	—
479	C₂×C₄×C₆₇	—	2	1	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	1	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	2	1	no	—
484	C₂×C₄×C₆₇	—	2	2	no	—
485	C₂×C₄×C₆₇	—	2	2	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	1	no	—
488	C₂×C₄×C₆₇	—	2	1	no	—
489	C₂×C₄×C₆₇	—	2	2	no	—
490	C₂×C₄×C₆₇	—	2	1	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	4	2	no	—
493	C₂×C₄×C₆₇	—	4	2	no	—
494	C₂×C₄×C₆₇	—	4	2	no	—
495	C₂×C₄×C₆₇	—	4	1	no	—
496	C₂×C₄×C₆₇	—	4	2	no	—
497	C₂×C₄×C₆₇	—	4	4	no	—
498	C₂×C₄×C₆₇	—	4	2	no	—
499	C₂×C₄×C₆₇	—	8	1	no	—
500	C₂×C₄×C₆₇	—	8	2	no	—
501	C₂×C₄×C₆₇	—	8	2	no	—
502	C₂×C₄×C₆₇	—	8	2	no	—
503	C₂×C₄×C₆₇	—	8	2	no	—
504	C₂×C₄×C₆₇	—	8	2	no	—
505	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
513	C₈×C₆₇	—	2	1	no	—
514	C₈×C₆₇	—	2	1	no	—
515	C₈×C₆₇	—	2	2	no	—
516	C₈×C₆₇	—	2	2	no	—
517	C₈×C₆₇	—	2	1	no	—
518	C₈×C₆₇	—	2	1	no	—
519	C₂²×C₆₇	—	2	2	no	—
520	C₂²×C₆₇	—	2	2	no	—
521	C₂²×C₆₇	—	2	1	no	—
522	C₂²×C₆₇	—	2	2	no	—
523	C₂²×C₆₇	—	2	1	no	—
524	C₂²×C₆₇	—	2	2	no	—
525	C₂²×C₆₇	—	2	1	no	—
526	C₂²×C₆₇	—	2	2	no	—
527	C₂²×C₆₇	—	4	1	no	—
528	C₂²×C₆₇	—	4	1	no	—
529	C₂²×C₆₇	—	4	1	no	—
530	C₂²×C₆₇	—	8	4	no	—
531	C₂²×C₆₇	C₂×#137	1	4	yes	—
532	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
533	C₄×C₆₇	—	2	1	no	—
534	C₄×C₆₇	—	2	1	no	—
535	C₄×C₆₇	—	2	1	no	—
536	C₄×C₆₇	—	2	2	no	—
537	C₄×C₆₇	—	2	2	no	—
538	C₄×C₆₇	—	2	1	no	—
539	C₄×C₆₇	—	4	1	no	—
540	C₄×C₆₇	—	4	1	no	—
541	C₄×C₆₇	—	4	2	no	—
542	C₄×C₆₇	—	4	1	no	—
543	C₄×C₆₇	—	4	2	no	—
544	C₄×C₆₇	—	4	1	no	—
545	C₄×C₆₇	—	4	1	no	—
546	C₄×C₆₇	—	4	2	no	—
547	C₄×C₆₇	—	4	1	no	—
548	C₄×C₆₇	—	4	1	no	—
549	C₄×C₆₇	—	4	2	no	—
550	C₄×C₆₇	C₂×#137	1	2	yes	—
551	C₄×C₆₇	#585	1	1	yes	characteristic
552	C₄×C₆₇	#585	1	1	yes	characteristic
553	#61742	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
554	C₂×C₆₇	—	2	4	no	—
555	C₂×C₆₇	—	4	2	no	—
556	C₂×C₆₇	—	4	1	no	—
557	C₂×C₆₇	—	8	1	no	—
558	C₂×C₆₇	#3485	1	1	yes	characteristic
559	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
560	C₂×C₆₇	#3584	1	1	yes	characteristic
561	#3501	C₂×C₆₇	1	1	yes	characteristic, complemented
562	#3475	C₂×C₆₇	1	1	yes	characteristic
563	#3357	C₂×C₆₇	1	1	yes	characteristic, complemented
564	#3356	C₂×C₆₇	1	1	yes	characteristic, complemented
565	#3346	C₂×C₆₇	1	2	yes	complemented
566	#3344	C₂×C₆₇	1	2	yes	complemented
567	#3338	C₂×C₆₇	1	1	yes	characteristic, complemented
568	#3335	C₂×C₆₇	1	1	yes	characteristic, complemented
569	#3329	C₂×C₆₇	1	1	yes	characteristic, complemented
570	#3328	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#3320	C₂×C₆₇	1	2	yes	complemented
572	#3312	C₂×C₆₇	1	2	yes	complemented
573	#3299	C₂×C₆₇	1	1	yes	characteristic, complemented
574	#3298	C₂×C₆₇	1	1	yes	characteristic, complemented
575	#3237	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#3231	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#3196	C₂×C₆₇	1	2	yes	complemented
578	#3190	C₂×C₆₇	1	2	yes	complemented
579	#3116	C₂×C₆₇	1	1	yes	characteristic, complemented
580	#3107	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#3095	C₂×C₆₇	1	2	yes	complemented
582	C₂×#485	C₂×C₆₇	1	2	yes	complemented
583	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
584	C₆₇	#61742	1	1	yes	characteristic, direct product factor, Sylow
585	#556	C₂²×C₆₇	1	1	yes	characteristic
586	#555	C₂²×C₆₇	1	1	yes	characteristic
587	#554	—	2	1	no	—
588	#554	—	2	2	no	—
589	#554	—	2	1	no	—
590	#554	C₂²×C₆₇	1	1	yes	characteristic
591	#554	C₂²×C₆₇	1	1	yes	characteristic
592	#554	C₂²×C₆₇	1	2	yes	—
593	#554	C₂²×C₆₇	1	1	yes	characteristic
594	#553	C₂²×C₆₇	1	2	yes	—
595	#552	—	2	1	no	—
596	#552	C₂²×C₆₇	1	2	yes	—
597	#551	—	2	2	no	—
598	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
599	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
600	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
601	#547	C₂²×C₆₇	1	1	yes	characteristic
602	#546	—	2	1	no	—
603	#544	—	2	1	no	—
604	#543	—	2	2	no	—
605	#533	C₂²×C₆₇	1	1	yes	characteristic
606	#533	C₂²×C₆₇	1	1	yes	characteristic
607	#533	C₂²×C₆₇	1	1	yes	characteristic
608	#529	—	2	2	no	—
609	#529	—	2	1	no	—
610	#525	C₂²×C₆₇	1	2	yes	—
611	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
612	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
613	#518	—	2	1	no	—
614	C₄×#41	—	2	1	no	—
615	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
616	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
617	C₂×#117	C₂²×C₆₇	1	2	yes	—
618	#501	C₂²×C₆₇	1	2	yes	complemented
619	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
620	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
621	#491	C₂²×C₆₇	1	2	yes	complemented
622	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
623	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
624	#485	C₂²×C₆₇	1	1	yes	characteristic
625	#485	C₂²×C₆₇	1	2	yes	—
626	#485	C₂²×C₆₇	1	2	yes	—
627	#485	C₂²×C₆₇	1	2	yes	—
628	#485	C₂²×C₆₇	1	1	yes	characteristic
629	#485	C₂²×C₆₇	1	2	yes	—
630	#485	C₂²×C₆₇	1	2	yes	—
631	#485	C₂²×C₆₇	1	2	yes	complemented
632	#485	C₂²×C₆₇	1	2	yes	complemented
633	#485	C₂²×C₆₇	1	2	yes	complemented
634	#485	C₂²×C₆₇	1	2	yes	complemented
635	#484	C₂²×C₆₇	1	2	yes	complemented
636	#484	C₂²×C₆₇	1	2	yes	complemented
637	#484	C₂²×C₆₇	1	2	yes	complemented
638	#483	C₂²×C₆₇	1	2	yes	complemented
639	#483	C₂²×C₆₇	1	2	yes	complemented
640	#483	C₂²×C₆₇	1	2	yes	complemented
641	#481	C₂²×C₆₇	1	2	yes	complemented
642	#480	C₂²×C₆₇	1	2	yes	complemented
643	#479	C₂²×C₆₇	1	2	yes	complemented
644	#479	C₂²×C₆₇	1	2	yes	complemented
645	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
646	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
647	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
648	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
649	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
650	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
651	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
652	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
653	#470	C₂²×C₆₇	1	2	yes	complemented
654	#470	C₂²×C₆₇	1	2	yes	complemented
655	#468	C₂²×C₆₇	1	2	yes	complemented
656	#468	C₂²×C₆₇	1	2	yes	complemented
657	#467	C₂²×C₆₇	1	2	yes	complemented
658	#467	C₂²×C₆₇	1	2	yes	complemented
659	#465	C₂²×C₆₇	1	2	yes	complemented
660	#465	C₂²×C₆₇	1	2	yes	complemented
661	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
662	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
663	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
665	#452	C₂²×C₆₇	1	1	yes	characteristic
666	#452	C₂²×C₆₇	1	1	yes	characteristic
667	#452	C₂²×C₆₇	1	2	yes	—
668	#451	C₂²×C₆₇	1	2	yes	complemented
669	#451	C₂²×C₆₇	1	2	yes	complemented
670	#448	C₂²×C₆₇	1	2	yes	complemented
671	#448	C₂²×C₆₇	1	2	yes	complemented
672	#441	C₂²×C₆₇	1	2	yes	complemented
673	#440	C₂²×C₆₇	1	2	yes	complemented
674	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
675	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
676	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
677	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
678	#436	C₂²×C₆₇	1	1	yes	characteristic
679	#436	C₂²×C₆₇	1	1	yes	characteristic
680	#435	C₂²×C₆₇	1	2	yes	—
681	#435	C₂²×C₆₇	1	2	yes	—
682	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
683	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
684	#432	C₂²×C₆₇	1	1	yes	characteristic
685	#431	C₂²×C₆₇	1	1	yes	characteristic
686	#428	C₂²×C₆₇	1	2	yes	complemented
687	#428	C₂²×C₆₇	1	2	yes	complemented
688	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
689	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
690	#419	C₂²×C₆₇	1	2	yes	complemented
691	#419	C₂²×C₆₇	1	2	yes	complemented
692	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
693	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
694	#407	C₂²×C₆₇	1	2	yes	—
695	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
696	C₂×#41	—	2	1	no	—
697	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
698	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
699	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
700	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
701	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
702	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
703	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
704	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
705	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
708	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
709	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
710	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
711	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
712	C₄⋊Q₈	—	2	1	no	—
713	C₄⋊Q₈	—	2	1	no	—
714	C₄⋊Q₈	—	2	2	no	—
715	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
717	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
718	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	1	no	—
726	#125	—	2	1	no	—
727	#125	—	2	1	no	—
728	#125	—	2	2	no	—
729	#125	—	2	1	no	—
730	#125	—	2	1	no	—
731	#125	C₂³×C₆₇	1	2	yes	—
732	#124	—	2	1	no	—
733	#124	—	2	2	no	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
757	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
758	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
765	#121	—	2	2	no	—
766	#121	—	2	1	no	—
767	#121	C₂³×C₆₇	1	2	yes	—
768	#121	C₂³×C₆₇	1	2	yes	—
769	#120	—	2	2	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
793	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
794	C₄×D₄	D₄×C₆₇	1	2	yes	—
795	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₆₇	1	2	yes	—
799	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
800	#117	—	2	2	no	—
801	#117	—	2	2	no	—
802	#117	—	2	1	no	—
803	#117	—	2	1	no	—
804	#117	—	2	1	no	—
805	#117	—	2	2	no	—
806	#117	—	2	1	no	—
807	#117	C₂³×C₆₇	1	1	yes	characteristic
808	#117	C₂³×C₆₇	1	2	yes	—
809	#117	C₂³×C₆₇	1	2	yes	—
810	#117	C₂³×C₆₇	1	2	yes	—
811	C₂×C₄⋊C₄	—	2	2	no	—
812	C₂×C₄⋊C₄	—	2	2	no	—
813	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
814	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
815	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
816	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
817	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
818	C₂×C₂²⋊C₄	—	2	2	no	—
819	C₂×C₂²⋊C₄	—	2	2	no	—
820	C₂×C₂²⋊C₄	—	2	2	no	—
821	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
822	C₂×C₄²	—	2	2	no	—
823	C₂×C₄²	—	2	1	no	—
824	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
825	#107	C₂³×C₆₇	1	1	yes	characteristic
826	#107	C₂³×C₆₇	1	2	yes	—
827	#107	C₂³×C₆₇	1	2	yes	—
828	#107	C₂³×C₆₇	1	2	yes	—
829	#107	C₂³×C₆₇	1	1	yes	characteristic
830	#107	C₂³×C₆₇	1	2	yes	—
831	#107	C₂³×C₆₇	1	2	yes	—
832	#106	C₂³×C₆₇	1	1	yes	characteristic
833	#106	C₂³×C₆₇	1	2	yes	—
834	#106	C₂³×C₆₇	1	2	yes	—
835	#106	C₂³×C₆₇	1	2	yes	—
836	#106	C₂³×C₆₇	1	1	yes	characteristic
837	#106	C₂³×C₆₇	1	2	yes	—
838	#106	C₂³×C₆₇	1	2	yes	—
839	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
843	#103	C₂³×C₆₇	1	1	yes	characteristic
844	#103	C₂³×C₆₇	1	1	yes	characteristic
845	#103	C₂³×C₆₇	1	2	yes	—
846	#103	C₂³×C₆₇	1	2	yes	—
847	#103	C₂³×C₆₇	1	2	yes	—
848	#103	C₂³×C₆₇	1	2	yes	—
849	#103	C₂³×C₆₇	1	2	yes	—
850	#103	C₂³×C₆₇	1	2	yes	—
851	#103	C₂³×C₆₇	1	1	yes	characteristic
852	#103	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
858	#103	C₂³×C₆₇	1	1	yes	characteristic
859	#103	C₂³×C₆₇	1	2	yes	—
860	#102	C₂³×C₆₇	1	1	yes	characteristic
861	#102	C₂³×C₆₇	1	1	yes	characteristic
862	#102	C₂³×C₆₇	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
864	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
870	#97	C₂³×C₆₇	1	2	yes	—
871	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
873	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
874	#41	—	4	1	no	—
875	#41	—	4	1	no	—
876	#41	—	4	4	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	1	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	2	1	no	—
881	C₂×Q₈	—	2	2	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	4	2	no	—
884	C₂×Q₈	—	4	2	no	—
885	C₂×Q₈	—	4	2	no	—
886	C₂×Q₈	—	4	2	no	—
887	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
889	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
891	C₂×D₄	—	2	4	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
896	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
897	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
898	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	—	4	2	no	—
910	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
911	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
912	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
913	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
914	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
915	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
917	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
918	Q₁₆	—	4	1	no	—
919	Q₁₆	—	4	2	no	—
920	Q₁₆	—	4	1	no	—
921	SD₁₆	—	4	1	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	1	no	—
924	M₁₆	—	4	2	no	—
925	M₁₆	—	4	2	no	—
926	C₂×C₈	—	4	2	no	—
927	C₂×C₈	—	4	2	no	—
928	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
933	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
963	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
964	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
965	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
968	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
969	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
990	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1003	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1004	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1006	C₂³	—	2	4	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	4	2	no	—
1009	C₂³	—	4	2	no	—
1010	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1011	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1012	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	2	no	—
1019	Q₈	—	2	1	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	8	2	no	—
1023	Q₈	—	8	2	no	—
1024	Q₈	—	8	1	no	—
1025	Q₈	—	8	1	no	—
1026	Q₈	—	8	1	no	—
1027	D₄	—	2	4	no	—
1028	D₄	—	2	2	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	4	4	no	—
1033	D₄	—	8	2	no	—
1034	D₄	#137×C₆₇	1	4	yes	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	4	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1073	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	8	4	no	—
1092	C₂²	C₂×#137×C₆₇	1	4	yes	—
1093	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1094	C₄	—	2	1	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	C₂×#137×C₆₇	1	2	yes	—
1112	C₄	#585×C₆₇	1	1	yes	characteristic
1113	C₄	#585×C₆₇	1	1	yes	characteristic
1114	C₂	—	2	4	no	—
1115	C₂	—	4	1	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	8	1	no	—
1118	C₂	C₆₇×#3485	1	1	yes	characteristic
1119	C₂	C₂²×#137×C₆₇	1	1	yes	characteristic
1120	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3475	C₂
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×#3501	C₂	semidirect
3. C₆₇×#3357	C₂	semidirect
4. C₆₇×#3356	C₂	semidirect
5. C₆₇×#3346	C₂	semidirect
6. C₆₇×#3344	C₂	semidirect
7. C₆₇×#3338	C₂	semidirect
8. C₆₇×#3335	C₂	semidirect
9. C₆₇×#3329	C₂	semidirect
10. C₆₇×#3328	C₂	semidirect
11. C₆₇×#3320	C₂	semidirect
12. C₆₇×#3312	C₂	semidirect
13. C₆₇×#3299	C₂	semidirect
14. C₆₇×#3298	C₂	semidirect
15. C₆₇×#3237	C₂	semidirect
16. C₆₇×#3231	C₂	semidirect
17. C₆₇×#3196	C₂	semidirect
18. C₆₇×#3190	C₂	semidirect
19. C₆₇×#3116	C₂	semidirect
20. C₆₇×#3107	C₂	semidirect
21. C₆₇×#3095	C₂	semidirect
22. C₂×#485×C₆₇	C₂	semidirect
23. C₆₇×#2974	C₂	semidirect
57. #501×C₆₇	C₂²	semidirect
58. #500×C₆₇	C₂²	semidirect
59. #498×C₆₇	C₂²	semidirect
60. #491×C₆₇	C₂²	semidirect
61. #487×C₆₇	C₂²	semidirect
62. #487×C₆₇	C₂²	semidirect
70. #485×C₆₇	C₂²	semidirect
71. #485×C₆₇	C₂²	semidirect
72. #485×C₆₇	C₂²	semidirect
73. #485×C₆₇	C₂²	semidirect
74. #484×C₆₇	C₂²	semidirect
75. #484×C₆₇	C₂²	semidirect
76. #484×C₆₇	C₂²	semidirect
77. #483×C₆₇	C₂²	semidirect
78. #483×C₆₇	C₂²	semidirect
79. #483×C₆₇	C₂²	semidirect
80. #481×C₆₇	C₂²	semidirect
81. #480×C₆₇	C₂²	semidirect
82. #479×C₆₇	C₂²	semidirect
83. #479×C₆₇	C₂²	semidirect
84. #477×C₆₇	C₂²	semidirect
85. #477×C₆₇	C₂²	semidirect
86. #477×C₆₇	C₂²	semidirect
87. #476×C₆₇	C₂²	semidirect
88. #475×C₆₇	C₂²	semidirect
89. #475×C₆₇	C₂²	semidirect
90. #475×C₆₇	C₂²	semidirect
91. #474×C₆₇	C₂²	semidirect
92. #470×C₆₇	C₂²	semidirect
93. #470×C₆₇	C₂²	semidirect
94. #468×C₆₇	C₂²	semidirect
95. #468×C₆₇	C₂²	semidirect
96. #467×C₆₇	C₂²	semidirect
97. #467×C₆₇	C₂²	semidirect
98. #465×C₆₇	C₂²	semidirect
99. #465×C₆₇	C₂²	semidirect
100. #462×C₆₇	C₂²	semidirect
101. #462×C₆₇	C₂²	semidirect
102. #461×C₆₇	C₂²	semidirect
103. #461×C₆₇	C₂²	semidirect
107. #451×C₆₇	C₂²	semidirect
108. #451×C₆₇	C₂²	semidirect
109. #448×C₆₇	C₂²	semidirect
110. #448×C₆₇	C₂²	semidirect
111. #441×C₆₇	C₂²	semidirect
112. #440×C₆₇	C₂²	semidirect
113. C₄×Q₁₆×C₆₇	C₂²	semidirect
114. C₄×Q₁₆×C₆₇	C₂²	semidirect
115. C₄×SD₁₆×C₆₇	C₂²	semidirect
116. C₄×SD₁₆×C₆₇	C₂²	semidirect
125. #428×C₆₇	C₂²	semidirect
126. #428×C₆₇	C₂²	semidirect
127. C₂×#107×C₆₇	C₂²	semidirect
128. C₂×#106×C₆₇	C₂²	semidirect
129. #419×C₆₇	C₂²	semidirect
130. #419×C₆₇	C₂²	semidirect
131. C₂×#103×C₆₇	C₂²	semidirect
132. C₂×#103×C₆₇	C₂²	semidirect
553. #61742	C₆₇	direct (N × H)
561. #3501	C₂×C₆₇	semidirect
563. #3357	C₂×C₆₇	semidirect
564. #3356	C₂×C₆₇	semidirect
565. #3346	C₂×C₆₇	semidirect
566. #3344	C₂×C₆₇	semidirect
567. #3338	C₂×C₆₇	semidirect
568. #3335	C₂×C₆₇	semidirect
569. #3329	C₂×C₆₇	semidirect
570. #3328	C₂×C₆₇	semidirect
571. #3320	C₂×C₆₇	semidirect
572. #3312	C₂×C₆₇	semidirect
573. #3299	C₂×C₆₇	semidirect
574. #3298	C₂×C₆₇	semidirect
575. #3237	C₂×C₆₇	semidirect
576. #3231	C₂×C₆₇	semidirect
577. #3196	C₂×C₆₇	semidirect
578. #3190	C₂×C₆₇	semidirect
579. #3116	C₂×C₆₇	semidirect
580. #3107	C₂×C₆₇	semidirect
581. #3095	C₂×C₆₇	semidirect
582. C₂×#485	C₂×C₆₇	semidirect
583. #2974	C₂×C₆₇	semidirect
584. C₆₇	#61742	direct (N × H)
618. #501	C₂²×C₆₇	semidirect
619. #500	C₂²×C₆₇	semidirect
620. #498	C₂²×C₆₇	semidirect
621. #491	C₂²×C₆₇	semidirect
622. #487	C₂²×C₆₇	semidirect
623. #487	C₂²×C₆₇	semidirect
631. #485	C₂²×C₆₇	semidirect
632. #485	C₂²×C₆₇	semidirect
633. #485	C₂²×C₆₇	semidirect
634. #485	C₂²×C₆₇	semidirect
635. #484	C₂²×C₆₇	semidirect
636. #484	C₂²×C₆₇	semidirect
637. #484	C₂²×C₆₇	semidirect
638. #483	C₂²×C₆₇	semidirect
639. #483	C₂²×C₆₇	semidirect
640. #483	C₂²×C₆₇	semidirect
641. #481	C₂²×C₆₇	semidirect
642. #480	C₂²×C₆₇	semidirect
643. #479	C₂²×C₆₇	semidirect
644. #479	C₂²×C₆₇	semidirect
645. #477	C₂²×C₆₇	semidirect
646. #477	C₂²×C₆₇	semidirect
647. #477	C₂²×C₆₇	semidirect
648. #476	C₂²×C₆₇	semidirect
649. #475	C₂²×C₆₇	semidirect
650. #475	C₂²×C₆₇	semidirect
651. #475	C₂²×C₆₇	semidirect
652. #474	C₂²×C₆₇	semidirect
653. #470	C₂²×C₆₇	semidirect
654. #470	C₂²×C₆₇	semidirect
655. #468	C₂²×C₆₇	semidirect
656. #468	C₂²×C₆₇	semidirect
657. #467	C₂²×C₆₇	semidirect
658. #467	C₂²×C₆₇	semidirect
659. #465	C₂²×C₆₇	semidirect
660. #465	C₂²×C₆₇	semidirect
661. #462	C₂²×C₆₇	semidirect
662. #462	C₂²×C₆₇	semidirect
663. #461	C₂²×C₆₇	semidirect
664. #461	C₂²×C₆₇	semidirect
668. #451	C₂²×C₆₇	semidirect
669. #451	C₂²×C₆₇	semidirect
670. #448	C₂²×C₆₇	semidirect
671. #448	C₂²×C₆₇	semidirect
672. #441	C₂²×C₆₇	semidirect
673. #440	C₂²×C₆₇	semidirect
674. C₄×Q₁₆	C₂²×C₆₇	semidirect
675. C₄×Q₁₆	C₂²×C₆₇	semidirect
676. C₄×SD₁₆	C₂²×C₆₇	semidirect
677. C₄×SD₁₆	C₂²×C₆₇	semidirect
686. #428	C₂²×C₆₇	semidirect
687. #428	C₂²×C₆₇	semidirect
688. C₂×#107	C₂²×C₆₇	semidirect
689. C₂×#106	C₂²×C₆₇	semidirect
690. #419	C₂²×C₆₇	semidirect
691. #419	C₂²×C₆₇	semidirect
692. C₂×#103	C₂²×C₆₇	semidirect
693. C₂×#103	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×#3501	2
C₆₇×#3475	2
C₆₇×#3357	2
C₆₇×#3356	2
C₆₇×#3346	2
C₆₇×#3344	2
C₆₇×#3338	2
C₆₇×#3335	2
C₆₇×#3329	2
C₆₇×#3328	2
C₆₇×#3320	2
C₆₇×#3312	2
C₆₇×#3299	2
C₆₇×#3298	2
C₆₇×#3237	2
C₆₇×#3231	2
C₆₇×#3196	2
C₆₇×#3190	2
C₆₇×#3116	2
C₆₇×#3107	2
C₆₇×#3095	2
C₂×#485×C₆₇	2
C₆₇×#2974	2
#61742	67

Subgroups — C67×#61742 #30740993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61742 #30740993