Subgroups — C₆₇×#61724 #30740975

Order 17152.

1756 conjugacy classes of subgroups.

The subgroup lattice has 1132 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	C₆₇×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3353	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3353	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3352	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3351	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3330	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3329	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3328	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3327	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3326	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3231	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×#3095	C₂	1	2	yes	maximal, complemented
22	C₆₇×#3093	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
24	#556×C₆₇	C₂²	1	1	yes	characteristic
25	#556×C₆₇	C₂²	1	1	yes	characteristic
26	#555×C₆₇	C₂²	1	1	yes	characteristic
27	#554×C₆₇	—	2	1	no	—
28	#554×C₆₇	C₂²	1	1	yes	characteristic
29	#553×C₆₇	C₂²	1	2	yes	—
30	#552×C₆₇	—	2	1	no	—
31	#552×C₆₇	C₂²	1	2	yes	—
32	#552×C₆₇	C₂²	1	2	yes	—
33	#551×C₆₇	—	2	2	no	—
34	#551×C₆₇	—	2	2	no	—
35	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	#548×C₆₇	C₂²	1	2	yes	—
37	#547×C₆₇	C₂²	1	1	yes	characteristic
38	#547×C₆₇	C₂²	1	1	yes	characteristic
39	#547×C₆₇	C₂²	1	1	yes	characteristic
40	#546×C₆₇	—	2	1	no	—
41	#546×C₆₇	—	2	1	no	—
42	#542×C₆₇	—	2	1	no	—
43	#539×C₆₇	—	2	2	no	—
44	#533×C₆₇	C₂²	1	1	yes	characteristic
45	#533×C₆₇	C₂²	1	1	yes	characteristic
46	#529×C₆₇	—	2	2	no	—
47	#529×C₆₇	—	2	1	no	—
48	#529×C₆₇	C₂²	1	1	yes	characteristic
49	#525×C₆₇	C₂²	1	2	yes	—
50	#525×C₆₇	C₂²	1	2	yes	—
51	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
52	#520×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	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#499×C₆₇	C₂²	1	2	yes	complemented
59	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#488×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	2	yes	—
64	#485×C₆₇	C₂²	1	2	yes	—
65	#485×C₆₇	C₂²	1	1	yes	characteristic
66	#485×C₆₇	C₂²	1	2	yes	—
67	#485×C₆₇	C₂²	1	2	yes	—
68	#485×C₆₇	C₂²	1	2	yes	complemented
69	#485×C₆₇	C₂²	1	2	yes	complemented
70	#485×C₆₇	C₂²	1	2	yes	complemented
71	#484×C₆₇	C₂²	1	2	yes	complemented
72	#484×C₆₇	C₂²	1	2	yes	complemented
73	#484×C₆₇	C₂²	1	2	yes	complemented
74	#483×C₆₇	C₂²	1	2	yes	complemented
75	#483×C₆₇	C₂²	1	2	yes	complemented
76	#482×C₆₇	C₂²	1	1	yes	characteristic
77	#482×C₆₇	C₂²	1	2	yes	—
78	#482×C₆₇	C₂²	1	2	yes	complemented
79	#482×C₆₇	C₂²	1	2	yes	complemented
80	#482×C₆₇	C₂²	1	2	yes	complemented
81	#481×C₆₇	C₂²	1	2	yes	complemented
82	#479×C₆₇	C₂²	1	2	yes	complemented
83	#479×C₆₇	C₂²	1	2	yes	complemented
84	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#478×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	#474×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	#470×C₆₇	C₂²	1	2	yes	complemented
95	#469×C₆₇	C₂²	1	2	yes	complemented
96	#468×C₆₇	C₂²	1	2	yes	complemented
97	#468×C₆₇	C₂²	1	2	yes	complemented
98	#468×C₆₇	C₂²	1	2	yes	complemented
99	#468×C₆₇	C₂²	1	2	yes	complemented
100	#464×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#463×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#462×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	2	yes	—
106	#452×C₆₇	C₂²	1	2	yes	complemented
107	#451×C₆₇	C₂²	1	2	yes	complemented
108	#449×C₆₇	C₂²	1	1	yes	characteristic
109	#449×C₆₇	C₂²	1	2	yes	complemented
110	#448×C₆₇	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
112	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
114	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#436×C₆₇	C₂²	1	2	yes	—
118	#436×C₆₇	C₂²	1	2	yes	—
119	#436×C₆₇	C₂²	1	1	yes	characteristic
120	#436×C₆₇	C₂²	1	1	yes	characteristic
121	#436×C₆₇	C₂²	1	1	yes	characteristic
122	#436×C₆₇	C₂²	1	1	yes	characteristic
123	#431×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	#428×C₆₇	C₂²	1	2	yes	complemented
128	#428×C₆₇	C₂²	1	2	yes	complemented
129	#419×C₆₇	C₂²	1	2	yes	complemented
130	#419×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	—
134	#407×C₆₇	C₂²	1	2	yes	—
135	C₂×#41×C₆₇	—	2	1	no	—
136	C₂×#41×C₆₇	—	2	1	no	—
137	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×#41×C₆₇	C₂³	1	2	yes	—
139	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
140	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
141	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
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×D₈×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₆₇	—	2	1	no	—
153	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
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	#126×C₆₇	—	2	2	no	—
158	#126×C₆₇	—	2	2	no	—
159	#126×C₆₇	—	2	2	no	—
160	#126×C₆₇	—	2	2	no	—
161	#126×C₆₇	—	2	2	no	—
162	#126×C₆₇	—	2	1	no	—
163	#125×C₆₇	—	2	2	no	—
164	#125×C₆₇	—	2	1	no	—
165	#125×C₆₇	—	2	2	no	—
166	#125×C₆₇	—	2	1	no	—
167	#125×C₆₇	C₂³	1	1	yes	characteristic
168	#125×C₆₇	C₂³	1	2	yes	—
169	#124×C₆₇	—	2	1	no	—
170	#124×C₆₇	—	2	1	no	—
171	#124×C₆₇	—	2	2	no	—
172	#124×C₆₇	—	2	2	no	—
173	#124×C₆₇	C₂³	1	1	yes	characteristic
174	#123×C₆₇	—	2	2	no	—
175	#123×C₆₇	—	2	2	no	—
176	#123×C₆₇	—	2	2	no	—
177	#123×C₆₇	—	2	2	no	—
178	#123×C₆₇	—	2	1	no	—
179	#123×C₆₇	—	2	2	no	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	—	2	2	no	—
182	#123×C₆₇	—	2	2	no	—
183	C₂²⋊Q₈×C₆₇	—	2	2	no	—
184	C₂²⋊Q₈×C₆₇	—	2	2	no	—
185	C₂²⋊Q₈×C₆₇	—	2	1	no	—
186	C₂²⋊Q₈×C₆₇	—	2	1	no	—
187	C₂²⋊Q₈×C₆₇	—	2	1	no	—
188	C₂²⋊Q₈×C₆₇	—	2	1	no	—
189	C₂²⋊Q₈×C₆₇	—	2	2	no	—
190	C₂²⋊Q₈×C₆₇	—	2	1	no	—
191	C₂²⋊Q₈×C₆₇	—	2	2	no	—
192	C₂²⋊Q₈×C₆₇	—	2	2	no	—
193	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
195	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
200	#121×C₆₇	—	2	2	no	—
201	#121×C₆₇	—	2	1	no	—
202	#121×C₆₇	—	2	2	no	—
203	#121×C₆₇	—	2	1	no	—
204	#121×C₆₇	C₂³	1	2	yes	—
205	#121×C₆₇	C₂³	1	1	yes	characteristic
206	#121×C₆₇	C₂³	1	2	yes	—
207	#121×C₆₇	C₂³	1	2	yes	—
208	#120×C₆₇	—	2	2	no	—
209	#120×C₆₇	—	2	2	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	—	2	1	no	—
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	1	no	—
221	C₄×D₄×C₆₇	—	2	2	no	—
222	C₄×D₄×C₆₇	—	2	1	no	—
223	C₄×D₄×C₆₇	—	2	1	no	—
224	C₄×D₄×C₆₇	—	2	2	no	—
225	C₄×D₄×C₆₇	—	2	2	no	—
226	C₄×D₄×C₆₇	—	2	2	no	—
227	C₄×D₄×C₆₇	—	2	1	no	—
228	C₄×D₄×C₆₇	—	2	2	no	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
231	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
232	C₄×D₄×C₆₇	D₄	1	2	yes	—
233	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
238	C₄×D₄×C₆₇	C₂³	1	2	yes	—
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	2	no	—
244	#117×C₆₇	—	2	2	no	—
245	#117×C₆₇	—	2	1	no	—
246	#117×C₆₇	—	2	1	no	—
247	#117×C₆₇	C₂³	1	1	yes	characteristic
248	#117×C₆₇	C₂³	1	2	yes	—
249	#117×C₆₇	C₂³	1	2	yes	—
250	#117×C₆₇	C₂³	1	2	yes	—
251	#117×C₆₇	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
253	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
254	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
269	#107×C₆₇	C₂³	1	1	yes	characteristic
270	#107×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
276	#106×C₆₇	C₂³	1	1	yes	characteristic
277	#106×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	1	yes	characteristic
294	#103×C₆₇	C₂³	1	1	yes	characteristic
295	#102×C₆₇	C₂³	1	1	yes	characteristic
296	#102×C₆₇	C₂³	1	2	yes	—
297	#102×C₆₇	C₂³	1	1	yes	characteristic
298	#102×C₆₇	C₂³	1	2	yes	—
299	#102×C₆₇	C₂³	1	2	yes	—
300	#102×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
303	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
309	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	2	yes	—
312	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
313	#41×C₆₇	—	4	1	no	—
314	#41×C₆₇	—	4	1	no	—
315	#41×C₆₇	—	4	2	no	—
316	#41×C₆₇	—	4	2	no	—
317	#41×C₆₇	—	4	4	no	—
318	#41×C₆₇	—	4	4	no	—
319	C₂×Q₈×C₆₇	—	2	1	no	—
320	C₂×Q₈×C₆₇	—	2	1	no	—
321	C₂×Q₈×C₆₇	—	2	1	no	—
322	C₂×Q₈×C₆₇	—	2	2	no	—
323	C₂×Q₈×C₆₇	—	4	2	no	—
324	C₂×Q₈×C₆₇	—	4	2	no	—
325	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₆₇	—	2	1	no	—
329	C₂×D₄×C₆₇	—	2	1	no	—
330	C₂×D₄×C₆₇	—	2	2	no	—
331	C₂×D₄×C₆₇	—	2	2	no	—
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	2	no	—
334	C₂×D₄×C₆₇	—	4	2	no	—
335	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
338	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
348	C₂²×C₄×C₆₇	—	2	2	no	—
349	C₂²×C₄×C₆₇	—	4	2	no	—
350	C₂²×C₄×C₆₇	—	4	2	no	—
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	1	yes	characteristic
354	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
355	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
356	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
359	Q₁₆×C₆₇	—	4	1	no	—
360	Q₁₆×C₆₇	—	4	2	no	—
361	SD₁₆×C₆₇	—	4	1	no	—
362	SD₁₆×C₆₇	—	4	2	no	—
363	SD₁₆×C₆₇	—	4	1	no	—
364	D₈×C₆₇	—	4	1	no	—
365	M₁₆×C₆₇	—	4	2	no	—
366	M₁₆×C₆₇	—	4	2	no	—
367	M₁₆×C₆₇	—	4	2	no	—
368	M₁₆×C₆₇	—	4	2	no	—
369	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
371	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
373	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₆₇	—	2	1	no	—
376	C₄⋊C₄×C₆₇	—	2	2	no	—
377	C₄⋊C₄×C₆₇	—	2	1	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	1	no	—
384	C₄⋊C₄×C₆₇	—	2	1	no	—
385	C₄⋊C₄×C₆₇	—	2	2	no	—
386	C₄⋊C₄×C₆₇	—	2	2	no	—
387	C₄⋊C₄×C₆₇	—	2	1	no	—
388	C₄⋊C₄×C₆₇	—	2	1	no	—
389	C₄⋊C₄×C₆₇	—	2	1	no	—
390	C₄⋊C₄×C₆₇	—	2	1	no	—
391	C₄⋊C₄×C₆₇	—	2	2	no	—
392	C₄⋊C₄×C₆₇	—	2	2	no	—
393	C₄⋊C₄×C₆₇	—	2	1	no	—
394	C₄⋊C₄×C₆₇	—	2	2	no	—
395	C₄⋊C₄×C₆₇	—	2	1	no	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	—	2	1	no	—
398	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄×C₆₇	—	2	1	no	—
409	C₂²⋊C₄×C₆₇	—	2	1	no	—
410	C₂²⋊C₄×C₆₇	—	2	2	no	—
411	C₂²⋊C₄×C₆₇	—	2	2	no	—
412	C₂²⋊C₄×C₆₇	—	2	2	no	—
413	C₂²⋊C₄×C₆₇	—	2	2	no	—
414	C₂²⋊C₄×C₆₇	—	2	2	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	1	no	—
421	C₂²⋊C₄×C₆₇	—	2	2	no	—
422	C₂²⋊C₄×C₆₇	—	2	1	no	—
423	C₂²⋊C₄×C₆₇	—	2	1	no	—
424	C₂²⋊C₄×C₆₇	—	2	1	no	—
425	C₂²⋊C₄×C₆₇	—	2	1	no	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₂²⋊C₄×C₆₇	—	2	1	no	—
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	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
433	C₄²×C₆₇	—	2	1	no	—
434	C₄²×C₆₇	—	2	2	no	—
435	C₄²×C₆₇	—	2	1	no	—
436	C₄²×C₆₇	—	2	2	no	—
437	C₄²×C₆₇	—	2	2	no	—
438	C₄²×C₆₇	—	2	1	no	—
439	C₄²×C₆₇	—	2	2	no	—
440	C₄²×C₆₇	—	2	2	no	—
441	C₄²×C₆₇	—	2	1	no	—
442	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
445	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
446	C₂³×C₆₇	—	2	1	no	—
447	C₂³×C₆₇	—	2	1	no	—
448	C₂³×C₆₇	—	4	2	no	—
449	C₂³×C₆₇	—	4	2	no	—
450	C₂³×C₆₇	—	4	2	no	—
451	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
452	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
453	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
454	Q₈×C₆₇	—	2	1	no	—
455	Q₈×C₆₇	—	2	1	no	—
456	Q₈×C₆₇	—	2	2	no	—
457	Q₈×C₆₇	—	2	1	no	—
458	Q₈×C₆₇	—	2	1	no	—
459	Q₈×C₆₇	—	2	2	no	—
460	Q₈×C₆₇	—	4	2	no	—
461	Q₈×C₆₇	—	4	2	no	—
462	Q₈×C₆₇	—	8	1	no	—
463	Q₈×C₆₇	—	8	2	no	—
464	D₄×C₆₇	—	2	2	no	—
465	D₄×C₆₇	—	2	2	no	—
466	D₄×C₆₇	—	2	1	no	—
467	D₄×C₆₇	—	2	1	no	—
468	D₄×C₆₇	—	2	1	no	—
469	D₄×C₆₇	—	2	1	no	—
470	D₄×C₆₇	—	4	2	no	—
471	D₄×C₆₇	—	4	2	no	—
472	D₄×C₆₇	—	4	2	no	—
473	D₄×C₆₇	—	4	4	no	—
474	D₄×C₆₇	—	4	4	no	—
475	D₄×C₆₇	—	8	2	no	—
476	D₄×C₆₇	—	8	2	no	—
477	C₂×C₄×C₆₇	—	2	2	no	—
478	C₂×C₄×C₆₇	—	2	2	no	—
479	C₂×C₄×C₆₇	—	2	2	no	—
480	C₂×C₄×C₆₇	—	2	2	no	—
481	C₂×C₄×C₆₇	—	2	2	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	2	1	no	—
484	C₂×C₄×C₆₇	—	2	1	no	—
485	C₂×C₄×C₆₇	—	2	1	no	—
486	C₂×C₄×C₆₇	—	2	1	no	—
487	C₂×C₄×C₆₇	—	2	1	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	2	2	no	—
490	C₂×C₄×C₆₇	—	2	2	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	2	2	no	—
493	C₂×C₄×C₆₇	—	2	1	no	—
494	C₂×C₄×C₆₇	—	4	2	no	—
495	C₂×C₄×C₆₇	—	4	2	no	—
496	C₂×C₄×C₆₇	—	4	2	no	—
497	C₂×C₄×C₆₇	—	4	1	no	—
498	C₂×C₄×C₆₇	—	4	2	no	—
499	C₂×C₄×C₆₇	—	4	4	no	—
500	C₂×C₄×C₆₇	—	4	4	no	—
501	C₂×C₄×C₆₇	—	4	2	no	—
502	C₂×C₄×C₆₇	—	4	2	no	—
503	C₂×C₄×C₆₇	—	8	1	no	—
504	C₂×C₄×C₆₇	—	8	2	no	—
505	C₂×C₄×C₆₇	—	8	2	no	—
506	C₂×C₄×C₆₇	—	8	2	no	—
507	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
515	C₈×C₆₇	—	2	1	no	—
516	C₈×C₆₇	—	2	1	no	—
517	C₈×C₆₇	—	2	1	no	—
518	C₈×C₆₇	—	2	2	no	—
519	C₈×C₆₇	—	2	2	no	—
520	C₈×C₆₇	—	2	1	no	—
521	C₂²×C₆₇	—	2	1	no	—
522	C₂²×C₆₇	—	2	2	no	—
523	C₂²×C₆₇	—	2	2	no	—
524	C₂²×C₆₇	—	2	1	no	—
525	C₂²×C₆₇	—	2	2	no	—
526	C₂²×C₆₇	—	2	2	no	—
527	C₂²×C₆₇	—	2	1	no	—
528	C₂²×C₆₇	—	2	2	no	—
529	C₂²×C₆₇	—	2	2	no	—
530	C₂²×C₆₇	—	4	1	no	—
531	C₂²×C₆₇	—	4	1	no	—
532	C₂²×C₆₇	—	4	1	no	—
533	C₂²×C₆₇	—	4	1	no	—
534	C₂²×C₆₇	—	4	1	no	—
535	C₂²×C₆₇	—	4	1	no	—
536	C₂²×C₆₇	—	8	4	no	—
537	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
538	C₄×C₆₇	—	2	1	no	—
539	C₄×C₆₇	—	2	1	no	—
540	C₄×C₆₇	—	2	1	no	—
541	C₄×C₆₇	—	2	2	no	—
542	C₄×C₆₇	—	2	2	no	—
543	C₄×C₆₇	—	2	1	no	—
544	C₄×C₆₇	—	4	1	no	—
545	C₄×C₆₇	—	4	2	no	—
546	C₄×C₆₇	—	4	1	no	—
547	C₄×C₆₇	—	4	1	no	—
548	C₄×C₆₇	—	4	2	no	—
549	C₄×C₆₇	—	4	1	no	—
550	C₄×C₆₇	—	4	1	no	—
551	C₄×C₆₇	—	4	1	no	—
552	C₄×C₆₇	—	4	2	no	—
553	C₄×C₆₇	—	4	2	no	—
554	C₄×C₆₇	#575	1	2	yes	—
555	C₄×C₆₇	#585	1	1	yes	characteristic
556	C₄×C₆₇	#585	1	1	yes	characteristic
557	#61724	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
558	C₂×C₆₇	—	4	2	no	—
559	C₂×C₆₇	—	4	2	no	—
560	C₂×C₆₇	—	4	1	no	—
561	C₂×C₆₇	—	8	1	no	—
562	C₂×C₆₇	—	8	1	no	—
563	C₂×C₆₇	#3485	1	1	yes	characteristic
564	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
565	C₂×C₆₇	#3586	1	1	yes	characteristic
566	#3520	C₂×C₆₇	1	1	yes	characteristic, complemented
567	#3475	C₂×C₆₇	1	1	yes	characteristic, complemented
568	#3356	C₂×C₆₇	1	1	yes	characteristic, complemented
569	#3354	C₂×C₆₇	1	1	yes	characteristic, complemented
570	#3353	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#3353	C₂×C₆₇	1	1	yes	characteristic, complemented
572	#3352	C₂×C₆₇	1	2	yes	complemented
573	#3351	C₂×C₆₇	1	2	yes	complemented
574	#3331	C₂×C₆₇	1	1	yes	characteristic, complemented
575	#3330	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#3329	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#3328	C₂×C₆₇	1	1	yes	characteristic, complemented
578	#3327	C₂×C₆₇	1	2	yes	complemented
579	#3326	C₂×C₆₇	1	2	yes	complemented
580	#3233	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#3231	C₂×C₆₇	1	1	yes	characteristic, complemented
582	#3197	C₂×C₆₇	1	2	yes	complemented
583	#3196	C₂×C₆₇	1	2	yes	complemented
584	#3107	C₂×C₆₇	1	1	yes	characteristic, complemented
585	#3102	C₂×C₆₇	1	1	yes	characteristic, complemented
586	#3095	C₂×C₆₇	1	2	yes	complemented
587	#3093	C₂×C₆₇	1	2	yes	complemented
588	#2975	C₂×C₆₇	1	1	yes	characteristic, complemented
589	C₆₇	#61724	1	1	yes	characteristic, direct product factor, Sylow
590	#556	C₂²×C₆₇	1	1	yes	characteristic
591	#556	C₂²×C₆₇	1	1	yes	characteristic
592	#555	C₂²×C₆₇	1	1	yes	characteristic
593	#554	—	2	1	no	—
594	#554	C₂²×C₆₇	1	1	yes	characteristic
595	#553	C₂²×C₆₇	1	2	yes	—
596	#552	—	2	1	no	—
597	#552	C₂²×C₆₇	1	2	yes	—
598	#552	C₂²×C₆₇	1	2	yes	—
599	#551	—	2	2	no	—
600	#551	—	2	2	no	—
601	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
602	#548	C₂²×C₆₇	1	2	yes	—
603	#547	C₂²×C₆₇	1	1	yes	characteristic
604	#547	C₂²×C₆₇	1	1	yes	characteristic
605	#547	C₂²×C₆₇	1	1	yes	characteristic
606	#546	—	2	1	no	—
607	#546	—	2	1	no	—
608	#542	—	2	1	no	—
609	#539	—	2	2	no	—
610	#533	C₂²×C₆₇	1	1	yes	characteristic
611	#533	C₂²×C₆₇	1	1	yes	characteristic
612	#529	—	2	2	no	—
613	#529	—	2	1	no	—
614	#529	C₂²×C₆₇	1	1	yes	characteristic
615	#525	C₂²×C₆₇	1	2	yes	—
616	#525	C₂²×C₆₇	1	2	yes	—
617	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
618	#520	—	2	1	no	—
619	C₄×#41	—	2	1	no	—
620	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
621	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
622	C₂×#117	C₂²×C₆₇	1	2	yes	—
623	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
624	#499	C₂²×C₆₇	1	2	yes	complemented
625	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
626	#488	C₂²×C₆₇	1	2	yes	complemented
627	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	#485	C₂²×C₆₇	1	2	yes	—
630	#485	C₂²×C₆₇	1	2	yes	—
631	#485	C₂²×C₆₇	1	1	yes	characteristic
632	#485	C₂²×C₆₇	1	2	yes	—
633	#485	C₂²×C₆₇	1	2	yes	—
634	#485	C₂²×C₆₇	1	2	yes	complemented
635	#485	C₂²×C₆₇	1	2	yes	complemented
636	#485	C₂²×C₆₇	1	2	yes	complemented
637	#484	C₂²×C₆₇	1	2	yes	complemented
638	#484	C₂²×C₆₇	1	2	yes	complemented
639	#484	C₂²×C₆₇	1	2	yes	complemented
640	#483	C₂²×C₆₇	1	2	yes	complemented
641	#483	C₂²×C₆₇	1	2	yes	complemented
642	#482	C₂²×C₆₇	1	1	yes	characteristic
643	#482	C₂²×C₆₇	1	2	yes	—
644	#482	C₂²×C₆₇	1	2	yes	complemented
645	#482	C₂²×C₆₇	1	2	yes	complemented
646	#482	C₂²×C₆₇	1	2	yes	complemented
647	#481	C₂²×C₆₇	1	2	yes	complemented
648	#479	C₂²×C₆₇	1	2	yes	complemented
649	#479	C₂²×C₆₇	1	1	yes	characteristic, complemented
650	#479	C₂²×C₆₇	1	2	yes	complemented
651	#478	C₂²×C₆₇	1	1	yes	characteristic, complemented
652	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
653	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
655	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
656	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
657	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
658	#470	C₂²×C₆₇	1	2	yes	complemented
659	#470	C₂²×C₆₇	1	2	yes	complemented
660	#470	C₂²×C₆₇	1	2	yes	complemented
661	#469	C₂²×C₆₇	1	2	yes	complemented
662	#468	C₂²×C₆₇	1	2	yes	complemented
663	#468	C₂²×C₆₇	1	2	yes	complemented
664	#468	C₂²×C₆₇	1	2	yes	complemented
665	#468	C₂²×C₆₇	1	2	yes	complemented
666	#464	C₂²×C₆₇	1	1	yes	characteristic, complemented
667	#463	C₂²×C₆₇	1	1	yes	characteristic, complemented
668	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
669	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
670	#452	C₂²×C₆₇	1	1	yes	characteristic
671	#452	C₂²×C₆₇	1	2	yes	—
672	#452	C₂²×C₆₇	1	2	yes	complemented
673	#451	C₂²×C₆₇	1	2	yes	complemented
674	#449	C₂²×C₆₇	1	1	yes	characteristic
675	#449	C₂²×C₆₇	1	2	yes	complemented
676	#448	C₂²×C₆₇	1	2	yes	complemented
677	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
678	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
679	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
680	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
681	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
682	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
683	#436	C₂²×C₆₇	1	1	yes	characteristic
684	#436	C₂²×C₆₇	1	1	yes	characteristic
685	#436	C₂²×C₆₇	1	1	yes	characteristic
686	#436	C₂²×C₆₇	1	1	yes	characteristic
687	#436	C₂²×C₆₇	1	2	yes	—
688	#436	C₂²×C₆₇	1	2	yes	—
689	#431	C₂²×C₆₇	1	1	yes	characteristic
690	#431	C₂²×C₆₇	1	1	yes	characteristic
691	#428	C₂²×C₆₇	1	2	yes	complemented
692	#428	C₂²×C₆₇	1	2	yes	complemented
693	#428	C₂²×C₆₇	1	2	yes	complemented
694	#428	C₂²×C₆₇	1	2	yes	complemented
695	#419	C₂²×C₆₇	1	2	yes	complemented
696	#419	C₂²×C₆₇	1	2	yes	complemented
697	#417	C₂²×C₆₇	1	2	yes	complemented
698	#417	C₂²×C₆₇	1	2	yes	complemented
699	#407	C₂²×C₆₇	1	2	yes	—
700	#407	C₂²×C₆₇	1	2	yes	—
701	C₂×#41	—	2	1	no	—
702	C₂×#41	—	2	1	no	—
703	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
704	C₂×#41	C₂³×C₆₇	1	2	yes	—
705	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
706	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
707	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
708	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
709	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
711	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
712	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
713	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
714	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
715	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
716	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
717	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	1	no	—
729	#125	—	2	2	no	—
730	#125	—	2	1	no	—
731	#125	—	2	2	no	—
732	#125	—	2	1	no	—
733	#125	C₂³×C₆₇	1	1	yes	characteristic
734	#125	C₂³×C₆₇	1	2	yes	—
735	#124	—	2	1	no	—
736	#124	—	2	1	no	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	C₂³×C₆₇	1	1	yes	characteristic
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	1	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
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	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
766	#121	—	2	2	no	—
767	#121	—	2	1	no	—
768	#121	—	2	2	no	—
769	#121	—	2	1	no	—
770	#121	C₂³×C₆₇	1	1	yes	characteristic
771	#121	C₂³×C₆₇	1	2	yes	—
772	#121	C₂³×C₆₇	1	2	yes	—
773	#121	C₂³×C₆₇	1	2	yes	—
774	#120	—	2	2	no	—
775	#120	—	2	2	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
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	—	2	2	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
797	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
798	C₄×D₄	D₄×C₆₇	1	2	yes	—
799	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₆₇	1	2	yes	—
805	#117	—	2	2	no	—
806	#117	—	2	2	no	—
807	#117	—	2	1	no	—
808	#117	—	2	1	no	—
809	#117	—	2	2	no	—
810	#117	—	2	2	no	—
811	#117	—	2	1	no	—
812	#117	—	2	1	no	—
813	#117	C₂³×C₆₇	1	1	yes	characteristic
814	#117	C₂³×C₆₇	1	2	yes	—
815	#117	C₂³×C₆₇	1	2	yes	—
816	#117	C₂³×C₆₇	1	2	yes	—
817	#117	C₂³×C₆₇	1	2	yes	—
818	C₂×C₄⋊C₄	—	2	2	no	—
819	C₂×C₄⋊C₄	—	2	1	no	—
820	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
821	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
822	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
823	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
824	C₂×C₂²⋊C₄	—	2	2	no	—
825	C₂×C₂²⋊C₄	—	2	2	no	—
826	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
827	C₂×C₄²	—	2	2	no	—
828	C₂×C₄²	—	2	1	no	—
829	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
830	#107	C₂³×C₆₇	1	1	yes	characteristic
831	#107	C₂³×C₆₇	1	2	yes	—
832	#107	C₂³×C₆₇	1	1	yes	characteristic
833	#107	C₂³×C₆₇	1	2	yes	—
834	#107	C₂³×C₆₇	1	2	yes	—
835	#107	C₂³×C₆₇	1	2	yes	—
836	#107	C₂³×C₆₇	1	2	yes	—
837	#106	C₂³×C₆₇	1	2	yes	—
838	#106	C₂³×C₆₇	1	1	yes	characteristic
839	#106	C₂³×C₆₇	1	1	yes	characteristic
840	#106	C₂³×C₆₇	1	2	yes	—
841	#106	C₂³×C₆₇	1	2	yes	—
842	#106	C₂³×C₆₇	1	2	yes	—
843	#106	C₂³×C₆₇	1	2	yes	—
844	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
852	#103	C₂³×C₆₇	1	1	yes	characteristic
853	#103	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
859	#103	C₂³×C₆₇	1	1	yes	characteristic
860	#103	C₂³×C₆₇	1	2	yes	—
861	#102	C₂³×C₆₇	1	1	yes	characteristic
862	#102	C₂³×C₆₇	1	1	yes	characteristic
863	#102	C₂³×C₆₇	1	2	yes	—
864	#102	C₂³×C₆₇	1	2	yes	—
865	#102	C₂³×C₆₇	1	1	yes	characteristic
866	#102	C₂³×C₆₇	1	1	yes	characteristic
867	#102	C₂³×C₆₇	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
869	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
870	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
875	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
876	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
877	C₄×C₈	C₂³×C₆₇	1	2	yes	—
878	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
879	#41	—	4	1	no	—
880	#41	—	4	1	no	—
881	#41	—	4	2	no	—
882	#41	—	4	2	no	—
883	#41	—	4	4	no	—
884	#41	—	4	4	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	4	2	no	—
890	C₂×Q₈	—	4	2	no	—
891	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
892	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
893	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	4	2	no	—
901	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
902	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
903	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
904	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
905	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	4	2	no	—
916	C₂²×C₄	—	4	2	no	—
917	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
918	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
919	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
920	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
921	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
922	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
924	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
925	Q₁₆	—	4	1	no	—
926	Q₁₆	—	4	2	no	—
927	SD₁₆	—	4	1	no	—
928	SD₁₆	—	4	2	no	—
929	SD₁₆	—	4	1	no	—
930	D₈	—	4	1	no	—
931	M₁₆	—	4	2	no	—
932	M₁₆	—	4	2	no	—
933	M₁₆	—	4	2	no	—
934	M₁₆	—	4	2	no	—
935	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
937	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
939	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
940	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
965	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
966	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
974	C₂²⋊C₄	—	2	1	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	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄×C₆₇	1	2	yes	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1009	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1010	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1011	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	4	2	no	—
1015	C₂³	—	4	2	no	—
1016	C₂³	—	4	2	no	—
1017	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1018	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1019	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	4	2	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	8	2	no	—
1029	Q₈	—	8	1	no	—
1030	D₄	—	2	2	no	—
1031	D₄	—	2	2	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	4	4	no	—
1038	D₄	—	4	4	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	8	2	no	—
1042	D₄	—	8	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	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	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	4	1	no	—
1064	C₂×C₄	—	4	2	no	—
1065	C₂×C₄	—	4	4	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	—	8	1	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1077	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1078	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1079	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1080	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1081	C₈	—	2	1	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	2	no	—
1085	C₈	—	2	2	no	—
1086	C₈	—	2	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	8	4	no	—
1103	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	#575×C₆₇	1	2	yes	—
1121	C₄	#585×C₆₇	1	1	yes	characteristic
1122	C₄	#585×C₆₇	1	1	yes	characteristic
1123	C₂	—	4	1	no	—
1124	C₂	—	4	2	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	8	1	no	—
1127	C₂	—	8	1	no	—
1128	C₂	C₆₇×#3485	1	1	yes	characteristic
1129	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
1130	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. C₆₇×#3475	C₂	semidirect
3. C₆₇×#3356	C₂	semidirect
4. C₆₇×#3354	C₂	semidirect
5. C₆₇×#3353	C₂	semidirect
6. C₆₇×#3353	C₂	semidirect
7. C₆₇×#3352	C₂	semidirect
8. C₆₇×#3351	C₂	semidirect
9. C₆₇×#3331	C₂	semidirect
10. C₆₇×#3330	C₂	semidirect
11. C₆₇×#3329	C₂	semidirect
12. C₆₇×#3328	C₂	semidirect
13. C₆₇×#3327	C₂	semidirect
14. C₆₇×#3326	C₂	semidirect
15. C₆₇×#3233	C₂	semidirect
16. C₆₇×#3231	C₂	semidirect
17. C₆₇×#3197	C₂	semidirect
18. C₆₇×#3196	C₂	semidirect
19. C₆₇×#3107	C₂	semidirect
20. C₆₇×#3102	C₂	semidirect
21. C₆₇×#3095	C₂	semidirect
22. C₆₇×#3093	C₂	semidirect
23. C₆₇×#2975	C₂	semidirect
57. #500×C₆₇	C₂²	semidirect
58. #499×C₆₇	C₂²	semidirect
59. #498×C₆₇	C₂²	semidirect
60. #488×C₆₇	C₂²	semidirect
61. #487×C₆₇	C₂²	semidirect
62. #487×C₆₇	C₂²	semidirect
68. #485×C₆₇	C₂²	semidirect
69. #485×C₆₇	C₂²	semidirect
70. #485×C₆₇	C₂²	semidirect
71. #484×C₆₇	C₂²	semidirect
72. #484×C₆₇	C₂²	semidirect
73. #484×C₆₇	C₂²	semidirect
74. #483×C₆₇	C₂²	semidirect
75. #483×C₆₇	C₂²	semidirect
78. #482×C₆₇	C₂²	semidirect
79. #482×C₆₇	C₂²	semidirect
80. #482×C₆₇	C₂²	semidirect
81. #481×C₆₇	C₂²	semidirect
82. #479×C₆₇	C₂²	semidirect
83. #479×C₆₇	C₂²	semidirect
84. #479×C₆₇	C₂²	semidirect
85. #478×C₆₇	C₂²	semidirect
86. #477×C₆₇	C₂²	semidirect
87. #476×C₆₇	C₂²	semidirect
88. #475×C₆₇	C₂²	semidirect
89. #475×C₆₇	C₂²	semidirect
90. #474×C₆₇	C₂²	semidirect
91. #474×C₆₇	C₂²	semidirect
92. #470×C₆₇	C₂²	semidirect
93. #470×C₆₇	C₂²	semidirect
94. #470×C₆₇	C₂²	semidirect
95. #469×C₆₇	C₂²	semidirect
96. #468×C₆₇	C₂²	semidirect
97. #468×C₆₇	C₂²	semidirect
98. #468×C₆₇	C₂²	semidirect
99. #468×C₆₇	C₂²	semidirect
100. #464×C₆₇	C₂²	semidirect
101. #463×C₆₇	C₂²	semidirect
102. #462×C₆₇	C₂²	semidirect
103. #461×C₆₇	C₂²	semidirect
106. #452×C₆₇	C₂²	semidirect
107. #451×C₆₇	C₂²	semidirect
109. #449×C₆₇	C₂²	semidirect
110. #448×C₆₇	C₂²	semidirect
111. C₄×Q₁₆×C₆₇	C₂²	semidirect
112. C₄×Q₁₆×C₆₇	C₂²	semidirect
113. C₄×SD₁₆×C₆₇	C₂²	semidirect
114. C₄×SD₁₆×C₆₇	C₂²	semidirect
115. C₄×SD₁₆×C₆₇	C₂²	semidirect
116. C₄×D₈×C₆₇	C₂²	semidirect
125. #428×C₆₇	C₂²	semidirect
126. #428×C₆₇	C₂²	semidirect
127. #428×C₆₇	C₂²	semidirect
128. #428×C₆₇	C₂²	semidirect
129. #419×C₆₇	C₂²	semidirect
130. #419×C₆₇	C₂²	semidirect
131. #417×C₆₇	C₂²	semidirect
132. #417×C₆₇	C₂²	semidirect
557. #61724	C₆₇	direct (N × H)
566. #3520	C₂×C₆₇	semidirect
567. #3475	C₂×C₆₇	semidirect
568. #3356	C₂×C₆₇	semidirect
569. #3354	C₂×C₆₇	semidirect
570. #3353	C₂×C₆₇	semidirect
571. #3353	C₂×C₆₇	semidirect
572. #3352	C₂×C₆₇	semidirect
573. #3351	C₂×C₆₇	semidirect
574. #3331	C₂×C₆₇	semidirect
575. #3330	C₂×C₆₇	semidirect
576. #3329	C₂×C₆₇	semidirect
577. #3328	C₂×C₆₇	semidirect
578. #3327	C₂×C₆₇	semidirect
579. #3326	C₂×C₆₇	semidirect
580. #3233	C₂×C₆₇	semidirect
581. #3231	C₂×C₆₇	semidirect
582. #3197	C₂×C₆₇	semidirect
583. #3196	C₂×C₆₇	semidirect
584. #3107	C₂×C₆₇	semidirect
585. #3102	C₂×C₆₇	semidirect
586. #3095	C₂×C₆₇	semidirect
587. #3093	C₂×C₆₇	semidirect
588. #2975	C₂×C₆₇	semidirect
589. C₆₇	#61724	direct (N × H)
623. #500	C₂²×C₆₇	semidirect
624. #499	C₂²×C₆₇	semidirect
625. #498	C₂²×C₆₇	semidirect
626. #488	C₂²×C₆₇	semidirect
627. #487	C₂²×C₆₇	semidirect
628. #487	C₂²×C₆₇	semidirect
634. #485	C₂²×C₆₇	semidirect
635. #485	C₂²×C₆₇	semidirect
636. #485	C₂²×C₆₇	semidirect
637. #484	C₂²×C₆₇	semidirect
638. #484	C₂²×C₆₇	semidirect
639. #484	C₂²×C₆₇	semidirect
640. #483	C₂²×C₆₇	semidirect
641. #483	C₂²×C₆₇	semidirect
644. #482	C₂²×C₆₇	semidirect
645. #482	C₂²×C₆₇	semidirect
646. #482	C₂²×C₆₇	semidirect
647. #481	C₂²×C₆₇	semidirect
648. #479	C₂²×C₆₇	semidirect
649. #479	C₂²×C₆₇	semidirect
650. #479	C₂²×C₆₇	semidirect
651. #478	C₂²×C₆₇	semidirect
652. #477	C₂²×C₆₇	semidirect
653. #476	C₂²×C₆₇	semidirect
654. #475	C₂²×C₆₇	semidirect
655. #475	C₂²×C₆₇	semidirect
656. #474	C₂²×C₆₇	semidirect
657. #474	C₂²×C₆₇	semidirect
658. #470	C₂²×C₆₇	semidirect
659. #470	C₂²×C₆₇	semidirect
660. #470	C₂²×C₆₇	semidirect
661. #469	C₂²×C₆₇	semidirect
662. #468	C₂²×C₆₇	semidirect
663. #468	C₂²×C₆₇	semidirect
664. #468	C₂²×C₆₇	semidirect
665. #468	C₂²×C₆₇	semidirect
666. #464	C₂²×C₆₇	semidirect
667. #463	C₂²×C₆₇	semidirect
668. #462	C₂²×C₆₇	semidirect
669. #461	C₂²×C₆₇	semidirect
672. #452	C₂²×C₆₇	semidirect
673. #451	C₂²×C₆₇	semidirect
675. #449	C₂²×C₆₇	semidirect
676. #448	C₂²×C₆₇	semidirect
677. C₄×Q₁₆	C₂²×C₆₇	semidirect
678. C₄×Q₁₆	C₂²×C₆₇	semidirect
679. C₄×SD₁₆	C₂²×C₆₇	semidirect
680. C₄×SD₁₆	C₂²×C₆₇	semidirect
681. C₄×SD₁₆	C₂²×C₆₇	semidirect
682. C₄×D₈	C₂²×C₆₇	semidirect
691. #428	C₂²×C₆₇	semidirect
692. #428	C₂²×C₆₇	semidirect
693. #428	C₂²×C₆₇	semidirect
694. #428	C₂²×C₆₇	semidirect
695. #419	C₂²×C₆₇	semidirect
696. #419	C₂²×C₆₇	semidirect
697. #417	C₂²×C₆₇	semidirect
698. #417	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
C₆₇×#3475	2
C₆₇×#3356	2
C₆₇×#3354	2
C₆₇×#3353	2
C₆₇×#3352	2
C₆₇×#3351	2
C₆₇×#3331	2
C₆₇×#3330	2
C₆₇×#3329	2
C₆₇×#3328	2
C₆₇×#3327	2
C₆₇×#3326	2
C₆₇×#3233	2
C₆₇×#3231	2
C₆₇×#3197	2
C₆₇×#3196	2
C₆₇×#3107	2
C₆₇×#3102	2
C₆₇×#3095	2
C₆₇×#3093	2
C₆₇×#2975	2
#61724	67

Subgroups — C67×#61724 #30740975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61724 #30740975