Subgroups — #31720156

Order 17152.

2628 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16864193	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	#22569122	C₂	1	2	yes	maximal, complemented
8	#22569117	C₂	1	4	yes	maximal, complemented
9	#22569114	C₂	1	4	yes	maximal, complemented
10	#22569109	C₂	1	4	yes	maximal, complemented
11	#22569107	C₂	1	4	yes	maximal, complemented
12	C₂×#16863443	C₂	1	1	yes	maximal, characteristic, complemented
13	#421×D₆₇	C₂	1	2	yes	maximal, complemented
14	#22568625	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	#16864193	C₄	1	4	yes	complemented
18	#16864193	C₄	1	4	yes	complemented
19	#16864193	C₂²	1	2	yes	—
20	#16864193	C₂²	1	2	yes	—
21	#16864193	C₂²	1	2	yes	—
22	#16864193	C₂²	1	2	yes	—
23	C₂×#14524075	C₄	1	2	yes	complemented
24	C₂×#14524072	C₄	1	2	yes	complemented
25	C₂×#14524070	C₄	1	2	yes	complemented
26	C₂×#14524067	C₄	1	2	yes	complemented
27	C₂×#14524065	C₂²	1	1	yes	characteristic
28	C₂×#14524063	C₂²	1	2	yes	—
29	#16864163	C₂²	1	2	yes	complemented
30	#16864162	—	2	4	no	—
31	#16864162	C₂²	1	2	yes	complemented
32	#16864162	C₂²	1	2	yes	complemented
33	#16864161	—	2	4	no	—
34	#16864161	C₂²	1	8	yes	complemented
35	#131×D₆₇	—	2	4	no	—
36	#131×D₆₇	C₂²	1	8	yes	complemented
37	C₂²×#11761611	C₂²	1	1	yes	characteristic
38	C₂×M₁₆×D₆₇	—	2	4	no	—
39	C₂×M₁₆×D₆₇	C₂²	1	2	yes	—
40	C₂×M₁₆×D₆₇	C₂²	1	1	yes	characteristic
41	#117×D₆₇	C₂²	1	1	yes	characteristic
42	#16863519	C₂²	1	4	yes	complemented
43	#16863518	C₂²	1	4	yes	complemented
44	#16863517	C₂²	1	4	yes	complemented
45	#16863516	C₂²	1	8	yes	complemented
46	#16863515	C₂²	1	8	yes	complemented
47	#16863514	C₂²	1	4	yes	complemented
48	#16863513	C₂²	1	4	yes	complemented
49	#16863512	C₂²	1	4	yes	complemented
50	#16863511	C₂²	1	8	yes	complemented
51	#16863510	C₂²	1	8	yes	complemented
52	#16863443	C₂²	1	2	yes	complemented
53	#16863443	C₂²	1	2	yes	complemented
54	#16863443	C₂²	1	2	yes	complemented
55	#16863443	C₂²	1	2	yes	complemented
56	C₂×#14523979	C₂²	1	1	yes	characteristic, complemented
57	C₂×#14523978	C₂²	1	2	yes	complemented
58	#16863414	C₂²	1	2	yes	complemented
59	#16863413	C₂²	1	2	yes	complemented
60	#16863412	C₂²	1	2	yes	complemented
61	#16863411	C₂²	1	8	yes	complemented
62	#104×D₆₇	C₂²	1	8	yes	complemented
63	#16863354	C₂²	1	1	yes	characteristic, complemented
64	#16863353	C₂²	1	2	yes	complemented
65	#16863352	C₂²	1	1	yes	characteristic, complemented
66	#16863351	C₂²	1	1	yes	characteristic, complemented
67	#16863350	C₂²	1	2	yes	complemented
68	#16863348	C₂²	1	2	yes	complemented
69	C₄×#11761611	C₂²	1	2	yes	complemented
70	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
71	#568×C₆₇	C₂²	1	2	yes	complemented
72	#444×C₆₇	C₂²	1	4	yes	complemented
73	#443×C₆₇	C₂²	1	4	yes	complemented
74	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#421×C₆₇	C₂²	1	2	yes	complemented
76	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	C₂×#11761629	C₂×C₄	1	2	yes	—
78	C₂×#11761628	—	2	2	no	—
79	C₂×#11761628	C₂³	1	2	yes	—
80	C₂×#11761627	—	2	2	no	—
81	C₂×#11761627	C₂×C₄	1	2	yes	—
82	#41×D₆₇	—	2	2	no	—
83	#41×D₆₇	—	2	2	no	—
84	#41×D₆₇	—	2	2	no	—
85	#41×D₆₇	—	2	2	no	—
86	#41×D₆₇	C₂×C₄	1	4	yes	—
87	#41×D₆₇	C₂×C₄	1	4	yes	—
88	#41×D₆₇	C₂³	1	4	yes	—
89	#41×D₆₇	C₂³	1	4	yes	—
90	C₂×Q₈×D₆₇	C₂×C₄	1	2	yes	—
91	C₂×D₄×D₆₇	—	2	2	no	—
92	C₂×D₄×D₆₇	C₂×C₄	1	2	yes	—
93	C₂²×C₄×D₆₇	—	2	2	no	—
94	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
95	#14524075	C₂×C₄	1	4	yes	—
96	#14524075	C₂×C₄	1	4	yes	—
97	#14524075	C₂×C₄	1	4	yes	complemented
98	#14524075	C₂×C₄	1	4	yes	complemented
99	#14524072	C₂×C₄	1	4	yes	—
100	#14524072	C₂×C₄	1	4	yes	—
101	#14524072	C₂×C₄	1	4	yes	complemented
102	#14524072	C₂×C₄	1	4	yes	complemented
103	#14524070	C₂×C₄	1	4	yes	—
104	#14524070	C₂×C₄	1	4	yes	—
105	#14524070	C₂×C₄	1	4	yes	complemented
106	#14524070	C₂×C₄	1	4	yes	complemented
107	#14524067	C₂×C₄	1	4	yes	—
108	#14524067	C₂×C₄	1	4	yes	—
109	#14524067	C₂×C₄	1	4	yes	complemented
110	#14524067	C₂×C₄	1	4	yes	complemented
111	#14524065	C₂×C₄	1	2	yes	complemented
112	#14524065	C₂×C₄	1	2	yes	complemented
113	#14524065	C₂³	1	2	yes	—
114	#14524065	C₂³	1	2	yes	—
115	#14524063	C₂×C₄	1	4	yes	complemented
116	#14524063	C₂×C₄	1	4	yes	complemented
117	#14524063	C₂³	1	4	yes	—
118	#14524063	C₂³	1	4	yes	—
119	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic, complemented
120	C₂×#11761618	C₂×C₄	1	2	yes	complemented
121	C₂×#11761617	C₂×C₄	1	2	yes	complemented
122	C₂×#11761616	C₂×C₄	1	2	yes	complemented
123	C₂×#11761615	C₂×C₄	1	2	yes	complemented
124	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic, complemented
125	C₂×#11761613	C₂×C₄	1	2	yes	complemented
126	#14524051	—	2	8	no	—
127	#14524051	—	2	8	no	—
128	#14524051	—	2	4	no	—
129	#14524051	C₂³	1	8	yes	complemented
130	#14524050	—	2	4	no	—
131	#14524050	C₂³	1	8	yes	complemented
132	#14524049	—	2	4	no	—
133	#14524049	—	2	8	no	—
134	#14524049	—	2	8	no	—
135	#14524049	C₂³	1	8	yes	complemented
136	C₂×#11761612	—	2	4	no	—
137	C₂×#11761612	C₂³	1	2	yes	—
138	C₂×#11761612	C₂³	1	1	yes	characteristic
139	C₂×#11761611	—	2	2	no	—
140	C₂×#11761611	—	2	8	no	—
141	C₂×#11761611	C₂×C₄	1	2	yes	—
142	C₂×#11761611	C₂×C₄	1	2	yes	—
143	C₂×#11761611	C₂×C₄	1	2	yes	—
144	C₂×#11761611	C₂×C₄	1	2	yes	—
145	C₂×#11761611	C₂³	1	1	yes	characteristic
146	C₂×#11761611	C₂³	1	1	yes	characteristic
147	C₂×#11761611	C₂³	1	1	yes	characteristic
148	C₂×#11761611	C₂³	1	1	yes	characteristic
149	C₂×#11761611	C₂³	1	2	yes	—
150	M₁₆×D₆₇	—	2	2	no	—
151	M₁₆×D₆₇	—	2	2	no	—
152	M₁₆×D₆₇	—	2	4	no	—
153	M₁₆×D₆₇	—	2	8	no	—
154	M₁₆×D₆₇	—	2	8	no	—
155	M₁₆×D₆₇	—	2	4	no	—
156	M₁₆×D₆₇	D₄	1	4	yes	—
157	M₁₆×D₆₇	D₄	1	4	yes	—
158	M₁₆×D₆₇	C₂³	1	4	yes	—
159	M₁₆×D₆₇	C₂³	1	4	yes	—
160	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
161	C₂×C₈×D₆₇	—	2	2	no	—
162	C₂×C₈×D₆₇	—	2	8	no	—
163	C₂×C₈×D₆₇	C₂³	1	2	yes	—
164	#14524002	C₂³	1	1	yes	characteristic
165	#14524001	—	2	1	no	—
166	#14524000	C₂³	1	2	yes	—
167	#14523999	—	2	1	no	—
168	C₄⋊C₄×D₆₇	—	2	1	no	—
169	C₂²⋊C₄×D₆₇	—	2	1	no	—
170	C₄²×D₆₇	C₂³	1	2	yes	—
171	#14523979	C₂³	1	2	yes	complemented
172	#14523979	C₂³	1	2	yes	complemented
173	#14523978	C₂³	1	4	yes	complemented
174	#14523978	C₂³	1	4	yes	complemented
175	#14523971	C₂³	1	8	yes	complemented
176	#14523970	C₂³	1	8	yes	complemented
177	#14523969	C₂³	1	8	yes	complemented
178	#14523954	C₂³	1	2	yes	complemented
179	#14523953	C₂³	1	2	yes	complemented
180	#14523953	C₂³	1	2	yes	complemented
181	C₄×C₆₇⋊C₈	C₂³	1	2	yes	complemented
182	C₈×Dic₆₇	C₂³	1	2	yes	complemented
183	C₈×Dic₆₇	C₂³	1	2	yes	complemented
184	C₂×#41×C₆₇	C₂³	1	2	yes	—
185	#135×C₆₇	C₂×C₄	1	2	yes	complemented
186	#135×C₆₇	C₂×C₄	1	2	yes	complemented
187	#135×C₆₇	C₂³	1	2	yes	—
188	#135×C₆₇	C₂³	1	2	yes	—
189	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
190	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	complemented
191	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
192	#131×C₆₇	—	2	4	no	—
193	#131×C₆₇	C₂³	1	8	yes	complemented
194	C₂×M₁₆×C₆₇	—	2	4	no	—
195	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
196	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
197	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
198	#117×C₆₇	C₂³	1	1	yes	characteristic
199	#108×C₆₇	C₂³	1	2	yes	complemented
200	#108×C₆₇	C₂³	1	2	yes	complemented
201	#104×C₆₇	C₂³	1	8	yes	complemented
202	#97×C₆₇	C₂³	1	2	yes	complemented
203	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
204	C₂³×D₆₇	—	2	2	no	—
205	C₂³×D₆₇	#41	1	1	yes	characteristic
206	#11761629	—	2	2	no	—
207	#11761629	—	2	2	no	—
208	#11761629	C₂²×C₄	1	4	yes	—
209	#11761629	C₂²×C₄	1	4	yes	—
210	#11761628	—	2	2	no	—
211	#11761628	—	2	2	no	—
212	#11761628	—	2	4	no	—
213	#11761628	—	2	4	no	—
214	#11761628	—	2	4	no	—
215	#11761628	—	2	4	no	—
216	#11761628	C₂²×C₄	1	4	yes	—
217	#11761628	C₂⁴	1	4	yes	—
218	#11761627	—	2	4	no	—
219	#11761627	—	2	4	no	—
220	#11761627	—	2	4	no	—
221	#11761627	—	2	4	no	—
222	#11761627	—	2	2	no	—
223	#11761627	—	2	2	no	—
224	#11761627	C₂²×C₄	1	4	yes	—
225	#11761627	C₂²×C₄	1	4	yes	—
226	C₂×Dic₁₃₄	—	2	2	no	—
227	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
228	Q₈×D₆₇	—	2	2	no	—
229	Q₈×D₆₇	—	2	2	no	—
230	Q₈×D₆₇	C₂²×C₄	1	4	yes	—
231	Q₈×D₆₇	C₂²×C₄	1	4	yes	—
232	C₂×D₂₆₈	—	2	2	no	—
233	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
234	C₂×C₂²⋊D₆₇	—	2	2	no	—
235	C₂×C₂²⋊D₆₇	—	2	2	no	—
236	C₂×C₂²⋊D₆₇	—	2	2	no	—
237	D₄×D₆₇	—	2	4	no	—
238	D₄×D₆₇	—	2	4	no	—
239	D₄×D₆₇	—	2	4	no	—
240	D₄×D₆₇	—	2	4	no	—
241	D₄×D₆₇	—	2	2	no	—
242	D₄×D₆₇	—	2	2	no	—
243	D₄×D₆₇	C₂²×C₄	1	4	yes	—
244	D₄×D₆₇	C₂²×C₄	1	4	yes	—
245	C₂²×Dic₆₇	—	2	2	no	—
246	C₂²×Dic₆₇	#41	1	1	yes	characteristic
247	C₂×C₄×D₆₇	—	2	2	no	—
248	C₂×C₄×D₆₇	—	2	2	no	—
249	C₂×C₄×D₆₇	—	2	2	no	—
250	C₂×C₄×D₆₇	—	2	4	no	—
251	C₂×C₄×D₆₇	—	2	4	no	—
252	C₂×C₄×D₆₇	—	2	4	no	—
253	C₂×C₄×D₆₇	—	2	4	no	—
254	C₂×C₄×D₆₇	—	2	2	no	—
255	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
256	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
257	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
258	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
259	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
260	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
261	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
263	Dic₂₆₈	C₂²×C₄	1	2	yes	—
264	Dic₂₆₈	C₂²×C₄	1	2	yes	—
265	#11761618	C₂²×C₄	1	4	yes	—
266	#11761618	C₂²×C₄	1	4	yes	—
267	#11761617	C₂²×C₄	1	4	yes	—
268	#11761617	C₂²×C₄	1	4	yes	—
269	#11761616	C₂²×C₄	1	4	yes	—
270	#11761616	C₂²×C₄	1	4	yes	—
271	#11761615	C₂²×C₄	1	4	yes	—
272	#11761615	C₂²×C₄	1	4	yes	—
273	D₅₃₆	C₂²×C₄	1	2	yes	—
274	D₅₃₆	C₂²×C₄	1	2	yes	—
275	#11761613	C₂²×C₄	1	4	yes	—
276	#11761613	C₂²×C₄	1	4	yes	—
277	#11761612	—	2	2	no	—
278	#11761612	—	2	8	no	—
279	#11761612	C₂×D₄	1	2	yes	—
280	#11761612	C₂×D₄	1	2	yes	—
281	#11761612	C₂⁴	1	4	yes	—
282	#11761611	—	2	4	no	—
283	#11761611	—	2	4	no	—
284	#11761611	—	2	8	no	—
285	#11761611	—	2	8	no	—
286	#11761611	C₂²×C₄	1	2	yes	—
287	#11761611	C₂²×C₄	1	2	yes	—
288	#11761611	C₂²×C₄	1	2	yes	—
289	#11761611	C₂²×C₄	1	2	yes	—
290	#11761611	C₂²×C₄	1	2	yes	—
291	#11761611	C₂²×C₄	1	2	yes	—
292	#11761611	C₂²×C₄	1	2	yes	—
293	#11761611	C₂²×C₄	1	2	yes	—
294	#11761611	C₂×D₄	1	8	yes	—
295	C₂×C₆₇⋊C₈	—	2	2	no	—
296	C₂×C₆₇⋊C₈	—	2	8	no	—
297	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
298	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
299	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
300	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
301	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
302	C₈×D₆₇	—	2	4	no	—
303	C₈×D₆₇	—	2	4	no	—
304	C₈×D₆₇	—	2	8	no	—
305	C₈×D₆₇	—	2	8	no	—
306	C₈×D₆₇	C₂×D₄	1	8	yes	—
307	C₄⋊Dic₆₇	—	2	1	no	—
308	Dic₆₇⋊C₄	—	2	2	no	—
309	C₂²⋊Dic₆₇	—	2	1	no	—
310	(C₂×D₆₇)⋊C₄	—	2	2	no	—
311	C₄×Dic₆₇	—	2	2	no	—
312	C₄×Dic₆₇	C₂⁴	1	2	yes	—
313	#41×C₆₇	—	2	2	no	—
314	#41×C₆₇	—	2	2	no	—
315	#41×C₆₇	C₂²×C₄	1	4	yes	—
316	#41×C₆₇	C₂⁴	1	4	yes	—
317	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
318	C₂×D₄×C₆₇	—	2	2	no	—
319	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
320	C₂²×C₄×C₆₇	—	2	2	no	—
321	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	Q₁₆×C₆₇	C₂²×C₄	1	2	yes	—
323	Q₁₆×C₆₇	C₂²×C₄	1	2	yes	—
324	SD₁₆×C₆₇	C₂²×C₄	1	4	yes	—
325	SD₁₆×C₆₇	C₂²×C₄	1	4	yes	—
326	D₈×C₆₇	C₂²×C₄	1	2	yes	—
327	D₈×C₆₇	C₂²×C₄	1	2	yes	—
328	M₁₆×C₆₇	—	2	2	no	—
329	M₁₆×C₆₇	—	2	8	no	—
330	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
331	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
332	M₁₆×C₆₇	C₂⁴	1	4	yes	—
333	C₂×C₈×C₆₇	—	2	2	no	—
334	C₂×C₈×C₆₇	—	2	8	no	—
335	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
336	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
337	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
338	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
339	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
340	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
341	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₆₇	—	2	1	no	—
343	C₂²⋊C₄×C₆₇	—	2	1	no	—
344	C₄²×C₆₇	C₂⁴	1	2	yes	—
345	C₂³×C₆₇	—	2	2	no	—
346	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
347	C₂²×D₆₇	—	2	2	no	—
348	C₂²×D₆₇	—	2	4	no	—
349	C₂²×D₆₇	—	2	4	no	—
350	C₂²×D₆₇	—	8	1	no	—
351	C₂²×D₆₇	—	8	4	no	—
352	C₂²×D₆₇	C₄×D₄	1	2	yes	—
353	C₂²×D₆₇	C₄×D₄	1	2	yes	—
354	C₂²×D₆₇	C₂×#41	1	1	yes	characteristic
355	C₂²×D₆₇	C₂×#41	1	1	yes	characteristic
356	Q₈×C₆₇	—	2	2	no	—
357	Q₈×C₆₇	C₂³×C₄	1	4	yes	—
358	D₄×C₆₇	—	2	4	no	—
359	D₄×C₆₇	—	2	4	no	—
360	D₄×C₆₇	—	2	2	no	—
361	D₄×C₆₇	C₂³×C₄	1	4	yes	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	4	no	—
364	C₂×C₄×C₆₇	—	2	4	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
367	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
368	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
371	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
372	C₂²⋊D₆₇	—	2	4	no	—
373	C₂²⋊D₆₇	—	2	4	no	—
374	C₂²⋊D₆₇	—	2	4	no	—
375	C₂²⋊D₆₇	—	2	4	no	—
376	C₂²⋊D₆₇	—	2	4	no	—
377	C₂²⋊D₆₇	—	2	4	no	—
378	C₂×Dic₆₇	—	2	2	no	—
379	C₂×Dic₆₇	—	2	4	no	—
380	C₂×Dic₆₇	—	2	4	no	—
381	C₂×Dic₆₇	—	2	2	no	—
382	C₂×Dic₆₇	C₄×D₄	1	2	yes	—
383	C₂×Dic₆₇	C₄×D₄	1	2	yes	—
384	C₂×Dic₆₇	C₂×#41	1	1	yes	characteristic
385	C₂×Dic₆₇	C₂×#41	1	1	yes	characteristic
386	D₂₆₈	—	2	4	no	—
387	D₂₆₈	—	2	4	no	—
388	D₂₆₈	—	2	2	no	—
389	D₂₆₈	C₂³×C₄	1	4	yes	—
390	C₄×D₆₇	—	2	4	no	—
391	C₄×D₆₇	—	2	4	no	—
392	C₄×D₆₇	—	2	4	no	—
393	C₄×D₆₇	—	2	4	no	—
394	C₄×D₆₇	—	2	4	no	—
395	C₄×D₆₇	—	2	4	no	—
396	C₄×D₆₇	—	8	2	no	—
397	C₄×D₆₇	C₄×D₄	1	2	yes	—
398	C₄×D₆₇	C₄×D₄	1	2	yes	—
399	C₄×D₆₇	C₄×D₄	1	2	yes	—
400	C₄×D₆₇	C₄×D₄	1	2	yes	—
401	C₄×D₆₇	C₂³×C₄	1	2	yes	—
402	C₄×D₆₇	C₂³×C₄	1	2	yes	—
403	C₄×D₆₇	C₂²×D₄	1	2	yes	—
404	C₄×D₆₇	C₂²×D₄	1	2	yes	—
405	Dic₁₃₄	—	2	2	no	—
406	Dic₁₃₄	—	2	4	no	—
407	Dic₁₃₄	—	2	4	no	—
408	Dic₁₃₄	C₂³×C₄	1	4	yes	—
409	C₈×C₆₇	—	2	4	no	—
410	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
411	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
412	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
413	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
414	C₈×C₆₇	C₂²×D₄	1	4	yes	—
415	C₆₇⋊C₈	—	2	4	no	—
416	C₆₇⋊C₈	C₂³×C₄	1	2	yes	—
417	C₆₇⋊C₈	C₂³×C₄	1	2	yes	—
418	C₆₇⋊C₈	C₂²×D₄	1	4	yes	—
419	C₂²×C₆₇	—	2	4	no	—
420	C₂²×C₆₇	—	4	1	no	—
421	C₂²×C₆₇	—	8	2	no	—
422	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
423	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
424	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
425	C₂×D₆₇	—	2	4	no	—
426	C₂×D₆₇	—	4	1	no	—
427	C₂×D₆₇	—	4	2	no	—
428	C₂×D₆₇	—	4	2	no	—
429	C₂×D₆₇	—	4	1	no	—
430	C₂×D₆₇	—	4	8	no	—
431	C₂×D₆₇	—	8	4	no	—
432	C₂×D₆₇	—	8	2	no	—
433	C₂×D₆₇	C₂×C₄×D₄	1	2	yes	—
434	C₂×D₆₇	C₂×C₄×D₄	1	2	yes	—
435	C₄×C₆₇	—	2	4	no	—
436	C₄×C₆₇	—	4	2	no	—
437	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
438	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
439	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
440	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
441	Dic₆₇	—	2	4	no	—
442	Dic₆₇	—	4	2	no	—
443	Dic₆₇	C₂×C₄×D₄	1	2	yes	—
444	Dic₆₇	C₂×C₄×D₄	1	2	yes	—
445	#60182	—	67	1	no	maximal, Sylow
446	C₂×C₆₇	—	2	1	no	—
447	C₂×C₆₇	—	2	1	no	—
448	C₂×C₆₇	—	2	1	no	—
449	C₂×C₆₇	—	4	4	no	—
450	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
451	D₆₇	—	2	2	no	—
452	D₆₇	—	2	2	no	—
453	D₆₇	—	4	4	no	—
454	C₂×#575	—	67	1	no	—
455	C₂×#568	—	67	2	no	—
456	#2957	—	67	1	no	—
457	#2957	—	67	2	no	—
458	#2957	—	67	1	no	—
459	#2957	—	67	1	no	—
460	#2957	—	67	2	no	—
461	#2957	D₆₇	1	1	yes	characteristic, complemented
462	#2956	—	67	4	no	—
463	#2956	—	67	4	no	—
464	#2955	—	67	4	no	—
465	#2955	—	67	4	no	—
466	C₂×#430	—	67	1	no	—
467	C₂×#421	—	67	2	no	—
468	#2873	—	67	1	no	—
469	C₆₇	#60182	1	1	yes	characteristic, complemented, Sylow
470	C₂²×#41	—	67	2	no	—
471	#575	—	67	4	no	—
472	#575	—	67	4	no	—
473	#575	—	67	2	no	—
474	#575	—	67	2	no	—
475	#575	—	67	2	no	—
476	#575	—	67	2	no	—
477	C₂×#137	—	67	2	no	—
478	C₂×#137	—	67	2	no	—
479	C₂×AGL(1,ℤ/8)	—	67	2	no	—
480	C₂×AGL(1,ℤ/8)	—	67	2	no	—
481	C₂×#135	—	67	2	no	—
482	C₂×#135	—	67	1	no	—
483	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
484	#568	—	67	2	no	—
485	#568	—	67	8	no	—
486	#568	—	67	2	no	—
487	#568	—	67	2	no	—
488	#568	—	134	4	no	—
489	#568	—	134	4	no	—
490	#568	C₂×D₆₇	1	2	yes	complemented
491	C₂×#131	—	67	8	no	—
492	C₂×#131	—	134	4	no	—
493	C₂²×M₁₆	—	67	1	no	—
494	C₂²×M₁₆	—	67	1	no	—
495	C₂²×M₁₆	—	67	2	no	—
496	C₂²×M₁₆	—	134	4	no	—
497	C₂×#117	—	67	1	no	—
498	#444	—	67	4	no	—
499	#444	—	67	8	no	—
500	#444	—	67	4	no	—
501	#444	—	67	8	no	—
502	#444	—	67	4	no	—
503	#444	C₂×D₆₇	1	4	yes	complemented
504	#443	—	67	4	no	—
505	#443	—	67	8	no	—
506	#443	—	67	4	no	—
507	#443	—	67	8	no	—
508	#443	—	67	4	no	—
509	#443	C₂×D₆₇	1	4	yes	complemented
510	#430	—	67	2	no	—
511	#430	—	67	2	no	—
512	#430	—	67	2	no	—
513	#430	—	67	2	no	—
514	C₂×#108	—	67	2	no	—
515	C₂×#108	—	67	1	no	—
516	C₂×#108	C₂×D₆₇	1	1	yes	characteristic, complemented
517	#421	—	67	2	no	—
518	#421	—	67	2	no	—
519	#421	—	67	2	no	—
520	#421	—	67	8	no	—
521	#421	C₂×D₆₇	1	2	yes	complemented
522	C₂×#104	—	67	8	no	—
523	#405	—	67	1	no	—
524	#405	—	67	1	no	—
525	#405	—	67	1	no	—
526	#405	—	67	2	no	—
527	#405	—	67	2	no	—
528	#405	C₂×D₆₇	1	1	yes	characteristic, complemented
529	C₄×M₁₆	—	67	2	no	—
530	C₄×M₁₆	—	67	2	no	—
531	C₂×#41	—	67	4	no	—
532	C₂×#41	—	67	4	no	—
533	C₂×#41	—	67	4	no	—
534	C₂×#41	—	67	4	no	—
535	C₂×#41	—	67	2	no	—
536	C₂×#41	—	67	2	no	—
537	C₂×#41	—	67	2	no	—
538	C₂×#41	—	134	2	no	—
539	C₂×#41	—	134	2	no	—
540	C₂×#41	—	134	2	no	—
541	C₂×#41	—	134	2	no	—
542	C₂×#41	—	134	2	no	—
543	C₂×#41	—	134	2	no	—
544	C₂×#41	C₂²×D₆₇	1	2	yes	—
545	C₂²×Q₈	—	67	2	no	—
546	C₂²×D₄	—	67	2	no	—
547	C₂²×D₄	—	134	2	no	—
548	C₂³×C₄	—	67	1	no	—
549	C₂³×C₄	—	134	2	no	—
550	#137	—	67	4	no	—
551	#137	—	67	4	no	—
552	#137	—	67	4	no	—
553	#137	—	67	4	no	—
554	#137	—	67	4	no	—
555	#137	—	67	4	no	—
556	#137	—	67	4	no	—
557	#137	—	67	4	no	—
558	AGL(1,ℤ/8)	—	67	4	no	—
559	AGL(1,ℤ/8)	—	67	4	no	—
560	AGL(1,ℤ/8)	—	67	4	no	—
561	AGL(1,ℤ/8)	—	67	4	no	—
562	AGL(1,ℤ/8)	—	67	4	no	—
563	AGL(1,ℤ/8)	—	67	4	no	—
564	AGL(1,ℤ/8)	—	67	4	no	—
565	AGL(1,ℤ/8)	—	67	4	no	—
566	#135	—	67	4	no	—
567	#135	—	67	4	no	—
568	#135	—	67	4	no	—
569	#135	—	67	4	no	—
570	#135	—	67	2	no	—
571	#135	—	67	2	no	—
572	#135	—	67	2	no	—
573	#135	—	67	2	no	—
574	#135	C₄×D₆₇	1	2	yes	complemented
575	#135	C₄×D₆₇	1	2	yes	complemented
576	#135	C₂²×D₆₇	1	2	yes	—
577	#135	C₂²×D₆₇	1	2	yes	—
578	C₂×Q₁₆	—	67	2	no	—
579	C₂×Q₁₆	—	67	1	no	—
580	C₂×Q₁₆	C₄×D₆₇	1	1	yes	characteristic, complemented
581	C₂×SD₁₆	—	67	2	no	—
582	C₂×SD₁₆	—	67	2	no	—
583	C₂×SD₁₆	—	67	2	no	—
584	C₂×SD₁₆	C₄×D₆₇	1	2	yes	complemented
585	C₂×D₈	—	67	2	no	—
586	C₂×D₈	—	67	1	no	—
587	C₂×D₈	C₄×D₆₇	1	1	yes	characteristic, complemented
588	#131	—	2	4	no	—
589	#131	—	67	8	no	—
590	#131	—	67	8	no	—
591	#131	—	67	8	no	—
592	#131	—	134	8	no	—
593	#131	—	134	4	no	—
594	#131	—	134	8	no	—
595	#131	—	134	8	no	—
596	#131	—	134	8	no	—
597	#131	—	134	4	no	—
598	#131	—	134	4	no	—
599	#131	C₂²×D₆₇	1	8	yes	complemented
600	C₂×M₁₆	—	2	4	no	—
601	C₂×M₁₆	—	67	1	no	—
602	C₂×M₁₆	—	67	4	no	—
603	C₂×M₁₆	—	67	4	no	—
604	C₂×M₁₆	—	67	2	no	—
605	C₂×M₁₆	—	67	2	no	—
606	C₂×M₁₆	—	67	2	no	—
607	C₂×M₁₆	—	67	2	no	—
608	C₂×M₁₆	—	67	2	no	—
609	C₂×M₁₆	—	67	1	no	—
610	C₂×M₁₆	—	67	1	no	—
611	C₂×M₁₆	—	67	1	no	—
612	C₂×M₁₆	—	67	1	no	—
613	C₂×M₁₆	—	67	2	no	—
614	C₂×M₁₆	—	67	4	no	—
615	C₂×M₁₆	—	67	4	no	—
616	C₂×M₁₆	—	134	8	no	—
617	C₂×M₁₆	—	134	2	no	—
618	C₂×M₁₆	—	134	8	no	—
619	C₂×M₁₆	—	134	4	no	—
620	C₂×M₁₆	—	134	8	no	—
621	C₂×M₁₆	—	134	2	no	—
622	C₂×M₁₆	—	134	2	no	—
623	C₂×M₁₆	—	134	4	no	—
624	C₂×M₁₆	—	134	4	no	—
625	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
626	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
627	C₂²×C₈	—	67	1	no	—
628	C₂²×C₈	—	67	2	no	—
629	C₂²×C₈	—	134	8	no	—
630	C₂²×C₈	—	134	2	no	—
631	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
632	#117	—	67	1	no	—
633	#117	—	67	2	no	—
634	#117	—	134	1	no	—
635	#117	—	134	1	no	—
636	#117	C₂²×D₆₇	1	1	yes	characteristic
637	C₂×C₄⋊C₄	—	134	1	no	—
638	C₂×C₂²⋊C₄	—	134	1	no	—
639	C₂×C₄²	—	67	2	no	—
640	#108	—	67	4	no	—
641	#108	—	67	4	no	—
642	#108	—	67	2	no	—
643	#108	—	67	2	no	—
644	#108	C₂²×D₆₇	1	2	yes	complemented
645	#108	C₂²×D₆₇	1	2	yes	complemented
646	#104	—	67	8	no	—
647	#104	—	67	8	no	—
648	#104	—	67	8	no	—
649	#104	C₂²×D₆₇	1	8	yes	complemented
650	#97	—	67	2	no	—
651	#97	—	67	2	no	—
652	#97	—	67	2	no	—
653	#97	C₂²×D₆₇	1	2	yes	complemented
654	C₄×C₈	—	67	2	no	—
655	C₄×C₈	—	67	2	no	—
656	C₄×C₈	—	67	2	no	—
657	C₄×C₈	C₂²×D₆₇	1	2	yes	complemented
658	C₂⁴	—	67	1	no	—
659	C₂⁴	—	134	2	no	—
660	#41	—	2	2	no	—
661	#41	—	2	2	no	—
662	#41	—	67	4	no	—
663	#41	—	67	4	no	—
664	#41	—	67	4	no	—
665	#41	—	67	4	no	—
666	#41	—	67	4	no	—
667	#41	—	67	4	no	—
668	#41	—	134	4	no	—
669	#41	—	134	4	no	—
670	#41	—	134	4	no	—
671	#41	—	134	4	no	—
672	#41	—	134	4	no	—
673	#41	—	134	4	no	—
674	#41	—	134	4	no	—
675	#41	—	134	4	no	—
676	#41	—	134	2	no	—
677	#41	—	134	2	no	—
678	#41	—	134	2	no	—
679	#41	—	134	2	no	—
680	#41	—	134	2	no	—
681	#41	—	134	2	no	—
682	#41	C₂×C₄×D₆₇	1	4	yes	—
683	#41	C₂³×D₆₇	1	4	yes	—
684	C₂×Q₈	—	67	4	no	—
685	C₂×Q₈	—	67	4	no	—
686	C₂×Q₈	—	67	2	no	—
687	C₂×Q₈	—	134	2	no	—
688	C₂×Q₈	—	134	2	no	—
689	C₂×Q₈	—	134	2	no	—
690	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	67	4	no	—
693	C₂×D₄	—	67	4	no	—
694	C₂×D₄	—	67	2	no	—
695	C₂×D₄	—	134	2	no	—
696	C₂×D₄	—	134	2	no	—
697	C₂×D₄	—	134	2	no	—
698	C₂×D₄	—	134	2	no	—
699	C₂×D₄	—	134	4	no	—
700	C₂×D₄	—	134	4	no	—
701	C₂×D₄	—	134	4	no	—
702	C₂×D₄	—	134	4	no	—
703	C₂×D₄	—	134	2	no	—
704	C₂×D₄	—	134	2	no	—
705	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	67	1	no	—
708	C₂²×C₄	—	67	2	no	—
709	C₂²×C₄	—	67	2	no	—
710	C₂²×C₄	—	67	2	no	—
711	C₂²×C₄	—	67	2	no	—
712	C₂²×C₄	—	67	1	no	—
713	C₂²×C₄	—	67	1	no	—
714	C₂²×C₄	—	67	1	no	—
715	C₂²×C₄	—	67	1	no	—
716	C₂²×C₄	—	134	2	no	—
717	C₂²×C₄	—	134	4	no	—
718	C₂²×C₄	—	134	4	no	—
719	C₂²×C₄	—	134	2	no	—
720	C₂²×C₄	—	134	4	no	—
721	C₂²×C₄	—	134	4	no	—
722	C₂²×C₄	—	134	2	no	—
723	C₂²×C₄	—	134	2	no	—
724	C₂²×C₄	—	134	2	no	—
725	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
726	Q₁₆	—	67	4	no	—
727	Q₁₆	—	67	4	no	—
728	Q₁₆	—	67	2	no	—
729	Q₁₆	—	67	2	no	—
730	Q₁₆	C₂×C₄×D₆₇	1	2	yes	—
731	Q₁₆	C₂×C₄×D₆₇	1	2	yes	—
732	SD₁₆	—	67	4	no	—
733	SD₁₆	—	67	4	no	—
734	SD₁₆	—	67	4	no	—
735	SD₁₆	—	67	4	no	—
736	SD₁₆	—	67	4	no	—
737	SD₁₆	—	67	4	no	—
738	SD₁₆	C₂×C₄×D₆₇	1	4	yes	—
739	SD₁₆	C₂×C₄×D₆₇	1	4	yes	—
740	D₈	—	67	4	no	—
741	D₈	—	67	4	no	—
742	D₈	—	67	2	no	—
743	D₈	—	67	2	no	—
744	D₈	C₂×C₄×D₆₇	1	2	yes	—
745	D₈	C₂×C₄×D₆₇	1	2	yes	—
746	M₁₆	—	2	2	no	—
747	M₁₆	—	2	8	no	—
748	M₁₆	—	67	2	no	—
749	M₁₆	—	67	2	no	—
750	M₁₆	—	67	2	no	—
751	M₁₆	—	67	2	no	—
752	M₁₆	—	67	2	no	—
753	M₁₆	—	67	2	no	—
754	M₁₆	—	67	2	no	—
755	M₁₆	—	67	2	no	—
756	M₁₆	—	67	2	no	—
757	M₁₆	—	67	2	no	—
758	M₁₆	—	67	8	no	—
759	M₁₆	—	67	4	no	—
760	M₁₆	—	134	8	no	—
761	M₁₆	—	134	4	no	—
762	M₁₆	—	134	4	no	—
763	M₁₆	—	134	8	no	—
764	M₁₆	—	134	2	no	—
765	M₁₆	—	134	8	no	—
766	M₁₆	D₄×D₆₇	1	2	yes	—
767	M₁₆	D₄×D₆₇	1	2	yes	—
768	M₁₆	C₂³×D₆₇	1	4	yes	—
769	C₂×C₈	—	2	2	no	—
770	C₂×C₈	—	2	8	no	—
771	C₂×C₈	—	67	2	no	—
772	C₂×C₈	—	67	2	no	—
773	C₂×C₈	—	67	1	no	—
774	C₂×C₈	—	67	1	no	—
775	C₂×C₈	—	67	2	no	—
776	C₂×C₈	—	67	8	no	—
777	C₂×C₈	—	134	8	no	—
778	C₂×C₈	—	134	4	no	—
779	C₂×C₈	—	134	4	no	—
780	C₂×C₈	—	134	8	no	—
781	C₂×C₈	—	134	2	no	—
782	C₂×C₈	—	134	8	no	—
783	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
784	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
785	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
786	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
787	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
788	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
789	C₂×C₈	C₂³×D₆₇	1	2	yes	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	134	2	no	—
792	C₄⋊C₄	—	134	1	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	—	134	2	no	—
795	C₂²⋊C₄	—	134	1	no	—
796	C₄²	—	67	2	no	—
797	C₄²	—	134	2	no	—
798	C₄²	C₂³×D₆₇	1	2	yes	—
799	C₂³	—	2	2	no	—
800	C₂³	—	536	1	no	—
801	C₂³	—	536	4	no	—
802	C₂³	—	67	2	no	—
803	C₂³	—	67	2	no	—
804	C₂³	—	67	1	no	—
805	C₂³	—	67	1	no	—
806	C₂³	—	134	4	no	—
807	C₂³	—	134	4	no	—
808	C₂³	—	134	2	no	—
809	C₂³	#41×D₆₇	1	1	yes	characteristic
810	Q₈	—	2	2	no	—
811	Q₈	—	67	4	no	—
812	Q₈	—	134	4	no	—
813	Q₈	—	134	4	no	—
814	Q₈	—	134	2	no	—
815	Q₈	C₂²×C₄×D₆₇	1	4	yes	—
816	D₄	—	2	4	no	—
817	D₄	—	2	4	no	—
818	D₄	—	2	2	no	—
819	D₄	—	67	4	no	—
820	D₄	—	134	4	no	—
821	D₄	—	134	4	no	—
822	D₄	—	134	4	no	—
823	D₄	—	134	4	no	—
824	D₄	—	134	4	no	—
825	D₄	—	134	4	no	—
826	D₄	—	134	4	no	—
827	D₄	—	134	4	no	—
828	D₄	—	134	2	no	—
829	D₄	C₂²×C₄×D₆₇	1	4	yes	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	536	2	no	—
835	C₂×C₄	—	67	2	no	—
836	C₂×C₄	—	67	2	no	—
837	C₂×C₄	—	67	1	no	—
838	C₂×C₄	—	67	1	no	—
839	C₂×C₄	—	67	2	no	—
840	C₂×C₄	—	67	2	no	—
841	C₂×C₄	—	67	2	no	—
842	C₂×C₄	—	67	2	no	—
843	C₂×C₄	—	67	2	no	—
844	C₂×C₄	—	67	2	no	—
845	C₂×C₄	—	67	2	no	—
846	C₂×C₄	—	67	2	no	—
847	C₂×C₄	—	134	4	no	—
848	C₂×C₄	—	134	4	no	—
849	C₂×C₄	—	134	4	no	—
850	C₂×C₄	—	134	4	no	—
851	C₂×C₄	—	134	2	no	—
852	C₂×C₄	—	134	4	no	—
853	C₂×C₄	—	134	4	no	—
854	C₂×C₄	—	134	2	no	—
855	C₂×C₄	—	134	4	no	—
856	C₂×C₄	—	134	4	no	—
857	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
858	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
859	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
860	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
861	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
862	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
863	C₈	—	2	4	no	—
864	C₈	—	67	2	no	—
865	C₈	—	67	2	no	—
866	C₈	—	67	4	no	—
867	C₈	—	134	4	no	—
868	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
869	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
870	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
871	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
872	C₈	C₂×D₄×D₆₇	1	4	yes	—
873	C₂²	—	2	4	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	8	2	no	—
876	C₂²	—	268	1	no	—
877	C₂²	—	268	2	no	—
878	C₂²	—	268	1	no	—
879	C₂²	—	268	2	no	—
880	C₂²	—	268	8	no	—
881	C₂²	—	536	2	no	—
882	C₂²	—	536	4	no	—
883	C₂²	—	67	2	no	—
884	C₂²	—	67	2	no	—
885	C₂²	—	134	4	no	—
886	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
887	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
888	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
889	C₄	—	2	4	no	—
890	C₄	—	4	2	no	—
891	C₄	—	268	2	no	—
892	C₄	—	67	2	no	—
893	C₄	—	67	2	no	—
894	C₄	—	134	4	no	—
895	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
896	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
897	C₄	C₂³×C₄×D₆₇	1	1	yes	characteristic
898	C₄	C₂²×D₄×D₆₇	1	1	yes	characteristic
899	C₂	—	2	1	no	—
900	C₂	—	2	1	no	—
901	C₂	—	2	1	no	—
902	C₂	—	4	4	no	—
903	C₂	—	268	4	no	—
904	C₂	—	134	2	no	—
905	C₂	—	134	2	no	—
906	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×#16864193	C₂
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	#2957	D₆₇
hypocenter	C₆₇	#60182
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. #22569122	C₂	semidirect
8. #22569117	C₂	semidirect
9. #22569114	C₂	semidirect
10. #22569109	C₂	semidirect
11. #22569107	C₂	semidirect
12. C₂×#16863443	C₂	semidirect
13. #421×D₆₇	C₂	semidirect
14. #22568625	C₂	semidirect
15. C₆₇×#2957	C₂	semidirect
17. #16864193	C₄	semidirect
18. #16864193	C₄	semidirect
23. C₂×#14524075	C₄	semidirect
24. C₂×#14524072	C₄	semidirect
25. C₂×#14524070	C₄	semidirect
26. C₂×#14524067	C₄	semidirect
29. #16864163	C₂²	semidirect
31. #16864162	C₂²	semidirect
32. #16864162	C₂²	semidirect
34. #16864161	C₂²	semidirect
36. #131×D₆₇	C₂²	semidirect
42. #16863519	C₂²	semidirect
43. #16863518	C₂²	semidirect
44. #16863517	C₂²	semidirect
45. #16863516	C₂²	semidirect
46. #16863515	C₂²	semidirect
47. #16863514	C₂²	semidirect
48. #16863513	C₂²	semidirect
49. #16863512	C₂²	semidirect
50. #16863511	C₂²	semidirect
51. #16863510	C₂²	semidirect
52. #16863443	C₂²	semidirect
53. #16863443	C₂²	semidirect
54. #16863443	C₂²	semidirect
55. #16863443	C₂²	semidirect
56. C₂×#14523979	C₂²	semidirect
57. C₂×#14523978	C₂²	semidirect
58. #16863414	C₂²	semidirect
59. #16863413	C₂²	semidirect
60. #16863412	C₂²	semidirect
61. #16863411	C₂²	semidirect
62. #104×D₆₇	C₂²	semidirect
63. #16863354	C₂²	semidirect
64. #16863353	C₂²	semidirect
65. #16863352	C₂²	semidirect
66. #16863351	C₂²	semidirect
67. #16863350	C₂²	semidirect
68. #16863348	C₂²	semidirect
69. C₄×#11761611	C₂²	semidirect
71. #568×C₆₇	C₂²	semidirect
72. #444×C₆₇	C₂²	semidirect
73. #443×C₆₇	C₂²	semidirect
74. C₂×#108×C₆₇	C₂²	semidirect
75. #421×C₆₇	C₂²	semidirect
76. #405×C₆₇	C₂²	semidirect
97. #14524075	C₂×C₄	semidirect
98. #14524075	C₂×C₄	semidirect
101. #14524072	C₂×C₄	semidirect
102. #14524072	C₂×C₄	semidirect
105. #14524070	C₂×C₄	semidirect
106. #14524070	C₂×C₄	semidirect
109. #14524067	C₂×C₄	semidirect
110. #14524067	C₂×C₄	semidirect
111. #14524065	C₂×C₄	semidirect
112. #14524065	C₂×C₄	semidirect
115. #14524063	C₂×C₄	semidirect
116. #14524063	C₂×C₄	semidirect
119. C₂×Dic₂₆₈	C₂×C₄	semidirect
120. C₂×#11761618	C₂×C₄	semidirect
121. C₂×#11761617	C₂×C₄	semidirect
122. C₂×#11761616	C₂×C₄	semidirect
123. C₂×#11761615	C₂×C₄	semidirect
124. C₂×D₅₃₆	C₂×C₄	semidirect
125. C₂×#11761613	C₂×C₄	semidirect
129. #14524051	C₂³	semidirect
131. #14524050	C₂³	semidirect
135. #14524049	C₂³	semidirect
171. #14523979	C₂³	semidirect
172. #14523979	C₂³	semidirect
173. #14523978	C₂³	semidirect
174. #14523978	C₂³	semidirect
175. #14523971	C₂³	semidirect
176. #14523970	C₂³	semidirect
177. #14523969	C₂³	semidirect
178. #14523954	C₂³	semidirect
179. #14523953	C₂³	semidirect
180. #14523953	C₂³	semidirect
181. C₄×C₆₇⋊C₈	C₂³	semidirect
182. C₈×Dic₆₇	C₂³	semidirect
183. C₈×Dic₆₇	C₂³	semidirect
185. #135×C₆₇	C₂×C₄	semidirect
186. #135×C₆₇	C₂×C₄	semidirect
189. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
190. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
191. C₂×D₈×C₆₇	C₂×C₄	semidirect
193. #131×C₆₇	C₂³	semidirect
199. #108×C₆₇	C₂³	semidirect
200. #108×C₆₇	C₂³	semidirect
201. #104×C₆₇	C₂³	semidirect
202. #97×C₆₇	C₂³	semidirect
203. C₄×C₈×C₆₇	C₂³	semidirect
461. #2957	D₆₇	semidirect
469. C₆₇	#60182	semidirect
490. #568	C₂×D₆₇	semidirect
503. #444	C₂×D₆₇	semidirect
509. #443	C₂×D₆₇	semidirect
516. C₂×#108	C₂×D₆₇	semidirect
521. #421	C₂×D₆₇	semidirect
528. #405	C₂×D₆₇	semidirect
574. #135	C₄×D₆₇	semidirect
575. #135	C₄×D₆₇	semidirect
580. C₂×Q₁₆	C₄×D₆₇	semidirect
584. C₂×SD₁₆	C₄×D₆₇	semidirect
587. C₂×D₈	C₄×D₆₇	semidirect
599. #131	C₂²×D₆₇	semidirect
644. #108	C₂²×D₆₇	semidirect
645. #108	C₂²×D₆₇	semidirect
649. #104	C₂²×D₆₇	semidirect
653. #97	C₂²×D₆₇	semidirect
657. 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×#16864193	2
#568×D₆₇	2
#22569127	2
#22569126	2
#22569125	2
#22569124	2
#22569122	2
#22569117	2
#22569114	2
#22569109	2
#22569107	2
C₂×#16863443	2
#421×D₆₇	2
#22568625	2
C₆₇×#2957	2
#60182	67