Subgroups — C₆₇×#61050 #30740301

Order 17152.

2870 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3282	C₂	1	4	yes	maximal, complemented
6	D₄×SD₁₆×C₆₇	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3266	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3265	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×#3050	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3043	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3042	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3010	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3009	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3004	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3003	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2949	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
21	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
22	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
24	#577×C₆₇	—	2	8	no	—
25	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
28	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
31	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
33	C₂²×SD₁₆×C₆₇	—	2	8	no	—
34	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
37	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
39	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
41	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	D₄×Q₈×C₆₇	—	2	2	no	—
44	D₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
45	#548×C₆₇	—	2	2	no	—
46	#548×C₆₇	C₂²	1	4	yes	complemented
47	#546×C₆₇	—	2	2	no	—
48	#546×C₆₇	C₂²	1	4	yes	—
49	D₄²×C₆₇	—	2	2	no	—
50	D₄²×C₆₇	C₂²	1	4	yes	—
51	#536×C₆₇	—	2	2	no	—
52	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#535×C₆₇	C₂²	1	1	yes	characteristic
55	#535×C₆₇	C₂²	1	1	yes	characteristic
56	#534×C₆₇	—	2	2	no	—
57	#525×C₆₇	—	2	2	no	—
58	#525×C₆₇	C₂²	1	1	yes	characteristic
59	#525×C₆₇	C₂²	1	1	yes	characteristic
60	#525×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×#120×C₆₇	—	2	2	no	—
62	#519×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#518×C₆₇	C₂²	1	1	yes	characteristic
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	#468×C₆₇	C₂²	1	4	yes	complemented
69	#467×C₆₇	C₂²	1	2	yes	complemented
70	#466×C₆₇	C₂²	1	2	yes	complemented
71	#465×C₆₇	C₂²	1	4	yes	complemented
72	#465×C₆₇	C₂²	1	2	yes	complemented
73	#465×C₆₇	C₂²	1	2	yes	complemented
74	#464×C₆₇	C₂²	1	4	yes	complemented
75	#463×C₆₇	C₂²	1	4	yes	complemented
76	#461×C₆₇	C₂²	1	4	yes	complemented
77	#460×C₆₇	C₂²	1	4	yes	complemented
78	#452×C₆₇	C₂²	1	4	yes	complemented
79	#451×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	#448×C₆₇	C₂²	1	4	yes	complemented
84	#448×C₆₇	C₂²	1	4	yes	complemented
85	#447×C₆₇	C₂²	1	4	yes	complemented
86	#440×C₆₇	C₂²	1	4	yes	complemented
87	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
88	#435×C₆₇	C₂²	1	4	yes	complemented
89	C₈×D₄×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	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#418×C₆₇	C₂²	1	1	yes	characteristic
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	2₋¹⁺⁴×C₆₇	—	2	4	no	—
103	2₋¹⁺⁴×C₆₇	—	4	2	no	—
104	H(5,𝔽₂)×C₆₇	—	2	4	no	—
105	H(5,𝔽₂)×C₆₇	—	4	2	no	—
106	C₂×#41×C₆₇	—	2	1	no	—
107	C₂×#41×C₆₇	—	2	2	no	—
108	C₂×#41×C₆₇	—	2	1	no	—
109	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
110	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
111	C₂×#41×C₆₇	C₂³	1	2	yes	—
112	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×#41×C₆₇	C₂³	1	2	yes	complemented
114	C₂²×Q₈×C₆₇	—	2	1	no	—
115	C₂²×Q₈×C₆₇	—	2	1	no	—
116	C₂²×Q₈×C₆₇	—	2	2	no	—
117	C₂²×Q₈×C₆₇	—	2	4	no	—
118	C₂²×Q₈×C₆₇	—	4	2	no	—
119	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
120	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
121	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₆₇	C₂³	1	2	yes	complemented
123	C₂²×D₄×C₆₇	—	2	4	no	—
124	C₂²×D₄×C₆₇	—	2	2	no	—
125	C₂²×D₄×C₆₇	—	2	1	no	—
126	C₂²×D₄×C₆₇	—	2	4	no	—
127	C₂²×D₄×C₆₇	—	2	1	no	—
128	C₂²×D₄×C₆₇	—	2	2	no	—
129	C₂²×D₄×C₆₇	—	4	2	no	—
130	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
132	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
133	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₇	—	2	1	no	—
135	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
136	#137×C₆₇	—	2	4	no	—
137	#137×C₆₇	—	2	8	no	—
138	#137×C₆₇	—	4	2	no	—
139	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
140	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
141	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
142	#135×C₆₇	—	2	8	no	—
143	#135×C₆₇	—	2	4	no	—
144	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	complemented
145	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
146	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	complemented
147	C₂×SD₁₆×C₆₇	—	2	4	no	—
148	C₂×SD₁₆×C₆₇	—	2	4	no	—
149	C₂×SD₁₆×C₆₇	—	2	16	no	—
150	C₂×SD₁₆×C₆₇	—	2	16	no	—
151	C₂×SD₁₆×C₆₇	—	2	8	no	—
152	C₂×SD₁₆×C₆₇	—	2	4	no	—
153	C₂×SD₁₆×C₆₇	D₄	1	8	yes	complemented
154	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
155	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
157	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
163	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
164	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
165	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
166	C₂×D₈×C₆₇	C₂³	1	2	yes	—
167	C₂×D₈×C₆₇	C₂³	1	2	yes	—
168	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
169	#131×C₆₇	—	2	4	no	—
170	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₆₇	C₂³	1	2	yes	complemented
173	C₂²×C₈×C₆₇	—	2	4	no	—
174	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
175	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
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	—	2	4	no	—
181	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
182	#127×C₆₇	—	2	1	no	—
183	#127×C₆₇	C₂³	1	2	yes	—
184	#124×C₆₇	—	2	1	no	—
185	#124×C₆₇	—	2	1	no	—
186	#124×C₆₇	—	2	4	no	—
187	#124×C₆₇	C₂³	1	2	yes	—
188	#124×C₆₇	C₂³	1	2	yes	complemented
189	#123×C₆₇	—	2	2	no	—
190	#123×C₆₇	—	2	1	no	—
191	#123×C₆₇	—	2	1	no	—
192	#123×C₆₇	—	2	4	no	—
193	#123×C₆₇	—	2	2	no	—
194	#123×C₆₇	D₄	1	2	yes	—
195	C₂²⋊Q₈×C₆₇	—	2	4	no	—
196	C₂²⋊Q₈×C₆₇	—	2	2	no	—
197	C₂²⋊Q₈×C₆₇	—	2	4	no	—
198	C₂²⋊Q₈×C₆₇	—	2	4	no	—
199	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
200	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
203	#121×C₆₇	—	2	4	no	—
204	#121×C₆₇	—	2	4	no	—
205	#121×C₆₇	—	2	2	no	—
206	#121×C₆₇	—	2	4	no	—
207	#121×C₆₇	D₄	1	2	yes	—
208	#121×C₆₇	C₂³	1	2	yes	—
209	#121×C₆₇	C₂³	1	4	yes	—
210	#121×C₆₇	C₂³	1	2	yes	—
211	#120×C₆₇	—	2	1	no	—
212	#120×C₆₇	—	2	1	no	—
213	#120×C₆₇	—	2	2	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×Q₈×C₆₇	—	2	2	no	—
220	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
221	C₄×D₄×C₆₇	—	2	4	no	—
222	C₄×D₄×C₆₇	—	2	2	no	—
223	C₄×D₄×C₆₇	—	2	2	no	—
224	C₄×D₄×C₆₇	—	2	2	no	—
225	C₄×D₄×C₆₇	—	2	4	no	—
226	C₄×D₄×C₆₇	C₂³	1	4	yes	—
227	C₄×D₄×C₆₇	C₂³	1	4	yes	—
228	#117×C₆₇	—	2	2	no	—
229	#117×C₆₇	C₂³	1	1	yes	characteristic
230	#117×C₆₇	C₂³	1	1	yes	characteristic
231	#117×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊C₄×C₆₇	—	2	2	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	4	yes	complemented
238	#103×C₆₇	C₂³	1	2	yes	complemented
239	#103×C₆₇	C₂³	1	4	yes	complemented
240	#103×C₆₇	C₂³	1	2	yes	complemented
241	#102×C₆₇	C₂³	1	4	yes	—
242	#102×C₆₇	C₂³	1	4	yes	—
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	4	no	—
251	C₂⁴×C₆₇	—	2	1	no	—
252	C₂⁴×C₆₇	—	2	2	no	—
253	C₂⁴×C₆₇	—	4	4	no	—
254	C₂⁴×C₆₇	—	8	4	no	—
255	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
256	#41×C₆₇	—	2	2	no	—
257	#41×C₆₇	—	2	2	no	—
258	#41×C₆₇	—	2	4	no	—
259	#41×C₆₇	—	2	4	no	—
260	#41×C₆₇	—	2	2	no	—
261	#41×C₆₇	—	2	2	no	—
262	#41×C₆₇	—	2	2	no	—
263	#41×C₆₇	—	2	2	no	—
264	#41×C₆₇	—	4	2	no	—
265	#41×C₆₇	—	4	2	no	—
266	#41×C₆₇	—	4	8	no	—
267	#41×C₆₇	—	4	4	no	—
268	#41×C₆₇	—	4	4	no	—
269	C₂×Q₈×C₆₇	—	2	1	no	—
270	C₂×Q₈×C₆₇	—	2	4	no	—
271	C₂×Q₈×C₆₇	—	2	1	no	—
272	C₂×Q₈×C₆₇	—	2	2	no	—
273	C₂×Q₈×C₆₇	—	2	2	no	—
274	C₂×Q₈×C₆₇	—	2	8	no	—
275	C₂×Q₈×C₆₇	—	2	4	no	—
276	C₂×Q₈×C₆₇	—	2	2	no	—
277	C₂×Q₈×C₆₇	—	2	2	no	—
278	C₂×Q₈×C₆₇	—	4	4	no	—
279	C₂×Q₈×C₆₇	—	4	4	no	—
280	C₂×Q₈×C₆₇	—	4	2	no	—
281	C₂×Q₈×C₆₇	—	4	8	no	—
282	C₂×Q₈×C₆₇	—	4	4	no	—
283	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
284	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	complemented
285	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
287	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
288	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
289	C₂×D₄×C₆₇	—	2	8	no	—
290	C₂×D₄×C₆₇	—	2	4	no	—
291	C₂×D₄×C₆₇	—	2	2	no	—
292	C₂×D₄×C₆₇	—	2	2	no	—
293	C₂×D₄×C₆₇	—	2	1	no	—
294	C₂×D₄×C₆₇	—	2	2	no	—
295	C₂×D₄×C₆₇	—	2	1	no	—
296	C₂×D₄×C₆₇	—	2	2	no	—
297	C₂×D₄×C₆₇	—	2	4	no	—
298	C₂×D₄×C₆₇	—	2	1	no	—
299	C₂×D₄×C₆₇	—	2	2	no	—
300	C₂×D₄×C₆₇	—	2	2	no	—
301	C₂×D₄×C₆₇	—	2	4	no	—
302	C₂×D₄×C₆₇	—	2	1	no	—
303	C₂×D₄×C₆₇	—	2	4	no	—
304	C₂×D₄×C₆₇	—	2	2	no	—
305	C₂×D₄×C₆₇	—	2	2	no	—
306	C₂×D₄×C₆₇	—	4	4	no	—
307	C₂×D₄×C₆₇	—	4	2	no	—
308	C₂×D₄×C₆₇	—	4	8	no	—
309	C₂×D₄×C₆₇	—	4	4	no	—
310	C₂×D₄×C₆₇	—	4	4	no	—
311	C₂×D₄×C₆₇	—	4	8	no	—
312	C₂×D₄×C₆₇	—	8	8	no	—
313	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
314	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
315	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
316	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
317	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
318	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₆₇	—	2	1	no	—
322	C₂²×C₄×C₆₇	—	2	2	no	—
323	C₂²×C₄×C₆₇	—	2	2	no	—
324	C₂²×C₄×C₆₇	—	2	4	no	—
325	C₂²×C₄×C₆₇	—	2	2	no	—
326	C₂²×C₄×C₆₇	—	2	1	no	—
327	C₂²×C₄×C₆₇	—	2	2	no	—
328	C₂²×C₄×C₆₇	—	2	1	no	—
329	C₂²×C₄×C₆₇	—	2	1	no	—
330	C₂²×C₄×C₆₇	—	2	2	no	—
331	C₂²×C₄×C₆₇	—	2	4	no	—
332	C₂²×C₄×C₆₇	—	4	4	no	—
333	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
334	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
338	Q₁₆×C₆₇	—	2	4	no	—
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	8	no	—
344	SD₁₆×C₆₇	—	2	4	no	—
345	SD₁₆×C₆₇	—	2	4	no	—
346	SD₁₆×C₆₇	—	2	4	no	—
347	SD₁₆×C₆₇	—	2	2	no	—
348	SD₁₆×C₆₇	—	2	2	no	—
349	SD₁₆×C₆₇	—	4	2	no	—
350	SD₁₆×C₆₇	—	4	2	no	—
351	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
352	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
353	D₈×C₆₇	—	2	4	no	—
354	D₈×C₆₇	—	2	2	no	—
355	D₈×C₆₇	—	4	2	no	—
356	M₁₆×C₆₇	—	2	2	no	—
357	M₁₆×C₆₇	—	2	2	no	—
358	M₁₆×C₆₇	—	2	4	no	—
359	C₂×C₈×C₆₇	—	2	2	no	—
360	C₂×C₈×C₆₇	—	2	4	no	—
361	C₂×C₈×C₆₇	—	2	4	no	—
362	C₂×C₈×C₆₇	—	2	4	no	—
363	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	complemented
364	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
365	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
366	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
367	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₆₇	—	2	4	no	—
370	C₄⋊C₄×C₆₇	—	2	2	no	—
371	C₄⋊C₄×C₆₇	—	2	4	no	—
372	C₄⋊C₄×C₆₇	—	2	2	no	—
373	C₄⋊C₄×C₆₇	—	2	4	no	—
374	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₆₇	C₂×D₄	1	4	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	2	no	—
380	C₂²⋊C₄×C₆₇	—	2	1	no	—
381	C₂²⋊C₄×C₆₇	—	2	2	no	—
382	C₂²⋊C₄×C₆₇	—	2	4	no	—
383	C₂²⋊C₄×C₆₇	—	2	4	no	—
384	C₂²⋊C₄×C₆₇	—	2	4	no	—
385	C₂²⋊C₄×C₆₇	—	2	4	no	—
386	C₂²⋊C₄×C₆₇	—	2	2	no	—
387	C₂²⋊C₄×C₆₇	—	2	4	no	—
388	C₂²⋊C₄×C₆₇	—	2	2	no	—
389	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
391	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
392	C₄²×C₆₇	—	2	4	no	—
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	4	no	—
398	C₂³×C₆₇	—	2	2	no	—
399	C₂³×C₆₇	—	2	4	no	—
400	C₂³×C₆₇	—	2	1	no	—
401	C₂³×C₆₇	—	2	2	no	—
402	C₂³×C₆₇	—	2	1	no	—
403	C₂³×C₆₇	—	4	8	no	—
404	C₂³×C₆₇	—	4	4	no	—
405	C₂³×C₆₇	—	4	2	no	—
406	C₂³×C₆₇	—	4	8	no	—
407	C₂³×C₆₇	—	8	2	no	—
408	C₂³×C₆₇	—	8	4	no	—
409	C₂³×C₆₇	—	8	2	no	—
410	C₂³×C₆₇	—	8	4	no	—
411	C₂³×C₆₇	—	8	16	no	—
412	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
413	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
414	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
415	Q₈×C₆₇	—	2	4	no	—
416	Q₈×C₆₇	—	2	2	no	—
417	Q₈×C₆₇	—	2	2	no	—
418	Q₈×C₆₇	—	2	2	no	—
419	Q₈×C₆₇	—	2	1	no	—
420	Q₈×C₆₇	—	2	1	no	—
421	Q₈×C₆₇	—	2	1	no	—
422	Q₈×C₆₇	—	2	2	no	—
423	Q₈×C₆₇	—	2	1	no	—
424	Q₈×C₆₇	—	4	8	no	—
425	Q₈×C₆₇	—	4	4	no	—
426	Q₈×C₆₇	—	4	2	no	—
427	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
428	D₄×C₆₇	—	2	4	no	—
429	D₄×C₆₇	—	2	8	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	1	no	—
437	D₄×C₆₇	—	2	2	no	—
438	D₄×C₆₇	—	2	1	no	—
439	D₄×C₆₇	—	4	8	no	—
440	D₄×C₆₇	—	4	4	no	—
441	D₄×C₆₇	—	4	4	no	—
442	D₄×C₆₇	—	4	4	no	—
443	D₄×C₆₇	—	4	2	no	—
444	D₄×C₆₇	—	4	2	no	—
445	D₄×C₆₇	—	4	4	no	—
446	D₄×C₆₇	—	4	4	no	—
447	D₄×C₆₇	—	4	2	no	—
448	D₄×C₆₇	—	8	4	no	—
449	D₄×C₆₇	—	8	4	no	—
450	D₄×C₆₇	C₂²×D₄	1	4	yes	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	2	4	no	—
453	C₂×C₄×C₆₇	—	2	2	no	—
454	C₂×C₄×C₆₇	—	2	4	no	—
455	C₂×C₄×C₆₇	—	2	2	no	—
456	C₂×C₄×C₆₇	—	2	2	no	—
457	C₂×C₄×C₆₇	—	2	2	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	1	no	—
462	C₂×C₄×C₆₇	—	2	2	no	—
463	C₂×C₄×C₆₇	—	2	1	no	—
464	C₂×C₄×C₆₇	—	4	4	no	—
465	C₂×C₄×C₆₇	—	4	8	no	—
466	C₂×C₄×C₆₇	—	4	4	no	—
467	C₂×C₄×C₆₇	—	4	4	no	—
468	C₂×C₄×C₆₇	—	4	2	no	—
469	C₂×C₄×C₆₇	—	4	2	no	—
470	C₂×C₄×C₆₇	—	4	2	no	—
471	C₂×C₄×C₆₇	—	8	4	no	—
472	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
473	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
477	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
478	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
479	C₈×C₆₇	—	2	2	no	—
480	C₈×C₆₇	—	2	2	no	—
481	C₈×C₆₇	—	2	2	no	—
482	C₈×C₆₇	C₂²×D₄	1	2	yes	—
483	C₈×C₆₇	C₂²×D₄	1	2	yes	—
484	C₂²×C₆₇	—	2	8	no	—
485	C₂²×C₆₇	—	2	2	no	—
486	C₂²×C₆₇	—	2	2	no	—
487	C₂²×C₆₇	—	2	2	no	—
488	C₂²×C₆₇	—	2	2	no	—
489	C₂²×C₆₇	—	2	4	no	—
490	C₂²×C₆₇	—	2	4	no	—
491	C₂²×C₆₇	—	4	4	no	—
492	C₂²×C₆₇	—	4	1	no	—
493	C₂²×C₆₇	—	4	1	no	—
494	C₂²×C₆₇	—	4	2	no	—
495	C₂²×C₆₇	—	4	2	no	—
496	C₂²×C₆₇	—	4	2	no	—
497	C₂²×C₆₇	—	4	4	no	—
498	C₂²×C₆₇	—	8	4	no	—
499	C₂²×C₆₇	—	8	16	no	—
500	C₂²×C₆₇	—	8	4	no	—
501	C₂²×C₆₇	—	16	4	no	—
502	C₂²×C₆₇	D₄²	1	2	yes	—
503	C₂²×C₆₇	#577	1	4	yes	complemented
504	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
505	C₄×C₆₇	—	2	2	no	—
506	C₄×C₆₇	—	2	4	no	—
507	C₄×C₆₇	—	2	2	no	—
508	C₄×C₆₇	—	2	4	no	—
509	C₄×C₆₇	—	4	1	no	—
510	C₄×C₆₇	—	4	1	no	—
511	C₄×C₆₇	—	4	2	no	—
512	C₄×C₆₇	—	4	2	no	—
513	C₄×C₆₇	—	4	2	no	—
514	C₄×C₆₇	D₄²	1	2	yes	—
515	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
516	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
517	#61050	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
518	C₂×C₆₇	—	2	2	no	—
519	C₂×C₆₇	—	2	4	no	—
520	C₂×C₆₇	—	4	2	no	—
521	C₂×C₆₇	—	4	4	no	—
522	C₂×C₆₇	—	8	1	no	—
523	C₂×C₆₇	—	8	2	no	—
524	C₂×C₆₇	—	8	1	no	—
525	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
526	C₂×C₆₇	C₂×#577	1	2	yes	—
527	C₂×#577	C₂×C₆₇	1	1	yes	characteristic, complemented
528	C₂³×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
529	#3486	C₂×C₆₇	1	1	yes	characteristic, complemented
530	#3484	C₂×C₆₇	1	1	yes	characteristic, complemented
531	#3282	C₂×C₆₇	1	4	yes	complemented
532	D₄×SD₁₆	C₂×C₆₇	1	4	yes	complemented
533	#3266	C₂×C₆₇	1	4	yes	complemented
534	#3265	C₂×C₆₇	1	4	yes	complemented
535	#3154	C₂×C₆₇	1	1	yes	characteristic, complemented
536	#3057	C₂×C₆₇	1	1	yes	characteristic, complemented
537	#3050	C₂×C₆₇	1	1	yes	characteristic, complemented
538	#3043	C₂×C₆₇	1	1	yes	characteristic, complemented
539	#3042	C₂×C₆₇	1	1	yes	characteristic, complemented
540	#3010	C₂×C₆₇	1	1	yes	characteristic, complemented
541	#3009	C₂×C₆₇	1	1	yes	characteristic, complemented
542	#3004	C₂×C₆₇	1	1	yes	characteristic, complemented
543	#3003	C₂×C₆₇	1	1	yes	characteristic, complemented
544	#2949	C₂×C₆₇	1	1	yes	characteristic, complemented
545	#2929	C₂×C₆₇	1	1	yes	characteristic, complemented
546	C₆₇	#61050	1	1	yes	characteristic, direct product factor, Sylow
547	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
548	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
549	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
550	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
551	#577	—	2	8	no	—
552	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
553	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
554	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
555	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
556	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
557	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
558	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
559	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
560	C₂²×SD₁₆	—	2	8	no	—
561	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
562	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
563	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
564	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
565	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
566	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
567	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
568	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
569	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
570	D₄×Q₈	—	2	2	no	—
571	D₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
572	#548	—	2	2	no	—
573	#548	C₂²×C₆₇	1	4	yes	complemented
574	#546	—	2	2	no	—
575	#546	C₂²×C₆₇	1	4	yes	—
576	D₄²	—	2	2	no	—
577	D₄²	C₂²×C₆₇	1	4	yes	—
578	#536	—	2	2	no	—
579	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
580	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
581	#535	C₂²×C₆₇	1	1	yes	characteristic
582	#535	C₂²×C₆₇	1	1	yes	characteristic
583	#534	—	2	2	no	—
584	#525	—	2	2	no	—
585	#525	C₂²×C₆₇	1	1	yes	characteristic
586	#525	C₂²×C₆₇	1	1	yes	characteristic
587	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
588	C₂×#120	—	2	2	no	—
589	#519	C₂²×C₆₇	1	1	yes	characteristic, complemented
590	#518	C₂²×C₆₇	1	1	yes	characteristic
591	#497	C₂²×C₆₇	1	2	yes	complemented
592	#496	C₂²×C₆₇	1	2	yes	complemented
593	#495	C₂²×C₆₇	1	2	yes	complemented
594	#492	C₂²×C₆₇	1	2	yes	complemented
595	#468	C₂²×C₆₇	1	4	yes	complemented
596	#467	C₂²×C₆₇	1	2	yes	complemented
597	#466	C₂²×C₆₇	1	2	yes	complemented
598	#465	C₂²×C₆₇	1	4	yes	complemented
599	#465	C₂²×C₆₇	1	2	yes	complemented
600	#465	C₂²×C₆₇	1	2	yes	complemented
601	#464	C₂²×C₆₇	1	4	yes	complemented
602	#463	C₂²×C₆₇	1	4	yes	complemented
603	#461	C₂²×C₆₇	1	4	yes	complemented
604	#460	C₂²×C₆₇	1	4	yes	complemented
605	#452	C₂²×C₆₇	1	4	yes	complemented
606	#451	C₂²×C₆₇	1	4	yes	complemented
607	#450	C₂²×C₆₇	1	4	yes	complemented
608	#450	C₂²×C₆₇	1	4	yes	complemented
609	#449	C₂²×C₆₇	1	4	yes	complemented
610	#448	C₂²×C₆₇	1	4	yes	complemented
611	#448	C₂²×C₆₇	1	4	yes	complemented
612	#447	C₂²×C₆₇	1	4	yes	complemented
613	#440	C₂²×C₆₇	1	4	yes	complemented
614	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
615	#435	C₂²×C₆₇	1	4	yes	complemented
616	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
617	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
618	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
619	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
620	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
621	#418	C₂²×C₆₇	1	1	yes	characteristic
622	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
623	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
624	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
626	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	C₂⁵	—	2	1	no	—
629	2₋¹⁺⁴	—	2	4	no	—
630	2₋¹⁺⁴	—	4	2	no	—
631	H(5,𝔽₂)	—	2	4	no	—
632	H(5,𝔽₂)	—	4	2	no	—
633	C₂×#41	—	2	1	no	—
634	C₂×#41	—	2	2	no	—
635	C₂×#41	—	2	1	no	—
636	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
637	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
638	C₂×#41	C₂³×C₆₇	1	2	yes	—
639	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
640	C₂×#41	C₂³×C₆₇	1	2	yes	complemented
641	C₂²×Q₈	—	2	1	no	—
642	C₂²×Q₈	—	2	1	no	—
643	C₂²×Q₈	—	2	2	no	—
644	C₂²×Q₈	—	2	4	no	—
645	C₂²×Q₈	—	4	2	no	—
646	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
647	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
648	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
649	C₂²×Q₈	C₂³×C₆₇	1	2	yes	complemented
650	C₂²×D₄	—	2	4	no	—
651	C₂²×D₄	—	2	2	no	—
652	C₂²×D₄	—	2	1	no	—
653	C₂²×D₄	—	2	4	no	—
654	C₂²×D₄	—	2	1	no	—
655	C₂²×D₄	—	2	2	no	—
656	C₂²×D₄	—	4	2	no	—
657	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
658	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
659	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
660	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
661	C₂³×C₄	—	2	1	no	—
662	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
663	#137	—	2	4	no	—
664	#137	—	2	8	no	—
665	#137	—	4	2	no	—
666	AGL(1,ℤ/8)	—	2	4	no	—
667	AGL(1,ℤ/8)	—	2	8	no	—
668	AGL(1,ℤ/8)	—	4	2	no	—
669	#135	—	2	8	no	—
670	#135	—	2	4	no	—
671	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	complemented
672	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
673	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	complemented
674	C₂×SD₁₆	—	2	4	no	—
675	C₂×SD₁₆	—	2	4	no	—
676	C₂×SD₁₆	—	2	16	no	—
677	C₂×SD₁₆	—	2	16	no	—
678	C₂×SD₁₆	—	2	8	no	—
679	C₂×SD₁₆	—	2	4	no	—
680	C₂×SD₁₆	D₄×C₆₇	1	8	yes	complemented
681	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
682	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
683	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
684	C₂×SD₁₆	C₂³×C₆₇	1	2	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	1	yes	characteristic, complemented
690	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
691	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
692	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
693	C₂×D₈	C₂³×C₆₇	1	2	yes	—
694	C₂×D₈	C₂³×C₆₇	1	2	yes	—
695	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
696	#131	—	2	4	no	—
697	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
698	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
699	C₂×M₁₆	C₂³×C₆₇	1	2	yes	complemented
700	C₂²×C₈	—	2	4	no	—
701	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
702	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
703	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
704	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
705	C₂²×C₈	C₂³×C₆₇	1	2	yes	complemented
706	C₄⋊Q₈	—	2	1	no	—
707	C₄⋊Q₈	—	2	4	no	—
708	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
709	#127	—	2	1	no	—
710	#127	C₂³×C₆₇	1	2	yes	—
711	#124	—	2	1	no	—
712	#124	—	2	1	no	—
713	#124	—	2	4	no	—
714	#124	C₂³×C₆₇	1	2	yes	—
715	#124	C₂³×C₆₇	1	2	yes	complemented
716	#123	—	2	2	no	—
717	#123	—	2	1	no	—
718	#123	—	2	1	no	—
719	#123	—	2	4	no	—
720	#123	—	2	2	no	—
721	#123	D₄×C₆₇	1	2	yes	—
722	C₂²⋊Q₈	—	2	4	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	4	no	—
725	C₂²⋊Q₈	—	2	4	no	—
726	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
727	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
728	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
729	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	complemented
730	#121	—	2	4	no	—
731	#121	—	2	4	no	—
732	#121	—	2	2	no	—
733	#121	—	2	4	no	—
734	#121	D₄×C₆₇	1	2	yes	—
735	#121	C₂³×C₆₇	1	2	yes	—
736	#121	C₂³×C₆₇	1	2	yes	—
737	#121	C₂³×C₆₇	1	4	yes	—
738	#120	—	2	1	no	—
739	#120	—	2	1	no	—
740	#120	—	2	2	no	—
741	#120	—	2	4	no	—
742	#120	—	2	2	no	—
743	#120	—	2	4	no	—
744	#120	—	2	4	no	—
745	#120	D₄×C₆₇	1	2	yes	—
746	C₄×Q₈	—	2	2	no	—
747	C₄×Q₈	C₂³×C₆₇	1	4	yes	complemented
748	C₄×D₄	—	2	4	no	—
749	C₄×D₄	—	2	2	no	—
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	2	2	no	—
752	C₄×D₄	—	2	4	no	—
753	C₄×D₄	C₂³×C₆₇	1	4	yes	—
754	C₄×D₄	C₂³×C₆₇	1	4	yes	—
755	#117	—	2	2	no	—
756	#117	C₂³×C₆₇	1	1	yes	characteristic
757	#117	C₂³×C₆₇	1	1	yes	characteristic
758	#117	C₂³×C₆₇	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	—	2	2	no	—
760	C₂×C₂²⋊C₄	—	2	4	no	—
761	#107	C₂³×C₆₇	1	2	yes	complemented
762	#106	C₂³×C₆₇	1	2	yes	complemented
763	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
764	#103	C₂³×C₆₇	1	2	yes	complemented
765	#103	C₂³×C₆₇	1	2	yes	complemented
766	#103	C₂³×C₆₇	1	4	yes	complemented
767	#103	C₂³×C₆₇	1	4	yes	complemented
768	#102	C₂³×C₆₇	1	4	yes	—
769	#102	C₂³×C₆₇	1	4	yes	—
770	#102	C₂³×C₆₇	1	2	yes	complemented
771	#102	C₂³×C₆₇	1	2	yes	complemented
772	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
773	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
774	#97	C₂³×C₆₇	1	2	yes	complemented
775	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
776	C₂⁴	—	2	1	no	—
777	C₂⁴	—	2	4	no	—
778	C₂⁴	—	2	1	no	—
779	C₂⁴	—	2	2	no	—
780	C₂⁴	—	4	4	no	—
781	C₂⁴	—	8	4	no	—
782	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
783	#41	—	2	2	no	—
784	#41	—	2	2	no	—
785	#41	—	2	4	no	—
786	#41	—	2	4	no	—
787	#41	—	2	2	no	—
788	#41	—	2	2	no	—
789	#41	—	2	2	no	—
790	#41	—	2	2	no	—
791	#41	—	4	2	no	—
792	#41	—	4	2	no	—
793	#41	—	4	8	no	—
794	#41	—	4	4	no	—
795	#41	—	4	4	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	4	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	2	no	—
800	C₂×Q₈	—	2	2	no	—
801	C₂×Q₈	—	2	8	no	—
802	C₂×Q₈	—	2	4	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	4	4	no	—
806	C₂×Q₈	—	4	4	no	—
807	C₂×Q₈	—	4	2	no	—
808	C₂×Q₈	—	4	8	no	—
809	C₂×Q₈	—	4	4	no	—
810	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
811	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	complemented
812	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
813	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
814	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
815	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
816	C₂×D₄	—	2	8	no	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	2	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	1	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	1	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	4	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	4	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	4	4	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	4	8	no	—
836	C₂×D₄	—	4	4	no	—
837	C₂×D₄	—	4	4	no	—
838	C₂×D₄	—	4	8	no	—
839	C₂×D₄	—	8	8	no	—
840	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
841	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
842	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
843	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
844	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
845	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
846	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
847	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	4	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	4	no	—
859	C₂²×C₄	—	4	4	no	—
860	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
861	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
863	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
865	Q₁₆	—	2	4	no	—
866	Q₁₆	—	2	2	no	—
867	Q₁₆	—	4	2	no	—
868	SD₁₆	—	2	8	no	—
869	SD₁₆	—	2	4	no	—
870	SD₁₆	—	2	8	no	—
871	SD₁₆	—	2	4	no	—
872	SD₁₆	—	2	4	no	—
873	SD₁₆	—	2	4	no	—
874	SD₁₆	—	2	2	no	—
875	SD₁₆	—	2	2	no	—
876	SD₁₆	—	4	2	no	—
877	SD₁₆	—	4	2	no	—
878	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
879	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
880	D₈	—	2	4	no	—
881	D₈	—	2	2	no	—
882	D₈	—	4	2	no	—
883	M₁₆	—	2	2	no	—
884	M₁₆	—	2	2	no	—
885	M₁₆	—	2	4	no	—
886	C₂×C₈	—	2	2	no	—
887	C₂×C₈	—	2	4	no	—
888	C₂×C₈	—	2	4	no	—
889	C₂×C₈	—	2	4	no	—
890	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	complemented
891	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
892	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
893	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
894	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
895	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
896	C₄⋊C₄	—	2	4	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	4	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	4	no	—
901	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
902	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
903	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
904	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
905	C₂²⋊C₄	—	2	1	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	1	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	4	no	—
910	C₂²⋊C₄	—	2	4	no	—
911	C₂²⋊C₄	—	2	4	no	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
917	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
918	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
919	C₄²	—	2	4	no	—
920	C₄²	—	2	1	no	—
921	C₄²	—	2	1	no	—
922	C₄²	C₂⁴×C₆₇	1	2	yes	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	4	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	4	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	2	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	4	8	no	—
931	C₂³	—	4	4	no	—
932	C₂³	—	4	2	no	—
933	C₂³	—	4	8	no	—
934	C₂³	—	8	2	no	—
935	C₂³	—	8	4	no	—
936	C₂³	—	8	2	no	—
937	C₂³	—	8	4	no	—
938	C₂³	—	8	16	no	—
939	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
940	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
941	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
942	Q₈	—	2	4	no	—
943	Q₈	—	2	2	no	—
944	Q₈	—	2	2	no	—
945	Q₈	—	2	2	no	—
946	Q₈	—	2	1	no	—
947	Q₈	—	2	1	no	—
948	Q₈	—	2	1	no	—
949	Q₈	—	2	2	no	—
950	Q₈	—	2	1	no	—
951	Q₈	—	4	8	no	—
952	Q₈	—	4	4	no	—
953	Q₈	—	4	2	no	—
954	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
955	D₄	—	2	4	no	—
956	D₄	—	2	8	no	—
957	D₄	—	2	4	no	—
958	D₄	—	2	2	no	—
959	D₄	—	2	1	no	—
960	D₄	—	2	1	no	—
961	D₄	—	2	2	no	—
962	D₄	—	2	2	no	—
963	D₄	—	2	1	no	—
964	D₄	—	2	2	no	—
965	D₄	—	2	1	no	—
966	D₄	—	4	8	no	—
967	D₄	—	4	4	no	—
968	D₄	—	4	4	no	—
969	D₄	—	4	4	no	—
970	D₄	—	4	2	no	—
971	D₄	—	4	2	no	—
972	D₄	—	4	4	no	—
973	D₄	—	4	4	no	—
974	D₄	—	4	2	no	—
975	D₄	—	8	4	no	—
976	D₄	—	8	4	no	—
977	D₄	C₂²×D₄×C₆₇	1	4	yes	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	4	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	4	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	4	4	no	—
992	C₂×C₄	—	4	8	no	—
993	C₂×C₄	—	4	4	no	—
994	C₂×C₄	—	4	4	no	—
995	C₂×C₄	—	4	2	no	—
996	C₂×C₄	—	4	2	no	—
997	C₂×C₄	—	4	2	no	—
998	C₂×C₄	—	8	4	no	—
999	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1000	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1001	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1002	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1003	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1004	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1005	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1006	C₈	—	2	2	no	—
1007	C₈	—	2	2	no	—
1008	C₈	—	2	2	no	—
1009	C₈	C₂²×D₄×C₆₇	1	2	yes	—
1010	C₈	C₂²×D₄×C₆₇	1	2	yes	—
1011	C₂²	—	2	8	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	4	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	4	no	—
1018	C₂²	—	4	4	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	4	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	1	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	8	4	no	—
1026	C₂²	—	8	16	no	—
1027	C₂²	—	8	4	no	—
1028	C₂²	—	16	4	no	—
1029	C₂²	D₄²×C₆₇	1	2	yes	—
1030	C₂²	#577×C₆₇	1	4	yes	complemented
1031	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1032	C₄	—	2	4	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	2	4	no	—
1035	C₄	—	2	2	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	2	no	—
1041	C₄	D₄²×C₆₇	1	2	yes	—
1042	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1043	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1044	C₂	—	2	2	no	—
1045	C₂	—	2	4	no	—
1046	C₂	—	4	2	no	—
1047	C₂	—	4	4	no	—
1048	C₂	—	8	2	no	—
1049	C₂	—	8	1	no	—
1050	C₂	—	8	1	no	—
1051	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1052	C₂	C₂×#577×C₆₇	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×#577×C₆₇	C₂	semidirect
2. C₂³×SD₁₆×C₆₇	C₂	semidirect
3. C₆₇×#3486	C₂	semidirect
4. C₆₇×#3484	C₂	semidirect
5. C₆₇×#3282	C₂	semidirect
6. D₄×SD₁₆×C₆₇	C₂	semidirect
7. C₆₇×#3266	C₂	semidirect
8. C₆₇×#3265	C₂	semidirect
9. C₆₇×#3154	C₂	semidirect
10. C₆₇×#3057	C₂	semidirect
11. C₆₇×#3050	C₂	semidirect
12. C₆₇×#3043	C₂	semidirect
13. C₆₇×#3042	C₂	semidirect
14. C₆₇×#3010	C₂	semidirect
15. C₆₇×#3009	C₂	semidirect
16. C₆₇×#3004	C₂	semidirect
17. C₆₇×#3003	C₂	semidirect
18. C₆₇×#2949	C₂	semidirect
19. C₆₇×#2929	C₂	semidirect
20. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
22. C₂³×Q₈×C₆₇	C₂²	semidirect
25. C₂×#137×C₆₇	C₂²	semidirect
26. C₂×#137×C₆₇	C₂²	semidirect
27. C₂×#137×C₆₇	C₂²	semidirect
29. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
30. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
31. C₂×#135×C₆₇	C₂²	semidirect
32. C₂×#135×C₆₇	C₂²	semidirect
36. C₂²×SD₁₆×C₆₇	C₂²	semidirect
37. C₂²×SD₁₆×C₆₇	C₂²	semidirect
38. C₂²×SD₁₆×C₆₇	C₂²	semidirect
39. C₂²×SD₁₆×C₆₇	C₂²	semidirect
40. C₂²×SD₁₆×C₆₇	C₂²	semidirect
41. C₂×#131×C₆₇	C₂²	semidirect
42. C₂³×C₈×C₆₇	C₂²	semidirect
44. D₄×Q₈×C₆₇	C₂²	semidirect
46. #548×C₆₇	C₂²	semidirect
52. #536×C₆₇	C₂²	semidirect
53. #536×C₆₇	C₂²	semidirect
60. #525×C₆₇	C₂²	semidirect
62. #519×C₆₇	C₂²	semidirect
64. #497×C₆₇	C₂²	semidirect
65. #496×C₆₇	C₂²	semidirect
66. #495×C₆₇	C₂²	semidirect
67. #492×C₆₇	C₂²	semidirect
68. #468×C₆₇	C₂²	semidirect
69. #467×C₆₇	C₂²	semidirect
70. #466×C₆₇	C₂²	semidirect
71. #465×C₆₇	C₂²	semidirect
72. #465×C₆₇	C₂²	semidirect
73. #465×C₆₇	C₂²	semidirect
74. #464×C₆₇	C₂²	semidirect
75. #463×C₆₇	C₂²	semidirect
76. #461×C₆₇	C₂²	semidirect
77. #460×C₆₇	C₂²	semidirect
78. #452×C₆₇	C₂²	semidirect
79. #451×C₆₇	C₂²	semidirect
80. #450×C₆₇	C₂²	semidirect
81. #450×C₆₇	C₂²	semidirect
82. #449×C₆₇	C₂²	semidirect
83. #448×C₆₇	C₂²	semidirect
84. #448×C₆₇	C₂²	semidirect
85. #447×C₆₇	C₂²	semidirect
86. #440×C₆₇	C₂²	semidirect
87. C₄×SD₁₆×C₆₇	C₂²	semidirect
88. #435×C₆₇	C₂²	semidirect
89. C₈×D₄×C₆₇	C₂²	semidirect
90. #427×C₆₇	C₂²	semidirect
91. #424×C₆₇	C₂²	semidirect
92. #419×C₆₇	C₂²	semidirect
93. #419×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
113. C₂×#41×C₆₇	C₂³	semidirect
122. C₂²×Q₈×C₆₇	C₂³	semidirect
144. C₂×Q₁₆×C₆₇	C₂³	semidirect
145. C₂×Q₁₆×C₆₇	C₂³	semidirect
146. C₂×Q₁₆×C₆₇	C₂³	semidirect
153. C₂×SD₁₆×C₆₇	D₄	semidirect
162. C₂×SD₁₆×C₆₇	C₂³	semidirect
163. C₂×SD₁₆×C₆₇	C₂³	semidirect
164. C₂×SD₁₆×C₆₇	C₂³	semidirect
165. C₂×SD₁₆×C₆₇	C₂³	semidirect
168. C₂×D₈×C₆₇	C₂³	semidirect
172. C₂×M₁₆×C₆₇	C₂³	semidirect
178. C₂²×C₈×C₆₇	C₂³	semidirect
181. C₄⋊Q₈×C₆₇	C₂³	semidirect
188. #124×C₆₇	C₂³	semidirect
202. C₂²⋊Q₈×C₆₇	C₂³	semidirect
220. C₄×Q₈×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
240. #103×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
284. C₂×Q₈×C₆₇	C₂×D₄	semidirect
351. SD₁₆×C₆₇	C₂×D₄	semidirect
352. SD₁₆×C₆₇	C₂×D₄	semidirect
363. C₂×C₈×C₆₇	C₂×D₄	semidirect
503. C₂²×C₆₇	#577	semidirect
517. #61050	C₆₇	direct (N × H)
527. C₂×#577	C₂×C₆₇	semidirect
528. C₂³×SD₁₆	C₂×C₆₇	semidirect
529. #3486	C₂×C₆₇	semidirect
530. #3484	C₂×C₆₇	semidirect
531. #3282	C₂×C₆₇	semidirect
532. D₄×SD₁₆	C₂×C₆₇	semidirect
533. #3266	C₂×C₆₇	semidirect
534. #3265	C₂×C₆₇	semidirect
535. #3154	C₂×C₆₇	semidirect
536. #3057	C₂×C₆₇	semidirect
537. #3050	C₂×C₆₇	semidirect
538. #3043	C₂×C₆₇	semidirect
539. #3042	C₂×C₆₇	semidirect
540. #3010	C₂×C₆₇	semidirect
541. #3009	C₂×C₆₇	semidirect
542. #3004	C₂×C₆₇	semidirect
543. #3003	C₂×C₆₇	semidirect
544. #2949	C₂×C₆₇	semidirect
545. #2929	C₂×C₆₇	semidirect
546. C₆₇	#61050	direct (N × H)
547. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
549. C₂³×Q₈	C₂²×C₆₇	semidirect
552. C₂×#137	C₂²×C₆₇	semidirect
553. C₂×#137	C₂²×C₆₇	semidirect
554. C₂×#137	C₂²×C₆₇	semidirect
556. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
557. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
558. C₂×#135	C₂²×C₆₇	semidirect
559. C₂×#135	C₂²×C₆₇	semidirect
563. C₂²×SD₁₆	C₂²×C₆₇	semidirect
564. C₂²×SD₁₆	C₂²×C₆₇	semidirect
565. C₂²×SD₁₆	C₂²×C₆₇	semidirect
566. C₂²×SD₁₆	C₂²×C₆₇	semidirect
567. C₂²×SD₁₆	C₂²×C₆₇	semidirect
568. C₂×#131	C₂²×C₆₇	semidirect
569. C₂³×C₈	C₂²×C₆₇	semidirect
571. D₄×Q₈	C₂²×C₆₇	semidirect
573. #548	C₂²×C₆₇	semidirect
579. #536	C₂²×C₆₇	semidirect
580. #536	C₂²×C₆₇	semidirect
587. #525	C₂²×C₆₇	semidirect
589. #519	C₂²×C₆₇	semidirect
591. #497	C₂²×C₆₇	semidirect
592. #496	C₂²×C₆₇	semidirect
593. #495	C₂²×C₆₇	semidirect
594. #492	C₂²×C₆₇	semidirect
595. #468	C₂²×C₆₇	semidirect
596. #467	C₂²×C₆₇	semidirect
597. #466	C₂²×C₆₇	semidirect
598. #465	C₂²×C₆₇	semidirect
599. #465	C₂²×C₆₇	semidirect
600. #465	C₂²×C₆₇	semidirect
601. #464	C₂²×C₆₇	semidirect
602. #463	C₂²×C₆₇	semidirect
603. #461	C₂²×C₆₇	semidirect
604. #460	C₂²×C₆₇	semidirect
605. #452	C₂²×C₆₇	semidirect
606. #451	C₂²×C₆₇	semidirect
607. #450	C₂²×C₆₇	semidirect
608. #450	C₂²×C₆₇	semidirect
609. #449	C₂²×C₆₇	semidirect
610. #448	C₂²×C₆₇	semidirect
611. #448	C₂²×C₆₇	semidirect
612. #447	C₂²×C₆₇	semidirect
613. #440	C₂²×C₆₇	semidirect
614. C₄×SD₁₆	C₂²×C₆₇	semidirect
615. #435	C₂²×C₆₇	semidirect
616. C₈×D₄	C₂²×C₆₇	semidirect
617. #427	C₂²×C₆₇	semidirect
618. #424	C₂²×C₆₇	semidirect
619. #419	C₂²×C₆₇	semidirect
620. #419	C₂²×C₆₇	semidirect
622. #418	C₂²×C₆₇	semidirect
623. #416	C₂²×C₆₇	semidirect
624. #416	C₂²×C₆₇	semidirect
625. #408	C₂²×C₆₇	semidirect
626. #407	C₂²×C₆₇	semidirect
627. #405	C₂²×C₆₇	semidirect
640. C₂×#41	C₂³×C₆₇	semidirect
649. C₂²×Q₈	C₂³×C₆₇	semidirect
671. C₂×Q₁₆	C₂³×C₆₇	semidirect
672. C₂×Q₁₆	C₂³×C₆₇	semidirect
673. C₂×Q₁₆	C₂³×C₆₇	semidirect
680. C₂×SD₁₆	D₄×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	C₂³×C₆₇	semidirect
699. C₂×M₁₆	C₂³×C₆₇	semidirect
705. C₂²×C₈	C₂³×C₆₇	semidirect
708. C₄⋊Q₈	C₂³×C₆₇	semidirect
715. #124	C₂³×C₆₇	semidirect
729. C₂²⋊Q₈	C₂³×C₆₇	semidirect
747. C₄×Q₈	C₂³×C₆₇	semidirect
761. #107	C₂³×C₆₇	semidirect
762. #106	C₂³×C₆₇	semidirect
763. C₄⋊C₈	C₂³×C₆₇	semidirect
764. #103	C₂³×C₆₇	semidirect
765. #103	C₂³×C₆₇	semidirect
766. #103	C₂³×C₆₇	semidirect
767. #103	C₂³×C₆₇	semidirect
770. #102	C₂³×C₆₇	semidirect
771. #102	C₂³×C₆₇	semidirect
773. C₂²⋊C₈	C₂³×C₆₇	semidirect
774. #97	C₂³×C₆₇	semidirect
775. C₄×C₈	C₂³×C₆₇	semidirect
811. C₂×Q₈	C₂×D₄×C₆₇	semidirect
878. SD₁₆	C₂×D₄×C₆₇	semidirect
879. SD₁₆	C₂×D₄×C₆₇	semidirect
890. C₂×C₈	C₂×D₄×C₆₇	semidirect
1030. C₂²	#577×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#577×C₆₇	2
C₂³×SD₁₆×C₆₇	2
C₆₇×#3486	2
C₆₇×#3484	2
C₆₇×#3282	2
D₄×SD₁₆×C₆₇	2
C₆₇×#3266	2
C₆₇×#3265	2
C₆₇×#3154	2
C₆₇×#3057	2
C₆₇×#3050	2
C₆₇×#3043	2
C₆₇×#3042	2
C₆₇×#3010	2
C₆₇×#3009	2
C₆₇×#3004	2
C₆₇×#3003	2
C₆₇×#2949	2
C₆₇×#2929	2
#61050	67

Subgroups — C67×#61050 #30740301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61050 #30740301