Subgroups — C₆₇×#60583 #30739834

Order 17152.

1998 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3495	C₂	1	1	yes	maximal, characteristic
2	C₂×#519×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3127	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3121	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3117	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3113	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3108	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3104	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3095	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3091	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#3082	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3044	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3004	C₂	1	1	yes	maximal, characteristic
14	C₂×#451×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2950	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2947	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#137×C₆₇	C₂²	1	2	yes	—
20	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	—
21	#556×C₆₇	—	2	1	no	—
22	#554×C₆₇	—	2	1	no	—
23	#552×C₆₇	—	2	2	no	—
24	#552×C₆₇	—	2	1	no	—
25	#552×C₆₇	—	2	1	no	—
26	#551×C₆₇	—	2	2	no	—
27	#544×C₆₇	C₂²	1	1	yes	characteristic
28	#542×C₆₇	C₂²	1	2	yes	—
29	#541×C₆₇	C₂²	1	2	yes	—
30	#536×C₆₇	C₂²	1	1	yes	characteristic
31	#533×C₆₇	C₂²	1	2	yes	—
32	#529×C₆₇	C₂²	1	2	yes	—
33	#525×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	#520×C₆₇	C₂²	1	1	yes	characteristic
36	#519×C₆₇	—	2	2	no	—
37	#519×C₆₇	—	2	1	no	—
38	#519×C₆₇	—	2	1	no	—
39	#519×C₆₇	C₂²	1	2	yes	—
40	#519×C₆₇	C₂²	1	4	yes	—
41	#519×C₆₇	C₂²	1	2	yes	—
42	#519×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
44	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
45	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
47	C₂×#117×C₆₇	—	2	2	no	—
48	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
50	#485×C₆₇	C₂²	1	2	yes	—
51	#485×C₆₇	C₂²	1	4	yes	—
52	#484×C₆₇	C₂²	1	1	yes	characteristic
53	#484×C₆₇	C₂²	1	2	yes	—
54	#483×C₆₇	C₂²	1	1	yes	characteristic
55	#483×C₆₇	C₂²	1	2	yes	—
56	#482×C₆₇	C₂²	1	2	yes	—
57	#481×C₆₇	C₂²	1	1	yes	characteristic
58	#480×C₆₇	C₂²	1	1	yes	characteristic
59	#479×C₆₇	C₂²	1	4	yes	complemented
60	#479×C₆₇	C₂²	1	4	yes	complemented
61	#477×C₆₇	C₂²	1	4	yes	complemented
62	#475×C₆₇	C₂²	1	4	yes	complemented
63	#464×C₆₇	C₂²	1	4	yes	complemented
64	#464×C₆₇	C₂²	1	4	yes	complemented
65	#462×C₆₇	C₂²	1	4	yes	complemented
66	#462×C₆₇	C₂²	1	4	yes	complemented
67	#451×C₆₇	C₂²	1	2	yes	—
68	#451×C₆₇	C₂²	1	2	yes	—
69	#451×C₆₇	C₂²	1	2	yes	—
70	#451×C₆₇	C₂²	1	4	yes	—
71	#451×C₆₇	C₂²	1	2	yes	—
72	#448×C₆₇	C₂²	1	2	yes	—
73	#448×C₆₇	C₂²	1	2	yes	—
74	#441×C₆₇	C₂²	1	4	yes	complemented
75	#441×C₆₇	C₂²	1	4	yes	complemented
76	#441×C₆₇	C₂²	1	4	yes	complemented
77	#440×C₆₇	C₂²	1	4	yes	complemented
78	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	complemented
79	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	complemented
80	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	complemented
81	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
82	#433×C₆₇	C₂²	1	4	yes	—
83	#432×C₆₇	C₂²	1	2	yes	—
84	#431×C₆₇	C₂²	1	2	yes	—
85	#428×C₆₇	C₂²	1	2	yes	—
86	#427×C₆₇	C₂²	1	2	yes	—
87	#424×C₆₇	C₂²	1	2	yes	—
88	#419×C₆₇	C₂²	1	2	yes	—
89	#419×C₆₇	C₂²	1	2	yes	—
90	#416×C₆₇	C₂²	1	2	yes	—
91	C₂×#103×C₆₇	C₂²	1	2	yes	—
92	#407×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
94	#405×C₆₇	C₂²	1	2	yes	—
95	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₆₇	—	2	8	no	—
97	C₂²×Q₈×C₆₇	—	2	1	no	—
98	C₂²×Q₈×C₆₇	—	2	1	no	—
99	C₂²×Q₈×C₆₇	—	2	1	no	—
100	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
101	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
102	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
104	C₂³×C₄×C₆₇	—	2	1	no	—
105	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
106	#137×C₆₇	—	2	8	no	—
107	C₂×Q₁₆×C₆₇	—	2	8	no	—
108	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
109	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
110	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
112	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
113	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₆₇	—	2	1	no	—
115	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
116	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
117	#126×C₆₇	—	2	2	no	—
118	#126×C₆₇	—	2	2	no	—
119	#126×C₆₇	—	2	2	no	—
120	#126×C₆₇	—	2	2	no	—
121	#125×C₆₇	—	2	2	no	—
122	#125×C₆₇	—	2	2	no	—
123	#125×C₆₇	—	2	1	no	—
124	#125×C₆₇	—	2	2	no	—
125	#125×C₆₇	C₂³	1	2	yes	—
126	#124×C₆₇	—	2	2	no	—
127	#124×C₆₇	C₂³	1	2	yes	—
128	#123×C₆₇	—	2	1	no	—
129	#123×C₆₇	—	2	2	no	—
130	#123×C₆₇	—	2	2	no	—
131	#123×C₆₇	—	2	2	no	—
132	C₂²⋊Q₈×C₆₇	—	2	1	no	—
133	C₂²⋊Q₈×C₆₇	—	2	1	no	—
134	C₂²⋊Q₈×C₆₇	—	2	2	no	—
135	C₂²⋊Q₈×C₆₇	—	2	1	no	—
136	C₂²⋊Q₈×C₆₇	—	2	1	no	—
137	C₂²⋊Q₈×C₆₇	—	2	2	no	—
138	C₂²⋊Q₈×C₆₇	—	2	2	no	—
139	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
140	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
141	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
142	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
143	#121×C₆₇	C₂³	1	1	yes	characteristic
144	#121×C₆₇	C₂³	1	1	yes	characteristic
145	#120×C₆₇	—	2	1	no	—
146	C₄×Q₈×C₆₇	—	2	2	no	—
147	C₄×Q₈×C₆₇	—	2	2	no	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	—	2	4	no	—
150	C₄×Q₈×C₆₇	—	2	2	no	—
151	C₄×Q₈×C₆₇	—	2	4	no	—
152	C₄×Q₈×C₆₇	—	2	1	no	—
153	C₄×Q₈×C₆₇	—	2	1	no	—
154	C₄×Q₈×C₆₇	—	2	2	no	—
155	C₄×Q₈×C₆₇	—	2	2	no	—
156	C₄×Q₈×C₆₇	—	2	2	no	—
157	C₄×Q₈×C₆₇	—	2	2	no	—
158	C₄×Q₈×C₆₇	—	2	2	no	—
159	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
160	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
161	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
162	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
163	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
164	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
165	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
166	C₄×D₄×C₆₇	—	2	1	no	—
167	C₄×D₄×C₆₇	—	2	1	no	—
168	C₄×D₄×C₆₇	—	2	2	no	—
169	C₄×D₄×C₆₇	—	2	2	no	—
170	C₄×D₄×C₆₇	C₂³	1	2	yes	—
171	#117×C₆₇	—	2	1	no	—
172	#117×C₆₇	—	2	1	no	—
173	#117×C₆₇	—	2	2	no	—
174	#117×C₆₇	—	2	1	no	—
175	#117×C₆₇	—	2	4	no	—
176	#117×C₆₇	—	2	4	no	—
177	#117×C₆₇	—	2	4	no	—
178	#117×C₆₇	—	2	4	no	—
179	#117×C₆₇	—	2	2	no	—
180	#117×C₆₇	—	2	2	no	—
181	#117×C₆₇	D₄	1	1	yes	characteristic
182	#117×C₆₇	D₄	1	2	yes	—
183	#117×C₆₇	D₄	1	1	yes	characteristic
184	#117×C₆₇	C₂³	1	2	yes	—
185	#117×C₆₇	C₂³	1	2	yes	—
186	#117×C₆₇	C₂³	1	1	yes	characteristic
187	#117×C₆₇	C₂³	1	1	yes	characteristic
188	#117×C₆₇	C₂³	1	1	yes	characteristic
189	#117×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
191	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
192	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
193	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
194	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
201	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
202	C₂×C₄²×C₆₇	—	2	2	no	—
203	C₂×C₄²×C₆₇	—	2	2	no	—
204	C₂×C₄²×C₆₇	—	2	1	no	—
205	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
206	#107×C₆₇	C₂³	1	2	yes	—
207	#107×C₆₇	C₂³	1	4	yes	—
208	#107×C₆₇	C₂³	1	2	yes	—
209	#106×C₆₇	C₂³	1	2	yes	—
210	#106×C₆₇	C₂³	1	4	yes	—
211	#106×C₆₇	C₂³	1	2	yes	—
212	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
213	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
214	#103×C₆₇	C₂³	1	4	yes	—
215	#103×C₆₇	C₂³	1	4	yes	—
216	#103×C₆₇	C₂³	1	4	yes	—
217	#103×C₆₇	C₂³	1	4	yes	—
218	#103×C₆₇	C₂³	1	2	yes	—
219	#103×C₆₇	C₂³	1	2	yes	—
220	#103×C₆₇	C₂³	1	4	yes	—
221	#103×C₆₇	C₂³	1	4	yes	—
222	#102×C₆₇	C₂³	1	2	yes	—
223	#102×C₆₇	C₂³	1	2	yes	—
224	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
225	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
226	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
229	#97×C₆₇	C₂³	1	4	yes	—
230	C₄×C₈×C₆₇	C₂³	1	4	yes	—
231	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
232	#41×C₆₇	—	2	4	no	—
233	C₂×Q₈×C₆₇	—	2	8	no	—
234	C₂×Q₈×C₆₇	—	2	8	no	—
235	C₂×Q₈×C₆₇	—	2	8	no	—
236	C₂×Q₈×C₆₇	—	2	8	no	—
237	C₂×Q₈×C₆₇	—	2	8	no	—
238	C₂×Q₈×C₆₇	—	2	2	no	—
239	C₂×Q₈×C₆₇	—	2	2	no	—
240	C₂×Q₈×C₆₇	—	2	2	no	—
241	C₂×Q₈×C₆₇	—	2	1	no	—
242	C₂×Q₈×C₆₇	—	2	2	no	—
243	C₂×Q₈×C₆₇	—	2	4	no	—
244	C₂×Q₈×C₆₇	—	2	4	no	—
245	C₂×Q₈×C₆₇	#41	1	8	yes	—
246	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
249	C₂×D₄×C₆₇	—	2	1	no	—
250	C₂×D₄×C₆₇	—	2	1	no	—
251	C₂×D₄×C₆₇	—	2	1	no	—
252	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	—	2	8	no	—
254	C₂²×C₄×C₆₇	—	2	2	no	—
255	C₂²×C₄×C₆₇	—	2	2	no	—
256	C₂²×C₄×C₆₇	—	2	2	no	—
257	C₂²×C₄×C₆₇	—	2	4	no	—
258	C₂²×C₄×C₆₇	—	2	1	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	—	2	1	no	—
263	C₂²×C₄×C₆₇	—	2	2	no	—
264	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	Q₁₆×C₆₇	—	2	8	no	—
273	Q₁₆×C₆₇	—	2	8	no	—
274	Q₁₆×C₆₇	—	2	8	no	—
275	SD₁₆×C₆₇	—	2	8	no	—
276	M₁₆×C₆₇	—	2	4	no	—
277	C₂×C₈×C₆₇	—	2	4	no	—
278	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
279	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
280	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
281	C₄⋊C₄×C₆₇	—	2	1	no	—
282	C₄⋊C₄×C₆₇	—	2	4	no	—
283	C₄⋊C₄×C₆₇	—	2	4	no	—
284	C₄⋊C₄×C₆₇	—	2	4	no	—
285	C₄⋊C₄×C₆₇	—	2	4	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	2	1	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	2	no	—
294	C₄⋊C₄×C₆₇	—	2	2	no	—
295	C₄⋊C₄×C₆₇	—	2	2	no	—
296	C₄⋊C₄×C₆₇	—	2	1	no	—
297	C₄⋊C₄×C₆₇	—	2	2	no	—
298	C₄⋊C₄×C₆₇	—	2	1	no	—
299	C₄⋊C₄×C₆₇	—	2	2	no	—
300	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
301	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
302	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
305	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
309	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂²⋊C₄×C₆₇	—	2	2	no	—
312	C₂²⋊C₄×C₆₇	—	2	2	no	—
313	C₂²⋊C₄×C₆₇	—	2	2	no	—
314	C₂²⋊C₄×C₆₇	—	2	2	no	—
315	C₂²⋊C₄×C₆₇	—	2	1	no	—
316	C₂²⋊C₄×C₆₇	—	2	1	no	—
317	C₂²⋊C₄×C₆₇	—	2	1	no	—
318	C₂²⋊C₄×C₆₇	—	2	1	no	—
319	C₂²⋊C₄×C₆₇	—	2	2	no	—
320	C₂²⋊C₄×C₆₇	—	2	2	no	—
321	C₂²⋊C₄×C₆₇	—	2	1	no	—
322	C₂²⋊C₄×C₆₇	—	2	2	no	—
323	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
327	C₄²×C₆₇	—	2	4	no	—
328	C₄²×C₆₇	—	2	4	no	—
329	C₄²×C₆₇	—	2	4	no	—
330	C₄²×C₆₇	—	2	4	no	—
331	C₄²×C₆₇	—	2	2	no	—
332	C₄²×C₆₇	—	2	2	no	—
333	C₄²×C₆₇	—	2	2	no	—
334	C₄²×C₆₇	—	2	2	no	—
335	C₄²×C₆₇	—	2	2	no	—
336	C₄²×C₆₇	—	2	1	no	—
337	C₄²×C₆₇	C₂×D₄	1	2	yes	—
338	C₄²×C₆₇	C₂×D₄	1	2	yes	—
339	C₄²×C₆₇	C₂⁴	1	2	yes	—
340	C₄²×C₆₇	C₂⁴	1	2	yes	—
341	C₂³×C₆₇	—	2	2	no	—
342	C₂³×C₆₇	—	2	2	no	—
343	C₂³×C₆₇	—	2	1	no	—
344	C₂³×C₆₇	—	4	1	no	—
345	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
346	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
347	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
348	Q₈×C₆₇	—	2	8	no	—
349	Q₈×C₆₇	—	2	8	no	—
350	Q₈×C₆₇	—	2	8	no	—
351	Q₈×C₆₇	—	2	4	no	—
352	Q₈×C₆₇	—	2	4	no	—
353	Q₈×C₆₇	—	2	2	no	—
354	Q₈×C₆₇	—	4	2	no	—
355	Q₈×C₆₇	—	8	2	no	—
356	Q₈×C₆₇	C₂×#41	1	8	yes	—
357	D₄×C₆₇	—	2	2	no	—
358	D₄×C₆₇	—	4	2	no	—
359	D₄×C₆₇	—	4	2	no	—
360	D₄×C₆₇	—	8	1	no	—
361	C₂×C₄×C₆₇	—	2	8	no	—
362	C₂×C₄×C₆₇	—	2	8	no	—
363	C₂×C₄×C₆₇	—	2	8	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	4	no	—
366	C₂×C₄×C₆₇	—	2	4	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	2	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	1	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	4	2	no	—
379	C₂×C₄×C₆₇	—	4	2	no	—
380	C₂×C₄×C₆₇	—	4	2	no	—
381	C₂×C₄×C₆₇	—	4	2	no	—
382	C₂×C₄×C₆₇	—	4	2	no	—
383	C₂×C₄×C₆₇	—	8	2	no	—
384	C₂×C₄×C₆₇	—	8	1	no	—
385	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
391	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
393	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
394	C₈×C₆₇	—	2	2	no	—
395	C₈×C₆₇	—	2	2	no	—
396	C₈×C₆₇	—	2	4	no	—
397	C₂²×C₆₇	—	2	1	no	—
398	C₂²×C₆₇	—	2	1	no	—
399	C₂²×C₆₇	—	2	1	no	—
400	C₂²×C₆₇	—	2	1	no	—
401	C₂²×C₆₇	—	2	1	no	—
402	C₂²×C₆₇	—	2	1	no	—
403	C₂²×C₆₇	—	2	1	no	—
404	C₂²×C₆₇	—	4	4	no	—
405	C₂²×C₆₇	—	4	1	no	—
406	C₂²×C₆₇	—	4	1	no	—
407	C₂²×C₆₇	—	4	1	no	—
408	C₂²×C₆₇	#525	1	2	yes	—
409	C₂²×C₆₇	#578	1	2	yes	—
410	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
411	C₄×C₆₇	—	2	2	no	—
412	C₄×C₆₇	—	2	2	no	—
413	C₄×C₆₇	—	2	8	no	—
414	C₄×C₆₇	—	2	1	no	—
415	C₄×C₆₇	—	2	1	no	—
416	C₄×C₆₇	—	2	2	no	—
417	C₄×C₆₇	—	2	2	no	—
418	C₄×C₆₇	—	4	2	no	—
419	C₄×C₆₇	—	4	2	no	—
420	C₄×C₆₇	—	4	1	no	—
421	C₄×C₆₇	—	4	1	no	—
422	C₄×C₆₇	—	4	2	no	—
423	C₄×C₆₇	—	4	2	no	—
424	C₄×C₆₇	—	4	1	no	—
425	C₄×C₆₇	#525	1	2	yes	—
426	C₄×C₆₇	C₂²×#41	1	2	yes	—
427	#60583	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
428	C₂×C₆₇	—	2	2	no	—
429	C₂×C₆₇	—	2	2	no	—
430	C₂×C₆₇	—	4	1	no	—
431	C₂×C₆₇	—	8	1	no	—
432	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
433	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
434	C₂×C₆₇	#3586	1	1	yes	characteristic
435	#3495	C₂×C₆₇	1	1	yes	characteristic
436	C₂×#519	C₂×C₆₇	1	1	yes	characteristic, complemented
437	#3127	C₂×C₆₇	1	4	yes	complemented
438	#3121	C₂×C₆₇	1	4	yes	complemented
439	#3117	C₂×C₆₇	1	2	yes	complemented
440	#3113	C₂×C₆₇	1	2	yes	complemented
441	#3108	C₂×C₆₇	1	2	yes	complemented
442	#3104	C₂×C₆₇	1	2	yes	complemented
443	#3095	C₂×C₆₇	1	1	yes	characteristic, complemented
444	#3091	C₂×C₆₇	1	1	yes	characteristic
445	#3082	C₂×C₆₇	1	2	yes	complemented
446	#3044	C₂×C₆₇	1	2	yes	complemented
447	#3004	C₂×C₆₇	1	1	yes	characteristic
448	C₂×#451	C₂×C₆₇	1	1	yes	characteristic, complemented
449	#2950	C₂×C₆₇	1	2	yes	complemented
450	#2947	C₂×C₆₇	1	2	yes	complemented
451	#2924	C₂×C₆₇	1	1	yes	characteristic, complemented
452	C₆₇	#60583	1	1	yes	characteristic, direct product factor, Sylow
453	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
454	C₂×#137	C₂²×C₆₇	1	2	yes	—
455	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	—
456	#556	—	2	1	no	—
457	#554	—	2	1	no	—
458	#552	—	2	2	no	—
459	#552	—	2	1	no	—
460	#552	—	2	1	no	—
461	#551	—	2	2	no	—
462	#544	C₂²×C₆₇	1	1	yes	characteristic
463	#542	C₂²×C₆₇	1	2	yes	—
464	#541	C₂²×C₆₇	1	2	yes	—
465	#536	C₂²×C₆₇	1	1	yes	characteristic
466	#533	C₂²×C₆₇	1	2	yes	—
467	#529	C₂²×C₆₇	1	2	yes	—
468	#525	C₂²×C₆₇	1	1	yes	characteristic
469	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
470	#520	C₂²×C₆₇	1	1	yes	characteristic
471	#519	—	2	2	no	—
472	#519	—	2	1	no	—
473	#519	—	2	1	no	—
474	#519	C₂²×C₆₇	1	2	yes	—
475	#519	C₂²×C₆₇	1	4	yes	—
476	#519	C₂²×C₆₇	1	2	yes	—
477	#519	C₂²×C₆₇	1	1	yes	characteristic
478	C₂×C₄×Q₈	—	2	1	no	—
479	C₂×C₄×Q₈	—	2	1	no	—
480	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
481	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
482	C₂×#117	—	2	2	no	—
483	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
484	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
485	#485	C₂²×C₆₇	1	2	yes	—
486	#485	C₂²×C₆₇	1	4	yes	—
487	#484	C₂²×C₆₇	1	1	yes	characteristic
488	#484	C₂²×C₆₇	1	2	yes	—
489	#483	C₂²×C₆₇	1	1	yes	characteristic
490	#483	C₂²×C₆₇	1	2	yes	—
491	#482	C₂²×C₆₇	1	2	yes	—
492	#481	C₂²×C₆₇	1	1	yes	characteristic
493	#480	C₂²×C₆₇	1	1	yes	characteristic
494	#479	C₂²×C₆₇	1	4	yes	complemented
495	#479	C₂²×C₆₇	1	4	yes	complemented
496	#477	C₂²×C₆₇	1	4	yes	complemented
497	#475	C₂²×C₆₇	1	4	yes	complemented
498	#464	C₂²×C₆₇	1	4	yes	complemented
499	#464	C₂²×C₆₇	1	4	yes	complemented
500	#462	C₂²×C₆₇	1	4	yes	complemented
501	#462	C₂²×C₆₇	1	4	yes	complemented
502	#451	C₂²×C₆₇	1	2	yes	—
503	#451	C₂²×C₆₇	1	2	yes	—
504	#451	C₂²×C₆₇	1	2	yes	—
505	#451	C₂²×C₆₇	1	4	yes	—
506	#451	C₂²×C₆₇	1	2	yes	—
507	#448	C₂²×C₆₇	1	2	yes	—
508	#448	C₂²×C₆₇	1	2	yes	—
509	#441	C₂²×C₆₇	1	4	yes	complemented
510	#441	C₂²×C₆₇	1	4	yes	complemented
511	#441	C₂²×C₆₇	1	4	yes	complemented
512	#440	C₂²×C₆₇	1	4	yes	complemented
513	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	complemented
514	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	complemented
515	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	complemented
516	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
517	#433	C₂²×C₆₇	1	4	yes	—
518	#432	C₂²×C₆₇	1	2	yes	—
519	#431	C₂²×C₆₇	1	2	yes	—
520	#428	C₂²×C₆₇	1	2	yes	—
521	#427	C₂²×C₆₇	1	2	yes	—
522	#424	C₂²×C₆₇	1	2	yes	—
523	#419	C₂²×C₆₇	1	2	yes	—
524	#419	C₂²×C₆₇	1	2	yes	—
525	#416	C₂²×C₆₇	1	2	yes	—
526	C₂×#103	C₂²×C₆₇	1	2	yes	—
527	#407	C₂²×C₆₇	1	1	yes	characteristic
528	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
529	#405	C₂²×C₆₇	1	2	yes	—
530	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
531	C₂²×Q₈	—	2	8	no	—
532	C₂²×Q₈	—	2	1	no	—
533	C₂²×Q₈	—	2	1	no	—
534	C₂²×Q₈	—	2	1	no	—
535	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
536	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
537	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
539	C₂³×C₄	—	2	1	no	—
540	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
541	#137	—	2	8	no	—
542	C₂×Q₁₆	—	2	8	no	—
543	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
544	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
545	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
546	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
547	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
548	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
551	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
552	#126	—	2	2	no	—
553	#126	—	2	2	no	—
554	#126	—	2	2	no	—
555	#126	—	2	2	no	—
556	#125	—	2	2	no	—
557	#125	—	2	2	no	—
558	#125	—	2	1	no	—
559	#125	—	2	2	no	—
560	#125	C₂³×C₆₇	1	2	yes	—
561	#124	—	2	2	no	—
562	#124	C₂³×C₆₇	1	2	yes	—
563	#123	—	2	1	no	—
564	#123	—	2	2	no	—
565	#123	—	2	2	no	—
566	#123	—	2	2	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
575	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
576	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
577	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
578	#121	C₂³×C₆₇	1	1	yes	characteristic
579	#121	C₂³×C₆₇	1	1	yes	characteristic
580	#120	—	2	1	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	4	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	4	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
595	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
596	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
597	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
598	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
599	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
600	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	C₂³×C₆₇	1	2	yes	—
606	#117	—	2	1	no	—
607	#117	—	2	1	no	—
608	#117	—	2	2	no	—
609	#117	—	2	1	no	—
610	#117	—	2	4	no	—
611	#117	—	2	4	no	—
612	#117	—	2	4	no	—
613	#117	—	2	4	no	—
614	#117	—	2	2	no	—
615	#117	—	2	2	no	—
616	#117	D₄×C₆₇	1	1	yes	characteristic
617	#117	D₄×C₆₇	1	2	yes	—
618	#117	D₄×C₆₇	1	1	yes	characteristic
619	#117	C₂³×C₆₇	1	2	yes	—
620	#117	C₂³×C₆₇	1	2	yes	—
621	#117	C₂³×C₆₇	1	1	yes	characteristic
622	#117	C₂³×C₆₇	1	1	yes	characteristic
623	#117	C₂³×C₆₇	1	1	yes	characteristic
624	#117	C₂³×C₆₇	1	2	yes	—
625	C₂×C₄⋊C₄	—	2	2	no	—
626	C₂×C₄⋊C₄	—	2	2	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
630	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
637	C₂×C₄²	—	2	2	no	—
638	C₂×C₄²	—	2	2	no	—
639	C₂×C₄²	—	2	1	no	—
640	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
641	#107	C₂³×C₆₇	1	2	yes	—
642	#107	C₂³×C₆₇	1	2	yes	—
643	#107	C₂³×C₆₇	1	4	yes	—
644	#106	C₂³×C₆₇	1	2	yes	—
645	#106	C₂³×C₆₇	1	2	yes	—
646	#106	C₂³×C₆₇	1	4	yes	—
647	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
648	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
649	#103	C₂³×C₆₇	1	4	yes	—
650	#103	C₂³×C₆₇	1	4	yes	—
651	#103	C₂³×C₆₇	1	2	yes	—
652	#103	C₂³×C₆₇	1	2	yes	—
653	#103	C₂³×C₆₇	1	4	yes	—
654	#103	C₂³×C₆₇	1	4	yes	—
655	#103	C₂³×C₆₇	1	4	yes	—
656	#103	C₂³×C₆₇	1	4	yes	—
657	#102	C₂³×C₆₇	1	2	yes	—
658	#102	C₂³×C₆₇	1	2	yes	—
659	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
660	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
661	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
662	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
663	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
664	#97	C₂³×C₆₇	1	4	yes	—
665	C₄×C₈	C₂³×C₆₇	1	4	yes	—
666	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
667	#41	—	2	4	no	—
668	C₂×Q₈	—	2	8	no	—
669	C₂×Q₈	—	2	8	no	—
670	C₂×Q₈	—	2	8	no	—
671	C₂×Q₈	—	2	8	no	—
672	C₂×Q₈	—	2	8	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	4	no	—
679	C₂×Q₈	—	2	4	no	—
680	C₂×Q₈	#41×C₆₇	1	8	yes	—
681	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
682	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
683	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
688	C₂²×C₄	—	2	8	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
700	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
702	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
707	Q₁₆	—	2	8	no	—
708	Q₁₆	—	2	8	no	—
709	Q₁₆	—	2	8	no	—
710	SD₁₆	—	2	8	no	—
711	M₁₆	—	2	4	no	—
712	C₂×C₈	—	2	4	no	—
713	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
714	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
715	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
736	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
737	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
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	2	yes	—
743	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
745	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
759	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
760	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
761	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
762	C₄²	—	2	4	no	—
763	C₄²	—	2	4	no	—
764	C₄²	—	2	4	no	—
765	C₄²	—	2	4	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	1	no	—
772	C₄²	C₂×D₄×C₆₇	1	2	yes	—
773	C₄²	C₂×D₄×C₆₇	1	2	yes	—
774	C₄²	C₂⁴×C₆₇	1	2	yes	—
775	C₄²	C₂⁴×C₆₇	1	2	yes	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	4	1	no	—
780	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
781	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
782	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
783	Q₈	—	2	8	no	—
784	Q₈	—	2	8	no	—
785	Q₈	—	2	8	no	—
786	Q₈	—	2	4	no	—
787	Q₈	—	2	4	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	4	2	no	—
790	Q₈	—	8	2	no	—
791	Q₈	C₂×#41×C₆₇	1	8	yes	—
792	D₄	—	2	2	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	2	no	—
795	D₄	—	8	1	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	2	8	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	8	2	no	—
819	C₂×C₄	—	8	1	no	—
820	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
821	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
827	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
828	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
829	C₈	—	2	2	no	—
830	C₈	—	2	2	no	—
831	C₈	—	2	4	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	4	4	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	#525×C₆₇	1	2	yes	—
844	C₂²	#578×C₆₇	1	2	yes	—
845	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
846	C₄	—	2	2	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	8	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	2	no	—
860	C₄	#525×C₆₇	1	2	yes	—
861	C₄	C₂²×#41×C₆₇	1	2	yes	—
862	C₂	—	2	2	no	—
863	C₂	—	2	2	no	—
864	C₂	—	4	1	no	—
865	C₂	—	8	1	no	—
866	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
867	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
868	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	#525×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#519×C₆₇	C₂	semidirect
3. C₆₇×#3127	C₂	semidirect
4. C₆₇×#3121	C₂	semidirect
5. C₆₇×#3117	C₂	semidirect
6. C₆₇×#3113	C₂	semidirect
7. C₆₇×#3108	C₂	semidirect
8. C₆₇×#3104	C₂	semidirect
9. C₆₇×#3095	C₂	semidirect
11. C₆₇×#3082	C₂	semidirect
12. C₆₇×#3044	C₂	semidirect
14. C₂×#451×C₆₇	C₂	semidirect
15. C₆₇×#2950	C₂	semidirect
16. C₆₇×#2947	C₂	semidirect
17. C₆₇×#2924	C₂	semidirect
59. #479×C₆₇	C₂²	semidirect
60. #479×C₆₇	C₂²	semidirect
61. #477×C₆₇	C₂²	semidirect
62. #475×C₆₇	C₂²	semidirect
63. #464×C₆₇	C₂²	semidirect
64. #464×C₆₇	C₂²	semidirect
65. #462×C₆₇	C₂²	semidirect
66. #462×C₆₇	C₂²	semidirect
74. #441×C₆₇	C₂²	semidirect
75. #441×C₆₇	C₂²	semidirect
76. #441×C₆₇	C₂²	semidirect
77. #440×C₆₇	C₂²	semidirect
78. C₄×Q₁₆×C₆₇	C₂²	semidirect
79. C₄×Q₁₆×C₆₇	C₂²	semidirect
80. C₄×Q₁₆×C₆₇	C₂²	semidirect
81. C₄×SD₁₆×C₆₇	C₂²	semidirect
427. #60583	C₆₇	direct (N × H)
436. C₂×#519	C₂×C₆₇	semidirect
437. #3127	C₂×C₆₇	semidirect
438. #3121	C₂×C₆₇	semidirect
439. #3117	C₂×C₆₇	semidirect
440. #3113	C₂×C₆₇	semidirect
441. #3108	C₂×C₆₇	semidirect
442. #3104	C₂×C₆₇	semidirect
443. #3095	C₂×C₆₇	semidirect
445. #3082	C₂×C₆₇	semidirect
446. #3044	C₂×C₆₇	semidirect
448. C₂×#451	C₂×C₆₇	semidirect
449. #2950	C₂×C₆₇	semidirect
450. #2947	C₂×C₆₇	semidirect
451. #2924	C₂×C₆₇	semidirect
452. C₆₇	#60583	direct (N × H)
494. #479	C₂²×C₆₇	semidirect
495. #479	C₂²×C₆₇	semidirect
496. #477	C₂²×C₆₇	semidirect
497. #475	C₂²×C₆₇	semidirect
498. #464	C₂²×C₆₇	semidirect
499. #464	C₂²×C₆₇	semidirect
500. #462	C₂²×C₆₇	semidirect
501. #462	C₂²×C₆₇	semidirect
509. #441	C₂²×C₆₇	semidirect
510. #441	C₂²×C₆₇	semidirect
511. #441	C₂²×C₆₇	semidirect
512. #440	C₂²×C₆₇	semidirect
513. C₄×Q₁₆	C₂²×C₆₇	semidirect
514. C₄×Q₁₆	C₂²×C₆₇	semidirect
515. C₄×Q₁₆	C₂²×C₆₇	semidirect
516. C₄×SD₁₆	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×#3495	2
C₂×#519×C₆₇	2
C₆₇×#3127	2
C₆₇×#3121	2
C₆₇×#3117	2
C₆₇×#3113	2
C₆₇×#3108	2
C₆₇×#3104	2
C₆₇×#3095	2
C₆₇×#3091	2
C₆₇×#3082	2
C₆₇×#3044	2
C₆₇×#3004	2
C₂×#451×C₆₇	2
C₆₇×#2950	2
C₆₇×#2947	2
C₆₇×#2924	2
#60583	67

Subgroups — C67×#60583 #30739834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60583 #30739834