Subgroups — C₆₇×#61716 #30740967

Order 17152.

1766 conjugacy classes of subgroups.

The subgroup lattice has 840 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
2	C₂×#552×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3352	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3351	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3327	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3323	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3232	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3196	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3195	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3193	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3108	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	C₂²	1	2	yes	—
18	#552×C₆₇	—	2	2	no	—
19	#552×C₆₇	—	2	2	no	—
20	#552×C₆₇	C₂²	1	4	yes	—
21	#552×C₆₇	C₂²	1	2	yes	—
22	#552×C₆₇	C₂²	1	4	yes	complemented
23	#551×C₆₇	—	2	2	no	—
24	#548×C₆₇	C₂²	1	2	yes	—
25	#546×C₆₇	C₂²	1	2	yes	—
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	—	2	1	no	—
32	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#525×C₆₇	C₂²	1	2	yes	—
34	C₂×#123×C₆₇	—	2	1	no	—
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
39	#518×C₆₇	—	2	1	no	—
40	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#117×C₆₇	—	2	1	no	—
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	#485×C₆₇	C₂²	1	4	yes	complemented
49	#484×C₆₇	C₂²	1	4	yes	complemented
50	#484×C₆₇	C₂²	1	2	yes	complemented
51	#484×C₆₇	C₂²	1	2	yes	complemented
52	#483×C₆₇	C₂²	1	2	yes	complemented
53	#483×C₆₇	C₂²	1	2	yes	complemented
54	#483×C₆₇	C₂²	1	2	yes	complemented
55	#482×C₆₇	C₂²	1	4	yes	complemented
56	#481×C₆₇	C₂²	1	2	yes	—
57	#481×C₆₇	C₂²	1	4	yes	complemented
58	#480×C₆₇	C₂²	1	2	yes	—
59	#480×C₆₇	C₂²	1	2	yes	—
60	#479×C₆₇	C₂²	1	4	yes	complemented
61	#479×C₆₇	C₂²	1	4	yes	complemented
62	#478×C₆₇	C₂²	1	4	yes	complemented
63	#470×C₆₇	C₂²	1	4	yes	complemented
64	#470×C₆₇	C₂²	1	4	yes	complemented
65	#468×C₆₇	C₂²	1	4	yes	complemented
66	#468×C₆₇	C₂²	1	4	yes	complemented
67	#464×C₆₇	C₂²	1	4	yes	complemented
68	#452×C₆₇	C₂²	1	4	yes	complemented
69	#451×C₆₇	C₂²	1	2	yes	complemented
70	#451×C₆₇	C₂²	1	2	yes	complemented
71	#450×C₆₇	C₂²	1	2	yes	complemented
72	#448×C₆₇	C₂²	1	2	yes	—
73	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	complemented
74	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
75	#436×C₆₇	C₂²	1	4	yes	—
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×Q₈×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₆₇	—	2	1	no	—
91	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
92	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₆₇	—	2	1	no	—
94	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
96	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
98	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
99	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
101	#126×C₆₇	—	2	2	no	—
102	#126×C₆₇	—	2	4	no	—
103	#126×C₆₇	—	2	4	no	—
104	#126×C₆₇	—	2	2	no	—
105	#126×C₆₇	—	2	2	no	—
106	#125×C₆₇	—	2	4	no	—
107	#125×C₆₇	—	2	4	no	—
108	#125×C₆₇	—	2	2	no	—
109	#125×C₆₇	—	2	2	no	—
110	#125×C₆₇	C₂³	1	4	yes	—
111	#125×C₆₇	C₂³	1	2	yes	—
112	#124×C₆₇	—	2	2	no	—
113	#124×C₆₇	C₂³	1	2	yes	—
114	#123×C₆₇	—	2	4	no	—
115	#123×C₆₇	—	2	4	no	—
116	#123×C₆₇	—	2	2	no	—
117	#123×C₆₇	—	2	2	no	—
118	#123×C₆₇	—	2	2	no	—
119	#123×C₆₇	—	2	2	no	—
120	#123×C₆₇	—	2	2	no	—
121	C₂²⋊Q₈×C₆₇	—	2	1	no	—
122	C₂²⋊Q₈×C₆₇	—	2	1	no	—
123	C₂²⋊Q₈×C₆₇	—	2	1	no	—
124	C₂²⋊Q₈×C₆₇	—	2	1	no	—
125	C₂²⋊Q₈×C₆₇	—	2	2	no	—
126	C₂²⋊Q₈×C₆₇	—	2	2	no	—
127	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
128	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
129	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
130	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
131	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
132	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
133	#121×C₆₇	—	2	2	no	—
134	#121×C₆₇	—	2	2	no	—
135	#121×C₆₇	—	2	1	no	—
136	#121×C₆₇	—	2	1	no	—
137	#121×C₆₇	—	2	2	no	—
138	#121×C₆₇	C₂³	1	2	yes	—
139	#121×C₆₇	C₂³	1	2	yes	—
140	#121×C₆₇	C₂³	1	2	yes	—
141	#120×C₆₇	—	2	2	no	—
142	#120×C₆₇	—	2	2	no	—
143	C₄×Q₈×C₆₇	—	2	2	no	—
144	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
145	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
146	C₄×D₄×C₆₇	—	2	2	no	—
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	2	no	—
151	C₄×D₄×C₆₇	D₄	1	2	yes	—
152	C₄×D₄×C₆₇	D₄	1	2	yes	—
153	C₄×D₄×C₆₇	C₂³	1	2	yes	—
154	C₄×D₄×C₆₇	C₂³	1	2	yes	—
155	C₄×D₄×C₆₇	C₂³	1	2	yes	—
156	#117×C₆₇	—	2	1	no	—
157	#117×C₆₇	—	2	1	no	—
158	#117×C₆₇	—	2	4	no	—
159	#117×C₆₇	—	2	4	no	—
160	#117×C₆₇	—	2	2	no	—
161	#117×C₆₇	—	2	2	no	—
162	#117×C₆₇	C₂³	1	2	yes	—
163	#117×C₆₇	C₂³	1	2	yes	—
164	#117×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
166	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
167	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
168	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
169	C₂×C₄⋊C₄×C₆₇	—	2	1	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	1	yes	characteristic
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
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	2	no	—
186	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₆₇	—	2	1	no	—
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	#103×C₆₇	C₂³	1	4	yes	—
202	#103×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	2	yes	—
208	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
209	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
210	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
211	C₄×C₈×C₆₇	C₂³	1	4	yes	—
212	C₂⁴×C₆₇	—	2	1	no	—
213	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
214	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
215	#41×C₆₇	—	4	4	no	—
216	C₂×Q₈×C₆₇	—	2	1	no	—
217	C₂×Q₈×C₆₇	—	2	1	no	—
218	C₂×Q₈×C₆₇	—	4	2	no	—
219	C₂×Q₈×C₆₇	—	4	2	no	—
220	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
221	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
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	1	no	—
227	C₂×D₄×C₆₇	—	4	2	no	—
228	C₂×D₄×C₆₇	—	4	2	no	—
229	C₂×D₄×C₆₇	—	4	4	no	—
230	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
231	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
232	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₆₇	—	2	1	no	—
234	C₂²×C₄×C₆₇	—	2	1	no	—
235	C₂²×C₄×C₆₇	—	2	1	no	—
236	C₂²×C₄×C₆₇	—	2	1	no	—
237	C₂²×C₄×C₆₇	—	2	1	no	—
238	C₂²×C₄×C₆₇	—	2	4	no	—
239	C₂²×C₄×C₆₇	—	2	1	no	—
240	C₂²×C₄×C₆₇	—	2	1	no	—
241	C₂²×C₄×C₆₇	—	2	2	no	—
242	C₂²×C₄×C₆₇	—	2	2	no	—
243	C₂²×C₄×C₆₇	—	4	2	no	—
244	C₂²×C₄×C₆₇	—	4	2	no	—
245	C₂²×C₄×C₆₇	—	4	4	no	—
246	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	Q₁₆×C₆₇	—	4	4	no	—
258	SD₁₆×C₆₇	—	4	4	no	—
259	M₁₆×C₆₇	—	4	2	no	—
260	M₁₆×C₆₇	—	4	4	no	—
261	M₁₆×C₆₇	—	4	2	no	—
262	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
263	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
264	C₄⋊C₄×C₆₇	—	2	1	no	—
265	C₄⋊C₄×C₆₇	—	2	1	no	—
266	C₄⋊C₄×C₆₇	—	2	4	no	—
267	C₄⋊C₄×C₆₇	—	2	2	no	—
268	C₄⋊C₄×C₆₇	—	2	2	no	—
269	C₄⋊C₄×C₆₇	—	2	4	no	—
270	C₄⋊C₄×C₆₇	—	2	2	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	2	no	—
273	C₄⋊C₄×C₆₇	—	2	4	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	—	2	1	no	—
276	C₄⋊C₄×C₆₇	—	2	1	no	—
277	C₄⋊C₄×C₆₇	—	2	1	no	—
278	C₄⋊C₄×C₆₇	—	2	2	no	—
279	C₄⋊C₄×C₆₇	—	2	2	no	—
280	C₄⋊C₄×C₆₇	—	2	2	no	—
281	C₄⋊C₄×C₆₇	—	2	2	no	—
282	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
283	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
284	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
289	C₂²⋊C₄×C₆₇	—	2	2	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	2	no	—
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	2	no	—
304	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
305	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
306	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
307	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
308	C₄²×C₆₇	—	2	2	no	—
309	C₄²×C₆₇	—	2	2	no	—
310	C₄²×C₆₇	—	2	4	no	—
311	C₄²×C₆₇	—	2	2	no	—
312	C₄²×C₆₇	—	2	2	no	—
313	C₄²×C₆₇	C₂×D₄	1	2	yes	—
314	C₄²×C₆₇	C₂⁴	1	2	yes	—
315	C₂³×C₆₇	—	2	2	no	—
316	C₂³×C₆₇	—	2	2	no	—
317	C₂³×C₆₇	—	2	2	no	—
318	C₂³×C₆₇	—	4	1	no	—
319	C₂³×C₆₇	—	4	1	no	—
320	C₂³×C₆₇	—	4	1	no	—
321	C₂³×C₆₇	—	4	1	no	—
322	C₂³×C₆₇	—	4	2	no	—
323	C₂³×C₆₇	—	8	1	no	—
324	C₂³×C₆₇	—	8	1	no	—
325	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
326	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
327	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
328	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
329	Q₈×C₆₇	—	2	4	no	—
330	Q₈×C₆₇	—	2	4	no	—
331	Q₈×C₆₇	—	4	2	no	—
332	Q₈×C₆₇	—	8	1	no	—
333	D₄×C₆₇	—	2	4	no	—
334	D₄×C₆₇	—	4	2	no	—
335	D₄×C₆₇	—	4	2	no	—
336	D₄×C₆₇	—	4	4	no	—
337	D₄×C₆₇	—	4	4	no	—
338	D₄×C₆₇	—	8	1	no	—
339	D₄×C₆₇	—	8	2	no	—
340	D₄×C₆₇	—	8	2	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	4	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	4	2	no	—
354	C₂×C₄×C₆₇	—	4	1	no	—
355	C₂×C₄×C₆₇	—	4	1	no	—
356	C₂×C₄×C₆₇	—	4	1	no	—
357	C₂×C₄×C₆₇	—	4	1	no	—
358	C₂×C₄×C₆₇	—	4	1	no	—
359	C₂×C₄×C₆₇	—	4	2	no	—
360	C₂×C₄×C₆₇	—	4	8	no	—
361	C₂×C₄×C₆₇	—	4	2	no	—
362	C₂×C₄×C₆₇	—	4	2	no	—
363	C₂×C₄×C₆₇	—	4	2	no	—
364	C₂×C₄×C₆₇	—	4	2	no	—
365	C₂×C₄×C₆₇	—	8	2	no	—
366	C₂×C₄×C₆₇	—	8	2	no	—
367	C₂×C₄×C₆₇	—	8	1	no	—
368	C₂×C₄×C₆₇	—	8	1	no	—
369	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
376	C₈×C₆₇	—	2	4	no	—
377	C₈×C₆₇	—	2	4	no	—
378	C₂²×C₆₇	—	2	1	no	—
379	C₂²×C₆₇	—	2	1	no	—
380	C₂²×C₆₇	—	2	1	no	—
381	C₂²×C₆₇	—	2	2	no	—
382	C₂²×C₆₇	—	2	1	no	—
383	C₂²×C₆₇	—	2	1	no	—
384	C₂²×C₆₇	—	2	2	no	—
385	C₂²×C₆₇	—	2	1	no	—
386	C₂²×C₆₇	—	2	2	no	—
387	C₂²×C₆₇	—	2	1	no	—
388	C₂²×C₆₇	—	2	1	no	—
389	C₂²×C₆₇	—	4	4	no	—
390	C₂²×C₆₇	—	4	2	no	—
391	C₂²×C₆₇	—	4	2	no	—
392	C₂²×C₆₇	—	4	2	no	—
393	C₂²×C₆₇	—	8	2	no	—
394	C₂²×C₆₇	—	16	2	no	—
395	C₂²×C₆₇	#575	1	2	yes	—
396	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
397	C₄×C₆₇	—	2	2	no	—
398	C₄×C₆₇	—	2	1	no	—
399	C₄×C₆₇	—	2	2	no	—
400	C₄×C₆₇	—	2	1	no	—
401	C₄×C₆₇	—	2	1	no	—
402	C₄×C₆₇	—	2	2	no	—
403	C₄×C₆₇	—	4	2	no	—
404	C₄×C₆₇	—	4	2	no	—
405	C₄×C₆₇	—	4	2	no	—
406	C₄×C₆₇	—	4	2	no	—
407	C₄×C₆₇	—	4	2	no	—
408	C₄×C₆₇	—	4	2	no	—
409	C₄×C₆₇	—	4	2	no	—
410	C₄×C₆₇	#585	1	2	yes	—
411	#61716	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₂×C₆₇	—	2	2	no	—
413	C₂×C₆₇	—	4	2	no	—
414	C₂×C₆₇	—	4	1	no	—
415	C₂×C₆₇	—	4	1	no	—
416	C₂×C₆₇	—	8	2	no	—
417	C₂×C₆₇	#3485	1	1	yes	characteristic
418	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
419	C₂×C₆₇	#3586	1	1	yes	characteristic
420	#3505	C₂×C₆₇	1	1	yes	characteristic
421	C₂×#552	C₂×C₆₇	1	1	yes	characteristic, complemented
422	#3352	C₂×C₆₇	1	4	yes	complemented
423	#3351	C₂×C₆₇	1	4	yes	complemented
424	#3327	C₂×C₆₇	1	4	yes	complemented
425	#3323	C₂×C₆₇	1	4	yes	complemented
426	#3232	C₂×C₆₇	1	2	yes	complemented
427	#3196	C₂×C₆₇	1	2	yes	complemented
428	#3195	C₂×C₆₇	1	1	yes	characteristic, complemented
429	#3193	C₂×C₆₇	1	1	yes	characteristic, complemented
430	#3108	C₂×C₆₇	1	2	yes	complemented
431	#3095	C₂×C₆₇	1	1	yes	characteristic, complemented
432	#3094	C₂×C₆₇	1	1	yes	characteristic, complemented
433	#3092	C₂×C₆₇	1	2	yes	complemented
434	#2975	C₂×C₆₇	1	1	yes	characteristic, complemented
435	C₆₇	#61716	1	1	yes	characteristic, direct product factor, Sylow
436	#553	—	2	2	no	—
437	#553	C₂²×C₆₇	1	2	yes	—
438	#552	—	2	2	no	—
439	#552	—	2	2	no	—
440	#552	C₂²×C₆₇	1	2	yes	—
441	#552	C₂²×C₆₇	1	4	yes	—
442	#552	C₂²×C₆₇	1	4	yes	complemented
443	#551	—	2	2	no	—
444	#548	C₂²×C₆₇	1	2	yes	—
445	#546	C₂²×C₆₇	1	2	yes	—
446	#539	—	2	1	no	—
447	#538	—	2	1	no	—
448	#534	—	2	1	no	—
449	#529	C₂²×C₆₇	1	2	yes	—
450	C₂×#126	—	2	1	no	—
451	C₂×#125	—	2	1	no	—
452	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
453	#525	C₂²×C₆₇	1	2	yes	—
454	C₂×#123	—	2	1	no	—
455	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
456	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
457	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
458	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
459	#518	—	2	1	no	—
460	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
461	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
462	C₂×#117	—	2	1	no	—
463	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
464	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
465	#499	C₂²×C₆₇	1	4	yes	complemented
466	#488	C₂²×C₆₇	1	4	yes	complemented
467	#485	C₂²×C₆₇	1	4	yes	complemented
468	#485	C₂²×C₆₇	1	4	yes	complemented
469	#484	C₂²×C₆₇	1	4	yes	complemented
470	#484	C₂²×C₆₇	1	2	yes	complemented
471	#484	C₂²×C₆₇	1	2	yes	complemented
472	#483	C₂²×C₆₇	1	2	yes	complemented
473	#483	C₂²×C₆₇	1	2	yes	complemented
474	#483	C₂²×C₆₇	1	2	yes	complemented
475	#482	C₂²×C₆₇	1	4	yes	complemented
476	#481	C₂²×C₆₇	1	2	yes	—
477	#481	C₂²×C₆₇	1	4	yes	complemented
478	#480	C₂²×C₆₇	1	2	yes	—
479	#480	C₂²×C₆₇	1	2	yes	—
480	#479	C₂²×C₆₇	1	4	yes	complemented
481	#479	C₂²×C₆₇	1	4	yes	complemented
482	#478	C₂²×C₆₇	1	4	yes	complemented
483	#470	C₂²×C₆₇	1	4	yes	complemented
484	#470	C₂²×C₆₇	1	4	yes	complemented
485	#468	C₂²×C₆₇	1	4	yes	complemented
486	#468	C₂²×C₆₇	1	4	yes	complemented
487	#464	C₂²×C₆₇	1	4	yes	complemented
488	#452	C₂²×C₆₇	1	4	yes	complemented
489	#451	C₂²×C₆₇	1	2	yes	complemented
490	#451	C₂²×C₆₇	1	2	yes	complemented
491	#450	C₂²×C₆₇	1	2	yes	complemented
492	#448	C₂²×C₆₇	1	2	yes	—
493	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	complemented
494	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
495	#436	C₂²×C₆₇	1	4	yes	—
496	#436	C₂²×C₆₇	1	4	yes	complemented
497	#431	C₂²×C₆₇	1	2	yes	complemented
498	#428	C₂²×C₆₇	1	4	yes	complemented
499	#428	C₂²×C₆₇	1	2	yes	complemented
500	#428	C₂²×C₆₇	1	2	yes	complemented
501	#419	C₂²×C₆₇	1	2	yes	complemented
502	#418	C₂²×C₆₇	1	2	yes	complemented
503	#417	C₂²×C₆₇	1	4	yes	complemented
504	#407	C₂²×C₆₇	1	1	yes	characteristic
505	#407	C₂²×C₆₇	1	1	yes	characteristic
506	#407	C₂²×C₆₇	1	2	yes	complemented
507	C₂×#41	C₂³×C₆₇	1	2	yes	—
508	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
509	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
510	C₂²×D₄	—	2	1	no	—
511	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
516	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
517	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
518	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
519	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
520	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
521	#126	—	2	2	no	—
522	#126	—	2	4	no	—
523	#126	—	2	4	no	—
524	#126	—	2	2	no	—
525	#126	—	2	2	no	—
526	#125	—	2	4	no	—
527	#125	—	2	4	no	—
528	#125	—	2	2	no	—
529	#125	—	2	2	no	—
530	#125	C₂³×C₆₇	1	4	yes	—
531	#125	C₂³×C₆₇	1	2	yes	—
532	#124	—	2	2	no	—
533	#124	C₂³×C₆₇	1	2	yes	—
534	#123	—	2	4	no	—
535	#123	—	2	4	no	—
536	#123	—	2	2	no	—
537	#123	—	2	2	no	—
538	#123	—	2	2	no	—
539	#123	—	2	2	no	—
540	#123	—	2	2	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	2	1	no	—
543	C₂²⋊Q₈	—	2	1	no	—
544	C₂²⋊Q₈	—	2	1	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
548	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
549	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
550	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
551	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
552	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
553	#121	—	2	2	no	—
554	#121	—	2	2	no	—
555	#121	—	2	1	no	—
556	#121	—	2	1	no	—
557	#121	—	2	2	no	—
558	#121	C₂³×C₆₇	1	2	yes	—
559	#121	C₂³×C₆₇	1	2	yes	—
560	#121	C₂³×C₆₇	1	2	yes	—
561	#120	—	2	2	no	—
562	#120	—	2	2	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
565	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	D₄×C₆₇	1	2	yes	—
572	C₄×D₄	D₄×C₆₇	1	2	yes	—
573	C₄×D₄	C₂³×C₆₇	1	2	yes	—
574	C₄×D₄	C₂³×C₆₇	1	2	yes	—
575	C₄×D₄	C₂³×C₆₇	1	2	yes	—
576	#117	—	2	1	no	—
577	#117	—	2	1	no	—
578	#117	—	2	4	no	—
579	#117	—	2	4	no	—
580	#117	—	2	2	no	—
581	#117	—	2	2	no	—
582	#117	C₂³×C₆₇	1	2	yes	—
583	#117	C₂³×C₆₇	1	2	yes	—
584	#117	C₂³×C₆₇	1	2	yes	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	2	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
597	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	—	2	1	no	—
602	C₂×C₂²⋊C₄	—	2	1	no	—
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	2	no	—
606	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
608	C₂×C₄²	—	2	1	no	—
609	C₂×C₄²	—	2	1	no	—
610	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
611	#107	C₂³×C₆₇	1	4	yes	—
612	#107	C₂³×C₆₇	1	4	yes	—
613	#107	C₂³×C₆₇	1	4	yes	—
614	#106	C₂³×C₆₇	1	4	yes	—
615	#106	C₂³×C₆₇	1	4	yes	—
616	#106	C₂³×C₆₇	1	4	yes	—
617	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
618	#103	C₂³×C₆₇	1	4	yes	—
619	#103	C₂³×C₆₇	1	4	yes	—
620	#103	C₂³×C₆₇	1	4	yes	—
621	#103	C₂³×C₆₇	1	4	yes	—
622	#103	C₂³×C₆₇	1	4	yes	—
623	#102	C₂³×C₆₇	1	4	yes	—
624	#102	C₂³×C₆₇	1	4	yes	—
625	#102	C₂³×C₆₇	1	4	yes	—
626	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
627	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
628	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
629	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
630	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
631	C₄×C₈	C₂³×C₆₇	1	4	yes	—
632	C₂⁴	—	2	1	no	—
633	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
634	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
635	#41	—	4	4	no	—
636	C₂×Q₈	—	2	1	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	4	2	no	—
639	C₂×Q₈	—	4	2	no	—
640	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
641	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	4	2	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
651	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
652	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	4	no	—
666	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
671	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
677	Q₁₆	—	4	4	no	—
678	SD₁₆	—	4	4	no	—
679	M₁₆	—	4	2	no	—
680	M₁₆	—	4	4	no	—
681	M₁₆	—	4	2	no	—
682	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
683	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
703	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
704	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
705	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
706	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
707	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
708	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
725	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
726	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
727	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	4	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	C₂×D₄×C₆₇	1	2	yes	—
734	C₄²	C₂⁴×C₆₇	1	2	yes	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	4	1	no	—
739	C₂³	—	4	1	no	—
740	C₂³	—	4	1	no	—
741	C₂³	—	4	1	no	—
742	C₂³	—	4	2	no	—
743	C₂³	—	8	1	no	—
744	C₂³	—	8	1	no	—
745	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
746	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
747	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
748	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
749	Q₈	—	2	4	no	—
750	Q₈	—	2	4	no	—
751	Q₈	—	4	2	no	—
752	Q₈	—	8	1	no	—
753	D₄	—	2	4	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	2	no	—
756	D₄	—	4	4	no	—
757	D₄	—	4	4	no	—
758	D₄	—	8	1	no	—
759	D₄	—	8	2	no	—
760	D₄	—	8	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	8	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	2	no	—
785	C₂×C₄	—	8	2	no	—
786	C₂×C₄	—	8	2	no	—
787	C₂×C₄	—	8	1	no	—
788	C₂×C₄	—	8	1	no	—
789	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
790	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
795	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
796	C₈	—	2	4	no	—
797	C₈	—	2	4	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	4	4	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	8	2	no	—
814	C₂²	—	16	2	no	—
815	C₂²	#575×C₆₇	1	2	yes	—
816	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	1	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	#585×C₆₇	1	2	yes	—
831	C₂	—	2	2	no	—
832	C₂	—	4	2	no	—
833	C₂	—	4	1	no	—
834	C₂	—	4	1	no	—
835	C₂	—	8	2	no	—
836	C₂	C₆₇×#3485	1	1	yes	characteristic
837	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
838	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3505	C₂
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
2. C₂×#552×C₆₇	C₂	semidirect
3. C₆₇×#3352	C₂	semidirect
4. C₆₇×#3351	C₂	semidirect
5. C₆₇×#3327	C₂	semidirect
6. C₆₇×#3323	C₂	semidirect
7. C₆₇×#3232	C₂	semidirect
8. C₆₇×#3196	C₂	semidirect
9. C₆₇×#3195	C₂	semidirect
10. C₆₇×#3193	C₂	semidirect
11. C₆₇×#3108	C₂	semidirect
12. C₆₇×#3095	C₂	semidirect
13. C₆₇×#3094	C₂	semidirect
14. C₆₇×#3092	C₂	semidirect
15. C₆₇×#2975	C₂	semidirect
22. #552×C₆₇	C₂²	semidirect
32. C₂×#125×C₆₇	C₂²	semidirect
37. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
40. C₂×C₄×Q₈×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. #485×C₆₇	C₂²	semidirect
49. #484×C₆₇	C₂²	semidirect
50. #484×C₆₇	C₂²	semidirect
51. #484×C₆₇	C₂²	semidirect
52. #483×C₆₇	C₂²	semidirect
53. #483×C₆₇	C₂²	semidirect
54. #483×C₆₇	C₂²	semidirect
55. #482×C₆₇	C₂²	semidirect
57. #481×C₆₇	C₂²	semidirect
60. #479×C₆₇	C₂²	semidirect
61. #479×C₆₇	C₂²	semidirect
62. #478×C₆₇	C₂²	semidirect
63. #470×C₆₇	C₂²	semidirect
64. #470×C₆₇	C₂²	semidirect
65. #468×C₆₇	C₂²	semidirect
66. #468×C₆₇	C₂²	semidirect
67. #464×C₆₇	C₂²	semidirect
68. #452×C₆₇	C₂²	semidirect
69. #451×C₆₇	C₂²	semidirect
70. #451×C₆₇	C₂²	semidirect
71. #450×C₆₇	C₂²	semidirect
73. C₄×Q₁₆×C₆₇	C₂²	semidirect
74. C₄×SD₁₆×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
411. #61716	C₆₇	direct (N × H)
421. C₂×#552	C₂×C₆₇	semidirect
422. #3352	C₂×C₆₇	semidirect
423. #3351	C₂×C₆₇	semidirect
424. #3327	C₂×C₆₇	semidirect
425. #3323	C₂×C₆₇	semidirect
426. #3232	C₂×C₆₇	semidirect
427. #3196	C₂×C₆₇	semidirect
428. #3195	C₂×C₆₇	semidirect
429. #3193	C₂×C₆₇	semidirect
430. #3108	C₂×C₆₇	semidirect
431. #3095	C₂×C₆₇	semidirect
432. #3094	C₂×C₆₇	semidirect
433. #3092	C₂×C₆₇	semidirect
434. #2975	C₂×C₆₇	semidirect
435. C₆₇	#61716	direct (N × H)
442. #552	C₂²×C₆₇	semidirect
452. C₂×#125	C₂²×C₆₇	semidirect
457. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
460. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
464. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
465. #499	C₂²×C₆₇	semidirect
466. #488	C₂²×C₆₇	semidirect
467. #485	C₂²×C₆₇	semidirect
468. #485	C₂²×C₆₇	semidirect
469. #484	C₂²×C₆₇	semidirect
470. #484	C₂²×C₆₇	semidirect
471. #484	C₂²×C₆₇	semidirect
472. #483	C₂²×C₆₇	semidirect
473. #483	C₂²×C₆₇	semidirect
474. #483	C₂²×C₆₇	semidirect
475. #482	C₂²×C₆₇	semidirect
477. #481	C₂²×C₆₇	semidirect
480. #479	C₂²×C₆₇	semidirect
481. #479	C₂²×C₆₇	semidirect
482. #478	C₂²×C₆₇	semidirect
483. #470	C₂²×C₆₇	semidirect
484. #470	C₂²×C₆₇	semidirect
485. #468	C₂²×C₆₇	semidirect
486. #468	C₂²×C₆₇	semidirect
487. #464	C₂²×C₆₇	semidirect
488. #452	C₂²×C₆₇	semidirect
489. #451	C₂²×C₆₇	semidirect
490. #451	C₂²×C₆₇	semidirect
491. #450	C₂²×C₆₇	semidirect
493. C₄×Q₁₆	C₂²×C₆₇	semidirect
494. C₄×SD₁₆	C₂²×C₆₇	semidirect
496. #436	C₂²×C₆₇	semidirect
497. #431	C₂²×C₆₇	semidirect
498. #428	C₂²×C₆₇	semidirect
499. #428	C₂²×C₆₇	semidirect
500. #428	C₂²×C₆₇	semidirect
501. #419	C₂²×C₆₇	semidirect
502. #418	C₂²×C₆₇	semidirect
503. #417	C₂²×C₆₇	semidirect
506. #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×#552×C₆₇	2
C₆₇×#3352	2
C₆₇×#3351	2
C₆₇×#3327	2
C₆₇×#3323	2
C₆₇×#3232	2
C₆₇×#3196	2
C₆₇×#3195	2
C₆₇×#3193	2
C₆₇×#3108	2
C₆₇×#3095	2
C₆₇×#3094	2
C₆₇×#3092	2
C₆₇×#2975	2
#61716	67

Subgroups — C67×#61716 #30740967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61716 #30740967