Subgroups — #31735846

Order 17152.

1896 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574085	C₂	1	1	yes	maximal, characteristic, complemented
2	#22574028	C₂	1	1	yes	maximal, characteristic, complemented
3	#22573021	C₂	1	2	yes	maximal, complemented
4	#22572999	C₂	1	2	yes	maximal, complemented
5	#22572936	C₂	1	2	yes	maximal, complemented
6	#22572914	C₂	1	2	yes	maximal, complemented
7	#22572903	C₂	1	2	yes	maximal, complemented
8	#22572878	C₂	1	2	yes	maximal, complemented
9	#22572867	C₂	1	2	yes	maximal, complemented
10	#22572842	C₂	1	2	yes	maximal, complemented
11	#22570567	C₂	1	2	yes	maximal, complemented
12	C₂×#16863743	C₂	1	1	yes	maximal, characteristic, complemented
13	#22570043	C₂	1	2	yes	maximal, complemented
14	#22570024	C₂	1	1	yes	maximal, characteristic, complemented
15	#22569746	C₂	1	2	yes	maximal, complemented
16	#22569689	C₂	1	1	yes	maximal, characteristic, complemented
17	#22569143	C₂	1	1	yes	maximal, characteristic, complemented
18	#22569044	C₂	1	2	yes	maximal, complemented
19	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14524068	C₂²	1	2	yes	—
21	#16864131	C₂²	1	2	yes	—
22	#16864131	C₂²	1	2	yes	—
23	Q₈×Dic₁₃₄	C₂²	1	2	yes	complemented
24	#16864125	C₂²	1	2	yes	complemented
25	#16864103	—	2	2	no	—
26	#16864103	C₂²	1	2	yes	complemented
27	#16864067	C₂²	1	2	yes	—
28	#16864067	C₂²	1	2	yes	—
29	D₄×Dic₁₃₄	—	2	2	no	—
30	D₄×Dic₁₃₄	C₂²	1	2	yes	complemented
31	#16864042	—	2	2	no	—
32	#16864042	—	2	2	no	—
33	#16864024	—	2	2	no	—
34	#16864024	C₂²	1	2	yes	—
35	#16864001	—	2	2	no	—
36	#16863960	C₂²	1	2	yes	—
37	#16863953	—	2	1	no	—
38	#16863953	C₂²	1	1	yes	characteristic
39	#16863946	—	2	1	no	—
40	#16863946	—	2	1	no	—
41	C₂×#14524043	—	2	1	no	—
42	C₂×#14524043	C₂²	1	1	yes	characteristic
43	C₂×#14524040	C₂²	1	1	yes	characteristic
44	#16863879	C₂²	1	2	yes	—
45	#16863870	C₂²	1	2	yes	—
46	#16863759	C₂²	1	4	yes	complemented
47	#16863757	C₂²	1	4	yes	complemented
48	#16863752	C₂²	1	4	yes	complemented
49	#16863743	C₂²	1	2	yes	—
50	#16863743	C₂²	1	2	yes	—
51	#16863743	C₂²	1	2	yes	—
52	#16863743	C₂²	1	2	yes	—
53	#16863741	C₂²	1	4	yes	complemented
54	#16863699	C₂²	1	4	yes	complemented
55	#16863695	C₂²	1	4	yes	complemented
56	#16863691	C₂²	1	2	yes	complemented
57	#16863686	C₂²	1	2	yes	complemented
58	#16863685	C₂²	1	4	yes	complemented
59	#16863681	C₂²	1	2	yes	complemented
60	#16863676	C₂²	1	2	yes	complemented
61	#16863675	C₂²	1	4	yes	complemented
62	#16863620	C₂²	1	4	yes	complemented
63	#16863613	C₂²	1	4	yes	complemented
64	#16863596	C₂²	1	2	yes	—
65	#16863596	C₂²	1	2	yes	—
66	#16863594	C₂²	1	4	yes	complemented
67	#16863591	C₂²	1	2	yes	—
68	#16863591	C₂²	1	2	yes	—
69	#16863589	C₂²	1	4	yes	complemented
70	#16863526	C₂²	1	2	yes	complemented
71	#16863526	C₂²	1	2	yes	complemented
72	C₈×Dic₁₃₄	C₂²	1	2	yes	complemented
73	C₈×Dic₁₃₄	C₂²	1	2	yes	complemented
74	#16863505	C₂²	1	4	yes	complemented
75	#16863499	C₂²	1	4	yes	complemented
76	#16863481	C₂²	1	4	yes	complemented
77	#16863476	C₂²	1	4	yes	complemented
78	#16863439	C₂²	1	2	yes	—
79	#16863422	C₂²	1	2	yes	—
80	#16863420	C₂²	1	1	yes	characteristic
81	#16863400	C₂²	1	2	yes	—
82	#16863397	C₂²	1	2	yes	—
83	C₂×#14523965	C₂²	1	2	yes	—
84	C₂×#14523965	C₂²	1	2	yes	—
85	#16863351	C₂²	1	2	yes	—
86	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
87	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
88	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
89	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#427×C₆₇	C₂²	1	1	yes	characteristic
98	#416×C₆₇	C₂²	1	1	yes	characteristic
99	#416×C₆₇	C₂²	1	1	yes	characteristic
100	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
101	C₂×#11761628	—	2	2	no	—
102	C₂×#11761628	—	2	2	no	—
103	C₂²×Dic₁₃₄	—	2	2	no	—
104	C₂²×Dic₁₃₄	—	2	1	no	—
105	C₂²×D₂₆₈	—	2	1	no	—
106	C₂²×D₂₆₈	—	2	1	no	—
107	C₂²×D₂₆₈	C₂³	1	2	yes	—
108	#14524068	—	2	8	no	—
109	C₂×#11761615	C₂³	1	4	yes	—
110	C₂×#11761613	C₂³	1	4	yes	—
111	C₂×#11761612	C₂³	1	2	yes	—
112	#14524043	—	2	2	no	—
113	#14524043	—	2	2	no	—
114	#14524043	—	2	2	no	—
115	#14524043	—	2	1	no	—
116	#14524043	—	2	1	no	—
117	#14524043	D₄	1	1	yes	characteristic
118	#14524043	D₄	1	1	yes	characteristic
119	#14524043	C₂³	1	2	yes	—
120	#14524043	C₂³	1	2	yes	—
121	#14524042	—	2	4	no	—
122	#14524042	C₂³	1	4	yes	—
123	#14524040	—	2	1	no	—
124	#14524040	—	2	1	no	—
125	#14524040	C₂³	1	2	yes	—
126	#14524040	C₂³	1	2	yes	—
127	#14524039	C₂³	1	4	yes	—
128	#14524035	—	2	2	no	—
129	#14524035	D₄	1	2	yes	—
130	#14524034	—	2	4	no	—
131	#14524034	C₂³	1	4	yes	—
132	#14524032	C₂³	1	4	yes	—
133	#14524031	—	2	2	no	—
134	#14524031	—	2	2	no	—
135	#14524028	—	2	4	no	—
136	#14524028	—	2	4	no	—
137	#14524022	—	2	2	no	—
138	#14524022	—	2	2	no	—
139	#14524022	D₄	1	2	yes	—
140	#14524022	D₄	1	2	yes	—
141	#14524020	—	2	4	no	—
142	#14524020	—	2	4	no	—
143	#14524020	—	2	4	no	—
144	#14524017	—	2	2	no	—
145	#14524017	—	2	2	no	—
146	#14524017	—	2	2	no	—
147	#14524017	—	2	2	no	—
148	#14524016	—	2	4	no	—
149	#14524016	—	2	4	no	—
150	#14524011	—	2	4	no	—
151	Q₈×Dic₆₇	C₂³	1	4	yes	—
152	C₄×Dic₁₃₄	—	2	2	no	—
153	C₄×Dic₁₃₄	—	2	2	no	—
154	C₄×Dic₁₃₄	C₂³	1	2	yes	—
155	C₄×Dic₁₃₄	C₂³	1	2	yes	—
156	C₄×D₂₆₈	—	2	2	no	—
157	C₄×D₂₆₈	—	2	2	no	—
158	C₄×D₂₆₈	—	2	2	no	—
159	C₄×D₂₆₈	—	2	2	no	—
160	D₄×Dic₆₇	—	2	4	no	—
161	D₄×Dic₆₇	C₂³	1	4	yes	—
162	#14524005	C₂³	1	4	yes	—
163	#14524005	C₂³	1	4	yes	—
164	#14524002	—	2	2	no	—
165	#14524002	C₂³	1	2	yes	—
166	C₂×C₄⋊Dic₆₇	—	2	2	no	—
167	C₂×C₄⋊Dic₆₇	—	2	2	no	—
168	C₂×C₄⋊Dic₆₇	—	2	1	no	—
169	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
170	C₂²⋊C₄×D₆₇	—	2	4	no	—
171	#14523976	C₂³	1	4	yes	—
172	#14523974	C₂³	1	4	yes	—
173	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
174	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
175	Dic₆₇⋊C₈	C₂³	1	4	yes	—
176	Dic₆₇⋊C₈	C₂³	1	4	yes	—
177	#14523967	C₂³	1	4	yes	—
178	#14523965	C₂³	1	4	yes	—
179	#14523965	C₂³	1	4	yes	—
180	#14523965	C₂³	1	4	yes	—
181	#14523965	C₂³	1	4	yes	—
182	#14523964	C₂³	1	4	yes	—
183	#14523963	C₂³	1	4	yes	—
184	#14523963	C₂³	1	4	yes	—
185	#14523953	C₂³	1	4	yes	—
186	C₈×Dic₆₇	C₂³	1	4	yes	—
187	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
189	#135×C₆₇	—	2	4	no	—
190	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
194	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
195	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
196	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
197	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
198	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
199	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
200	C₄×D₄×C₆₇	—	2	1	no	—
201	C₄×D₄×C₆₇	—	2	1	no	—
202	C₄×D₄×C₆₇	—	2	1	no	—
203	C₄×D₄×C₆₇	—	2	1	no	—
204	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
208	#117×C₆₇	—	2	1	no	—
209	#117×C₆₇	—	2	1	no	—
210	#117×C₆₇	C₂³	1	1	yes	characteristic
211	#117×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₆₇	—	2	1	no	—
213	C₂×C₄²×C₆₇	—	2	1	no	—
214	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
215	#107×C₆₇	C₂³	1	1	yes	characteristic
216	#107×C₆₇	C₂³	1	1	yes	characteristic
217	#106×C₆₇	C₂³	1	1	yes	characteristic
218	#106×C₆₇	C₂³	1	1	yes	characteristic
219	#103×C₆₇	C₂³	1	1	yes	characteristic
220	#103×C₆₇	C₂³	1	1	yes	characteristic
221	#103×C₆₇	C₂³	1	1	yes	characteristic
222	#103×C₆₇	C₂³	1	1	yes	characteristic
223	#102×C₆₇	C₂³	1	1	yes	characteristic
224	#102×C₆₇	C₂³	1	1	yes	characteristic
225	#102×C₆₇	C₂³	1	1	yes	characteristic
226	#102×C₆₇	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
229	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
230	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
231	C₂³×D₆₇	—	2	2	no	—
232	#11761628	—	8	4	no	—
233	#11761628	—	8	4	no	—
234	C₂×Dic₁₃₄	—	2	2	no	—
235	C₂×Dic₁₃₄	—	2	2	no	—
236	C₂×Dic₁₃₄	—	2	4	no	—
237	C₂×Dic₁₃₄	—	8	4	no	—
238	C₂×Dic₁₃₄	—	8	2	no	—
239	C₂×Dic₁₃₄	C₂×D₄	1	2	yes	—
240	C₂×Dic₁₃₄	C₂×D₄	1	2	yes	—
241	C₂×D₂₆₈	—	2	4	no	—
242	C₂×D₂₆₈	—	2	4	no	—
243	C₂×D₂₆₈	—	2	2	no	—
244	C₂×D₂₆₈	—	2	2	no	—
245	C₂×D₂₆₈	—	2	2	no	—
246	C₂×D₂₆₈	—	2	2	no	—
247	C₂×D₂₆₈	—	2	2	no	—
248	C₂×D₂₆₈	—	8	2	no	—
249	C₂×D₂₆₈	—	8	2	no	—
250	C₂×D₂₆₈	C₂⁴	1	4	yes	—
251	C₂×C₂²⋊D₆₇	—	2	4	no	—
252	C₂×C₂²⋊D₆₇	—	2	4	no	—
253	C₂²×Dic₆₇	—	2	2	no	—
254	C₂²×Dic₆₇	—	2	4	no	—
255	C₂×C₄×D₆₇	—	2	4	no	—
256	C₂×C₄×D₆₇	—	2	4	no	—
257	#11761615	—	2	8	no	—
258	#11761613	—	2	8	no	—
259	#11761612	—	2	4	no	—
260	C₂×C₆₇⋊C₈	C₂⁴	1	4	yes	—
261	C₄⋊Dic₆₇	—	2	2	no	—
262	C₄⋊Dic₆₇	—	2	2	no	—
263	C₄⋊Dic₆₇	—	2	2	no	—
264	C₄⋊Dic₆₇	—	2	4	no	—
265	C₄⋊Dic₆₇	—	2	4	no	—
266	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
267	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
268	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
269	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
270	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
271	Dic₆₇⋊C₄	—	2	4	no	—
272	Dic₆₇⋊C₄	—	2	4	no	—
273	Dic₆₇⋊C₄	C₂×D₄	1	4	yes	—
274	Dic₆₇⋊C₄	C₂×D₄	1	4	yes	—
275	C₂²⋊Dic₆₇	—	2	4	no	—
276	C₂²⋊Dic₆₇	C₂×D₄	1	4	yes	—
277	(C₂×D₆₇)⋊C₄	—	2	4	no	—
278	(C₂×D₆₇)⋊C₄	—	2	4	no	—
279	(C₂×D₆₇)⋊C₄	—	2	4	no	—
280	(C₂×D₆₇)⋊C₄	—	2	4	no	—
281	C₄×Dic₆₇	—	2	4	no	—
282	C₄×Dic₆₇	C₂⁴	1	4	yes	—
283	#41×C₆₇	—	2	2	no	—
284	#41×C₆₇	—	2	2	no	—
285	#41×C₆₇	—	2	2	no	—
286	#41×C₆₇	#41	1	4	yes	complemented
287	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂×D₄×C₆₇	—	2	1	no	—
290	C₂×D₄×C₆₇	—	2	1	no	—
291	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
292	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	—	2	1	no	—
294	C₂²×C₄×C₆₇	—	2	1	no	—
295	C₂²×C₄×C₆₇	—	2	1	no	—
296	C₂²×C₄×C₆₇	—	2	1	no	—
297	C₂²×C₄×C₆₇	—	2	1	no	—
298	C₂²×C₄×C₆₇	—	2	1	no	—
299	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
302	Q₁₆×C₆₇	—	2	2	no	—
303	SD₁₆×C₆₇	—	2	2	no	—
304	SD₁₆×C₆₇	—	2	2	no	—
305	D₈×C₆₇	—	2	2	no	—
306	C₂×C₈×C₆₇	—	2	2	no	—
307	C₂×C₈×C₆₇	—	2	2	no	—
308	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₆₇	—	2	1	no	—
313	C₄⋊C₄×C₆₇	—	2	1	no	—
314	C₄⋊C₄×C₆₇	—	2	1	no	—
315	C₄⋊C₄×C₆₇	—	2	1	no	—
316	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
317	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂²⋊C₄×C₆₇	—	2	1	no	—
321	C₂²⋊C₄×C₆₇	—	2	1	no	—
322	C₂²⋊C₄×C₆₇	—	2	1	no	—
323	C₂²⋊C₄×C₆₇	—	2	1	no	—
324	C₂²⋊C₄×C₆₇	—	2	1	no	—
325	C₂²⋊C₄×C₆₇	—	2	1	no	—
326	C₄²×C₆₇	—	2	1	no	—
327	C₄²×C₆₇	—	2	1	no	—
328	C₄²×C₆₇	—	2	1	no	—
329	C₄²×C₆₇	—	2	1	no	—
330	C₄²×C₆₇	—	2	1	no	—
331	C₄²×C₆₇	—	2	1	no	—
332	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
336	C₂³×C₆₇	—	2	1	no	—
337	C₂³×C₆₇	—	2	1	no	—
338	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
339	C₂²×D₆₇	—	2	4	no	—
340	C₂²×D₆₇	—	4	4	no	—
341	C₂²×D₆₇	—	8	2	no	—
342	C₂²×D₆₇	—	8	2	no	—
343	Q₈×C₆₇	—	2	1	no	—
344	Q₈×C₆₇	—	2	1	no	—
345	Q₈×C₆₇	—	2	1	no	—
346	Q₈×C₆₇	C₂×#41	1	2	yes	—
347	D₄×C₆₇	—	2	4	no	—
348	D₄×C₆₇	—	2	1	no	—
349	D₄×C₆₇	—	2	1	no	—
350	D₄×C₆₇	—	2	1	no	—
351	D₄×C₆₇	—	4	2	no	—
352	D₄×C₆₇	C₂×#41	1	2	yes	—
353	C₂×C₄×C₆₇	—	2	1	no	—
354	C₂×C₄×C₆₇	—	2	4	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	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	—	4	2	no	—
363	C₂×C₄×C₆₇	—	4	2	no	—
364	C₂×C₄×C₆₇	—	4	2	no	—
365	C₂×C₄×C₆₇	—	4	2	no	—
366	C₂×C₄×C₆₇	—	4	2	no	—
367	C₂×C₄×C₆₇	C₂²×D₄	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	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
373	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
374	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
375	C₂²⋊D₆₇	—	8	4	no	—
376	C₂²⋊D₆₇	—	8	4	no	—
377	C₂×Dic₆₇	—	2	4	no	—
378	C₂×Dic₆₇	—	8	4	no	—
379	C₂×Dic₆₇	—	8	2	no	—
380	C₂×Dic₆₇	C₂²×D₄	1	4	yes	—
381	C₂×Dic₆₇	C₂²×D₄	1	4	yes	—
382	D₂₆₈	—	2	4	no	—
383	D₂₆₈	—	2	4	no	—
384	D₂₆₈	—	4	4	no	—
385	D₂₆₈	—	4	4	no	—
386	D₂₆₈	—	4	4	no	—
387	D₂₆₈	—	8	2	no	—
388	D₂₆₈	—	8	2	no	—
389	C₄×D₆₇	—	8	4	no	—
390	C₄×D₆₇	—	8	4	no	—
391	Dic₁₃₄	—	2	4	no	—
392	Dic₁₃₄	—	2	4	no	—
393	Dic₁₃₄	—	4	4	no	—
394	Dic₁₃₄	—	8	4	no	—
395	Dic₁₃₄	—	8	2	no	—
396	C₈×C₆₇	—	2	1	no	—
397	C₈×C₆₇	—	2	1	no	—
398	C₈×C₆₇	—	2	1	no	—
399	C₈×C₆₇	—	2	1	no	—
400	C₆₇⋊C₈	—	2	4	no	—
401	C₂²×C₆₇	—	2	1	no	—
402	C₂²×C₆₇	—	2	1	no	—
403	C₂²×C₆₇	—	2	2	no	—
404	C₂²×C₆₇	—	4	1	no	—
405	C₂²×C₆₇	—	4	1	no	—
406	C₂²×C₆₇	—	4	1	no	—
407	C₂²×C₆₇	—	4	1	no	—
408	C₂²×C₆₇	—	4	1	no	—
409	C₂²×C₆₇	#548	1	2	yes	—
410	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
411	C₂×D₆₇	—	4	4	no	—
412	C₂×D₆₇	—	4	4	no	—
413	C₂×D₆₇	—	4	4	no	—
414	C₂×D₆₇	—	16	4	no	—
415	C₄×C₆₇	—	2	2	no	—
416	C₄×C₆₇	—	2	1	no	—
417	C₄×C₆₇	—	2	1	no	—
418	C₄×C₆₇	—	4	1	no	—
419	C₄×C₆₇	—	4	1	no	—
420	C₄×C₆₇	—	4	1	no	—
421	C₄×C₆₇	—	4	1	no	—
422	C₄×C₆₇	—	4	1	no	—
423	C₄×C₆₇	#548	1	2	yes	—
424	C₄×C₆₇	#576	1	2	yes	—
425	C₄×C₆₇	#577	1	2	yes	—
426	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
427	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
428	Dic₆₇	—	2	4	no	—
429	Dic₆₇	—	2	4	no	—
430	Dic₆₇	—	4	4	no	—
431	#61329	—	67	1	no	maximal, Sylow
432	C₂×C₆₇	—	2	2	no	—
433	C₂×C₆₇	—	4	2	no	—
434	C₂×C₆₇	—	8	1	no	—
435	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
436	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
437	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
438	D₆₇	—	8	4	no	—
439	#3508	—	67	1	no	—
440	#3503	—	67	1	no	—
441	#3375	—	67	2	no	—
442	#3373	—	67	2	no	—
443	#3368	—	67	2	no	—
444	#3366	—	67	2	no	—
445	#3365	—	67	2	no	—
446	#3362	—	67	2	no	—
447	#3361	—	67	2	no	—
448	#3358	—	67	2	no	—
449	#3136	—	67	2	no	—
450	C₂×#486	—	67	1	no	—
451	#3081	—	67	2	no	—
452	#3079	—	67	1	no	—
453	#3045	—	67	2	no	—
454	#3038	—	67	1	no	—
455	#2960	—	67	1	no	—
456	#2946	—	67	2	no	—
457	C₄×#135	D₆₇	1	1	yes	characteristic, complemented
458	C₆₇	#61329	1	1	yes	characteristic, complemented, Sylow
459	C₂×AGL(1,ℤ/8)	—	67	2	no	—
460	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
461	#559	—	67	2	no	—
462	#559	—	67	2	no	—
463	Q₈²	—	67	2	no	—
464	#557	—	67	2	no	—
465	#554	—	67	2	no	—
466	#554	—	134	2	no	—
467	#550	—	67	2	no	—
468	#550	—	67	2	no	—
469	D₄×Q₈	—	67	2	no	—
470	D₄×Q₈	—	134	2	no	—
471	#546	—	134	2	no	—
472	#546	—	134	2	no	—
473	#544	—	67	2	no	—
474	#544	—	134	2	no	—
475	#540	—	134	2	no	—
476	#535	—	67	2	no	—
477	#533	—	67	1	no	—
478	#533	—	134	1	no	—
479	#532	—	134	1	no	—
480	#532	—	134	1	no	—
481	C₂×C₄⋊Q₈	—	67	1	no	—
482	C₂×C₄⋊Q₈	—	134	1	no	—
483	C₂×#127	—	67	1	no	—
484	#520	—	67	2	no	—
485	#518	—	67	2	no	—
486	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
487	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
488	#490	—	67	4	no	—
489	#489	—	67	4	no	—
490	#488	—	67	4	no	—
491	#486	—	67	4	no	—
492	#486	—	67	2	no	—
493	#486	—	67	2	no	—
494	#486	—	67	2	no	—
495	#486	—	67	2	no	—
496	#478	—	67	4	no	—
497	#478	—	67	4	no	—
498	#477	—	67	2	no	—
499	#476	—	67	2	no	—
500	#476	—	67	4	no	—
501	#475	—	67	2	no	—
502	#474	—	67	2	no	—
503	#474	—	67	4	no	—
504	#464	—	67	4	no	—
505	#463	—	67	4	no	—
506	#460	—	67	4	no	—
507	#460	—	67	2	no	—
508	#460	—	67	2	no	—
509	#459	—	67	4	no	—
510	#459	—	67	2	no	—
511	#459	—	67	2	no	—
512	#446	—	67	2	no	—
513	#446	—	67	2	no	—
514	C₈×Q₈	—	67	2	no	—
515	C₈×Q₈	—	67	2	no	—
516	#442	—	67	4	no	—
517	#440	—	67	4	no	—
518	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
519	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
520	C₄×SD₁₆	—	67	4	no	—
521	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
522	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
523	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
524	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
525	C₄×D₈	—	67	4	no	—
526	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic, complemented
527	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic, complemented
528	#428	—	67	2	no	—
529	#427	C₂×D₆₇	1	1	yes	characteristic
530	#424	—	67	2	no	—
531	#423	—	67	1	no	—
532	#418	—	67	2	no	—
533	#417	—	67	2	no	—
534	#416	C₂×D₆₇	1	1	yes	characteristic
535	#416	C₂×D₆₇	1	1	yes	characteristic
536	C₂×#102	—	67	2	no	—
537	C₂×#102	—	67	2	no	—
538	#405	—	67	2	no	—
539	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
540	C₂×#41	—	134	2	no	—
541	C₂×#41	—	134	2	no	—
542	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
543	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
544	C₂²×Q₈	—	134	2	no	—
545	C₂²×Q₈	—	134	1	no	—
546	C₂²×D₄	—	67	2	no	—
547	C₂²×D₄	—	134	1	no	—
548	C₂²×D₄	—	134	1	no	—
549	AGL(1,ℤ/8)	—	134	8	no	—
550	#135	—	2	4	no	—
551	C₂×Q₁₆	C₂²×D₆₇	1	1	yes	characteristic
552	C₂×SD₁₆	—	67	4	no	—
553	C₂×SD₁₆	C₂²×D₆₇	1	1	yes	characteristic
554	C₂×SD₁₆	C₂²×D₆₇	1	1	yes	characteristic
555	C₂×D₈	—	67	4	no	—
556	C₂×D₈	C₂²×D₆₇	1	1	yes	characteristic
557	C₂×M₁₆	—	67	2	no	—
558	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
559	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
560	C₄⋊Q₈	—	67	4	no	—
561	C₄⋊Q₈	—	67	1	no	—
562	C₄⋊Q₈	—	67	1	no	—
563	C₄⋊Q₈	—	67	2	no	—
564	C₄⋊Q₈	—	67	2	no	—
565	C₄⋊Q₈	—	134	2	no	—
566	C₄⋊Q₈	—	134	2	no	—
567	C₄⋊Q₈	—	134	2	no	—
568	C₄⋊Q₈	—	134	4	no	—
569	C₄⋊Q₈	—	134	1	no	—
570	C₄⋊Q₈	—	134	1	no	—
571	#127	—	67	4	no	—
572	#127	—	67	2	no	—
573	#127	—	67	2	no	—
574	#127	—	134	1	no	—
575	#127	—	134	1	no	—
576	#125	—	67	4	no	—
577	#125	—	67	2	no	—
578	#125	—	134	2	no	—
579	#125	—	134	4	no	—
580	#124	—	67	4	no	—
581	#124	—	134	2	no	—
582	#124	—	134	2	no	—
583	#123	—	134	4	no	—
584	#123	—	134	4	no	—
585	C₂²⋊Q₈	—	67	2	no	—
586	C₂²⋊Q₈	—	67	2	no	—
587	C₂²⋊Q₈	—	134	4	no	—
588	C₂²⋊Q₈	—	134	4	no	—
589	C₂²⋊Q₈	—	134	4	no	—
590	C₂²⋊Q₈	—	134	2	no	—
591	C₂²⋊Q₈	—	134	2	no	—
592	#121	—	134	4	no	—
593	#121	—	134	4	no	—
594	#121	—	134	2	no	—
595	#121	—	134	2	no	—
596	#121	—	134	2	no	—
597	#121	—	134	2	no	—
598	#120	—	134	4	no	—
599	C₄×Q₈	—	67	2	no	—
600	C₄×Q₈	—	67	2	no	—
601	C₄×Q₈	—	67	4	no	—
602	C₄×Q₈	—	134	2	no	—
603	C₄×Q₈	—	134	2	no	—
604	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
605	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
606	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
607	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	67	4	no	—
613	C₄×D₄	—	67	4	no	—
614	C₄×D₄	—	67	4	no	—
615	C₄×D₄	—	134	2	no	—
616	C₄×D₄	—	134	2	no	—
617	C₄×D₄	—	134	2	no	—
618	C₄×D₄	—	134	2	no	—
619	C₄×D₄	—	134	4	no	—
620	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
621	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
622	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
623	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
624	#117	—	2	1	no	—
625	#117	—	2	1	no	—
626	#117	—	67	2	no	—
627	#117	—	134	2	no	—
628	#117	C₂²×D₆₇	1	1	yes	characteristic
629	#117	C₂²×D₆₇	1	1	yes	characteristic
630	C₂×C₄⋊C₄	—	67	2	no	—
631	C₂×C₄⋊C₄	—	134	2	no	—
632	C₂×C₄⋊C₄	—	134	2	no	—
633	C₂×C₄⋊C₄	—	134	1	no	—
634	C₂×C₂²⋊C₄	—	134	4	no	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
638	#107	—	67	4	no	—
639	#107	C₂²×D₆₇	1	1	yes	characteristic
640	#107	C₂²×D₆₇	1	1	yes	characteristic
641	#106	—	67	4	no	—
642	#106	C₂²×D₆₇	1	1	yes	characteristic
643	#106	C₂²×D₆₇	1	1	yes	characteristic
644	C₄⋊C₈	—	67	4	no	—
645	C₄⋊C₈	—	67	4	no	—
646	C₄⋊C₈	—	67	2	no	—
647	C₄⋊C₈	—	67	2	no	—
648	#103	—	67	4	no	—
649	#103	C₂²×D₆₇	1	1	yes	characteristic
650	#103	C₂²×D₆₇	1	1	yes	characteristic
651	#103	C₂²×D₆₇	1	1	yes	characteristic
652	#103	C₂²×D₆₇	1	1	yes	characteristic
653	#102	—	67	4	no	—
654	#102	—	67	4	no	—
655	#102	—	67	4	no	—
656	#102	—	67	4	no	—
657	#102	—	67	4	no	—
658	#102	—	67	4	no	—
659	#102	—	67	4	no	—
660	#102	C₂²×D₆₇	1	1	yes	characteristic
661	#102	C₂²×D₆₇	1	1	yes	characteristic
662	#102	C₂²×D₆₇	1	1	yes	characteristic
663	#102	C₂²×D₆₇	1	1	yes	characteristic
664	#97	—	67	4	no	—
665	C₄×C₈	—	67	4	no	—
666	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
667	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
668	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
669	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
670	C₂⁴	—	134	2	no	—
671	#41	—	2	2	no	—
672	#41	—	2	2	no	—
673	#41	—	2	2	no	—
674	#41	—	536	4	no	—
675	#41	—	536	4	no	—
676	#41	#11761628	1	4	yes	complemented
677	C₂×Q₈	—	536	2	no	—
678	C₂×Q₈	—	536	4	no	—
679	C₂×Q₈	—	67	2	no	—
680	C₂×Q₈	—	67	2	no	—
681	C₂×Q₈	—	134	4	no	—
682	C₂×Q₈	—	134	2	no	—
683	C₂×Q₈	—	134	2	no	—
684	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
685	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	536	2	no	—
689	C₂×D₄	—	536	2	no	—
690	C₂×D₄	—	67	4	no	—
691	C₂×D₄	—	134	4	no	—
692	C₂×D₄	—	134	4	no	—
693	C₂×D₄	—	134	2	no	—
694	C₂×D₄	—	134	2	no	—
695	C₂×D₄	—	134	2	no	—
696	C₂×D₄	—	134	2	no	—
697	C₂×D₄	—	134	2	no	—
698	C₂×D₄	—	134	4	no	—
699	C₂×D₄	—	134	4	no	—
700	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
701	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	134	4	no	—
709	C₂²×C₄	—	134	4	no	—
710	C₂²×C₄	—	134	4	no	—
711	C₂²×C₄	—	134	2	no	—
712	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
713	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
714	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
715	Q₁₆	—	2	2	no	—
716	SD₁₆	—	2	2	no	—
717	SD₁₆	—	2	2	no	—
718	SD₁₆	—	134	8	no	—
719	D₈	—	2	2	no	—
720	D₈	—	134	8	no	—
721	M₁₆	—	134	4	no	—
722	C₂×C₈	—	2	2	no	—
723	C₂×C₈	—	2	2	no	—
724	C₂×C₈	—	67	4	no	—
725	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
726	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
727	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
728	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	67	2	no	—
734	C₄⋊C₄	—	67	2	no	—
735	C₄⋊C₄	—	67	2	no	—
736	C₄⋊C₄	—	67	2	no	—
737	C₄⋊C₄	—	67	4	no	—
738	C₄⋊C₄	—	67	4	no	—
739	C₄⋊C₄	—	67	4	no	—
740	C₄⋊C₄	—	134	4	no	—
741	C₄⋊C₄	—	134	4	no	—
742	C₄⋊C₄	—	134	4	no	—
743	C₄⋊C₄	—	134	4	no	—
744	C₄⋊C₄	—	134	2	no	—
745	C₄⋊C₄	—	134	2	no	—
746	C₄⋊C₄	—	134	2	no	—
747	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
748	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
749	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
750	C₄⋊C₄	C₂³×D₆₇	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	—	2	1	no	—
757	C₂²⋊C₄	—	67	4	no	—
758	C₂²⋊C₄	—	134	4	no	—
759	C₂²⋊C₄	—	134	4	no	—
760	C₂²⋊C₄	—	134	4	no	—
761	C₂²⋊C₄	—	134	4	no	—
762	C₂²⋊C₄	—	134	4	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	1	no	—
768	C₄²	—	2	1	no	—
769	C₄²	—	67	4	no	—
770	C₄²	—	134	4	no	—
771	C₄²	D₄×D₆₇	1	1	yes	characteristic
772	C₄²	D₄×D₆₇	1	1	yes	characteristic
773	C₄²	C₂³×D₆₇	1	1	yes	characteristic
774	C₄²	C₂³×D₆₇	1	1	yes	characteristic
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	268	4	no	—
778	C₂³	—	536	2	no	—
779	C₂³	—	536	2	no	—
780	C₂³	—	134	4	no	—
781	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
782	Q₈	—	2	1	no	—
783	Q₈	—	2	1	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	268	4	no	—
786	Q₈	—	536	2	no	—
787	Q₈	—	536	4	no	—
788	Q₈	—	134	4	no	—
789	Q₈	—	134	4	no	—
790	Q₈	C₂×#11761628	1	2	yes	—
791	D₄	—	2	4	no	—
792	D₄	—	2	1	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	1	no	—
795	D₄	—	4	2	no	—
796	D₄	—	268	4	no	—
797	D₄	—	268	4	no	—
798	D₄	—	268	4	no	—
799	D₄	—	536	2	no	—
800	D₄	—	536	2	no	—
801	D₄	—	536	4	no	—
802	D₄	—	536	4	no	—
803	D₄	—	134	4	no	—
804	D₄	—	134	4	no	—
805	D₄	C₂×#11761628	1	2	yes	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	536	4	no	—
821	C₂×C₄	—	536	4	no	—
822	C₂×C₄	—	536	2	no	—
823	C₂×C₄	—	536	4	no	—
824	C₂×C₄	—	67	4	no	—
825	C₂×C₄	—	67	4	no	—
826	C₂×C₄	—	134	4	no	—
827	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
828	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
829	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
830	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
831	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
832	C₂×C₄	C₂×#11761628	1	2	yes	—
833	C₂×C₄	#14524090	1	2	yes	—
834	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
835	C₈	—	2	1	no	—
836	C₈	—	2	1	no	—
837	C₈	—	2	1	no	—
838	C₈	—	2	1	no	—
839	C₈	—	134	4	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	268	4	no	—
849	C₂²	—	268	4	no	—
850	C₂²	—	268	4	no	—
851	C₂²	—	1072	4	no	—
852	C₂²	#16864055	1	2	yes	—
853	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
854	C₄	—	2	2	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	268	4	no	—
863	C₄	—	134	4	no	—
864	C₄	—	134	4	no	—
865	C₄	#16864055	1	2	yes	—
866	C₄	#16864198	1	2	yes	—
867	C₄	#16864203	1	2	yes	—
868	C₄	C₂²×#11761628	1	1	yes	characteristic
869	C₄	C₂×#14524090	1	1	yes	characteristic
870	C₂	—	2	2	no	—
871	C₂	—	4	2	no	—
872	C₂	—	8	1	no	—
873	C₂	—	536	4	no	—
874	C₂	C₂×#16864055	1	1	yes	characteristic
875	C₂	C₂×#16864198	1	1	yes	characteristic
876	C₂	C₂×#16864203	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₆₇
commutator, cosocle	C₂×C₄×C₆₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₄×#135×C₆₇	C₂
socle	C₂²×C₆₇	C₂³×D₄
hypercenter	C₄×#135	D₆₇
hypocenter	C₆₇	#61329
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #22574085	C₂	semidirect
2. #22574028	C₂	semidirect
3. #22573021	C₂	semidirect
4. #22572999	C₂	semidirect
5. #22572936	C₂	semidirect
6. #22572914	C₂	semidirect
7. #22572903	C₂	semidirect
8. #22572878	C₂	semidirect
9. #22572867	C₂	semidirect
10. #22572842	C₂	semidirect
11. #22570567	C₂	semidirect
12. C₂×#16863743	C₂	semidirect
13. #22570043	C₂	semidirect
14. #22570024	C₂	semidirect
15. #22569746	C₂	semidirect
16. #22569689	C₂	semidirect
17. #22569143	C₂	semidirect
18. #22569044	C₂	semidirect
19. C₄×#135×C₆₇	C₂	semidirect
23. Q₈×Dic₁₃₄	C₂²	semidirect
24. #16864125	C₂²	semidirect
26. #16864103	C₂²	semidirect
30. D₄×Dic₁₃₄	C₂²	semidirect
46. #16863759	C₂²	semidirect
47. #16863757	C₂²	semidirect
48. #16863752	C₂²	semidirect
53. #16863741	C₂²	semidirect
54. #16863699	C₂²	semidirect
55. #16863695	C₂²	semidirect
56. #16863691	C₂²	semidirect
57. #16863686	C₂²	semidirect
58. #16863685	C₂²	semidirect
59. #16863681	C₂²	semidirect
60. #16863676	C₂²	semidirect
61. #16863675	C₂²	semidirect
62. #16863620	C₂²	semidirect
63. #16863613	C₂²	semidirect
66. #16863594	C₂²	semidirect
69. #16863589	C₂²	semidirect
70. #16863526	C₂²	semidirect
71. #16863526	C₂²	semidirect
72. C₈×Dic₁₃₄	C₂²	semidirect
73. C₈×Dic₁₃₄	C₂²	semidirect
74. #16863505	C₂²	semidirect
75. #16863499	C₂²	semidirect
76. #16863481	C₂²	semidirect
77. #16863476	C₂²	semidirect
89. C₄×Q₁₆×C₆₇	C₂²	semidirect
90. C₄×Q₁₆×C₆₇	C₂²	semidirect
91. C₄×SD₁₆×C₆₇	C₂²	semidirect
92. C₄×SD₁₆×C₆₇	C₂²	semidirect
93. C₄×SD₁₆×C₆₇	C₂²	semidirect
94. C₄×SD₁₆×C₆₇	C₂²	semidirect
95. C₄×D₈×C₆₇	C₂²	semidirect
96. C₄×D₈×C₆₇	C₂²	semidirect
286. #41×C₆₇	#41	semidirect
457. C₄×#135	D₆₇	semidirect
458. C₆₇	#61329	semidirect
518. C₄×Q₁₆	C₂×D₆₇	semidirect
519. C₄×Q₁₆	C₂×D₆₇	semidirect
521. C₄×SD₁₆	C₂×D₆₇	semidirect
522. C₄×SD₁₆	C₂×D₆₇	semidirect
523. C₄×SD₁₆	C₂×D₆₇	semidirect
524. C₄×SD₁₆	C₂×D₆₇	semidirect
526. C₄×D₈	C₂×D₆₇	semidirect
527. C₄×D₈	C₂×D₆₇	semidirect
676. #41	#11761628	semidirect

Maximal subgroups

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

subgroup	index
#22574085	2
#22574028	2
#22573021	2
#22572999	2
#22572936	2
#22572914	2
#22572903	2
#22572878	2
#22572867	2
#22572842	2
#22570567	2
C₂×#16863743	2
#22570043	2
#22570024	2
#22569746	2
#22569689	2
#22569143	2
#22569044	2
C₄×#135×C₆₇	2
#61329	67