Subgroups — #30861693

Order 17152.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16864163	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863513	C₂	1	1	yes	maximal, characteristic, complemented
4	#22568913	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560538	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560538	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560512	C₂	1	1	yes	maximal, characteristic, complemented
8	#22560486	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560486	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560416	C₂	1	1	yes	maximal, characteristic, complemented
11	#22560153	C₂	1	1	yes	maximal, characteristic, complemented
12	#22560056	C₂	1	1	yes	maximal, characteristic, complemented
13	#22560049	C₂	1	1	yes	maximal, characteristic, complemented
14	#22559995	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3002	C₂	1	1	yes	maximal, characteristic
16	#16864163	—	2	4	no	—
17	#16864163	—	2	4	no	—
18	C₂×#14524050	—	2	1	no	—
19	C₂×#14524050	—	2	1	no	—
20	C₂×#14524050	C₂²	1	1	yes	characteristic
21	C₂×#14524050	C₂²	1	1	yes	characteristic
22	C₂×#14524050	C₂²	1	1	yes	characteristic
23	C₂×#14524050	C₂²	1	1	yes	characteristic
24	C₂×#14524050	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#11761612	—	2	1	no	—
26	C₂²×#11761612	—	2	1	no	—
27	C₂²×#11761612	C₂²	1	1	yes	characteristic
28	C₂²×#11761612	C₂²	1	1	yes	characteristic
29	#16863518	—	2	4	no	—
30	#16863513	—	2	4	no	—
31	#16863474	—	2	1	no	—
32	#16863474	—	2	1	no	—
33	#16863468	—	2	1	no	—
34	#16863468	—	2	1	no	—
35	C₂×#14523979	C₂²	1	1	yes	characteristic, complemented
36	C₂×#14523979	C₂²	1	1	yes	characteristic, complemented
37	#16863423	C₂²	1	1	yes	characteristic, complemented
38	C₂×#14523970	C₂²	1	1	yes	characteristic
39	C₂×#14523970	C₂²	1	1	yes	characteristic
40	C₂×#14523970	C₂²	1	1	yes	characteristic
41	C₂×#14523970	C₂²	1	1	yes	characteristic
42	C₂×#14523970	C₂²	1	1	yes	characteristic, complemented
43	C₂×#14523970	C₂²	1	1	yes	characteristic, complemented
44	#16863363	C₂²	1	1	yes	characteristic, complemented
45	#16863360	C₂²	1	1	yes	characteristic
46	#16863352	C₂²	1	1	yes	characteristic, complemented
47	C₂×#14523953	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
49	C₄×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
50	#16863161	C₂²	1	1	yes	characteristic, complemented
51	#16863161	C₂²	1	1	yes	characteristic, complemented
52	#16863155	C₂²	1	1	yes	characteristic, complemented
53	#16863155	C₂²	1	1	yes	characteristic, complemented
54	#16863150	C₂²	1	1	yes	characteristic, complemented
55	#16863150	C₂²	1	1	yes	characteristic, complemented
56	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
57	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
59	#525×C₆₇	C₂²	1	1	yes	characteristic
60	#452×C₆₇	C₄	1	1	yes	characteristic, complemented
61	#452×C₆₇	C₄	1	1	yes	characteristic, complemented
62	#451×C₆₇	C₄	1	1	yes	characteristic, complemented
63	#450×C₆₇	C₄	1	1	yes	characteristic, complemented
64	#449×C₆₇	C₄	1	1	yes	characteristic, complemented
65	#449×C₆₇	C₄	1	1	yes	characteristic, complemented
66	#448×C₆₇	C₄	1	1	yes	characteristic, complemented
67	#447×C₆₇	C₄	1	1	yes	characteristic, complemented
68	#416×C₆₇	C₂²	1	1	yes	characteristic
69	#416×C₆₇	C₂²	1	1	yes	characteristic
70	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
71	#14524050	—	2	8	no	—
72	#14524050	—	2	8	no	—
73	#14524050	—	2	2	no	—
74	#14524050	—	2	2	no	—
75	#14524050	—	2	2	no	—
76	#14524050	—	2	2	no	—
77	#14524050	—	2	2	no	—
78	#14524050	—	2	2	no	—
79	#14524050	—	2	2	no	—
80	#14524050	—	2	2	no	—
81	#14524050	D₄	1	4	yes	complemented
82	#14524050	D₄	1	4	yes	complemented
83	C₂×#11761612	—	2	8	no	—
84	C₂×#11761612	—	2	8	no	—
85	C₂×#11761612	—	2	2	no	—
86	C₂×#11761612	—	2	2	no	—
87	C₂×#11761612	—	2	1	no	—
88	C₂×#11761612	—	2	1	no	—
89	C₂×#11761612	—	2	1	no	—
90	C₂×#11761612	—	2	1	no	—
91	C₂×#11761612	—	2	2	no	—
92	C₂×#11761612	—	2	2	no	—
93	C₂×#11761612	—	2	1	no	—
94	C₂×#11761612	—	2	1	no	—
95	C₂×#11761612	D₄	1	1	yes	characteristic
96	C₂×#11761612	D₄	1	1	yes	characteristic
97	C₂×#11761612	D₄	1	1	yes	characteristic
98	C₂×#11761612	D₄	1	1	yes	characteristic
99	C₂×#11761612	C₂³	1	1	yes	characteristic
100	C₂×#11761612	C₂³	1	1	yes	characteristic
101	C₂×#11761612	C₂³	1	1	yes	characteristic
102	C₂×#11761612	C₂³	1	1	yes	characteristic
103	C₂²×C₆₇⋊C₈	—	2	1	no	—
104	C₂²×C₆₇⋊C₈	—	2	1	no	—
105	C₂²×C₆₇⋊C₈	—	2	1	no	—
106	C₂²×C₆₇⋊C₈	—	2	1	no	—
107	C₂²×C₆₇⋊C₈	—	2	1	no	—
108	C₂²×C₆₇⋊C₈	—	2	1	no	—
109	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
110	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
112	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
114	#14523979	—	2	2	no	—
115	#14523979	—	2	2	no	—
116	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
117	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
118	#14523970	—	2	2	no	—
119	#14523970	—	2	2	no	—
120	#14523970	—	2	2	no	—
121	#14523970	—	2	2	no	—
122	#14523970	—	2	2	no	—
123	#14523970	—	2	2	no	—
124	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
125	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
126	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
127	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
128	#14523954	—	2	1	no	—
129	#14523953	—	2	2	no	—
130	C₄×C₆₇⋊C₈	—	2	1	no	—
131	C₈×Dic₆₇	—	2	2	no	—
132	C₆₇⋊#95	—	2	1	no	—
133	C₂×#41×C₆₇	—	2	2	no	—
134	C₂×#41×C₆₇	—	2	2	no	—
135	C₂×#41×C₆₇	—	2	2	no	—
136	C₂×#41×C₆₇	—	2	2	no	—
137	C₂×#41×C₆₇	—	2	1	no	—
138	C₂×#41×C₆₇	—	2	1	no	—
139	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
140	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
145	C₂²×D₄×C₆₇	—	2	1	no	—
146	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
147	C₂³×C₄×C₆₇	—	2	1	no	—
148	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
149	#135×C₆₇	—	2	2	no	—
150	#135×C₆₇	—	2	2	no	—
151	#135×C₆₇	—	2	2	no	—
152	#135×C₆₇	—	2	2	no	—
153	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
154	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
155	C₂×SD₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
156	C₂×SD₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
157	C₂×SD₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
158	C₂×SD₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
159	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
160	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
161	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
163	#123×C₆₇	—	2	1	no	—
164	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
165	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
166	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
167	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
168	#120×C₆₇	—	2	1	no	—
169	C₄×D₄×C₆₇	—	2	1	no	—
170	C₄×D₄×C₆₇	—	2	1	no	—
171	#117×C₆₇	C₂³	1	1	yes	characteristic
172	#103×C₆₇	C₂×C₄	1	1	yes	characteristic
173	#103×C₆₇	C₂×C₄	1	1	yes	characteristic
174	#103×C₆₇	C₂×C₄	1	1	yes	characteristic
175	#103×C₆₇	C₂×C₄	1	1	yes	characteristic
176	#102×C₆₇	C₂×C₄	1	1	yes	characteristic
177	#102×C₆₇	C₂×C₄	1	1	yes	characteristic
178	#102×C₆₇	C₂×C₄	1	1	yes	characteristic
179	#102×C₆₇	C₂×C₄	1	1	yes	characteristic
180	C₂²⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
181	C₂²⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
182	C₂²⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
183	C₂²⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
184	C₂²×Dic₆₇	—	2	1	no	—
185	C₂²×Dic₆₇	—	2	1	no	—
186	#11761612	—	2	4	no	—
187	#11761612	—	2	4	no	—
188	#11761612	—	2	4	no	—
189	#11761612	—	2	1	no	—
190	#11761612	—	2	1	no	—
191	#11761612	—	2	2	no	—
192	#11761612	—	2	2	no	—
193	#11761612	—	2	4	no	—
194	#11761612	—	2	4	no	—
195	#11761612	—	2	2	no	—
196	#11761612	—	2	2	no	—
197	#11761612	—	2	1	no	—
198	#11761612	—	2	1	no	—
199	#11761612	—	2	1	no	—
200	#11761612	—	2	1	no	—
201	#11761612	—	4	2	no	—
202	#11761612	C₂×D₄	1	2	yes	—
203	#11761612	C₂×D₄	1	2	yes	—
204	C₂×C₆₇⋊C₈	—	2	4	no	—
205	C₂×C₆₇⋊C₈	—	2	4	no	—
206	C₂×C₆₇⋊C₈	—	2	4	no	—
207	C₂×C₆₇⋊C₈	—	2	1	no	—
208	C₂×C₆₇⋊C₈	—	2	1	no	—
209	C₂×C₆₇⋊C₈	—	2	1	no	—
210	C₂×C₆₇⋊C₈	—	2	1	no	—
211	C₂×C₆₇⋊C₈	—	2	4	no	—
212	C₂×C₆₇⋊C₈	—	2	4	no	—
213	C₂×C₆₇⋊C₈	—	2	1	no	—
214	C₂×C₆₇⋊C₈	—	2	1	no	—
215	C₂×C₆₇⋊C₈	—	4	2	no	—
216	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
217	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
218	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
219	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
220	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
221	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
222	C₂²⋊Dic₆₇	—	4	2	no	—
223	C₄×Dic₆₇	—	2	1	no	—
224	C₄×Dic₆₇	—	2	1	no	—
225	C₄×Dic₆₇	—	2	1	no	—
226	C₄×Dic₆₇	—	2	1	no	—
227	C₂⁴×C₆₇	—	2	1	no	—
228	C₂⁴×C₆₇	#41	1	1	yes	characteristic
229	#41×C₆₇	—	2	4	no	—
230	#41×C₆₇	—	2	4	no	—
231	#41×C₆₇	—	2	4	no	—
232	#41×C₆₇	—	2	4	no	—
233	#41×C₆₇	—	2	2	no	—
234	#41×C₆₇	—	2	2	no	—
235	#41×C₆₇	—	2	2	no	—
236	#41×C₆₇	—	2	2	no	—
237	#41×C₆₇	—	2	1	no	—
238	#41×C₆₇	—	2	1	no	—
239	#41×C₆₇	—	2	1	no	—
240	#41×C₆₇	—	2	1	no	—
241	#41×C₆₇	—	2	1	no	—
242	#41×C₆₇	—	2	1	no	—
243	#41×C₆₇	—	2	1	no	—
244	#41×C₆₇	—	2	1	no	—
245	#41×C₆₇	C₂×D₄	1	2	yes	—
246	#41×C₆₇	C₂×D₄	1	2	yes	—
247	#41×C₆₇	#41	1	2	yes	—
248	#41×C₆₇	#41	1	2	yes	—
249	C₂×Q₈×C₆₇	—	2	2	no	—
250	C₂×Q₈×C₆₇	—	2	2	no	—
251	C₂×Q₈×C₆₇	—	2	1	no	—
252	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
253	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
254	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
255	C₂×D₄×C₆₇	—	2	4	no	—
256	C₂×D₄×C₆₇	—	2	4	no	—
257	C₂×D₄×C₆₇	—	2	1	no	—
258	C₂×D₄×C₆₇	—	2	1	no	—
259	C₂×D₄×C₆₇	—	2	1	no	—
260	C₂×D₄×C₆₇	—	2	1	no	—
261	C₂×D₄×C₆₇	—	2	2	no	—
262	C₂×D₄×C₆₇	—	2	2	no	—
263	C₂×D₄×C₆₇	—	2	1	no	—
264	C₂×D₄×C₆₇	—	2	1	no	—
265	C₂×D₄×C₆₇	—	2	1	no	—
266	C₂×D₄×C₆₇	—	2	1	no	—
267	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
268	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
269	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	—	2	4	no	—
271	C₂²×C₄×C₆₇	—	2	4	no	—
272	C₂²×C₄×C₆₇	—	2	1	no	—
273	C₂²×C₄×C₆₇	—	2	1	no	—
274	C₂²×C₄×C₆₇	—	2	1	no	—
275	C₂²×C₄×C₆₇	—	2	1	no	—
276	C₂²×C₄×C₆₇	—	2	1	no	—
277	C₂²×C₄×C₆₇	—	2	1	no	—
278	C₂²×C₄×C₆₇	—	2	1	no	—
279	C₂²×C₄×C₆₇	—	2	1	no	—
280	C₂²×C₄×C₆₇	—	2	1	no	—
281	C₂²×C₄×C₆₇	—	2	1	no	—
282	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
284	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
287	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
288	Q₁₆×C₆₇	—	2	2	no	—
289	Q₁₆×C₆₇	—	2	2	no	—
290	SD₁₆×C₆₇	—	2	2	no	—
291	SD₁₆×C₆₇	—	2	2	no	—
292	SD₁₆×C₆₇	—	2	2	no	—
293	SD₁₆×C₆₇	—	2	2	no	—
294	D₈×C₆₇	—	2	2	no	—
295	D₈×C₆₇	—	2	2	no	—
296	C₂×C₈×C₆₇	—	2	1	no	—
297	C₂×C₈×C₆₇	—	2	1	no	—
298	C₂×C₈×C₆₇	—	2	1	no	—
299	C₂×C₈×C₆₇	—	2	1	no	—
300	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
301	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
302	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
303	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
304	C₄⋊C₄×C₆₇	—	2	1	no	—
305	C₄⋊C₄×C₆₇	—	2	1	no	—
306	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
307	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
308	C₂²⋊C₄×C₆₇	—	2	1	no	—
309	C₂²⋊C₄×C₆₇	—	2	1	no	—
310	C₂²⋊C₄×C₆₇	—	2	1	no	—
311	C₂²⋊C₄×C₆₇	—	2	1	no	—
312	C₂²⋊C₄×C₆₇	—	2	1	no	—
313	C₄²×C₆₇	—	2	1	no	—
314	C₂³×C₆₇	—	2	4	no	—
315	C₂³×C₆₇	—	2	1	no	—
316	C₂³×C₆₇	—	2	1	no	—
317	C₂³×C₆₇	—	2	1	no	—
318	C₂³×C₆₇	—	2	1	no	—
319	C₂³×C₆₇	—	2	1	no	—
320	C₂³×C₆₇	—	4	1	no	—
321	C₂³×C₆₇	—	4	1	no	—
322	C₂³×C₆₇	—	8	1	no	—
323	C₂³×C₆₇	—	8	1	no	—
324	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
325	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
326	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
327	Q₈×C₆₇	—	2	4	no	—
328	Q₈×C₆₇	—	2	1	no	—
329	Q₈×C₆₇	—	2	1	no	—
330	Q₈×C₆₇	—	2	1	no	—
331	Q₈×C₆₇	—	2	1	no	—
332	Q₈×C₆₇	C₄×D₄	1	2	yes	—
333	Q₈×C₆₇	C₄×D₄	1	2	yes	—
334	D₄×C₆₇	—	2	4	no	—
335	D₄×C₆₇	—	2	4	no	—
336	D₄×C₆₇	—	2	4	no	—
337	D₄×C₆₇	—	2	2	no	—
338	D₄×C₆₇	—	2	2	no	—
339	D₄×C₆₇	—	2	2	no	—
340	D₄×C₆₇	—	2	2	no	—
341	D₄×C₆₇	—	2	1	no	—
342	D₄×C₆₇	—	2	1	no	—
343	D₄×C₆₇	—	2	1	no	—
344	D₄×C₆₇	—	2	1	no	—
345	D₄×C₆₇	—	4	1	no	—
346	D₄×C₆₇	—	4	1	no	—
347	D₄×C₆₇	—	8	1	no	—
348	D₄×C₆₇	—	8	1	no	—
349	D₄×C₆₇	C₄×D₄	1	2	yes	—
350	D₄×C₆₇	C₄×D₄	1	2	yes	—
351	C₂×C₄×C₆₇	—	2	4	no	—
352	C₂×C₄×C₆₇	—	2	4	no	—
353	C₂×C₄×C₆₇	—	2	4	no	—
354	C₂×C₄×C₆₇	—	2	1	no	—
355	C₂×C₄×C₆₇	—	2	1	no	—
356	C₂×C₄×C₆₇	—	2	1	no	—
357	C₂×C₄×C₆₇	—	2	1	no	—
358	C₂×C₄×C₆₇	—	2	1	no	—
359	C₂×C₄×C₆₇	—	2	1	no	—
360	C₂×C₄×C₆₇	—	2	1	no	—
361	C₂×C₄×C₆₇	—	2	1	no	—
362	C₂×C₄×C₆₇	—	2	1	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	1	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	1	no	—
370	C₂×C₄×C₆₇	—	2	1	no	—
371	C₂×C₄×C₆₇	—	2	1	no	—
372	C₂×C₄×C₆₇	—	2	1	no	—
373	C₂×C₄×C₆₇	—	4	1	no	—
374	C₂×C₄×C₆₇	—	4	1	no	—
375	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
376	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
377	C₂×C₄×C₆₇	C₂³×C₄	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	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
382	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
383	C₂×Dic₆₇	—	2	2	no	—
384	C₂×Dic₆₇	—	4	1	no	—
385	C₂×Dic₆₇	—	4	1	no	—
386	C₂×Dic₆₇	—	4	1	no	—
387	C₂×Dic₆₇	—	4	1	no	—
388	C₂×Dic₆₇	—	4	1	no	—
389	C₈×C₆₇	—	2	1	no	—
390	C₈×C₆₇	—	2	1	no	—
391	C₈×C₆₇	—	2	1	no	—
392	C₈×C₆₇	—	2	1	no	—
393	C₆₇⋊C₈	—	2	2	no	—
394	C₆₇⋊C₈	—	2	2	no	—
395	C₆₇⋊C₈	—	2	1	no	—
396	C₆₇⋊C₈	—	2	1	no	—
397	C₆₇⋊C₈	—	4	1	no	—
398	C₆₇⋊C₈	—	4	1	no	—
399	C₆₇⋊C₈	#120	1	2	yes	—
400	C₆₇⋊C₈	#120	1	2	yes	—
401	C₂²×C₆₇	—	2	1	no	—
402	C₂²×C₆₇	—	2	1	no	—
403	C₂²×C₆₇	—	2	1	no	—
404	C₂²×C₆₇	—	2	1	no	—
405	C₂²×C₆₇	—	2	1	no	—
406	C₂²×C₆₇	—	2	1	no	—
407	C₂²×C₆₇	—	2	1	no	—
408	C₂²×C₆₇	—	2	1	no	—
409	C₂²×C₆₇	—	2	2	no	—
410	C₂²×C₆₇	—	2	2	no	—
411	C₂²×C₆₇	—	4	1	no	—
412	C₂²×C₆₇	—	4	1	no	—
413	C₂²×C₆₇	—	4	1	no	—
414	C₂²×C₆₇	—	4	1	no	—
415	C₂²×C₆₇	—	4	1	no	—
416	C₂²×C₆₇	—	4	1	no	—
417	C₂²×C₆₇	—	4	1	no	—
418	C₂²×C₆₇	—	8	1	no	—
419	C₂²×C₆₇	—	8	1	no	—
420	C₂²×C₆₇	—	8	4	no	—
421	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
422	C₂²×C₆₇	#525	1	1	yes	characteristic
423	C₂²×C₆₇	#525	1	1	yes	characteristic
424	C₄×C₆₇	—	2	1	no	—
425	C₄×C₆₇	—	2	2	no	—
426	C₄×C₆₇	—	2	2	no	—
427	C₄×C₆₇	—	2	1	no	—
428	C₄×C₆₇	—	4	1	no	—
429	C₄×C₆₇	—	4	1	no	—
430	C₄×C₆₇	—	4	1	no	—
431	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
432	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
433	C₄×C₆₇	C₂×#120	1	1	yes	characteristic
434	C₄×C₆₇	#525	1	1	yes	characteristic
435	Dic₆₇	—	4	2	no	—
436	Dic₆₇	—	8	1	no	—
437	#21468	—	67	1	no	maximal, Sylow
438	C₂×C₆₇	—	2	1	no	—
439	C₂×C₆₇	—	2	1	no	—
440	C₂×C₆₇	—	4	1	no	—
441	C₂×C₆₇	—	4	1	no	—
442	C₂×C₆₇	—	4	2	no	—
443	C₂×C₆₇	—	4	2	no	—
444	C₂×C₆₇	—	8	1	no	—
445	C₂×C₆₇	C₄×#120	1	1	yes	characteristic
446	C₂×C₆₇	#2956	1	1	yes	characteristic
447	C₂×C₆₇	#2957	1	1	yes	characteristic
448	C₂×#568	—	67	1	no	—
449	#3002	D₆₇	1	1	yes	characteristic
450	C₂×#444	—	67	1	no	—
451	C₂×#443	—	67	1	no	—
452	#2930	—	67	1	no	—
453	#1876	—	67	1	no	—
454	#1876	—	67	1	no	—
455	#1871	—	67	1	no	—
456	#1866	—	67	1	no	—
457	#1866	—	67	1	no	—
458	#1855	—	67	1	no	—
459	#1789	—	67	1	no	—
460	#1765	—	67	1	no	—
461	#1764	—	67	1	no	—
462	#1753	—	67	1	no	—
463	C₆₇	#21468	1	1	yes	characteristic, complemented, Sylow
464	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
465	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
466	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
467	#568	—	134	4	no	—
468	#568	—	134	4	no	—
469	C₂×#131	—	67	1	no	—
470	C₂×#131	—	67	1	no	—
471	C₂×#131	—	67	1	no	—
472	C₂×#131	—	67	1	no	—
473	C₂×#131	—	67	1	no	—
474	C₂×#131	—	134	1	no	—
475	C₂×#131	—	134	1	no	—
476	C₂²×M₁₆	—	67	1	no	—
477	C₂²×M₁₆	—	67	1	no	—
478	C₂²×M₁₆	—	134	1	no	—
479	C₂²×M₁₆	—	134	1	no	—
480	#525	C₂×D₆₇	1	1	yes	characteristic
481	#452	Dic₆₇	1	1	yes	characteristic, complemented
482	#452	Dic₆₇	1	1	yes	characteristic, complemented
483	#451	Dic₆₇	1	1	yes	characteristic, complemented
484	#450	Dic₆₇	1	1	yes	characteristic, complemented
485	#449	Dic₆₇	1	1	yes	characteristic, complemented
486	#449	Dic₆₇	1	1	yes	characteristic, complemented
487	#448	Dic₆₇	1	1	yes	characteristic, complemented
488	#447	Dic₆₇	1	1	yes	characteristic, complemented
489	#444	—	134	4	no	—
490	#443	—	134	4	no	—
491	#436	—	134	1	no	—
492	#436	—	134	1	no	—
493	#435	—	134	1	no	—
494	#435	—	134	1	no	—
495	C₂×#108	—	67	1	no	—
496	C₂×#108	—	67	1	no	—
497	#424	—	67	1	no	—
498	C₂×#104	—	67	1	no	—
499	C₂×#104	—	67	1	no	—
500	C₂×#104	—	67	1	no	—
501	C₂×#104	—	67	1	no	—
502	C₂×#104	—	67	1	no	—
503	C₂×#104	—	67	1	no	—
504	#416	C₂×D₆₇	1	1	yes	characteristic
505	#416	C₂×D₆₇	1	1	yes	characteristic
506	#408	—	67	1	no	—
507	#407	—	67	1	no	—
508	C₂×C₂²⋊C₈	C₂×D₆₇	1	1	yes	characteristic
509	#405	—	67	1	no	—
510	C₂×#97	—	67	1	no	—
511	C₂×C₄×C₈	—	67	1	no	—
512	C₄×C₂²⋊C₄	—	67	1	no	—
513	#341	—	67	1	no	—
514	#341	—	67	1	no	—
515	#339	—	67	1	no	—
516	#339	—	67	1	no	—
517	#336	—	67	1	no	—
518	#336	—	67	1	no	—
519	C₂×#41	—	2	2	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	—	2	2	no	—
522	C₂×#41	—	2	2	no	—
523	C₂×#41	—	2	1	no	—
524	C₂×#41	—	2	1	no	—
525	C₂×#41	C₂×Dic₆₇	1	1	yes	characteristic
526	C₂×#41	C₂×Dic₆₇	1	1	yes	characteristic
527	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
528	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
529	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
530	C₂²×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	C₂×Dic₆₇	1	1	yes	characteristic
533	C₂³×C₄	—	2	1	no	—
534	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
535	#135	—	2	2	no	—
536	#135	—	2	2	no	—
537	#135	—	2	2	no	—
538	#135	—	2	2	no	—
539	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic
540	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic
541	C₂×SD₁₆	C₂×Dic₆₇	1	1	yes	characteristic
542	C₂×SD₁₆	C₂×Dic₆₇	1	1	yes	characteristic
543	C₂×SD₁₆	C₂×Dic₆₇	1	1	yes	characteristic
544	C₂×SD₁₆	C₂×Dic₆₇	1	1	yes	characteristic
545	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
546	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
547	#131	—	67	4	no	—
548	#131	—	67	4	no	—
549	#131	—	134	2	no	—
550	#131	—	134	2	no	—
551	#131	—	134	2	no	—
552	#131	—	134	2	no	—
553	#131	—	134	2	no	—
554	#131	—	134	2	no	—
555	#131	—	134	8	no	—
556	#131	—	134	8	no	—
557	#131	—	134	2	no	—
558	#131	—	134	2	no	—
559	C₂×M₁₆	—	67	1	no	—
560	C₂×M₁₆	—	67	1	no	—
561	C₂×M₁₆	—	67	1	no	—
562	C₂×M₁₆	—	67	1	no	—
563	C₂×M₁₆	—	67	1	no	—
564	C₂×M₁₆	—	67	1	no	—
565	C₂×M₁₆	—	67	1	no	—
566	C₂×M₁₆	—	67	1	no	—
567	C₂×M₁₆	—	134	1	no	—
568	C₂×M₁₆	—	134	2	no	—
569	C₂×M₁₆	—	134	2	no	—
570	C₂×M₁₆	—	134	1	no	—
571	C₂×M₁₆	—	134	1	no	—
572	C₂×M₁₆	—	134	1	no	—
573	C₂×M₁₆	—	134	1	no	—
574	C₂×M₁₆	—	134	2	no	—
575	C₂×M₁₆	—	134	2	no	—
576	C₂×M₁₆	—	134	8	no	—
577	C₂×M₁₆	—	134	8	no	—
578	C₂×M₁₆	—	134	1	no	—
579	C₂²×C₈	—	67	1	no	—
580	C₂²×C₈	—	67	1	no	—
581	C₂²×C₈	—	134	1	no	—
582	C₂²×C₈	—	134	1	no	—
583	C₂²×C₈	—	134	1	no	—
584	C₂²×C₈	—	134	1	no	—
585	C₂²×C₈	—	134	1	no	—
586	C₂²×C₈	—	134	1	no	—
587	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
588	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
589	#123	—	2	1	no	—
590	C₂²⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
591	C₂²⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
592	#121	C₂×Dic₆₇	1	1	yes	characteristic
593	#121	C₂×Dic₆₇	1	1	yes	characteristic
594	#120	—	2	1	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	#117	C₂²×D₆₇	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	—	134	1	no	—
599	C₂×C₄²	—	67	1	no	—
600	C₂×C₄²	—	67	1	no	—
601	#108	—	134	2	no	—
602	#108	—	134	2	no	—
603	C₄⋊C₈	—	134	1	no	—
604	C₄⋊C₈	—	134	1	no	—
605	#104	—	134	2	no	—
606	#104	—	134	2	no	—
607	#104	—	134	2	no	—
608	#104	—	134	2	no	—
609	#104	—	134	2	no	—
610	#104	—	134	2	no	—
611	#103	C₂×Dic₆₇	1	1	yes	characteristic
612	#103	C₂×Dic₆₇	1	1	yes	characteristic
613	#103	C₂×Dic₆₇	1	1	yes	characteristic
614	#103	C₂×Dic₆₇	1	1	yes	characteristic
615	#102	C₂×Dic₆₇	1	1	yes	characteristic
616	#102	C₂×Dic₆₇	1	1	yes	characteristic
617	#102	C₂×Dic₆₇	1	1	yes	characteristic
618	#102	C₂×Dic₆₇	1	1	yes	characteristic
619	C₂²⋊C₈	—	134	1	no	—
620	C₂²⋊C₈	—	134	1	no	—
621	C₂²⋊C₈	—	134	1	no	—
622	C₂²⋊C₈	—	134	1	no	—
623	C₂²⋊C₈	C₂×Dic₆₇	1	1	yes	characteristic
624	C₂²⋊C₈	C₂×Dic₆₇	1	1	yes	characteristic
625	C₂²⋊C₈	C₂×Dic₆₇	1	1	yes	characteristic
626	C₂²⋊C₈	C₂×Dic₆₇	1	1	yes	characteristic
627	#97	—	134	1	no	—
628	#97	—	134	2	no	—
629	C₄×C₈	—	134	1	no	—
630	C₄×C₈	—	134	2	no	—
631	#95	—	134	1	no	—
632	C₂⁴	—	2	1	no	—
633	C₂⁴	#11761627	1	1	yes	characteristic
634	#41	—	2	4	no	—
635	#41	—	2	4	no	—
636	#41	—	2	4	no	—
637	#41	—	2	4	no	—
638	#41	—	2	2	no	—
639	#41	—	2	2	no	—
640	#41	—	2	2	no	—
641	#41	—	2	2	no	—
642	#41	—	2	1	no	—
643	#41	—	2	1	no	—
644	#41	—	2	1	no	—
645	#41	—	2	1	no	—
646	#41	—	2	1	no	—
647	#41	—	2	1	no	—
648	#41	—	2	1	no	—
649	#41	—	2	1	no	—
650	#41	D₄×D₆₇	1	2	yes	—
651	#41	D₄×D₆₇	1	2	yes	—
652	#41	#11761627	1	2	yes	—
653	#41	#11761627	1	2	yes	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	C₂²×Dic₆₇	1	1	yes	characteristic
658	C₂×Q₈	C₂²×Dic₆₇	1	1	yes	characteristic
659	C₂×Q₈	C₂²×Dic₆₇	1	1	yes	characteristic
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
673	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
674	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	134	1	no	—
688	C₂²×C₄	—	134	1	no	—
689	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
690	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
691	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
692	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
693	C₂²×C₄	#11761627	1	1	yes	characteristic
694	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
695	Q₁₆	—	2	2	no	—
696	Q₁₆	—	2	2	no	—
697	SD₁₆	—	2	2	no	—
698	SD₁₆	—	2	2	no	—
699	SD₁₆	—	2	2	no	—
700	SD₁₆	—	2	2	no	—
701	D₈	—	2	2	no	—
702	D₈	—	2	2	no	—
703	M₁₆	—	268	2	no	—
704	M₁₆	—	67	2	no	—
705	M₁₆	—	67	2	no	—
706	M₁₆	—	134	1	no	—
707	M₁₆	—	134	1	no	—
708	M₁₆	—	134	1	no	—
709	M₁₆	—	134	1	no	—
710	M₁₆	—	134	2	no	—
711	M₁₆	—	134	2	no	—
712	M₁₆	—	134	2	no	—
713	M₁₆	—	134	2	no	—
714	M₁₆	—	134	4	no	—
715	M₁₆	—	134	4	no	—
716	M₁₆	—	134	4	no	—
717	M₁₆	—	134	4	no	—
718	M₁₆	—	134	4	no	—
719	M₁₆	—	134	1	no	—
720	M₁₆	—	134	1	no	—
721	C₂×C₈	—	2	1	no	—
722	C₂×C₈	—	2	1	no	—
723	C₂×C₈	—	2	1	no	—
724	C₂×C₈	—	2	1	no	—
725	C₂×C₈	—	268	2	no	—
726	C₂×C₈	—	67	2	no	—
727	C₂×C₈	—	67	2	no	—
728	C₂×C₈	—	67	1	no	—
729	C₂×C₈	—	67	1	no	—
730	C₂×C₈	—	67	1	no	—
731	C₂×C₈	—	67	1	no	—
732	C₂×C₈	—	134	1	no	—
733	C₂×C₈	—	134	1	no	—
734	C₂×C₈	—	134	4	no	—
735	C₂×C₈	—	134	4	no	—
736	C₂×C₈	—	134	4	no	—
737	C₂×C₈	—	134	4	no	—
738	C₂×C₈	—	134	4	no	—
739	C₂×C₈	—	134	1	no	—
740	C₂×C₈	—	134	1	no	—
741	C₂×C₈	—	134	1	no	—
742	C₂×C₈	—	134	1	no	—
743	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
744	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
745	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
746	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
750	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	268	2	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	134	1	no	—
759	C₄²	—	134	1	no	—
760	C₄²	—	134	1	no	—
761	C₄²	—	134	1	no	—
762	C₂³	—	2	4	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	4	1	no	—
769	C₂³	—	4	1	no	—
770	C₂³	—	8	1	no	—
771	C₂³	—	8	1	no	—
772	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
773	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
774	C₂³	C₂×#11761627	1	1	yes	characteristic
775	Q₈	—	2	4	no	—
776	Q₈	—	2	1	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	2	1	no	—
779	Q₈	—	2	1	no	—
780	Q₈	D₄×Dic₆₇	1	2	yes	—
781	Q₈	D₄×Dic₆₇	1	2	yes	—
782	D₄	—	2	4	no	—
783	D₄	—	2	4	no	—
784	D₄	—	2	4	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	2	1	no	—
792	D₄	—	2	1	no	—
793	D₄	—	4	1	no	—
794	D₄	—	4	1	no	—
795	D₄	—	8	1	no	—
796	D₄	—	8	1	no	—
797	D₄	D₄×Dic₆₇	1	2	yes	—
798	D₄	D₄×Dic₆₇	1	2	yes	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	268	1	no	—
824	C₂×C₄	—	268	1	no	—
825	C₂×C₄	—	268	1	no	—
826	C₂×C₄	—	268	1	no	—
827	C₂×C₄	—	268	1	no	—
828	C₂×C₄	—	134	2	no	—
829	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
830	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
831	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
832	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
833	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
834	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
835	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
836	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
837	C₈	—	2	1	no	—
838	C₈	—	2	1	no	—
839	C₈	—	2	1	no	—
840	C₈	—	2	1	no	—
841	C₈	—	268	1	no	—
842	C₈	—	268	1	no	—
843	C₈	—	67	2	no	—
844	C₈	—	67	2	no	—
845	C₈	—	134	1	no	—
846	C₈	—	134	1	no	—
847	C₈	—	134	2	no	—
848	C₈	—	134	2	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	8	1	no	—
867	C₂²	—	8	1	no	—
868	C₂²	—	8	4	no	—
869	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
870	C₂²	#16863902	1	1	yes	characteristic
871	C₂²	#16863902	1	1	yes	characteristic
872	C₄	—	2	1	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	1	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	268	2	no	—
880	C₄	—	536	1	no	—
881	C₄	C₂×D₄×Dic₆₇	1	1	yes	characteristic
882	C₄	C₂×D₄×Dic₆₇	1	1	yes	characteristic
883	C₄	#120×D₆₇	1	1	yes	characteristic
884	C₄	#16863902	1	1	yes	characteristic
885	C₂	—	2	1	no	—
886	C₂	—	2	1	no	—
887	C₂	—	4	1	no	—
888	C₂	—	4	1	no	—
889	C₂	—	4	2	no	—
890	C₂	—	4	2	no	—
891	C₂	—	8	1	no	—
892	C₂	#120×Dic₆₇	1	1	yes	characteristic
893	C₂	#22569119	1	1	yes	characteristic
894	C₂	#22569126	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting, prime radical	C₆₇×#3002	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#3002	D₆₇
hypocenter	C₆₇	#21468
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3002

Complements

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

N	H ≅ G/N	type
1. C₂×#16864163	C₂	semidirect
2. C₂×#16863518	C₂	semidirect
3. C₂×#16863513	C₂	semidirect
4. #22568913	C₂	semidirect
5. #22560538	C₂	semidirect
6. #22560538	C₂	semidirect
7. #22560512	C₂	semidirect
8. #22560486	C₂	semidirect
9. #22560486	C₂	semidirect
10. #22560416	C₂	semidirect
11. #22560153	C₂	semidirect
12. #22560056	C₂	semidirect
13. #22560049	C₂	semidirect
14. #22559995	C₂	semidirect
24. C₂×#14524050	C₂²	semidirect
35. C₂×#14523979	C₂²	semidirect
36. C₂×#14523979	C₂²	semidirect
37. #16863423	C₂²	semidirect
42. C₂×#14523970	C₂²	semidirect
43. C₂×#14523970	C₂²	semidirect
44. #16863363	C₂²	semidirect
46. #16863352	C₂²	semidirect
47. C₂×#14523953	C₂²	semidirect
48. C₂×C₈×Dic₆₇	C₂²	semidirect
50. #16863161	C₂²	semidirect
51. #16863161	C₂²	semidirect
52. #16863155	C₂²	semidirect
53. #16863155	C₂²	semidirect
54. #16863150	C₂²	semidirect
55. #16863150	C₂²	semidirect
60. #452×C₆₇	C₄	semidirect
61. #452×C₆₇	C₄	semidirect
62. #451×C₆₇	C₄	semidirect
63. #450×C₆₇	C₄	semidirect
64. #449×C₆₇	C₄	semidirect
65. #449×C₆₇	C₄	semidirect
66. #448×C₆₇	C₄	semidirect
67. #447×C₆₇	C₄	semidirect
81. #14524050	D₄	semidirect
82. #14524050	D₄	semidirect
463. C₆₇	#21468	semidirect
481. #452	Dic₆₇	semidirect
482. #452	Dic₆₇	semidirect
483. #451	Dic₆₇	semidirect
484. #450	Dic₆₇	semidirect
485. #449	Dic₆₇	semidirect
486. #449	Dic₆₇	semidirect
487. #448	Dic₆₇	semidirect
488. #447	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16864163	2
C₂×#16863518	2
C₂×#16863513	2
#22568913	2
#22560538	2
#22560512	2
#22560486	2
#22560416	2
#22560153	2
#22560056	2
#22560049	2
#22559995	2
C₆₇×#3002	2
#21468	67