Subgroups — C₆₇×#61344 #30740595

Order 17152.

1748 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3510	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3377	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3377	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3375	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3371	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3371	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3369	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3365	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3364	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3136	C₂	1	1	yes	maximal, characteristic
14	C₆₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3081	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3043	C₂	1	1	yes	maximal, characteristic
19	C₂×#464×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2950	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2949	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
27	#559×C₆₇	C₂²	1	2	yes	—
28	#559×C₆₇	C₂²	1	2	yes	—
29	Q₈²×C₆₇	—	2	1	no	—
30	Q₈²×C₆₇	C₂²	1	2	yes	complemented
31	#557×C₆₇	—	2	1	no	—
32	#557×C₆₇	—	2	1	no	—
33	#557×C₆₇	—	2	1	no	—
34	#557×C₆₇	C₂²	1	2	yes	complemented
35	#557×C₆₇	C₂²	1	2	yes	complemented
36	#557×C₆₇	C₂²	1	2	yes	complemented
37	#556×C₆₇	C₂²	1	2	yes	—
38	#556×C₆₇	C₂²	1	2	yes	—
39	#551×C₆₇	—	2	2	no	—
40	#551×C₆₇	—	2	2	no	—
41	#544×C₆₇	—	2	2	no	—
42	#544×C₆₇	C₂²	1	1	yes	characteristic
43	#544×C₆₇	C₂²	1	1	yes	characteristic
44	#542×C₆₇	—	2	1	no	—
45	#542×C₆₇	—	2	1	no	—
46	#536×C₆₇	C₂²	1	1	yes	characteristic
47	#535×C₆₇	C₂²	1	1	yes	characteristic
48	#533×C₆₇	—	2	2	no	—
49	#533×C₆₇	C₂²	1	1	yes	characteristic
50	#533×C₆₇	C₂²	1	1	yes	characteristic
51	#529×C₆₇	—	2	1	no	—
52	#529×C₆₇	—	2	1	no	—
53	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
54	#519×C₆₇	C₂²	1	1	yes	characteristic
55	#519×C₆₇	C₂²	1	1	yes	characteristic
56	#519×C₆₇	C₂²	1	1	yes	characteristic
57	#518×C₆₇	C₂²	1	1	yes	characteristic
58	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
60	#491×C₆₇	C₂²	1	2	yes	complemented
61	#490×C₆₇	C₂²	1	2	yes	—
62	#489×C₆₇	C₂²	1	2	yes	—
63	#489×C₆₇	C₂²	1	2	yes	—
64	#489×C₆₇	C₂²	1	2	yes	—
65	#489×C₆₇	C₂²	1	2	yes	complemented
66	#488×C₆₇	C₂²	1	2	yes	—
67	#488×C₆₇	C₂²	1	2	yes	—
68	#488×C₆₇	C₂²	1	2	yes	—
69	#488×C₆₇	C₂²	1	2	yes	complemented
70	#487×C₆₇	C₂²	1	2	yes	complemented
71	#486×C₆₇	C₂²	1	2	yes	—
72	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#479×C₆₇	C₂²	1	2	yes	complemented
75	#479×C₆₇	C₂²	1	2	yes	complemented
76	#478×C₆₇	C₂²	1	2	yes	—
77	#478×C₆₇	C₂²	1	2	yes	—
78	#478×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	#478×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#477×C₆₇	C₂²	1	2	yes	complemented
82	#476×C₆₇	C₂²	1	2	yes	—
83	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#475×C₆₇	C₂²	1	2	yes	complemented
86	#474×C₆₇	C₂²	1	2	yes	—
87	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#464×C₆₇	C₂²	1	2	yes	—
89	#464×C₆₇	C₂²	1	2	yes	—
90	#464×C₆₇	C₂²	1	2	yes	—
91	#464×C₆₇	C₂²	1	2	yes	—
92	#464×C₆₇	C₂²	1	2	yes	—
93	#464×C₆₇	C₂²	1	2	yes	—
94	#464×C₆₇	C₂²	1	2	yes	complemented
95	#464×C₆₇	C₂²	1	2	yes	complemented
96	#462×C₆₇	C₂²	1	2	yes	complemented
97	#462×C₆₇	C₂²	1	2	yes	complemented
98	#460×C₆₇	C₂²	1	2	yes	—
99	#460×C₆₇	C₂²	1	2	yes	—
100	#446×C₆₇	C₂²	1	2	yes	complemented
101	#446×C₆₇	C₂²	1	2	yes	complemented
102	#446×C₆₇	C₂²	1	2	yes	complemented
103	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
104	#441×C₆₇	C₂²	1	2	yes	complemented
105	#441×C₆₇	C₂²	1	2	yes	complemented
106	#441×C₆₇	C₂²	1	2	yes	complemented
107	#440×C₆₇	C₂²	1	2	yes	—
108	#440×C₆₇	C₂²	1	2	yes	—
109	#440×C₆₇	C₂²	1	2	yes	complemented
110	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
112	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
116	#428×C₆₇	C₂²	1	1	yes	characteristic
117	#427×C₆₇	C₂²	1	1	yes	characteristic
118	#427×C₆₇	C₂²	1	1	yes	characteristic
119	#424×C₆₇	C₂²	1	1	yes	characteristic
120	#424×C₆₇	C₂²	1	1	yes	characteristic
121	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
122	#419×C₆₇	C₂²	1	1	yes	characteristic
123	#419×C₆₇	C₂²	1	1	yes	characteristic
124	#419×C₆₇	C₂²	1	1	yes	characteristic
125	#418×C₆₇	C₂²	1	1	yes	characteristic
126	#418×C₆₇	C₂²	1	1	yes	characteristic
127	#417×C₆₇	C₂²	1	1	yes	characteristic
128	#416×C₆₇	C₂²	1	1	yes	characteristic
129	#416×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	#405×C₆₇	C₂²	1	1	yes	characteristic
133	#405×C₆₇	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
139	#137×C₆₇	—	2	4	no	—
140	C₂×Q₁₆×C₆₇	—	2	4	no	—
141	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₆₇	—	2	4	no	—
145	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×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	C₄⋊Q₈×C₆₇	—	2	2	no	—
153	C₄⋊Q₈×C₆₇	—	2	2	no	—
154	C₄⋊Q₈×C₆₇	—	2	2	no	—
155	C₄⋊Q₈×C₆₇	—	2	2	no	—
156	C₄⋊Q₈×C₆₇	—	2	2	no	—
157	C₄⋊Q₈×C₆₇	—	2	2	no	—
158	C₄⋊Q₈×C₆₇	—	2	1	no	—
159	C₄⋊Q₈×C₆₇	—	2	1	no	—
160	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
161	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
162	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
164	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
167	#127×C₆₇	C₂³	1	2	yes	—
168	#126×C₆₇	—	2	2	no	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#126×C₆₇	—	2	2	no	—
172	#125×C₆₇	—	2	2	no	—
173	#125×C₆₇	—	2	2	no	—
174	#125×C₆₇	—	2	2	no	—
175	#125×C₆₇	—	2	2	no	—
176	#125×C₆₇	—	2	2	no	—
177	#125×C₆₇	—	2	2	no	—
178	#125×C₆₇	—	2	1	no	—
179	#125×C₆₇	—	2	1	no	—
180	#125×C₆₇	D₄	1	1	yes	characteristic
181	#125×C₆₇	D₄	1	1	yes	characteristic
182	#125×C₆₇	C₂³	1	2	yes	—
183	#125×C₆₇	C₂³	1	1	yes	characteristic
184	#125×C₆₇	C₂³	1	1	yes	characteristic
185	#125×C₆₇	C₂³	1	2	yes	—
186	#124×C₆₇	—	2	2	no	—
187	#124×C₆₇	—	2	2	no	—
188	#124×C₆₇	—	2	1	no	—
189	#124×C₆₇	—	2	1	no	—
190	#124×C₆₇	C₂³	1	2	yes	—
191	#124×C₆₇	C₂³	1	2	yes	—
192	#124×C₆₇	C₂³	1	2	yes	—
193	#124×C₆₇	C₂³	1	2	yes	—
194	#123×C₆₇	—	2	2	no	—
195	#123×C₆₇	—	2	2	no	—
196	#123×C₆₇	—	2	2	no	—
197	#123×C₆₇	—	2	2	no	—
198	#123×C₆₇	—	2	2	no	—
199	C₂²⋊Q₈×C₆₇	—	2	2	no	—
200	C₂²⋊Q₈×C₆₇	—	2	2	no	—
201	C₂²⋊Q₈×C₆₇	—	2	1	no	—
202	C₂²⋊Q₈×C₆₇	—	2	1	no	—
203	C₂²⋊Q₈×C₆₇	—	2	1	no	—
204	C₂²⋊Q₈×C₆₇	—	2	1	no	—
205	C₂²⋊Q₈×C₆₇	—	2	2	no	—
206	C₂²⋊Q₈×C₆₇	—	2	2	no	—
207	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
208	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
209	#121×C₆₇	—	2	1	no	—
210	#121×C₆₇	—	2	1	no	—
211	#120×C₆₇	—	2	2	no	—
212	C₄×Q₈×C₆₇	—	2	2	no	—
213	C₄×Q₈×C₆₇	—	2	1	no	—
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	1	no	—
219	C₄×Q₈×C₆₇	—	2	2	no	—
220	C₄×Q₈×C₆₇	—	2	2	no	—
221	C₄×Q₈×C₆₇	—	2	2	no	—
222	C₄×Q₈×C₆₇	—	2	1	no	—
223	C₄×Q₈×C₆₇	—	2	1	no	—
224	C₄×Q₈×C₆₇	—	2	1	no	—
225	C₄×Q₈×C₆₇	—	2	1	no	—
226	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
227	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
228	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
229	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
230	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
231	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
232	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
234	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
235	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
237	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
238	C₄×D₄×C₆₇	—	2	1	no	—
239	C₄×D₄×C₆₇	—	2	1	no	—
240	C₄×D₄×C₆₇	—	2	1	no	—
241	C₄×D₄×C₆₇	—	2	1	no	—
242	C₄×D₄×C₆₇	—	2	2	no	—
243	C₄×D₄×C₆₇	—	2	2	no	—
244	C₄×D₄×C₆₇	C₂³	1	2	yes	—
245	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₇	C₂³	1	2	yes	—
247	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
248	#117×C₆₇	—	2	2	no	—
249	#117×C₆₇	—	2	2	no	—
250	#117×C₆₇	—	2	2	no	—
251	#117×C₆₇	—	2	2	no	—
252	#117×C₆₇	—	2	2	no	—
253	#117×C₆₇	—	2	1	no	—
254	#117×C₆₇	C₂³	1	1	yes	characteristic
255	#117×C₆₇	C₂³	1	1	yes	characteristic
256	#117×C₆₇	C₂³	1	1	yes	characteristic
257	#117×C₆₇	C₂³	1	1	yes	characteristic
258	#117×C₆₇	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
260	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
262	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
264	C₂×C₄²×C₆₇	—	2	1	no	—
265	C₂×C₄²×C₆₇	—	2	1	no	—
266	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
267	#107×C₆₇	C₂³	1	1	yes	characteristic
268	#107×C₆₇	C₂³	1	2	yes	—
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	#106×C₆₇	C₂³	1	1	yes	characteristic
273	#106×C₆₇	C₂³	1	1	yes	characteristic
274	#106×C₆₇	C₂³	1	2	yes	—
275	#106×C₆₇	C₂³	1	1	yes	characteristic
276	#106×C₆₇	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
278	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
279	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
285	#103×C₆₇	C₂³	1	1	yes	characteristic
286	#103×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	2	yes	—
297	#103×C₆₇	C₂³	1	2	yes	—
298	#102×C₆₇	C₂³	1	1	yes	characteristic
299	#102×C₆₇	C₂³	1	1	yes	characteristic
300	#102×C₆₇	C₂³	1	2	yes	—
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	1	yes	characteristic
305	#102×C₆₇	C₂³	1	1	yes	characteristic
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	2	yes	—
308	#102×C₆₇	C₂³	1	2	yes	—
309	#97×C₆₇	C₂³	1	2	yes	—
310	#97×C₆₇	C₂³	1	2	yes	—
311	#97×C₆₇	C₂³	1	2	yes	—
312	C₄×C₈×C₆₇	C₂³	1	2	yes	—
313	C₄×C₈×C₆₇	C₂³	1	2	yes	—
314	C₄×C₈×C₆₇	C₂³	1	2	yes	—
315	C₂⁴×C₆₇	—	2	1	no	—
316	#41×C₆₇	—	2	2	no	—
317	#41×C₆₇	—	2	2	no	—
318	C₂×Q₈×C₆₇	—	2	1	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	—	2	2	no	—
324	C₂×Q₈×C₆₇	—	2	2	no	—
325	C₂×Q₈×C₆₇	—	2	2	no	—
326	C₂×Q₈×C₆₇	—	2	2	no	—
327	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
328	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
329	C₂×Q₈×C₆₇	#41	1	4	yes	—
330	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
333	C₂×D₄×C₆₇	—	2	1	no	—
334	C₂×D₄×C₆₇	—	2	1	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	2	no	—
337	C₂×D₄×C₆₇	—	2	2	no	—
338	C₂×D₄×C₆₇	—	2	2	no	—
339	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
340	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₆₇	—	2	1	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	2	no	—
348	C₂²×C₄×C₆₇	—	2	2	no	—
349	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
352	Q₁₆×C₆₇	—	2	4	no	—
353	Q₁₆×C₆₇	—	2	4	no	—
354	Q₁₆×C₆₇	—	2	4	no	—
355	SD₁₆×C₆₇	—	2	4	no	—
356	SD₁₆×C₆₇	—	2	4	no	—
357	SD₁₆×C₆₇	—	2	4	no	—
358	M₁₆×C₆₇	—	2	2	no	—
359	M₁₆×C₆₇	—	2	2	no	—
360	C₂×C₈×C₆₇	—	2	2	no	—
361	C₂×C₈×C₆₇	—	2	2	no	—
362	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
363	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
366	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₆₇	—	2	2	no	—
369	C₄⋊C₄×C₆₇	—	2	2	no	—
370	C₄⋊C₄×C₆₇	—	2	1	no	—
371	C₄⋊C₄×C₆₇	—	2	1	no	—
372	C₄⋊C₄×C₆₇	—	2	1	no	—
373	C₄⋊C₄×C₆₇	—	2	2	no	—
374	C₄⋊C₄×C₆₇	—	2	2	no	—
375	C₄⋊C₄×C₆₇	—	2	2	no	—
376	C₄⋊C₄×C₆₇	—	2	2	no	—
377	C₄⋊C₄×C₆₇	—	2	2	no	—
378	C₄⋊C₄×C₆₇	—	2	2	no	—
379	C₄⋊C₄×C₆₇	—	2	2	no	—
380	C₄⋊C₄×C₆₇	—	2	2	no	—
381	C₄⋊C₄×C₆₇	—	2	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	2	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	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	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
409	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂²⋊C₄×C₆₇	—	2	1	no	—
411	C₂²⋊C₄×C₆₇	—	2	1	no	—
412	C₂²⋊C₄×C₆₇	—	2	1	no	—
413	C₂²⋊C₄×C₆₇	—	2	2	no	—
414	C₂²⋊C₄×C₆₇	—	2	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	1	no	—
420	C₂²⋊C₄×C₆₇	—	2	1	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	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
427	C₄²×C₆₇	—	2	1	no	—
428	C₄²×C₆₇	—	2	1	no	—
429	C₄²×C₆₇	—	2	1	no	—
430	C₄²×C₆₇	—	2	2	no	—
431	C₄²×C₆₇	—	2	2	no	—
432	C₄²×C₆₇	—	2	2	no	—
433	C₄²×C₆₇	—	2	2	no	—
434	C₄²×C₆₇	—	2	2	no	—
435	C₄²×C₆₇	—	2	2	no	—
436	C₄²×C₆₇	—	2	2	no	—
437	C₄²×C₆₇	—	2	2	no	—
438	C₄²×C₆₇	—	2	1	no	—
439	C₄²×C₆₇	—	2	1	no	—
440	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
443	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
444	C₄²×C₆₇	C₂⁴	1	2	yes	—
445	C₄²×C₆₇	C₂⁴	1	2	yes	—
446	C₂³×C₆₇	—	2	2	no	—
447	C₂³×C₆₇	—	2	1	no	—
448	C₂³×C₆₇	—	4	2	no	—
449	C₂³×C₆₇	—	8	1	no	—
450	C₂³×C₆₇	—	8	1	no	—
451	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
452	Q₈×C₆₇	—	2	4	no	—
453	Q₈×C₆₇	—	2	2	no	—
454	Q₈×C₆₇	—	2	2	no	—
455	Q₈×C₆₇	—	2	1	no	—
456	Q₈×C₆₇	—	2	2	no	—
457	Q₈×C₆₇	—	2	1	no	—
458	Q₈×C₆₇	—	4	2	no	—
459	Q₈×C₆₇	—	4	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	Q₈×C₆₇	—	8	2	no	—
465	Q₈×C₆₇	C₂×#41	1	4	yes	—
466	D₄×C₆₇	—	2	2	no	—
467	D₄×C₆₇	—	2	1	no	—
468	D₄×C₆₇	—	2	2	no	—
469	D₄×C₆₇	—	2	1	no	—
470	D₄×C₆₇	—	4	2	no	—
471	D₄×C₆₇	—	4	2	no	—
472	D₄×C₆₇	—	8	2	no	—
473	D₄×C₆₇	—	8	2	no	—
474	C₂×C₄×C₆₇	—	2	4	no	—
475	C₂×C₄×C₆₇	—	2	2	no	—
476	C₂×C₄×C₆₇	—	2	1	no	—
477	C₂×C₄×C₆₇	—	2	1	no	—
478	C₂×C₄×C₆₇	—	2	1	no	—
479	C₂×C₄×C₆₇	—	2	1	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	1	no	—
482	C₂×C₄×C₆₇	—	2	2	no	—
483	C₂×C₄×C₆₇	—	2	1	no	—
484	C₂×C₄×C₆₇	—	2	2	no	—
485	C₂×C₄×C₆₇	—	4	1	no	—
486	C₂×C₄×C₆₇	—	4	1	no	—
487	C₂×C₄×C₆₇	—	4	2	no	—
488	C₂×C₄×C₆₇	—	4	2	no	—
489	C₂×C₄×C₆₇	—	8	1	no	—
490	C₂×C₄×C₆₇	—	8	2	no	—
491	C₂×C₄×C₆₇	—	8	1	no	—
492	C₂×C₄×C₆₇	—	8	2	no	—
493	C₂×C₄×C₆₇	—	8	1	no	—
494	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
504	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
505	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
506	C₈×C₆₇	—	2	1	no	—
507	C₈×C₆₇	—	2	1	no	—
508	C₈×C₆₇	—	2	1	no	—
509	C₈×C₆₇	—	2	1	no	—
510	C₈×C₆₇	—	2	2	no	—
511	C₈×C₆₇	—	2	2	no	—
512	C₂²×C₆₇	—	2	1	no	—
513	C₂²×C₆₇	—	2	1	no	—
514	C₂²×C₆₇	—	4	1	no	—
515	C₂²×C₆₇	—	4	2	no	—
516	C₂²×C₆₇	—	4	1	no	—
517	C₂²×C₆₇	—	4	2	no	—
518	C₂²×C₆₇	—	4	1	no	—
519	C₂²×C₆₇	—	4	2	no	—
520	C₂²×C₆₇	—	16	2	no	—
521	C₂²×C₆₇	#548	1	2	yes	—
522	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
523	C₄×C₆₇	—	2	1	no	—
524	C₄×C₆₇	—	2	1	no	—
525	C₄×C₆₇	—	2	2	no	—
526	C₄×C₆₇	—	2	2	no	—
527	C₄×C₆₇	—	2	1	no	—
528	C₄×C₆₇	—	2	1	no	—
529	C₄×C₆₇	—	2	2	no	—
530	C₄×C₆₇	—	2	2	no	—
531	C₄×C₆₇	—	2	4	no	—
532	C₄×C₆₇	—	4	1	no	—
533	C₄×C₆₇	—	4	2	no	—
534	C₄×C₆₇	—	4	1	no	—
535	C₄×C₆₇	—	4	1	no	—
536	C₄×C₆₇	—	4	1	no	—
537	C₄×C₆₇	—	4	1	no	—
538	C₄×C₆₇	—	4	1	no	—
539	C₄×C₆₇	—	4	1	no	—
540	C₄×C₆₇	—	4	2	no	—
541	C₄×C₆₇	#548	1	2	yes	—
542	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
543	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
544	#61344	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
545	C₂×C₆₇	—	2	2	no	—
546	C₂×C₆₇	—	8	1	no	—
547	C₂×C₆₇	—	8	2	no	—
548	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
549	C₂×C₆₇	#3584	1	1	yes	characteristic
550	C₂×C₆₇	#3586	1	1	yes	characteristic
551	#3510	C₂×C₆₇	1	1	yes	characteristic
552	#3502	C₂×C₆₇	1	1	yes	characteristic, complemented
553	#3377	C₂×C₆₇	1	2	yes	complemented
554	#3377	C₂×C₆₇	1	2	yes	complemented
555	#3375	C₂×C₆₇	1	2	yes	complemented
556	#3371	C₂×C₆₇	1	2	yes	complemented
557	#3371	C₂×C₆₇	1	2	yes	complemented
558	#3369	C₂×C₆₇	1	2	yes	complemented
559	#3365	C₂×C₆₇	1	2	yes	complemented
560	#3364	C₂×C₆₇	1	2	yes	complemented
561	#3140	C₂×C₆₇	1	1	yes	characteristic, complemented
562	#3137	C₂×C₆₇	1	1	yes	characteristic, complemented
563	#3136	C₂×C₆₇	1	1	yes	characteristic
564	#3082	C₂×C₆₇	1	1	yes	characteristic, complemented
565	#3081	C₂×C₆₇	1	1	yes	characteristic, complemented
566	#3076	C₂×C₆₇	1	1	yes	characteristic, complemented
567	#3044	C₂×C₆₇	1	1	yes	characteristic, complemented
568	#3043	C₂×C₆₇	1	1	yes	characteristic
569	C₂×#464	C₂×C₆₇	1	1	yes	characteristic, complemented
570	#2962	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#2950	C₂×C₆₇	1	1	yes	characteristic, complemented
572	#2949	C₂×C₆₇	1	1	yes	characteristic, complemented
573	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
574	C₆₇	#61344	1	1	yes	characteristic, direct product factor, Sylow
575	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
576	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
577	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
578	#559	C₂²×C₆₇	1	2	yes	—
579	#559	C₂²×C₆₇	1	2	yes	—
580	Q₈²	—	2	1	no	—
581	Q₈²	C₂²×C₆₇	1	2	yes	complemented
582	#557	—	2	1	no	—
583	#557	—	2	1	no	—
584	#557	—	2	1	no	—
585	#557	C₂²×C₆₇	1	2	yes	complemented
586	#557	C₂²×C₆₇	1	2	yes	complemented
587	#557	C₂²×C₆₇	1	2	yes	complemented
588	#556	C₂²×C₆₇	1	2	yes	—
589	#556	C₂²×C₆₇	1	2	yes	—
590	#551	—	2	2	no	—
591	#551	—	2	2	no	—
592	#544	—	2	2	no	—
593	#544	C₂²×C₆₇	1	1	yes	characteristic
594	#544	C₂²×C₆₇	1	1	yes	characteristic
595	#542	—	2	1	no	—
596	#542	—	2	1	no	—
597	#536	C₂²×C₆₇	1	1	yes	characteristic
598	#535	C₂²×C₆₇	1	1	yes	characteristic
599	#533	—	2	2	no	—
600	#533	C₂²×C₆₇	1	1	yes	characteristic
601	#533	C₂²×C₆₇	1	1	yes	characteristic
602	#529	—	2	1	no	—
603	#529	—	2	1	no	—
604	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
605	#519	C₂²×C₆₇	1	1	yes	characteristic
606	#519	C₂²×C₆₇	1	1	yes	characteristic
607	#519	C₂²×C₆₇	1	1	yes	characteristic
608	#518	C₂²×C₆₇	1	1	yes	characteristic
609	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
610	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
611	#491	C₂²×C₆₇	1	2	yes	complemented
612	#490	C₂²×C₆₇	1	2	yes	—
613	#489	C₂²×C₆₇	1	2	yes	—
614	#489	C₂²×C₆₇	1	2	yes	—
615	#489	C₂²×C₆₇	1	2	yes	—
616	#489	C₂²×C₆₇	1	2	yes	complemented
617	#488	C₂²×C₆₇	1	2	yes	—
618	#488	C₂²×C₆₇	1	2	yes	—
619	#488	C₂²×C₆₇	1	2	yes	—
620	#488	C₂²×C₆₇	1	2	yes	complemented
621	#487	C₂²×C₆₇	1	2	yes	complemented
622	#486	C₂²×C₆₇	1	2	yes	—
623	#479	C₂²×C₆₇	1	1	yes	characteristic, complemented
624	#479	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	#479	C₂²×C₆₇	1	2	yes	complemented
626	#479	C₂²×C₆₇	1	2	yes	complemented
627	#478	C₂²×C₆₇	1	2	yes	—
628	#478	C₂²×C₆₇	1	2	yes	—
629	#478	C₂²×C₆₇	1	1	yes	characteristic, complemented
630	#478	C₂²×C₆₇	1	1	yes	characteristic, complemented
631	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
632	#477	C₂²×C₆₇	1	2	yes	complemented
633	#476	C₂²×C₆₇	1	2	yes	—
634	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
635	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
636	#475	C₂²×C₆₇	1	2	yes	complemented
637	#474	C₂²×C₆₇	1	2	yes	—
638	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
639	#464	C₂²×C₆₇	1	2	yes	—
640	#464	C₂²×C₆₇	1	2	yes	—
641	#464	C₂²×C₆₇	1	2	yes	—
642	#464	C₂²×C₆₇	1	2	yes	—
643	#464	C₂²×C₆₇	1	2	yes	—
644	#464	C₂²×C₆₇	1	2	yes	—
645	#464	C₂²×C₆₇	1	2	yes	complemented
646	#464	C₂²×C₆₇	1	2	yes	complemented
647	#462	C₂²×C₆₇	1	2	yes	complemented
648	#462	C₂²×C₆₇	1	2	yes	complemented
649	#460	C₂²×C₆₇	1	2	yes	—
650	#460	C₂²×C₆₇	1	2	yes	—
651	#446	C₂²×C₆₇	1	2	yes	complemented
652	#446	C₂²×C₆₇	1	2	yes	complemented
653	#446	C₂²×C₆₇	1	2	yes	complemented
654	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
655	#441	C₂²×C₆₇	1	2	yes	complemented
656	#441	C₂²×C₆₇	1	2	yes	complemented
657	#441	C₂²×C₆₇	1	2	yes	complemented
658	#440	C₂²×C₆₇	1	2	yes	—
659	#440	C₂²×C₆₇	1	2	yes	—
660	#440	C₂²×C₆₇	1	2	yes	complemented
661	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
662	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
663	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
664	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
665	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
666	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
667	#428	C₂²×C₆₇	1	1	yes	characteristic
668	#427	C₂²×C₆₇	1	1	yes	characteristic
669	#427	C₂²×C₆₇	1	1	yes	characteristic
670	#424	C₂²×C₆₇	1	1	yes	characteristic
671	#424	C₂²×C₆₇	1	1	yes	characteristic
672	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
673	#419	C₂²×C₆₇	1	1	yes	characteristic
674	#419	C₂²×C₆₇	1	1	yes	characteristic
675	#419	C₂²×C₆₇	1	1	yes	characteristic
676	#418	C₂²×C₆₇	1	1	yes	characteristic
677	#418	C₂²×C₆₇	1	1	yes	characteristic
678	#417	C₂²×C₆₇	1	1	yes	characteristic
679	#416	C₂²×C₆₇	1	1	yes	characteristic
680	#416	C₂²×C₆₇	1	1	yes	characteristic
681	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
682	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
683	#405	C₂²×C₆₇	1	1	yes	characteristic
684	#405	C₂²×C₆₇	1	1	yes	characteristic
685	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
686	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
687	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
688	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
689	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
690	#137	—	2	4	no	—
691	C₂×Q₁₆	—	2	4	no	—
692	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
693	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
694	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
695	C₂×SD₁₆	—	2	4	no	—
696	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
697	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
698	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
699	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
700	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
701	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
702	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
703	C₄⋊Q₈	—	2	2	no	—
704	C₄⋊Q₈	—	2	2	no	—
705	C₄⋊Q₈	—	2	2	no	—
706	C₄⋊Q₈	—	2	2	no	—
707	C₄⋊Q₈	—	2	2	no	—
708	C₄⋊Q₈	—	2	2	no	—
709	C₄⋊Q₈	—	2	1	no	—
710	C₄⋊Q₈	—	2	1	no	—
711	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
712	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
713	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
714	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
717	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
718	#127	C₂³×C₆₇	1	2	yes	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	1	no	—
730	#125	—	2	1	no	—
731	#125	D₄×C₆₇	1	1	yes	characteristic
732	#125	D₄×C₆₇	1	1	yes	characteristic
733	#125	C₂³×C₆₇	1	1	yes	characteristic
734	#125	C₂³×C₆₇	1	1	yes	characteristic
735	#125	C₂³×C₆₇	1	2	yes	—
736	#125	C₂³×C₆₇	1	2	yes	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	—	2	1	no	—
740	#124	—	2	1	no	—
741	#124	C₂³×C₆₇	1	2	yes	—
742	#124	C₂³×C₆₇	1	2	yes	—
743	#124	C₂³×C₆₇	1	2	yes	—
744	#124	C₂³×C₆₇	1	2	yes	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
759	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
760	#121	—	2	1	no	—
761	#121	—	2	1	no	—
762	#120	—	2	2	no	—
763	C₄×Q₈	—	2	2	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	2	no	—
771	C₄×Q₈	—	2	2	no	—
772	C₄×Q₈	—	2	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
778	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
779	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
782	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
783	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
784	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
785	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
786	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
787	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
788	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
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	C₂³×C₆₇	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₆₇	1	2	yes	—
798	C₄×D₄	C₂³×C₆₇	1	2	yes	—
799	#117	—	2	2	no	—
800	#117	—	2	2	no	—
801	#117	—	2	2	no	—
802	#117	—	2	2	no	—
803	#117	—	2	2	no	—
804	#117	—	2	1	no	—
805	#117	C₂³×C₆₇	1	1	yes	characteristic
806	#117	C₂³×C₆₇	1	1	yes	characteristic
807	#117	C₂³×C₆₇	1	1	yes	characteristic
808	#117	C₂³×C₆₇	1	1	yes	characteristic
809	#117	C₂³×C₆₇	1	1	yes	characteristic
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
812	C₂×C₂²⋊C₄	—	2	1	no	—
813	C₂×C₂²⋊C₄	—	2	1	no	—
814	C₂×C₂²⋊C₄	—	2	2	no	—
815	C₂×C₄²	—	2	1	no	—
816	C₂×C₄²	—	2	1	no	—
817	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
818	#107	C₂³×C₆₇	1	1	yes	characteristic
819	#107	C₂³×C₆₇	1	1	yes	characteristic
820	#107	C₂³×C₆₇	1	1	yes	characteristic
821	#107	C₂³×C₆₇	1	1	yes	characteristic
822	#107	C₂³×C₆₇	1	2	yes	—
823	#106	C₂³×C₆₇	1	1	yes	characteristic
824	#106	C₂³×C₆₇	1	1	yes	characteristic
825	#106	C₂³×C₆₇	1	1	yes	characteristic
826	#106	C₂³×C₆₇	1	1	yes	characteristic
827	#106	C₂³×C₆₇	1	2	yes	—
828	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
833	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
834	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
835	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
836	#103	C₂³×C₆₇	1	2	yes	—
837	#103	C₂³×C₆₇	1	2	yes	—
838	#103	C₂³×C₆₇	1	1	yes	characteristic
839	#103	C₂³×C₆₇	1	1	yes	characteristic
840	#103	C₂³×C₆₇	1	1	yes	characteristic
841	#103	C₂³×C₆₇	1	1	yes	characteristic
842	#103	C₂³×C₆₇	1	2	yes	—
843	#103	C₂³×C₆₇	1	2	yes	—
844	#103	C₂³×C₆₇	1	2	yes	—
845	#103	C₂³×C₆₇	1	2	yes	—
846	#103	C₂³×C₆₇	1	2	yes	—
847	#103	C₂³×C₆₇	1	2	yes	—
848	#103	C₂³×C₆₇	1	2	yes	—
849	#102	C₂³×C₆₇	1	2	yes	—
850	#102	C₂³×C₆₇	1	2	yes	—
851	#102	C₂³×C₆₇	1	1	yes	characteristic
852	#102	C₂³×C₆₇	1	1	yes	characteristic
853	#102	C₂³×C₆₇	1	1	yes	characteristic
854	#102	C₂³×C₆₇	1	1	yes	characteristic
855	#102	C₂³×C₆₇	1	2	yes	—
856	#102	C₂³×C₆₇	1	2	yes	—
857	#102	C₂³×C₆₇	1	2	yes	—
858	#102	C₂³×C₆₇	1	2	yes	—
859	#102	C₂³×C₆₇	1	2	yes	—
860	#97	C₂³×C₆₇	1	2	yes	—
861	#97	C₂³×C₆₇	1	2	yes	—
862	#97	C₂³×C₆₇	1	2	yes	—
863	C₄×C₈	C₂³×C₆₇	1	2	yes	—
864	C₄×C₈	C₂³×C₆₇	1	2	yes	—
865	C₄×C₈	C₂³×C₆₇	1	2	yes	—
866	C₂⁴	—	2	1	no	—
867	#41	—	2	2	no	—
868	#41	—	2	2	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	2	2	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
879	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
880	C₂×Q₈	#41×C₆₇	1	4	yes	—
881	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
882	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
883	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
891	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
901	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
903	Q₁₆	—	2	4	no	—
904	Q₁₆	—	2	4	no	—
905	Q₁₆	—	2	4	no	—
906	SD₁₆	—	2	4	no	—
907	SD₁₆	—	2	4	no	—
908	SD₁₆	—	2	4	no	—
909	M₁₆	—	2	2	no	—
910	M₁₆	—	2	2	no	—
911	C₂×C₈	—	2	2	no	—
912	C₂×C₈	—	2	2	no	—
913	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
914	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
917	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
918	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
947	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
949	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
950	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
951	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
952	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
953	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
955	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
956	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
959	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
960	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
977	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	1	no	—
991	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
992	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
993	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
994	C₄²	C₂⁴×C₆₇	1	2	yes	—
995	C₄²	C₂⁴×C₆₇	1	2	yes	—
996	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
997	C₂³	—	2	2	no	—
998	C₂³	—	2	1	no	—
999	C₂³	—	4	2	no	—
1000	C₂³	—	8	1	no	—
1001	C₂³	—	8	1	no	—
1002	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1003	Q₈	—	2	4	no	—
1004	Q₈	—	2	2	no	—
1005	Q₈	—	2	2	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	4	2	no	—
1010	Q₈	—	4	2	no	—
1011	Q₈	—	4	2	no	—
1012	Q₈	—	4	2	no	—
1013	Q₈	—	8	1	no	—
1014	Q₈	—	8	2	no	—
1015	Q₈	—	8	2	no	—
1016	Q₈	C₂×#41×C₆₇	1	4	yes	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	1	no	—
1019	D₄	—	2	2	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	4	2	no	—
1023	D₄	—	8	2	no	—
1024	D₄	—	8	2	no	—
1025	C₂×C₄	—	2	4	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	4	1	no	—
1037	C₂×C₄	—	4	1	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	8	1	no	—
1041	C₂×C₄	—	8	2	no	—
1042	C₂×C₄	—	8	1	no	—
1043	C₂×C₄	—	8	2	no	—
1044	C₂×C₄	—	8	1	no	—
1045	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1046	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1048	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1049	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1051	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1052	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1054	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1055	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1056	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	1	no	—
1061	C₈	—	2	2	no	—
1062	C₈	—	2	2	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	16	2	no	—
1072	C₂²	#548×C₆₇	1	2	yes	—
1073	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	1	no	—
1079	C₄	—	2	1	no	—
1080	C₄	—	2	2	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	2	4	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	#548×C₆₇	1	2	yes	—
1093	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1094	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1095	C₂	—	2	2	no	—
1096	C₂	—	8	2	no	—
1097	C₂	—	8	1	no	—
1098	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
1099	C₂	C₆₇×#3584	1	1	yes	characteristic
1100	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	#535×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #533×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#3502	C₂	semidirect
3. C₆₇×#3377	C₂	semidirect
4. C₆₇×#3377	C₂	semidirect
5. C₆₇×#3375	C₂	semidirect
6. C₆₇×#3371	C₂	semidirect
7. C₆₇×#3371	C₂	semidirect
8. C₆₇×#3369	C₂	semidirect
9. C₆₇×#3365	C₂	semidirect
10. C₆₇×#3364	C₂	semidirect
11. C₆₇×#3140	C₂	semidirect
12. C₆₇×#3137	C₂	semidirect
14. C₆₇×#3082	C₂	semidirect
15. C₆₇×#3081	C₂	semidirect
16. C₆₇×#3076	C₂	semidirect
17. C₆₇×#3044	C₂	semidirect
19. C₂×#464×C₆₇	C₂	semidirect
20. C₆₇×#2962	C₂	semidirect
21. C₆₇×#2950	C₂	semidirect
22. C₆₇×#2949	C₂	semidirect
23. C₄×#137×C₆₇	C₂	semidirect
30. Q₈²×C₆₇	C₂²	semidirect
34. #557×C₆₇	C₂²	semidirect
35. #557×C₆₇	C₂²	semidirect
36. #557×C₆₇	C₂²	semidirect
60. #491×C₆₇	C₂²	semidirect
65. #489×C₆₇	C₂²	semidirect
69. #488×C₆₇	C₂²	semidirect
70. #487×C₆₇	C₂²	semidirect
72. #479×C₆₇	C₂²	semidirect
73. #479×C₆₇	C₂²	semidirect
74. #479×C₆₇	C₂²	semidirect
75. #479×C₆₇	C₂²	semidirect
78. #478×C₆₇	C₂²	semidirect
79. #478×C₆₇	C₂²	semidirect
80. #477×C₆₇	C₂²	semidirect
81. #477×C₆₇	C₂²	semidirect
83. #476×C₆₇	C₂²	semidirect
84. #475×C₆₇	C₂²	semidirect
85. #475×C₆₇	C₂²	semidirect
87. #474×C₆₇	C₂²	semidirect
94. #464×C₆₇	C₂²	semidirect
95. #464×C₆₇	C₂²	semidirect
96. #462×C₆₇	C₂²	semidirect
97. #462×C₆₇	C₂²	semidirect
100. #446×C₆₇	C₂²	semidirect
101. #446×C₆₇	C₂²	semidirect
102. #446×C₆₇	C₂²	semidirect
103. C₈×Q₈×C₆₇	C₂²	semidirect
104. #441×C₆₇	C₂²	semidirect
105. #441×C₆₇	C₂²	semidirect
106. #441×C₆₇	C₂²	semidirect
109. #440×C₆₇	C₂²	semidirect
110. C₄×Q₁₆×C₆₇	C₂²	semidirect
111. C₄×Q₁₆×C₆₇	C₂²	semidirect
112. C₄×Q₁₆×C₆₇	C₂²	semidirect
115. C₄×SD₁₆×C₆₇	C₂²	semidirect
544. #61344	C₆₇	direct (N × H)
552. #3502	C₂×C₆₇	semidirect
553. #3377	C₂×C₆₇	semidirect
554. #3377	C₂×C₆₇	semidirect
555. #3375	C₂×C₆₇	semidirect
556. #3371	C₂×C₆₇	semidirect
557. #3371	C₂×C₆₇	semidirect
558. #3369	C₂×C₆₇	semidirect
559. #3365	C₂×C₆₇	semidirect
560. #3364	C₂×C₆₇	semidirect
561. #3140	C₂×C₆₇	semidirect
562. #3137	C₂×C₆₇	semidirect
564. #3082	C₂×C₆₇	semidirect
565. #3081	C₂×C₆₇	semidirect
566. #3076	C₂×C₆₇	semidirect
567. #3044	C₂×C₆₇	semidirect
569. C₂×#464	C₂×C₆₇	semidirect
570. #2962	C₂×C₆₇	semidirect
571. #2950	C₂×C₆₇	semidirect
572. #2949	C₂×C₆₇	semidirect
573. C₄×#137	C₂×C₆₇	semidirect
574. C₆₇	#61344	direct (N × H)
581. Q₈²	C₂²×C₆₇	semidirect
585. #557	C₂²×C₆₇	semidirect
586. #557	C₂²×C₆₇	semidirect
587. #557	C₂²×C₆₇	semidirect
611. #491	C₂²×C₆₇	semidirect
616. #489	C₂²×C₆₇	semidirect
620. #488	C₂²×C₆₇	semidirect
621. #487	C₂²×C₆₇	semidirect
623. #479	C₂²×C₆₇	semidirect
624. #479	C₂²×C₆₇	semidirect
625. #479	C₂²×C₆₇	semidirect
626. #479	C₂²×C₆₇	semidirect
629. #478	C₂²×C₆₇	semidirect
630. #478	C₂²×C₆₇	semidirect
631. #477	C₂²×C₆₇	semidirect
632. #477	C₂²×C₆₇	semidirect
634. #476	C₂²×C₆₇	semidirect
635. #475	C₂²×C₆₇	semidirect
636. #475	C₂²×C₆₇	semidirect
638. #474	C₂²×C₆₇	semidirect
645. #464	C₂²×C₆₇	semidirect
646. #464	C₂²×C₆₇	semidirect
647. #462	C₂²×C₆₇	semidirect
648. #462	C₂²×C₆₇	semidirect
651. #446	C₂²×C₆₇	semidirect
652. #446	C₂²×C₆₇	semidirect
653. #446	C₂²×C₆₇	semidirect
654. C₈×Q₈	C₂²×C₆₇	semidirect
655. #441	C₂²×C₆₇	semidirect
656. #441	C₂²×C₆₇	semidirect
657. #441	C₂²×C₆₇	semidirect
660. #440	C₂²×C₆₇	semidirect
661. C₄×Q₁₆	C₂²×C₆₇	semidirect
662. C₄×Q₁₆	C₂²×C₆₇	semidirect
663. C₄×Q₁₆	C₂²×C₆₇	semidirect
666. C₄×SD₁₆	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×#3510	2
C₆₇×#3502	2
C₆₇×#3377	2
C₆₇×#3375	2
C₆₇×#3371	2
C₆₇×#3369	2
C₆₇×#3365	2
C₆₇×#3364	2
C₆₇×#3140	2
C₆₇×#3137	2
C₆₇×#3136	2
C₆₇×#3082	2
C₆₇×#3081	2
C₆₇×#3076	2
C₆₇×#3044	2
C₆₇×#3043	2
C₂×#464×C₆₇	2
C₆₇×#2962	2
C₆₇×#2950	2
C₆₇×#2949	2
C₄×#137×C₆₇	2
#61344	67

Subgroups — C67×#61344 #30740595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61344 #30740595