Subgroups — C₆₇×#60567 #30739818

Order 17152.

2074 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3125	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3124	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3121	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3118	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3095	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3079	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3040	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3006	C₂	1	1	yes	maximal, characteristic
13	C₄×#137×C₆₇	C₂	1	2	yes	maximal, complemented
14	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2921	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×#137×C₆₇	C₂²	1	2	yes	—
18	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
19	#542×C₆₇	—	2	2	no	—
20	#542×C₆₇	—	2	2	no	—
21	#542×C₆₇	C₂²	1	4	yes	—
22	#542×C₆₇	C₂²	1	4	yes	complemented
23	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	C₂×#126×C₆₇	—	2	1	no	—
25	C₂×#124×C₆₇	—	2	1	no	—
26	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#123×C₆₇	—	2	1	no	—
28	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
31	#520×C₆₇	—	2	1	no	—
32	#520×C₆₇	—	2	1	no	—
33	#520×C₆₇	C₂²	1	2	yes	complemented
34	#520×C₆₇	C₂²	1	2	yes	complemented
35	#519×C₆₇	C₂²	1	2	yes	complemented
36	#518×C₆₇	—	2	1	no	—
37	#518×C₆₇	—	2	1	no	—
38	#518×C₆₇	C₂²	1	2	yes	complemented
39	C₄×#41×C₆₇	—	2	2	no	—
40	C₄×#41×C₆₇	C₂²	1	2	yes	—
41	C₄×#41×C₆₇	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂×#117×C₆₇	—	2	2	no	—
45	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
47	#485×C₆₇	C₂²	1	4	yes	complemented
48	#484×C₆₇	C₂²	1	2	yes	complemented
49	#483×C₆₇	C₂²	1	2	yes	complemented
50	#482×C₆₇	C₂²	1	4	yes	—
51	#481×C₆₇	C₂²	1	2	yes	complemented
52	#480×C₆₇	C₂²	1	2	yes	complemented
53	#477×C₆₇	C₂²	1	4	yes	complemented
54	#476×C₆₇	C₂²	1	4	yes	complemented
55	#475×C₆₇	C₂²	1	4	yes	complemented
56	#474×C₆₇	C₂²	1	4	yes	complemented
57	#464×C₆₇	C₂²	1	4	yes	complemented
58	#464×C₆₇	C₂²	1	4	yes	complemented
59	#463×C₆₇	C₂²	1	4	yes	complemented
60	#463×C₆₇	C₂²	1	4	yes	complemented
61	#452×C₆₇	C₂²	1	4	yes	complemented
62	#451×C₆₇	C₂²	1	2	yes	complemented
63	#450×C₆₇	C₂²	1	2	yes	complemented
64	#449×C₆₇	C₂²	1	4	yes	—
65	#448×C₆₇	C₂²	1	2	yes	—
66	#447×C₆₇	C₂²	1	2	yes	—
67	#442×C₆₇	C₂²	1	4	yes	complemented
68	#441×C₆₇	C₂²	1	4	yes	complemented
69	#440×C₆₇	C₂²	1	4	yes	complemented
70	#440×C₆₇	C₂²	1	4	yes	complemented
71	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	complemented
72	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
73	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
74	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
75	#433×C₆₇	C₂²	1	4	yes	complemented
76	#433×C₆₇	C₂²	1	4	yes	complemented
77	#428×C₆₇	C₂²	1	2	yes	complemented
78	#428×C₆₇	C₂²	1	2	yes	complemented
79	#423×C₆₇	C₂²	1	2	yes	complemented
80	#419×C₆₇	C₂²	1	2	yes	complemented
81	#418×C₆₇	C₂²	1	2	yes	complemented
82	#417×C₆₇	C₂²	1	2	yes	—
83	#417×C₆₇	C₂²	1	2	yes	—
84	#407×C₆₇	C₂²	1	1	yes	characteristic
85	#407×C₆₇	C₂²	1	1	yes	characteristic
86	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
87	C₂×#41×C₆₇	—	2	8	no	—
88	C₂×#41×C₆₇	—	2	1	no	—
89	C₂×#41×C₆₇	—	2	1	no	—
90	C₂×#41×C₆₇	C₂³	1	2	yes	—
91	C₂×#41×C₆₇	C₂³	1	2	yes	—
92	C₂²×Q₈×C₆₇	—	2	1	no	—
93	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₆₇	—	2	1	no	—
96	C₂²×D₄×C₆₇	—	2	1	no	—
97	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₆₇	—	2	1	no	—
100	C₂³×C₄×C₆₇	—	2	1	no	—
101	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
102	#137×C₆₇	—	2	8	no	—
103	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
104	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
107	C₂×D₈×C₆₇	C₂³	1	4	yes	—
108	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
109	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
110	C₄⋊Q₈×C₆₇	—	2	2	no	—
111	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
112	#126×C₆₇	—	2	4	no	—
113	#126×C₆₇	—	2	4	no	—
114	#124×C₆₇	—	2	4	no	—
115	#124×C₆₇	—	2	4	no	—
116	#124×C₆₇	—	2	2	no	—
117	#124×C₆₇	C₂³	1	4	yes	—
118	#123×C₆₇	—	2	4	no	—
119	#123×C₆₇	—	2	4	no	—
120	C₂²⋊Q₈×C₆₇	—	2	1	no	—
121	C₂²⋊Q₈×C₆₇	—	2	1	no	—
122	C₂²⋊Q₈×C₆₇	—	2	4	no	—
123	C₂²⋊Q₈×C₆₇	—	2	4	no	—
124	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
125	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
126	#121×C₆₇	—	2	1	no	—
127	#121×C₆₇	—	2	1	no	—
128	#121×C₆₇	C₂³	1	2	yes	—
129	#121×C₆₇	C₂³	1	2	yes	—
130	C₄×Q₈×C₆₇	—	2	2	no	—
131	C₄×Q₈×C₆₇	—	2	2	no	—
132	C₄×Q₈×C₆₇	—	2	2	no	—
133	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
134	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
135	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
136	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
137	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
138	C₄×D₄×C₆₇	—	2	2	no	—
139	C₄×D₄×C₆₇	—	2	2	no	—
140	C₄×D₄×C₆₇	—	2	2	no	—
141	C₄×D₄×C₆₇	—	2	2	no	—
142	C₄×D₄×C₆₇	—	2	2	no	—
143	C₄×D₄×C₆₇	—	2	2	no	—
144	C₄×D₄×C₆₇	—	2	2	no	—
145	C₄×D₄×C₆₇	—	2	2	no	—
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	C₂³	1	2	yes	—
150	C₄×D₄×C₆₇	C₂³	1	2	yes	—
151	C₄×D₄×C₆₇	C₂³	1	4	yes	—
152	C₄×D₄×C₆₇	C₂³	1	2	yes	—
153	C₄×D₄×C₆₇	C₂³	1	2	yes	—
154	#117×C₆₇	—	2	1	no	—
155	#117×C₆₇	—	2	1	no	—
156	#117×C₆₇	—	2	2	no	—
157	#117×C₆₇	—	2	2	no	—
158	#117×C₆₇	—	2	2	no	—
159	#117×C₆₇	—	2	2	no	—
160	#117×C₆₇	—	2	2	no	—
161	#117×C₆₇	—	2	2	no	—
162	#117×C₆₇	D₄	1	2	yes	—
163	#117×C₆₇	D₄	1	2	yes	—
164	#117×C₆₇	C₂³	1	2	yes	—
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	1	no	—
170	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
171	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
172	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
173	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	D₄	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	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
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	—	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	—	2	1	no	—
191	C₂×C₄²×C₆₇	—	2	2	no	—
192	C₂×C₄²×C₆₇	—	2	2	no	—
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
195	#107×C₆₇	C₂³	1	4	yes	—
196	#107×C₆₇	C₂³	1	4	yes	—
197	#106×C₆₇	C₂³	1	4	yes	—
198	#106×C₆₇	C₂³	1	4	yes	—
199	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
200	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
201	#103×C₆₇	C₂³	1	4	yes	—
202	#103×C₆₇	C₂³	1	4	yes	—
203	#103×C₆₇	C₂³	1	4	yes	—
204	#103×C₆₇	C₂³	1	4	yes	—
205	#102×C₆₇	C₂³	1	4	yes	—
206	#102×C₆₇	C₂³	1	4	yes	—
207	#102×C₆₇	C₂³	1	4	yes	—
208	#102×C₆₇	C₂³	1	4	yes	—
209	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
210	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
211	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
213	#97×C₆₇	C₂³	1	4	yes	—
214	C₄×C₈×C₆₇	C₂³	1	4	yes	—
215	C₂⁴×C₆₇	—	2	1	no	—
216	C₂⁴×C₆₇	—	2	1	no	—
217	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
218	#41×C₆₇	—	2	8	no	—
219	#41×C₆₇	—	2	8	no	—
220	#41×C₆₇	—	2	4	no	—
221	#41×C₆₇	—	2	4	no	—
222	#41×C₆₇	—	2	4	no	—
223	#41×C₆₇	#41	1	8	yes	—
224	C₂×Q₈×C₆₇	—	2	4	no	—
225	C₂×Q₈×C₆₇	—	2	1	no	—
226	C₂×Q₈×C₆₇	—	2	1	no	—
227	C₂×Q₈×C₆₇	—	2	4	no	—
228	C₂×Q₈×C₆₇	—	2	4	no	—
229	C₂×Q₈×C₆₇	—	8	2	no	—
230	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
231	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
232	C₂×D₄×C₆₇	—	2	8	no	—
233	C₂×D₄×C₆₇	—	2	2	no	—
234	C₂×D₄×C₆₇	—	2	2	no	—
235	C₂×D₄×C₆₇	—	2	4	no	—
236	C₂×D₄×C₆₇	—	2	2	no	—
237	C₂×D₄×C₆₇	—	2	2	no	—
238	C₂×D₄×C₆₇	—	2	1	no	—
239	C₂×D₄×C₆₇	—	2	1	no	—
240	C₂×D₄×C₆₇	—	2	4	no	—
241	C₂×D₄×C₆₇	—	8	2	no	—
242	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
243	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₆₇	—	2	8	no	—
245	C₂²×C₄×C₆₇	—	2	1	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	—	2	1	no	—
250	C₂²×C₄×C₆₇	—	2	1	no	—
251	C₂²×C₄×C₆₇	—	2	1	no	—
252	C₂²×C₄×C₆₇	—	2	1	no	—
253	C₂²×C₄×C₆₇	—	2	1	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	2	no	—
258	C₂²×C₄×C₆₇	—	2	4	no	—
259	C₂²×C₄×C₆₇	—	8	2	no	—
260	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	Q₁₆×C₆₇	—	2	8	no	—
271	SD₁₆×C₆₇	—	2	8	no	—
272	SD₁₆×C₆₇	—	2	8	no	—
273	D₈×C₆₇	—	2	8	no	—
274	M₁₆×C₆₇	—	2	4	no	—
275	M₁₆×C₆₇	—	2	4	no	—
276	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
277	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
278	C₄⋊C₄×C₆₇	—	2	1	no	—
279	C₄⋊C₄×C₆₇	—	2	1	no	—
280	C₄⋊C₄×C₆₇	—	2	2	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	4	no	—
285	C₄⋊C₄×C₆₇	—	2	2	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	4	no	—
288	C₄⋊C₄×C₆₇	—	2	1	no	—
289	C₄⋊C₄×C₆₇	—	2	1	no	—
290	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
291	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
292	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
293	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
295	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
296	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
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	—	2	2	no	—
305	C₂²⋊C₄×C₆₇	—	2	2	no	—
306	C₂²⋊C₄×C₆₇	—	2	4	no	—
307	C₂²⋊C₄×C₆₇	—	2	2	no	—
308	C₂²⋊C₄×C₆₇	—	2	2	no	—
309	C₂²⋊C₄×C₆₇	—	2	4	no	—
310	C₂²⋊C₄×C₆₇	—	2	4	no	—
311	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
312	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
313	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
314	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
315	C₄²×C₆₇	—	2	2	no	—
316	C₄²×C₆₇	—	2	2	no	—
317	C₄²×C₆₇	—	2	2	no	—
318	C₄²×C₆₇	—	2	2	no	—
319	C₄²×C₆₇	—	2	2	no	—
320	C₄²×C₆₇	—	2	2	no	—
321	C₄²×C₆₇	—	2	4	no	—
322	C₄²×C₆₇	C₂×D₄	1	2	yes	—
323	C₄²×C₆₇	C₂×D₄	1	2	yes	—
324	C₄²×C₆₇	C₂⁴	1	2	yes	—
325	C₄²×C₆₇	C₂⁴	1	2	yes	—
326	C₂³×C₆₇	—	2	4	no	—
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	—	2	2	no	—
329	C₂³×C₆₇	—	2	2	no	—
330	C₂³×C₆₇	—	4	1	no	—
331	C₂³×C₆₇	—	4	1	no	—
332	C₂³×C₆₇	—	4	2	no	—
333	C₂³×C₆₇	—	4	2	no	—
334	C₂³×C₆₇	—	4	2	no	—
335	C₂³×C₆₇	—	8	1	no	—
336	C₂³×C₆₇	—	8	1	no	—
337	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
338	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
339	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₆₇	—	2	4	no	—
341	Q₈×C₆₇	—	2	2	no	—
342	Q₈×C₆₇	—	2	4	no	—
343	Q₈×C₆₇	—	4	2	no	—
344	Q₈×C₆₇	—	8	4	no	—
345	Q₈×C₆₇	C₂×#41	1	4	yes	—
346	D₄×C₆₇	—	2	8	no	—
347	D₄×C₆₇	—	2	4	no	—
348	D₄×C₆₇	—	2	8	no	—
349	D₄×C₆₇	—	2	2	no	—
350	D₄×C₆₇	—	2	4	no	—
351	D₄×C₆₇	—	4	2	no	—
352	D₄×C₆₇	—	8	2	no	—
353	D₄×C₆₇	—	8	2	no	—
354	D₄×C₆₇	C₂×#41	1	4	yes	—
355	C₂×C₄×C₆₇	—	2	4	no	—
356	C₂×C₄×C₆₇	—	2	8	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	8	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	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	—	4	1	no	—
370	C₂×C₄×C₆₇	—	4	1	no	—
371	C₂×C₄×C₆₇	—	4	1	no	—
372	C₂×C₄×C₆₇	—	4	1	no	—
373	C₂×C₄×C₆₇	—	4	2	no	—
374	C₂×C₄×C₆₇	—	4	2	no	—
375	C₂×C₄×C₆₇	—	4	2	no	—
376	C₂×C₄×C₆₇	—	8	2	no	—
377	C₂×C₄×C₆₇	—	8	2	no	—
378	C₂×C₄×C₆₇	—	8	2	no	—
379	C₂×C₄×C₆₇	—	8	2	no	—
380	C₂×C₄×C₆₇	—	8	4	no	—
381	C₂×C₄×C₆₇	—	8	1	no	—
382	C₂×C₄×C₆₇	—	8	1	no	—
383	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
389	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
391	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
392	C₈×C₆₇	—	2	4	no	—
393	C₈×C₆₇	—	2	4	no	—
394	C₂²×C₆₇	—	2	1	no	—
395	C₂²×C₆₇	—	2	1	no	—
396	C₂²×C₆₇	—	2	1	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	4	no	—
403	C₂²×C₆₇	—	4	2	no	—
404	C₂²×C₆₇	—	4	2	no	—
405	C₂²×C₆₇	—	4	2	no	—
406	C₂²×C₆₇	—	4	2	no	—
407	C₂²×C₆₇	—	4	2	no	—
408	C₂²×C₆₇	—	8	2	no	—
409	C₂²×C₆₇	—	8	4	no	—
410	C₂²×C₆₇	—	8	4	no	—
411	C₂²×C₆₇	#525	1	2	yes	—
412	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
413	C₄×C₆₇	—	2	2	no	—
414	C₄×C₆₇	—	2	2	no	—
415	C₄×C₆₇	—	2	2	no	—
416	C₄×C₆₇	—	2	2	no	—
417	C₄×C₆₇	—	2	1	no	—
418	C₄×C₆₇	—	2	4	no	—
419	C₄×C₆₇	—	2	1	no	—
420	C₄×C₆₇	—	4	2	no	—
421	C₄×C₆₇	—	4	2	no	—
422	C₄×C₆₇	—	4	2	no	—
423	C₄×C₆₇	—	4	2	no	—
424	C₄×C₆₇	—	4	2	no	—
425	C₄×C₆₇	#525	1	2	yes	—
426	C₄×C₆₇	C₂²×#41	1	2	yes	—
427	#60567	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
428	C₂×C₆₇	—	2	2	no	—
429	C₂×C₆₇	—	4	1	no	—
430	C₂×C₆₇	—	4	1	no	—
431	C₂×C₆₇	—	4	4	no	—
432	C₂×C₆₇	—	8	2	no	—
433	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
434	C₂×C₆₇	#3585	1	1	yes	characteristic
435	C₂×C₆₇	#3586	1	1	yes	characteristic
436	C₂×#542	C₂×C₆₇	1	1	yes	characteristic, complemented
437	#3428	C₂×C₆₇	1	1	yes	characteristic, complemented
438	#3125	C₂×C₆₇	1	4	yes	complemented
439	#3124	C₂×C₆₇	1	4	yes	complemented
440	#3121	C₂×C₆₇	1	4	yes	complemented
441	#3118	C₂×C₆₇	1	4	yes	complemented
442	#3095	C₂×C₆₇	1	1	yes	characteristic, complemented
443	#3094	C₂×C₆₇	1	1	yes	characteristic, complemented
444	#3079	C₂×C₆₇	1	2	yes	complemented
445	#3040	C₂×C₆₇	1	2	yes	complemented
446	#3007	C₂×C₆₇	1	1	yes	characteristic, complemented
447	#3006	C₂×C₆₇	1	1	yes	characteristic
448	C₄×#137	C₂×C₆₇	1	2	yes	complemented
449	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	2	yes	complemented
450	#2921	C₂×C₆₇	1	1	yes	characteristic, complemented
451	C₆₇	#60567	1	1	yes	characteristic, direct product factor, Sylow
452	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
453	C₂×#137	C₂²×C₆₇	1	2	yes	—
454	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
455	#542	—	2	2	no	—
456	#542	—	2	2	no	—
457	#542	C₂²×C₆₇	1	4	yes	—
458	#542	C₂²×C₆₇	1	4	yes	complemented
459	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
460	C₂×#126	—	2	1	no	—
461	C₂×#124	—	2	1	no	—
462	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
463	C₂×#123	—	2	1	no	—
464	C₂×C₂²⋊Q₈	—	2	1	no	—
465	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
466	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
467	#520	—	2	1	no	—
468	#520	—	2	1	no	—
469	#520	C₂²×C₆₇	1	2	yes	complemented
470	#520	C₂²×C₆₇	1	2	yes	complemented
471	#519	C₂²×C₆₇	1	2	yes	complemented
472	#518	—	2	1	no	—
473	#518	—	2	1	no	—
474	#518	C₂²×C₆₇	1	2	yes	complemented
475	C₄×#41	—	2	2	no	—
476	C₄×#41	C₂²×C₆₇	1	2	yes	—
477	C₄×#41	C₂²×C₆₇	1	2	yes	—
478	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
479	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
480	C₂×#117	—	2	2	no	—
481	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
482	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
483	#485	C₂²×C₆₇	1	4	yes	complemented
484	#484	C₂²×C₆₇	1	2	yes	complemented
485	#483	C₂²×C₆₇	1	2	yes	complemented
486	#482	C₂²×C₆₇	1	4	yes	—
487	#481	C₂²×C₆₇	1	2	yes	complemented
488	#480	C₂²×C₆₇	1	2	yes	complemented
489	#477	C₂²×C₆₇	1	4	yes	complemented
490	#476	C₂²×C₆₇	1	4	yes	complemented
491	#475	C₂²×C₆₇	1	4	yes	complemented
492	#474	C₂²×C₆₇	1	4	yes	complemented
493	#464	C₂²×C₆₇	1	4	yes	complemented
494	#464	C₂²×C₆₇	1	4	yes	complemented
495	#463	C₂²×C₆₇	1	4	yes	complemented
496	#463	C₂²×C₆₇	1	4	yes	complemented
497	#452	C₂²×C₆₇	1	4	yes	complemented
498	#451	C₂²×C₆₇	1	2	yes	complemented
499	#450	C₂²×C₆₇	1	2	yes	complemented
500	#449	C₂²×C₆₇	1	4	yes	—
501	#448	C₂²×C₆₇	1	2	yes	—
502	#447	C₂²×C₆₇	1	2	yes	—
503	#442	C₂²×C₆₇	1	4	yes	complemented
504	#441	C₂²×C₆₇	1	4	yes	complemented
505	#440	C₂²×C₆₇	1	4	yes	complemented
506	#440	C₂²×C₆₇	1	4	yes	complemented
507	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	complemented
508	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
509	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
510	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
511	#433	C₂²×C₆₇	1	4	yes	complemented
512	#433	C₂²×C₆₇	1	4	yes	complemented
513	#428	C₂²×C₆₇	1	2	yes	complemented
514	#428	C₂²×C₆₇	1	2	yes	complemented
515	#423	C₂²×C₆₇	1	2	yes	complemented
516	#419	C₂²×C₆₇	1	2	yes	complemented
517	#418	C₂²×C₆₇	1	2	yes	complemented
518	#417	C₂²×C₆₇	1	2	yes	—
519	#417	C₂²×C₆₇	1	2	yes	—
520	#407	C₂²×C₆₇	1	1	yes	characteristic
521	#407	C₂²×C₆₇	1	1	yes	characteristic
522	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
523	C₂×#41	—	2	8	no	—
524	C₂×#41	—	2	1	no	—
525	C₂×#41	—	2	1	no	—
526	C₂×#41	C₂³×C₆₇	1	2	yes	—
527	C₂×#41	C₂³×C₆₇	1	2	yes	—
528	C₂²×Q₈	—	2	1	no	—
529	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
530	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	—	2	1	no	—
533	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
534	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
535	C₂³×C₄	—	2	1	no	—
536	C₂³×C₄	—	2	1	no	—
537	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
538	#137	—	2	8	no	—
539	AGL(1,ℤ/8)	—	2	8	no	—
540	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
541	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
542	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
543	C₂×D₈	C₂³×C₆₇	1	4	yes	—
544	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
545	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
546	C₄⋊Q₈	—	2	2	no	—
547	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
548	#126	—	2	4	no	—
549	#126	—	2	4	no	—
550	#124	—	2	4	no	—
551	#124	—	2	4	no	—
552	#124	—	2	2	no	—
553	#124	C₂³×C₆₇	1	4	yes	—
554	#123	—	2	4	no	—
555	#123	—	2	4	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	—	2	4	no	—
559	C₂²⋊Q₈	—	2	4	no	—
560	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
561	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
562	#121	—	2	1	no	—
563	#121	—	2	1	no	—
564	#121	C₂³×C₆₇	1	2	yes	—
565	#121	C₂³×C₆₇	1	2	yes	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×Q₈	—	2	2	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
570	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
571	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
572	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
573	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	C₂³×C₆₇	1	4	yes	—
586	C₄×D₄	C₂³×C₆₇	1	2	yes	—
587	C₄×D₄	C₂³×C₆₇	1	2	yes	—
588	C₄×D₄	C₂³×C₆₇	1	2	yes	—
589	C₄×D₄	C₂³×C₆₇	1	2	yes	—
590	#117	—	2	1	no	—
591	#117	—	2	1	no	—
592	#117	—	2	2	no	—
593	#117	—	2	2	no	—
594	#117	—	2	2	no	—
595	#117	—	2	2	no	—
596	#117	—	2	2	no	—
597	#117	—	2	2	no	—
598	#117	D₄×C₆₇	1	2	yes	—
599	#117	D₄×C₆₇	1	2	yes	—
600	#117	C₂³×C₆₇	1	2	yes	—
601	#117	C₂³×C₆₇	1	2	yes	—
602	#117	C₂³×C₆₇	1	2	yes	—
603	#117	C₂³×C₆₇	1	2	yes	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	—	2	2	no	—
609	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
610	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	2	no	—
622	C₂×C₂²⋊C₄	—	2	2	no	—
623	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
625	C₂×C₄²	—	2	1	no	—
626	C₂×C₄²	—	2	1	no	—
627	C₂×C₄²	—	2	2	no	—
628	C₂×C₄²	—	2	2	no	—
629	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
631	#107	C₂³×C₆₇	1	4	yes	—
632	#107	C₂³×C₆₇	1	4	yes	—
633	#106	C₂³×C₆₇	1	4	yes	—
634	#106	C₂³×C₆₇	1	4	yes	—
635	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
636	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
637	#103	C₂³×C₆₇	1	4	yes	—
638	#103	C₂³×C₆₇	1	4	yes	—
639	#103	C₂³×C₆₇	1	4	yes	—
640	#103	C₂³×C₆₇	1	4	yes	—
641	#102	C₂³×C₆₇	1	4	yes	—
642	#102	C₂³×C₆₇	1	4	yes	—
643	#102	C₂³×C₆₇	1	4	yes	—
644	#102	C₂³×C₆₇	1	4	yes	—
645	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
646	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
647	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
648	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
649	#97	C₂³×C₆₇	1	4	yes	—
650	C₄×C₈	C₂³×C₆₇	1	4	yes	—
651	C₂⁴	—	2	1	no	—
652	C₂⁴	—	2	1	no	—
653	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
654	#41	—	2	8	no	—
655	#41	—	2	8	no	—
656	#41	—	2	4	no	—
657	#41	—	2	4	no	—
658	#41	—	2	4	no	—
659	#41	#41×C₆₇	1	8	yes	—
660	C₂×Q₈	—	2	4	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	4	no	—
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	8	2	no	—
666	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
667	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
668	C₂×D₄	—	2	8	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	8	2	no	—
678	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
679	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
680	C₂²×C₄	—	2	8	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	8	2	no	—
696	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
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	C₂⁴×C₆₇	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
706	Q₁₆	—	2	8	no	—
707	SD₁₆	—	2	8	no	—
708	SD₁₆	—	2	8	no	—
709	D₈	—	2	8	no	—
710	M₁₆	—	2	4	no	—
711	M₁₆	—	2	4	no	—
712	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
713	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
727	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
728	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
729	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
732	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
748	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
749	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
750	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	4	no	—
758	C₄²	C₂×D₄×C₆₇	1	2	yes	—
759	C₄²	C₂×D₄×C₆₇	1	2	yes	—
760	C₄²	C₂⁴×C₆₇	1	2	yes	—
761	C₄²	C₂⁴×C₆₇	1	2	yes	—
762	C₂³	—	2	4	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	4	1	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	2	no	—
769	C₂³	—	4	2	no	—
770	C₂³	—	4	2	no	—
771	C₂³	—	8	1	no	—
772	C₂³	—	8	1	no	—
773	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
774	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
775	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
776	Q₈	—	2	4	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	2	4	no	—
779	Q₈	—	4	2	no	—
780	Q₈	—	8	4	no	—
781	Q₈	C₂×#41×C₆₇	1	4	yes	—
782	D₄	—	2	8	no	—
783	D₄	—	2	4	no	—
784	D₄	—	2	8	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	4	no	—
787	D₄	—	4	2	no	—
788	D₄	—	8	2	no	—
789	D₄	—	8	2	no	—
790	D₄	C₂×#41×C₆₇	1	4	yes	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	8	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	8	4	no	—
813	C₂×C₄	—	8	2	no	—
814	C₂×C₄	—	8	2	no	—
815	C₂×C₄	—	8	2	no	—
816	C₂×C₄	—	8	2	no	—
817	C₂×C₄	—	8	1	no	—
818	C₂×C₄	—	8	1	no	—
819	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
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	C₂×#41×C₆₇	1	4	yes	—
827	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
828	C₈	—	2	4	no	—
829	C₈	—	2	4	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	2	1	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	4	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	8	2	no	—
845	C₂²	—	8	4	no	—
846	C₂²	—	8	4	no	—
847	C₂²	#525×C₆₇	1	2	yes	—
848	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	1	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	#525×C₆₇	1	2	yes	—
862	C₄	C₂²×#41×C₆₇	1	2	yes	—
863	C₂	—	2	2	no	—
864	C₂	—	4	1	no	—
865	C₂	—	4	1	no	—
866	C₂	—	4	4	no	—
867	C₂	—	8	2	no	—
868	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
869	C₂	C₆₇×#3585	1	1	yes	characteristic
870	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×#3006	C₂
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
1. C₂×#542×C₆₇	C₂	semidirect
2. C₆₇×#3428	C₂	semidirect
3. C₆₇×#3125	C₂	semidirect
4. C₆₇×#3124	C₂	semidirect
5. C₆₇×#3121	C₂	semidirect
6. C₆₇×#3118	C₂	semidirect
7. C₆₇×#3095	C₂	semidirect
8. C₆₇×#3094	C₂	semidirect
9. C₆₇×#3079	C₂	semidirect
10. C₆₇×#3040	C₂	semidirect
11. C₆₇×#3007	C₂	semidirect
13. C₄×#137×C₆₇	C₂	semidirect
14. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
15. C₆₇×#2921	C₂	semidirect
22. #542×C₆₇	C₂²	semidirect
23. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
26. C₂×#124×C₆₇	C₂²	semidirect
33. #520×C₆₇	C₂²	semidirect
34. #520×C₆₇	C₂²	semidirect
35. #519×C₆₇	C₂²	semidirect
38. #518×C₆₇	C₂²	semidirect
42. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
43. C₂×C₄×D₄×C₆₇	C₂²	semidirect
47. #485×C₆₇	C₂²	semidirect
48. #484×C₆₇	C₂²	semidirect
49. #483×C₆₇	C₂²	semidirect
51. #481×C₆₇	C₂²	semidirect
52. #480×C₆₇	C₂²	semidirect
53. #477×C₆₇	C₂²	semidirect
54. #476×C₆₇	C₂²	semidirect
55. #475×C₆₇	C₂²	semidirect
56. #474×C₆₇	C₂²	semidirect
57. #464×C₆₇	C₂²	semidirect
58. #464×C₆₇	C₂²	semidirect
59. #463×C₆₇	C₂²	semidirect
60. #463×C₆₇	C₂²	semidirect
61. #452×C₆₇	C₂²	semidirect
62. #451×C₆₇	C₂²	semidirect
63. #450×C₆₇	C₂²	semidirect
67. #442×C₆₇	C₂²	semidirect
68. #441×C₆₇	C₂²	semidirect
69. #440×C₆₇	C₂²	semidirect
70. #440×C₆₇	C₂²	semidirect
71. C₄×Q₁₆×C₆₇	C₂²	semidirect
72. C₄×SD₁₆×C₆₇	C₂²	semidirect
73. C₄×SD₁₆×C₆₇	C₂²	semidirect
74. C₄×D₈×C₆₇	C₂²	semidirect
75. #433×C₆₇	C₂²	semidirect
76. #433×C₆₇	C₂²	semidirect
77. #428×C₆₇	C₂²	semidirect
78. #428×C₆₇	C₂²	semidirect
79. #423×C₆₇	C₂²	semidirect
80. #419×C₆₇	C₂²	semidirect
81. #418×C₆₇	C₂²	semidirect
86. C₄×M₁₆×C₆₇	C₂²	semidirect
427. #60567	C₆₇	direct (N × H)
436. C₂×#542	C₂×C₆₇	semidirect
437. #3428	C₂×C₆₇	semidirect
438. #3125	C₂×C₆₇	semidirect
439. #3124	C₂×C₆₇	semidirect
440. #3121	C₂×C₆₇	semidirect
441. #3118	C₂×C₆₇	semidirect
442. #3095	C₂×C₆₇	semidirect
443. #3094	C₂×C₆₇	semidirect
444. #3079	C₂×C₆₇	semidirect
445. #3040	C₂×C₆₇	semidirect
446. #3007	C₂×C₆₇	semidirect
448. C₄×#137	C₂×C₆₇	semidirect
449. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
450. #2921	C₂×C₆₇	semidirect
451. C₆₇	#60567	direct (N × H)
458. #542	C₂²×C₆₇	semidirect
459. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
462. C₂×#124	C₂²×C₆₇	semidirect
469. #520	C₂²×C₆₇	semidirect
470. #520	C₂²×C₆₇	semidirect
471. #519	C₂²×C₆₇	semidirect
474. #518	C₂²×C₆₇	semidirect
478. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
479. C₂×C₄×D₄	C₂²×C₆₇	semidirect
483. #485	C₂²×C₆₇	semidirect
484. #484	C₂²×C₆₇	semidirect
485. #483	C₂²×C₆₇	semidirect
487. #481	C₂²×C₆₇	semidirect
488. #480	C₂²×C₆₇	semidirect
489. #477	C₂²×C₆₇	semidirect
490. #476	C₂²×C₆₇	semidirect
491. #475	C₂²×C₆₇	semidirect
492. #474	C₂²×C₆₇	semidirect
493. #464	C₂²×C₆₇	semidirect
494. #464	C₂²×C₆₇	semidirect
495. #463	C₂²×C₆₇	semidirect
496. #463	C₂²×C₆₇	semidirect
497. #452	C₂²×C₆₇	semidirect
498. #451	C₂²×C₆₇	semidirect
499. #450	C₂²×C₆₇	semidirect
503. #442	C₂²×C₆₇	semidirect
504. #441	C₂²×C₆₇	semidirect
505. #440	C₂²×C₆₇	semidirect
506. #440	C₂²×C₆₇	semidirect
507. C₄×Q₁₆	C₂²×C₆₇	semidirect
508. C₄×SD₁₆	C₂²×C₆₇	semidirect
509. C₄×SD₁₆	C₂²×C₆₇	semidirect
510. C₄×D₈	C₂²×C₆₇	semidirect
511. #433	C₂²×C₆₇	semidirect
512. #433	C₂²×C₆₇	semidirect
513. #428	C₂²×C₆₇	semidirect
514. #428	C₂²×C₆₇	semidirect
515. #423	C₂²×C₆₇	semidirect
516. #419	C₂²×C₆₇	semidirect
517. #418	C₂²×C₆₇	semidirect
522. C₄×M₁₆	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#542×C₆₇	2
C₆₇×#3428	2
C₆₇×#3125	2
C₆₇×#3124	2
C₆₇×#3121	2
C₆₇×#3118	2
C₆₇×#3095	2
C₆₇×#3094	2
C₆₇×#3079	2
C₆₇×#3040	2
C₆₇×#3007	2
C₆₇×#3006	2
C₄×#137×C₆₇	2
C₄×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#2921	2
#60567	67

Subgroups — C67×#60567 #30739818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60567 #30739818