Subgroups — C₆₇×#59927 #30739178

Order 17152.

1496 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2806	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2805	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2734	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2726	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#2612	C₂	1	2	yes	maximal
6	C₆₇×#2590	C₂	1	2	yes	maximal
7	C₆₇×#2588	C₂	1	2	yes	maximal
8	C₆₇×#2588	C₂	1	2	yes	maximal
9	C₆₇×#2586	C₂	1	2	yes	maximal
10	C₆₇×#2585	C₂	1	2	yes	maximal
11	C₆₇×#2585	C₂	1	2	yes	maximal
12	C₆₇×#2462	C₂	1	2	yes	maximal
13	C₆₇×#2446	C₂	1	2	yes	maximal
14	C₆₇×#2371	C₂	1	2	yes	maximal
15	C₆₇×#2370	C₂	1	2	yes	maximal
16	C₆₇×#2369	C₂	1	2	yes	maximal
17	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic
18	C₆₇×#2295	C₂	1	1	yes	maximal, characteristic
19	C₆₇×#2295	C₂	1	1	yes	maximal, characteristic
20	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
21	C₂×#125×C₆₇	C₂²	1	2	yes	—
22	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	#400×C₆₇	C₂²	1	2	yes	—
26	#400×C₆₇	C₂²	1	2	yes	—
27	#400×C₆₇	C₂²	1	2	yes	—
28	#400×C₆₇	C₂²	1	2	yes	—
29	#398×C₆₇	C₂²	1	2	yes	—
30	#398×C₆₇	C₂²	1	2	yes	—
31	#398×C₆₇	C₂²	1	2	yes	—
32	#398×C₆₇	C₂²	1	2	yes	—
33	#398×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	#395×C₆₇	C₂²	1	2	yes	—
38	#395×C₆₇	C₂²	1	2	yes	—
39	#395×C₆₇	C₂²	1	2	yes	—
40	#395×C₆₇	C₂²	1	2	yes	—
41	#391×C₆₇	C₂²	1	1	yes	characteristic
42	#391×C₆₇	C₂²	1	1	yes	characteristic
43	#391×C₆₇	C₂²	1	2	yes	—
44	#391×C₆₇	C₂²	1	1	yes	characteristic
45	#391×C₆₇	C₂²	1	1	yes	characteristic
46	#391×C₆₇	C₂²	1	2	yes	—
47	#391×C₆₇	C₂²	1	2	yes	—
48	#391×C₆₇	C₂²	1	2	yes	—
49	#391×C₆₇	C₂²	1	2	yes	—
50	#389×C₆₇	C₂²	1	1	yes	characteristic
51	#389×C₆₇	C₂²	1	1	yes	characteristic
52	#389×C₆₇	C₂²	1	2	yes	—
53	#389×C₆₇	C₂²	1	1	yes	characteristic
54	#389×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
63	#389×C₆₇	C₂²	1	2	yes	—
64	#389×C₆₇	C₂²	1	2	yes	—
65	#387×C₆₇	C₂²	1	2	yes	—
66	#387×C₆₇	C₂²	1	2	yes	—
67	#387×C₆₇	C₂²	1	2	yes	—
68	#387×C₆₇	C₂²	1	2	yes	—
69	#387×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	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	#382×C₆₇	C₂²	1	1	yes	characteristic
90	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
104	#376×C₆₇	C₂²	1	2	yes	—
105	#376×C₆₇	C₂²	1	2	yes	—
106	C₄³×C₆₇	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₆₇	—	2	8	no	—
111	#125×C₆₇	—	2	8	no	—
112	#125×C₆₇	Q₈	1	8	yes	complemented
113	C₄×Q₈×C₆₇	—	2	4	no	—
114	C₄×Q₈×C₆₇	—	2	4	no	—
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
165	#95×C₆₇	C₂³	1	2	yes	—
166	#95×C₆₇	C₂³	1	2	yes	—
167	#95×C₆₇	C₂³	1	2	yes	—
168	#95×C₆₇	C₂³	1	2	yes	—
169	#95×C₆₇	C₂³	1	2	yes	—
170	#95×C₆₇	C₂³	1	2	yes	—
171	#95×C₆₇	C₂³	1	2	yes	—
172	#95×C₆₇	C₂³	1	2	yes	—
173	#95×C₆₇	C₂³	1	2	yes	—
174	#95×C₆₇	C₂³	1	2	yes	—
175	#95×C₆₇	C₂³	1	2	yes	—
176	#95×C₆₇	C₂³	1	2	yes	—
177	#95×C₆₇	C₂³	1	2	yes	—
178	#95×C₆₇	C₂³	1	2	yes	—
179	#95×C₆₇	C₂³	1	2	yes	—
180	#95×C₆₇	C₂³	1	2	yes	—
181	#95×C₆₇	C₂³	1	2	yes	—
182	#95×C₆₇	C₂³	1	2	yes	—
183	#95×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
186	#95×C₆₇	C₂³	1	2	yes	—
187	#95×C₆₇	C₂³	1	2	yes	—
188	#95×C₆₇	C₂³	1	2	yes	—
189	#95×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	2	yes	—
191	#95×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	2	yes	—
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	C₂×Q₈×C₆₇	—	2	2	no	—
200	C₂×Q₈×C₆₇	—	2	4	no	—
201	C₂×Q₈×C₆₇	—	4	1	no	—
202	C₂×Q₈×C₆₇	—	4	1	no	—
203	C₂×Q₈×C₆₇	—	4	1	no	—
204	C₂×Q₈×C₆₇	—	4	1	no	—
205	C₂×Q₈×C₆₇	—	4	2	no	—
206	C₂×Q₈×C₆₇	—	4	2	no	—
207	C₂×Q₈×C₆₇	#41	1	4	yes	—
208	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
227	C₄⋊C₄×C₆₇	—	2	4	no	—
228	C₄⋊C₄×C₆₇	—	2	2	no	—
229	C₄⋊C₄×C₆₇	—	2	4	no	—
230	C₄⋊C₄×C₆₇	—	2	4	no	—
231	C₄⋊C₄×C₆₇	—	2	4	no	—
232	C₄⋊C₄×C₆₇	—	2	4	no	—
233	C₄⋊C₄×C₆₇	—	2	4	no	—
234	C₄⋊C₄×C₆₇	—	2	4	no	—
235	C₄⋊C₄×C₆₇	—	2	4	no	—
236	C₄⋊C₄×C₆₇	—	2	4	no	—
237	C₄⋊C₄×C₆₇	—	2	4	no	—
238	C₄⋊C₄×C₆₇	—	2	4	no	—
239	C₄⋊C₄×C₆₇	—	2	4	no	—
240	C₄⋊C₄×C₆₇	—	2	4	no	—
241	C₄⋊C₄×C₆₇	—	4	2	no	—
242	C₄⋊C₄×C₆₇	—	4	2	no	—
243	C₄⋊C₄×C₆₇	—	4	1	no	—
244	C₄⋊C₄×C₆₇	—	4	1	no	—
245	C₄⋊C₄×C₆₇	—	4	1	no	—
246	C₄⋊C₄×C₆₇	—	4	1	no	—
247	C₄⋊C₄×C₆₇	—	4	1	no	—
248	C₄⋊C₄×C₆₇	—	4	1	no	—
249	C₄⋊C₄×C₆₇	—	4	2	no	—
250	C₄⋊C₄×C₆₇	—	4	2	no	—
251	C₄⋊C₄×C₆₇	—	4	2	no	—
252	C₄⋊C₄×C₆₇	—	4	2	no	—
253	C₄⋊C₄×C₆₇	—	4	2	no	—
254	C₄⋊C₄×C₆₇	—	4	2	no	—
255	C₄⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
256	C₄⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
257	C₄⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
258	C₄⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
259	C₄⋊C₄×C₆₇	#41	1	4	yes	—
260	C₄²×C₆₇	—	2	4	no	—
261	C₄²×C₆₇	—	2	2	no	—
262	C₄²×C₆₇	—	2	2	no	—
263	C₄²×C₆₇	—	2	4	no	—
264	C₄²×C₆₇	—	2	4	no	—
265	C₄²×C₆₇	—	2	4	no	—
266	C₄²×C₆₇	—	2	2	no	—
267	C₄²×C₆₇	—	4	1	no	—
268	C₄²×C₆₇	—	4	1	no	—
269	C₄²×C₆₇	—	4	2	no	—
270	C₄²×C₆₇	—	4	2	no	—
271	C₄²×C₆₇	—	4	2	no	—
272	C₄²×C₆₇	—	4	2	no	—
273	C₄²×C₆₇	—	4	2	no	—
274	C₄²×C₆₇	—	4	2	no	—
275	C₄²×C₆₇	—	4	1	no	—
276	C₄²×C₆₇	C₂×Q₈	1	4	yes	—
277	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
278	Q₈×C₆₇	—	4	4	no	—
279	Q₈×C₆₇	—	4	4	no	—
280	Q₈×C₆₇	—	8	4	no	—
281	C₂×C₄×C₆₇	—	2	1	no	—
282	C₂×C₄×C₆₇	—	2	1	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	1	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	1	no	—
289	C₂×C₄×C₆₇	—	2	1	no	—
290	C₂×C₄×C₆₇	—	2	1	no	—
291	C₂×C₄×C₆₇	—	2	1	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	2	no	—
294	C₂×C₄×C₆₇	—	2	1	no	—
295	C₂×C₄×C₆₇	—	2	1	no	—
296	C₂×C₄×C₆₇	—	2	1	no	—
297	C₂×C₄×C₆₇	—	2	1	no	—
298	C₂×C₄×C₆₇	—	2	1	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	1	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	2	1	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	1	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
329	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
330	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
331	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
332	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
333	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
334	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
335	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
336	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
337	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
338	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
339	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
340	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
341	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
342	C₂²×C₆₇	#585	1	1	yes	characteristic
343	C₂²×C₆₇	#585	1	1	yes	characteristic
344	C₂²×C₆₇	#585	1	1	yes	characteristic
345	C₄×C₆₇	—	2	2	no	—
346	C₄×C₆₇	—	2	2	no	—
347	C₄×C₆₇	—	2	4	no	—
348	C₄×C₆₇	—	2	4	no	—
349	C₄×C₆₇	—	2	4	no	—
350	C₄×C₆₇	—	2	2	no	—
351	C₄×C₆₇	—	2	4	no	—
352	C₄×C₆₇	—	2	2	no	—
353	C₄×C₆₇	—	2	2	no	—
354	C₄×C₆₇	—	2	2	no	—
355	C₄×C₆₇	—	4	1	no	—
356	C₄×C₆₇	—	4	2	no	—
357	C₄×C₆₇	—	4	2	no	—
358	C₄×C₆₇	—	4	2	no	—
359	C₄×C₆₇	—	4	2	no	—
360	C₄×C₆₇	—	4	2	no	—
361	C₄×C₆₇	—	4	2	no	—
362	C₄×C₆₇	—	4	2	no	—
363	C₄×C₆₇	—	4	2	no	—
364	#59927	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
365	C₂×C₆₇	Q₈×#41	1	1	yes	characteristic
366	C₂×C₆₇	Q₈×#41	1	1	yes	characteristic
367	C₂×C₆₇	#3482	1	1	yes	characteristic
368	C₂×C₆₇	#3491	1	1	yes	characteristic
369	C₂×C₆₇	#3493	1	1	yes	characteristic
370	C₂×C₆₇	#3502	1	1	yes	characteristic
371	C₂×C₆₇	#3553	1	1	yes	characteristic
372	#2806	C₂×C₆₇	1	1	yes	characteristic
373	#2805	C₂×C₆₇	1	1	yes	characteristic
374	#2734	C₂×C₆₇	1	1	yes	characteristic
375	#2726	C₂×C₆₇	1	1	yes	characteristic
376	#2612	C₂×C₆₇	1	2	yes	—
377	#2590	C₂×C₆₇	1	2	yes	—
378	#2588	C₂×C₆₇	1	2	yes	—
379	#2588	C₂×C₆₇	1	2	yes	—
380	#2586	C₂×C₆₇	1	2	yes	—
381	#2585	C₂×C₆₇	1	2	yes	—
382	#2585	C₂×C₆₇	1	2	yes	—
383	#2462	C₂×C₆₇	1	2	yes	—
384	#2446	C₂×C₆₇	1	2	yes	—
385	#2371	C₂×C₆₇	1	2	yes	—
386	#2370	C₂×C₆₇	1	2	yes	—
387	#2369	C₂×C₆₇	1	2	yes	—
388	C₄×#125	C₂×C₆₇	1	1	yes	characteristic
389	#2295	C₂×C₆₇	1	1	yes	characteristic
390	#2295	C₂×C₆₇	1	1	yes	characteristic
391	C₆₇	#59927	1	1	yes	characteristic, direct product factor, Sylow
392	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
393	C₂×#125	C₂²×C₆₇	1	2	yes	—
394	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
395	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
396	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
397	#400	C₂²×C₆₇	1	2	yes	—
398	#400	C₂²×C₆₇	1	2	yes	—
399	#400	C₂²×C₆₇	1	2	yes	—
400	#400	C₂²×C₆₇	1	2	yes	—
401	#398	C₂²×C₆₇	1	2	yes	—
402	#398	C₂²×C₆₇	1	2	yes	—
403	#398	C₂²×C₆₇	1	2	yes	—
404	#398	C₂²×C₆₇	1	2	yes	—
405	#398	C₂²×C₆₇	1	2	yes	—
406	#398	C₂²×C₆₇	1	2	yes	—
407	#398	C₂²×C₆₇	1	2	yes	—
408	#398	C₂²×C₆₇	1	2	yes	—
409	#395	C₂²×C₆₇	1	2	yes	—
410	#395	C₂²×C₆₇	1	2	yes	—
411	#395	C₂²×C₆₇	1	2	yes	—
412	#395	C₂²×C₆₇	1	2	yes	—
413	#391	C₂²×C₆₇	1	1	yes	characteristic
414	#391	C₂²×C₆₇	1	2	yes	—
415	#391	C₂²×C₆₇	1	2	yes	—
416	#391	C₂²×C₆₇	1	2	yes	—
417	#391	C₂²×C₆₇	1	2	yes	—
418	#391	C₂²×C₆₇	1	1	yes	characteristic
419	#391	C₂²×C₆₇	1	2	yes	—
420	#391	C₂²×C₆₇	1	1	yes	characteristic
421	#391	C₂²×C₆₇	1	1	yes	characteristic
422	#389	C₂²×C₆₇	1	1	yes	characteristic
423	#389	C₂²×C₆₇	1	1	yes	characteristic
424	#389	C₂²×C₆₇	1	1	yes	characteristic
425	#389	C₂²×C₆₇	1	2	yes	—
426	#389	C₂²×C₆₇	1	2	yes	—
427	#389	C₂²×C₆₇	1	2	yes	—
428	#389	C₂²×C₆₇	1	2	yes	—
429	#389	C₂²×C₆₇	1	2	yes	—
430	#389	C₂²×C₆₇	1	2	yes	—
431	#389	C₂²×C₆₇	1	2	yes	—
432	#389	C₂²×C₆₇	1	2	yes	—
433	#389	C₂²×C₆₇	1	2	yes	—
434	#389	C₂²×C₆₇	1	1	yes	characteristic
435	#389	C₂²×C₆₇	1	1	yes	characteristic
436	#389	C₂²×C₆₇	1	1	yes	characteristic
437	#387	C₂²×C₆₇	1	2	yes	—
438	#387	C₂²×C₆₇	1	2	yes	—
439	#387	C₂²×C₆₇	1	2	yes	—
440	#387	C₂²×C₆₇	1	2	yes	—
441	#387	C₂²×C₆₇	1	2	yes	—
442	#387	C₂²×C₆₇	1	2	yes	—
443	#387	C₂²×C₆₇	1	2	yes	—
444	#387	C₂²×C₆₇	1	2	yes	—
445	#387	C₂²×C₆₇	1	2	yes	—
446	#387	C₂²×C₆₇	1	2	yes	—
447	#387	C₂²×C₆₇	1	2	yes	—
448	#387	C₂²×C₆₇	1	2	yes	—
449	#387	C₂²×C₆₇	1	2	yes	—
450	#387	C₂²×C₆₇	1	2	yes	—
451	#387	C₂²×C₆₇	1	2	yes	—
452	#387	C₂²×C₆₇	1	2	yes	—
453	#387	C₂²×C₆₇	1	2	yes	—
454	#387	C₂²×C₆₇	1	2	yes	—
455	#387	C₂²×C₆₇	1	2	yes	—
456	#387	C₂²×C₆₇	1	2	yes	—
457	#387	C₂²×C₆₇	1	2	yes	—
458	#387	C₂²×C₆₇	1	2	yes	—
459	#387	C₂²×C₆₇	1	2	yes	—
460	#387	C₂²×C₆₇	1	2	yes	—
461	#382	C₂²×C₆₇	1	1	yes	characteristic
462	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
463	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
464	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
465	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
466	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
467	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
468	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
470	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
471	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
473	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
474	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
475	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
476	#376	C₂²×C₆₇	1	2	yes	—
477	#376	C₂²×C₆₇	1	2	yes	—
478	C₄³	C₂²×C₆₇	1	1	yes	characteristic
479	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
480	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
481	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
482	C₄⋊Q₈	—	2	8	no	—
483	#125	—	2	8	no	—
484	#125	Q₈×C₆₇	1	8	yes	complemented
485	C₄×Q₈	—	2	4	no	—
486	C₄×Q₈	—	2	4	no	—
487	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
521	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
522	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
523	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
524	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
525	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
526	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
531	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
532	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
533	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
534	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
535	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
536	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
537	#95	C₂³×C₆₇	1	2	yes	—
538	#95	C₂³×C₆₇	1	2	yes	—
539	#95	C₂³×C₆₇	1	2	yes	—
540	#95	C₂³×C₆₇	1	2	yes	—
541	#95	C₂³×C₆₇	1	2	yes	—
542	#95	C₂³×C₆₇	1	2	yes	—
543	#95	C₂³×C₆₇	1	2	yes	—
544	#95	C₂³×C₆₇	1	2	yes	—
545	#95	C₂³×C₆₇	1	2	yes	—
546	#95	C₂³×C₆₇	1	2	yes	—
547	#95	C₂³×C₆₇	1	2	yes	—
548	#95	C₂³×C₆₇	1	2	yes	—
549	#95	C₂³×C₆₇	1	2	yes	—
550	#95	C₂³×C₆₇	1	2	yes	—
551	#95	C₂³×C₆₇	1	2	yes	—
552	#95	C₂³×C₆₇	1	2	yes	—
553	#95	C₂³×C₆₇	1	2	yes	—
554	#95	C₂³×C₆₇	1	2	yes	—
555	#95	C₂³×C₆₇	1	2	yes	—
556	#95	C₂³×C₆₇	1	2	yes	—
557	#95	C₂³×C₆₇	1	2	yes	—
558	#95	C₂³×C₆₇	1	2	yes	—
559	#95	C₂³×C₆₇	1	2	yes	—
560	#95	C₂³×C₆₇	1	2	yes	—
561	#95	C₂³×C₆₇	1	2	yes	—
562	#95	C₂³×C₆₇	1	2	yes	—
563	#95	C₂³×C₆₇	1	2	yes	—
564	#95	C₂³×C₆₇	1	2	yes	—
565	#95	C₂³×C₆₇	1	2	yes	—
566	#95	C₂³×C₆₇	1	2	yes	—
567	#95	C₂³×C₆₇	1	2	yes	—
568	#95	C₂³×C₆₇	1	2	yes	—
569	#95	C₂³×C₆₇	1	2	yes	—
570	#95	C₂³×C₆₇	1	2	yes	—
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	—	2	4	no	—
573	C₂×Q₈	—	4	1	no	—
574	C₂×Q₈	—	4	1	no	—
575	C₂×Q₈	—	4	1	no	—
576	C₂×Q₈	—	4	1	no	—
577	C₂×Q₈	—	4	2	no	—
578	C₂×Q₈	—	4	2	no	—
579	C₂×Q₈	#41×C₆₇	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	1	no	—
616	C₄⋊C₄	—	4	1	no	—
617	C₄⋊C₄	—	4	1	no	—
618	C₄⋊C₄	—	4	1	no	—
619	C₄⋊C₄	—	4	1	no	—
620	C₄⋊C₄	—	4	1	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
628	C₄⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
629	C₄⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
630	C₄⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
631	C₄⋊C₄	#41×C₆₇	1	4	yes	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	4	1	no	—
640	C₄²	—	4	1	no	—
641	C₄²	—	4	2	no	—
642	C₄²	—	4	2	no	—
643	C₄²	—	4	2	no	—
644	C₄²	—	4	2	no	—
645	C₄²	—	4	2	no	—
646	C₄²	—	4	2	no	—
647	C₄²	—	4	1	no	—
648	C₄²	C₂×Q₈×C₆₇	1	4	yes	—
649	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
650	Q₈	—	4	4	no	—
651	Q₈	—	4	4	no	—
652	Q₈	—	8	4	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
701	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
702	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
703	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
704	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
705	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
706	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
707	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
708	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
709	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
710	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
711	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
712	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
713	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
714	C₂²	#585×C₆₇	1	1	yes	characteristic
715	C₂²	#585×C₆₇	1	1	yes	characteristic
716	C₂²	#585×C₆₇	1	1	yes	characteristic
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	4	no	—
721	C₄	—	2	4	no	—
722	C₄	—	2	4	no	—
723	C₄	—	2	4	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	2	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₂	Q₈×#41×C₆₇	1	1	yes	characteristic
737	C₂	Q₈×#41×C₆₇	1	1	yes	characteristic
738	C₂	C₆₇×#3482	1	1	yes	characteristic
739	C₂	C₆₇×#3491	1	1	yes	characteristic
740	C₂	C₆₇×#3493	1	1	yes	characteristic
741	C₂	C₆₇×#3502	1	1	yes	characteristic
742	C₂	C₆₇×#3553	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
112. #125×C₆₇	Q₈	semidirect
364. #59927	C₆₇	direct (N × H)
391. C₆₇	#59927	direct (N × H)
484. #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×#2806	2
C₆₇×#2805	2
C₆₇×#2734	2
C₆₇×#2726	2
C₆₇×#2612	2
C₆₇×#2590	2
C₆₇×#2588	2
C₆₇×#2586	2
C₆₇×#2585	2
C₆₇×#2462	2
C₆₇×#2446	2
C₆₇×#2371	2
C₆₇×#2370	2
C₆₇×#2369	2
C₄×#125×C₆₇	2
C₆₇×#2295	2
#59927	67

Subgroups — C67×#59927 #30739178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59927 #30739178