Subgroups — C₆₇×#32910 #30712161

Order 17152.

1494 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#464×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#463×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#452×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#449×C₆₇	C₂	1	1	yes	maximal, characteristic
6	C₆₇×#2850	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1880	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1879	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1877	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#1873	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#1797	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
24	C₄×#41×C₆₇	—	2	4	no	—
25	C₄×#41×C₆₇	—	2	4	no	—
26	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	—	2	1	no	—
29	C₂×C₄×D₄×C₆₇	—	2	1	no	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#117×C₆₇	—	2	1	no	—
33	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₆₇	—	2	1	no	—
35	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
36	#464×C₆₇	—	2	4	no	—
37	#463×C₆₇	—	2	4	no	—
38	#452×C₆₇	—	2	4	no	—
39	#449×C₆₇	—	2	4	no	—
40	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
52	#391×C₆₇	C₂²	1	1	yes	characteristic
53	#390×C₆₇	C₂²	1	1	yes	characteristic
54	#388×C₆₇	—	2	1	no	—
55	#388×C₆₇	—	2	1	no	—
56	#386×C₆₇	—	2	1	no	—
57	#386×C₆₇	—	2	1	no	—
58	#382×C₆₇	C₂²	1	1	yes	characteristic
59	#340×C₆₇	C₂²	1	1	yes	characteristic
60	#340×C₆₇	C₂²	1	1	yes	characteristic
61	#340×C₆₇	C₂²	1	1	yes	characteristic
62	#340×C₆₇	C₂²	1	1	yes	characteristic
63	#336×C₆₇	C₂²	1	1	yes	characteristic
64	#336×C₆₇	C₂²	1	1	yes	characteristic
65	C₂×#41×C₆₇	—	2	2	no	—
66	C₂×#41×C₆₇	—	2	2	no	—
67	C₂×#41×C₆₇	—	2	2	no	—
68	C₂×#41×C₆₇	—	2	2	no	—
69	C₂×#41×C₆₇	—	2	2	no	—
70	C₂×#41×C₆₇	D₄	1	4	yes	—
71	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₆₇	—	2	1	no	—
74	C₂²×D₄×C₆₇	—	2	1	no	—
75	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₆₇	—	2	1	no	—
78	C₂³×C₄×C₆₇	—	2	1	no	—
79	C₂³×C₄×C₆₇	—	2	1	no	—
80	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
83	C₂×Q₁₆×C₆₇	—	2	2	no	—
84	C₂×Q₁₆×C₆₇	—	2	2	no	—
85	C₂×Q₁₆×C₆₇	—	2	2	no	—
86	C₂×SD₁₆×C₆₇	—	2	2	no	—
87	C₂×SD₁₆×C₆₇	—	2	2	no	—
88	C₂×SD₁₆×C₆₇	—	2	2	no	—
89	C₂×SD₁₆×C₆₇	—	2	2	no	—
90	C₂×SD₁₆×C₆₇	—	2	2	no	—
91	C₂×SD₁₆×C₆₇	—	2	2	no	—
92	C₂×D₈×C₆₇	—	2	2	no	—
93	C₂×D₈×C₆₇	—	2	2	no	—
94	C₂×D₈×C₆₇	—	2	2	no	—
95	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
99	#124×C₆₇	—	2	2	no	—
100	#124×C₆₇	—	2	2	no	—
101	C₂²⋊Q₈×C₆₇	—	2	2	no	—
102	C₂²⋊Q₈×C₆₇	—	2	2	no	—
103	#121×C₆₇	—	2	2	no	—
104	#121×C₆₇	—	2	2	no	—
105	C₄×Q₈×C₆₇	—	2	2	no	—
106	C₄×Q₈×C₆₇	—	2	2	no	—
107	C₄×Q₈×C₆₇	—	2	2	no	—
108	C₄×Q₈×C₆₇	D₄	1	4	yes	complemented
109	C₄×D₄×C₆₇	—	2	8	no	—
110	C₄×D₄×C₆₇	—	2	8	no	—
111	C₄×D₄×C₆₇	—	2	2	no	—
112	C₄×D₄×C₆₇	—	2	2	no	—
113	C₄×D₄×C₆₇	—	2	2	no	—
114	C₄×D₄×C₆₇	D₄	1	4	yes	complemented
115	#117×C₆₇	—	2	8	no	—
116	#117×C₆₇	—	2	2	no	—
117	#117×C₆₇	—	2	2	no	—
118	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
119	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
120	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
134	C₂×C₄²×C₆₇	—	2	8	no	—
135	C₂×C₄²×C₆₇	—	2	1	no	—
136	C₂×C₄²×C₆₇	—	2	1	no	—
137	C₂×C₄²×C₆₇	—	2	1	no	—
138	C₂×C₄²×C₆₇	—	2	2	no	—
139	C₂×C₄²×C₆₇	—	2	2	no	—
140	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
141	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
142	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
144	C₄⋊C₈×C₆₇	—	2	2	no	—
145	C₄⋊C₈×C₆₇	—	2	2	no	—
146	#103×C₆₇	—	2	2	no	—
147	#103×C₆₇	—	2	2	no	—
148	#103×C₆₇	—	2	2	no	—
149	#103×C₆₇	—	2	2	no	—
150	#102×C₆₇	—	2	2	no	—
151	#102×C₆₇	—	2	2	no	—
152	#102×C₆₇	—	2	2	no	—
153	#102×C₆₇	—	2	2	no	—
154	C₂²⋊C₈×C₆₇	—	2	2	no	—
155	C₂²⋊C₈×C₆₇	—	2	2	no	—
156	#95×C₆₇	—	2	1	no	—
157	#95×C₆₇	—	2	1	no	—
158	#95×C₆₇	—	2	1	no	—
159	#95×C₆₇	—	2	1	no	—
160	C₂⁴×C₆₇	—	2	1	no	—
161	C₂⁴×C₆₇	—	2	1	no	—
162	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
163	#41×C₆₇	—	2	8	no	—
164	#41×C₆₇	—	2	8	no	—
165	#41×C₆₇	—	2	8	no	—
166	#41×C₆₇	—	2	8	no	—
167	C₂×Q₈×C₆₇	—	2	1	no	—
168	C₂×Q₈×C₆₇	—	2	1	no	—
169	C₂×Q₈×C₆₇	—	2	1	no	—
170	C₂×Q₈×C₆₇	—	2	1	no	—
171	C₂×Q₈×C₆₇	—	2	1	no	—
172	C₂×Q₈×C₆₇	—	2	1	no	—
173	C₂×Q₈×C₆₇	—	2	1	no	—
174	C₂×Q₈×C₆₇	—	2	1	no	—
175	C₂×Q₈×C₆₇	—	2	1	no	—
176	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
177	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
178	C₂×Q₈×C₆₇	#41	1	2	yes	—
179	C₂×D₄×C₆₇	—	2	4	no	—
180	C₂×D₄×C₆₇	—	2	4	no	—
181	C₂×D₄×C₆₇	—	2	4	no	—
182	C₂×D₄×C₆₇	—	2	1	no	—
183	C₂×D₄×C₆₇	—	2	1	no	—
184	C₂×D₄×C₆₇	—	2	1	no	—
185	C₂×D₄×C₆₇	—	2	1	no	—
186	C₂×D₄×C₆₇	—	2	1	no	—
187	C₂×D₄×C₆₇	—	2	1	no	—
188	C₂×D₄×C₆₇	—	2	1	no	—
189	C₂×D₄×C₆₇	—	2	1	no	—
190	C₂×D₄×C₆₇	—	2	1	no	—
191	C₂×D₄×C₆₇	—	4	2	no	—
192	C₂×D₄×C₆₇	—	4	2	no	—
193	C₂×D₄×C₆₇	—	4	2	no	—
194	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
195	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
196	C₂×D₄×C₆₇	#41	1	2	yes	—
197	C₂²×C₄×C₆₇	—	2	4	no	—
198	C₂²×C₄×C₆₇	—	2	4	no	—
199	C₂²×C₄×C₆₇	—	2	1	no	—
200	C₂²×C₄×C₆₇	—	2	4	no	—
201	C₂²×C₄×C₆₇	—	2	1	no	—
202	C₂²×C₄×C₆₇	—	2	1	no	—
203	C₂²×C₄×C₆₇	—	2	1	no	—
204	C₂²×C₄×C₆₇	—	2	1	no	—
205	C₂²×C₄×C₆₇	—	2	4	no	—
206	C₂²×C₄×C₆₇	—	2	1	no	—
207	C₂²×C₄×C₆₇	—	2	1	no	—
208	C₂²×C₄×C₆₇	—	2	2	no	—
209	C₂²×C₄×C₆₇	—	2	2	no	—
210	C₂²×C₄×C₆₇	—	2	4	no	—
211	C₂²×C₄×C₆₇	—	2	2	no	—
212	C₂²×C₄×C₆₇	—	2	1	no	—
213	C₂²×C₄×C₆₇	—	2	1	no	—
214	C₂²×C₄×C₆₇	—	2	1	no	—
215	C₂²×C₄×C₆₇	—	4	1	no	—
216	C₂²×C₄×C₆₇	—	4	1	no	—
217	C₂²×C₄×C₆₇	—	4	1	no	—
218	C₂²×C₄×C₆₇	—	4	2	no	—
219	C₂²×C₄×C₆₇	—	4	2	no	—
220	C₂²×C₄×C₆₇	—	4	2	no	—
221	C₂²×C₄×C₆₇	—	4	2	no	—
222	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₆₇	#41	1	2	yes	—
229	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
230	Q₁₆×C₆₇	—	4	4	no	—
231	SD₁₆×C₆₇	—	4	4	no	—
232	SD₁₆×C₆₇	—	4	4	no	—
233	D₈×C₆₇	—	4	4	no	—
234	C₂×C₈×C₆₇	—	2	1	no	—
235	C₂×C₈×C₆₇	—	2	1	no	—
236	C₂×C₈×C₆₇	—	2	1	no	—
237	C₂×C₈×C₆₇	—	2	1	no	—
238	C₂×C₈×C₆₇	—	2	1	no	—
239	C₂×C₈×C₆₇	—	2	1	no	—
240	C₂×C₈×C₆₇	—	2	1	no	—
241	C₂×C₈×C₆₇	—	2	1	no	—
242	C₂×C₈×C₆₇	—	2	1	no	—
243	C₂×C₈×C₆₇	—	2	1	no	—
244	C₂×C₈×C₆₇	—	2	1	no	—
245	C₂×C₈×C₆₇	—	2	1	no	—
246	C₄⋊C₄×C₆₇	—	2	4	no	—
247	C₄⋊C₄×C₆₇	—	2	4	no	—
248	C₄⋊C₄×C₆₇	—	2	1	no	—
249	C₄⋊C₄×C₆₇	—	2	1	no	—
250	C₄⋊C₄×C₆₇	—	2	1	no	—
251	C₄⋊C₄×C₆₇	—	2	1	no	—
252	C₄⋊C₄×C₆₇	—	2	1	no	—
253	C₄⋊C₄×C₆₇	—	2	1	no	—
254	C₄⋊C₄×C₆₇	—	4	2	no	—
255	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
257	C₂²⋊C₄×C₆₇	—	2	4	no	—
258	C₂²⋊C₄×C₆₇	—	2	4	no	—
259	C₂²⋊C₄×C₆₇	—	2	4	no	—
260	C₂²⋊C₄×C₆₇	—	4	2	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	C₄²×C₆₇	—	2	4	no	—
267	C₄²×C₆₇	—	2	4	no	—
268	C₄²×C₆₇	—	2	2	no	—
269	C₄²×C₆₇	—	2	4	no	—
270	C₄²×C₆₇	—	2	2	no	—
271	C₄²×C₆₇	—	2	1	no	—
272	C₄²×C₆₇	—	2	1	no	—
273	C₄²×C₆₇	C₂×D₄	1	2	yes	—
274	C₄²×C₆₇	C₂×D₄	1	2	yes	—
275	C₂³×C₆₇	—	2	1	no	—
276	C₂³×C₆₇	—	2	2	no	—
277	C₂³×C₆₇	—	2	2	no	—
278	C₂³×C₆₇	—	2	1	no	—
279	C₂³×C₆₇	—	2	2	no	—
280	C₂³×C₆₇	—	2	1	no	—
281	C₂³×C₆₇	—	2	1	no	—
282	C₂³×C₆₇	—	2	1	no	—
283	C₂³×C₆₇	—	2	1	no	—
284	C₂³×C₆₇	—	4	1	no	—
285	C₂³×C₆₇	—	4	1	no	—
286	C₂³×C₆₇	—	4	1	no	—
287	C₂³×C₆₇	—	4	1	no	—
288	C₂³×C₆₇	—	4	1	no	—
289	C₂³×C₆₇	—	4	1	no	—
290	C₂³×C₆₇	—	4	1	no	—
291	C₂³×C₆₇	—	4	1	no	—
292	C₂³×C₆₇	—	4	1	no	—
293	C₂³×C₆₇	—	4	1	no	—
294	C₂³×C₆₇	—	4	1	no	—
295	C₂³×C₆₇	#121	1	2	yes	—
296	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
297	Q₈×C₆₇	—	2	2	no	—
298	Q₈×C₆₇	—	2	2	no	—
299	Q₈×C₆₇	—	2	2	no	—
300	Q₈×C₆₇	—	4	1	no	—
301	Q₈×C₆₇	—	4	1	no	—
302	Q₈×C₆₇	—	4	1	no	—
303	Q₈×C₆₇	—	4	1	no	—
304	Q₈×C₆₇	#121	1	4	yes	—
305	D₄×C₆₇	—	2	16	no	—
306	D₄×C₆₇	—	2	2	no	—
307	D₄×C₆₇	—	2	2	no	—
308	D₄×C₆₇	—	2	2	no	—
309	D₄×C₆₇	—	4	1	no	—
310	D₄×C₆₇	—	4	1	no	—
311	D₄×C₆₇	—	4	1	no	—
312	D₄×C₆₇	—	4	1	no	—
313	D₄×C₆₇	—	8	4	no	—
314	D₄×C₆₇	#121	1	4	yes	—
315	C₂×C₄×C₆₇	—	2	16	no	—
316	C₂×C₄×C₆₇	—	2	1	no	—
317	C₂×C₄×C₆₇	—	2	1	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	1	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	1	no	—
323	C₂×C₄×C₆₇	—	2	1	no	—
324	C₂×C₄×C₆₇	—	2	1	no	—
325	C₂×C₄×C₆₇	—	2	1	no	—
326	C₂×C₄×C₆₇	—	2	1	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	1	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	1	no	—
335	C₂×C₄×C₆₇	—	2	1	no	—
336	C₂×C₄×C₆₇	—	4	4	no	—
337	C₂×C₄×C₆₇	—	4	8	no	—
338	C₂×C₄×C₆₇	—	4	4	no	—
339	C₂×C₄×C₆₇	—	4	8	no	—
340	C₂×C₄×C₆₇	—	4	1	no	—
341	C₂×C₄×C₆₇	—	4	1	no	—
342	C₂×C₄×C₆₇	—	4	1	no	—
343	C₂×C₄×C₆₇	—	4	1	no	—
344	C₂×C₄×C₆₇	—	4	1	no	—
345	C₂×C₄×C₆₇	—	4	1	no	—
346	C₂×C₄×C₆₇	—	4	1	no	—
347	C₂×C₄×C₆₇	—	4	1	no	—
348	C₂×C₄×C₆₇	—	4	1	no	—
349	C₂×C₄×C₆₇	—	4	1	no	—
350	C₂×C₄×C₆₇	—	4	1	no	—
351	C₂×C₄×C₆₇	—	4	1	no	—
352	C₂×C₄×C₆₇	—	4	1	no	—
353	C₂×C₄×C₆₇	#120	1	2	yes	—
354	C₂×C₄×C₆₇	#120	1	2	yes	—
355	C₂×C₄×C₆₇	#121	1	2	yes	—
356	C₂×C₄×C₆₇	#135	1	2	yes	—
357	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
362	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
363	C₈×C₆₇	—	4	1	no	—
364	C₈×C₆₇	—	4	1	no	—
365	C₈×C₆₇	—	4	1	no	—
366	C₈×C₆₇	—	4	1	no	—
367	C₂²×C₆₇	—	2	2	no	—
368	C₂²×C₆₇	—	2	4	no	—
369	C₂²×C₆₇	—	2	2	no	—
370	C₂²×C₆₇	—	2	2	no	—
371	C₂²×C₆₇	—	4	1	no	—
372	C₂²×C₆₇	—	4	2	no	—
373	C₂²×C₆₇	—	4	1	no	—
374	C₂²×C₆₇	—	4	2	no	—
375	C₂²×C₆₇	—	4	1	no	—
376	C₂²×C₆₇	—	4	2	no	—
377	C₂²×C₆₇	—	4	1	no	—
378	C₂²×C₆₇	—	4	2	no	—
379	C₂²×C₆₇	—	4	2	no	—
380	C₂²×C₆₇	—	4	2	no	—
381	C₂²×C₆₇	—	8	1	no	—
382	C₂²×C₆₇	—	8	1	no	—
383	C₂²×C₆₇	—	8	1	no	—
384	C₂²×C₆₇	—	8	1	no	—
385	C₂²×C₆₇	—	8	1	no	—
386	C₂²×C₆₇	—	8	1	no	—
387	C₂²×C₆₇	—	8	1	no	—
388	C₂²×C₆₇	C₂×#120	1	1	yes	characteristic
389	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
390	C₂²×C₆₇	#525	1	1	yes	characteristic
391	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
392	C₂²×C₆₇	#575	1	1	yes	characteristic
393	C₂²×C₆₇	#575	1	1	yes	characteristic
394	C₂²×C₆₇	#575	1	1	yes	characteristic
395	C₄×C₆₇	—	2	2	no	—
396	C₄×C₆₇	—	2	4	no	—
397	C₄×C₆₇	—	2	2	no	—
398	C₄×C₆₇	—	2	2	no	—
399	C₄×C₆₇	—	2	2	no	—
400	C₄×C₆₇	—	4	2	no	—
401	C₄×C₆₇	—	4	1	no	—
402	C₄×C₆₇	—	4	2	no	—
403	C₄×C₆₇	—	8	1	no	—
404	C₄×C₆₇	—	8	1	no	—
405	C₄×C₆₇	—	8	1	no	—
406	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
407	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
408	C₄×C₆₇	#525	1	1	yes	characteristic
409	C₄×C₆₇	#525	1	1	yes	characteristic
410	#32910	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
411	C₂×C₆₇	—	4	2	no	—
412	C₂×C₆₇	—	4	4	no	—
413	C₂×C₆₇	—	16	1	no	—
414	C₂×C₆₇	#2847	1	1	yes	characteristic
415	C₂×C₆₇	#3002	1	1	yes	characteristic
416	C₂×C₆₇	#3005	1	1	yes	characteristic
417	C₂×C₆₇	#3035	1	1	yes	characteristic
418	C₂×C₆₇	#3040	1	1	yes	characteristic
419	C₂×C₆₇	#3102	1	1	yes	characteristic
420	C₂×C₆₇	#3111	1	1	yes	characteristic
421	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
422	C₂×#464	C₂×C₆₇	1	1	yes	characteristic, complemented
423	C₂×#463	C₂×C₆₇	1	1	yes	characteristic, complemented
424	C₂×#452	C₂×C₆₇	1	1	yes	characteristic, complemented
425	C₂×#449	C₂×C₆₇	1	1	yes	characteristic
426	#2850	C₂×C₆₇	1	1	yes	characteristic, complemented
427	#1880	C₂×C₆₇	1	1	yes	characteristic, complemented
428	#1879	C₂×C₆₇	1	1	yes	characteristic, complemented
429	#1878	C₂×C₆₇	1	1	yes	characteristic, complemented
430	#1877	C₂×C₆₇	1	1	yes	characteristic, complemented
431	#1875	C₂×C₆₇	1	1	yes	characteristic, complemented
432	#1873	C₂×C₆₇	1	1	yes	characteristic, complemented
433	#1805	C₂×C₆₇	1	1	yes	characteristic, complemented
434	#1804	C₂×C₆₇	1	1	yes	characteristic, complemented
435	#1797	C₂×C₆₇	1	1	yes	characteristic, complemented
436	C₆₇	#32910	1	1	yes	characteristic, direct product factor, Sylow
437	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
438	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
439	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
440	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
441	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
442	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
443	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
444	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
445	C₄×#41	—	2	4	no	—
446	C₄×#41	—	2	4	no	—
447	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
448	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
449	C₂×C₄×D₄	—	2	1	no	—
450	C₂×C₄×D₄	—	2	1	no	—
451	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
453	C₂×#117	—	2	1	no	—
454	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
455	C₂²×C₄²	—	2	1	no	—
456	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
457	#464	—	2	4	no	—
458	#463	—	2	4	no	—
459	#452	—	2	4	no	—
460	#449	—	2	4	no	—
461	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
462	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
463	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
464	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
465	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
466	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
467	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
468	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
469	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
470	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
471	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
472	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
473	#391	C₂²×C₆₇	1	1	yes	characteristic
474	#390	C₂²×C₆₇	1	1	yes	characteristic
475	#388	—	2	1	no	—
476	#388	—	2	1	no	—
477	#386	—	2	1	no	—
478	#386	—	2	1	no	—
479	#382	C₂²×C₆₇	1	1	yes	characteristic
480	#340	C₂²×C₆₇	1	1	yes	characteristic
481	#340	C₂²×C₆₇	1	1	yes	characteristic
482	#340	C₂²×C₆₇	1	1	yes	characteristic
483	#340	C₂²×C₆₇	1	1	yes	characteristic
484	#336	C₂²×C₆₇	1	1	yes	characteristic
485	#336	C₂²×C₆₇	1	1	yes	characteristic
486	C₂×#41	—	2	2	no	—
487	C₂×#41	—	2	2	no	—
488	C₂×#41	—	2	2	no	—
489	C₂×#41	—	2	2	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	D₄×C₆₇	1	4	yes	—
492	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
493	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
498	C₂³×C₄	—	2	1	no	—
499	C₂³×C₄	—	2	1	no	—
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
502	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
504	C₂×Q₁₆	—	2	2	no	—
505	C₂×Q₁₆	—	2	2	no	—
506	C₂×Q₁₆	—	2	2	no	—
507	C₂×SD₁₆	—	2	2	no	—
508	C₂×SD₁₆	—	2	2	no	—
509	C₂×SD₁₆	—	2	2	no	—
510	C₂×SD₁₆	—	2	2	no	—
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	2	2	no	—
513	C₂×D₈	—	2	2	no	—
514	C₂×D₈	—	2	2	no	—
515	C₂×D₈	—	2	2	no	—
516	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
517	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
518	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
519	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
520	#124	—	2	2	no	—
521	#124	—	2	2	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	#121	—	2	2	no	—
525	#121	—	2	2	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	—	2	2	no	—
529	C₄×Q₈	D₄×C₆₇	1	4	yes	complemented
530	C₄×D₄	—	2	8	no	—
531	C₄×D₄	—	2	8	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	D₄×C₆₇	1	4	yes	complemented
536	#117	—	2	8	no	—
537	#117	—	2	2	no	—
538	#117	—	2	2	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	2	1	no	—
542	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₄²	—	2	8	no	—
556	C₂×C₄²	—	2	1	no	—
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	—	2	1	no	—
559	C₂×C₄²	—	2	2	no	—
560	C₂×C₄²	—	2	2	no	—
561	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
562	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
565	C₄⋊C₈	—	2	2	no	—
566	C₄⋊C₈	—	2	2	no	—
567	#103	—	2	2	no	—
568	#103	—	2	2	no	—
569	#103	—	2	2	no	—
570	#103	—	2	2	no	—
571	#102	—	2	2	no	—
572	#102	—	2	2	no	—
573	#102	—	2	2	no	—
574	#102	—	2	2	no	—
575	C₂²⋊C₈	—	2	2	no	—
576	C₂²⋊C₈	—	2	2	no	—
577	#95	—	2	1	no	—
578	#95	—	2	1	no	—
579	#95	—	2	1	no	—
580	#95	—	2	1	no	—
581	C₂⁴	—	2	1	no	—
582	C₂⁴	—	2	1	no	—
583	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
584	#41	—	2	8	no	—
585	#41	—	2	8	no	—
586	#41	—	2	8	no	—
587	#41	—	2	8	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
598	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
599	C₂×Q₈	#41×C₆₇	1	2	yes	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	4	2	no	—
613	C₂×D₄	—	4	2	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
616	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
617	C₂×D₄	#41×C₆₇	1	2	yes	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	4	1	no	—
637	C₂²×C₄	—	4	1	no	—
638	C₂²×C₄	—	4	1	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
648	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
649	C₂²×C₄	#41×C₆₇	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
651	Q₁₆	—	4	4	no	—
652	SD₁₆	—	4	4	no	—
653	SD₁₆	—	4	4	no	—
654	D₈	—	4	4	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	2	1	no	—
662	C₂×C₈	—	2	1	no	—
663	C₂×C₈	—	2	1	no	—
664	C₂×C₈	—	2	1	no	—
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	—	2	1	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
677	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	2	no	—
685	C₂²⋊C₄	—	4	2	no	—
686	C₂²⋊C₄	—	4	2	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	4	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	1	no	—
693	C₄²	—	2	1	no	—
694	C₄²	C₂×D₄×C₆₇	1	2	yes	—
695	C₄²	C₂×D₄×C₆₇	1	2	yes	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	—	4	1	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	#121×C₆₇	1	2	yes	—
717	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	4	1	no	—
722	Q₈	—	4	1	no	—
723	Q₈	—	4	1	no	—
724	Q₈	—	4	1	no	—
725	Q₈	#121×C₆₇	1	4	yes	—
726	D₄	—	2	16	no	—
727	D₄	—	2	2	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	2	no	—
730	D₄	—	4	1	no	—
731	D₄	—	4	1	no	—
732	D₄	—	4	1	no	—
733	D₄	—	4	1	no	—
734	D₄	—	8	4	no	—
735	D₄	#121×C₆₇	1	4	yes	—
736	C₂×C₄	—	2	16	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	4	4	no	—
758	C₂×C₄	—	4	8	no	—
759	C₂×C₄	—	4	4	no	—
760	C₂×C₄	—	4	8	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	#120×C₆₇	1	2	yes	—
775	C₂×C₄	#120×C₆₇	1	2	yes	—
776	C₂×C₄	#121×C₆₇	1	2	yes	—
777	C₂×C₄	#135×C₆₇	1	2	yes	—
778	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
781	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
782	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
783	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
784	C₈	—	4	1	no	—
785	C₈	—	4	1	no	—
786	C₈	—	4	1	no	—
787	C₈	—	4	1	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	4	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	8	1	no	—
803	C₂²	—	8	1	no	—
804	C₂²	—	8	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	—	8	1	no	—
808	C₂²	—	8	1	no	—
809	C₂²	C₂×#120×C₆₇	1	1	yes	characteristic
810	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
811	C₂²	#525×C₆₇	1	1	yes	characteristic
812	C₂²	C₂×#135×C₆₇	1	1	yes	characteristic
813	C₂²	#575×C₆₇	1	1	yes	characteristic
814	C₂²	#575×C₆₇	1	1	yes	characteristic
815	C₂²	#575×C₆₇	1	1	yes	characteristic
816	C₄	—	2	2	no	—
817	C₄	—	2	4	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	2	no	—
824	C₄	—	8	1	no	—
825	C₄	—	8	1	no	—
826	C₄	—	8	1	no	—
827	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
828	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
829	C₄	#525×C₆₇	1	1	yes	characteristic
830	C₄	#525×C₆₇	1	1	yes	characteristic
831	C₂	—	4	2	no	—
832	C₂	—	4	4	no	—
833	C₂	—	16	1	no	—
834	C₂	C₆₇×#2847	1	1	yes	characteristic
835	C₂	C₆₇×#3002	1	1	yes	characteristic
836	C₂	C₆₇×#3005	1	1	yes	characteristic
837	C₂	C₆₇×#3035	1	1	yes	characteristic
838	C₂	C₆₇×#3040	1	1	yes	characteristic
839	C₂	C₆₇×#3102	1	1	yes	characteristic
840	C₂	C₆₇×#3111	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂×#449×C₆₇	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×#41×C₆₇	C₂	semidirect
2. C₂×#464×C₆₇	C₂	semidirect
3. C₂×#463×C₆₇	C₂	semidirect
4. C₂×#452×C₆₇	C₂	semidirect
6. C₆₇×#2850	C₂	semidirect
7. C₆₇×#1880	C₂	semidirect
8. C₆₇×#1879	C₂	semidirect
9. C₆₇×#1878	C₂	semidirect
10. C₆₇×#1877	C₂	semidirect
11. C₆₇×#1875	C₂	semidirect
12. C₆₇×#1873	C₂	semidirect
13. C₆₇×#1805	C₂	semidirect
14. C₆₇×#1804	C₂	semidirect
15. C₆₇×#1797	C₂	semidirect
108. C₄×Q₈×C₆₇	D₄	semidirect
114. C₄×D₄×C₆₇	D₄	semidirect
410. #32910	C₆₇	direct (N × H)
421. C₂×C₄×#41	C₂×C₆₇	semidirect
422. C₂×#464	C₂×C₆₇	semidirect
423. C₂×#463	C₂×C₆₇	semidirect
424. C₂×#452	C₂×C₆₇	semidirect
426. #2850	C₂×C₆₇	semidirect
427. #1880	C₂×C₆₇	semidirect
428. #1879	C₂×C₆₇	semidirect
429. #1878	C₂×C₆₇	semidirect
430. #1877	C₂×C₆₇	semidirect
431. #1875	C₂×C₆₇	semidirect
432. #1873	C₂×C₆₇	semidirect
433. #1805	C₂×C₆₇	semidirect
434. #1804	C₂×C₆₇	semidirect
435. #1797	C₂×C₆₇	semidirect
436. C₆₇	#32910	direct (N × H)
529. C₄×Q₈	D₄×C₆₇	semidirect
535. C₄×D₄	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₆₇	2
C₂×#464×C₆₇	2
C₂×#463×C₆₇	2
C₂×#452×C₆₇	2
C₂×#449×C₆₇	2
C₆₇×#2850	2
C₆₇×#1880	2
C₆₇×#1879	2
C₆₇×#1878	2
C₆₇×#1877	2
C₆₇×#1875	2
C₆₇×#1873	2
C₆₇×#1805	2
C₆₇×#1804	2
C₆₇×#1797	2
#32910	67

Subgroups — C67×#32910 #30712161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#32910 #30712161