Subgroups — C₆₇×#34439 #30713690

Order 17152.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2378	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2376	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2374	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2368	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2367	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2365	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2365	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2341	C₂	1	1	yes	maximal, characteristic
11	Q₈×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2339	C₂	1	1	yes	maximal, characteristic
14	C₆₇×#2335	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2335	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2332	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2329	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2327	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2326	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2314	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2298	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	#536×C₆₇	C₄	1	16	yes	complemented
27	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#123×C₆₇	C₂²	1	2	yes	—
32	C₂×#123×C₆₇	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
44	#391×C₆₇	C₂²	1	1	yes	characteristic
45	#391×C₆₇	C₂²	1	1	yes	characteristic
46	#391×C₆₇	C₂²	1	1	yes	characteristic
47	#391×C₆₇	C₂²	1	1	yes	characteristic
48	#391×C₆₇	C₂²	1	1	yes	characteristic
49	#391×C₆₇	C₂²	1	1	yes	characteristic
50	#391×C₆₇	C₂²	1	2	yes	—
51	#391×C₆₇	C₂²	1	2	yes	—
52	#391×C₆₇	C₂²	1	2	yes	—
53	#391×C₆₇	C₂²	1	2	yes	—
54	#390×C₆₇	C₂²	1	1	yes	characteristic
55	#390×C₆₇	C₂²	1	1	yes	characteristic
56	#390×C₆₇	C₂²	1	2	yes	—
57	#390×C₆₇	C₂²	1	2	yes	—
58	#389×C₆₇	C₂²	1	2	yes	—
59	#389×C₆₇	C₂²	1	2	yes	—
60	#389×C₆₇	C₂²	1	2	yes	—
61	#389×C₆₇	C₂²	1	2	yes	—
62	#388×C₆₇	C₂²	1	1	yes	characteristic
63	#388×C₆₇	C₂²	1	1	yes	characteristic
64	#388×C₆₇	C₂²	1	1	yes	characteristic
65	#388×C₆₇	C₂²	1	1	yes	characteristic
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	2	yes	—
71	#388×C₆₇	C₂²	1	2	yes	—
72	#388×C₆₇	C₂²	1	2	yes	—
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	1	yes	characteristic
77	#387×C₆₇	C₂²	1	1	yes	characteristic
78	#387×C₆₇	C₂²	1	1	yes	characteristic
79	#387×C₆₇	C₂²	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
90	#386×C₆₇	C₂²	1	2	yes	—
91	#386×C₆₇	C₂²	1	2	yes	—
92	#385×C₆₇	C₂²	1	2	yes	—
93	#385×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	#382×C₆₇	C₂²	1	1	yes	characteristic
98	#381×C₆₇	C₂²	1	2	yes	—
99	#380×C₆₇	C₂²	1	1	yes	characteristic
100	#380×C₆₇	C₂²	1	1	yes	characteristic
101	#380×C₆₇	C₂²	1	2	yes	—
102	#380×C₆₇	C₂²	1	2	yes	—
103	#380×C₆₇	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
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×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	#376×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×#95×C₆₇	C₂²	1	2	yes	—
123	C₄³×C₆₇	C₂²	1	1	yes	characteristic
124	C₂×#41×C₆₇	—	4	2	no	—
125	C₂×#41×C₆₇	—	4	2	no	—
126	C₂×#41×C₆₇	C₂×C₄	1	8	yes	—
127	C₂²×Q₈×C₆₇	—	4	2	no	—
128	C₂²×Q₈×C₆₇	—	4	2	no	—
129	C₂²×Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
134	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
139	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
140	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
141	C₄⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
142	C₄⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
143	#124×C₆₇	C₂×C₄	1	8	yes	—
144	#124×C₆₇	C₂×C₄	1	8	yes	—
145	#123×C₆₇	C₂×C₄	1	16	yes	complemented
146	#123×C₆₇	C₂×C₄	1	16	yes	complemented
147	C₂²⋊Q₈×C₆₇	C₂×C₄	1	16	yes	complemented
148	C₂²⋊Q₈×C₆₇	C₂×C₄	1	16	yes	complemented
149	C₄×Q₈×C₆₇	—	4	2	no	—
150	C₄×Q₈×C₆₇	—	4	2	no	—
151	C₄×Q₈×C₆₇	—	4	2	no	—
152	C₄×Q₈×C₆₇	—	4	2	no	—
153	C₄×Q₈×C₆₇	—	4	2	no	—
154	C₄×Q₈×C₆₇	—	4	2	no	—
155	C₄×D₄×C₆₇	—	4	2	no	—
156	C₄×D₄×C₆₇	—	4	2	no	—
157	#117×C₆₇	C₂×C₄	1	8	yes	complemented
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	1	yes	characteristic
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
203	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
205	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
206	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
207	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
208	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
209	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
210	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
213	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
214	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×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	2	yes	—
219	#95×C₆₇	C₂³	1	2	yes	—
220	#95×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
226	#95×C₆₇	C₂³	1	1	yes	characteristic
227	#95×C₆₇	C₂³	1	1	yes	characteristic
228	#95×C₆₇	C₂³	1	2	yes	—
229	#95×C₆₇	C₂³	1	1	yes	characteristic
230	#95×C₆₇	C₂³	1	2	yes	—
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	1	yes	characteristic
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	#95×C₆₇	C₂³	1	2	yes	—
240	#95×C₆₇	C₂³	1	2	yes	—
241	#95×C₆₇	C₂³	1	2	yes	—
242	#95×C₆₇	C₂³	1	2	yes	—
243	#95×C₆₇	C₂³	1	2	yes	—
244	#95×C₆₇	C₂³	1	1	yes	characteristic
245	#95×C₆₇	C₂³	1	1	yes	characteristic
246	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
247	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
248	#41×C₆₇	—	4	16	no	—
249	C₂×Q₈×C₆₇	—	2	2	no	—
250	C₂×Q₈×C₆₇	—	2	2	no	—
251	C₂×Q₈×C₆₇	—	2	2	no	—
252	C₂×Q₈×C₆₇	—	2	2	no	—
253	C₂×Q₈×C₆₇	—	2	2	no	—
254	C₂×Q₈×C₆₇	—	2	2	no	—
255	C₂×Q₈×C₆₇	—	4	2	no	—
256	C₂×Q₈×C₆₇	—	4	2	no	—
257	C₂×Q₈×C₆₇	—	4	16	no	—
258	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
259	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
260	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
261	C₂×Q₈×C₆₇	C₂²×C₄	1	8	yes	—
262	C₂×D₄×C₆₇	—	2	2	no	—
263	C₂×D₄×C₆₇	—	2	2	no	—
264	C₂×D₄×C₆₇	—	4	2	no	—
265	C₂×D₄×C₆₇	—	4	2	no	—
266	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
267	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
268	C₂²×C₄×C₆₇	—	2	2	no	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	2	4	no	—
271	C₂²×C₄×C₆₇	—	4	2	no	—
272	C₂²×C₄×C₆₇	—	4	2	no	—
273	C₂²×C₄×C₆₇	—	4	2	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	—	4	2	no	—
278	C₂²×C₄×C₆₇	—	4	2	no	—
279	C₂²×C₄×C₆₇	—	4	2	no	—
280	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
281	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
282	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
283	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	2	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	no	—
309	C₄⋊C₄×C₆₇	—	2	2	no	—
310	C₄⋊C₄×C₆₇	—	4	1	no	—
311	C₄⋊C₄×C₆₇	—	4	1	no	—
312	C₄⋊C₄×C₆₇	—	4	2	no	—
313	C₄⋊C₄×C₆₇	—	4	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	2	no	—
318	C₄⋊C₄×C₆₇	—	4	2	no	—
319	C₄⋊C₄×C₆₇	—	4	2	no	—
320	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
321	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
322	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
323	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
324	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
325	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
326	C₂²⋊C₄×C₆₇	—	2	2	no	—
327	C₂²⋊C₄×C₆₇	—	2	4	no	—
328	C₂²⋊C₄×C₆₇	—	2	2	no	—
329	C₂²⋊C₄×C₆₇	—	4	2	no	—
330	C₂²⋊C₄×C₆₇	—	4	2	no	—
331	C₂²⋊C₄×C₆₇	—	4	1	no	—
332	C₂²⋊C₄×C₆₇	—	4	2	no	—
333	C₂²⋊C₄×C₆₇	—	4	1	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	C₂²×C₄	1	4	yes	—
339	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
340	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
341	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
342	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
343	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
344	C₄²×C₆₇	—	2	2	no	—
345	C₄²×C₆₇	—	2	2	no	—
346	C₄²×C₆₇	—	2	2	no	—
347	C₄²×C₆₇	—	2	2	no	—
348	C₄²×C₆₇	—	2	2	no	—
349	C₄²×C₆₇	—	2	2	no	—
350	C₄²×C₆₇	—	4	2	no	—
351	C₄²×C₆₇	—	4	2	no	—
352	C₄²×C₆₇	—	4	1	no	—
353	C₄²×C₆₇	—	4	1	no	—
354	C₄²×C₆₇	—	4	2	no	—
355	C₄²×C₆₇	—	4	2	no	—
356	C₄²×C₆₇	—	4	2	no	—
357	C₄²×C₆₇	—	4	2	no	—
358	C₄²×C₆₇	—	4	2	no	—
359	C₄²×C₆₇	—	4	2	no	—
360	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
361	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	2	2	no	—
364	C₂³×C₆₇	—	2	1	no	—
365	C₂³×C₆₇	—	2	1	no	—
366	C₂³×C₆₇	—	2	1	no	—
367	C₂³×C₆₇	—	2	2	no	—
368	C₂³×C₆₇	—	2	1	no	—
369	C₂³×C₆₇	—	2	2	no	—
370	C₂³×C₆₇	—	2	1	no	—
371	C₂³×C₆₇	—	2	1	no	—
372	C₂³×C₆₇	—	2	2	no	—
373	C₂³×C₆₇	—	2	2	no	—
374	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
375	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
376	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
377	Q₈×C₆₇	—	2	8	no	—
378	Q₈×C₆₇	—	2	8	no	—
379	Q₈×C₆₇	—	2	8	no	—
380	Q₈×C₆₇	—	4	8	no	—
381	D₄×C₆₇	—	2	8	no	—
382	D₄×C₆₇	—	4	8	no	—
383	C₂×C₄×C₆₇	—	2	1	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	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	1	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	1	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	8	no	—
404	C₂×C₄×C₆₇	—	2	1	no	—
405	C₂×C₄×C₆₇	—	2	1	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	1	no	—
408	C₂×C₄×C₆₇	—	2	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	1	no	—
419	C₂×C₄×C₆₇	—	2	1	no	—
420	C₂×C₄×C₆₇	—	2	2	no	—
421	C₂×C₄×C₆₇	—	2	2	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	2	no	—
426	C₂×C₄×C₆₇	—	2	2	no	—
427	C₂×C₄×C₆₇	—	2	2	no	—
428	C₂×C₄×C₆₇	—	2	1	no	—
429	C₂×C₄×C₆₇	—	2	1	no	—
430	C₂×C₄×C₆₇	—	2	2	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	1	no	—
433	C₂×C₄×C₆₇	—	2	1	no	—
434	C₂×C₄×C₆₇	—	4	8	no	—
435	C₂×C₄×C₆₇	—	4	8	no	—
436	C₂×C₄×C₆₇	—	8	4	no	—
437	C₂×C₄×C₆₇	—	8	4	no	—
438	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
439	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
440	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
441	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
442	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
443	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
444	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
445	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
446	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
447	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
448	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
449	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
450	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
451	C₂²×C₆₇	—	2	2	no	—
452	C₂²×C₆₇	—	2	4	no	—
453	C₂²×C₆₇	—	2	2	no	—
454	C₂²×C₆₇	—	2	2	no	—
455	C₂²×C₆₇	—	2	4	no	—
456	C₂²×C₆₇	—	2	4	no	—
457	C₂²×C₆₇	—	4	2	no	—
458	C₂²×C₆₇	—	4	1	no	—
459	C₂²×C₆₇	—	4	2	no	—
460	C₂²×C₆₇	—	4	1	no	—
461	C₂²×C₆₇	—	4	2	no	—
462	C₂²×C₆₇	—	4	1	no	—
463	C₂²×C₆₇	—	4	2	no	—
464	C₂²×C₆₇	—	4	1	no	—
465	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
466	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
469	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
470	C₂²×C₆₇	#585	1	1	yes	characteristic
471	C₂²×C₆₇	#585	1	1	yes	characteristic
472	C₄×C₆₇	—	2	2	no	—
473	C₄×C₆₇	—	2	4	no	—
474	C₄×C₆₇	—	2	4	no	—
475	C₄×C₆₇	—	2	4	no	—
476	C₄×C₆₇	—	2	2	no	—
477	C₄×C₆₇	—	2	2	no	—
478	C₄×C₆₇	—	2	2	no	—
479	C₄×C₆₇	—	2	2	no	—
480	C₄×C₆₇	—	2	2	no	—
481	C₄×C₆₇	—	2	2	no	—
482	C₄×C₆₇	—	4	1	no	—
483	C₄×C₆₇	—	4	1	no	—
484	C₄×C₆₇	—	4	1	no	—
485	C₄×C₆₇	—	4	2	no	—
486	C₄×C₆₇	—	4	1	no	—
487	C₄×C₆₇	—	4	2	no	—
488	C₄×C₆₇	—	4	1	no	—
489	C₄×C₆₇	—	4	2	no	—
490	C₄×C₆₇	—	4	2	no	—
491	C₄×C₆₇	—	4	1	no	—
492	C₄×C₆₇	#518	1	4	yes	—
493	#34439	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
494	C₂×C₆₇	—	4	2	no	—
495	C₂×C₆₇	—	4	4	no	—
496	C₂×C₆₇	C₂×#518	1	1	yes	characteristic
497	C₂×C₆₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
498	C₂×C₆₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
499	C₂×C₆₇	#3552	1	1	yes	characteristic
500	C₂×C₆₇	#3554	1	1	yes	characteristic
501	C₂×C₆₇	#3561	1	1	yes	characteristic
502	C₂×C₆₇	#3562	1	1	yes	characteristic
503	C₂×#536	C₂×C₆₇	1	1	yes	characteristic
504	#2378	C₂×C₆₇	1	2	yes	complemented
505	#2376	C₂×C₆₇	1	2	yes	complemented
506	#2374	C₂×C₆₇	1	2	yes	complemented
507	#2368	C₂×C₆₇	1	2	yes	complemented
508	#2367	C₂×C₆₇	1	1	yes	characteristic, complemented
509	#2367	C₂×C₆₇	1	1	yes	characteristic, complemented
510	#2365	C₂×C₆₇	1	1	yes	characteristic, complemented
511	#2365	C₂×C₆₇	1	1	yes	characteristic, complemented
512	#2341	C₂×C₆₇	1	1	yes	characteristic
513	Q₈×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
514	Q₈×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
515	#2339	C₂×C₆₇	1	1	yes	characteristic
516	#2335	C₂×C₆₇	1	2	yes	complemented
517	#2335	C₂×C₆₇	1	2	yes	complemented
518	#2332	C₂×C₆₇	1	2	yes	complemented
519	#2329	C₂×C₆₇	1	2	yes	complemented
520	#2327	C₂×C₆₇	1	1	yes	characteristic, complemented
521	#2326	C₂×C₆₇	1	1	yes	characteristic, complemented
522	#2314	C₂×C₆₇	1	1	yes	characteristic, complemented
523	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
524	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
525	#2298	C₂×C₆₇	1	1	yes	characteristic, complemented
526	C₆₇	#34439	1	1	yes	characteristic, direct product factor, Sylow
527	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
528	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
529	#536	C₄×C₆₇	1	16	yes	complemented
530	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
531	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
532	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
533	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
534	C₂×#123	C₂²×C₆₇	1	2	yes	—
535	C₂×#123	C₂²×C₆₇	1	2	yes	—
536	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
537	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
538	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
539	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
540	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
541	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
542	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
543	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
544	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
545	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
546	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
547	#391	C₂²×C₆₇	1	1	yes	characteristic
548	#391	C₂²×C₆₇	1	1	yes	characteristic
549	#391	C₂²×C₆₇	1	1	yes	characteristic
550	#391	C₂²×C₆₇	1	1	yes	characteristic
551	#391	C₂²×C₆₇	1	1	yes	characteristic
552	#391	C₂²×C₆₇	1	2	yes	—
553	#391	C₂²×C₆₇	1	2	yes	—
554	#391	C₂²×C₆₇	1	2	yes	—
555	#391	C₂²×C₆₇	1	2	yes	—
556	#391	C₂²×C₆₇	1	1	yes	characteristic
557	#390	C₂²×C₆₇	1	1	yes	characteristic
558	#390	C₂²×C₆₇	1	2	yes	—
559	#390	C₂²×C₆₇	1	2	yes	—
560	#390	C₂²×C₆₇	1	1	yes	characteristic
561	#389	C₂²×C₆₇	1	2	yes	—
562	#389	C₂²×C₆₇	1	2	yes	—
563	#389	C₂²×C₆₇	1	2	yes	—
564	#389	C₂²×C₆₇	1	2	yes	—
565	#388	C₂²×C₆₇	1	2	yes	—
566	#388	C₂²×C₆₇	1	2	yes	—
567	#388	C₂²×C₆₇	1	2	yes	—
568	#388	C₂²×C₆₇	1	2	yes	—
569	#388	C₂²×C₆₇	1	2	yes	—
570	#388	C₂²×C₆₇	1	2	yes	—
571	#388	C₂²×C₆₇	1	2	yes	—
572	#388	C₂²×C₆₇	1	1	yes	characteristic
573	#388	C₂²×C₆₇	1	1	yes	characteristic
574	#388	C₂²×C₆₇	1	2	yes	—
575	#388	C₂²×C₆₇	1	2	yes	—
576	#388	C₂²×C₆₇	1	1	yes	characteristic
577	#388	C₂²×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
586	#387	C₂²×C₆₇	1	2	yes	—
587	#387	C₂²×C₆₇	1	1	yes	characteristic
588	#387	C₂²×C₆₇	1	2	yes	—
589	#387	C₂²×C₆₇	1	2	yes	—
590	#387	C₂²×C₆₇	1	2	yes	—
591	#387	C₂²×C₆₇	1	1	yes	characteristic
592	#387	C₂²×C₆₇	1	1	yes	characteristic
593	#386	C₂²×C₆₇	1	2	yes	—
594	#386	C₂²×C₆₇	1	2	yes	—
595	#385	C₂²×C₆₇	1	2	yes	—
596	#385	C₂²×C₆₇	1	2	yes	—
597	#385	C₂²×C₆₇	1	2	yes	—
598	#385	C₂²×C₆₇	1	2	yes	—
599	#384	C₂²×C₆₇	1	1	yes	characteristic
600	#382	C₂²×C₆₇	1	1	yes	characteristic
601	#381	C₂²×C₆₇	1	2	yes	—
602	#380	C₂²×C₆₇	1	1	yes	characteristic
603	#380	C₂²×C₆₇	1	1	yes	characteristic
604	#380	C₂²×C₆₇	1	2	yes	—
605	#380	C₂²×C₆₇	1	2	yes	—
606	#380	C₂²×C₆₇	1	2	yes	—
607	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
608	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
609	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
610	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
611	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
612	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
613	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
614	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
615	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
616	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
617	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
618	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
619	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
620	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
621	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
622	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
623	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
624	#376	C₂²×C₆₇	1	1	yes	characteristic
625	C₂×#95	C₂²×C₆₇	1	2	yes	—
626	C₄³	C₂²×C₆₇	1	1	yes	characteristic
627	C₂×#41	—	4	2	no	—
628	C₂×#41	—	4	2	no	—
629	C₂×#41	C₂×C₄×C₆₇	1	8	yes	—
630	C₂²×Q₈	—	4	2	no	—
631	C₂²×Q₈	—	4	2	no	—
632	C₂²×Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
633	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
634	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
635	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
636	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
637	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
638	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
639	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
640	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
641	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
642	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
643	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
644	C₄⋊Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
645	C₄⋊Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
646	#124	C₂×C₄×C₆₇	1	8	yes	—
647	#124	C₂×C₄×C₆₇	1	8	yes	—
648	#123	C₂×C₄×C₆₇	1	16	yes	complemented
649	#123	C₂×C₄×C₆₇	1	16	yes	complemented
650	C₂²⋊Q₈	C₂×C₄×C₆₇	1	16	yes	complemented
651	C₂²⋊Q₈	C₂×C₄×C₆₇	1	16	yes	complemented
652	C₄×Q₈	—	4	2	no	—
653	C₄×Q₈	—	4	2	no	—
654	C₄×Q₈	—	4	2	no	—
655	C₄×Q₈	—	4	2	no	—
656	C₄×Q₈	—	4	2	no	—
657	C₄×Q₈	—	4	2	no	—
658	C₄×D₄	—	4	2	no	—
659	C₄×D₄	—	4	2	no	—
660	#117	C₂×C₄×C₆₇	1	8	yes	complemented
661	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
674	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
690	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
696	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
701	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
708	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
709	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
710	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
711	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
712	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
713	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
716	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
717	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
718	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
719	#95	C₂³×C₆₇	1	1	yes	characteristic
720	#95	C₂³×C₆₇	1	2	yes	—
721	#95	C₂³×C₆₇	1	2	yes	—
722	#95	C₂³×C₆₇	1	2	yes	—
723	#95	C₂³×C₆₇	1	1	yes	characteristic
724	#95	C₂³×C₆₇	1	1	yes	characteristic
725	#95	C₂³×C₆₇	1	1	yes	characteristic
726	#95	C₂³×C₆₇	1	1	yes	characteristic
727	#95	C₂³×C₆₇	1	1	yes	characteristic
728	#95	C₂³×C₆₇	1	2	yes	—
729	#95	C₂³×C₆₇	1	1	yes	characteristic
730	#95	C₂³×C₆₇	1	1	yes	characteristic
731	#95	C₂³×C₆₇	1	2	yes	—
732	#95	C₂³×C₆₇	1	2	yes	—
733	#95	C₂³×C₆₇	1	1	yes	characteristic
734	#95	C₂³×C₆₇	1	2	yes	—
735	#95	C₂³×C₆₇	1	2	yes	—
736	#95	C₂³×C₆₇	1	1	yes	characteristic
737	#95	C₂³×C₆₇	1	2	yes	—
738	#95	C₂³×C₆₇	1	2	yes	—
739	#95	C₂³×C₆₇	1	2	yes	—
740	#95	C₂³×C₆₇	1	2	yes	—
741	#95	C₂³×C₆₇	1	2	yes	—
742	#95	C₂³×C₆₇	1	2	yes	—
743	#95	C₂³×C₆₇	1	2	yes	—
744	#95	C₂³×C₆₇	1	2	yes	—
745	#95	C₂³×C₆₇	1	2	yes	—
746	#95	C₂³×C₆₇	1	2	yes	—
747	#95	C₂³×C₆₇	1	1	yes	characteristic
748	#95	C₂³×C₆₇	1	1	yes	characteristic
749	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
750	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
751	#41	—	4	16	no	—
752	C₂×Q₈	—	2	2	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	—	2	2	no	—
755	C₂×Q₈	—	2	2	no	—
756	C₂×Q₈	—	2	2	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×Q₈	—	4	2	no	—
760	C₂×Q₈	—	4	16	no	—
761	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
762	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
763	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
764	C₂×Q₈	C₂²×C₄×C₆₇	1	8	yes	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	4	2	no	—
768	C₂×D₄	—	4	2	no	—
769	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
770	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	4	no	—
774	C₂²×C₄	—	4	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	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	2	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
784	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
785	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
786	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
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	2	yes	—
793	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
802	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
803	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₄⋊C₄	—	4	2	no	—
819	C₄⋊C₄	—	4	1	no	—
820	C₄⋊C₄	—	4	1	no	—
821	C₄⋊C₄	—	4	2	no	—
822	C₄⋊C₄	—	4	2	no	—
823	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
824	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
825	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
826	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
827	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
828	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	1	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	1	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
842	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
843	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
844	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
845	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
846	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	4	2	no	—
854	C₄²	—	4	2	no	—
855	C₄²	—	4	2	no	—
856	C₄²	—	4	2	no	—
857	C₄²	—	4	2	no	—
858	C₄²	—	4	2	no	—
859	C₄²	—	4	2	no	—
860	C₄²	—	4	2	no	—
861	C₄²	—	4	1	no	—
862	C₄²	—	4	1	no	—
863	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
864	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	1	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	2	no	—
876	C₂³	—	2	2	no	—
877	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
878	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
879	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
880	Q₈	—	2	8	no	—
881	Q₈	—	2	8	no	—
882	Q₈	—	2	8	no	—
883	Q₈	—	4	8	no	—
884	D₄	—	2	8	no	—
885	D₄	—	4	8	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	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	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	8	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	4	8	no	—
938	C₂×C₄	—	4	8	no	—
939	C₂×C₄	—	8	4	no	—
940	C₂×C₄	—	8	4	no	—
941	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
942	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
943	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
944	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
945	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
946	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
947	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
948	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
949	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
950	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
951	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
952	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
953	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
954	C₂²	—	2	2	no	—
955	C₂²	—	2	4	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	4	no	—
959	C₂²	—	2	4	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	1	no	—
968	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
969	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
970	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
971	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
972	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
973	C₂²	#585×C₆₇	1	1	yes	characteristic
974	C₂²	#585×C₆₇	1	1	yes	characteristic
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	4	no	—
979	C₄	—	2	4	no	—
980	C₄	—	2	4	no	—
981	C₄	—	2	2	no	—
982	C₄	—	2	2	no	—
983	C₄	—	2	2	no	—
984	C₄	—	2	2	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	2	no	—
995	C₄	#518×C₆₇	1	4	yes	—
996	C₂	—	4	2	no	—
997	C₂	—	4	4	no	—
998	C₂	C₂×#518×C₆₇	1	1	yes	characteristic
999	C₂	C₄×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1000	C₂	C₄×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1001	C₂	C₆₇×#3552	1	1	yes	characteristic
1002	C₂	C₆₇×#3554	1	1	yes	characteristic
1003	C₂	C₆₇×#3561	1	1	yes	characteristic
1004	C₂	C₆₇×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂²×#41×C₆₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2378	C₂	semidirect
3. C₆₇×#2376	C₂	semidirect
4. C₆₇×#2374	C₂	semidirect
5. C₆₇×#2368	C₂	semidirect
6. C₆₇×#2367	C₂	semidirect
7. C₆₇×#2367	C₂	semidirect
8. C₆₇×#2365	C₂	semidirect
9. C₆₇×#2365	C₂	semidirect
11. Q₈×C₂²⋊C₄×C₆₇	C₂	semidirect
12. Q₈×C₂²⋊C₄×C₆₇	C₂	semidirect
14. C₆₇×#2335	C₂	semidirect
15. C₆₇×#2335	C₂	semidirect
16. C₆₇×#2332	C₂	semidirect
17. C₆₇×#2329	C₂	semidirect
18. C₆₇×#2327	C₂	semidirect
19. C₆₇×#2326	C₂	semidirect
20. C₆₇×#2314	C₂	semidirect
21. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
22. C₄×#124×C₆₇	C₂	semidirect
23. C₆₇×#2298	C₂	semidirect
26. #536×C₆₇	C₄	semidirect
129. C₂²×Q₈×C₆₇	C₂×C₄	semidirect
141. C₄⋊Q₈×C₆₇	C₂×C₄	semidirect
142. C₄⋊Q₈×C₆₇	C₂×C₄	semidirect
145. #123×C₆₇	C₂×C₄	semidirect
146. #123×C₆₇	C₂×C₄	semidirect
147. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
148. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
157. #117×C₆₇	C₂×C₄	semidirect
493. #34439	C₆₇	direct (N × H)
504. #2378	C₂×C₆₇	semidirect
505. #2376	C₂×C₆₇	semidirect
506. #2374	C₂×C₆₇	semidirect
507. #2368	C₂×C₆₇	semidirect
508. #2367	C₂×C₆₇	semidirect
509. #2367	C₂×C₆₇	semidirect
510. #2365	C₂×C₆₇	semidirect
511. #2365	C₂×C₆₇	semidirect
513. Q₈×C₂²⋊C₄	C₂×C₆₇	semidirect
514. Q₈×C₂²⋊C₄	C₂×C₆₇	semidirect
516. #2335	C₂×C₆₇	semidirect
517. #2335	C₂×C₆₇	semidirect
518. #2332	C₂×C₆₇	semidirect
519. #2329	C₂×C₆₇	semidirect
520. #2327	C₂×C₆₇	semidirect
521. #2326	C₂×C₆₇	semidirect
522. #2314	C₂×C₆₇	semidirect
523. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
524. C₄×#124	C₂×C₆₇	semidirect
525. #2298	C₂×C₆₇	semidirect
526. C₆₇	#34439	direct (N × H)
529. #536	C₄×C₆₇	semidirect
632. C₂²×Q₈	C₂×C₄×C₆₇	semidirect
644. C₄⋊Q₈	C₂×C₄×C₆₇	semidirect
645. C₄⋊Q₈	C₂×C₄×C₆₇	semidirect
648. #123	C₂×C₄×C₆₇	semidirect
649. #123	C₂×C₄×C₆₇	semidirect
650. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
651. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
660. #117	C₂×C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#536×C₆₇	2
C₆₇×#2378	2
C₆₇×#2376	2
C₆₇×#2374	2
C₆₇×#2368	2
C₆₇×#2367	2
C₆₇×#2365	2
C₆₇×#2341	2
Q₈×C₂²⋊C₄×C₆₇	2
C₆₇×#2339	2
C₆₇×#2335	2
C₆₇×#2332	2
C₆₇×#2329	2
C₆₇×#2327	2
C₆₇×#2326	2
C₆₇×#2314	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#124×C₆₇	2
C₆₇×#2298	2
#34439	67

Subgroups — C67×#34439 #30713690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34439 #30713690