Subgroups — C₆₇×#61058 #30740309

Order 17152.

2890 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#576×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3485	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3273	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3272	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3267	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3264	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3154	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3057	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3042	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3041	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3009	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3005	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3003	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2948	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	#576×C₆₇	—	2	8	no	—
25	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
27	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
29	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
30	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
33	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
34	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
36	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
41	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#547×C₆₇	—	2	2	no	—
44	#547×C₆₇	C₂²	1	4	yes	complemented
45	#546×C₆₇	—	2	2	no	—
46	#546×C₆₇	—	2	2	no	—
47	#546×C₆₇	C₂²	1	4	yes	complemented
48	#546×C₆₇	C₂²	1	4	yes	complemented
49	D₄²×C₆₇	—	2	2	no	—
50	D₄²×C₆₇	C₂²	1	4	yes	complemented
51	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#535×C₆₇	C₂²	1	1	yes	characteristic
54	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	#534×C₆₇	—	2	2	no	—
56	#534×C₆₇	—	2	2	no	—
57	#525×C₆₇	C₂²	1	1	yes	characteristic
58	#525×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#525×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	C₂×#123×C₆₇	—	2	2	no	—
61	C₂×#120×C₆₇	—	2	2	no	—
62	#518×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#518×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#497×C₆₇	C₂²	1	2	yes	complemented
65	#496×C₆₇	C₂²	1	2	yes	complemented
66	#495×C₆₇	C₂²	1	2	yes	complemented
67	#492×C₆₇	C₂²	1	2	yes	complemented
68	#470×C₆₇	C₂²	1	2	yes	complemented
69	#469×C₆₇	C₂²	1	2	yes	complemented
70	#468×C₆₇	C₂²	1	4	yes	complemented
71	#468×C₆₇	C₂²	1	2	yes	complemented
72	#468×C₆₇	C₂²	1	2	yes	complemented
73	#465×C₆₇	C₂²	1	4	yes	complemented
74	#463×C₆₇	C₂²	1	4	yes	complemented
75	#463×C₆₇	C₂²	1	4	yes	complemented
76	#461×C₆₇	C₂²	1	4	yes	complemented
77	#459×C₆₇	C₂²	1	4	yes	complemented
78	#452×C₆₇	C₂²	1	4	yes	complemented
79	#452×C₆₇	C₂²	1	4	yes	complemented
80	#450×C₆₇	C₂²	1	4	yes	complemented
81	#450×C₆₇	C₂²	1	4	yes	complemented
82	#449×C₆₇	C₂²	1	4	yes	complemented
83	#449×C₆₇	C₂²	1	4	yes	complemented
84	#447×C₆₇	C₂²	1	4	yes	complemented
85	#447×C₆₇	C₂²	1	4	yes	complemented
86	#442×C₆₇	C₂²	1	4	yes	complemented
87	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
88	#436×C₆₇	C₂²	1	4	yes	complemented
89	#435×C₆₇	C₂²	1	4	yes	complemented
90	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₂⁵×C₆₇	—	2	1	no	—
102	H(5,𝔽₂)×C₆₇	—	2	4	no	—
103	H(5,𝔽₂)×C₆₇	—	2	4	no	—
104	H(5,𝔽₂)×C₆₇	—	4	2	no	—
105	H(5,𝔽₂)×C₆₇	—	4	2	no	—
106	C₂×#41×C₆₇	—	2	1	no	—
107	C₂×#41×C₆₇	—	2	1	no	—
108	C₂×#41×C₆₇	—	2	2	no	—
109	C₂×#41×C₆₇	—	2	4	no	—
110	C₂×#41×C₆₇	—	4	2	no	—
111	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×#41×C₆₇	C₂³	1	4	yes	—
114	C₂×#41×C₆₇	C₂³	1	2	yes	—
115	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
116	C₂×#41×C₆₇	C₂³	1	2	yes	complemented
117	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₆₇	—	2	4	no	—
119	C₂²×D₄×C₆₇	—	2	1	no	—
120	C₂²×D₄×C₆₇	—	2	2	no	—
121	C₂²×D₄×C₆₇	—	2	2	no	—
122	C₂²×D₄×C₆₇	—	2	1	no	—
123	C₂²×D₄×C₆₇	—	2	1	no	—
124	C₂²×D₄×C₆₇	—	2	4	no	—
125	C₂²×D₄×C₆₇	—	2	1	no	—
126	C₂²×D₄×C₆₇	—	2	2	no	—
127	C₂²×D₄×C₆₇	—	4	2	no	—
128	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
130	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
131	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₆₇	C₂³	1	2	yes	complemented
134	C₂³×C₄×C₆₇	—	2	1	no	—
135	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
136	#137×C₆₇	—	4	2	no	—
137	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
138	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
139	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
140	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
141	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
142	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
143	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
144	#135×C₆₇	—	2	8	no	—
145	#135×C₆₇	—	2	4	no	—
146	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
147	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	complemented
148	C₂×SD₁₆×C₆₇	—	2	4	no	—
149	C₂×SD₁₆×C₆₇	—	2	4	no	—
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
152	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
156	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
157	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
158	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
159	C₂×D₈×C₆₇	—	2	4	no	—
160	C₂×D₈×C₆₇	—	2	8	no	—
161	C₂×D₈×C₆₇	D₄	1	8	yes	complemented
162	C₂×D₈×C₆₇	C₂³	1	4	yes	—
163	C₂×D₈×C₆₇	C₂³	1	2	yes	—
164	C₂×D₈×C₆₇	C₂³	1	2	yes	—
165	C₂×D₈×C₆₇	C₂³	1	2	yes	—
166	C₂×D₈×C₆₇	C₂³	1	2	yes	—
167	C₂×D₈×C₆₇	C₂³	1	2	yes	complemented
168	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
169	#131×C₆₇	—	2	4	no	—
170	C₂×M₁₆×C₆₇	—	2	4	no	—
171	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
172	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
173	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×M₁₆×C₆₇	C₂³	1	2	yes	complemented
176	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₆₇	C₂³	1	2	yes	complemented
179	C₄⋊Q₈×C₆₇	—	2	1	no	—
180	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
181	#127×C₆₇	—	2	1	no	—
182	#127×C₆₇	C₂³	1	2	yes	—
183	#124×C₆₇	—	2	1	no	—
184	#124×C₆₇	—	2	1	no	—
185	#124×C₆₇	C₂³	1	2	yes	—
186	#124×C₆₇	C₂³	1	2	yes	complemented
187	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	—	2	1	no	—
189	#123×C₆₇	—	2	1	no	—
190	#123×C₆₇	—	2	4	no	—
191	#123×C₆₇	—	2	4	no	—
192	#123×C₆₇	—	2	2	no	—
193	#123×C₆₇	—	2	4	no	—
194	#123×C₆₇	—	2	4	no	—
195	#123×C₆₇	D₄	1	2	yes	—
196	C₂²⋊Q₈×C₆₇	—	2	2	no	—
197	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
198	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
201	#121×C₆₇	—	2	4	no	—
202	#121×C₆₇	—	2	4	no	—
203	#121×C₆₇	—	2	2	no	—
204	#121×C₆₇	—	2	4	no	—
205	#121×C₆₇	—	2	4	no	—
206	#121×C₆₇	D₄	1	2	yes	—
207	#121×C₆₇	C₂³	1	2	yes	—
208	#121×C₆₇	C₂³	1	4	yes	—
209	#121×C₆₇	C₂³	1	2	yes	—
210	#120×C₆₇	—	2	1	no	—
211	#120×C₆₇	—	2	1	no	—
212	#120×C₆₇	—	2	2	no	—
213	#120×C₆₇	—	2	4	no	—
214	#120×C₆₇	—	2	4	no	—
215	#120×C₆₇	—	2	2	no	—
216	#120×C₆₇	—	2	4	no	—
217	#120×C₆₇	—	2	4	no	—
218	#120×C₆₇	D₄	1	2	yes	—
219	C₄×D₄×C₆₇	—	2	2	no	—
220	C₄×D₄×C₆₇	—	2	2	no	—
221	C₄×D₄×C₆₇	—	2	2	no	—
222	C₄×D₄×C₆₇	—	2	2	no	—
223	C₄×D₄×C₆₇	C₂³	1	4	yes	—
224	C₄×D₄×C₆₇	C₂³	1	4	yes	—
225	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
226	#117×C₆₇	C₂³	1	1	yes	characteristic
227	#117×C₆₇	C₂³	1	1	yes	characteristic
228	#117×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
230	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
231	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
232	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
233	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
234	#107×C₆₇	C₂³	1	2	yes	complemented
235	#106×C₆₇	C₂³	1	2	yes	complemented
236	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
237	#103×C₆₇	C₂³	1	2	yes	complemented
238	#103×C₆₇	C₂³	1	4	yes	complemented
239	#103×C₆₇	C₂³	1	2	yes	complemented
240	#102×C₆₇	C₂³	1	4	yes	—
241	#102×C₆₇	C₂³	1	4	yes	—
242	#102×C₆₇	C₂³	1	4	yes	complemented
243	#102×C₆₇	C₂³	1	2	yes	complemented
244	#102×C₆₇	C₂³	1	2	yes	complemented
245	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
246	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	complemented
247	#97×C₆₇	C₂³	1	2	yes	complemented
248	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
249	C₂⁴×C₆₇	—	2	1	no	—
250	C₂⁴×C₆₇	—	2	1	no	—
251	C₂⁴×C₆₇	—	2	4	no	—
252	C₂⁴×C₆₇	—	2	2	no	—
253	C₂⁴×C₆₇	—	2	1	no	—
254	C₂⁴×C₆₇	—	2	2	no	—
255	C₂⁴×C₆₇	—	4	4	no	—
256	C₂⁴×C₆₇	—	8	4	no	—
257	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
258	#41×C₆₇	—	2	2	no	—
259	#41×C₆₇	—	2	2	no	—
260	#41×C₆₇	—	2	4	no	—
261	#41×C₆₇	—	2	4	no	—
262	#41×C₆₇	—	2	8	no	—
263	#41×C₆₇	—	2	2	no	—
264	#41×C₆₇	—	2	2	no	—
265	#41×C₆₇	—	2	2	no	—
266	#41×C₆₇	—	2	2	no	—
267	#41×C₆₇	—	4	4	no	—
268	#41×C₆₇	—	4	2	no	—
269	#41×C₆₇	—	4	2	no	—
270	#41×C₆₇	—	4	8	no	—
271	#41×C₆₇	—	4	4	no	—
272	#41×C₆₇	—	4	4	no	—
273	C₂×Q₈×C₆₇	—	2	1	no	—
274	C₂×Q₈×C₆₇	—	2	2	no	—
275	C₂×Q₈×C₆₇	—	2	2	no	—
276	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
277	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
278	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
279	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
280	C₂×D₄×C₆₇	—	2	4	no	—
281	C₂×D₄×C₆₇	—	2	4	no	—
282	C₂×D₄×C₆₇	—	2	8	no	—
283	C₂×D₄×C₆₇	—	2	2	no	—
284	C₂×D₄×C₆₇	—	2	1	no	—
285	C₂×D₄×C₆₇	—	2	2	no	—
286	C₂×D₄×C₆₇	—	2	4	no	—
287	C₂×D₄×C₆₇	—	2	1	no	—
288	C₂×D₄×C₆₇	—	2	2	no	—
289	C₂×D₄×C₆₇	—	2	2	no	—
290	C₂×D₄×C₆₇	—	2	4	no	—
291	C₂×D₄×C₆₇	—	2	1	no	—
292	C₂×D₄×C₆₇	—	2	1	no	—
293	C₂×D₄×C₆₇	—	2	2	no	—
294	C₂×D₄×C₆₇	—	2	2	no	—
295	C₂×D₄×C₆₇	—	2	4	no	—
296	C₂×D₄×C₆₇	—	2	2	no	—
297	C₂×D₄×C₆₇	—	2	1	no	—
298	C₂×D₄×C₆₇	—	2	4	no	—
299	C₂×D₄×C₆₇	—	2	2	no	—
300	C₂×D₄×C₆₇	—	2	2	no	—
301	C₂×D₄×C₆₇	—	2	2	no	—
302	C₂×D₄×C₆₇	—	4	4	no	—
303	C₂×D₄×C₆₇	—	4	2	no	—
304	C₂×D₄×C₆₇	—	4	2	no	—
305	C₂×D₄×C₆₇	—	4	8	no	—
306	C₂×D₄×C₆₇	—	4	4	no	—
307	C₂×D₄×C₆₇	—	4	4	no	—
308	C₂×D₄×C₆₇	—	4	4	no	—
309	C₂×D₄×C₆₇	—	4	8	no	—
310	C₂×D₄×C₆₇	—	4	8	no	—
311	C₂×D₄×C₆₇	—	4	4	no	—
312	C₂×D₄×C₆₇	—	8	8	no	—
313	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
314	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
315	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
316	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
317	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	complemented
318	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
319	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
322	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₆₇	—	2	2	no	—
324	C₂²×C₄×C₆₇	—	2	2	no	—
325	C₂²×C₄×C₆₇	—	2	1	no	—
326	C₂²×C₄×C₆₇	—	2	2	no	—
327	C₂²×C₄×C₆₇	—	2	4	no	—
328	C₂²×C₄×C₆₇	—	2	2	no	—
329	C₂²×C₄×C₆₇	—	2	1	no	—
330	C₂²×C₄×C₆₇	—	2	1	no	—
331	C₂²×C₄×C₆₇	—	2	4	no	—
332	C₂²×C₄×C₆₇	—	2	4	no	—
333	C₂²×C₄×C₆₇	—	4	4	no	—
334	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
335	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
339	Q₁₆×C₆₇	—	2	2	no	—
340	Q₁₆×C₆₇	—	4	2	no	—
341	SD₁₆×C₆₇	—	2	8	no	—
342	SD₁₆×C₆₇	—	2	4	no	—
343	SD₁₆×C₆₇	—	2	4	no	—
344	SD₁₆×C₆₇	—	2	4	no	—
345	SD₁₆×C₆₇	—	2	4	no	—
346	SD₁₆×C₆₇	—	2	2	no	—
347	SD₁₆×C₆₇	—	2	2	no	—
348	SD₁₆×C₆₇	—	4	2	no	—
349	SD₁₆×C₆₇	—	4	2	no	—
350	D₈×C₆₇	—	2	4	no	—
351	D₈×C₆₇	—	2	8	no	—
352	D₈×C₆₇	—	2	4	no	—
353	D₈×C₆₇	—	2	2	no	—
354	D₈×C₆₇	—	4	2	no	—
355	D₈×C₆₇	C₂×D₄	1	8	yes	complemented
356	D₈×C₆₇	C₂×D₄	1	8	yes	complemented
357	M₁₆×C₆₇	—	2	2	no	—
358	M₁₆×C₆₇	—	2	2	no	—
359	M₁₆×C₆₇	—	2	4	no	—
360	M₁₆×C₆₇	—	2	4	no	—
361	M₁₆×C₆₇	—	2	4	no	—
362	C₂×C₈×C₆₇	—	2	2	no	—
363	C₂×C₈×C₆₇	—	2	4	no	—
364	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	complemented
365	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
366	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
367	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
368	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₆₇	—	2	2	no	—
371	C₄⋊C₄×C₆₇	—	2	4	no	—
372	C₄⋊C₄×C₆₇	—	2	4	no	—
373	C₄⋊C₄×C₆₇	—	2	2	no	—
374	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
375	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
377	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
378	C₂²⋊C₄×C₆₇	—	2	1	no	—
379	C₂²⋊C₄×C₆₇	—	2	1	no	—
380	C₂²⋊C₄×C₆₇	—	2	2	no	—
381	C₂²⋊C₄×C₆₇	—	2	4	no	—
382	C₂²⋊C₄×C₆₇	—	2	2	no	—
383	C₂²⋊C₄×C₆₇	—	2	2	no	—
384	C₂²⋊C₄×C₆₇	—	2	4	no	—
385	C₂²⋊C₄×C₆₇	—	2	4	no	—
386	C₂²⋊C₄×C₆₇	—	2	4	no	—
387	C₂²⋊C₄×C₆₇	—	2	4	no	—
388	C₂²⋊C₄×C₆₇	—	2	4	no	—
389	C₂²⋊C₄×C₆₇	—	2	2	no	—
390	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
392	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
393	C₄²×C₆₇	—	2	1	no	—
394	C₄²×C₆₇	—	2	1	no	—
395	C₄²×C₆₇	C₂⁴	1	2	yes	—
396	C₂³×C₆₇	—	2	2	no	—
397	C₂³×C₆₇	—	2	2	no	—
398	C₂³×C₆₇	—	2	2	no	—
399	C₂³×C₆₇	—	2	4	no	—
400	C₂³×C₆₇	—	2	4	no	—
401	C₂³×C₆₇	—	2	1	no	—
402	C₂³×C₆₇	—	2	2	no	—
403	C₂³×C₆₇	—	2	1	no	—
404	C₂³×C₆₇	—	4	2	no	—
405	C₂³×C₆₇	—	4	8	no	—
406	C₂³×C₆₇	—	4	4	no	—
407	C₂³×C₆₇	—	4	4	no	—
408	C₂³×C₆₇	—	4	8	no	—
409	C₂³×C₆₇	—	4	2	no	—
410	C₂³×C₆₇	—	8	2	no	—
411	C₂³×C₆₇	—	8	2	no	—
412	C₂³×C₆₇	—	8	2	no	—
413	C₂³×C₆₇	—	8	4	no	—
414	C₂³×C₆₇	—	8	4	no	—
415	C₂³×C₆₇	—	8	4	no	—
416	C₂³×C₆₇	—	8	16	no	—
417	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
418	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
419	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
420	Q₈×C₆₇	—	2	2	no	—
421	Q₈×C₆₇	—	2	2	no	—
422	Q₈×C₆₇	—	2	1	no	—
423	Q₈×C₆₇	—	2	1	no	—
424	Q₈×C₆₇	—	2	1	no	—
425	Q₈×C₆₇	—	2	2	no	—
426	Q₈×C₆₇	—	2	1	no	—
427	Q₈×C₆₇	—	4	2	no	—
428	D₄×C₆₇	—	2	4	no	—
429	D₄×C₆₇	—	2	4	no	—
430	D₄×C₆₇	—	2	4	no	—
431	D₄×C₆₇	—	2	2	no	—
432	D₄×C₆₇	—	2	1	no	—
433	D₄×C₆₇	—	2	1	no	—
434	D₄×C₆₇	—	2	2	no	—
435	D₄×C₆₇	—	2	2	no	—
436	D₄×C₆₇	—	2	2	no	—
437	D₄×C₆₇	—	2	1	no	—
438	D₄×C₆₇	—	2	2	no	—
439	D₄×C₆₇	—	2	1	no	—
440	D₄×C₆₇	—	4	4	no	—
441	D₄×C₆₇	—	4	8	no	—
442	D₄×C₆₇	—	4	4	no	—
443	D₄×C₆₇	—	4	4	no	—
444	D₄×C₆₇	—	4	4	no	—
445	D₄×C₆₇	—	4	4	no	—
446	D₄×C₆₇	—	4	8	no	—
447	D₄×C₆₇	—	4	4	no	—
448	D₄×C₆₇	—	4	2	no	—
449	D₄×C₆₇	—	4	2	no	—
450	D₄×C₆₇	—	4	2	no	—
451	D₄×C₆₇	—	8	4	no	—
452	D₄×C₆₇	—	8	2	no	—
453	D₄×C₆₇	—	8	4	no	—
454	D₄×C₆₇	C₂²×D₄	1	4	yes	—
455	D₄×C₆₇	C₂²×D₄	1	4	yes	—
456	C₂×C₄×C₆₇	—	2	2	no	—
457	C₂×C₄×C₆₇	—	2	4	no	—
458	C₂×C₄×C₆₇	—	2	2	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	2	no	—
461	C₂×C₄×C₆₇	—	2	2	no	—
462	C₂×C₄×C₆₇	—	2	2	no	—
463	C₂×C₄×C₆₇	—	2	2	no	—
464	C₂×C₄×C₆₇	—	2	1	no	—
465	C₂×C₄×C₆₇	—	2	2	no	—
466	C₂×C₄×C₆₇	—	2	1	no	—
467	C₂×C₄×C₆₇	—	4	8	no	—
468	C₂×C₄×C₆₇	—	4	4	no	—
469	C₂×C₄×C₆₇	—	4	4	no	—
470	C₂×C₄×C₆₇	—	4	2	no	—
471	C₂×C₄×C₆₇	—	4	2	no	—
472	C₂×C₄×C₆₇	—	4	2	no	—
473	C₂×C₄×C₆₇	—	8	4	no	—
474	C₂×C₄×C₆₇	—	8	4	no	—
475	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
476	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
477	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
478	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
481	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
482	C₈×C₆₇	—	2	2	no	—
483	C₈×C₆₇	—	2	2	no	—
484	C₈×C₆₇	—	2	2	no	—
485	C₈×C₆₇	C₂²×D₄	1	2	yes	—
486	C₈×C₆₇	C₂²×D₄	1	2	yes	—
487	C₂²×C₆₇	—	2	2	no	—
488	C₂²×C₆₇	—	2	2	no	—
489	C₂²×C₆₇	—	2	4	no	—
490	C₂²×C₆₇	—	2	2	no	—
491	C₂²×C₆₇	—	2	2	no	—
492	C₂²×C₆₇	—	2	2	no	—
493	C₂²×C₆₇	—	2	4	no	—
494	C₂²×C₆₇	—	2	4	no	—
495	C₂²×C₆₇	—	4	4	no	—
496	C₂²×C₆₇	—	4	4	no	—
497	C₂²×C₆₇	—	4	4	no	—
498	C₂²×C₆₇	—	4	2	no	—
499	C₂²×C₆₇	—	4	4	no	—
500	C₂²×C₆₇	—	4	2	no	—
501	C₂²×C₆₇	—	4	1	no	—
502	C₂²×C₆₇	—	4	1	no	—
503	C₂²×C₆₇	—	4	2	no	—
504	C₂²×C₆₇	—	8	4	no	—
505	C₂²×C₆₇	—	8	4	no	—
506	C₂²×C₆₇	—	8	4	no	—
507	C₂²×C₆₇	—	8	16	no	—
508	C₂²×C₆₇	—	16	4	no	—
509	C₂²×C₆₇	—	16	4	no	—
510	C₂²×C₆₇	D₄²	1	2	yes	—
511	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
512	C₄×C₆₇	—	2	4	no	—
513	C₄×C₆₇	—	2	2	no	—
514	C₄×C₆₇	—	2	2	no	—
515	C₄×C₆₇	—	4	2	no	—
516	C₄×C₆₇	—	4	2	no	—
517	C₄×C₆₇	—	4	1	no	—
518	C₄×C₆₇	—	4	1	no	—
519	C₄×C₆₇	—	4	2	no	—
520	C₄×C₆₇	D₄²	1	2	yes	—
521	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
522	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
523	#61058	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
524	C₂×C₆₇	—	2	2	no	—
525	C₂×C₆₇	—	4	2	no	—
526	C₂×C₆₇	—	4	2	no	—
527	C₂×C₆₇	—	4	4	no	—
528	C₂×C₆₇	—	4	4	no	—
529	C₂×C₆₇	—	8	2	no	—
530	C₂×C₆₇	—	8	1	no	—
531	C₂×C₆₇	—	8	1	no	—
532	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
533	C₂×C₆₇	#3585	1	2	yes	—
534	C₂×#576	C₂×C₆₇	1	1	yes	characteristic, complemented
535	C₂²×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
536	#3485	C₂×C₆₇	1	1	yes	characteristic, complemented
537	#3484	C₂×C₆₇	1	1	yes	characteristic, complemented
538	#3273	C₂×C₆₇	1	4	yes	complemented
539	#3272	C₂×C₆₇	1	4	yes	complemented
540	#3267	C₂×C₆₇	1	4	yes	complemented
541	#3264	C₂×C₆₇	1	4	yes	complemented
542	#3154	C₂×C₆₇	1	1	yes	characteristic, complemented
543	#3057	C₂×C₆₇	1	1	yes	characteristic, complemented
544	#3054	C₂×C₆₇	1	1	yes	characteristic, complemented
545	#3042	C₂×C₆₇	1	1	yes	characteristic, complemented
546	#3041	C₂×C₆₇	1	1	yes	characteristic, complemented
547	#3009	C₂×C₆₇	1	1	yes	characteristic, complemented
548	#3008	C₂×C₆₇	1	1	yes	characteristic, complemented
549	#3005	C₂×C₆₇	1	1	yes	characteristic, complemented
550	#3003	C₂×C₆₇	1	1	yes	characteristic, complemented
551	#2948	C₂×C₆₇	1	1	yes	characteristic, complemented
552	#2930	C₂×C₆₇	1	1	yes	characteristic, complemented
553	C₆₇	#61058	1	1	yes	characteristic, direct product factor, Sylow
554	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
555	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
556	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
557	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
558	#576	—	2	8	no	—
559	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
560	C₂×AGL(1,ℤ/8)	—	2	8	no	—
561	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
562	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
563	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
564	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
565	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
566	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
567	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
568	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
569	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
570	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
571	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
572	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
573	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
574	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
575	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
576	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
577	#547	—	2	2	no	—
578	#547	C₂²×C₆₇	1	4	yes	complemented
579	#546	—	2	2	no	—
580	#546	—	2	2	no	—
581	#546	C₂²×C₆₇	1	4	yes	complemented
582	#546	C₂²×C₆₇	1	4	yes	complemented
583	D₄²	—	2	2	no	—
584	D₄²	C₂²×C₆₇	1	4	yes	complemented
585	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
586	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
587	#535	C₂²×C₆₇	1	1	yes	characteristic
588	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
589	#534	—	2	2	no	—
590	#534	—	2	2	no	—
591	#525	C₂²×C₆₇	1	1	yes	characteristic
592	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
593	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
594	C₂×#123	—	2	2	no	—
595	C₂×#120	—	2	2	no	—
596	#518	C₂²×C₆₇	1	1	yes	characteristic, complemented
597	#518	C₂²×C₆₇	1	1	yes	characteristic, complemented
598	#497	C₂²×C₆₇	1	2	yes	complemented
599	#496	C₂²×C₆₇	1	2	yes	complemented
600	#495	C₂²×C₆₇	1	2	yes	complemented
601	#492	C₂²×C₆₇	1	2	yes	complemented
602	#470	C₂²×C₆₇	1	2	yes	complemented
603	#469	C₂²×C₆₇	1	2	yes	complemented
604	#468	C₂²×C₆₇	1	4	yes	complemented
605	#468	C₂²×C₆₇	1	2	yes	complemented
606	#468	C₂²×C₆₇	1	2	yes	complemented
607	#465	C₂²×C₆₇	1	4	yes	complemented
608	#463	C₂²×C₆₇	1	4	yes	complemented
609	#463	C₂²×C₆₇	1	4	yes	complemented
610	#461	C₂²×C₆₇	1	4	yes	complemented
611	#459	C₂²×C₆₇	1	4	yes	complemented
612	#452	C₂²×C₆₇	1	4	yes	complemented
613	#452	C₂²×C₆₇	1	4	yes	complemented
614	#450	C₂²×C₆₇	1	4	yes	complemented
615	#450	C₂²×C₆₇	1	4	yes	complemented
616	#449	C₂²×C₆₇	1	4	yes	complemented
617	#449	C₂²×C₆₇	1	4	yes	complemented
618	#447	C₂²×C₆₇	1	4	yes	complemented
619	#447	C₂²×C₆₇	1	4	yes	complemented
620	#442	C₂²×C₆₇	1	4	yes	complemented
621	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
622	#436	C₂²×C₆₇	1	4	yes	complemented
623	#435	C₂²×C₆₇	1	4	yes	complemented
624	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
626	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
630	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
631	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
632	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
633	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
634	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
635	C₂⁵	—	2	1	no	—
636	H(5,𝔽₂)	—	2	4	no	—
637	H(5,𝔽₂)	—	2	4	no	—
638	H(5,𝔽₂)	—	4	2	no	—
639	H(5,𝔽₂)	—	4	2	no	—
640	C₂×#41	—	2	1	no	—
641	C₂×#41	—	2	1	no	—
642	C₂×#41	—	2	2	no	—
643	C₂×#41	—	2	4	no	—
644	C₂×#41	—	4	2	no	—
645	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
646	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
647	C₂×#41	C₂³×C₆₇	1	2	yes	—
648	C₂×#41	C₂³×C₆₇	1	4	yes	—
649	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
650	C₂×#41	C₂³×C₆₇	1	2	yes	complemented
651	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
652	C₂²×D₄	—	2	4	no	—
653	C₂²×D₄	—	2	1	no	—
654	C₂²×D₄	—	2	2	no	—
655	C₂²×D₄	—	2	2	no	—
656	C₂²×D₄	—	2	1	no	—
657	C₂²×D₄	—	2	1	no	—
658	C₂²×D₄	—	2	4	no	—
659	C₂²×D₄	—	2	1	no	—
660	C₂²×D₄	—	2	2	no	—
661	C₂²×D₄	—	4	2	no	—
662	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
663	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
664	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
665	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
666	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
667	C₂²×D₄	C₂³×C₆₇	1	2	yes	complemented
668	C₂³×C₄	—	2	1	no	—
669	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
670	#137	—	4	2	no	—
671	AGL(1,ℤ/8)	—	2	4	no	—
672	AGL(1,ℤ/8)	—	2	4	no	—
673	AGL(1,ℤ/8)	—	2	16	no	—
674	AGL(1,ℤ/8)	—	2	16	no	—
675	AGL(1,ℤ/8)	—	2	8	no	—
676	AGL(1,ℤ/8)	—	2	8	no	—
677	AGL(1,ℤ/8)	—	4	2	no	—
678	#135	—	2	8	no	—
679	#135	—	2	4	no	—
680	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
681	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	complemented
682	C₂×SD₁₆	—	2	4	no	—
683	C₂×SD₁₆	—	2	4	no	—
684	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
685	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
686	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
689	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
690	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
691	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
692	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
693	C₂×D₈	—	2	4	no	—
694	C₂×D₈	—	2	8	no	—
695	C₂×D₈	D₄×C₆₇	1	8	yes	complemented
696	C₂×D₈	C₂³×C₆₇	1	2	yes	—
697	C₂×D₈	C₂³×C₆₇	1	4	yes	—
698	C₂×D₈	C₂³×C₆₇	1	2	yes	—
699	C₂×D₈	C₂³×C₆₇	1	2	yes	—
700	C₂×D₈	C₂³×C₆₇	1	2	yes	—
701	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
702	C₂×D₈	C₂³×C₆₇	1	2	yes	complemented
703	#131	—	2	4	no	—
704	C₂×M₁₆	—	2	4	no	—
705	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
706	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
707	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
708	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
709	C₂×M₁₆	C₂³×C₆₇	1	2	yes	complemented
710	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
711	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
712	C₂²×C₈	C₂³×C₆₇	1	2	yes	complemented
713	C₄⋊Q₈	—	2	1	no	—
714	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
715	#127	—	2	1	no	—
716	#127	C₂³×C₆₇	1	2	yes	—
717	#124	—	2	1	no	—
718	#124	—	2	1	no	—
719	#124	C₂³×C₆₇	1	2	yes	—
720	#124	C₂³×C₆₇	1	2	yes	complemented
721	#123	—	2	2	no	—
722	#123	—	2	1	no	—
723	#123	—	2	1	no	—
724	#123	—	2	4	no	—
725	#123	—	2	4	no	—
726	#123	—	2	2	no	—
727	#123	—	2	4	no	—
728	#123	—	2	4	no	—
729	#123	D₄×C₆₇	1	2	yes	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
732	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
733	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
734	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	complemented
735	#121	—	2	4	no	—
736	#121	—	2	4	no	—
737	#121	—	2	2	no	—
738	#121	—	2	4	no	—
739	#121	—	2	4	no	—
740	#121	D₄×C₆₇	1	2	yes	—
741	#121	C₂³×C₆₇	1	2	yes	—
742	#121	C₂³×C₆₇	1	2	yes	—
743	#121	C₂³×C₆₇	1	4	yes	—
744	#120	—	2	1	no	—
745	#120	—	2	1	no	—
746	#120	—	2	2	no	—
747	#120	—	2	4	no	—
748	#120	—	2	4	no	—
749	#120	—	2	2	no	—
750	#120	—	2	4	no	—
751	#120	—	2	4	no	—
752	#120	D₄×C₆₇	1	2	yes	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	C₂³×C₆₇	1	4	yes	—
758	C₄×D₄	C₂³×C₆₇	1	4	yes	—
759	C₄×D₄	C₂³×C₆₇	1	4	yes	complemented
760	#117	C₂³×C₆₇	1	1	yes	characteristic
761	#117	C₂³×C₆₇	1	1	yes	characteristic
762	#117	C₂³×C₆₇	1	1	yes	characteristic
763	C₂×C₄⋊C₄	—	2	4	no	—
764	C₂×C₂²⋊C₄	—	2	2	no	—
765	C₂×C₂²⋊C₄	—	2	2	no	—
766	C₂×C₂²⋊C₄	—	2	4	no	—
767	C₂×C₂²⋊C₄	—	2	4	no	—
768	#107	C₂³×C₆₇	1	2	yes	complemented
769	#106	C₂³×C₆₇	1	2	yes	complemented
770	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
771	#103	C₂³×C₆₇	1	2	yes	complemented
772	#103	C₂³×C₆₇	1	2	yes	complemented
773	#103	C₂³×C₆₇	1	4	yes	complemented
774	#102	C₂³×C₆₇	1	4	yes	—
775	#102	C₂³×C₆₇	1	4	yes	—
776	#102	C₂³×C₆₇	1	2	yes	complemented
777	#102	C₂³×C₆₇	1	2	yes	complemented
778	#102	C₂³×C₆₇	1	4	yes	complemented
779	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
780	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
781	#97	C₂³×C₆₇	1	2	yes	complemented
782	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
783	C₂⁴	—	2	1	no	—
784	C₂⁴	—	2	1	no	—
785	C₂⁴	—	2	4	no	—
786	C₂⁴	—	2	2	no	—
787	C₂⁴	—	2	1	no	—
788	C₂⁴	—	2	2	no	—
789	C₂⁴	—	4	4	no	—
790	C₂⁴	—	8	4	no	—
791	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
792	#41	—	2	2	no	—
793	#41	—	2	2	no	—
794	#41	—	2	4	no	—
795	#41	—	2	4	no	—
796	#41	—	2	8	no	—
797	#41	—	2	2	no	—
798	#41	—	2	2	no	—
799	#41	—	2	2	no	—
800	#41	—	2	2	no	—
801	#41	—	4	4	no	—
802	#41	—	4	2	no	—
803	#41	—	4	2	no	—
804	#41	—	4	8	no	—
805	#41	—	4	4	no	—
806	#41	—	4	4	no	—
807	C₂×Q₈	—	2	1	no	—
808	C₂×Q₈	—	2	2	no	—
809	C₂×Q₈	—	2	2	no	—
810	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
811	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
812	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
813	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
814	C₂×D₄	—	2	4	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	8	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	4	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	1	no	—
826	C₂×D₄	—	2	1	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	4	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	4	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	4	4	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	—	4	2	no	—
839	C₂×D₄	—	4	8	no	—
840	C₂×D₄	—	4	4	no	—
841	C₂×D₄	—	4	4	no	—
842	C₂×D₄	—	4	4	no	—
843	C₂×D₄	—	4	8	no	—
844	C₂×D₄	—	4	8	no	—
845	C₂×D₄	—	4	4	no	—
846	C₂×D₄	—	8	8	no	—
847	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
848	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
849	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
850	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
851	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	complemented
852	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
853	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
854	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
855	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
856	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	4	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	4	no	—
866	C₂²×C₄	—	2	4	no	—
867	C₂²×C₄	—	4	4	no	—
868	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
869	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
871	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
873	Q₁₆	—	2	2	no	—
874	Q₁₆	—	4	2	no	—
875	SD₁₆	—	2	8	no	—
876	SD₁₆	—	2	4	no	—
877	SD₁₆	—	2	4	no	—
878	SD₁₆	—	2	4	no	—
879	SD₁₆	—	2	4	no	—
880	SD₁₆	—	2	2	no	—
881	SD₁₆	—	2	2	no	—
882	SD₁₆	—	4	2	no	—
883	SD₁₆	—	4	2	no	—
884	D₈	—	2	4	no	—
885	D₈	—	2	8	no	—
886	D₈	—	2	4	no	—
887	D₈	—	2	2	no	—
888	D₈	—	4	2	no	—
889	D₈	C₂×D₄×C₆₇	1	8	yes	complemented
890	D₈	C₂×D₄×C₆₇	1	8	yes	complemented
891	M₁₆	—	2	2	no	—
892	M₁₆	—	2	2	no	—
893	M₁₆	—	2	4	no	—
894	M₁₆	—	2	4	no	—
895	M₁₆	—	2	4	no	—
896	C₂×C₈	—	2	2	no	—
897	C₂×C₈	—	2	4	no	—
898	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	complemented
899	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
900	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
901	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
902	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	4	no	—
906	C₄⋊C₄	—	2	4	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
909	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
910	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
911	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
912	C₂²⋊C₄	—	2	1	no	—
913	C₂²⋊C₄	—	2	1	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	4	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
925	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
926	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
927	C₄²	—	2	1	no	—
928	C₄²	—	2	1	no	—
929	C₄²	C₂⁴×C₆₇	1	2	yes	—
930	C₂³	—	2	2	no	—
931	C₂³	—	2	2	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	4	no	—
934	C₂³	—	2	4	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	4	2	no	—
939	C₂³	—	4	8	no	—
940	C₂³	—	4	4	no	—
941	C₂³	—	4	4	no	—
942	C₂³	—	4	8	no	—
943	C₂³	—	4	2	no	—
944	C₂³	—	8	2	no	—
945	C₂³	—	8	2	no	—
946	C₂³	—	8	4	no	—
947	C₂³	—	8	2	no	—
948	C₂³	—	8	4	no	—
949	C₂³	—	8	4	no	—
950	C₂³	—	8	16	no	—
951	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
952	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
953	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
954	Q₈	—	2	2	no	—
955	Q₈	—	2	2	no	—
956	Q₈	—	2	1	no	—
957	Q₈	—	2	1	no	—
958	Q₈	—	2	1	no	—
959	Q₈	—	2	2	no	—
960	Q₈	—	2	1	no	—
961	Q₈	—	4	2	no	—
962	D₄	—	2	4	no	—
963	D₄	—	2	4	no	—
964	D₄	—	2	4	no	—
965	D₄	—	2	2	no	—
966	D₄	—	2	1	no	—
967	D₄	—	2	1	no	—
968	D₄	—	2	2	no	—
969	D₄	—	2	2	no	—
970	D₄	—	2	2	no	—
971	D₄	—	2	1	no	—
972	D₄	—	2	2	no	—
973	D₄	—	2	1	no	—
974	D₄	—	4	4	no	—
975	D₄	—	4	8	no	—
976	D₄	—	4	4	no	—
977	D₄	—	4	4	no	—
978	D₄	—	4	4	no	—
979	D₄	—	4	4	no	—
980	D₄	—	4	8	no	—
981	D₄	—	4	4	no	—
982	D₄	—	4	2	no	—
983	D₄	—	4	2	no	—
984	D₄	—	4	2	no	—
985	D₄	—	8	4	no	—
986	D₄	—	8	4	no	—
987	D₄	—	8	2	no	—
988	D₄	C₂²×D₄×C₆₇	1	4	yes	—
989	D₄	C₂²×D₄×C₆₇	1	4	yes	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	4	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	4	8	no	—
1002	C₂×C₄	—	4	4	no	—
1003	C₂×C₄	—	4	4	no	—
1004	C₂×C₄	—	4	2	no	—
1005	C₂×C₄	—	4	2	no	—
1006	C₂×C₄	—	4	2	no	—
1007	C₂×C₄	—	8	4	no	—
1008	C₂×C₄	—	8	4	no	—
1009	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1010	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1011	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1012	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1013	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1014	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1015	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1016	C₈	—	2	2	no	—
1017	C₈	—	2	2	no	—
1018	C₈	—	2	2	no	—
1019	C₈	C₂²×D₄×C₆₇	1	2	yes	—
1020	C₈	C₂²×D₄×C₆₇	1	2	yes	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	2	no	—
1023	C₂²	—	2	4	no	—
1024	C₂²	—	2	2	no	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	4	no	—
1028	C₂²	—	2	4	no	—
1029	C₂²	—	4	4	no	—
1030	C₂²	—	4	4	no	—
1031	C₂²	—	4	4	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	—	4	4	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	1	no	—
1036	C₂²	—	4	1	no	—
1037	C₂²	—	4	2	no	—
1038	C₂²	—	8	4	no	—
1039	C₂²	—	8	4	no	—
1040	C₂²	—	8	4	no	—
1041	C₂²	—	8	16	no	—
1042	C₂²	—	16	4	no	—
1043	C₂²	—	16	4	no	—
1044	C₂²	D₄²×C₆₇	1	2	yes	—
1045	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1046	C₄	—	2	4	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	2	no	—
1054	C₄	D₄²×C₆₇	1	2	yes	—
1055	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1056	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1057	C₂	—	2	2	no	—
1058	C₂	—	4	2	no	—
1059	C₂	—	4	2	no	—
1060	C₂	—	4	4	no	—
1061	C₂	—	4	4	no	—
1062	C₂	—	8	2	no	—
1063	C₂	—	8	1	no	—
1064	C₂	—	8	1	no	—
1065	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1066	C₂	C₆₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#576×C₆₇	C₂	semidirect
2. C₂²×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
3. C₆₇×#3485	C₂	semidirect
4. C₆₇×#3484	C₂	semidirect
5. C₆₇×#3273	C₂	semidirect
6. C₆₇×#3272	C₂	semidirect
7. C₆₇×#3267	C₂	semidirect
8. C₆₇×#3264	C₂	semidirect
9. C₆₇×#3154	C₂	semidirect
10. C₆₇×#3057	C₂	semidirect
11. C₆₇×#3054	C₂	semidirect
12. C₆₇×#3042	C₂	semidirect
13. C₆₇×#3041	C₂	semidirect
14. C₆₇×#3009	C₂	semidirect
15. C₆₇×#3008	C₂	semidirect
16. C₆₇×#3005	C₂	semidirect
17. C₆₇×#3003	C₂	semidirect
18. C₆₇×#2948	C₂	semidirect
19. C₆₇×#2930	C₂	semidirect
21. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
22. C₂²×#41×C₆₇	C₂²	semidirect
23. C₂³×D₄×C₆₇	C₂²	semidirect
25. C₂×#137×C₆₇	C₂²	semidirect
28. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
29. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
30. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
31. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
32. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
33. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
34. C₂×#135×C₆₇	C₂²	semidirect
35. C₂×#135×C₆₇	C₂²	semidirect
36. C₂²×SD₁₆×C₆₇	C₂²	semidirect
37. C₂²×SD₁₆×C₆₇	C₂²	semidirect
39. C₂²×D₈×C₆₇	C₂²	semidirect
40. C₂²×D₈×C₆₇	C₂²	semidirect
41. C₂×#131×C₆₇	C₂²	semidirect
42. C₂²×M₁₆×C₆₇	C₂²	semidirect
44. #547×C₆₇	C₂²	semidirect
47. #546×C₆₇	C₂²	semidirect
48. #546×C₆₇	C₂²	semidirect
50. D₄²×C₆₇	C₂²	semidirect
51. #536×C₆₇	C₂²	semidirect
52. #536×C₆₇	C₂²	semidirect
54. #535×C₆₇	C₂²	semidirect
58. #525×C₆₇	C₂²	semidirect
59. #525×C₆₇	C₂²	semidirect
62. #518×C₆₇	C₂²	semidirect
63. #518×C₆₇	C₂²	semidirect
64. #497×C₆₇	C₂²	semidirect
65. #496×C₆₇	C₂²	semidirect
66. #495×C₆₇	C₂²	semidirect
67. #492×C₆₇	C₂²	semidirect
68. #470×C₆₇	C₂²	semidirect
69. #469×C₆₇	C₂²	semidirect
70. #468×C₆₇	C₂²	semidirect
71. #468×C₆₇	C₂²	semidirect
72. #468×C₆₇	C₂²	semidirect
73. #465×C₆₇	C₂²	semidirect
74. #463×C₆₇	C₂²	semidirect
75. #463×C₆₇	C₂²	semidirect
76. #461×C₆₇	C₂²	semidirect
77. #459×C₆₇	C₂²	semidirect
78. #452×C₆₇	C₂²	semidirect
79. #452×C₆₇	C₂²	semidirect
80. #450×C₆₇	C₂²	semidirect
81. #450×C₆₇	C₂²	semidirect
82. #449×C₆₇	C₂²	semidirect
83. #449×C₆₇	C₂²	semidirect
84. #447×C₆₇	C₂²	semidirect
85. #447×C₆₇	C₂²	semidirect
86. #442×C₆₇	C₂²	semidirect
87. C₄×D₈×C₆₇	C₂²	semidirect
88. #436×C₆₇	C₂²	semidirect
89. #435×C₆₇	C₂²	semidirect
90. #427×C₆₇	C₂²	semidirect
91. #424×C₆₇	C₂²	semidirect
92. #419×C₆₇	C₂²	semidirect
93. #418×C₆₇	C₂²	semidirect
94. #418×C₆₇	C₂²	semidirect
95. #418×C₆₇	C₂²	semidirect
96. #416×C₆₇	C₂²	semidirect
97. #416×C₆₇	C₂²	semidirect
98. #408×C₆₇	C₂²	semidirect
99. #407×C₆₇	C₂²	semidirect
100. #405×C₆₇	C₂²	semidirect
116. C₂×#41×C₆₇	C₂³	semidirect
133. C₂²×D₄×C₆₇	C₂³	semidirect
146. C₂×Q₁₆×C₆₇	C₂³	semidirect
147. C₂×Q₁₆×C₆₇	C₂³	semidirect
155. C₂×SD₁₆×C₆₇	C₂³	semidirect
156. C₂×SD₁₆×C₆₇	C₂³	semidirect
157. C₂×SD₁₆×C₆₇	C₂³	semidirect
158. C₂×SD₁₆×C₆₇	C₂³	semidirect
161. C₂×D₈×C₆₇	D₄	semidirect
167. C₂×D₈×C₆₇	C₂³	semidirect
168. C₂×D₈×C₆₇	C₂³	semidirect
175. C₂×M₁₆×C₆₇	C₂³	semidirect
178. C₂²×C₈×C₆₇	C₂³	semidirect
180. C₄⋊Q₈×C₆₇	C₂³	semidirect
186. #124×C₆₇	C₂³	semidirect
200. C₂²⋊Q₈×C₆₇	C₂³	semidirect
225. C₄×D₄×C₆₇	C₂³	semidirect
234. #107×C₆₇	C₂³	semidirect
235. #106×C₆₇	C₂³	semidirect
236. C₄⋊C₈×C₆₇	C₂³	semidirect
237. #103×C₆₇	C₂³	semidirect
238. #103×C₆₇	C₂³	semidirect
239. #103×C₆₇	C₂³	semidirect
242. #102×C₆₇	C₂³	semidirect
243. #102×C₆₇	C₂³	semidirect
244. #102×C₆₇	C₂³	semidirect
246. C₂²⋊C₈×C₆₇	C₂³	semidirect
247. #97×C₆₇	C₂³	semidirect
248. C₄×C₈×C₆₇	C₂³	semidirect
317. C₂×D₄×C₆₇	C₂×D₄	semidirect
355. D₈×C₆₇	C₂×D₄	semidirect
356. D₈×C₆₇	C₂×D₄	semidirect
364. C₂×C₈×C₆₇	C₂×D₄	semidirect
523. #61058	C₆₇	direct (N × H)
534. C₂×#576	C₂×C₆₇	semidirect
535. C₂²×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
536. #3485	C₂×C₆₇	semidirect
537. #3484	C₂×C₆₇	semidirect
538. #3273	C₂×C₆₇	semidirect
539. #3272	C₂×C₆₇	semidirect
540. #3267	C₂×C₆₇	semidirect
541. #3264	C₂×C₆₇	semidirect
542. #3154	C₂×C₆₇	semidirect
543. #3057	C₂×C₆₇	semidirect
544. #3054	C₂×C₆₇	semidirect
545. #3042	C₂×C₆₇	semidirect
546. #3041	C₂×C₆₇	semidirect
547. #3009	C₂×C₆₇	semidirect
548. #3008	C₂×C₆₇	semidirect
549. #3005	C₂×C₆₇	semidirect
550. #3003	C₂×C₆₇	semidirect
551. #2948	C₂×C₆₇	semidirect
552. #2930	C₂×C₆₇	semidirect
553. C₆₇	#61058	direct (N × H)
555. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
556. C₂²×#41	C₂²×C₆₇	semidirect
557. C₂³×D₄	C₂²×C₆₇	semidirect
559. C₂×#137	C₂²×C₆₇	semidirect
562. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
563. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
564. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
565. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
566. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
567. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
568. C₂×#135	C₂²×C₆₇	semidirect
569. C₂×#135	C₂²×C₆₇	semidirect
570. C₂²×SD₁₆	C₂²×C₆₇	semidirect
571. C₂²×SD₁₆	C₂²×C₆₇	semidirect
573. C₂²×D₈	C₂²×C₆₇	semidirect
574. C₂²×D₈	C₂²×C₆₇	semidirect
575. C₂×#131	C₂²×C₆₇	semidirect
576. C₂²×M₁₆	C₂²×C₆₇	semidirect
578. #547	C₂²×C₆₇	semidirect
581. #546	C₂²×C₆₇	semidirect
582. #546	C₂²×C₆₇	semidirect
584. D₄²	C₂²×C₆₇	semidirect
585. #536	C₂²×C₆₇	semidirect
586. #536	C₂²×C₆₇	semidirect
588. #535	C₂²×C₆₇	semidirect
592. #525	C₂²×C₆₇	semidirect
593. #525	C₂²×C₆₇	semidirect
596. #518	C₂²×C₆₇	semidirect
597. #518	C₂²×C₆₇	semidirect
598. #497	C₂²×C₆₇	semidirect
599. #496	C₂²×C₆₇	semidirect
600. #495	C₂²×C₆₇	semidirect
601. #492	C₂²×C₆₇	semidirect
602. #470	C₂²×C₆₇	semidirect
603. #469	C₂²×C₆₇	semidirect
604. #468	C₂²×C₆₇	semidirect
605. #468	C₂²×C₆₇	semidirect
606. #468	C₂²×C₆₇	semidirect
607. #465	C₂²×C₆₇	semidirect
608. #463	C₂²×C₆₇	semidirect
609. #463	C₂²×C₆₇	semidirect
610. #461	C₂²×C₆₇	semidirect
611. #459	C₂²×C₆₇	semidirect
612. #452	C₂²×C₆₇	semidirect
613. #452	C₂²×C₆₇	semidirect
614. #450	C₂²×C₆₇	semidirect
615. #450	C₂²×C₆₇	semidirect
616. #449	C₂²×C₆₇	semidirect
617. #449	C₂²×C₆₇	semidirect
618. #447	C₂²×C₆₇	semidirect
619. #447	C₂²×C₆₇	semidirect
620. #442	C₂²×C₆₇	semidirect
621. C₄×D₈	C₂²×C₆₇	semidirect
622. #436	C₂²×C₆₇	semidirect
623. #435	C₂²×C₆₇	semidirect
624. #427	C₂²×C₆₇	semidirect
625. #424	C₂²×C₆₇	semidirect
626. #419	C₂²×C₆₇	semidirect
627. #418	C₂²×C₆₇	semidirect
628. #418	C₂²×C₆₇	semidirect
629. #418	C₂²×C₆₇	semidirect
630. #416	C₂²×C₆₇	semidirect
631. #416	C₂²×C₆₇	semidirect
632. #408	C₂²×C₆₇	semidirect
633. #407	C₂²×C₆₇	semidirect
634. #405	C₂²×C₆₇	semidirect
650. C₂×#41	C₂³×C₆₇	semidirect
667. C₂²×D₄	C₂³×C₆₇	semidirect
680. C₂×Q₁₆	C₂³×C₆₇	semidirect
681. C₂×Q₁₆	C₂³×C₆₇	semidirect
689. C₂×SD₁₆	C₂³×C₆₇	semidirect
690. C₂×SD₁₆	C₂³×C₆₇	semidirect
691. C₂×SD₁₆	C₂³×C₆₇	semidirect
692. C₂×SD₁₆	C₂³×C₆₇	semidirect
695. C₂×D₈	D₄×C₆₇	semidirect
701. C₂×D₈	C₂³×C₆₇	semidirect
702. C₂×D₈	C₂³×C₆₇	semidirect
709. C₂×M₁₆	C₂³×C₆₇	semidirect
712. C₂²×C₈	C₂³×C₆₇	semidirect
714. C₄⋊Q₈	C₂³×C₆₇	semidirect
720. #124	C₂³×C₆₇	semidirect
734. C₂²⋊Q₈	C₂³×C₆₇	semidirect
759. C₄×D₄	C₂³×C₆₇	semidirect
768. #107	C₂³×C₆₇	semidirect
769. #106	C₂³×C₆₇	semidirect
770. C₄⋊C₈	C₂³×C₆₇	semidirect
771. #103	C₂³×C₆₇	semidirect
772. #103	C₂³×C₆₇	semidirect
773. #103	C₂³×C₆₇	semidirect
776. #102	C₂³×C₆₇	semidirect
777. #102	C₂³×C₆₇	semidirect
778. #102	C₂³×C₆₇	semidirect
780. C₂²⋊C₈	C₂³×C₆₇	semidirect
781. #97	C₂³×C₆₇	semidirect
782. C₄×C₈	C₂³×C₆₇	semidirect
851. C₂×D₄	C₂×D₄×C₆₇	semidirect
889. D₈	C₂×D₄×C₆₇	semidirect
890. D₈	C₂×D₄×C₆₇	semidirect
898. C₂×C₈	C₂×D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#576×C₆₇	2
C₂²×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#3485	2
C₆₇×#3484	2
C₆₇×#3273	2
C₆₇×#3272	2
C₆₇×#3267	2
C₆₇×#3264	2
C₆₇×#3154	2
C₆₇×#3057	2
C₆₇×#3054	2
C₆₇×#3042	2
C₆₇×#3041	2
C₆₇×#3009	2
C₆₇×#3008	2
C₆₇×#3005	2
C₆₇×#3003	2
C₆₇×#2948	2
C₆₇×#2930	2
#61058	67

Subgroups — C67×#61058 #30740309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61058 #30740309