Subgroups — C₆₇×#59587 #30738838

Order 17152.

1488 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2791	C₂	1	2	yes	maximal
2	C₆₇×#2755	C₂	1	2	yes	maximal
3	C₆₇×#2590	C₂	1	2	yes	maximal
4	C₆₇×#2585	C₂	1	2	yes	maximal
5	C₆₇×#2570	C₂	1	1	yes	maximal, characteristic
6	C₆₇×#2552	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#2550	C₂	1	1	yes	maximal, characteristic
8	C₆₇×#2550	C₂	1	1	yes	maximal, characteristic
9	C₆₇×#2520	C₂	1	2	yes	maximal
10	C₆₇×#2508	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#2508	C₂	1	1	yes	maximal, characteristic
12	C₆₇×#2508	C₂	1	1	yes	maximal, characteristic
13	C₆₇×#2508	C₂	1	2	yes	maximal
14	C₆₇×#2507	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2462	C₂	1	2	yes	maximal
16	C₆₇×#2370	C₂	1	1	yes	maximal, characteristic
17	C₆₇×#2370	C₂	1	1	yes	maximal, characteristic
18	C₆₇×#2370	C₂	1	1	yes	maximal, characteristic
19	C₆₇×#2365	C₂	1	1	yes	maximal, characteristic
20	C₆₇×#2355	C₂	1	2	yes	maximal
21	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic
22	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic
23	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
30	#400×C₆₇	C₂²	1	2	yes	—
31	#400×C₆₇	C₂²	1	2	yes	—
32	#400×C₆₇	C₂²	1	2	yes	—
33	#400×C₆₇	C₂²	1	2	yes	—
34	#398×C₆₇	C₂²	1	2	yes	—
35	#398×C₆₇	C₂²	1	2	yes	—
36	#398×C₆₇	C₂²	1	2	yes	—
37	#398×C₆₇	C₂²	1	2	yes	—
38	#398×C₆₇	C₂²	1	2	yes	—
39	#398×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	#395×C₆₇	C₂²	1	2	yes	—
45	#395×C₆₇	C₂²	1	2	yes	—
46	#391×C₆₇	C₂²	1	2	yes	—
47	#391×C₆₇	C₂²	1	2	yes	—
48	#391×C₆₇	C₂²	1	2	yes	—
49	#389×C₆₇	C₂²	1	1	yes	characteristic
50	#389×C₆₇	C₂²	1	2	yes	—
51	#389×C₆₇	C₂²	1	1	yes	characteristic
52	#389×C₆₇	C₂²	1	1	yes	characteristic
53	#389×C₆₇	C₂²	1	2	yes	—
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	1	yes	characteristic
60	#389×C₆₇	C₂²	1	2	yes	—
61	#389×C₆₇	C₂²	1	1	yes	characteristic
62	#389×C₆₇	C₂²	1	1	yes	characteristic
63	#389×C₆₇	C₂²	1	1	yes	characteristic
64	#389×C₆₇	C₂²	1	1	yes	characteristic
65	#389×C₆₇	C₂²	1	1	yes	characteristic
66	#389×C₆₇	C₂²	1	2	yes	—
67	#389×C₆₇	C₂²	1	2	yes	—
68	#389×C₆₇	C₂²	1	1	yes	characteristic
69	#389×C₆₇	C₂²	1	2	yes	—
70	#387×C₆₇	C₂²	1	2	yes	—
71	#387×C₆₇	C₂²	1	2	yes	—
72	#387×C₆₇	C₂²	1	2	yes	—
73	#387×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
78	#387×C₆₇	C₂²	1	2	yes	—
79	#387×C₆₇	C₂²	1	2	yes	—
80	#387×C₆₇	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
88	#387×C₆₇	C₂²	1	1	yes	characteristic
89	#387×C₆₇	C₂²	1	1	yes	characteristic
90	#387×C₆₇	C₂²	1	2	yes	—
91	#387×C₆₇	C₂²	1	2	yes	—
92	#384×C₆₇	C₂²	1	1	yes	characteristic
93	#384×C₆₇	C₂²	1	2	yes	—
94	#382×C₆₇	C₂²	1	2	yes	—
95	#382×C₆₇	C₂²	1	2	yes	—
96	#382×C₆₇	C₂²	1	1	yes	characteristic
97	#382×C₆₇	C₂²	1	1	yes	characteristic
98	#382×C₆₇	C₂²	1	2	yes	—
99	#382×C₆₇	C₂²	1	1	yes	characteristic
100	#382×C₆₇	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×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	2	yes	—
108	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
122	C₄³×C₆₇	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
124	C₄⋊Q₈×C₆₇	—	2	4	no	—
125	#125×C₆₇	—	2	4	no	—
126	#125×C₆₇	—	2	4	no	—
127	#125×C₆₇	—	2	4	no	—
128	#125×C₆₇	Q₈	1	8	yes	complemented
129	C₄×Q₈×C₆₇	—	2	8	no	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	#95×C₆₇	C₂³	1	1	yes	characteristic
191	#95×C₆₇	C₂³	1	1	yes	characteristic
192	#95×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
197	#95×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
203	#95×C₆₇	C₂³	1	1	yes	characteristic
204	#95×C₆₇	C₂³	1	1	yes	characteristic
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
214	#95×C₆₇	C₂³	1	1	yes	characteristic
215	#95×C₆₇	C₂³	1	2	yes	—
216	#95×C₆₇	C₂³	1	2	yes	—
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	C₂×Q₈×C₆₇	—	2	4	no	—
229	C₂×Q₈×C₆₇	—	2	4	no	—
230	C₂×Q₈×C₆₇	—	4	2	no	—
231	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₄⋊C₄×C₆₇	—	2	4	no	—
255	C₄⋊C₄×C₆₇	—	2	4	no	—
256	C₄⋊C₄×C₆₇	—	2	2	no	—
257	C₄⋊C₄×C₆₇	—	2	2	no	—
258	C₄⋊C₄×C₆₇	—	2	2	no	—
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	4	no	—
264	C₄⋊C₄×C₆₇	—	2	2	no	—
265	C₄⋊C₄×C₆₇	—	2	2	no	—
266	C₄⋊C₄×C₆₇	—	2	2	no	—
267	C₄⋊C₄×C₆₇	—	2	4	no	—
268	C₄⋊C₄×C₆₇	—	2	2	no	—
269	C₄⋊C₄×C₆₇	—	2	2	no	—
270	C₄⋊C₄×C₆₇	—	2	2	no	—
271	C₄⋊C₄×C₆₇	—	4	2	no	—
272	C₄⋊C₄×C₆₇	—	4	2	no	—
273	C₄⋊C₄×C₆₇	—	4	2	no	—
274	C₄⋊C₄×C₆₇	—	4	1	no	—
275	C₄⋊C₄×C₆₇	—	4	1	no	—
276	C₄⋊C₄×C₆₇	—	4	1	no	—
277	C₄⋊C₄×C₆₇	—	4	2	no	—
278	C₄⋊C₄×C₆₇	—	4	2	no	—
279	C₄⋊C₄×C₆₇	—	4	2	no	—
280	C₄⋊C₄×C₆₇	—	4	2	no	—
281	C₄⋊C₄×C₆₇	—	4	1	no	—
282	C₄⋊C₄×C₆₇	—	4	1	no	—
283	C₄⋊C₄×C₆₇	—	4	2	no	—
284	C₄⋊C₄×C₆₇	—	4	1	no	—
285	C₄⋊C₄×C₆₇	—	4	2	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	C₂×Q₈	1	8	yes	—
290	C₄⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
291	C₄⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
292	C₄⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
293	C₄⋊C₄×C₆₇	#41	1	4	yes	—
294	C₄⋊C₄×C₆₇	#41	1	4	yes	—
295	C₄²×C₆₇	—	2	4	no	—
296	C₄²×C₆₇	—	2	4	no	—
297	C₄²×C₆₇	—	2	4	no	—
298	C₄²×C₆₇	—	2	2	no	—
299	C₄²×C₆₇	—	2	2	no	—
300	C₄²×C₆₇	—	2	2	no	—
301	C₄²×C₆₇	—	2	2	no	—
302	C₄²×C₆₇	—	2	2	no	—
303	C₄²×C₆₇	—	2	2	no	—
304	C₄²×C₆₇	—	2	2	no	—
305	C₄²×C₆₇	—	4	1	no	—
306	C₄²×C₆₇	—	4	2	no	—
307	C₄²×C₆₇	—	4	2	no	—
308	C₄²×C₆₇	—	4	2	no	—
309	C₄²×C₆₇	—	4	1	no	—
310	C₄²×C₆₇	—	4	2	no	—
311	C₄²×C₆₇	—	4	2	no	—
312	C₄²×C₆₇	—	4	1	no	—
313	C₄²×C₆₇	C₂×Q₈	1	4	yes	—
314	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
315	Q₈×C₆₇	—	4	8	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	1	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	1	no	—
320	C₂×C₄×C₆₇	—	2	1	no	—
321	C₂×C₄×C₆₇	—	2	1	no	—
322	C₂×C₄×C₆₇	—	2	1	no	—
323	C₂×C₄×C₆₇	—	2	1	no	—
324	C₂×C₄×C₆₇	—	2	1	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	1	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	1	no	—
331	C₂×C₄×C₆₇	—	2	1	no	—
332	C₂×C₄×C₆₇	—	2	1	no	—
333	C₂×C₄×C₆₇	—	2	1	no	—
334	C₂×C₄×C₆₇	—	2	1	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	1	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	1	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	1	no	—
346	C₂×C₄×C₆₇	—	2	1	no	—
347	C₂×C₄×C₆₇	—	2	1	no	—
348	C₂×C₄×C₆₇	—	2	1	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	1	no	—
353	C₂×C₄×C₆₇	—	2	1	no	—
354	C₂×C₄×C₆₇	—	2	1	no	—
355	C₂×C₄×C₆₇	—	2	1	no	—
356	C₂×C₄×C₆₇	—	2	1	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	1	no	—
360	C₂×C₄×C₆₇	—	2	2	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	1	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	1	no	—
369	C₂×C₄×C₆₇	—	2	1	no	—
370	C₂×C₄×C₆₇	—	2	1	no	—
371	C₂×C₄×C₆₇	—	2	1	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
375	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
376	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
377	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
378	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
379	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
380	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
381	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
382	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
383	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
384	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
385	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
386	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
387	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
388	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
389	C₂²×C₆₇	#585	1	1	yes	characteristic
390	C₂²×C₆₇	#585	1	1	yes	characteristic
391	C₂²×C₆₇	#585	1	1	yes	characteristic
392	C₄×C₆₇	—	2	4	no	—
393	C₄×C₆₇	—	2	2	no	—
394	C₄×C₆₇	—	2	4	no	—
395	C₄×C₆₇	—	2	2	no	—
396	C₄×C₆₇	—	2	2	no	—
397	C₄×C₆₇	—	2	4	no	—
398	C₄×C₆₇	—	2	2	no	—
399	C₄×C₆₇	—	2	2	no	—
400	C₄×C₆₇	—	4	1	no	—
401	C₄×C₆₇	—	4	1	no	—
402	C₄×C₆₇	—	4	2	no	—
403	C₄×C₆₇	—	4	2	no	—
404	C₄×C₆₇	—	4	1	no	—
405	C₄×C₆₇	—	4	1	no	—
406	C₄×C₆₇	—	4	1	no	—
407	C₄×C₆₇	—	4	1	no	—
408	C₄×C₆₇	—	4	2	no	—
409	C₄×C₆₇	—	4	2	no	—
410	C₄×C₆₇	—	4	1	no	—
411	C₄×C₆₇	—	4	1	no	—
412	C₄×C₆₇	—	4	1	no	—
413	C₄×C₆₇	—	4	2	no	—
414	C₄×C₆₇	#557	1	4	yes	—
415	#59587	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
416	C₂×C₆₇	#3475	1	1	yes	characteristic
417	C₂×C₆₇	C₂×#557	1	1	yes	characteristic
418	C₂×C₆₇	Q₈×#41	1	1	yes	characteristic
419	C₂×C₆₇	#3504	1	1	yes	characteristic
420	C₂×C₆₇	#3515	1	1	yes	characteristic
421	C₂×C₆₇	#3524	1	1	yes	characteristic
422	C₂×C₆₇	#3565	1	1	yes	characteristic
423	#2791	C₂×C₆₇	1	2	yes	—
424	#2755	C₂×C₆₇	1	2	yes	—
425	#2590	C₂×C₆₇	1	2	yes	—
426	#2585	C₂×C₆₇	1	2	yes	—
427	#2570	C₂×C₆₇	1	1	yes	characteristic
428	#2552	C₂×C₆₇	1	1	yes	characteristic
429	#2550	C₂×C₆₇	1	1	yes	characteristic
430	#2550	C₂×C₆₇	1	1	yes	characteristic
431	#2520	C₂×C₆₇	1	2	yes	—
432	#2508	C₂×C₆₇	1	1	yes	characteristic
433	#2508	C₂×C₆₇	1	2	yes	—
434	#2508	C₂×C₆₇	1	1	yes	characteristic
435	#2508	C₂×C₆₇	1	1	yes	characteristic
436	#2507	C₂×C₆₇	1	1	yes	characteristic
437	#2462	C₂×C₆₇	1	2	yes	—
438	#2370	C₂×C₆₇	1	1	yes	characteristic
439	#2370	C₂×C₆₇	1	1	yes	characteristic
440	#2370	C₂×C₆₇	1	1	yes	characteristic
441	#2365	C₂×C₆₇	1	1	yes	characteristic
442	#2355	C₂×C₆₇	1	2	yes	—
443	C₄×#125	C₂×C₆₇	1	1	yes	characteristic
444	C₄×#125	C₂×C₆₇	1	1	yes	characteristic
445	C₄×#125	C₂×C₆₇	1	1	yes	characteristic
446	C₆₇	#59587	1	1	yes	characteristic, direct product factor, Sylow
447	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
448	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
449	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
450	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
451	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
452	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
453	#400	C₂²×C₆₇	1	2	yes	—
454	#400	C₂²×C₆₇	1	2	yes	—
455	#400	C₂²×C₆₇	1	2	yes	—
456	#400	C₂²×C₆₇	1	2	yes	—
457	#398	C₂²×C₆₇	1	2	yes	—
458	#398	C₂²×C₆₇	1	2	yes	—
459	#398	C₂²×C₆₇	1	2	yes	—
460	#398	C₂²×C₆₇	1	2	yes	—
461	#398	C₂²×C₆₇	1	2	yes	—
462	#398	C₂²×C₆₇	1	2	yes	—
463	#398	C₂²×C₆₇	1	2	yes	—
464	#398	C₂²×C₆₇	1	2	yes	—
465	#398	C₂²×C₆₇	1	2	yes	—
466	#398	C₂²×C₆₇	1	2	yes	—
467	#395	C₂²×C₆₇	1	2	yes	—
468	#395	C₂²×C₆₇	1	2	yes	—
469	#391	C₂²×C₆₇	1	2	yes	—
470	#391	C₂²×C₆₇	1	2	yes	—
471	#391	C₂²×C₆₇	1	2	yes	—
472	#389	C₂²×C₆₇	1	1	yes	characteristic
473	#389	C₂²×C₆₇	1	1	yes	characteristic
474	#389	C₂²×C₆₇	1	1	yes	characteristic
475	#389	C₂²×C₆₇	1	1	yes	characteristic
476	#389	C₂²×C₆₇	1	1	yes	characteristic
477	#389	C₂²×C₆₇	1	1	yes	characteristic
478	#389	C₂²×C₆₇	1	1	yes	characteristic
479	#389	C₂²×C₆₇	1	1	yes	characteristic
480	#389	C₂²×C₆₇	1	2	yes	—
481	#389	C₂²×C₆₇	1	2	yes	—
482	#389	C₂²×C₆₇	1	2	yes	—
483	#389	C₂²×C₆₇	1	2	yes	—
484	#389	C₂²×C₆₇	1	2	yes	—
485	#389	C₂²×C₆₇	1	2	yes	—
486	#389	C₂²×C₆₇	1	1	yes	characteristic
487	#389	C₂²×C₆₇	1	1	yes	characteristic
488	#389	C₂²×C₆₇	1	1	yes	characteristic
489	#389	C₂²×C₆₇	1	2	yes	—
490	#389	C₂²×C₆₇	1	1	yes	characteristic
491	#389	C₂²×C₆₇	1	1	yes	characteristic
492	#389	C₂²×C₆₇	1	1	yes	characteristic
493	#387	C₂²×C₆₇	1	1	yes	characteristic
494	#387	C₂²×C₆₇	1	2	yes	—
495	#387	C₂²×C₆₇	1	1	yes	characteristic
496	#387	C₂²×C₆₇	1	1	yes	characteristic
497	#387	C₂²×C₆₇	1	2	yes	—
498	#387	C₂²×C₆₇	1	2	yes	—
499	#387	C₂²×C₆₇	1	2	yes	—
500	#387	C₂²×C₆₇	1	1	yes	characteristic
501	#387	C₂²×C₆₇	1	2	yes	—
502	#387	C₂²×C₆₇	1	2	yes	—
503	#387	C₂²×C₆₇	1	2	yes	—
504	#387	C₂²×C₆₇	1	2	yes	—
505	#387	C₂²×C₆₇	1	2	yes	—
506	#387	C₂²×C₆₇	1	2	yes	—
507	#387	C₂²×C₆₇	1	2	yes	—
508	#387	C₂²×C₆₇	1	2	yes	—
509	#387	C₂²×C₆₇	1	2	yes	—
510	#387	C₂²×C₆₇	1	2	yes	—
511	#387	C₂²×C₆₇	1	2	yes	—
512	#387	C₂²×C₆₇	1	2	yes	—
513	#387	C₂²×C₆₇	1	2	yes	—
514	#387	C₂²×C₆₇	1	2	yes	—
515	#384	C₂²×C₆₇	1	1	yes	characteristic
516	#384	C₂²×C₆₇	1	2	yes	—
517	#382	C₂²×C₆₇	1	1	yes	characteristic
518	#382	C₂²×C₆₇	1	1	yes	characteristic
519	#382	C₂²×C₆₇	1	1	yes	characteristic
520	#382	C₂²×C₆₇	1	1	yes	characteristic
521	#382	C₂²×C₆₇	1	2	yes	—
522	#382	C₂²×C₆₇	1	2	yes	—
523	#382	C₂²×C₆₇	1	2	yes	—
524	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
525	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
526	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
527	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
528	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
529	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
530	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
531	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
532	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
533	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
534	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
535	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
536	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
537	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
538	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
539	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
540	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
541	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
542	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
543	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
544	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
545	C₄³	C₂²×C₆₇	1	1	yes	characteristic
546	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
547	C₄⋊Q₈	—	2	4	no	—
548	#125	—	2	4	no	—
549	#125	—	2	4	no	—
550	#125	—	2	4	no	—
551	#125	Q₈×C₆₇	1	8	yes	complemented
552	C₄×Q₈	—	2	8	no	—
553	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
595	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
596	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
597	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
608	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
609	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
610	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
611	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
612	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
613	#95	C₂³×C₆₇	1	1	yes	characteristic
614	#95	C₂³×C₆₇	1	1	yes	characteristic
615	#95	C₂³×C₆₇	1	1	yes	characteristic
616	#95	C₂³×C₆₇	1	1	yes	characteristic
617	#95	C₂³×C₆₇	1	2	yes	—
618	#95	C₂³×C₆₇	1	2	yes	—
619	#95	C₂³×C₆₇	1	1	yes	characteristic
620	#95	C₂³×C₆₇	1	2	yes	—
621	#95	C₂³×C₆₇	1	1	yes	characteristic
622	#95	C₂³×C₆₇	1	2	yes	—
623	#95	C₂³×C₆₇	1	2	yes	—
624	#95	C₂³×C₆₇	1	1	yes	characteristic
625	#95	C₂³×C₆₇	1	2	yes	—
626	#95	C₂³×C₆₇	1	1	yes	characteristic
627	#95	C₂³×C₆₇	1	1	yes	characteristic
628	#95	C₂³×C₆₇	1	2	yes	—
629	#95	C₂³×C₆₇	1	2	yes	—
630	#95	C₂³×C₆₇	1	2	yes	—
631	#95	C₂³×C₆₇	1	2	yes	—
632	#95	C₂³×C₆₇	1	1	yes	characteristic
633	#95	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
642	#95	C₂³×C₆₇	1	2	yes	—
643	#95	C₂³×C₆₇	1	1	yes	characteristic
644	#95	C₂³×C₆₇	1	2	yes	—
645	#95	C₂³×C₆₇	1	2	yes	—
646	#95	C₂³×C₆₇	1	2	yes	—
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	C₂×Q₈	—	2	4	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	4	2	no	—
654	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	1	no	—
698	C₄⋊C₄	—	4	1	no	—
699	C₄⋊C₄	—	4	1	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	1	no	—
705	C₄⋊C₄	—	4	1	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	1	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
713	C₄⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
714	C₄⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
715	C₄⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
716	C₄⋊C₄	#41×C₆₇	1	4	yes	—
717	C₄⋊C₄	#41×C₆₇	1	4	yes	—
718	C₄²	—	2	4	no	—
719	C₄²	—	2	4	no	—
720	C₄²	—	2	4	no	—
721	C₄²	—	2	2	no	—
722	C₄²	—	2	2	no	—
723	C₄²	—	2	2	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	2	2	no	—
726	C₄²	—	2	2	no	—
727	C₄²	—	2	2	no	—
728	C₄²	—	4	1	no	—
729	C₄²	—	4	2	no	—
730	C₄²	—	4	2	no	—
731	C₄²	—	4	2	no	—
732	C₄²	—	4	1	no	—
733	C₄²	—	4	2	no	—
734	C₄²	—	4	2	no	—
735	C₄²	—	4	1	no	—
736	C₄²	C₂×Q₈×C₆₇	1	4	yes	—
737	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
738	Q₈	—	4	8	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	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	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
798	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
799	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
800	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
801	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
802	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
803	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
804	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
805	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
806	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
807	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
808	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
809	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
810	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
811	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
812	C₂²	#585×C₆₇	1	1	yes	characteristic
813	C₂²	#585×C₆₇	1	1	yes	characteristic
814	C₂²	#585×C₆₇	1	1	yes	characteristic
815	C₄	—	2	2	no	—
816	C₄	—	2	4	no	—
817	C₄	—	2	4	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	4	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	2	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	1	no	—
837	C₄	#557×C₆₇	1	4	yes	—
838	C₂	C₆₇×#3475	1	1	yes	characteristic
839	C₂	C₂×#557×C₆₇	1	1	yes	characteristic
840	C₂	Q₈×#41×C₆₇	1	1	yes	characteristic
841	C₂	C₆₇×#3504	1	1	yes	characteristic
842	C₂	C₆₇×#3515	1	1	yes	characteristic
843	C₂	C₆₇×#3524	1	1	yes	characteristic
844	C₂	C₆₇×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
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
128. #125×C₆₇	Q₈	semidirect
415. #59587	C₆₇	direct (N × H)
446. C₆₇	#59587	direct (N × H)
551. #125	Q₈×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2791	2
C₆₇×#2755	2
C₆₇×#2590	2
C₆₇×#2585	2
C₆₇×#2570	2
C₆₇×#2552	2
C₆₇×#2550	2
C₆₇×#2520	2
C₆₇×#2508	2
C₆₇×#2507	2
C₆₇×#2462	2
C₆₇×#2370	2
C₆₇×#2365	2
C₆₇×#2355	2
C₄×#125×C₆₇	2
#59587	67

Subgroups — C67×#59587 #30738838

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59587 #30738838