Subgroups — C₆₇×#59352 #30738603

Order 17152.

2034 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2736	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2685	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2670	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2610	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2607	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2600	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2599	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2574	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2521	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2518	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2479	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2468	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2467	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2459	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2373	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2367	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2357	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2280	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#126×C₆₇	C₂²	1	2	yes	—
22	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
23	C₂×#124×C₆₇	C₂²	1	2	yes	—
24	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	C₂×#120×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
32	#399×C₆₇	C₂²	1	2	yes	—
33	#399×C₆₇	C₂²	1	2	yes	complemented
34	#398×C₆₇	C₂²	1	2	yes	complemented
35	#398×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#397×C₆₇	C₂²	1	2	yes	—
37	#397×C₆₇	C₂²	1	1	yes	characteristic
38	#396×C₆₇	C₂²	1	2	yes	—
39	#395×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#395×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#394×C₆₇	C₂²	1	2	yes	—
42	#394×C₆₇	C₂²	1	2	yes	—
43	#394×C₆₇	C₂²	1	2	yes	—
44	#394×C₆₇	C₂²	1	2	yes	—
45	#394×C₆₇	C₂²	1	2	yes	—
46	#394×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#393×C₆₇	C₂²	1	2	yes	—
48	#393×C₆₇	C₂²	1	1	yes	characteristic
49	#393×C₆₇	C₂²	1	1	yes	characteristic
50	#392×C₆₇	C₂²	1	1	yes	characteristic
51	#392×C₆₇	C₂²	1	2	yes	—
52	#391×C₆₇	C₂²	1	2	yes	complemented
53	#391×C₆₇	C₂²	1	2	yes	complemented
54	#390×C₆₇	C₂²	1	2	yes	—
55	#390×C₆₇	C₂²	1	2	yes	—
56	#390×C₆₇	C₂²	1	2	yes	—
57	#389×C₆₇	C₂²	1	2	yes	complemented
58	#388×C₆₇	C₂²	1	2	yes	—
59	#388×C₆₇	C₂²	1	2	yes	—
60	#388×C₆₇	C₂²	1	2	yes	—
61	#388×C₆₇	C₂²	1	2	yes	—
62	#388×C₆₇	C₂²	1	2	yes	—
63	#388×C₆₇	C₂²	1	2	yes	—
64	#388×C₆₇	C₂²	1	2	yes	—
65	#388×C₆₇	C₂²	1	2	yes	complemented
66	#388×C₆₇	C₂²	1	2	yes	complemented
67	#388×C₆₇	C₂²	1	2	yes	complemented
68	#388×C₆₇	C₂²	1	2	yes	complemented
69	#388×C₆₇	C₂²	1	2	yes	complemented
70	#388×C₆₇	C₂²	1	2	yes	complemented
71	#388×C₆₇	C₂²	1	2	yes	complemented
72	#387×C₆₇	C₂²	1	2	yes	complemented
73	#387×C₆₇	C₂²	1	2	yes	complemented
74	#387×C₆₇	C₂²	1	2	yes	complemented
75	#387×C₆₇	C₂²	1	2	yes	complemented
76	#387×C₆₇	C₂²	1	2	yes	complemented
77	#387×C₆₇	C₂²	1	2	yes	complemented
78	#386×C₆₇	C₂²	1	2	yes	—
79	#386×C₆₇	C₂²	1	2	yes	—
80	#386×C₆₇	C₂²	1	2	yes	—
81	#386×C₆₇	C₂²	1	2	yes	complemented
82	#385×C₆₇	C₂²	1	2	yes	—
83	#385×C₆₇	C₂²	1	2	yes	—
84	#385×C₆₇	C₂²	1	2	yes	—
85	#385×C₆₇	C₂²	1	2	yes	complemented
86	#383×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#382×C₆₇	C₂²	1	2	yes	complemented
88	#381×C₆₇	C₂²	1	1	yes	characteristic
89	#381×C₆₇	C₂²	1	1	yes	characteristic
90	#381×C₆₇	C₂²	1	2	yes	complemented
91	#380×C₆₇	C₂²	1	2	yes	—
92	#380×C₆₇	C₂²	1	2	yes	—
93	#379×C₆₇	C₂²	1	1	yes	characteristic
94	#379×C₆₇	C₂²	1	1	yes	characteristic
95	#379×C₆₇	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
106	#376×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
113	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₆₇	—	2	4	no	—
115	C₂³×C₄×C₆₇	—	4	2	no	—
116	C₂³×C₄×C₆₇	—	4	2	no	—
117	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
122	#126×C₆₇	—	2	8	no	—
123	#126×C₆₇	—	4	4	no	—
124	#124×C₆₇	—	2	8	no	—
125	#124×C₆₇	—	4	2	no	—
126	#120×C₆₇	—	2	8	no	—
127	C₄×Q₈×C₆₇	—	4	2	no	—
128	C₄×D₄×C₆₇	—	2	8	no	—
129	C₄×D₄×C₆₇	—	4	4	no	—
130	C₄×D₄×C₆₇	—	4	4	no	—
131	#117×C₆₇	—	4	2	no	—
132	#117×C₆₇	—	4	2	no	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	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	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
186	#95×C₆₇	C₂³	1	1	yes	characteristic
187	#95×C₆₇	C₂³	1	1	yes	characteristic
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	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	1	yes	characteristic
203	#95×C₆₇	C₂³	1	1	yes	characteristic
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	C₂⁴×C₆₇	—	2	4	no	—
209	C₂⁴×C₆₇	—	2	2	no	—
210	C₂⁴×C₆₇	—	4	1	no	—
211	C₂⁴×C₆₇	—	4	1	no	—
212	C₂⁴×C₆₇	—	4	2	no	—
213	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
214	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
216	C₂×Q₈×C₆₇	—	2	4	no	—
217	C₂×Q₈×C₆₇	—	4	1	no	—
218	C₂×Q₈×C₆₇	—	4	1	no	—
219	C₂×Q₈×C₆₇	—	4	2	no	—
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	2	4	no	—
222	C₂×D₄×C₆₇	—	2	4	no	—
223	C₂×D₄×C₆₇	—	2	4	no	—
224	C₂×D₄×C₆₇	—	2	4	no	—
225	C₂×D₄×C₆₇	—	4	2	no	—
226	C₂×D₄×C₆₇	—	4	2	no	—
227	C₂×D₄×C₆₇	—	4	2	no	—
228	C₂×D₄×C₆₇	—	4	2	no	—
229	C₂×D₄×C₆₇	—	4	1	no	—
230	C₂×D₄×C₆₇	—	4	2	no	—
231	C₂²×C₄×C₆₇	—	2	2	no	—
232	C₂²×C₄×C₆₇	—	2	2	no	—
233	C₂²×C₄×C₆₇	—	2	2	no	—
234	C₂²×C₄×C₆₇	—	2	4	no	—
235	C₂²×C₄×C₆₇	—	2	4	no	—
236	C₂²×C₄×C₆₇	—	2	4	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	2	4	no	—
239	C₂²×C₄×C₆₇	—	4	2	no	—
240	C₂²×C₄×C₆₇	—	4	1	no	—
241	C₂²×C₄×C₆₇	—	4	1	no	—
242	C₂²×C₄×C₆₇	—	4	2	no	—
243	C₂²×C₄×C₆₇	—	4	2	no	—
244	C₂²×C₄×C₆₇	—	4	2	no	—
245	C₂²×C₄×C₆₇	—	4	16	no	—
246	C₂²×C₄×C₆₇	#41	1	4	yes	—
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	1	yes	characteristic
251	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	2	yes	—
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₄⋊C₄×C₆₇	—	2	4	no	—
264	C₄⋊C₄×C₆₇	—	2	4	no	—
265	C₄⋊C₄×C₆₇	—	2	4	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	—	4	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	C₂²⋊C₄×C₆₇	—	2	4	no	—
279	C₂²⋊C₄×C₆₇	—	2	4	no	—
280	C₂²⋊C₄×C₆₇	—	2	4	no	—
281	C₂²⋊C₄×C₆₇	—	2	4	no	—
282	C₂²⋊C₄×C₆₇	—	2	4	no	—
283	C₂²⋊C₄×C₆₇	—	2	4	no	—
284	C₂²⋊C₄×C₆₇	—	2	4	no	—
285	C₂²⋊C₄×C₆₇	—	2	4	no	—
286	C₂²⋊C₄×C₆₇	—	2	4	no	—
287	C₂²⋊C₄×C₆₇	—	2	4	no	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	—	4	2	no	—
290	C₂²⋊C₄×C₆₇	—	4	2	no	—
291	C₂²⋊C₄×C₆₇	—	4	2	no	—
292	C₂²⋊C₄×C₆₇	—	4	2	no	—
293	C₂²⋊C₄×C₆₇	—	4	2	no	—
294	C₂²⋊C₄×C₆₇	—	4	2	no	—
295	C₂²⋊C₄×C₆₇	—	4	1	no	—
296	C₂²⋊C₄×C₆₇	—	4	1	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	C₂²⋊C₄×C₆₇	—	4	2	no	—
302	C₂²⋊C₄×C₆₇	—	4	2	no	—
303	C₂²⋊C₄×C₆₇	—	4	2	no	—
304	C₂²⋊C₄×C₆₇	#41	1	8	yes	—
305	C₄²×C₆₇	—	2	4	no	—
306	C₄²×C₆₇	—	2	4	no	—
307	C₄²×C₆₇	—	2	4	no	—
308	C₄²×C₆₇	—	2	2	no	—
309	C₄²×C₆₇	—	2	2	no	—
310	C₄²×C₆₇	—	4	2	no	—
311	C₄²×C₆₇	—	4	2	no	—
312	C₄²×C₆₇	—	4	2	no	—
313	C₄²×C₆₇	—	4	2	no	—
314	C₄²×C₆₇	—	4	2	no	—
315	C₂³×C₆₇	—	2	2	no	—
316	C₂³×C₆₇	—	2	2	no	—
317	C₂³×C₆₇	—	2	2	no	—
318	C₂³×C₆₇	—	2	1	no	—
319	C₂³×C₆₇	—	2	1	no	—
320	C₂³×C₆₇	—	2	2	no	—
321	C₂³×C₆₇	—	2	2	no	—
322	C₂³×C₆₇	—	2	2	no	—
323	C₂³×C₆₇	—	2	2	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	—	2	2	no	—
329	C₂³×C₆₇	—	2	2	no	—
330	C₂³×C₆₇	—	2	2	no	—
331	C₂³×C₆₇	—	2	2	no	—
332	C₂³×C₆₇	—	4	8	no	—
333	C₂³×C₆₇	—	4	4	no	—
334	C₂³×C₆₇	—	4	4	no	—
335	C₂³×C₆₇	—	4	8	no	—
336	C₂³×C₆₇	—	4	4	no	—
337	C₂³×C₆₇	C₂×#41	1	4	yes	—
338	C₂³×C₆₇	C₂×#41	1	2	yes	—
339	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
340	Q₈×C₆₇	—	4	4	no	—
341	Q₈×C₆₇	—	8	2	no	—
342	D₄×C₆₇	—	4	8	no	—
343	D₄×C₆₇	—	4	8	no	—
344	D₄×C₆₇	—	4	8	no	—
345	D₄×C₆₇	—	8	2	no	—
346	C₂×C₄×C₆₇	—	2	8	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	1	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	2	no	—
355	C₂×C₄×C₆₇	—	2	1	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	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	1	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	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	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	4	4	no	—
387	C₂×C₄×C₆₇	—	4	8	no	—
388	C₂×C₄×C₆₇	—	4	8	no	—
389	C₂×C₄×C₆₇	—	8	4	no	—
390	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
391	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
392	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
393	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
394	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
395	C₂²×C₆₇	—	2	4	no	—
396	C₂²×C₆₇	—	2	4	no	—
397	C₂²×C₆₇	—	2	4	no	—
398	C₂²×C₆₇	—	2	2	no	—
399	C₂²×C₆₇	—	2	4	no	—
400	C₂²×C₆₇	—	4	16	no	—
401	C₂²×C₆₇	—	4	2	no	—
402	C₂²×C₆₇	—	4	1	no	—
403	C₂²×C₆₇	—	4	2	no	—
404	C₂²×C₆₇	—	4	2	no	—
405	C₂²×C₆₇	—	4	2	no	—
406	C₂²×C₆₇	—	4	1	no	—
407	C₂²×C₆₇	—	4	2	no	—
408	C₂²×C₆₇	—	4	2	no	—
409	C₂²×C₆₇	—	4	2	no	—
410	C₂²×C₆₇	—	4	2	no	—
411	C₂²×C₆₇	—	4	2	no	—
412	C₂²×C₆₇	—	4	2	no	—
413	C₂²×C₆₇	—	4	2	no	—
414	C₂²×C₆₇	—	4	2	no	—
415	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
416	C₂²×C₆₇	C₂²×#41	1	2	yes	—
417	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂²×C₆₇	#585	1	2	yes	—
420	C₄×C₆₇	—	2	4	no	—
421	C₄×C₆₇	—	2	4	no	—
422	C₄×C₆₇	—	2	2	no	—
423	C₄×C₆₇	—	2	2	no	—
424	C₄×C₆₇	—	2	4	no	—
425	C₄×C₆₇	—	4	2	no	—
426	C₄×C₆₇	—	4	1	no	—
427	C₄×C₆₇	—	4	1	no	—
428	C₄×C₆₇	—	4	2	no	—
429	C₄×C₆₇	—	4	2	no	—
430	C₄×C₆₇	—	4	2	no	—
431	C₄×C₆₇	—	4	2	no	—
432	C₄×C₆₇	—	4	2	no	—
433	C₄×C₆₇	—	4	1	no	—
434	C₄×C₆₇	—	4	1	no	—
435	C₄×C₆₇	—	4	2	no	—
436	#59352	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
437	C₂×C₆₇	—	4	2	no	—
438	C₂×C₆₇	—	4	4	no	—
439	C₂×C₆₇	—	8	2	no	—
440	C₂×C₆₇	#3475	1	2	yes	—
441	C₂×C₆₇	#3481	1	1	yes	characteristic
442	C₂×C₆₇	#3490	1	1	yes	characteristic
443	C₂×C₆₇	#3506	1	2	yes	—
444	C₂×C₆₇	#3540	1	1	yes	characteristic
445	#2736	C₂×C₆₇	1	1	yes	characteristic, complemented
446	#2685	C₂×C₆₇	1	2	yes	complemented
447	#2670	C₂×C₆₇	1	1	yes	characteristic
448	#2610	C₂×C₆₇	1	1	yes	characteristic, complemented
449	#2607	C₂×C₆₇	1	1	yes	characteristic, complemented
450	#2600	C₂×C₆₇	1	1	yes	characteristic, complemented
451	#2599	C₂×C₆₇	1	1	yes	characteristic, complemented
452	#2574	C₂×C₆₇	1	2	yes	complemented
453	#2521	C₂×C₆₇	1	2	yes	complemented
454	#2518	C₂×C₆₇	1	2	yes	complemented
455	#2479	C₂×C₆₇	1	2	yes	complemented
456	#2468	C₂×C₆₇	1	2	yes	complemented
457	#2467	C₂×C₆₇	1	2	yes	complemented
458	#2459	C₂×C₆₇	1	2	yes	complemented
459	#2373	C₂×C₆₇	1	2	yes	complemented
460	#2367	C₂×C₆₇	1	2	yes	complemented
461	#2357	C₂×C₆₇	1	2	yes	complemented
462	C₄×#120	C₂×C₆₇	1	2	yes	complemented
463	#2280	C₂×C₆₇	1	1	yes	characteristic, complemented
464	C₆₇	#59352	1	1	yes	characteristic, direct product factor, Sylow
465	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
466	C₂×#126	C₂²×C₆₇	1	2	yes	—
467	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
468	C₂×#124	C₂²×C₆₇	1	2	yes	—
469	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
470	C₂×#120	C₂²×C₆₇	1	2	yes	—
471	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
472	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
473	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
474	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
475	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
476	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
477	#399	C₂²×C₆₇	1	2	yes	—
478	#399	C₂²×C₆₇	1	2	yes	complemented
479	#398	C₂²×C₆₇	1	2	yes	complemented
480	#398	C₂²×C₆₇	1	1	yes	characteristic, complemented
481	#397	C₂²×C₆₇	1	1	yes	characteristic
482	#397	C₂²×C₆₇	1	2	yes	—
483	#396	C₂²×C₆₇	1	2	yes	—
484	#395	C₂²×C₆₇	1	1	yes	characteristic, complemented
485	#395	C₂²×C₆₇	1	1	yes	characteristic, complemented
486	#394	C₂²×C₆₇	1	2	yes	—
487	#394	C₂²×C₆₇	1	2	yes	—
488	#394	C₂²×C₆₇	1	2	yes	—
489	#394	C₂²×C₆₇	1	2	yes	—
490	#394	C₂²×C₆₇	1	2	yes	—
491	#394	C₂²×C₆₇	1	1	yes	characteristic, complemented
492	#393	C₂²×C₆₇	1	2	yes	—
493	#393	C₂²×C₆₇	1	1	yes	characteristic
494	#393	C₂²×C₆₇	1	1	yes	characteristic
495	#392	C₂²×C₆₇	1	1	yes	characteristic
496	#392	C₂²×C₆₇	1	2	yes	—
497	#391	C₂²×C₆₇	1	2	yes	complemented
498	#391	C₂²×C₆₇	1	2	yes	complemented
499	#390	C₂²×C₆₇	1	2	yes	—
500	#390	C₂²×C₆₇	1	2	yes	—
501	#390	C₂²×C₆₇	1	2	yes	—
502	#389	C₂²×C₆₇	1	2	yes	complemented
503	#388	C₂²×C₆₇	1	2	yes	—
504	#388	C₂²×C₆₇	1	2	yes	—
505	#388	C₂²×C₆₇	1	2	yes	—
506	#388	C₂²×C₆₇	1	2	yes	—
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	complemented
511	#388	C₂²×C₆₇	1	2	yes	complemented
512	#388	C₂²×C₆₇	1	2	yes	complemented
513	#388	C₂²×C₆₇	1	2	yes	complemented
514	#388	C₂²×C₆₇	1	2	yes	complemented
515	#388	C₂²×C₆₇	1	2	yes	complemented
516	#388	C₂²×C₆₇	1	2	yes	complemented
517	#387	C₂²×C₆₇	1	2	yes	complemented
518	#387	C₂²×C₆₇	1	2	yes	complemented
519	#387	C₂²×C₆₇	1	2	yes	complemented
520	#387	C₂²×C₆₇	1	2	yes	complemented
521	#387	C₂²×C₆₇	1	2	yes	complemented
522	#387	C₂²×C₆₇	1	2	yes	complemented
523	#386	C₂²×C₆₇	1	2	yes	—
524	#386	C₂²×C₆₇	1	2	yes	—
525	#386	C₂²×C₆₇	1	2	yes	—
526	#386	C₂²×C₆₇	1	2	yes	complemented
527	#385	C₂²×C₆₇	1	2	yes	—
528	#385	C₂²×C₆₇	1	2	yes	—
529	#385	C₂²×C₆₇	1	2	yes	—
530	#385	C₂²×C₆₇	1	2	yes	complemented
531	#383	C₂²×C₆₇	1	1	yes	characteristic, complemented
532	#382	C₂²×C₆₇	1	2	yes	complemented
533	#381	C₂²×C₆₇	1	1	yes	characteristic
534	#381	C₂²×C₆₇	1	1	yes	characteristic
535	#381	C₂²×C₆₇	1	2	yes	complemented
536	#380	C₂²×C₆₇	1	2	yes	—
537	#380	C₂²×C₆₇	1	2	yes	—
538	#379	C₂²×C₆₇	1	1	yes	characteristic
539	#379	C₂²×C₆₇	1	1	yes	characteristic
540	#379	C₂²×C₆₇	1	2	yes	—
541	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
542	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
543	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
544	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
545	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
546	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
547	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
548	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
549	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
550	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
551	#376	C₂²×C₆₇	1	1	yes	characteristic, complemented
552	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
553	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
554	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
556	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
557	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
558	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
559	C₂³×C₄	—	2	4	no	—
560	C₂³×C₄	—	4	2	no	—
561	C₂³×C₄	—	4	2	no	—
562	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
564	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
565	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
566	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
567	#126	—	2	8	no	—
568	#126	—	4	4	no	—
569	#124	—	2	8	no	—
570	#124	—	4	2	no	—
571	#120	—	2	8	no	—
572	C₄×Q₈	—	4	2	no	—
573	C₄×D₄	—	2	8	no	—
574	C₄×D₄	—	4	4	no	—
575	C₄×D₄	—	4	4	no	—
576	#117	—	4	2	no	—
577	#117	—	4	2	no	—
578	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
623	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
624	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
625	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
626	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
627	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
628	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
630	#95	C₂³×C₆₇	1	2	yes	—
631	#95	C₂³×C₆₇	1	1	yes	characteristic
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	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	2	yes	—
642	#95	C₂³×C₆₇	1	2	yes	—
643	#95	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
648	#95	C₂³×C₆₇	1	1	yes	characteristic
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	C₂⁴	—	2	4	no	—
654	C₂⁴	—	2	2	no	—
655	C₂⁴	—	4	1	no	—
656	C₂⁴	—	4	1	no	—
657	C₂⁴	—	4	2	no	—
658	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
659	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
660	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
661	C₂×Q₈	—	2	4	no	—
662	C₂×Q₈	—	4	1	no	—
663	C₂×Q₈	—	4	1	no	—
664	C₂×Q₈	—	4	2	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	4	2	no	—
671	C₂×D₄	—	4	2	no	—
672	C₂×D₄	—	4	2	no	—
673	C₂×D₄	—	4	2	no	—
674	C₂×D₄	—	4	1	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	1	no	—
686	C₂²×C₄	—	4	1	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	16	no	—
691	C₂²×C₄	#41×C₆₇	1	4	yes	—
692	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
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	4	no	—
715	C₄⋊C₄	—	4	1	no	—
716	C₄⋊C₄	—	4	1	no	—
717	C₄⋊C₄	—	4	1	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	4	1	no	—
735	C₂²⋊C₄	—	4	1	no	—
736	C₂²⋊C₄	—	4	1	no	—
737	C₂²⋊C₄	—	4	1	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	4	no	—
752	C₄²	—	2	4	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	4	2	no	—
756	C₄²	—	4	2	no	—
757	C₄²	—	4	2	no	—
758	C₄²	—	4	2	no	—
759	C₄²	—	4	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	4	8	no	—
778	C₂³	—	4	4	no	—
779	C₂³	—	4	4	no	—
780	C₂³	—	4	8	no	—
781	C₂³	—	4	4	no	—
782	C₂³	C₂×#41×C₆₇	1	4	yes	—
783	C₂³	C₂×#41×C₆₇	1	2	yes	—
784	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
785	Q₈	—	4	4	no	—
786	Q₈	—	8	2	no	—
787	D₄	—	4	8	no	—
788	D₄	—	4	8	no	—
789	D₄	—	4	8	no	—
790	D₄	—	8	2	no	—
791	C₂×C₄	—	2	8	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	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	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	8	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	8	4	no	—
835	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
836	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
837	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
838	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
839	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	4	16	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
861	C₂²	C₂²×#41×C₆₇	1	2	yes	—
862	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
863	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
864	C₂²	#585×C₆₇	1	2	yes	—
865	C₄	—	2	4	no	—
866	C₄	—	2	4	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	4	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₂	—	4	2	no	—
882	C₂	—	4	4	no	—
883	C₂	—	8	2	no	—
884	C₂	C₆₇×#3475	1	2	yes	—
885	C₂	C₆₇×#3481	1	1	yes	characteristic
886	C₂	C₆₇×#3490	1	1	yes	characteristic
887	C₂	C₆₇×#3506	1	2	yes	—
888	C₂	C₆₇×#3540	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2670	C₂
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
1. C₆₇×#2736	C₂	semidirect
2. C₆₇×#2685	C₂	semidirect
4. C₆₇×#2610	C₂	semidirect
5. C₆₇×#2607	C₂	semidirect
6. C₆₇×#2600	C₂	semidirect
7. C₆₇×#2599	C₂	semidirect
8. C₆₇×#2574	C₂	semidirect
9. C₆₇×#2521	C₂	semidirect
10. C₆₇×#2518	C₂	semidirect
11. C₆₇×#2479	C₂	semidirect
12. C₆₇×#2468	C₂	semidirect
13. C₆₇×#2467	C₂	semidirect
14. C₆₇×#2459	C₂	semidirect
15. C₆₇×#2373	C₂	semidirect
16. C₆₇×#2367	C₂	semidirect
17. C₆₇×#2357	C₂	semidirect
18. C₄×#120×C₆₇	C₂	semidirect
19. C₆₇×#2280	C₂	semidirect
22. C₂×#126×C₆₇	C₂²	semidirect
24. C₂×#124×C₆₇	C₂²	semidirect
26. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
33. #399×C₆₇	C₂²	semidirect
34. #398×C₆₇	C₂²	semidirect
35. #398×C₆₇	C₂²	semidirect
39. #395×C₆₇	C₂²	semidirect
40. #395×C₆₇	C₂²	semidirect
46. #394×C₆₇	C₂²	semidirect
52. #391×C₆₇	C₂²	semidirect
53. #391×C₆₇	C₂²	semidirect
57. #389×C₆₇	C₂²	semidirect
65. #388×C₆₇	C₂²	semidirect
66. #388×C₆₇	C₂²	semidirect
67. #388×C₆₇	C₂²	semidirect
68. #388×C₆₇	C₂²	semidirect
69. #388×C₆₇	C₂²	semidirect
70. #388×C₆₇	C₂²	semidirect
71. #388×C₆₇	C₂²	semidirect
72. #387×C₆₇	C₂²	semidirect
73. #387×C₆₇	C₂²	semidirect
74. #387×C₆₇	C₂²	semidirect
75. #387×C₆₇	C₂²	semidirect
76. #387×C₆₇	C₂²	semidirect
77. #387×C₆₇	C₂²	semidirect
81. #386×C₆₇	C₂²	semidirect
85. #385×C₆₇	C₂²	semidirect
86. #383×C₆₇	C₂²	semidirect
87. #382×C₆₇	C₂²	semidirect
90. #381×C₆₇	C₂²	semidirect
96. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
97. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
98. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
99. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
106. #376×C₆₇	C₂²	semidirect
436. #59352	C₆₇	direct (N × H)
445. #2736	C₂×C₆₇	semidirect
446. #2685	C₂×C₆₇	semidirect
448. #2610	C₂×C₆₇	semidirect
449. #2607	C₂×C₆₇	semidirect
450. #2600	C₂×C₆₇	semidirect
451. #2599	C₂×C₆₇	semidirect
452. #2574	C₂×C₆₇	semidirect
453. #2521	C₂×C₆₇	semidirect
454. #2518	C₂×C₆₇	semidirect
455. #2479	C₂×C₆₇	semidirect
456. #2468	C₂×C₆₇	semidirect
457. #2467	C₂×C₆₇	semidirect
458. #2459	C₂×C₆₇	semidirect
459. #2373	C₂×C₆₇	semidirect
460. #2367	C₂×C₆₇	semidirect
461. #2357	C₂×C₆₇	semidirect
462. C₄×#120	C₂×C₆₇	semidirect
463. #2280	C₂×C₆₇	semidirect
464. C₆₇	#59352	direct (N × H)
467. C₂×#126	C₂²×C₆₇	semidirect
469. C₂×#124	C₂²×C₆₇	semidirect
471. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
478. #399	C₂²×C₆₇	semidirect
479. #398	C₂²×C₆₇	semidirect
480. #398	C₂²×C₆₇	semidirect
484. #395	C₂²×C₆₇	semidirect
485. #395	C₂²×C₆₇	semidirect
491. #394	C₂²×C₆₇	semidirect
497. #391	C₂²×C₆₇	semidirect
498. #391	C₂²×C₆₇	semidirect
502. #389	C₂²×C₆₇	semidirect
510. #388	C₂²×C₆₇	semidirect
511. #388	C₂²×C₆₇	semidirect
512. #388	C₂²×C₆₇	semidirect
513. #388	C₂²×C₆₇	semidirect
514. #388	C₂²×C₆₇	semidirect
515. #388	C₂²×C₆₇	semidirect
516. #388	C₂²×C₆₇	semidirect
517. #387	C₂²×C₆₇	semidirect
518. #387	C₂²×C₆₇	semidirect
519. #387	C₂²×C₆₇	semidirect
520. #387	C₂²×C₆₇	semidirect
521. #387	C₂²×C₆₇	semidirect
522. #387	C₂²×C₆₇	semidirect
526. #386	C₂²×C₆₇	semidirect
530. #385	C₂²×C₆₇	semidirect
531. #383	C₂²×C₆₇	semidirect
532. #382	C₂²×C₆₇	semidirect
535. #381	C₂²×C₆₇	semidirect
541. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
542. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
543. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
544. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
550. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
551. #376	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×#2736	2
C₆₇×#2685	2
C₆₇×#2670	2
C₆₇×#2610	2
C₆₇×#2607	2
C₆₇×#2600	2
C₆₇×#2599	2
C₆₇×#2574	2
C₆₇×#2521	2
C₆₇×#2518	2
C₆₇×#2479	2
C₆₇×#2468	2
C₆₇×#2467	2
C₆₇×#2459	2
C₆₇×#2373	2
C₆₇×#2367	2
C₆₇×#2357	2
C₄×#120×C₆₇	2
C₆₇×#2280	2
#59352	67

Subgroups — C67×#59352 #30738603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59352 #30738603