Subgroups — C₆₇×#35162 #30714413

Order 17152.

1602 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2865	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2863	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2653	C₂	1	2	yes	maximal
4	C₆₇×#2652	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2532	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2528	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2523	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2518	C₂	1	2	yes	maximal
9	C₆₇×#2514	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2507	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2499	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2495	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2492	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2485	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2439	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2415	C₂	1	1	yes	maximal, characteristic
17	C₆₇×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2323	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2320	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2314	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2290	C₂	1	1	yes	maximal, characteristic
23	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
33	#401×C₆₇	C₂²	1	2	yes	—
34	#400×C₆₇	C₂²	1	2	yes	—
35	#400×C₆₇	C₂²	1	2	yes	—
36	#400×C₆₇	C₂²	1	2	yes	—
37	#398×C₆₇	C₂²	1	2	yes	—
38	#398×C₆₇	C₂²	1	2	yes	—
39	#397×C₆₇	C₂²	1	2	yes	—
40	#397×C₆₇	C₂²	1	2	yes	—
41	#397×C₆₇	C₂²	1	2	yes	—
42	#397×C₆₇	C₂²	1	2	yes	—
43	#397×C₆₇	C₂²	1	2	yes	—
44	#396×C₆₇	C₂²	1	2	yes	—
45	#394×C₆₇	C₂²	1	2	yes	—
46	#394×C₆₇	C₂²	1	2	yes	—
47	#393×C₆₇	C₂²	1	2	yes	—
48	#393×C₆₇	C₂²	1	2	yes	—
49	#391×C₆₇	C₂²	1	1	yes	characteristic
50	#391×C₆₇	C₂²	1	1	yes	characteristic
51	#391×C₆₇	C₂²	1	1	yes	characteristic
52	#391×C₆₇	C₂²	1	1	yes	characteristic
53	#391×C₆₇	C₂²	1	2	yes	—
54	#391×C₆₇	C₂²	1	2	yes	—
55	#391×C₆₇	C₂²	1	2	yes	—
56	#391×C₆₇	C₂²	1	2	yes	—
57	#389×C₆₇	C₂²	1	2	yes	—
58	#389×C₆₇	C₂²	1	1	yes	characteristic
59	#389×C₆₇	C₂²	1	1	yes	characteristic
60	#389×C₆₇	C₂²	1	1	yes	characteristic
61	#389×C₆₇	C₂²	1	1	yes	characteristic
62	#389×C₆₇	C₂²	1	1	yes	characteristic
63	#389×C₆₇	C₂²	1	2	yes	—
64	#389×C₆₇	C₂²	1	1	yes	characteristic
65	#389×C₆₇	C₂²	1	2	yes	—
66	#388×C₆₇	C₂²	1	2	yes	—
67	#388×C₆₇	C₂²	1	2	yes	—
68	#388×C₆₇	C₂²	1	2	yes	—
69	#388×C₆₇	C₂²	1	2	yes	—
70	#388×C₆₇	C₂²	1	1	yes	characteristic
71	#388×C₆₇	C₂²	1	2	yes	—
72	#388×C₆₇	C₂²	1	2	yes	—
73	#388×C₆₇	C₂²	1	1	yes	characteristic
74	#388×C₆₇	C₂²	1	2	yes	—
75	#388×C₆₇	C₂²	1	2	yes	—
76	#387×C₆₇	C₂²	1	2	yes	—
77	#387×C₆₇	C₂²	1	2	yes	—
78	#387×C₆₇	C₂²	1	2	yes	—
79	#387×C₆₇	C₂²	1	2	yes	—
80	#387×C₆₇	C₂²	1	2	yes	—
81	#387×C₆₇	C₂²	1	2	yes	—
82	#387×C₆₇	C₂²	1	2	yes	—
83	#387×C₆₇	C₂²	1	1	yes	characteristic
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	2	yes	—
92	#386×C₆₇	C₂²	1	1	yes	characteristic
93	#386×C₆₇	C₂²	1	1	yes	characteristic
94	#385×C₆₇	C₂²	1	1	yes	characteristic
95	#385×C₆₇	C₂²	1	1	yes	characteristic
96	#385×C₆₇	C₂²	1	2	yes	—
97	#384×C₆₇	C₂²	1	1	yes	characteristic
98	#383×C₆₇	C₂²	1	2	yes	—
99	#383×C₆₇	C₂²	1	2	yes	—
100	#383×C₆₇	C₂²	1	2	yes	—
101	#382×C₆₇	C₂²	1	1	yes	characteristic
102	#382×C₆₇	C₂²	1	1	yes	characteristic
103	#382×C₆₇	C₂²	1	2	yes	—
104	#380×C₆₇	C₂²	1	1	yes	characteristic
105	#380×C₆₇	C₂²	1	1	yes	characteristic
106	#380×C₆₇	C₂²	1	1	yes	characteristic
107	#380×C₆₇	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×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	2	yes	—
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
120	#376×C₆₇	C₂²	1	2	yes	—
121	#376×C₆₇	C₂²	1	1	yes	characteristic
122	C₄³×C₆₇	C₂²	1	2	yes	—
123	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
125	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₄⋊Q₈×C₆₇	—	2	4	no	—
131	C₂²⋊Q₈×C₆₇	—	2	4	no	—
132	C₂²⋊Q₈×C₆₇	—	2	4	no	—
133	C₄×Q₈×C₆₇	—	2	4	no	—
134	C₄×D₄×C₆₇	—	2	4	no	—
135	#117×C₆₇	—	2	4	no	—
136	#117×C₆₇	—	2	4	no	—
137	#117×C₆₇	—	2	4	no	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	—	2	4	no	—
179	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
192	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	1	yes	characteristic
199	#95×C₆₇	C₂³	1	1	yes	characteristic
200	#95×C₆₇	C₂³	1	1	yes	characteristic
201	#95×C₆₇	C₂³	1	1	yes	characteristic
202	#95×C₆₇	C₂³	1	1	yes	characteristic
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	1	yes	characteristic
206	#95×C₆₇	C₂³	1	1	yes	characteristic
207	#95×C₆₇	C₂³	1	1	yes	characteristic
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	1	yes	characteristic
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	1	yes	characteristic
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
219	#95×C₆₇	C₂³	1	2	yes	—
220	#95×C₆₇	C₂³	1	2	yes	—
221	#95×C₆₇	C₂³	1	2	yes	—
222	#95×C₆₇	C₂³	1	2	yes	—
223	#95×C₆₇	C₂³	1	2	yes	—
224	#95×C₆₇	C₂³	1	2	yes	—
225	#95×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
230	#95×C₆₇	C₂³	1	2	yes	—
231	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
232	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₂×Q₈×C₆₇	—	2	2	no	—
234	C₂×Q₈×C₆₇	—	2	2	no	—
235	C₂×Q₈×C₆₇	—	2	2	no	—
236	C₂×Q₈×C₆₇	—	2	4	no	—
237	C₂×Q₈×C₆₇	—	4	2	no	—
238	C₂×Q₈×C₆₇	—	4	2	no	—
239	C₂×D₄×C₆₇	—	2	2	no	—
240	C₂×D₄×C₆₇	—	4	1	no	—
241	C₂×D₄×C₆₇	—	4	1	no	—
242	C₂²×C₄×C₆₇	—	2	2	no	—
243	C₂²×C₄×C₆₇	—	2	2	no	—
244	C₂²×C₄×C₆₇	—	2	2	no	—
245	C₂²×C₄×C₆₇	—	2	2	no	—
246	C₂²×C₄×C₆₇	—	2	2	no	—
247	C₂²×C₄×C₆₇	—	2	2	no	—
248	C₂²×C₄×C₆₇	—	2	2	no	—
249	C₂²×C₄×C₆₇	—	2	2	no	—
250	C₂²×C₄×C₆₇	—	4	1	no	—
251	C₂²×C₄×C₆₇	—	4	1	no	—
252	C₂²×C₄×C₆₇	—	4	1	no	—
253	C₂²×C₄×C₆₇	#41	1	4	yes	—
254	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₄⋊C₄×C₆₇	—	2	2	no	—
276	C₄⋊C₄×C₆₇	—	2	2	no	—
277	C₄⋊C₄×C₆₇	—	2	2	no	—
278	C₄⋊C₄×C₆₇	—	2	2	no	—
279	C₄⋊C₄×C₆₇	—	2	2	no	—
280	C₄⋊C₄×C₆₇	—	2	2	no	—
281	C₄⋊C₄×C₆₇	—	2	2	no	—
282	C₄⋊C₄×C₆₇	—	2	4	no	—
283	C₄⋊C₄×C₆₇	—	2	2	no	—
284	C₄⋊C₄×C₆₇	—	2	4	no	—
285	C₄⋊C₄×C₆₇	—	2	4	no	—
286	C₄⋊C₄×C₆₇	—	2	4	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	4	2	no	—
290	C₄⋊C₄×C₆₇	—	4	2	no	—
291	C₄⋊C₄×C₆₇	—	4	2	no	—
292	C₄⋊C₄×C₆₇	—	4	2	no	—
293	C₄⋊C₄×C₆₇	—	4	2	no	—
294	C₄⋊C₄×C₆₇	—	4	2	no	—
295	C₄⋊C₄×C₆₇	—	4	2	no	—
296	C₄⋊C₄×C₆₇	—	4	2	no	—
297	C₄⋊C₄×C₆₇	—	4	1	no	—
298	C₄⋊C₄×C₆₇	#41	1	4	yes	—
299	C₂²⋊C₄×C₆₇	—	2	4	no	—
300	C₂²⋊C₄×C₆₇	—	2	2	no	—
301	C₂²⋊C₄×C₆₇	—	2	4	no	—
302	C₂²⋊C₄×C₆₇	—	2	2	no	—
303	C₂²⋊C₄×C₆₇	—	2	2	no	—
304	C₂²⋊C₄×C₆₇	—	2	4	no	—
305	C₂²⋊C₄×C₆₇	—	2	2	no	—
306	C₂²⋊C₄×C₆₇	—	2	4	no	—
307	C₂²⋊C₄×C₆₇	—	2	2	no	—
308	C₂²⋊C₄×C₆₇	—	4	2	no	—
309	C₂²⋊C₄×C₆₇	—	4	2	no	—
310	C₂²⋊C₄×C₆₇	—	4	2	no	—
311	C₂²⋊C₄×C₆₇	—	4	2	no	—
312	C₂²⋊C₄×C₆₇	—	4	1	no	—
313	C₂²⋊C₄×C₆₇	—	4	1	no	—
314	C₂²⋊C₄×C₆₇	—	4	1	no	—
315	C₄²×C₆₇	—	2	2	no	—
316	C₄²×C₆₇	—	2	2	no	—
317	C₄²×C₆₇	—	2	2	no	—
318	C₄²×C₆₇	—	2	4	no	—
319	C₄²×C₆₇	—	2	4	no	—
320	C₄²×C₆₇	—	2	2	no	—
321	C₄²×C₆₇	—	2	2	no	—
322	C₄²×C₆₇	—	2	4	no	—
323	C₄²×C₆₇	—	2	2	no	—
324	C₄²×C₆₇	—	2	4	no	—
325	C₄²×C₆₇	—	4	2	no	—
326	C₄²×C₆₇	—	4	2	no	—
327	C₄²×C₆₇	—	4	2	no	—
328	C₄²×C₆₇	—	4	2	no	—
329	C₄²×C₆₇	#41	1	4	yes	—
330	C₂³×C₆₇	—	2	1	no	—
331	C₂³×C₆₇	—	2	1	no	—
332	C₂³×C₆₇	—	2	1	no	—
333	C₂³×C₆₇	—	2	1	no	—
334	C₂³×C₆₇	—	2	1	no	—
335	C₂³×C₆₇	—	2	1	no	—
336	C₂³×C₆₇	—	2	1	no	—
337	C₂³×C₆₇	—	2	1	no	—
338	C₂³×C₆₇	—	2	1	no	—
339	C₂³×C₆₇	—	2	1	no	—
340	C₂³×C₆₇	—	2	1	no	—
341	C₂³×C₆₇	—	2	1	no	—
342	C₂³×C₆₇	—	2	1	no	—
343	C₂³×C₆₇	C₂×#41	1	2	yes	—
344	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
345	Q₈×C₆₇	—	4	4	no	—
346	Q₈×C₆₇	—	8	4	no	—
347	D₄×C₆₇	—	4	4	no	—
348	C₂×C₄×C₆₇	—	2	1	no	—
349	C₂×C₄×C₆₇	—	2	1	no	—
350	C₂×C₄×C₆₇	—	2	1	no	—
351	C₂×C₄×C₆₇	—	2	1	no	—
352	C₂×C₄×C₆₇	—	2	1	no	—
353	C₂×C₄×C₆₇	—	2	1	no	—
354	C₂×C₄×C₆₇	—	2	1	no	—
355	C₂×C₄×C₆₇	—	2	1	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	8	no	—
359	C₂×C₄×C₆₇	—	2	1	no	—
360	C₂×C₄×C₆₇	—	2	1	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	1	no	—
364	C₂×C₄×C₆₇	—	2	1	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	1	no	—
368	C₂×C₄×C₆₇	—	2	1	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	1	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	1	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	2	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	2	no	—
379	C₂×C₄×C₆₇	—	2	2	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	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	1	no	—
392	C₂×C₄×C₆₇	—	2	1	no	—
393	C₂×C₄×C₆₇	—	2	1	no	—
394	C₂×C₄×C₆₇	—	2	1	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	2	1	no	—
397	C₂×C₄×C₆₇	—	2	1	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	1	no	—
402	C₂×C₄×C₆₇	—	2	1	no	—
403	C₂×C₄×C₆₇	—	2	1	no	—
404	C₂×C₄×C₆₇	—	4	4	no	—
405	C₂×C₄×C₆₇	—	4	4	no	—
406	C₂×C₄×C₆₇	—	4	4	no	—
407	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
408	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
409	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
410	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
411	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
412	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
413	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
414	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
415	C₂²×C₆₇	—	2	2	no	—
416	C₂²×C₆₇	—	2	2	no	—
417	C₂²×C₆₇	—	2	2	no	—
418	C₂²×C₆₇	—	4	1	no	—
419	C₂²×C₆₇	—	4	1	no	—
420	C₂²×C₆₇	—	4	1	no	—
421	C₂²×C₆₇	—	4	1	no	—
422	C₂²×C₆₇	—	4	1	no	—
423	C₂²×C₆₇	—	4	1	no	—
424	C₂²×C₆₇	—	4	1	no	—
425	C₂²×C₆₇	—	4	1	no	—
426	C₂²×C₆₇	—	4	1	no	—
427	C₂²×C₆₇	—	4	1	no	—
428	C₂²×C₆₇	—	4	1	no	—
429	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
430	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
431	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
432	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
433	C₂²×C₆₇	#585	1	1	yes	characteristic
434	C₂²×C₆₇	#585	1	1	yes	characteristic
435	C₂²×C₆₇	#585	1	1	yes	characteristic
436	C₄×C₆₇	—	2	2	no	—
437	C₄×C₆₇	—	2	2	no	—
438	C₄×C₆₇	—	2	2	no	—
439	C₄×C₆₇	—	2	2	no	—
440	C₄×C₆₇	—	2	4	no	—
441	C₄×C₆₇	—	4	1	no	—
442	C₄×C₆₇	—	4	2	no	—
443	C₄×C₆₇	—	4	2	no	—
444	C₄×C₆₇	—	4	2	no	—
445	C₄×C₆₇	—	4	1	no	—
446	C₄×C₆₇	—	4	1	no	—
447	C₄×C₆₇	—	4	2	no	—
448	C₄×C₆₇	—	4	1	no	—
449	C₄×C₆₇	—	4	2	no	—
450	C₄×C₆₇	—	4	1	no	—
451	C₄×C₆₇	—	4	1	no	—
452	C₄×C₆₇	—	4	2	no	—
453	C₄×C₆₇	—	4	1	no	—
454	C₄×C₆₇	—	4	2	no	—
455	C₄×C₆₇	—	4	1	no	—
456	C₄×C₆₇	#529	1	4	yes	—
457	#35162	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
458	C₂×C₆₇	—	4	2	no	—
459	C₂×C₆₇	—	8	1	no	—
460	C₂×C₆₇	C₂×#529	1	1	yes	characteristic
461	C₂×C₆₇	#3455	1	1	yes	characteristic
462	C₂×C₆₇	#3461	1	1	yes	characteristic
463	C₂×C₆₇	#3493	1	1	yes	characteristic
464	C₂×C₆₇	#3495	1	1	yes	characteristic
465	C₂×C₆₇	#3518	1	1	yes	characteristic
466	C₂×C₆₇	#3521	1	1	yes	characteristic
467	#2865	C₂×C₆₇	1	2	yes	complemented
468	#2863	C₂×C₆₇	1	2	yes	complemented
469	#2653	C₂×C₆₇	1	2	yes	—
470	#2652	C₂×C₆₇	1	2	yes	complemented
471	#2532	C₂×C₆₇	1	2	yes	complemented
472	#2528	C₂×C₆₇	1	2	yes	complemented
473	#2523	C₂×C₆₇	1	2	yes	complemented
474	#2518	C₂×C₆₇	1	2	yes	—
475	#2514	C₂×C₆₇	1	1	yes	characteristic, complemented
476	#2507	C₂×C₆₇	1	1	yes	characteristic, complemented
477	#2499	C₂×C₆₇	1	1	yes	characteristic, complemented
478	#2495	C₂×C₆₇	1	1	yes	characteristic, complemented
479	#2492	C₂×C₆₇	1	1	yes	characteristic, complemented
480	#2485	C₂×C₆₇	1	1	yes	characteristic
481	#2439	C₂×C₆₇	1	1	yes	characteristic, complemented
482	#2415	C₂×C₆₇	1	1	yes	characteristic
483	#2331	C₂×C₆₇	1	1	yes	characteristic, complemented
484	#2323	C₂×C₆₇	1	1	yes	characteristic, complemented
485	#2320	C₂×C₆₇	1	1	yes	characteristic, complemented
486	#2314	C₂×C₆₇	1	1	yes	characteristic, complemented
487	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
488	#2290	C₂×C₆₇	1	1	yes	characteristic
489	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
490	C₆₇	#35162	1	1	yes	characteristic, direct product factor, Sylow
491	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
492	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
494	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
495	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
496	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
497	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
498	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
499	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
500	#401	C₂²×C₆₇	1	2	yes	—
501	#400	C₂²×C₆₇	1	2	yes	—
502	#400	C₂²×C₆₇	1	2	yes	—
503	#400	C₂²×C₆₇	1	2	yes	—
504	#398	C₂²×C₆₇	1	2	yes	—
505	#398	C₂²×C₆₇	1	2	yes	—
506	#397	C₂²×C₆₇	1	2	yes	—
507	#397	C₂²×C₆₇	1	2	yes	—
508	#397	C₂²×C₆₇	1	2	yes	—
509	#397	C₂²×C₆₇	1	2	yes	—
510	#397	C₂²×C₆₇	1	2	yes	—
511	#396	C₂²×C₆₇	1	2	yes	—
512	#394	C₂²×C₆₇	1	2	yes	—
513	#394	C₂²×C₆₇	1	2	yes	—
514	#393	C₂²×C₆₇	1	2	yes	—
515	#393	C₂²×C₆₇	1	2	yes	—
516	#391	C₂²×C₆₇	1	1	yes	characteristic
517	#391	C₂²×C₆₇	1	1	yes	characteristic
518	#391	C₂²×C₆₇	1	1	yes	characteristic
519	#391	C₂²×C₆₇	1	2	yes	—
520	#391	C₂²×C₆₇	1	2	yes	—
521	#391	C₂²×C₆₇	1	2	yes	—
522	#391	C₂²×C₆₇	1	2	yes	—
523	#391	C₂²×C₆₇	1	1	yes	characteristic
524	#389	C₂²×C₆₇	1	1	yes	characteristic
525	#389	C₂²×C₆₇	1	1	yes	characteristic
526	#389	C₂²×C₆₇	1	2	yes	—
527	#389	C₂²×C₆₇	1	1	yes	characteristic
528	#389	C₂²×C₆₇	1	1	yes	characteristic
529	#389	C₂²×C₆₇	1	1	yes	characteristic
530	#389	C₂²×C₆₇	1	2	yes	—
531	#389	C₂²×C₆₇	1	2	yes	—
532	#389	C₂²×C₆₇	1	1	yes	characteristic
533	#388	C₂²×C₆₇	1	2	yes	—
534	#388	C₂²×C₆₇	1	2	yes	—
535	#388	C₂²×C₆₇	1	2	yes	—
536	#388	C₂²×C₆₇	1	2	yes	—
537	#388	C₂²×C₆₇	1	1	yes	characteristic
538	#388	C₂²×C₆₇	1	2	yes	—
539	#388	C₂²×C₆₇	1	2	yes	—
540	#388	C₂²×C₆₇	1	2	yes	—
541	#388	C₂²×C₆₇	1	2	yes	—
542	#388	C₂²×C₆₇	1	1	yes	characteristic
543	#387	C₂²×C₆₇	1	2	yes	—
544	#387	C₂²×C₆₇	1	2	yes	—
545	#387	C₂²×C₆₇	1	2	yes	—
546	#387	C₂²×C₆₇	1	2	yes	—
547	#387	C₂²×C₆₇	1	2	yes	—
548	#387	C₂²×C₆₇	1	2	yes	—
549	#387	C₂²×C₆₇	1	2	yes	—
550	#387	C₂²×C₆₇	1	1	yes	characteristic
551	#387	C₂²×C₆₇	1	2	yes	—
552	#387	C₂²×C₆₇	1	2	yes	—
553	#387	C₂²×C₆₇	1	2	yes	—
554	#387	C₂²×C₆₇	1	2	yes	—
555	#387	C₂²×C₆₇	1	2	yes	—
556	#387	C₂²×C₆₇	1	2	yes	—
557	#387	C₂²×C₆₇	1	2	yes	—
558	#387	C₂²×C₆₇	1	1	yes	characteristic
559	#386	C₂²×C₆₇	1	1	yes	characteristic
560	#386	C₂²×C₆₇	1	1	yes	characteristic
561	#385	C₂²×C₆₇	1	1	yes	characteristic
562	#385	C₂²×C₆₇	1	2	yes	—
563	#385	C₂²×C₆₇	1	1	yes	characteristic
564	#384	C₂²×C₆₇	1	1	yes	characteristic
565	#383	C₂²×C₆₇	1	2	yes	—
566	#383	C₂²×C₆₇	1	2	yes	—
567	#383	C₂²×C₆₇	1	2	yes	—
568	#382	C₂²×C₆₇	1	1	yes	characteristic
569	#382	C₂²×C₆₇	1	2	yes	—
570	#382	C₂²×C₆₇	1	1	yes	characteristic
571	#380	C₂²×C₆₇	1	1	yes	characteristic
572	#380	C₂²×C₆₇	1	1	yes	characteristic
573	#380	C₂²×C₆₇	1	1	yes	characteristic
574	#380	C₂²×C₆₇	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
581	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
582	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
583	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
584	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
585	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
586	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
587	#376	C₂²×C₆₇	1	1	yes	characteristic
588	#376	C₂²×C₆₇	1	2	yes	—
589	C₄³	C₂²×C₆₇	1	2	yes	—
590	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
591	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
592	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
593	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
594	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
595	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
596	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
597	C₄⋊Q₈	—	2	4	no	—
598	C₂²⋊Q₈	—	2	4	no	—
599	C₂²⋊Q₈	—	2	4	no	—
600	C₄×Q₈	—	2	4	no	—
601	C₄×D₄	—	2	4	no	—
602	#117	—	2	4	no	—
603	#117	—	2	4	no	—
604	#117	—	2	4	no	—
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
645	C₂×C₄²	—	2	4	no	—
646	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
647	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
648	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
651	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
654	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
657	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
658	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
659	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
660	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
661	#95	C₂³×C₆₇	1	2	yes	—
662	#95	C₂³×C₆₇	1	2	yes	—
663	#95	C₂³×C₆₇	1	2	yes	—
664	#95	C₂³×C₆₇	1	2	yes	—
665	#95	C₂³×C₆₇	1	1	yes	characteristic
666	#95	C₂³×C₆₇	1	1	yes	characteristic
667	#95	C₂³×C₆₇	1	1	yes	characteristic
668	#95	C₂³×C₆₇	1	1	yes	characteristic
669	#95	C₂³×C₆₇	1	1	yes	characteristic
670	#95	C₂³×C₆₇	1	2	yes	—
671	#95	C₂³×C₆₇	1	2	yes	—
672	#95	C₂³×C₆₇	1	1	yes	characteristic
673	#95	C₂³×C₆₇	1	1	yes	characteristic
674	#95	C₂³×C₆₇	1	1	yes	characteristic
675	#95	C₂³×C₆₇	1	2	yes	—
676	#95	C₂³×C₆₇	1	1	yes	characteristic
677	#95	C₂³×C₆₇	1	2	yes	—
678	#95	C₂³×C₆₇	1	2	yes	—
679	#95	C₂³×C₆₇	1	1	yes	characteristic
680	#95	C₂³×C₆₇	1	2	yes	—
681	#95	C₂³×C₆₇	1	2	yes	—
682	#95	C₂³×C₆₇	1	2	yes	—
683	#95	C₂³×C₆₇	1	2	yes	—
684	#95	C₂³×C₆₇	1	2	yes	—
685	#95	C₂³×C₆₇	1	2	yes	—
686	#95	C₂³×C₆₇	1	2	yes	—
687	#95	C₂³×C₆₇	1	2	yes	—
688	#95	C₂³×C₆₇	1	2	yes	—
689	#95	C₂³×C₆₇	1	2	yes	—
690	#95	C₂³×C₆₇	1	2	yes	—
691	#95	C₂³×C₆₇	1	2	yes	—
692	#95	C₂³×C₆₇	1	2	yes	—
693	#95	C₂³×C₆₇	1	2	yes	—
694	#95	C₂³×C₆₇	1	2	yes	—
695	#95	C₂³×C₆₇	1	2	yes	—
696	#95	C₂³×C₆₇	1	2	yes	—
697	#95	C₂³×C₆₇	1	2	yes	—
698	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
699	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	4	no	—
704	C₂×Q₈	—	4	2	no	—
705	C₂×Q₈	—	4	2	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	4	1	no	—
708	C₂×D₄	—	4	1	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	4	1	no	—
718	C₂²×C₄	—	4	1	no	—
719	C₂²×C₄	—	4	1	no	—
720	C₂²×C₄	#41×C₆₇	1	4	yes	—
721	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	1	no	—
765	C₄⋊C₄	#41×C₆₇	1	4	yes	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	—	4	1	no	—
780	C₂²⋊C₄	—	4	1	no	—
781	C₂²⋊C₄	—	4	1	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	4	no	—
786	C₄²	—	2	4	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	4	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	4	no	—
792	C₄²	—	4	2	no	—
793	C₄²	—	4	2	no	—
794	C₄²	—	4	2	no	—
795	C₄²	—	4	2	no	—
796	C₄²	#41×C₆₇	1	4	yes	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	1	no	—
810	C₂³	C₂×#41×C₆₇	1	2	yes	—
811	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
812	Q₈	—	4	4	no	—
813	Q₈	—	8	4	no	—
814	D₄	—	4	4	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	8	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	4	4	no	—
872	C₂×C₄	—	4	4	no	—
873	C₂×C₄	—	4	4	no	—
874	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
875	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
876	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
877	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
878	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
879	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
880	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
881	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	1	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	1	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	1	no	—
896	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
897	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
898	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
899	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
900	C₂²	#585×C₆₇	1	1	yes	characteristic
901	C₂²	#585×C₆₇	1	1	yes	characteristic
902	C₂²	#585×C₆₇	1	1	yes	characteristic
903	C₄	—	2	4	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	2	no	—
915	C₄	—	4	1	no	—
916	C₄	—	4	2	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	1	no	—
923	C₄	#529×C₆₇	1	4	yes	—
924	C₂	—	4	2	no	—
925	C₂	—	8	1	no	—
926	C₂	C₂×#529×C₆₇	1	1	yes	characteristic
927	C₂	C₆₇×#3455	1	1	yes	characteristic
928	C₂	C₆₇×#3461	1	1	yes	characteristic
929	C₂	C₆₇×#3493	1	1	yes	characteristic
930	C₂	C₆₇×#3495	1	1	yes	characteristic
931	C₂	C₆₇×#3518	1	1	yes	characteristic
932	C₂	C₆₇×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂²×D₄×C₆₇	C₂³
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×#2865	C₂	semidirect
2. C₆₇×#2863	C₂	semidirect
4. C₆₇×#2652	C₂	semidirect
5. C₆₇×#2532	C₂	semidirect
6. C₆₇×#2528	C₂	semidirect
7. C₆₇×#2523	C₂	semidirect
9. C₆₇×#2514	C₂	semidirect
10. C₆₇×#2507	C₂	semidirect
11. C₆₇×#2499	C₂	semidirect
12. C₆₇×#2495	C₂	semidirect
13. C₆₇×#2492	C₂	semidirect
15. C₆₇×#2439	C₂	semidirect
17. C₆₇×#2331	C₂	semidirect
18. C₆₇×#2323	C₂	semidirect
19. C₆₇×#2320	C₂	semidirect
20. C₆₇×#2314	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
23. C₄×#117×C₆₇	C₂	semidirect
457. #35162	C₆₇	direct (N × H)
467. #2865	C₂×C₆₇	semidirect
468. #2863	C₂×C₆₇	semidirect
470. #2652	C₂×C₆₇	semidirect
471. #2532	C₂×C₆₇	semidirect
472. #2528	C₂×C₆₇	semidirect
473. #2523	C₂×C₆₇	semidirect
475. #2514	C₂×C₆₇	semidirect
476. #2507	C₂×C₆₇	semidirect
477. #2499	C₂×C₆₇	semidirect
478. #2495	C₂×C₆₇	semidirect
479. #2492	C₂×C₆₇	semidirect
481. #2439	C₂×C₆₇	semidirect
483. #2331	C₂×C₆₇	semidirect
484. #2323	C₂×C₆₇	semidirect
485. #2320	C₂×C₆₇	semidirect
486. #2314	C₂×C₆₇	semidirect
487. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
489. C₄×#117	C₂×C₆₇	semidirect
490. C₆₇	#35162	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×#2865	2
C₆₇×#2863	2
C₆₇×#2653	2
C₆₇×#2652	2
C₆₇×#2532	2
C₆₇×#2528	2
C₆₇×#2523	2
C₆₇×#2518	2
C₆₇×#2514	2
C₆₇×#2507	2
C₆₇×#2499	2
C₆₇×#2495	2
C₆₇×#2492	2
C₆₇×#2485	2
C₆₇×#2439	2
C₆₇×#2415	2
C₆₇×#2331	2
C₆₇×#2323	2
C₆₇×#2320	2
C₆₇×#2314	2
C₄×C₂²⋊Q₈×C₆₇	2
C₆₇×#2290	2
C₄×#117×C₆₇	2
#35162	67

Subgroups — C67×#35162 #30714413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35162 #30714413