Subgroups — C₆₇×#61060 #30740311

Order 17152.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1030 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	C₂²×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3276	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3275	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3269	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3266	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3156	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3059	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3044	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3042	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3009	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3005	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3004	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2949	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
23	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	#577×C₆₇	—	2	8	no	—
25	C₂×#137×C₆₇	—	2	8	no	—
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
29	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
30	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
31	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
34	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
36	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
41	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×M₁₆×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	#547×C₆₇	—	2	2	no	—
48	#547×C₆₇	C₂²	1	4	yes	—
49	#546×C₆₇	—	2	2	no	—
50	#546×C₆₇	C₂²	1	4	yes	—
51	#536×C₆₇	—	2	2	no	—
52	#536×C₆₇	C₂²	1	1	yes	characteristic
53	#536×C₆₇	C₂²	1	1	yes	characteristic
54	#536×C₆₇	C₂²	1	1	yes	characteristic
55	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
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×#123×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	#497×C₆₇	C₂²	1	2	yes	complemented
66	#495×C₆₇	C₂²	1	2	yes	complemented
67	#494×C₆₇	C₂²	1	2	yes	complemented
68	#470×C₆₇	C₂²	1	4	yes	complemented
69	#470×C₆₇	C₂²	1	2	yes	complemented
70	#469×C₆₇	C₂²	1	2	yes	complemented
71	#468×C₆₇	C₂²	1	2	yes	complemented
72	#468×C₆₇	C₂²	1	2	yes	complemented
73	#467×C₆₇	C₂²	1	4	yes	complemented
74	#464×C₆₇	C₂²	1	4	yes	complemented
75	#463×C₆₇	C₂²	1	4	yes	complemented
76	#462×C₆₇	C₂²	1	4	yes	complemented
77	#461×C₆₇	C₂²	1	4	yes	complemented
78	#452×C₆₇	C₂²	1	4	yes	complemented
79	#452×C₆₇	C₂²	1	4	yes	complemented
80	#452×C₆₇	C₂²	1	4	yes	complemented
81	#451×C₆₇	C₂²	1	4	yes	complemented
82	#451×C₆₇	C₂²	1	4	yes	complemented
83	#450×C₆₇	C₂²	1	4	yes	complemented
84	#449×C₆₇	C₂²	1	4	yes	complemented
85	#448×C₆₇	C₂²	1	4	yes	complemented
86	#440×C₆₇	C₂²	1	4	yes	complemented
87	C₄×SD₁₆×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	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#418×C₆₇	C₂²	1	1	yes	characteristic
96	#416×C₆₇	C₂²	1	1	yes	characteristic
97	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#408×C₆₇	C₂²	1	1	yes	characteristic
99	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	2₋¹⁺⁴×C₆₇	—	2	4	no	—
102	2₋¹⁺⁴×C₆₇	—	4	2	no	—
103	H(5,𝔽₂)×C₆₇	—	2	4	no	—
104	H(5,𝔽₂)×C₆₇	—	4	2	no	—
105	C₂×#41×C₆₇	—	2	1	no	—
106	C₂×#41×C₆₇	—	2	2	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	2	yes	—
116	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₆₇	—	2	1	no	—
118	C₂²×Q₈×C₆₇	—	2	1	no	—
119	C₂²×Q₈×C₆₇	—	2	2	no	—
120	C₂²×Q₈×C₆₇	—	2	4	no	—
121	C₂²×Q₈×C₆₇	—	4	2	no	—
122	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
125	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
126	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₇	—	2	1	no	—
128	C₂²×D₄×C₆₇	—	2	2	no	—
129	C₂²×D₄×C₆₇	—	2	1	no	—
130	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
131	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₆₇	—	2	1	no	—
133	C₂³×C₄×C₆₇	—	2	1	no	—
134	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
135	#137×C₆₇	—	2	4	no	—
136	#137×C₆₇	—	2	16	no	—
137	#137×C₆₇	—	2	16	no	—
138	#137×C₆₇	—	2	8	no	—
139	#137×C₆₇	—	4	2	no	—
140	#137×C₆₇	—	4	2	no	—
141	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
142	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
143	#135×C₆₇	—	2	8	no	—
144	#135×C₆₇	—	2	4	no	—
145	C₂×Q₁₆×C₆₇	—	2	4	no	—
146	C₂×Q₁₆×C₆₇	—	2	4	no	—
147	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
149	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	—	2	4	no	—
155	C₂×SD₁₆×C₆₇	—	2	8	no	—
156	C₂×SD₁₆×C₆₇	D₄	1	8	yes	complemented
157	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
159	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
166	C₂×D₈×C₆₇	C₂³	1	2	yes	—
167	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
168	#131×C₆₇	—	2	4	no	—
169	C₂×M₁₆×C₆₇	—	2	4	no	—
170	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
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	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	C₄⋊Q₈×C₆₇	—	2	1	no	—
179	C₄⋊Q₈×C₆₇	—	2	1	no	—
180	C₄⋊Q₈×C₆₇	—	2	4	no	—
181	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
182	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
183	#124×C₆₇	—	2	1	no	—
184	#124×C₆₇	—	2	1	no	—
185	#124×C₆₇	—	2	4	no	—
186	#124×C₆₇	C₂³	1	2	yes	—
187	#124×C₆₇	C₂³	1	2	yes	—
188	#123×C₆₇	—	2	2	no	—
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	—	2	4	no	—
195	#123×C₆₇	—	2	2	no	—
196	#123×C₆₇	—	2	4	no	—
197	#123×C₆₇	D₄	1	2	yes	—
198	C₂²⋊Q₈×C₆₇	—	2	4	no	—
199	C₂²⋊Q₈×C₆₇	—	2	2	no	—
200	C₂²⋊Q₈×C₆₇	—	2	2	no	—
201	C₂²⋊Q₈×C₆₇	—	2	4	no	—
202	C₂²⋊Q₈×C₆₇	—	2	4	no	—
203	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
204	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
205	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
207	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
208	#121×C₆₇	—	2	4	no	—
209	#121×C₆₇	—	2	4	no	—
210	#121×C₆₇	—	2	4	no	—
211	#121×C₆₇	D₄	1	2	yes	—
212	#121×C₆₇	C₂³	1	2	yes	—
213	#121×C₆₇	C₂³	1	2	yes	—
214	#120×C₆₇	—	2	1	no	—
215	#120×C₆₇	—	2	1	no	—
216	#120×C₆₇	—	2	4	no	—
217	#120×C₆₇	D₄	1	2	yes	—
218	C₄×Q₈×C₆₇	—	2	2	no	—
219	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
220	C₄×D₄×C₆₇	—	2	4	no	—
221	C₄×D₄×C₆₇	—	2	2	no	—
222	C₄×D₄×C₆₇	—	2	2	no	—
223	C₄×D₄×C₆₇	—	2	2	no	—
224	C₄×D₄×C₆₇	—	2	4	no	—
225	C₄×D₄×C₆₇	C₂³	1	4	yes	—
226	C₄×D₄×C₆₇	C₂³	1	4	yes	—
227	#117×C₆₇	—	2	2	no	—
228	#117×C₆₇	C₂³	1	1	yes	characteristic
229	#117×C₆₇	C₂³	1	1	yes	characteristic
230	#117×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
232	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
233	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
234	#107×C₆₇	C₂³	1	2	yes	—
235	#106×C₆₇	C₂³	1	2	yes	—
236	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
237	#103×C₆₇	C₂³	1	4	yes	—
238	#103×C₆₇	C₂³	1	4	yes	—
239	#103×C₆₇	C₂³	1	4	yes	—
240	#103×C₆₇	C₂³	1	2	yes	—
241	#103×C₆₇	C₂³	1	2	yes	—
242	#102×C₆₇	C₂³	1	4	yes	—
243	#102×C₆₇	C₂³	1	2	yes	—
244	#102×C₆₇	C₂³	1	2	yes	—
245	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
246	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
247	#97×C₆₇	C₂³	1	2	yes	—
248	C₄×C₈×C₆₇	C₂³	1	2	yes	—
249	C₂⁴×C₆₇	—	2	1	no	—
250	C₂⁴×C₆₇	—	2	2	no	—
251	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
252	#41×C₆₇	—	2	2	no	—
253	#41×C₆₇	—	2	2	no	—
254	#41×C₆₇	—	2	4	no	—
255	#41×C₆₇	—	2	4	no	—
256	#41×C₆₇	—	2	8	no	—
257	#41×C₆₇	—	2	2	no	—
258	#41×C₆₇	—	2	2	no	—
259	#41×C₆₇	—	2	2	no	—
260	#41×C₆₇	—	2	2	no	—
261	#41×C₆₇	—	4	4	no	—
262	#41×C₆₇	—	4	2	no	—
263	#41×C₆₇	—	4	2	no	—
264	#41×C₆₇	—	4	8	no	—
265	#41×C₆₇	—	4	8	no	—
266	#41×C₆₇	—	4	4	no	—
267	#41×C₆₇	—	4	4	no	—
268	C₂×Q₈×C₆₇	—	2	1	no	—
269	C₂×Q₈×C₆₇	—	2	4	no	—
270	C₂×Q₈×C₆₇	—	2	1	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	4	no	—
275	C₂×Q₈×C₆₇	—	2	8	no	—
276	C₂×Q₈×C₆₇	—	2	2	no	—
277	C₂×Q₈×C₆₇	—	2	2	no	—
278	C₂×Q₈×C₆₇	—	2	2	no	—
279	C₂×Q₈×C₆₇	—	2	2	no	—
280	C₂×Q₈×C₆₇	—	4	4	no	—
281	C₂×Q₈×C₆₇	—	4	4	no	—
282	C₂×Q₈×C₆₇	—	4	2	no	—
283	C₂×Q₈×C₆₇	—	4	8	no	—
284	C₂×Q₈×C₆₇	—	4	4	no	—
285	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
286	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
287	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
288	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
289	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
292	C₂×D₄×C₆₇	—	2	4	no	—
293	C₂×D₄×C₆₇	—	2	2	no	—
294	C₂×D₄×C₆₇	—	2	4	no	—
295	C₂×D₄×C₆₇	—	2	1	no	—
296	C₂×D₄×C₆₇	—	2	1	no	—
297	C₂×D₄×C₆₇	—	2	2	no	—
298	C₂×D₄×C₆₇	—	2	2	no	—
299	C₂×D₄×C₆₇	—	2	2	no	—
300	C₂×D₄×C₆₇	—	2	1	no	—
301	C₂×D₄×C₆₇	—	2	2	no	—
302	C₂×D₄×C₆₇	—	2	2	no	—
303	C₂×D₄×C₆₇	—	4	2	no	—
304	C₂×D₄×C₆₇	—	4	4	no	—
305	C₂×D₄×C₆₇	—	4	8	no	—
306	C₂×D₄×C₆₇	—	4	4	no	—
307	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
308	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
309	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
310	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
311	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
313	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₆₇	—	2	1	no	—
315	C₂²×C₄×C₆₇	—	2	2	no	—
316	C₂²×C₄×C₆₇	—	2	2	no	—
317	C₂²×C₄×C₆₇	—	2	4	no	—
318	C₂²×C₄×C₆₇	—	2	2	no	—
319	C₂²×C₄×C₆₇	—	2	1	no	—
320	C₂²×C₄×C₆₇	—	2	1	no	—
321	C₂²×C₄×C₆₇	—	2	4	no	—
322	C₂²×C₄×C₆₇	—	2	2	no	—
323	C₂²×C₄×C₆₇	—	2	1	no	—
324	C₂²×C₄×C₆₇	—	2	2	no	—
325	C₂²×C₄×C₆₇	—	2	1	no	—
326	C₂²×C₄×C₆₇	—	2	4	no	—
327	C₂²×C₄×C₆₇	—	4	4	no	—
328	C₂²×C₄×C₆₇	—	4	4	no	—
329	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
330	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
334	Q₁₆×C₆₇	—	2	8	no	—
335	Q₁₆×C₆₇	—	2	4	no	—
336	Q₁₆×C₆₇	—	2	4	no	—
337	Q₁₆×C₆₇	—	2	4	no	—
338	Q₁₆×C₆₇	—	2	2	no	—
339	Q₁₆×C₆₇	—	4	2	no	—
340	Q₁₆×C₆₇	—	4	2	no	—
341	SD₁₆×C₆₇	—	2	4	no	—
342	SD₁₆×C₆₇	—	2	4	no	—
343	SD₁₆×C₆₇	—	2	8	no	—
344	SD₁₆×C₆₇	—	2	2	no	—
345	SD₁₆×C₆₇	—	2	2	no	—
346	SD₁₆×C₆₇	—	4	2	no	—
347	SD₁₆×C₆₇	—	4	2	no	—
348	SD₁₆×C₆₇	C₂×D₄	1	8	yes	—
349	SD₁₆×C₆₇	C₂×D₄	1	8	yes	—
350	D₈×C₆₇	—	2	4	no	—
351	D₈×C₆₇	—	2	2	no	—
352	M₁₆×C₆₇	—	2	2	no	—
353	M₁₆×C₆₇	—	2	2	no	—
354	M₁₆×C₆₇	—	2	4	no	—
355	M₁₆×C₆₇	—	2	4	no	—
356	M₁₆×C₆₇	—	2	4	no	—
357	C₂×C₈×C₆₇	—	2	2	no	—
358	C₂×C₈×C₆₇	—	2	4	no	—
359	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
360	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
361	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
362	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
363	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₆₇	—	2	2	no	—
366	C₄⋊C₄×C₆₇	—	2	4	no	—
367	C₄⋊C₄×C₆₇	—	2	4	no	—
368	C₄⋊C₄×C₆₇	—	2	4	no	—
369	C₄⋊C₄×C₆₇	—	2	4	no	—
370	C₄⋊C₄×C₆₇	—	2	4	no	—
371	C₄⋊C₄×C₆₇	—	2	2	no	—
372	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
373	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
375	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
376	C₂²⋊C₄×C₆₇	—	2	1	no	—
377	C₂²⋊C₄×C₆₇	—	2	4	no	—
378	C₂²⋊C₄×C₆₇	—	2	1	no	—
379	C₂²⋊C₄×C₆₇	—	2	2	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	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	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
389	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
390	C₄²×C₆₇	—	2	4	no	—
391	C₄²×C₆₇	—	2	1	no	—
392	C₄²×C₆₇	—	2	1	no	—
393	C₄²×C₆₇	C₂⁴	1	2	yes	—
394	C₂³×C₆₇	—	2	2	no	—
395	C₂³×C₆₇	—	2	2	no	—
396	C₂³×C₆₇	—	2	4	no	—
397	C₂³×C₆₇	—	2	1	no	—
398	C₂³×C₆₇	—	2	1	no	—
399	C₂³×C₆₇	—	4	2	no	—
400	C₂³×C₆₇	—	4	4	no	—
401	C₂³×C₆₇	—	8	2	no	—
402	C₂³×C₆₇	—	8	4	no	—
403	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
404	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
405	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
406	Q₈×C₆₇	—	2	4	no	—
407	Q₈×C₆₇	—	2	2	no	—
408	Q₈×C₆₇	—	2	2	no	—
409	Q₈×C₆₇	—	2	1	no	—
410	Q₈×C₆₇	—	2	2	no	—
411	Q₈×C₆₇	—	2	1	no	—
412	Q₈×C₆₇	—	2	2	no	—
413	Q₈×C₆₇	—	2	2	no	—
414	Q₈×C₆₇	—	2	2	no	—
415	Q₈×C₆₇	—	2	1	no	—
416	Q₈×C₆₇	—	2	1	no	—
417	Q₈×C₆₇	—	4	8	no	—
418	Q₈×C₆₇	—	4	4	no	—
419	Q₈×C₆₇	—	4	2	no	—
420	Q₈×C₆₇	—	4	2	no	—
421	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
422	D₄×C₆₇	—	2	4	no	—
423	D₄×C₆₇	—	2	4	no	—
424	D₄×C₆₇	—	2	2	no	—
425	D₄×C₆₇	—	2	1	no	—
426	D₄×C₆₇	—	2	1	no	—
427	D₄×C₆₇	—	2	2	no	—
428	D₄×C₆₇	—	2	1	no	—
429	D₄×C₆₇	—	2	1	no	—
430	D₄×C₆₇	—	4	4	no	—
431	D₄×C₆₇	—	4	4	no	—
432	D₄×C₆₇	—	4	4	no	—
433	D₄×C₆₇	—	4	4	no	—
434	D₄×C₆₇	—	4	8	no	—
435	D₄×C₆₇	—	4	4	no	—
436	D₄×C₆₇	—	4	2	no	—
437	D₄×C₆₇	—	4	2	no	—
438	D₄×C₆₇	—	8	2	no	—
439	D₄×C₆₇	C₂²×D₄	1	4	yes	—
440	C₂×C₄×C₆₇	—	2	2	no	—
441	C₂×C₄×C₆₇	—	2	4	no	—
442	C₂×C₄×C₆₇	—	2	2	no	—
443	C₂×C₄×C₆₇	—	2	4	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	2	no	—
446	C₂×C₄×C₆₇	—	2	2	no	—
447	C₂×C₄×C₆₇	—	2	2	no	—
448	C₂×C₄×C₆₇	—	2	2	no	—
449	C₂×C₄×C₆₇	—	2	2	no	—
450	C₂×C₄×C₆₇	—	2	2	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	2	1	no	—
453	C₂×C₄×C₆₇	—	2	1	no	—
454	C₂×C₄×C₆₇	—	4	4	no	—
455	C₂×C₄×C₆₇	—	4	8	no	—
456	C₂×C₄×C₆₇	—	4	8	no	—
457	C₂×C₄×C₆₇	—	4	4	no	—
458	C₂×C₄×C₆₇	—	4	4	no	—
459	C₂×C₄×C₆₇	—	4	2	no	—
460	C₂×C₄×C₆₇	—	4	2	no	—
461	C₂×C₄×C₆₇	—	4	2	no	—
462	C₂×C₄×C₆₇	—	4	2	no	—
463	C₂×C₄×C₆₇	—	8	4	no	—
464	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
465	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
470	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
471	C₈×C₆₇	—	2	2	no	—
472	C₈×C₆₇	—	2	2	no	—
473	C₈×C₆₇	—	2	2	no	—
474	C₈×C₆₇	C₂²×D₄	1	2	yes	—
475	C₈×C₆₇	C₂²×D₄	1	2	yes	—
476	C₂²×C₆₇	—	2	2	no	—
477	C₂²×C₆₇	—	2	2	no	—
478	C₂²×C₆₇	—	2	4	no	—
479	C₂²×C₆₇	—	2	2	no	—
480	C₂²×C₆₇	—	2	2	no	—
481	C₂²×C₆₇	—	2	2	no	—
482	C₂²×C₆₇	—	2	4	no	—
483	C₂²×C₆₇	—	4	4	no	—
484	C₂²×C₆₇	—	4	4	no	—
485	C₂²×C₆₇	—	4	2	no	—
486	C₂²×C₆₇	—	4	2	no	—
487	C₂²×C₆₇	—	4	1	no	—
488	C₂²×C₆₇	—	4	1	no	—
489	C₂²×C₆₇	—	8	4	no	—
490	C₂²×C₆₇	—	16	4	no	—
491	C₂²×C₆₇	D₄²	1	2	yes	—
492	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
493	C₄×C₆₇	—	2	4	no	—
494	C₄×C₆₇	—	2	2	no	—
495	C₄×C₆₇	—	2	4	no	—
496	C₄×C₆₇	—	2	2	no	—
497	C₄×C₆₇	—	4	2	no	—
498	C₄×C₆₇	—	4	2	no	—
499	C₄×C₆₇	—	4	1	no	—
500	C₄×C₆₇	—	4	2	no	—
501	C₄×C₆₇	—	4	1	no	—
502	C₄×C₆₇	—	4	2	no	—
503	C₄×C₆₇	D₄²	1	2	yes	—
504	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
505	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
506	#61060	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
507	C₂×C₆₇	—	2	2	no	—
508	C₂×C₆₇	—	4	2	no	—
509	C₂×C₆₇	—	4	2	no	—
510	C₂×C₆₇	—	4	4	no	—
511	C₂×C₆₇	—	8	1	no	—
512	C₂×C₆₇	—	8	1	no	—
513	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
514	C₂×C₆₇	#3586	1	2	yes	—
515	C₂×#577	C₂×C₆₇	1	1	yes	characteristic, complemented
516	C₂²×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
517	#3486	C₂×C₆₇	1	1	yes	characteristic, complemented
518	#3485	C₂×C₆₇	1	1	yes	characteristic, complemented
519	#3276	C₂×C₆₇	1	4	yes	complemented
520	#3275	C₂×C₆₇	1	4	yes	complemented
521	#3269	C₂×C₆₇	1	4	yes	complemented
522	#3266	C₂×C₆₇	1	4	yes	complemented
523	#3156	C₂×C₆₇	1	1	yes	characteristic, complemented
524	#3059	C₂×C₆₇	1	1	yes	characteristic, complemented
525	#3054	C₂×C₆₇	1	1	yes	characteristic, complemented
526	#3044	C₂×C₆₇	1	1	yes	characteristic, complemented
527	#3042	C₂×C₆₇	1	1	yes	characteristic, complemented
528	#3011	C₂×C₆₇	1	1	yes	characteristic, complemented
529	#3009	C₂×C₆₇	1	1	yes	characteristic, complemented
530	#3005	C₂×C₆₇	1	1	yes	characteristic, complemented
531	#3004	C₂×C₆₇	1	1	yes	characteristic, complemented
532	#2949	C₂×C₆₇	1	1	yes	characteristic, complemented
533	#2930	C₂×C₆₇	1	1	yes	characteristic, complemented
534	C₆₇	#61060	1	1	yes	characteristic, direct product factor, Sylow
535	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
536	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
537	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
538	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
539	#577	—	2	8	no	—
540	C₂×#137	—	2	8	no	—
541	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
542	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
543	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
544	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
545	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
546	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
547	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
548	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
549	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
550	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
551	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
552	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
553	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
554	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
555	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
556	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
557	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
558	D₄×Q₈	—	2	2	no	—
559	D₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
560	#548	—	2	2	no	—
561	#548	C₂²×C₆₇	1	4	yes	complemented
562	#547	—	2	2	no	—
563	#547	C₂²×C₆₇	1	4	yes	—
564	#546	—	2	2	no	—
565	#546	C₂²×C₆₇	1	4	yes	—
566	#536	—	2	2	no	—
567	#536	C₂²×C₆₇	1	1	yes	characteristic
568	#536	C₂²×C₆₇	1	1	yes	characteristic
569	#536	C₂²×C₆₇	1	1	yes	characteristic
570	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
571	#534	—	2	2	no	—
572	#525	—	2	2	no	—
573	#525	C₂²×C₆₇	1	1	yes	characteristic
574	#525	C₂²×C₆₇	1	1	yes	characteristic
575	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
576	C₂×#123	—	2	2	no	—
577	#519	C₂²×C₆₇	1	1	yes	characteristic, complemented
578	#518	C₂²×C₆₇	1	1	yes	characteristic
579	#497	C₂²×C₆₇	1	2	yes	complemented
580	#497	C₂²×C₆₇	1	2	yes	complemented
581	#495	C₂²×C₆₇	1	2	yes	complemented
582	#494	C₂²×C₆₇	1	2	yes	complemented
583	#470	C₂²×C₆₇	1	4	yes	complemented
584	#470	C₂²×C₆₇	1	2	yes	complemented
585	#469	C₂²×C₆₇	1	2	yes	complemented
586	#468	C₂²×C₆₇	1	2	yes	complemented
587	#468	C₂²×C₆₇	1	2	yes	complemented
588	#467	C₂²×C₆₇	1	4	yes	complemented
589	#464	C₂²×C₆₇	1	4	yes	complemented
590	#463	C₂²×C₆₇	1	4	yes	complemented
591	#462	C₂²×C₆₇	1	4	yes	complemented
592	#461	C₂²×C₆₇	1	4	yes	complemented
593	#452	C₂²×C₆₇	1	4	yes	complemented
594	#452	C₂²×C₆₇	1	4	yes	complemented
595	#452	C₂²×C₆₇	1	4	yes	complemented
596	#451	C₂²×C₆₇	1	4	yes	complemented
597	#451	C₂²×C₆₇	1	4	yes	complemented
598	#450	C₂²×C₆₇	1	4	yes	complemented
599	#449	C₂²×C₆₇	1	4	yes	complemented
600	#448	C₂²×C₆₇	1	4	yes	complemented
601	#440	C₂²×C₆₇	1	4	yes	complemented
602	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
603	#436	C₂²×C₆₇	1	4	yes	complemented
604	#435	C₂²×C₆₇	1	4	yes	complemented
605	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
606	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
607	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
608	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
609	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
610	#418	C₂²×C₆₇	1	1	yes	characteristic
611	#416	C₂²×C₆₇	1	1	yes	characteristic
612	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
613	#408	C₂²×C₆₇	1	1	yes	characteristic
614	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
615	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
616	2₋¹⁺⁴	—	2	4	no	—
617	2₋¹⁺⁴	—	4	2	no	—
618	H(5,𝔽₂)	—	2	4	no	—
619	H(5,𝔽₂)	—	4	2	no	—
620	C₂×#41	—	2	1	no	—
621	C₂×#41	—	2	2	no	—
622	C₂×#41	—	2	1	no	—
623	C₂×#41	—	2	2	no	—
624	C₂×#41	—	2	4	no	—
625	C₂×#41	—	4	2	no	—
626	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
627	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
628	C₂×#41	C₂³×C₆₇	1	4	yes	—
629	C₂×#41	C₂³×C₆₇	1	2	yes	—
630	C₂×#41	C₂³×C₆₇	1	2	yes	—
631	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
632	C₂²×Q₈	—	2	1	no	—
633	C₂²×Q₈	—	2	1	no	—
634	C₂²×Q₈	—	2	2	no	—
635	C₂²×Q₈	—	2	4	no	—
636	C₂²×Q₈	—	4	2	no	—
637	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
638	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
639	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
640	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
641	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
642	C₂²×D₄	—	2	1	no	—
643	C₂²×D₄	—	2	2	no	—
644	C₂²×D₄	—	2	1	no	—
645	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
646	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
647	C₂³×C₄	—	2	1	no	—
648	C₂³×C₄	—	2	1	no	—
649	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
650	#137	—	2	4	no	—
651	#137	—	2	16	no	—
652	#137	—	2	16	no	—
653	#137	—	2	8	no	—
654	#137	—	4	2	no	—
655	#137	—	4	2	no	—
656	AGL(1,ℤ/8)	—	2	4	no	—
657	AGL(1,ℤ/8)	—	2	8	no	—
658	#135	—	2	8	no	—
659	#135	—	2	4	no	—
660	C₂×Q₁₆	—	2	4	no	—
661	C₂×Q₁₆	—	2	4	no	—
662	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
663	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
664	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
665	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
666	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
667	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
668	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
669	C₂×SD₁₆	—	2	4	no	—
670	C₂×SD₁₆	—	2	8	no	—
671	C₂×SD₁₆	D₄×C₆₇	1	8	yes	complemented
672	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
673	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
674	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
675	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
676	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
677	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
680	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
681	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
682	C₂×D₈	C₂³×C₆₇	1	2	yes	—
683	#131	—	2	4	no	—
684	C₂×M₁₆	—	2	4	no	—
685	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
686	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
687	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
688	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
689	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
690	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
691	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
692	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	—	2	4	no	—
696	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
697	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
698	#124	—	2	1	no	—
699	#124	—	2	1	no	—
700	#124	—	2	4	no	—
701	#124	C₂³×C₆₇	1	2	yes	—
702	#124	C₂³×C₆₇	1	2	yes	—
703	#123	—	2	2	no	—
704	#123	—	2	2	no	—
705	#123	—	2	1	no	—
706	#123	—	2	1	no	—
707	#123	—	2	4	no	—
708	#123	—	2	2	no	—
709	#123	—	2	4	no	—
710	#123	—	2	2	no	—
711	#123	—	2	4	no	—
712	#123	D₄×C₆₇	1	2	yes	—
713	C₂²⋊Q₈	—	2	4	no	—
714	C₂²⋊Q₈	—	2	2	no	—
715	C₂²⋊Q₈	—	2	2	no	—
716	C₂²⋊Q₈	—	2	4	no	—
717	C₂²⋊Q₈	—	2	4	no	—
718	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
719	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
720	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
721	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
722	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
723	#121	—	2	4	no	—
724	#121	—	2	4	no	—
725	#121	—	2	4	no	—
726	#121	D₄×C₆₇	1	2	yes	—
727	#121	C₂³×C₆₇	1	2	yes	—
728	#121	C₂³×C₆₇	1	2	yes	—
729	#120	—	2	1	no	—
730	#120	—	2	1	no	—
731	#120	—	2	4	no	—
732	#120	D₄×C₆₇	1	2	yes	—
733	C₄×Q₈	—	2	2	no	—
734	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
735	C₄×D₄	—	2	4	no	—
736	C₄×D₄	—	2	2	no	—
737	C₄×D₄	—	2	2	no	—
738	C₄×D₄	—	2	2	no	—
739	C₄×D₄	—	2	4	no	—
740	C₄×D₄	C₂³×C₆₇	1	4	yes	—
741	C₄×D₄	C₂³×C₆₇	1	4	yes	—
742	#117	—	2	2	no	—
743	#117	C₂³×C₆₇	1	1	yes	characteristic
744	#117	C₂³×C₆₇	1	1	yes	characteristic
745	#117	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×C₄⋊C₄	—	2	4	no	—
747	C₂×C₂²⋊C₄	—	2	2	no	—
748	C₂×C₂²⋊C₄	—	2	4	no	—
749	#107	C₂³×C₆₇	1	2	yes	—
750	#106	C₂³×C₆₇	1	2	yes	—
751	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
752	#103	C₂³×C₆₇	1	2	yes	—
753	#103	C₂³×C₆₇	1	2	yes	—
754	#103	C₂³×C₆₇	1	4	yes	—
755	#103	C₂³×C₆₇	1	4	yes	—
756	#103	C₂³×C₆₇	1	4	yes	—
757	#102	C₂³×C₆₇	1	2	yes	—
758	#102	C₂³×C₆₇	1	2	yes	—
759	#102	C₂³×C₆₇	1	4	yes	—
760	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
761	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
762	#97	C₂³×C₆₇	1	2	yes	—
763	C₄×C₈	C₂³×C₆₇	1	2	yes	—
764	C₂⁴	—	2	1	no	—
765	C₂⁴	—	2	2	no	—
766	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
767	#41	—	2	2	no	—
768	#41	—	2	2	no	—
769	#41	—	2	4	no	—
770	#41	—	2	4	no	—
771	#41	—	2	8	no	—
772	#41	—	2	2	no	—
773	#41	—	2	2	no	—
774	#41	—	2	2	no	—
775	#41	—	2	2	no	—
776	#41	—	4	4	no	—
777	#41	—	4	2	no	—
778	#41	—	4	2	no	—
779	#41	—	4	8	no	—
780	#41	—	4	8	no	—
781	#41	—	4	4	no	—
782	#41	—	4	4	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	4	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	2	2	no	—
789	C₂×Q₈	—	2	4	no	—
790	C₂×Q₈	—	2	8	no	—
791	C₂×Q₈	—	2	2	no	—
792	C₂×Q₈	—	2	2	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	—	2	2	no	—
795	C₂×Q₈	—	4	4	no	—
796	C₂×Q₈	—	4	4	no	—
797	C₂×Q₈	—	4	2	no	—
798	C₂×Q₈	—	4	8	no	—
799	C₂×Q₈	—	4	4	no	—
800	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
801	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
802	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
803	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
804	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
805	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
806	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	4	no	—
820	C₂×D₄	—	4	8	no	—
821	C₂×D₄	—	4	4	no	—
822	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
823	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
824	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
825	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
826	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
827	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
828	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	4	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	4	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	2	4	no	—
842	C₂²×C₄	—	4	4	no	—
843	C₂²×C₄	—	4	4	no	—
844	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
845	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
849	Q₁₆	—	2	8	no	—
850	Q₁₆	—	2	4	no	—
851	Q₁₆	—	2	4	no	—
852	Q₁₆	—	2	4	no	—
853	Q₁₆	—	2	2	no	—
854	Q₁₆	—	4	2	no	—
855	Q₁₆	—	4	2	no	—
856	SD₁₆	—	2	4	no	—
857	SD₁₆	—	2	4	no	—
858	SD₁₆	—	2	8	no	—
859	SD₁₆	—	2	2	no	—
860	SD₁₆	—	2	2	no	—
861	SD₁₆	—	4	2	no	—
862	SD₁₆	—	4	2	no	—
863	SD₁₆	C₂×D₄×C₆₇	1	8	yes	—
864	SD₁₆	C₂×D₄×C₆₇	1	8	yes	—
865	D₈	—	2	4	no	—
866	D₈	—	2	2	no	—
867	M₁₆	—	2	2	no	—
868	M₁₆	—	2	2	no	—
869	M₁₆	—	2	4	no	—
870	M₁₆	—	2	4	no	—
871	M₁₆	—	2	4	no	—
872	C₂×C₈	—	2	2	no	—
873	C₂×C₈	—	2	4	no	—
874	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
875	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
876	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
877	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
878	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
879	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	4	no	—
882	C₄⋊C₄	—	2	4	no	—
883	C₄⋊C₄	—	2	4	no	—
884	C₄⋊C₄	—	2	4	no	—
885	C₄⋊C₄	—	2	4	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
888	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
889	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
890	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
891	C₂²⋊C₄	—	2	1	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
903	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
904	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
905	C₄²	—	2	4	no	—
906	C₄²	—	2	1	no	—
907	C₄²	—	2	1	no	—
908	C₄²	C₂⁴×C₆₇	1	2	yes	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	4	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	4	2	no	—
915	C₂³	—	4	4	no	—
916	C₂³	—	8	2	no	—
917	C₂³	—	8	4	no	—
918	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
919	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
920	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
921	Q₈	—	2	4	no	—
922	Q₈	—	2	2	no	—
923	Q₈	—	2	2	no	—
924	Q₈	—	2	1	no	—
925	Q₈	—	2	2	no	—
926	Q₈	—	2	1	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	2	2	no	—
929	Q₈	—	2	2	no	—
930	Q₈	—	2	1	no	—
931	Q₈	—	2	1	no	—
932	Q₈	—	4	8	no	—
933	Q₈	—	4	4	no	—
934	Q₈	—	4	2	no	—
935	Q₈	—	4	2	no	—
936	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
937	D₄	—	2	4	no	—
938	D₄	—	2	4	no	—
939	D₄	—	2	2	no	—
940	D₄	—	2	1	no	—
941	D₄	—	2	1	no	—
942	D₄	—	2	2	no	—
943	D₄	—	2	1	no	—
944	D₄	—	2	1	no	—
945	D₄	—	4	4	no	—
946	D₄	—	4	4	no	—
947	D₄	—	4	4	no	—
948	D₄	—	4	4	no	—
949	D₄	—	4	8	no	—
950	D₄	—	4	4	no	—
951	D₄	—	4	2	no	—
952	D₄	—	4	2	no	—
953	D₄	—	8	2	no	—
954	D₄	C₂²×D₄×C₆₇	1	4	yes	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	4	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	4	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	4	4	no	—
970	C₂×C₄	—	4	8	no	—
971	C₂×C₄	—	4	8	no	—
972	C₂×C₄	—	4	4	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	2	no	—
975	C₂×C₄	—	4	2	no	—
976	C₂×C₄	—	4	2	no	—
977	C₂×C₄	—	4	2	no	—
978	C₂×C₄	—	8	4	no	—
979	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
980	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
981	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
982	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
983	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
984	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
985	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
986	C₈	—	2	2	no	—
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₈	C₂²×D₄×C₆₇	1	2	yes	—
990	C₈	C₂²×D₄×C₆₇	1	2	yes	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	4	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	4	no	—
998	C₂²	—	4	4	no	—
999	C₂²	—	4	4	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	1	no	—
1003	C₂²	—	4	1	no	—
1004	C₂²	—	8	4	no	—
1005	C₂²	—	16	4	no	—
1006	C₂²	D₄²×C₆₇	1	2	yes	—
1007	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1008	C₄	—	2	4	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	4	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	2	no	—
1018	C₄	D₄²×C₆₇	1	2	yes	—
1019	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1020	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1021	C₂	—	2	2	no	—
1022	C₂	—	4	2	no	—
1023	C₂	—	4	2	no	—
1024	C₂	—	4	4	no	—
1025	C₂	—	8	1	no	—
1026	C₂	—	8	1	no	—
1027	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1028	C₂	C₆₇×#3586	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. C₂²×#137×C₆₇	C₂	semidirect
3. C₆₇×#3486	C₂	semidirect
4. C₆₇×#3485	C₂	semidirect
5. C₆₇×#3276	C₂	semidirect
6. C₆₇×#3275	C₂	semidirect
7. C₆₇×#3269	C₂	semidirect
8. C₆₇×#3266	C₂	semidirect
9. C₆₇×#3156	C₂	semidirect
10. C₆₇×#3059	C₂	semidirect
11. C₆₇×#3054	C₂	semidirect
12. C₆₇×#3044	C₂	semidirect
13. C₆₇×#3042	C₂	semidirect
14. C₆₇×#3011	C₂	semidirect
15. C₆₇×#3009	C₂	semidirect
16. C₆₇×#3005	C₂	semidirect
17. C₆₇×#3004	C₂	semidirect
18. C₆₇×#2949	C₂	semidirect
19. C₆₇×#2930	C₂	semidirect
23. C₂³×Q₈×C₆₇	C₂²	semidirect
28. C₂×#137×C₆₇	C₂²	semidirect
29. C₂×#137×C₆₇	C₂²	semidirect
30. C₂×#137×C₆₇	C₂²	semidirect
31. C₂×#137×C₆₇	C₂²	semidirect
33. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
35. C₂×#135×C₆₇	C₂²	semidirect
36. C₂²×Q₁₆×C₆₇	C₂²	semidirect
37. C₂²×Q₁₆×C₆₇	C₂²	semidirect
40. C₂²×SD₁₆×C₆₇	C₂²	semidirect
42. C₂²×M₁₆×C₆₇	C₂²	semidirect
44. D₄×Q₈×C₆₇	C₂²	semidirect
46. #548×C₆₇	C₂²	semidirect
55. #536×C₆₇	C₂²	semidirect
60. #525×C₆₇	C₂²	semidirect
62. #519×C₆₇	C₂²	semidirect
64. #497×C₆₇	C₂²	semidirect
65. #497×C₆₇	C₂²	semidirect
66. #495×C₆₇	C₂²	semidirect
67. #494×C₆₇	C₂²	semidirect
68. #470×C₆₇	C₂²	semidirect
69. #470×C₆₇	C₂²	semidirect
70. #469×C₆₇	C₂²	semidirect
71. #468×C₆₇	C₂²	semidirect
72. #468×C₆₇	C₂²	semidirect
73. #467×C₆₇	C₂²	semidirect
74. #464×C₆₇	C₂²	semidirect
75. #463×C₆₇	C₂²	semidirect
76. #462×C₆₇	C₂²	semidirect
77. #461×C₆₇	C₂²	semidirect
78. #452×C₆₇	C₂²	semidirect
79. #452×C₆₇	C₂²	semidirect
80. #452×C₆₇	C₂²	semidirect
81. #451×C₆₇	C₂²	semidirect
82. #451×C₆₇	C₂²	semidirect
83. #450×C₆₇	C₂²	semidirect
84. #449×C₆₇	C₂²	semidirect
85. #448×C₆₇	C₂²	semidirect
86. #440×C₆₇	C₂²	semidirect
87. C₄×SD₁₆×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. #419×C₆₇	C₂²	semidirect
94. #419×C₆₇	C₂²	semidirect
97. #416×C₆₇	C₂²	semidirect
99. #407×C₆₇	C₂²	semidirect
100. #405×C₆₇	C₂²	semidirect
156. C₂×SD₁₆×C₆₇	D₄	semidirect
506. #61060	C₆₇	direct (N × H)
515. C₂×#577	C₂×C₆₇	semidirect
516. C₂²×#137	C₂×C₆₇	semidirect
517. #3486	C₂×C₆₇	semidirect
518. #3485	C₂×C₆₇	semidirect
519. #3276	C₂×C₆₇	semidirect
520. #3275	C₂×C₆₇	semidirect
521. #3269	C₂×C₆₇	semidirect
522. #3266	C₂×C₆₇	semidirect
523. #3156	C₂×C₆₇	semidirect
524. #3059	C₂×C₆₇	semidirect
525. #3054	C₂×C₆₇	semidirect
526. #3044	C₂×C₆₇	semidirect
527. #3042	C₂×C₆₇	semidirect
528. #3011	C₂×C₆₇	semidirect
529. #3009	C₂×C₆₇	semidirect
530. #3005	C₂×C₆₇	semidirect
531. #3004	C₂×C₆₇	semidirect
532. #2949	C₂×C₆₇	semidirect
533. #2930	C₂×C₆₇	semidirect
534. C₆₇	#61060	direct (N × H)
538. C₂³×Q₈	C₂²×C₆₇	semidirect
543. C₂×#137	C₂²×C₆₇	semidirect
544. C₂×#137	C₂²×C₆₇	semidirect
545. C₂×#137	C₂²×C₆₇	semidirect
546. C₂×#137	C₂²×C₆₇	semidirect
548. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
550. C₂×#135	C₂²×C₆₇	semidirect
551. C₂²×Q₁₆	C₂²×C₆₇	semidirect
552. C₂²×Q₁₆	C₂²×C₆₇	semidirect
555. C₂²×SD₁₆	C₂²×C₆₇	semidirect
557. C₂²×M₁₆	C₂²×C₆₇	semidirect
559. D₄×Q₈	C₂²×C₆₇	semidirect
561. #548	C₂²×C₆₇	semidirect
570. #536	C₂²×C₆₇	semidirect
575. #525	C₂²×C₆₇	semidirect
577. #519	C₂²×C₆₇	semidirect
579. #497	C₂²×C₆₇	semidirect
580. #497	C₂²×C₆₇	semidirect
581. #495	C₂²×C₆₇	semidirect
582. #494	C₂²×C₆₇	semidirect
583. #470	C₂²×C₆₇	semidirect
584. #470	C₂²×C₆₇	semidirect
585. #469	C₂²×C₆₇	semidirect
586. #468	C₂²×C₆₇	semidirect
587. #468	C₂²×C₆₇	semidirect
588. #467	C₂²×C₆₇	semidirect
589. #464	C₂²×C₆₇	semidirect
590. #463	C₂²×C₆₇	semidirect
591. #462	C₂²×C₆₇	semidirect
592. #461	C₂²×C₆₇	semidirect
593. #452	C₂²×C₆₇	semidirect
594. #452	C₂²×C₆₇	semidirect
595. #452	C₂²×C₆₇	semidirect
596. #451	C₂²×C₆₇	semidirect
597. #451	C₂²×C₆₇	semidirect
598. #450	C₂²×C₆₇	semidirect
599. #449	C₂²×C₆₇	semidirect
600. #448	C₂²×C₆₇	semidirect
601. #440	C₂²×C₆₇	semidirect
602. C₄×SD₁₆	C₂²×C₆₇	semidirect
603. #436	C₂²×C₆₇	semidirect
604. #435	C₂²×C₆₇	semidirect
605. #427	C₂²×C₆₇	semidirect
606. #424	C₂²×C₆₇	semidirect
607. #419	C₂²×C₆₇	semidirect
608. #419	C₂²×C₆₇	semidirect
609. #419	C₂²×C₆₇	semidirect
612. #416	C₂²×C₆₇	semidirect
614. #407	C₂²×C₆₇	semidirect
615. #405	C₂²×C₆₇	semidirect
671. C₂×SD₁₆	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×#577×C₆₇	2
C₂²×#137×C₆₇	2
C₆₇×#3486	2
C₆₇×#3485	2
C₆₇×#3276	2
C₆₇×#3275	2
C₆₇×#3269	2
C₆₇×#3266	2
C₆₇×#3156	2
C₆₇×#3059	2
C₆₇×#3054	2
C₆₇×#3044	2
C₆₇×#3042	2
C₆₇×#3011	2
C₆₇×#3009	2
C₆₇×#3005	2
C₆₇×#3004	2
C₆₇×#2949	2
C₆₇×#2930	2
#61060	67

Subgroups — C67×#61060 #30740311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61060 #30740311