Subgroups — C₆₇×#59502 #30738753

Order 17152.

1642 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2762	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2698	C₂	1	2	yes	maximal
3	C₆₇×#2611	C₂	1	2	yes	maximal
4	C₆₇×#2590	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2575	C₂	1	2	yes	maximal
6	C₆₇×#2570	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2528	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2509	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2506	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2494	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#2462	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2440	C₂	1	1	yes	maximal, characteristic
14	C₆₇×#2423	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2421	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2362	C₂	1	2	yes	maximal
17	C₆₇×#2360	C₂	1	1	yes	maximal, characteristic
18	C₆₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2351	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2344	C₂	1	1	yes	maximal, characteristic
21	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#126×C₆₇	C₂	1	1	yes	maximal, characteristic
23	C₆₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#125×C₆₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
33	C₂×#117×C₆₇	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
35	#401×C₆₇	C₂²	1	2	yes	—
36	#400×C₆₇	C₂²	1	2	yes	—
37	#400×C₆₇	C₂²	1	2	yes	—
38	#400×C₆₇	C₂²	1	2	yes	—
39	#400×C₆₇	C₂²	1	2	yes	—
40	#400×C₆₇	C₂²	1	2	yes	—
41	#399×C₆₇	C₂²	1	2	yes	—
42	#398×C₆₇	C₂²	1	2	yes	—
43	#398×C₆₇	C₂²	1	2	yes	—
44	#398×C₆₇	C₂²	1	2	yes	—
45	#398×C₆₇	C₂²	1	2	yes	—
46	#398×C₆₇	C₂²	1	2	yes	—
47	#397×C₆₇	C₂²	1	2	yes	—
48	#397×C₆₇	C₂²	1	2	yes	—
49	#395×C₆₇	C₂²	1	2	yes	—
50	#395×C₆₇	C₂²	1	2	yes	—
51	#391×C₆₇	C₂²	1	2	yes	—
52	#391×C₆₇	C₂²	1	2	yes	—
53	#391×C₆₇	C₂²	1	1	yes	characteristic
54	#391×C₆₇	C₂²	1	1	yes	characteristic
55	#391×C₆₇	C₂²	1	1	yes	characteristic
56	#389×C₆₇	C₂²	1	1	yes	characteristic
57	#389×C₆₇	C₂²	1	1	yes	characteristic
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	2	yes	—
62	#389×C₆₇	C₂²	1	1	yes	characteristic
63	#389×C₆₇	C₂²	1	1	yes	characteristic
64	#389×C₆₇	C₂²	1	2	yes	—
65	#389×C₆₇	C₂²	1	1	yes	characteristic
66	#389×C₆₇	C₂²	1	1	yes	characteristic
67	#389×C₆₇	C₂²	1	2	yes	—
68	#389×C₆₇	C₂²	1	2	yes	—
69	#389×C₆₇	C₂²	1	2	yes	—
70	#388×C₆₇	C₂²	1	1	yes	characteristic
71	#388×C₆₇	C₂²	1	1	yes	characteristic
72	#388×C₆₇	C₂²	1	1	yes	characteristic
73	#388×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
87	#387×C₆₇	C₂²	1	2	yes	—
88	#387×C₆₇	C₂²	1	2	yes	—
89	#387×C₆₇	C₂²	1	1	yes	characteristic
90	#387×C₆₇	C₂²	1	1	yes	characteristic
91	#387×C₆₇	C₂²	1	2	yes	—
92	#387×C₆₇	C₂²	1	2	yes	—
93	#387×C₆₇	C₂²	1	2	yes	—
94	#385×C₆₇	C₂²	1	2	yes	—
95	#385×C₆₇	C₂²	1	2	yes	—
96	#384×C₆₇	C₂²	1	1	yes	characteristic
97	#384×C₆₇	C₂²	1	1	yes	characteristic
98	#383×C₆₇	C₂²	1	1	yes	characteristic
99	#382×C₆₇	C₂²	1	2	yes	—
100	#382×C₆₇	C₂²	1	1	yes	characteristic
101	#382×C₆₇	C₂²	1	2	yes	—
102	#382×C₆₇	C₂²	1	1	yes	characteristic
103	#381×C₆₇	C₂²	1	2	yes	—
104	#380×C₆₇	C₂²	1	1	yes	characteristic
105	#380×C₆₇	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×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	2	yes	—
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
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×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
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	2	yes	—
121	#376×C₆₇	C₂²	1	2	yes	—
122	C₄³×C₆₇	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
124	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
127	C₄⋊Q₈×C₆₇	—	2	4	no	—
128	#126×C₆₇	—	2	4	no	—
129	#125×C₆₇	—	4	4	no	—
130	C₂²⋊Q₈×C₆₇	—	2	4	no	—
131	C₂²⋊Q₈×C₆₇	—	2	8	no	—
132	C₄×Q₈×C₆₇	—	2	4	no	—
133	C₄×Q₈×C₆₇	—	2	4	no	—
134	C₄×Q₈×C₆₇	—	2	4	no	—
135	C₄×Q₈×C₆₇	—	4	4	no	—
136	#117×C₆₇	—	4	4	no	—
137	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
184	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	1	yes	characteristic
202	#95×C₆₇	C₂³	1	1	yes	characteristic
203	#95×C₆₇	C₂³	1	1	yes	characteristic
204	#95×C₆₇	C₂³	1	1	yes	characteristic
205	#95×C₆₇	C₂³	1	1	yes	characteristic
206	#95×C₆₇	C₂³	1	1	yes	characteristic
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
215	#95×C₆₇	C₂³	1	1	yes	characteristic
216	#95×C₆₇	C₂³	1	1	yes	characteristic
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	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	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂×Q₈×C₆₇	—	2	2	no	—
235	C₂×Q₈×C₆₇	—	2	4	no	—
236	C₂×Q₈×C₆₇	—	2	4	no	—
237	C₂×Q₈×C₆₇	—	2	2	no	—
238	C₂×Q₈×C₆₇	—	4	2	no	—
239	C₂×Q₈×C₆₇	#41	1	4	yes	—
240	C₂²×C₄×C₆₇	—	2	4	no	—
241	C₂²×C₄×C₆₇	—	2	4	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	—	4	2	no	—
246	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₄⋊C₄×C₆₇	—	2	4	no	—
269	C₄⋊C₄×C₆₇	—	2	2	no	—
270	C₄⋊C₄×C₆₇	—	2	4	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	2	2	no	—
274	C₄⋊C₄×C₆₇	—	2	2	no	—
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	—	2	2	no	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	—	2	4	no	—
279	C₄⋊C₄×C₆₇	—	2	4	no	—
280	C₄⋊C₄×C₆₇	—	2	2	no	—
281	C₄⋊C₄×C₆₇	—	2	2	no	—
282	C₄⋊C₄×C₆₇	—	2	2	no	—
283	C₄⋊C₄×C₆₇	—	2	4	no	—
284	C₄⋊C₄×C₆₇	—	2	2	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	—	2	4	no	—
290	C₄⋊C₄×C₆₇	—	2	4	no	—
291	C₄⋊C₄×C₆₇	—	2	2	no	—
292	C₄⋊C₄×C₆₇	—	2	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	2	no	—
298	C₄⋊C₄×C₆₇	—	4	2	no	—
299	C₄⋊C₄×C₆₇	#41	1	4	yes	—
300	C₂²⋊C₄×C₆₇	—	2	4	no	—
301	C₂²⋊C₄×C₆₇	—	2	2	no	—
302	C₂²⋊C₄×C₆₇	—	2	2	no	—
303	C₂²⋊C₄×C₆₇	—	2	4	no	—
304	C₂²⋊C₄×C₆₇	—	2	2	no	—
305	C₂²⋊C₄×C₆₇	—	2	2	no	—
306	C₂²⋊C₄×C₆₇	—	2	2	no	—
307	C₂²⋊C₄×C₆₇	—	4	2	no	—
308	C₂²⋊C₄×C₆₇	#41	1	4	yes	—
309	C₄²×C₆₇	—	2	4	no	—
310	C₄²×C₆₇	—	2	4	no	—
311	C₄²×C₆₇	—	2	2	no	—
312	C₄²×C₆₇	—	2	2	no	—
313	C₄²×C₆₇	—	2	4	no	—
314	C₄²×C₆₇	—	2	2	no	—
315	C₄²×C₆₇	—	2	2	no	—
316	C₄²×C₆₇	—	2	2	no	—
317	C₄²×C₆₇	—	2	4	no	—
318	C₄²×C₆₇	—	2	2	no	—
319	C₄²×C₆₇	—	2	2	no	—
320	C₄²×C₆₇	—	2	2	no	—
321	C₄²×C₆₇	—	2	2	no	—
322	C₄²×C₆₇	—	2	2	no	—
323	C₄²×C₆₇	—	4	2	no	—
324	C₄²×C₆₇	—	4	2	no	—
325	C₄²×C₆₇	—	4	2	no	—
326	C₂³×C₆₇	—	2	1	no	—
327	C₂³×C₆₇	—	2	1	no	—
328	C₂³×C₆₇	—	2	1	no	—
329	C₂³×C₆₇	—	2	1	no	—
330	C₂³×C₆₇	—	2	1	no	—
331	C₂³×C₆₇	—	2	1	no	—
332	C₂³×C₆₇	C₂×#41	1	2	yes	—
333	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
334	Q₈×C₆₇	—	2	8	no	—
335	Q₈×C₆₇	—	4	8	no	—
336	C₂×C₄×C₆₇	—	2	1	no	—
337	C₂×C₄×C₆₇	—	2	1	no	—
338	C₂×C₄×C₆₇	—	2	1	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	1	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	1	no	—
343	C₂×C₄×C₆₇	—	2	1	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	1	no	—
346	C₂×C₄×C₆₇	—	2	1	no	—
347	C₂×C₄×C₆₇	—	2	1	no	—
348	C₂×C₄×C₆₇	—	2	1	no	—
349	C₂×C₄×C₆₇	—	2	2	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	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	1	no	—
358	C₂×C₄×C₆₇	—	2	1	no	—
359	C₂×C₄×C₆₇	—	2	2	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	2	no	—
368	C₂×C₄×C₆₇	—	2	2	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	2	no	—
373	C₂×C₄×C₆₇	—	2	2	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	1	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	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	1	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	1	no	—
392	C₂×C₄×C₆₇	—	4	8	no	—
393	C₂×C₄×C₆₇	—	4	4	no	—
394	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
395	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
396	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
397	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
398	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
399	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
400	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
401	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
402	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
403	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
404	C₂²×C₆₇	—	2	2	no	—
405	C₂²×C₆₇	—	2	2	no	—
406	C₂²×C₆₇	—	2	2	no	—
407	C₂²×C₆₇	—	4	1	no	—
408	C₂²×C₆₇	—	4	1	no	—
409	C₂²×C₆₇	—	4	1	no	—
410	C₂²×C₆₇	—	4	1	no	—
411	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
412	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
413	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
414	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
415	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
416	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
417	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
418	C₄×C₆₇	—	2	4	no	—
419	C₄×C₆₇	—	2	4	no	—
420	C₄×C₆₇	—	2	2	no	—
421	C₄×C₆₇	—	2	2	no	—
422	C₄×C₆₇	—	2	2	no	—
423	C₄×C₆₇	—	2	2	no	—
424	C₄×C₆₇	—	2	2	no	—
425	C₄×C₆₇	—	4	1	no	—
426	C₄×C₆₇	—	4	1	no	—
427	C₄×C₆₇	—	4	2	no	—
428	C₄×C₆₇	—	4	2	no	—
429	C₄×C₆₇	—	4	1	no	—
430	C₄×C₆₇	—	4	2	no	—
431	C₄×C₆₇	—	4	1	no	—
432	C₄×C₆₇	—	4	1	no	—
433	C₄×C₆₇	—	4	2	no	—
434	C₄×C₆₇	—	4	1	no	—
435	C₄×C₆₇	—	4	2	no	—
436	C₄×C₆₇	—	4	1	no	—
437	C₄×C₆₇	—	4	2	no	—
438	C₄×C₆₇	—	4	1	no	—
439	C₄×C₆₇	#552	1	4	yes	—
440	#59502	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
441	C₂×C₆₇	—	4	2	no	—
442	C₂×C₆₇	C₂×#552	1	1	yes	characteristic
443	C₂×C₆₇	#3481	1	1	yes	characteristic
444	C₂×C₆₇	#3482	1	1	yes	characteristic
445	C₂×C₆₇	#3509	1	1	yes	characteristic
446	C₂×C₆₇	#3522	1	1	yes	characteristic
447	C₂×C₆₇	#3523	1	1	yes	characteristic
448	C₂×C₆₇	#3552	1	1	yes	characteristic
449	#2762	C₂×C₆₇	1	2	yes	complemented
450	#2698	C₂×C₆₇	1	2	yes	—
451	#2611	C₂×C₆₇	1	2	yes	—
452	#2590	C₂×C₆₇	1	2	yes	complemented
453	#2575	C₂×C₆₇	1	2	yes	—
454	#2570	C₂×C₆₇	1	1	yes	characteristic, complemented
455	#2528	C₂×C₆₇	1	2	yes	complemented
456	#2509	C₂×C₆₇	1	1	yes	characteristic, complemented
457	#2506	C₂×C₆₇	1	1	yes	characteristic, complemented
458	#2494	C₂×C₆₇	1	1	yes	characteristic
459	#2462	C₂×C₆₇	1	2	yes	complemented
460	#2451	C₂×C₆₇	1	1	yes	characteristic, complemented
461	#2440	C₂×C₆₇	1	1	yes	characteristic
462	#2423	C₂×C₆₇	1	1	yes	characteristic
463	#2421	C₂×C₆₇	1	1	yes	characteristic
464	#2362	C₂×C₆₇	1	2	yes	—
465	#2360	C₂×C₆₇	1	1	yes	characteristic
466	#2355	C₂×C₆₇	1	1	yes	characteristic, complemented
467	#2351	C₂×C₆₇	1	1	yes	characteristic, complemented
468	#2344	C₂×C₆₇	1	1	yes	characteristic
469	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
470	C₄×#126	C₂×C₆₇	1	1	yes	characteristic
471	#2295	C₂×C₆₇	1	1	yes	characteristic, complemented
472	C₆₇	#59502	1	1	yes	characteristic, direct product factor, Sylow
473	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
474	C₂×#126	C₂²×C₆₇	1	1	yes	characteristic
475	C₂×#125	C₂²×C₆₇	1	2	yes	—
476	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
477	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
478	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
479	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
480	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
481	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
482	C₂×#117	C₂²×C₆₇	1	2	yes	—
483	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
484	#401	C₂²×C₆₇	1	2	yes	—
485	#400	C₂²×C₆₇	1	2	yes	—
486	#400	C₂²×C₆₇	1	2	yes	—
487	#400	C₂²×C₆₇	1	2	yes	—
488	#400	C₂²×C₆₇	1	2	yes	—
489	#400	C₂²×C₆₇	1	2	yes	—
490	#399	C₂²×C₆₇	1	2	yes	—
491	#398	C₂²×C₆₇	1	2	yes	—
492	#398	C₂²×C₆₇	1	2	yes	—
493	#398	C₂²×C₆₇	1	2	yes	—
494	#398	C₂²×C₆₇	1	2	yes	—
495	#398	C₂²×C₆₇	1	2	yes	—
496	#397	C₂²×C₆₇	1	2	yes	—
497	#397	C₂²×C₆₇	1	2	yes	—
498	#395	C₂²×C₆₇	1	2	yes	—
499	#395	C₂²×C₆₇	1	2	yes	—
500	#391	C₂²×C₆₇	1	2	yes	—
501	#391	C₂²×C₆₇	1	1	yes	characteristic
502	#391	C₂²×C₆₇	1	1	yes	characteristic
503	#391	C₂²×C₆₇	1	2	yes	—
504	#391	C₂²×C₆₇	1	1	yes	characteristic
505	#389	C₂²×C₆₇	1	1	yes	characteristic
506	#389	C₂²×C₆₇	1	2	yes	—
507	#389	C₂²×C₆₇	1	1	yes	characteristic
508	#389	C₂²×C₆₇	1	1	yes	characteristic
509	#389	C₂²×C₆₇	1	1	yes	characteristic
510	#389	C₂²×C₆₇	1	2	yes	—
511	#389	C₂²×C₆₇	1	2	yes	—
512	#389	C₂²×C₆₇	1	2	yes	—
513	#389	C₂²×C₆₇	1	1	yes	characteristic
514	#389	C₂²×C₆₇	1	2	yes	—
515	#389	C₂²×C₆₇	1	1	yes	characteristic
516	#389	C₂²×C₆₇	1	1	yes	characteristic
517	#389	C₂²×C₆₇	1	1	yes	characteristic
518	#389	C₂²×C₆₇	1	1	yes	characteristic
519	#388	C₂²×C₆₇	1	1	yes	characteristic
520	#388	C₂²×C₆₇	1	1	yes	characteristic
521	#388	C₂²×C₆₇	1	1	yes	characteristic
522	#388	C₂²×C₆₇	1	2	yes	—
523	#388	C₂²×C₆₇	1	2	yes	—
524	#388	C₂²×C₆₇	1	2	yes	—
525	#387	C₂²×C₆₇	1	1	yes	characteristic
526	#387	C₂²×C₆₇	1	1	yes	characteristic
527	#387	C₂²×C₆₇	1	1	yes	characteristic
528	#387	C₂²×C₆₇	1	2	yes	—
529	#387	C₂²×C₆₇	1	2	yes	—
530	#387	C₂²×C₆₇	1	2	yes	—
531	#387	C₂²×C₆₇	1	2	yes	—
532	#387	C₂²×C₆₇	1	2	yes	—
533	#387	C₂²×C₆₇	1	2	yes	—
534	#387	C₂²×C₆₇	1	2	yes	—
535	#387	C₂²×C₆₇	1	2	yes	—
536	#387	C₂²×C₆₇	1	2	yes	—
537	#387	C₂²×C₆₇	1	2	yes	—
538	#387	C₂²×C₆₇	1	2	yes	—
539	#387	C₂²×C₆₇	1	2	yes	—
540	#387	C₂²×C₆₇	1	2	yes	—
541	#387	C₂²×C₆₇	1	2	yes	—
542	#387	C₂²×C₆₇	1	2	yes	—
543	#385	C₂²×C₆₇	1	2	yes	—
544	#385	C₂²×C₆₇	1	2	yes	—
545	#384	C₂²×C₆₇	1	1	yes	characteristic
546	#384	C₂²×C₆₇	1	1	yes	characteristic
547	#383	C₂²×C₆₇	1	1	yes	characteristic
548	#382	C₂²×C₆₇	1	1	yes	characteristic
549	#382	C₂²×C₆₇	1	1	yes	characteristic
550	#382	C₂²×C₆₇	1	2	yes	—
551	#382	C₂²×C₆₇	1	2	yes	—
552	#381	C₂²×C₆₇	1	2	yes	—
553	#380	C₂²×C₆₇	1	1	yes	characteristic
554	#380	C₂²×C₆₇	1	1	yes	characteristic
555	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
556	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
558	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
559	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
560	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
561	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
563	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
565	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
566	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
567	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
568	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
569	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
570	#376	C₂²×C₆₇	1	2	yes	—
571	C₄³	C₂²×C₆₇	1	1	yes	characteristic
572	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
573	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
576	C₄⋊Q₈	—	2	4	no	—
577	#126	—	2	4	no	—
578	#125	—	4	4	no	—
579	C₂²⋊Q₈	—	2	4	no	—
580	C₂²⋊Q₈	—	2	8	no	—
581	C₄×Q₈	—	2	4	no	—
582	C₄×Q₈	—	2	4	no	—
583	C₄×Q₈	—	2	4	no	—
584	C₄×Q₈	—	4	4	no	—
585	#117	—	4	4	no	—
586	C₂×C₄⋊C₄	—	2	4	no	—
587	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	2	yes	—
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	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
632	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
635	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
636	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
643	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
644	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
645	#95	C₂³×C₆₇	1	2	yes	—
646	#95	C₂³×C₆₇	1	2	yes	—
647	#95	C₂³×C₆₇	1	2	yes	—
648	#95	C₂³×C₆₇	1	2	yes	—
649	#95	C₂³×C₆₇	1	2	yes	—
650	#95	C₂³×C₆₇	1	1	yes	characteristic
651	#95	C₂³×C₆₇	1	1	yes	characteristic
652	#95	C₂³×C₆₇	1	1	yes	characteristic
653	#95	C₂³×C₆₇	1	1	yes	characteristic
654	#95	C₂³×C₆₇	1	1	yes	characteristic
655	#95	C₂³×C₆₇	1	1	yes	characteristic
656	#95	C₂³×C₆₇	1	2	yes	—
657	#95	C₂³×C₆₇	1	1	yes	characteristic
658	#95	C₂³×C₆₇	1	2	yes	—
659	#95	C₂³×C₆₇	1	2	yes	—
660	#95	C₂³×C₆₇	1	2	yes	—
661	#95	C₂³×C₆₇	1	1	yes	characteristic
662	#95	C₂³×C₆₇	1	2	yes	—
663	#95	C₂³×C₆₇	1	2	yes	—
664	#95	C₂³×C₆₇	1	1	yes	characteristic
665	#95	C₂³×C₆₇	1	1	yes	characteristic
666	#95	C₂³×C₆₇	1	2	yes	—
667	#95	C₂³×C₆₇	1	1	yes	characteristic
668	#95	C₂³×C₆₇	1	1	yes	characteristic
669	#95	C₂³×C₆₇	1	2	yes	—
670	#95	C₂³×C₆₇	1	2	yes	—
671	#95	C₂³×C₆₇	1	2	yes	—
672	#95	C₂³×C₆₇	1	2	yes	—
673	#95	C₂³×C₆₇	1	2	yes	—
674	#95	C₂³×C₆₇	1	2	yes	—
675	#95	C₂³×C₆₇	1	2	yes	—
676	#95	C₂³×C₆₇	1	2	yes	—
677	#95	C₂³×C₆₇	1	2	yes	—
678	#95	C₂³×C₆₇	1	2	yes	—
679	#95	C₂³×C₆₇	1	2	yes	—
680	#95	C₂³×C₆₇	1	2	yes	—
681	#95	C₂³×C₆₇	1	2	yes	—
682	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	4	no	—
685	C₂×Q₈	—	2	4	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	4	2	no	—
688	C₂×Q₈	#41×C₆₇	1	4	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	#41×C₆₇	1	4	yes	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	#41×C₆₇	1	4	yes	—
758	C₄²	—	2	4	no	—
759	C₄²	—	2	4	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	4	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	4	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	4	2	no	—
773	C₄²	—	4	2	no	—
774	C₄²	—	4	2	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	C₂×#41×C₆₇	1	2	yes	—
782	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
783	Q₈	—	2	8	no	—
784	Q₈	—	4	8	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	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	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	4	8	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
844	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
845	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
846	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
847	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
848	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
849	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
850	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
851	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
852	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
861	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
862	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
863	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
864	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
865	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
866	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	4	no	—
871	C₄	—	2	4	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	1	no	—
888	C₄	#552×C₆₇	1	4	yes	—
889	C₂	—	4	2	no	—
890	C₂	C₂×#552×C₆₇	1	1	yes	characteristic
891	C₂	C₆₇×#3481	1	1	yes	characteristic
892	C₂	C₆₇×#3482	1	1	yes	characteristic
893	C₂	C₆₇×#3509	1	1	yes	characteristic
894	C₂	C₆₇×#3522	1	1	yes	characteristic
895	C₂	C₆₇×#3523	1	1	yes	characteristic
896	C₂	C₆₇×#3552	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂⁴×C₆₇	C₂⁴
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×#2762	C₂	semidirect
4. C₆₇×#2590	C₂	semidirect
6. C₆₇×#2570	C₂	semidirect
7. C₆₇×#2528	C₂	semidirect
8. C₆₇×#2509	C₂	semidirect
9. C₆₇×#2506	C₂	semidirect
11. C₆₇×#2462	C₂	semidirect
12. C₆₇×#2451	C₂	semidirect
18. C₆₇×#2355	C₂	semidirect
19. C₆₇×#2351	C₂	semidirect
21. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
23. C₆₇×#2295	C₂	semidirect
440. #59502	C₆₇	direct (N × H)
449. #2762	C₂×C₆₇	semidirect
452. #2590	C₂×C₆₇	semidirect
454. #2570	C₂×C₆₇	semidirect
455. #2528	C₂×C₆₇	semidirect
456. #2509	C₂×C₆₇	semidirect
457. #2506	C₂×C₆₇	semidirect
459. #2462	C₂×C₆₇	semidirect
460. #2451	C₂×C₆₇	semidirect
466. #2355	C₂×C₆₇	semidirect
467. #2351	C₂×C₆₇	semidirect
469. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
471. #2295	C₂×C₆₇	semidirect
472. C₆₇	#59502	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×#2762	2
C₆₇×#2698	2
C₆₇×#2611	2
C₆₇×#2590	2
C₆₇×#2575	2
C₆₇×#2570	2
C₆₇×#2528	2
C₆₇×#2509	2
C₆₇×#2506	2
C₆₇×#2494	2
C₆₇×#2462	2
C₆₇×#2451	2
C₆₇×#2440	2
C₆₇×#2423	2
C₆₇×#2421	2
C₆₇×#2362	2
C₆₇×#2360	2
C₆₇×#2355	2
C₆₇×#2351	2
C₆₇×#2344	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#126×C₆₇	2
C₆₇×#2295	2
#59502	67

Subgroups — C67×#59502 #30738753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59502 #30738753