Subgroups — C₆₇×#61709 #30740960

Order 17152.

1806 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3505	C₂	1	1	yes	maximal, characteristic
2	C₂×#554×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3346	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3344	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3316	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3314	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3239	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3196	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3189	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3187	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3117	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3092	C₂	1	2	yes	maximal, complemented
13	C₂×#484×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#481×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	#554×C₆₇	—	2	2	no	—
17	#554×C₆₇	—	2	2	no	—
18	#554×C₆₇	C₂²	1	4	yes	—
19	#554×C₆₇	C₂²	1	4	yes	complemented
20	#553×C₆₇	—	2	2	no	—
21	#553×C₆₇	C₂²	1	2	yes	—
22	#552×C₆₇	C₂²	1	2	yes	—
23	#551×C₆₇	—	2	2	no	—
24	#548×C₆₇	C₂²	1	2	yes	—
25	#546×C₆₇	C₂²	1	2	yes	—
26	#539×C₆₇	—	2	1	no	—
27	#538×C₆₇	—	2	1	no	—
28	#534×C₆₇	—	2	1	no	—
29	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#529×C₆₇	C₂²	1	2	yes	—
31	C₂×#125×C₆₇	—	2	1	no	—
32	#525×C₆₇	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
39	#518×C₆₇	—	2	1	no	—
40	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₆₇	—	2	1	no	—
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#501×C₆₇	C₂²	1	4	yes	complemented
46	#489×C₆₇	C₂²	1	4	yes	complemented
47	#485×C₆₇	C₂²	1	4	yes	complemented
48	#484×C₆₇	C₂²	1	4	yes	complemented
49	#484×C₆₇	C₂²	1	2	yes	complemented
50	#484×C₆₇	C₂²	1	2	yes	complemented
51	#484×C₆₇	C₂²	1	2	yes	complemented
52	#484×C₆₇	C₂²	1	2	yes	complemented
53	#483×C₆₇	C₂²	1	4	yes	complemented
54	#483×C₆₇	C₂²	1	2	yes	complemented
55	#481×C₆₇	C₂²	1	2	yes	—
56	#481×C₆₇	C₂²	1	2	yes	—
57	#481×C₆₇	C₂²	1	2	yes	—
58	#481×C₆₇	C₂²	1	4	yes	complemented
59	#480×C₆₇	C₂²	1	4	yes	complemented
60	#479×C₆₇	C₂²	1	4	yes	complemented
61	#475×C₆₇	C₂²	1	4	yes	complemented
62	#474×C₆₇	C₂²	1	4	yes	complemented
63	#470×C₆₇	C₂²	1	4	yes	complemented
64	#468×C₆₇	C₂²	1	4	yes	complemented
65	#467×C₆₇	C₂²	1	4	yes	complemented
66	#465×C₆₇	C₂²	1	4	yes	complemented
67	#464×C₆₇	C₂²	1	4	yes	complemented
68	#452×C₆₇	C₂²	1	4	yes	complemented
69	#451×C₆₇	C₂²	1	2	yes	complemented
70	#451×C₆₇	C₂²	1	2	yes	complemented
71	#450×C₆₇	C₂²	1	2	yes	complemented
72	#448×C₆₇	C₂²	1	2	yes	—
73	#441×C₆₇	C₂²	1	4	yes	complemented
74	#440×C₆₇	C₂²	1	4	yes	complemented
75	#435×C₆₇	C₂²	1	4	yes	—
76	#435×C₆₇	C₂²	1	4	yes	complemented
77	#432×C₆₇	C₂²	1	2	yes	complemented
78	#428×C₆₇	C₂²	1	4	yes	complemented
79	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
80	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
81	#417×C₆₇	C₂²	1	4	yes	complemented
82	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
83	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
84	#407×C₆₇	C₂²	1	2	yes	complemented
85	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
86	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
87	C₂×#41×C₆₇	C₂³	1	2	yes	—
88	C₂²×Q₈×C₆₇	—	2	1	no	—
89	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₆₇	—	2	1	no	—
92	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₆₇	—	2	1	no	—
95	C₂³×C₄×C₆₇	—	2	1	no	—
96	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
101	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
102	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
103	C₄⋊Q₈×C₆₇	—	2	2	no	—
104	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
105	#126×C₆₇	—	2	2	no	—
106	#126×C₆₇	—	2	2	no	—
107	#126×C₆₇	—	2	2	no	—
108	#125×C₆₇	—	2	4	no	—
109	#125×C₆₇	—	2	4	no	—
110	#125×C₆₇	—	2	2	no	—
111	#125×C₆₇	C₂³	1	2	yes	—
112	#124×C₆₇	—	2	2	no	—
113	#124×C₆₇	C₂³	1	2	yes	—
114	#123×C₆₇	—	2	2	no	—
115	#123×C₆₇	—	2	2	no	—
116	#123×C₆₇	—	2	2	no	—
117	#123×C₆₇	—	2	2	no	—
118	#123×C₆₇	—	2	2	no	—
119	C₂²⋊Q₈×C₆₇	—	2	1	no	—
120	C₂²⋊Q₈×C₆₇	—	2	1	no	—
121	C₂²⋊Q₈×C₆₇	—	2	1	no	—
122	C₂²⋊Q₈×C₆₇	—	2	1	no	—
123	C₂²⋊Q₈×C₆₇	—	2	2	no	—
124	C₂²⋊Q₈×C₆₇	—	2	2	no	—
125	C₂²⋊Q₈×C₆₇	—	2	4	no	—
126	C₂²⋊Q₈×C₆₇	—	2	4	no	—
127	C₂²⋊Q₈×C₆₇	—	2	4	no	—
128	C₂²⋊Q₈×C₆₇	—	2	4	no	—
129	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
130	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
131	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
132	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
133	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
134	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
135	#121×C₆₇	—	2	2	no	—
136	#121×C₆₇	—	2	2	no	—
137	#121×C₆₇	—	2	1	no	—
138	#121×C₆₇	—	2	1	no	—
139	#121×C₆₇	—	2	2	no	—
140	#121×C₆₇	C₂³	1	2	yes	—
141	#121×C₆₇	C₂³	1	2	yes	—
142	#121×C₆₇	C₂³	1	2	yes	—
143	#120×C₆₇	—	2	2	no	—
144	#120×C₆₇	—	2	2	no	—
145	C₄×Q₈×C₆₇	—	2	2	no	—
146	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
147	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
148	C₄×D₄×C₆₇	—	2	4	no	—
149	C₄×D₄×C₆₇	—	2	4	no	—
150	C₄×D₄×C₆₇	—	2	2	no	—
151	C₄×D₄×C₆₇	—	2	2	no	—
152	C₄×D₄×C₆₇	—	2	2	no	—
153	C₄×D₄×C₆₇	—	2	2	no	—
154	C₄×D₄×C₆₇	—	2	2	no	—
155	C₄×D₄×C₆₇	D₄	1	2	yes	—
156	C₄×D₄×C₆₇	D₄	1	2	yes	—
157	C₄×D₄×C₆₇	C₂³	1	2	yes	—
158	C₄×D₄×C₆₇	C₂³	1	2	yes	—
159	C₄×D₄×C₆₇	C₂³	1	2	yes	—
160	#117×C₆₇	—	2	2	no	—
161	#117×C₆₇	—	2	2	no	—
162	#117×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
164	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
165	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
166	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
167	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
168	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
169	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
170	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
171	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
172	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
173	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
187	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₆₇	—	2	1	no	—
190	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	#107×C₆₇	C₂³	1	4	yes	—
192	#107×C₆₇	C₂³	1	4	yes	—
193	#107×C₆₇	C₂³	1	4	yes	—
194	#106×C₆₇	C₂³	1	4	yes	—
195	#106×C₆₇	C₂³	1	4	yes	—
196	#106×C₆₇	C₂³	1	4	yes	—
197	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
198	#103×C₆₇	C₂³	1	4	yes	—
199	#103×C₆₇	C₂³	1	4	yes	—
200	#103×C₆₇	C₂³	1	4	yes	—
201	#103×C₆₇	C₂³	1	4	yes	—
202	#103×C₆₇	C₂³	1	4	yes	—
203	#102×C₆₇	C₂³	1	4	yes	—
204	#102×C₆₇	C₂³	1	4	yes	—
205	#102×C₆₇	C₂³	1	4	yes	—
206	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
208	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
209	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
210	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
211	#97×C₆₇	C₂³	1	4	yes	—
212	C₂⁴×C₆₇	—	2	1	no	—
213	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
214	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
215	#41×C₆₇	—	4	4	no	—
216	C₂×Q₈×C₆₇	—	2	1	no	—
217	C₂×Q₈×C₆₇	—	2	1	no	—
218	C₂×Q₈×C₆₇	—	2	4	no	—
219	C₂×Q₈×C₆₇	—	4	2	no	—
220	C₂×Q₈×C₆₇	—	4	2	no	—
221	C₂×Q₈×C₆₇	—	8	2	no	—
222	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
224	C₂×D₄×C₆₇	—	2	4	no	—
225	C₂×D₄×C₆₇	—	2	2	no	—
226	C₂×D₄×C₆₇	—	2	2	no	—
227	C₂×D₄×C₆₇	—	2	2	no	—
228	C₂×D₄×C₆₇	—	2	2	no	—
229	C₂×D₄×C₆₇	—	2	1	no	—
230	C₂×D₄×C₆₇	—	4	2	no	—
231	C₂×D₄×C₆₇	—	4	4	no	—
232	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₆₇	—	2	1	no	—
236	C₂²×C₄×C₆₇	—	2	1	no	—
237	C₂²×C₄×C₆₇	—	2	1	no	—
238	C₂²×C₄×C₆₇	—	2	1	no	—
239	C₂²×C₄×C₆₇	—	2	1	no	—
240	C₂²×C₄×C₆₇	—	2	1	no	—
241	C₂²×C₄×C₆₇	—	2	1	no	—
242	C₂²×C₄×C₆₇	—	2	4	no	—
243	C₂²×C₄×C₆₇	—	2	2	no	—
244	C₂²×C₄×C₆₇	—	2	2	no	—
245	C₂²×C₄×C₆₇	—	2	2	no	—
246	C₂²×C₄×C₆₇	—	2	2	no	—
247	C₂²×C₄×C₆₇	—	4	2	no	—
248	C₂²×C₄×C₆₇	—	4	2	no	—
249	C₂²×C₄×C₆₇	—	8	2	no	—
250	C₂²×C₄×C₆₇	—	8	2	no	—
251	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	Q₁₆×C₆₇	—	4	4	no	—
263	SD₁₆×C₆₇	—	4	4	no	—
264	M₁₆×C₆₇	—	4	4	no	—
265	C₂×C₈×C₆₇	—	4	2	no	—
266	C₂×C₈×C₆₇	—	4	2	no	—
267	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
268	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
269	C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₄⋊C₄×C₆₇	—	2	4	no	—
271	C₄⋊C₄×C₆₇	—	2	2	no	—
272	C₄⋊C₄×C₆₇	—	2	2	no	—
273	C₄⋊C₄×C₆₇	—	2	1	no	—
274	C₄⋊C₄×C₆₇	—	2	1	no	—
275	C₄⋊C₄×C₆₇	—	2	2	no	—
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	—	2	2	no	—
279	C₄⋊C₄×C₆₇	—	2	4	no	—
280	C₄⋊C₄×C₆₇	—	2	2	no	—
281	C₄⋊C₄×C₆₇	—	2	2	no	—
282	C₄⋊C₄×C₆₇	—	2	1	no	—
283	C₄⋊C₄×C₆₇	—	2	1	no	—
284	C₄⋊C₄×C₆₇	—	2	2	no	—
285	C₄⋊C₄×C₆₇	—	2	2	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
289	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
290	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
291	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
292	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
293	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
294	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
295	C₂²⋊C₄×C₆₇	—	2	2	no	—
296	C₂²⋊C₄×C₆₇	—	2	2	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	2	no	—
301	C₂²⋊C₄×C₆₇	—	2	2	no	—
302	C₂²⋊C₄×C₆₇	—	2	2	no	—
303	C₂²⋊C₄×C₆₇	—	2	2	no	—
304	C₂²⋊C₄×C₆₇	—	2	2	no	—
305	C₂²⋊C₄×C₆₇	—	2	2	no	—
306	C₂²⋊C₄×C₆₇	—	2	2	no	—
307	C₂²⋊C₄×C₆₇	—	2	2	no	—
308	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
309	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
310	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
311	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
312	C₄²×C₆₇	—	2	4	no	—
313	C₄²×C₆₇	—	2	2	no	—
314	C₄²×C₆₇	—	2	2	no	—
315	C₄²×C₆₇	C₂×D₄	1	2	yes	—
316	C₄²×C₆₇	C₂⁴	1	2	yes	—
317	C₂³×C₆₇	—	2	2	no	—
318	C₂³×C₆₇	—	2	2	no	—
319	C₂³×C₆₇	—	4	1	no	—
320	C₂³×C₆₇	—	4	1	no	—
321	C₂³×C₆₇	—	4	1	no	—
322	C₂³×C₆₇	—	4	1	no	—
323	C₂³×C₆₇	—	4	2	no	—
324	C₂³×C₆₇	—	8	1	no	—
325	C₂³×C₆₇	—	8	1	no	—
326	C₂³×C₆₇	#137	1	4	yes	—
327	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
328	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
329	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
330	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
331	Q₈×C₆₇	—	2	4	no	—
332	Q₈×C₆₇	—	2	4	no	—
333	Q₈×C₆₇	—	4	2	no	—
334	Q₈×C₆₇	—	8	1	no	—
335	Q₈×C₆₇	—	8	4	no	—
336	D₄×C₆₇	—	2	4	no	—
337	D₄×C₆₇	—	2	4	no	—
338	D₄×C₆₇	—	2	4	no	—
339	D₄×C₆₇	—	4	4	no	—
340	D₄×C₆₇	—	4	4	no	—
341	D₄×C₆₇	—	8	1	no	—
342	D₄×C₆₇	—	8	2	no	—
343	D₄×C₆₇	—	8	2	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	4	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	2	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	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	4	2	no	—
357	C₂×C₄×C₆₇	—	4	1	no	—
358	C₂×C₄×C₆₇	—	4	1	no	—
359	C₂×C₄×C₆₇	—	4	1	no	—
360	C₂×C₄×C₆₇	—	4	1	no	—
361	C₂×C₄×C₆₇	—	4	1	no	—
362	C₂×C₄×C₆₇	—	4	2	no	—
363	C₂×C₄×C₆₇	—	4	2	no	—
364	C₂×C₄×C₆₇	—	4	2	no	—
365	C₂×C₄×C₆₇	—	4	2	no	—
366	C₂×C₄×C₆₇	—	4	2	no	—
367	C₂×C₄×C₆₇	—	8	2	no	—
368	C₂×C₄×C₆₇	—	8	2	no	—
369	C₂×C₄×C₆₇	—	8	1	no	—
370	C₂×C₄×C₆₇	—	8	2	no	—
371	C₂×C₄×C₆₇	—	8	2	no	—
372	C₂×C₄×C₆₇	—	8	4	no	—
373	C₂×C₄×C₆₇	—	8	1	no	—
374	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
381	C₈×C₆₇	—	2	4	no	—
382	C₈×C₆₇	—	2	4	no	—
383	C₂²×C₆₇	—	2	1	no	—
384	C₂²×C₆₇	—	2	1	no	—
385	C₂²×C₆₇	—	2	1	no	—
386	C₂²×C₆₇	—	2	1	no	—
387	C₂²×C₆₇	—	2	1	no	—
388	C₂²×C₆₇	—	2	1	no	—
389	C₂²×C₆₇	—	2	2	no	—
390	C₂²×C₆₇	—	2	2	no	—
391	C₂²×C₆₇	—	2	2	no	—
392	C₂²×C₆₇	—	4	4	no	—
393	C₂²×C₆₇	—	4	4	no	—
394	C₂²×C₆₇	—	4	2	no	—
395	C₂²×C₆₇	—	4	2	no	—
396	C₂²×C₆₇	—	4	2	no	—
397	C₂²×C₆₇	—	16	2	no	—
398	C₂²×C₆₇	C₂×#137	1	2	yes	—
399	C₂²×C₆₇	C₂×#137	1	2	yes	—
400	C₂²×C₆₇	C₂×#137	1	2	yes	—
401	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
402	C₄×C₆₇	—	2	2	no	—
403	C₄×C₆₇	—	2	1	no	—
404	C₄×C₆₇	—	2	2	no	—
405	C₄×C₆₇	—	2	1	no	—
406	C₄×C₆₇	—	2	1	no	—
407	C₄×C₆₇	—	2	2	no	—
408	C₄×C₆₇	—	4	2	no	—
409	C₄×C₆₇	—	4	2	no	—
410	C₄×C₆₇	—	4	2	no	—
411	C₄×C₆₇	—	4	2	no	—
412	C₄×C₆₇	—	4	2	no	—
413	C₄×C₆₇	—	4	2	no	—
414	C₄×C₆₇	—	4	2	no	—
415	C₄×C₆₇	#585	1	2	yes	—
416	#61709	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
417	C₂×C₆₇	—	2	2	no	—
418	C₂×C₆₇	—	2	2	no	—
419	C₂×C₆₇	—	2	2	no	—
420	C₂×C₆₇	—	4	2	no	—
421	C₂×C₆₇	—	8	2	no	—
422	C₂×C₆₇	#3485	1	1	yes	characteristic
423	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
424	C₂×C₆₇	#3585	1	1	yes	characteristic
425	#3505	C₂×C₆₇	1	1	yes	characteristic
426	C₂×#554	C₂×C₆₇	1	1	yes	characteristic, complemented
427	#3346	C₂×C₆₇	1	4	yes	complemented
428	#3344	C₂×C₆₇	1	4	yes	complemented
429	#3316	C₂×C₆₇	1	4	yes	complemented
430	#3314	C₂×C₆₇	1	4	yes	complemented
431	#3239	C₂×C₆₇	1	2	yes	complemented
432	#3196	C₂×C₆₇	1	2	yes	complemented
433	#3189	C₂×C₆₇	1	1	yes	characteristic, complemented
434	#3187	C₂×C₆₇	1	1	yes	characteristic, complemented
435	#3117	C₂×C₆₇	1	2	yes	complemented
436	#3092	C₂×C₆₇	1	2	yes	complemented
437	C₂×#484	C₂×C₆₇	1	1	yes	characteristic, complemented
438	C₂×#481	C₂×C₆₇	1	1	yes	characteristic, complemented
439	#2973	C₂×C₆₇	1	1	yes	characteristic, complemented
440	C₆₇	#61709	1	1	yes	characteristic, direct product factor, Sylow
441	#554	—	2	2	no	—
442	#554	—	2	2	no	—
443	#554	C₂²×C₆₇	1	4	yes	—
444	#554	C₂²×C₆₇	1	4	yes	complemented
445	#553	—	2	2	no	—
446	#553	C₂²×C₆₇	1	2	yes	—
447	#552	C₂²×C₆₇	1	2	yes	—
448	#551	—	2	2	no	—
449	#548	C₂²×C₆₇	1	2	yes	—
450	#546	C₂²×C₆₇	1	2	yes	—
451	#539	—	2	1	no	—
452	#538	—	2	1	no	—
453	#534	—	2	1	no	—
454	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
455	#529	C₂²×C₆₇	1	2	yes	—
456	C₂×#125	—	2	1	no	—
457	#525	C₂²×C₆₇	1	2	yes	—
458	C₂×C₂²⋊Q₈	—	2	1	no	—
459	C₂×C₂²⋊Q₈	—	2	1	no	—
460	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
461	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
462	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
463	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
464	#518	—	2	1	no	—
465	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
466	C₂×C₄×D₄	—	2	1	no	—
467	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
468	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
469	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
470	#501	C₂²×C₆₇	1	4	yes	complemented
471	#489	C₂²×C₆₇	1	4	yes	complemented
472	#485	C₂²×C₆₇	1	4	yes	complemented
473	#484	C₂²×C₆₇	1	4	yes	complemented
474	#484	C₂²×C₆₇	1	2	yes	complemented
475	#484	C₂²×C₆₇	1	2	yes	complemented
476	#484	C₂²×C₆₇	1	2	yes	complemented
477	#484	C₂²×C₆₇	1	2	yes	complemented
478	#483	C₂²×C₆₇	1	2	yes	complemented
479	#483	C₂²×C₆₇	1	4	yes	complemented
480	#481	C₂²×C₆₇	1	2	yes	—
481	#481	C₂²×C₆₇	1	2	yes	—
482	#481	C₂²×C₆₇	1	2	yes	—
483	#481	C₂²×C₆₇	1	4	yes	complemented
484	#480	C₂²×C₆₇	1	4	yes	complemented
485	#479	C₂²×C₆₇	1	4	yes	complemented
486	#475	C₂²×C₆₇	1	4	yes	complemented
487	#474	C₂²×C₆₇	1	4	yes	complemented
488	#470	C₂²×C₆₇	1	4	yes	complemented
489	#468	C₂²×C₆₇	1	4	yes	complemented
490	#467	C₂²×C₆₇	1	4	yes	complemented
491	#465	C₂²×C₆₇	1	4	yes	complemented
492	#464	C₂²×C₆₇	1	4	yes	complemented
493	#452	C₂²×C₆₇	1	4	yes	complemented
494	#451	C₂²×C₆₇	1	2	yes	complemented
495	#451	C₂²×C₆₇	1	2	yes	complemented
496	#450	C₂²×C₆₇	1	2	yes	complemented
497	#448	C₂²×C₆₇	1	2	yes	—
498	#441	C₂²×C₆₇	1	4	yes	complemented
499	#440	C₂²×C₆₇	1	4	yes	complemented
500	#435	C₂²×C₆₇	1	4	yes	—
501	#435	C₂²×C₆₇	1	4	yes	complemented
502	#432	C₂²×C₆₇	1	2	yes	complemented
503	#428	C₂²×C₆₇	1	4	yes	complemented
504	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
505	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
506	#417	C₂²×C₆₇	1	4	yes	complemented
507	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
508	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
509	#407	C₂²×C₆₇	1	2	yes	complemented
510	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
511	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
512	C₂×#41	C₂³×C₆₇	1	2	yes	—
513	C₂²×Q₈	—	2	1	no	—
514	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
515	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
516	C₂²×D₄	—	2	1	no	—
517	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
518	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	—	2	1	no	—
521	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
523	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
524	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
525	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
526	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
527	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
528	C₄⋊Q₈	—	2	2	no	—
529	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
530	#126	—	2	2	no	—
531	#126	—	2	2	no	—
532	#126	—	2	2	no	—
533	#125	—	2	4	no	—
534	#125	—	2	4	no	—
535	#125	—	2	2	no	—
536	#125	C₂³×C₆₇	1	2	yes	—
537	#124	—	2	2	no	—
538	#124	C₂³×C₆₇	1	2	yes	—
539	#123	—	2	2	no	—
540	#123	—	2	2	no	—
541	#123	—	2	2	no	—
542	#123	—	2	2	no	—
543	#123	—	2	2	no	—
544	C₂²⋊Q₈	—	2	1	no	—
545	C₂²⋊Q₈	—	2	1	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	—	2	1	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	4	no	—
551	C₂²⋊Q₈	—	2	4	no	—
552	C₂²⋊Q₈	—	2	4	no	—
553	C₂²⋊Q₈	—	2	4	no	—
554	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
555	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
556	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
557	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
558	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
559	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
560	#121	—	2	2	no	—
561	#121	—	2	2	no	—
562	#121	—	2	1	no	—
563	#121	—	2	1	no	—
564	#121	—	2	2	no	—
565	#121	C₂³×C₆₇	1	2	yes	—
566	#121	C₂³×C₆₇	1	2	yes	—
567	#121	C₂³×C₆₇	1	2	yes	—
568	#120	—	2	2	no	—
569	#120	—	2	2	no	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
572	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
573	C₄×D₄	—	2	4	no	—
574	C₄×D₄	—	2	4	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	D₄×C₆₇	1	2	yes	—
581	C₄×D₄	D₄×C₆₇	1	2	yes	—
582	C₄×D₄	C₂³×C₆₇	1	2	yes	—
583	C₄×D₄	C₂³×C₆₇	1	2	yes	—
584	C₄×D₄	C₂³×C₆₇	1	2	yes	—
585	#117	—	2	2	no	—
586	#117	—	2	2	no	—
587	#117	C₂³×C₆₇	1	2	yes	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	2	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	2	no	—
612	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
614	C₂×C₄²	—	2	1	no	—
615	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
616	#107	C₂³×C₆₇	1	4	yes	—
617	#107	C₂³×C₆₇	1	4	yes	—
618	#107	C₂³×C₆₇	1	4	yes	—
619	#106	C₂³×C₆₇	1	4	yes	—
620	#106	C₂³×C₆₇	1	4	yes	—
621	#106	C₂³×C₆₇	1	4	yes	—
622	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
623	#103	C₂³×C₆₇	1	4	yes	—
624	#103	C₂³×C₆₇	1	4	yes	—
625	#103	C₂³×C₆₇	1	4	yes	—
626	#103	C₂³×C₆₇	1	4	yes	—
627	#103	C₂³×C₆₇	1	4	yes	—
628	#102	C₂³×C₆₇	1	4	yes	—
629	#102	C₂³×C₆₇	1	4	yes	—
630	#102	C₂³×C₆₇	1	4	yes	—
631	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
632	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
633	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
634	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
635	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
636	#97	C₂³×C₆₇	1	4	yes	—
637	C₂⁴	—	2	1	no	—
638	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
639	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
640	#41	—	4	4	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	4	no	—
644	C₂×Q₈	—	4	2	no	—
645	C₂×Q₈	—	4	2	no	—
646	C₂×Q₈	—	8	2	no	—
647	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
648	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
658	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
659	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
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	1	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	8	2	no	—
675	C₂²×C₄	—	8	2	no	—
676	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
687	Q₁₆	—	4	4	no	—
688	SD₁₆	—	4	4	no	—
689	M₁₆	—	4	4	no	—
690	C₂×C₈	—	4	2	no	—
691	C₂×C₈	—	4	2	no	—
692	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
693	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
714	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
715	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
719	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
734	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
735	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
736	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	C₂×D₄×C₆₇	1	2	yes	—
741	C₄²	C₂⁴×C₆₇	1	2	yes	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	—	4	2	no	—
749	C₂³	—	8	1	no	—
750	C₂³	—	8	1	no	—
751	C₂³	#137×C₆₇	1	4	yes	—
752	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
753	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
754	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
755	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
756	Q₈	—	2	4	no	—
757	Q₈	—	2	4	no	—
758	Q₈	—	4	2	no	—
759	Q₈	—	8	1	no	—
760	Q₈	—	8	4	no	—
761	D₄	—	2	4	no	—
762	D₄	—	2	4	no	—
763	D₄	—	2	4	no	—
764	D₄	—	4	4	no	—
765	D₄	—	4	4	no	—
766	D₄	—	8	1	no	—
767	D₄	—	8	2	no	—
768	D₄	—	8	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	4	2	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	8	2	no	—
793	C₂×C₄	—	8	2	no	—
794	C₂×C₄	—	8	2	no	—
795	C₂×C₄	—	8	2	no	—
796	C₂×C₄	—	8	4	no	—
797	C₂×C₄	—	8	1	no	—
798	C₂×C₄	—	8	1	no	—
799	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
801	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
802	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
805	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
806	C₈	—	2	4	no	—
807	C₈	—	2	4	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	1	no	—
811	C₂²	—	2	1	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	4	4	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	16	2	no	—
823	C₂²	C₂×#137×C₆₇	1	2	yes	—
824	C₂²	C₂×#137×C₆₇	1	2	yes	—
825	C₂²	C₂×#137×C₆₇	1	2	yes	—
826	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
827	C₄	—	2	2	no	—
828	C₄	—	2	2	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	#585×C₆₇	1	2	yes	—
841	C₂	—	2	2	no	—
842	C₂	—	2	2	no	—
843	C₂	—	2	2	no	—
844	C₂	—	4	2	no	—
845	C₂	—	8	2	no	—
846	C₂	C₆₇×#3485	1	1	yes	characteristic
847	C₂	C₂²×#137×C₆₇	1	1	yes	characteristic
848	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3505	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#554×C₆₇	C₂	semidirect
3. C₆₇×#3346	C₂	semidirect
4. C₆₇×#3344	C₂	semidirect
5. C₆₇×#3316	C₂	semidirect
6. C₆₇×#3314	C₂	semidirect
7. C₆₇×#3239	C₂	semidirect
8. C₆₇×#3196	C₂	semidirect
9. C₆₇×#3189	C₂	semidirect
10. C₆₇×#3187	C₂	semidirect
11. C₆₇×#3117	C₂	semidirect
12. C₆₇×#3092	C₂	semidirect
13. C₂×#484×C₆₇	C₂	semidirect
14. C₂×#481×C₆₇	C₂	semidirect
15. C₆₇×#2973	C₂	semidirect
19. #554×C₆₇	C₂²	semidirect
29. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
37. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
40. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
44. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
45. #501×C₆₇	C₂²	semidirect
46. #489×C₆₇	C₂²	semidirect
47. #485×C₆₇	C₂²	semidirect
48. #484×C₆₇	C₂²	semidirect
49. #484×C₆₇	C₂²	semidirect
50. #484×C₆₇	C₂²	semidirect
51. #484×C₆₇	C₂²	semidirect
52. #484×C₆₇	C₂²	semidirect
53. #483×C₆₇	C₂²	semidirect
54. #483×C₆₇	C₂²	semidirect
58. #481×C₆₇	C₂²	semidirect
59. #480×C₆₇	C₂²	semidirect
60. #479×C₆₇	C₂²	semidirect
61. #475×C₆₇	C₂²	semidirect
62. #474×C₆₇	C₂²	semidirect
63. #470×C₆₇	C₂²	semidirect
64. #468×C₆₇	C₂²	semidirect
65. #467×C₆₇	C₂²	semidirect
66. #465×C₆₇	C₂²	semidirect
67. #464×C₆₇	C₂²	semidirect
68. #452×C₆₇	C₂²	semidirect
69. #451×C₆₇	C₂²	semidirect
70. #451×C₆₇	C₂²	semidirect
71. #450×C₆₇	C₂²	semidirect
73. #441×C₆₇	C₂²	semidirect
74. #440×C₆₇	C₂²	semidirect
76. #435×C₆₇	C₂²	semidirect
77. #432×C₆₇	C₂²	semidirect
78. #428×C₆₇	C₂²	semidirect
79. C₂×#107×C₆₇	C₂²	semidirect
80. C₂×#106×C₆₇	C₂²	semidirect
81. #417×C₆₇	C₂²	semidirect
82. C₂×#103×C₆₇	C₂²	semidirect
83. C₂×#102×C₆₇	C₂²	semidirect
84. #407×C₆₇	C₂²	semidirect
416. #61709	C₆₇	direct (N × H)
426. C₂×#554	C₂×C₆₇	semidirect
427. #3346	C₂×C₆₇	semidirect
428. #3344	C₂×C₆₇	semidirect
429. #3316	C₂×C₆₇	semidirect
430. #3314	C₂×C₆₇	semidirect
431. #3239	C₂×C₆₇	semidirect
432. #3196	C₂×C₆₇	semidirect
433. #3189	C₂×C₆₇	semidirect
434. #3187	C₂×C₆₇	semidirect
435. #3117	C₂×C₆₇	semidirect
436. #3092	C₂×C₆₇	semidirect
437. C₂×#484	C₂×C₆₇	semidirect
438. C₂×#481	C₂×C₆₇	semidirect
439. #2973	C₂×C₆₇	semidirect
440. C₆₇	#61709	direct (N × H)
444. #554	C₂²×C₆₇	semidirect
454. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
462. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
465. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
469. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
470. #501	C₂²×C₆₇	semidirect
471. #489	C₂²×C₆₇	semidirect
472. #485	C₂²×C₆₇	semidirect
473. #484	C₂²×C₆₇	semidirect
474. #484	C₂²×C₆₇	semidirect
475. #484	C₂²×C₆₇	semidirect
476. #484	C₂²×C₆₇	semidirect
477. #484	C₂²×C₆₇	semidirect
478. #483	C₂²×C₆₇	semidirect
479. #483	C₂²×C₆₇	semidirect
483. #481	C₂²×C₆₇	semidirect
484. #480	C₂²×C₆₇	semidirect
485. #479	C₂²×C₆₇	semidirect
486. #475	C₂²×C₆₇	semidirect
487. #474	C₂²×C₆₇	semidirect
488. #470	C₂²×C₆₇	semidirect
489. #468	C₂²×C₆₇	semidirect
490. #467	C₂²×C₆₇	semidirect
491. #465	C₂²×C₆₇	semidirect
492. #464	C₂²×C₆₇	semidirect
493. #452	C₂²×C₆₇	semidirect
494. #451	C₂²×C₆₇	semidirect
495. #451	C₂²×C₆₇	semidirect
496. #450	C₂²×C₆₇	semidirect
498. #441	C₂²×C₆₇	semidirect
499. #440	C₂²×C₆₇	semidirect
501. #435	C₂²×C₆₇	semidirect
502. #432	C₂²×C₆₇	semidirect
503. #428	C₂²×C₆₇	semidirect
504. C₂×#107	C₂²×C₆₇	semidirect
505. C₂×#106	C₂²×C₆₇	semidirect
506. #417	C₂²×C₆₇	semidirect
507. C₂×#103	C₂²×C₆₇	semidirect
508. C₂×#102	C₂²×C₆₇	semidirect
509. #407	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3505	2
C₂×#554×C₆₇	2
C₆₇×#3346	2
C₆₇×#3344	2
C₆₇×#3316	2
C₆₇×#3314	2
C₆₇×#3239	2
C₆₇×#3196	2
C₆₇×#3189	2
C₆₇×#3187	2
C₆₇×#3117	2
C₆₇×#3092	2
C₂×#484×C₆₇	2
C₂×#481×C₆₇	2
C₆₇×#2973	2
#61709	67

Subgroups — C67×#61709 #30740960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61709 #30740960