Subgroups — C₆₇×#61263 #30740514

Order 17152.

1824 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3494	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3350	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3348	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3346	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3343	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3340	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3337	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3337	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3335	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3095	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3081	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#465×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2912	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#427×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
27	#556×C₆₇	C₂²	1	2	yes	complemented
28	#555×C₆₇	C₂²	1	2	yes	—
29	#554×C₆₇	C₂²	1	2	yes	complemented
30	#553×C₆₇	C₂²	1	2	yes	—
31	#553×C₆₇	C₂²	1	2	yes	—
32	#552×C₆₇	—	2	2	no	—
33	#552×C₆₇	C₂²	1	2	yes	complemented
34	#552×C₆₇	C₂²	1	2	yes	complemented
35	#551×C₆₇	—	2	2	no	—
36	#551×C₆₇	—	2	2	no	—
37	#547×C₆₇	C₂²	1	2	yes	—
38	#546×C₆₇	—	2	2	no	—
39	#544×C₆₇	C₂²	1	1	yes	characteristic
40	#544×C₆₇	C₂²	1	1	yes	characteristic
41	#542×C₆₇	—	2	1	no	—
42	#542×C₆₇	—	2	1	no	—
43	#541×C₆₇	—	2	1	no	—
44	#540×C₆₇	—	2	1	no	—
45	#536×C₆₇	C₂²	1	1	yes	characteristic
46	#535×C₆₇	C₂²	1	1	yes	characteristic
47	#533×C₆₇	—	2	1	no	—
48	#532×C₆₇	—	2	1	no	—
49	#529×C₆₇	—	2	1	no	—
50	#529×C₆₇	—	2	1	no	—
51	#525×C₆₇	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
54	#520×C₆₇	C₂²	1	1	yes	characteristic
55	#520×C₆₇	C₂²	1	1	yes	characteristic
56	#519×C₆₇	C₂²	1	1	yes	characteristic
57	#518×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
60	#501×C₆₇	C₂²	1	2	yes	complemented
61	#501×C₆₇	C₂²	1	2	yes	complemented
62	#499×C₆₇	C₂²	1	2	yes	complemented
63	#498×C₆₇	C₂²	1	2	yes	complemented
64	#485×C₆₇	C₂²	1	2	yes	complemented
65	#485×C₆₇	C₂²	1	2	yes	complemented
66	#485×C₆₇	C₂²	1	2	yes	complemented
67	#485×C₆₇	C₂²	1	2	yes	complemented
68	#484×C₆₇	C₂²	1	2	yes	complemented
69	#484×C₆₇	C₂²	1	2	yes	complemented
70	#483×C₆₇	C₂²	1	2	yes	complemented
71	#483×C₆₇	C₂²	1	2	yes	complemented
72	#482×C₆₇	C₂²	1	2	yes	—
73	#482×C₆₇	C₂²	1	2	yes	—
74	#482×C₆₇	C₂²	1	2	yes	complemented
75	#482×C₆₇	C₂²	1	2	yes	complemented
76	#481×C₆₇	C₂²	1	2	yes	—
77	#481×C₆₇	C₂²	1	2	yes	complemented
78	#480×C₆₇	C₂²	1	2	yes	—
79	#480×C₆₇	C₂²	1	2	yes	complemented
80	#479×C₆₇	C₂²	1	2	yes	complemented
81	#479×C₆₇	C₂²	1	2	yes	complemented
82	#478×C₆₇	C₂²	1	2	yes	complemented
83	#478×C₆₇	C₂²	1	2	yes	complemented
84	#477×C₆₇	C₂²	1	2	yes	complemented
85	#476×C₆₇	C₂²	1	2	yes	complemented
86	#475×C₆₇	C₂²	1	2	yes	complemented
87	#474×C₆₇	C₂²	1	2	yes	complemented
88	#468×C₆₇	C₂²	1	2	yes	complemented
89	#468×C₆₇	C₂²	1	2	yes	complemented
90	#465×C₆₇	C₂²	1	2	yes	—
91	#465×C₆₇	C₂²	1	2	yes	—
92	#465×C₆₇	C₂²	1	2	yes	—
93	#465×C₆₇	C₂²	1	2	yes	—
94	#465×C₆₇	C₂²	1	2	yes	complemented
95	#465×C₆₇	C₂²	1	2	yes	complemented
96	#440×C₆₇	C₂²	1	2	yes	complemented
97	#440×C₆₇	C₂²	1	2	yes	complemented
98	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
99	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
100	#435×C₆₇	C₂²	1	2	yes	complemented
101	#435×C₆₇	C₂²	1	2	yes	complemented
102	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
103	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
104	#428×C₆₇	C₂²	1	1	yes	characteristic
105	#428×C₆₇	C₂²	1	1	yes	characteristic
106	#428×C₆₇	C₂²	1	1	yes	characteristic
107	#428×C₆₇	C₂²	1	1	yes	characteristic
108	#428×C₆₇	C₂²	1	2	yes	complemented
109	#428×C₆₇	C₂²	1	2	yes	complemented
110	#427×C₆₇	C₂²	1	1	yes	characteristic
111	#427×C₆₇	C₂²	1	1	yes	characteristic
112	#427×C₆₇	C₂²	1	1	yes	characteristic
113	#427×C₆₇	C₂²	1	1	yes	characteristic
114	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	#427×C₆₇	C₂²	1	2	yes	complemented
116	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
124	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#424×C₆₇	C₂²	1	1	yes	characteristic
126	#419×C₆₇	C₂²	1	1	yes	characteristic
127	#419×C₆₇	C₂²	1	1	yes	characteristic
128	#418×C₆₇	C₂²	1	1	yes	characteristic
129	#418×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
131	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	#407×C₆₇	C₂²	1	1	yes	characteristic
134	#405×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₇	—	2	2	no	—
136	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₆₇	—	2	1	no	—
139	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₆₇	—	2	4	no	—
142	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
144	#131×C₆₇	—	2	4	no	—
145	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₆₇	—	2	4	no	—
149	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
154	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₆₇	—	2	1	no	—
157	C₄⋊Q₈×C₆₇	—	2	1	no	—
158	C₄⋊Q₈×C₆₇	—	2	1	no	—
159	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
161	#127×C₆₇	—	2	1	no	—
162	#126×C₆₇	—	2	2	no	—
163	#126×C₆₇	—	2	2	no	—
164	#126×C₆₇	—	2	2	no	—
165	#126×C₆₇	—	2	2	no	—
166	#126×C₆₇	—	2	2	no	—
167	#126×C₆₇	—	2	2	no	—
168	#125×C₆₇	—	2	1	no	—
169	#125×C₆₇	—	2	1	no	—
170	#125×C₆₇	—	2	2	no	—
171	#125×C₆₇	—	2	2	no	—
172	#125×C₆₇	—	2	2	no	—
173	#125×C₆₇	C₂³	1	2	yes	—
174	#125×C₆₇	C₂³	1	2	yes	—
175	#124×C₆₇	—	2	1	no	—
176	#124×C₆₇	—	2	1	no	—
177	#124×C₆₇	—	2	2	no	—
178	#124×C₆₇	—	2	2	no	—
179	#124×C₆₇	—	2	2	no	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	—	2	2	no	—
182	#123×C₆₇	—	2	2	no	—
183	#123×C₆₇	—	2	2	no	—
184	#123×C₆₇	—	2	2	no	—
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	D₄	1	2	yes	—
188	C₂²⋊Q₈×C₆₇	—	2	1	no	—
189	C₂²⋊Q₈×C₆₇	—	2	1	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	D₄	1	1	yes	characteristic
196	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
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	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
201	#121×C₆₇	—	2	2	no	—
202	#121×C₆₇	—	2	2	no	—
203	#121×C₆₇	—	2	2	no	—
204	#121×C₆₇	—	2	1	no	—
205	#121×C₆₇	—	2	1	no	—
206	#121×C₆₇	D₄	1	1	yes	characteristic
207	#121×C₆₇	D₄	1	1	yes	characteristic
208	#121×C₆₇	C₂³	1	2	yes	—
209	#121×C₆₇	C₂³	1	2	yes	—
210	#121×C₆₇	C₂³	1	2	yes	—
211	#121×C₆₇	C₂³	1	2	yes	—
212	#120×C₆₇	—	2	2	no	—
213	#120×C₆₇	D₄	1	2	yes	—
214	C₄×Q₈×C₆₇	—	2	1	no	—
215	C₄×Q₈×C₆₇	—	2	1	no	—
216	C₄×Q₈×C₆₇	—	2	1	no	—
217	C₄×Q₈×C₆₇	—	2	1	no	—
218	C₄×Q₈×C₆₇	—	2	2	no	—
219	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
220	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
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	2	no	—
225	C₄×D₄×C₆₇	—	2	2	no	—
226	C₄×D₄×C₆₇	—	2	1	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	C₂³	1	2	yes	—
231	C₄×D₄×C₆₇	C₂³	1	2	yes	—
232	C₄×D₄×C₆₇	C₂³	1	2	yes	—
233	C₄×D₄×C₆₇	C₂³	1	2	yes	—
234	#117×C₆₇	—	2	1	no	—
235	#117×C₆₇	—	2	1	no	—
236	#117×C₆₇	—	2	1	no	—
237	#117×C₆₇	—	2	1	no	—
238	#117×C₆₇	—	2	2	no	—
239	#117×C₆₇	—	2	2	no	—
240	#117×C₆₇	—	2	2	no	—
241	#117×C₆₇	—	2	2	no	—
242	#117×C₆₇	C₂³	1	1	yes	characteristic
243	#117×C₆₇	C₂³	1	1	yes	characteristic
244	#117×C₆₇	C₂³	1	2	yes	—
245	#117×C₆₇	C₂³	1	1	yes	characteristic
246	#117×C₆₇	C₂³	1	1	yes	characteristic
247	#117×C₆₇	C₂³	1	2	yes	—
248	#117×C₆₇	C₂³	1	1	yes	characteristic
249	#117×C₆₇	C₂³	1	1	yes	characteristic
250	#117×C₆₇	C₂³	1	1	yes	characteristic
251	#117×C₆₇	C₂³	1	1	yes	characteristic
252	#117×C₆₇	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
254	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
267	C₂×C₄²×C₆₇	—	2	1	no	—
268	C₂×C₄²×C₆₇	—	2	1	no	—
269	#107×C₆₇	C₂³	1	1	yes	characteristic
270	#107×C₆₇	C₂³	1	1	yes	characteristic
271	#107×C₆₇	C₂³	1	1	yes	characteristic
272	#107×C₆₇	C₂³	1	2	yes	—
273	#107×C₆₇	C₂³	1	1	yes	characteristic
274	#107×C₆₇	C₂³	1	2	yes	—
275	#107×C₆₇	C₂³	1	1	yes	characteristic
276	#107×C₆₇	C₂³	1	1	yes	characteristic
277	#107×C₆₇	C₂³	1	2	yes	—
278	#107×C₆₇	C₂³	1	2	yes	—
279	#107×C₆₇	C₂³	1	1	yes	characteristic
280	#107×C₆₇	C₂³	1	1	yes	characteristic
281	#106×C₆₇	C₂³	1	2	yes	—
282	#106×C₆₇	C₂³	1	2	yes	—
283	#106×C₆₇	C₂³	1	1	yes	characteristic
284	#106×C₆₇	C₂³	1	1	yes	characteristic
285	#106×C₆₇	C₂³	1	1	yes	characteristic
286	#106×C₆₇	C₂³	1	2	yes	—
287	#106×C₆₇	C₂³	1	1	yes	characteristic
288	#106×C₆₇	C₂³	1	2	yes	—
289	#106×C₆₇	C₂³	1	1	yes	characteristic
290	#106×C₆₇	C₂³	1	1	yes	characteristic
291	#106×C₆₇	C₂³	1	2	yes	—
292	#106×C₆₇	C₂³	1	2	yes	—
293	#106×C₆₇	C₂³	1	1	yes	characteristic
294	#106×C₆₇	C₂³	1	1	yes	characteristic
295	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
296	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
297	#103×C₆₇	C₂³	1	2	yes	—
298	#103×C₆₇	C₂³	1	2	yes	—
299	#103×C₆₇	C₂³	1	2	yes	—
300	#103×C₆₇	C₂³	1	2	yes	—
301	#103×C₆₇	C₂³	1	2	yes	—
302	#103×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	2	yes	—
305	#102×C₆₇	C₂³	1	2	yes	—
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	2	yes	—
308	#102×C₆₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
313	#97×C₆₇	C₂³	1	2	yes	—
314	C₄×C₈×C₆₇	C₂³	1	2	yes	—
315	C₂⁴×C₆₇	—	2	1	no	—
316	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
317	#41×C₆₇	—	2	2	no	—
318	#41×C₆₇	—	2	2	no	—
319	#41×C₆₇	—	8	4	no	—
320	C₂×Q₈×C₆₇	—	2	1	no	—
321	C₂×Q₈×C₆₇	—	2	2	no	—
322	C₂×Q₈×C₆₇	—	2	2	no	—
323	C₂×Q₈×C₆₇	—	2	2	no	—
324	C₂×Q₈×C₆₇	—	2	2	no	—
325	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
327	C₂×D₄×C₆₇	—	2	2	no	—
328	C₂×D₄×C₆₇	—	2	2	no	—
329	C₂×D₄×C₆₇	—	2	2	no	—
330	C₂×D₄×C₆₇	—	2	2	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	—	8	2	no	—
335	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
338	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₆₇	—	2	2	no	—
341	C₂²×C₄×C₆₇	—	2	2	no	—
342	C₂²×C₄×C₆₇	—	2	1	no	—
343	C₂²×C₄×C₆₇	—	2	1	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	1	no	—
349	C₂²×C₄×C₆₇	—	2	2	no	—
350	C₂²×C₄×C₆₇	—	2	2	no	—
351	C₂²×C₄×C₆₇	—	2	2	no	—
352	C₂²×C₄×C₆₇	—	2	2	no	—
353	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
360	SD₁₆×C₆₇	—	2	4	no	—
361	SD₁₆×C₆₇	—	2	4	no	—
362	M₁₆×C₆₇	—	2	2	no	—
363	M₁₆×C₆₇	—	2	2	no	—
364	M₁₆×C₆₇	—	2	4	no	—
365	C₂×C₈×C₆₇	—	2	2	no	—
366	C₂×C₈×C₆₇	—	2	2	no	—
367	C₂×C₈×C₆₇	—	2	2	no	—
368	C₂×C₈×C₆₇	—	2	2	no	—
369	C₂×C₈×C₆₇	—	2	2	no	—
370	C₂×C₈×C₆₇	—	2	4	no	—
371	C₂×C₈×C₆₇	#41	1	4	yes	complemented
372	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
374	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
376	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₆₇	—	2	2	no	—
379	C₄⋊C₄×C₆₇	—	2	2	no	—
380	C₄⋊C₄×C₆₇	—	2	1	no	—
381	C₄⋊C₄×C₆₇	—	2	1	no	—
382	C₄⋊C₄×C₆₇	—	2	1	no	—
383	C₄⋊C₄×C₆₇	—	2	1	no	—
384	C₄⋊C₄×C₆₇	—	2	1	no	—
385	C₄⋊C₄×C₆₇	—	2	1	no	—
386	C₄⋊C₄×C₆₇	—	2	2	no	—
387	C₄⋊C₄×C₆₇	—	2	2	no	—
388	C₄⋊C₄×C₆₇	—	2	2	no	—
389	C₄⋊C₄×C₆₇	—	2	2	no	—
390	C₄⋊C₄×C₆₇	—	2	2	no	—
391	C₄⋊C₄×C₆₇	—	2	2	no	—
392	C₄⋊C₄×C₆₇	—	2	2	no	—
393	C₄⋊C₄×C₆₇	—	2	2	no	—
394	C₄⋊C₄×C₆₇	—	2	2	no	—
395	C₄⋊C₄×C₆₇	—	2	2	no	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	—	2	2	no	—
398	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
411	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₆₇	—	2	1	no	—
413	C₂²⋊C₄×C₆₇	—	2	1	no	—
414	C₂²⋊C₄×C₆₇	—	2	1	no	—
415	C₂²⋊C₄×C₆₇	—	2	1	no	—
416	C₂²⋊C₄×C₆₇	—	2	1	no	—
417	C₂²⋊C₄×C₆₇	—	2	1	no	—
418	C₂²⋊C₄×C₆₇	—	2	1	no	—
419	C₂²⋊C₄×C₆₇	—	2	1	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	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	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
437	C₄²×C₆₇	—	2	1	no	—
438	C₄²×C₆₇	—	2	1	no	—
439	C₄²×C₆₇	—	2	1	no	—
440	C₄²×C₆₇	—	2	1	no	—
441	C₄²×C₆₇	—	2	1	no	—
442	C₄²×C₆₇	—	2	1	no	—
443	C₄²×C₆₇	—	2	1	no	—
444	C₄²×C₆₇	—	2	1	no	—
445	C₄²×C₆₇	—	2	2	no	—
446	C₄²×C₆₇	—	2	2	no	—
447	C₄²×C₆₇	—	2	2	no	—
448	C₄²×C₆₇	—	2	2	no	—
449	C₄²×C₆₇	C₂⁴	1	2	yes	—
450	C₂³×C₆₇	—	2	2	no	—
451	C₂³×C₆₇	—	2	2	no	—
452	C₂³×C₆₇	—	2	2	no	—
453	C₂³×C₆₇	—	4	1	no	—
454	C₂³×C₆₇	—	4	2	no	—
455	C₂³×C₆₇	—	8	1	no	—
456	C₂³×C₆₇	—	8	1	no	—
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	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
461	Q₈×C₆₇	—	2	2	no	—
462	Q₈×C₆₇	—	2	2	no	—
463	Q₈×C₆₇	—	2	2	no	—
464	Q₈×C₆₇	—	4	2	no	—
465	Q₈×C₆₇	—	8	2	no	—
466	Q₈×C₆₇	—	8	2	no	—
467	D₄×C₆₇	—	2	4	no	—
468	D₄×C₆₇	—	2	4	no	—
469	D₄×C₆₇	—	2	2	no	—
470	D₄×C₆₇	—	2	2	no	—
471	D₄×C₆₇	—	2	2	no	—
472	D₄×C₆₇	—	4	2	no	—
473	D₄×C₆₇	—	4	4	no	—
474	D₄×C₆₇	—	4	2	no	—
475	D₄×C₆₇	—	8	2	no	—
476	D₄×C₆₇	—	8	2	no	—
477	D₄×C₆₇	—	8	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	1	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	2	2	no	—
484	C₂×C₄×C₆₇	—	2	1	no	—
485	C₂×C₄×C₆₇	—	2	1	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	1	no	—
490	C₂×C₄×C₆₇	—	2	1	no	—
491	C₂×C₄×C₆₇	—	2	2	no	—
492	C₂×C₄×C₆₇	—	2	1	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	2	no	—
498	C₂×C₄×C₆₇	—	4	2	no	—
499	C₂×C₄×C₆₇	—	4	2	no	—
500	C₂×C₄×C₆₇	—	4	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	1	no	—
505	C₂×C₄×C₆₇	—	8	1	no	—
506	C₂×C₄×C₆₇	—	8	1	no	—
507	C₂×C₄×C₆₇	—	8	1	no	—
508	C₂×C₄×C₆₇	—	8	2	no	—
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	2	yes	—
512	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
516	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
517	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
518	C₈×C₆₇	—	2	1	no	—
519	C₈×C₆₇	—	2	1	no	—
520	C₈×C₆₇	—	2	2	no	—
521	C₈×C₆₇	—	2	2	no	—
522	C₈×C₆₇	C₂×#41	1	2	yes	—
523	C₈×C₆₇	C₂×#41	1	2	yes	—
524	C₂²×C₆₇	—	2	1	no	—
525	C₂²×C₆₇	—	2	1	no	—
526	C₂²×C₆₇	—	2	1	no	—
527	C₂²×C₆₇	—	2	1	no	—
528	C₂²×C₆₇	—	2	2	no	—
529	C₂²×C₆₇	—	2	1	no	—
530	C₂²×C₆₇	—	2	1	no	—
531	C₂²×C₆₇	—	2	2	no	—
532	C₂²×C₆₇	—	2	2	no	—
533	C₂²×C₆₇	—	2	1	no	—
534	C₂²×C₆₇	—	4	4	no	—
535	C₂²×C₆₇	—	4	2	no	—
536	C₂²×C₆₇	—	4	2	no	—
537	C₂²×C₆₇	—	4	2	no	—
538	C₂²×C₆₇	—	16	2	no	—
539	C₂²×C₆₇	#547	1	2	yes	—
540	C₂²×C₆₇	#577	1	2	yes	—
541	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
542	C₄×C₆₇	—	2	2	no	—
543	C₄×C₆₇	—	2	1	no	—
544	C₄×C₆₇	—	2	1	no	—
545	C₄×C₆₇	—	2	2	no	—
546	C₄×C₆₇	—	2	2	no	—
547	C₄×C₆₇	—	4	1	no	—
548	C₄×C₆₇	—	4	1	no	—
549	C₄×C₆₇	—	4	2	no	—
550	C₄×C₆₇	—	4	1	no	—
551	C₄×C₆₇	—	4	1	no	—
552	C₄×C₆₇	—	4	2	no	—
553	C₄×C₆₇	—	4	1	no	—
554	C₄×C₆₇	—	4	1	no	—
555	C₄×C₆₇	—	4	1	no	—
556	C₄×C₆₇	—	4	1	no	—
557	C₄×C₆₇	—	4	2	no	—
558	C₄×C₆₇	#547	1	2	yes	—
559	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
560	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
561	#61263	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
562	C₂×C₆₇	—	2	2	no	—
563	C₂×C₆₇	—	2	2	no	—
564	C₂×C₆₇	—	4	2	no	—
565	C₂×C₆₇	—	4	1	no	—
566	C₂×C₆₇	—	8	2	no	—
567	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
568	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
569	C₂×C₆₇	#3584	1	1	yes	characteristic
570	#3495	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#3494	C₂×C₆₇	1	1	yes	characteristic
572	#3350	C₂×C₆₇	1	2	yes	complemented
573	#3348	C₂×C₆₇	1	2	yes	complemented
574	#3346	C₂×C₆₇	1	2	yes	complemented
575	#3343	C₂×C₆₇	1	2	yes	complemented
576	#3340	C₂×C₆₇	1	2	yes	complemented
577	#3337	C₂×C₆₇	1	2	yes	complemented
578	#3337	C₂×C₆₇	1	2	yes	complemented
579	#3335	C₂×C₆₇	1	2	yes	complemented
580	#3163	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#3097	C₂×C₆₇	1	1	yes	characteristic, complemented
582	#3096	C₂×C₆₇	1	1	yes	characteristic, complemented
583	#3095	C₂×C₆₇	1	1	yes	characteristic, complemented
584	#3094	C₂×C₆₇	1	1	yes	characteristic, complemented
585	#3082	C₂×C₆₇	1	1	yes	characteristic, complemented
586	#3081	C₂×C₆₇	1	1	yes	characteristic, complemented
587	#3057	C₂×C₆₇	1	1	yes	characteristic, complemented
588	C₂×#465	C₂×C₆₇	1	1	yes	characteristic, complemented
589	#2949	C₂×C₆₇	1	1	yes	characteristic, complemented
590	#2929	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#2912	C₂×C₆₇	1	1	yes	characteristic, complemented
592	C₂×#427	C₂×C₆₇	1	1	yes	characteristic, complemented
593	C₆₇	#61263	1	1	yes	characteristic, direct product factor, Sylow
594	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
595	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
596	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
597	#556	C₂²×C₆₇	1	2	yes	complemented
598	#555	C₂²×C₆₇	1	2	yes	—
599	#554	C₂²×C₆₇	1	2	yes	complemented
600	#553	C₂²×C₆₇	1	2	yes	—
601	#553	C₂²×C₆₇	1	2	yes	—
602	#552	—	2	2	no	—
603	#552	C₂²×C₆₇	1	2	yes	complemented
604	#552	C₂²×C₆₇	1	2	yes	complemented
605	#551	—	2	2	no	—
606	#551	—	2	2	no	—
607	#547	C₂²×C₆₇	1	2	yes	—
608	#546	—	2	2	no	—
609	#544	C₂²×C₆₇	1	1	yes	characteristic
610	#544	C₂²×C₆₇	1	1	yes	characteristic
611	#542	—	2	1	no	—
612	#542	—	2	1	no	—
613	#541	—	2	1	no	—
614	#540	—	2	1	no	—
615	#536	C₂²×C₆₇	1	1	yes	characteristic
616	#535	C₂²×C₆₇	1	1	yes	characteristic
617	#533	—	2	1	no	—
618	#532	—	2	1	no	—
619	#529	—	2	1	no	—
620	#529	—	2	1	no	—
621	#525	C₂²×C₆₇	1	1	yes	characteristic
622	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
623	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
624	#520	C₂²×C₆₇	1	1	yes	characteristic
625	#520	C₂²×C₆₇	1	1	yes	characteristic
626	#519	C₂²×C₆₇	1	1	yes	characteristic
627	#518	C₂²×C₆₇	1	1	yes	characteristic
628	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
629	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
630	#501	C₂²×C₆₇	1	2	yes	complemented
631	#501	C₂²×C₆₇	1	2	yes	complemented
632	#499	C₂²×C₆₇	1	2	yes	complemented
633	#498	C₂²×C₆₇	1	2	yes	complemented
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	#485	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	2	yes	—
643	#482	C₂²×C₆₇	1	2	yes	—
644	#482	C₂²×C₆₇	1	2	yes	complemented
645	#482	C₂²×C₆₇	1	2	yes	complemented
646	#481	C₂²×C₆₇	1	2	yes	—
647	#481	C₂²×C₆₇	1	2	yes	complemented
648	#480	C₂²×C₆₇	1	2	yes	—
649	#480	C₂²×C₆₇	1	2	yes	complemented
650	#479	C₂²×C₆₇	1	2	yes	complemented
651	#479	C₂²×C₆₇	1	2	yes	complemented
652	#478	C₂²×C₆₇	1	2	yes	complemented
653	#478	C₂²×C₆₇	1	2	yes	complemented
654	#477	C₂²×C₆₇	1	2	yes	complemented
655	#476	C₂²×C₆₇	1	2	yes	complemented
656	#475	C₂²×C₆₇	1	2	yes	complemented
657	#474	C₂²×C₆₇	1	2	yes	complemented
658	#468	C₂²×C₆₇	1	2	yes	complemented
659	#468	C₂²×C₆₇	1	2	yes	complemented
660	#465	C₂²×C₆₇	1	2	yes	—
661	#465	C₂²×C₆₇	1	2	yes	—
662	#465	C₂²×C₆₇	1	2	yes	—
663	#465	C₂²×C₆₇	1	2	yes	—
664	#465	C₂²×C₆₇	1	2	yes	complemented
665	#465	C₂²×C₆₇	1	2	yes	complemented
666	#440	C₂²×C₆₇	1	2	yes	complemented
667	#440	C₂²×C₆₇	1	2	yes	complemented
668	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
669	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
670	#435	C₂²×C₆₇	1	2	yes	complemented
671	#435	C₂²×C₆₇	1	2	yes	complemented
672	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
673	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
674	#428	C₂²×C₆₇	1	1	yes	characteristic
675	#428	C₂²×C₆₇	1	1	yes	characteristic
676	#428	C₂²×C₆₇	1	1	yes	characteristic
677	#428	C₂²×C₆₇	1	1	yes	characteristic
678	#428	C₂²×C₆₇	1	2	yes	complemented
679	#428	C₂²×C₆₇	1	2	yes	complemented
680	#427	C₂²×C₆₇	1	1	yes	characteristic
681	#427	C₂²×C₆₇	1	1	yes	characteristic
682	#427	C₂²×C₆₇	1	1	yes	characteristic
683	#427	C₂²×C₆₇	1	1	yes	characteristic
684	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
685	#427	C₂²×C₆₇	1	2	yes	complemented
686	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
689	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
691	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
692	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
694	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
695	#424	C₂²×C₆₇	1	1	yes	characteristic
696	#419	C₂²×C₆₇	1	1	yes	characteristic
697	#419	C₂²×C₆₇	1	1	yes	characteristic
698	#418	C₂²×C₆₇	1	1	yes	characteristic
699	#418	C₂²×C₆₇	1	1	yes	characteristic
700	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
701	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
702	#408	C₂²×C₆₇	1	1	yes	characteristic
703	#407	C₂²×C₆₇	1	1	yes	characteristic
704	#405	C₂²×C₆₇	1	1	yes	characteristic
705	C₂×#41	—	2	2	no	—
706	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
707	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
708	C₂²×D₄	—	2	1	no	—
709	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
710	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
711	C₂×SD₁₆	—	2	4	no	—
712	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
714	#131	—	2	4	no	—
715	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
716	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
717	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
718	C₂²×C₈	—	2	4	no	—
719	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
720	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
721	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
722	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
723	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
724	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
725	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
726	C₄⋊Q₈	—	2	1	no	—
727	C₄⋊Q₈	—	2	1	no	—
728	C₄⋊Q₈	—	2	1	no	—
729	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
730	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
731	#127	—	2	1	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#125	—	2	1	no	—
739	#125	—	2	1	no	—
740	#125	—	2	2	no	—
741	#125	—	2	2	no	—
742	#125	—	2	2	no	—
743	#125	C₂³×C₆₇	1	2	yes	—
744	#125	C₂³×C₆₇	1	2	yes	—
745	#124	—	2	1	no	—
746	#124	—	2	1	no	—
747	#124	—	2	2	no	—
748	#124	—	2	2	no	—
749	#124	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	D₄×C₆₇	1	2	yes	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
766	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
767	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	—	2	1	no	—
775	#121	—	2	1	no	—
776	#121	D₄×C₆₇	1	1	yes	characteristic
777	#121	D₄×C₆₇	1	1	yes	characteristic
778	#121	C₂³×C₆₇	1	2	yes	—
779	#121	C₂³×C₆₇	1	2	yes	—
780	#121	C₂³×C₆₇	1	2	yes	—
781	#121	C₂³×C₆₇	1	2	yes	—
782	#120	—	2	2	no	—
783	#120	D₄×C₆₇	1	2	yes	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	2	no	—
789	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
790	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	C₂³×C₆₇	1	2	yes	—
801	C₄×D₄	C₂³×C₆₇	1	2	yes	—
802	C₄×D₄	C₂³×C₆₇	1	2	yes	—
803	C₄×D₄	C₂³×C₆₇	1	2	yes	—
804	#117	—	2	1	no	—
805	#117	—	2	1	no	—
806	#117	—	2	1	no	—
807	#117	—	2	1	no	—
808	#117	—	2	2	no	—
809	#117	—	2	2	no	—
810	#117	—	2	2	no	—
811	#117	—	2	2	no	—
812	#117	C₂³×C₆₇	1	1	yes	characteristic
813	#117	C₂³×C₆₇	1	1	yes	characteristic
814	#117	C₂³×C₆₇	1	1	yes	characteristic
815	#117	C₂³×C₆₇	1	1	yes	characteristic
816	#117	C₂³×C₆₇	1	1	yes	characteristic
817	#117	C₂³×C₆₇	1	1	yes	characteristic
818	#117	C₂³×C₆₇	1	1	yes	characteristic
819	#117	C₂³×C₆₇	1	1	yes	characteristic
820	#117	C₂³×C₆₇	1	2	yes	—
821	#117	C₂³×C₆₇	1	2	yes	—
822	#117	C₂³×C₆₇	1	1	yes	characteristic
823	C₂×C₄⋊C₄	—	2	1	no	—
824	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
825	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
826	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
827	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
828	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
829	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
830	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
831	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
832	C₂×C₂²⋊C₄	—	2	1	no	—
833	C₂×C₂²⋊C₄	—	2	1	no	—
834	C₂×C₂²⋊C₄	—	2	1	no	—
835	C₂×C₂²⋊C₄	—	2	1	no	—
836	C₂×C₂²⋊C₄	—	2	2	no	—
837	C₂×C₄²	—	2	1	no	—
838	C₂×C₄²	—	2	1	no	—
839	#107	C₂³×C₆₇	1	1	yes	characteristic
840	#107	C₂³×C₆₇	1	1	yes	characteristic
841	#107	C₂³×C₆₇	1	1	yes	characteristic
842	#107	C₂³×C₆₇	1	1	yes	characteristic
843	#107	C₂³×C₆₇	1	1	yes	characteristic
844	#107	C₂³×C₆₇	1	1	yes	characteristic
845	#107	C₂³×C₆₇	1	1	yes	characteristic
846	#107	C₂³×C₆₇	1	1	yes	characteristic
847	#107	C₂³×C₆₇	1	2	yes	—
848	#107	C₂³×C₆₇	1	2	yes	—
849	#107	C₂³×C₆₇	1	2	yes	—
850	#107	C₂³×C₆₇	1	2	yes	—
851	#106	C₂³×C₆₇	1	2	yes	—
852	#106	C₂³×C₆₇	1	2	yes	—
853	#106	C₂³×C₆₇	1	1	yes	characteristic
854	#106	C₂³×C₆₇	1	1	yes	characteristic
855	#106	C₂³×C₆₇	1	1	yes	characteristic
856	#106	C₂³×C₆₇	1	1	yes	characteristic
857	#106	C₂³×C₆₇	1	1	yes	characteristic
858	#106	C₂³×C₆₇	1	1	yes	characteristic
859	#106	C₂³×C₆₇	1	1	yes	characteristic
860	#106	C₂³×C₆₇	1	1	yes	characteristic
861	#106	C₂³×C₆₇	1	2	yes	—
862	#106	C₂³×C₆₇	1	2	yes	—
863	#106	C₂³×C₆₇	1	2	yes	—
864	#106	C₂³×C₆₇	1	2	yes	—
865	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
866	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
867	#103	C₂³×C₆₇	1	2	yes	—
868	#103	C₂³×C₆₇	1	2	yes	—
869	#103	C₂³×C₆₇	1	2	yes	—
870	#103	C₂³×C₆₇	1	2	yes	—
871	#103	C₂³×C₆₇	1	2	yes	—
872	#103	C₂³×C₆₇	1	2	yes	—
873	#102	C₂³×C₆₇	1	2	yes	—
874	#102	C₂³×C₆₇	1	2	yes	—
875	#102	C₂³×C₆₇	1	2	yes	—
876	#102	C₂³×C₆₇	1	2	yes	—
877	#102	C₂³×C₆₇	1	2	yes	—
878	#102	C₂³×C₆₇	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
883	#97	C₂³×C₆₇	1	2	yes	—
884	C₄×C₈	C₂³×C₆₇	1	2	yes	—
885	C₂⁴	—	2	1	no	—
886	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
887	#41	—	2	2	no	—
888	#41	—	2	2	no	—
889	#41	—	8	4	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	2	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	2	no	—
895	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	8	2	no	—
905	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
906	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
907	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
908	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
909	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
924	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
925	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
927	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
928	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
930	SD₁₆	—	2	4	no	—
931	SD₁₆	—	2	4	no	—
932	M₁₆	—	2	2	no	—
933	M₁₆	—	2	2	no	—
934	M₁₆	—	2	4	no	—
935	C₂×C₈	—	2	2	no	—
936	C₂×C₈	—	2	2	no	—
937	C₂×C₈	—	2	2	no	—
938	C₂×C₈	—	2	2	no	—
939	C₂×C₈	—	2	2	no	—
940	C₂×C₈	—	2	4	no	—
941	C₂×C₈	#41×C₆₇	1	4	yes	complemented
942	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
943	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
945	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
947	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
971	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
979	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1003	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1004	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1005	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	C₂⁴×C₆₇	1	2	yes	—
1020	C₂³	—	2	2	no	—
1021	C₂³	—	2	2	no	—
1022	C₂³	—	2	2	no	—
1023	C₂³	—	4	1	no	—
1024	C₂³	—	4	2	no	—
1025	C₂³	—	8	1	no	—
1026	C₂³	—	8	1	no	—
1027	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1028	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1029	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1030	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1031	Q₈	—	2	2	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	2	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	8	2	no	—
1036	Q₈	—	8	2	no	—
1037	D₄	—	2	4	no	—
1038	D₄	—	2	4	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	2	no	—
1047	D₄	—	8	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	1	no	—
1077	C₂×C₄	—	8	1	no	—
1078	C₂×C₄	—	8	1	no	—
1079	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1081	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1082	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1085	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1086	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1087	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	2	no	—
1091	C₈	—	2	2	no	—
1092	C₈	C₂×#41×C₆₇	1	2	yes	—
1093	C₈	C₂×#41×C₆₇	1	2	yes	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	4	4	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	16	2	no	—
1109	C₂²	#547×C₆₇	1	2	yes	—
1110	C₂²	#577×C₆₇	1	2	yes	—
1111	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1112	C₄	—	2	2	no	—
1113	C₄	—	2	2	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	2	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	#547×C₆₇	1	2	yes	—
1129	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1130	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1131	C₂	—	2	2	no	—
1132	C₂	—	2	2	no	—
1133	C₂	—	4	1	no	—
1134	C₂	—	4	2	no	—
1135	C₂	—	8	2	no	—
1136	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
1137	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1138	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×#3494	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×#3495	C₂	semidirect
3. C₆₇×#3350	C₂	semidirect
4. C₆₇×#3348	C₂	semidirect
5. C₆₇×#3346	C₂	semidirect
6. C₆₇×#3343	C₂	semidirect
7. C₆₇×#3340	C₂	semidirect
8. C₆₇×#3337	C₂	semidirect
9. C₆₇×#3337	C₂	semidirect
10. C₆₇×#3335	C₂	semidirect
11. C₆₇×#3163	C₂	semidirect
12. C₆₇×#3097	C₂	semidirect
13. C₆₇×#3096	C₂	semidirect
14. C₆₇×#3095	C₂	semidirect
15. C₆₇×#3094	C₂	semidirect
16. C₆₇×#3082	C₂	semidirect
17. C₆₇×#3081	C₂	semidirect
18. C₆₇×#3057	C₂	semidirect
19. C₂×#465×C₆₇	C₂	semidirect
20. C₆₇×#2949	C₂	semidirect
21. C₆₇×#2929	C₂	semidirect
22. C₆₇×#2912	C₂	semidirect
23. C₂×#427×C₆₇	C₂	semidirect
27. #556×C₆₇	C₂²	semidirect
29. #554×C₆₇	C₂²	semidirect
33. #552×C₆₇	C₂²	semidirect
34. #552×C₆₇	C₂²	semidirect
60. #501×C₆₇	C₂²	semidirect
61. #501×C₆₇	C₂²	semidirect
62. #499×C₆₇	C₂²	semidirect
63. #498×C₆₇	C₂²	semidirect
64. #485×C₆₇	C₂²	semidirect
65. #485×C₆₇	C₂²	semidirect
66. #485×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
68. #484×C₆₇	C₂²	semidirect
69. #484×C₆₇	C₂²	semidirect
70. #483×C₆₇	C₂²	semidirect
71. #483×C₆₇	C₂²	semidirect
74. #482×C₆₇	C₂²	semidirect
75. #482×C₆₇	C₂²	semidirect
77. #481×C₆₇	C₂²	semidirect
79. #480×C₆₇	C₂²	semidirect
80. #479×C₆₇	C₂²	semidirect
81. #479×C₆₇	C₂²	semidirect
82. #478×C₆₇	C₂²	semidirect
83. #478×C₆₇	C₂²	semidirect
84. #477×C₆₇	C₂²	semidirect
85. #476×C₆₇	C₂²	semidirect
86. #475×C₆₇	C₂²	semidirect
87. #474×C₆₇	C₂²	semidirect
88. #468×C₆₇	C₂²	semidirect
89. #468×C₆₇	C₂²	semidirect
94. #465×C₆₇	C₂²	semidirect
95. #465×C₆₇	C₂²	semidirect
96. #440×C₆₇	C₂²	semidirect
97. #440×C₆₇	C₂²	semidirect
98. C₄×SD₁₆×C₆₇	C₂²	semidirect
99. C₄×SD₁₆×C₆₇	C₂²	semidirect
100. #435×C₆₇	C₂²	semidirect
101. #435×C₆₇	C₂²	semidirect
102. C₈×D₄×C₆₇	C₂²	semidirect
103. C₈×D₄×C₆₇	C₂²	semidirect
108. #428×C₆₇	C₂²	semidirect
109. #428×C₆₇	C₂²	semidirect
114. #427×C₆₇	C₂²	semidirect
115. #427×C₆₇	C₂²	semidirect
116. #427×C₆₇	C₂²	semidirect
117. #427×C₆₇	C₂²	semidirect
118. #427×C₆₇	C₂²	semidirect
119. C₂×#107×C₆₇	C₂²	semidirect
120. C₂×#107×C₆₇	C₂²	semidirect
122. C₂×#106×C₆₇	C₂²	semidirect
123. C₂×#106×C₆₇	C₂²	semidirect
124. C₂×#106×C₆₇	C₂²	semidirect
371. C₂×C₈×C₆₇	#41	semidirect
561. #61263	C₆₇	direct (N × H)
570. #3495	C₂×C₆₇	semidirect
572. #3350	C₂×C₆₇	semidirect
573. #3348	C₂×C₆₇	semidirect
574. #3346	C₂×C₆₇	semidirect
575. #3343	C₂×C₆₇	semidirect
576. #3340	C₂×C₆₇	semidirect
577. #3337	C₂×C₆₇	semidirect
578. #3337	C₂×C₆₇	semidirect
579. #3335	C₂×C₆₇	semidirect
580. #3163	C₂×C₆₇	semidirect
581. #3097	C₂×C₆₇	semidirect
582. #3096	C₂×C₆₇	semidirect
583. #3095	C₂×C₆₇	semidirect
584. #3094	C₂×C₆₇	semidirect
585. #3082	C₂×C₆₇	semidirect
586. #3081	C₂×C₆₇	semidirect
587. #3057	C₂×C₆₇	semidirect
588. C₂×#465	C₂×C₆₇	semidirect
589. #2949	C₂×C₆₇	semidirect
590. #2929	C₂×C₆₇	semidirect
591. #2912	C₂×C₆₇	semidirect
592. C₂×#427	C₂×C₆₇	semidirect
593. C₆₇	#61263	direct (N × H)
597. #556	C₂²×C₆₇	semidirect
599. #554	C₂²×C₆₇	semidirect
603. #552	C₂²×C₆₇	semidirect
604. #552	C₂²×C₆₇	semidirect
630. #501	C₂²×C₆₇	semidirect
631. #501	C₂²×C₆₇	semidirect
632. #499	C₂²×C₆₇	semidirect
633. #498	C₂²×C₆₇	semidirect
634. #485	C₂²×C₆₇	semidirect
635. #485	C₂²×C₆₇	semidirect
636. #485	C₂²×C₆₇	semidirect
637. #485	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
647. #481	C₂²×C₆₇	semidirect
649. #480	C₂²×C₆₇	semidirect
650. #479	C₂²×C₆₇	semidirect
651. #479	C₂²×C₆₇	semidirect
652. #478	C₂²×C₆₇	semidirect
653. #478	C₂²×C₆₇	semidirect
654. #477	C₂²×C₆₇	semidirect
655. #476	C₂²×C₆₇	semidirect
656. #475	C₂²×C₆₇	semidirect
657. #474	C₂²×C₆₇	semidirect
658. #468	C₂²×C₆₇	semidirect
659. #468	C₂²×C₆₇	semidirect
664. #465	C₂²×C₆₇	semidirect
665. #465	C₂²×C₆₇	semidirect
666. #440	C₂²×C₆₇	semidirect
667. #440	C₂²×C₆₇	semidirect
668. C₄×SD₁₆	C₂²×C₆₇	semidirect
669. C₄×SD₁₆	C₂²×C₆₇	semidirect
670. #435	C₂²×C₆₇	semidirect
671. #435	C₂²×C₆₇	semidirect
672. C₈×D₄	C₂²×C₆₇	semidirect
673. C₈×D₄	C₂²×C₆₇	semidirect
678. #428	C₂²×C₆₇	semidirect
679. #428	C₂²×C₆₇	semidirect
684. #427	C₂²×C₆₇	semidirect
685. #427	C₂²×C₆₇	semidirect
686. #427	C₂²×C₆₇	semidirect
687. #427	C₂²×C₆₇	semidirect
688. #427	C₂²×C₆₇	semidirect
689. C₂×#107	C₂²×C₆₇	semidirect
690. C₂×#107	C₂²×C₆₇	semidirect
692. C₂×#106	C₂²×C₆₇	semidirect
693. C₂×#106	C₂²×C₆₇	semidirect
694. C₂×#106	C₂²×C₆₇	semidirect
941. C₂×C₈	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3495	2
C₆₇×#3494	2
C₆₇×#3350	2
C₆₇×#3348	2
C₆₇×#3346	2
C₆₇×#3343	2
C₆₇×#3340	2
C₆₇×#3337	2
C₆₇×#3335	2
C₆₇×#3163	2
C₆₇×#3097	2
C₆₇×#3096	2
C₆₇×#3095	2
C₆₇×#3094	2
C₆₇×#3082	2
C₆₇×#3081	2
C₆₇×#3057	2
C₂×#465×C₆₇	2
C₆₇×#2949	2
C₆₇×#2929	2
C₆₇×#2912	2
C₂×#427×C₆₇	2
#61263	67

Subgroups — C67×#61263 #30740514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61263 #30740514