Subgroups — #25119151

Order 11008.

880 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144176	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583020	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143320	C₂	1	2	yes	maximal, complemented
4	#19135486	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135346	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135242	C₂	1	2	yes	maximal, complemented
7	#19134897	C₂	1	2	yes	maximal, complemented
8	#19134867	C₂	1	2	yes	maximal, complemented
9	#19134482	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134371	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#108×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	1	yes	characteristic
13	C₂×#13063333	C₂²	1	2	yes	—
14	#14583410	C₂²	1	2	yes	—
15	#14583140	C₄	1	1	yes	characteristic, complemented
16	#14583140	C₄	1	1	yes	characteristic, complemented
17	#14583135	C₄	1	1	yes	characteristic, complemented
18	#14583135	C₄	1	1	yes	characteristic, complemented
19	#14583128	C₄	1	2	yes	complemented
20	#14583128	C₄	1	2	yes	complemented
21	#14583020	—	2	4	no	—
22	#14582975	—	2	2	no	—
23	#14582970	—	2	2	no	—
24	#14582968	—	2	2	no	—
25	C₈×C₂²⋊D₄₃	—	2	2	no	—
26	#14582937	C₂²	1	1	yes	characteristic
27	#14582927	C₂²	1	2	yes	—
28	C₂×#13063251	C₂²	1	2	yes	—
29	C₂×#13063251	C₂²	1	2	yes	—
30	#14582896	C₂²	1	2	yes	—
31	#14582867	C₂²	1	2	yes	—
32	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
33	#14582857	C₂²	1	2	yes	—
34	C₂×#13063235	C₂²	1	1	yes	characteristic
35	C₂×#13063235	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
37	#14582660	C₂²	1	2	yes	—
38	#14582660	C₂²	1	2	yes	—
39	#14582653	C₂²	1	1	yes	characteristic
40	#14582653	C₂²	1	1	yes	characteristic
41	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
42	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₂×#108×C₄₃	—	2	4	no	—
44	C₂×#108×C₄₃	C₂²	1	2	yes	—
45	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
46	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621898	C₂³	1	2	yes	—
48	#13063347	—	2	2	no	—
49	#13063347	—	2	2	no	—
50	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
51	C₂×#10621873	C₂×C₄	1	2	yes	—
52	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic
53	#13063333	—	2	4	no	—
54	#13063333	—	4	2	no	—
55	C₂×#10621872	—	2	2	no	—
56	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₄₃	—	2	2	no	—
59	#13063308	—	2	2	no	—
60	#13063304	C₂×C₄	1	2	yes	—
61	#13063304	C₂×C₄	1	2	yes	—
62	#13063299	C₂×C₄	1	2	yes	—
63	#13063299	C₂×C₄	1	2	yes	—
64	#13063294	—	2	2	no	—
65	C₄×C₂²⋊D₄₃	—	2	2	no	—
66	C₄×C₂²⋊D₄₃	—	2	2	no	—
67	#13063284	C₂³	1	2	yes	—
68	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
69	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
71	#13063259	C₂×C₄	1	1	yes	characteristic
72	#13063259	C₂×C₄	1	1	yes	characteristic
73	#13063257	C₂×C₄	1	2	yes	—
74	Dic₄₃⋊C₈	—	2	2	no	—
75	Dic₄₃⋊C₈	—	2	2	no	—
76	#13063251	—	2	4	no	—
77	#13063251	—	4	2	no	—
78	#13063250	C₂×C₄	1	2	yes	—
79	#13063250	C₂×C₄	1	2	yes	—
80	#13063247	C₂×C₄	1	2	yes	—
81	#13063247	C₂×C₄	1	2	yes	—
82	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
83	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
84	(C₂×D₄₃)⋊C₈	—	2	2	no	—
85	(C₂×D₄₃)⋊C₈	—	2	2	no	—
86	#13063235	—	2	2	no	—
87	#13063235	—	2	2	no	—
88	#13063235	—	2	2	no	—
89	C₈×Dic₄₃	—	2	2	no	—
90	C₄₃⋊#95	—	2	1	no	—
91	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₄₃	—	2	2	no	—
93	C₂×M₁₆×C₄₃	—	2	4	no	—
94	C₂×M₁₆×C₄₃	—	4	2	no	—
95	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
96	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
97	C₂²×C₈×C₄₃	—	2	2	no	—
98	C₂²×C₈×C₄₃	—	2	2	no	—
99	C₂²×C₈×C₄₃	—	2	2	no	—
100	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
101	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
102	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
103	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
104	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
106	#108×C₄₃	—	2	4	no	—
107	#108×C₄₃	—	2	2	no	—
108	#108×C₄₃	D₄	1	4	yes	complemented
109	C₂⁴×C₄₃	#41	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	—	2	1	no	—
113	C₂²×C₄×C₄₃	—	2	1	no	—
114	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
120	C₂×C₂²⋊D₄₃	—	2	2	no	—
121	C₂×C₂²⋊D₄₃	—	2	2	no	—
122	C₂×C₂²⋊D₄₃	—	2	2	no	—
123	C₂²×Dic₄₃	—	2	1	no	—
124	C₂²×Dic₄₃	—	2	1	no	—
125	#10621898	—	2	2	no	—
126	#10621898	—	2	2	no	—
127	#10621898	—	2	2	no	—
128	#10621898	—	2	2	no	—
129	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
130	C₂×C₄×D₄₃	—	2	2	no	—
131	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
132	M₁₆×C₄₃	—	2	2	no	—
133	M₁₆×C₄₃	—	2	2	no	—
134	M₁₆×C₄₃	—	2	2	no	—
135	M₁₆×C₄₃	—	4	4	no	—
136	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
137	C₂×C₈×C₄₃	—	2	1	no	—
138	C₂×C₈×C₄₃	—	2	2	no	—
139	C₂×C₈×C₄₃	—	2	1	no	—
140	C₂×C₈×C₄₃	—	2	2	no	—
141	C₂×C₈×C₄₃	—	2	2	no	—
142	C₂×C₈×C₄₃	—	2	2	no	—
143	C₂×C₈×C₄₃	—	2	2	no	—
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₂×C₈×C₄₃	—	4	4	no	—
146	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₄₃	#41	1	2	yes	—
152	C₂²⋊Dic₄₃	—	2	2	no	—
153	C₂²⋊Dic₄₃	—	2	2	no	—
154	C₂²⋊Dic₄₃	—	2	2	no	—
155	C₂²⋊Dic₄₃	—	4	2	no	—
156	(C₂×D₄₃)⋊C₄	—	2	2	no	—
157	(C₂×D₄₃)⋊C₄	—	2	2	no	—
158	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
159	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
160	Dic₄₃⋊C₄	—	2	2	no	—
161	Dic₄₃⋊C₄	—	2	2	no	—
162	C₄×Dic₄₃	—	2	2	no	—
163	C₄×Dic₄₃	—	2	1	no	—
164	C₄×Dic₄₃	—	2	1	no	—
165	C₄×Dic₄₃	—	2	1	no	—
166	C₄×Dic₄₃	—	2	1	no	—
167	C₂×C₄₃⋊C₈	—	2	1	no	—
168	C₂×C₄₃⋊C₈	—	2	1	no	—
169	C₂×C₄₃⋊C₈	—	2	1	no	—
170	C₂×C₄₃⋊C₈	—	2	1	no	—
171	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
172	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
173	Dic₁₇₂	—	2	2	no	—
174	D₃₄₄	—	2	2	no	—
175	#10621873	—	2	4	no	—
176	#10621872	—	4	4	no	—
177	C₈×D₄₃	—	4	4	no	—
178	C₂³×C₄₃	—	2	1	no	—
179	C₂³×C₄₃	—	2	1	no	—
180	C₂³×C₄₃	—	2	2	no	—
181	C₂³×C₄₃	—	4	1	no	—
182	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
183	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
184	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
185	C₂²×D₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	1	no	—
188	C₂×C₄×C₄₃	—	2	1	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	1	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	1	no	—
193	C₂×C₄×C₄₃	—	2	1	no	—
194	C₂×C₄×C₄₃	—	2	1	no	—
195	C₂×C₄×C₄₃	—	2	1	no	—
196	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
204	C₂²⋊D₄₃	—	4	2	no	—
205	C₂²⋊D₄₃	—	4	2	no	—
206	C₂²⋊D₄₃	—	4	4	no	—
207	C₂²⋊D₄₃	—	8	2	no	—
208	C₂×Dic₄₃	—	2	2	no	—
209	C₂×Dic₄₃	—	2	2	no	—
210	C₂×Dic₄₃	—	2	2	no	—
211	C₂×Dic₄₃	—	4	1	no	—
212	C₂×Dic₄₃	—	4	1	no	—
213	C₂×Dic₄₃	—	4	1	no	—
214	C₂×Dic₄₃	—	4	1	no	—
215	C₂×Dic₄₃	—	4	1	no	—
216	C₂×Dic₄₃	—	4	1	no	—
217	D₁₇₂	—	2	2	no	—
218	D₁₇₂	—	2	2	no	—
219	C₄×D₄₃	—	4	2	no	—
220	C₄×D₄₃	—	4	2	no	—
221	Dic₈₆	—	2	2	no	—
222	Dic₈₆	—	2	2	no	—
223	C₈×C₄₃	—	2	1	no	—
224	C₈×C₄₃	—	2	1	no	—
225	C₈×C₄₃	—	2	4	no	—
226	C₈×C₄₃	—	4	2	no	—
227	C₈×C₄₃	C₄×D₄	1	2	yes	—
228	C₈×C₄₃	C₄×D₄	1	2	yes	—
229	C₄₃⋊C₈	—	2	2	no	—
230	C₄₃⋊C₈	—	2	2	no	—
231	#23019	—	43	1	no	maximal, Sylow
232	C₂²×C₄₃	—	2	1	no	—
233	C₂²×C₄₃	—	2	1	no	—
234	C₂²×C₄₃	—	2	1	no	—
235	C₂²×C₄₃	—	2	1	no	—
236	C₂²×C₄₃	—	2	1	no	—
237	C₂²×C₄₃	—	2	1	no	—
238	C₂²×C₄₃	—	2	1	no	—
239	C₂²×C₄₃	—	4	2	no	—
240	C₂²×C₄₃	—	4	2	no	—
241	C₂²×C₄₃	#444	1	2	yes	complemented
242	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
243	C₂²×C₄₃	#548	1	1	yes	characteristic
244	C₂²×C₄₃	#553	1	1	yes	characteristic
245	C₂×D₄₃	—	4	2	no	—
246	C₂×D₄₃	—	4	2	no	—
247	C₂×D₄₃	—	4	2	no	—
248	C₄×C₄₃	—	2	1	no	—
249	C₄×C₄₃	—	2	1	no	—
250	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
251	C₄×C₄₃	#520	1	1	yes	characteristic
252	C₄×C₄₃	D₄²	1	1	yes	characteristic
253	C₄×C₄₃	#547	1	1	yes	characteristic
254	Dic₄₃	—	4	2	no	—
255	Dic₄₃	—	4	2	no	—
256	Dic₄₃	—	4	2	no	—
257	Dic₄₃	—	8	1	no	—
258	Dic₄₃	—	8	1	no	—
259	#3050	—	43	1	no	—
260	C₂×#444	—	43	1	no	—
261	#2933	—	43	2	no	—
262	C₂²×#108	D₄₃	1	1	yes	characteristic, complemented
263	#1975	—	43	1	no	—
264	#1946	—	43	1	no	—
265	#1929	—	43	2	no	—
266	#1871	—	43	2	no	—
267	#1866	—	43	2	no	—
268	#1773	—	43	1	no	—
269	#1752	—	43	1	no	—
270	C₂×C₄₃	—	2	1	no	—
271	C₂×C₄₃	—	2	1	no	—
272	C₂×C₄₃	—	2	2	no	—
273	C₂×C₄₃	—	4	1	no	—
274	C₂×C₄₃	#2361	1	1	yes	characteristic
275	C₂×C₄₃	C₂×#444	1	1	yes	characteristic
276	C₂×C₄₃	#2957	1	1	yes	characteristic
277	D₄₃	—	8	2	no	—
278	C₂×#135	—	43	1	no	—
279	C₂×#131	—	43	2	no	—
280	C₂²×M₁₆	C₂×D₄₃	1	2	yes	—
281	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
282	#525	—	43	2	no	—
283	#467	—	43	1	no	—
284	#467	—	43	1	no	—
285	#466	—	43	1	no	—
286	#466	—	43	1	no	—
287	#465	—	43	2	no	—
288	#465	—	43	2	no	—
289	#444	—	86	4	no	—
290	#436	—	86	2	no	—
291	#435	—	86	2	no	—
292	#435	—	86	2	no	—
293	C₈×D₄	—	86	2	no	—
294	C₂×#108	—	2	4	no	—
295	C₂×#108	C₂×D₄₃	1	2	yes	—
296	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
297	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
298	#427	—	43	1	no	—
299	#424	—	43	2	no	—
300	C₂×#104	—	43	2	no	—
301	C₂×#104	—	43	2	no	—
302	#416	—	43	2	no	—
303	#408	—	43	2	no	—
304	C₂×C₂²⋊C₈	—	43	1	no	—
305	#405	—	43	2	no	—
306	C₂×#97	—	43	1	no	—
307	C₂×#97	—	43	1	no	—
308	C₄×C₂²⋊C₄	—	43	1	no	—
309	#339	—	43	2	no	—
310	#339	—	43	2	no	—
311	#336	—	43	1	no	—
312	#336	—	43	1	no	—
313	C₄₃	#23019	1	1	yes	characteristic, complemented, Sylow
314	C₂×#41	—	43	2	no	—
315	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
316	#135	—	86	2	no	—
317	#135	—	86	2	no	—
318	C₂×Q₁₆	—	43	1	no	—
319	C₂×SD₁₆	—	43	2	no	—
320	C₂×D₈	—	43	1	no	—
321	#131	—	86	4	no	—
322	#131	—	172	2	no	—
323	C₂×M₁₆	—	2	2	no	—
324	C₂×M₁₆	—	2	4	no	—
325	C₂×M₁₆	—	4	2	no	—
326	C₂×M₁₆	—	86	2	no	—
327	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
328	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
329	C₂²×C₈	—	2	2	no	—
330	C₂²×C₈	—	2	2	no	—
331	C₂²×C₈	—	2	2	no	—
332	C₂²×C₈	—	43	1	no	—
333	C₂²×C₈	—	43	1	no	—
334	C₂²×C₈	—	86	2	no	—
335	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
336	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
337	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
338	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
339	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
340	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
341	#123	—	86	2	no	—
342	C₂²⋊Q₈	—	43	2	no	—
343	C₂²⋊Q₈	—	43	2	no	—
344	#121	—	43	2	no	—
345	#121	—	43	2	no	—
346	#120	—	86	2	no	—
347	C₄×D₄	—	86	2	no	—
348	C₄×D₄	—	86	2	no	—
349	#117	—	43	2	no	—
350	C₂×C₂²⋊C₄	—	86	1	no	—
351	C₂×C₄²	—	43	1	no	—
352	C₂×C₄²	—	43	1	no	—
353	#108	—	2	4	no	—
354	#108	—	2	2	no	—
355	#108	C₂²⋊D₄₃	1	4	yes	complemented
356	#107	—	43	1	no	—
357	#107	—	43	1	no	—
358	#106	—	43	2	no	—
359	C₄⋊C₈	—	86	2	no	—
360	C₄⋊C₈	—	86	2	no	—
361	#104	—	86	4	no	—
362	#104	—	172	2	no	—
363	#103	—	43	2	no	—
364	#103	—	43	2	no	—
365	#102	—	43	2	no	—
366	#102	—	43	2	no	—
367	C₂²⋊C₈	—	43	2	no	—
368	C₂²⋊C₈	—	43	2	no	—
369	C₂²⋊C₈	—	86	2	no	—
370	C₂²⋊C₈	—	86	2	no	—
371	#97	—	86	2	no	—
372	#97	—	86	2	no	—
373	#97	—	86	2	no	—
374	C₄×C₈	—	86	2	no	—
375	#95	—	86	1	no	—
376	C₂⁴	#10621902	1	1	yes	characteristic
377	#41	—	86	2	no	—
378	#41	—	86	2	no	—
379	#41	—	86	2	no	—
380	#41	—	86	2	no	—
381	C₂×Q₈	—	43	2	no	—
382	C₂×D₄	—	43	2	no	—
383	C₂×D₄	—	86	2	no	—
384	C₂×D₄	—	86	2	no	—
385	C₂×D₄	—	86	2	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	86	2	no	—
391	C₂²×C₄	—	86	1	no	—
392	C₂²×C₄	—	86	1	no	—
393	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
395	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
396	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
397	C₂²×C₄	#10621902	1	1	yes	characteristic
398	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
399	Q₁₆	—	86	2	no	—
400	SD₁₆	—	86	4	no	—
401	D₈	—	86	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	2	2	no	—
405	M₁₆	—	4	4	no	—
406	M₁₆	—	172	4	no	—
407	M₁₆	C₂×C₂²⋊D₄₃	1	4	yes	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	4	4	no	—
417	C₂×C₈	—	43	2	no	—
418	C₂×C₈	—	43	2	no	—
419	C₂×C₈	—	86	1	no	—
420	C₂×C₈	—	86	1	no	—
421	C₂×C₈	—	86	1	no	—
422	C₂×C₈	—	86	1	no	—
423	C₂×C₈	—	172	4	no	—
424	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
425	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
426	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
427	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
428	C₂×C₈	#10621898	1	2	yes	—
429	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
430	C₄⋊C₄	—	43	2	no	—
431	C₄⋊C₄	—	43	2	no	—
432	C₄⋊C₄	—	86	2	no	—
433	C₄⋊C₄	—	86	2	no	—
434	C₂²⋊C₄	—	86	2	no	—
435	C₂²⋊C₄	—	86	2	no	—
436	C₂²⋊C₄	—	86	2	no	—
437	C₂²⋊C₄	—	86	2	no	—
438	C₂²⋊C₄	—	86	2	no	—
439	C₂²⋊C₄	—	172	2	no	—
440	C₄²	—	86	2	no	—
441	C₄²	—	86	1	no	—
442	C₄²	—	86	1	no	—
443	C₄²	—	86	1	no	—
444	C₄²	—	86	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	86	2	no	—
450	C₂³	#13063287	1	1	yes	characteristic
451	C₂³	#13063287	1	1	yes	characteristic
452	C₂³	C₂×#10621902	1	1	yes	characteristic
453	Q₈	—	86	2	no	—
454	Q₈	—	86	2	no	—
455	D₄	—	86	2	no	—
456	D₄	—	86	2	no	—
457	D₄	—	344	2	no	—
458	D₄	—	172	2	no	—
459	D₄	—	172	2	no	—
460	D₄	—	172	4	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	86	2	no	—
472	C₂×C₄	—	86	2	no	—
473	C₂×C₄	—	86	2	no	—
474	C₂×C₄	—	172	1	no	—
475	C₂×C₄	—	172	1	no	—
476	C₂×C₄	—	172	1	no	—
477	C₂×C₄	—	172	1	no	—
478	C₂×C₄	—	172	1	no	—
479	C₂×C₄	—	172	1	no	—
480	C₂×C₄	—	172	2	no	—
481	C₂×C₄	—	172	2	no	—
482	C₂×C₄	#13063287	1	1	yes	characteristic
483	C₂×C₄	#13063287	1	1	yes	characteristic
484	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
485	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
487	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
488	C₂×C₄	#13063370	1	1	yes	characteristic
489	C₂×C₄	#13063373	1	1	yes	characteristic
490	C₈	—	2	1	no	—
491	C₈	—	2	1	no	—
492	C₈	—	2	4	no	—
493	C₈	—	4	2	no	—
494	C₈	—	86	2	no	—
495	C₈	—	86	2	no	—
496	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
497	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	172	2	no	—
508	C₂²	—	172	2	no	—
509	C₂²	—	172	2	no	—
510	C₂²	#14583020	1	2	yes	complemented
511	C₂²	C₂×#13063287	1	1	yes	characteristic
512	C₂²	#14583560	1	1	yes	characteristic
513	C₂²	#14583597	1	1	yes	characteristic
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	344	1	no	—
517	C₄	—	344	1	no	—
518	C₄	—	172	2	no	—
519	C₄	—	172	2	no	—
520	C₄	—	172	2	no	—
521	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
522	C₄	#14583380	1	1	yes	characteristic
523	C₄	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
524	C₄	#14583550	1	1	yes	characteristic
525	C₂	—	2	1	no	—
526	C₂	—	2	1	no	—
527	C₂	—	2	2	no	—
528	C₂	—	4	1	no	—
529	C₂	—	344	2	no	—
530	C₂	#19137611	1	1	yes	characteristic
531	C₂	C₂×#14583020	1	1	yes	characteristic
532	C₂	#19143511	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂²×#108×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#19144176	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂²×#108	D₄₃
hypocenter	C₄₃	#23019
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
2. C₂×#14583020	C₂	semidirect
3. #19143320	C₂	semidirect
4. #19135486	C₂	semidirect
5. #19135346	C₂	semidirect
6. #19135242	C₂	semidirect
7. #19134897	C₂	semidirect
8. #19134867	C₂	semidirect
9. #19134482	C₂	semidirect
10. #19134371	C₂	semidirect
11. C₂²×#108×C₄₃	C₂	semidirect
15. #14583140	C₄	semidirect
16. #14583140	C₄	semidirect
17. #14583135	C₄	semidirect
18. #14583135	C₄	semidirect
19. #14583128	C₄	semidirect
20. #14583128	C₄	semidirect
108. #108×C₄₃	D₄	semidirect
241. C₂²×C₄₃	#444	semidirect
262. C₂²×#108	D₄₃	semidirect
313. C₄₃	#23019	semidirect
355. #108	C₂²⋊D₄₃	semidirect
510. C₂²	#14583020	semidirect

Maximal subgroups

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

subgroup	index
#19144176	2
C₂×#14583020	2
#19143320	2
#19135486	2
#19135346	2
#19135242	2
#19134897	2
#19134867	2
#19134482	2
#19134371	2
C₂²×#108×C₄₃	2
#23019	43