Subgroups — C₆₇×#61339 #30740590

Order 17152.

1912 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3373	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3370	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3366	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3366	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3361	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3358	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3136	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3081	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3041	C₂	1	2	yes	maximal, complemented
14	C₂×#459×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2948	C₂	1	2	yes	maximal, complemented
17	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
20	#559×C₆₇	C₂²	1	2	yes	complemented
21	#559×C₆₇	C₂²	1	2	yes	complemented
22	#554×C₆₇	—	2	1	no	—
23	#554×C₆₇	—	2	2	no	—
24	#554×C₆₇	C₂²	1	2	yes	complemented
25	#554×C₆₇	C₂²	1	4	yes	complemented
26	#550×C₆₇	C₂²	1	2	yes	complemented
27	#550×C₆₇	C₂²	1	2	yes	complemented
28	D₄×Q₈×C₆₇	—	2	1	no	—
29	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
30	#546×C₆₇	—	2	2	no	—
31	#546×C₆₇	—	2	2	no	—
32	#544×C₆₇	C₂²	1	2	yes	—
33	#543×C₆₇	—	2	2	no	—
34	#540×C₆₇	—	2	2	no	—
35	#535×C₆₇	C₂²	1	2	yes	—
36	#533×C₆₇	C₂²	1	1	yes	characteristic
37	#533×C₆₇	C₂²	1	1	yes	characteristic
38	#532×C₆₇	—	2	1	no	—
39	#532×C₆₇	—	2	1	no	—
40	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
42	#518×C₆₇	C₂²	1	2	yes	—
43	#518×C₆₇	C₂²	1	2	yes	—
44	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	#490×C₆₇	C₂²	1	4	yes	complemented
47	#490×C₆₇	C₂²	1	4	yes	complemented
48	#489×C₆₇	C₂²	1	4	yes	complemented
49	#488×C₆₇	C₂²	1	4	yes	complemented
50	#486×C₆₇	C₂²	1	4	yes	complemented
51	#486×C₆₇	C₂²	1	2	yes	complemented
52	#486×C₆₇	C₂²	1	2	yes	complemented
53	#479×C₆₇	C₂²	1	2	yes	complemented
54	#478×C₆₇	C₂²	1	2	yes	complemented
55	#478×C₆₇	C₂²	1	4	yes	complemented
56	#478×C₆₇	C₂²	1	4	yes	complemented
57	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#476×C₆₇	C₂²	1	4	yes	complemented
60	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#474×C₆₇	C₂²	1	4	yes	complemented
63	#463×C₆₇	C₂²	1	4	yes	complemented
64	#463×C₆₇	C₂²	1	4	yes	complemented
65	#459×C₆₇	C₂²	1	2	yes	—
66	#459×C₆₇	C₂²	1	4	yes	—
67	#459×C₆₇	C₂²	1	2	yes	—
68	#459×C₆₇	C₂²	1	4	yes	complemented
69	#459×C₆₇	C₂²	1	4	yes	complemented
70	#446×C₆₇	C₂²	1	4	yes	complemented
71	#446×C₆₇	C₂²	1	2	yes	complemented
72	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
73	#442×C₆₇	C₂²	1	2	yes	complemented
74	#442×C₆₇	C₂²	1	4	yes	complemented
75	#442×C₆₇	C₂²	1	4	yes	complemented
76	#440×C₆₇	C₂²	1	2	yes	complemented
77	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
78	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
79	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
80	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
81	#428×C₆₇	C₂²	1	1	yes	characteristic
82	#427×C₆₇	C₂²	1	2	yes	—
83	#424×C₆₇	C₂²	1	2	yes	—
84	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
85	#418×C₆₇	C₂²	1	2	yes	—
86	#418×C₆₇	C₂²	1	2	yes	—
87	#418×C₆₇	C₂²	1	1	yes	characteristic
88	#417×C₆₇	C₂²	1	1	yes	characteristic
89	#416×C₆₇	C₂²	1	2	yes	—
90	C₂×#102×C₆₇	C₂²	1	2	yes	—
91	#405×C₆₇	C₂²	1	2	yes	—
92	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×#41×C₆₇	—	2	2	no	—
94	C₂×#41×C₆₇	—	2	2	no	—
95	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₆₇	—	2	2	no	—
97	C₂²×D₄×C₆₇	—	2	1	no	—
98	C₂²×D₄×C₆₇	—	2	1	no	—
99	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
100	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₆₇	—	2	1	no	—
102	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
103	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
104	C₂×D₈×C₆₇	—	2	8	no	—
105	C₂×D₈×C₆₇	C₂³	1	4	yes	—
106	C₂×D₈×C₆₇	C₂³	1	4	yes	—
107	C₂×D₈×C₆₇	C₂³	1	2	yes	—
108	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₆₇	—	2	2	no	—
112	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
116	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
117	#127×C₆₇	—	2	1	no	—
118	#127×C₆₇	—	2	1	no	—
119	#127×C₆₇	C₂³	1	2	yes	—
120	#127×C₆₇	C₂³	1	2	yes	—
121	#127×C₆₇	C₂³	1	4	yes	—
122	#125×C₆₇	—	2	2	no	—
123	#125×C₆₇	D₄	1	2	yes	—
124	#125×C₆₇	C₂³	1	4	yes	—
125	#125×C₆₇	C₂³	1	2	yes	—
126	#124×C₆₇	—	2	2	no	—
127	#124×C₆₇	—	2	2	no	—
128	#124×C₆₇	C₂³	1	4	yes	—
129	#123×C₆₇	—	2	4	no	—
130	#123×C₆₇	—	2	4	no	—
131	C₂²⋊Q₈×C₆₇	—	2	2	no	—
132	C₂²⋊Q₈×C₆₇	—	2	4	no	—
133	C₂²⋊Q₈×C₆₇	—	2	1	no	—
134	C₂²⋊Q₈×C₆₇	—	2	1	no	—
135	C₂²⋊Q₈×C₆₇	—	2	2	no	—
136	C₂²⋊Q₈×C₆₇	—	2	4	no	—
137	C₂²⋊Q₈×C₆₇	—	2	4	no	—
138	C₂²⋊Q₈×C₆₇	—	2	4	no	—
139	C₂²⋊Q₈×C₆₇	—	2	4	no	—
140	C₂²⋊Q₈×C₆₇	—	2	4	no	—
141	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
142	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
143	#121×C₆₇	—	2	2	no	—
144	#121×C₆₇	—	2	2	no	—
145	#121×C₆₇	—	2	2	no	—
146	#121×C₆₇	—	2	2	no	—
147	#121×C₆₇	—	2	4	no	—
148	#121×C₆₇	—	2	4	no	—
149	#120×C₆₇	—	2	4	no	—
150	C₄×Q₈×C₆₇	—	2	1	no	—
151	C₄×Q₈×C₆₇	—	2	1	no	—
152	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
155	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
156	C₄×D₄×C₆₇	—	2	1	no	—
157	C₄×D₄×C₆₇	—	2	1	no	—
158	C₄×D₄×C₆₇	—	2	2	no	—
159	C₄×D₄×C₆₇	—	2	2	no	—
160	C₄×D₄×C₆₇	—	2	2	no	—
161	C₄×D₄×C₆₇	—	2	2	no	—
162	C₄×D₄×C₆₇	—	2	2	no	—
163	C₄×D₄×C₆₇	—	2	2	no	—
164	C₄×D₄×C₆₇	—	2	1	no	—
165	C₄×D₄×C₆₇	—	2	1	no	—
166	C₄×D₄×C₆₇	C₂³	1	2	yes	—
167	C₄×D₄×C₆₇	C₂³	1	2	yes	—
168	C₄×D₄×C₆₇	C₂³	1	4	yes	—
169	C₄×D₄×C₆₇	C₂³	1	4	yes	—
170	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₄×D₄×C₆₇	C₂³	1	4	yes	—
172	C₄×D₄×C₆₇	C₂³	1	4	yes	—
173	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
174	#117×C₆₇	—	2	1	no	—
175	#117×C₆₇	C₂³	1	1	yes	characteristic
176	#117×C₆₇	C₂³	1	2	yes	—
177	#117×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
179	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
183	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
184	C₂×C₄²×C₆₇	—	2	1	no	—
185	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
186	#107×C₆₇	C₂³	1	2	yes	—
187	#107×C₆₇	C₂³	1	2	yes	—
188	#107×C₆₇	C₂³	1	2	yes	—
189	#106×C₆₇	C₂³	1	2	yes	—
190	#106×C₆₇	C₂³	1	2	yes	—
191	#106×C₆₇	C₂³	1	2	yes	—
192	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
194	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
195	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
196	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
197	#103×C₆₇	C₂³	1	2	yes	—
198	#103×C₆₇	C₂³	1	2	yes	—
199	#103×C₆₇	C₂³	1	2	yes	—
200	#102×C₆₇	C₂³	1	4	yes	—
201	#102×C₆₇	C₂³	1	4	yes	—
202	#102×C₆₇	C₂³	1	2	yes	—
203	#102×C₆₇	C₂³	1	2	yes	—
204	#102×C₆₇	C₂³	1	4	yes	—
205	#102×C₆₇	C₂³	1	4	yes	—
206	#102×C₆₇	C₂³	1	4	yes	—
207	#102×C₆₇	C₂³	1	2	yes	—
208	#102×C₆₇	C₂³	1	4	yes	—
209	#102×C₆₇	C₂³	1	2	yes	—
210	#102×C₆₇	C₂³	1	2	yes	—
211	#97×C₆₇	C₂³	1	4	yes	—
212	#97×C₆₇	C₂³	1	2	yes	—
213	C₄×C₈×C₆₇	C₂³	1	2	yes	—
214	C₄×C₈×C₆₇	C₂³	1	4	yes	—
215	C₂⁴×C₆₇	—	2	1	no	—
216	C₂⁴×C₆₇	—	2	2	no	—
217	#41×C₆₇	—	2	2	no	—
218	#41×C₆₇	—	2	2	no	—
219	#41×C₆₇	—	8	4	no	—
220	#41×C₆₇	—	8	4	no	—
221	C₂×Q₈×C₆₇	—	2	1	no	—
222	C₂×Q₈×C₆₇	—	2	1	no	—
223	C₂×Q₈×C₆₇	—	2	4	no	—
224	C₂×Q₈×C₆₇	—	8	4	no	—
225	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
228	C₂×D₄×C₆₇	—	2	1	no	—
229	C₂×D₄×C₆₇	—	2	1	no	—
230	C₂×D₄×C₆₇	—	2	2	no	—
231	C₂×D₄×C₆₇	—	2	2	no	—
232	C₂×D₄×C₆₇	—	2	2	no	—
233	C₂×D₄×C₆₇	—	2	4	no	—
234	C₂×D₄×C₆₇	—	2	4	no	—
235	C₂×D₄×C₆₇	—	2	2	no	—
236	C₂×D₄×C₆₇	—	2	2	no	—
237	C₂×D₄×C₆₇	—	2	4	no	—
238	C₂×D₄×C₆₇	—	2	2	no	—
239	C₂×D₄×C₆₇	—	2	4	no	—
240	C₂×D₄×C₆₇	—	8	2	no	—
241	C₂×D₄×C₆₇	—	8	2	no	—
242	C₂×D₄×C₆₇	#41	1	4	yes	complemented
243	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
244	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₆₇	—	2	1	no	—
247	C₂²×C₄×C₆₇	—	2	1	no	—
248	C₂²×C₄×C₆₇	—	2	1	no	—
249	C₂²×C₄×C₆₇	—	2	1	no	—
250	C₂²×C₄×C₆₇	—	2	2	no	—
251	C₂²×C₄×C₆₇	—	2	4	no	—
252	C₂²×C₄×C₆₇	—	2	4	no	—
253	C₂²×C₄×C₆₇	—	2	4	no	—
254	C₂²×C₄×C₆₇	—	2	4	no	—
255	C₂²×C₄×C₆₇	—	2	2	no	—
256	C₂²×C₄×C₆₇	—	8	2	no	—
257	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
260	SD₁₆×C₆₇	—	2	4	no	—
261	D₈×C₆₇	—	2	8	no	—
262	D₈×C₆₇	—	2	8	no	—
263	D₈×C₆₇	—	2	4	no	—
264	M₁₆×C₆₇	—	2	2	no	—
265	M₁₆×C₆₇	—	2	2	no	—
266	C₂×C₈×C₆₇	—	2	4	no	—
267	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
268	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
269	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
270	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
271	C₄⋊C₄×C₆₇	—	2	2	no	—
272	C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₄⋊C₄×C₆₇	—	2	4	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	—	2	1	no	—
277	C₄⋊C₄×C₆₇	—	2	1	no	—
278	C₄⋊C₄×C₆₇	—	2	1	no	—
279	C₄⋊C₄×C₆₇	—	2	2	no	—
280	C₄⋊C₄×C₆₇	—	2	1	no	—
281	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
283	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
284	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
286	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
287	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
292	C₂²⋊C₄×C₆₇	—	2	1	no	—
293	C₂²⋊C₄×C₆₇	—	2	2	no	—
294	C₂²⋊C₄×C₆₇	—	2	4	no	—
295	C₂²⋊C₄×C₆₇	—	2	4	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	2	4	no	—
298	C₂²⋊C₄×C₆₇	—	2	2	no	—
299	C₂²⋊C₄×C₆₇	—	2	2	no	—
300	C₂²⋊C₄×C₆₇	—	2	1	no	—
301	C₂²⋊C₄×C₆₇	—	2	1	no	—
302	C₂²⋊C₄×C₆₇	—	2	4	no	—
303	C₂²⋊C₄×C₆₇	—	2	4	no	—
304	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
305	C₄²×C₆₇	—	2	1	no	—
306	C₄²×C₆₇	—	2	1	no	—
307	C₄²×C₆₇	—	2	1	no	—
308	C₄²×C₆₇	—	2	2	no	—
309	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
313	C₄²×C₆₇	C₂⁴	1	4	yes	—
314	C₂³×C₆₇	—	2	2	no	—
315	C₂³×C₆₇	—	2	4	no	—
316	C₂³×C₆₇	—	2	4	no	—
317	C₂³×C₆₇	—	2	1	no	—
318	C₂³×C₆₇	—	4	4	no	—
319	C₂³×C₆₇	—	8	1	no	—
320	C₂³×C₆₇	—	8	1	no	—
321	C₂³×C₆₇	—	8	2	no	—
322	C₂³×C₆₇	—	8	2	no	—
323	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
324	Q₈×C₆₇	—	2	4	no	—
325	Q₈×C₆₇	—	2	1	no	—
326	Q₈×C₆₇	—	2	1	no	—
327	Q₈×C₆₇	—	4	2	no	—
328	Q₈×C₆₇	—	4	2	no	—
329	Q₈×C₆₇	—	8	1	no	—
330	Q₈×C₆₇	—	8	4	no	—
331	D₄×C₆₇	—	2	4	no	—
332	D₄×C₆₇	—	2	4	no	—
333	D₄×C₆₇	—	2	1	no	—
334	D₄×C₆₇	—	2	2	no	—
335	D₄×C₆₇	—	2	4	no	—
336	D₄×C₆₇	—	2	1	no	—
337	D₄×C₆₇	—	4	4	no	—
338	D₄×C₆₇	—	4	2	no	—
339	D₄×C₆₇	—	4	4	no	—
340	D₄×C₆₇	—	4	4	no	—
341	D₄×C₆₇	—	8	2	no	—
342	D₄×C₆₇	—	8	2	no	—
343	D₄×C₆₇	—	8	4	no	—
344	D₄×C₆₇	—	8	4	no	—
345	D₄×C₆₇	C₂×#41	1	4	yes	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	1	no	—
348	C₂×C₄×C₆₇	—	2	1	no	—
349	C₂×C₄×C₆₇	—	2	1	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	4	1	no	—
354	C₂×C₄×C₆₇	—	4	2	no	—
355	C₂×C₄×C₆₇	—	4	2	no	—
356	C₂×C₄×C₆₇	—	4	4	no	—
357	C₂×C₄×C₆₇	—	4	2	no	—
358	C₂×C₄×C₆₇	—	8	4	no	—
359	C₂×C₄×C₆₇	—	8	2	no	—
360	C₂×C₄×C₆₇	—	8	4	no	—
361	C₂×C₄×C₆₇	—	8	4	no	—
362	C₂×C₄×C₆₇	—	8	4	no	—
363	C₂×C₄×C₆₇	—	8	1	no	—
364	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
368	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
369	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
372	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
373	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
374	C₈×C₆₇	—	2	2	no	—
375	C₈×C₆₇	—	2	2	no	—
376	C₈×C₆₇	—	2	2	no	—
377	C₈×C₆₇	—	2	2	no	—
378	C₂²×C₆₇	—	2	1	no	—
379	C₂²×C₆₇	—	2	1	no	—
380	C₂²×C₆₇	—	2	4	no	—
381	C₂²×C₆₇	—	4	2	no	—
382	C₂²×C₆₇	—	4	2	no	—
383	C₂²×C₆₇	—	4	1	no	—
384	C₂²×C₆₇	—	4	4	no	—
385	C₂²×C₆₇	—	4	1	no	—
386	C₂²×C₆₇	—	4	4	no	—
387	C₂²×C₆₇	—	4	1	no	—
388	C₂²×C₆₇	—	4	4	no	—
389	C₂²×C₆₇	—	8	4	no	—
390	C₂²×C₆₇	—	16	4	no	—
391	C₂²×C₆₇	#548	1	2	yes	—
392	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
393	C₄×C₆₇	—	2	1	no	—
394	C₄×C₆₇	—	2	1	no	—
395	C₄×C₆₇	—	2	4	no	—
396	C₄×C₆₇	—	2	1	no	—
397	C₄×C₆₇	—	2	4	no	—
398	C₄×C₆₇	—	4	1	no	—
399	C₄×C₆₇	—	4	2	no	—
400	C₄×C₆₇	—	4	1	no	—
401	C₄×C₆₇	—	4	1	no	—
402	C₄×C₆₇	—	4	2	no	—
403	C₄×C₆₇	—	4	2	no	—
404	C₄×C₆₇	#548	1	2	yes	—
405	C₄×C₆₇	#576	1	2	yes	—
406	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
407	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
408	#61339	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
409	C₂×C₆₇	—	2	2	no	—
410	C₂×C₆₇	—	4	4	no	—
411	C₂×C₆₇	—	8	1	no	—
412	C₂×C₆₇	—	8	4	no	—
413	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
414	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
415	C₂×C₆₇	#3585	1	1	yes	characteristic
416	#3508	C₂×C₆₇	1	1	yes	characteristic, complemented
417	#3501	C₂×C₆₇	1	1	yes	characteristic, complemented
418	#3373	C₂×C₆₇	1	2	yes	complemented
419	#3370	C₂×C₆₇	1	4	yes	complemented
420	#3366	C₂×C₆₇	1	2	yes	complemented
421	#3366	C₂×C₆₇	1	4	yes	complemented
422	#3361	C₂×C₆₇	1	2	yes	complemented
423	#3358	C₂×C₆₇	1	2	yes	complemented
424	#3138	C₂×C₆₇	1	1	yes	characteristic, complemented
425	#3136	C₂×C₆₇	1	2	yes	complemented
426	#3081	C₂×C₆₇	1	2	yes	complemented
427	#3076	C₂×C₆₇	1	1	yes	characteristic, complemented
428	#3041	C₂×C₆₇	1	2	yes	complemented
429	C₂×#459	C₂×C₆₇	1	1	yes	characteristic, complemented
430	#2962	C₂×C₆₇	1	1	yes	characteristic, complemented
431	#2948	C₂×C₆₇	1	2	yes	complemented
432	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
433	C₆₇	#61339	1	1	yes	characteristic, direct product factor, Sylow
434	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
435	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
436	#559	C₂²×C₆₇	1	2	yes	complemented
437	#559	C₂²×C₆₇	1	2	yes	complemented
438	#554	—	2	1	no	—
439	#554	—	2	2	no	—
440	#554	C₂²×C₆₇	1	2	yes	complemented
441	#554	C₂²×C₆₇	1	4	yes	complemented
442	#550	C₂²×C₆₇	1	2	yes	complemented
443	#550	C₂²×C₆₇	1	2	yes	complemented
444	D₄×Q₈	—	2	1	no	—
445	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
446	#546	—	2	2	no	—
447	#546	—	2	2	no	—
448	#544	C₂²×C₆₇	1	2	yes	—
449	#543	—	2	2	no	—
450	#540	—	2	2	no	—
451	#535	C₂²×C₆₇	1	2	yes	—
452	#533	C₂²×C₆₇	1	1	yes	characteristic
453	#533	C₂²×C₆₇	1	1	yes	characteristic
454	#532	—	2	1	no	—
455	#532	—	2	1	no	—
456	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
457	C₂×C₂²⋊Q₈	—	2	2	no	—
458	#518	C₂²×C₆₇	1	2	yes	—
459	#518	C₂²×C₆₇	1	2	yes	—
460	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
462	#490	C₂²×C₆₇	1	4	yes	complemented
463	#490	C₂²×C₆₇	1	4	yes	complemented
464	#489	C₂²×C₆₇	1	4	yes	complemented
465	#488	C₂²×C₆₇	1	4	yes	complemented
466	#486	C₂²×C₆₇	1	4	yes	complemented
467	#486	C₂²×C₆₇	1	2	yes	complemented
468	#486	C₂²×C₆₇	1	2	yes	complemented
469	#479	C₂²×C₆₇	1	2	yes	complemented
470	#478	C₂²×C₆₇	1	2	yes	complemented
471	#478	C₂²×C₆₇	1	4	yes	complemented
472	#478	C₂²×C₆₇	1	4	yes	complemented
473	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
474	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
475	#476	C₂²×C₆₇	1	4	yes	complemented
476	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
477	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
478	#474	C₂²×C₆₇	1	4	yes	complemented
479	#463	C₂²×C₆₇	1	4	yes	complemented
480	#463	C₂²×C₆₇	1	4	yes	complemented
481	#459	C₂²×C₆₇	1	2	yes	—
482	#459	C₂²×C₆₇	1	4	yes	—
483	#459	C₂²×C₆₇	1	2	yes	—
484	#459	C₂²×C₆₇	1	4	yes	complemented
485	#459	C₂²×C₆₇	1	4	yes	complemented
486	#446	C₂²×C₆₇	1	4	yes	complemented
487	#446	C₂²×C₆₇	1	2	yes	complemented
488	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
489	#442	C₂²×C₆₇	1	2	yes	complemented
490	#442	C₂²×C₆₇	1	4	yes	complemented
491	#442	C₂²×C₆₇	1	4	yes	complemented
492	#440	C₂²×C₆₇	1	2	yes	complemented
493	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
494	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
495	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
496	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
497	#428	C₂²×C₆₇	1	1	yes	characteristic
498	#427	C₂²×C₆₇	1	2	yes	—
499	#424	C₂²×C₆₇	1	2	yes	—
500	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
501	#418	C₂²×C₆₇	1	2	yes	—
502	#418	C₂²×C₆₇	1	2	yes	—
503	#418	C₂²×C₆₇	1	1	yes	characteristic
504	#417	C₂²×C₆₇	1	1	yes	characteristic
505	#416	C₂²×C₆₇	1	2	yes	—
506	C₂×#102	C₂²×C₆₇	1	2	yes	—
507	#405	C₂²×C₆₇	1	2	yes	—
508	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
509	C₂×#41	—	2	2	no	—
510	C₂×#41	—	2	2	no	—
511	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
512	C₂²×Q₈	—	2	2	no	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	—	2	1	no	—
515	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
516	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
517	C₂³×C₄	—	2	1	no	—
518	AGL(1,ℤ/8)	—	2	4	no	—
519	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
520	C₂×D₈	—	2	8	no	—
521	C₂×D₈	C₂³×C₆₇	1	4	yes	—
522	C₂×D₈	C₂³×C₆₇	1	4	yes	—
523	C₂×D₈	C₂³×C₆₇	1	2	yes	—
524	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
525	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
526	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
527	C₄⋊Q₈	—	2	2	no	—
528	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
529	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
532	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
533	#127	—	2	1	no	—
534	#127	—	2	1	no	—
535	#127	C₂³×C₆₇	1	2	yes	—
536	#127	C₂³×C₆₇	1	2	yes	—
537	#127	C₂³×C₆₇	1	4	yes	—
538	#125	—	2	2	no	—
539	#125	D₄×C₆₇	1	2	yes	—
540	#125	C₂³×C₆₇	1	2	yes	—
541	#125	C₂³×C₆₇	1	4	yes	—
542	#124	—	2	2	no	—
543	#124	—	2	2	no	—
544	#124	C₂³×C₆₇	1	4	yes	—
545	#123	—	2	4	no	—
546	#123	—	2	4	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	4	no	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	—	2	1	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	—	2	4	no	—
553	C₂²⋊Q₈	—	2	4	no	—
554	C₂²⋊Q₈	—	2	4	no	—
555	C₂²⋊Q₈	—	2	4	no	—
556	C₂²⋊Q₈	—	2	4	no	—
557	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
558	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
559	#121	—	2	2	no	—
560	#121	—	2	2	no	—
561	#121	—	2	2	no	—
562	#121	—	2	2	no	—
563	#121	—	2	4	no	—
564	#121	—	2	4	no	—
565	#120	—	2	4	no	—
566	C₄×Q₈	—	2	1	no	—
567	C₄×Q₈	—	2	1	no	—
568	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
569	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
570	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
571	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	C₂³×C₆₇	1	2	yes	—
583	C₄×D₄	C₂³×C₆₇	1	2	yes	—
584	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
585	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
586	C₄×D₄	C₂³×C₆₇	1	4	yes	—
587	C₄×D₄	C₂³×C₆₇	1	4	yes	—
588	C₄×D₄	C₂³×C₆₇	1	4	yes	—
589	C₄×D₄	C₂³×C₆₇	1	4	yes	—
590	#117	—	2	1	no	—
591	#117	C₂³×C₆₇	1	1	yes	characteristic
592	#117	C₂³×C₆₇	1	2	yes	—
593	#117	C₂³×C₆₇	1	2	yes	—
594	C₂×C₄⋊C₄	—	2	4	no	—
595	C₂×C₄⋊C₄	—	2	2	no	—
596	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	4	no	—
599	C₂×C₂²⋊C₄	—	2	4	no	—
600	C₂×C₄²	—	2	1	no	—
601	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
602	#107	C₂³×C₆₇	1	2	yes	—
603	#107	C₂³×C₆₇	1	2	yes	—
604	#107	C₂³×C₆₇	1	2	yes	—
605	#106	C₂³×C₆₇	1	2	yes	—
606	#106	C₂³×C₆₇	1	2	yes	—
607	#106	C₂³×C₆₇	1	2	yes	—
608	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
609	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
610	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
611	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
612	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
613	#103	C₂³×C₆₇	1	2	yes	—
614	#103	C₂³×C₆₇	1	2	yes	—
615	#103	C₂³×C₆₇	1	2	yes	—
616	#102	C₂³×C₆₇	1	4	yes	—
617	#102	C₂³×C₆₇	1	4	yes	—
618	#102	C₂³×C₆₇	1	2	yes	—
619	#102	C₂³×C₆₇	1	2	yes	—
620	#102	C₂³×C₆₇	1	2	yes	—
621	#102	C₂³×C₆₇	1	2	yes	—
622	#102	C₂³×C₆₇	1	2	yes	—
623	#102	C₂³×C₆₇	1	4	yes	—
624	#102	C₂³×C₆₇	1	4	yes	—
625	#102	C₂³×C₆₇	1	4	yes	—
626	#102	C₂³×C₆₇	1	4	yes	—
627	#97	C₂³×C₆₇	1	2	yes	—
628	#97	C₂³×C₆₇	1	4	yes	—
629	C₄×C₈	C₂³×C₆₇	1	2	yes	—
630	C₄×C₈	C₂³×C₆₇	1	4	yes	—
631	C₂⁴	—	2	1	no	—
632	C₂⁴	—	2	2	no	—
633	#41	—	2	2	no	—
634	#41	—	2	2	no	—
635	#41	—	8	4	no	—
636	#41	—	8	4	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	4	no	—
640	C₂×Q₈	—	8	4	no	—
641	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
642	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
643	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	8	2	no	—
657	C₂×D₄	—	8	2	no	—
658	C₂×D₄	#41×C₆₇	1	4	yes	complemented
659	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
660	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
661	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	8	2	no	—
673	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
676	SD₁₆	—	2	4	no	—
677	D₈	—	2	8	no	—
678	D₈	—	2	8	no	—
679	D₈	—	2	4	no	—
680	M₁₆	—	2	2	no	—
681	M₁₆	—	2	2	no	—
682	C₂×C₈	—	2	4	no	—
683	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
684	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
685	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
686	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
698	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
699	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
700	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
701	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
702	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
703	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
704	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
705	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
706	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
707	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	—	2	1	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
721	C₄²	—	2	1	no	—
722	C₄²	—	2	1	no	—
723	C₄²	—	2	1	no	—
724	C₄²	—	2	2	no	—
725	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
726	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
727	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
728	C₄²	C₂⁴×C₆₇	1	4	yes	—
729	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
730	C₂³	—	2	2	no	—
731	C₂³	—	2	4	no	—
732	C₂³	—	2	4	no	—
733	C₂³	—	2	1	no	—
734	C₂³	—	4	4	no	—
735	C₂³	—	8	1	no	—
736	C₂³	—	8	1	no	—
737	C₂³	—	8	2	no	—
738	C₂³	—	8	2	no	—
739	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
740	Q₈	—	2	4	no	—
741	Q₈	—	2	1	no	—
742	Q₈	—	2	1	no	—
743	Q₈	—	4	2	no	—
744	Q₈	—	4	2	no	—
745	Q₈	—	8	4	no	—
746	Q₈	—	8	1	no	—
747	D₄	—	2	4	no	—
748	D₄	—	2	4	no	—
749	D₄	—	2	1	no	—
750	D₄	—	2	2	no	—
751	D₄	—	2	4	no	—
752	D₄	—	2	1	no	—
753	D₄	—	4	4	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	4	no	—
756	D₄	—	4	4	no	—
757	D₄	—	8	2	no	—
758	D₄	—	8	2	no	—
759	D₄	—	8	4	no	—
760	D₄	—	8	4	no	—
761	D₄	C₂×#41×C₆₇	1	4	yes	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	2	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	8	2	no	—
775	C₂×C₄	—	8	4	no	—
776	C₂×C₄	—	8	4	no	—
777	C₂×C₄	—	8	4	no	—
778	C₂×C₄	—	8	4	no	—
779	C₂×C₄	—	8	1	no	—
780	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
784	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
785	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
787	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
788	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
789	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
790	C₈	—	2	2	no	—
791	C₈	—	2	2	no	—
792	C₈	—	2	2	no	—
793	C₈	—	2	2	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	4	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	4	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	4	no	—
805	C₂²	—	8	4	no	—
806	C₂²	—	16	4	no	—
807	C₂²	#548×C₆₇	1	2	yes	—
808	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
809	C₄	—	2	1	no	—
810	C₄	—	2	4	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	4	no	—
814	C₄	—	4	1	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	1	no	—
820	C₄	#548×C₆₇	1	2	yes	—
821	C₄	#576×C₆₇	1	2	yes	—
822	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
823	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
824	C₂	—	2	2	no	—
825	C₂	—	4	4	no	—
826	C₂	—	8	4	no	—
827	C₂	—	8	1	no	—
828	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
829	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
830	C₂	C₆₇×#3585	1	1	yes	characteristic

	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 ◁ #533×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3508	C₂	semidirect
2. C₆₇×#3501	C₂	semidirect
3. C₆₇×#3373	C₂	semidirect
4. C₆₇×#3370	C₂	semidirect
5. C₆₇×#3366	C₂	semidirect
6. C₆₇×#3366	C₂	semidirect
7. C₆₇×#3361	C₂	semidirect
8. C₆₇×#3358	C₂	semidirect
9. C₆₇×#3138	C₂	semidirect
10. C₆₇×#3136	C₂	semidirect
11. C₆₇×#3081	C₂	semidirect
12. C₆₇×#3076	C₂	semidirect
13. C₆₇×#3041	C₂	semidirect
14. C₂×#459×C₆₇	C₂	semidirect
15. C₆₇×#2962	C₂	semidirect
16. C₆₇×#2948	C₂	semidirect
17. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
20. #559×C₆₇	C₂²	semidirect
21. #559×C₆₇	C₂²	semidirect
24. #554×C₆₇	C₂²	semidirect
25. #554×C₆₇	C₂²	semidirect
26. #550×C₆₇	C₂²	semidirect
27. #550×C₆₇	C₂²	semidirect
29. D₄×Q₈×C₆₇	C₂²	semidirect
46. #490×C₆₇	C₂²	semidirect
47. #490×C₆₇	C₂²	semidirect
48. #489×C₆₇	C₂²	semidirect
49. #488×C₆₇	C₂²	semidirect
50. #486×C₆₇	C₂²	semidirect
51. #486×C₆₇	C₂²	semidirect
52. #486×C₆₇	C₂²	semidirect
53. #479×C₆₇	C₂²	semidirect
54. #478×C₆₇	C₂²	semidirect
55. #478×C₆₇	C₂²	semidirect
56. #478×C₆₇	C₂²	semidirect
57. #477×C₆₇	C₂²	semidirect
58. #476×C₆₇	C₂²	semidirect
59. #476×C₆₇	C₂²	semidirect
60. #475×C₆₇	C₂²	semidirect
61. #474×C₆₇	C₂²	semidirect
62. #474×C₆₇	C₂²	semidirect
63. #463×C₆₇	C₂²	semidirect
64. #463×C₆₇	C₂²	semidirect
68. #459×C₆₇	C₂²	semidirect
69. #459×C₆₇	C₂²	semidirect
70. #446×C₆₇	C₂²	semidirect
71. #446×C₆₇	C₂²	semidirect
72. C₈×Q₈×C₆₇	C₂²	semidirect
73. #442×C₆₇	C₂²	semidirect
74. #442×C₆₇	C₂²	semidirect
75. #442×C₆₇	C₂²	semidirect
76. #440×C₆₇	C₂²	semidirect
77. C₄×SD₁₆×C₆₇	C₂²	semidirect
78. C₄×D₈×C₆₇	C₂²	semidirect
79. C₄×D₈×C₆₇	C₂²	semidirect
80. C₄×D₈×C₆₇	C₂²	semidirect
242. C₂×D₄×C₆₇	#41	semidirect
408. #61339	C₆₇	direct (N × H)
416. #3508	C₂×C₆₇	semidirect
417. #3501	C₂×C₆₇	semidirect
418. #3373	C₂×C₆₇	semidirect
419. #3370	C₂×C₆₇	semidirect
420. #3366	C₂×C₆₇	semidirect
421. #3366	C₂×C₆₇	semidirect
422. #3361	C₂×C₆₇	semidirect
423. #3358	C₂×C₆₇	semidirect
424. #3138	C₂×C₆₇	semidirect
425. #3136	C₂×C₆₇	semidirect
426. #3081	C₂×C₆₇	semidirect
427. #3076	C₂×C₆₇	semidirect
428. #3041	C₂×C₆₇	semidirect
429. C₂×#459	C₂×C₆₇	semidirect
430. #2962	C₂×C₆₇	semidirect
431. #2948	C₂×C₆₇	semidirect
432. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
433. C₆₇	#61339	direct (N × H)
436. #559	C₂²×C₆₇	semidirect
437. #559	C₂²×C₆₇	semidirect
440. #554	C₂²×C₆₇	semidirect
441. #554	C₂²×C₆₇	semidirect
442. #550	C₂²×C₆₇	semidirect
443. #550	C₂²×C₆₇	semidirect
445. D₄×Q₈	C₂²×C₆₇	semidirect
462. #490	C₂²×C₆₇	semidirect
463. #490	C₂²×C₆₇	semidirect
464. #489	C₂²×C₆₇	semidirect
465. #488	C₂²×C₆₇	semidirect
466. #486	C₂²×C₆₇	semidirect
467. #486	C₂²×C₆₇	semidirect
468. #486	C₂²×C₆₇	semidirect
469. #479	C₂²×C₆₇	semidirect
470. #478	C₂²×C₆₇	semidirect
471. #478	C₂²×C₆₇	semidirect
472. #478	C₂²×C₆₇	semidirect
473. #477	C₂²×C₆₇	semidirect
474. #476	C₂²×C₆₇	semidirect
475. #476	C₂²×C₆₇	semidirect
476. #475	C₂²×C₆₇	semidirect
477. #474	C₂²×C₆₇	semidirect
478. #474	C₂²×C₆₇	semidirect
479. #463	C₂²×C₆₇	semidirect
480. #463	C₂²×C₆₇	semidirect
484. #459	C₂²×C₆₇	semidirect
485. #459	C₂²×C₆₇	semidirect
486. #446	C₂²×C₆₇	semidirect
487. #446	C₂²×C₆₇	semidirect
488. C₈×Q₈	C₂²×C₆₇	semidirect
489. #442	C₂²×C₆₇	semidirect
490. #442	C₂²×C₆₇	semidirect
491. #442	C₂²×C₆₇	semidirect
492. #440	C₂²×C₆₇	semidirect
493. C₄×SD₁₆	C₂²×C₆₇	semidirect
494. C₄×D₈	C₂²×C₆₇	semidirect
495. C₄×D₈	C₂²×C₆₇	semidirect
496. C₄×D₈	C₂²×C₆₇	semidirect
658. C₂×D₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3508	2
C₆₇×#3501	2
C₆₇×#3373	2
C₆₇×#3370	2
C₆₇×#3366	2
C₆₇×#3361	2
C₆₇×#3358	2
C₆₇×#3138	2
C₆₇×#3136	2
C₆₇×#3081	2
C₆₇×#3076	2
C₆₇×#3041	2
C₂×#459×C₆₇	2
C₆₇×#2962	2
C₆₇×#2948	2
C₄×AGL(1,ℤ/8)×C₆₇	2
#61339	67

Subgroups — C67×#61339 #30740590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61339 #30740590