Subgroups — C₆₇×#61257 #30740508

Order 17152.

1828 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3475	C₂	1	1	yes	maximal, characteristic
2	C₂×#556×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3356	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3353	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3350	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3349	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3342	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3340	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3095	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3093	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3056	C₂	1	2	yes	maximal, complemented
15	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2911	C₂	1	2	yes	maximal, complemented
18	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
20	#556×C₆₇	—	2	1	no	—
21	#556×C₆₇	—	2	2	no	—
22	#556×C₆₇	—	2	1	no	—
23	#556×C₆₇	C₂²	1	2	yes	—
24	#556×C₆₇	C₂²	1	1	yes	characteristic
25	#556×C₆₇	C₂²	1	4	yes	—
26	#556×C₆₇	C₂²	1	2	yes	—
27	#555×C₆₇	C₂²	1	1	yes	characteristic
28	#554×C₆₇	C₂²	1	1	yes	characteristic
29	#553×C₆₇	C₂²	1	2	yes	—
30	#552×C₆₇	—	2	1	no	—
31	#552×C₆₇	C₂²	1	2	yes	—
32	#551×C₆₇	—	2	2	no	—
33	#547×C₆₇	C₂²	1	1	yes	characteristic
34	#546×C₆₇	—	2	1	no	—
35	#533×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	#529×C₆₇	—	2	2	no	—
38	#529×C₆₇	—	2	1	no	—
39	C₂×#126×C₆₇	—	2	2	no	—
40	C₂×#124×C₆₇	—	2	1	no	—
41	#525×C₆₇	C₂²	1	2	yes	—
42	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
43	C₄×#41×C₆₇	—	2	1	no	—
44	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
46	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×#117×C₆₇	C₂²	1	2	yes	—
49	C₂×#117×C₆₇	C₂²	1	2	yes	—
50	#501×C₆₇	C₂²	1	4	yes	complemented
51	#500×C₆₇	C₂²	1	2	yes	complemented
52	#498×C₆₇	C₂²	1	2	yes	complemented
53	#485×C₆₇	C₂²	1	4	yes	complemented
54	#485×C₆₇	C₂²	1	4	yes	complemented
55	#485×C₆₇	C₂²	1	4	yes	complemented
56	#485×C₆₇	C₂²	1	4	yes	complemented
57	#484×C₆₇	C₂²	1	4	yes	complemented
58	#483×C₆₇	C₂²	1	4	yes	complemented
59	#482×C₆₇	C₂²	1	4	yes	complemented
60	#482×C₆₇	C₂²	1	4	yes	complemented
61	#479×C₆₇	C₂²	1	4	yes	complemented
62	#477×C₆₇	C₂²	1	2	yes	complemented
63	#477×C₆₇	C₂²	1	2	yes	complemented
64	#476×C₆₇	C₂²	1	2	yes	complemented
65	#475×C₆₇	C₂²	1	2	yes	complemented
66	#475×C₆₇	C₂²	1	2	yes	complemented
67	#474×C₆₇	C₂²	1	2	yes	complemented
68	#470×C₆₇	C₂²	1	4	yes	complemented
69	#468×C₆₇	C₂²	1	4	yes	complemented
70	#467×C₆₇	C₂²	1	4	yes	complemented
71	#465×C₆₇	C₂²	1	4	yes	complemented
72	#441×C₆₇	C₂²	1	2	yes	complemented
73	#440×C₆₇	C₂²	1	2	yes	complemented
74	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
75	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
76	#436×C₆₇	C₂²	1	2	yes	—
77	#435×C₆₇	C₂²	1	4	yes	—
78	C₈×D₄×C₆₇	C₂²	1	2	yes	—
79	#428×C₆₇	C₂²	1	2	yes	—
80	#428×C₆₇	C₂²	1	2	yes	—
81	#428×C₆₇	C₂²	1	2	yes	—
82	#428×C₆₇	C₂²	1	2	yes	—
83	#428×C₆₇	C₂²	1	1	yes	characteristic
84	#428×C₆₇	C₂²	1	4	yes	complemented
85	#428×C₆₇	C₂²	1	4	yes	complemented
86	#427×C₆₇	C₂²	1	4	yes	complemented
87	#427×C₆₇	C₂²	1	4	yes	complemented
88	#423×C₆₇	C₂²	1	1	yes	characteristic
89	#419×C₆₇	C₂²	1	2	yes	—
90	#419×C₆₇	C₂²	1	1	yes	characteristic
91	#417×C₆₇	C₂²	1	2	yes	—
92	#417×C₆₇	C₂²	1	1	yes	characteristic
93	#407×C₆₇	C₂²	1	2	yes	—
94	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
95	C₂×#41×C₆₇	—	2	1	no	—
96	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₆₇	—	2	1	no	—
98	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
100	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
101	#137×C₆₇	—	2	4	no	—
102	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
104	C₂×M₁₆×C₆₇	—	2	8	no	—
105	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
106	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
107	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
110	C₄⋊Q₈×C₆₇	—	2	1	no	—
111	C₄⋊Q₈×C₆₇	—	2	1	no	—
112	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
116	#126×C₆₇	—	2	2	no	—
117	#126×C₆₇	—	2	4	no	—
118	#126×C₆₇	—	2	4	no	—
119	#126×C₆₇	—	2	4	no	—
120	#126×C₆₇	—	2	4	no	—
121	#126×C₆₇	—	2	2	no	—
122	#126×C₆₇	—	2	2	no	—
123	#125×C₆₇	—	2	2	no	—
124	#125×C₆₇	—	2	1	no	—
125	#125×C₆₇	C₂³	1	2	yes	—
126	#124×C₆₇	—	2	2	no	—
127	#124×C₆₇	—	2	2	no	—
128	#124×C₆₇	—	2	4	no	—
129	#124×C₆₇	—	2	1	no	—
130	#124×C₆₇	—	2	2	no	—
131	#123×C₆₇	—	2	2	no	—
132	#123×C₆₇	—	2	2	no	—
133	#123×C₆₇	—	2	2	no	—
134	#123×C₆₇	—	2	2	no	—
135	C₂²⋊Q₈×C₆₇	—	2	2	no	—
136	C₂²⋊Q₈×C₆₇	—	2	2	no	—
137	C₂²⋊Q₈×C₆₇	—	2	1	no	—
138	C₂²⋊Q₈×C₆₇	—	2	1	no	—
139	C₂²⋊Q₈×C₆₇	—	2	1	no	—
140	C₂²⋊Q₈×C₆₇	—	2	2	no	—
141	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
142	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
143	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
144	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
145	#121×C₆₇	—	2	2	no	—
146	#121×C₆₇	—	2	1	no	—
147	#121×C₆₇	C₂³	1	2	yes	—
148	#121×C₆₇	C₂³	1	2	yes	—
149	#120×C₆₇	—	2	2	no	—
150	C₄×Q₈×C₆₇	—	2	2	no	—
151	C₄×Q₈×C₆₇	—	2	2	no	—
152	C₄×Q₈×C₆₇	—	2	4	no	—
153	C₄×Q₈×C₆₇	—	2	1	no	—
154	C₄×Q₈×C₆₇	—	2	1	no	—
155	C₄×Q₈×C₆₇	—	2	1	no	—
156	C₄×Q₈×C₆₇	—	2	1	no	—
157	C₄×Q₈×C₆₇	—	2	1	no	—
158	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
160	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
162	C₄×D₄×C₆₇	—	2	1	no	—
163	C₄×D₄×C₆₇	—	2	2	no	—
164	C₄×D₄×C₆₇	—	2	1	no	—
165	C₄×D₄×C₆₇	—	2	1	no	—
166	C₄×D₄×C₆₇	—	2	2	no	—
167	C₄×D₄×C₆₇	—	2	2	no	—
168	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
169	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
170	C₄×D₄×C₆₇	D₄	1	2	yes	—
171	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₆₇	C₂³	1	2	yes	—
175	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
176	#117×C₆₇	—	2	2	no	—
177	#117×C₆₇	—	2	2	no	—
178	#117×C₆₇	—	2	2	no	—
179	#117×C₆₇	—	2	2	no	—
180	#117×C₆₇	—	2	1	no	—
181	#117×C₆₇	—	2	2	no	—
182	#117×C₆₇	—	2	1	no	—
183	#117×C₆₇	C₂³	1	4	yes	—
184	#117×C₆₇	C₂³	1	4	yes	—
185	#117×C₆₇	C₂³	1	2	yes	—
186	#117×C₆₇	C₂³	1	2	yes	—
187	#117×C₆₇	C₂³	1	1	yes	characteristic
188	#117×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
190	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
191	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
192	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
201	C₂×C₄²×C₆₇	—	2	2	no	—
202	C₂×C₄²×C₆₇	—	2	2	no	—
203	C₂×C₄²×C₆₇	—	2	1	no	—
204	C₂×C₄²×C₆₇	—	2	1	no	—
205	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
206	#107×C₆₇	C₂³	1	4	yes	—
207	#107×C₆₇	C₂³	1	4	yes	—
208	#107×C₆₇	C₂³	1	4	yes	—
209	#107×C₆₇	C₂³	1	4	yes	—
210	#107×C₆₇	C₂³	1	2	yes	—
211	#106×C₆₇	C₂³	1	4	yes	—
212	#106×C₆₇	C₂³	1	4	yes	—
213	#106×C₆₇	C₂³	1	4	yes	—
214	#106×C₆₇	C₂³	1	4	yes	—
215	#106×C₆₇	C₂³	1	2	yes	—
216	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
217	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
218	#103×C₆₇	C₂³	1	4	yes	—
219	#103×C₆₇	C₂³	1	4	yes	—
220	#103×C₆₇	C₂³	1	4	yes	—
221	#103×C₆₇	C₂³	1	2	yes	—
222	#103×C₆₇	C₂³	1	2	yes	—
223	#103×C₆₇	C₂³	1	2	yes	—
224	#102×C₆₇	C₂³	1	4	yes	—
225	#102×C₆₇	C₂³	1	2	yes	—
226	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
228	#97×C₆₇	C₂³	1	2	yes	—
229	C₄×C₈×C₆₇	C₂³	1	2	yes	—
230	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
231	#41×C₆₇	—	2	2	no	—
232	#41×C₆₇	—	2	2	no	—
233	#41×C₆₇	—	4	4	no	—
234	C₂×Q₈×C₆₇	—	2	1	no	—
235	C₂×Q₈×C₆₇	—	2	1	no	—
236	C₂×Q₈×C₆₇	—	2	2	no	—
237	C₂×Q₈×C₆₇	—	2	2	no	—
238	C₂×Q₈×C₆₇	—	2	1	no	—
239	C₂×Q₈×C₆₇	—	2	2	no	—
240	C₂×Q₈×C₆₇	—	2	2	no	—
241	C₂×Q₈×C₆₇	—	4	4	no	—
242	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₆₇	—	2	1	no	—
245	C₂×D₄×C₆₇	—	2	2	no	—
246	C₂×D₄×C₆₇	—	2	2	no	—
247	C₂×D₄×C₆₇	—	4	2	no	—
248	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
249	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	—	2	4	no	—
253	C₂²×C₄×C₆₇	—	2	4	no	—
254	C₂²×C₄×C₆₇	—	2	1	no	—
255	C₂²×C₄×C₆₇	—	2	1	no	—
256	C₂²×C₄×C₆₇	—	2	2	no	—
257	C₂²×C₄×C₆₇	—	2	2	no	—
258	C₂²×C₄×C₆₇	—	2	2	no	—
259	C₂²×C₄×C₆₇	—	2	1	no	—
260	C₂²×C₄×C₆₇	—	2	1	no	—
261	C₂²×C₄×C₆₇	—	2	1	no	—
262	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	Q₁₆×C₆₇	—	2	4	no	—
271	SD₁₆×C₆₇	—	2	4	no	—
272	M₁₆×C₆₇	—	2	4	no	—
273	M₁₆×C₆₇	—	2	2	no	—
274	M₁₆×C₆₇	—	2	8	no	—
275	M₁₆×C₆₇	#41	1	4	yes	complemented
276	C₂×C₈×C₆₇	—	2	8	no	—
277	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
278	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
279	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₆₇	—	2	4	no	—
281	C₄⋊C₄×C₆₇	—	2	4	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	—	2	2	no	—
286	C₄⋊C₄×C₆₇	—	2	1	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	2	2	no	—
290	C₄⋊C₄×C₆₇	—	2	1	no	—
291	C₄⋊C₄×C₆₇	—	2	2	no	—
292	C₄⋊C₄×C₆₇	—	2	2	no	—
293	C₄⋊C₄×C₆₇	—	2	1	no	—
294	C₄⋊C₄×C₆₇	—	2	1	no	—
295	C₄⋊C₄×C₆₇	—	2	2	no	—
296	C₄⋊C₄×C₆₇	—	2	2	no	—
297	C₄⋊C₄×C₆₇	—	2	1	no	—
298	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
303	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
305	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
307	C₂²⋊C₄×C₆₇	—	2	1	no	—
308	C₂²⋊C₄×C₆₇	—	2	2	no	—
309	C₂²⋊C₄×C₆₇	—	2	2	no	—
310	C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂²⋊C₄×C₆₇	—	2	4	no	—
312	C₂²⋊C₄×C₆₇	—	2	4	no	—
313	C₂²⋊C₄×C₆₇	—	2	4	no	—
314	C₂²⋊C₄×C₆₇	—	2	4	no	—
315	C₂²⋊C₄×C₆₇	—	2	2	no	—
316	C₂²⋊C₄×C₆₇	—	2	2	no	—
317	C₂²⋊C₄×C₆₇	—	2	2	no	—
318	C₂²⋊C₄×C₆₇	—	2	1	no	—
319	C₂²⋊C₄×C₆₇	—	2	1	no	—
320	C₂²⋊C₄×C₆₇	—	2	2	no	—
321	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
325	C₄²×C₆₇	—	2	1	no	—
326	C₄²×C₆₇	—	2	2	no	—
327	C₄²×C₆₇	—	2	1	no	—
328	C₄²×C₆₇	—	2	2	no	—
329	C₄²×C₆₇	—	2	2	no	—
330	C₄²×C₆₇	—	2	4	no	—
331	C₄²×C₆₇	—	2	4	no	—
332	C₄²×C₆₇	—	2	1	no	—
333	C₄²×C₆₇	—	2	2	no	—
334	C₄²×C₆₇	—	2	2	no	—
335	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
338	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
339	C₂³×C₆₇	—	2	4	no	—
340	C₂³×C₆₇	—	2	1	no	—
341	C₂³×C₆₇	—	4	2	no	—
342	C₂³×C₆₇	—	4	2	no	—
343	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
344	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
345	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
346	Q₈×C₆₇	—	2	2	no	—
347	Q₈×C₆₇	—	2	1	no	—
348	Q₈×C₆₇	—	2	2	no	—
349	Q₈×C₆₇	—	2	1	no	—
350	Q₈×C₆₇	—	4	4	no	—
351	Q₈×C₆₇	—	4	2	no	—
352	Q₈×C₆₇	—	4	4	no	—
353	Q₈×C₆₇	—	4	2	no	—
354	Q₈×C₆₇	—	8	1	no	—
355	D₄×C₆₇	—	2	2	no	—
356	D₄×C₆₇	—	2	2	no	—
357	D₄×C₆₇	—	2	1	no	—
358	D₄×C₆₇	—	2	1	no	—
359	D₄×C₆₇	—	4	2	no	—
360	D₄×C₆₇	—	4	4	no	—
361	D₄×C₆₇	—	4	2	no	—
362	D₄×C₆₇	—	8	2	no	—
363	C₂×C₄×C₆₇	—	2	4	no	—
364	C₂×C₄×C₆₇	—	2	4	no	—
365	C₂×C₄×C₆₇	—	2	4	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	1	no	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	1	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	4	no	—
379	C₂×C₄×C₆₇	—	4	1	no	—
380	C₂×C₄×C₆₇	—	4	2	no	—
381	C₂×C₄×C₆₇	—	4	4	no	—
382	C₂×C₄×C₆₇	—	4	4	no	—
383	C₂×C₄×C₆₇	—	4	2	no	—
384	C₂×C₄×C₆₇	—	4	2	no	—
385	C₂×C₄×C₆₇	—	4	2	no	—
386	C₂×C₄×C₆₇	—	8	1	no	—
387	C₂×C₄×C₆₇	—	8	2	no	—
388	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
396	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
397	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
398	C₈×C₆₇	—	2	4	no	—
399	C₈×C₆₇	—	2	2	no	—
400	C₈×C₆₇	C₂×#41	1	4	yes	—
401	C₂²×C₆₇	—	2	1	no	—
402	C₂²×C₆₇	—	2	1	no	—
403	C₂²×C₆₇	—	2	2	no	—
404	C₂²×C₆₇	—	2	2	no	—
405	C₂²×C₆₇	—	2	2	no	—
406	C₂²×C₆₇	—	2	2	no	—
407	C₂²×C₆₇	—	2	2	no	—
408	C₂²×C₆₇	—	2	2	no	—
409	C₂²×C₆₇	—	4	1	no	—
410	C₂²×C₆₇	—	4	1	no	—
411	C₂²×C₆₇	—	4	1	no	—
412	C₂²×C₆₇	—	8	4	no	—
413	C₂²×C₆₇	#547	1	2	yes	—
414	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₆₇	—	2	1	no	—
416	C₄×C₆₇	—	2	1	no	—
417	C₄×C₆₇	—	2	2	no	—
418	C₄×C₆₇	—	2	2	no	—
419	C₄×C₆₇	—	2	1	no	—
420	C₄×C₆₇	—	4	2	no	—
421	C₄×C₆₇	—	4	1	no	—
422	C₄×C₆₇	—	4	2	no	—
423	C₄×C₆₇	—	4	1	no	—
424	C₄×C₆₇	—	4	2	no	—
425	C₄×C₆₇	—	4	1	no	—
426	C₄×C₆₇	—	4	2	no	—
427	C₄×C₆₇	—	4	4	no	—
428	C₄×C₆₇	#547	1	2	yes	—
429	C₄×C₆₇	#575	1	2	yes	—
430	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
431	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
432	#61257	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
433	C₂×C₆₇	—	2	2	no	—
434	C₂×C₆₇	—	4	2	no	—
435	C₂×C₆₇	—	4	2	no	—
436	C₂×C₆₇	—	8	1	no	—
437	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
438	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
439	C₂×C₆₇	#3586	1	1	yes	characteristic
440	#3475	C₂×C₆₇	1	1	yes	characteristic
441	C₂×#556	C₂×C₆₇	1	1	yes	characteristic, complemented
442	#3356	C₂×C₆₇	1	2	yes	complemented
443	#3353	C₂×C₆₇	1	2	yes	complemented
444	#3350	C₂×C₆₇	1	4	yes	complemented
445	#3349	C₂×C₆₇	1	4	yes	complemented
446	#3342	C₂×C₆₇	1	2	yes	complemented
447	#3340	C₂×C₆₇	1	2	yes	complemented
448	#3165	C₂×C₆₇	1	1	yes	characteristic, complemented
449	#3095	C₂×C₆₇	1	2	yes	complemented
450	#3093	C₂×C₆₇	1	2	yes	complemented
451	#3079	C₂×C₆₇	1	1	yes	characteristic, complemented
452	#3078	C₂×C₆₇	1	1	yes	characteristic, complemented
453	#3056	C₂×C₆₇	1	2	yes	complemented
454	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
455	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#2911	C₂×C₆₇	1	2	yes	complemented
457	C₆₇	#61257	1	1	yes	characteristic, direct product factor, Sylow
458	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
459	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
460	#556	—	2	1	no	—
461	#556	—	2	2	no	—
462	#556	—	2	1	no	—
463	#556	C₂²×C₆₇	1	2	yes	—
464	#556	C₂²×C₆₇	1	1	yes	characteristic
465	#556	C₂²×C₆₇	1	4	yes	—
466	#556	C₂²×C₆₇	1	2	yes	—
467	#555	C₂²×C₆₇	1	1	yes	characteristic
468	#554	C₂²×C₆₇	1	1	yes	characteristic
469	#553	C₂²×C₆₇	1	2	yes	—
470	#552	—	2	1	no	—
471	#552	C₂²×C₆₇	1	2	yes	—
472	#551	—	2	2	no	—
473	#547	C₂²×C₆₇	1	1	yes	characteristic
474	#546	—	2	1	no	—
475	#533	C₂²×C₆₇	1	1	yes	characteristic
476	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
477	#529	—	2	2	no	—
478	#529	—	2	1	no	—
479	C₂×#126	—	2	2	no	—
480	C₂×#124	—	2	1	no	—
481	#525	C₂²×C₆₇	1	2	yes	—
482	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
483	C₄×#41	—	2	1	no	—
484	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
485	C₂×C₄×Q₈	—	2	1	no	—
486	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
487	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
488	C₂×#117	C₂²×C₆₇	1	2	yes	—
489	C₂×#117	C₂²×C₆₇	1	2	yes	—
490	#501	C₂²×C₆₇	1	4	yes	complemented
491	#500	C₂²×C₆₇	1	2	yes	complemented
492	#498	C₂²×C₆₇	1	2	yes	complemented
493	#485	C₂²×C₆₇	1	4	yes	complemented
494	#485	C₂²×C₆₇	1	4	yes	complemented
495	#485	C₂²×C₆₇	1	4	yes	complemented
496	#485	C₂²×C₆₇	1	4	yes	complemented
497	#484	C₂²×C₆₇	1	4	yes	complemented
498	#483	C₂²×C₆₇	1	4	yes	complemented
499	#482	C₂²×C₆₇	1	4	yes	complemented
500	#482	C₂²×C₆₇	1	4	yes	complemented
501	#479	C₂²×C₆₇	1	4	yes	complemented
502	#477	C₂²×C₆₇	1	2	yes	complemented
503	#477	C₂²×C₆₇	1	2	yes	complemented
504	#476	C₂²×C₆₇	1	2	yes	complemented
505	#475	C₂²×C₆₇	1	2	yes	complemented
506	#475	C₂²×C₆₇	1	2	yes	complemented
507	#474	C₂²×C₆₇	1	2	yes	complemented
508	#470	C₂²×C₆₇	1	4	yes	complemented
509	#468	C₂²×C₆₇	1	4	yes	complemented
510	#467	C₂²×C₆₇	1	4	yes	complemented
511	#465	C₂²×C₆₇	1	4	yes	complemented
512	#441	C₂²×C₆₇	1	2	yes	complemented
513	#440	C₂²×C₆₇	1	2	yes	complemented
514	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
515	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
516	#436	C₂²×C₆₇	1	2	yes	—
517	#435	C₂²×C₆₇	1	4	yes	—
518	C₈×D₄	C₂²×C₆₇	1	2	yes	—
519	#428	C₂²×C₆₇	1	2	yes	—
520	#428	C₂²×C₆₇	1	2	yes	—
521	#428	C₂²×C₆₇	1	2	yes	—
522	#428	C₂²×C₆₇	1	2	yes	—
523	#428	C₂²×C₆₇	1	1	yes	characteristic
524	#428	C₂²×C₆₇	1	4	yes	complemented
525	#428	C₂²×C₆₇	1	4	yes	complemented
526	#427	C₂²×C₆₇	1	4	yes	complemented
527	#427	C₂²×C₆₇	1	4	yes	complemented
528	#423	C₂²×C₆₇	1	1	yes	characteristic
529	#419	C₂²×C₆₇	1	2	yes	—
530	#419	C₂²×C₆₇	1	1	yes	characteristic
531	#417	C₂²×C₆₇	1	2	yes	—
532	#417	C₂²×C₆₇	1	1	yes	characteristic
533	#407	C₂²×C₆₇	1	2	yes	—
534	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
535	C₂×#41	—	2	1	no	—
536	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
537	C₂²×Q₈	—	2	1	no	—
538	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
539	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
541	#137	—	2	4	no	—
542	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
543	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
544	C₂×M₁₆	—	2	8	no	—
545	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
546	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
547	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
548	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
549	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	1	no	—
552	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
554	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
555	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
556	#126	—	2	2	no	—
557	#126	—	2	4	no	—
558	#126	—	2	4	no	—
559	#126	—	2	4	no	—
560	#126	—	2	4	no	—
561	#126	—	2	2	no	—
562	#126	—	2	2	no	—
563	#125	—	2	2	no	—
564	#125	—	2	1	no	—
565	#125	C₂³×C₆₇	1	2	yes	—
566	#124	—	2	2	no	—
567	#124	—	2	2	no	—
568	#124	—	2	4	no	—
569	#124	—	2	1	no	—
570	#124	—	2	2	no	—
571	#123	—	2	2	no	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
582	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
583	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
584	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
585	#121	—	2	2	no	—
586	#121	—	2	1	no	—
587	#121	C₂³×C₆₇	1	2	yes	—
588	#121	C₂³×C₆₇	1	2	yes	—
589	#120	—	2	2	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	—	2	4	no	—
593	C₄×Q₈	—	2	1	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
599	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
600	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
609	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
610	C₄×D₄	D₄×C₆₇	1	2	yes	—
611	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
612	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
613	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₆₇	1	2	yes	—
615	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
616	#117	—	2	2	no	—
617	#117	—	2	2	no	—
618	#117	—	2	2	no	—
619	#117	—	2	2	no	—
620	#117	—	2	1	no	—
621	#117	—	2	2	no	—
622	#117	—	2	1	no	—
623	#117	C₂³×C₆₇	1	1	yes	characteristic
624	#117	C₂³×C₆₇	1	2	yes	—
625	#117	C₂³×C₆₇	1	2	yes	—
626	#117	C₂³×C₆₇	1	2	yes	—
627	#117	C₂³×C₆₇	1	4	yes	—
628	#117	C₂³×C₆₇	1	4	yes	—
629	C₂×C₄⋊C₄	—	2	2	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₂²⋊C₄	—	2	2	no	—
639	C₂×C₂²⋊C₄	—	2	2	no	—
640	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
641	C₂×C₄²	—	2	2	no	—
642	C₂×C₄²	—	2	2	no	—
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	—	2	1	no	—
645	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
646	#107	C₂³×C₆₇	1	2	yes	—
647	#107	C₂³×C₆₇	1	4	yes	—
648	#107	C₂³×C₆₇	1	4	yes	—
649	#107	C₂³×C₆₇	1	4	yes	—
650	#107	C₂³×C₆₇	1	4	yes	—
651	#106	C₂³×C₆₇	1	2	yes	—
652	#106	C₂³×C₆₇	1	4	yes	—
653	#106	C₂³×C₆₇	1	4	yes	—
654	#106	C₂³×C₆₇	1	4	yes	—
655	#106	C₂³×C₆₇	1	4	yes	—
656	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
657	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
658	#103	C₂³×C₆₇	1	2	yes	—
659	#103	C₂³×C₆₇	1	4	yes	—
660	#103	C₂³×C₆₇	1	2	yes	—
661	#103	C₂³×C₆₇	1	2	yes	—
662	#103	C₂³×C₆₇	1	4	yes	—
663	#103	C₂³×C₆₇	1	4	yes	—
664	#102	C₂³×C₆₇	1	2	yes	—
665	#102	C₂³×C₆₇	1	4	yes	—
666	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
667	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
668	#97	C₂³×C₆₇	1	2	yes	—
669	C₄×C₈	C₂³×C₆₇	1	2	yes	—
670	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
671	#41	—	2	2	no	—
672	#41	—	2	2	no	—
673	#41	—	4	4	no	—
674	C₂×Q₈	—	2	1	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	1	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	4	4	no	—
682	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
683	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	4	2	no	—
688	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
689	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
690	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
691	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
704	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
705	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
706	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
710	Q₁₆	—	2	4	no	—
711	SD₁₆	—	2	4	no	—
712	M₁₆	—	2	4	no	—
713	M₁₆	—	2	2	no	—
714	M₁₆	—	2	8	no	—
715	M₁₆	#41×C₆₇	1	4	yes	complemented
716	C₂×C₈	—	2	8	no	—
717	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
718	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
719	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
739	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
740	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
743	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
744	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
745	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
746	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
762	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
763	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
764	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	1	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	4	no	—
771	C₄²	—	2	4	no	—
772	C₄²	—	2	1	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
776	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
777	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
778	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
779	C₂³	—	2	4	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	4	2	no	—
782	C₂³	—	4	2	no	—
783	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
784	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
785	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
786	Q₈	—	2	2	no	—
787	Q₈	—	2	1	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	2	1	no	—
790	Q₈	—	4	4	no	—
791	Q₈	—	4	2	no	—
792	Q₈	—	4	4	no	—
793	Q₈	—	4	2	no	—
794	Q₈	—	8	1	no	—
795	D₄	—	2	2	no	—
796	D₄	—	2	2	no	—
797	D₄	—	2	1	no	—
798	D₄	—	2	1	no	—
799	D₄	—	4	2	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	2	no	—
802	D₄	—	8	2	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	8	1	no	—
827	C₂×C₄	—	8	2	no	—
828	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
829	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
831	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
835	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
836	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
837	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
838	C₈	—	2	4	no	—
839	C₈	—	2	2	no	—
840	C₈	C₂×#41×C₆₇	1	4	yes	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	8	4	no	—
853	C₂²	#547×C₆₇	1	2	yes	—
854	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	4	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	#547×C₆₇	1	2	yes	—
869	C₄	#575×C₆₇	1	2	yes	—
870	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
871	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
872	C₂	—	2	2	no	—
873	C₂	—	4	2	no	—
874	C₂	—	4	2	no	—
875	C₂	—	8	1	no	—
876	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
877	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
878	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×#3475	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×#556×C₆₇	C₂	semidirect
3. C₆₇×#3356	C₂	semidirect
4. C₆₇×#3353	C₂	semidirect
5. C₆₇×#3350	C₂	semidirect
6. C₆₇×#3349	C₂	semidirect
7. C₆₇×#3342	C₂	semidirect
8. C₆₇×#3340	C₂	semidirect
9. C₆₇×#3165	C₂	semidirect
10. C₆₇×#3095	C₂	semidirect
11. C₆₇×#3093	C₂	semidirect
12. C₆₇×#3079	C₂	semidirect
13. C₆₇×#3078	C₂	semidirect
14. C₆₇×#3056	C₂	semidirect
15. C₄×#137×C₆₇	C₂	semidirect
16. D₄×M₁₆×C₆₇	C₂	semidirect
17. C₆₇×#2911	C₂	semidirect
50. #501×C₆₇	C₂²	semidirect
51. #500×C₆₇	C₂²	semidirect
52. #498×C₆₇	C₂²	semidirect
53. #485×C₆₇	C₂²	semidirect
54. #485×C₆₇	C₂²	semidirect
55. #485×C₆₇	C₂²	semidirect
56. #485×C₆₇	C₂²	semidirect
57. #484×C₆₇	C₂²	semidirect
58. #483×C₆₇	C₂²	semidirect
59. #482×C₆₇	C₂²	semidirect
60. #482×C₆₇	C₂²	semidirect
61. #479×C₆₇	C₂²	semidirect
62. #477×C₆₇	C₂²	semidirect
63. #477×C₆₇	C₂²	semidirect
64. #476×C₆₇	C₂²	semidirect
65. #475×C₆₇	C₂²	semidirect
66. #475×C₆₇	C₂²	semidirect
67. #474×C₆₇	C₂²	semidirect
68. #470×C₆₇	C₂²	semidirect
69. #468×C₆₇	C₂²	semidirect
70. #467×C₆₇	C₂²	semidirect
71. #465×C₆₇	C₂²	semidirect
72. #441×C₆₇	C₂²	semidirect
73. #440×C₆₇	C₂²	semidirect
74. C₄×Q₁₆×C₆₇	C₂²	semidirect
75. C₄×SD₁₆×C₆₇	C₂²	semidirect
84. #428×C₆₇	C₂²	semidirect
85. #428×C₆₇	C₂²	semidirect
86. #427×C₆₇	C₂²	semidirect
87. #427×C₆₇	C₂²	semidirect
275. M₁₆×C₆₇	#41	semidirect
432. #61257	C₆₇	direct (N × H)
441. C₂×#556	C₂×C₆₇	semidirect
442. #3356	C₂×C₆₇	semidirect
443. #3353	C₂×C₆₇	semidirect
444. #3350	C₂×C₆₇	semidirect
445. #3349	C₂×C₆₇	semidirect
446. #3342	C₂×C₆₇	semidirect
447. #3340	C₂×C₆₇	semidirect
448. #3165	C₂×C₆₇	semidirect
449. #3095	C₂×C₆₇	semidirect
450. #3093	C₂×C₆₇	semidirect
451. #3079	C₂×C₆₇	semidirect
452. #3078	C₂×C₆₇	semidirect
453. #3056	C₂×C₆₇	semidirect
454. C₄×#137	C₂×C₆₇	semidirect
455. D₄×M₁₆	C₂×C₆₇	semidirect
456. #2911	C₂×C₆₇	semidirect
457. C₆₇	#61257	direct (N × H)
490. #501	C₂²×C₆₇	semidirect
491. #500	C₂²×C₆₇	semidirect
492. #498	C₂²×C₆₇	semidirect
493. #485	C₂²×C₆₇	semidirect
494. #485	C₂²×C₆₇	semidirect
495. #485	C₂²×C₆₇	semidirect
496. #485	C₂²×C₆₇	semidirect
497. #484	C₂²×C₆₇	semidirect
498. #483	C₂²×C₆₇	semidirect
499. #482	C₂²×C₆₇	semidirect
500. #482	C₂²×C₆₇	semidirect
501. #479	C₂²×C₆₇	semidirect
502. #477	C₂²×C₆₇	semidirect
503. #477	C₂²×C₆₇	semidirect
504. #476	C₂²×C₆₇	semidirect
505. #475	C₂²×C₆₇	semidirect
506. #475	C₂²×C₆₇	semidirect
507. #474	C₂²×C₆₇	semidirect
508. #470	C₂²×C₆₇	semidirect
509. #468	C₂²×C₆₇	semidirect
510. #467	C₂²×C₆₇	semidirect
511. #465	C₂²×C₆₇	semidirect
512. #441	C₂²×C₆₇	semidirect
513. #440	C₂²×C₆₇	semidirect
514. C₄×Q₁₆	C₂²×C₆₇	semidirect
515. C₄×SD₁₆	C₂²×C₆₇	semidirect
524. #428	C₂²×C₆₇	semidirect
525. #428	C₂²×C₆₇	semidirect
526. #427	C₂²×C₆₇	semidirect
527. #427	C₂²×C₆₇	semidirect
715. M₁₆	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3475	2
C₂×#556×C₆₇	2
C₆₇×#3356	2
C₆₇×#3353	2
C₆₇×#3350	2
C₆₇×#3349	2
C₆₇×#3342	2
C₆₇×#3340	2
C₆₇×#3165	2
C₆₇×#3095	2
C₆₇×#3093	2
C₆₇×#3079	2
C₆₇×#3078	2
C₆₇×#3056	2
C₄×#137×C₆₇	2
D₄×M₁₆×C₆₇	2
C₆₇×#2911	2
#61257	67

Subgroups — C67×#61257 #30740508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61257 #30740508