Subgroups — C₆₇×#61266 #30740517

Order 17152.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3356	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3355	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3354	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3352	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3350	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3348	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3346	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3343	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3093	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3092	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3084	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3060	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3054	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2913	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#428×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
27	#556×C₆₇	—	2	1	no	—
28	#556×C₆₇	C₂²	1	2	yes	—
29	#555×C₆₇	—	2	1	no	—
30	#555×C₆₇	C₂²	1	2	yes	—
31	#554×C₆₇	—	2	1	no	—
32	#554×C₆₇	C₂²	1	2	yes	—
33	#553×C₆₇	—	2	1	no	—
34	#553×C₆₇	—	2	1	no	—
35	#553×C₆₇	C₂²	1	2	yes	—
36	#553×C₆₇	C₂²	1	2	yes	—
37	#552×C₆₇	—	2	1	no	—
38	#552×C₆₇	—	2	1	no	—
39	#552×C₆₇	C₂²	1	2	yes	—
40	#552×C₆₇	C₂²	1	2	yes	—
41	#547×C₆₇	—	2	1	no	—
42	#547×C₆₇	C₂²	1	2	yes	—
43	#544×C₆₇	C₂²	1	1	yes	characteristic
44	#544×C₆₇	C₂²	1	1	yes	characteristic
45	#539×C₆₇	—	2	2	no	—
46	#538×C₆₇	—	2	2	no	—
47	#537×C₆₇	C₂²	1	1	yes	characteristic
48	#537×C₆₇	C₂²	1	1	yes	characteristic
49	#529×C₆₇	—	2	2	no	—
50	#525×C₆₇	—	2	2	no	—
51	#525×C₆₇	C₂²	1	1	yes	characteristic
52	#525×C₆₇	C₂²	1	1	yes	characteristic
53	#525×C₆₇	C₂²	1	1	yes	characteristic
54	#520×C₆₇	C₂²	1	1	yes	characteristic
55	#520×C₆₇	C₂²	1	1	yes	characteristic
56	#520×C₆₇	C₂²	1	1	yes	characteristic
57	#520×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
59	C₂²×C₄⋊C₄×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	—
65	#485×C₆₇	C₂²	1	2	yes	—
66	#485×C₆₇	C₂²	1	2	yes	complemented
67	#485×C₆₇	C₂²	1	2	yes	complemented
68	#484×C₆₇	C₂²	1	2	yes	—
69	#484×C₆₇	C₂²	1	2	yes	complemented
70	#483×C₆₇	C₂²	1	2	yes	—
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	#470×C₆₇	C₂²	1	1	yes	characteristic
89	#470×C₆₇	C₂²	1	1	yes	characteristic
90	#470×C₆₇	C₂²	1	2	yes	complemented
91	#469×C₆₇	C₂²	1	1	yes	characteristic
92	#469×C₆₇	C₂²	1	1	yes	characteristic
93	#469×C₆₇	C₂²	1	2	yes	complemented
94	#468×C₆₇	C₂²	1	1	yes	characteristic
95	#468×C₆₇	C₂²	1	1	yes	characteristic
96	#468×C₆₇	C₂²	1	1	yes	characteristic
97	#468×C₆₇	C₂²	1	1	yes	characteristic
98	#465×C₆₇	C₂²	1	2	yes	complemented
99	#465×C₆₇	C₂²	1	2	yes	complemented
100	#440×C₆₇	C₂²	1	2	yes	complemented
101	#440×C₆₇	C₂²	1	2	yes	complemented
102	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
103	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
104	#436×C₆₇	C₂²	1	2	yes	—
105	#436×C₆₇	C₂²	1	2	yes	—
106	#435×C₆₇	C₂²	1	2	yes	—
107	#435×C₆₇	C₂²	1	2	yes	—
108	#428×C₆₇	C₂²	1	1	yes	characteristic
109	#428×C₆₇	C₂²	1	1	yes	characteristic
110	#428×C₆₇	C₂²	1	2	yes	—
111	#428×C₆₇	C₂²	1	2	yes	—
112	#428×C₆₇	C₂²	1	1	yes	characteristic
113	#428×C₆₇	C₂²	1	1	yes	characteristic
114	#428×C₆₇	C₂²	1	2	yes	—
115	#428×C₆₇	C₂²	1	2	yes	—
116	#428×C₆₇	C₂²	1	2	yes	complemented
117	#428×C₆₇	C₂²	1	2	yes	complemented
118	#427×C₆₇	C₂²	1	1	yes	characteristic
119	#427×C₆₇	C₂²	1	2	yes	complemented
120	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
121	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
123	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
124	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
125	#424×C₆₇	C₂²	1	1	yes	characteristic
126	#417×C₆₇	C₂²	1	1	yes	characteristic
127	#417×C₆₇	C₂²	1	1	yes	characteristic
128	#417×C₆₇	C₂²	1	1	yes	characteristic
129	#417×C₆₇	C₂²	1	1	yes	characteristic
130	#416×C₆₇	C₂²	1	1	yes	characteristic
131	#416×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	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₇	—	2	1	no	—
140	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
141	#135×C₆₇	—	2	4	no	—
142	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
146	#131×C₆₇	—	2	4	no	—
147	C₂×M₁₆×C₆₇	—	2	4	no	—
148	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
156	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₇	—	2	1	no	—
159	C₄⋊Q₈×C₆₇	—	2	1	no	—
160	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
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	2	no	—
169	#125×C₆₇	—	2	2	no	—
170	#125×C₆₇	—	2	2	no	—
171	#125×C₆₇	—	2	1	no	—
172	#125×C₆₇	—	2	1	no	—
173	#125×C₆₇	C₂³	1	2	yes	—
174	#125×C₆₇	C₂³	1	2	yes	—
175	#124×C₆₇	—	2	2	no	—
176	#124×C₆₇	—	2	2	no	—
177	#124×C₆₇	—	2	2	no	—
178	#123×C₆₇	—	2	2	no	—
179	#123×C₆₇	—	2	2	no	—
180	#123×C₆₇	—	2	1	no	—
181	#123×C₆₇	—	2	1	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	D₄	1	2	yes	—
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	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	D₄	1	1	yes	characteristic
195	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
196	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
199	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
200	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
201	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
202	#121×C₆₇	—	2	2	no	—
203	#121×C₆₇	—	2	2	no	—
204	#121×C₆₇	—	2	2	no	—
205	#121×C₆₇	—	2	1	no	—
206	#121×C₆₇	—	2	1	no	—
207	#121×C₆₇	—	2	2	no	—
208	#121×C₆₇	—	2	2	no	—
209	#121×C₆₇	D₄	1	1	yes	characteristic
210	#121×C₆₇	D₄	1	1	yes	characteristic
211	#121×C₆₇	C₂³	1	2	yes	—
212	#121×C₆₇	C₂³	1	2	yes	—
213	#121×C₆₇	C₂³	1	1	yes	characteristic
214	#121×C₆₇	C₂³	1	1	yes	characteristic
215	#121×C₆₇	C₂³	1	1	yes	characteristic
216	#121×C₆₇	C₂³	1	1	yes	characteristic
217	#120×C₆₇	—	2	1	no	—
218	#120×C₆₇	—	2	1	no	—
219	#120×C₆₇	D₄	1	2	yes	—
220	C₄×Q₈×C₆₇	—	2	1	no	—
221	C₄×Q₈×C₆₇	—	2	1	no	—
222	C₄×Q₈×C₆₇	—	2	2	no	—
223	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
224	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
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	1	no	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	—	2	1	no	—
231	C₄×D₄×C₆₇	—	2	1	no	—
232	C₄×D₄×C₆₇	—	2	1	no	—
233	C₄×D₄×C₆₇	—	2	1	no	—
234	C₄×D₄×C₆₇	—	2	2	no	—
235	C₄×D₄×C₆₇	—	2	2	no	—
236	C₄×D₄×C₆₇	—	2	2	no	—
237	C₄×D₄×C₆₇	—	2	2	no	—
238	C₄×D₄×C₆₇	C₂³	1	2	yes	—
239	C₄×D₄×C₆₇	C₂³	1	2	yes	—
240	C₄×D₄×C₆₇	C₂³	1	2	yes	—
241	C₄×D₄×C₆₇	C₂³	1	2	yes	—
242	#117×C₆₇	—	2	1	no	—
243	#117×C₆₇	—	2	1	no	—
244	#117×C₆₇	—	2	1	no	—
245	#117×C₆₇	—	2	1	no	—
246	#117×C₆₇	—	2	2	no	—
247	#117×C₆₇	—	2	2	no	—
248	#117×C₆₇	—	2	2	no	—
249	#117×C₆₇	C₂³	1	2	yes	—
250	#117×C₆₇	C₂³	1	2	yes	—
251	#117×C₆₇	C₂³	1	2	yes	—
252	#117×C₆₇	C₂³	1	2	yes	—
253	#117×C₆₇	C₂³	1	1	yes	characteristic
254	#117×C₆₇	C₂³	1	1	yes	characteristic
255	#117×C₆₇	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
257	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
258	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
259	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
260	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
270	C₂×C₄²×C₆₇	—	2	1	no	—
271	#107×C₆₇	C₂³	1	1	yes	characteristic
272	#107×C₆₇	C₂³	1	1	yes	characteristic
273	#107×C₆₇	C₂³	1	2	yes	—
274	#107×C₆₇	C₂³	1	2	yes	—
275	#107×C₆₇	C₂³	1	2	yes	—
276	#107×C₆₇	C₂³	1	2	yes	—
277	#107×C₆₇	C₂³	1	2	yes	—
278	#107×C₆₇	C₂³	1	2	yes	—
279	#107×C₆₇	C₂³	1	2	yes	—
280	#107×C₆₇	C₂³	1	2	yes	—
281	#106×C₆₇	C₂³	1	2	yes	—
282	#106×C₆₇	C₂³	1	1	yes	characteristic
283	#106×C₆₇	C₂³	1	1	yes	characteristic
284	#106×C₆₇	C₂³	1	2	yes	—
285	#106×C₆₇	C₂³	1	2	yes	—
286	#106×C₆₇	C₂³	1	2	yes	—
287	#106×C₆₇	C₂³	1	2	yes	—
288	#106×C₆₇	C₂³	1	2	yes	—
289	#106×C₆₇	C₂³	1	2	yes	—
290	#106×C₆₇	C₂³	1	2	yes	—
291	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
292	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	1	yes	characteristic
296	#103×C₆₇	C₂³	1	1	yes	characteristic
297	#103×C₆₇	C₂³	1	1	yes	characteristic
298	#103×C₆₇	C₂³	1	1	yes	characteristic
299	#103×C₆₇	C₂³	1	2	yes	—
300	#103×C₆₇	C₂³	1	2	yes	—
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	1	yes	characteristic
304	#102×C₆₇	C₂³	1	1	yes	characteristic
305	#102×C₆₇	C₂³	1	1	yes	characteristic
306	#102×C₆₇	C₂³	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
316	#41×C₆₇	—	2	2	no	—
317	#41×C₆₇	—	2	2	no	—
318	#41×C₆₇	—	2	2	no	—
319	#41×C₆₇	—	2	2	no	—
320	#41×C₆₇	—	2	2	no	—
321	#41×C₆₇	—	2	2	no	—
322	#41×C₆₇	—	8	4	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	1	yes	characteristic
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	1	no	—
331	C₂×D₄×C₆₇	—	2	1	no	—
332	C₂×D₄×C₆₇	—	2	1	no	—
333	C₂×D₄×C₆₇	—	2	1	no	—
334	C₂×D₄×C₆₇	—	2	2	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₆₇	—	2	2	no	—
343	C₂²×C₄×C₆₇	—	2	2	no	—
344	C₂²×C₄×C₆₇	—	2	2	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	—	2	1	no	—
350	C₂²×C₄×C₆₇	—	2	2	no	—
351	C₂²×C₄×C₆₇	—	2	2	no	—
352	C₂²×C₄×C₆₇	—	2	1	no	—
353	C₂²×C₄×C₆₇	—	2	1	no	—
354	C₂²×C₄×C₆₇	—	2	2	no	—
355	C₂²×C₄×C₆₇	—	2	2	no	—
356	C₂²×C₄×C₆₇	—	8	2	no	—
357	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
364	Q₁₆×C₆₇	—	2	2	no	—
365	SD₁₆×C₆₇	—	2	2	no	—
366	SD₁₆×C₆₇	—	2	2	no	—
367	D₈×C₆₇	—	2	2	no	—
368	M₁₆×C₆₇	—	2	2	no	—
369	M₁₆×C₆₇	—	2	2	no	—
370	M₁₆×C₆₇	—	2	2	no	—
371	M₁₆×C₆₇	—	2	2	no	—
372	M₁₆×C₆₇	—	2	2	no	—
373	M₁₆×C₆₇	—	2	2	no	—
374	M₁₆×C₆₇	—	2	4	no	—
375	C₂×C₈×C₆₇	—	2	2	no	—
376	C₂×C₈×C₆₇	—	2	4	no	—
377	C₂×C₈×C₆₇	#41	1	4	yes	complemented
378	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
379	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
382	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
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	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	2	no	—
393	C₄⋊C₄×C₆₇	—	2	2	no	—
394	C₄⋊C₄×C₆₇	—	2	1	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	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	1	no	—
400	C₄⋊C₄×C₆₇	—	2	1	no	—
401	C₄⋊C₄×C₆₇	—	2	2	no	—
402	C₄⋊C₄×C₆₇	—	2	2	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	2	1	no	—
405	C₄⋊C₄×C₆₇	—	2	2	no	—
406	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	—	2	1	no	—
427	C₂²⋊C₄×C₆₇	—	2	1	no	—
428	C₂²⋊C₄×C₆₇	—	2	1	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	1	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	no	—
433	C₂²⋊C₄×C₆₇	—	2	2	no	—
434	C₂²⋊C₄×C₆₇	—	2	1	no	—
435	C₂²⋊C₄×C₆₇	—	2	2	no	—
436	C₂²⋊C₄×C₆₇	—	2	1	no	—
437	C₂²⋊C₄×C₆₇	—	2	1	no	—
438	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
443	C₄²×C₆₇	—	2	2	no	—
444	C₄²×C₆₇	—	2	2	no	—
445	C₄²×C₆₇	—	2	2	no	—
446	C₄²×C₆₇	—	2	2	no	—
447	C₄²×C₆₇	—	2	2	no	—
448	C₄²×C₆₇	—	2	2	no	—
449	C₄²×C₆₇	—	2	1	no	—
450	C₄²×C₆₇	—	2	1	no	—
451	C₄²×C₆₇	C₂⁴	1	2	yes	—
452	C₂³×C₆₇	—	2	2	no	—
453	C₂³×C₆₇	—	2	1	no	—
454	C₂³×C₆₇	—	2	1	no	—
455	C₂³×C₆₇	—	4	1	no	—
456	C₂³×C₆₇	—	4	1	no	—
457	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
458	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
460	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
461	Q₈×C₆₇	—	2	2	no	—
462	Q₈×C₆₇	—	2	1	no	—
463	Q₈×C₆₇	—	2	1	no	—
464	Q₈×C₆₇	—	2	1	no	—
465	Q₈×C₆₇	—	2	1	no	—
466	Q₈×C₆₇	—	8	2	no	—
467	Q₈×C₆₇	—	8	2	no	—
468	D₄×C₆₇	—	2	4	no	—
469	D₄×C₆₇	—	2	2	no	—
470	D₄×C₆₇	—	2	1	no	—
471	D₄×C₆₇	—	2	1	no	—
472	D₄×C₆₇	—	2	1	no	—
473	D₄×C₆₇	—	2	1	no	—
474	D₄×C₆₇	—	4	2	no	—
475	D₄×C₆₇	—	4	2	no	—
476	D₄×C₆₇	—	4	2	no	—
477	D₄×C₆₇	—	4	2	no	—
478	D₄×C₆₇	—	4	2	no	—
479	D₄×C₆₇	—	4	2	no	—
480	D₄×C₆₇	—	8	1	no	—
481	D₄×C₆₇	—	8	2	no	—
482	D₄×C₆₇	—	8	1	no	—
483	D₄×C₆₇	—	8	2	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	2	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	1	no	—
492	C₂×C₄×C₆₇	—	2	2	no	—
493	C₂×C₄×C₆₇	—	2	2	no	—
494	C₂×C₄×C₆₇	—	2	1	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	1	no	—
498	C₂×C₄×C₆₇	—	2	2	no	—
499	C₂×C₄×C₆₇	—	2	2	no	—
500	C₂×C₄×C₆₇	—	2	1	no	—
501	C₂×C₄×C₆₇	—	2	1	no	—
502	C₂×C₄×C₆₇	—	2	2	no	—
503	C₂×C₄×C₆₇	—	4	4	no	—
504	C₂×C₄×C₆₇	—	4	2	no	—
505	C₂×C₄×C₆₇	—	4	2	no	—
506	C₂×C₄×C₆₇	—	8	2	no	—
507	C₂×C₄×C₆₇	—	8	2	no	—
508	C₂×C₄×C₆₇	—	8	1	no	—
509	C₂×C₄×C₆₇	—	8	2	no	—
510	C₂×C₄×C₆₇	—	8	1	no	—
511	C₂×C₄×C₆₇	—	8	1	no	—
512	C₂×C₄×C₆₇	—	8	2	no	—
513	C₂×C₄×C₆₇	—	8	1	no	—
514	C₂×C₄×C₆₇	—	8	2	no	—
515	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
522	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
523	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
524	C₈×C₆₇	—	2	1	no	—
525	C₈×C₆₇	—	2	1	no	—
526	C₈×C₆₇	—	2	2	no	—
527	C₈×C₆₇	—	2	2	no	—
528	C₈×C₆₇	C₂×#41	1	2	yes	—
529	C₈×C₆₇	C₂×#41	1	2	yes	—
530	C₂²×C₆₇	—	2	1	no	—
531	C₂²×C₆₇	—	2	1	no	—
532	C₂²×C₆₇	—	2	1	no	—
533	C₂²×C₆₇	—	2	2	no	—
534	C₂²×C₆₇	—	2	1	no	—
535	C₂²×C₆₇	—	2	1	no	—
536	C₂²×C₆₇	—	2	2	no	—
537	C₂²×C₆₇	—	2	1	no	—
538	C₂²×C₆₇	—	2	1	no	—
539	C₂²×C₆₇	—	2	1	no	—
540	C₂²×C₆₇	—	2	2	no	—
541	C₂²×C₆₇	—	4	4	no	—
542	C₂²×C₆₇	—	4	1	no	—
543	C₂²×C₆₇	—	4	1	no	—
544	C₂²×C₆₇	—	4	1	no	—
545	C₂²×C₆₇	—	4	1	no	—
546	C₂²×C₆₇	—	4	1	no	—
547	C₂²×C₆₇	—	4	1	no	—
548	C₂²×C₆₇	#547	1	2	yes	—
549	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
550	C₄×C₆₇	—	2	2	no	—
551	C₄×C₆₇	—	2	2	no	—
552	C₄×C₆₇	—	2	1	no	—
553	C₄×C₆₇	—	2	1	no	—
554	C₄×C₆₇	—	2	2	no	—
555	C₄×C₆₇	—	4	2	no	—
556	C₄×C₆₇	—	4	2	no	—
557	C₄×C₆₇	—	4	2	no	—
558	C₄×C₆₇	—	4	1	no	—
559	C₄×C₆₇	—	4	1	no	—
560	C₄×C₆₇	—	4	2	no	—
561	C₄×C₆₇	—	4	1	no	—
562	C₄×C₆₇	—	4	1	no	—
563	C₄×C₆₇	—	4	1	no	—
564	C₄×C₆₇	—	4	1	no	—
565	C₄×C₆₇	#547	1	2	yes	—
566	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
567	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
568	#61266	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
569	C₂×C₆₇	—	2	2	no	—
570	C₂×C₆₇	—	4	2	no	—
571	C₂×C₆₇	—	4	1	no	—
572	C₂×C₆₇	—	4	1	no	—
573	C₂×C₆₇	—	8	1	no	—
574	C₂×C₆₇	—	8	1	no	—
575	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
576	C₂×C₆₇	#3585	1	1	yes	characteristic
577	C₂×C₆₇	#3586	1	1	yes	characteristic
578	#3493	C₂×C₆₇	1	1	yes	characteristic, complemented
579	#3492	C₂×C₆₇	1	1	yes	characteristic, complemented
580	#3356	C₂×C₆₇	1	2	yes	complemented
581	#3355	C₂×C₆₇	1	2	yes	complemented
582	#3354	C₂×C₆₇	1	2	yes	complemented
583	#3352	C₂×C₆₇	1	2	yes	complemented
584	#3350	C₂×C₆₇	1	2	yes	complemented
585	#3348	C₂×C₆₇	1	2	yes	complemented
586	#3346	C₂×C₆₇	1	2	yes	complemented
587	#3343	C₂×C₆₇	1	2	yes	complemented
588	#3163	C₂×C₆₇	1	1	yes	characteristic, complemented
589	#3099	C₂×C₆₇	1	1	yes	characteristic, complemented
590	#3098	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#3093	C₂×C₆₇	1	1	yes	characteristic, complemented
592	#3092	C₂×C₆₇	1	1	yes	characteristic, complemented
593	#3084	C₂×C₆₇	1	1	yes	characteristic, complemented
594	#3083	C₂×C₆₇	1	1	yes	characteristic, complemented
595	#3060	C₂×C₆₇	1	1	yes	characteristic, complemented
596	#3054	C₂×C₆₇	1	1	yes	characteristic, complemented
597	#2951	C₂×C₆₇	1	1	yes	characteristic, complemented
598	#2930	C₂×C₆₇	1	1	yes	characteristic, complemented
599	#2913	C₂×C₆₇	1	1	yes	characteristic, complemented
600	C₂×#428	C₂×C₆₇	1	1	yes	characteristic, complemented
601	C₆₇	#61266	1	1	yes	characteristic, direct product factor, Sylow
602	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
603	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
604	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
605	#556	—	2	1	no	—
606	#556	C₂²×C₆₇	1	2	yes	—
607	#555	—	2	1	no	—
608	#555	C₂²×C₆₇	1	2	yes	—
609	#554	—	2	1	no	—
610	#554	C₂²×C₆₇	1	2	yes	—
611	#553	—	2	1	no	—
612	#553	—	2	1	no	—
613	#553	C₂²×C₆₇	1	2	yes	—
614	#553	C₂²×C₆₇	1	2	yes	—
615	#552	—	2	1	no	—
616	#552	—	2	1	no	—
617	#552	C₂²×C₆₇	1	2	yes	—
618	#552	C₂²×C₆₇	1	2	yes	—
619	#547	—	2	1	no	—
620	#547	C₂²×C₆₇	1	2	yes	—
621	#544	C₂²×C₆₇	1	1	yes	characteristic
622	#544	C₂²×C₆₇	1	1	yes	characteristic
623	#539	—	2	2	no	—
624	#538	—	2	2	no	—
625	#537	C₂²×C₆₇	1	1	yes	characteristic
626	#537	C₂²×C₆₇	1	1	yes	characteristic
627	#529	—	2	2	no	—
628	#525	—	2	2	no	—
629	#525	C₂²×C₆₇	1	1	yes	characteristic
630	#525	C₂²×C₆₇	1	1	yes	characteristic
631	#525	C₂²×C₆₇	1	1	yes	characteristic
632	#520	C₂²×C₆₇	1	1	yes	characteristic
633	#520	C₂²×C₆₇	1	1	yes	characteristic
634	#520	C₂²×C₆₇	1	1	yes	characteristic
635	#520	C₂²×C₆₇	1	1	yes	characteristic
636	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
637	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
638	#501	C₂²×C₆₇	1	2	yes	complemented
639	#501	C₂²×C₆₇	1	2	yes	complemented
640	#499	C₂²×C₆₇	1	2	yes	complemented
641	#498	C₂²×C₆₇	1	2	yes	complemented
642	#485	C₂²×C₆₇	1	2	yes	—
643	#485	C₂²×C₆₇	1	2	yes	—
644	#485	C₂²×C₆₇	1	2	yes	complemented
645	#485	C₂²×C₆₇	1	2	yes	complemented
646	#484	C₂²×C₆₇	1	2	yes	—
647	#484	C₂²×C₆₇	1	2	yes	complemented
648	#483	C₂²×C₆₇	1	2	yes	—
649	#483	C₂²×C₆₇	1	2	yes	complemented
650	#482	C₂²×C₆₇	1	2	yes	—
651	#482	C₂²×C₆₇	1	2	yes	—
652	#482	C₂²×C₆₇	1	2	yes	complemented
653	#482	C₂²×C₆₇	1	2	yes	complemented
654	#481	C₂²×C₆₇	1	2	yes	—
655	#481	C₂²×C₆₇	1	2	yes	complemented
656	#480	C₂²×C₆₇	1	2	yes	—
657	#480	C₂²×C₆₇	1	2	yes	complemented
658	#479	C₂²×C₆₇	1	2	yes	complemented
659	#479	C₂²×C₆₇	1	2	yes	complemented
660	#478	C₂²×C₆₇	1	2	yes	complemented
661	#478	C₂²×C₆₇	1	2	yes	complemented
662	#477	C₂²×C₆₇	1	2	yes	complemented
663	#476	C₂²×C₆₇	1	2	yes	complemented
664	#475	C₂²×C₆₇	1	2	yes	complemented
665	#474	C₂²×C₆₇	1	2	yes	complemented
666	#470	C₂²×C₆₇	1	1	yes	characteristic
667	#470	C₂²×C₆₇	1	1	yes	characteristic
668	#470	C₂²×C₆₇	1	2	yes	complemented
669	#469	C₂²×C₆₇	1	1	yes	characteristic
670	#469	C₂²×C₆₇	1	1	yes	characteristic
671	#469	C₂²×C₆₇	1	2	yes	complemented
672	#468	C₂²×C₆₇	1	1	yes	characteristic
673	#468	C₂²×C₆₇	1	1	yes	characteristic
674	#468	C₂²×C₆₇	1	1	yes	characteristic
675	#468	C₂²×C₆₇	1	1	yes	characteristic
676	#465	C₂²×C₆₇	1	2	yes	complemented
677	#465	C₂²×C₆₇	1	2	yes	complemented
678	#440	C₂²×C₆₇	1	2	yes	complemented
679	#440	C₂²×C₆₇	1	2	yes	complemented
680	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
681	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
682	#436	C₂²×C₆₇	1	2	yes	—
683	#436	C₂²×C₆₇	1	2	yes	—
684	#435	C₂²×C₆₇	1	2	yes	—
685	#435	C₂²×C₆₇	1	2	yes	—
686	#428	C₂²×C₆₇	1	1	yes	characteristic
687	#428	C₂²×C₆₇	1	1	yes	characteristic
688	#428	C₂²×C₆₇	1	2	yes	—
689	#428	C₂²×C₆₇	1	2	yes	—
690	#428	C₂²×C₆₇	1	1	yes	characteristic
691	#428	C₂²×C₆₇	1	1	yes	characteristic
692	#428	C₂²×C₆₇	1	2	yes	—
693	#428	C₂²×C₆₇	1	2	yes	—
694	#428	C₂²×C₆₇	1	2	yes	complemented
695	#428	C₂²×C₆₇	1	2	yes	complemented
696	#427	C₂²×C₆₇	1	1	yes	characteristic
697	#427	C₂²×C₆₇	1	2	yes	complemented
698	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
699	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
700	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
701	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
702	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
703	#424	C₂²×C₆₇	1	1	yes	characteristic
704	#417	C₂²×C₆₇	1	1	yes	characteristic
705	#417	C₂²×C₆₇	1	1	yes	characteristic
706	#417	C₂²×C₆₇	1	1	yes	characteristic
707	#417	C₂²×C₆₇	1	1	yes	characteristic
708	#416	C₂²×C₆₇	1	1	yes	characteristic
709	#416	C₂²×C₆₇	1	1	yes	characteristic
710	#408	C₂²×C₆₇	1	1	yes	characteristic
711	#407	C₂²×C₆₇	1	1	yes	characteristic
712	#405	C₂²×C₆₇	1	1	yes	characteristic
713	C₂×#41	—	2	2	no	—
714	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
715	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
716	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
717	C₂³×C₄	—	2	1	no	—
718	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
719	#135	—	2	4	no	—
720	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
721	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
722	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
723	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
724	#131	—	2	4	no	—
725	C₂×M₁₆	—	2	4	no	—
726	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
727	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
729	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
731	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
732	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
733	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
734	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
735	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	—	2	1	no	—
738	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
739	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#125	—	2	2	no	—
747	#125	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	1	no	—
750	#125	—	2	1	no	—
751	#125	C₂³×C₆₇	1	2	yes	—
752	#125	C₂³×C₆₇	1	2	yes	—
753	#124	—	2	2	no	—
754	#124	—	2	2	no	—
755	#124	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	1	no	—
759	#123	—	2	1	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	D₄×C₆₇	1	2	yes	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
773	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
774	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
776	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
778	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
779	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	1	no	—
784	#121	—	2	1	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	D₄×C₆₇	1	1	yes	characteristic
788	#121	D₄×C₆₇	1	1	yes	characteristic
789	#121	C₂³×C₆₇	1	1	yes	characteristic
790	#121	C₂³×C₆₇	1	1	yes	characteristic
791	#121	C₂³×C₆₇	1	1	yes	characteristic
792	#121	C₂³×C₆₇	1	1	yes	characteristic
793	#121	C₂³×C₆₇	1	2	yes	—
794	#121	C₂³×C₆₇	1	2	yes	—
795	#120	—	2	1	no	—
796	#120	—	2	1	no	—
797	#120	D₄×C₆₇	1	2	yes	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	2	no	—
801	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
802	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	C₂³×C₆₇	1	2	yes	—
817	C₄×D₄	C₂³×C₆₇	1	2	yes	—
818	C₄×D₄	C₂³×C₆₇	1	2	yes	—
819	C₄×D₄	C₂³×C₆₇	1	2	yes	—
820	#117	—	2	1	no	—
821	#117	—	2	1	no	—
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	—	2	2	no	—
826	#117	—	2	2	no	—
827	#117	C₂³×C₆₇	1	2	yes	—
828	#117	C₂³×C₆₇	1	2	yes	—
829	#117	C₂³×C₆₇	1	1	yes	characteristic
830	#117	C₂³×C₆₇	1	1	yes	characteristic
831	#117	C₂³×C₆₇	1	2	yes	—
832	#117	C₂³×C₆₇	1	2	yes	—
833	#117	C₂³×C₆₇	1	1	yes	characteristic
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
842	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
843	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
845	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
846	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
847	C₂×C₂²⋊C₄	—	2	1	no	—
848	C₂×C₄²	—	2	1	no	—
849	#107	C₂³×C₆₇	1	2	yes	—
850	#107	C₂³×C₆₇	1	2	yes	—
851	#107	C₂³×C₆₇	1	2	yes	—
852	#107	C₂³×C₆₇	1	2	yes	—
853	#107	C₂³×C₆₇	1	1	yes	characteristic
854	#107	C₂³×C₆₇	1	2	yes	—
855	#107	C₂³×C₆₇	1	2	yes	—
856	#107	C₂³×C₆₇	1	1	yes	characteristic
857	#107	C₂³×C₆₇	1	2	yes	—
858	#107	C₂³×C₆₇	1	2	yes	—
859	#106	C₂³×C₆₇	1	2	yes	—
860	#106	C₂³×C₆₇	1	2	yes	—
861	#106	C₂³×C₆₇	1	2	yes	—
862	#106	C₂³×C₆₇	1	2	yes	—
863	#106	C₂³×C₆₇	1	1	yes	characteristic
864	#106	C₂³×C₆₇	1	1	yes	characteristic
865	#106	C₂³×C₆₇	1	2	yes	—
866	#106	C₂³×C₆₇	1	2	yes	—
867	#106	C₂³×C₆₇	1	2	yes	—
868	#106	C₂³×C₆₇	1	2	yes	—
869	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
870	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
871	#103	C₂³×C₆₇	1	1	yes	characteristic
872	#103	C₂³×C₆₇	1	1	yes	characteristic
873	#103	C₂³×C₆₇	1	1	yes	characteristic
874	#103	C₂³×C₆₇	1	1	yes	characteristic
875	#103	C₂³×C₆₇	1	2	yes	—
876	#103	C₂³×C₆₇	1	2	yes	—
877	#103	C₂³×C₆₇	1	2	yes	—
878	#103	C₂³×C₆₇	1	2	yes	—
879	#102	C₂³×C₆₇	1	1	yes	characteristic
880	#102	C₂³×C₆₇	1	1	yes	characteristic
881	#102	C₂³×C₆₇	1	1	yes	characteristic
882	#102	C₂³×C₆₇	1	1	yes	characteristic
883	#102	C₂³×C₆₇	1	2	yes	—
884	#102	C₂³×C₆₇	1	2	yes	—
885	#102	C₂³×C₆₇	1	2	yes	—
886	#102	C₂³×C₆₇	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
891	#97	C₂³×C₆₇	1	2	yes	—
892	C₄×C₈	C₂³×C₆₇	1	2	yes	—
893	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
894	#41	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	2	2	no	—
897	#41	—	2	2	no	—
898	#41	—	2	2	no	—
899	#41	—	2	2	no	—
900	#41	—	8	4	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
905	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
915	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
916	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
917	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
918	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	8	2	no	—
935	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
936	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
937	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
939	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
942	Q₁₆	—	2	2	no	—
943	SD₁₆	—	2	2	no	—
944	SD₁₆	—	2	2	no	—
945	D₈	—	2	2	no	—
946	M₁₆	—	2	2	no	—
947	M₁₆	—	2	2	no	—
948	M₁₆	—	2	2	no	—
949	M₁₆	—	2	2	no	—
950	M₁₆	—	2	2	no	—
951	M₁₆	—	2	2	no	—
952	M₁₆	—	2	4	no	—
953	C₂×C₈	—	2	2	no	—
954	C₂×C₈	—	2	4	no	—
955	C₂×C₈	#41×C₆₇	1	4	yes	complemented
956	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
957	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
958	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
986	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
987	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
988	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
989	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
990	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1018	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1019	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1020	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	C₂⁴×C₆₇	1	2	yes	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	4	1	no	—
1034	C₂³	—	4	1	no	—
1035	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1036	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1037	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1038	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	8	2	no	—
1045	Q₈	—	8	2	no	—
1046	D₄	—	2	4	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	1	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	4	4	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	—	8	1	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	—	8	1	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	1	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	1	no	—
1093	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1094	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1095	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1096	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1098	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1099	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1100	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1101	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1102	C₈	—	2	1	no	—
1103	C₈	—	2	1	no	—
1104	C₈	—	2	2	no	—
1105	C₈	—	2	2	no	—
1106	C₈	C₂×#41×C₆₇	1	2	yes	—
1107	C₈	C₂×#41×C₆₇	1	2	yes	—
1108	C₂²	—	2	1	no	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	4	4	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	#547×C₆₇	1	2	yes	—
1127	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1128	C₄	—	2	2	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	1	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	2	no	—
1135	C₄	—	4	2	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	#547×C₆₇	1	2	yes	—
1144	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1145	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1146	C₂	—	2	2	no	—
1147	C₂	—	4	1	no	—
1148	C₂	—	4	1	no	—
1149	C₂	—	4	2	no	—
1150	C₂	—	8	1	no	—
1151	C₂	—	8	1	no	—
1152	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
1153	C₂	C₆₇×#3585	1	1	yes	characteristic
1154	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 ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3493	C₂	semidirect
2. C₆₇×#3492	C₂	semidirect
3. C₆₇×#3356	C₂	semidirect
4. C₆₇×#3355	C₂	semidirect
5. C₆₇×#3354	C₂	semidirect
6. C₆₇×#3352	C₂	semidirect
7. C₆₇×#3350	C₂	semidirect
8. C₆₇×#3348	C₂	semidirect
9. C₆₇×#3346	C₂	semidirect
10. C₆₇×#3343	C₂	semidirect
11. C₆₇×#3163	C₂	semidirect
12. C₆₇×#3099	C₂	semidirect
13. C₆₇×#3098	C₂	semidirect
14. C₆₇×#3093	C₂	semidirect
15. C₆₇×#3092	C₂	semidirect
16. C₆₇×#3084	C₂	semidirect
17. C₆₇×#3083	C₂	semidirect
18. C₆₇×#3060	C₂	semidirect
19. C₆₇×#3054	C₂	semidirect
20. C₆₇×#2951	C₂	semidirect
21. C₆₇×#2930	C₂	semidirect
22. C₆₇×#2913	C₂	semidirect
23. C₂×#428×C₆₇	C₂	semidirect
60. #501×C₆₇	C₂²	semidirect
61. #501×C₆₇	C₂²	semidirect
62. #499×C₆₇	C₂²	semidirect
63. #498×C₆₇	C₂²	semidirect
66. #485×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
69. #484×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
90. #470×C₆₇	C₂²	semidirect
93. #469×C₆₇	C₂²	semidirect
98. #465×C₆₇	C₂²	semidirect
99. #465×C₆₇	C₂²	semidirect
100. #440×C₆₇	C₂²	semidirect
101. #440×C₆₇	C₂²	semidirect
102. C₄×Q₁₆×C₆₇	C₂²	semidirect
103. C₄×D₈×C₆₇	C₂²	semidirect
116. #428×C₆₇	C₂²	semidirect
117. #428×C₆₇	C₂²	semidirect
119. #427×C₆₇	C₂²	semidirect
122. C₂×#107×C₆₇	C₂²	semidirect
377. C₂×C₈×C₆₇	#41	semidirect
568. #61266	C₆₇	direct (N × H)
578. #3493	C₂×C₆₇	semidirect
579. #3492	C₂×C₆₇	semidirect
580. #3356	C₂×C₆₇	semidirect
581. #3355	C₂×C₆₇	semidirect
582. #3354	C₂×C₆₇	semidirect
583. #3352	C₂×C₆₇	semidirect
584. #3350	C₂×C₆₇	semidirect
585. #3348	C₂×C₆₇	semidirect
586. #3346	C₂×C₆₇	semidirect
587. #3343	C₂×C₆₇	semidirect
588. #3163	C₂×C₆₇	semidirect
589. #3099	C₂×C₆₇	semidirect
590. #3098	C₂×C₆₇	semidirect
591. #3093	C₂×C₆₇	semidirect
592. #3092	C₂×C₆₇	semidirect
593. #3084	C₂×C₆₇	semidirect
594. #3083	C₂×C₆₇	semidirect
595. #3060	C₂×C₆₇	semidirect
596. #3054	C₂×C₆₇	semidirect
597. #2951	C₂×C₆₇	semidirect
598. #2930	C₂×C₆₇	semidirect
599. #2913	C₂×C₆₇	semidirect
600. C₂×#428	C₂×C₆₇	semidirect
601. C₆₇	#61266	direct (N × H)
638. #501	C₂²×C₆₇	semidirect
639. #501	C₂²×C₆₇	semidirect
640. #499	C₂²×C₆₇	semidirect
641. #498	C₂²×C₆₇	semidirect
644. #485	C₂²×C₆₇	semidirect
645. #485	C₂²×C₆₇	semidirect
647. #484	C₂²×C₆₇	semidirect
649. #483	C₂²×C₆₇	semidirect
652. #482	C₂²×C₆₇	semidirect
653. #482	C₂²×C₆₇	semidirect
655. #481	C₂²×C₆₇	semidirect
657. #480	C₂²×C₆₇	semidirect
658. #479	C₂²×C₆₇	semidirect
659. #479	C₂²×C₆₇	semidirect
660. #478	C₂²×C₆₇	semidirect
661. #478	C₂²×C₆₇	semidirect
662. #477	C₂²×C₆₇	semidirect
663. #476	C₂²×C₆₇	semidirect
664. #475	C₂²×C₆₇	semidirect
665. #474	C₂²×C₆₇	semidirect
668. #470	C₂²×C₆₇	semidirect
671. #469	C₂²×C₆₇	semidirect
676. #465	C₂²×C₆₇	semidirect
677. #465	C₂²×C₆₇	semidirect
678. #440	C₂²×C₆₇	semidirect
679. #440	C₂²×C₆₇	semidirect
680. C₄×Q₁₆	C₂²×C₆₇	semidirect
681. C₄×D₈	C₂²×C₆₇	semidirect
694. #428	C₂²×C₆₇	semidirect
695. #428	C₂²×C₆₇	semidirect
697. #427	C₂²×C₆₇	semidirect
700. C₂×#107	C₂²×C₆₇	semidirect
955. 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×#3493	2
C₆₇×#3492	2
C₆₇×#3356	2
C₆₇×#3355	2
C₆₇×#3354	2
C₆₇×#3352	2
C₆₇×#3350	2
C₆₇×#3348	2
C₆₇×#3346	2
C₆₇×#3343	2
C₆₇×#3163	2
C₆₇×#3099	2
C₆₇×#3098	2
C₆₇×#3093	2
C₆₇×#3092	2
C₆₇×#3084	2
C₆₇×#3083	2
C₆₇×#3060	2
C₆₇×#3054	2
C₆₇×#2951	2
C₆₇×#2930	2
C₆₇×#2913	2
C₂×#428×C₆₇	2
#61266	67

Subgroups — C67×#61266 #30740517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61266 #30740517