Subgroups — C₆₇×#22495 #30701746

Order 17152.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#435×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1987	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1895	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1874	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1823	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#1762	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#1736	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#340×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	—	2	1	no	—
17	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
19	#547×C₆₇	—	2	4	no	—
20	#547×C₆₇	C₄	1	8	yes	complemented
21	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#123×C₆₇	—	2	1	no	—
23	C₂×#123×C₆₇	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
25	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×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	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
33	#435×C₆₇	—	2	4	no	—
34	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
42	#388×C₆₇	—	2	1	no	—
43	#387×C₆₇	—	2	1	no	—
44	#386×C₆₇	—	2	1	no	—
45	#382×C₆₇	C₂²	1	1	yes	characteristic
46	#380×C₆₇	C₂²	1	1	yes	characteristic
47	#380×C₆₇	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
50	#340×C₆₇	C₂²	1	1	yes	characteristic
51	#340×C₆₇	C₂²	1	1	yes	characteristic
52	#340×C₆₇	C₂²	1	1	yes	characteristic
53	#340×C₆₇	C₂²	1	1	yes	characteristic
54	#340×C₆₇	C₂²	1	1	yes	characteristic
55	#340×C₆₇	C₂²	1	1	yes	characteristic
56	#340×C₆₇	C₂²	1	1	yes	characteristic
57	#340×C₆₇	C₂²	1	1	yes	characteristic
58	#340×C₆₇	C₂²	1	1	yes	characteristic
59	#340×C₆₇	C₂²	1	1	yes	characteristic
60	#340×C₆₇	C₂²	1	1	yes	characteristic
61	#340×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×#41×C₆₇	—	2	8	no	—
63	C₂×#41×C₆₇	—	4	4	no	—
64	C₂×#41×C₆₇	—	4	4	no	—
65	C₂²×Q₈×C₆₇	—	2	1	no	—
66	C₂²×D₄×C₆₇	—	2	1	no	—
67	C₂²×D₄×C₆₇	—	2	1	no	—
68	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
69	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₆₇	—	2	1	no	—
71	C₂³×C₄×C₆₇	—	2	1	no	—
72	C₂³×C₄×C₆₇	—	2	1	no	—
73	C₂³×C₄×C₆₇	—	2	1	no	—
74	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₆₇	—	2	2	no	—
77	C₂×M₁₆×C₆₇	—	2	2	no	—
78	C₂×M₁₆×C₆₇	—	4	1	no	—
79	C₂²×C₈×C₆₇	—	2	2	no	—
80	C₂²×C₈×C₆₇	—	2	2	no	—
81	C₂²×C₈×C₆₇	—	4	1	no	—
82	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₄⋊Q₈×C₆₇	—	2	2	no	—
87	C₄⋊Q₈×C₆₇	C₂×C₄	1	4	yes	complemented
88	#123×C₆₇	—	2	8	no	—
89	#123×C₆₇	—	2	8	no	—
90	C₂²⋊Q₈×C₆₇	—	2	8	no	—
91	#121×C₆₇	—	2	2	no	—
92	#121×C₆₇	—	2	2	no	—
93	#121×C₆₇	C₂×C₄	1	4	yes	—
94	#121×C₆₇	C₂×C₄	1	4	yes	complemented
95	C₄×D₄×C₆₇	—	2	2	no	—
96	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
97	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	complemented
98	C₄×D₄×C₆₇	D₄	1	4	yes	—
99	#117×C₆₇	—	2	2	no	—
100	#117×C₆₇	—	4	1	no	—
101	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
102	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
103	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
104	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
105	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
106	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
107	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
108	C₂×C₄⋊C₄×C₆₇	—	4	1	no	—
109	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
110	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	complemented
111	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₆₇	—	2	1	no	—
128	C₂×C₄²×C₆₇	—	2	1	no	—
129	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
130	C₄⋊C₈×C₆₇	—	2	2	no	—
131	#102×C₆₇	—	2	2	no	—
132	#102×C₆₇	—	2	2	no	—
133	#102×C₆₇	—	4	1	no	—
134	#102×C₆₇	—	4	1	no	—
135	C₂²⋊C₈×C₆₇	—	2	2	no	—
136	C₂²⋊C₈×C₆₇	—	2	2	no	—
137	#97×C₆₇	—	2	2	no	—
138	#95×C₆₇	—	2	1	no	—
139	#95×C₆₇	—	2	1	no	—
140	#95×C₆₇	—	2	1	no	—
141	#95×C₆₇	—	2	1	no	—
142	#95×C₆₇	—	2	1	no	—
143	C₂⁴×C₆₇	—	2	1	no	—
144	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
145	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
146	#41×C₆₇	—	4	32	no	—
147	C₂×Q₈×C₆₇	—	2	4	no	—
148	C₂×Q₈×C₆₇	—	4	2	no	—
149	C₂×Q₈×C₆₇	—	4	2	no	—
150	C₂×D₄×C₆₇	—	2	2	no	—
151	C₂×D₄×C₆₇	—	2	2	no	—
152	C₂×D₄×C₆₇	—	2	4	no	—
153	C₂×D₄×C₆₇	—	2	4	no	—
154	C₂×D₄×C₆₇	—	2	1	no	—
155	C₂×D₄×C₆₇	—	2	1	no	—
156	C₂×D₄×C₆₇	—	2	1	no	—
157	C₂×D₄×C₆₇	—	2	1	no	—
158	C₂×D₄×C₆₇	—	2	1	no	—
159	C₂×D₄×C₆₇	—	4	2	no	—
160	C₂×D₄×C₆₇	—	4	2	no	—
161	C₂×D₄×C₆₇	—	4	2	no	—
162	C₂×D₄×C₆₇	—	4	2	no	—
163	C₂×D₄×C₆₇	C₂²⋊C₄	1	4	yes	—
164	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
165	C₂²×C₄×C₆₇	—	2	1	no	—
166	C₂²×C₄×C₆₇	—	2	1	no	—
167	C₂²×C₄×C₆₇	—	2	1	no	—
168	C₂²×C₄×C₆₇	—	2	1	no	—
169	C₂²×C₄×C₆₇	—	2	1	no	—
170	C₂²×C₄×C₆₇	—	2	1	no	—
171	C₂²×C₄×C₆₇	—	2	1	no	—
172	C₂²×C₄×C₆₇	—	2	1	no	—
173	C₂²×C₄×C₆₇	—	2	4	no	—
174	C₂²×C₄×C₆₇	—	2	4	no	—
175	C₂²×C₄×C₆₇	—	2	1	no	—
176	C₂²×C₄×C₆₇	—	2	1	no	—
177	C₂²×C₄×C₆₇	—	2	1	no	—
178	C₂²×C₄×C₆₇	—	2	1	no	—
179	C₂²×C₄×C₆₇	—	2	4	no	—
180	C₂²×C₄×C₆₇	—	2	1	no	—
181	C₂²×C₄×C₆₇	—	2	1	no	—
182	C₂²×C₄×C₆₇	—	2	1	no	—
183	C₂²×C₄×C₆₇	—	4	2	no	—
184	C₂²×C₄×C₆₇	—	4	2	no	—
185	C₂²×C₄×C₆₇	—	4	2	no	—
186	C₂²×C₄×C₆₇	—	4	2	no	—
187	C₂²×C₄×C₆₇	—	4	2	no	—
188	C₂²×C₄×C₆₇	—	4	2	no	—
189	C₂²×C₄×C₆₇	—	4	2	no	—
190	C₂²×C₄×C₆₇	—	4	2	no	—
191	C₂²×C₄×C₆₇	—	8	1	no	—
192	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
193	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
194	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
201	M₁₆×C₆₇	—	4	4	no	—
202	C₂×C₈×C₆₇	—	2	1	no	—
203	C₂×C₈×C₆₇	—	2	1	no	—
204	C₂×C₈×C₆₇	—	2	1	no	—
205	C₂×C₈×C₆₇	—	2	1	no	—
206	C₂×C₈×C₆₇	—	2	1	no	—
207	C₂×C₈×C₆₇	—	2	1	no	—
208	C₂×C₈×C₆₇	—	2	1	no	—
209	C₂×C₈×C₆₇	—	2	1	no	—
210	C₂×C₈×C₆₇	—	2	1	no	—
211	C₂×C₈×C₆₇	—	2	1	no	—
212	C₂×C₈×C₆₇	—	2	1	no	—
213	C₂×C₈×C₆₇	—	4	4	no	—
214	C₂×C₈×C₆₇	#41	1	2	yes	complemented
215	C₄⋊C₄×C₆₇	—	2	4	no	—
216	C₄⋊C₄×C₆₇	—	2	4	no	—
217	C₄⋊C₄×C₆₇	—	2	4	no	—
218	C₄⋊C₄×C₆₇	—	2	1	no	—
219	C₄⋊C₄×C₆₇	—	2	1	no	—
220	C₄⋊C₄×C₆₇	—	2	1	no	—
221	C₄⋊C₄×C₆₇	—	2	1	no	—
222	C₄⋊C₄×C₆₇	—	2	1	no	—
223	C₄⋊C₄×C₆₇	—	2	1	no	—
224	C₄⋊C₄×C₆₇	—	2	1	no	—
225	C₄⋊C₄×C₆₇	—	2	1	no	—
226	C₄⋊C₄×C₆₇	—	2	1	no	—
227	C₄⋊C₄×C₆₇	—	2	1	no	—
228	C₄⋊C₄×C₆₇	—	4	2	no	—
229	C₄⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
230	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
231	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
232	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
233	C₄⋊C₄×C₆₇	#41	1	2	yes	complemented
234	C₂²⋊C₄×C₆₇	—	2	4	no	—
235	C₂²⋊C₄×C₆₇	—	2	4	no	—
236	C₂²⋊C₄×C₆₇	—	2	4	no	—
237	C₂²⋊C₄×C₆₇	—	4	2	no	—
238	C₂²⋊C₄×C₆₇	—	4	2	no	—
239	C₂²⋊C₄×C₆₇	—	8	1	no	—
240	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
241	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
242	C₄²×C₆₇	—	4	2	no	—
243	C₄²×C₆₇	—	8	1	no	—
244	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
245	C₄²×C₆₇	C₂×D₄	1	2	yes	—
246	C₂³×C₆₇	—	2	1	no	—
247	C₂³×C₆₇	—	2	1	no	—
248	C₂³×C₆₇	—	2	1	no	—
249	C₂³×C₆₇	—	2	1	no	—
250	C₂³×C₆₇	—	2	1	no	—
251	C₂³×C₆₇	—	2	1	no	—
252	C₂³×C₆₇	—	2	1	no	—
253	C₂³×C₆₇	—	2	1	no	—
254	C₂³×C₆₇	—	2	1	no	—
255	C₂³×C₆₇	—	2	1	no	—
256	C₂³×C₆₇	—	2	2	no	—
257	C₂³×C₆₇	—	4	1	no	—
258	C₂³×C₆₇	—	4	1	no	—
259	C₂³×C₆₇	—	4	1	no	—
260	C₂³×C₆₇	—	4	1	no	—
261	C₂³×C₆₇	—	4	1	no	—
262	C₂³×C₆₇	—	4	1	no	—
263	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
264	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
265	C₂³×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
266	C₂³×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
267	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
268	Q₈×C₆₇	—	4	8	no	—
269	D₄×C₆₇	—	2	8	no	—
270	D₄×C₆₇	—	2	2	no	—
271	D₄×C₆₇	—	2	2	no	—
272	D₄×C₆₇	—	4	8	no	—
273	D₄×C₆₇	—	4	8	no	—
274	D₄×C₆₇	—	4	1	no	—
275	D₄×C₆₇	—	4	1	no	—
276	C₂×C₄×C₆₇	—	2	1	no	—
277	C₂×C₄×C₆₇	—	2	1	no	—
278	C₂×C₄×C₆₇	—	2	1	no	—
279	C₂×C₄×C₆₇	—	2	1	no	—
280	C₂×C₄×C₆₇	—	2	1	no	—
281	C₂×C₄×C₆₇	—	2	1	no	—
282	C₂×C₄×C₆₇	—	2	1	no	—
283	C₂×C₄×C₆₇	—	2	1	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	2	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	2	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	2	no	—
294	C₂×C₄×C₆₇	—	2	2	no	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	4	8	no	—
297	C₂×C₄×C₆₇	—	4	8	no	—
298	C₂×C₄×C₆₇	—	4	1	no	—
299	C₂×C₄×C₆₇	—	4	1	no	—
300	C₂×C₄×C₆₇	—	4	1	no	—
301	C₂×C₄×C₆₇	—	4	1	no	—
302	C₂×C₄×C₆₇	—	4	1	no	—
303	C₂×C₄×C₆₇	—	4	1	no	—
304	C₂×C₄×C₆₇	—	4	1	no	—
305	C₂×C₄×C₆₇	—	4	1	no	—
306	C₂×C₄×C₆₇	—	4	8	no	—
307	C₂×C₄×C₆₇	—	4	1	no	—
308	C₂×C₄×C₆₇	—	4	1	no	—
309	C₂×C₄×C₆₇	—	4	1	no	—
310	C₂×C₄×C₆₇	—	4	1	no	—
311	C₂×C₄×C₆₇	—	4	1	no	—
312	C₂×C₄×C₆₇	—	4	1	no	—
313	C₂×C₄×C₆₇	—	4	1	no	—
314	C₂×C₄×C₆₇	—	4	1	no	—
315	C₂×C₄×C₆₇	—	4	1	no	—
316	C₂×C₄×C₆₇	—	8	4	no	—
317	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
318	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
319	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
320	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
321	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
322	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
327	C₈×C₆₇	—	2	2	no	—
328	C₈×C₆₇	—	4	1	no	—
329	C₈×C₆₇	—	4	1	no	—
330	C₈×C₆₇	—	4	1	no	—
331	C₂²×C₆₇	—	2	2	no	—
332	C₂²×C₆₇	—	2	2	no	—
333	C₂²×C₆₇	—	2	2	no	—
334	C₂²×C₆₇	—	2	2	no	—
335	C₂²×C₆₇	—	2	2	no	—
336	C₂²×C₆₇	—	2	2	no	—
337	C₂²×C₆₇	—	2	2	no	—
338	C₂²×C₆₇	—	2	2	no	—
339	C₂²×C₆₇	—	2	2	no	—
340	C₂²×C₆₇	—	4	1	no	—
341	C₂²×C₆₇	—	4	1	no	—
342	C₂²×C₆₇	—	4	1	no	—
343	C₂²×C₆₇	—	4	1	no	—
344	C₂²×C₆₇	—	4	2	no	—
345	C₂²×C₆₇	—	4	2	no	—
346	C₂²×C₆₇	—	4	2	no	—
347	C₂²×C₆₇	—	8	1	no	—
348	C₂²×C₆₇	—	8	1	no	—
349	C₂²×C₆₇	—	8	1	no	—
350	C₂²×C₆₇	—	8	1	no	—
351	C₂²×C₆₇	#418	1	4	yes	—
352	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
353	C₂²×C₆₇	#546	1	1	yes	characteristic
354	C₂²×C₆₇	#547	1	1	yes	characteristic
355	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
356	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
357	C₂²×C₆₇	#577	1	1	yes	characteristic
358	C₂²×C₆₇	#578	1	1	yes	characteristic
359	C₄×C₆₇	—	2	2	no	—
360	C₄×C₆₇	—	2	2	no	—
361	C₄×C₆₇	—	2	2	no	—
362	C₄×C₆₇	—	2	2	no	—
363	C₄×C₆₇	—	4	2	no	—
364	C₄×C₆₇	—	4	2	no	—
365	C₄×C₆₇	—	4	2	no	—
366	C₄×C₆₇	—	4	2	no	—
367	C₄×C₆₇	—	8	1	no	—
368	C₄×C₆₇	—	8	1	no	—
369	C₄×C₆₇	—	8	1	no	—
370	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
371	C₄×C₆₇	#520	1	1	yes	characteristic
372	C₄×C₆₇	#546	1	1	yes	characteristic
373	C₄×C₆₇	#547	1	1	yes	characteristic
374	#22495	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
375	C₂×C₆₇	—	2	4	no	—
376	C₂×C₆₇	—	4	2	no	—
377	C₂×C₆₇	—	8	2	no	—
378	C₂×C₆₇	#2339	1	1	yes	characteristic
379	C₂×C₆₇	C₂×#418	1	1	yes	characteristic
380	C₂×C₆₇	#2898	1	1	yes	characteristic
381	C₂×C₆₇	#3306	1	1	yes	characteristic
382	C₂×C₆₇	#3308	1	1	yes	characteristic
383	C₂×C₆₇	#3343	1	1	yes	characteristic
384	C₂×C₆₇	#3345	1	1	yes	characteristic
385	C₂×#547	C₂×C₆₇	1	1	yes	characteristic
386	C₂×#435	C₂×C₆₇	1	1	yes	characteristic, complemented
387	#2352	C₂×C₆₇	1	1	yes	characteristic, complemented
388	#1993	C₂×C₆₇	1	1	yes	characteristic, complemented
389	#1987	C₂×C₆₇	1	1	yes	characteristic, complemented
390	#1895	C₂×C₆₇	1	1	yes	characteristic, complemented
391	#1893	C₂×C₆₇	1	1	yes	characteristic, complemented
392	#1875	C₂×C₆₇	1	1	yes	characteristic, complemented
393	#1874	C₂×C₆₇	1	1	yes	characteristic, complemented
394	#1824	C₂×C₆₇	1	1	yes	characteristic, complemented
395	#1823	C₂×C₆₇	1	1	yes	characteristic, complemented
396	#1804	C₂×C₆₇	1	1	yes	characteristic, complemented
397	#1762	C₂×C₆₇	1	1	yes	characteristic, complemented
398	#1736	C₂×C₆₇	1	1	yes	characteristic, complemented
399	C₂×#340	C₂×C₆₇	1	1	yes	characteristic, complemented
400	C₆₇	#22495	1	1	yes	characteristic, direct product factor, Sylow
401	C₂²×#41	—	2	1	no	—
402	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
403	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
404	#547	—	2	4	no	—
405	#547	C₄×C₆₇	1	8	yes	complemented
406	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
407	C₂×#123	—	2	1	no	—
408	C₂×#123	—	2	1	no	—
409	C₂×C₂²⋊Q₈	—	2	1	no	—
410	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
411	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
412	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
413	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
414	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
415	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
416	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
417	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
418	#435	—	2	4	no	—
419	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
420	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
421	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
422	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
423	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
424	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
425	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
426	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
427	#388	—	2	1	no	—
428	#387	—	2	1	no	—
429	#386	—	2	1	no	—
430	#382	C₂²×C₆₇	1	1	yes	characteristic
431	#380	C₂²×C₆₇	1	1	yes	characteristic
432	#380	C₂²×C₆₇	1	1	yes	characteristic
433	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
434	C₄×C₂²⋊C₄	—	2	1	no	—
435	#340	C₂²×C₆₇	1	1	yes	characteristic
436	#340	C₂²×C₆₇	1	1	yes	characteristic
437	#340	C₂²×C₆₇	1	1	yes	characteristic
438	#340	C₂²×C₆₇	1	1	yes	characteristic
439	#340	C₂²×C₆₇	1	1	yes	characteristic
440	#340	C₂²×C₆₇	1	1	yes	characteristic
441	#340	C₂²×C₆₇	1	1	yes	characteristic
442	#340	C₂²×C₆₇	1	1	yes	characteristic
443	#340	C₂²×C₆₇	1	1	yes	characteristic
444	#340	C₂²×C₆₇	1	1	yes	characteristic
445	#340	C₂²×C₆₇	1	1	yes	characteristic
446	#340	C₂²×C₆₇	1	1	yes	characteristic
447	C₂×#41	—	2	8	no	—
448	C₂×#41	—	4	4	no	—
449	C₂×#41	—	4	4	no	—
450	C₂²×Q₈	—	2	1	no	—
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
454	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
455	C₂³×C₄	—	2	1	no	—
456	C₂³×C₄	—	2	1	no	—
457	C₂³×C₄	—	2	1	no	—
458	C₂³×C₄	—	2	1	no	—
459	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
461	C₂×M₁₆	—	2	2	no	—
462	C₂×M₁₆	—	2	2	no	—
463	C₂×M₁₆	—	4	1	no	—
464	C₂²×C₈	—	2	2	no	—
465	C₂²×C₈	—	2	2	no	—
466	C₂²×C₈	—	4	1	no	—
467	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
471	C₄⋊Q₈	—	2	2	no	—
472	C₄⋊Q₈	C₂×C₄×C₆₇	1	4	yes	complemented
473	#123	—	2	8	no	—
474	#123	—	2	8	no	—
475	C₂²⋊Q₈	—	2	8	no	—
476	#121	—	2	2	no	—
477	#121	—	2	2	no	—
478	#121	C₂×C₄×C₆₇	1	4	yes	—
479	#121	C₂×C₄×C₆₇	1	4	yes	complemented
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
482	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	complemented
483	C₄×D₄	D₄×C₆₇	1	4	yes	—
484	#117	—	2	2	no	—
485	#117	—	4	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	—	2	2	no	—
489	C₂×C₄⋊C₄	—	2	2	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	2	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	4	1	no	—
494	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
495	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	4	yes	complemented
496	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
512	C₂×C₄²	—	2	1	no	—
513	C₂×C₄²	—	2	1	no	—
514	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
515	C₄⋊C₈	—	2	2	no	—
516	#102	—	2	2	no	—
517	#102	—	2	2	no	—
518	#102	—	4	1	no	—
519	#102	—	4	1	no	—
520	C₂²⋊C₈	—	2	2	no	—
521	C₂²⋊C₈	—	2	2	no	—
522	#97	—	2	2	no	—
523	#95	—	2	1	no	—
524	#95	—	2	1	no	—
525	#95	—	2	1	no	—
526	#95	—	2	1	no	—
527	#95	—	2	1	no	—
528	C₂⁴	—	2	1	no	—
529	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
530	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
531	#41	—	4	32	no	—
532	C₂×Q₈	—	2	4	no	—
533	C₂×Q₈	—	4	2	no	—
534	C₂×Q₈	—	4	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	4	2	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	2	no	—
547	C₂×D₄	—	4	2	no	—
548	C₂×D₄	C₂²⋊C₄×C₆₇	1	4	yes	—
549	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	4	2	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	8	1	no	—
577	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
578	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
579	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
584	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
586	M₁₆	—	4	4	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	4	4	no	—
599	C₂×C₈	#41×C₆₇	1	2	yes	complemented
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
615	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
616	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
617	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
618	C₄⋊C₄	#41×C₆₇	1	2	yes	complemented
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₂²⋊C₄	—	4	2	no	—
624	C₂²⋊C₄	—	8	1	no	—
625	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
626	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
627	C₄²	—	4	2	no	—
628	C₄²	—	8	1	no	—
629	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
630	C₄²	C₂×D₄×C₆₇	1	2	yes	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
649	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
650	C₂³	AGL(1,ℤ/8)×C₆₇	1	2	yes	—
651	C₂³	AGL(1,ℤ/8)×C₆₇	1	2	yes	—
652	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
653	Q₈	—	4	8	no	—
654	D₄	—	2	8	no	—
655	D₄	—	2	2	no	—
656	D₄	—	2	2	no	—
657	D₄	—	4	8	no	—
658	D₄	—	4	8	no	—
659	D₄	—	4	1	no	—
660	D₄	—	4	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	4	8	no	—
682	C₂×C₄	—	4	8	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	8	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
703	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
704	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
705	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
706	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
708	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
709	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
710	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
711	C₂×C₄	2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
712	C₈	—	2	2	no	—
713	C₈	—	4	1	no	—
714	C₈	—	4	1	no	—
715	C₈	—	4	1	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	8	1	no	—
733	C₂²	—	8	1	no	—
734	C₂²	—	8	1	no	—
735	C₂²	—	8	1	no	—
736	C₂²	#418×C₆₇	1	4	yes	—
737	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
738	C₂²	#546×C₆₇	1	1	yes	characteristic
739	C₂²	#547×C₆₇	1	1	yes	characteristic
740	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
741	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
742	C₂²	#577×C₆₇	1	1	yes	characteristic
743	C₂²	#578×C₆₇	1	1	yes	characteristic
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	8	1	no	—
753	C₄	—	8	1	no	—
754	C₄	—	8	1	no	—
755	C₄	C₄×#41×C₆₇	1	1	yes	characteristic
756	C₄	#520×C₆₇	1	1	yes	characteristic
757	C₄	#546×C₆₇	1	1	yes	characteristic
758	C₄	#547×C₆₇	1	1	yes	characteristic
759	C₂	—	2	4	no	—
760	C₂	—	4	2	no	—
761	C₂	—	8	2	no	—
762	C₂	C₆₇×#2339	1	1	yes	characteristic
763	C₂	C₂×#418×C₆₇	1	1	yes	characteristic
764	C₂	C₆₇×#2898	1	1	yes	characteristic
765	C₂	C₆₇×#3306	1	1	yes	characteristic
766	C₂	C₆₇×#3308	1	1	yes	characteristic
767	C₂	C₆₇×#3343	1	1	yes	characteristic
768	C₂	C₆₇×#3345	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂×#547×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×#435×C₆₇	C₂	semidirect
3. C₆₇×#2352	C₂	semidirect
4. C₆₇×#1993	C₂	semidirect
5. C₆₇×#1987	C₂	semidirect
6. C₆₇×#1895	C₂	semidirect
7. C₆₇×#1893	C₂	semidirect
8. C₆₇×#1875	C₂	semidirect
9. C₆₇×#1874	C₂	semidirect
10. C₆₇×#1824	C₂	semidirect
11. C₆₇×#1823	C₂	semidirect
12. C₆₇×#1804	C₂	semidirect
13. C₆₇×#1762	C₂	semidirect
14. C₆₇×#1736	C₂	semidirect
15. C₂×#340×C₆₇	C₂	semidirect
20. #547×C₆₇	C₄	semidirect
87. C₄⋊Q₈×C₆₇	C₂×C₄	semidirect
94. #121×C₆₇	C₂×C₄	semidirect
97. C₄×D₄×C₆₇	C₂×C₄	semidirect
110. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
214. C₂×C₈×C₆₇	#41	semidirect
233. C₄⋊C₄×C₆₇	#41	semidirect
374. #22495	C₆₇	direct (N × H)
386. C₂×#435	C₂×C₆₇	semidirect
387. #2352	C₂×C₆₇	semidirect
388. #1993	C₂×C₆₇	semidirect
389. #1987	C₂×C₆₇	semidirect
390. #1895	C₂×C₆₇	semidirect
391. #1893	C₂×C₆₇	semidirect
392. #1875	C₂×C₆₇	semidirect
393. #1874	C₂×C₆₇	semidirect
394. #1824	C₂×C₆₇	semidirect
395. #1823	C₂×C₆₇	semidirect
396. #1804	C₂×C₆₇	semidirect
397. #1762	C₂×C₆₇	semidirect
398. #1736	C₂×C₆₇	semidirect
399. C₂×#340	C₂×C₆₇	semidirect
400. C₆₇	#22495	direct (N × H)
405. #547	C₄×C₆₇	semidirect
472. C₄⋊Q₈	C₂×C₄×C₆₇	semidirect
479. #121	C₂×C₄×C₆₇	semidirect
482. C₄×D₄	C₂×C₄×C₆₇	semidirect
495. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect
599. C₂×C₈	#41×C₆₇	semidirect
618. C₄⋊C₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₆₇	2
C₂×#435×C₆₇	2
C₆₇×#2352	2
C₆₇×#1993	2
C₆₇×#1987	2
C₆₇×#1895	2
C₆₇×#1893	2
C₆₇×#1875	2
C₆₇×#1874	2
C₆₇×#1824	2
C₆₇×#1823	2
C₆₇×#1804	2
C₆₇×#1762	2
C₆₇×#1736	2
C₂×#340×C₆₇	2
#22495	67

Subgroups — C67×#22495 #30701746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#22495 #30701746