Subgroups — #2957×D₆₇ #31720146

Order 17152.

2642 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#135×D₆₇	C₂	1	1	yes	maximal, characteristic
2	#568×D₆₇	C₂	1	2	yes	maximal, complemented
3	#22569127	C₂	1	1	yes	maximal, characteristic, complemented
4	#22569126	C₂	1	1	yes	maximal, characteristic, complemented
5	#22569125	C₂	1	1	yes	maximal, characteristic, complemented
6	#22569124	C₂	1	2	yes	maximal, complemented
7	#22569123	C₂	1	4	yes	maximal, complemented
8	#22569122	C₂	1	2	yes	maximal, complemented
9	#22569121	C₂	1	4	yes	maximal, complemented
10	#444×D₆₇	C₂	1	4	yes	maximal, complemented
11	#443×D₆₇	C₂	1	4	yes	maximal, complemented
12	C₂×#108×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#421×D₆₇	C₂	1	2	yes	maximal, complemented
14	#405×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2957	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×D₆₇	C₂²	1	2	yes	—
17	C₂×#14524066	C₄	1	1	yes	characteristic, complemented
18	C₂×#14524065	C₂²	1	1	yes	characteristic
19	C₂×#14524064	C₄	1	2	yes	complemented
20	C₂×#14524063	C₂²	1	2	yes	—
21	C₂×#14524062	C₄	1	1	yes	characteristic, complemented
22	#135×D₆₇	C₄	1	2	yes	complemented
23	#135×D₆₇	C₄	1	2	yes	complemented
24	#135×D₆₇	C₄	1	2	yes	complemented
25	#135×D₆₇	C₄	1	2	yes	complemented
26	#135×D₆₇	C₂²	1	2	yes	—
27	#135×D₆₇	C₂²	1	2	yes	—
28	#135×D₆₇	C₂²	1	2	yes	—
29	#135×D₆₇	C₂²	1	2	yes	—
30	C₂×Q₁₆×D₆₇	C₄	1	1	yes	characteristic, complemented
31	C₂×SD₁₆×D₆₇	C₄	1	2	yes	complemented
32	C₂×D₈×D₆₇	C₄	1	1	yes	characteristic, complemented
33	#16864163	C₂²	1	2	yes	complemented
34	#16864162	—	2	4	no	—
35	#16864162	C₂²	1	2	yes	complemented
36	#16864162	C₂²	1	2	yes	complemented
37	#16864161	—	2	4	no	—
38	#16864161	C₂²	1	8	yes	complemented
39	#131×D₆₇	—	2	4	no	—
40	#131×D₆₇	C₂²	1	8	yes	complemented
41	C₂×M₁₆×D₆₇	—	2	4	no	—
42	C₂×M₁₆×D₆₇	C₂²	1	2	yes	—
43	C₂×M₁₆×D₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
45	#117×D₆₇	C₂²	1	1	yes	characteristic
46	#16863519	C₂²	1	4	yes	complemented
47	#16863518	C₂²	1	4	yes	complemented
48	#16863517	C₂²	1	4	yes	complemented
49	#16863516	C₂²	1	8	yes	complemented
50	#16863515	C₂²	1	8	yes	complemented
51	#16863514	C₂²	1	4	yes	complemented
52	#16863513	C₂²	1	4	yes	complemented
53	#16863512	C₂²	1	4	yes	complemented
54	#16863511	C₂²	1	8	yes	complemented
55	#16863510	C₂²	1	8	yes	complemented
56	C₂×#14523979	C₂²	1	1	yes	characteristic, complemented
57	C₂×#14523978	C₂²	1	2	yes	complemented
58	#108×D₆₇	C₂²	1	2	yes	complemented
59	#108×D₆₇	C₂²	1	2	yes	complemented
60	#108×D₆₇	C₂²	1	2	yes	complemented
61	#108×D₆₇	C₂²	1	2	yes	complemented
62	#16863414	C₂²	1	2	yes	complemented
63	#16863413	C₂²	1	2	yes	complemented
64	#16863412	C₂²	1	2	yes	complemented
65	#16863411	C₂²	1	8	yes	complemented
66	#104×D₆₇	C₂²	1	8	yes	complemented
67	#16863354	C₂²	1	1	yes	characteristic, complemented
68	#16863353	C₂²	1	2	yes	complemented
69	#16863352	C₂²	1	1	yes	characteristic, complemented
70	#16863351	C₂²	1	1	yes	characteristic, complemented
71	#16863350	C₂²	1	2	yes	complemented
72	#97×D₆₇	C₂²	1	2	yes	complemented
73	C₄×C₈×D₆₇	C₂²	1	2	yes	complemented
74	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
75	#568×C₆₇	C₂²	1	2	yes	complemented
76	#444×C₆₇	C₂²	1	4	yes	complemented
77	#443×C₆₇	C₂²	1	4	yes	complemented
78	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	#421×C₆₇	C₂²	1	2	yes	complemented
80	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	C₂×#11761629	C₂×C₄	1	2	yes	—
82	C₂×#11761628	—	2	2	no	—
83	C₂×#11761628	C₂³	1	2	yes	—
84	C₂×#11761627	—	2	2	no	—
85	C₂×#11761627	C₂×C₄	1	2	yes	—
86	#41×D₆₇	—	2	2	no	—
87	#41×D₆₇	—	2	2	no	—
88	#41×D₆₇	—	2	2	no	—
89	#41×D₆₇	—	2	2	no	—
90	#41×D₆₇	C₂×C₄	1	4	yes	—
91	#41×D₆₇	C₂×C₄	1	4	yes	—
92	#41×D₆₇	C₂³	1	4	yes	—
93	#41×D₆₇	C₂³	1	4	yes	—
94	C₂×Q₈×D₆₇	C₂×C₄	1	2	yes	—
95	C₂×D₄×D₆₇	—	2	2	no	—
96	C₂×D₄×D₆₇	C₂×C₄	1	2	yes	—
97	C₂²×C₄×D₆₇	—	2	2	no	—
98	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
99	#14524066	C₂×C₄	1	2	yes	—
100	#14524066	C₂×C₄	1	2	yes	—
101	#14524066	C₂×C₄	1	2	yes	complemented
102	#14524066	C₂×C₄	1	2	yes	complemented
103	#14524065	C₂×C₄	1	2	yes	complemented
104	#14524065	C₂×C₄	1	2	yes	complemented
105	#14524065	C₂³	1	2	yes	—
106	#14524065	C₂³	1	2	yes	—
107	#14524064	C₂×C₄	1	4	yes	—
108	#14524064	C₂×C₄	1	4	yes	—
109	#14524064	C₂×C₄	1	4	yes	complemented
110	#14524064	C₂×C₄	1	4	yes	complemented
111	#14524063	C₂×C₄	1	4	yes	complemented
112	#14524063	C₂×C₄	1	4	yes	complemented
113	#14524063	C₂³	1	4	yes	—
114	#14524063	C₂³	1	4	yes	—
115	#14524062	C₂×C₄	1	2	yes	—
116	#14524062	C₂×C₄	1	2	yes	—
117	#14524062	C₂×C₄	1	2	yes	complemented
118	#14524062	C₂×C₄	1	2	yes	complemented
119	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic, complemented
120	C₂×#11761618	C₂×C₄	1	2	yes	complemented
121	Q₁₆×D₆₇	C₂×C₄	1	2	yes	—
122	Q₁₆×D₆₇	C₂×C₄	1	2	yes	—
123	Q₁₆×D₆₇	C₂×C₄	1	2	yes	complemented
124	Q₁₆×D₆₇	C₂×C₄	1	2	yes	complemented
125	C₂×#11761617	C₂×C₄	1	2	yes	complemented
126	C₂×#11761616	C₂×C₄	1	2	yes	complemented
127	C₂×#11761615	C₂×C₄	1	2	yes	complemented
128	SD₁₆×D₆₇	C₂×C₄	1	4	yes	—
129	SD₁₆×D₆₇	C₂×C₄	1	4	yes	—
130	SD₁₆×D₆₇	C₂×C₄	1	4	yes	complemented
131	SD₁₆×D₆₇	C₂×C₄	1	4	yes	complemented
132	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic, complemented
133	C₂×#11761613	C₂×C₄	1	2	yes	complemented
134	D₈×D₆₇	C₂×C₄	1	2	yes	—
135	D₈×D₆₇	C₂×C₄	1	2	yes	—
136	D₈×D₆₇	C₂×C₄	1	2	yes	complemented
137	D₈×D₆₇	C₂×C₄	1	2	yes	complemented
138	#14524051	—	2	8	no	—
139	#14524051	—	2	8	no	—
140	#14524051	—	2	4	no	—
141	#14524051	C₂³	1	8	yes	complemented
142	#14524050	—	2	4	no	—
143	#14524050	C₂³	1	8	yes	complemented
144	#14524049	—	2	4	no	—
145	#14524049	—	2	8	no	—
146	#14524049	—	2	8	no	—
147	#14524049	C₂³	1	8	yes	complemented
148	C₂×#11761612	—	2	4	no	—
149	C₂×#11761612	C₂³	1	2	yes	—
150	C₂×#11761612	C₂³	1	1	yes	characteristic
151	C₂×#11761611	—	2	2	no	—
152	C₂×#11761611	—	2	8	no	—
153	C₂×#11761611	C₂³	1	2	yes	—
154	M₁₆×D₆₇	—	2	2	no	—
155	M₁₆×D₆₇	—	2	2	no	—
156	M₁₆×D₆₇	—	2	4	no	—
157	M₁₆×D₆₇	—	2	8	no	—
158	M₁₆×D₆₇	—	2	8	no	—
159	M₁₆×D₆₇	—	2	4	no	—
160	M₁₆×D₆₇	D₄	1	2	yes	—
161	M₁₆×D₆₇	D₄	1	2	yes	—
162	M₁₆×D₆₇	D₄	1	2	yes	—
163	M₁₆×D₆₇	D₄	1	2	yes	—
164	M₁₆×D₆₇	C₂³	1	4	yes	—
165	M₁₆×D₆₇	C₂³	1	4	yes	—
166	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
167	C₂×C₈×D₆₇	—	2	2	no	—
168	C₂×C₈×D₆₇	—	2	8	no	—
169	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
170	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
171	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
172	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
173	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
174	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
175	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
176	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
177	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₈×D₆₇	C₂³	1	2	yes	—
182	#14524002	C₂³	1	1	yes	characteristic
183	#14524001	—	2	1	no	—
184	#14524000	C₂³	1	2	yes	—
185	#14523999	—	2	1	no	—
186	C₄⋊C₄×D₆₇	—	2	1	no	—
187	C₂²⋊C₄×D₆₇	—	2	1	no	—
188	C₄²×D₆₇	C₂³	1	2	yes	—
189	#14523979	C₂³	1	2	yes	complemented
190	#14523979	C₂³	1	2	yes	complemented
191	#14523978	C₂³	1	4	yes	complemented
192	#14523978	C₂³	1	4	yes	complemented
193	#14523971	C₂³	1	8	yes	complemented
194	#14523970	C₂³	1	8	yes	complemented
195	#14523969	C₂³	1	8	yes	complemented
196	#14523954	C₂³	1	2	yes	complemented
197	#14523953	C₂³	1	2	yes	complemented
198	#14523953	C₂³	1	2	yes	complemented
199	C₄×C₆₇⋊C₈	C₂³	1	2	yes	complemented
200	C₈×Dic₆₇	C₂³	1	2	yes	complemented
201	C₈×Dic₆₇	C₂³	1	2	yes	complemented
202	C₂×#41×C₆₇	C₂³	1	2	yes	—
203	#135×C₆₇	C₂×C₄	1	2	yes	complemented
204	#135×C₆₇	C₂×C₄	1	2	yes	complemented
205	#135×C₆₇	C₂³	1	2	yes	—
206	#135×C₆₇	C₂³	1	2	yes	—
207	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
208	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	complemented
209	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
210	#131×C₆₇	—	2	4	no	—
211	#131×C₆₇	C₂³	1	8	yes	complemented
212	C₂×M₁₆×C₆₇	—	2	4	no	—
213	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
214	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
215	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
216	#117×C₆₇	C₂³	1	1	yes	characteristic
217	#108×C₆₇	C₂³	1	2	yes	complemented
218	#108×C₆₇	C₂³	1	2	yes	complemented
219	#104×C₆₇	C₂³	1	8	yes	complemented
220	#97×C₆₇	C₂³	1	2	yes	complemented
221	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
222	C₂³×D₆₇	—	2	2	no	—
223	C₂³×D₆₇	#41	1	1	yes	characteristic
224	#11761629	—	2	2	no	—
225	#11761629	—	2	2	no	—
226	#11761629	C₂²×C₄	1	4	yes	—
227	#11761629	C₂²×C₄	1	4	yes	—
228	#11761628	—	2	2	no	—
229	#11761628	—	2	2	no	—
230	#11761628	—	2	4	no	—
231	#11761628	—	2	4	no	—
232	#11761628	—	2	4	no	—
233	#11761628	—	2	4	no	—
234	#11761628	C₂²×C₄	1	4	yes	—
235	#11761628	C₂⁴	1	4	yes	—
236	#11761627	—	2	4	no	—
237	#11761627	—	2	4	no	—
238	#11761627	—	2	4	no	—
239	#11761627	—	2	4	no	—
240	#11761627	—	2	2	no	—
241	#11761627	—	2	2	no	—
242	#11761627	C₂²×C₄	1	4	yes	—
243	#11761627	C₂²×C₄	1	4	yes	—
244	C₂×Dic₁₃₄	—	2	2	no	—
245	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
246	Q₈×D₆₇	—	2	2	no	—
247	Q₈×D₆₇	—	2	2	no	—
248	Q₈×D₆₇	C₂²×C₄	1	4	yes	—
249	Q₈×D₆₇	C₂²×C₄	1	4	yes	—
250	C₂×D₂₆₈	—	2	2	no	—
251	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
252	C₂×C₂²⋊D₆₇	—	2	2	no	—
253	C₂×C₂²⋊D₆₇	—	2	2	no	—
254	C₂×C₂²⋊D₆₇	—	2	2	no	—
255	D₄×D₆₇	—	2	4	no	—
256	D₄×D₆₇	—	2	4	no	—
257	D₄×D₆₇	—	2	4	no	—
258	D₄×D₆₇	—	2	4	no	—
259	D₄×D₆₇	—	2	2	no	—
260	D₄×D₆₇	—	2	2	no	—
261	D₄×D₆₇	C₂²×C₄	1	4	yes	—
262	D₄×D₆₇	C₂²×C₄	1	4	yes	—
263	C₂²×Dic₆₇	—	2	2	no	—
264	C₂²×Dic₆₇	#41	1	1	yes	characteristic
265	C₂×C₄×D₆₇	—	2	2	no	—
266	C₂×C₄×D₆₇	—	2	2	no	—
267	C₂×C₄×D₆₇	—	2	2	no	—
268	C₂×C₄×D₆₇	—	2	4	no	—
269	C₂×C₄×D₆₇	—	2	4	no	—
270	C₂×C₄×D₆₇	—	2	4	no	—
271	C₂×C₄×D₆₇	—	2	4	no	—
272	C₂×C₄×D₆₇	—	2	2	no	—
273	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
274	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
275	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
276	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
277	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
278	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
279	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
280	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
281	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
282	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
283	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
285	Dic₂₆₈	C₂²×C₄	1	2	yes	—
286	Dic₂₆₈	C₂²×C₄	1	2	yes	—
287	#11761618	C₂²×C₄	1	4	yes	—
288	#11761618	C₂²×C₄	1	4	yes	—
289	#11761617	C₂²×C₄	1	4	yes	—
290	#11761617	C₂²×C₄	1	4	yes	—
291	#11761616	C₂²×C₄	1	4	yes	—
292	#11761616	C₂²×C₄	1	4	yes	—
293	#11761615	C₂²×C₄	1	4	yes	—
294	#11761615	C₂²×C₄	1	4	yes	—
295	D₅₃₆	C₂²×C₄	1	2	yes	—
296	D₅₃₆	C₂²×C₄	1	2	yes	—
297	#11761613	C₂²×C₄	1	4	yes	—
298	#11761613	C₂²×C₄	1	4	yes	—
299	#11761612	—	2	2	no	—
300	#11761612	—	2	8	no	—
301	#11761612	C₂×D₄	1	2	yes	—
302	#11761612	C₂×D₄	1	2	yes	—
303	#11761612	C₂⁴	1	4	yes	—
304	#11761611	—	2	4	no	—
305	#11761611	—	2	4	no	—
306	#11761611	—	2	8	no	—
307	#11761611	—	2	8	no	—
308	#11761611	C₂×D₄	1	4	yes	—
309	#11761611	C₂×D₄	1	4	yes	—
310	C₂×C₆₇⋊C₈	—	2	2	no	—
311	C₂×C₆₇⋊C₈	—	2	8	no	—
312	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
313	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
314	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
315	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
316	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
317	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
318	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
319	C₈×D₆₇	—	2	4	no	—
320	C₈×D₆₇	—	2	4	no	—
321	C₈×D₆₇	—	2	8	no	—
322	C₈×D₆₇	—	2	8	no	—
323	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
324	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
325	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
326	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
327	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
328	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
329	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
330	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
331	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
332	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
333	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
334	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
335	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
336	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
337	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
338	C₈×D₆₇	C₂²×C₄	1	1	yes	characteristic
339	C₈×D₆₇	C₂×D₄	1	4	yes	—
340	C₈×D₆₇	C₂×D₄	1	4	yes	—
341	C₄⋊Dic₆₇	—	2	1	no	—
342	Dic₆₇⋊C₄	—	2	2	no	—
343	C₂²⋊Dic₆₇	—	2	1	no	—
344	(C₂×D₆₇)⋊C₄	—	2	2	no	—
345	C₄×Dic₆₇	—	2	2	no	—
346	C₄×Dic₆₇	C₂⁴	1	2	yes	—
347	#41×C₆₇	—	2	2	no	—
348	#41×C₆₇	—	2	2	no	—
349	#41×C₆₇	C₂²×C₄	1	4	yes	—
350	#41×C₆₇	C₂⁴	1	4	yes	—
351	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
352	C₂×D₄×C₆₇	—	2	2	no	—
353	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
354	C₂²×C₄×C₆₇	—	2	2	no	—
355	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
356	Q₁₆×C₆₇	C₂²×C₄	1	2	yes	—
357	Q₁₆×C₆₇	C₂²×C₄	1	2	yes	—
358	SD₁₆×C₆₇	C₂²×C₄	1	4	yes	—
359	SD₁₆×C₆₇	C₂²×C₄	1	4	yes	—
360	D₈×C₆₇	C₂²×C₄	1	2	yes	—
361	D₈×C₆₇	C₂²×C₄	1	2	yes	—
362	M₁₆×C₆₇	—	2	2	no	—
363	M₁₆×C₆₇	—	2	8	no	—
364	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
365	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
366	M₁₆×C₆₇	C₂⁴	1	4	yes	—
367	C₂×C₈×C₆₇	—	2	2	no	—
368	C₂×C₈×C₆₇	—	2	8	no	—
369	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
370	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
371	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
372	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
373	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₆₇	—	2	1	no	—
377	C₂²⋊C₄×C₆₇	—	2	1	no	—
378	C₄²×C₆₇	C₂⁴	1	2	yes	—
379	C₂³×C₆₇	—	2	2	no	—
380	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
381	C₂²×D₆₇	—	2	2	no	—
382	C₂²×D₆₇	—	2	4	no	—
383	C₂²×D₆₇	—	2	4	no	—
384	C₂²×D₆₇	—	4	2	no	—
385	C₂²×D₆₇	—	8	4	no	—
386	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
387	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
388	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
389	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
390	C₂²×D₆₇	C₂×#41	1	1	yes	characteristic
391	C₂²×D₆₇	C₂×#41	1	1	yes	characteristic
392	Q₈×C₆₇	—	2	2	no	—
393	Q₈×C₆₇	C₂³×C₄	1	4	yes	—
394	D₄×C₆₇	—	2	4	no	—
395	D₄×C₆₇	—	2	4	no	—
396	D₄×C₆₇	—	2	2	no	—
397	D₄×C₆₇	C₂³×C₄	1	4	yes	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	4	no	—
400	C₂×C₄×C₆₇	—	2	4	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
403	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
404	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
407	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
408	C₂²⋊D₆₇	—	2	4	no	—
409	C₂²⋊D₆₇	—	2	4	no	—
410	C₂²⋊D₆₇	—	2	4	no	—
411	C₂²⋊D₆₇	—	2	4	no	—
412	C₂²⋊D₆₇	—	2	4	no	—
413	C₂²⋊D₆₇	—	2	4	no	—
414	C₂×Dic₆₇	—	2	2	no	—
415	C₂×Dic₆₇	—	2	4	no	—
416	C₂×Dic₆₇	—	2	4	no	—
417	C₂×Dic₆₇	—	2	2	no	—
418	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
419	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
420	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
421	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
422	C₂×Dic₆₇	C₂×#41	1	1	yes	characteristic
423	C₂×Dic₆₇	C₂×#41	1	1	yes	characteristic
424	D₂₆₈	—	2	4	no	—
425	D₂₆₈	—	2	4	no	—
426	D₂₆₈	—	2	2	no	—
427	D₂₆₈	C₂³×C₄	1	4	yes	—
428	C₄×D₆₇	—	2	4	no	—
429	C₄×D₆₇	—	2	4	no	—
430	C₄×D₆₇	—	2	4	no	—
431	C₄×D₆₇	—	2	4	no	—
432	C₄×D₆₇	—	2	4	no	—
433	C₄×D₆₇	—	2	4	no	—
434	C₄×D₆₇	—	4	4	no	—
435	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
436	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
437	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
438	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
439	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
440	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
441	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
442	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
443	C₄×D₆₇	C₂³×C₄	1	1	yes	characteristic
444	C₄×D₆₇	C₂³×C₄	1	1	yes	characteristic
445	C₄×D₆₇	C₂³×C₄	1	1	yes	characteristic
446	C₄×D₆₇	C₂³×C₄	1	1	yes	characteristic
447	C₄×D₆₇	C₂²×D₄	1	1	yes	characteristic
448	C₄×D₆₇	C₂²×D₄	1	1	yes	characteristic
449	C₄×D₆₇	C₂²×D₄	1	1	yes	characteristic
450	C₄×D₆₇	C₂²×D₄	1	1	yes	characteristic
451	Dic₁₃₄	—	2	2	no	—
452	Dic₁₃₄	—	2	4	no	—
453	Dic₁₃₄	—	2	4	no	—
454	Dic₁₃₄	C₂³×C₄	1	4	yes	—
455	C₈×C₆₇	—	2	4	no	—
456	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
457	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
458	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
459	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
460	C₈×C₆₇	C₂²×D₄	1	4	yes	—
461	C₆₇⋊C₈	—	2	4	no	—
462	C₆₇⋊C₈	C₂³×C₄	1	1	yes	characteristic
463	C₆₇⋊C₈	C₂³×C₄	1	1	yes	characteristic
464	C₆₇⋊C₈	C₂³×C₄	1	1	yes	characteristic
465	C₆₇⋊C₈	C₂³×C₄	1	1	yes	characteristic
466	C₆₇⋊C₈	C₂²×D₄	1	4	yes	—
467	C₂²×C₆₇	—	2	4	no	—
468	C₂²×C₆₇	—	4	1	no	—
469	C₂²×C₆₇	—	8	2	no	—
470	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
471	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
472	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
473	C₂×D₆₇	—	2	2	no	—
474	C₂×D₆₇	—	2	2	no	—
475	C₂×D₆₇	—	2	2	no	—
476	C₂×D₆₇	—	2	4	no	—
477	C₂×D₆₇	—	4	1	no	—
478	C₂×D₆₇	—	4	1	no	—
479	C₂×D₆₇	—	4	1	no	—
480	C₂×D₆₇	—	4	8	no	—
481	C₂×D₆₇	—	8	4	no	—
482	C₂×D₆₇	—	8	2	no	—
483	C₂×D₆₇	C₂×C₄×D₄	1	1	yes	characteristic
484	C₂×D₆₇	C₂×C₄×D₄	1	1	yes	characteristic
485	C₂×D₆₇	C₂×C₄×D₄	1	1	yes	characteristic
486	C₂×D₆₇	C₂×C₄×D₄	1	1	yes	characteristic
487	C₄×C₆₇	—	2	4	no	—
488	C₄×C₆₇	—	4	2	no	—
489	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
490	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
491	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
492	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
493	Dic₆₇	—	2	4	no	—
494	Dic₆₇	—	4	2	no	—
495	Dic₆₇	C₂×C₄×D₄	1	1	yes	characteristic
496	Dic₆₇	C₂×C₄×D₄	1	1	yes	characteristic
497	Dic₆₇	C₂×C₄×D₄	1	1	yes	characteristic
498	Dic₆₇	C₂×C₄×D₄	1	1	yes	characteristic
499	C₂×#2957	—	67	1	no	maximal, Sylow
500	C₂×C₆₇	—	2	1	no	—
501	C₂×C₆₇	—	2	1	no	—
502	C₂×C₆₇	—	2	1	no	—
503	C₂×C₆₇	—	4	4	no	—
504	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
505	D₆₇	—	2	1	no	—
506	D₆₇	—	2	1	no	—
507	D₆₇	—	2	1	no	—
508	D₆₇	—	4	4	no	—
509	D₆₇	#2957	1	2	yes	direct product factor
510	C₂²×#135	—	67	1	no	—
511	C₂×#568	—	67	2	no	—
512	#2957	—	67	4	no	—
513	#2957	—	67	4	no	—
514	#2957	—	67	1	no	—
515	#2957	—	67	2	no	—
516	#2957	—	67	1	no	—
517	#2957	—	67	1	no	—
518	#2957	—	67	2	no	—
519	#2957	D₆₇	1	1	yes	characteristic, direct product factor
520	C₂×#444	—	67	4	no	—
521	C₂×#443	—	67	4	no	—
522	C₂²×#108	—	67	1	no	—
523	C₂×#421	—	67	2	no	—
524	C₂×#405	—	67	1	no	—
525	C₆₇	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
526	C₂²×#41	—	67	2	no	—
527	C₂×#135	—	67	2	no	—
528	C₂×#135	—	67	2	no	—
529	C₂×#135	—	67	2	no	—
530	C₂×#135	—	67	2	no	—
531	C₂×#135	—	67	2	no	—
532	C₂×#135	—	67	2	no	—
533	C₂×#135	—	67	2	no	—
534	C₂×#135	—	67	2	no	—
535	C₂×#135	—	67	2	no	—
536	C₂×#135	—	67	1	no	—
537	C₂×#135	—	67	2	no	—
538	C₂×#135	—	67	1	no	—
539	C₂×#135	—	67	1	no	—
540	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
541	C₂²×Q₁₆	—	67	1	no	—
542	C₂²×SD₁₆	—	67	2	no	—
543	C₂²×D₈	—	67	1	no	—
544	#568	—	67	2	no	—
545	#568	—	67	8	no	—
546	#568	—	67	2	no	—
547	#568	—	67	2	no	—
548	#568	—	134	4	no	—
549	#568	—	134	4	no	—
550	#568	C₂×D₆₇	1	2	yes	complemented
551	C₂×#131	—	67	8	no	—
552	C₂×#131	—	134	4	no	—
553	C₂²×M₁₆	—	67	1	no	—
554	C₂²×M₁₆	—	67	2	no	—
555	C₂²×M₁₆	—	134	4	no	—
556	C₂³×C₈	—	67	1	no	—
557	C₂×#117	—	67	1	no	—
558	#444	—	67	4	no	—
559	#444	—	67	8	no	—
560	#444	—	67	4	no	—
561	#444	—	67	8	no	—
562	#444	—	67	4	no	—
563	#444	C₂×D₆₇	1	4	yes	complemented
564	#443	—	67	4	no	—
565	#443	—	67	8	no	—
566	#443	—	67	4	no	—
567	#443	—	67	8	no	—
568	#443	—	67	4	no	—
569	#443	C₂×D₆₇	1	4	yes	complemented
570	C₂×#108	—	67	2	no	—
571	C₂×#108	—	67	1	no	—
572	C₂×#108	—	67	2	no	—
573	C₂×#108	—	67	2	no	—
574	C₂×#108	—	67	2	no	—
575	C₂×#108	—	67	2	no	—
576	C₂×#108	C₂×D₆₇	1	1	yes	characteristic, complemented
577	#421	—	67	2	no	—
578	#421	—	67	2	no	—
579	#421	—	67	2	no	—
580	#421	—	67	8	no	—
581	#421	C₂×D₆₇	1	2	yes	complemented
582	C₂×#104	—	67	8	no	—
583	#405	—	67	1	no	—
584	#405	—	67	1	no	—
585	#405	—	67	1	no	—
586	#405	—	67	2	no	—
587	#405	—	67	2	no	—
588	#405	C₂×D₆₇	1	1	yes	characteristic, complemented
589	C₂×#97	—	67	2	no	—
590	C₂×C₄×C₈	—	67	2	no	—
591	C₂×#41	—	67	4	no	—
592	C₂×#41	—	67	4	no	—
593	C₂×#41	—	67	4	no	—
594	C₂×#41	—	67	4	no	—
595	C₂×#41	—	67	2	no	—
596	C₂×#41	—	67	2	no	—
597	C₂×#41	—	67	2	no	—
598	C₂×#41	—	134	2	no	—
599	C₂×#41	—	134	2	no	—
600	C₂×#41	—	134	2	no	—
601	C₂×#41	—	134	2	no	—
602	C₂×#41	—	134	2	no	—
603	C₂×#41	—	134	2	no	—
604	C₂×#41	C₂²×D₆₇	1	2	yes	—
605	C₂²×Q₈	—	67	2	no	—
606	C₂²×D₄	—	67	2	no	—
607	C₂²×D₄	—	134	2	no	—
608	C₂³×C₄	—	67	1	no	—
609	C₂³×C₄	—	134	2	no	—
610	#135	—	67	4	no	—
611	#135	—	67	4	no	—
612	#135	—	67	4	no	—
613	#135	—	67	4	no	—
614	#135	—	67	2	no	—
615	#135	—	67	2	no	—
616	#135	—	67	2	no	—
617	#135	—	67	2	no	—
618	#135	—	67	4	no	—
619	#135	—	67	4	no	—
620	#135	—	67	4	no	—
621	#135	—	67	4	no	—
622	#135	—	67	2	no	—
623	#135	—	67	2	no	—
624	#135	—	67	2	no	—
625	#135	—	67	2	no	—
626	#135	—	67	2	no	—
627	#135	—	67	2	no	—
628	#135	—	67	2	no	—
629	#135	—	67	2	no	—
630	#135	C₄×D₆₇	1	2	yes	complemented
631	#135	C₄×D₆₇	1	2	yes	complemented
632	#135	C₂²×D₆₇	1	2	yes	—
633	#135	C₂²×D₆₇	1	2	yes	—
634	C₂×Q₁₆	—	67	2	no	—
635	C₂×Q₁₆	—	67	2	no	—
636	C₂×Q₁₆	—	67	2	no	—
637	C₂×Q₁₆	—	67	2	no	—
638	C₂×Q₁₆	—	67	2	no	—
639	C₂×Q₁₆	—	67	1	no	—
640	C₂×Q₁₆	C₄×D₆₇	1	1	yes	characteristic, complemented
641	C₂×SD₁₆	—	67	2	no	—
642	C₂×SD₁₆	—	67	2	no	—
643	C₂×SD₁₆	—	67	4	no	—
644	C₂×SD₁₆	—	67	4	no	—
645	C₂×SD₁₆	—	67	4	no	—
646	C₂×SD₁₆	—	67	4	no	—
647	C₂×SD₁₆	—	67	2	no	—
648	C₂×SD₁₆	C₄×D₆₇	1	2	yes	complemented
649	C₂×D₈	—	67	2	no	—
650	C₂×D₈	—	67	2	no	—
651	C₂×D₈	—	67	2	no	—
652	C₂×D₈	—	67	2	no	—
653	C₂×D₈	—	67	2	no	—
654	C₂×D₈	—	67	1	no	—
655	C₂×D₈	C₄×D₆₇	1	1	yes	characteristic, complemented
656	#131	—	2	4	no	—
657	#131	—	67	8	no	—
658	#131	—	67	8	no	—
659	#131	—	67	8	no	—
660	#131	—	134	8	no	—
661	#131	—	134	4	no	—
662	#131	—	134	8	no	—
663	#131	—	134	8	no	—
664	#131	—	134	8	no	—
665	#131	—	134	4	no	—
666	#131	—	134	4	no	—
667	#131	C₂²×D₆₇	1	8	yes	complemented
668	C₂×M₁₆	—	2	4	no	—
669	C₂×M₁₆	—	67	1	no	—
670	C₂×M₁₆	—	67	2	no	—
671	C₂×M₁₆	—	67	2	no	—
672	C₂×M₁₆	—	67	2	no	—
673	C₂×M₁₆	—	67	2	no	—
674	C₂×M₁₆	—	67	2	no	—
675	C₂×M₁₆	—	67	2	no	—
676	C₂×M₁₆	—	67	4	no	—
677	C₂×M₁₆	—	67	4	no	—
678	C₂×M₁₆	—	134	8	no	—
679	C₂×M₁₆	—	134	2	no	—
680	C₂×M₁₆	—	134	8	no	—
681	C₂×M₁₆	—	134	4	no	—
682	C₂×M₁₆	—	134	8	no	—
683	C₂×M₁₆	—	134	2	no	—
684	C₂×M₁₆	—	134	2	no	—
685	C₂×M₁₆	—	134	4	no	—
686	C₂×M₁₆	—	134	4	no	—
687	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
688	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
689	C₂²×C₈	—	67	1	no	—
690	C₂²×C₈	—	67	1	no	—
691	C₂²×C₈	—	67	1	no	—
692	C₂²×C₈	—	67	1	no	—
693	C₂²×C₈	—	67	1	no	—
694	C₂²×C₈	—	67	1	no	—
695	C₂²×C₈	—	67	1	no	—
696	C₂²×C₈	—	67	1	no	—
697	C₂²×C₈	—	67	1	no	—
698	C₂²×C₈	—	67	1	no	—
699	C₂²×C₈	—	67	1	no	—
700	C₂²×C₈	—	67	1	no	—
701	C₂²×C₈	—	67	1	no	—
702	C₂²×C₈	—	67	2	no	—
703	C₂²×C₈	—	134	8	no	—
704	C₂²×C₈	—	134	2	no	—
705	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
706	#117	—	67	1	no	—
707	#117	—	67	2	no	—
708	#117	—	134	1	no	—
709	#117	—	134	1	no	—
710	#117	C₂²×D₆₇	1	1	yes	characteristic
711	C₂×C₄⋊C₄	—	134	1	no	—
712	C₂×C₂²⋊C₄	—	134	1	no	—
713	C₂×C₄²	—	67	2	no	—
714	#108	—	67	4	no	—
715	#108	—	67	4	no	—
716	#108	—	67	2	no	—
717	#108	—	67	2	no	—
718	#108	C₂²×D₆₇	1	2	yes	complemented
719	#108	C₂²×D₆₇	1	2	yes	complemented
720	#104	—	67	8	no	—
721	#104	—	67	8	no	—
722	#104	—	67	8	no	—
723	#104	C₂²×D₆₇	1	8	yes	complemented
724	#97	—	67	2	no	—
725	#97	—	67	2	no	—
726	#97	—	67	2	no	—
727	#97	C₂²×D₆₇	1	2	yes	complemented
728	C₄×C₈	—	67	2	no	—
729	C₄×C₈	—	67	2	no	—
730	C₄×C₈	—	67	2	no	—
731	C₄×C₈	C₂²×D₆₇	1	2	yes	complemented
732	C₂⁴	—	67	1	no	—
733	C₂⁴	—	134	2	no	—
734	#41	—	2	2	no	—
735	#41	—	2	2	no	—
736	#41	—	67	4	no	—
737	#41	—	67	4	no	—
738	#41	—	67	4	no	—
739	#41	—	67	4	no	—
740	#41	—	67	4	no	—
741	#41	—	67	4	no	—
742	#41	—	134	4	no	—
743	#41	—	134	4	no	—
744	#41	—	134	4	no	—
745	#41	—	134	4	no	—
746	#41	—	134	4	no	—
747	#41	—	134	4	no	—
748	#41	—	134	4	no	—
749	#41	—	134	4	no	—
750	#41	—	134	2	no	—
751	#41	—	134	2	no	—
752	#41	—	134	2	no	—
753	#41	—	134	2	no	—
754	#41	—	134	2	no	—
755	#41	—	134	2	no	—
756	#41	C₂×C₄×D₆₇	1	4	yes	—
757	#41	C₂³×D₆₇	1	4	yes	—
758	C₂×Q₈	—	67	4	no	—
759	C₂×Q₈	—	67	4	no	—
760	C₂×Q₈	—	67	2	no	—
761	C₂×Q₈	—	134	2	no	—
762	C₂×Q₈	—	134	2	no	—
763	C₂×Q₈	—	134	2	no	—
764	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	67	4	no	—
767	C₂×D₄	—	67	4	no	—
768	C₂×D₄	—	67	2	no	—
769	C₂×D₄	—	134	2	no	—
770	C₂×D₄	—	134	2	no	—
771	C₂×D₄	—	134	2	no	—
772	C₂×D₄	—	134	2	no	—
773	C₂×D₄	—	134	4	no	—
774	C₂×D₄	—	134	4	no	—
775	C₂×D₄	—	134	4	no	—
776	C₂×D₄	—	134	4	no	—
777	C₂×D₄	—	134	2	no	—
778	C₂×D₄	—	134	2	no	—
779	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	67	1	no	—
782	C₂²×C₄	—	67	1	no	—
783	C₂²×C₄	—	67	1	no	—
784	C₂²×C₄	—	67	1	no	—
785	C₂²×C₄	—	67	1	no	—
786	C₂²×C₄	—	67	1	no	—
787	C₂²×C₄	—	67	1	no	—
788	C₂²×C₄	—	67	1	no	—
789	C₂²×C₄	—	67	1	no	—
790	C₂²×C₄	—	67	1	no	—
791	C₂²×C₄	—	67	1	no	—
792	C₂²×C₄	—	67	1	no	—
793	C₂²×C₄	—	67	1	no	—
794	C₂²×C₄	—	134	2	no	—
795	C₂²×C₄	—	134	4	no	—
796	C₂²×C₄	—	134	4	no	—
797	C₂²×C₄	—	134	2	no	—
798	C₂²×C₄	—	134	4	no	—
799	C₂²×C₄	—	134	4	no	—
800	C₂²×C₄	—	134	2	no	—
801	C₂²×C₄	—	134	2	no	—
802	C₂²×C₄	—	134	2	no	—
803	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
804	Q₁₆	—	67	4	no	—
805	Q₁₆	—	67	4	no	—
806	Q₁₆	—	67	2	no	—
807	Q₁₆	—	67	2	no	—
808	Q₁₆	C₂×C₄×D₆₇	1	2	yes	—
809	Q₁₆	C₂×C₄×D₆₇	1	2	yes	—
810	SD₁₆	—	67	4	no	—
811	SD₁₆	—	67	4	no	—
812	SD₁₆	—	67	4	no	—
813	SD₁₆	—	67	4	no	—
814	SD₁₆	—	67	4	no	—
815	SD₁₆	—	67	4	no	—
816	SD₁₆	C₂×C₄×D₆₇	1	4	yes	—
817	SD₁₆	C₂×C₄×D₆₇	1	4	yes	—
818	D₈	—	67	4	no	—
819	D₈	—	67	4	no	—
820	D₈	—	67	2	no	—
821	D₈	—	67	2	no	—
822	D₈	C₂×C₄×D₆₇	1	2	yes	—
823	D₈	C₂×C₄×D₆₇	1	2	yes	—
824	M₁₆	—	2	2	no	—
825	M₁₆	—	2	8	no	—
826	M₁₆	—	67	2	no	—
827	M₁₆	—	67	2	no	—
828	M₁₆	—	67	4	no	—
829	M₁₆	—	67	4	no	—
830	M₁₆	—	67	4	no	—
831	M₁₆	—	134	8	no	—
832	M₁₆	—	134	4	no	—
833	M₁₆	—	134	4	no	—
834	M₁₆	—	134	8	no	—
835	M₁₆	—	134	2	no	—
836	M₁₆	—	134	8	no	—
837	M₁₆	D₄×D₆₇	1	2	yes	—
838	M₁₆	D₄×D₆₇	1	2	yes	—
839	M₁₆	C₂³×D₆₇	1	4	yes	—
840	C₂×C₈	—	2	2	no	—
841	C₂×C₈	—	2	8	no	—
842	C₂×C₈	—	67	1	no	—
843	C₂×C₈	—	67	1	no	—
844	C₂×C₈	—	67	1	no	—
845	C₂×C₈	—	67	1	no	—
846	C₂×C₈	—	67	1	no	—
847	C₂×C₈	—	67	2	no	—
848	C₂×C₈	—	67	1	no	—
849	C₂×C₈	—	67	1	no	—
850	C₂×C₈	—	67	1	no	—
851	C₂×C₈	—	67	1	no	—
852	C₂×C₈	—	67	1	no	—
853	C₂×C₈	—	67	1	no	—
854	C₂×C₈	—	67	1	no	—
855	C₂×C₈	—	67	1	no	—
856	C₂×C₈	—	67	1	no	—
857	C₂×C₈	—	67	1	no	—
858	C₂×C₈	—	67	1	no	—
859	C₂×C₈	—	67	1	no	—
860	C₂×C₈	—	67	1	no	—
861	C₂×C₈	—	67	1	no	—
862	C₂×C₈	—	67	1	no	—
863	C₂×C₈	—	67	1	no	—
864	C₂×C₈	—	67	1	no	—
865	C₂×C₈	—	67	4	no	—
866	C₂×C₈	—	67	4	no	—
867	C₂×C₈	—	134	8	no	—
868	C₂×C₈	—	134	4	no	—
869	C₂×C₈	—	134	4	no	—
870	C₂×C₈	—	134	8	no	—
871	C₂×C₈	—	134	2	no	—
872	C₂×C₈	—	134	8	no	—
873	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
874	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
875	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
876	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
877	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
878	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
879	C₂×C₈	C₂³×D₆₇	1	2	yes	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	134	2	no	—
882	C₄⋊C₄	—	134	1	no	—
883	C₂²⋊C₄	—	2	1	no	—
884	C₂²⋊C₄	—	134	2	no	—
885	C₂²⋊C₄	—	134	1	no	—
886	C₄²	—	67	2	no	—
887	C₄²	—	134	2	no	—
888	C₄²	C₂³×D₆₇	1	2	yes	—
889	C₂³	—	2	2	no	—
890	C₂³	—	268	2	no	—
891	C₂³	—	536	4	no	—
892	C₂³	—	67	1	no	—
893	C₂³	—	67	1	no	—
894	C₂³	—	67	1	no	—
895	C₂³	—	67	1	no	—
896	C₂³	—	67	1	no	—
897	C₂³	—	67	1	no	—
898	C₂³	—	134	4	no	—
899	C₂³	—	134	4	no	—
900	C₂³	—	134	2	no	—
901	C₂³	#41×D₆₇	1	1	yes	characteristic
902	Q₈	—	2	2	no	—
903	Q₈	—	67	4	no	—
904	Q₈	—	134	4	no	—
905	Q₈	—	134	4	no	—
906	Q₈	—	134	2	no	—
907	Q₈	C₂²×C₄×D₆₇	1	4	yes	—
908	D₄	—	2	4	no	—
909	D₄	—	2	4	no	—
910	D₄	—	2	2	no	—
911	D₄	—	67	4	no	—
912	D₄	—	134	4	no	—
913	D₄	—	134	4	no	—
914	D₄	—	134	4	no	—
915	D₄	—	134	4	no	—
916	D₄	—	134	4	no	—
917	D₄	—	134	4	no	—
918	D₄	—	134	4	no	—
919	D₄	—	134	4	no	—
920	D₄	—	134	2	no	—
921	D₄	C₂²×C₄×D₆₇	1	4	yes	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	4	no	—
924	C₂×C₄	—	2	4	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	268	4	no	—
927	C₂×C₄	—	67	1	no	—
928	C₂×C₄	—	67	1	no	—
929	C₂×C₄	—	67	1	no	—
930	C₂×C₄	—	67	1	no	—
931	C₂×C₄	—	67	1	no	—
932	C₂×C₄	—	67	1	no	—
933	C₂×C₄	—	67	1	no	—
934	C₂×C₄	—	67	1	no	—
935	C₂×C₄	—	67	1	no	—
936	C₂×C₄	—	67	1	no	—
937	C₂×C₄	—	67	1	no	—
938	C₂×C₄	—	67	1	no	—
939	C₂×C₄	—	67	1	no	—
940	C₂×C₄	—	67	1	no	—
941	C₂×C₄	—	67	1	no	—
942	C₂×C₄	—	67	1	no	—
943	C₂×C₄	—	67	1	no	—
944	C₂×C₄	—	67	1	no	—
945	C₂×C₄	—	67	1	no	—
946	C₂×C₄	—	67	1	no	—
947	C₂×C₄	—	67	1	no	—
948	C₂×C₄	—	67	1	no	—
949	C₂×C₄	—	134	4	no	—
950	C₂×C₄	—	134	4	no	—
951	C₂×C₄	—	134	4	no	—
952	C₂×C₄	—	134	4	no	—
953	C₂×C₄	—	134	2	no	—
954	C₂×C₄	—	134	4	no	—
955	C₂×C₄	—	134	4	no	—
956	C₂×C₄	—	134	2	no	—
957	C₂×C₄	—	134	4	no	—
958	C₂×C₄	—	134	4	no	—
959	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
960	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
961	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
962	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
963	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
964	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
965	C₈	—	2	4	no	—
966	C₈	—	67	1	no	—
967	C₈	—	67	1	no	—
968	C₈	—	67	1	no	—
969	C₈	—	67	1	no	—
970	C₈	—	67	4	no	—
971	C₈	—	134	4	no	—
972	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
973	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
974	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
975	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
976	C₈	C₂×D₄×D₆₇	1	4	yes	—
977	C₂²	—	2	4	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	8	2	no	—
980	C₂²	—	268	1	no	—
981	C₂²	—	268	1	no	—
982	C₂²	—	268	1	no	—
983	C₂²	—	268	8	no	—
984	C₂²	—	536	2	no	—
985	C₂²	—	536	4	no	—
986	C₂²	—	67	1	no	—
987	C₂²	—	67	1	no	—
988	C₂²	—	67	1	no	—
989	C₂²	—	67	1	no	—
990	C₂²	—	134	2	no	—
991	C₂²	—	134	2	no	—
992	C₂²	—	134	2	no	—
993	C₂²	—	134	4	no	—
994	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
995	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
996	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
997	C₄	—	2	4	no	—
998	C₄	—	4	2	no	—
999	C₄	—	268	2	no	—
1000	C₄	—	67	1	no	—
1001	C₄	—	67	1	no	—
1002	C₄	—	67	1	no	—
1003	C₄	—	67	1	no	—
1004	C₄	—	134	4	no	—
1005	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
1006	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
1007	C₄	C₂³×C₄×D₆₇	1	1	yes	characteristic
1008	C₄	C₂²×D₄×D₆₇	1	1	yes	characteristic
1009	C₂	—	2	1	no	—
1010	C₂	—	2	1	no	—
1011	C₂	—	2	1	no	—
1012	C₂	—	4	4	no	—
1013	C₂	—	268	4	no	—
1014	C₂	—	67	2	no	—
1015	C₂	—	134	1	no	—
1016	C₂	—	134	1	no	—
1017	C₂	—	134	1	no	—
1018	C₂	C₂×C₄×D₄×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₆₇
commutator	C₄×C₆₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₆₇×#2957	C₂
socle	C₂×C₆₇	C₂²×C₄×D₄
prime radical	C₂×#135×D₆₇	C₂
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	#2957	D₆₇
hypocenter	C₆₇	C₂×#2957
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #2957

Complements

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

N	H ≅ G/N	type
2. #568×D₆₇	C₂	semidirect
3. #22569127	C₂	semidirect
4. #22569126	C₂	semidirect
5. #22569125	C₂	semidirect
6. #22569124	C₂	semidirect
7. #22569123	C₂	semidirect
8. #22569122	C₂	semidirect
9. #22569121	C₂	semidirect
10. #444×D₆₇	C₂	semidirect
11. #443×D₆₇	C₂	semidirect
12. C₂×#108×D₆₇	C₂	semidirect
13. #421×D₆₇	C₂	semidirect
14. #405×D₆₇	C₂	semidirect
15. C₆₇×#2957	C₂	semidirect
17. C₂×#14524066	C₄	semidirect
19. C₂×#14524064	C₄	semidirect
21. C₂×#14524062	C₄	semidirect
22. #135×D₆₇	C₄	semidirect
23. #135×D₆₇	C₄	semidirect
24. #135×D₆₇	C₄	semidirect
25. #135×D₆₇	C₄	semidirect
30. C₂×Q₁₆×D₆₇	C₄	semidirect
31. C₂×SD₁₆×D₆₇	C₄	semidirect
32. C₂×D₈×D₆₇	C₄	semidirect
33. #16864163	C₂²	semidirect
35. #16864162	C₂²	semidirect
36. #16864162	C₂²	semidirect
38. #16864161	C₂²	semidirect
40. #131×D₆₇	C₂²	semidirect
46. #16863519	C₂²	semidirect
47. #16863518	C₂²	semidirect
48. #16863517	C₂²	semidirect
49. #16863516	C₂²	semidirect
50. #16863515	C₂²	semidirect
51. #16863514	C₂²	semidirect
52. #16863513	C₂²	semidirect
53. #16863512	C₂²	semidirect
54. #16863511	C₂²	semidirect
55. #16863510	C₂²	semidirect
56. C₂×#14523979	C₂²	semidirect
57. C₂×#14523978	C₂²	semidirect
58. #108×D₆₇	C₂²	semidirect
59. #108×D₆₇	C₂²	semidirect
60. #108×D₆₇	C₂²	semidirect
61. #108×D₆₇	C₂²	semidirect
62. #16863414	C₂²	semidirect
63. #16863413	C₂²	semidirect
64. #16863412	C₂²	semidirect
65. #16863411	C₂²	semidirect
66. #104×D₆₇	C₂²	semidirect
67. #16863354	C₂²	semidirect
68. #16863353	C₂²	semidirect
69. #16863352	C₂²	semidirect
70. #16863351	C₂²	semidirect
71. #16863350	C₂²	semidirect
72. #97×D₆₇	C₂²	semidirect
73. C₄×C₈×D₆₇	C₂²	semidirect
75. #568×C₆₇	C₂²	semidirect
76. #444×C₆₇	C₂²	semidirect
77. #443×C₆₇	C₂²	semidirect
78. C₂×#108×C₆₇	C₂²	semidirect
79. #421×C₆₇	C₂²	semidirect
80. #405×C₆₇	C₂²	semidirect
101. #14524066	C₂×C₄	semidirect
102. #14524066	C₂×C₄	semidirect
103. #14524065	C₂×C₄	semidirect
104. #14524065	C₂×C₄	semidirect
109. #14524064	C₂×C₄	semidirect
110. #14524064	C₂×C₄	semidirect
111. #14524063	C₂×C₄	semidirect
112. #14524063	C₂×C₄	semidirect
117. #14524062	C₂×C₄	semidirect
118. #14524062	C₂×C₄	semidirect
119. C₂×Dic₂₆₈	C₂×C₄	semidirect
120. C₂×#11761618	C₂×C₄	semidirect
123. Q₁₆×D₆₇	C₂×C₄	semidirect
124. Q₁₆×D₆₇	C₂×C₄	semidirect
125. C₂×#11761617	C₂×C₄	semidirect
126. C₂×#11761616	C₂×C₄	semidirect
127. C₂×#11761615	C₂×C₄	semidirect
130. SD₁₆×D₆₇	C₂×C₄	semidirect
131. SD₁₆×D₆₇	C₂×C₄	semidirect
132. C₂×D₅₃₆	C₂×C₄	semidirect
133. C₂×#11761613	C₂×C₄	semidirect
136. D₈×D₆₇	C₂×C₄	semidirect
137. D₈×D₆₇	C₂×C₄	semidirect
141. #14524051	C₂³	semidirect
143. #14524050	C₂³	semidirect
147. #14524049	C₂³	semidirect
189. #14523979	C₂³	semidirect
190. #14523979	C₂³	semidirect
191. #14523978	C₂³	semidirect
192. #14523978	C₂³	semidirect
193. #14523971	C₂³	semidirect
194. #14523970	C₂³	semidirect
195. #14523969	C₂³	semidirect
196. #14523954	C₂³	semidirect
197. #14523953	C₂³	semidirect
198. #14523953	C₂³	semidirect
199. C₄×C₆₇⋊C₈	C₂³	semidirect
200. C₈×Dic₆₇	C₂³	semidirect
201. C₈×Dic₆₇	C₂³	semidirect
203. #135×C₆₇	C₂×C₄	semidirect
204. #135×C₆₇	C₂×C₄	semidirect
207. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
208. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
209. C₂×D₈×C₆₇	C₂×C₄	semidirect
211. #131×C₆₇	C₂³	semidirect
217. #108×C₆₇	C₂³	semidirect
218. #108×C₆₇	C₂³	semidirect
219. #104×C₆₇	C₂³	semidirect
220. #97×C₆₇	C₂³	semidirect
221. C₄×C₈×C₆₇	C₂³	semidirect
509. D₆₇	#2957	direct (N × H)
519. #2957	D₆₇	direct (N × H)
525. C₆₇	C₂×#2957	semidirect
550. #568	C₂×D₆₇	semidirect
563. #444	C₂×D₆₇	semidirect
569. #443	C₂×D₆₇	semidirect
576. C₂×#108	C₂×D₆₇	semidirect
581. #421	C₂×D₆₇	semidirect
588. #405	C₂×D₆₇	semidirect
630. #135	C₄×D₆₇	semidirect
631. #135	C₄×D₆₇	semidirect
640. C₂×Q₁₆	C₄×D₆₇	semidirect
648. C₂×SD₁₆	C₄×D₆₇	semidirect
655. C₂×D₈	C₄×D₆₇	semidirect
667. #131	C₂²×D₆₇	semidirect
718. #108	C₂²×D₆₇	semidirect
719. #108	C₂²×D₆₇	semidirect
723. #104	C₂²×D₆₇	semidirect
727. #97	C₂²×D₆₇	semidirect
731. C₄×C₈	C₂²×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#135×D₆₇	2
#568×D₆₇	2
#22569127	2
#22569126	2
#22569125	2
#22569124	2
#22569123	2
#22569122	2
#22569121	2
#444×D₆₇	2
#443×D₆₇	2
C₂×#108×D₆₇	2
#421×D₆₇	2
#405×D₆₇	2
C₆₇×#2957	2
C₂×#2957	67

Subgroups — #2957×D67 #31720146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2957×D₆₇ #31720146