Subgroups — C₆₇×#61003 #30740254

Order 17152.

1792 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3494	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3256	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3253	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3251	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3244	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3241	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3224	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3220	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3197	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3194	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3192	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3184	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3183	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3171	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3125	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3122	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3119	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2921	C₂	1	1	yes	maximal, characteristic, complemented
20	#555×C₆₇	—	2	2	no	—
21	#553×C₆₇	—	2	2	no	—
22	#553×C₆₇	—	2	2	no	—
23	#551×C₆₇	—	2	2	no	—
24	#551×C₆₇	—	2	2	no	—
25	#547×C₆₇	—	2	2	no	—
26	#546×C₆₇	—	2	2	no	—
27	#546×C₆₇	—	2	2	no	—
28	#544×C₆₇	C₂²	1	2	yes	complemented
29	#542×C₆₇	C₂²	1	2	yes	—
30	#542×C₆₇	C₂²	1	2	yes	—
31	#540×C₆₇	C₂²	1	2	yes	—
32	#540×C₆₇	C₂²	1	2	yes	—
33	#535×C₆₇	C₂²	1	2	yes	complemented
34	#532×C₆₇	C₂²	1	2	yes	complemented
35	#532×C₆₇	C₂²	1	2	yes	complemented
36	#529×C₆₇	C₂²	1	2	yes	complemented
37	#529×C₆₇	C₂²	1	2	yes	complemented
38	#525×C₆₇	C₂²	1	2	yes	—
39	C₂×#121×C₆₇	C₂²	1	2	yes	—
40	#520×C₆₇	C₂²	1	2	yes	complemented
41	#518×C₆₇	C₂²	1	2	yes	complemented
42	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
43	#501×C₆₇	C₂²	1	2	yes	complemented
44	#499×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#496×C₆₇	C₂²	1	2	yes	complemented
47	#495×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#490×C₆₇	C₂²	1	2	yes	complemented
50	#489×C₆₇	C₂²	1	2	yes	complemented
51	#488×C₆₇	C₂²	1	2	yes	complemented
52	#486×C₆₇	C₂²	1	2	yes	complemented
53	#485×C₆₇	C₂²	1	2	yes	complemented
54	#483×C₆₇	C₂²	1	2	yes	complemented
55	#482×C₆₇	C₂²	1	2	yes	—
56	#482×C₆₇	C₂²	1	2	yes	—
57	#482×C₆₇	C₂²	1	2	yes	complemented
58	#481×C₆₇	C₂²	1	2	yes	—
59	#481×C₆₇	C₂²	1	2	yes	—
60	#480×C₆₇	C₂²	1	2	yes	complemented
61	#479×C₆₇	C₂²	1	2	yes	complemented
62	#478×C₆₇	C₂²	1	2	yes	complemented
63	#478×C₆₇	C₂²	1	2	yes	complemented
64	#478×C₆₇	C₂²	1	2	yes	complemented
65	#476×C₆₇	C₂²	1	2	yes	complemented
66	#476×C₆₇	C₂²	1	2	yes	complemented
67	#475×C₆₇	C₂²	1	2	yes	complemented
68	#474×C₆₇	C₂²	1	2	yes	complemented
69	#470×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#469×C₆₇	C₂²	1	2	yes	—
71	#469×C₆₇	C₂²	1	1	yes	characteristic
72	#469×C₆₇	C₂²	1	1	yes	characteristic
73	#469×C₆₇	C₂²	1	2	yes	complemented
74	#469×C₆₇	C₂²	1	2	yes	complemented
75	#469×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#468×C₆₇	C₂²	1	2	yes	complemented
77	#468×C₆₇	C₂²	1	2	yes	complemented
78	#468×C₆₇	C₂²	1	2	yes	complemented
79	#464×C₆₇	C₂²	1	2	yes	complemented
80	#463×C₆₇	C₂²	1	2	yes	complemented
81	#463×C₆₇	C₂²	1	2	yes	complemented
82	#463×C₆₇	C₂²	1	2	yes	complemented
83	#460×C₆₇	C₂²	1	2	yes	complemented
84	#459×C₆₇	C₂²	1	2	yes	complemented
85	#459×C₆₇	C₂²	1	2	yes	complemented
86	#459×C₆₇	C₂²	1	2	yes	complemented
87	#452×C₆₇	C₂²	1	2	yes	complemented
88	#450×C₆₇	C₂²	1	2	yes	complemented
89	#449×C₆₇	C₂²	1	2	yes	—
90	#449×C₆₇	C₂²	1	2	yes	—
91	#449×C₆₇	C₂²	1	2	yes	complemented
92	#447×C₆₇	C₂²	1	2	yes	—
93	#447×C₆₇	C₂²	1	2	yes	—
94	#447×C₆₇	C₂²	1	2	yes	complemented
95	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#442×C₆₇	C₂²	1	2	yes	complemented
99	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#440×C₆₇	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
103	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
104	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
105	#433×C₆₇	C₂²	1	2	yes	complemented
106	#433×C₆₇	C₂²	1	2	yes	complemented
107	#433×C₆₇	C₂²	1	2	yes	complemented
108	#433×C₆₇	C₂²	1	2	yes	complemented
109	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#407×C₆₇	C₂²	1	1	yes	characteristic
112	#407×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₆₇	—	2	2	no	—
116	C₂×#41×C₆₇	—	2	2	no	—
117	C₂×#41×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	—	2	2	no	—
119	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
125	C₂×D₈×C₆₇	C₂³	1	2	yes	—
126	C₂×D₈×C₆₇	C₂³	1	2	yes	—
127	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×D₈×C₆₇	C₂³	1	2	yes	—
130	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
134	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
135	C₄⋊Q₈×C₆₇	—	2	2	no	—
136	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
138	#127×C₆₇	C₂³	1	2	yes	—
139	#127×C₆₇	C₂³	1	2	yes	—
140	#126×C₆₇	—	2	2	no	—
141	#126×C₆₇	—	2	2	no	—
142	#126×C₆₇	—	2	2	no	—
143	#126×C₆₇	—	2	2	no	—
144	#125×C₆₇	—	2	2	no	—
145	#125×C₆₇	C₂³	1	2	yes	—
146	#125×C₆₇	C₂³	1	2	yes	—
147	#124×C₆₇	—	2	2	no	—
148	#124×C₆₇	—	2	2	no	—
149	#124×C₆₇	—	2	2	no	—
150	#124×C₆₇	—	2	2	no	—
151	#124×C₆₇	C₂³	1	2	yes	—
152	#124×C₆₇	C₂³	1	2	yes	—
153	#123×C₆₇	—	2	2	no	—
154	#123×C₆₇	—	2	2	no	—
155	#123×C₆₇	—	2	2	no	—
156	#123×C₆₇	—	2	2	no	—
157	#123×C₆₇	—	2	2	no	—
158	#123×C₆₇	—	2	2	no	—
159	#123×C₆₇	—	2	2	no	—
160	#123×C₆₇	—	2	2	no	—
161	#123×C₆₇	—	2	2	no	—
162	C₂²⋊Q₈×C₆₇	—	2	2	no	—
163	C₂²⋊Q₈×C₆₇	—	2	2	no	—
164	C₂²⋊Q₈×C₆₇	—	2	2	no	—
165	C₂²⋊Q₈×C₆₇	—	2	2	no	—
166	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
167	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
168	#121×C₆₇	—	2	2	no	—
169	#121×C₆₇	—	2	2	no	—
170	#121×C₆₇	—	2	2	no	—
171	#121×C₆₇	—	2	2	no	—
172	#121×C₆₇	—	2	2	no	—
173	#121×C₆₇	—	2	2	no	—
174	#121×C₆₇	—	2	2	no	—
175	#121×C₆₇	—	2	2	no	—
176	#121×C₆₇	—	2	2	no	—
177	#121×C₆₇	—	2	2	no	—
178	#121×C₆₇	C₂³	1	2	yes	—
179	#121×C₆₇	C₂³	1	2	yes	—
180	#121×C₆₇	C₂³	1	2	yes	—
181	#121×C₆₇	C₂³	1	2	yes	—
182	#121×C₆₇	C₂³	1	2	yes	—
183	#121×C₆₇	C₂³	1	2	yes	—
184	#120×C₆₇	—	2	2	no	—
185	#120×C₆₇	—	2	2	no	—
186	#120×C₆₇	—	2	2	no	—
187	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
188	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
189	C₄×D₄×C₆₇	—	2	2	no	—
190	C₄×D₄×C₆₇	—	2	2	no	—
191	C₄×D₄×C₆₇	—	2	2	no	—
192	C₄×D₄×C₆₇	—	2	2	no	—
193	C₄×D₄×C₆₇	—	2	2	no	—
194	C₄×D₄×C₆₇	—	2	2	no	—
195	C₄×D₄×C₆₇	—	2	2	no	—
196	C₄×D₄×C₆₇	—	2	2	no	—
197	C₄×D₄×C₆₇	—	2	2	no	—
198	C₄×D₄×C₆₇	—	2	2	no	—
199	C₄×D₄×C₆₇	C₂³	1	2	yes	—
200	C₄×D₄×C₆₇	C₂³	1	2	yes	—
201	C₄×D₄×C₆₇	C₂³	1	2	yes	—
202	C₄×D₄×C₆₇	C₂³	1	2	yes	—
203	C₄×D₄×C₆₇	C₂³	1	2	yes	—
204	C₄×D₄×C₆₇	C₂³	1	2	yes	—
205	#117×C₆₇	—	2	2	no	—
206	#117×C₆₇	—	2	2	no	—
207	#117×C₆₇	—	2	2	no	—
208	#117×C₆₇	D₄	1	2	yes	—
209	#117×C₆₇	D₄	1	2	yes	—
210	#117×C₆₇	C₂³	1	2	yes	—
211	#117×C₆₇	C₂³	1	2	yes	—
212	#117×C₆₇	C₂³	1	2	yes	—
213	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
214	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
215	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
217	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
218	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
219	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
220	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
222	#107×C₆₇	C₂³	1	2	yes	—
223	#107×C₆₇	C₂³	1	2	yes	—
224	#107×C₆₇	C₂³	1	2	yes	—
225	#106×C₆₇	C₂³	1	2	yes	—
226	#106×C₆₇	C₂³	1	1	yes	characteristic
227	#106×C₆₇	C₂³	1	1	yes	characteristic
228	#106×C₆₇	C₂³	1	2	yes	—
229	#106×C₆₇	C₂³	1	2	yes	—
230	#106×C₆₇	C₂³	1	1	yes	characteristic
231	#106×C₆₇	C₂³	1	1	yes	characteristic
232	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
233	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
234	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
235	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
236	#103×C₆₇	C₂³	1	2	yes	—
237	#103×C₆₇	C₂³	1	2	yes	—
238	#103×C₆₇	C₂³	1	2	yes	—
239	#103×C₆₇	C₂³	1	2	yes	—
240	#102×C₆₇	C₂³	1	2	yes	—
241	#102×C₆₇	C₂³	1	2	yes	—
242	#102×C₆₇	C₂³	1	2	yes	—
243	#102×C₆₇	C₂³	1	2	yes	—
244	#102×C₆₇	C₂³	1	2	yes	—
245	#102×C₆₇	C₂³	1	2	yes	—
246	#102×C₆₇	C₂³	1	2	yes	—
247	#102×C₆₇	C₂³	1	2	yes	—
248	#102×C₆₇	C₂³	1	2	yes	—
249	#102×C₆₇	C₂³	1	2	yes	—
250	#102×C₆₇	C₂³	1	2	yes	—
251	#102×C₆₇	C₂³	1	2	yes	—
252	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
253	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
254	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
255	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
256	#97×C₆₇	C₂³	1	2	yes	—
257	#97×C₆₇	C₂³	1	1	yes	characteristic
258	#97×C₆₇	C₂³	1	1	yes	characteristic
259	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
260	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₆₇	C₂³	1	2	yes	—
262	C₂⁴×C₆₇	—	2	2	no	—
263	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
264	#41×C₆₇	—	4	2	no	—
265	#41×C₆₇	—	4	2	no	—
266	#41×C₆₇	—	8	4	no	—
267	#41×C₆₇	—	8	4	no	—
268	C₂×Q₈×C₆₇	—	2	2	no	—
269	C₂×Q₈×C₆₇	—	2	2	no	—
270	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
271	C₂×D₄×C₆₇	—	2	2	no	—
272	C₂×D₄×C₆₇	—	2	2	no	—
273	C₂×D₄×C₆₇	—	2	2	no	—
274	C₂×D₄×C₆₇	—	2	2	no	—
275	C₂×D₄×C₆₇	—	2	2	no	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	2	2	no	—
278	C₂×D₄×C₆₇	—	2	2	no	—
279	C₂×D₄×C₆₇	—	2	2	no	—
280	C₂×D₄×C₆₇	—	2	2	no	—
281	C₂×D₄×C₆₇	—	2	2	no	—
282	C₂×D₄×C₆₇	—	2	2	no	—
283	C₂×D₄×C₆₇	—	4	2	no	—
284	C₂×D₄×C₆₇	—	4	2	no	—
285	C₂×D₄×C₆₇	—	8	4	no	—
286	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
287	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₆₇	—	2	2	no	—
290	C₂²×C₄×C₆₇	—	2	2	no	—
291	C₂²×C₄×C₆₇	—	2	2	no	—
292	C₂²×C₄×C₆₇	—	2	2	no	—
293	C₂²×C₄×C₆₇	—	2	2	no	—
294	C₂²×C₄×C₆₇	—	2	2	no	—
295	C₂²×C₄×C₆₇	—	2	2	no	—
296	C₂²×C₄×C₆₇	—	2	2	no	—
297	C₂²×C₄×C₆₇	—	4	1	no	—
298	C₂²×C₄×C₆₇	—	4	1	no	—
299	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
300	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
301	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
302	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
305	Q₁₆×C₆₇	—	4	1	no	—
306	SD₁₆×C₆₇	—	4	2	no	—
307	SD₁₆×C₆₇	—	4	2	no	—
308	SD₁₆×C₆₇	—	4	2	no	—
309	D₈×C₆₇	—	4	2	no	—
310	D₈×C₆₇	—	4	1	no	—
311	D₈×C₆₇	—	4	1	no	—
312	D₈×C₆₇	—	4	2	no	—
313	D₈×C₆₇	—	4	2	no	—
314	D₈×C₆₇	—	4	1	no	—
315	M₁₆×C₆₇	—	4	1	no	—
316	M₁₆×C₆₇	—	4	1	no	—
317	M₁₆×C₆₇	—	4	1	no	—
318	M₁₆×C₆₇	—	4	1	no	—
319	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
322	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
323	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₄⋊C₄×C₆₇	—	2	2	no	—
326	C₄⋊C₄×C₆₇	—	2	2	no	—
327	C₄⋊C₄×C₆₇	—	2	2	no	—
328	C₄⋊C₄×C₆₇	—	2	2	no	—
329	C₄⋊C₄×C₆₇	—	2	2	no	—
330	C₄⋊C₄×C₆₇	—	2	2	no	—
331	C₄⋊C₄×C₆₇	—	2	2	no	—
332	C₄⋊C₄×C₆₇	—	2	2	no	—
333	C₄⋊C₄×C₆₇	—	2	2	no	—
334	C₄⋊C₄×C₆₇	—	2	2	no	—
335	C₄⋊C₄×C₆₇	—	2	2	no	—
336	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
338	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
339	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
340	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
341	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
343	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
344	C₂²⋊C₄×C₆₇	—	2	2	no	—
345	C₂²⋊C₄×C₆₇	—	2	2	no	—
346	C₂²⋊C₄×C₆₇	—	2	2	no	—
347	C₂²⋊C₄×C₆₇	—	2	2	no	—
348	C₂²⋊C₄×C₆₇	—	2	2	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	—	2	2	no	—
354	C₂²⋊C₄×C₆₇	—	2	2	no	—
355	C₂²⋊C₄×C₆₇	—	2	2	no	—
356	C₂²⋊C₄×C₆₇	—	2	2	no	—
357	C₂²⋊C₄×C₆₇	—	2	2	no	—
358	C₂²⋊C₄×C₆₇	—	2	2	no	—
359	C₂²⋊C₄×C₆₇	—	2	2	no	—
360	C₂²⋊C₄×C₆₇	—	2	2	no	—
361	C₂²⋊C₄×C₆₇	—	2	2	no	—
362	C₂²⋊C₄×C₆₇	—	2	2	no	—
363	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
364	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
365	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
366	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
367	C₄²×C₆₇	—	2	2	no	—
368	C₄²×C₆₇	—	2	2	no	—
369	C₄²×C₆₇	—	2	2	no	—
370	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₆₇	C₂×D₄	1	2	yes	—
372	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₆₇	C₂⁴	1	2	yes	—
374	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂³×C₆₇	—	2	2	no	—
377	C₂³×C₆₇	—	2	2	no	—
378	C₂³×C₆₇	—	2	2	no	—
379	C₂³×C₆₇	—	4	1	no	—
380	C₂³×C₆₇	—	4	2	no	—
381	C₂³×C₆₇	—	4	4	no	—
382	C₂³×C₆₇	—	8	2	no	—
383	C₂³×C₆₇	—	8	2	no	—
384	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
385	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
386	Q₈×C₆₇	—	2	2	no	—
387	Q₈×C₆₇	—	2	2	no	—
388	Q₈×C₆₇	—	8	2	no	—
389	Q₈×C₆₇	—	8	2	no	—
390	D₄×C₆₇	—	2	2	no	—
391	D₄×C₆₇	—	2	2	no	—
392	D₄×C₆₇	—	2	2	no	—
393	D₄×C₆₇	—	2	2	no	—
394	D₄×C₆₇	—	2	2	no	—
395	D₄×C₆₇	—	2	2	no	—
396	D₄×C₆₇	—	4	4	no	—
397	D₄×C₆₇	—	4	4	no	—
398	D₄×C₆₇	—	4	4	no	—
399	D₄×C₆₇	—	4	4	no	—
400	D₄×C₆₇	—	4	4	no	—
401	D₄×C₆₇	—	8	2	no	—
402	D₄×C₆₇	—	8	2	no	—
403	D₄×C₆₇	—	8	2	no	—
404	D₄×C₆₇	—	8	2	no	—
405	D₄×C₆₇	—	8	2	no	—
406	D₄×C₆₇	—	8	2	no	—
407	D₄×C₆₇	—	8	2	no	—
408	C₂×C₄×C₆₇	—	2	1	no	—
409	C₂×C₄×C₆₇	—	2	1	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	2	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	2	2	no	—
414	C₂×C₄×C₆₇	—	2	2	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	2	no	—
417	C₂×C₄×C₆₇	—	4	1	no	—
418	C₂×C₄×C₆₇	—	4	2	no	—
419	C₂×C₄×C₆₇	—	4	2	no	—
420	C₂×C₄×C₆₇	—	4	2	no	—
421	C₂×C₄×C₆₇	—	4	4	no	—
422	C₂×C₄×C₆₇	—	8	2	no	—
423	C₂×C₄×C₆₇	—	8	2	no	—
424	C₂×C₄×C₆₇	—	8	2	no	—
425	C₂×C₄×C₆₇	—	8	2	no	—
426	C₂×C₄×C₆₇	—	8	2	no	—
427	C₂×C₄×C₆₇	—	8	2	no	—
428	C₂×C₄×C₆₇	—	8	2	no	—
429	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
436	C₈×C₆₇	—	2	1	no	—
437	C₈×C₆₇	—	2	1	no	—
438	C₈×C₆₇	—	2	2	no	—
439	C₈×C₆₇	—	2	2	no	—
440	C₈×C₆₇	—	2	1	no	—
441	C₈×C₆₇	—	2	1	no	—
442	C₂²×C₆₇	—	2	2	no	—
443	C₂²×C₆₇	—	2	2	no	—
444	C₂²×C₆₇	—	2	2	no	—
445	C₂²×C₆₇	—	2	2	no	—
446	C₂²×C₆₇	—	2	1	no	—
447	C₂²×C₆₇	—	4	2	no	—
448	C₂²×C₆₇	—	4	2	no	—
449	C₂²×C₆₇	—	4	2	no	—
450	C₂²×C₆₇	—	4	2	no	—
451	C₂²×C₆₇	—	4	2	no	—
452	C₂²×C₆₇	—	4	2	no	—
453	C₂²×C₆₇	—	4	2	no	—
454	C₂²×C₆₇	—	4	2	no	—
455	C₂²×C₆₇	—	4	2	no	—
456	C₂²×C₆₇	—	8	2	no	—
457	C₂²×C₆₇	—	16	4	no	—
458	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
459	C₄×C₆₇	—	2	2	no	—
460	C₄×C₆₇	—	2	2	no	—
461	C₄×C₆₇	—	2	2	no	—
462	C₄×C₆₇	—	2	2	no	—
463	C₄×C₆₇	—	2	2	no	—
464	C₄×C₆₇	—	2	1	no	—
465	C₄×C₆₇	—	4	2	no	—
466	C₄×C₆₇	—	4	2	no	—
467	C₄×C₆₇	—	4	2	no	—
468	C₄×C₆₇	—	4	2	no	—
469	C₄×C₆₇	—	4	2	no	—
470	C₄×C₆₇	#585	1	1	yes	characteristic
471	C₄×C₆₇	#585	1	1	yes	characteristic
472	#61003	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
473	C₂×C₆₇	—	4	1	no	—
474	C₂×C₆₇	—	4	2	no	—
475	C₂×C₆₇	—	8	2	no	—
476	C₂×C₆₇	—	8	2	no	—
477	C₂×C₆₇	—	8	2	no	—
478	C₂×C₆₇	#3449	1	1	yes	characteristic
479	C₂×C₆₇	#3585	1	2	yes	—
480	#3494	C₂×C₆₇	1	2	yes	complemented
481	#3256	C₂×C₆₇	1	1	yes	characteristic, complemented
482	#3253	C₂×C₆₇	1	1	yes	characteristic, complemented
483	#3251	C₂×C₆₇	1	2	yes	complemented
484	#3244	C₂×C₆₇	1	2	yes	complemented
485	#3241	C₂×C₆₇	1	2	yes	complemented
486	#3224	C₂×C₆₇	1	2	yes	complemented
487	#3220	C₂×C₆₇	1	2	yes	complemented
488	#3197	C₂×C₆₇	1	1	yes	characteristic, complemented
489	#3194	C₂×C₆₇	1	2	yes	complemented
490	#3192	C₂×C₆₇	1	1	yes	characteristic, complemented
491	#3184	C₂×C₆₇	1	1	yes	characteristic, complemented
492	#3183	C₂×C₆₇	1	1	yes	characteristic, complemented
493	#3171	C₂×C₆₇	1	2	yes	complemented
494	#3125	C₂×C₆₇	1	2	yes	complemented
495	#3122	C₂×C₆₇	1	2	yes	complemented
496	#3119	C₂×C₆₇	1	2	yes	complemented
497	#3118	C₂×C₆₇	1	2	yes	complemented
498	#2921	C₂×C₆₇	1	1	yes	characteristic, complemented
499	C₆₇	#61003	1	1	yes	characteristic, direct product factor, Sylow
500	#555	—	2	2	no	—
501	#553	—	2	2	no	—
502	#553	—	2	2	no	—
503	#551	—	2	2	no	—
504	#551	—	2	2	no	—
505	#547	—	2	2	no	—
506	#546	—	2	2	no	—
507	#546	—	2	2	no	—
508	#544	C₂²×C₆₇	1	2	yes	complemented
509	#542	C₂²×C₆₇	1	2	yes	—
510	#542	C₂²×C₆₇	1	2	yes	—
511	#540	C₂²×C₆₇	1	2	yes	—
512	#540	C₂²×C₆₇	1	2	yes	—
513	#535	C₂²×C₆₇	1	2	yes	complemented
514	#532	C₂²×C₆₇	1	2	yes	complemented
515	#532	C₂²×C₆₇	1	2	yes	complemented
516	#529	C₂²×C₆₇	1	2	yes	complemented
517	#529	C₂²×C₆₇	1	2	yes	complemented
518	#525	C₂²×C₆₇	1	2	yes	—
519	C₂×#121	C₂²×C₆₇	1	2	yes	—
520	#520	C₂²×C₆₇	1	2	yes	complemented
521	#518	C₂²×C₆₇	1	2	yes	complemented
522	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
523	#501	C₂²×C₆₇	1	2	yes	complemented
524	#499	C₂²×C₆₇	1	1	yes	characteristic, complemented
525	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
526	#496	C₂²×C₆₇	1	2	yes	complemented
527	#495	C₂²×C₆₇	1	1	yes	characteristic, complemented
528	#493	C₂²×C₆₇	1	1	yes	characteristic, complemented
529	#490	C₂²×C₆₇	1	2	yes	complemented
530	#489	C₂²×C₆₇	1	2	yes	complemented
531	#488	C₂²×C₆₇	1	2	yes	complemented
532	#486	C₂²×C₆₇	1	2	yes	complemented
533	#485	C₂²×C₆₇	1	2	yes	complemented
534	#483	C₂²×C₆₇	1	2	yes	complemented
535	#482	C₂²×C₆₇	1	2	yes	—
536	#482	C₂²×C₆₇	1	2	yes	—
537	#482	C₂²×C₆₇	1	2	yes	complemented
538	#481	C₂²×C₆₇	1	2	yes	—
539	#481	C₂²×C₆₇	1	2	yes	—
540	#480	C₂²×C₆₇	1	2	yes	complemented
541	#479	C₂²×C₆₇	1	2	yes	complemented
542	#478	C₂²×C₆₇	1	2	yes	complemented
543	#478	C₂²×C₆₇	1	2	yes	complemented
544	#478	C₂²×C₆₇	1	2	yes	complemented
545	#476	C₂²×C₆₇	1	2	yes	complemented
546	#476	C₂²×C₆₇	1	2	yes	complemented
547	#475	C₂²×C₆₇	1	2	yes	complemented
548	#474	C₂²×C₆₇	1	2	yes	complemented
549	#470	C₂²×C₆₇	1	1	yes	characteristic, complemented
550	#469	C₂²×C₆₇	1	2	yes	—
551	#469	C₂²×C₆₇	1	1	yes	characteristic
552	#469	C₂²×C₆₇	1	1	yes	characteristic
553	#469	C₂²×C₆₇	1	2	yes	complemented
554	#469	C₂²×C₆₇	1	2	yes	complemented
555	#469	C₂²×C₆₇	1	1	yes	characteristic, complemented
556	#468	C₂²×C₆₇	1	2	yes	complemented
557	#468	C₂²×C₆₇	1	2	yes	complemented
558	#468	C₂²×C₆₇	1	2	yes	complemented
559	#464	C₂²×C₆₇	1	2	yes	complemented
560	#463	C₂²×C₆₇	1	2	yes	complemented
561	#463	C₂²×C₆₇	1	2	yes	complemented
562	#463	C₂²×C₆₇	1	2	yes	complemented
563	#460	C₂²×C₆₇	1	2	yes	complemented
564	#459	C₂²×C₆₇	1	2	yes	complemented
565	#459	C₂²×C₆₇	1	2	yes	complemented
566	#459	C₂²×C₆₇	1	2	yes	complemented
567	#452	C₂²×C₆₇	1	2	yes	complemented
568	#450	C₂²×C₆₇	1	2	yes	complemented
569	#449	C₂²×C₆₇	1	2	yes	—
570	#449	C₂²×C₆₇	1	2	yes	—
571	#449	C₂²×C₆₇	1	2	yes	complemented
572	#447	C₂²×C₆₇	1	2	yes	—
573	#447	C₂²×C₆₇	1	2	yes	—
574	#447	C₂²×C₆₇	1	2	yes	complemented
575	#442	C₂²×C₆₇	1	1	yes	characteristic, complemented
576	#442	C₂²×C₆₇	1	1	yes	characteristic, complemented
577	#442	C₂²×C₆₇	1	1	yes	characteristic, complemented
578	#442	C₂²×C₆₇	1	2	yes	complemented
579	#441	C₂²×C₆₇	1	1	yes	characteristic, complemented
580	#440	C₂²×C₆₇	1	2	yes	complemented
581	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
582	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
583	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
584	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
585	#433	C₂²×C₆₇	1	2	yes	complemented
586	#433	C₂²×C₆₇	1	2	yes	complemented
587	#433	C₂²×C₆₇	1	2	yes	complemented
588	#433	C₂²×C₆₇	1	2	yes	complemented
589	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
590	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
591	#407	C₂²×C₆₇	1	1	yes	characteristic
592	#407	C₂²×C₆₇	1	1	yes	characteristic
593	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
594	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
595	C₂×#41	—	2	2	no	—
596	C₂×#41	—	2	2	no	—
597	C₂×#41	C₂³×C₆₇	1	2	yes	—
598	C₂²×D₄	—	2	2	no	—
599	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
600	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
601	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
602	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
603	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
604	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
605	C₂×D₈	C₂³×C₆₇	1	2	yes	—
606	C₂×D₈	C₂³×C₆₇	1	2	yes	—
607	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
608	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
609	C₂×D₈	C₂³×C₆₇	1	2	yes	—
610	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
612	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
613	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
614	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
615	C₄⋊Q₈	—	2	2	no	—
616	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
617	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
618	#127	C₂³×C₆₇	1	2	yes	—
619	#127	C₂³×C₆₇	1	2	yes	—
620	#126	—	2	2	no	—
621	#126	—	2	2	no	—
622	#126	—	2	2	no	—
623	#126	—	2	2	no	—
624	#125	—	2	2	no	—
625	#125	C₂³×C₆₇	1	2	yes	—
626	#125	C₂³×C₆₇	1	2	yes	—
627	#124	—	2	2	no	—
628	#124	—	2	2	no	—
629	#124	—	2	2	no	—
630	#124	—	2	2	no	—
631	#124	C₂³×C₆₇	1	2	yes	—
632	#124	C₂³×C₆₇	1	2	yes	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
647	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	2	no	—
656	#121	—	2	2	no	—
657	#121	—	2	2	no	—
658	#121	C₂³×C₆₇	1	2	yes	—
659	#121	C₂³×C₆₇	1	2	yes	—
660	#121	C₂³×C₆₇	1	2	yes	—
661	#121	C₂³×C₆₇	1	2	yes	—
662	#121	C₂³×C₆₇	1	2	yes	—
663	#121	C₂³×C₆₇	1	2	yes	—
664	#120	—	2	2	no	—
665	#120	—	2	2	no	—
666	#120	—	2	2	no	—
667	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
668	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	C₂³×C₆₇	1	2	yes	—
680	C₄×D₄	C₂³×C₆₇	1	2	yes	—
681	C₄×D₄	C₂³×C₆₇	1	2	yes	—
682	C₄×D₄	C₂³×C₆₇	1	2	yes	—
683	C₄×D₄	C₂³×C₆₇	1	2	yes	—
684	C₄×D₄	C₂³×C₆₇	1	2	yes	—
685	#117	—	2	2	no	—
686	#117	—	2	2	no	—
687	#117	—	2	2	no	—
688	#117	D₄×C₆₇	1	2	yes	—
689	#117	D₄×C₆₇	1	2	yes	—
690	#117	C₂³×C₆₇	1	2	yes	—
691	#117	C₂³×C₆₇	1	2	yes	—
692	#117	C₂³×C₆₇	1	2	yes	—
693	C₂×C₄⋊C₄	—	2	2	no	—
694	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
696	C₂×C₂²⋊C₄	—	2	2	no	—
697	C₂×C₂²⋊C₄	—	2	2	no	—
698	C₂×C₂²⋊C₄	—	2	2	no	—
699	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
700	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
702	#107	C₂³×C₆₇	1	2	yes	—
703	#107	C₂³×C₆₇	1	2	yes	—
704	#107	C₂³×C₆₇	1	2	yes	—
705	#106	C₂³×C₆₇	1	2	yes	—
706	#106	C₂³×C₆₇	1	2	yes	—
707	#106	C₂³×C₆₇	1	1	yes	characteristic
708	#106	C₂³×C₆₇	1	1	yes	characteristic
709	#106	C₂³×C₆₇	1	2	yes	—
710	#106	C₂³×C₆₇	1	1	yes	characteristic
711	#106	C₂³×C₆₇	1	1	yes	characteristic
712	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
713	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
714	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
715	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
716	#103	C₂³×C₆₇	1	2	yes	—
717	#103	C₂³×C₆₇	1	2	yes	—
718	#103	C₂³×C₆₇	1	2	yes	—
719	#103	C₂³×C₆₇	1	2	yes	—
720	#102	C₂³×C₆₇	1	2	yes	—
721	#102	C₂³×C₆₇	1	2	yes	—
722	#102	C₂³×C₆₇	1	2	yes	—
723	#102	C₂³×C₆₇	1	2	yes	—
724	#102	C₂³×C₆₇	1	2	yes	—
725	#102	C₂³×C₆₇	1	2	yes	—
726	#102	C₂³×C₆₇	1	2	yes	—
727	#102	C₂³×C₆₇	1	2	yes	—
728	#102	C₂³×C₆₇	1	2	yes	—
729	#102	C₂³×C₆₇	1	2	yes	—
730	#102	C₂³×C₆₇	1	2	yes	—
731	#102	C₂³×C₆₇	1	2	yes	—
732	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
733	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
734	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
735	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
736	#97	C₂³×C₆₇	1	1	yes	characteristic
737	#97	C₂³×C₆₇	1	1	yes	characteristic
738	#97	C₂³×C₆₇	1	2	yes	—
739	C₄×C₈	C₂³×C₆₇	1	2	yes	—
740	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
741	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
742	C₂⁴	—	2	2	no	—
743	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
744	#41	—	4	2	no	—
745	#41	—	4	2	no	—
746	#41	—	8	4	no	—
747	#41	—	8	4	no	—
748	C₂×Q₈	—	2	2	no	—
749	C₂×Q₈	—	2	2	no	—
750	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	4	2	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	8	4	no	—
766	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
767	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
768	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	4	1	no	—
778	C₂²×C₄	—	4	1	no	—
779	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
780	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
781	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
782	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
785	Q₁₆	—	4	1	no	—
786	SD₁₆	—	4	2	no	—
787	SD₁₆	—	4	2	no	—
788	SD₁₆	—	4	2	no	—
789	D₈	—	4	2	no	—
790	D₈	—	4	1	no	—
791	D₈	—	4	1	no	—
792	D₈	—	4	2	no	—
793	D₈	—	4	2	no	—
794	D₈	—	4	1	no	—
795	M₁₆	—	4	1	no	—
796	M₁₆	—	4	1	no	—
797	M₁₆	—	4	1	no	—
798	M₁₆	—	4	1	no	—
799	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
800	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
801	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
802	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
803	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
804	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
817	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
818	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
819	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
821	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
822	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
823	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
844	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
845	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
846	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
851	C₄²	C₂×D₄×C₆₇	1	2	yes	—
852	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
853	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
854	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
855	C₄²	C₂⁴×C₆₇	1	2	yes	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	4	1	no	—
860	C₂³	—	4	2	no	—
861	C₂³	—	4	4	no	—
862	C₂³	—	8	2	no	—
863	C₂³	—	8	2	no	—
864	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
865	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
866	Q₈	—	2	2	no	—
867	Q₈	—	2	2	no	—
868	Q₈	—	8	2	no	—
869	Q₈	—	8	2	no	—
870	D₄	—	2	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	2	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	4	no	—
879	D₄	—	4	4	no	—
880	D₄	—	4	4	no	—
881	D₄	—	8	2	no	—
882	D₄	—	8	2	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	—	8	2	no	—
886	D₄	—	8	2	no	—
887	D₄	—	8	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	4	1	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	2	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	8	2	no	—
903	C₂×C₄	—	8	2	no	—
904	C₂×C₄	—	8	2	no	—
905	C₂×C₄	—	8	2	no	—
906	C₂×C₄	—	8	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
910	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
911	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
912	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
913	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
914	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
915	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
916	C₈	—	2	1	no	—
917	C₈	—	2	1	no	—
918	C₈	—	2	2	no	—
919	C₈	—	2	2	no	—
920	C₈	—	2	1	no	—
921	C₈	—	2	1	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	8	2	no	—
937	C₂²	—	16	4	no	—
938	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	2	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	#585×C₆₇	1	1	yes	characteristic
951	C₄	#585×C₆₇	1	1	yes	characteristic
952	C₂	—	4	2	no	—
953	C₂	—	4	1	no	—
954	C₂	—	8	2	no	—
955	C₂	—	8	2	no	—
956	C₂	—	8	2	no	—
957	C₂	C₆₇×#3449	1	1	yes	characteristic
958	C₂	C₆₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3494	C₂	semidirect
2. C₆₇×#3256	C₂	semidirect
3. C₆₇×#3253	C₂	semidirect
4. C₆₇×#3251	C₂	semidirect
5. C₆₇×#3244	C₂	semidirect
6. C₆₇×#3241	C₂	semidirect
7. C₆₇×#3224	C₂	semidirect
8. C₆₇×#3220	C₂	semidirect
9. C₆₇×#3197	C₂	semidirect
10. C₆₇×#3194	C₂	semidirect
11. C₆₇×#3192	C₂	semidirect
12. C₆₇×#3184	C₂	semidirect
13. C₆₇×#3183	C₂	semidirect
14. C₆₇×#3171	C₂	semidirect
15. C₆₇×#3125	C₂	semidirect
16. C₆₇×#3122	C₂	semidirect
17. C₆₇×#3119	C₂	semidirect
18. C₆₇×#3118	C₂	semidirect
19. C₆₇×#2921	C₂	semidirect
28. #544×C₆₇	C₂²	semidirect
33. #535×C₆₇	C₂²	semidirect
34. #532×C₆₇	C₂²	semidirect
35. #532×C₆₇	C₂²	semidirect
36. #529×C₆₇	C₂²	semidirect
37. #529×C₆₇	C₂²	semidirect
40. #520×C₆₇	C₂²	semidirect
41. #518×C₆₇	C₂²	semidirect
43. #501×C₆₇	C₂²	semidirect
44. #499×C₆₇	C₂²	semidirect
45. #498×C₆₇	C₂²	semidirect
46. #496×C₆₇	C₂²	semidirect
47. #495×C₆₇	C₂²	semidirect
48. #493×C₆₇	C₂²	semidirect
49. #490×C₆₇	C₂²	semidirect
50. #489×C₆₇	C₂²	semidirect
51. #488×C₆₇	C₂²	semidirect
52. #486×C₆₇	C₂²	semidirect
53. #485×C₆₇	C₂²	semidirect
54. #483×C₆₇	C₂²	semidirect
57. #482×C₆₇	C₂²	semidirect
60. #480×C₆₇	C₂²	semidirect
61. #479×C₆₇	C₂²	semidirect
62. #478×C₆₇	C₂²	semidirect
63. #478×C₆₇	C₂²	semidirect
64. #478×C₆₇	C₂²	semidirect
65. #476×C₆₇	C₂²	semidirect
66. #476×C₆₇	C₂²	semidirect
67. #475×C₆₇	C₂²	semidirect
68. #474×C₆₇	C₂²	semidirect
69. #470×C₆₇	C₂²	semidirect
73. #469×C₆₇	C₂²	semidirect
74. #469×C₆₇	C₂²	semidirect
75. #469×C₆₇	C₂²	semidirect
76. #468×C₆₇	C₂²	semidirect
77. #468×C₆₇	C₂²	semidirect
78. #468×C₆₇	C₂²	semidirect
79. #464×C₆₇	C₂²	semidirect
80. #463×C₆₇	C₂²	semidirect
81. #463×C₆₇	C₂²	semidirect
82. #463×C₆₇	C₂²	semidirect
83. #460×C₆₇	C₂²	semidirect
84. #459×C₆₇	C₂²	semidirect
85. #459×C₆₇	C₂²	semidirect
86. #459×C₆₇	C₂²	semidirect
87. #452×C₆₇	C₂²	semidirect
88. #450×C₆₇	C₂²	semidirect
91. #449×C₆₇	C₂²	semidirect
94. #447×C₆₇	C₂²	semidirect
95. #442×C₆₇	C₂²	semidirect
96. #442×C₆₇	C₂²	semidirect
97. #442×C₆₇	C₂²	semidirect
98. #442×C₆₇	C₂²	semidirect
99. #441×C₆₇	C₂²	semidirect
100. #440×C₆₇	C₂²	semidirect
101. C₄×SD₁₆×C₆₇	C₂²	semidirect
102. C₄×SD₁₆×C₆₇	C₂²	semidirect
103. C₄×D₈×C₆₇	C₂²	semidirect
104. C₄×D₈×C₆₇	C₂²	semidirect
105. #433×C₆₇	C₂²	semidirect
106. #433×C₆₇	C₂²	semidirect
107. #433×C₆₇	C₂²	semidirect
108. #433×C₆₇	C₂²	semidirect
109. #423×C₆₇	C₂²	semidirect
110. #423×C₆₇	C₂²	semidirect
113. C₄×M₁₆×C₆₇	C₂²	semidirect
114. C₄×M₁₆×C₆₇	C₂²	semidirect
472. #61003	C₆₇	direct (N × H)
480. #3494	C₂×C₆₇	semidirect
481. #3256	C₂×C₆₇	semidirect
482. #3253	C₂×C₆₇	semidirect
483. #3251	C₂×C₆₇	semidirect
484. #3244	C₂×C₆₇	semidirect
485. #3241	C₂×C₆₇	semidirect
486. #3224	C₂×C₆₇	semidirect
487. #3220	C₂×C₆₇	semidirect
488. #3197	C₂×C₆₇	semidirect
489. #3194	C₂×C₆₇	semidirect
490. #3192	C₂×C₆₇	semidirect
491. #3184	C₂×C₆₇	semidirect
492. #3183	C₂×C₆₇	semidirect
493. #3171	C₂×C₆₇	semidirect
494. #3125	C₂×C₆₇	semidirect
495. #3122	C₂×C₆₇	semidirect
496. #3119	C₂×C₆₇	semidirect
497. #3118	C₂×C₆₇	semidirect
498. #2921	C₂×C₆₇	semidirect
499. C₆₇	#61003	direct (N × H)
508. #544	C₂²×C₆₇	semidirect
513. #535	C₂²×C₆₇	semidirect
514. #532	C₂²×C₆₇	semidirect
515. #532	C₂²×C₆₇	semidirect
516. #529	C₂²×C₆₇	semidirect
517. #529	C₂²×C₆₇	semidirect
520. #520	C₂²×C₆₇	semidirect
521. #518	C₂²×C₆₇	semidirect
523. #501	C₂²×C₆₇	semidirect
524. #499	C₂²×C₆₇	semidirect
525. #498	C₂²×C₆₇	semidirect
526. #496	C₂²×C₆₇	semidirect
527. #495	C₂²×C₆₇	semidirect
528. #493	C₂²×C₆₇	semidirect
529. #490	C₂²×C₆₇	semidirect
530. #489	C₂²×C₆₇	semidirect
531. #488	C₂²×C₆₇	semidirect
532. #486	C₂²×C₆₇	semidirect
533. #485	C₂²×C₆₇	semidirect
534. #483	C₂²×C₆₇	semidirect
537. #482	C₂²×C₆₇	semidirect
540. #480	C₂²×C₆₇	semidirect
541. #479	C₂²×C₆₇	semidirect
542. #478	C₂²×C₆₇	semidirect
543. #478	C₂²×C₆₇	semidirect
544. #478	C₂²×C₆₇	semidirect
545. #476	C₂²×C₆₇	semidirect
546. #476	C₂²×C₆₇	semidirect
547. #475	C₂²×C₆₇	semidirect
548. #474	C₂²×C₆₇	semidirect
549. #470	C₂²×C₆₇	semidirect
553. #469	C₂²×C₆₇	semidirect
554. #469	C₂²×C₆₇	semidirect
555. #469	C₂²×C₆₇	semidirect
556. #468	C₂²×C₆₇	semidirect
557. #468	C₂²×C₆₇	semidirect
558. #468	C₂²×C₆₇	semidirect
559. #464	C₂²×C₆₇	semidirect
560. #463	C₂²×C₆₇	semidirect
561. #463	C₂²×C₆₇	semidirect
562. #463	C₂²×C₆₇	semidirect
563. #460	C₂²×C₆₇	semidirect
564. #459	C₂²×C₆₇	semidirect
565. #459	C₂²×C₆₇	semidirect
566. #459	C₂²×C₆₇	semidirect
567. #452	C₂²×C₆₇	semidirect
568. #450	C₂²×C₆₇	semidirect
571. #449	C₂²×C₆₇	semidirect
574. #447	C₂²×C₆₇	semidirect
575. #442	C₂²×C₆₇	semidirect
576. #442	C₂²×C₆₇	semidirect
577. #442	C₂²×C₆₇	semidirect
578. #442	C₂²×C₆₇	semidirect
579. #441	C₂²×C₆₇	semidirect
580. #440	C₂²×C₆₇	semidirect
581. C₄×SD₁₆	C₂²×C₆₇	semidirect
582. C₄×SD₁₆	C₂²×C₆₇	semidirect
583. C₄×D₈	C₂²×C₆₇	semidirect
584. C₄×D₈	C₂²×C₆₇	semidirect
585. #433	C₂²×C₆₇	semidirect
586. #433	C₂²×C₆₇	semidirect
587. #433	C₂²×C₆₇	semidirect
588. #433	C₂²×C₆₇	semidirect
589. #423	C₂²×C₆₇	semidirect
590. #423	C₂²×C₆₇	semidirect
593. C₄×M₁₆	C₂²×C₆₇	semidirect
594. C₄×M₁₆	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×#3494	2
C₆₇×#3256	2
C₆₇×#3253	2
C₆₇×#3251	2
C₆₇×#3244	2
C₆₇×#3241	2
C₆₇×#3224	2
C₆₇×#3220	2
C₆₇×#3197	2
C₆₇×#3194	2
C₆₇×#3192	2
C₆₇×#3184	2
C₆₇×#3183	2
C₆₇×#3171	2
C₆₇×#3125	2
C₆₇×#3122	2
C₆₇×#3119	2
C₆₇×#3118	2
C₆₇×#2921	2
#61003	67

Subgroups — C67×#61003 #30740254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61003 #30740254