Subgroups — C₆₇×#34424 #30713675

Order 17152.

2442 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#538×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2379	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2376	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2367	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2352	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2349	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2334	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2334	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2329	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2325	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2325	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2324	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2315	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#388×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#538×C₆₇	C₄	1	16	yes	complemented
21	C₂×#126×C₆₇	C₂²	1	2	yes	—
22	C₂×#124×C₆₇	C₂²	1	2	yes	—
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#121×C₆₇	C₂²	1	2	yes	—
27	C₂×#120×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
36	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
40	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
42	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#391×C₆₇	C₂²	1	2	yes	complemented
44	#390×C₆₇	C₂²	1	2	yes	—
45	#390×C₆₇	C₂²	1	2	yes	—
46	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#389×C₆₇	C₂²	1	2	yes	complemented
50	#389×C₆₇	C₂²	1	2	yes	complemented
51	#389×C₆₇	C₂²	1	2	yes	complemented
52	#388×C₆₇	C₂²	1	2	yes	—
53	#388×C₆₇	C₂²	1	2	yes	—
54	#388×C₆₇	C₂²	1	2	yes	—
55	#388×C₆₇	C₂²	1	2	yes	—
56	#388×C₆₇	C₂²	1	2	yes	—
57	#388×C₆₇	C₂²	1	2	yes	—
58	#388×C₆₇	C₂²	1	2	yes	—
59	#388×C₆₇	C₂²	1	2	yes	—
60	#388×C₆₇	C₂²	1	2	yes	complemented
61	#388×C₆₇	C₂²	1	2	yes	complemented
62	#388×C₆₇	C₂²	1	2	yes	complemented
63	#388×C₆₇	C₂²	1	2	yes	complemented
64	#387×C₆₇	C₂²	1	2	yes	complemented
65	#387×C₆₇	C₂²	1	2	yes	complemented
66	#387×C₆₇	C₂²	1	2	yes	complemented
67	#387×C₆₇	C₂²	1	2	yes	complemented
68	#387×C₆₇	C₂²	1	2	yes	complemented
69	#387×C₆₇	C₂²	1	2	yes	complemented
70	#386×C₆₇	C₂²	1	2	yes	—
71	#386×C₆₇	C₂²	1	2	yes	—
72	#386×C₆₇	C₂²	1	2	yes	—
73	#386×C₆₇	C₂²	1	2	yes	—
74	#386×C₆₇	C₂²	1	2	yes	—
75	#386×C₆₇	C₂²	1	2	yes	—
76	#386×C₆₇	C₂²	1	2	yes	complemented
77	#385×C₆₇	C₂²	1	2	yes	—
78	#385×C₆₇	C₂²	1	2	yes	—
79	#385×C₆₇	C₂²	1	2	yes	—
80	#385×C₆₇	C₂²	1	2	yes	—
81	#385×C₆₇	C₂²	1	2	yes	—
82	#385×C₆₇	C₂²	1	2	yes	—
83	#385×C₆₇	C₂²	1	2	yes	—
84	#385×C₆₇	C₂²	1	2	yes	—
85	#385×C₆₇	C₂²	1	2	yes	complemented
86	#385×C₆₇	C₂²	1	2	yes	complemented
87	#385×C₆₇	C₂²	1	2	yes	complemented
88	#382×C₆₇	C₂²	1	2	yes	complemented
89	#382×C₆₇	C₂²	1	2	yes	complemented
90	#380×C₆₇	C₂²	1	1	yes	characteristic
91	#380×C₆₇	C₂²	1	1	yes	characteristic
92	#380×C₆₇	C₂²	1	2	yes	—
93	#380×C₆₇	C₂²	1	2	yes	complemented
94	#380×C₆₇	C₂²	1	2	yes	complemented
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
105	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
106	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
107	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
108	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
113	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
125	#126×C₆₇	C₂×C₄	1	16	yes	complemented
126	#124×C₆₇	C₂×C₄	1	16	yes	complemented
127	#123×C₆₇	C₂×C₄	1	16	yes	complemented
128	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
129	#121×C₆₇	C₂×C₄	1	16	yes	complemented
130	#121×C₆₇	C₂×C₄	1	8	yes	complemented
131	#120×C₆₇	C₂×C₄	1	16	yes	complemented
132	C₄×Q₈×C₆₇	—	4	2	no	—
133	C₄×D₄×C₆₇	—	4	4	no	—
134	C₄×D₄×C₆₇	—	4	2	no	—
135	C₄×D₄×C₆₇	—	4	4	no	—
136	C₄×D₄×C₆₇	—	4	4	no	—
137	C₄×D₄×C₆₇	—	4	4	no	—
138	C₄×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
139	#117×C₆₇	—	4	4	no	—
140	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	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	1	yes	characteristic
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
160	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
161	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
162	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	8	yes	complemented
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₆₇	—	4	2	no	—
185	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	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	2	yes	—
202	#95×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
215	#95×C₆₇	C₂³	1	2	yes	—
216	C₂⁴×C₆₇	—	2	2	no	—
217	C₂⁴×C₆₇	—	2	2	no	—
218	C₂⁴×C₆₇	—	4	1	no	—
219	C₂⁴×C₆₇	—	4	1	no	—
220	C₂⁴×C₆₇	—	4	1	no	—
221	C₂⁴×C₆₇	—	4	1	no	—
222	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
223	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
224	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
225	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
226	C₂×Q₈×C₆₇	—	4	1	no	—
227	C₂×Q₈×C₆₇	—	4	1	no	—
228	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
229	C₂×D₄×C₆₇	—	2	4	no	—
230	C₂×D₄×C₆₇	—	2	4	no	—
231	C₂×D₄×C₆₇	—	4	2	no	—
232	C₂×D₄×C₆₇	—	4	1	no	—
233	C₂×D₄×C₆₇	—	4	2	no	—
234	C₂×D₄×C₆₇	—	4	2	no	—
235	C₂×D₄×C₆₇	—	4	1	no	—
236	C₂×D₄×C₆₇	—	4	2	no	—
237	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
238	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
239	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
240	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
241	C₂²×C₄×C₆₇	—	2	2	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	4	no	—
248	C₂²×C₄×C₆₇	—	4	1	no	—
249	C₂²×C₄×C₆₇	—	4	1	no	—
250	C₂²×C₄×C₆₇	—	4	1	no	—
251	C₂²×C₄×C₆₇	—	4	2	no	—
252	C₂²×C₄×C₆₇	—	4	1	no	—
253	C₂²×C₄×C₆₇	—	4	2	no	—
254	C₂²×C₄×C₆₇	—	4	1	no	—
255	C₂²×C₄×C₆₇	—	4	1	no	—
256	C₂²×C₄×C₆₇	—	4	1	no	—
257	C₂²×C₄×C₆₇	—	4	2	no	—
258	C₂²×C₄×C₆₇	—	4	2	no	—
259	C₂²×C₄×C₆₇	—	4	1	no	—
260	C₂²×C₄×C₆₇	—	4	1	no	—
261	C₂²×C₄×C₆₇	—	4	2	no	—
262	C₂²×C₄×C₆₇	—	4	2	no	—
263	C₂²×C₄×C₆₇	—	4	2	no	—
264	C₂²×C₄×C₆₇	—	4	2	no	—
265	C₂²×C₄×C₆₇	—	4	2	no	—
266	C₂²×C₄×C₆₇	—	4	2	no	—
267	C₂²×C₄×C₆₇	—	4	2	no	—
268	C₂²×C₄×C₆₇	—	4	2	no	—
269	C₂²×C₄×C₆₇	—	4	1	no	—
270	C₂²×C₄×C₆₇	—	4	2	no	—
271	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
272	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
273	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
274	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₄⋊C₄×C₆₇	—	2	4	no	—
291	C₄⋊C₄×C₆₇	—	2	4	no	—
292	C₄⋊C₄×C₆₇	—	4	2	no	—
293	C₄⋊C₄×C₆₇	—	4	2	no	—
294	C₄⋊C₄×C₆₇	—	4	1	no	—
295	C₄⋊C₄×C₆₇	—	4	2	no	—
296	C₄⋊C₄×C₆₇	—	4	1	no	—
297	C₄⋊C₄×C₆₇	—	4	2	no	—
298	C₄⋊C₄×C₆₇	—	4	2	no	—
299	C₄⋊C₄×C₆₇	—	4	2	no	—
300	C₄⋊C₄×C₆₇	—	4	1	no	—
301	C₄⋊C₄×C₆₇	—	4	2	no	—
302	C₄⋊C₄×C₆₇	—	4	2	no	—
303	C₄⋊C₄×C₆₇	—	4	1	no	—
304	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
305	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
306	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
307	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
308	C₂²⋊C₄×C₆₇	—	2	4	no	—
309	C₂²⋊C₄×C₆₇	—	2	4	no	—
310	C₂²⋊C₄×C₆₇	—	2	4	no	—
311	C₂²⋊C₄×C₆₇	—	2	4	no	—
312	C₂²⋊C₄×C₆₇	—	2	4	no	—
313	C₂²⋊C₄×C₆₇	—	4	2	no	—
314	C₂²⋊C₄×C₆₇	—	4	2	no	—
315	C₂²⋊C₄×C₆₇	—	4	2	no	—
316	C₂²⋊C₄×C₆₇	—	4	2	no	—
317	C₂²⋊C₄×C₆₇	—	4	2	no	—
318	C₂²⋊C₄×C₆₇	—	4	2	no	—
319	C₂²⋊C₄×C₆₇	—	4	2	no	—
320	C₂²⋊C₄×C₆₇	—	4	2	no	—
321	C₂²⋊C₄×C₆₇	—	4	2	no	—
322	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
323	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
324	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
325	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
326	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
327	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
328	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
329	C₄²×C₆₇	—	2	2	no	—
330	C₄²×C₆₇	—	2	2	no	—
331	C₄²×C₆₇	—	2	4	no	—
332	C₄²×C₆₇	—	4	1	no	—
333	C₄²×C₆₇	—	4	1	no	—
334	C₄²×C₆₇	—	4	2	no	—
335	C₄²×C₆₇	—	4	2	no	—
336	C₄²×C₆₇	—	4	2	no	—
337	C₄²×C₆₇	—	4	2	no	—
338	C₄²×C₆₇	—	4	2	no	—
339	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
340	C₂³×C₆₇	—	2	1	no	—
341	C₂³×C₆₇	—	2	1	no	—
342	C₂³×C₆₇	—	2	1	no	—
343	C₂³×C₆₇	—	2	1	no	—
344	C₂³×C₆₇	—	2	2	no	—
345	C₂³×C₆₇	—	2	2	no	—
346	C₂³×C₆₇	—	2	2	no	—
347	C₂³×C₆₇	—	2	2	no	—
348	C₂³×C₆₇	—	2	2	no	—
349	C₂³×C₆₇	—	2	2	no	—
350	C₂³×C₆₇	—	2	2	no	—
351	C₂³×C₆₇	—	2	2	no	—
352	C₂³×C₆₇	—	2	2	no	—
353	C₂³×C₆₇	—	2	2	no	—
354	C₂³×C₆₇	—	2	2	no	—
355	C₂³×C₆₇	—	2	2	no	—
356	C₂³×C₆₇	—	2	8	no	—
357	C₂³×C₆₇	—	4	4	no	—
358	C₂³×C₆₇	—	4	4	no	—
359	C₂³×C₆₇	—	8	2	no	—
360	C₂³×C₆₇	—	8	2	no	—
361	C₂³×C₆₇	—	8	2	no	—
362	C₂³×C₆₇	—	8	2	no	—
363	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
364	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
365	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
366	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
367	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
368	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
369	Q₈×C₆₇	—	4	4	no	—
370	D₄×C₆₇	—	2	16	no	—
371	D₄×C₆₇	—	4	8	no	—
372	D₄×C₆₇	—	4	4	no	—
373	D₄×C₆₇	—	4	8	no	—
374	C₂×C₄×C₆₇	—	2	1	no	—
375	C₂×C₄×C₆₇	—	2	1	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	1	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	2	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	1	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	1	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	1	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	2	no	—
404	C₂×C₄×C₆₇	—	2	1	no	—
405	C₂×C₄×C₆₇	—	2	1	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	2	1	no	—
409	C₂×C₄×C₆₇	—	2	2	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	—	4	4	no	—
415	C₂×C₄×C₆₇	—	4	8	no	—
416	C₂×C₄×C₆₇	—	4	4	no	—
417	C₂×C₄×C₆₇	—	4	4	no	—
418	C₂×C₄×C₆₇	—	4	4	no	—
419	C₂×C₄×C₆₇	—	8	4	no	—
420	C₂×C₄×C₆₇	—	8	2	no	—
421	C₂×C₄×C₆₇	—	8	2	no	—
422	C₂×C₄×C₆₇	—	8	4	no	—
423	C₂×C₄×C₆₇	—	8	4	no	—
424	C₂×C₄×C₆₇	—	8	4	no	—
425	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
426	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
427	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
428	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
429	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
430	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
431	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
432	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
433	C₂²×C₆₇	—	2	2	no	—
434	C₂²×C₆₇	—	2	2	no	—
435	C₂²×C₆₇	—	2	2	no	—
436	C₂²×C₆₇	—	2	2	no	—
437	C₂²×C₆₇	—	2	2	no	—
438	C₂²×C₆₇	—	2	2	no	—
439	C₂²×C₆₇	—	2	4	no	—
440	C₂²×C₆₇	—	2	4	no	—
441	C₂²×C₆₇	—	2	4	no	—
442	C₂²×C₆₇	—	2	4	no	—
443	C₂²×C₆₇	—	2	4	no	—
444	C₂²×C₆₇	—	2	4	no	—
445	C₂²×C₆₇	—	4	2	no	—
446	C₂²×C₆₇	—	4	2	no	—
447	C₂²×C₆₇	—	4	2	no	—
448	C₂²×C₆₇	—	4	2	no	—
449	C₂²×C₆₇	—	4	2	no	—
450	C₂²×C₆₇	—	4	2	no	—
451	C₂²×C₆₇	—	4	2	no	—
452	C₂²×C₆₇	—	4	2	no	—
453	C₂²×C₆₇	—	8	8	no	—
454	C₂²×C₆₇	#520	1	4	yes	—
455	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
456	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
460	C₂²×C₆₇	#585	1	1	yes	characteristic
461	C₂²×C₆₇	#585	1	1	yes	characteristic
462	C₄×C₆₇	—	2	4	no	—
463	C₄×C₆₇	—	2	4	no	—
464	C₄×C₆₇	—	2	4	no	—
465	C₄×C₆₇	—	2	2	no	—
466	C₄×C₆₇	—	2	2	no	—
467	C₄×C₆₇	—	2	4	no	—
468	C₄×C₆₇	—	2	2	no	—
469	C₄×C₆₇	—	2	2	no	—
470	C₄×C₆₇	—	4	1	no	—
471	C₄×C₆₇	—	4	2	no	—
472	C₄×C₆₇	—	4	2	no	—
473	C₄×C₆₇	—	4	1	no	—
474	C₄×C₆₇	—	4	2	no	—
475	C₄×C₆₇	—	4	2	no	—
476	C₄×C₆₇	—	4	2	no	—
477	C₄×C₆₇	—	4	2	no	—
478	#34424	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
479	C₂×C₆₇	—	2	4	no	—
480	C₂×C₆₇	—	4	4	no	—
481	C₂×C₆₇	—	4	4	no	—
482	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
483	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
484	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
485	C₂×C₆₇	#3534	1	1	yes	characteristic
486	C₂×C₆₇	#3536	1	1	yes	characteristic
487	C₂×C₆₇	#3558	1	1	yes	characteristic
488	C₂×C₆₇	#3564	1	1	yes	characteristic
489	C₂×#538	C₂×C₆₇	1	1	yes	characteristic
490	#2379	C₂×C₆₇	1	2	yes	complemented
491	#2376	C₂×C₆₇	1	2	yes	complemented
492	#2367	C₂×C₆₇	1	2	yes	complemented
493	#2359	C₂×C₆₇	1	2	yes	complemented
494	#2358	C₂×C₆₇	1	2	yes	complemented
495	#2358	C₂×C₆₇	1	2	yes	complemented
496	#2352	C₂×C₆₇	1	2	yes	complemented
497	#2349	C₂×C₆₇	1	2	yes	complemented
498	#2334	C₂×C₆₇	1	2	yes	complemented
499	#2334	C₂×C₆₇	1	2	yes	complemented
500	#2329	C₂×C₆₇	1	1	yes	characteristic, complemented
501	#2325	C₂×C₆₇	1	1	yes	characteristic, complemented
502	#2325	C₂×C₆₇	1	2	yes	complemented
503	#2324	C₂×C₆₇	1	2	yes	complemented
504	#2315	C₂×C₆₇	1	1	yes	characteristic, complemented
505	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
506	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
507	C₂×#388	C₂×C₆₇	1	1	yes	characteristic, complemented
508	C₆₇	#34424	1	1	yes	characteristic, direct product factor, Sylow
509	#538	C₄×C₆₇	1	16	yes	complemented
510	C₂×#126	C₂²×C₆₇	1	2	yes	—
511	C₂×#124	C₂²×C₆₇	1	2	yes	—
512	C₂×#123	C₂²×C₆₇	1	2	yes	—
513	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
514	C₂×#121	C₂²×C₆₇	1	2	yes	—
515	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
516	C₂×#120	C₂²×C₆₇	1	2	yes	—
517	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
518	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
519	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
520	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
521	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
522	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
523	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
524	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
525	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
526	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
527	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
528	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
529	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
530	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
531	#391	C₂²×C₆₇	1	2	yes	complemented
532	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
533	#390	C₂²×C₆₇	1	2	yes	—
534	#390	C₂²×C₆₇	1	2	yes	—
535	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
536	#389	C₂²×C₆₇	1	2	yes	complemented
537	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
538	#389	C₂²×C₆₇	1	2	yes	complemented
539	#389	C₂²×C₆₇	1	2	yes	complemented
540	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
541	#388	C₂²×C₆₇	1	2	yes	—
542	#388	C₂²×C₆₇	1	2	yes	—
543	#388	C₂²×C₆₇	1	2	yes	—
544	#388	C₂²×C₆₇	1	2	yes	—
545	#388	C₂²×C₆₇	1	2	yes	—
546	#388	C₂²×C₆₇	1	2	yes	—
547	#388	C₂²×C₆₇	1	2	yes	—
548	#388	C₂²×C₆₇	1	2	yes	—
549	#388	C₂²×C₆₇	1	2	yes	complemented
550	#388	C₂²×C₆₇	1	2	yes	complemented
551	#388	C₂²×C₆₇	1	2	yes	complemented
552	#388	C₂²×C₆₇	1	2	yes	complemented
553	#387	C₂²×C₆₇	1	2	yes	complemented
554	#387	C₂²×C₆₇	1	2	yes	complemented
555	#387	C₂²×C₆₇	1	2	yes	complemented
556	#387	C₂²×C₆₇	1	2	yes	complemented
557	#387	C₂²×C₆₇	1	2	yes	complemented
558	#387	C₂²×C₆₇	1	2	yes	complemented
559	#386	C₂²×C₆₇	1	2	yes	—
560	#386	C₂²×C₆₇	1	2	yes	—
561	#386	C₂²×C₆₇	1	2	yes	—
562	#386	C₂²×C₆₇	1	2	yes	—
563	#386	C₂²×C₆₇	1	2	yes	—
564	#386	C₂²×C₆₇	1	2	yes	—
565	#386	C₂²×C₆₇	1	2	yes	complemented
566	#385	C₂²×C₆₇	1	2	yes	—
567	#385	C₂²×C₆₇	1	2	yes	—
568	#385	C₂²×C₆₇	1	2	yes	—
569	#385	C₂²×C₆₇	1	2	yes	—
570	#385	C₂²×C₆₇	1	2	yes	—
571	#385	C₂²×C₆₇	1	2	yes	—
572	#385	C₂²×C₆₇	1	2	yes	—
573	#385	C₂²×C₆₇	1	2	yes	—
574	#385	C₂²×C₆₇	1	2	yes	complemented
575	#385	C₂²×C₆₇	1	2	yes	complemented
576	#385	C₂²×C₆₇	1	2	yes	complemented
577	#382	C₂²×C₆₇	1	2	yes	complemented
578	#382	C₂²×C₆₇	1	2	yes	complemented
579	#380	C₂²×C₆₇	1	1	yes	characteristic
580	#380	C₂²×C₆₇	1	1	yes	characteristic
581	#380	C₂²×C₆₇	1	2	yes	—
582	#380	C₂²×C₆₇	1	2	yes	complemented
583	#380	C₂²×C₆₇	1	2	yes	complemented
584	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
585	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
586	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
587	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
588	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
589	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
590	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
591	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
592	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
593	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
594	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
595	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
596	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
597	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
598	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
599	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
600	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
601	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
602	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
608	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
609	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
610	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
611	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
614	#126	C₂×C₄×C₆₇	1	16	yes	complemented
615	#124	C₂×C₄×C₆₇	1	16	yes	complemented
616	#123	C₂×C₄×C₆₇	1	16	yes	complemented
617	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
618	#121	C₂×C₄×C₆₇	1	16	yes	complemented
619	#121	C₂×C₄×C₆₇	1	8	yes	complemented
620	#120	C₂×C₄×C₆₇	1	16	yes	complemented
621	C₄×Q₈	—	4	2	no	—
622	C₄×D₄	—	4	4	no	—
623	C₄×D₄	—	4	2	no	—
624	C₄×D₄	—	4	4	no	—
625	C₄×D₄	—	4	4	no	—
626	C₄×D₄	—	4	4	no	—
627	C₄×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
628	#117	—	4	4	no	—
629	C₂×C₄⋊C₄	—	4	2	no	—
630	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	—	4	2	no	—
649	C₂×C₂²⋊C₄	—	4	2	no	—
650	C₂×C₂²⋊C₄	—	4	4	no	—
651	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	8	yes	complemented
652	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
673	C₂×C₄²	—	4	2	no	—
674	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
675	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
678	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
679	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
680	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
681	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
682	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
684	C₂×C₄²	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	#95	C₂³×C₆₇	1	2	yes	—
699	#95	C₂³×C₆₇	1	2	yes	—
700	#95	C₂³×C₆₇	1	2	yes	—
701	#95	C₂³×C₆₇	1	2	yes	—
702	#95	C₂³×C₆₇	1	2	yes	—
703	#95	C₂³×C₆₇	1	2	yes	—
704	#95	C₂³×C₆₇	1	2	yes	—
705	C₂⁴	—	2	2	no	—
706	C₂⁴	—	2	2	no	—
707	C₂⁴	—	4	1	no	—
708	C₂⁴	—	4	1	no	—
709	C₂⁴	—	4	1	no	—
710	C₂⁴	—	4	1	no	—
711	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
712	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
713	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
714	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
715	C₂×Q₈	—	4	1	no	—
716	C₂×Q₈	—	4	1	no	—
717	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	4	2	no	—
721	C₂×D₄	—	4	1	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	1	no	—
725	C₂×D₄	—	4	2	no	—
726	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
727	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
728	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
729	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	4	1	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	1	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	1	no	—
744	C₂²×C₄	—	4	1	no	—
745	C₂²×C₄	—	4	1	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	1	no	—
749	C₂²×C₄	—	4	1	no	—
750	C₂²×C₄	—	4	2	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	—	4	2	no	—
753	C₂²×C₄	—	4	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	1	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
761	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
762	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
763	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	4	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	1	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	1	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	1	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	1	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
794	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
795	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
796	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
812	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
813	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
814	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
815	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
816	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
817	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	4	no	—
821	C₄²	—	4	1	no	—
822	C₄²	—	4	1	no	—
823	C₄²	—	4	2	no	—
824	C₄²	—	4	2	no	—
825	C₄²	—	4	2	no	—
826	C₄²	—	4	2	no	—
827	C₄²	—	4	2	no	—
828	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	8	no	—
846	C₂³	—	4	4	no	—
847	C₂³	—	4	4	no	—
848	C₂³	—	8	2	no	—
849	C₂³	—	8	2	no	—
850	C₂³	—	8	2	no	—
851	C₂³	—	8	2	no	—
852	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
853	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
854	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
855	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
856	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
857	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
858	Q₈	—	4	4	no	—
859	D₄	—	2	16	no	—
860	D₄	—	4	8	no	—
861	D₄	—	4	4	no	—
862	D₄	—	4	8	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	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	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	8	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	4	4	no	—
908	C₂×C₄	—	8	4	no	—
909	C₂×C₄	—	8	2	no	—
910	C₂×C₄	—	8	2	no	—
911	C₂×C₄	—	8	4	no	—
912	C₂×C₄	—	8	4	no	—
913	C₂×C₄	—	8	4	no	—
914	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
915	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
916	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
917	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
918	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
919	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
920	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
921	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	4	no	—
929	C₂²	—	2	4	no	—
930	C₂²	—	2	4	no	—
931	C₂²	—	2	4	no	—
932	C₂²	—	2	4	no	—
933	C₂²	—	2	4	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	8	8	no	—
943	C₂²	#520×C₆₇	1	4	yes	—
944	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
945	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
946	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
947	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
948	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
949	C₂²	#585×C₆₇	1	1	yes	characteristic
950	C₂²	#585×C₆₇	1	1	yes	characteristic
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	4	no	—
954	C₄	—	2	4	no	—
955	C₄	—	2	4	no	—
956	C₄	—	2	2	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	4	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	1	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₂	—	2	4	no	—
968	C₂	—	4	4	no	—
969	C₂	—	4	4	no	—
970	C₂	C₂×#520×C₆₇	1	1	yes	characteristic
971	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
972	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
973	C₂	C₆₇×#3534	1	1	yes	characteristic
974	C₂	C₆₇×#3536	1	1	yes	characteristic
975	C₂	C₆₇×#3558	1	1	yes	characteristic
976	C₂	C₆₇×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#538×C₆₇	C₂
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×#2379	C₂	semidirect
3. C₆₇×#2376	C₂	semidirect
4. C₆₇×#2367	C₂	semidirect
5. C₆₇×#2359	C₂	semidirect
6. C₆₇×#2358	C₂	semidirect
7. C₆₇×#2358	C₂	semidirect
8. C₆₇×#2352	C₂	semidirect
9. C₆₇×#2349	C₂	semidirect
10. C₆₇×#2334	C₂	semidirect
11. C₆₇×#2334	C₂	semidirect
12. C₆₇×#2329	C₂	semidirect
13. C₆₇×#2325	C₂	semidirect
14. C₆₇×#2325	C₂	semidirect
15. C₆₇×#2324	C₂	semidirect
16. C₆₇×#2315	C₂	semidirect
17. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
18. C₄×#121×C₆₇	C₂	semidirect
19. C₂×#388×C₆₇	C₂	semidirect
20. #538×C₆₇	C₄	semidirect
28. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
34. C₂×C₄×D₄×C₆₇	C₂²	semidirect
35. C₂×#117×C₆₇	C₂²	semidirect
42. #391×C₆₇	C₂²	semidirect
43. #391×C₆₇	C₂²	semidirect
46. #390×C₆₇	C₂²	semidirect
47. #389×C₆₇	C₂²	semidirect
48. #389×C₆₇	C₂²	semidirect
49. #389×C₆₇	C₂²	semidirect
50. #389×C₆₇	C₂²	semidirect
51. #389×C₆₇	C₂²	semidirect
60. #388×C₆₇	C₂²	semidirect
61. #388×C₆₇	C₂²	semidirect
62. #388×C₆₇	C₂²	semidirect
63. #388×C₆₇	C₂²	semidirect
64. #387×C₆₇	C₂²	semidirect
65. #387×C₆₇	C₂²	semidirect
66. #387×C₆₇	C₂²	semidirect
67. #387×C₆₇	C₂²	semidirect
68. #387×C₆₇	C₂²	semidirect
69. #387×C₆₇	C₂²	semidirect
76. #386×C₆₇	C₂²	semidirect
85. #385×C₆₇	C₂²	semidirect
86. #385×C₆₇	C₂²	semidirect
87. #385×C₆₇	C₂²	semidirect
88. #382×C₆₇	C₂²	semidirect
89. #382×C₆₇	C₂²	semidirect
93. #380×C₆₇	C₂²	semidirect
94. #380×C₆₇	C₂²	semidirect
95. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
96. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
97. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
98. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
99. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
107. C₂×#95×C₆₇	C₂²	semidirect
125. #126×C₆₇	C₂×C₄	semidirect
126. #124×C₆₇	C₂×C₄	semidirect
127. #123×C₆₇	C₂×C₄	semidirect
128. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
129. #121×C₆₇	C₂×C₄	semidirect
130. #121×C₆₇	C₂×C₄	semidirect
131. #120×C₆₇	C₂×C₄	semidirect
138. C₄×D₄×C₆₇	C₂×C₄	semidirect
162. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
478. #34424	C₆₇	direct (N × H)
490. #2379	C₂×C₆₇	semidirect
491. #2376	C₂×C₆₇	semidirect
492. #2367	C₂×C₆₇	semidirect
493. #2359	C₂×C₆₇	semidirect
494. #2358	C₂×C₆₇	semidirect
495. #2358	C₂×C₆₇	semidirect
496. #2352	C₂×C₆₇	semidirect
497. #2349	C₂×C₆₇	semidirect
498. #2334	C₂×C₆₇	semidirect
499. #2334	C₂×C₆₇	semidirect
500. #2329	C₂×C₆₇	semidirect
501. #2325	C₂×C₆₇	semidirect
502. #2325	C₂×C₆₇	semidirect
503. #2324	C₂×C₆₇	semidirect
504. #2315	C₂×C₆₇	semidirect
505. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
506. C₄×#121	C₂×C₆₇	semidirect
507. C₂×#388	C₂×C₆₇	semidirect
508. C₆₇	#34424	direct (N × H)
509. #538	C₄×C₆₇	semidirect
517. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
523. C₂×C₄×D₄	C₂²×C₆₇	semidirect
524. C₂×#117	C₂²×C₆₇	semidirect
531. #391	C₂²×C₆₇	semidirect
532. #391	C₂²×C₆₇	semidirect
535. #390	C₂²×C₆₇	semidirect
536. #389	C₂²×C₆₇	semidirect
537. #389	C₂²×C₆₇	semidirect
538. #389	C₂²×C₆₇	semidirect
539. #389	C₂²×C₆₇	semidirect
540. #389	C₂²×C₆₇	semidirect
549. #388	C₂²×C₆₇	semidirect
550. #388	C₂²×C₆₇	semidirect
551. #388	C₂²×C₆₇	semidirect
552. #388	C₂²×C₆₇	semidirect
553. #387	C₂²×C₆₇	semidirect
554. #387	C₂²×C₆₇	semidirect
555. #387	C₂²×C₆₇	semidirect
556. #387	C₂²×C₆₇	semidirect
557. #387	C₂²×C₆₇	semidirect
558. #387	C₂²×C₆₇	semidirect
565. #386	C₂²×C₆₇	semidirect
574. #385	C₂²×C₆₇	semidirect
575. #385	C₂²×C₆₇	semidirect
576. #385	C₂²×C₆₇	semidirect
577. #382	C₂²×C₆₇	semidirect
578. #382	C₂²×C₆₇	semidirect
582. #380	C₂²×C₆₇	semidirect
583. #380	C₂²×C₆₇	semidirect
584. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
585. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
586. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
587. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
588. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
593. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
596. C₂×#95	C₂²×C₆₇	semidirect
614. #126	C₂×C₄×C₆₇	semidirect
615. #124	C₂×C₄×C₆₇	semidirect
616. #123	C₂×C₄×C₆₇	semidirect
617. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
618. #121	C₂×C₄×C₆₇	semidirect
619. #121	C₂×C₄×C₆₇	semidirect
620. #120	C₂×C₄×C₆₇	semidirect
627. C₄×D₄	C₂×C₄×C₆₇	semidirect
651. C₂×C₂²⋊C₄	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×#538×C₆₇	2
C₆₇×#2379	2
C₆₇×#2376	2
C₆₇×#2367	2
C₆₇×#2359	2
C₆₇×#2358	2
C₆₇×#2352	2
C₆₇×#2349	2
C₆₇×#2334	2
C₆₇×#2329	2
C₆₇×#2325	2
C₆₇×#2324	2
C₆₇×#2315	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#121×C₆₇	2
C₂×#388×C₆₇	2
#34424	67

Subgroups — C67×#34424 #30713675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34424 #30713675