Subgroups — C₆₇×#59638 #30738889

Order 17152.

1906 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2798	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2754	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2607	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2592	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2589	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2582	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2511	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2511	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2501	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#2498	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2488	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2447	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2436	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2419	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2367	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2344	C₂	1	1	yes	maximal, characteristic, complemented
20	Q₈×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic
23	C₂×#391×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#123×C₆₇	C₂²	1	2	yes	—
28	C₂×#123×C₆₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#117×C₆₇	C₂²	1	2	yes	—
37	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
39	#400×C₆₇	C₂²	1	2	yes	—
40	#400×C₆₇	C₂²	1	2	yes	—
41	#400×C₆₇	C₂²	1	2	yes	—
42	#400×C₆₇	C₂²	1	2	yes	—
43	#399×C₆₇	C₂²	1	2	yes	—
44	#399×C₆₇	C₂²	1	2	yes	—
45	#399×C₆₇	C₂²	1	2	yes	—
46	#398×C₆₇	C₂²	1	2	yes	—
47	#398×C₆₇	C₂²	1	2	yes	—
48	#397×C₆₇	C₂²	1	2	yes	—
49	#397×C₆₇	C₂²	1	2	yes	—
50	#397×C₆₇	C₂²	1	2	yes	—
51	#397×C₆₇	C₂²	1	2	yes	—
52	#393×C₆₇	C₂²	1	2	yes	—
53	#393×C₆₇	C₂²	1	2	yes	—
54	#393×C₆₇	C₂²	1	2	yes	—
55	#391×C₆₇	C₂²	1	2	yes	—
56	#391×C₆₇	C₂²	1	2	yes	—
57	#391×C₆₇	C₂²	1	1	yes	characteristic
58	#391×C₆₇	C₂²	1	1	yes	characteristic
59	#391×C₆₇	C₂²	1	1	yes	characteristic
60	#391×C₆₇	C₂²	1	1	yes	characteristic
61	#391×C₆₇	C₂²	1	1	yes	characteristic
62	#391×C₆₇	C₂²	1	2	yes	—
63	#391×C₆₇	C₂²	1	1	yes	characteristic
64	#391×C₆₇	C₂²	1	2	yes	—
65	#391×C₆₇	C₂²	1	1	yes	characteristic
66	#391×C₆₇	C₂²	1	1	yes	characteristic
67	#391×C₆₇	C₂²	1	2	yes	—
68	#391×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	#389×C₆₇	C₂²	1	1	yes	characteristic
73	#389×C₆₇	C₂²	1	1	yes	characteristic
74	#389×C₆₇	C₂²	1	2	yes	—
75	#389×C₆₇	C₂²	1	1	yes	characteristic
76	#389×C₆₇	C₂²	1	1	yes	characteristic
77	#388×C₆₇	C₂²	1	2	yes	—
78	#388×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
83	#388×C₆₇	C₂²	1	2	yes	—
84	#387×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	2	yes	—
88	#387×C₆₇	C₂²	1	2	yes	—
89	#387×C₆₇	C₂²	1	2	yes	—
90	#387×C₆₇	C₂²	1	2	yes	—
91	#387×C₆₇	C₂²	1	1	yes	characteristic
92	#387×C₆₇	C₂²	1	2	yes	—
93	#387×C₆₇	C₂²	1	2	yes	—
94	#386×C₆₇	C₂²	1	2	yes	—
95	#386×C₆₇	C₂²	1	2	yes	—
96	#386×C₆₇	C₂²	1	2	yes	—
97	#385×C₆₇	C₂²	1	1	yes	characteristic
98	#385×C₆₇	C₂²	1	1	yes	characteristic
99	#385×C₆₇	C₂²	1	2	yes	—
100	#385×C₆₇	C₂²	1	2	yes	—
101	#384×C₆₇	C₂²	1	1	yes	characteristic
102	#384×C₆₇	C₂²	1	1	yes	characteristic
103	#382×C₆₇	C₂²	1	2	yes	—
104	#381×C₆₇	C₂²	1	2	yes	—
105	#381×C₆₇	C₂²	1	2	yes	—
106	#380×C₆₇	C₂²	1	1	yes	characteristic
107	#380×C₆₇	C₂²	1	2	yes	—
108	#380×C₆₇	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
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	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₂×#95×C₆₇	C₂²	1	2	yes	—
122	C₂×#95×C₆₇	C₂²	1	2	yes	—
123	C₂²×Q₈×C₆₇	—	2	4	no	—
124	C₂²×Q₈×C₆₇	—	2	4	no	—
125	C₂²×Q₈×C₆₇	—	4	2	no	—
126	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
129	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
131	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
137	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
138	#124×C₆₇	—	2	4	no	—
139	#124×C₆₇	—	4	2	no	—
140	#123×C₆₇	—	2	8	no	—
141	#123×C₆₇	—	4	4	no	—
142	C₂²⋊Q₈×C₆₇	—	2	4	no	—
143	#121×C₆₇	—	2	4	no	—
144	C₄×Q₈×C₆₇	—	2	4	no	—
145	C₄×Q₈×C₆₇	—	4	2	no	—
146	C₄×Q₈×C₆₇	—	4	2	no	—
147	C₄×D₄×C₆₇	—	4	2	no	—
148	C₄×D₄×C₆₇	—	4	4	no	—
149	#117×C₆₇	—	4	4	no	—
150	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
192	C₂×C₄²×C₆₇	—	4	2	no	—
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
204	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
205	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	1	yes	characteristic
215	#95×C₆₇	C₂³	1	2	yes	—
216	#95×C₆₇	C₂³	1	2	yes	—
217	#95×C₆₇	C₂³	1	2	yes	—
218	#95×C₆₇	C₂³	1	1	yes	characteristic
219	#95×C₆₇	C₂³	1	1	yes	characteristic
220	#95×C₆₇	C₂³	1	2	yes	—
221	#95×C₆₇	C₂³	1	1	yes	characteristic
222	#95×C₆₇	C₂³	1	1	yes	characteristic
223	#95×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	2	yes	—
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	2	yes	—
229	#95×C₆₇	C₂³	1	1	yes	characteristic
230	#95×C₆₇	C₂³	1	1	yes	characteristic
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	2	yes	—
235	#95×C₆₇	C₂³	1	2	yes	—
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	2	yes	—
239	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
240	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₆₇	—	2	2	no	—
242	C₂×Q₈×C₆₇	—	2	2	no	—
243	C₂×Q₈×C₆₇	—	2	4	no	—
244	C₂×Q₈×C₆₇	—	2	4	no	—
245	C₂×Q₈×C₆₇	—	2	2	no	—
246	C₂×Q₈×C₆₇	—	2	2	no	—
247	C₂×Q₈×C₆₇	—	2	2	no	—
248	C₂×Q₈×C₆₇	—	2	2	no	—
249	C₂×Q₈×C₆₇	—	2	2	no	—
250	C₂×Q₈×C₆₇	—	4	1	no	—
251	C₂×Q₈×C₆₇	—	4	2	no	—
252	C₂×Q₈×C₆₇	—	4	16	no	—
253	C₂×Q₈×C₆₇	#41	1	4	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	2	no	—
258	C₂×D₄×C₆₇	—	2	2	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂²×C₄×C₆₇	—	2	2	no	—
261	C₂²×C₄×C₆₇	—	2	2	no	—
262	C₂²×C₄×C₆₇	—	2	4	no	—
263	C₂²×C₄×C₆₇	—	2	2	no	—
264	C₂²×C₄×C₆₇	—	2	4	no	—
265	C₂²×C₄×C₆₇	—	2	4	no	—
266	C₂²×C₄×C₆₇	—	2	4	no	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	4	no	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	2	2	no	—
271	C₂²×C₄×C₆₇	—	2	4	no	—
272	C₂²×C₄×C₆₇	—	4	1	no	—
273	C₂²×C₄×C₆₇	—	4	1	no	—
274	C₂²×C₄×C₆₇	—	4	2	no	—
275	C₂²×C₄×C₆₇	—	4	2	no	—
276	C₂²×C₄×C₆₇	—	4	2	no	—
277	C₂²×C₄×C₆₇	#41	1	4	yes	—
278	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	1	yes	characteristic
299	C₄⋊C₄×C₆₇	—	2	4	no	—
300	C₄⋊C₄×C₆₇	—	2	2	no	—
301	C₄⋊C₄×C₆₇	—	2	2	no	—
302	C₄⋊C₄×C₆₇	—	2	4	no	—
303	C₄⋊C₄×C₆₇	—	2	2	no	—
304	C₄⋊C₄×C₆₇	—	2	2	no	—
305	C₄⋊C₄×C₆₇	—	2	2	no	—
306	C₄⋊C₄×C₆₇	—	2	2	no	—
307	C₄⋊C₄×C₆₇	—	2	2	no	—
308	C₄⋊C₄×C₆₇	—	2	4	no	—
309	C₄⋊C₄×C₆₇	—	2	4	no	—
310	C₄⋊C₄×C₆₇	—	2	2	no	—
311	C₄⋊C₄×C₆₇	—	2	2	no	—
312	C₄⋊C₄×C₆₇	—	2	2	no	—
313	C₄⋊C₄×C₆₇	—	2	2	no	—
314	C₄⋊C₄×C₆₇	—	4	2	no	—
315	C₄⋊C₄×C₆₇	—	4	2	no	—
316	C₄⋊C₄×C₆₇	—	4	2	no	—
317	C₄⋊C₄×C₆₇	—	4	1	no	—
318	C₄⋊C₄×C₆₇	—	4	1	no	—
319	C₄⋊C₄×C₆₇	—	4	2	no	—
320	C₄⋊C₄×C₆₇	—	4	1	no	—
321	C₄⋊C₄×C₆₇	—	4	2	no	—
322	C₄⋊C₄×C₆₇	—	4	2	no	—
323	C₂²⋊C₄×C₆₇	—	2	2	no	—
324	C₂²⋊C₄×C₆₇	—	2	2	no	—
325	C₂²⋊C₄×C₆₇	—	2	4	no	—
326	C₂²⋊C₄×C₆₇	—	2	2	no	—
327	C₂²⋊C₄×C₆₇	—	2	4	no	—
328	C₂²⋊C₄×C₆₇	—	2	4	no	—
329	C₂²⋊C₄×C₆₇	—	2	4	no	—
330	C₂²⋊C₄×C₆₇	—	2	4	no	—
331	C₂²⋊C₄×C₆₇	—	2	4	no	—
332	C₂²⋊C₄×C₆₇	—	2	4	no	—
333	C₂²⋊C₄×C₆₇	—	4	2	no	—
334	C₂²⋊C₄×C₆₇	—	4	2	no	—
335	C₂²⋊C₄×C₆₇	—	4	2	no	—
336	C₂²⋊C₄×C₆₇	—	4	2	no	—
337	C₂²⋊C₄×C₆₇	—	4	2	no	—
338	C₂²⋊C₄×C₆₇	—	4	2	no	—
339	C₂²⋊C₄×C₆₇	#41	1	4	yes	—
340	C₄²×C₆₇	—	2	4	no	—
341	C₄²×C₆₇	—	2	2	no	—
342	C₄²×C₆₇	—	2	2	no	—
343	C₄²×C₆₇	—	2	2	no	—
344	C₄²×C₆₇	—	2	2	no	—
345	C₄²×C₆₇	—	2	2	no	—
346	C₄²×C₆₇	—	2	2	no	—
347	C₄²×C₆₇	—	4	1	no	—
348	C₄²×C₆₇	—	4	1	no	—
349	C₄²×C₆₇	—	4	2	no	—
350	C₄²×C₆₇	—	4	2	no	—
351	C₄²×C₆₇	—	4	2	no	—
352	C₄²×C₆₇	—	4	2	no	—
353	C₂³×C₆₇	—	2	1	no	—
354	C₂³×C₆₇	—	2	1	no	—
355	C₂³×C₆₇	—	2	1	no	—
356	C₂³×C₆₇	—	2	1	no	—
357	C₂³×C₆₇	—	2	2	no	—
358	C₂³×C₆₇	—	2	2	no	—
359	C₂³×C₆₇	—	2	2	no	—
360	C₂³×C₆₇	—	2	2	no	—
361	C₂³×C₆₇	—	2	2	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	2	2	no	—
364	C₂³×C₆₇	C₂×#41	1	2	yes	—
365	C₂³×C₆₇	C₂×#41	1	2	yes	—
366	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
367	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
368	Q₈×C₆₇	—	2	8	no	—
369	Q₈×C₆₇	—	4	4	no	—
370	Q₈×C₆₇	—	4	8	no	—
371	Q₈×C₆₇	—	4	4	no	—
372	D₄×C₆₇	—	4	8	no	—
373	D₄×C₆₇	—	4	4	no	—
374	C₂×C₄×C₆₇	—	2	1	no	—
375	C₂×C₄×C₆₇	—	2	1	no	—
376	C₂×C₄×C₆₇	—	2	1	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	1	no	—
379	C₂×C₄×C₆₇	—	2	1	no	—
380	C₂×C₄×C₆₇	—	2	1	no	—
381	C₂×C₄×C₆₇	—	2	1	no	—
382	C₂×C₄×C₆₇	—	2	1	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	1	no	—
385	C₂×C₄×C₆₇	—	2	1	no	—
386	C₂×C₄×C₆₇	—	2	8	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	1	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	1	no	—
391	C₂×C₄×C₆₇	—	2	1	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	1	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	1	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	2	no	—
408	C₂×C₄×C₆₇	—	2	1	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	2	no	—
413	C₂×C₄×C₆₇	—	2	2	no	—
414	C₂×C₄×C₆₇	—	2	1	no	—
415	C₂×C₄×C₆₇	—	2	1	no	—
416	C₂×C₄×C₆₇	—	2	1	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	2	2	no	—
419	C₂×C₄×C₆₇	—	2	2	no	—
420	C₂×C₄×C₆₇	—	2	1	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	1	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	—	4	4	no	—
430	C₂×C₄×C₆₇	—	4	4	no	—
431	C₂×C₄×C₆₇	—	4	8	no	—
432	C₂×C₄×C₆₇	—	4	8	no	—
433	C₂×C₄×C₆₇	—	8	4	no	—
434	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
435	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
436	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
437	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
438	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
439	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
440	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
441	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
442	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
443	C₂²×C₆₇	—	2	2	no	—
444	C₂²×C₆₇	—	2	2	no	—
445	C₂²×C₆₇	—	2	2	no	—
446	C₂²×C₆₇	—	2	2	no	—
447	C₂²×C₆₇	—	2	2	no	—
448	C₂²×C₆₇	—	2	2	no	—
449	C₂²×C₆₇	—	4	2	no	—
450	C₂²×C₆₇	—	4	2	no	—
451	C₂²×C₆₇	—	4	2	no	—
452	C₂²×C₆₇	—	4	2	no	—
453	C₂²×C₆₇	—	4	2	no	—
454	C₂²×C₆₇	—	4	2	no	—
455	C₂²×C₆₇	—	4	2	no	—
456	C₂²×C₆₇	#559	1	4	yes	—
457	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
458	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
459	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
460	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
463	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
464	C₄×C₆₇	—	2	2	no	—
465	C₄×C₆₇	—	2	4	no	—
466	C₄×C₆₇	—	2	2	no	—
467	C₄×C₆₇	—	2	2	no	—
468	C₄×C₆₇	—	2	2	no	—
469	C₄×C₆₇	—	2	2	no	—
470	C₄×C₆₇	—	4	2	no	—
471	C₄×C₆₇	—	4	2	no	—
472	C₄×C₆₇	—	4	2	no	—
473	C₄×C₆₇	—	4	2	no	—
474	C₄×C₆₇	—	4	1	no	—
475	C₄×C₆₇	—	4	1	no	—
476	C₄×C₆₇	—	4	1	no	—
477	C₄×C₆₇	—	4	1	no	—
478	C₄×C₆₇	—	4	2	no	—
479	C₄×C₆₇	—	4	1	no	—
480	C₄×C₆₇	—	4	1	no	—
481	C₄×C₆₇	—	4	1	no	—
482	C₄×C₆₇	—	4	1	no	—
483	C₄×C₆₇	—	4	2	no	—
484	C₄×C₆₇	#551	1	4	yes	—
485	#59638	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
486	C₂×C₆₇	—	2	4	no	—
487	C₂×C₆₇	—	8	2	no	—
488	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
489	C₂×C₆₇	C₂×#559	1	1	yes	characteristic
490	C₂×C₆₇	#3482	1	1	yes	characteristic
491	C₂×C₆₇	#3509	1	1	yes	characteristic
492	C₂×C₆₇	#3520	1	1	yes	characteristic
493	C₂×C₆₇	#3522	1	1	yes	characteristic
494	C₂×C₆₇	#3536	1	1	yes	characteristic
495	#2798	C₂×C₆₇	1	2	yes	complemented
496	#2754	C₂×C₆₇	1	2	yes	complemented
497	#2607	C₂×C₆₇	1	2	yes	complemented
498	#2592	C₂×C₆₇	1	1	yes	characteristic, complemented
499	#2589	C₂×C₆₇	1	2	yes	complemented
500	#2582	C₂×C₆₇	1	1	yes	characteristic, complemented
501	#2511	C₂×C₆₇	1	1	yes	characteristic, complemented
502	#2511	C₂×C₆₇	1	1	yes	characteristic, complemented
503	#2501	C₂×C₆₇	1	1	yes	characteristic
504	#2498	C₂×C₆₇	1	2	yes	complemented
505	#2488	C₂×C₆₇	1	2	yes	complemented
506	#2448	C₂×C₆₇	1	1	yes	characteristic, complemented
507	#2447	C₂×C₆₇	1	1	yes	characteristic, complemented
508	#2436	C₂×C₆₇	1	1	yes	characteristic
509	#2419	C₂×C₆₇	1	2	yes	complemented
510	#2367	C₂×C₆₇	1	1	yes	characteristic, complemented
511	#2359	C₂×C₆₇	1	2	yes	complemented
512	#2355	C₂×C₆₇	1	1	yes	characteristic, complemented
513	#2344	C₂×C₆₇	1	1	yes	characteristic, complemented
514	Q₈×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
515	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
516	C₄×#121	C₂×C₆₇	1	1	yes	characteristic
517	C₂×#391	C₂×C₆₇	1	1	yes	characteristic, complemented
518	C₆₇	#59638	1	1	yes	characteristic, direct product factor, Sylow
519	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
520	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
521	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
522	C₂×#123	C₂²×C₆₇	1	2	yes	—
523	C₂×#123	C₂²×C₆₇	1	2	yes	—
524	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
525	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
526	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
527	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
528	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
529	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
530	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
531	C₂×#117	C₂²×C₆₇	1	2	yes	—
532	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
533	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
534	#400	C₂²×C₆₇	1	2	yes	—
535	#400	C₂²×C₆₇	1	2	yes	—
536	#400	C₂²×C₆₇	1	2	yes	—
537	#400	C₂²×C₆₇	1	2	yes	—
538	#399	C₂²×C₆₇	1	2	yes	—
539	#399	C₂²×C₆₇	1	2	yes	—
540	#399	C₂²×C₆₇	1	2	yes	—
541	#398	C₂²×C₆₇	1	2	yes	—
542	#398	C₂²×C₆₇	1	2	yes	—
543	#397	C₂²×C₆₇	1	2	yes	—
544	#397	C₂²×C₆₇	1	2	yes	—
545	#397	C₂²×C₆₇	1	2	yes	—
546	#397	C₂²×C₆₇	1	2	yes	—
547	#393	C₂²×C₆₇	1	2	yes	—
548	#393	C₂²×C₆₇	1	2	yes	—
549	#393	C₂²×C₆₇	1	2	yes	—
550	#391	C₂²×C₆₇	1	2	yes	—
551	#391	C₂²×C₆₇	1	1	yes	characteristic
552	#391	C₂²×C₆₇	1	1	yes	characteristic
553	#391	C₂²×C₆₇	1	2	yes	—
554	#391	C₂²×C₆₇	1	2	yes	—
555	#391	C₂²×C₆₇	1	1	yes	characteristic
556	#391	C₂²×C₆₇	1	1	yes	characteristic
557	#391	C₂²×C₆₇	1	2	yes	—
558	#391	C₂²×C₆₇	1	1	yes	characteristic
559	#391	C₂²×C₆₇	1	1	yes	characteristic
560	#391	C₂²×C₆₇	1	1	yes	characteristic
561	#391	C₂²×C₆₇	1	1	yes	characteristic
562	#391	C₂²×C₆₇	1	1	yes	characteristic
563	#391	C₂²×C₆₇	1	2	yes	—
564	#390	C₂²×C₆₇	1	1	yes	characteristic
565	#390	C₂²×C₆₇	1	1	yes	characteristic
566	#390	C₂²×C₆₇	1	1	yes	characteristic
567	#389	C₂²×C₆₇	1	1	yes	characteristic
568	#389	C₂²×C₆₇	1	2	yes	—
569	#389	C₂²×C₆₇	1	1	yes	characteristic
570	#389	C₂²×C₆₇	1	1	yes	characteristic
571	#389	C₂²×C₆₇	1	1	yes	characteristic
572	#388	C₂²×C₆₇	1	2	yes	—
573	#388	C₂²×C₆₇	1	2	yes	—
574	#388	C₂²×C₆₇	1	2	yes	—
575	#388	C₂²×C₆₇	1	2	yes	—
576	#388	C₂²×C₆₇	1	2	yes	—
577	#388	C₂²×C₆₇	1	2	yes	—
578	#388	C₂²×C₆₇	1	2	yes	—
579	#387	C₂²×C₆₇	1	2	yes	—
580	#387	C₂²×C₆₇	1	2	yes	—
581	#387	C₂²×C₆₇	1	2	yes	—
582	#387	C₂²×C₆₇	1	2	yes	—
583	#387	C₂²×C₆₇	1	2	yes	—
584	#387	C₂²×C₆₇	1	2	yes	—
585	#387	C₂²×C₆₇	1	2	yes	—
586	#387	C₂²×C₆₇	1	2	yes	—
587	#387	C₂²×C₆₇	1	1	yes	characteristic
588	#387	C₂²×C₆₇	1	1	yes	characteristic
589	#386	C₂²×C₆₇	1	2	yes	—
590	#386	C₂²×C₆₇	1	2	yes	—
591	#386	C₂²×C₆₇	1	2	yes	—
592	#385	C₂²×C₆₇	1	2	yes	—
593	#385	C₂²×C₆₇	1	2	yes	—
594	#385	C₂²×C₆₇	1	1	yes	characteristic
595	#385	C₂²×C₆₇	1	1	yes	characteristic
596	#384	C₂²×C₆₇	1	1	yes	characteristic
597	#384	C₂²×C₆₇	1	1	yes	characteristic
598	#382	C₂²×C₆₇	1	2	yes	—
599	#381	C₂²×C₆₇	1	2	yes	—
600	#381	C₂²×C₆₇	1	2	yes	—
601	#380	C₂²×C₆₇	1	1	yes	characteristic
602	#380	C₂²×C₆₇	1	2	yes	—
603	#380	C₂²×C₆₇	1	1	yes	characteristic
604	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
605	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
606	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
607	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
608	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
609	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
610	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
611	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
612	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
613	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
614	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
615	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
616	C₂×#95	C₂²×C₆₇	1	2	yes	—
617	C₂×#95	C₂²×C₆₇	1	2	yes	—
618	C₂²×Q₈	—	2	4	no	—
619	C₂²×Q₈	—	2	4	no	—
620	C₂²×Q₈	—	4	2	no	—
621	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
622	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
623	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
624	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
625	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
626	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
628	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
629	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
630	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
631	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
632	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
633	#124	—	2	4	no	—
634	#124	—	4	2	no	—
635	#123	—	2	8	no	—
636	#123	—	4	4	no	—
637	C₂²⋊Q₈	—	2	4	no	—
638	#121	—	2	4	no	—
639	C₄×Q₈	—	2	4	no	—
640	C₄×Q₈	—	4	2	no	—
641	C₄×Q₈	—	4	2	no	—
642	C₄×D₄	—	4	2	no	—
643	C₄×D₄	—	4	4	no	—
644	#117	—	4	4	no	—
645	C₂×C₄⋊C₄	—	2	4	no	—
646	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
687	C₂×C₄²	—	4	2	no	—
688	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
693	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
696	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
697	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
698	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
699	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
701	#95	C₂³×C₆₇	1	2	yes	—
702	#95	C₂³×C₆₇	1	2	yes	—
703	#95	C₂³×C₆₇	1	2	yes	—
704	#95	C₂³×C₆₇	1	2	yes	—
705	#95	C₂³×C₆₇	1	2	yes	—
706	#95	C₂³×C₆₇	1	2	yes	—
707	#95	C₂³×C₆₇	1	2	yes	—
708	#95	C₂³×C₆₇	1	2	yes	—
709	#95	C₂³×C₆₇	1	1	yes	characteristic
710	#95	C₂³×C₆₇	1	2	yes	—
711	#95	C₂³×C₆₇	1	2	yes	—
712	#95	C₂³×C₆₇	1	2	yes	—
713	#95	C₂³×C₆₇	1	1	yes	characteristic
714	#95	C₂³×C₆₇	1	1	yes	characteristic
715	#95	C₂³×C₆₇	1	2	yes	—
716	#95	C₂³×C₆₇	1	1	yes	characteristic
717	#95	C₂³×C₆₇	1	1	yes	characteristic
718	#95	C₂³×C₆₇	1	1	yes	characteristic
719	#95	C₂³×C₆₇	1	1	yes	characteristic
720	#95	C₂³×C₆₇	1	1	yes	characteristic
721	#95	C₂³×C₆₇	1	2	yes	—
722	#95	C₂³×C₆₇	1	2	yes	—
723	#95	C₂³×C₆₇	1	2	yes	—
724	#95	C₂³×C₆₇	1	1	yes	characteristic
725	#95	C₂³×C₆₇	1	1	yes	characteristic
726	#95	C₂³×C₆₇	1	2	yes	—
727	#95	C₂³×C₆₇	1	2	yes	—
728	#95	C₂³×C₆₇	1	2	yes	—
729	#95	C₂³×C₆₇	1	2	yes	—
730	#95	C₂³×C₆₇	1	2	yes	—
731	#95	C₂³×C₆₇	1	2	yes	—
732	#95	C₂³×C₆₇	1	2	yes	—
733	#95	C₂³×C₆₇	1	2	yes	—
734	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
735	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	2	no	—
738	C₂×Q₈	—	2	4	no	—
739	C₂×Q₈	—	2	4	no	—
740	C₂×Q₈	—	2	2	no	—
741	C₂×Q₈	—	2	2	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	2	2	no	—
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	—	4	1	no	—
746	C₂×Q₈	—	4	2	no	—
747	C₂×Q₈	—	4	16	no	—
748	C₂×Q₈	#41×C₆₇	1	4	yes	—
749	C₂×D₄	—	2	4	no	—
750	C₂×D₄	—	2	4	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	4	1	no	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	#41×C₆₇	1	4	yes	—
773	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
794	C₄⋊C₄	—	2	4	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	1	no	—
813	C₄⋊C₄	—	4	1	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	1	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	#41×C₆₇	1	4	yes	—
835	C₄²	—	2	4	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	4	1	no	—
843	C₄²	—	4	1	no	—
844	C₄²	—	4	2	no	—
845	C₄²	—	4	2	no	—
846	C₄²	—	4	2	no	—
847	C₄²	—	4	2	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	C₂×#41×C₆₇	1	2	yes	—
860	C₂³	C₂×#41×C₆₇	1	2	yes	—
861	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
862	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
863	Q₈	—	2	8	no	—
864	Q₈	—	4	8	no	—
865	Q₈	—	4	4	no	—
866	Q₈	—	4	4	no	—
867	D₄	—	4	8	no	—
868	D₄	—	4	4	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	8	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	4	8	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	8	no	—
928	C₂×C₄	—	8	4	no	—
929	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
930	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
931	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
932	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
933	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
934	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
935	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
936	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
937	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	#559×C₆₇	1	4	yes	—
952	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
953	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
954	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
955	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
956	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
957	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
958	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	4	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	1	no	—
971	C₄	—	4	1	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	1	no	—
978	C₄	—	4	1	no	—
979	C₄	#551×C₆₇	1	4	yes	—
980	C₂	—	2	4	no	—
981	C₂	—	8	2	no	—
982	C₂	C₂×#551×C₆₇	1	1	yes	characteristic
983	C₂	C₂×#559×C₆₇	1	1	yes	characteristic
984	C₂	C₆₇×#3482	1	1	yes	characteristic
985	C₂	C₆₇×#3509	1	1	yes	characteristic
986	C₂	C₆₇×#3520	1	1	yes	characteristic
987	C₂	C₆₇×#3522	1	1	yes	characteristic
988	C₂	C₆₇×#3536	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#121×C₆₇	C₂²
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×#2798	C₂	semidirect
2. C₆₇×#2754	C₂	semidirect
3. C₆₇×#2607	C₂	semidirect
4. C₆₇×#2592	C₂	semidirect
5. C₆₇×#2589	C₂	semidirect
6. C₆₇×#2582	C₂	semidirect
7. C₆₇×#2511	C₂	semidirect
8. C₆₇×#2511	C₂	semidirect
10. C₆₇×#2498	C₂	semidirect
11. C₆₇×#2488	C₂	semidirect
12. C₆₇×#2448	C₂	semidirect
13. C₆₇×#2447	C₂	semidirect
15. C₆₇×#2419	C₂	semidirect
16. C₆₇×#2367	C₂	semidirect
17. C₆₇×#2359	C₂	semidirect
18. C₆₇×#2355	C₂	semidirect
19. C₆₇×#2344	C₂	semidirect
20. Q₈×C₂²⋊C₄×C₆₇	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
23. C₂×#391×C₆₇	C₂	semidirect
485. #59638	C₆₇	direct (N × H)
495. #2798	C₂×C₆₇	semidirect
496. #2754	C₂×C₆₇	semidirect
497. #2607	C₂×C₆₇	semidirect
498. #2592	C₂×C₆₇	semidirect
499. #2589	C₂×C₆₇	semidirect
500. #2582	C₂×C₆₇	semidirect
501. #2511	C₂×C₆₇	semidirect
502. #2511	C₂×C₆₇	semidirect
504. #2498	C₂×C₆₇	semidirect
505. #2488	C₂×C₆₇	semidirect
506. #2448	C₂×C₆₇	semidirect
507. #2447	C₂×C₆₇	semidirect
509. #2419	C₂×C₆₇	semidirect
510. #2367	C₂×C₆₇	semidirect
511. #2359	C₂×C₆₇	semidirect
512. #2355	C₂×C₆₇	semidirect
513. #2344	C₂×C₆₇	semidirect
514. Q₈×C₂²⋊C₄	C₂×C₆₇	semidirect
515. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
517. C₂×#391	C₂×C₆₇	semidirect
518. C₆₇	#59638	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2798	2
C₆₇×#2754	2
C₆₇×#2607	2
C₆₇×#2592	2
C₆₇×#2589	2
C₆₇×#2582	2
C₆₇×#2511	2
C₆₇×#2501	2
C₆₇×#2498	2
C₆₇×#2488	2
C₆₇×#2448	2
C₆₇×#2447	2
C₆₇×#2436	2
C₆₇×#2419	2
C₆₇×#2367	2
C₆₇×#2359	2
C₆₇×#2355	2
C₆₇×#2344	2
Q₈×C₂²⋊C₄×C₆₇	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#121×C₆₇	2
C₂×#391×C₆₇	2
#59638	67

Subgroups — C67×#59638 #30738889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59638 #30738889