Subgroups — #25976007

Order 11008.

1882 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148449	C₂	1	2	yes	maximal, complemented
2	#19147199	C₂	1	4	yes	maximal, complemented
3	#19147189	C₂	1	4	yes	maximal, complemented
4	#19147017	C₂	1	2	yes	maximal, complemented
5	#19146996	C₂	1	4	yes	maximal, complemented
6	#19146942	C₂	1	2	yes	maximal, complemented
7	#19144556	C₂	1	4	yes	maximal, complemented
8	#19144388	C₂	1	2	yes	maximal, complemented
9	#19144244	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×D₃₄₄	C₂	1	1	yes	maximal, characteristic, complemented
11	#19143308	C₂	1	1	yes	maximal, characteristic, complemented
12	#19143192	C₂	1	2	yes	maximal, complemented
13	C₄₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
15	C₂×#13063331	C₂²	1	2	yes	—
16	#14583634	—	2	4	no	—
17	#14583622	—	2	2	no	—
18	#14583615	C₂²	1	4	yes	complemented
19	#14583602	C₂²	1	8	yes	complemented
20	#14583571	—	2	2	no	—
21	#14583552	C₂²	1	4	yes	complemented
22	#14583489	—	2	4	no	—
23	#14583468	C₂²	1	4	yes	—
24	#14583449	C₂²	1	1	yes	characteristic
25	#14583412	—	2	4	no	—
26	#14583379	C₂²	1	4	yes	—
27	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
28	#14583226	C₂²	1	8	yes	complemented
29	#14583225	C₂²	1	8	yes	complemented
30	#14583219	C₂²	1	8	yes	complemented
31	#14583214	C₂²	1	8	yes	complemented
32	#14583196	C₂²	1	8	yes	complemented
33	#14583186	C₂²	1	4	yes	complemented
34	#14583176	C₂²	1	4	yes	complemented
35	#14583153	C₂²	1	8	yes	—
36	#14583136	C₂²	1	4	yes	—
37	#14583136	C₂²	1	4	yes	—
38	C₄×D₃₄₄	C₂²	1	2	yes	—
39	C₄×D₃₄₄	C₂²	1	2	yes	—
40	C₄×D₃₄₄	C₂²	1	2	yes	—
41	C₄×D₃₄₄	C₂²	1	2	yes	—
42	#14582978	C₂²	1	2	yes	complemented
43	#14582978	C₂²	1	2	yes	complemented
44	C₈×D₁₇₂	C₂²	1	2	yes	complemented
45	C₈×D₁₇₂	C₂²	1	2	yes	complemented
46	#14582942	C₂²	1	4	yes	—
47	#14582938	C₂²	1	8	yes	complemented
48	#14582936	C₂²	1	4	yes	complemented
49	C₂×#13063259	C₂²	1	1	yes	characteristic
50	#107×D₄₃	C₂²	1	4	yes	complemented
51	#14582923	C₂²	1	1	yes	characteristic
52	#14582903	C₂²	1	4	yes	—
53	C₂×#13063247	C₂²	1	2	yes	—
54	#14582865	C₂²	1	2	yes	—
55	C₄₃×#533	C₂²	1	2	yes	—
56	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
57	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
58	C₄₃×#499	C₂²	1	2	yes	complemented
59	C₄₃×#499	C₂²	1	2	yes	complemented
60	C₄₃×#498	C₂²	1	2	yes	complemented
61	C₄₃×#427	C₂²	1	2	yes	—
62	C₄₃×#427	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
64	C₂×#10621902	—	2	4	no	—
65	C₂×#10621898	C₂³	1	2	yes	—
66	C₂²×D₁₇₂	C₂³	1	2	yes	—
67	C₂²×C₄×D₄₃	—	2	2	no	—
68	C₂×D₃₄₄	—	2	4	no	—
69	C₂×D₃₄₄	C₂³	1	2	yes	—
70	C₂×D₃₄₄	C₂³	1	2	yes	—
71	#13063331	—	2	8	no	—
72	C₂×#10621877	C₂³	1	2	yes	—
73	C₂×#10621872	C₂³	1	4	yes	—
74	C₂×C₈×D₄₃	C₂³	1	4	yes	—
75	#13063325	D₄	1	1	yes	characteristic
76	#13063322	—	2	4	no	—
77	#13063322	D₄	1	1	yes	characteristic
78	#13063320	—	2	8	no	—
79	#13063314	—	2	8	no	—
80	#13063313	—	2	4	no	—
81	#13063313	D₄	1	2	yes	—
82	#13063310	—	2	8	no	—
83	#13063310	—	2	8	no	—
84	#13063301	—	2	4	no	—
85	#13063300	—	2	8	no	—
86	#13063300	—	2	4	no	—
87	#13063300	C₂³	1	8	yes	—
88	#13063300	C₂³	1	8	yes	—
89	#13063299	D₄	1	2	yes	—
90	#13063299	D₄	1	2	yes	—
91	#13063295	—	2	8	no	—
92	C₄×Dic₈₆	—	2	4	no	—
93	C₄×D₁₇₂	—	2	4	no	—
94	C₄×D₁₇₂	—	2	2	no	—
95	C₄×D₁₇₂	—	2	2	no	—
96	C₄×D₁₇₂	C₂³	1	2	yes	—
97	C₄×D₁₇₂	C₂³	1	2	yes	—
98	C₄×D₁₇₂	C₂³	1	4	yes	—
99	C₄×D₁₇₂	C₂³	1	4	yes	—
100	#13063287	—	2	8	no	—
101	(C₂²⋊D₄₃)⋊C₄	—	2	8	no	—
102	#13063283	—	2	4	no	—
103	#13063283	C₂³	1	8	yes	—
104	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
105	C₄⋊C₄×D₄₃	C₂³	1	8	yes	—
106	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
107	#13063259	C₂³	1	2	yes	—
108	#13063259	C₂³	1	2	yes	—
109	#13063258	C₂³	1	8	yes	—
110	#13063256	C₂³	1	8	yes	—
111	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
112	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
113	#13063247	C₂³	1	4	yes	—
114	#13063247	C₂³	1	4	yes	—
115	#13063245	C₂³	1	8	yes	—
116	#13063245	C₂³	1	8	yes	—
117	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
118	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
119	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
122	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
123	#125×C₄₃	C₂³	1	4	yes	—
124	C₂²⋊Q₈×C₄₃	—	2	2	no	—
125	C₂²⋊Q₈×C₄₃	—	2	2	no	—
126	C₄×Q₈×C₄₃	—	2	2	no	—
127	C₄×Q₈×C₄₃	—	2	2	no	—
128	#117×C₄₃	C₂³	1	4	yes	—
129	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
130	#107×C₄₃	C₂³	1	2	yes	—
131	#107×C₄₃	C₂³	1	2	yes	—
132	#107×C₄₃	C₂³	1	2	yes	—
133	#107×C₄₃	C₂³	1	2	yes	—
134	#106×C₄₃	C₂³	1	4	yes	—
135	#106×C₄₃	C₂³	1	4	yes	—
136	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
140	C₂³×D₄₃	—	2	2	no	—
141	C₂×Q₈×C₄₃	—	2	2	no	—
142	C₂×Q₈×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
146	C₂×C₂²⋊D₄₃	C₂×D₄	1	4	yes	—
147	C₂²×Dic₄₃	—	2	2	no	—
148	#10621902	—	8	8	no	—
149	#10621898	—	2	4	no	—
150	#10621898	—	2	4	no	—
151	C₂×D₁₇₂	—	2	2	no	—
152	C₂×D₁₇₂	—	2	8	no	—
153	C₂×D₁₇₂	—	2	8	no	—
154	C₂×D₁₇₂	—	2	4	no	—
155	C₂×D₁₇₂	—	2	4	no	—
156	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
157	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
158	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
159	C₂×D₁₇₂	C₂⁴	1	4	yes	—
160	C₂×C₄×D₄₃	—	2	4	no	—
161	C₂×C₄×D₄₃	—	2	4	no	—
162	C₂×C₄×D₄₃	—	2	8	no	—
163	C₂×C₄×D₄₃	—	8	4	no	—
164	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
165	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₄₃	—	2	2	no	—
167	C₂×C₈×C₄₃	#41	1	4	yes	complemented
168	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
172	C₄⋊C₄×C₄₃	—	2	4	no	—
173	C₄⋊C₄×C₄₃	—	2	4	no	—
174	C₄⋊C₄×C₄₃	—	2	2	no	—
175	C₄⋊C₄×C₄₃	—	2	2	no	—
176	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
177	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
178	C₂²⋊C₄×C₄₃	—	2	4	no	—
179	C₄²×C₄₃	—	2	4	no	—
180	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
183	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
184	(C₂×D₄₃)⋊C₄	—	2	4	no	—
185	(C₂×D₄₃)⋊C₄	—	2	4	no	—
186	(C₂×D₄₃)⋊C₄	—	2	8	no	—
187	(C₂×D₄₃)⋊C₄	—	2	8	no	—
188	(C₂×D₄₃)⋊C₄	—	2	8	no	—
189	(C₂×D₄₃)⋊C₄	C₂×D₄	1	4	yes	—
190	(C₂×D₄₃)⋊C₄	C₂×D₄	1	4	yes	—
191	C₄⋊Dic₄₃	—	2	2	no	—
192	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
193	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
194	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
195	Dic₄₃⋊C₄	—	2	8	no	—
196	C₄×Dic₄₃	—	2	8	no	—
197	#10621877	—	2	4	no	—
198	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
199	D₃₄₄	—	2	4	no	—
200	D₃₄₄	—	2	4	no	—
201	#10621872	—	2	8	no	—
202	C₈×D₄₃	—	2	8	no	—
203	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
204	C₂²×D₄₃	—	2	4	no	—
205	C₂²×D₄₃	—	4	4	no	—
206	C₂²×D₄₃	—	8	2	no	—
207	C₂²×D₄₃	—	8	2	no	—
208	C₂²×D₄₃	C₂²×D₄	1	4	yes	—
209	Q₈×C₄₃	—	4	4	no	—
210	Q₈×C₄₃	—	8	2	no	—
211	C₂×C₄×C₄₃	—	2	2	no	—
212	C₂×C₄×C₄₃	—	2	4	no	—
213	C₂×C₄×C₄₃	—	2	4	no	—
214	C₂×C₄×C₄₃	—	4	1	no	—
215	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
221	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
222	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
223	C₂²⋊D₄₃	—	2	8	no	—
224	C₂×Dic₄₃	—	2	4	no	—
225	C₂×Dic₄₃	—	8	2	no	—
226	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
227	D₁₇₂	—	2	4	no	—
228	D₁₇₂	—	2	4	no	—
229	D₁₇₂	—	2	4	no	—
230	D₁₇₂	—	2	4	no	—
231	D₁₇₂	—	4	2	no	—
232	D₁₇₂	—	4	4	no	—
233	D₁₇₂	—	8	8	no	—
234	D₁₇₂	—	8	8	no	—
235	C₄×D₄₃	—	2	4	no	—
236	C₄×D₄₃	—	2	4	no	—
237	C₄×D₄₃	—	4	8	no	—
238	C₄×D₄₃	—	8	4	no	—
239	C₄×D₄₃	—	8	8	no	—
240	Dic₈₆	—	2	4	no	—
241	C₈×C₄₃	—	2	1	no	—
242	C₈×C₄₃	—	2	1	no	—
243	C₈×C₄₃	C₂×#41	1	2	yes	—
244	C₈×C₄₃	C₂×#41	1	2	yes	—
245	C₄₃⋊C₈	—	2	4	no	—
246	#61284	—	43	1	no	maximal, Sylow
247	C₂²×C₄₃	—	2	1	no	—
248	C₂²×C₄₃	—	2	1	no	—
249	C₂²×C₄₃	#547	1	2	yes	—
250	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
251	C₂×D₄₃	—	2	4	no	—
252	C₂×D₄₃	—	2	4	no	—
253	C₂×D₄₃	—	2	4	no	—
254	C₂×D₄₃	—	4	4	no	—
255	C₂×D₄₃	—	4	4	no	—
256	C₂×D₄₃	—	4	4	no	—
257	C₂×D₄₃	—	8	8	no	—
258	C₄×C₄₃	—	2	1	no	—
259	C₄×C₄₃	—	2	1	no	—
260	C₄×C₄₃	—	2	1	no	—
261	C₄×C₄₃	—	4	4	no	—
262	C₄×C₄₃	—	4	4	no	—
263	C₄×C₄₃	#547	1	2	yes	—
264	C₄×C₄₃	#576	1	2	yes	—
265	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
266	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
267	Dic₄₃	—	2	4	no	—
268	Dic₄₃	—	4	4	no	—
269	#3506	—	43	2	no	—
270	#3355	—	43	4	no	—
271	#3354	—	43	4	no	—
272	#3341	—	43	2	no	—
273	#3339	—	43	4	no	—
274	#3334	—	43	2	no	—
275	#3160	D₄₃	1	1	yes	characteristic, complemented
276	#3096	—	43	4	no	—
277	#3077	—	43	2	no	—
278	#3058	—	43	2	no	—
279	C₂×C₄×D₈	—	43	1	no	—
280	#2931	—	43	1	no	—
281	#2913	—	43	2	no	—
282	C₂×C₄₃	—	2	2	no	—
283	C₂×C₄₃	C₂×#547	1	1	yes	characteristic
284	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
285	C₂×C₄₃	#3584	1	1	yes	characteristic
286	D₄₃	—	4	4	no	—
287	D₄₃	—	8	4	no	—
288	C₂²×D₈	—	43	1	no	—
289	C₂×#131	—	43	2	no	—
290	#559	—	86	4	no	—
291	#556	—	86	2	no	—
292	#555	—	43	4	no	—
293	#553	—	43	8	no	—
294	#550	—	86	2	no	—
295	#547	—	43	4	no	—
296	#538	—	86	4	no	—
297	#535	—	43	4	no	—
298	#533	C₂×D₄₃	1	2	yes	—
299	#532	—	43	1	no	—
300	#525	—	86	4	no	—
301	#520	—	43	4	no	—
302	C₂×C₄×D₄	—	43	2	no	—
303	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
304	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
305	#499	C₂×D₄₃	1	2	yes	complemented
306	#499	C₂×D₄₃	1	2	yes	complemented
307	#498	C₂×D₄₃	1	2	yes	complemented
308	#482	—	43	8	no	—
309	#482	—	43	8	no	—
310	#481	—	43	8	no	—
311	#480	—	43	8	no	—
312	#478	—	43	8	no	—
313	#476	—	43	4	no	—
314	#474	—	43	4	no	—
315	#469	—	43	8	no	—
316	#466	—	43	4	no	—
317	#466	—	43	4	no	—
318	C₄×D₈	—	43	2	no	—
319	C₄×D₈	—	43	2	no	—
320	C₄×D₈	—	43	2	no	—
321	C₄×D₈	—	43	2	no	—
322	#436	—	43	2	no	—
323	#436	—	43	2	no	—
324	C₈×D₄	—	43	2	no	—
325	C₈×D₄	—	43	2	no	—
326	#428	—	43	4	no	—
327	#428	—	43	8	no	—
328	#427	—	43	4	no	—
329	#427	C₂×D₄₃	1	2	yes	—
330	#427	C₂×D₄₃	1	2	yes	—
331	C₂×#107	—	43	1	no	—
332	C₂×#107	—	43	4	no	—
333	#423	—	43	1	no	—
334	#418	—	43	4	no	—
335	C₂×#102	—	43	2	no	—
336	#408	—	43	2	no	—
337	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
338	C₄₃	#61284	1	1	yes	characteristic, complemented, Sylow
339	C₂×#41	—	43	2	no	—
340	C₂×#41	—	86	4	no	—
341	C₂²×D₄	—	43	2	no	—
342	C₂³×C₄	—	86	2	no	—
343	C₂×D₈	—	43	2	no	—
344	C₂×D₈	—	43	2	no	—
345	C₂×D₈	—	86	4	no	—
346	#131	—	86	8	no	—
347	C₂×M₁₆	—	43	2	no	—
348	C₂×M₁₆	—	43	4	no	—
349	C₂²×C₈	—	43	4	no	—
350	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
351	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
352	C₄⋊Q₈	—	43	1	no	—
353	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
354	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
355	#127	—	43	1	no	—
356	#127	—	86	4	no	—
357	#126	—	86	8	no	—
358	#125	C₂²×D₄₃	1	4	yes	—
359	#124	—	43	2	no	—
360	#124	—	86	4	no	—
361	#124	—	86	8	no	—
362	#123	—	86	8	no	—
363	#123	—	86	8	no	—
364	C₂²⋊Q₈	—	2	2	no	—
365	C₂²⋊Q₈	—	2	2	no	—
366	C₂²⋊Q₈	—	86	4	no	—
367	#121	—	43	2	no	—
368	#121	—	43	2	no	—
369	#121	—	43	8	no	—
370	#121	—	43	8	no	—
371	#121	—	86	4	no	—
372	#121	—	86	8	no	—
373	#120	—	86	8	no	—
374	C₄×Q₈	—	2	2	no	—
375	C₄×Q₈	—	2	2	no	—
376	C₄×Q₈	—	86	4	no	—
377	C₄×D₄	—	43	2	no	—
378	C₄×D₄	—	43	2	no	—
379	C₄×D₄	—	43	4	no	—
380	C₄×D₄	—	43	4	no	—
381	C₄×D₄	—	86	4	no	—
382	C₄×D₄	—	86	8	no	—
383	C₄×D₄	—	86	8	no	—
384	C₄×D₄	—	86	2	no	—
385	C₄×D₄	—	86	2	no	—
386	#117	—	43	8	no	—
387	#117	—	86	4	no	—
388	#117	C₂²×D₄₃	1	4	yes	—
389	C₂×C₄⋊C₄	—	43	2	no	—
390	C₂×C₄⋊C₄	—	43	8	no	—
391	C₂×C₂²⋊C₄	—	86	2	no	—
392	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
393	#107	—	43	2	no	—
394	#107	—	43	2	no	—
395	#107	—	43	8	no	—
396	#107	C₂²×D₄₃	1	2	yes	—
397	#107	C₂²×D₄₃	1	2	yes	—
398	#107	C₂²×D₄₃	1	2	yes	—
399	#107	C₂²×D₄₃	1	2	yes	—
400	#106	—	43	8	no	—
401	#106	C₂²×D₄₃	1	4	yes	—
402	#106	C₂²×D₄₃	1	4	yes	—
403	C₄⋊C₈	—	43	2	no	—
404	C₄⋊C₈	—	43	2	no	—
405	#102	—	43	4	no	—
406	#102	—	43	4	no	—
407	#102	—	43	8	no	—
408	#102	—	43	8	no	—
409	C₂²⋊C₈	—	43	4	no	—
410	C₂²⋊C₈	—	43	4	no	—
411	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
412	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
413	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
414	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
415	C₂⁴	—	86	2	no	—
416	#41	—	86	4	no	—
417	#41	—	86	4	no	—
418	#41	—	344	8	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	43	2	no	—
422	C₂×D₄	—	43	4	no	—
423	C₂×D₄	—	43	2	no	—
424	C₂×D₄	—	43	2	no	—
425	C₂×D₄	—	43	2	no	—
426	C₂×D₄	—	43	4	no	—
427	C₂×D₄	—	86	8	no	—
428	C₂×D₄	—	86	8	no	—
429	C₂×D₄	—	86	2	no	—
430	C₂×D₄	—	86	4	no	—
431	C₂×D₄	—	86	4	no	—
432	C₂²×C₄	—	43	4	no	—
433	C₂²×C₄	—	86	8	no	—
434	C₂²×C₄	—	86	2	no	—
435	C₂²×C₄	—	86	4	no	—
436	C₂²×C₄	—	86	4	no	—
437	C₂²×C₄	—	344	4	no	—
438	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
439	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
440	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
441	D₈	—	86	4	no	—
442	D₈	—	86	4	no	—
443	M₁₆	—	86	4	no	—
444	M₁₆	—	86	8	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	43	4	no	—
447	C₂×C₈	—	86	8	no	—
448	C₂×C₈	#10621902	1	4	yes	complemented
449	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
450	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
451	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
452	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	43	2	no	—
458	C₄⋊C₄	—	43	2	no	—
459	C₄⋊C₄	—	43	4	no	—
460	C₄⋊C₄	—	86	8	no	—
461	C₄⋊C₄	—	86	2	no	—
462	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
463	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	43	4	no	—
466	C₂²⋊C₄	—	43	4	no	—
467	C₂²⋊C₄	—	86	8	no	—
468	C₂²⋊C₄	—	86	8	no	—
469	C₂²⋊C₄	—	86	8	no	—
470	C₂²⋊C₄	—	86	4	no	—
471	C₂²⋊C₄	—	86	4	no	—
472	C₄²	—	2	4	no	—
473	C₄²	—	86	8	no	—
474	C₄²	D₄×D₄₃	1	1	yes	characteristic
475	C₄²	D₄×D₄₃	1	1	yes	characteristic
476	C₄²	C₂³×D₄₃	1	1	yes	characteristic
477	C₄²	C₂³×D₄₃	1	1	yes	characteristic
478	C₂³	—	43	4	no	—
479	C₂³	—	86	4	no	—
480	C₂³	—	344	2	no	—
481	C₂³	—	344	2	no	—
482	C₂³	—	172	4	no	—
483	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
484	Q₈	—	4	4	no	—
485	Q₈	—	8	2	no	—
486	Q₈	—	86	4	no	—
487	D₄	—	86	8	no	—
488	D₄	—	86	4	no	—
489	D₄	—	86	4	no	—
490	D₄	—	86	4	no	—
491	D₄	—	86	4	no	—
492	D₄	—	344	8	no	—
493	D₄	—	344	8	no	—
494	D₄	—	172	2	no	—
495	D₄	—	172	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	43	4	no	—
501	C₂×C₄	—	86	4	no	—
502	C₂×C₄	—	86	4	no	—
503	C₂×C₄	—	86	4	no	—
504	C₂×C₄	—	344	4	no	—
505	C₂×C₄	—	344	8	no	—
506	C₂×C₄	—	344	2	no	—
507	C₂×C₄	—	172	8	no	—
508	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
509	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
510	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
511	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
512	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
513	C₂×C₄	C₂×#10621902	1	2	yes	—
514	C₂×C₄	#13063373	1	2	yes	—
515	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
516	C₈	—	2	1	no	—
517	C₈	—	2	1	no	—
518	C₈	—	86	4	no	—
519	C₈	C₂×#10621902	1	2	yes	—
520	C₈	C₂×#10621902	1	2	yes	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	86	4	no	—
524	C₂²	—	86	4	no	—
525	C₂²	—	86	4	no	—
526	C₂²	—	344	8	no	—
527	C₂²	—	172	4	no	—
528	C₂²	—	172	4	no	—
529	C₂²	—	172	4	no	—
530	C₂²	#14583552	1	2	yes	—
531	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	4	no	—
537	C₄	—	86	4	no	—
538	C₄	—	172	4	no	—
539	C₄	#14583552	1	2	yes	—
540	C₄	#14583701	1	2	yes	—
541	C₄	C₂²×#10621902	1	1	yes	characteristic
542	C₄	C₂×#13063373	1	1	yes	characteristic
543	C₂	—	2	2	no	—
544	C₂	—	344	4	no	—
545	C₂	—	172	4	no	—
546	C₂	C₂×#14583552	1	1	yes	characteristic
547	C₂	C₂×#14583701	1	1	yes	characteristic
548	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3160	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3160	D₄₃
hypocenter	C₄₃	#61284
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

Complements

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

N	H ≅ G/N	type
1. #19148449	C₂	semidirect
2. #19147199	C₂	semidirect
3. #19147189	C₂	semidirect
4. #19147017	C₂	semidirect
5. #19146996	C₂	semidirect
6. #19146942	C₂	semidirect
7. #19144556	C₂	semidirect
8. #19144388	C₂	semidirect
9. #19144244	C₂	semidirect
10. C₂×C₄×D₃₄₄	C₂	semidirect
11. #19143308	C₂	semidirect
12. #19143192	C₂	semidirect
13. C₄₃×#3160	C₂	semidirect
18. #14583615	C₂²	semidirect
19. #14583602	C₂²	semidirect
21. #14583552	C₂²	semidirect
28. #14583226	C₂²	semidirect
29. #14583225	C₂²	semidirect
30. #14583219	C₂²	semidirect
31. #14583214	C₂²	semidirect
32. #14583196	C₂²	semidirect
33. #14583186	C₂²	semidirect
34. #14583176	C₂²	semidirect
42. #14582978	C₂²	semidirect
43. #14582978	C₂²	semidirect
44. C₈×D₁₇₂	C₂²	semidirect
45. C₈×D₁₇₂	C₂²	semidirect
47. #14582938	C₂²	semidirect
48. #14582936	C₂²	semidirect
50. #107×D₄₃	C₂²	semidirect
56. C₄₃×#500	C₂²	semidirect
57. C₄₃×#500	C₂²	semidirect
58. C₄₃×#499	C₂²	semidirect
59. C₄₃×#499	C₂²	semidirect
60. C₄₃×#498	C₂²	semidirect
167. C₂×C₈×C₄₃	#41	semidirect
275. #3160	D₄₃	semidirect
303. #500	C₂×D₄₃	semidirect
304. #500	C₂×D₄₃	semidirect
305. #499	C₂×D₄₃	semidirect
306. #499	C₂×D₄₃	semidirect
307. #498	C₂×D₄₃	semidirect
338. C₄₃	#61284	semidirect
448. C₂×C₈	#10621902	semidirect

Maximal subgroups

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

subgroup	index
#19148449	2
#19147199	2
#19147189	2
#19147017	2
#19146996	2
#19146942	2
#19144556	2
#19144388	2
#19144244	2
C₂×C₄×D₃₄₄	2
#19143308	2
#19143192	2
C₄₃×#3160	2
#61284	43