Subgroups — C₆₇×#60593 #30739844

Order 17152.

2110 conjugacy classes of subgroups.

The subgroup lattice has 916 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	C₄×2₋¹⁺⁴×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3126	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3119	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3115	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3112	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3106	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3103	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3096	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#460×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3010	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2949	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2946	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
20	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
21	#559×C₆₇	—	2	1	no	—
22	#559×C₆₇	—	2	1	no	—
23	#550×C₆₇	—	2	1	no	—
24	#550×C₆₇	—	2	1	no	—
25	#546×C₆₇	—	2	2	no	—
26	#546×C₆₇	—	2	2	no	—
27	#540×C₆₇	C₂²	1	4	yes	—
28	#535×C₆₇	C₂²	1	2	yes	—
29	#533×C₆₇	C₂²	1	1	yes	characteristic
30	#532×C₆₇	C₂²	1	2	yes	—
31	#532×C₆₇	C₂²	1	2	yes	—
32	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
33	#520×C₆₇	—	2	2	no	—
34	#520×C₆₇	—	2	1	no	—
35	#520×C₆₇	C₂²	1	1	yes	characteristic
36	#520×C₆₇	C₂²	1	1	yes	characteristic
37	#520×C₆₇	C₂²	1	2	yes	complemented
38	#519×C₆₇	—	2	1	no	—
39	#519×C₆₇	C₂²	1	1	yes	characteristic
40	#519×C₆₇	C₂²	1	2	yes	complemented
41	#518×C₆₇	C₂²	1	2	yes	—
42	C₄×#41×C₆₇	—	2	2	no	—
43	C₄×#41×C₆₇	—	2	1	no	—
44	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
45	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
46	C₄×#41×C₆₇	C₂²	1	2	yes	complemented
47	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
48	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
50	#482×C₆₇	C₂²	1	4	yes	complemented
51	#482×C₆₇	C₂²	1	4	yes	complemented
52	#481×C₆₇	C₂²	1	4	yes	complemented
53	#480×C₆₇	C₂²	1	4	yes	complemented
54	#479×C₆₇	C₂²	1	2	yes	complemented
55	#479×C₆₇	C₂²	1	4	yes	complemented
56	#478×C₆₇	C₂²	1	2	yes	complemented
57	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#477×C₆₇	C₂²	1	2	yes	complemented
59	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#475×C₆₇	C₂²	1	2	yes	complemented
62	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#460×C₆₇	C₂²	1	2	yes	—
64	#460×C₆₇	C₂²	1	2	yes	—
65	#460×C₆₇	C₂²	1	4	yes	—
66	#460×C₆₇	C₂²	1	2	yes	—
67	#460×C₆₇	C₂²	1	2	yes	—
68	#459×C₆₇	C₂²	1	2	yes	—
69	#459×C₆₇	C₂²	1	2	yes	—
70	#449×C₆₇	C₂²	1	4	yes	complemented
71	#449×C₆₇	C₂²	1	4	yes	complemented
72	#448×C₆₇	C₂²	1	4	yes	complemented
73	#448×C₆₇	C₂²	1	4	yes	complemented
74	#442×C₆₇	C₂²	1	4	yes	complemented
75	#440×C₆₇	C₂²	1	4	yes	complemented
76	#440×C₆₇	C₂²	1	4	yes	complemented
77	#440×C₆₇	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
81	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
82	#433×C₆₇	C₂²	1	4	yes	complemented
83	#432×C₆₇	C₂²	1	2	yes	complemented
84	#431×C₆₇	C₂²	1	2	yes	complemented
85	#428×C₆₇	C₂²	1	2	yes	—
86	#427×C₆₇	C₂²	1	2	yes	—
87	#423×C₆₇	C₂²	1	1	yes	characteristic
88	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
89	#419×C₆₇	C₂²	1	2	yes	—
90	#418×C₆₇	C₂²	1	2	yes	—
91	#416×C₆₇	C₂²	1	2	yes	—
92	C₂×#102×C₆₇	C₂²	1	2	yes	—
93	#408×C₆₇	C₂²	1	2	yes	—
94	#405×C₆₇	C₂²	1	2	yes	—
95	2₋¹⁺⁴×C₆₇	—	2	4	no	—
96	2₋¹⁺⁴×C₆₇	—	2	4	no	—
97	C₂×#41×C₆₇	—	2	2	no	—
98	C₂×#41×C₆₇	—	2	1	no	—
99	C₂×#41×C₆₇	—	2	2	no	—
100	C₂×#41×C₆₇	—	2	2	no	—
101	C₂×#41×C₆₇	C₂³	1	2	yes	—
102	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
103	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×Q₈×C₆₇	—	2	1	no	—
105	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
106	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₂²×D₄×C₆₇	—	2	1	no	—
108	C₂²×D₄×C₆₇	—	2	1	no	—
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
111	C₂×SD₁₆×C₆₇	—	2	8	no	—
112	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
115	C₂×D₈×C₆₇	C₂³	1	4	yes	—
116	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
117	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
120	#127×C₆₇	—	2	2	no	—
121	#127×C₆₇	—	2	1	no	—
122	#127×C₆₇	—	2	1	no	—
123	#127×C₆₇	C₂³	1	2	yes	—
124	#127×C₆₇	C₂³	1	2	yes	—
125	#125×C₆₇	C₂³	1	2	yes	—
126	#124×C₆₇	—	2	2	no	—
127	#124×C₆₇	—	2	2	no	—
128	#124×C₆₇	—	2	2	no	—
129	#123×C₆₇	—	2	4	no	—
130	#123×C₆₇	—	2	4	no	—
131	C₂²⋊Q₈×C₆₇	—	2	1	no	—
132	C₂²⋊Q₈×C₆₇	—	2	1	no	—
133	#121×C₆₇	—	2	2	no	—
134	#121×C₆₇	—	2	2	no	—
135	#121×C₆₇	—	2	4	no	—
136	#121×C₆₇	—	2	4	no	—
137	#121×C₆₇	C₂³	1	4	yes	—
138	#121×C₆₇	C₂³	1	4	yes	—
139	#120×C₆₇	—	2	4	no	—
140	C₄×Q₈×C₆₇	—	2	1	no	—
141	C₄×Q₈×C₆₇	—	2	1	no	—
142	C₄×Q₈×C₆₇	—	2	2	no	—
143	C₄×Q₈×C₆₇	—	2	1	no	—
144	C₄×Q₈×C₆₇	—	2	2	no	—
145	C₄×Q₈×C₆₇	—	2	1	no	—
146	C₄×Q₈×C₆₇	—	2	2	no	—
147	C₄×Q₈×C₆₇	—	2	1	no	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	—	2	1	no	—
150	C₄×Q₈×C₆₇	—	2	1	no	—
151	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
152	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
153	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
154	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
156	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
159	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
160	C₄×D₄×C₆₇	—	2	2	no	—
161	C₄×D₄×C₆₇	—	2	1	no	—
162	C₄×D₄×C₆₇	—	2	1	no	—
163	C₄×D₄×C₆₇	—	2	2	no	—
164	C₄×D₄×C₆₇	—	2	1	no	—
165	C₄×D₄×C₆₇	—	2	2	no	—
166	C₄×D₄×C₆₇	—	2	2	no	—
167	C₄×D₄×C₆₇	—	2	2	no	—
168	C₄×D₄×C₆₇	—	2	2	no	—
169	C₄×D₄×C₆₇	—	2	2	no	—
170	C₄×D₄×C₆₇	—	2	2	no	—
171	C₄×D₄×C₆₇	—	2	2	no	—
172	C₄×D₄×C₆₇	—	2	2	no	—
173	C₄×D₄×C₆₇	D₄	1	2	yes	—
174	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
175	C₄×D₄×C₆₇	D₄	1	2	yes	—
176	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
177	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₆₇	C₂³	1	2	yes	—
180	C₄×D₄×C₆₇	C₂³	1	4	yes	—
181	C₄×D₄×C₆₇	C₂³	1	4	yes	—
182	#117×C₆₇	—	2	1	no	—
183	#117×C₆₇	—	2	2	no	—
184	#117×C₆₇	—	2	2	no	—
185	#117×C₆₇	—	2	2	no	—
186	#117×C₆₇	—	2	2	no	—
187	#117×C₆₇	—	2	1	no	—
188	#117×C₆₇	—	2	2	no	—
189	#117×C₆₇	C₂³	1	2	yes	—
190	#117×C₆₇	C₂³	1	1	yes	characteristic
191	#117×C₆₇	C₂³	1	2	yes	—
192	#117×C₆₇	C₂³	1	1	yes	characteristic
193	#117×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
195	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
196	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
197	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
201	C₂×C₄²×C₆₇	—	2	1	no	—
202	C₂×C₄²×C₆₇	—	2	2	no	—
203	C₂×C₄²×C₆₇	—	2	1	no	—
204	C₂×C₄²×C₆₇	—	2	2	no	—
205	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
207	#107×C₆₇	C₂³	1	2	yes	—
208	#107×C₆₇	C₂³	1	2	yes	—
209	#107×C₆₇	C₂³	1	4	yes	—
210	#106×C₆₇	C₂³	1	2	yes	—
211	#106×C₆₇	C₂³	1	4	yes	—
212	#106×C₆₇	C₂³	1	2	yes	—
213	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
214	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
215	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
217	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
218	#103×C₆₇	C₂³	1	2	yes	—
219	#103×C₆₇	C₂³	1	2	yes	—
220	#103×C₆₇	C₂³	1	4	yes	—
221	#103×C₆₇	C₂³	1	4	yes	—
222	#102×C₆₇	C₂³	1	2	yes	—
223	#102×C₆₇	C₂³	1	2	yes	—
224	#102×C₆₇	C₂³	1	4	yes	—
225	#102×C₆₇	C₂³	1	4	yes	—
226	#102×C₆₇	C₂³	1	4	yes	—
227	#102×C₆₇	C₂³	1	4	yes	—
228	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
229	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
230	#97×C₆₇	C₂³	1	4	yes	—
231	C₄×C₈×C₆₇	C₂³	1	4	yes	—
232	C₂⁴×C₆₇	—	2	2	no	—
233	#41×C₆₇	—	2	16	no	—
234	#41×C₆₇	—	2	8	no	—
235	#41×C₆₇	—	2	4	no	—
236	#41×C₆₇	—	2	4	no	—
237	#41×C₆₇	—	2	2	no	—
238	#41×C₆₇	—	2	2	no	—
239	#41×C₆₇	—	2	2	no	—
240	#41×C₆₇	—	8	4	no	—
241	#41×C₆₇	—	8	4	no	—
242	#41×C₆₇	#41	1	4	yes	complemented
243	C₂×Q₈×C₆₇	—	2	8	no	—
244	C₂×Q₈×C₆₇	—	2	4	no	—
245	C₂×Q₈×C₆₇	—	2	4	no	—
246	C₂×Q₈×C₆₇	—	2	2	no	—
247	C₂×Q₈×C₆₇	—	2	1	no	—
248	C₂×Q₈×C₆₇	—	2	1	no	—
249	C₂×Q₈×C₆₇	—	2	1	no	—
250	C₂×Q₈×C₆₇	—	2	2	no	—
251	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
252	C₂×Q₈×C₆₇	#41	1	4	yes	complemented
253	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
255	C₂×D₄×C₆₇	—	2	2	no	—
256	C₂×D₄×C₆₇	—	2	1	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	4	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂×D₄×C₆₇	—	2	2	no	—
261	C₂×D₄×C₆₇	—	2	2	no	—
262	C₂×D₄×C₆₇	—	2	2	no	—
263	C₂×D₄×C₆₇	—	2	2	no	—
264	C₂×D₄×C₆₇	—	2	4	no	—
265	C₂×D₄×C₆₇	—	2	4	no	—
266	C₂×D₄×C₆₇	—	8	2	no	—
267	C₂×D₄×C₆₇	—	8	2	no	—
268	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
269	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
270	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
271	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	—	2	2	no	—
273	C₂²×C₄×C₆₇	—	2	1	no	—
274	C₂²×C₄×C₆₇	—	2	2	no	—
275	C₂²×C₄×C₆₇	—	2	1	no	—
276	C₂²×C₄×C₆₇	—	2	2	no	—
277	C₂²×C₄×C₆₇	—	2	1	no	—
278	C₂²×C₄×C₆₇	—	2	1	no	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	2	1	no	—
281	C₂²×C₄×C₆₇	—	2	4	no	—
282	C₂²×C₄×C₆₇	—	2	4	no	—
283	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	SD₁₆×C₆₇	—	2	8	no	—
290	SD₁₆×C₆₇	—	2	8	no	—
291	SD₁₆×C₆₇	—	2	8	no	—
292	D₈×C₆₇	—	2	8	no	—
293	M₁₆×C₆₇	—	2	4	no	—
294	C₂×C₈×C₆₇	—	2	4	no	—
295	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
296	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
297	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
298	C₄⋊C₄×C₆₇	—	2	2	no	—
299	C₄⋊C₄×C₆₇	—	2	2	no	—
300	C₄⋊C₄×C₆₇	—	2	2	no	—
301	C₄⋊C₄×C₆₇	—	2	2	no	—
302	C₄⋊C₄×C₆₇	—	2	1	no	—
303	C₄⋊C₄×C₆₇	—	2	2	no	—
304	C₄⋊C₄×C₆₇	—	2	1	no	—
305	C₄⋊C₄×C₆₇	—	2	2	no	—
306	C₄⋊C₄×C₆₇	—	2	1	no	—
307	C₄⋊C₄×C₆₇	—	2	1	no	—
308	C₄⋊C₄×C₆₇	—	2	1	no	—
309	C₄⋊C₄×C₆₇	—	2	2	no	—
310	C₄⋊C₄×C₆₇	—	2	2	no	—
311	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
312	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
314	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
315	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
316	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
317	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
319	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
320	C₂²⋊C₄×C₆₇	—	2	2	no	—
321	C₂²⋊C₄×C₆₇	—	2	2	no	—
322	C₂²⋊C₄×C₆₇	—	2	1	no	—
323	C₂²⋊C₄×C₆₇	—	2	4	no	—
324	C₂²⋊C₄×C₆₇	—	2	4	no	—
325	C₂²⋊C₄×C₆₇	—	2	1	no	—
326	C₂²⋊C₄×C₆₇	—	2	2	no	—
327	C₂²⋊C₄×C₆₇	—	2	1	no	—
328	C₂²⋊C₄×C₆₇	—	2	4	no	—
329	C₂²⋊C₄×C₆₇	—	2	4	no	—
330	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
333	C₄²×C₆₇	—	2	2	no	—
334	C₄²×C₆₇	—	2	1	no	—
335	C₄²×C₆₇	—	2	2	no	—
336	C₄²×C₆₇	—	2	1	no	—
337	C₄²×C₆₇	—	2	2	no	—
338	C₄²×C₆₇	—	2	2	no	—
339	C₄²×C₆₇	—	2	2	no	—
340	C₄²×C₆₇	—	2	2	no	—
341	C₄²×C₆₇	—	2	1	no	—
342	C₄²×C₆₇	—	2	2	no	—
343	C₄²×C₆₇	C₂×D₄	1	2	yes	—
344	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
345	C₄²×C₆₇	C₂×D₄	1	2	yes	—
346	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₄²×C₆₇	C₂⁴	1	2	yes	—
350	C₂³×C₆₇	—	2	1	no	—
351	C₂³×C₆₇	—	2	4	no	—
352	C₂³×C₆₇	—	4	4	no	—
353	C₂³×C₆₇	—	8	2	no	—
354	C₂³×C₆₇	—	8	2	no	—
355	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
356	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₆₇	—	2	8	no	—
358	Q₈×C₆₇	—	2	2	no	—
359	Q₈×C₆₇	—	2	4	no	—
360	Q₈×C₆₇	—	2	1	no	—
361	Q₈×C₆₇	—	2	2	no	—
362	Q₈×C₆₇	—	4	2	no	—
363	Q₈×C₆₇	—	4	2	no	—
364	Q₈×C₆₇	C₂×#41	1	2	yes	—
365	Q₈×C₆₇	C₂×#41	1	4	yes	—
366	D₄×C₆₇	—	2	8	no	—
367	D₄×C₆₇	—	2	4	no	—
368	D₄×C₆₇	—	2	4	no	—
369	D₄×C₆₇	—	2	2	no	—
370	D₄×C₆₇	—	2	1	no	—
371	D₄×C₆₇	—	2	4	no	—
372	D₄×C₆₇	—	2	4	no	—
373	D₄×C₆₇	—	4	4	no	—
374	D₄×C₆₇	—	4	4	no	—
375	D₄×C₆₇	—	4	4	no	—
376	D₄×C₆₇	—	8	2	no	—
377	D₄×C₆₇	—	8	2	no	—
378	D₄×C₆₇	—	8	4	no	—
379	D₄×C₆₇	—	8	4	no	—
380	D₄×C₆₇	C₂×#41	1	2	yes	—
381	C₂×C₄×C₆₇	—	2	8	no	—
382	C₂×C₄×C₆₇	—	2	8	no	—
383	C₂×C₄×C₆₇	—	2	4	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	1	no	—
386	C₂×C₄×C₆₇	—	2	4	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	4	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	1	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	1	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	4	1	no	—
397	C₂×C₄×C₆₇	—	4	2	no	—
398	C₂×C₄×C₆₇	—	4	2	no	—
399	C₂×C₄×C₆₇	—	8	2	no	—
400	C₂×C₄×C₆₇	—	8	1	no	—
401	C₂×C₄×C₆₇	—	8	4	no	—
402	C₂×C₄×C₆₇	—	8	4	no	—
403	C₂×C₄×C₆₇	—	8	1	no	—
404	C₂×C₄×C₆₇	—	8	2	no	—
405	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
414	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
415	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
416	C₈×C₆₇	—	2	2	no	—
417	C₈×C₆₇	—	2	2	no	—
418	C₈×C₆₇	—	2	4	no	—
419	C₂²×C₆₇	—	2	1	no	—
420	C₂²×C₆₇	—	2	1	no	—
421	C₂²×C₆₇	—	2	2	no	—
422	C₂²×C₆₇	—	2	2	no	—
423	C₂²×C₆₇	—	2	2	no	—
424	C₂²×C₆₇	—	2	2	no	—
425	C₂²×C₆₇	—	4	1	no	—
426	C₂²×C₆₇	—	4	1	no	—
427	C₂²×C₆₇	—	4	4	no	—
428	C₂²×C₆₇	—	4	4	no	—
429	C₂²×C₆₇	—	4	4	no	—
430	C₂²×C₆₇	—	16	4	no	—
431	C₂²×C₆₇	#525	1	2	yes	—
432	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
433	C₄×C₆₇	—	2	1	no	—
434	C₄×C₆₇	—	2	2	no	—
435	C₄×C₆₇	—	2	1	no	—
436	C₄×C₆₇	—	2	4	no	—
437	C₄×C₆₇	—	2	2	no	—
438	C₄×C₆₇	—	2	2	no	—
439	C₄×C₆₇	—	2	2	no	—
440	C₄×C₆₇	—	2	1	no	—
441	C₄×C₆₇	—	4	2	no	—
442	C₄×C₆₇	—	4	1	no	—
443	C₄×C₆₇	—	4	2	no	—
444	C₄×C₆₇	—	4	1	no	—
445	C₄×C₆₇	—	4	2	no	—
446	C₄×C₆₇	#525	1	2	yes	—
447	C₄×C₆₇	#577	1	2	yes	—
448	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
449	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
450	#60593	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂×C₆₇	—	2	2	no	—
452	C₂×C₆₇	—	4	2	no	—
453	C₂×C₆₇	—	4	2	no	—
454	C₂×C₆₇	—	8	4	no	—
455	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
456	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
457	C₂×C₆₇	#3585	1	1	yes	characteristic
458	#3508	C₂×C₆₇	1	1	yes	characteristic, complemented
459	C₄×2₋¹⁺⁴	C₂×C₆₇	1	1	yes	characteristic, complemented
460	#3126	C₂×C₆₇	1	4	yes	complemented
461	#3119	C₂×C₆₇	1	4	yes	complemented
462	#3115	C₂×C₆₇	1	2	yes	complemented
463	#3112	C₂×C₆₇	1	2	yes	complemented
464	#3106	C₂×C₆₇	1	2	yes	complemented
465	#3103	C₂×C₆₇	1	2	yes	complemented
466	#3096	C₂×C₆₇	1	2	yes	complemented
467	#3078	C₂×C₆₇	1	1	yes	characteristic, complemented
468	#3076	C₂×C₆₇	1	1	yes	characteristic, complemented
469	#3038	C₂×C₆₇	1	1	yes	characteristic, complemented
470	C₂×#460	C₂×C₆₇	1	1	yes	characteristic, complemented
471	#3010	C₂×C₆₇	1	2	yes	complemented
472	#2949	C₂×C₆₇	1	2	yes	complemented
473	#2946	C₂×C₆₇	1	2	yes	complemented
474	#2925	C₂×C₆₇	1	1	yes	characteristic, complemented
475	C₆₇	#60593	1	1	yes	characteristic, direct product factor, Sylow
476	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
477	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
478	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
479	#559	—	2	1	no	—
480	#559	—	2	1	no	—
481	#550	—	2	1	no	—
482	#550	—	2	1	no	—
483	#546	—	2	2	no	—
484	#546	—	2	2	no	—
485	#540	C₂²×C₆₇	1	4	yes	—
486	#535	C₂²×C₆₇	1	2	yes	—
487	#533	C₂²×C₆₇	1	1	yes	characteristic
488	#532	C₂²×C₆₇	1	2	yes	—
489	#532	C₂²×C₆₇	1	2	yes	—
490	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
491	#520	—	2	2	no	—
492	#520	—	2	1	no	—
493	#520	C₂²×C₆₇	1	1	yes	characteristic
494	#520	C₂²×C₆₇	1	1	yes	characteristic
495	#520	C₂²×C₆₇	1	2	yes	complemented
496	#519	—	2	1	no	—
497	#519	C₂²×C₆₇	1	1	yes	characteristic
498	#519	C₂²×C₆₇	1	2	yes	complemented
499	#518	C₂²×C₆₇	1	2	yes	—
500	C₄×#41	—	2	2	no	—
501	C₄×#41	—	2	1	no	—
502	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
503	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
504	C₄×#41	C₂²×C₆₇	1	2	yes	complemented
505	C₂×C₄×Q₈	—	2	1	no	—
506	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
507	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
508	#482	C₂²×C₆₇	1	4	yes	complemented
509	#482	C₂²×C₆₇	1	4	yes	complemented
510	#481	C₂²×C₆₇	1	4	yes	complemented
511	#480	C₂²×C₆₇	1	4	yes	complemented
512	#479	C₂²×C₆₇	1	2	yes	complemented
513	#479	C₂²×C₆₇	1	4	yes	complemented
514	#478	C₂²×C₆₇	1	2	yes	complemented
515	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
516	#477	C₂²×C₆₇	1	2	yes	complemented
517	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
518	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
519	#475	C₂²×C₆₇	1	2	yes	complemented
520	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
521	#460	C₂²×C₆₇	1	2	yes	—
522	#460	C₂²×C₆₇	1	2	yes	—
523	#460	C₂²×C₆₇	1	2	yes	—
524	#460	C₂²×C₆₇	1	4	yes	—
525	#460	C₂²×C₆₇	1	2	yes	—
526	#459	C₂²×C₆₇	1	2	yes	—
527	#459	C₂²×C₆₇	1	2	yes	—
528	#449	C₂²×C₆₇	1	4	yes	complemented
529	#449	C₂²×C₆₇	1	4	yes	complemented
530	#448	C₂²×C₆₇	1	4	yes	complemented
531	#448	C₂²×C₆₇	1	4	yes	complemented
532	#442	C₂²×C₆₇	1	4	yes	complemented
533	#440	C₂²×C₆₇	1	4	yes	complemented
534	#440	C₂²×C₆₇	1	4	yes	complemented
535	#440	C₂²×C₆₇	1	4	yes	complemented
536	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
537	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
538	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
539	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
540	#433	C₂²×C₆₇	1	4	yes	complemented
541	#432	C₂²×C₆₇	1	2	yes	complemented
542	#431	C₂²×C₆₇	1	2	yes	complemented
543	#428	C₂²×C₆₇	1	2	yes	—
544	#427	C₂²×C₆₇	1	2	yes	—
545	#423	C₂²×C₆₇	1	1	yes	characteristic
546	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
547	#419	C₂²×C₆₇	1	2	yes	—
548	#418	C₂²×C₆₇	1	2	yes	—
549	#416	C₂²×C₆₇	1	2	yes	—
550	C₂×#102	C₂²×C₆₇	1	2	yes	—
551	#408	C₂²×C₆₇	1	2	yes	—
552	#405	C₂²×C₆₇	1	2	yes	—
553	2₋¹⁺⁴	—	2	4	no	—
554	2₋¹⁺⁴	—	2	4	no	—
555	C₂×#41	—	2	2	no	—
556	C₂×#41	—	2	1	no	—
557	C₂×#41	—	2	2	no	—
558	C₂×#41	—	2	2	no	—
559	C₂×#41	C₂³×C₆₇	1	2	yes	—
560	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
561	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
562	C₂²×Q₈	—	2	1	no	—
563	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
564	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
568	AGL(1,ℤ/8)	—	2	8	no	—
569	C₂×SD₁₆	—	2	8	no	—
570	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
571	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
572	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
573	C₂×D₈	C₂³×C₆₇	1	4	yes	—
574	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
575	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
576	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
577	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
578	#127	—	2	2	no	—
579	#127	—	2	1	no	—
580	#127	—	2	1	no	—
581	#127	C₂³×C₆₇	1	2	yes	—
582	#127	C₂³×C₆₇	1	2	yes	—
583	#125	C₂³×C₆₇	1	2	yes	—
584	#124	—	2	2	no	—
585	#124	—	2	2	no	—
586	#124	—	2	2	no	—
587	#123	—	2	4	no	—
588	#123	—	2	4	no	—
589	C₂²⋊Q₈	—	2	1	no	—
590	C₂²⋊Q₈	—	2	1	no	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	4	no	—
594	#121	—	2	4	no	—
595	#121	C₂³×C₆₇	1	4	yes	—
596	#121	C₂³×C₆₇	1	4	yes	—
597	#120	—	2	4	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	—	2	1	no	—
600	C₄×Q₈	—	2	2	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	2	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	2	no	—
607	C₄×Q₈	—	2	1	no	—
608	C₄×Q₈	—	2	1	no	—
609	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
610	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
611	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
612	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
613	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
614	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
615	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
616	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
617	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	D₄×C₆₇	1	2	yes	—
632	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
633	C₄×D₄	D₄×C₆₇	1	2	yes	—
634	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
635	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
636	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₆₇	1	2	yes	—
638	C₄×D₄	C₂³×C₆₇	1	4	yes	—
639	C₄×D₄	C₂³×C₆₇	1	4	yes	—
640	#117	—	2	1	no	—
641	#117	—	2	2	no	—
642	#117	—	2	2	no	—
643	#117	—	2	2	no	—
644	#117	—	2	2	no	—
645	#117	—	2	1	no	—
646	#117	—	2	2	no	—
647	#117	C₂³×C₆₇	1	1	yes	characteristic
648	#117	C₂³×C₆₇	1	2	yes	—
649	#117	C₂³×C₆₇	1	2	yes	—
650	#117	C₂³×C₆₇	1	1	yes	characteristic
651	#117	C₂³×C₆₇	1	2	yes	—
652	C₂×C₄⋊C₄	—	2	1	no	—
653	C₂×C₄⋊C₄	—	2	2	no	—
654	C₂×C₄⋊C₄	—	2	1	no	—
655	C₂×C₄⋊C₄	—	2	2	no	—
656	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₂²⋊C₄	—	2	4	no	—
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	—	2	2	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	—	2	2	no	—
663	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
665	#107	C₂³×C₆₇	1	2	yes	—
666	#107	C₂³×C₆₇	1	2	yes	—
667	#107	C₂³×C₆₇	1	4	yes	—
668	#106	C₂³×C₆₇	1	2	yes	—
669	#106	C₂³×C₆₇	1	2	yes	—
670	#106	C₂³×C₆₇	1	4	yes	—
671	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
672	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
673	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
674	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
675	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
676	#103	C₂³×C₆₇	1	2	yes	—
677	#103	C₂³×C₆₇	1	2	yes	—
678	#103	C₂³×C₆₇	1	4	yes	—
679	#103	C₂³×C₆₇	1	4	yes	—
680	#102	C₂³×C₆₇	1	4	yes	—
681	#102	C₂³×C₆₇	1	4	yes	—
682	#102	C₂³×C₆₇	1	2	yes	—
683	#102	C₂³×C₆₇	1	2	yes	—
684	#102	C₂³×C₆₇	1	4	yes	—
685	#102	C₂³×C₆₇	1	4	yes	—
686	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
687	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
688	#97	C₂³×C₆₇	1	4	yes	—
689	C₄×C₈	C₂³×C₆₇	1	4	yes	—
690	C₂⁴	—	2	2	no	—
691	#41	—	2	16	no	—
692	#41	—	2	8	no	—
693	#41	—	2	4	no	—
694	#41	—	2	4	no	—
695	#41	—	2	2	no	—
696	#41	—	2	2	no	—
697	#41	—	2	2	no	—
698	#41	—	8	4	no	—
699	#41	—	8	4	no	—
700	#41	#41×C₆₇	1	4	yes	complemented
701	C₂×Q₈	—	2	8	no	—
702	C₂×Q₈	—	2	4	no	—
703	C₂×Q₈	—	2	4	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	1	no	—
707	C₂×Q₈	—	2	1	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
710	C₂×Q₈	#41×C₆₇	1	4	yes	complemented
711	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
712	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	8	2	no	—
725	C₂×D₄	—	8	2	no	—
726	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
727	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
728	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
729	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
742	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
744	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
747	SD₁₆	—	2	8	no	—
748	SD₁₆	—	2	8	no	—
749	SD₁₆	—	2	8	no	—
750	D₈	—	2	8	no	—
751	M₁₆	—	2	4	no	—
752	C₂×C₈	—	2	4	no	—
753	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
754	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
755	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
770	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
771	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
772	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
773	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
774	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
775	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
776	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
777	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	1	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	1	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
789	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
790	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	1	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	1	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	1	no	—
800	C₄²	—	2	2	no	—
801	C₄²	C₂×D₄×C₆₇	1	2	yes	—
802	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
803	C₄²	C₂×D₄×C₆₇	1	2	yes	—
804	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
805	C₄²	C₂⁴×C₆₇	1	2	yes	—
806	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
807	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
808	C₂³	—	2	1	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	4	4	no	—
811	C₂³	—	8	2	no	—
812	C₂³	—	8	2	no	—
813	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
814	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
815	Q₈	—	2	8	no	—
816	Q₈	—	2	2	no	—
817	Q₈	—	2	4	no	—
818	Q₈	—	2	1	no	—
819	Q₈	—	2	2	no	—
820	Q₈	—	4	2	no	—
821	Q₈	—	4	2	no	—
822	Q₈	C₂×#41×C₆₇	1	2	yes	—
823	Q₈	C₂×#41×C₆₇	1	4	yes	—
824	D₄	—	2	8	no	—
825	D₄	—	2	4	no	—
826	D₄	—	2	4	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	1	no	—
829	D₄	—	2	4	no	—
830	D₄	—	2	4	no	—
831	D₄	—	4	4	no	—
832	D₄	—	4	4	no	—
833	D₄	—	4	4	no	—
834	D₄	—	8	2	no	—
835	D₄	—	8	2	no	—
836	D₄	—	8	4	no	—
837	D₄	—	8	4	no	—
838	D₄	C₂×#41×C₆₇	1	2	yes	—
839	C₂×C₄	—	2	8	no	—
840	C₂×C₄	—	2	8	no	—
841	C₂×C₄	—	2	4	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	4	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	8	4	no	—
858	C₂×C₄	—	8	4	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	—	8	1	no	—
861	C₂×C₄	—	8	1	no	—
862	C₂×C₄	—	8	2	no	—
863	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
864	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
865	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
866	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
867	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
868	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
870	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
871	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
872	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
873	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
874	C₈	—	2	2	no	—
875	C₈	—	2	2	no	—
876	C₈	—	2	4	no	—
877	C₂²	—	2	1	no	—
878	C₂²	—	2	1	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	4	no	—
886	C₂²	—	4	4	no	—
887	C₂²	—	4	4	no	—
888	C₂²	—	16	4	no	—
889	C₂²	#525×C₆₇	1	2	yes	—
890	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	4	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₄	#525×C₆₇	1	2	yes	—
905	C₄	#577×C₆₇	1	2	yes	—
906	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
907	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
908	C₂	—	2	2	no	—
909	C₂	—	4	2	no	—
910	C₂	—	4	2	no	—
911	C₂	—	8	4	no	—
912	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
913	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
914	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 ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3508	C₂	semidirect
2. C₄×2₋¹⁺⁴×C₆₇	C₂	semidirect
3. C₆₇×#3126	C₂	semidirect
4. C₆₇×#3119	C₂	semidirect
5. C₆₇×#3115	C₂	semidirect
6. C₆₇×#3112	C₂	semidirect
7. C₆₇×#3106	C₂	semidirect
8. C₆₇×#3103	C₂	semidirect
9. C₆₇×#3096	C₂	semidirect
10. C₆₇×#3078	C₂	semidirect
11. C₆₇×#3076	C₂	semidirect
12. C₆₇×#3038	C₂	semidirect
13. C₂×#460×C₆₇	C₂	semidirect
14. C₆₇×#3010	C₂	semidirect
15. C₆₇×#2949	C₂	semidirect
16. C₆₇×#2946	C₂	semidirect
17. C₆₇×#2925	C₂	semidirect
37. #520×C₆₇	C₂²	semidirect
40. #519×C₆₇	C₂²	semidirect
46. C₄×#41×C₆₇	C₂²	semidirect
49. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
50. #482×C₆₇	C₂²	semidirect
51. #482×C₆₇	C₂²	semidirect
52. #481×C₆₇	C₂²	semidirect
53. #480×C₆₇	C₂²	semidirect
54. #479×C₆₇	C₂²	semidirect
55. #479×C₆₇	C₂²	semidirect
56. #478×C₆₇	C₂²	semidirect
57. #477×C₆₇	C₂²	semidirect
58. #477×C₆₇	C₂²	semidirect
59. #476×C₆₇	C₂²	semidirect
60. #475×C₆₇	C₂²	semidirect
61. #475×C₆₇	C₂²	semidirect
62. #474×C₆₇	C₂²	semidirect
70. #449×C₆₇	C₂²	semidirect
71. #449×C₆₇	C₂²	semidirect
72. #448×C₆₇	C₂²	semidirect
73. #448×C₆₇	C₂²	semidirect
74. #442×C₆₇	C₂²	semidirect
75. #440×C₆₇	C₂²	semidirect
76. #440×C₆₇	C₂²	semidirect
77. #440×C₆₇	C₂²	semidirect
78. C₄×SD₁₆×C₆₇	C₂²	semidirect
79. C₄×SD₁₆×C₆₇	C₂²	semidirect
80. C₄×SD₁₆×C₆₇	C₂²	semidirect
81. C₄×D₈×C₆₇	C₂²	semidirect
82. #433×C₆₇	C₂²	semidirect
83. #432×C₆₇	C₂²	semidirect
84. #431×C₆₇	C₂²	semidirect
242. #41×C₆₇	#41	semidirect
252. C₂×Q₈×C₆₇	#41	semidirect
450. #60593	C₆₇	direct (N × H)
458. #3508	C₂×C₆₇	semidirect
459. C₄×2₋¹⁺⁴	C₂×C₆₇	semidirect
460. #3126	C₂×C₆₇	semidirect
461. #3119	C₂×C₆₇	semidirect
462. #3115	C₂×C₆₇	semidirect
463. #3112	C₂×C₆₇	semidirect
464. #3106	C₂×C₆₇	semidirect
465. #3103	C₂×C₆₇	semidirect
466. #3096	C₂×C₆₇	semidirect
467. #3078	C₂×C₆₇	semidirect
468. #3076	C₂×C₆₇	semidirect
469. #3038	C₂×C₆₇	semidirect
470. C₂×#460	C₂×C₆₇	semidirect
471. #3010	C₂×C₆₇	semidirect
472. #2949	C₂×C₆₇	semidirect
473. #2946	C₂×C₆₇	semidirect
474. #2925	C₂×C₆₇	semidirect
475. C₆₇	#60593	direct (N × H)
495. #520	C₂²×C₆₇	semidirect
498. #519	C₂²×C₆₇	semidirect
504. C₄×#41	C₂²×C₆₇	semidirect
507. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
508. #482	C₂²×C₆₇	semidirect
509. #482	C₂²×C₆₇	semidirect
510. #481	C₂²×C₆₇	semidirect
511. #480	C₂²×C₆₇	semidirect
512. #479	C₂²×C₆₇	semidirect
513. #479	C₂²×C₆₇	semidirect
514. #478	C₂²×C₆₇	semidirect
515. #477	C₂²×C₆₇	semidirect
516. #477	C₂²×C₆₇	semidirect
517. #476	C₂²×C₆₇	semidirect
518. #475	C₂²×C₆₇	semidirect
519. #475	C₂²×C₆₇	semidirect
520. #474	C₂²×C₆₇	semidirect
528. #449	C₂²×C₆₇	semidirect
529. #449	C₂²×C₆₇	semidirect
530. #448	C₂²×C₆₇	semidirect
531. #448	C₂²×C₆₇	semidirect
532. #442	C₂²×C₆₇	semidirect
533. #440	C₂²×C₆₇	semidirect
534. #440	C₂²×C₆₇	semidirect
535. #440	C₂²×C₆₇	semidirect
536. C₄×SD₁₆	C₂²×C₆₇	semidirect
537. C₄×SD₁₆	C₂²×C₆₇	semidirect
538. C₄×SD₁₆	C₂²×C₆₇	semidirect
539. C₄×D₈	C₂²×C₆₇	semidirect
540. #433	C₂²×C₆₇	semidirect
541. #432	C₂²×C₆₇	semidirect
542. #431	C₂²×C₆₇	semidirect
700. #41	#41×C₆₇	semidirect
710. C₂×Q₈	#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
C₄×2₋¹⁺⁴×C₆₇	2
C₆₇×#3126	2
C₆₇×#3119	2
C₆₇×#3115	2
C₆₇×#3112	2
C₆₇×#3106	2
C₆₇×#3103	2
C₆₇×#3096	2
C₆₇×#3078	2
C₆₇×#3076	2
C₆₇×#3038	2
C₂×#460×C₆₇	2
C₆₇×#3010	2
C₆₇×#2949	2
C₆₇×#2946	2
C₆₇×#2925	2
#60593	67

Subgroups — C67×#60593 #30739844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60593 #30739844