Subgroups — #25966675

Order 11008.

1970 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148011	C₂	1	2	yes	maximal, complemented
2	#19145333	C₂	1	2	yes	maximal, complemented
3	#19145324	C₂	1	2	yes	maximal, complemented
4	#19145293	C₂	1	4	yes	maximal, complemented
5	#19145278	C₂	1	4	yes	maximal, complemented
6	#19145245	C₂	1	2	yes	maximal, complemented
7	#19145212	C₂	1	2	yes	maximal, complemented
8	#19145126	C₂	1	1	yes	maximal, characteristic, complemented
9	#19145081	C₂	1	1	yes	maximal, characteristic, complemented
10	#19144951	C₂	1	2	yes	maximal, complemented
11	#19144275	C₂	1	2	yes	maximal, complemented
12	#19144257	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144243	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#13063353	C₂	1	2	yes	maximal, complemented
15	#19143397	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14583012	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13063353	C₂²	1	2	yes	—
19	C₂×#13063347	C₂²	1	1	yes	characteristic
20	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
21	#14583527	C₂²	1	2	yes	—
22	#14583521	—	2	2	no	—
23	#14583520	C₂²	1	4	yes	complemented
24	#14583504	C₂²	1	4	yes	complemented
25	#14583500	—	2	2	no	—
26	#14583482	—	2	4	no	—
27	#14583477	C₂²	1	2	yes	—
28	#14583468	C₂²	1	2	yes	—
29	#14583463	C₂²	1	2	yes	—
30	#14583449	C₂²	1	4	yes	complemented
31	#14583446	—	2	2	no	—
32	#14583436	—	2	2	no	—
33	#14583433	C₂²	1	4	yes	complemented
34	#14583408	—	2	4	no	—
35	C₄×#10621898	C₂²	1	2	yes	—
36	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
37	#14583308	C₂²	1	4	yes	complemented
38	#14583301	C₂²	1	2	yes	complemented
39	#14583297	C₂²	1	2	yes	complemented
40	#14583288	C₂²	1	4	yes	—
41	#14583283	C₂²	1	2	yes	—
42	#14583276	C₂²	1	2	yes	—
43	#14583264	C₂²	1	4	yes	complemented
44	#14583259	C₂²	1	4	yes	complemented
45	#14583254	C₂²	1	4	yes	complemented
46	#14583246	C₂²	1	4	yes	complemented
47	#14583157	C₂²	1	2	yes	complemented
48	#14583152	C₂²	1	2	yes	—
49	#14583152	C₂²	1	2	yes	—
50	#14583152	C₂²	1	2	yes	complemented
51	#14583152	C₂²	1	4	yes	complemented
52	#14583145	C₂²	1	4	yes	complemented
53	#14583135	C₂²	1	4	yes	—
54	#14583135	C₂²	1	4	yes	complemented
55	#14583128	C₂²	1	4	yes	complemented
56	#14583128	C₂²	1	4	yes	complemented
57	#14583012	C₂²	1	2	yes	—
58	#14583012	C₂²	1	2	yes	—
59	#14583012	C₂²	1	2	yes	—
60	#14583012	C₂²	1	2	yes	—
61	#14583012	C₂²	1	1	yes	characteristic, complemented
62	#14583012	C₂²	1	4	yes	complemented
63	#14583012	C₂²	1	1	yes	characteristic, complemented
64	#14583007	C₂²	1	1	yes	characteristic, complemented
65	#14583007	C₂²	1	1	yes	characteristic, complemented
66	#14583001	C₂²	1	2	yes	complemented
67	#14583001	C₂²	1	2	yes	complemented
68	#14583001	C₂²	1	4	yes	complemented
69	C₄×#10621873	C₂²	1	4	yes	complemented
70	C₄×D₃₄₄	C₂²	1	4	yes	complemented
71	#14582941	C₂²	1	2	yes	—
72	#14582937	C₂²	1	1	yes	characteristic
73	C₂×#13063257	C₂²	1	1	yes	characteristic
74	#14582905	C₂²	1	2	yes	—
75	#14582901	C₂²	1	2	yes	—
76	#14582896	C₂²	1	2	yes	—
77	C₂×#13063247	C₂²	1	2	yes	—
78	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
79	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
80	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
81	C₄₃×#405	C₂²	1	1	yes	characteristic
82	C₄₃×#405	C₂²	1	1	yes	characteristic
83	C₄₃×#405	C₂²	1	2	yes	complemented
84	C₄₃×#405	C₂²	1	2	yes	complemented
85	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
86	C₄×M₁₆×C₄₃	C₂²	1	2	yes	complemented
87	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
88	C₂×#97×C₄₃	C₂²	1	2	yes	complemented
89	C₂×#10621898	—	2	4	no	—
90	C₂×#10621898	C₂³	1	2	yes	—
91	C₂²×D₁₇₂	C₂³	1	2	yes	—
92	C₂²×C₄×D₄₃	—	2	2	no	—
93	#13063353	—	2	8	no	—
94	#13063347	—	2	4	no	—
95	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
96	C₂×#10621873	C₂³	1	2	yes	—
97	C₂×#10621873	C₂³	1	4	yes	—
98	C₂×D₃₄₄	—	2	4	no	—
99	C₂×D₃₄₄	C₂³	1	2	yes	—
100	C₂×D₃₄₄	C₂³	1	4	yes	—
101	C₂×D₃₄₄	C₂³	1	2	yes	—
102	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
103	#13063325	C₂³	1	4	yes	—
104	#13063324	—	2	2	no	—
105	#13063322	C₂³	1	4	yes	—
106	#13063321	—	2	2	no	—
107	#13063320	—	2	4	no	—
108	#13063319	—	2	4	no	—
109	#13063317	C₂³	1	4	yes	—
110	#13063316	—	2	2	no	—
111	#13063314	—	2	2	no	—
112	#13063313	—	2	4	no	—
113	#13063313	C₂³	1	4	yes	—
114	#13063311	—	2	4	no	—
115	#13063310	—	2	4	no	—
116	#13063310	—	2	4	no	—
117	#13063308	—	2	4	no	—
118	#13063307	—	2	4	no	—
119	#13063304	C₂³	1	4	yes	—
120	#13063303	—	2	4	no	—
121	#13063302	—	2	4	no	—
122	#13063301	—	2	2	no	—
123	#13063300	—	2	2	no	—
124	#13063300	—	2	2	no	—
125	#13063299	—	2	4	no	—
126	#13063299	C₂³	1	4	yes	—
127	#13063299	C₂³	1	4	yes	—
128	#13063299	C₂³	1	4	yes	—
129	#13063298	—	2	4	no	—
130	#13063298	—	2	4	no	—
131	#13063297	—	2	4	no	—
132	#13063296	—	2	2	no	—
133	#13063295	—	2	4	no	—
134	#13063293	—	2	4	no	—
135	C₄×Dic₈₆	C₂³	1	2	yes	—
136	C₄×Dic₈₆	C₂³	1	2	yes	—
137	C₄×D₁₇₂	—	2	2	no	—
138	C₄×D₁₇₂	—	2	2	no	—
139	C₄×D₁₇₂	—	2	4	no	—
140	C₄×D₁₇₂	C₂³	1	4	yes	—
141	C₄×D₁₇₂	C₂³	1	4	yes	—
142	C₄×D₁₇₂	C₂³	1	2	yes	—
143	C₄×D₁₇₂	C₂³	1	2	yes	—
144	C₄×C₂²⋊D₄₃	—	2	2	no	—
145	C₄×C₂²⋊D₄₃	—	2	2	no	—
146	C₄×C₂²⋊D₄₃	—	2	4	no	—
147	#13063284	C₂³	1	2	yes	—
148	#13063282	—	2	2	no	—
149	#13063282	—	2	4	no	—
150	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
151	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
152	C₄²×D₄₃	—	2	2	no	—
153	#13063259	C₂³	1	4	yes	—
154	#13063259	C₂³	1	2	yes	—
155	#13063257	C₂³	1	1	yes	characteristic
156	#13063257	C₂³	1	2	yes	—
157	#13063257	C₂³	1	4	yes	—
158	#13063257	C₂³	1	1	yes	characteristic
159	#13063257	C₂³	1	2	yes	—
160	#13063250	C₂³	1	2	yes	—
161	#13063250	C₂³	1	4	yes	—
162	#13063250	C₂³	1	2	yes	—
163	#13063247	C₂³	1	4	yes	—
164	#13063247	C₂³	1	4	yes	—
165	#13063247	C₂³	1	4	yes	—
166	#13063247	C₂³	1	4	yes	—
167	#13063247	C₂³	1	2	yes	—
168	#13063247	C₂³	1	4	yes	—
169	#13063247	C₂³	1	2	yes	—
170	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
171	#131×C₄₃	—	2	4	no	—
172	#131×C₄₃	—	2	4	no	—
173	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
174	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
175	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
176	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
178	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
179	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
181	C₄×Q₈×C₄₃	D₄	1	2	yes	—
182	C₄×D₄×C₄₃	D₄	1	4	yes	—
183	C₄×D₄×C₄₃	D₄	1	2	yes	—
184	#117×C₄₃	C₂³	1	1	yes	characteristic
185	#117×C₄₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
188	#97×C₄₃	C₂³	1	2	yes	—
189	#97×C₄₃	C₂³	1	1	yes	characteristic
190	#97×C₄₃	C₂³	1	1	yes	characteristic
191	#97×C₄₃	C₂³	1	1	yes	characteristic
192	#97×C₄₃	C₂³	1	1	yes	characteristic
193	#97×C₄₃	C₂³	1	2	yes	—
194	#97×C₄₃	C₂³	1	2	yes	—
195	C₄×C₈×C₄₃	C₂³	1	2	yes	—
196	C₄×C₈×C₄₃	C₂³	1	2	yes	—
197	C₄×C₈×C₄₃	C₂³	1	2	yes	—
198	C₂³×D₄₃	—	2	2	no	—
199	#41×C₄₃	—	2	2	no	—
200	#41×C₄₃	—	2	2	no	—
201	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
202	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
203	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
206	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
208	C₂×C₂²⋊D₄₃	—	2	2	no	—
209	C₂×C₂²⋊D₄₃	—	2	4	no	—
210	C₂×C₂²⋊D₄₃	—	2	4	no	—
211	C₂×C₂²⋊D₄₃	—	2	4	no	—
212	C₂²×Dic₄₃	—	2	2	no	—
213	#10621898	—	2	4	no	—
214	#10621898	—	2	4	no	—
215	#10621898	—	8	8	no	—
216	C₂×D₁₇₂	—	2	2	no	—
217	C₂×D₁₇₂	—	2	4	no	—
218	C₂×D₁₇₂	—	2	4	no	—
219	C₂×D₁₇₂	—	2	4	no	—
220	C₂×D₁₇₂	—	2	4	no	—
221	C₂×D₁₇₂	C₂⁴	1	4	yes	—
222	C₂×D₁₇₂	C₂⁴	1	2	yes	—
223	C₂×C₄×D₄₃	—	2	2	no	—
224	C₂×C₄×D₄₃	—	2	2	no	—
225	C₂×C₄×D₄₃	—	2	4	no	—
226	C₂×C₄×D₄₃	—	2	2	no	—
227	C₂×C₄×D₄₃	—	2	4	no	—
228	C₂×C₄×D₄₃	—	8	4	no	—
229	C₂×Dic₈₆	—	2	4	no	—
230	C₂×Dic₈₆	C₂⁴	1	2	yes	—
231	M₁₆×C₄₃	—	2	2	no	—
232	M₁₆×C₄₃	—	2	4	no	—
233	M₁₆×C₄₃	—	2	4	no	—
234	M₁₆×C₄₃	#41	1	4	yes	complemented
235	C₂×C₈×C₄₃	—	2	2	no	—
236	C₂×C₈×C₄₃	—	2	4	no	—
237	C₂×C₈×C₄₃	—	2	4	no	—
238	C₂×C₈×C₄₃	#41	1	4	yes	complemented
239	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
240	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
245	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
246	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
247	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
248	C₂²⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
249	C₄²×C₄₃	C₂×D₄	1	2	yes	—
250	C₄²×C₄₃	C₂×D₄	1	4	yes	—
251	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
252	C₄²×C₄₃	C₂⁴	1	2	yes	—
253	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
254	C₂²⋊Dic₄₃	—	2	2	no	—
255	C₂²⋊Dic₄₃	—	2	4	no	—
256	(C₂×D₄₃)⋊C₄	—	2	4	no	—
257	(C₂×D₄₃)⋊C₄	—	2	4	no	—
258	(C₂×D₄₃)⋊C₄	—	2	2	no	—
259	(C₂×D₄₃)⋊C₄	—	2	2	no	—
260	(C₂×D₄₃)⋊C₄	—	2	4	no	—
261	(C₂×D₄₃)⋊C₄	—	2	4	no	—
262	(C₂×D₄₃)⋊C₄	—	2	4	no	—
263	(C₂×D₄₃)⋊C₄	—	2	4	no	—
264	(C₂×D₄₃)⋊C₄	—	2	4	no	—
265	C₄⋊Dic₄₃	—	2	2	no	—
266	C₄⋊Dic₄₃	—	2	4	no	—
267	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
268	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
269	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
270	Dic₄₃⋊C₄	—	2	2	no	—
271	Dic₄₃⋊C₄	—	2	2	no	—
272	Dic₄₃⋊C₄	—	2	4	no	—
273	Dic₄₃⋊C₄	—	2	4	no	—
274	Dic₄₃⋊C₄	—	2	4	no	—
275	C₄×Dic₄₃	—	2	2	no	—
276	C₄×Dic₄₃	—	2	2	no	—
277	C₄×Dic₄₃	—	2	2	no	—
278	Dic₁₇₂	—	2	2	no	—
279	D₃₄₄	—	2	4	no	—
280	D₃₄₄	—	2	4	no	—
281	D₃₄₄	—	2	2	no	—
282	D₃₄₄	—	2	8	no	—
283	#10621873	—	2	4	no	—
284	#10621873	—	2	8	no	—
285	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
286	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
287	C₂²×D₄₃	—	2	4	no	—
288	C₂²×D₄₃	—	2	2	no	—
289	C₂²×D₄₃	—	4	4	no	—
290	C₂²×D₄₃	—	8	2	no	—
291	C₂²×D₄₃	—	8	2	no	—
292	Q₈×C₄₃	—	2	2	no	—
293	D₄×C₄₃	—	2	4	no	—
294	D₄×C₄₃	—	2	2	no	—
295	C₂×C₄×C₄₃	—	2	2	no	—
296	C₂×C₄×C₄₃	—	2	2	no	—
297	C₂×C₄×C₄₃	—	4	2	no	—
298	C₂×C₄×C₄₃	—	4	4	no	—
299	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
302	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
305	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
306	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
307	C₂²⋊D₄₃	—	4	4	no	—
308	C₂²⋊D₄₃	—	8	4	no	—
309	C₂²⋊D₄₃	—	8	4	no	—
310	C₂²⋊D₄₃	—	8	4	no	—
311	C₂×Dic₄₃	—	2	2	no	—
312	C₂×Dic₄₃	—	2	2	no	—
313	C₂×Dic₄₃	—	2	2	no	—
314	C₂×Dic₄₃	—	2	4	no	—
315	C₂×Dic₄₃	—	8	2	no	—
316	D₁₇₂	—	2	4	no	—
317	D₁₇₂	—	2	2	no	—
318	D₁₇₂	—	2	4	no	—
319	D₁₇₂	—	2	2	no	—
320	D₁₇₂	—	4	4	no	—
321	D₁₇₂	—	8	4	no	—
322	D₁₇₂	—	8	4	no	—
323	C₄×D₄₃	—	4	8	no	—
324	C₄×D₄₃	—	4	4	no	—
325	C₄×D₄₃	—	4	4	no	—
326	C₄×D₄₃	—	8	2	no	—
327	C₄×D₄₃	—	8	4	no	—
328	Dic₈₆	—	2	2	no	—
329	Dic₈₆	—	2	2	no	—
330	Dic₈₆	—	8	4	no	—
331	C₈×C₄₃	—	2	1	no	—
332	C₈×C₄₃	—	2	1	no	—
333	C₈×C₄₃	—	2	2	no	—
334	C₈×C₄₃	C₂×#41	1	2	yes	—
335	C₈×C₄₃	C₂×#41	1	4	yes	—
336	C₈×C₄₃	C₂×#41	1	2	yes	—
337	#60698	—	43	1	no	maximal, Sylow
338	C₂²×C₄₃	—	2	2	no	—
339	C₂²×C₄₃	—	2	4	no	—
340	C₂²×C₄₃	—	2	2	no	—
341	C₂²×C₄₃	#532	1	2	yes	—
342	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
343	C₂×D₄₃	—	4	4	no	—
344	C₂×D₄₃	—	4	4	no	—
345	C₂×D₄₃	—	4	2	no	—
346	C₂×D₄₃	—	4	2	no	—
347	C₂×D₄₃	—	4	4	no	—
348	C₂×D₄₃	—	4	2	no	—
349	C₂×D₄₃	—	8	8	no	—
350	C₄×C₄₃	—	2	4	no	—
351	C₄×C₄₃	—	2	2	no	—
352	C₄×C₄₃	—	2	2	no	—
353	C₄×C₄₃	—	2	2	no	—
354	C₄×C₄₃	#532	1	2	yes	—
355	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
356	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
357	Dic₄₃	—	4	2	no	—
358	Dic₄₃	—	4	4	no	—
359	Dic₄₃	—	4	2	no	—
360	Dic₄₃	—	4	2	no	—
361	#3460	—	43	2	no	—
362	#3184	—	43	2	no	—
363	#3183	—	43	2	no	—
364	#3180	—	43	4	no	—
365	#3179	—	43	4	no	—
366	#3176	—	43	2	no	—
367	#3173	—	43	2	no	—
368	#3163	—	43	1	no	—
369	#3155	—	43	1	no	—
370	#3136	—	43	2	no	—
371	#3062	—	43	2	no	—
372	#3060	—	43	1	no	—
373	#3058	—	43	1	no	—
374	C₄×AGL(1,ℤ/8)	—	43	2	no	—
375	#2943	—	43	1	no	—
376	C₂×#442	—	43	1	no	—
377	#2875	D₄₃	1	1	yes	characteristic, complemented
378	C₂×C₄₃	—	2	2	no	—
379	C₂×C₄₃	—	4	2	no	—
380	C₂×C₄₃	C₂×#532	1	1	yes	characteristic
381	C₂×C₄₃	#3585	1	2	yes	—
382	D₄₃	—	8	2	no	—
383	D₄₃	—	8	4	no	—
384	C₂×AGL(1,ℤ/8)	—	43	2	no	—
385	C₂×#135	—	43	1	no	—
386	C₂²×D₈	—	43	1	no	—
387	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
388	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
389	#544	—	43	2	no	—
390	#542	—	43	4	no	—
391	#542	—	86	2	no	—
392	#540	—	43	4	no	—
393	#540	—	86	2	no	—
394	#538	—	86	4	no	—
395	#537	—	43	2	no	—
396	#535	—	43	2	no	—
397	#535	—	43	2	no	—
398	#532	—	43	4	no	—
399	#532	—	86	2	no	—
400	#529	—	43	4	no	—
401	#529	—	86	2	no	—
402	#525	—	86	4	no	—
403	C₄×#41	—	43	2	no	—
404	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
405	C₂×C₄×D₄	—	43	2	no	—
406	#501	—	43	4	no	—
407	#499	—	43	2	no	—
408	#498	—	43	2	no	—
409	#496	—	43	4	no	—
410	#495	—	43	2	no	—
411	#493	—	43	2	no	—
412	#490	—	43	4	no	—
413	#489	—	43	4	no	—
414	#488	—	43	4	no	—
415	#486	—	43	4	no	—
416	#470	—	43	2	no	—
417	#469	—	43	2	no	—
418	#469	—	43	2	no	—
419	#469	—	43	2	no	—
420	#469	—	43	4	no	—
421	#468	—	43	4	no	—
422	#466	—	43	4	no	—
423	#466	—	43	4	no	—
424	#465	—	43	4	no	—
425	#465	—	43	4	no	—
426	#442	—	43	2	no	—
427	#442	—	43	1	no	—
428	#442	—	43	2	no	—
429	#442	—	43	2	no	—
430	#442	—	43	4	no	—
431	#442	—	43	2	no	—
432	#442	—	43	1	no	—
433	#441	—	43	1	no	—
434	#441	—	43	1	no	—
435	#440	—	43	2	no	—
436	#440	—	43	2	no	—
437	#440	—	43	4	no	—
438	C₄×SD₁₆	—	43	4	no	—
439	C₄×D₈	—	43	4	no	—
440	#428	—	43	2	no	—
441	#427	—	43	1	no	—
442	C₂×#106	—	43	1	no	—
443	#418	—	43	2	no	—
444	#417	—	43	2	no	—
445	#416	—	43	2	no	—
446	C₂×#102	—	43	2	no	—
447	#405	C₂×D₄₃	1	1	yes	characteristic
448	#405	C₂×D₄₃	1	1	yes	characteristic
449	#405	C₂×D₄₃	1	2	yes	complemented
450	#405	C₂×D₄₃	1	2	yes	complemented
451	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
452	C₄×M₁₆	C₂×D₄₃	1	2	yes	complemented
453	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
454	C₂×#97	C₂×D₄₃	1	2	yes	complemented
455	C₄₃	#60698	1	1	yes	characteristic, complemented, Sylow
456	C₂×#41	—	43	2	no	—
457	C₂×#41	—	86	4	no	—
458	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
459	C₂²×D₄	—	43	2	no	—
460	C₂³×C₄	—	86	2	no	—
461	AGL(1,ℤ/8)	—	86	8	no	—
462	#135	—	86	4	no	—
463	C₂×Q₁₆	—	43	1	no	—
464	C₂×SD₁₆	—	43	2	no	—
465	C₂×SD₁₆	—	43	4	no	—
466	C₂×D₈	—	43	2	no	—
467	C₂×D₈	—	43	2	no	—
468	C₂×D₈	—	43	1	no	—
469	C₂×D₈	—	43	4	no	—
470	C₂×D₈	—	86	4	no	—
471	#131	—	2	4	no	—
472	#131	—	2	4	no	—
473	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
474	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
475	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
476	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
477	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
478	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
479	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
480	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
481	C₄⋊Q₈	—	43	4	no	—
482	C₄⋊Q₈	—	86	2	no	—
483	#127	—	43	4	no	—
484	#127	—	86	2	no	—
485	#126	—	86	4	no	—
486	#126	—	86	4	no	—
487	#125	—	43	4	no	—
488	#125	—	86	2	no	—
489	#124	—	43	4	no	—
490	#124	—	86	2	no	—
491	#124	—	86	4	no	—
492	#124	—	86	4	no	—
493	#123	—	86	4	no	—
494	#123	—	86	4	no	—
495	#123	—	86	4	no	—
496	#123	—	86	4	no	—
497	C₂²⋊Q₈	—	43	4	no	—
498	C₂²⋊Q₈	—	86	2	no	—
499	C₂²⋊Q₈	—	86	4	no	—
500	C₂²⋊Q₈	—	86	4	no	—
501	#121	—	43	4	no	—
502	#121	—	43	4	no	—
503	#121	—	43	4	no	—
504	#121	—	86	4	no	—
505	#121	—	86	2	no	—
506	#121	—	86	4	no	—
507	#121	—	86	2	no	—
508	#121	—	86	2	no	—
509	#121	—	86	4	no	—
510	#121	—	86	4	no	—
511	#120	—	86	4	no	—
512	#120	—	86	4	no	—
513	C₄×Q₈	—	43	2	no	—
514	C₄×Q₈	—	43	2	no	—
515	C₄×Q₈	D₁₇₂	1	2	yes	—
516	C₄×D₄	—	43	4	no	—
517	C₄×D₄	—	43	4	no	—
518	C₄×D₄	—	43	2	no	—
519	C₄×D₄	—	43	2	no	—
520	C₄×D₄	—	86	2	no	—
521	C₄×D₄	—	86	2	no	—
522	C₄×D₄	—	86	4	no	—
523	C₄×D₄	—	86	2	no	—
524	C₄×D₄	—	86	2	no	—
525	C₄×D₄	—	86	4	no	—
526	C₄×D₄	D₁₇₂	1	4	yes	—
527	C₄×D₄	D₁₇₂	1	2	yes	—
528	#117	—	43	2	no	—
529	#117	—	86	2	no	—
530	#117	—	86	4	no	—
531	#117	C₂²×D₄₃	1	1	yes	characteristic
532	#117	C₂²×D₄₃	1	2	yes	—
533	C₂×C₄⋊C₄	—	43	2	no	—
534	C₂×C₂²⋊C₄	—	86	2	no	—
535	C₂×C₄²	—	86	2	no	—
536	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
537	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
538	#107	—	43	2	no	—
539	#107	—	43	4	no	—
540	#106	—	43	2	no	—
541	#106	—	43	2	no	—
542	#106	—	43	1	no	—
543	#106	—	43	1	no	—
544	#106	—	43	4	no	—
545	#103	—	43	2	no	—
546	#103	—	43	2	no	—
547	#103	—	43	4	no	—
548	#102	—	43	4	no	—
549	#102	—	43	4	no	—
550	#102	—	43	2	no	—
551	#102	—	43	2	no	—
552	#102	—	43	4	no	—
553	#102	—	43	4	no	—
554	#102	—	43	4	no	—
555	#97	C₂²×D₄₃	1	1	yes	characteristic
556	#97	C₂²×D₄₃	1	1	yes	characteristic
557	#97	C₂²×D₄₃	1	1	yes	characteristic
558	#97	C₂²×D₄₃	1	1	yes	characteristic
559	#97	C₂²×D₄₃	1	2	yes	—
560	#97	C₂²×D₄₃	1	2	yes	—
561	#97	C₂²×D₄₃	1	2	yes	—
562	C₄×C₈	C₂²×D₄₃	1	2	yes	—
563	C₄×C₈	C₂²×D₄₃	1	2	yes	—
564	C₄×C₈	C₂²×D₄₃	1	2	yes	—
565	C₂⁴	—	86	2	no	—
566	#41	—	2	2	no	—
567	#41	—	2	2	no	—
568	#41	—	86	4	no	—
569	#41	—	86	4	no	—
570	#41	—	344	8	no	—
571	C₂×Q₈	—	43	2	no	—
572	C₂×Q₈	—	86	4	no	—
573	C₂×Q₈	C₂×D₁₇₂	1	1	yes	characteristic
574	C₂×D₄	—	43	4	no	—
575	C₂×D₄	—	43	2	no	—
576	C₂×D₄	—	86	4	no	—
577	C₂×D₄	—	86	4	no	—
578	C₂×D₄	—	86	4	no	—
579	C₂×D₄	—	86	2	no	—
580	C₂×D₄	—	86	4	no	—
581	C₂×D₄	—	86	4	no	—
582	C₂×D₄	—	86	2	no	—
583	C₂×D₄	—	86	4	no	—
584	C₂×D₄	—	86	4	no	—
585	C₂×D₄	C₂×D₁₇₂	1	2	yes	—
586	C₂×D₄	C₂×D₁₇₂	1	1	yes	characteristic
587	C₂²×C₄	—	86	2	no	—
588	C₂²×C₄	—	86	2	no	—
589	C₂²×C₄	—	86	4	no	—
590	C₂²×C₄	—	86	2	no	—
591	C₂²×C₄	—	86	2	no	—
592	C₂²×C₄	—	86	4	no	—
593	C₂²×C₄	—	344	4	no	—
594	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
595	C₂²×C₄	C₂×D₁₇₂	1	4	yes	—
596	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
597	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
598	Q₁₆	—	86	2	no	—
599	SD₁₆	—	86	4	no	—
600	SD₁₆	—	86	8	no	—
601	D₈	—	86	4	no	—
602	D₈	—	86	4	no	—
603	D₈	—	86	2	no	—
604	D₈	—	86	8	no	—
605	M₁₆	—	2	2	no	—
606	M₁₆	—	2	4	no	—
607	M₁₆	—	2	4	no	—
608	M₁₆	#10621898	1	4	yes	complemented
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	—	2	4	no	—
611	C₂×C₈	—	2	4	no	—
612	C₂×C₈	#10621898	1	4	yes	complemented
613	C₂×C₈	C₂³×D₄₃	1	2	yes	—
614	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
615	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
616	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
617	C₂×C₈	C₂³×D₄₃	1	2	yes	—
618	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
619	C₄⋊C₄	—	43	4	no	—
620	C₄⋊C₄	—	43	2	no	—
621	C₄⋊C₄	—	43	2	no	—
622	C₄⋊C₄	—	86	2	no	—
623	C₄⋊C₄	—	86	2	no	—
624	C₄⋊C₄	—	86	2	no	—
625	C₄⋊C₄	—	86	4	no	—
626	C₄⋊C₄	—	86	4	no	—
627	C₄⋊C₄	—	86	4	no	—
628	C₄⋊C₄	—	86	4	no	—
629	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
630	C₄⋊C₄	C₂×D₁₇₂	1	4	yes	—
631	C₂²⋊C₄	—	86	2	no	—
632	C₂²⋊C₄	—	86	4	no	—
633	C₂²⋊C₄	—	86	4	no	—
634	C₂²⋊C₄	—	86	4	no	—
635	C₂²⋊C₄	—	86	2	no	—
636	C₂²⋊C₄	—	86	2	no	—
637	C₂²⋊C₄	—	86	4	no	—
638	C₂²⋊C₄	—	86	4	no	—
639	C₂²⋊C₄	—	86	4	no	—
640	C₂²⋊C₄	—	86	4	no	—
641	C₂²⋊C₄	—	86	4	no	—
642	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
643	C₂²⋊C₄	C₂×D₁₇₂	1	4	yes	—
644	C₄²	—	86	2	no	—
645	C₄²	—	86	2	no	—
646	C₄²	—	86	2	no	—
647	C₄²	C₂×D₁₇₂	1	2	yes	—
648	C₄²	C₂×D₁₇₂	1	4	yes	—
649	C₄²	C₂³×D₄₃	1	1	yes	characteristic
650	C₄²	C₂³×D₄₃	1	2	yes	—
651	C₄²	C₂³×D₄₃	1	1	yes	characteristic
652	C₂³	—	86	4	no	—
653	C₂³	—	86	2	no	—
654	C₂³	—	344	2	no	—
655	C₂³	—	344	2	no	—
656	C₂³	—	172	4	no	—
657	C₂³	C₂²×D₁₇₂	1	2	yes	—
658	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
659	Q₈	—	2	2	no	—
660	Q₈	—	86	2	no	—
661	Q₈	—	86	2	no	—
662	Q₈	—	344	4	no	—
663	D₄	—	2	4	no	—
664	D₄	—	2	2	no	—
665	D₄	—	86	4	no	—
666	D₄	—	86	2	no	—
667	D₄	—	86	4	no	—
668	D₄	—	86	2	no	—
669	D₄	—	344	4	no	—
670	D₄	—	344	4	no	—
671	D₄	—	344	4	no	—
672	D₄	—	344	4	no	—
673	D₄	—	344	4	no	—
674	D₄	—	172	4	no	—
675	D₄	—	172	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	4	2	no	—
679	C₂×C₄	—	4	4	no	—
680	C₂×C₄	—	86	2	no	—
681	C₂×C₄	—	86	2	no	—
682	C₂×C₄	—	86	2	no	—
683	C₂×C₄	—	86	4	no	—
684	C₂×C₄	—	344	4	no	—
685	C₂×C₄	—	344	2	no	—
686	C₂×C₄	—	344	2	no	—
687	C₂×C₄	—	172	8	no	—
688	C₂×C₄	—	172	4	no	—
689	C₂×C₄	—	172	4	no	—
690	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
691	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
692	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
693	C₂×C₄	C₂²×D₁₇₂	1	4	yes	—
694	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
695	C₂×C₄	C₂×#10621898	1	2	yes	—
696	C₂×C₄	C₂×#10621898	1	2	yes	—
697	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
698	C₈	—	2	1	no	—
699	C₈	—	2	1	no	—
700	C₈	—	2	2	no	—
701	C₈	C₂×#10621898	1	2	yes	—
702	C₈	C₂×#10621898	1	4	yes	—
703	C₈	C₂×#10621898	1	2	yes	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	344	8	no	—
708	C₂²	—	172	4	no	—
709	C₂²	—	172	2	no	—
710	C₂²	—	172	2	no	—
711	C₂²	—	172	4	no	—
712	C₂²	—	172	2	no	—
713	C₂²	—	172	4	no	—
714	C₂²	#14583449	1	2	yes	—
715	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	4	no	—
719	C₄	—	2	2	no	—
720	C₄	—	172	4	no	—
721	C₄	—	172	2	no	—
722	C₄	—	172	2	no	—
723	C₄	—	172	2	no	—
724	C₄	#14583449	1	2	yes	—
725	C₄	C₂²×#10621898	1	1	yes	characteristic
726	C₄	C₂²×#10621898	1	1	yes	characteristic
727	C₂	—	2	2	no	—
728	C₂	—	4	2	no	—
729	C₂	—	344	4	no	—
730	C₂	—	344	2	no	—
731	C₂	C₂×#14583449	1	1	yes	characteristic
732	C₂	#19149376	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂³×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#2875	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#2875	D₄₃
hypocenter	C₄₃	#60698
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #2875

Complements

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

N	H ≅ G/N	type
1. #19148011	C₂	semidirect
2. #19145333	C₂	semidirect
3. #19145324	C₂	semidirect
4. #19145293	C₂	semidirect
5. #19145278	C₂	semidirect
6. #19145245	C₂	semidirect
7. #19145212	C₂	semidirect
8. #19145126	C₂	semidirect
9. #19145081	C₂	semidirect
10. #19144951	C₂	semidirect
11. #19144275	C₂	semidirect
12. #19144257	C₂	semidirect
13. #19144243	C₂	semidirect
14. C₄×#13063353	C₂	semidirect
15. #19143397	C₂	semidirect
16. C₂×#14583012	C₂	semidirect
17. C₄₃×#2875	C₂	semidirect
23. #14583520	C₂²	semidirect
24. #14583504	C₂²	semidirect
30. #14583449	C₂²	semidirect
33. #14583433	C₂²	semidirect
37. #14583308	C₂²	semidirect
38. #14583301	C₂²	semidirect
39. #14583297	C₂²	semidirect
43. #14583264	C₂²	semidirect
44. #14583259	C₂²	semidirect
45. #14583254	C₂²	semidirect
46. #14583246	C₂²	semidirect
47. #14583157	C₂²	semidirect
50. #14583152	C₂²	semidirect
51. #14583152	C₂²	semidirect
52. #14583145	C₂²	semidirect
54. #14583135	C₂²	semidirect
55. #14583128	C₂²	semidirect
56. #14583128	C₂²	semidirect
61. #14583012	C₂²	semidirect
62. #14583012	C₂²	semidirect
63. #14583012	C₂²	semidirect
64. #14583007	C₂²	semidirect
65. #14583007	C₂²	semidirect
66. #14583001	C₂²	semidirect
67. #14583001	C₂²	semidirect
68. #14583001	C₂²	semidirect
69. C₄×#10621873	C₂²	semidirect
70. C₄×D₃₄₄	C₂²	semidirect
83. C₄₃×#405	C₂²	semidirect
84. C₄₃×#405	C₂²	semidirect
86. C₄×M₁₆×C₄₃	C₂²	semidirect
88. C₂×#97×C₄₃	C₂²	semidirect
234. M₁₆×C₄₃	#41	semidirect
238. C₂×C₈×C₄₃	#41	semidirect
377. #2875	D₄₃	semidirect
449. #405	C₂×D₄₃	semidirect
450. #405	C₂×D₄₃	semidirect
452. C₄×M₁₆	C₂×D₄₃	semidirect
454. C₂×#97	C₂×D₄₃	semidirect
455. C₄₃	#60698	semidirect
608. M₁₆	#10621898	semidirect
612. C₂×C₈	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148011	2
#19145333	2
#19145324	2
#19145293	2
#19145278	2
#19145245	2
#19145212	2
#19145126	2
#19145081	2
#19144951	2
#19144275	2
#19144257	2
#19144243	2
C₄×#13063353	2
#19143397	2
C₂×#14583012	2
C₄₃×#2875	2
#60698	43