Subgroups — C₆₇×#61718 #30740969

Order 17152.

1830 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#553×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3355	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3351	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3326	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3322	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3232	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3194	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3193	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3192	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3105	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3095	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3092	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
16	#553×C₆₇	—	2	2	no	—
17	#553×C₆₇	—	2	2	no	—
18	#553×C₆₇	—	2	2	no	—
19	#553×C₆₇	C₂²	1	4	yes	—
20	#553×C₆₇	C₂²	1	4	yes	complemented
21	#553×C₆₇	C₂²	1	2	yes	complemented
22	#552×C₆₇	C₂²	1	2	yes	complemented
23	#551×C₆₇	—	2	2	no	—
24	#548×C₆₇	C₂²	1	2	yes	complemented
25	#546×C₆₇	C₂²	1	2	yes	complemented
26	#539×C₆₇	—	2	1	no	—
27	#538×C₆₇	—	2	1	no	—
28	#534×C₆₇	—	2	1	no	—
29	#529×C₆₇	C₂²	1	2	yes	—
30	C₂×#126×C₆₇	—	2	1	no	—
31	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	#525×C₆₇	C₂²	1	2	yes	—
33	C₂×#123×C₆₇	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#121×C₆₇	—	2	1	no	—
36	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#518×C₆₇	—	2	1	no	—
40	C₂×C₄×D₄×C₆₇	—	2	1	no	—
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#499×C₆₇	C₂²	1	4	yes	complemented
46	#488×C₆₇	C₂²	1	4	yes	complemented
47	#485×C₆₇	C₂²	1	4	yes	complemented
48	#484×C₆₇	C₂²	1	2	yes	complemented
49	#484×C₆₇	C₂²	1	2	yes	complemented
50	#483×C₆₇	C₂²	1	4	yes	complemented
51	#483×C₆₇	C₂²	1	2	yes	complemented
52	#482×C₆₇	C₂²	1	4	yes	complemented
53	#482×C₆₇	C₂²	1	4	yes	complemented
54	#481×C₆₇	C₂²	1	2	yes	—
55	#481×C₆₇	C₂²	1	2	yes	—
56	#481×C₆₇	C₂²	1	2	yes	complemented
57	#480×C₆₇	C₂²	1	2	yes	—
58	#480×C₆₇	C₂²	1	4	yes	complemented
59	#480×C₆₇	C₂²	1	2	yes	complemented
60	#479×C₆₇	C₂²	1	4	yes	complemented
61	#478×C₆₇	C₂²	1	4	yes	complemented
62	#478×C₆₇	C₂²	1	4	yes	complemented
63	#469×C₆₇	C₂²	1	4	yes	complemented
64	#469×C₆₇	C₂²	1	4	yes	complemented
65	#468×C₆₇	C₂²	1	4	yes	complemented
66	#468×C₆₇	C₂²	1	4	yes	complemented
67	#463×C₆₇	C₂²	1	4	yes	complemented
68	#450×C₆₇	C₂²	1	2	yes	complemented
69	#449×C₆₇	C₂²	1	4	yes	complemented
70	#448×C₆₇	C₂²	1	2	yes	complemented
71	#447×C₆₇	C₂²	1	2	yes	—
72	#447×C₆₇	C₂²	1	2	yes	complemented
73	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
74	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
75	#436×C₆₇	C₂²	1	4	yes	complemented
76	#436×C₆₇	C₂²	1	4	yes	complemented
77	#431×C₆₇	C₂²	1	2	yes	complemented
78	#428×C₆₇	C₂²	1	4	yes	complemented
79	#428×C₆₇	C₂²	1	2	yes	complemented
80	#428×C₆₇	C₂²	1	2	yes	complemented
81	#419×C₆₇	C₂²	1	2	yes	complemented
82	#418×C₆₇	C₂²	1	2	yes	complemented
83	#417×C₆₇	C₂²	1	4	yes	complemented
84	#407×C₆₇	C₂²	1	1	yes	characteristic
85	#407×C₆₇	C₂²	1	1	yes	characteristic
86	#407×C₆₇	C₂²	1	2	yes	complemented
87	C₂×#41×C₆₇	C₂³	1	2	yes	—
88	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₇	—	2	1	no	—
90	C₂²×D₄×C₆₇	—	2	1	no	—
91	C₂²×D₄×C₆₇	—	2	1	no	—
92	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₆₇	—	2	1	no	—
96	C₂³×C₄×C₆₇	—	2	1	no	—
97	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×D₈×C₆₇	C₂³	1	4	yes	—
101	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
102	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
103	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
104	#126×C₆₇	—	2	4	no	—
105	#126×C₆₇	—	2	4	no	—
106	#126×C₆₇	—	2	2	no	—
107	#126×C₆₇	—	2	2	no	—
108	#126×C₆₇	—	2	2	no	—
109	#125×C₆₇	—	2	2	no	—
110	#125×C₆₇	—	2	2	no	—
111	#125×C₆₇	C₂³	1	2	yes	—
112	#125×C₆₇	C₂³	1	4	yes	—
113	#124×C₆₇	—	2	2	no	—
114	#124×C₆₇	C₂³	1	2	yes	—
115	#123×C₆₇	—	2	2	no	—
116	#123×C₆₇	—	2	2	no	—
117	#123×C₆₇	—	2	2	no	—
118	#123×C₆₇	—	2	2	no	—
119	#123×C₆₇	—	2	4	no	—
120	#123×C₆₇	—	2	4	no	—
121	#123×C₆₇	—	2	2	no	—
122	C₂²⋊Q₈×C₆₇	—	2	1	no	—
123	C₂²⋊Q₈×C₆₇	—	2	1	no	—
124	C₂²⋊Q₈×C₆₇	—	2	2	no	—
125	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
126	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
127	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
128	#121×C₆₇	—	2	4	no	—
129	#121×C₆₇	—	2	4	no	—
130	#121×C₆₇	—	2	2	no	—
131	#121×C₆₇	—	2	2	no	—
132	#121×C₆₇	—	2	1	no	—
133	#121×C₆₇	—	2	1	no	—
134	#121×C₆₇	—	2	1	no	—
135	#121×C₆₇	—	2	1	no	—
136	#121×C₆₇	—	2	2	no	—
137	#121×C₆₇	—	2	2	no	—
138	#121×C₆₇	C₂³	1	2	yes	—
139	#121×C₆₇	C₂³	1	4	yes	—
140	#121×C₆₇	C₂³	1	2	yes	—
141	#121×C₆₇	C₂³	1	2	yes	—
142	#121×C₆₇	C₂³	1	2	yes	—
143	#121×C₆₇	C₂³	1	2	yes	—
144	#120×C₆₇	—	2	2	no	—
145	#120×C₆₇	—	2	2	no	—
146	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
147	C₄×D₄×C₆₇	—	2	2	no	—
148	C₄×D₄×C₆₇	—	2	2	no	—
149	C₄×D₄×C₆₇	—	2	2	no	—
150	C₄×D₄×C₆₇	—	2	4	no	—
151	C₄×D₄×C₆₇	—	2	4	no	—
152	C₄×D₄×C₆₇	—	2	2	no	—
153	C₄×D₄×C₆₇	—	2	2	no	—
154	C₄×D₄×C₆₇	—	2	2	no	—
155	C₄×D₄×C₆₇	D₄	1	2	yes	—
156	C₄×D₄×C₆₇	D₄	1	2	yes	—
157	C₄×D₄×C₆₇	C₂³	1	4	yes	—
158	C₄×D₄×C₆₇	C₂³	1	2	yes	—
159	C₄×D₄×C₆₇	C₂³	1	2	yes	—
160	C₄×D₄×C₆₇	C₂³	1	2	yes	—
161	#117×C₆₇	—	2	1	no	—
162	#117×C₆₇	—	2	1	no	—
163	#117×C₆₇	—	2	2	no	—
164	#117×C₆₇	—	2	2	no	—
165	#117×C₆₇	C₂³	1	2	yes	—
166	#117×C₆₇	C₂³	1	2	yes	—
167	#117×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
169	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
170	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
171	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
172	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
173	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
181	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
187	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₆₇	—	2	1	no	—
190	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	#107×C₆₇	C₂³	1	4	yes	—
192	#107×C₆₇	C₂³	1	4	yes	—
193	#107×C₆₇	C₂³	1	4	yes	—
194	#106×C₆₇	C₂³	1	4	yes	—
195	#106×C₆₇	C₂³	1	4	yes	—
196	#106×C₆₇	C₂³	1	4	yes	—
197	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
198	#103×C₆₇	C₂³	1	4	yes	—
199	#103×C₆₇	C₂³	1	4	yes	—
200	#103×C₆₇	C₂³	1	4	yes	—
201	#102×C₆₇	C₂³	1	4	yes	—
202	#102×C₆₇	C₂³	1	4	yes	—
203	#102×C₆₇	C₂³	1	4	yes	—
204	#102×C₆₇	C₂³	1	4	yes	—
205	#102×C₆₇	C₂³	1	4	yes	—
206	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
208	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
209	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
210	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
211	C₄×C₈×C₆₇	C₂³	1	4	yes	—
212	C₂⁴×C₆₇	—	2	1	no	—
213	C₂⁴×C₆₇	—	2	1	no	—
214	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
215	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
216	#41×C₆₇	—	4	4	no	—
217	C₂×Q₈×C₆₇	—	2	1	no	—
218	C₂×Q₈×C₆₇	—	4	2	no	—
219	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
220	C₂×D₄×C₆₇	—	2	2	no	—
221	C₂×D₄×C₆₇	—	2	4	no	—
222	C₂×D₄×C₆₇	—	2	2	no	—
223	C₂×D₄×C₆₇	—	2	2	no	—
224	C₂×D₄×C₆₇	—	2	2	no	—
225	C₂×D₄×C₆₇	—	2	2	no	—
226	C₂×D₄×C₆₇	—	2	2	no	—
227	C₂×D₄×C₆₇	—	2	1	no	—
228	C₂×D₄×C₆₇	—	2	1	no	—
229	C₂×D₄×C₆₇	—	4	2	no	—
230	C₂×D₄×C₆₇	—	4	2	no	—
231	C₂×D₄×C₆₇	—	4	2	no	—
232	C₂×D₄×C₆₇	—	4	4	no	—
233	C₂×D₄×C₆₇	—	4	4	no	—
234	C₂×D₄×C₆₇	—	8	2	no	—
235	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
238	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₆₇	—	2	1	no	—
240	C₂²×C₄×C₆₇	—	2	1	no	—
241	C₂²×C₄×C₆₇	—	2	1	no	—
242	C₂²×C₄×C₆₇	—	2	1	no	—
243	C₂²×C₄×C₆₇	—	2	1	no	—
244	C₂²×C₄×C₆₇	—	2	1	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	—	2	2	no	—
247	C₂²×C₄×C₆₇	—	2	2	no	—
248	C₂²×C₄×C₆₇	—	2	4	no	—
249	C₂²×C₄×C₆₇	—	4	2	no	—
250	C₂²×C₄×C₆₇	—	4	2	no	—
251	C₂²×C₄×C₆₇	—	8	2	no	—
252	C₂²×C₄×C₆₇	—	8	2	no	—
253	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	SD₁₆×C₆₇	—	4	4	no	—
265	D₈×C₆₇	—	4	4	no	—
266	M₁₆×C₆₇	—	4	2	no	—
267	M₁₆×C₆₇	—	4	4	no	—
268	M₁₆×C₆₇	—	4	2	no	—
269	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
270	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
271	C₄⋊C₄×C₆₇	—	2	1	no	—
272	C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₄⋊C₄×C₆₇	—	2	4	no	—
274	C₄⋊C₄×C₆₇	—	2	2	no	—
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	—	2	2	no	—
278	C₄⋊C₄×C₆₇	—	2	1	no	—
279	C₄⋊C₄×C₆₇	—	2	1	no	—
280	C₄⋊C₄×C₆₇	—	2	1	no	—
281	C₄⋊C₄×C₆₇	—	2	2	no	—
282	C₄⋊C₄×C₆₇	—	2	2	no	—
283	C₄⋊C₄×C₆₇	—	2	2	no	—
284	C₄⋊C₄×C₆₇	—	2	2	no	—
285	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
286	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
287	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
291	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
292	C₂²⋊C₄×C₆₇	—	2	2	no	—
293	C₂²⋊C₄×C₆₇	—	2	2	no	—
294	C₂²⋊C₄×C₆₇	—	2	2	no	—
295	C₂²⋊C₄×C₆₇	—	2	2	no	—
296	C₂²⋊C₄×C₆₇	—	2	2	no	—
297	C₂²⋊C₄×C₆₇	—	2	2	no	—
298	C₂²⋊C₄×C₆₇	—	2	2	no	—
299	C₂²⋊C₄×C₆₇	—	2	2	no	—
300	C₂²⋊C₄×C₆₇	—	2	2	no	—
301	C₂²⋊C₄×C₆₇	—	2	2	no	—
302	C₂²⋊C₄×C₆₇	—	2	2	no	—
303	C₂²⋊C₄×C₆₇	—	2	4	no	—
304	C₂²⋊C₄×C₆₇	—	2	2	no	—
305	C₂²⋊C₄×C₆₇	—	2	4	no	—
306	C₂²⋊C₄×C₆₇	—	2	2	no	—
307	C₂²⋊C₄×C₆₇	—	2	2	no	—
308	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
309	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
310	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
311	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
312	C₄²×C₆₇	—	2	2	no	—
313	C₄²×C₆₇	—	2	2	no	—
314	C₄²×C₆₇	—	2	2	no	—
315	C₄²×C₆₇	—	2	2	no	—
316	C₄²×C₆₇	C₂×D₄	1	2	yes	—
317	C₄²×C₆₇	C₂⁴	1	2	yes	—
318	C₂³×C₆₇	—	2	2	no	—
319	C₂³×C₆₇	—	2	2	no	—
320	C₂³×C₆₇	—	2	2	no	—
321	C₂³×C₆₇	—	2	2	no	—
322	C₂³×C₆₇	—	4	1	no	—
323	C₂³×C₆₇	—	4	1	no	—
324	C₂³×C₆₇	—	4	1	no	—
325	C₂³×C₆₇	—	4	1	no	—
326	C₂³×C₆₇	—	4	2	no	—
327	C₂³×C₆₇	—	4	2	no	—
328	C₂³×C₆₇	—	4	2	no	—
329	C₂³×C₆₇	—	4	2	no	—
330	C₂³×C₆₇	—	8	1	no	—
331	C₂³×C₆₇	—	8	1	no	—
332	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
333	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
334	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
335	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₆₇	—	2	4	no	—
337	Q₈×C₆₇	—	8	1	no	—
338	D₄×C₆₇	—	2	4	no	—
339	D₄×C₆₇	—	2	4	no	—
340	D₄×C₆₇	—	4	2	no	—
341	D₄×C₆₇	—	4	2	no	—
342	D₄×C₆₇	—	4	2	no	—
343	D₄×C₆₇	—	4	4	no	—
344	D₄×C₆₇	—	4	8	no	—
345	D₄×C₆₇	—	4	4	no	—
346	D₄×C₆₇	—	8	1	no	—
347	D₄×C₆₇	—	8	2	no	—
348	D₄×C₆₇	—	8	2	no	—
349	D₄×C₆₇	—	8	2	no	—
350	D₄×C₆₇	—	8	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	4	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	4	2	no	—
363	C₂×C₄×C₆₇	—	4	1	no	—
364	C₂×C₄×C₆₇	—	4	1	no	—
365	C₂×C₄×C₆₇	—	4	1	no	—
366	C₂×C₄×C₆₇	—	4	1	no	—
367	C₂×C₄×C₆₇	—	4	1	no	—
368	C₂×C₄×C₆₇	—	4	2	no	—
369	C₂×C₄×C₆₇	—	4	2	no	—
370	C₂×C₄×C₆₇	—	4	2	no	—
371	C₂×C₄×C₆₇	—	4	2	no	—
372	C₂×C₄×C₆₇	—	8	2	no	—
373	C₂×C₄×C₆₇	—	8	4	no	—
374	C₂×C₄×C₆₇	—	8	2	no	—
375	C₂×C₄×C₆₇	—	8	1	no	—
376	C₂×C₄×C₆₇	—	8	4	no	—
377	C₂×C₄×C₆₇	—	8	1	no	—
378	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
385	C₈×C₆₇	—	2	4	no	—
386	C₈×C₆₇	—	2	4	no	—
387	C₂²×C₆₇	—	2	1	no	—
388	C₂²×C₆₇	—	2	1	no	—
389	C₂²×C₆₇	—	2	2	no	—
390	C₂²×C₆₇	—	2	1	no	—
391	C₂²×C₆₇	—	2	1	no	—
392	C₂²×C₆₇	—	2	1	no	—
393	C₂²×C₆₇	—	2	2	no	—
394	C₂²×C₆₇	—	2	1	no	—
395	C₂²×C₆₇	—	2	1	no	—
396	C₂²×C₆₇	—	2	2	no	—
397	C₂²×C₆₇	—	2	1	no	—
398	C₂²×C₆₇	—	4	4	no	—
399	C₂²×C₆₇	—	4	2	no	—
400	C₂²×C₆₇	—	4	2	no	—
401	C₂²×C₆₇	—	4	2	no	—
402	C₂²×C₆₇	—	4	2	no	—
403	C₂²×C₆₇	—	4	2	no	—
404	C₂²×C₆₇	—	4	2	no	—
405	C₂²×C₆₇	—	8	2	no	—
406	C₂²×C₆₇	—	8	4	no	—
407	C₂²×C₆₇	—	16	2	no	—
408	C₂²×C₆₇	#575	1	2	yes	—
409	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
410	C₄×C₆₇	—	2	2	no	—
411	C₄×C₆₇	—	2	1	no	—
412	C₄×C₆₇	—	2	2	no	—
413	C₄×C₆₇	—	2	1	no	—
414	C₄×C₆₇	—	2	1	no	—
415	C₄×C₆₇	—	2	2	no	—
416	C₄×C₆₇	—	4	2	no	—
417	C₄×C₆₇	—	4	2	no	—
418	C₄×C₆₇	—	4	2	no	—
419	C₄×C₆₇	—	4	2	no	—
420	C₄×C₆₇	—	4	2	no	—
421	C₄×C₆₇	—	4	2	no	—
422	C₄×C₆₇	#585	1	2	yes	—
423	#61718	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
424	C₂×C₆₇	—	2	2	no	—
425	C₂×C₆₇	—	4	2	no	—
426	C₂×C₆₇	—	4	1	no	—
427	C₂×C₆₇	—	4	1	no	—
428	C₂×C₆₇	—	8	2	no	—
429	C₂×C₆₇	—	8	2	no	—
430	C₂×C₆₇	#3485	1	1	yes	characteristic
431	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
432	C₂×C₆₇	#3585	1	1	yes	characteristic
433	#3505	C₂×C₆₇	1	1	yes	characteristic, complemented
434	C₂×#553	C₂×C₆₇	1	1	yes	characteristic, complemented
435	#3355	C₂×C₆₇	1	4	yes	complemented
436	#3351	C₂×C₆₇	1	4	yes	complemented
437	#3326	C₂×C₆₇	1	4	yes	complemented
438	#3322	C₂×C₆₇	1	4	yes	complemented
439	#3232	C₂×C₆₇	1	2	yes	complemented
440	#3194	C₂×C₆₇	1	2	yes	complemented
441	#3193	C₂×C₆₇	1	1	yes	characteristic, complemented
442	#3192	C₂×C₆₇	1	1	yes	characteristic, complemented
443	#3105	C₂×C₆₇	1	2	yes	complemented
444	#3095	C₂×C₆₇	1	1	yes	characteristic, complemented
445	#3094	C₂×C₆₇	1	1	yes	characteristic, complemented
446	#3092	C₂×C₆₇	1	2	yes	complemented
447	#2975	C₂×C₆₇	1	1	yes	characteristic, complemented
448	C₆₇	#61718	1	1	yes	characteristic, direct product factor, Sylow
449	#553	—	2	2	no	—
450	#553	—	2	2	no	—
451	#553	—	2	2	no	—
452	#553	C₂²×C₆₇	1	4	yes	—
453	#553	C₂²×C₆₇	1	2	yes	complemented
454	#553	C₂²×C₆₇	1	4	yes	complemented
455	#552	C₂²×C₆₇	1	2	yes	complemented
456	#551	—	2	2	no	—
457	#548	C₂²×C₆₇	1	2	yes	complemented
458	#546	C₂²×C₆₇	1	2	yes	complemented
459	#539	—	2	1	no	—
460	#538	—	2	1	no	—
461	#534	—	2	1	no	—
462	#529	C₂²×C₆₇	1	2	yes	—
463	C₂×#126	—	2	1	no	—
464	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
465	#525	C₂²×C₆₇	1	2	yes	—
466	C₂×#123	—	2	1	no	—
467	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
468	C₂×#121	—	2	1	no	—
469	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
470	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
471	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
472	#518	—	2	1	no	—
473	C₂×C₄×D₄	—	2	1	no	—
474	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
475	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
476	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
477	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
478	#499	C₂²×C₆₇	1	4	yes	complemented
479	#488	C₂²×C₆₇	1	4	yes	complemented
480	#485	C₂²×C₆₇	1	4	yes	complemented
481	#484	C₂²×C₆₇	1	2	yes	complemented
482	#484	C₂²×C₆₇	1	2	yes	complemented
483	#483	C₂²×C₆₇	1	4	yes	complemented
484	#483	C₂²×C₆₇	1	2	yes	complemented
485	#482	C₂²×C₆₇	1	4	yes	complemented
486	#482	C₂²×C₆₇	1	4	yes	complemented
487	#481	C₂²×C₆₇	1	2	yes	—
488	#481	C₂²×C₆₇	1	2	yes	—
489	#481	C₂²×C₆₇	1	2	yes	complemented
490	#480	C₂²×C₆₇	1	2	yes	—
491	#480	C₂²×C₆₇	1	4	yes	complemented
492	#480	C₂²×C₆₇	1	2	yes	complemented
493	#479	C₂²×C₆₇	1	4	yes	complemented
494	#478	C₂²×C₆₇	1	4	yes	complemented
495	#478	C₂²×C₆₇	1	4	yes	complemented
496	#469	C₂²×C₆₇	1	4	yes	complemented
497	#469	C₂²×C₆₇	1	4	yes	complemented
498	#468	C₂²×C₆₇	1	4	yes	complemented
499	#468	C₂²×C₆₇	1	4	yes	complemented
500	#463	C₂²×C₆₇	1	4	yes	complemented
501	#450	C₂²×C₆₇	1	2	yes	complemented
502	#449	C₂²×C₆₇	1	4	yes	complemented
503	#448	C₂²×C₆₇	1	2	yes	complemented
504	#447	C₂²×C₆₇	1	2	yes	—
505	#447	C₂²×C₆₇	1	2	yes	complemented
506	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
507	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
508	#436	C₂²×C₆₇	1	4	yes	complemented
509	#436	C₂²×C₆₇	1	4	yes	complemented
510	#431	C₂²×C₆₇	1	2	yes	complemented
511	#428	C₂²×C₆₇	1	4	yes	complemented
512	#428	C₂²×C₆₇	1	2	yes	complemented
513	#428	C₂²×C₆₇	1	2	yes	complemented
514	#419	C₂²×C₆₇	1	2	yes	complemented
515	#418	C₂²×C₆₇	1	2	yes	complemented
516	#417	C₂²×C₆₇	1	4	yes	complemented
517	#407	C₂²×C₆₇	1	1	yes	characteristic
518	#407	C₂²×C₆₇	1	1	yes	characteristic
519	#407	C₂²×C₆₇	1	2	yes	complemented
520	C₂×#41	C₂³×C₆₇	1	2	yes	—
521	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
526	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
528	C₂³×C₄	—	2	1	no	—
529	C₂³×C₄	—	2	1	no	—
530	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
532	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
533	C₂×D₈	C₂³×C₆₇	1	4	yes	—
534	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
535	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
536	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
537	#126	—	2	4	no	—
538	#126	—	2	4	no	—
539	#126	—	2	2	no	—
540	#126	—	2	2	no	—
541	#126	—	2	2	no	—
542	#125	—	2	2	no	—
543	#125	—	2	2	no	—
544	#125	C₂³×C₆₇	1	4	yes	—
545	#125	C₂³×C₆₇	1	2	yes	—
546	#124	—	2	2	no	—
547	#124	C₂³×C₆₇	1	2	yes	—
548	#123	—	2	2	no	—
549	#123	—	2	2	no	—
550	#123	—	2	2	no	—
551	#123	—	2	2	no	—
552	#123	—	2	4	no	—
553	#123	—	2	4	no	—
554	#123	—	2	2	no	—
555	C₂²⋊Q₈	—	2	1	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
559	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
560	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
561	#121	—	2	4	no	—
562	#121	—	2	4	no	—
563	#121	—	2	2	no	—
564	#121	—	2	2	no	—
565	#121	—	2	1	no	—
566	#121	—	2	1	no	—
567	#121	—	2	1	no	—
568	#121	—	2	1	no	—
569	#121	—	2	2	no	—
570	#121	—	2	2	no	—
571	#121	C₂³×C₆₇	1	2	yes	—
572	#121	C₂³×C₆₇	1	2	yes	—
573	#121	C₂³×C₆₇	1	2	yes	—
574	#121	C₂³×C₆₇	1	2	yes	—
575	#121	C₂³×C₆₇	1	4	yes	—
576	#121	C₂³×C₆₇	1	2	yes	—
577	#120	—	2	2	no	—
578	#120	—	2	2	no	—
579	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	4	no	—
584	C₄×D₄	—	2	4	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	D₄×C₆₇	1	2	yes	—
589	C₄×D₄	D₄×C₆₇	1	2	yes	—
590	C₄×D₄	C₂³×C₆₇	1	4	yes	—
591	C₄×D₄	C₂³×C₆₇	1	2	yes	—
592	C₄×D₄	C₂³×C₆₇	1	2	yes	—
593	C₄×D₄	C₂³×C₆₇	1	2	yes	—
594	#117	—	2	1	no	—
595	#117	—	2	1	no	—
596	#117	—	2	2	no	—
597	#117	—	2	2	no	—
598	#117	C₂³×C₆₇	1	2	yes	—
599	#117	C₂³×C₆₇	1	2	yes	—
600	#117	C₂³×C₆₇	1	2	yes	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	2	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
610	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	2	no	—
620	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
622	C₂×C₄²	—	2	1	no	—
623	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
624	#107	C₂³×C₆₇	1	4	yes	—
625	#107	C₂³×C₆₇	1	4	yes	—
626	#107	C₂³×C₆₇	1	4	yes	—
627	#106	C₂³×C₆₇	1	4	yes	—
628	#106	C₂³×C₆₇	1	4	yes	—
629	#106	C₂³×C₆₇	1	4	yes	—
630	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
631	#103	C₂³×C₆₇	1	4	yes	—
632	#103	C₂³×C₆₇	1	4	yes	—
633	#103	C₂³×C₆₇	1	4	yes	—
634	#102	C₂³×C₆₇	1	4	yes	—
635	#102	C₂³×C₆₇	1	4	yes	—
636	#102	C₂³×C₆₇	1	4	yes	—
637	#102	C₂³×C₆₇	1	4	yes	—
638	#102	C₂³×C₆₇	1	4	yes	—
639	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
640	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
641	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
642	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
643	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
644	C₄×C₈	C₂³×C₆₇	1	4	yes	—
645	C₂⁴	—	2	1	no	—
646	C₂⁴	—	2	1	no	—
647	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
648	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
649	#41	—	4	4	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	4	2	no	—
652	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	4	2	no	—
663	C₂×D₄	—	4	2	no	—
664	C₂×D₄	—	4	2	no	—
665	C₂×D₄	—	4	4	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	—	8	2	no	—
668	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
669	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
670	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
671	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	8	2	no	—
685	C₂²×C₄	—	8	2	no	—
686	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
697	SD₁₆	—	4	4	no	—
698	D₈	—	4	4	no	—
699	M₁₆	—	4	2	no	—
700	M₁₆	—	4	4	no	—
701	M₁₆	—	4	2	no	—
702	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
703	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
719	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
720	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
723	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
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	—	2	2	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
742	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
743	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
744	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	C₂×D₄×C₆₇	1	2	yes	—
750	C₄²	C₂⁴×C₆₇	1	2	yes	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	4	1	no	—
756	C₂³	—	4	1	no	—
757	C₂³	—	4	1	no	—
758	C₂³	—	4	1	no	—
759	C₂³	—	4	2	no	—
760	C₂³	—	4	2	no	—
761	C₂³	—	4	2	no	—
762	C₂³	—	4	2	no	—
763	C₂³	—	8	1	no	—
764	C₂³	—	8	1	no	—
765	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
766	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
767	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
768	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
769	Q₈	—	2	4	no	—
770	Q₈	—	8	1	no	—
771	D₄	—	2	4	no	—
772	D₄	—	2	4	no	—
773	D₄	—	4	2	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	4	no	—
777	D₄	—	4	8	no	—
778	D₄	—	4	4	no	—
779	D₄	—	8	1	no	—
780	D₄	—	8	2	no	—
781	D₄	—	8	2	no	—
782	D₄	—	8	2	no	—
783	D₄	—	8	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	4	2	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	8	4	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	4	no	—
809	C₂×C₄	—	8	1	no	—
810	C₂×C₄	—	8	1	no	—
811	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
815	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
817	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
818	C₈	—	2	4	no	—
819	C₈	—	2	4	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	8	2	no	—
839	C₂²	—	8	4	no	—
840	C₂²	—	16	2	no	—
841	C₂²	#575×C₆₇	1	2	yes	—
842	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	1	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	1	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	#585×C₆₇	1	2	yes	—
856	C₂	—	2	2	no	—
857	C₂	—	4	2	no	—
858	C₂	—	4	1	no	—
859	C₂	—	4	1	no	—
860	C₂	—	8	2	no	—
861	C₂	—	8	2	no	—
862	C₂	C₆₇×#3485	1	1	yes	characteristic
863	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
864	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3505	C₂	semidirect
2. C₂×#553×C₆₇	C₂	semidirect
3. C₆₇×#3355	C₂	semidirect
4. C₆₇×#3351	C₂	semidirect
5. C₆₇×#3326	C₂	semidirect
6. C₆₇×#3322	C₂	semidirect
7. C₆₇×#3232	C₂	semidirect
8. C₆₇×#3194	C₂	semidirect
9. C₆₇×#3193	C₂	semidirect
10. C₆₇×#3192	C₂	semidirect
11. C₆₇×#3105	C₂	semidirect
12. C₆₇×#3095	C₂	semidirect
13. C₆₇×#3094	C₂	semidirect
14. C₆₇×#3092	C₂	semidirect
15. C₆₇×#2975	C₂	semidirect
20. #553×C₆₇	C₂²	semidirect
21. #553×C₆₇	C₂²	semidirect
22. #552×C₆₇	C₂²	semidirect
24. #548×C₆₇	C₂²	semidirect
25. #546×C₆₇	C₂²	semidirect
31. C₂×#125×C₆₇	C₂²	semidirect
38. C₂×#121×C₆₇	C₂²	semidirect
42. C₂×C₄×D₄×C₆₇	C₂²	semidirect
44. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
45. #499×C₆₇	C₂²	semidirect
46. #488×C₆₇	C₂²	semidirect
47. #485×C₆₇	C₂²	semidirect
48. #484×C₆₇	C₂²	semidirect
49. #484×C₆₇	C₂²	semidirect
50. #483×C₆₇	C₂²	semidirect
51. #483×C₆₇	C₂²	semidirect
52. #482×C₆₇	C₂²	semidirect
53. #482×C₆₇	C₂²	semidirect
56. #481×C₆₇	C₂²	semidirect
58. #480×C₆₇	C₂²	semidirect
59. #480×C₆₇	C₂²	semidirect
60. #479×C₆₇	C₂²	semidirect
61. #478×C₆₇	C₂²	semidirect
62. #478×C₆₇	C₂²	semidirect
63. #469×C₆₇	C₂²	semidirect
64. #469×C₆₇	C₂²	semidirect
65. #468×C₆₇	C₂²	semidirect
66. #468×C₆₇	C₂²	semidirect
67. #463×C₆₇	C₂²	semidirect
68. #450×C₆₇	C₂²	semidirect
69. #449×C₆₇	C₂²	semidirect
70. #448×C₆₇	C₂²	semidirect
72. #447×C₆₇	C₂²	semidirect
73. C₄×SD₁₆×C₆₇	C₂²	semidirect
74. C₄×D₈×C₆₇	C₂²	semidirect
75. #436×C₆₇	C₂²	semidirect
76. #436×C₆₇	C₂²	semidirect
77. #431×C₆₇	C₂²	semidirect
78. #428×C₆₇	C₂²	semidirect
79. #428×C₆₇	C₂²	semidirect
80. #428×C₆₇	C₂²	semidirect
81. #419×C₆₇	C₂²	semidirect
82. #418×C₆₇	C₂²	semidirect
83. #417×C₆₇	C₂²	semidirect
86. #407×C₆₇	C₂²	semidirect
423. #61718	C₆₇	direct (N × H)
433. #3505	C₂×C₆₇	semidirect
434. C₂×#553	C₂×C₆₇	semidirect
435. #3355	C₂×C₆₇	semidirect
436. #3351	C₂×C₆₇	semidirect
437. #3326	C₂×C₆₇	semidirect
438. #3322	C₂×C₆₇	semidirect
439. #3232	C₂×C₆₇	semidirect
440. #3194	C₂×C₆₇	semidirect
441. #3193	C₂×C₆₇	semidirect
442. #3192	C₂×C₆₇	semidirect
443. #3105	C₂×C₆₇	semidirect
444. #3095	C₂×C₆₇	semidirect
445. #3094	C₂×C₆₇	semidirect
446. #3092	C₂×C₆₇	semidirect
447. #2975	C₂×C₆₇	semidirect
448. C₆₇	#61718	direct (N × H)
453. #553	C₂²×C₆₇	semidirect
454. #553	C₂²×C₆₇	semidirect
455. #552	C₂²×C₆₇	semidirect
457. #548	C₂²×C₆₇	semidirect
458. #546	C₂²×C₆₇	semidirect
464. C₂×#125	C₂²×C₆₇	semidirect
471. C₂×#121	C₂²×C₆₇	semidirect
475. C₂×C₄×D₄	C₂²×C₆₇	semidirect
477. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
478. #499	C₂²×C₆₇	semidirect
479. #488	C₂²×C₆₇	semidirect
480. #485	C₂²×C₆₇	semidirect
481. #484	C₂²×C₆₇	semidirect
482. #484	C₂²×C₆₇	semidirect
483. #483	C₂²×C₆₇	semidirect
484. #483	C₂²×C₆₇	semidirect
485. #482	C₂²×C₆₇	semidirect
486. #482	C₂²×C₆₇	semidirect
489. #481	C₂²×C₆₇	semidirect
491. #480	C₂²×C₆₇	semidirect
492. #480	C₂²×C₆₇	semidirect
493. #479	C₂²×C₆₇	semidirect
494. #478	C₂²×C₆₇	semidirect
495. #478	C₂²×C₆₇	semidirect
496. #469	C₂²×C₆₇	semidirect
497. #469	C₂²×C₆₇	semidirect
498. #468	C₂²×C₆₇	semidirect
499. #468	C₂²×C₆₇	semidirect
500. #463	C₂²×C₆₇	semidirect
501. #450	C₂²×C₆₇	semidirect
502. #449	C₂²×C₆₇	semidirect
503. #448	C₂²×C₆₇	semidirect
505. #447	C₂²×C₆₇	semidirect
506. C₄×SD₁₆	C₂²×C₆₇	semidirect
507. C₄×D₈	C₂²×C₆₇	semidirect
508. #436	C₂²×C₆₇	semidirect
509. #436	C₂²×C₆₇	semidirect
510. #431	C₂²×C₆₇	semidirect
511. #428	C₂²×C₆₇	semidirect
512. #428	C₂²×C₆₇	semidirect
513. #428	C₂²×C₆₇	semidirect
514. #419	C₂²×C₆₇	semidirect
515. #418	C₂²×C₆₇	semidirect
516. #417	C₂²×C₆₇	semidirect
519. #407	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3505	2
C₂×#553×C₆₇	2
C₆₇×#3355	2
C₆₇×#3351	2
C₆₇×#3326	2
C₆₇×#3322	2
C₆₇×#3232	2
C₆₇×#3194	2
C₆₇×#3193	2
C₆₇×#3192	2
C₆₇×#3105	2
C₆₇×#3095	2
C₆₇×#3094	2
C₆₇×#3092	2
C₆₇×#2975	2
#61718	67

Subgroups — C67×#61718 #30740969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61718 #30740969