Subgroups — C₆₇×#34763 #30714014

Order 17152.

2428 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2521	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2519	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2512	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2506	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2501	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2496	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2488	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2486	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2440	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2425	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2416	C₂	1	1	yes	maximal, characteristic
14	C₆₇×#2396	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2395	C₂	1	2	yes	maximal, complemented
16	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#123×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	#529×C₆₇	—	2	16	no	—
26	C₂×#126×C₆₇	C₂²	1	2	yes	—
27	C₂×#126×C₆₇	C₂²	1	2	yes	—
28	C₂×#125×C₆₇	C₂²	1	2	yes	—
29	C₂×#124×C₆₇	C₂²	1	2	yes	—
30	C₂×#123×C₆₇	C₂²	1	2	yes	—
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×#121×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#121×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#117×C₆₇	C₂²	1	2	yes	—
45	C₂×#117×C₆₇	C₂²	1	2	yes	—
46	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
50	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
51	#400×C₆₇	C₂²	1	2	yes	—
52	#400×C₆₇	C₂²	1	2	yes	—
53	#399×C₆₇	C₂²	1	2	yes	—
54	#399×C₆₇	C₂²	1	2	yes	—
55	#398×C₆₇	C₂²	1	2	yes	—
56	#398×C₆₇	C₂²	1	2	yes	—
57	#398×C₆₇	C₂²	1	2	yes	—
58	#397×C₆₇	C₂²	1	2	yes	—
59	#397×C₆₇	C₂²	1	2	yes	—
60	#397×C₆₇	C₂²	1	2	yes	—
61	#396×C₆₇	C₂²	1	2	yes	—
62	#396×C₆₇	C₂²	1	2	yes	—
63	#395×C₆₇	C₂²	1	2	yes	—
64	#394×C₆₇	C₂²	1	2	yes	—
65	#394×C₆₇	C₂²	1	2	yes	—
66	#393×C₆₇	C₂²	1	2	yes	—
67	#391×C₆₇	C₂²	1	2	yes	—
68	#390×C₆₇	C₂²	1	1	yes	characteristic
69	#390×C₆₇	C₂²	1	1	yes	characteristic
70	#390×C₆₇	C₂²	1	1	yes	characteristic
71	#390×C₆₇	C₂²	1	1	yes	characteristic
72	#389×C₆₇	C₂²	1	1	yes	characteristic
73	#389×C₆₇	C₂²	1	1	yes	characteristic
74	#389×C₆₇	C₂²	1	1	yes	characteristic
75	#389×C₆₇	C₂²	1	1	yes	characteristic
76	#389×C₆₇	C₂²	1	1	yes	characteristic
77	#389×C₆₇	C₂²	1	2	yes	—
78	#389×C₆₇	C₂²	1	1	yes	characteristic
79	#388×C₆₇	C₂²	1	2	yes	—
80	#388×C₆₇	C₂²	1	2	yes	—
81	#388×C₆₇	C₂²	1	2	yes	—
82	#388×C₆₇	C₂²	1	2	yes	—
83	#388×C₆₇	C₂²	1	2	yes	—
84	#388×C₆₇	C₂²	1	2	yes	—
85	#387×C₆₇	C₂²	1	2	yes	—
86	#387×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	2	yes	—
89	#386×C₆₇	C₂²	1	2	yes	—
90	#385×C₆₇	C₂²	1	2	yes	—
91	#384×C₆₇	C₂²	1	1	yes	characteristic
92	#384×C₆₇	C₂²	1	1	yes	characteristic
93	#384×C₆₇	C₂²	1	1	yes	characteristic
94	#382×C₆₇	C₂²	1	2	yes	—
95	#381×C₆₇	C₂²	1	2	yes	—
96	#380×C₆₇	C₂²	1	2	yes	—
97	#380×C₆₇	C₂²	1	1	yes	characteristic
98	#380×C₆₇	C₂²	1	1	yes	characteristic
99	#380×C₆₇	C₂²	1	1	yes	characteristic
100	#380×C₆₇	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
122	C₂×#95×C₆₇	C₂²	1	2	yes	—
123	C₄³×C₆₇	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
125	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
126	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
128	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₆₇	—	2	4	no	—
139	#126×C₆₇	—	2	8	no	—
140	#126×C₆₇	—	2	8	no	—
141	#125×C₆₇	—	2	8	no	—
142	#124×C₆₇	—	2	8	no	—
143	#123×C₆₇	—	2	8	no	—
144	#123×C₆₇	—	2	8	no	—
145	#123×C₆₇	—	2	8	no	—
146	C₂²⋊Q₈×C₆₇	—	2	8	no	—
147	#121×C₆₇	—	2	8	no	—
148	#121×C₆₇	—	2	4	no	—
149	#121×C₆₇	—	2	4	no	—
150	C₄×Q₈×C₆₇	—	2	8	no	—
151	C₄×D₄×C₆₇	—	2	8	no	—
152	C₄×D₄×C₆₇	—	2	8	no	—
153	C₄×D₄×C₆₇	—	2	4	no	—
154	C₄×D₄×C₆₇	—	2	4	no	—
155	C₄×D₄×C₆₇	—	2	4	no	—
156	C₄×D₄×C₆₇	D₄	1	8	yes	complemented
157	#117×C₆₇	—	2	8	no	—
158	#117×C₆₇	—	2	8	no	—
159	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
160	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
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	2	yes	—
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	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₆₇	—	2	8	no	—
208	C₂×C₄²×C₆₇	—	2	4	no	—
209	C₂×C₄²×C₆₇	—	2	4	no	—
210	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
211	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
212	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
220	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
221	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
224	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	#95×C₆₇	C₂³	1	2	yes	—
229	#95×C₆₇	C₂³	1	2	yes	—
230	#95×C₆₇	C₂³	1	2	yes	—
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	1	yes	characteristic
233	#95×C₆₇	C₂³	1	1	yes	characteristic
234	#95×C₆₇	C₂³	1	1	yes	characteristic
235	#95×C₆₇	C₂³	1	1	yes	characteristic
236	#95×C₆₇	C₂³	1	1	yes	characteristic
237	#95×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
245	#95×C₆₇	C₂³	1	2	yes	—
246	#95×C₆₇	C₂³	1	2	yes	—
247	#95×C₆₇	C₂³	1	2	yes	—
248	#95×C₆₇	C₂³	1	2	yes	—
249	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
250	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂×Q₈×C₆₇	—	2	4	no	—
253	C₂×Q₈×C₆₇	—	2	4	no	—
254	C₂×Q₈×C₆₇	—	4	2	no	—
255	C₂×D₄×C₆₇	—	2	2	no	—
256	C₂×D₄×C₆₇	—	2	2	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	4	no	—
259	C₂×D₄×C₆₇	—	2	4	no	—
260	C₂×D₄×C₆₇	—	2	4	no	—
261	C₂×D₄×C₆₇	—	2	2	no	—
262	C₂×D₄×C₆₇	—	2	4	no	—
263	C₂×D₄×C₆₇	—	2	2	no	—
264	C₂×D₄×C₆₇	—	2	2	no	—
265	C₂×D₄×C₆₇	—	4	2	no	—
266	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	2	no	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	2	2	no	—
271	C₂²×C₄×C₆₇	—	2	2	no	—
272	C₂²×C₄×C₆₇	—	2	2	no	—
273	C₂²×C₄×C₆₇	—	2	4	no	—
274	C₂²×C₄×C₆₇	—	2	4	no	—
275	C₂²×C₄×C₆₇	—	2	4	no	—
276	C₂²×C₄×C₆₇	—	2	2	no	—
277	C₂²×C₄×C₆₇	—	2	4	no	—
278	C₂²×C₄×C₆₇	—	2	4	no	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	2	2	no	—
281	C₂²×C₄×C₆₇	—	2	2	no	—
282	C₂²×C₄×C₆₇	—	2	4	no	—
283	C₂²×C₄×C₆₇	—	2	2	no	—
284	C₂²×C₄×C₆₇	—	2	2	no	—
285	C₂²×C₄×C₆₇	—	2	4	no	—
286	C₂²×C₄×C₆₇	—	2	2	no	—
287	C₂²×C₄×C₆₇	—	2	4	no	—
288	C₂²×C₄×C₆₇	—	4	1	no	—
289	C₂²×C₄×C₆₇	—	4	1	no	—
290	C₂²×C₄×C₆₇	—	4	2	no	—
291	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
292	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
293	C₂²×C₄×C₆₇	#41	1	4	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₆₇	—	2	4	no	—
315	C₄⋊C₄×C₆₇	—	2	4	no	—
316	C₄⋊C₄×C₆₇	—	2	4	no	—
317	C₄⋊C₄×C₆₇	—	2	4	no	—
318	C₄⋊C₄×C₆₇	—	2	4	no	—
319	C₄⋊C₄×C₆₇	—	2	4	no	—
320	C₄⋊C₄×C₆₇	—	2	4	no	—
321	C₄⋊C₄×C₆₇	—	2	4	no	—
322	C₄⋊C₄×C₆₇	—	2	4	no	—
323	C₄⋊C₄×C₆₇	—	2	4	no	—
324	C₄⋊C₄×C₆₇	—	2	4	no	—
325	C₄⋊C₄×C₆₇	—	2	2	no	—
326	C₄⋊C₄×C₆₇	—	2	2	no	—
327	C₄⋊C₄×C₆₇	—	2	2	no	—
328	C₄⋊C₄×C₆₇	—	2	2	no	—
329	C₄⋊C₄×C₆₇	—	2	2	no	—
330	C₄⋊C₄×C₆₇	—	2	2	no	—
331	C₄⋊C₄×C₆₇	—	2	2	no	—
332	C₄⋊C₄×C₆₇	—	2	4	no	—
333	C₄⋊C₄×C₆₇	—	2	4	no	—
334	C₄⋊C₄×C₆₇	—	2	4	no	—
335	C₄⋊C₄×C₆₇	—	2	2	no	—
336	C₄⋊C₄×C₆₇	—	4	2	no	—
337	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
338	C₄⋊C₄×C₆₇	#41	1	4	yes	—
339	C₂²⋊C₄×C₆₇	—	2	4	no	—
340	C₂²⋊C₄×C₆₇	—	2	4	no	—
341	C₂²⋊C₄×C₆₇	—	2	4	no	—
342	C₂²⋊C₄×C₆₇	—	2	4	no	—
343	C₂²⋊C₄×C₆₇	—	2	2	no	—
344	C₂²⋊C₄×C₆₇	—	2	4	no	—
345	C₂²⋊C₄×C₆₇	—	2	4	no	—
346	C₂²⋊C₄×C₆₇	—	2	4	no	—
347	C₂²⋊C₄×C₆₇	—	2	4	no	—
348	C₂²⋊C₄×C₆₇	—	2	2	no	—
349	C₂²⋊C₄×C₆₇	—	2	4	no	—
350	C₂²⋊C₄×C₆₇	—	2	2	no	—
351	C₂²⋊C₄×C₆₇	—	2	4	no	—
352	C₂²⋊C₄×C₆₇	—	2	4	no	—
353	C₂²⋊C₄×C₆₇	—	2	4	no	—
354	C₂²⋊C₄×C₆₇	—	2	4	no	—
355	C₂²⋊C₄×C₆₇	—	4	2	no	—
356	C₂²⋊C₄×C₆₇	—	4	2	no	—
357	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
358	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
359	C₂²⋊C₄×C₆₇	#41	1	4	yes	—
360	C₄²×C₆₇	—	2	4	no	—
361	C₄²×C₆₇	—	2	4	no	—
362	C₄²×C₆₇	—	2	4	no	—
363	C₄²×C₆₇	—	2	4	no	—
364	C₄²×C₆₇	—	2	4	no	—
365	C₄²×C₆₇	—	2	2	no	—
366	C₄²×C₆₇	—	2	2	no	—
367	C₄²×C₆₇	—	2	2	no	—
368	C₄²×C₆₇	—	2	2	no	—
369	C₄²×C₆₇	—	2	2	no	—
370	C₄²×C₆₇	—	2	2	no	—
371	C₄²×C₆₇	—	2	2	no	—
372	C₄²×C₆₇	—	2	2	no	—
373	C₄²×C₆₇	—	2	2	no	—
374	C₄²×C₆₇	—	2	2	no	—
375	C₄²×C₆₇	—	4	1	no	—
376	C₄²×C₆₇	C₂×D₄	1	4	yes	—
377	C₄²×C₆₇	#41	1	4	yes	—
378	C₂³×C₆₇	—	2	1	no	—
379	C₂³×C₆₇	—	2	1	no	—
380	C₂³×C₆₇	—	2	1	no	—
381	C₂³×C₆₇	—	2	1	no	—
382	C₂³×C₆₇	—	2	1	no	—
383	C₂³×C₆₇	—	2	1	no	—
384	C₂³×C₆₇	—	2	1	no	—
385	C₂³×C₆₇	—	2	1	no	—
386	C₂³×C₆₇	—	2	1	no	—
387	C₂³×C₆₇	—	2	1	no	—
388	C₂³×C₆₇	—	2	2	no	—
389	C₂³×C₆₇	—	2	2	no	—
390	C₂³×C₆₇	—	2	2	no	—
391	C₂³×C₆₇	—	2	2	no	—
392	C₂³×C₆₇	—	2	2	no	—
393	C₂³×C₆₇	—	2	2	no	—
394	C₂³×C₆₇	—	2	2	no	—
395	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
396	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
397	C₂³×C₆₇	C₂×#41	1	2	yes	—
398	C₂³×C₆₇	C₂×#41	1	2	yes	—
399	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
400	Q₈×C₆₇	—	4	8	no	—
401	D₄×C₆₇	—	2	8	no	—
402	D₄×C₆₇	—	4	8	no	—
403	D₄×C₆₇	—	4	8	no	—
404	D₄×C₆₇	—	4	4	no	—
405	C₂×C₄×C₆₇	—	2	2	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	1	no	—
411	C₂×C₄×C₆₇	—	2	1	no	—
412	C₂×C₄×C₆₇	—	2	1	no	—
413	C₂×C₄×C₆₇	—	2	1	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	1	no	—
418	C₂×C₄×C₆₇	—	2	1	no	—
419	C₂×C₄×C₆₇	—	2	1	no	—
420	C₂×C₄×C₆₇	—	2	1	no	—
421	C₂×C₄×C₆₇	—	2	1	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	2	8	no	—
424	C₂×C₄×C₆₇	—	2	8	no	—
425	C₂×C₄×C₆₇	—	2	8	no	—
426	C₂×C₄×C₆₇	—	2	2	no	—
427	C₂×C₄×C₆₇	—	2	2	no	—
428	C₂×C₄×C₆₇	—	2	2	no	—
429	C₂×C₄×C₆₇	—	2	2	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	—	2	1	no	—
435	C₂×C₄×C₆₇	—	2	1	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	2	no	—
438	C₂×C₄×C₆₇	—	2	2	no	—
439	C₂×C₄×C₆₇	—	2	2	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	2	2	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	2	no	—
446	C₂×C₄×C₆₇	—	2	2	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	2	2	no	—
449	C₂×C₄×C₆₇	—	2	1	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	2	2	no	—
453	C₂×C₄×C₆₇	—	4	4	no	—
454	C₂×C₄×C₆₇	—	4	8	no	—
455	C₂×C₄×C₆₇	—	4	4	no	—
456	C₂×C₄×C₆₇	—	4	8	no	—
457	C₂×C₄×C₆₇	—	4	4	no	—
458	C₂×C₄×C₆₇	—	4	8	no	—
459	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
465	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
466	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
467	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
468	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
469	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
470	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
471	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
472	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
473	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
474	C₂²×C₆₇	—	2	2	no	—
475	C₂²×C₆₇	—	2	2	no	—
476	C₂²×C₆₇	—	2	2	no	—
477	C₂²×C₆₇	—	2	2	no	—
478	C₂²×C₆₇	—	2	2	no	—
479	C₂²×C₆₇	—	2	2	no	—
480	C₂²×C₆₇	—	2	2	no	—
481	C₂²×C₆₇	—	2	2	no	—
482	C₂²×C₆₇	—	2	2	no	—
483	C₂²×C₆₇	—	4	1	no	—
484	C₂²×C₆₇	—	4	1	no	—
485	C₂²×C₆₇	—	4	1	no	—
486	C₂²×C₆₇	—	4	1	no	—
487	C₂²×C₆₇	—	4	2	no	—
488	C₂²×C₆₇	—	4	2	no	—
489	C₂²×C₆₇	—	4	2	no	—
490	C₂²×C₆₇	—	4	2	no	—
491	C₂²×C₆₇	—	4	2	no	—
492	C₂²×C₆₇	—	4	2	no	—
493	C₂²×C₆₇	—	4	2	no	—
494	C₂²×C₆₇	#532	1	4	yes	—
495	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
496	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
497	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
498	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
499	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
500	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
501	C₂²×C₆₇	#585	1	1	yes	characteristic
502	C₄×C₆₇	—	2	2	no	—
503	C₄×C₆₇	—	2	2	no	—
504	C₄×C₆₇	—	2	2	no	—
505	C₄×C₆₇	—	2	2	no	—
506	C₄×C₆₇	—	2	4	no	—
507	C₄×C₆₇	—	2	2	no	—
508	C₄×C₆₇	—	2	2	no	—
509	C₄×C₆₇	—	2	2	no	—
510	C₄×C₆₇	—	2	2	no	—
511	C₄×C₆₇	—	4	1	no	—
512	C₄×C₆₇	—	4	2	no	—
513	C₄×C₆₇	—	4	2	no	—
514	C₄×C₆₇	—	4	2	no	—
515	C₄×C₆₇	—	4	1	no	—
516	C₄×C₆₇	—	4	2	no	—
517	C₄×C₆₇	—	4	2	no	—
518	C₄×C₆₇	—	4	2	no	—
519	C₄×C₆₇	—	4	1	no	—
520	C₄×C₆₇	#529	1	4	yes	complemented
521	C₄×C₆₇	#547	1	4	yes	—
522	#34763	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
523	C₂×C₆₇	—	2	4	no	—
524	C₂×C₆₇	—	4	2	no	—
525	C₂×C₆₇	—	8	2	no	—
526	C₂×C₆₇	C₂×#529	1	1	yes	characteristic
527	C₂×C₆₇	C₂×#532	1	1	yes	characteristic
528	C₂×C₆₇	#3461	1	1	yes	characteristic
529	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
530	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
531	C₂×C₆₇	#3475	1	1	yes	characteristic
532	C₂×C₆₇	#3482	1	1	yes	characteristic
533	C₂×#529	C₂×C₆₇	1	2	yes	complemented
534	#2521	C₂×C₆₇	1	2	yes	complemented
535	#2519	C₂×C₆₇	1	2	yes	complemented
536	#2512	C₂×C₆₇	1	1	yes	characteristic, complemented
537	#2506	C₂×C₆₇	1	1	yes	characteristic, complemented
538	#2501	C₂×C₆₇	1	1	yes	characteristic, complemented
539	#2496	C₂×C₆₇	1	1	yes	characteristic, complemented
540	#2491	C₂×C₆₇	1	1	yes	characteristic, complemented
541	#2488	C₂×C₆₇	1	2	yes	complemented
542	#2486	C₂×C₆₇	1	1	yes	characteristic, complemented
543	#2440	C₂×C₆₇	1	1	yes	characteristic, complemented
544	#2425	C₂×C₆₇	1	2	yes	complemented
545	#2416	C₂×C₆₇	1	1	yes	characteristic
546	#2396	C₂×C₆₇	1	2	yes	complemented
547	#2395	C₂×C₆₇	1	2	yes	complemented
548	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
549	C₄×#123	C₂×C₆₇	1	2	yes	complemented
550	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
551	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
552	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
553	#2285	C₂×C₆₇	1	1	yes	characteristic, complemented
554	C₄²×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
555	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
556	C₆₇	#34763	1	1	yes	characteristic, direct product factor, Sylow
557	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
558	#529	—	2	16	no	—
559	C₂×#126	C₂²×C₆₇	1	2	yes	—
560	C₂×#126	C₂²×C₆₇	1	2	yes	—
561	C₂×#125	C₂²×C₆₇	1	2	yes	—
562	C₂×#124	C₂²×C₆₇	1	2	yes	—
563	C₂×#123	C₂²×C₆₇	1	2	yes	—
564	C₂×#123	C₂²×C₆₇	1	2	yes	—
565	C₂×#123	C₂²×C₆₇	1	2	yes	—
566	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
567	C₂×#121	C₂²×C₆₇	1	2	yes	—
568	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
569	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
570	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
571	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
572	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
573	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
574	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
575	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
576	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
577	C₂×#117	C₂²×C₆₇	1	2	yes	—
578	C₂×#117	C₂²×C₆₇	1	2	yes	—
579	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
580	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
581	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
582	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
583	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
584	#400	C₂²×C₆₇	1	2	yes	—
585	#400	C₂²×C₆₇	1	2	yes	—
586	#399	C₂²×C₆₇	1	2	yes	—
587	#399	C₂²×C₆₇	1	2	yes	—
588	#398	C₂²×C₆₇	1	2	yes	—
589	#398	C₂²×C₆₇	1	2	yes	—
590	#398	C₂²×C₆₇	1	2	yes	—
591	#397	C₂²×C₆₇	1	2	yes	—
592	#397	C₂²×C₆₇	1	2	yes	—
593	#397	C₂²×C₆₇	1	2	yes	—
594	#396	C₂²×C₆₇	1	2	yes	—
595	#396	C₂²×C₆₇	1	2	yes	—
596	#395	C₂²×C₆₇	1	2	yes	—
597	#394	C₂²×C₆₇	1	2	yes	—
598	#394	C₂²×C₆₇	1	2	yes	—
599	#393	C₂²×C₆₇	1	2	yes	—
600	#391	C₂²×C₆₇	1	2	yes	—
601	#390	C₂²×C₆₇	1	1	yes	characteristic
602	#390	C₂²×C₆₇	1	1	yes	characteristic
603	#390	C₂²×C₆₇	1	1	yes	characteristic
604	#390	C₂²×C₆₇	1	1	yes	characteristic
605	#389	C₂²×C₆₇	1	1	yes	characteristic
606	#389	C₂²×C₆₇	1	2	yes	—
607	#389	C₂²×C₆₇	1	1	yes	characteristic
608	#389	C₂²×C₆₇	1	1	yes	characteristic
609	#389	C₂²×C₆₇	1	1	yes	characteristic
610	#389	C₂²×C₆₇	1	1	yes	characteristic
611	#389	C₂²×C₆₇	1	1	yes	characteristic
612	#388	C₂²×C₆₇	1	2	yes	—
613	#388	C₂²×C₆₇	1	2	yes	—
614	#388	C₂²×C₆₇	1	2	yes	—
615	#388	C₂²×C₆₇	1	2	yes	—
616	#388	C₂²×C₆₇	1	2	yes	—
617	#388	C₂²×C₆₇	1	2	yes	—
618	#387	C₂²×C₆₇	1	2	yes	—
619	#387	C₂²×C₆₇	1	2	yes	—
620	#386	C₂²×C₆₇	1	2	yes	—
621	#386	C₂²×C₆₇	1	2	yes	—
622	#386	C₂²×C₆₇	1	2	yes	—
623	#385	C₂²×C₆₇	1	2	yes	—
624	#384	C₂²×C₆₇	1	1	yes	characteristic
625	#384	C₂²×C₆₇	1	1	yes	characteristic
626	#384	C₂²×C₆₇	1	1	yes	characteristic
627	#382	C₂²×C₆₇	1	2	yes	—
628	#381	C₂²×C₆₇	1	2	yes	—
629	#380	C₂²×C₆₇	1	1	yes	characteristic
630	#380	C₂²×C₆₇	1	2	yes	—
631	#380	C₂²×C₆₇	1	1	yes	characteristic
632	#380	C₂²×C₆₇	1	1	yes	characteristic
633	#380	C₂²×C₆₇	1	1	yes	characteristic
634	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
635	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
636	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
637	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
638	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
639	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
640	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
641	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
642	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
643	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
644	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
645	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
646	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
647	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
648	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
649	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
650	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
651	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
652	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
653	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
654	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
655	C₂×#95	C₂²×C₆₇	1	2	yes	—
656	C₄³	C₂²×C₆₇	1	1	yes	characteristic
657	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
658	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
659	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
660	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
661	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
662	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
663	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
664	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
665	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
666	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
667	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
668	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
669	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
670	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
671	C₄⋊Q₈	—	2	4	no	—
672	#126	—	2	8	no	—
673	#126	—	2	8	no	—
674	#125	—	2	8	no	—
675	#124	—	2	8	no	—
676	#123	—	2	8	no	—
677	#123	—	2	8	no	—
678	#123	—	2	8	no	—
679	C₂²⋊Q₈	—	2	8	no	—
680	#121	—	2	8	no	—
681	#121	—	2	4	no	—
682	#121	—	2	4	no	—
683	C₄×Q₈	—	2	8	no	—
684	C₄×D₄	—	2	8	no	—
685	C₄×D₄	—	2	8	no	—
686	C₄×D₄	—	2	4	no	—
687	C₄×D₄	—	2	4	no	—
688	C₄×D₄	—	2	4	no	—
689	C₄×D₄	D₄×C₆₇	1	8	yes	complemented
690	#117	—	2	8	no	—
691	#117	—	2	8	no	—
692	C₂×C₄⋊C₄	—	2	4	no	—
693	C₂×C₄⋊C₄	—	2	4	no	—
694	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
708	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
709	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
710	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
711	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
713	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
719	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
729	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×C₄²	—	2	8	no	—
741	C₂×C₄²	—	2	4	no	—
742	C₂×C₄²	—	2	4	no	—
743	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
744	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
745	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
746	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
747	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
748	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
749	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
750	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
751	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
754	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
755	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
756	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
757	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
758	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
759	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
760	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
761	#95	C₂³×C₆₇	1	2	yes	—
762	#95	C₂³×C₆₇	1	2	yes	—
763	#95	C₂³×C₆₇	1	2	yes	—
764	#95	C₂³×C₆₇	1	2	yes	—
765	#95	C₂³×C₆₇	1	1	yes	characteristic
766	#95	C₂³×C₆₇	1	1	yes	characteristic
767	#95	C₂³×C₆₇	1	1	yes	characteristic
768	#95	C₂³×C₆₇	1	1	yes	characteristic
769	#95	C₂³×C₆₇	1	1	yes	characteristic
770	#95	C₂³×C₆₇	1	1	yes	characteristic
771	#95	C₂³×C₆₇	1	2	yes	—
772	#95	C₂³×C₆₇	1	2	yes	—
773	#95	C₂³×C₆₇	1	2	yes	—
774	#95	C₂³×C₆₇	1	2	yes	—
775	#95	C₂³×C₆₇	1	2	yes	—
776	#95	C₂³×C₆₇	1	2	yes	—
777	#95	C₂³×C₆₇	1	2	yes	—
778	#95	C₂³×C₆₇	1	2	yes	—
779	#95	C₂³×C₆₇	1	2	yes	—
780	#95	C₂³×C₆₇	1	2	yes	—
781	#95	C₂³×C₆₇	1	2	yes	—
782	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
783	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
784	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
785	C₂×Q₈	—	2	4	no	—
786	C₂×Q₈	—	2	4	no	—
787	C₂×Q₈	—	4	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	4	no	—
791	C₂×D₄	—	2	4	no	—
792	C₂×D₄	—	2	4	no	—
793	C₂×D₄	—	2	4	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	4	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	2	4	no	—
808	C₂²×C₄	—	2	4	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	4	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	4	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	4	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	4	no	—
821	C₂²×C₄	—	4	1	no	—
822	C₂²×C₄	—	4	1	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
825	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
826	C₂²×C₄	#41×C₆₇	1	4	yes	—
827	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
845	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
847	C₄⋊C₄	—	2	4	no	—
848	C₄⋊C₄	—	2	4	no	—
849	C₄⋊C₄	—	2	4	no	—
850	C₄⋊C₄	—	2	4	no	—
851	C₄⋊C₄	—	2	4	no	—
852	C₄⋊C₄	—	2	4	no	—
853	C₄⋊C₄	—	2	4	no	—
854	C₄⋊C₄	—	2	4	no	—
855	C₄⋊C₄	—	2	4	no	—
856	C₄⋊C₄	—	2	4	no	—
857	C₄⋊C₄	—	2	4	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	4	no	—
866	C₄⋊C₄	—	2	4	no	—
867	C₄⋊C₄	—	2	4	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	4	2	no	—
870	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
871	C₄⋊C₄	#41×C₆₇	1	4	yes	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	2	4	no	—
874	C₂²⋊C₄	—	2	4	no	—
875	C₂²⋊C₄	—	2	4	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	4	no	—
878	C₂²⋊C₄	—	2	4	no	—
879	C₂²⋊C₄	—	2	4	no	—
880	C₂²⋊C₄	—	2	4	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	4	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	4	no	—
885	C₂²⋊C₄	—	2	4	no	—
886	C₂²⋊C₄	—	2	4	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	4	2	no	—
889	C₂²⋊C₄	—	4	2	no	—
890	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
891	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
892	C₂²⋊C₄	#41×C₆₇	1	4	yes	—
893	C₄²	—	2	4	no	—
894	C₄²	—	2	4	no	—
895	C₄²	—	2	4	no	—
896	C₄²	—	2	4	no	—
897	C₄²	—	2	4	no	—
898	C₄²	—	2	2	no	—
899	C₄²	—	2	2	no	—
900	C₄²	—	2	2	no	—
901	C₄²	—	2	2	no	—
902	C₄²	—	2	2	no	—
903	C₄²	—	2	2	no	—
904	C₄²	—	2	2	no	—
905	C₄²	—	2	2	no	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	4	1	no	—
909	C₄²	C₂×D₄×C₆₇	1	4	yes	—
910	C₄²	#41×C₆₇	1	4	yes	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	2	2	no	—
928	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
929	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
930	C₂³	C₂×#41×C₆₇	1	2	yes	—
931	C₂³	C₂×#41×C₆₇	1	2	yes	—
932	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
933	Q₈	—	4	8	no	—
934	D₄	—	2	8	no	—
935	D₄	—	4	8	no	—
936	D₄	—	4	8	no	—
937	D₄	—	4	4	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	8	no	—
957	C₂×C₄	—	2	8	no	—
958	C₂×C₄	—	2	8	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	4	4	no	—
987	C₂×C₄	—	4	8	no	—
988	C₂×C₄	—	4	4	no	—
989	C₂×C₄	—	4	8	no	—
990	C₂×C₄	—	4	4	no	—
991	C₂×C₄	—	4	8	no	—
992	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
993	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
994	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
995	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
996	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
997	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
998	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
999	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1000	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1001	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
1002	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1003	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1004	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1005	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1006	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	#532×C₆₇	1	4	yes	—
1028	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1029	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1030	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1031	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1032	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1033	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1034	C₂²	#585×C₆₇	1	1	yes	characteristic
1035	C₄	—	2	2	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	4	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	2	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	1	no	—
1053	C₄	#529×C₆₇	1	4	yes	complemented
1054	C₄	#547×C₆₇	1	4	yes	—
1055	C₂	—	2	4	no	—
1056	C₂	—	4	2	no	—
1057	C₂	—	8	2	no	—
1058	C₂	C₂×#529×C₆₇	1	1	yes	characteristic
1059	C₂	C₂×#532×C₆₇	1	1	yes	characteristic
1060	C₂	C₆₇×#3461	1	1	yes	characteristic
1061	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
1062	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1063	C₂	C₆₇×#3475	1	1	yes	characteristic
1064	C₂	C₆₇×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	C₆₇×#2416	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#529×C₆₇	C₂	semidirect
2. C₆₇×#2521	C₂	semidirect
3. C₆₇×#2519	C₂	semidirect
4. C₆₇×#2512	C₂	semidirect
5. C₆₇×#2506	C₂	semidirect
6. C₆₇×#2501	C₂	semidirect
7. C₆₇×#2496	C₂	semidirect
8. C₆₇×#2491	C₂	semidirect
9. C₆₇×#2488	C₂	semidirect
10. C₆₇×#2486	C₂	semidirect
11. C₆₇×#2440	C₂	semidirect
12. C₆₇×#2425	C₂	semidirect
14. C₆₇×#2396	C₂	semidirect
15. C₆₇×#2395	C₂	semidirect
16. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
17. C₄×#123×C₆₇	C₂	semidirect
18. C₄×#121×C₆₇	C₂	semidirect
19. C₄×#121×C₆₇	C₂	semidirect
20. C₆₇×#2293	C₂	semidirect
21. C₆₇×#2285	C₂	semidirect
22. C₄²×D₄×C₆₇	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₆₇	C₂	semidirect
156. C₄×D₄×C₆₇	D₄	semidirect
520. C₄×C₆₇	#529	semidirect
522. #34763	C₆₇	direct (N × H)
533. C₂×#529	C₂×C₆₇	semidirect
534. #2521	C₂×C₆₇	semidirect
535. #2519	C₂×C₆₇	semidirect
536. #2512	C₂×C₆₇	semidirect
537. #2506	C₂×C₆₇	semidirect
538. #2501	C₂×C₆₇	semidirect
539. #2496	C₂×C₆₇	semidirect
540. #2491	C₂×C₆₇	semidirect
541. #2488	C₂×C₆₇	semidirect
542. #2486	C₂×C₆₇	semidirect
543. #2440	C₂×C₆₇	semidirect
544. #2425	C₂×C₆₇	semidirect
546. #2396	C₂×C₆₇	semidirect
547. #2395	C₂×C₆₇	semidirect
548. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
549. C₄×#123	C₂×C₆₇	semidirect
550. C₄×#121	C₂×C₆₇	semidirect
551. C₄×#121	C₂×C₆₇	semidirect
552. #2293	C₂×C₆₇	semidirect
553. #2285	C₂×C₆₇	semidirect
554. C₄²×D₄	C₂×C₆₇	semidirect
555. C₂×C₄×C₄⋊C₄	C₂×C₆₇	semidirect
556. C₆₇	#34763	direct (N × H)
689. C₄×D₄	D₄×C₆₇	semidirect
1053. C₄	#529×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₆₇	2
C₆₇×#2521	2
C₆₇×#2519	2
C₆₇×#2512	2
C₆₇×#2506	2
C₆₇×#2501	2
C₆₇×#2496	2
C₆₇×#2491	2
C₆₇×#2488	2
C₆₇×#2486	2
C₆₇×#2440	2
C₆₇×#2425	2
C₆₇×#2416	2
C₆₇×#2396	2
C₆₇×#2395	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#123×C₆₇	2
C₄×#121×C₆₇	2
C₆₇×#2293	2
C₆₇×#2285	2
C₄²×D₄×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
#34763	67

Subgroups — C67×#34763 #30714014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34763 #30714014