Subgroups — C₆₇×#59392 #30738643

Order 17152.

2396 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2691	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2688	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2600	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2537	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2512	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2506	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2496	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2481	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2476	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2460	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2457	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2428	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2428	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2422	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2416	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2366	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
19	D₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2344	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#123×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	#553×C₆₇	—	2	16	no	—
25	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#126×C₆₇	C₂²	1	2	yes	—
27	C₂×#126×C₆₇	C₂²	1	2	yes	—
28	C₂×#125×C₆₇	C₂²	1	2	yes	—
29	C₂×#123×C₆₇	C₂²	1	2	yes	—
30	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#121×C₆₇	C₂²	1	2	yes	—
34	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#121×C₆₇	C₂²	1	2	yes	—
36	C₂×#121×C₆₇	C₂²	1	2	yes	—
37	C₂×#121×C₆₇	C₂²	1	2	yes	—
38	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×#117×C₆₇	C₂²	1	2	yes	—
49	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
50	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
51	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
52	#400×C₆₇	C₂²	1	2	yes	—
53	#400×C₆₇	C₂²	1	2	yes	—
54	#398×C₆₇	C₂²	1	2	yes	—
55	#397×C₆₇	C₂²	1	2	yes	—
56	#397×C₆₇	C₂²	1	2	yes	—
57	#397×C₆₇	C₂²	1	2	yes	—
58	#396×C₆₇	C₂²	1	2	yes	—
59	#396×C₆₇	C₂²	1	2	yes	—
60	#394×C₆₇	C₂²	1	2	yes	—
61	#394×C₆₇	C₂²	1	2	yes	—
62	#394×C₆₇	C₂²	1	2	yes	—
63	#394×C₆₇	C₂²	1	2	yes	—
64	#394×C₆₇	C₂²	1	2	yes	—
65	#394×C₆₇	C₂²	1	2	yes	—
66	#392×C₆₇	C₂²	1	2	yes	—
67	#392×C₆₇	C₂²	1	2	yes	—
68	#390×C₆₇	C₂²	1	1	yes	characteristic
69	#390×C₆₇	C₂²	1	1	yes	characteristic
70	#390×C₆₇	C₂²	1	1	yes	characteristic
71	#390×C₆₇	C₂²	1	1	yes	characteristic
72	#390×C₆₇	C₂²	1	2	yes	—
73	#389×C₆₇	C₂²	1	1	yes	characteristic
74	#389×C₆₇	C₂²	1	1	yes	characteristic
75	#389×C₆₇	C₂²	1	1	yes	characteristic
76	#389×C₆₇	C₂²	1	1	yes	characteristic
77	#389×C₆₇	C₂²	1	1	yes	characteristic
78	#389×C₆₇	C₂²	1	1	yes	characteristic
79	#388×C₆₇	C₂²	1	2	yes	—
80	#388×C₆₇	C₂²	1	2	yes	—
81	#388×C₆₇	C₂²	1	2	yes	—
82	#388×C₆₇	C₂²	1	1	yes	characteristic
83	#388×C₆₇	C₂²	1	1	yes	characteristic
84	#388×C₆₇	C₂²	1	2	yes	—
85	#387×C₆₇	C₂²	1	2	yes	—
86	#387×C₆₇	C₂²	1	1	yes	characteristic
87	#387×C₆₇	C₂²	1	1	yes	characteristic
88	#387×C₆₇	C₂²	1	2	yes	—
89	#387×C₆₇	C₂²	1	2	yes	—
90	#387×C₆₇	C₂²	1	2	yes	—
91	#386×C₆₇	C₂²	1	2	yes	—
92	#386×C₆₇	C₂²	1	2	yes	—
93	#386×C₆₇	C₂²	1	1	yes	characteristic
94	#386×C₆₇	C₂²	1	2	yes	—
95	#386×C₆₇	C₂²	1	2	yes	—
96	#386×C₆₇	C₂²	1	2	yes	—
97	#386×C₆₇	C₂²	1	2	yes	—
98	#386×C₆₇	C₂²	1	2	yes	—
99	#386×C₆₇	C₂²	1	2	yes	—
100	#385×C₆₇	C₂²	1	1	yes	characteristic
101	#385×C₆₇	C₂²	1	2	yes	—
102	#385×C₆₇	C₂²	1	2	yes	—
103	#385×C₆₇	C₂²	1	2	yes	—
104	#385×C₆₇	C₂²	1	2	yes	—
105	#384×C₆₇	C₂²	1	1	yes	characteristic
106	#384×C₆₇	C₂²	1	1	yes	characteristic
107	#381×C₆₇	C₂²	1	1	yes	characteristic
108	#381×C₆₇	C₂²	1	2	yes	—
109	#380×C₆₇	C₂²	1	1	yes	characteristic
110	#380×C₆₇	C₂²	1	1	yes	characteristic
111	#380×C₆₇	C₂²	1	2	yes	—
112	#380×C₆₇	C₂²	1	1	yes	characteristic
113	#380×C₆₇	C₂²	1	2	yes	—
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×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
124	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
126	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
127	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
128	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
129	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
131	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
132	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
139	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
140	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
142	#127×C₆₇	—	2	4	no	—
143	#126×C₆₇	—	2	8	no	—
144	#126×C₆₇	—	2	8	no	—
145	#125×C₆₇	—	2	8	no	—
146	#123×C₆₇	—	2	8	no	—
147	#123×C₆₇	D₄	1	8	yes	complemented
148	#121×C₆₇	—	2	8	no	—
149	#121×C₆₇	—	2	8	no	—
150	#121×C₆₇	—	2	4	no	—
151	#121×C₆₇	—	2	4	no	—
152	#121×C₆₇	—	2	4	no	—
153	#121×C₆₇	—	2	8	no	—
154	#121×C₆₇	—	2	8	no	—
155	#121×C₆₇	—	4	2	no	—
156	C₄×D₄×C₆₇	—	2	8	no	—
157	C₄×D₄×C₆₇	—	2	8	no	—
158	C₄×D₄×C₆₇	—	2	8	no	—
159	C₄×D₄×C₆₇	—	2	4	no	—
160	C₄×D₄×C₆₇	—	2	8	no	—
161	C₄×D₄×C₆₇	—	4	2	no	—
162	C₄×D₄×C₆₇	—	4	2	no	—
163	C₄×D₄×C₆₇	—	4	2	no	—
164	C₄×D₄×C₆₇	—	4	2	no	—
165	#117×C₆₇	—	2	8	no	—
166	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
167	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₆₇	—	4	2	no	—
218	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
221	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
222	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
223	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	#95×C₆₇	C₂³	1	2	yes	—
229	#95×C₆₇	C₂³	1	2	yes	—
230	#95×C₆₇	C₂³	1	2	yes	—
231	#95×C₆₇	C₂³	1	1	yes	characteristic
232	#95×C₆₇	C₂³	1	1	yes	characteristic
233	#95×C₆₇	C₂³	1	1	yes	characteristic
234	#95×C₆₇	C₂³	1	1	yes	characteristic
235	#95×C₆₇	C₂³	1	1	yes	characteristic
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	1	yes	characteristic
238	#95×C₆₇	C₂³	1	1	yes	characteristic
239	#95×C₆₇	C₂³	1	1	yes	characteristic
240	#95×C₆₇	C₂³	1	2	yes	—
241	#95×C₆₇	C₂³	1	2	yes	—
242	#95×C₆₇	C₂³	1	1	yes	characteristic
243	#95×C₆₇	C₂³	1	2	yes	—
244	#95×C₆₇	C₂³	1	1	yes	characteristic
245	#95×C₆₇	C₂³	1	2	yes	—
246	#95×C₆₇	C₂³	1	2	yes	—
247	#95×C₆₇	C₂³	1	2	yes	—
248	#95×C₆₇	C₂³	1	2	yes	—
249	#95×C₆₇	C₂³	1	2	yes	—
250	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
251	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
254	C₂×D₄×C₆₇	—	2	4	no	—
255	C₂×D₄×C₆₇	—	2	4	no	—
256	C₂×D₄×C₆₇	—	2	4	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	4	no	—
259	C₂×D₄×C₆₇	—	2	4	no	—
260	C₂×D₄×C₆₇	—	2	4	no	—
261	C₂×D₄×C₆₇	—	2	4	no	—
262	C₂×D₄×C₆₇	—	2	4	no	—
263	C₂×D₄×C₆₇	—	2	2	no	—
264	C₂×D₄×C₆₇	—	2	4	no	—
265	C₂×D₄×C₆₇	—	2	2	no	—
266	C₂×D₄×C₆₇	—	2	2	no	—
267	C₂×D₄×C₆₇	—	2	2	no	—
268	C₂×D₄×C₆₇	—	2	2	no	—
269	C₂×D₄×C₆₇	—	4	1	no	—
270	C₂×D₄×C₆₇	—	4	2	no	—
271	C₂×D₄×C₆₇	—	4	1	no	—
272	C₂×D₄×C₆₇	—	4	2	no	—
273	C₂×D₄×C₆₇	—	4	2	no	—
274	C₂×D₄×C₆₇	—	4	2	no	—
275	C₂×D₄×C₆₇	—	4	2	no	—
276	C₂×D₄×C₆₇	—	4	2	no	—
277	C₂×D₄×C₆₇	—	4	2	no	—
278	C₂×D₄×C₆₇	—	4	2	no	—
279	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
280	C₂×D₄×C₆₇	#41	1	4	yes	—
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	2	no	—
285	C₂²×C₄×C₆₇	—	2	4	no	—
286	C₂²×C₄×C₆₇	—	2	2	no	—
287	C₂²×C₄×C₆₇	—	2	2	no	—
288	C₂²×C₄×C₆₇	—	2	2	no	—
289	C₂²×C₄×C₆₇	—	2	2	no	—
290	C₂²×C₄×C₆₇	—	2	2	no	—
291	C₂²×C₄×C₆₇	—	2	4	no	—
292	C₂²×C₄×C₆₇	—	2	4	no	—
293	C₂²×C₄×C₆₇	—	2	4	no	—
294	C₂²×C₄×C₆₇	—	4	1	no	—
295	C₂²×C₄×C₆₇	—	4	1	no	—
296	C₂²×C₄×C₆₇	—	4	2	no	—
297	C₂²×C₄×C₆₇	—	4	1	no	—
298	C₂²×C₄×C₆₇	—	4	2	no	—
299	C₂²×C₄×C₆₇	—	4	1	no	—
300	C₂²×C₄×C₆₇	—	4	1	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	—	4	2	no	—
305	C₂²×C₄×C₆₇	—	4	2	no	—
306	C₂²×C₄×C₆₇	—	4	2	no	—
307	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
308	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
327	C₄⋊C₄×C₆₇	—	2	4	no	—
328	C₄⋊C₄×C₆₇	—	2	4	no	—
329	C₄⋊C₄×C₆₇	—	2	4	no	—
330	C₄⋊C₄×C₆₇	—	2	4	no	—
331	C₄⋊C₄×C₆₇	—	2	4	no	—
332	C₄⋊C₄×C₆₇	—	2	4	no	—
333	C₄⋊C₄×C₆₇	—	2	4	no	—
334	C₄⋊C₄×C₆₇	—	2	4	no	—
335	C₄⋊C₄×C₆₇	—	2	4	no	—
336	C₄⋊C₄×C₆₇	—	2	2	no	—
337	C₄⋊C₄×C₆₇	—	2	2	no	—
338	C₄⋊C₄×C₆₇	—	2	2	no	—
339	C₄⋊C₄×C₆₇	—	2	2	no	—
340	C₄⋊C₄×C₆₇	—	2	2	no	—
341	C₄⋊C₄×C₆₇	—	4	1	no	—
342	C₄⋊C₄×C₆₇	—	4	1	no	—
343	C₄⋊C₄×C₆₇	—	4	2	no	—
344	C₄⋊C₄×C₆₇	—	4	2	no	—
345	C₄⋊C₄×C₆₇	—	4	1	no	—
346	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
347	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
348	C₄⋊C₄×C₆₇	#41	1	4	yes	—
349	C₂²⋊C₄×C₆₇	—	2	4	no	—
350	C₂²⋊C₄×C₆₇	—	2	4	no	—
351	C₂²⋊C₄×C₆₇	—	2	4	no	—
352	C₂²⋊C₄×C₆₇	—	2	4	no	—
353	C₂²⋊C₄×C₆₇	—	2	4	no	—
354	C₂²⋊C₄×C₆₇	—	2	4	no	—
355	C₂²⋊C₄×C₆₇	—	2	4	no	—
356	C₂²⋊C₄×C₆₇	—	2	4	no	—
357	C₂²⋊C₄×C₆₇	—	2	4	no	—
358	C₂²⋊C₄×C₆₇	—	2	4	no	—
359	C₂²⋊C₄×C₆₇	—	2	4	no	—
360	C₂²⋊C₄×C₆₇	—	4	1	no	—
361	C₂²⋊C₄×C₆₇	—	4	2	no	—
362	C₂²⋊C₄×C₆₇	—	4	2	no	—
363	C₂²⋊C₄×C₆₇	—	4	2	no	—
364	C₂²⋊C₄×C₆₇	—	4	2	no	—
365	C₂²⋊C₄×C₆₇	—	4	1	no	—
366	C₂²⋊C₄×C₆₇	—	4	1	no	—
367	C₂²⋊C₄×C₆₇	—	4	2	no	—
368	C₂²⋊C₄×C₆₇	—	4	2	no	—
369	C₂²⋊C₄×C₆₇	—	4	1	no	—
370	C₂²⋊C₄×C₆₇	—	4	1	no	—
371	C₂²⋊C₄×C₆₇	—	4	2	no	—
372	C₂²⋊C₄×C₆₇	—	4	2	no	—
373	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
374	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
375	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
376	C₄²×C₆₇	—	2	4	no	—
377	C₄²×C₆₇	—	2	4	no	—
378	C₄²×C₆₇	—	2	4	no	—
379	C₄²×C₆₇	—	2	2	no	—
380	C₄²×C₆₇	—	2	2	no	—
381	C₄²×C₆₇	—	2	2	no	—
382	C₄²×C₆₇	—	2	2	no	—
383	C₄²×C₆₇	—	2	2	no	—
384	C₄²×C₆₇	—	4	1	no	—
385	C₄²×C₆₇	—	4	1	no	—
386	C₂³×C₆₇	—	2	2	no	—
387	C₂³×C₆₇	—	2	2	no	—
388	C₂³×C₆₇	—	2	1	no	—
389	C₂³×C₆₇	—	2	1	no	—
390	C₂³×C₆₇	—	2	1	no	—
391	C₂³×C₆₇	—	2	1	no	—
392	C₂³×C₆₇	—	2	2	no	—
393	C₂³×C₆₇	—	2	1	no	—
394	C₂³×C₆₇	—	2	1	no	—
395	C₂³×C₆₇	—	2	1	no	—
396	C₂³×C₆₇	—	2	1	no	—
397	C₂³×C₆₇	—	2	2	no	—
398	C₂³×C₆₇	—	2	1	no	—
399	C₂³×C₆₇	—	2	2	no	—
400	C₂³×C₆₇	—	2	1	no	—
401	C₂³×C₆₇	—	2	1	no	—
402	C₂³×C₆₇	—	2	2	no	—
403	C₂³×C₆₇	—	2	1	no	—
404	C₂³×C₆₇	—	2	2	no	—
405	C₂³×C₆₇	—	2	2	no	—
406	C₂³×C₆₇	—	2	2	no	—
407	C₂³×C₆₇	—	2	2	no	—
408	C₂³×C₆₇	—	2	2	no	—
409	C₂³×C₆₇	—	2	2	no	—
410	C₂³×C₆₇	—	2	2	no	—
411	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
412	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
413	C₂³×C₆₇	C₂×#41	1	4	yes	—
414	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
415	D₄×C₆₇	—	2	8	no	—
416	D₄×C₆₇	—	4	4	no	—
417	D₄×C₆₇	—	4	8	no	—
418	D₄×C₆₇	—	4	8	no	—
419	D₄×C₆₇	—	4	8	no	—
420	D₄×C₆₇	—	4	8	no	—
421	D₄×C₆₇	—	4	4	no	—
422	D₄×C₆₇	—	8	4	no	—
423	D₄×C₆₇	—	8	4	no	—
424	C₂×C₄×C₆₇	—	2	2	no	—
425	C₂×C₄×C₆₇	—	2	1	no	—
426	C₂×C₄×C₆₇	—	2	1	no	—
427	C₂×C₄×C₆₇	—	2	1	no	—
428	C₂×C₄×C₆₇	—	2	1	no	—
429	C₂×C₄×C₆₇	—	2	1	no	—
430	C₂×C₄×C₆₇	—	2	1	no	—
431	C₂×C₄×C₆₇	—	2	1	no	—
432	C₂×C₄×C₆₇	—	2	1	no	—
433	C₂×C₄×C₆₇	—	2	1	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	1	no	—
436	C₂×C₄×C₆₇	—	2	2	no	—
437	C₂×C₄×C₆₇	—	2	2	no	—
438	C₂×C₄×C₆₇	—	2	2	no	—
439	C₂×C₄×C₆₇	—	2	2	no	—
440	C₂×C₄×C₆₇	—	2	2	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	1	no	—
444	C₂×C₄×C₆₇	—	2	1	no	—
445	C₂×C₄×C₆₇	—	2	1	no	—
446	C₂×C₄×C₆₇	—	2	2	no	—
447	C₂×C₄×C₆₇	—	2	2	no	—
448	C₂×C₄×C₆₇	—	2	2	no	—
449	C₂×C₄×C₆₇	—	2	1	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	2	1	no	—
453	C₂×C₄×C₆₇	—	2	1	no	—
454	C₂×C₄×C₆₇	—	2	1	no	—
455	C₂×C₄×C₆₇	—	2	2	no	—
456	C₂×C₄×C₆₇	—	2	2	no	—
457	C₂×C₄×C₆₇	—	2	1	no	—
458	C₂×C₄×C₆₇	—	2	1	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	1	no	—
461	C₂×C₄×C₆₇	—	2	1	no	—
462	C₂×C₄×C₆₇	—	2	1	no	—
463	C₂×C₄×C₆₇	—	2	1	no	—
464	C₂×C₄×C₆₇	—	2	1	no	—
465	C₂×C₄×C₆₇	—	2	2	no	—
466	C₂×C₄×C₆₇	—	2	2	no	—
467	C₂×C₄×C₆₇	—	2	1	no	—
468	C₂×C₄×C₆₇	—	2	1	no	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	2	no	—
471	C₂×C₄×C₆₇	—	2	2	no	—
472	C₂×C₄×C₆₇	—	4	4	no	—
473	C₂×C₄×C₆₇	—	4	8	no	—
474	C₂×C₄×C₆₇	—	4	8	no	—
475	C₂×C₄×C₆₇	—	4	4	no	—
476	C₂×C₄×C₆₇	—	4	4	no	—
477	C₂×C₄×C₆₇	—	4	4	no	—
478	C₂×C₄×C₆₇	—	8	4	no	—
479	C₂×C₄×C₆₇	—	8	4	no	—
480	C₂×C₄×C₆₇	—	8	4	no	—
481	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
487	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
488	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
489	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
490	C₂²×C₆₇	—	2	2	no	—
491	C₂²×C₆₇	—	2	4	no	—
492	C₂²×C₆₇	—	2	2	no	—
493	C₂²×C₆₇	—	2	2	no	—
494	C₂²×C₆₇	—	2	2	no	—
495	C₂²×C₆₇	—	2	4	no	—
496	C₂²×C₆₇	—	2	2	no	—
497	C₂²×C₆₇	—	2	2	no	—
498	C₂²×C₆₇	—	2	4	no	—
499	C₂²×C₆₇	—	4	2	no	—
500	C₂²×C₆₇	—	4	1	no	—
501	C₂²×C₆₇	—	4	1	no	—
502	C₂²×C₆₇	—	4	2	no	—
503	C₂²×C₆₇	—	4	1	no	—
504	C₂²×C₆₇	—	4	1	no	—
505	C₂²×C₆₇	—	4	2	no	—
506	C₂²×C₆₇	—	4	1	no	—
507	C₂²×C₆₇	—	4	1	no	—
508	C₂²×C₆₇	—	4	1	no	—
509	C₂²×C₆₇	—	4	2	no	—
510	C₂²×C₆₇	—	4	1	no	—
511	C₂²×C₆₇	—	4	2	no	—
512	C₂²×C₆₇	—	4	2	no	—
513	C₂²×C₆₇	—	4	2	no	—
514	C₂²×C₆₇	—	4	2	no	—
515	C₂²×C₆₇	—	4	2	no	—
516	C₂²×C₆₇	—	4	2	no	—
517	C₂²×C₆₇	—	4	2	no	—
518	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
519	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
520	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
521	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
522	C₂²×C₆₇	#585	1	1	yes	characteristic
523	C₂²×C₆₇	#585	1	1	yes	characteristic
524	C₂²×C₆₇	#585	1	1	yes	characteristic
525	C₄×C₆₇	—	2	2	no	—
526	C₄×C₆₇	—	2	4	no	—
527	C₄×C₆₇	—	2	2	no	—
528	C₄×C₆₇	—	2	2	no	—
529	C₄×C₆₇	—	2	2	no	—
530	C₄×C₆₇	—	2	2	no	—
531	C₄×C₆₇	—	4	2	no	—
532	C₄×C₆₇	—	4	2	no	—
533	C₄×C₆₇	—	4	2	no	—
534	C₄×C₆₇	—	4	1	no	—
535	C₄×C₆₇	—	4	1	no	—
536	C₄×C₆₇	—	4	2	no	—
537	C₄×C₆₇	—	4	2	no	—
538	C₄×C₆₇	—	4	1	no	—
539	C₄×C₆₇	—	4	1	no	—
540	C₄×C₆₇	—	4	1	no	—
541	C₄×C₆₇	—	4	1	no	—
542	C₄×C₆₇	—	4	1	no	—
543	C₄×C₆₇	#553	1	4	yes	complemented
544	#59392	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
545	C₂×C₆₇	—	4	2	no	—
546	C₂×C₆₇	—	4	4	no	—
547	C₂×C₆₇	—	4	2	no	—
548	C₂×C₆₇	—	8	2	no	—
549	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
550	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
551	C₂×C₆₇	C₂×#553	1	1	yes	characteristic
552	C₂×C₆₇	#3496	1	1	yes	characteristic
553	C₂×C₆₇	#3521	1	1	yes	characteristic
554	C₂×C₆₇	#3524	1	1	yes	characteristic
555	C₂×C₆₇	#3539	1	1	yes	characteristic
556	C₂×#553	C₂×C₆₇	1	2	yes	complemented
557	#2691	C₂×C₆₇	1	2	yes	complemented
558	#2688	C₂×C₆₇	1	2	yes	complemented
559	#2600	C₂×C₆₇	1	2	yes	complemented
560	#2537	C₂×C₆₇	1	1	yes	characteristic, complemented
561	#2512	C₂×C₆₇	1	1	yes	characteristic, complemented
562	#2506	C₂×C₆₇	1	1	yes	characteristic, complemented
563	#2496	C₂×C₆₇	1	1	yes	characteristic, complemented
564	#2481	C₂×C₆₇	1	2	yes	complemented
565	#2476	C₂×C₆₇	1	2	yes	complemented
566	#2460	C₂×C₆₇	1	2	yes	complemented
567	#2457	C₂×C₆₇	1	2	yes	complemented
568	#2428	C₂×C₆₇	1	1	yes	characteristic, complemented
569	#2428	C₂×C₆₇	1	1	yes	characteristic, complemented
570	#2422	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#2416	C₂×C₆₇	1	1	yes	characteristic, complemented
572	#2366	C₂×C₆₇	1	1	yes	characteristic, complemented
573	#2361	C₂×C₆₇	1	1	yes	characteristic, complemented
574	D₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
575	#2344	C₂×C₆₇	1	1	yes	characteristic, complemented
576	C₄×#123	C₂×C₆₇	1	1	yes	characteristic, complemented
577	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
578	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
579	C₆₇	#59392	1	1	yes	characteristic, direct product factor, Sylow
580	#553	—	2	16	no	—
581	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
582	C₂×#126	C₂²×C₆₇	1	2	yes	—
583	C₂×#126	C₂²×C₆₇	1	2	yes	—
584	C₂×#125	C₂²×C₆₇	1	2	yes	—
585	C₂×#123	C₂²×C₆₇	1	2	yes	—
586	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
587	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
588	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
589	C₂×#121	C₂²×C₆₇	1	2	yes	—
590	C₂×#121	C₂²×C₆₇	1	2	yes	—
591	C₂×#121	C₂²×C₆₇	1	2	yes	—
592	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
593	C₂×#121	C₂²×C₆₇	1	2	yes	—
594	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
595	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
596	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
597	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
598	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
599	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
600	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
601	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
602	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
603	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
604	C₂×#117	C₂²×C₆₇	1	2	yes	—
605	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
606	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
607	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
608	#400	C₂²×C₆₇	1	2	yes	—
609	#400	C₂²×C₆₇	1	2	yes	—
610	#398	C₂²×C₆₇	1	2	yes	—
611	#397	C₂²×C₆₇	1	2	yes	—
612	#397	C₂²×C₆₇	1	2	yes	—
613	#397	C₂²×C₆₇	1	2	yes	—
614	#396	C₂²×C₆₇	1	2	yes	—
615	#396	C₂²×C₆₇	1	2	yes	—
616	#394	C₂²×C₆₇	1	2	yes	—
617	#394	C₂²×C₆₇	1	2	yes	—
618	#394	C₂²×C₆₇	1	2	yes	—
619	#394	C₂²×C₆₇	1	2	yes	—
620	#394	C₂²×C₆₇	1	2	yes	—
621	#394	C₂²×C₆₇	1	2	yes	—
622	#392	C₂²×C₆₇	1	2	yes	—
623	#392	C₂²×C₆₇	1	2	yes	—
624	#390	C₂²×C₆₇	1	1	yes	characteristic
625	#390	C₂²×C₆₇	1	1	yes	characteristic
626	#390	C₂²×C₆₇	1	2	yes	—
627	#390	C₂²×C₆₇	1	1	yes	characteristic
628	#390	C₂²×C₆₇	1	1	yes	characteristic
629	#389	C₂²×C₆₇	1	1	yes	characteristic
630	#389	C₂²×C₆₇	1	1	yes	characteristic
631	#389	C₂²×C₆₇	1	1	yes	characteristic
632	#389	C₂²×C₆₇	1	1	yes	characteristic
633	#389	C₂²×C₆₇	1	1	yes	characteristic
634	#389	C₂²×C₆₇	1	1	yes	characteristic
635	#388	C₂²×C₆₇	1	2	yes	—
636	#388	C₂²×C₆₇	1	2	yes	—
637	#388	C₂²×C₆₇	1	1	yes	characteristic
638	#388	C₂²×C₆₇	1	2	yes	—
639	#388	C₂²×C₆₇	1	1	yes	characteristic
640	#388	C₂²×C₆₇	1	2	yes	—
641	#387	C₂²×C₆₇	1	2	yes	—
642	#387	C₂²×C₆₇	1	2	yes	—
643	#387	C₂²×C₆₇	1	2	yes	—
644	#387	C₂²×C₆₇	1	1	yes	characteristic
645	#387	C₂²×C₆₇	1	2	yes	—
646	#387	C₂²×C₆₇	1	1	yes	characteristic
647	#386	C₂²×C₆₇	1	2	yes	—
648	#386	C₂²×C₆₇	1	2	yes	—
649	#386	C₂²×C₆₇	1	2	yes	—
650	#386	C₂²×C₆₇	1	2	yes	—
651	#386	C₂²×C₆₇	1	2	yes	—
652	#386	C₂²×C₆₇	1	2	yes	—
653	#386	C₂²×C₆₇	1	1	yes	characteristic
654	#386	C₂²×C₆₇	1	2	yes	—
655	#386	C₂²×C₆₇	1	2	yes	—
656	#385	C₂²×C₆₇	1	2	yes	—
657	#385	C₂²×C₆₇	1	2	yes	—
658	#385	C₂²×C₆₇	1	2	yes	—
659	#385	C₂²×C₆₇	1	2	yes	—
660	#385	C₂²×C₆₇	1	1	yes	characteristic
661	#384	C₂²×C₆₇	1	1	yes	characteristic
662	#384	C₂²×C₆₇	1	1	yes	characteristic
663	#381	C₂²×C₆₇	1	2	yes	—
664	#381	C₂²×C₆₇	1	1	yes	characteristic
665	#380	C₂²×C₆₇	1	1	yes	characteristic
666	#380	C₂²×C₆₇	1	2	yes	—
667	#380	C₂²×C₆₇	1	1	yes	characteristic
668	#380	C₂²×C₆₇	1	2	yes	—
669	#380	C₂²×C₆₇	1	1	yes	characteristic
670	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
671	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
672	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
673	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
674	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
675	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
676	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
677	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
678	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
679	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
680	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
681	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
682	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
683	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
684	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
685	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
686	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
687	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
688	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
689	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
690	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
691	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
692	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
693	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
694	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
695	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
696	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
697	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
698	#127	—	2	4	no	—
699	#126	—	2	8	no	—
700	#126	—	2	8	no	—
701	#125	—	2	8	no	—
702	#123	—	2	8	no	—
703	#123	D₄×C₆₇	1	8	yes	complemented
704	#121	—	2	8	no	—
705	#121	—	2	8	no	—
706	#121	—	2	4	no	—
707	#121	—	2	4	no	—
708	#121	—	2	4	no	—
709	#121	—	2	8	no	—
710	#121	—	2	8	no	—
711	#121	—	4	2	no	—
712	C₄×D₄	—	2	8	no	—
713	C₄×D₄	—	2	8	no	—
714	C₄×D₄	—	2	8	no	—
715	C₄×D₄	—	2	4	no	—
716	C₄×D₄	—	2	8	no	—
717	C₄×D₄	—	4	2	no	—
718	C₄×D₄	—	4	2	no	—
719	C₄×D₄	—	4	2	no	—
720	C₄×D₄	—	4	2	no	—
721	#117	—	2	8	no	—
722	C₂×C₄⋊C₄	—	2	8	no	—
723	C₂×C₄⋊C₄	—	2	4	no	—
724	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
731	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
734	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
735	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
764	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
765	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
771	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
772	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
773	C₂×C₄²	—	4	2	no	—
774	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
775	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
776	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
777	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
778	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
779	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
780	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
781	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
782	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
783	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
784	#95	C₂³×C₆₇	1	2	yes	—
785	#95	C₂³×C₆₇	1	2	yes	—
786	#95	C₂³×C₆₇	1	2	yes	—
787	#95	C₂³×C₆₇	1	1	yes	characteristic
788	#95	C₂³×C₆₇	1	1	yes	characteristic
789	#95	C₂³×C₆₇	1	1	yes	characteristic
790	#95	C₂³×C₆₇	1	1	yes	characteristic
791	#95	C₂³×C₆₇	1	1	yes	characteristic
792	#95	C₂³×C₆₇	1	2	yes	—
793	#95	C₂³×C₆₇	1	1	yes	characteristic
794	#95	C₂³×C₆₇	1	1	yes	characteristic
795	#95	C₂³×C₆₇	1	1	yes	characteristic
796	#95	C₂³×C₆₇	1	2	yes	—
797	#95	C₂³×C₆₇	1	2	yes	—
798	#95	C₂³×C₆₇	1	1	yes	characteristic
799	#95	C₂³×C₆₇	1	2	yes	—
800	#95	C₂³×C₆₇	1	1	yes	characteristic
801	#95	C₂³×C₆₇	1	2	yes	—
802	#95	C₂³×C₆₇	1	2	yes	—
803	#95	C₂³×C₆₇	1	2	yes	—
804	#95	C₂³×C₆₇	1	2	yes	—
805	#95	C₂³×C₆₇	1	2	yes	—
806	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
807	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
808	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
809	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
810	C₂×D₄	—	2	4	no	—
811	C₂×D₄	—	2	4	no	—
812	C₂×D₄	—	2	4	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	2	4	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	4	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	4	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	4	1	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	—	4	1	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	—	4	2	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
836	C₂×D₄	#41×C₆₇	1	4	yes	—
837	C₂²×C₄	—	2	4	no	—
838	C₂²×C₄	—	2	4	no	—
839	C₂²×C₄	—	2	4	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	4	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	4	no	—
848	C₂²×C₄	—	2	4	no	—
849	C₂²×C₄	—	2	4	no	—
850	C₂²×C₄	—	4	1	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	4	1	no	—
854	C₂²×C₄	—	4	2	no	—
855	C₂²×C₄	—	4	1	no	—
856	C₂²×C₄	—	4	1	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
864	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
871	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
882	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
883	C₄⋊C₄	—	2	4	no	—
884	C₄⋊C₄	—	2	4	no	—
885	C₄⋊C₄	—	2	4	no	—
886	C₄⋊C₄	—	2	4	no	—
887	C₄⋊C₄	—	2	4	no	—
888	C₄⋊C₄	—	2	4	no	—
889	C₄⋊C₄	—	2	4	no	—
890	C₄⋊C₄	—	2	4	no	—
891	C₄⋊C₄	—	2	4	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	4	1	no	—
898	C₄⋊C₄	—	4	1	no	—
899	C₄⋊C₄	—	4	1	no	—
900	C₄⋊C₄	—	4	2	no	—
901	C₄⋊C₄	—	4	2	no	—
902	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
903	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
904	C₄⋊C₄	#41×C₆₇	1	4	yes	—
905	C₂²⋊C₄	—	2	4	no	—
906	C₂²⋊C₄	—	2	4	no	—
907	C₂²⋊C₄	—	2	4	no	—
908	C₂²⋊C₄	—	2	4	no	—
909	C₂²⋊C₄	—	2	4	no	—
910	C₂²⋊C₄	—	2	4	no	—
911	C₂²⋊C₄	—	2	4	no	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	1	no	—
919	C₂²⋊C₄	—	4	1	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	2	no	—
922	C₂²⋊C₄	—	4	1	no	—
923	C₂²⋊C₄	—	4	2	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	2	no	—
927	C₂²⋊C₄	—	4	1	no	—
928	C₂²⋊C₄	—	4	1	no	—
929	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
930	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
931	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
932	C₄²	—	2	4	no	—
933	C₄²	—	2	4	no	—
934	C₄²	—	2	4	no	—
935	C₄²	—	2	2	no	—
936	C₄²	—	2	2	no	—
937	C₄²	—	2	2	no	—
938	C₄²	—	2	2	no	—
939	C₄²	—	2	2	no	—
940	C₄²	—	4	1	no	—
941	C₄²	—	4	1	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	2	no	—
964	C₂³	—	2	2	no	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
968	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
969	C₂³	C₂×#41×C₆₇	1	4	yes	—
970	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
971	D₄	—	2	8	no	—
972	D₄	—	4	4	no	—
973	D₄	—	4	8	no	—
974	D₄	—	4	8	no	—
975	D₄	—	4	8	no	—
976	D₄	—	4	8	no	—
977	D₄	—	4	4	no	—
978	D₄	—	8	4	no	—
979	D₄	—	8	4	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	4	4	no	—
1029	C₂×C₄	—	4	8	no	—
1030	C₂×C₄	—	4	8	no	—
1031	C₂×C₄	—	4	4	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	—	8	4	no	—
1035	C₂×C₄	—	8	4	no	—
1036	C₂×C₄	—	8	4	no	—
1037	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1039	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1040	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1041	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1042	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
1043	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1044	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1045	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1046	C₂²	—	2	4	no	—
1047	C₂²	—	2	2	no	—
1048	C₂²	—	2	4	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	4	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1075	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1076	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1077	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1078	C₂²	#585×C₆₇	1	1	yes	characteristic
1079	C₂²	#585×C₆₇	1	1	yes	characteristic
1080	C₂²	#585×C₆₇	1	1	yes	characteristic
1081	C₄	—	2	2	no	—
1082	C₄	—	2	4	no	—
1083	C₄	—	2	2	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	2	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	2	no	—
1099	C₄	#553×C₆₇	1	4	yes	complemented
1100	C₂	—	4	4	no	—
1101	C₂	—	4	2	no	—
1102	C₂	—	4	2	no	—
1103	C₂	—	8	2	no	—
1104	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1105	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1106	C₂	C₂×#553×C₆₇	1	1	yes	characteristic
1107	C₂	C₆₇×#3496	1	1	yes	characteristic
1108	C₂	C₆₇×#3521	1	1	yes	characteristic
1109	C₂	C₆₇×#3524	1	1	yes	characteristic
1110	C₂	C₆₇×#3539	1	1	yes	characteristic

	subgroup	G/H
center, socle	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
1. C₂×#553×C₆₇	C₂	semidirect
2. C₆₇×#2691	C₂	semidirect
3. C₆₇×#2688	C₂	semidirect
4. C₆₇×#2600	C₂	semidirect
5. C₆₇×#2537	C₂	semidirect
6. C₆₇×#2512	C₂	semidirect
7. C₆₇×#2506	C₂	semidirect
8. C₆₇×#2496	C₂	semidirect
9. C₆₇×#2481	C₂	semidirect
10. C₆₇×#2476	C₂	semidirect
11. C₆₇×#2460	C₂	semidirect
12. C₆₇×#2457	C₂	semidirect
13. C₆₇×#2428	C₂	semidirect
14. C₆₇×#2428	C₂	semidirect
15. C₆₇×#2422	C₂	semidirect
16. C₆₇×#2416	C₂	semidirect
17. C₆₇×#2366	C₂	semidirect
18. C₆₇×#2361	C₂	semidirect
19. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
20. C₆₇×#2344	C₂	semidirect
21. C₄×#123×C₆₇	C₂	semidirect
22. C₄×#121×C₆₇	C₂	semidirect
23. C₄×#121×C₆₇	C₂	semidirect
147. #123×C₆₇	D₄	semidirect
543. C₄×C₆₇	#553	semidirect
544. #59392	C₆₇	direct (N × H)
556. C₂×#553	C₂×C₆₇	semidirect
557. #2691	C₂×C₆₇	semidirect
558. #2688	C₂×C₆₇	semidirect
559. #2600	C₂×C₆₇	semidirect
560. #2537	C₂×C₆₇	semidirect
561. #2512	C₂×C₆₇	semidirect
562. #2506	C₂×C₆₇	semidirect
563. #2496	C₂×C₆₇	semidirect
564. #2481	C₂×C₆₇	semidirect
565. #2476	C₂×C₆₇	semidirect
566. #2460	C₂×C₆₇	semidirect
567. #2457	C₂×C₆₇	semidirect
568. #2428	C₂×C₆₇	semidirect
569. #2428	C₂×C₆₇	semidirect
570. #2422	C₂×C₆₇	semidirect
571. #2416	C₂×C₆₇	semidirect
572. #2366	C₂×C₆₇	semidirect
573. #2361	C₂×C₆₇	semidirect
574. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
575. #2344	C₂×C₆₇	semidirect
576. C₄×#123	C₂×C₆₇	semidirect
577. C₄×#121	C₂×C₆₇	semidirect
578. C₄×#121	C₂×C₆₇	semidirect
579. C₆₇	#59392	direct (N × H)
703. #123	D₄×C₆₇	semidirect
1099. C₄	#553×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₆₇	2
C₆₇×#2691	2
C₆₇×#2688	2
C₆₇×#2600	2
C₆₇×#2537	2
C₆₇×#2512	2
C₆₇×#2506	2
C₆₇×#2496	2
C₆₇×#2481	2
C₆₇×#2476	2
C₆₇×#2460	2
C₆₇×#2457	2
C₆₇×#2428	2
C₆₇×#2422	2
C₆₇×#2416	2
C₆₇×#2366	2
C₆₇×#2361	2
D₄×C₄⋊C₄×C₆₇	2
C₆₇×#2344	2
C₄×#123×C₆₇	2
C₄×#121×C₆₇	2
#59392	67

Subgroups — C67×#59392 #30738643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59392 #30738643