Subgroups — C₆₇×#59505 #30738756

Order 17152.

1528 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2793	C₂	1	2	yes	maximal
2	C₆₇×#2767	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2596	C₂	1	2	yes	maximal
4	C₆₇×#2570	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2570	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2533	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2529	C₂	1	2	yes	maximal
8	C₆₇×#2519	C₂	1	2	yes	maximal
9	C₆₇×#2508	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2506	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2497	C₂	1	1	yes	maximal, characteristic
12	C₆₇×#2453	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2441	C₂	1	1	yes	maximal, characteristic
14	C₆₇×#2421	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2421	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2371	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2362	C₂	1	1	yes	maximal, characteristic
18	C₆₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
19	Q₈×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2346	C₂	1	1	yes	maximal, characteristic
21	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#126×C₆₇	C₂	1	1	yes	maximal, characteristic
23	C₆₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₆₇	C₂²	1	2	yes	—
26	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
32	#400×C₆₇	C₂²	1	2	yes	—
33	#400×C₆₇	C₂²	1	2	yes	—
34	#400×C₆₇	C₂²	1	2	yes	—
35	#400×C₆₇	C₂²	1	2	yes	—
36	#400×C₆₇	C₂²	1	2	yes	—
37	#400×C₆₇	C₂²	1	2	yes	—
38	#400×C₆₇	C₂²	1	2	yes	—
39	#399×C₆₇	C₂²	1	2	yes	—
40	#398×C₆₇	C₂²	1	2	yes	—
41	#398×C₆₇	C₂²	1	2	yes	—
42	#398×C₆₇	C₂²	1	2	yes	—
43	#398×C₆₇	C₂²	1	2	yes	—
44	#397×C₆₇	C₂²	1	2	yes	—
45	#397×C₆₇	C₂²	1	2	yes	—
46	#396×C₆₇	C₂²	1	2	yes	—
47	#396×C₆₇	C₂²	1	2	yes	—
48	#391×C₆₇	C₂²	1	1	yes	characteristic
49	#391×C₆₇	C₂²	1	1	yes	characteristic
50	#391×C₆₇	C₂²	1	1	yes	characteristic
51	#389×C₆₇	C₂²	1	1	yes	characteristic
52	#389×C₆₇	C₂²	1	1	yes	characteristic
53	#389×C₆₇	C₂²	1	1	yes	characteristic
54	#389×C₆₇	C₂²	1	1	yes	characteristic
55	#389×C₆₇	C₂²	1	1	yes	characteristic
56	#389×C₆₇	C₂²	1	1	yes	characteristic
57	#389×C₆₇	C₂²	1	1	yes	characteristic
58	#389×C₆₇	C₂²	1	2	yes	—
59	#389×C₆₇	C₂²	1	2	yes	—
60	#389×C₆₇	C₂²	1	2	yes	—
61	#389×C₆₇	C₂²	1	2	yes	—
62	#389×C₆₇	C₂²	1	1	yes	characteristic
63	#389×C₆₇	C₂²	1	1	yes	characteristic
64	#388×C₆₇	C₂²	1	2	yes	—
65	#388×C₆₇	C₂²	1	2	yes	—
66	#388×C₆₇	C₂²	1	2	yes	—
67	#388×C₆₇	C₂²	1	2	yes	—
68	#388×C₆₇	C₂²	1	2	yes	—
69	#388×C₆₇	C₂²	1	1	yes	characteristic
70	#388×C₆₇	C₂²	1	2	yes	—
71	#388×C₆₇	C₂²	1	1	yes	characteristic
72	#388×C₆₇	C₂²	1	2	yes	—
73	#388×C₆₇	C₂²	1	1	yes	characteristic
74	#387×C₆₇	C₂²	1	2	yes	—
75	#387×C₆₇	C₂²	1	2	yes	—
76	#387×C₆₇	C₂²	1	2	yes	—
77	#387×C₆₇	C₂²	1	1	yes	characteristic
78	#387×C₆₇	C₂²	1	2	yes	—
79	#387×C₆₇	C₂²	1	2	yes	—
80	#387×C₆₇	C₂²	1	2	yes	—
81	#387×C₆₇	C₂²	1	2	yes	—
82	#387×C₆₇	C₂²	1	2	yes	—
83	#387×C₆₇	C₂²	1	2	yes	—
84	#387×C₆₇	C₂²	1	2	yes	—
85	#387×C₆₇	C₂²	1	2	yes	—
86	#387×C₆₇	C₂²	1	2	yes	—
87	#387×C₆₇	C₂²	1	2	yes	—
88	#387×C₆₇	C₂²	1	2	yes	—
89	#387×C₆₇	C₂²	1	2	yes	—
90	#387×C₆₇	C₂²	1	2	yes	—
91	#387×C₆₇	C₂²	1	1	yes	characteristic
92	#387×C₆₇	C₂²	1	1	yes	characteristic
93	#384×C₆₇	C₂²	1	1	yes	characteristic
94	#384×C₆₇	C₂²	1	1	yes	characteristic
95	#384×C₆₇	C₂²	1	2	yes	—
96	#383×C₆₇	C₂²	1	1	yes	characteristic
97	#382×C₆₇	C₂²	1	2	yes	—
98	#382×C₆₇	C₂²	1	1	yes	characteristic
99	#382×C₆₇	C₂²	1	2	yes	—
100	#382×C₆₇	C₂²	1	2	yes	—
101	#382×C₆₇	C₂²	1	1	yes	characteristic
102	#380×C₆₇	C₂²	1	1	yes	characteristic
103	#380×C₆₇	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
120	#376×C₆₇	C₂²	1	2	yes	—
121	#376×C₆₇	C₂²	1	2	yes	—
122	C₄³×C₆₇	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
125	#126×C₆₇	—	2	4	no	—
126	#125×C₆₇	—	2	4	no	—
127	#125×C₆₇	—	2	8	no	—
128	C₂²⋊Q₈×C₆₇	—	2	4	no	—
129	C₄×Q₈×C₆₇	—	2	4	no	—
130	C₄×Q₈×C₆₇	—	2	4	no	—
131	C₄×Q₈×C₆₇	—	2	4	no	—
132	#117×C₆₇	—	2	4	no	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
192	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	1	yes	characteristic
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	1	yes	characteristic
202	#95×C₆₇	C₂³	1	1	yes	characteristic
203	#95×C₆₇	C₂³	1	1	yes	characteristic
204	#95×C₆₇	C₂³	1	1	yes	characteristic
205	#95×C₆₇	C₂³	1	1	yes	characteristic
206	#95×C₆₇	C₂³	1	1	yes	characteristic
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	1	yes	characteristic
214	#95×C₆₇	C₂³	1	1	yes	characteristic
215	#95×C₆₇	C₂³	1	1	yes	characteristic
216	#95×C₆₇	C₂³	1	1	yes	characteristic
217	#95×C₆₇	C₂³	1	2	yes	—
218	#95×C₆₇	C₂³	1	2	yes	—
219	#95×C₆₇	C₂³	1	2	yes	—
220	#95×C₆₇	C₂³	1	1	yes	characteristic
221	#95×C₆₇	C₂³	1	2	yes	—
222	#95×C₆₇	C₂³	1	2	yes	—
223	#95×C₆₇	C₂³	1	2	yes	—
224	#95×C₆₇	C₂³	1	2	yes	—
225	#95×C₆₇	C₂³	1	2	yes	—
226	#95×C₆₇	C₂³	1	2	yes	—
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	2	yes	—
229	#95×C₆₇	C₂³	1	2	yes	—
230	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂×Q₈×C₆₇	—	2	2	no	—
232	C₂×Q₈×C₆₇	—	2	2	no	—
233	C₂×Q₈×C₆₇	#41	1	4	yes	—
234	C₂²×C₄×C₆₇	—	2	2	no	—
235	C₂²×C₄×C₆₇	—	2	2	no	—
236	C₂²×C₄×C₆₇	—	2	2	no	—
237	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₄⋊C₄×C₆₇	—	2	2	no	—
260	C₄⋊C₄×C₆₇	—	2	4	no	—
261	C₄⋊C₄×C₆₇	—	2	4	no	—
262	C₄⋊C₄×C₆₇	—	2	4	no	—
263	C₄⋊C₄×C₆₇	—	2	2	no	—
264	C₄⋊C₄×C₆₇	—	2	2	no	—
265	C₄⋊C₄×C₆₇	—	2	2	no	—
266	C₄⋊C₄×C₆₇	—	2	4	no	—
267	C₄⋊C₄×C₆₇	—	2	4	no	—
268	C₄⋊C₄×C₆₇	—	2	4	no	—
269	C₄⋊C₄×C₆₇	—	2	4	no	—
270	C₄⋊C₄×C₆₇	—	2	4	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	2	4	no	—
274	C₄⋊C₄×C₆₇	—	2	2	no	—
275	C₄⋊C₄×C₆₇	—	2	2	no	—
276	C₄⋊C₄×C₆₇	—	2	2	no	—
277	C₄⋊C₄×C₆₇	—	2	2	no	—
278	C₄⋊C₄×C₆₇	—	2	2	no	—
279	C₄⋊C₄×C₆₇	—	4	2	no	—
280	C₄⋊C₄×C₆₇	—	4	1	no	—
281	C₄⋊C₄×C₆₇	—	4	2	no	—
282	C₄⋊C₄×C₆₇	—	4	2	no	—
283	C₄⋊C₄×C₆₇	—	4	2	no	—
284	C₄⋊C₄×C₆₇	—	4	2	no	—
285	C₄⋊C₄×C₆₇	—	4	1	no	—
286	C₄⋊C₄×C₆₇	—	4	2	no	—
287	C₄⋊C₄×C₆₇	—	4	2	no	—
288	C₄⋊C₄×C₆₇	—	4	2	no	—
289	C₄⋊C₄×C₆₇	#41	1	4	yes	—
290	C₄⋊C₄×C₆₇	#41	1	4	yes	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	4	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	—	4	2	no	—
300	C₂²⋊C₄×C₆₇	—	4	2	no	—
301	C₄²×C₆₇	—	2	4	no	—
302	C₄²×C₆₇	—	2	4	no	—
303	C₄²×C₆₇	—	2	4	no	—
304	C₄²×C₆₇	—	2	4	no	—
305	C₄²×C₆₇	—	2	2	no	—
306	C₄²×C₆₇	—	2	2	no	—
307	C₄²×C₆₇	—	2	2	no	—
308	C₄²×C₆₇	—	2	4	no	—
309	C₄²×C₆₇	—	2	2	no	—
310	C₄²×C₆₇	—	2	2	no	—
311	C₄²×C₆₇	—	2	2	no	—
312	C₄²×C₆₇	—	2	4	no	—
313	C₄²×C₆₇	—	2	2	no	—
314	C₄²×C₆₇	—	2	2	no	—
315	C₄²×C₆₇	—	4	2	no	—
316	C₄²×C₆₇	—	4	1	no	—
317	C₄²×C₆₇	—	4	2	no	—
318	C₄²×C₆₇	—	4	1	no	—
319	C₂³×C₆₇	—	2	1	no	—
320	C₂³×C₆₇	—	2	1	no	—
321	C₂³×C₆₇	—	2	1	no	—
322	C₂³×C₆₇	—	2	1	no	—
323	C₂³×C₆₇	—	2	1	no	—
324	C₂³×C₆₇	—	2	1	no	—
325	C₂³×C₆₇	—	2	1	no	—
326	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
327	Q₈×C₆₇	—	2	8	no	—
328	C₂×C₄×C₆₇	—	2	1	no	—
329	C₂×C₄×C₆₇	—	2	1	no	—
330	C₂×C₄×C₆₇	—	2	1	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	1	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	1	no	—
335	C₂×C₄×C₆₇	—	2	1	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	1	no	—
338	C₂×C₄×C₆₇	—	2	1	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	1	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	1	no	—
343	C₂×C₄×C₆₇	—	2	1	no	—
344	C₂×C₄×C₆₇	—	2	1	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	1	no	—
347	C₂×C₄×C₆₇	—	2	1	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	1	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	1	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	1	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	1	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	1	no	—
361	C₂×C₄×C₆₇	—	2	1	no	—
362	C₂×C₄×C₆₇	—	2	1	no	—
363	C₂×C₄×C₆₇	—	2	1	no	—
364	C₂×C₄×C₆₇	—	2	1	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	1	no	—
368	C₂×C₄×C₆₇	—	2	1	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	1	no	—
372	C₂×C₄×C₆₇	—	2	1	no	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	1	no	—
376	C₂×C₄×C₆₇	—	2	1	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	1	no	—
381	C₂×C₄×C₆₇	—	2	1	no	—
382	C₂×C₄×C₆₇	—	2	1	no	—
383	C₂×C₄×C₆₇	—	2	1	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	4	4	no	—
386	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
387	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
388	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
389	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
390	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
391	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
392	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
393	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
394	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
395	C₂²×C₆₇	—	4	1	no	—
396	C₂²×C₆₇	—	4	1	no	—
397	C₂²×C₆₇	—	4	1	no	—
398	C₂²×C₆₇	—	4	1	no	—
399	C₂²×C₆₇	—	4	1	no	—
400	C₂²×C₆₇	—	4	1	no	—
401	C₂²×C₆₇	—	4	1	no	—
402	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
403	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
404	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
405	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
406	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
407	C₂²×C₆₇	#585	1	1	yes	characteristic
408	C₂²×C₆₇	#585	1	1	yes	characteristic
409	C₄×C₆₇	—	2	4	no	—
410	C₄×C₆₇	—	2	2	no	—
411	C₄×C₆₇	—	2	2	no	—
412	C₄×C₆₇	—	2	2	no	—
413	C₄×C₆₇	—	2	4	no	—
414	C₄×C₆₇	—	2	2	no	—
415	C₄×C₆₇	—	4	1	no	—
416	C₄×C₆₇	—	4	2	no	—
417	C₄×C₆₇	—	4	1	no	—
418	C₄×C₆₇	—	4	2	no	—
419	C₄×C₆₇	—	4	2	no	—
420	C₄×C₆₇	—	4	1	no	—
421	C₄×C₆₇	—	4	1	no	—
422	C₄×C₆₇	—	4	1	no	—
423	C₄×C₆₇	—	4	2	no	—
424	C₄×C₆₇	—	4	1	no	—
425	C₄×C₆₇	—	4	2	no	—
426	C₄×C₆₇	—	4	1	no	—
427	C₄×C₆₇	—	4	2	no	—
428	C₄×C₆₇	—	4	1	no	—
429	C₄×C₆₇	—	4	1	no	—
430	C₄×C₆₇	#552	1	4	yes	—
431	#59505	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
432	C₂×C₆₇	—	8	1	no	—
433	C₂×C₆₇	C₂×#552	1	1	yes	characteristic
434	C₂×C₆₇	#3480	1	1	yes	characteristic
435	C₂×C₆₇	#3482	1	1	yes	characteristic
436	C₂×C₆₇	#3515	1	1	yes	characteristic
437	C₂×C₆₇	#3518	1	1	yes	characteristic
438	C₂×C₆₇	#3524	1	1	yes	characteristic
439	C₂×C₆₇	#3563	1	1	yes	characteristic
440	#2793	C₂×C₆₇	1	2	yes	—
441	#2767	C₂×C₆₇	1	2	yes	complemented
442	#2596	C₂×C₆₇	1	2	yes	—
443	#2570	C₂×C₆₇	1	1	yes	characteristic, complemented
444	#2570	C₂×C₆₇	1	2	yes	complemented
445	#2533	C₂×C₆₇	1	2	yes	complemented
446	#2529	C₂×C₆₇	1	2	yes	—
447	#2519	C₂×C₆₇	1	2	yes	—
448	#2508	C₂×C₆₇	1	1	yes	characteristic, complemented
449	#2506	C₂×C₆₇	1	1	yes	characteristic, complemented
450	#2497	C₂×C₆₇	1	1	yes	characteristic
451	#2453	C₂×C₆₇	1	1	yes	characteristic, complemented
452	#2441	C₂×C₆₇	1	1	yes	characteristic
453	#2421	C₂×C₆₇	1	1	yes	characteristic
454	#2421	C₂×C₆₇	1	1	yes	characteristic
455	#2371	C₂×C₆₇	1	2	yes	complemented
456	#2362	C₂×C₆₇	1	1	yes	characteristic
457	#2355	C₂×C₆₇	1	1	yes	characteristic, complemented
458	Q₈×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
459	#2346	C₂×C₆₇	1	1	yes	characteristic
460	C₄×#125	C₂×C₆₇	1	1	yes	characteristic, complemented
461	C₄×#126	C₂×C₆₇	1	1	yes	characteristic
462	#2295	C₂×C₆₇	1	1	yes	characteristic, complemented
463	C₆₇	#59505	1	1	yes	characteristic, direct product factor, Sylow
464	C₂×#126	C₂²×C₆₇	1	1	yes	characteristic
465	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
466	C₂×#125	C₂²×C₆₇	1	2	yes	—
467	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
468	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
469	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
470	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
471	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
472	#400	C₂²×C₆₇	1	2	yes	—
473	#400	C₂²×C₆₇	1	2	yes	—
474	#400	C₂²×C₆₇	1	2	yes	—
475	#400	C₂²×C₆₇	1	2	yes	—
476	#400	C₂²×C₆₇	1	2	yes	—
477	#400	C₂²×C₆₇	1	2	yes	—
478	#400	C₂²×C₆₇	1	2	yes	—
479	#399	C₂²×C₆₇	1	2	yes	—
480	#398	C₂²×C₆₇	1	2	yes	—
481	#398	C₂²×C₆₇	1	2	yes	—
482	#398	C₂²×C₆₇	1	2	yes	—
483	#398	C₂²×C₆₇	1	2	yes	—
484	#397	C₂²×C₆₇	1	2	yes	—
485	#397	C₂²×C₆₇	1	2	yes	—
486	#396	C₂²×C₆₇	1	2	yes	—
487	#396	C₂²×C₆₇	1	2	yes	—
488	#391	C₂²×C₆₇	1	1	yes	characteristic
489	#391	C₂²×C₆₇	1	1	yes	characteristic
490	#391	C₂²×C₆₇	1	1	yes	characteristic
491	#389	C₂²×C₆₇	1	1	yes	characteristic
492	#389	C₂²×C₆₇	1	1	yes	characteristic
493	#389	C₂²×C₆₇	1	1	yes	characteristic
494	#389	C₂²×C₆₇	1	2	yes	—
495	#389	C₂²×C₆₇	1	1	yes	characteristic
496	#389	C₂²×C₆₇	1	2	yes	—
497	#389	C₂²×C₆₇	1	2	yes	—
498	#389	C₂²×C₆₇	1	1	yes	characteristic
499	#389	C₂²×C₆₇	1	1	yes	characteristic
500	#389	C₂²×C₆₇	1	2	yes	—
501	#389	C₂²×C₆₇	1	1	yes	characteristic
502	#389	C₂²×C₆₇	1	1	yes	characteristic
503	#389	C₂²×C₆₇	1	1	yes	characteristic
504	#388	C₂²×C₆₇	1	1	yes	characteristic
505	#388	C₂²×C₆₇	1	1	yes	characteristic
506	#388	C₂²×C₆₇	1	1	yes	characteristic
507	#388	C₂²×C₆₇	1	2	yes	—
508	#388	C₂²×C₆₇	1	2	yes	—
509	#388	C₂²×C₆₇	1	2	yes	—
510	#388	C₂²×C₆₇	1	2	yes	—
511	#388	C₂²×C₆₇	1	2	yes	—
512	#388	C₂²×C₆₇	1	2	yes	—
513	#388	C₂²×C₆₇	1	2	yes	—
514	#387	C₂²×C₆₇	1	1	yes	characteristic
515	#387	C₂²×C₆₇	1	1	yes	characteristic
516	#387	C₂²×C₆₇	1	1	yes	characteristic
517	#387	C₂²×C₆₇	1	2	yes	—
518	#387	C₂²×C₆₇	1	2	yes	—
519	#387	C₂²×C₆₇	1	2	yes	—
520	#387	C₂²×C₆₇	1	2	yes	—
521	#387	C₂²×C₆₇	1	2	yes	—
522	#387	C₂²×C₆₇	1	2	yes	—
523	#387	C₂²×C₆₇	1	2	yes	—
524	#387	C₂²×C₆₇	1	2	yes	—
525	#387	C₂²×C₆₇	1	2	yes	—
526	#387	C₂²×C₆₇	1	2	yes	—
527	#387	C₂²×C₆₇	1	2	yes	—
528	#387	C₂²×C₆₇	1	2	yes	—
529	#387	C₂²×C₆₇	1	2	yes	—
530	#387	C₂²×C₆₇	1	2	yes	—
531	#387	C₂²×C₆₇	1	2	yes	—
532	#387	C₂²×C₆₇	1	2	yes	—
533	#384	C₂²×C₆₇	1	1	yes	characteristic
534	#384	C₂²×C₆₇	1	2	yes	—
535	#384	C₂²×C₆₇	1	1	yes	characteristic
536	#383	C₂²×C₆₇	1	1	yes	characteristic
537	#382	C₂²×C₆₇	1	1	yes	characteristic
538	#382	C₂²×C₆₇	1	2	yes	—
539	#382	C₂²×C₆₇	1	1	yes	characteristic
540	#382	C₂²×C₆₇	1	2	yes	—
541	#382	C₂²×C₆₇	1	2	yes	—
542	#380	C₂²×C₆₇	1	1	yes	characteristic
543	#380	C₂²×C₆₇	1	1	yes	characteristic
544	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
545	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
546	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
547	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
548	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
549	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
550	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
551	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
553	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
554	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
555	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
556	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
557	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
558	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
559	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
560	#376	C₂²×C₆₇	1	2	yes	—
561	#376	C₂²×C₆₇	1	2	yes	—
562	C₄³	C₂²×C₆₇	1	1	yes	characteristic
563	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
564	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
565	#126	—	2	4	no	—
566	#125	—	2	4	no	—
567	#125	—	2	8	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₄×Q₈	—	2	4	no	—
570	C₄×Q₈	—	2	4	no	—
571	C₄×Q₈	—	2	4	no	—
572	#117	—	2	4	no	—
573	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
616	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
618	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
621	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
622	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
624	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
632	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
633	#95	C₂³×C₆₇	1	1	yes	characteristic
634	#95	C₂³×C₆₇	1	2	yes	—
635	#95	C₂³×C₆₇	1	2	yes	—
636	#95	C₂³×C₆₇	1	2	yes	—
637	#95	C₂³×C₆₇	1	2	yes	—
638	#95	C₂³×C₆₇	1	2	yes	—
639	#95	C₂³×C₆₇	1	2	yes	—
640	#95	C₂³×C₆₇	1	2	yes	—
641	#95	C₂³×C₆₇	1	1	yes	characteristic
642	#95	C₂³×C₆₇	1	1	yes	characteristic
643	#95	C₂³×C₆₇	1	1	yes	characteristic
644	#95	C₂³×C₆₇	1	1	yes	characteristic
645	#95	C₂³×C₆₇	1	1	yes	characteristic
646	#95	C₂³×C₆₇	1	1	yes	characteristic
647	#95	C₂³×C₆₇	1	2	yes	—
648	#95	C₂³×C₆₇	1	2	yes	—
649	#95	C₂³×C₆₇	1	2	yes	—
650	#95	C₂³×C₆₇	1	2	yes	—
651	#95	C₂³×C₆₇	1	2	yes	—
652	#95	C₂³×C₆₇	1	2	yes	—
653	#95	C₂³×C₆₇	1	1	yes	characteristic
654	#95	C₂³×C₆₇	1	1	yes	characteristic
655	#95	C₂³×C₆₇	1	1	yes	characteristic
656	#95	C₂³×C₆₇	1	1	yes	characteristic
657	#95	C₂³×C₆₇	1	2	yes	—
658	#95	C₂³×C₆₇	1	2	yes	—
659	#95	C₂³×C₆₇	1	2	yes	—
660	#95	C₂³×C₆₇	1	1	yes	characteristic
661	#95	C₂³×C₆₇	1	2	yes	—
662	#95	C₂³×C₆₇	1	2	yes	—
663	#95	C₂³×C₆₇	1	2	yes	—
664	#95	C₂³×C₆₇	1	2	yes	—
665	#95	C₂³×C₆₇	1	2	yes	—
666	#95	C₂³×C₆₇	1	2	yes	—
667	#95	C₂³×C₆₇	1	2	yes	—
668	#95	C₂³×C₆₇	1	2	yes	—
669	#95	C₂³×C₆₇	1	2	yes	—
670	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	#41×C₆₇	1	4	yes	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	1	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	1	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	#41×C₆₇	1	4	yes	—
730	C₄⋊C₄	#41×C₆₇	1	4	yes	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	4	1	no	—
738	C₂²⋊C₄	—	4	1	no	—
739	C₂²⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₄²	—	2	4	no	—
742	C₄²	—	2	4	no	—
743	C₄²	—	2	4	no	—
744	C₄²	—	2	4	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	4	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	4	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	4	2	no	—
756	C₄²	—	4	1	no	—
757	C₄²	—	4	2	no	—
758	C₄²	—	4	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
767	Q₈	—	2	8	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
827	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
828	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
829	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
830	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
831	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
832	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
833	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
834	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
843	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
844	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
845	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
846	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
847	C₂²	#585×C₆₇	1	1	yes	characteristic
848	C₂²	#585×C₆₇	1	1	yes	characteristic
849	C₄	—	2	2	no	—
850	C₄	—	2	4	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	4	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	#552×C₆₇	1	4	yes	—
871	C₂	—	8	1	no	—
872	C₂	C₂×#552×C₆₇	1	1	yes	characteristic
873	C₂	C₆₇×#3480	1	1	yes	characteristic
874	C₂	C₆₇×#3482	1	1	yes	characteristic
875	C₂	C₆₇×#3515	1	1	yes	characteristic
876	C₂	C₆₇×#3518	1	1	yes	characteristic
877	C₂	C₆₇×#3524	1	1	yes	characteristic
878	C₂	C₆₇×#3563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂⁴×C₆₇	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2767	C₂	semidirect
4. C₆₇×#2570	C₂	semidirect
5. C₆₇×#2570	C₂	semidirect
6. C₆₇×#2533	C₂	semidirect
9. C₆₇×#2508	C₂	semidirect
10. C₆₇×#2506	C₂	semidirect
12. C₆₇×#2453	C₂	semidirect
16. C₆₇×#2371	C₂	semidirect
18. C₆₇×#2355	C₂	semidirect
19. Q₈×C₄⋊C₄×C₆₇	C₂	semidirect
21. C₄×#125×C₆₇	C₂	semidirect
23. C₆₇×#2295	C₂	semidirect
431. #59505	C₆₇	direct (N × H)
441. #2767	C₂×C₆₇	semidirect
443. #2570	C₂×C₆₇	semidirect
444. #2570	C₂×C₆₇	semidirect
445. #2533	C₂×C₆₇	semidirect
448. #2508	C₂×C₆₇	semidirect
449. #2506	C₂×C₆₇	semidirect
451. #2453	C₂×C₆₇	semidirect
455. #2371	C₂×C₆₇	semidirect
457. #2355	C₂×C₆₇	semidirect
458. Q₈×C₄⋊C₄	C₂×C₆₇	semidirect
460. C₄×#125	C₂×C₆₇	semidirect
462. #2295	C₂×C₆₇	semidirect
463. C₆₇	#59505	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2793	2
C₆₇×#2767	2
C₆₇×#2596	2
C₆₇×#2570	2
C₆₇×#2533	2
C₆₇×#2529	2
C₆₇×#2519	2
C₆₇×#2508	2
C₆₇×#2506	2
C₆₇×#2497	2
C₆₇×#2453	2
C₆₇×#2441	2
C₆₇×#2421	2
C₆₇×#2371	2
C₆₇×#2362	2
C₆₇×#2355	2
Q₈×C₄⋊C₄×C₆₇	2
C₆₇×#2346	2
C₄×#125×C₆₇	2
C₄×#126×C₆₇	2
C₆₇×#2295	2
#59505	67

Subgroups — C67×#59505 #30738756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59505 #30738756