Subgroups — #25961164

Order 11008.

1878 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19147985	C₂	1	1	yes	maximal, characteristic
2	#19143595	C₂	1	8	yes	maximal, complemented
3	#19143585	C₂	1	8	yes	maximal, complemented
4	#19143535	C₂	1	1	yes	maximal, characteristic, complemented
5	#19143529	C₂	1	1	yes	maximal, characteristic, complemented
6	#19143314	C₂	1	1	yes	maximal, characteristic, complemented
7	#19143308	C₂	1	1	yes	maximal, characteristic, complemented
8	#19143298	C₂	1	2	yes	maximal, complemented
9	#19143289	C₂	1	2	yes	maximal, complemented
10	#19143237	C₂	1	2	yes	maximal, complemented
11	#19143233	C₂	1	1	yes	maximal, characteristic, complemented
12	#19143020	C₂	1	2	yes	maximal, complemented
13	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13063331	C₂²	1	2	yes	—
15	C₂×#13063331	C₂²	1	2	yes	—
16	#14583520	C₄	1	4	yes	—
17	#14583511	C₄	1	2	yes	—
18	#14583504	C₄	1	2	yes	—
19	#14583496	C₄	1	4	yes	—
20	#14583487	C₄	1	4	yes	—
21	#14583456	C₂²	1	1	yes	characteristic
22	#14583449	C₂²	1	1	yes	characteristic
23	#14583427	C₂²	1	8	yes	—
24	#14583410	C₂²	1	2	yes	—
25	C₄×#10621898	C₂²	1	2	yes	—
26	#14583029	C₂²	1	4	yes	complemented
27	#14583027	C₂²	1	8	yes	complemented
28	C₈×Dic₈₆	C₂²	1	4	yes	complemented
29	#14582978	C₂²	1	4	yes	complemented
30	#14582975	C₂²	1	8	yes	—
31	#14582972	C₂²	1	8	yes	complemented
32	#14582970	C₂²	1	8	yes	—
33	#14582968	C₂²	1	8	yes	—
34	C₈×D₁₇₂	C₂²	1	4	yes	complemented
35	C₈×C₂²⋊D₄₃	C₂²	1	8	yes	—
36	#14582960	C₂²	1	8	yes	—
37	#14582958	C₂²	1	8	yes	complemented
38	#14582950	C₂²	1	8	yes	complemented
39	#14582925	C₂²	1	2	yes	—
40	#14582925	C₂²	1	2	yes	—
41	#14582923	C₂²	1	1	yes	characteristic
42	#14582923	C₂²	1	1	yes	characteristic
43	#14582865	C₂²	1	2	yes	—
44	#14582865	C₂²	1	2	yes	—
45	#14582863	C₂²	1	2	yes	—
46	#14582856	C₂²	1	4	yes	complemented
47	#14582856	C₂²	1	4	yes	complemented
48	#14582854	C₂²	1	2	yes	—
49	#14582854	C₂²	1	2	yes	—
50	C₄×#10621877	C₂²	1	2	yes	—
51	#14582851	C₂²	1	4	yes	complemented
52	#97×D₄₃	C₂²	1	4	yes	complemented
53	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
54	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
55	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
56	C₄₃×#405	C₂²	1	4	yes	—
57	C₄₃×#405	C₂²	1	4	yes	—
58	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
59	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
60	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
61	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
62	C₂×#10621898	C₂³	1	2	yes	—
63	#13063331	—	2	8	no	—
64	#13063331	—	2	8	no	—
65	C₂×#10621877	C₂³	1	2	yes	—
66	C₂×#10621877	C₂³	1	2	yes	—
67	C₂×#10621872	C₂³	1	4	yes	—
68	C₂×#10621872	C₂³	1	4	yes	—
69	C₂×C₈×D₄₃	C₂³	1	4	yes	—
70	C₂×C₈×D₄₃	C₂³	1	4	yes	—
71	#13063325	C₂×C₄	1	1	yes	characteristic
72	#13063325	C₂×C₄	1	2	yes	—
73	#13063322	C₂×C₄	1	1	yes	characteristic
74	#13063320	C₂×C₄	1	8	yes	—
75	#13063318	C₂×C₄	1	8	yes	—
76	#13063317	C₂×C₄	1	2	yes	—
77	#13063315	C₂×C₄	1	8	yes	—
78	#13063313	C₂×C₄	1	2	yes	—
79	#13063311	C₂×C₄	1	8	yes	—
80	#13063310	C₂×C₄	1	8	yes	—
81	#13063308	C₂×C₄	1	4	yes	—
82	#13063307	C₂×C₄	1	8	yes	—
83	#13063304	C₂×C₄	1	4	yes	—
84	#13063304	C₂×C₄	1	4	yes	—
85	#13063303	C₂×C₄	1	8	yes	—
86	#13063299	C₂×C₄	1	4	yes	—
87	#13063299	C₂×C₄	1	4	yes	—
88	#13063298	C₂×C₄	1	8	yes	—
89	#13063294	C₂×C₄	1	4	yes	—
90	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
91	C₄×Dic₈₆	C₂³	1	4	yes	—
92	C₄×D₁₇₂	C₂×C₄	1	4	yes	—
93	C₄×D₁₇₂	C₂³	1	4	yes	—
94	C₄×C₂²⋊D₄₃	C₂×C₄	1	8	yes	—
95	C₄×C₂²⋊D₄₃	C₂³	1	8	yes	—
96	#13063284	C₂³	1	2	yes	—
97	#13063282	C₂³	1	4	yes	—
98	C₄²×D₄₃	C₂³	1	4	yes	—
99	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
100	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
101	Dic₄₃⋊C₈	C₂³	1	8	yes	—
102	Dic₄₃⋊C₈	C₂³	1	8	yes	—
103	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
104	(C₂×D₄₃)⋊C₈	C₂³	1	8	yes	—
105	(C₂×D₄₃)⋊C₈	C₂³	1	8	yes	—
106	#13063236	C₂³	1	4	yes	—
107	#13063235	C₂³	1	4	yes	—
108	#13063235	C₂³	1	4	yes	—
109	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
110	C₈×Dic₄₃	C₂³	1	4	yes	—
111	C₈×Dic₄₃	C₂³	1	4	yes	—
112	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
113	C₂×M₁₆×C₄₃	—	2	4	no	—
114	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
115	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
116	C₂²×C₈×C₄₃	—	2	4	no	—
117	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
119	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
122	#117×C₄₃	C₂×C₄	1	2	yes	—
123	#117×C₄₃	C₂×C₄	1	2	yes	—
124	#117×C₄₃	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
126	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
127	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
129	#97×C₄₃	C₂³	1	2	yes	—
130	#97×C₄₃	C₂³	1	2	yes	—
131	#97×C₄₃	C₂³	1	4	yes	—
132	C₄×C₈×C₄₃	C₂³	1	4	yes	—
133	C₄×C₈×C₄₃	C₂³	1	2	yes	—
134	C₄×C₈×C₄₃	C₂³	1	2	yes	—
135	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
144	C₂×C₂²⋊D₄₃	C₂²×C₄	1	4	yes	—
145	C₂×C₂²⋊D₄₃	C₂²×C₄	1	8	yes	—
146	#10621898	—	2	4	no	—
147	#10621898	—	2	4	no	—
148	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
149	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
150	C₂×C₄×D₄₃	C₂²×C₄	1	8	yes	—
151	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
152	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
153	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
154	M₁₆×C₄₃	—	2	4	no	—
155	M₁₆×C₄₃	—	2	4	no	—
156	C₂×C₈×C₄₃	—	2	2	no	—
157	C₂×C₈×C₄₃	—	2	2	no	—
158	C₂×C₈×C₄₃	—	2	8	no	—
159	C₂×C₈×C₄₃	#41	1	4	yes	—
160	C₂×C₈×C₄₃	#41	1	4	yes	—
161	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
162	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
163	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
166	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
167	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
168	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
169	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
170	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
171	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₄₃	C₂⁴	1	2	yes	—
174	C₄²×C₄₃	C₂⁴	1	2	yes	—
175	C₂²⋊Dic₄₃	C₂²×C₄	1	4	yes	—
176	C₂²⋊Dic₄₃	C₂²×C₄	1	8	yes	—
177	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	8	yes	—
178	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	8	yes	—
179	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	8	yes	—
180	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
181	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
182	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
183	Dic₄₃⋊C₄	C₂²×C₄	1	8	yes	—
184	Dic₄₃⋊C₄	C₂²×C₄	1	8	yes	—
185	Dic₄₃⋊C₄	C₂²×C₄	1	8	yes	—
186	C₄×Dic₄₃	C₂²×C₄	1	8	yes	—
187	C₄×Dic₄₃	C₂⁴	1	4	yes	—
188	#10621877	—	2	4	no	—
189	#10621877	—	2	4	no	—
190	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
191	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
192	#10621872	—	2	8	no	—
193	#10621872	—	2	8	no	—
194	C₈×D₄₃	—	2	8	no	—
195	C₈×D₄₃	—	2	8	no	—
196	C₂³×C₄₃	—	2	2	no	—
197	C₂³×C₄₃	—	4	2	no	—
198	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
199	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
200	C₂²×D₄₃	C₂³×C₄	1	4	yes	—
201	C₂×C₄×C₄₃	—	2	2	no	—
202	C₂×C₄×C₄₃	—	2	4	no	—
203	C₂×C₄×C₄₃	—	2	2	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	4	2	no	—
206	C₂×C₄×C₄₃	—	4	2	no	—
207	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
208	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
209	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
210	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
211	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
213	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
214	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
215	C₂²⋊D₄₃	—	2	8	no	—
216	C₂²⋊D₄₃	—	4	8	no	—
217	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
218	C₂×Dic₄₃	C₂³×C₄	1	8	yes	—
219	D₁₇₂	—	2	4	no	—
220	D₁₇₂	—	4	4	no	—
221	C₄×D₄₃	—	2	4	no	—
222	C₄×D₄₃	—	2	4	no	—
223	C₄×D₄₃	—	4	8	no	—
224	Dic₈₆	—	2	4	no	—
225	Dic₈₆	—	4	4	no	—
226	C₈×C₄₃	—	2	2	no	—
227	C₈×C₄₃	—	2	2	no	—
228	C₈×C₄₃	C₂×#41	1	2	yes	—
229	C₈×C₄₃	C₂×#41	1	4	yes	—
230	C₈×C₄₃	C₂×#41	1	2	yes	—
231	C₄₃⋊C₈	—	2	4	no	—
232	C₄₃⋊C₈	—	2	4	no	—
233	#60209	—	43	1	no	maximal, Sylow
234	C₂²×C₄₃	—	2	2	no	—
235	C₂²×C₄₃	—	2	2	no	—
236	C₂²×C₄₃	—	2	4	no	—
237	C₂²×C₄₃	—	4	4	no	—
238	C₂²×C₄₃	C₄×#41	1	2	yes	—
239	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
240	C₂×D₄₃	—	2	4	no	—
241	C₂×D₄₃	—	2	8	no	—
242	C₄×C₄₃	—	2	2	no	—
243	C₄×C₄₃	—	2	2	no	—
244	C₄×C₄₃	—	2	4	no	—
245	C₄×C₄₃	—	2	2	no	—
246	C₄×C₄₃	C₄×#41	1	2	yes	—
247	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
248	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
249	Dic₄₃	—	2	4	no	—
250	Dic₄₃	—	2	8	no	—
251	#3455	—	43	1	no	—
252	#2969	—	43	8	no	—
253	#2968	—	43	8	no	—
254	#2961	—	43	1	no	—
255	#2960	—	43	1	no	—
256	#2932	—	43	1	no	—
257	#2931	—	43	1	no	—
258	#2930	—	43	2	no	—
259	#2929	—	43	2	no	—
260	#2922	—	43	2	no	—
261	#2921	—	43	1	no	—
262	#2875	—	43	2	no	—
263	C₂×#405	D₄₃	1	1	yes	characteristic, complemented
264	C₂×C₄₃	—	2	2	no	—
265	C₂×C₄₃	—	4	2	no	—
266	C₂×C₄₃	C₂×C₄×#41	1	1	yes	characteristic
267	C₂×C₄₃	#3573	1	2	yes	—
268	D₄₃	—	4	4	no	—
269	C₂×#131	—	43	2	no	—
270	C₂×#131	—	43	2	no	—
271	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
272	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
273	#542	—	43	4	no	—
274	#541	—	43	2	no	—
275	#540	—	43	2	no	—
276	#539	—	43	4	no	—
277	#538	—	43	4	no	—
278	#533	—	43	1	no	—
279	#532	—	43	1	no	—
280	#529	—	43	8	no	—
281	#525	—	43	2	no	—
282	C₄×#41	—	43	2	no	—
283	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
284	#446	—	43	8	no	—
285	#446	—	43	4	no	—
286	C₈×Q₈	—	43	4	no	—
287	#436	—	43	8	no	—
288	#436	—	43	4	no	—
289	#435	—	43	8	no	—
290	#435	—	43	8	no	—
291	#435	—	43	8	no	—
292	C₈×D₄	—	43	8	no	—
293	C₈×D₄	—	43	4	no	—
294	#433	—	43	8	no	—
295	#433	—	43	8	no	—
296	#431	—	43	8	no	—
297	#424	—	43	2	no	—
298	#424	—	43	2	no	—
299	#423	—	43	1	no	—
300	#423	—	43	1	no	—
301	#408	—	43	2	no	—
302	#408	—	43	2	no	—
303	#407	—	43	2	no	—
304	#405	—	43	2	no	—
305	#405	—	43	2	no	—
306	#405	—	43	4	no	—
307	#405	—	43	4	no	—
308	#405	C₂×D₄₃	1	4	yes	—
309	#405	C₂×D₄₃	1	4	yes	—
310	C₄×M₁₆	—	43	2	no	—
311	C₄×M₁₆	—	43	4	no	—
312	C₂×#97	—	43	4	no	—
313	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
314	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
315	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
316	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
317	C₄₃	#60209	1	1	yes	characteristic, complemented, Sylow
318	C₂×#41	—	43	2	no	—
319	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
320	#131	—	86	8	no	—
321	#131	—	86	8	no	—
322	C₂×M₁₆	—	2	4	no	—
323	C₂×M₁₆	—	43	2	no	—
324	C₂×M₁₆	—	43	2	no	—
325	C₂×M₁₆	—	43	4	no	—
326	C₂×M₁₆	—	43	4	no	—
327	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
328	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
329	C₂²×C₈	—	2	4	no	—
330	C₂²×C₈	—	43	4	no	—
331	C₂²×C₈	—	43	4	no	—
332	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
333	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
334	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
335	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
336	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
337	C₄⋊Q₈	—	43	1	no	—
338	C₄⋊Q₈	—	43	2	no	—
339	#127	—	43	1	no	—
340	#126	—	43	8	no	—
341	#126	—	43	8	no	—
342	#125	—	43	8	no	—
343	#125	—	43	2	no	—
344	#124	—	43	8	no	—
345	#124	—	43	2	no	—
346	#123	—	43	4	no	—
347	#123	—	43	8	no	—
348	#123	—	43	8	no	—
349	C₂²⋊Q₈	—	43	4	no	—
350	C₂²⋊Q₈	—	43	4	no	—
351	C₂²⋊Q₈	—	43	8	no	—
352	#121	—	43	4	no	—
353	#121	—	43	4	no	—
354	#121	—	43	8	no	—
355	#120	—	43	4	no	—
356	C₄×Q₈	—	43	4	no	—
357	C₄×Q₈	—	43	4	no	—
358	C₄×D₄	—	43	8	no	—
359	C₄×D₄	—	43	8	no	—
360	C₄×D₄	—	43	4	no	—
361	C₄×D₄	—	43	4	no	—
362	#117	—	43	2	no	—
363	#117	—	43	4	no	—
364	#117	C₄×D₄₃	1	2	yes	—
365	#117	C₄×D₄₃	1	2	yes	—
366	#117	C₂²×D₄₃	1	4	yes	—
367	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
368	C₂×C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
369	C₂×C₄²	—	43	4	no	—
370	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
371	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
372	C₄⋊C₈	—	43	8	no	—
373	C₄⋊C₈	—	43	8	no	—
374	C₄⋊C₈	—	43	4	no	—
375	C₄⋊C₈	—	43	4	no	—
376	C₂²⋊C₈	—	43	8	no	—
377	C₂²⋊C₈	—	43	8	no	—
378	C₂²⋊C₈	—	43	8	no	—
379	#97	—	43	4	no	—
380	#97	—	43	4	no	—
381	#97	—	43	4	no	—
382	#97	C₂²×D₄₃	1	2	yes	—
383	#97	C₂²×D₄₃	1	2	yes	—
384	#97	C₂²×D₄₃	1	4	yes	—
385	C₄×C₈	—	43	4	no	—
386	C₄×C₈	—	43	4	no	—
387	C₄×C₈	—	43	4	no	—
388	C₄×C₈	C₂²×D₄₃	1	4	yes	—
389	C₄×C₈	C₂²×D₄₃	1	2	yes	—
390	C₄×C₈	C₂²×D₄₃	1	2	yes	—
391	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
392	#41	—	86	4	no	—
393	#41	—	86	4	no	—
394	C₂×Q₈	—	43	2	no	—
395	C₂×Q₈	—	43	4	no	—
396	C₂×D₄	—	43	4	no	—
397	C₂×D₄	—	43	8	no	—
398	C₂×D₄	—	43	2	no	—
399	C₂×D₄	—	43	4	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	43	4	no	—
403	C₂²×C₄	—	43	8	no	—
404	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
405	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
406	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
407	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
408	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
409	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
410	M₁₆	—	2	4	no	—
411	M₁₆	—	2	4	no	—
412	M₁₆	—	86	4	no	—
413	M₁₆	—	86	4	no	—
414	M₁₆	—	86	8	no	—
415	M₁₆	—	86	8	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	8	no	—
419	C₂×C₈	—	43	4	no	—
420	C₂×C₈	—	43	4	no	—
421	C₂×C₈	—	86	8	no	—
422	C₂×C₈	—	86	8	no	—
423	C₂×C₈	#10621898	1	4	yes	—
424	C₂×C₈	#10621898	1	4	yes	—
425	C₂×C₈	C₂³×D₄₃	1	2	yes	—
426	C₂×C₈	C₂³×D₄₃	1	2	yes	—
427	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
428	C₂×C₈	C₂³×D₄₃	1	2	yes	—
429	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
430	C₄⋊C₄	—	43	4	no	—
431	C₄⋊C₄	—	43	8	no	—
432	C₄⋊C₄	—	43	4	no	—
433	C₄⋊C₄	—	43	8	no	—
434	C₄⋊C₄	—	43	8	no	—
435	C₄⋊C₄	—	43	4	no	—
436	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
437	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
438	C₂²⋊C₄	—	43	4	no	—
439	C₂²⋊C₄	—	43	8	no	—
440	C₂²⋊C₄	—	43	8	no	—
441	C₂²⋊C₄	—	43	8	no	—
442	C₂²⋊C₄	—	43	8	no	—
443	C₂²⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
444	C₂²⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
445	C₄²	—	43	8	no	—
446	C₄²	—	43	4	no	—
447	C₄²	C₂×C₄×D₄₃	1	2	yes	—
448	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
449	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
450	C₄²	C₂³×D₄₃	1	2	yes	—
451	C₄²	C₂³×D₄₃	1	2	yes	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	43	4	no	—
455	C₂³	C₂²×C₄×D₄₃	1	2	yes	—
456	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
457	Q₈	—	86	4	no	—
458	Q₈	—	172	4	no	—
459	D₄	—	86	8	no	—
460	D₄	—	86	4	no	—
461	D₄	—	172	4	no	—
462	D₄	—	172	8	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	43	8	no	—
470	C₂×C₄	—	43	4	no	—
471	C₂×C₄	—	86	4	no	—
472	C₂×C₄	—	86	4	no	—
473	C₂×C₄	—	172	8	no	—
474	C₂×C₄	C₂²×C₄×D₄₃	1	4	yes	—
475	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
476	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
477	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
478	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
479	C₂×C₄	C₂×#10621898	1	2	yes	—
480	C₂×C₄	C₂×#10621898	1	2	yes	—
481	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
482	C₈	—	2	2	no	—
483	C₈	—	2	2	no	—
484	C₈	—	86	4	no	—
485	C₈	—	86	4	no	—
486	C₈	C₂×#10621898	1	4	yes	—
487	C₈	C₂×#10621898	1	2	yes	—
488	C₈	C₂×#10621898	1	2	yes	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	86	8	no	—
494	C₂²	—	86	4	no	—
495	C₂²	C₄×#10621898	1	2	yes	—
496	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
497	C₄	—	2	4	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	86	8	no	—
502	C₄	—	86	4	no	—
503	C₄	C₄×#10621898	1	2	yes	—
504	C₄	C₂²×#10621898	1	1	yes	characteristic
505	C₄	C₂²×#10621898	1	1	yes	characteristic
506	C₂	—	2	2	no	—
507	C₂	—	4	2	no	—
508	C₂	—	172	4	no	—
509	C₂	C₂×C₄×#10621898	1	1	yes	characteristic
510	C₂	#19149306	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁴×C₄
Fitting	C₂×C₄₃×#405	C₂
prime radical	#19147985	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	#60209
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. #19143595	C₂	semidirect
3. #19143585	C₂	semidirect
4. #19143535	C₂	semidirect
5. #19143529	C₂	semidirect
6. #19143314	C₂	semidirect
7. #19143308	C₂	semidirect
8. #19143298	C₂	semidirect
9. #19143289	C₂	semidirect
10. #19143237	C₂	semidirect
11. #19143233	C₂	semidirect
12. #19143020	C₂	semidirect
13. C₂×C₄₃×#405	C₂	semidirect
26. #14583029	C₂²	semidirect
27. #14583027	C₂²	semidirect
28. C₈×Dic₈₆	C₂²	semidirect
29. #14582978	C₂²	semidirect
31. #14582972	C₂²	semidirect
34. C₈×D₁₇₂	C₂²	semidirect
37. #14582958	C₂²	semidirect
38. #14582950	C₂²	semidirect
46. #14582856	C₂²	semidirect
47. #14582856	C₂²	semidirect
51. #14582851	C₂²	semidirect
52. #97×D₄₃	C₂²	semidirect
263. C₂×#405	D₄₃	semidirect
317. C₄₃	#60209	semidirect

Maximal subgroups

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

subgroup	index
#19147985	2
#19143595	2
#19143585	2
#19143535	2
#19143529	2
#19143314	2
#19143308	2
#19143298	2
#19143289	2
#19143237	2
#19143233	2
#19143020	2
C₂×C₄₃×#405	2
#60209	43