Subgroups — C₆₇×#59586 #30738837

Order 17152.

2194 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#552×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2696	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2690	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2581	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2560	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2535	C₂	1	1	yes	maximal, characteristic
8	C₆₇×#2492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2489	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2489	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2481	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2477	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2461	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2442	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2439	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2427	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2427	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2363	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2352	C₂	1	2	yes	maximal, complemented
21	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	#554×C₆₇	—	2	8	no	—
25	#552×C₆₇	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#126×C₆₇	C₂²	1	2	yes	—
28	C₂×#125×C₆₇	C₂²	1	2	yes	—
29	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#123×C₆₇	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
39	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
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	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
50	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
51	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
52	#400×C₆₇	C₂²	1	2	yes	—
53	#400×C₆₇	C₂²	1	2	yes	—
54	#400×C₆₇	C₂²	1	2	yes	—
55	#400×C₆₇	C₂²	1	2	yes	—
56	#398×C₆₇	C₂²	1	2	yes	—
57	#397×C₆₇	C₂²	1	2	yes	—
58	#397×C₆₇	C₂²	1	2	yes	—
59	#397×C₆₇	C₂²	1	2	yes	—
60	#397×C₆₇	C₂²	1	2	yes	—
61	#396×C₆₇	C₂²	1	2	yes	—
62	#395×C₆₇	C₂²	1	2	yes	—
63	#394×C₆₇	C₂²	1	2	yes	—
64	#394×C₆₇	C₂²	1	2	yes	—
65	#393×C₆₇	C₂²	1	2	yes	—
66	#393×C₆₇	C₂²	1	2	yes	—
67	#392×C₆₇	C₂²	1	2	yes	—
68	#391×C₆₇	C₂²	1	1	yes	characteristic
69	#391×C₆₇	C₂²	1	1	yes	characteristic
70	#391×C₆₇	C₂²	1	2	yes	—
71	#391×C₆₇	C₂²	1	1	yes	characteristic
72	#391×C₆₇	C₂²	1	1	yes	characteristic
73	#391×C₆₇	C₂²	1	2	yes	—
74	#390×C₆₇	C₂²	1	1	yes	characteristic
75	#390×C₆₇	C₂²	1	1	yes	characteristic
76	#390×C₆₇	C₂²	1	2	yes	—
77	#389×C₆₇	C₂²	1	1	yes	characteristic
78	#389×C₆₇	C₂²	1	1	yes	characteristic
79	#389×C₆₇	C₂²	1	1	yes	characteristic
80	#389×C₆₇	C₂²	1	1	yes	characteristic
81	#388×C₆₇	C₂²	1	1	yes	characteristic
82	#388×C₆₇	C₂²	1	1	yes	characteristic
83	#388×C₆₇	C₂²	1	2	yes	—
84	#388×C₆₇	C₂²	1	2	yes	—
85	#388×C₆₇	C₂²	1	1	yes	characteristic
86	#388×C₆₇	C₂²	1	1	yes	characteristic
87	#388×C₆₇	C₂²	1	2	yes	—
88	#388×C₆₇	C₂²	1	2	yes	—
89	#388×C₆₇	C₂²	1	2	yes	—
90	#388×C₆₇	C₂²	1	2	yes	—
91	#387×C₆₇	C₂²	1	2	yes	—
92	#387×C₆₇	C₂²	1	2	yes	—
93	#387×C₆₇	C₂²	1	2	yes	—
94	#387×C₆₇	C₂²	1	2	yes	—
95	#387×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	#386×C₆₇	C₂²	1	2	yes	—
101	#386×C₆₇	C₂²	1	2	yes	—
102	#385×C₆₇	C₂²	1	2	yes	—
103	#385×C₆₇	C₂²	1	2	yes	—
104	#382×C₆₇	C₂²	1	1	yes	characteristic
105	#382×C₆₇	C₂²	1	1	yes	characteristic
106	#382×C₆₇	C₂²	1	1	yes	characteristic
107	#382×C₆₇	C₂²	1	2	yes	—
108	#380×C₆₇	C₂²	1	1	yes	characteristic
109	#380×C₆₇	C₂²	1	1	yes	characteristic
110	#380×C₆₇	C₂²	1	2	yes	—
111	#380×C₆₇	C₂²	1	2	yes	—
112	#380×C₆₇	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
123	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
124	C₄³×C₆₇	C₂²	1	1	yes	characteristic
125	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×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	1	yes	characteristic
131	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
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	C₄⋊Q₈×C₆₇	—	2	4	no	—
139	#126×C₆₇	—	2	8	no	—
140	#125×C₆₇	—	2	8	no	—
141	#125×C₆₇	—	2	4	no	—
142	#125×C₆₇	D₄	1	8	yes	complemented
143	#124×C₆₇	—	2	4	no	—
144	#124×C₆₇	—	2	4	no	—
145	#123×C₆₇	—	2	8	no	—
146	C₂²⋊Q₈×C₆₇	—	2	4	no	—
147	C₂²⋊Q₈×C₆₇	—	2	4	no	—
148	C₂²⋊Q₈×C₆₇	—	2	8	no	—
149	C₂²⋊Q₈×C₆₇	—	2	8	no	—
150	C₂²⋊Q₈×C₆₇	—	2	8	no	—
151	#121×C₆₇	—	2	4	no	—
152	#121×C₆₇	—	2	4	no	—
153	C₄×Q₈×C₆₇	—	2	4	no	—
154	C₄×Q₈×C₆₇	—	2	4	no	—
155	C₄×D₄×C₆₇	—	2	4	no	—
156	C₄×D₄×C₆₇	—	2	4	no	—
157	C₄×D₄×C₆₇	—	2	8	no	—
158	C₄×D₄×C₆₇	—	2	4	no	—
159	C₄×D₄×C₆₇	—	2	4	no	—
160	#117×C₆₇	—	2	4	no	—
161	#117×C₆₇	—	2	8	no	—
162	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
163	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
212	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
213	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
216	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
223	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
224	#95×C₆₇	C₂³	1	1	yes	characteristic
225	#95×C₆₇	C₂³	1	1	yes	characteristic
226	#95×C₆₇	C₂³	1	1	yes	characteristic
227	#95×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
236	#95×C₆₇	C₂³	1	1	yes	characteristic
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	2	yes	—
239	#95×C₆₇	C₂³	1	2	yes	—
240	#95×C₆₇	C₂³	1	2	yes	—
241	#95×C₆₇	C₂³	1	2	yes	—
242	#95×C₆₇	C₂³	1	2	yes	—
243	#95×C₆₇	C₂³	1	2	yes	—
244	#95×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
251	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
252	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂×Q₈×C₆₇	—	2	2	no	—
254	C₂×Q₈×C₆₇	—	2	2	no	—
255	C₂×Q₈×C₆₇	—	2	4	no	—
256	C₂×Q₈×C₆₇	—	2	2	no	—
257	C₂×Q₈×C₆₇	—	2	2	no	—
258	C₂×Q₈×C₆₇	—	2	2	no	—
259	C₂×Q₈×C₆₇	—	4	1	no	—
260	C₂×Q₈×C₆₇	—	4	2	no	—
261	C₂×Q₈×C₆₇	—	4	2	no	—
262	C₂×D₄×C₆₇	—	2	4	no	—
263	C₂×D₄×C₆₇	—	2	4	no	—
264	C₂×D₄×C₆₇	—	2	2	no	—
265	C₂×D₄×C₆₇	—	2	4	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	2	no	—
272	C₂×D₄×C₆₇	—	4	2	no	—
273	C₂×D₄×C₆₇	#41	1	4	yes	—
274	C₂²×C₄×C₆₇	—	2	4	no	—
275	C₂²×C₄×C₆₇	—	2	4	no	—
276	C₂²×C₄×C₆₇	—	2	4	no	—
277	C₂²×C₄×C₆₇	—	2	2	no	—
278	C₂²×C₄×C₆₇	—	2	2	no	—
279	C₂²×C₄×C₆₇	—	2	4	no	—
280	C₂²×C₄×C₆₇	—	2	2	no	—
281	C₂²×C₄×C₆₇	—	2	2	no	—
282	C₂²×C₄×C₆₇	—	2	2	no	—
283	C₂²×C₄×C₆₇	—	2	2	no	—
284	C₂²×C₄×C₆₇	—	2	4	no	—
285	C₂²×C₄×C₆₇	—	2	4	no	—
286	C₂²×C₄×C₆₇	—	4	2	no	—
287	C₂²×C₄×C₆₇	—	4	2	no	—
288	C₂²×C₄×C₆₇	—	4	2	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	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₆₇	C₂⁴	1	2	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	C₄⋊C₄×C₆₇	—	2	2	no	—
313	C₄⋊C₄×C₆₇	—	2	2	no	—
314	C₄⋊C₄×C₆₇	—	2	4	no	—
315	C₄⋊C₄×C₆₇	—	2	4	no	—
316	C₄⋊C₄×C₆₇	—	2	4	no	—
317	C₄⋊C₄×C₆₇	—	2	4	no	—
318	C₄⋊C₄×C₆₇	—	2	2	no	—
319	C₄⋊C₄×C₆₇	—	2	2	no	—
320	C₄⋊C₄×C₆₇	—	2	2	no	—
321	C₄⋊C₄×C₆₇	—	2	2	no	—
322	C₄⋊C₄×C₆₇	—	2	4	no	—
323	C₄⋊C₄×C₆₇	—	2	4	no	—
324	C₄⋊C₄×C₆₇	—	2	4	no	—
325	C₄⋊C₄×C₆₇	—	2	4	no	—
326	C₄⋊C₄×C₆₇	—	2	2	no	—
327	C₄⋊C₄×C₆₇	—	2	2	no	—
328	C₄⋊C₄×C₆₇	—	4	2	no	—
329	C₄⋊C₄×C₆₇	—	4	2	no	—
330	C₄⋊C₄×C₆₇	—	4	2	no	—
331	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
332	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
333	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
334	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
335	C₂²⋊C₄×C₆₇	—	2	4	no	—
336	C₂²⋊C₄×C₆₇	—	2	4	no	—
337	C₂²⋊C₄×C₆₇	—	2	4	no	—
338	C₂²⋊C₄×C₆₇	—	2	4	no	—
339	C₂²⋊C₄×C₆₇	—	2	2	no	—
340	C₂²⋊C₄×C₆₇	—	2	2	no	—
341	C₂²⋊C₄×C₆₇	—	2	4	no	—
342	C₂²⋊C₄×C₆₇	—	2	4	no	—
343	C₂²⋊C₄×C₆₇	—	2	4	no	—
344	C₂²⋊C₄×C₆₇	—	2	4	no	—
345	C₂²⋊C₄×C₆₇	—	2	4	no	—
346	C₂²⋊C₄×C₆₇	—	2	2	no	—
347	C₂²⋊C₄×C₆₇	—	2	4	no	—
348	C₂²⋊C₄×C₆₇	—	2	4	no	—
349	C₂²⋊C₄×C₆₇	—	2	2	no	—
350	C₂²⋊C₄×C₆₇	—	2	2	no	—
351	C₂²⋊C₄×C₆₇	—	4	2	no	—
352	C₂²⋊C₄×C₆₇	—	4	1	no	—
353	C₂²⋊C₄×C₆₇	—	4	1	no	—
354	C₂²⋊C₄×C₆₇	—	4	1	no	—
355	C₂²⋊C₄×C₆₇	—	4	1	no	—
356	C₂²⋊C₄×C₆₇	—	4	2	no	—
357	C₂²⋊C₄×C₆₇	—	4	2	no	—
358	C₂²⋊C₄×C₆₇	#41	1	4	yes	—
359	C₄²×C₆₇	—	2	4	no	—
360	C₄²×C₆₇	—	2	4	no	—
361	C₄²×C₆₇	—	2	2	no	—
362	C₄²×C₆₇	—	2	2	no	—
363	C₄²×C₆₇	—	2	4	no	—
364	C₄²×C₆₇	—	2	2	no	—
365	C₄²×C₆₇	—	2	2	no	—
366	C₄²×C₆₇	—	2	2	no	—
367	C₄²×C₆₇	—	4	1	no	—
368	C₄²×C₆₇	—	4	2	no	—
369	C₄²×C₆₇	—	4	1	no	—
370	C₄²×C₆₇	—	4	1	no	—
371	C₄²×C₆₇	C₂×D₄	1	4	yes	—
372	C₂³×C₆₇	—	2	2	no	—
373	C₂³×C₆₇	—	2	1	no	—
374	C₂³×C₆₇	—	2	2	no	—
375	C₂³×C₆₇	—	2	1	no	—
376	C₂³×C₆₇	—	2	1	no	—
377	C₂³×C₆₇	—	2	2	no	—
378	C₂³×C₆₇	—	2	1	no	—
379	C₂³×C₆₇	—	2	2	no	—
380	C₂³×C₆₇	—	2	1	no	—
381	C₂³×C₆₇	—	2	1	no	—
382	C₂³×C₆₇	—	2	2	no	—
383	C₂³×C₆₇	—	2	2	no	—
384	C₂³×C₆₇	—	2	1	no	—
385	C₂³×C₆₇	—	2	1	no	—
386	C₂³×C₆₇	—	2	1	no	—
387	C₂³×C₆₇	—	2	1	no	—
388	C₂³×C₆₇	—	2	1	no	—
389	C₂³×C₆₇	—	2	1	no	—
390	C₂³×C₆₇	—	2	1	no	—
391	C₂³×C₆₇	C₂×#41	1	4	yes	—
392	C₂³×C₆₇	C₂×#41	1	2	yes	—
393	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
394	Q₈×C₆₇	—	4	4	no	—
395	Q₈×C₆₇	—	4	4	no	—
396	Q₈×C₆₇	—	8	4	no	—
397	D₄×C₆₇	—	2	8	no	—
398	D₄×C₆₇	—	4	4	no	—
399	D₄×C₆₇	—	4	8	no	—
400	D₄×C₆₇	—	8	4	no	—
401	C₂×C₄×C₆₇	—	2	1	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	1	no	—
404	C₂×C₄×C₆₇	—	2	1	no	—
405	C₂×C₄×C₆₇	—	2	1	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	1	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	2	1	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	2	no	—
412	C₂×C₄×C₆₇	—	2	1	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	2	2	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	1	no	—
417	C₂×C₄×C₆₇	—	2	1	no	—
418	C₂×C₄×C₆₇	—	2	1	no	—
419	C₂×C₄×C₆₇	—	2	1	no	—
420	C₂×C₄×C₆₇	—	2	2	no	—
421	C₂×C₄×C₆₇	—	2	1	no	—
422	C₂×C₄×C₆₇	—	2	1	no	—
423	C₂×C₄×C₆₇	—	2	1	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	2	no	—
428	C₂×C₄×C₆₇	—	2	1	no	—
429	C₂×C₄×C₆₇	—	2	2	no	—
430	C₂×C₄×C₆₇	—	2	2	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	1	no	—
433	C₂×C₄×C₆₇	—	2	1	no	—
434	C₂×C₄×C₆₇	—	2	1	no	—
435	C₂×C₄×C₆₇	—	2	2	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	1	no	—
438	C₂×C₄×C₆₇	—	2	1	no	—
439	C₂×C₄×C₆₇	—	2	2	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	2	no	—
443	C₂×C₄×C₆₇	—	2	2	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	1	no	—
449	C₂×C₄×C₆₇	—	2	1	no	—
450	C₂×C₄×C₆₇	—	2	2	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	4	8	no	—
453	C₂×C₄×C₆₇	—	4	8	no	—
454	C₂×C₄×C₆₇	—	4	4	no	—
455	C₂×C₄×C₆₇	—	4	4	no	—
456	C₂×C₄×C₆₇	—	8	4	no	—
457	C₂×C₄×C₆₇	—	8	4	no	—
458	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
460	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
462	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
464	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
465	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
466	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
467	C₂²×C₆₇	—	2	4	no	—
468	C₂²×C₆₇	—	2	2	no	—
469	C₂²×C₆₇	—	2	2	no	—
470	C₂²×C₆₇	—	2	4	no	—
471	C₂²×C₆₇	—	2	2	no	—
472	C₂²×C₆₇	—	2	4	no	—
473	C₂²×C₆₇	—	4	1	no	—
474	C₂²×C₆₇	—	4	2	no	—
475	C₂²×C₆₇	—	4	2	no	—
476	C₂²×C₆₇	—	4	1	no	—
477	C₂²×C₆₇	—	4	2	no	—
478	C₂²×C₆₇	—	4	1	no	—
479	C₂²×C₆₇	—	4	1	no	—
480	C₂²×C₆₇	—	4	2	no	—
481	C₂²×C₆₇	—	4	1	no	—
482	C₂²×C₆₇	—	4	1	no	—
483	C₂²×C₆₇	—	4	1	no	—
484	C₂²×C₆₇	—	4	1	no	—
485	C₂²×C₆₇	—	4	1	no	—
486	C₂²×C₆₇	—	4	1	no	—
487	C₂²×C₆₇	—	4	1	no	—
488	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
489	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
490	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
491	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
492	C₂²×C₆₇	#585	1	1	yes	characteristic
493	C₂²×C₆₇	#585	1	1	yes	characteristic
494	C₂²×C₆₇	#585	1	1	yes	characteristic
495	C₄×C₆₇	—	2	4	no	—
496	C₄×C₆₇	—	2	2	no	—
497	C₄×C₆₇	—	2	2	no	—
498	C₄×C₆₇	—	2	2	no	—
499	C₄×C₆₇	—	2	4	no	—
500	C₄×C₆₇	—	2	2	no	—
501	C₄×C₆₇	—	4	1	no	—
502	C₄×C₆₇	—	4	1	no	—
503	C₄×C₆₇	—	4	2	no	—
504	C₄×C₆₇	—	4	2	no	—
505	C₄×C₆₇	—	4	1	no	—
506	C₄×C₆₇	—	4	1	no	—
507	C₄×C₆₇	—	4	2	no	—
508	C₄×C₆₇	—	4	1	no	—
509	C₄×C₆₇	—	4	2	no	—
510	C₄×C₆₇	—	4	1	no	—
511	C₄×C₆₇	—	4	1	no	—
512	C₄×C₆₇	—	4	2	no	—
513	C₄×C₆₇	—	4	1	no	—
514	C₄×C₆₇	#548	1	4	yes	—
515	#59586	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
516	C₂×C₆₇	—	4	4	no	—
517	C₂×C₆₇	—	4	2	no	—
518	C₂×C₆₇	—	8	1	no	—
519	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
520	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
521	C₂×C₆₇	#3475	1	1	yes	characteristic
522	C₂×C₆₇	#3500	1	1	yes	characteristic
523	C₂×C₆₇	#3515	1	1	yes	characteristic
524	C₂×C₆₇	#3521	1	1	yes	characteristic
525	C₂×C₆₇	#3565	1	1	yes	characteristic
526	C₂×#554	C₂×C₆₇	1	1	yes	characteristic, complemented
527	C₂×#552	C₂×C₆₇	1	1	yes	characteristic, complemented
528	#2696	C₂×C₆₇	1	2	yes	complemented
529	#2690	C₂×C₆₇	1	2	yes	complemented
530	#2581	C₂×C₆₇	1	1	yes	characteristic, complemented
531	#2560	C₂×C₆₇	1	2	yes	complemented
532	#2535	C₂×C₆₇	1	1	yes	characteristic
533	#2492	C₂×C₆₇	1	1	yes	characteristic, complemented
534	#2489	C₂×C₆₇	1	1	yes	characteristic, complemented
535	#2489	C₂×C₆₇	1	2	yes	complemented
536	#2481	C₂×C₆₇	1	2	yes	complemented
537	#2477	C₂×C₆₇	1	2	yes	complemented
538	#2461	C₂×C₆₇	1	2	yes	complemented
539	#2442	C₂×C₆₇	1	1	yes	characteristic, complemented
540	#2439	C₂×C₆₇	1	1	yes	characteristic, complemented
541	#2427	C₂×C₆₇	1	1	yes	characteristic, complemented
542	#2427	C₂×C₆₇	1	1	yes	characteristic, complemented
543	#2363	C₂×C₆₇	1	1	yes	characteristic, complemented
544	#2361	C₂×C₆₇	1	1	yes	characteristic, complemented
545	#2352	C₂×C₆₇	1	2	yes	complemented
546	C₄×#125	C₂×C₆₇	1	1	yes	characteristic, complemented
547	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
548	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
549	C₆₇	#59586	1	1	yes	characteristic, direct product factor, Sylow
550	#554	—	2	8	no	—
551	#552	—	2	8	no	—
552	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
553	C₂×#126	C₂²×C₆₇	1	2	yes	—
554	C₂×#125	C₂²×C₆₇	1	2	yes	—
555	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
556	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
557	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
558	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
559	C₂×#123	C₂²×C₆₇	1	2	yes	—
560	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
561	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
562	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
563	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
564	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
565	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
566	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
567	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
568	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
569	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
570	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
571	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
572	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
573	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
574	C₂×#117	C₂²×C₆₇	1	2	yes	—
575	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
576	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
577	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
578	#400	C₂²×C₆₇	1	2	yes	—
579	#400	C₂²×C₆₇	1	2	yes	—
580	#400	C₂²×C₆₇	1	2	yes	—
581	#400	C₂²×C₆₇	1	2	yes	—
582	#398	C₂²×C₆₇	1	2	yes	—
583	#397	C₂²×C₆₇	1	2	yes	—
584	#397	C₂²×C₆₇	1	2	yes	—
585	#397	C₂²×C₆₇	1	2	yes	—
586	#397	C₂²×C₆₇	1	2	yes	—
587	#396	C₂²×C₆₇	1	2	yes	—
588	#395	C₂²×C₆₇	1	2	yes	—
589	#394	C₂²×C₆₇	1	2	yes	—
590	#394	C₂²×C₆₇	1	2	yes	—
591	#393	C₂²×C₆₇	1	2	yes	—
592	#393	C₂²×C₆₇	1	2	yes	—
593	#392	C₂²×C₆₇	1	2	yes	—
594	#391	C₂²×C₆₇	1	2	yes	—
595	#391	C₂²×C₆₇	1	1	yes	characteristic
596	#391	C₂²×C₆₇	1	1	yes	characteristic
597	#391	C₂²×C₆₇	1	1	yes	characteristic
598	#391	C₂²×C₆₇	1	2	yes	—
599	#391	C₂²×C₆₇	1	1	yes	characteristic
600	#390	C₂²×C₆₇	1	2	yes	—
601	#390	C₂²×C₆₇	1	1	yes	characteristic
602	#390	C₂²×C₆₇	1	1	yes	characteristic
603	#389	C₂²×C₆₇	1	1	yes	characteristic
604	#389	C₂²×C₆₇	1	1	yes	characteristic
605	#389	C₂²×C₆₇	1	1	yes	characteristic
606	#389	C₂²×C₆₇	1	1	yes	characteristic
607	#388	C₂²×C₆₇	1	1	yes	characteristic
608	#388	C₂²×C₆₇	1	2	yes	—
609	#388	C₂²×C₆₇	1	2	yes	—
610	#388	C₂²×C₆₇	1	1	yes	characteristic
611	#388	C₂²×C₆₇	1	2	yes	—
612	#388	C₂²×C₆₇	1	2	yes	—
613	#388	C₂²×C₆₇	1	2	yes	—
614	#388	C₂²×C₆₇	1	2	yes	—
615	#388	C₂²×C₆₇	1	1	yes	characteristic
616	#388	C₂²×C₆₇	1	1	yes	characteristic
617	#387	C₂²×C₆₇	1	2	yes	—
618	#387	C₂²×C₆₇	1	2	yes	—
619	#387	C₂²×C₆₇	1	2	yes	—
620	#387	C₂²×C₆₇	1	2	yes	—
621	#387	C₂²×C₆₇	1	2	yes	—
622	#386	C₂²×C₆₇	1	2	yes	—
623	#386	C₂²×C₆₇	1	2	yes	—
624	#386	C₂²×C₆₇	1	2	yes	—
625	#386	C₂²×C₆₇	1	2	yes	—
626	#386	C₂²×C₆₇	1	2	yes	—
627	#386	C₂²×C₆₇	1	2	yes	—
628	#385	C₂²×C₆₇	1	2	yes	—
629	#385	C₂²×C₆₇	1	2	yes	—
630	#382	C₂²×C₆₇	1	1	yes	characteristic
631	#382	C₂²×C₆₇	1	2	yes	—
632	#382	C₂²×C₆₇	1	1	yes	characteristic
633	#382	C₂²×C₆₇	1	1	yes	characteristic
634	#380	C₂²×C₆₇	1	2	yes	—
635	#380	C₂²×C₆₇	1	2	yes	—
636	#380	C₂²×C₆₇	1	2	yes	—
637	#380	C₂²×C₆₇	1	1	yes	characteristic
638	#380	C₂²×C₆₇	1	1	yes	characteristic
639	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
640	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
641	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
642	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
643	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
644	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
645	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
646	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
647	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
648	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
649	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
650	C₄³	C₂²×C₆₇	1	1	yes	characteristic
651	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
652	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
653	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
654	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
655	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
656	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
657	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
658	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
659	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
660	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
661	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
662	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
663	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
664	C₄⋊Q₈	—	2	4	no	—
665	#126	—	2	8	no	—
666	#125	—	2	8	no	—
667	#125	—	2	4	no	—
668	#125	D₄×C₆₇	1	8	yes	complemented
669	#124	—	2	4	no	—
670	#124	—	2	4	no	—
671	#123	—	2	8	no	—
672	C₂²⋊Q₈	—	2	4	no	—
673	C₂²⋊Q₈	—	2	4	no	—
674	C₂²⋊Q₈	—	2	8	no	—
675	C₂²⋊Q₈	—	2	8	no	—
676	C₂²⋊Q₈	—	2	8	no	—
677	#121	—	2	4	no	—
678	#121	—	2	4	no	—
679	C₄×Q₈	—	2	4	no	—
680	C₄×Q₈	—	2	4	no	—
681	C₄×D₄	—	2	4	no	—
682	C₄×D₄	—	2	4	no	—
683	C₄×D₄	—	2	8	no	—
684	C₄×D₄	—	2	4	no	—
685	C₄×D₄	—	2	4	no	—
686	#117	—	2	4	no	—
687	#117	—	2	8	no	—
688	C₂×C₄⋊C₄	—	2	4	no	—
689	C₂×C₄⋊C₄	—	2	8	no	—
690	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
706	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
707	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
708	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
709	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
710	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
711	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
714	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
720	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
729	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
733	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
734	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
738	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
739	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
742	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
743	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
744	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
745	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
747	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
748	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
749	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
750	#95	C₂³×C₆₇	1	1	yes	characteristic
751	#95	C₂³×C₆₇	1	1	yes	characteristic
752	#95	C₂³×C₆₇	1	1	yes	characteristic
753	#95	C₂³×C₆₇	1	2	yes	—
754	#95	C₂³×C₆₇	1	2	yes	—
755	#95	C₂³×C₆₇	1	2	yes	—
756	#95	C₂³×C₆₇	1	2	yes	—
757	#95	C₂³×C₆₇	1	1	yes	characteristic
758	#95	C₂³×C₆₇	1	1	yes	characteristic
759	#95	C₂³×C₆₇	1	1	yes	characteristic
760	#95	C₂³×C₆₇	1	1	yes	characteristic
761	#95	C₂³×C₆₇	1	2	yes	—
762	#95	C₂³×C₆₇	1	1	yes	characteristic
763	#95	C₂³×C₆₇	1	2	yes	—
764	#95	C₂³×C₆₇	1	2	yes	—
765	#95	C₂³×C₆₇	1	2	yes	—
766	#95	C₂³×C₆₇	1	2	yes	—
767	#95	C₂³×C₆₇	1	2	yes	—
768	#95	C₂³×C₆₇	1	2	yes	—
769	#95	C₂³×C₆₇	1	2	yes	—
770	#95	C₂³×C₆₇	1	2	yes	—
771	#95	C₂³×C₆₇	1	2	yes	—
772	#95	C₂³×C₆₇	1	2	yes	—
773	#95	C₂³×C₆₇	1	2	yes	—
774	#95	C₂³×C₆₇	1	2	yes	—
775	#95	C₂³×C₆₇	1	2	yes	—
776	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
777	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
778	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	2	2	no	—
781	C₂×Q₈	—	2	4	no	—
782	C₂×Q₈	—	2	2	no	—
783	C₂×Q₈	—	2	2	no	—
784	C₂×Q₈	—	2	2	no	—
785	C₂×Q₈	—	4	1	no	—
786	C₂×Q₈	—	4	2	no	—
787	C₂×Q₈	—	4	2	no	—
788	C₂×D₄	—	2	4	no	—
789	C₂×D₄	—	2	4	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	4	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	4	1	no	—
796	C₂×D₄	—	4	2	no	—
797	C₂×D₄	—	4	2	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	#41×C₆₇	1	4	yes	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	4	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
820	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
829	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	4	no	—
841	C₄⋊C₄	—	2	4	no	—
842	C₄⋊C₄	—	2	4	no	—
843	C₄⋊C₄	—	2	4	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	4	no	—
849	C₄⋊C₄	—	2	4	no	—
850	C₄⋊C₄	—	2	4	no	—
851	C₄⋊C₄	—	2	4	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	4	2	no	—
855	C₄⋊C₄	—	4	2	no	—
856	C₄⋊C₄	—	4	2	no	—
857	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
858	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
859	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
860	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	4	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	4	no	—
874	C₂²⋊C₄	—	2	4	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	1	no	—
879	C₂²⋊C₄	—	4	1	no	—
880	C₂²⋊C₄	—	4	1	no	—
881	C₂²⋊C₄	—	4	1	no	—
882	C₂²⋊C₄	—	4	2	no	—
883	C₂²⋊C₄	—	4	2	no	—
884	C₂²⋊C₄	#41×C₆₇	1	4	yes	—
885	C₄²	—	2	4	no	—
886	C₄²	—	2	4	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	4	no	—
890	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	4	1	no	—
894	C₄²	—	4	2	no	—
895	C₄²	—	4	1	no	—
896	C₄²	—	4	1	no	—
897	C₄²	C₂×D₄×C₆₇	1	4	yes	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	1	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	1	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	1	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	1	no	—
917	C₂³	C₂×#41×C₆₇	1	4	yes	—
918	C₂³	C₂×#41×C₆₇	1	2	yes	—
919	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
920	Q₈	—	4	4	no	—
921	Q₈	—	4	4	no	—
922	Q₈	—	8	4	no	—
923	D₄	—	2	8	no	—
924	D₄	—	4	4	no	—
925	D₄	—	4	8	no	—
926	D₄	—	8	4	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	4	8	no	—
979	C₂×C₄	—	4	8	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	8	4	no	—
983	C₂×C₄	—	8	4	no	—
984	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
985	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
986	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
987	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
988	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
989	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
990	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
991	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
992	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
993	C₂²	—	2	4	no	—
994	C₂²	—	2	4	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	4	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	1	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	1	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	1	no	—
1014	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1015	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1016	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1017	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1018	C₂²	#585×C₆₇	1	1	yes	characteristic
1019	C₂²	#585×C₆₇	1	1	yes	characteristic
1020	C₂²	#585×C₆₇	1	1	yes	characteristic
1021	C₄	—	2	4	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	2	4	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	1	no	—
1029	C₄	—	4	1	no	—
1030	C₄	—	4	1	no	—
1031	C₄	—	4	1	no	—
1032	C₄	—	4	2	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	2	no	—
1039	C₄	—	4	1	no	—
1040	C₄	#548×C₆₇	1	4	yes	—
1041	C₂	—	4	4	no	—
1042	C₂	—	4	2	no	—
1043	C₂	—	8	1	no	—
1044	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
1045	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1046	C₂	C₆₇×#3475	1	1	yes	characteristic
1047	C₂	C₆₇×#3500	1	1	yes	characteristic
1048	C₂	C₆₇×#3515	1	1	yes	characteristic
1049	C₂	C₆₇×#3521	1	1	yes	characteristic
1050	C₂	C₆₇×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2535	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. C₂×#554×C₆₇	C₂	semidirect
2. C₂×#552×C₆₇	C₂	semidirect
3. C₆₇×#2696	C₂	semidirect
4. C₆₇×#2690	C₂	semidirect
5. C₆₇×#2581	C₂	semidirect
6. C₆₇×#2560	C₂	semidirect
8. C₆₇×#2492	C₂	semidirect
9. C₆₇×#2489	C₂	semidirect
10. C₆₇×#2489	C₂	semidirect
11. C₆₇×#2481	C₂	semidirect
12. C₆₇×#2477	C₂	semidirect
13. C₆₇×#2461	C₂	semidirect
14. C₆₇×#2442	C₂	semidirect
15. C₆₇×#2439	C₂	semidirect
16. C₆₇×#2427	C₂	semidirect
17. C₆₇×#2427	C₂	semidirect
18. C₆₇×#2363	C₂	semidirect
19. C₆₇×#2361	C₂	semidirect
20. C₆₇×#2352	C₂	semidirect
21. C₄×#125×C₆₇	C₂	semidirect
22. C₄×#124×C₆₇	C₂	semidirect
23. C₄×#124×C₆₇	C₂	semidirect
142. #125×C₆₇	D₄	semidirect
515. #59586	C₆₇	direct (N × H)
526. C₂×#554	C₂×C₆₇	semidirect
527. C₂×#552	C₂×C₆₇	semidirect
528. #2696	C₂×C₆₇	semidirect
529. #2690	C₂×C₆₇	semidirect
530. #2581	C₂×C₆₇	semidirect
531. #2560	C₂×C₆₇	semidirect
533. #2492	C₂×C₆₇	semidirect
534. #2489	C₂×C₆₇	semidirect
535. #2489	C₂×C₆₇	semidirect
536. #2481	C₂×C₆₇	semidirect
537. #2477	C₂×C₆₇	semidirect
538. #2461	C₂×C₆₇	semidirect
539. #2442	C₂×C₆₇	semidirect
540. #2439	C₂×C₆₇	semidirect
541. #2427	C₂×C₆₇	semidirect
542. #2427	C₂×C₆₇	semidirect
543. #2363	C₂×C₆₇	semidirect
544. #2361	C₂×C₆₇	semidirect
545. #2352	C₂×C₆₇	semidirect
546. C₄×#125	C₂×C₆₇	semidirect
547. C₄×#124	C₂×C₆₇	semidirect
548. C₄×#124	C₂×C₆₇	semidirect
549. C₆₇	#59586	direct (N × H)
668. #125	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₆₇	2
C₂×#552×C₆₇	2
C₆₇×#2696	2
C₆₇×#2690	2
C₆₇×#2581	2
C₆₇×#2560	2
C₆₇×#2535	2
C₆₇×#2492	2
C₆₇×#2489	2
C₆₇×#2481	2
C₆₇×#2477	2
C₆₇×#2461	2
C₆₇×#2442	2
C₆₇×#2439	2
C₆₇×#2427	2
C₆₇×#2363	2
C₆₇×#2361	2
C₆₇×#2352	2
C₄×#125×C₆₇	2
C₄×#124×C₆₇	2
#59586	67

Subgroups — C67×#59586 #30738837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59586 #30738837