Subgroups — #25114208

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143253	C₂	1	2	yes	maximal
2	#19135349	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135344	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135196	C₂	1	2	yes	maximal, complemented
5	#19135196	C₂	1	2	yes	maximal, complemented
6	#19134694	C₂	1	2	yes	maximal
7	#19134637	C₂	1	1	yes	maximal, characteristic
8	#19134481	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134476	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134376	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#2911	C₂	1	1	yes	maximal, characteristic
12	#14582960	—	2	2	no	—
13	#14582960	—	2	2	no	—
14	#14582956	—	2	2	no	—
15	#14582952	—	2	2	no	—
16	C₂×#13063261	C₂²	1	1	yes	characteristic
17	C₂×#13063261	C₂²	1	1	yes	characteristic
18	#14582926	C₂²	1	2	yes	—
19	#14582926	C₂²	1	2	yes	—
20	#14582863	C₂²	1	2	yes	—
21	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
22	#14582855	C₂²	1	2	yes	—
23	#14582855	C₂²	1	2	yes	—
24	C₂×#13063235	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
27	#14582664	C₂²	1	2	yes	—
28	#14582658	C₂²	1	2	yes	—
29	#14582658	C₂²	1	2	yes	—
30	#14582658	C₂²	1	2	yes	—
31	#14582658	C₂²	1	2	yes	—
32	#14582653	C₂²	1	1	yes	characteristic
33	#14582653	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₃	C₂²	1	2	yes	—
36	C₄₃×#428	C₄	1	2	yes	complemented
37	C₄₃×#428	C₄	1	2	yes	complemented
38	C₄₃×#428	C₄	1	2	yes	complemented
39	C₄₃×#428	C₄	1	2	yes	complemented
40	C₄₃×#427	C₂²	1	1	yes	characteristic
41	C₄₃×#427	C₂²	1	1	yes	characteristic
42	C₄₃×#427	C₂²	1	2	yes	—
43	C₂×#10621877	C₂³	1	2	yes	—
44	C₂×#10621877	C₂³	1	2	yes	—
45	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
47	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
48	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
49	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
50	#13063261	—	2	2	no	—
51	#13063261	—	2	2	no	—
52	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
53	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
54	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
55	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
56	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
57	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
58	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
59	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
60	#13063236	—	2	2	no	—
61	#13063236	—	2	2	no	—
62	#13063235	—	2	2	no	—
63	C₄×C₄₃⋊C₈	—	2	2	no	—
64	C₄×C₄₃⋊C₈	—	2	2	no	—
65	C₈×Dic₄₃	—	2	2	no	—
66	C₄₃⋊#95	—	2	1	no	—
67	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₄₃	—	2	2	no	—
69	C₂×M₁₆×C₄₃	—	2	2	no	—
70	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
71	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
74	#117×C₄₃	—	2	2	no	—
75	#117×C₄₃	—	2	2	no	—
76	#117×C₄₃	C₂×C₄	1	2	yes	—
77	#117×C₄₃	C₂×C₄	1	2	yes	—
78	#117×C₄₃	C₂³	1	2	yes	—
79	#117×C₄₃	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
83	C₂×C₄²×C₄₃	—	2	2	no	—
84	#107×C₄₃	C₂×C₄	1	2	yes	—
85	#107×C₄₃	C₂×C₄	1	2	yes	—
86	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
87	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
88	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
89	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
90	#106×C₄₃	C₂×C₄	1	2	yes	—
91	#106×C₄₃	C₂×C₄	1	2	yes	—
92	#106×C₄₃	C₂×C₄	1	2	yes	—
93	#106×C₄₃	C₂×C₄	1	2	yes	—
94	C₂⁴×C₄₃	#41	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	—	2	1	no	—
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	—	2	1	no	—
98	C₂²×C₄×C₄₃	—	2	1	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₃	—	2	1	no	—
106	C₂²×Dic₄₃	—	2	1	no	—
107	M₁₆×C₄₃	—	2	4	no	—
108	M₁₆×C₄₃	—	2	4	no	—
109	C₂×C₈×C₄₃	—	2	1	no	—
110	C₂×C₈×C₄₃	—	2	1	no	—
111	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₄₃	#41	1	2	yes	—
115	C₂×C₈×C₄₃	#41	1	2	yes	—
116	C₄⋊C₄×C₄₃	—	2	2	no	—
117	C₄⋊C₄×C₄₃	—	2	2	no	—
118	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
119	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
120	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
121	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
122	C₂²⋊C₄×C₄₃	—	2	2	no	—
123	C₂²⋊C₄×C₄₃	—	2	2	no	—
124	C₂²⋊C₄×C₄₃	—	2	2	no	—
125	C₂²⋊C₄×C₄₃	—	2	2	no	—
126	C₄²×C₄₃	—	2	2	no	—
127	C₄²×C₄₃	—	2	2	no	—
128	C₄²×C₄₃	—	2	2	no	—
129	C₄²×C₄₃	—	2	2	no	—
130	C₂²⋊Dic₄₃	—	4	2	no	—
131	C₄×Dic₄₃	—	2	1	no	—
132	C₄×Dic₄₃	—	2	1	no	—
133	C₄×Dic₄₃	—	2	1	no	—
134	C₄×Dic₄₃	—	2	1	no	—
135	#10621877	—	2	2	no	—
136	#10621877	—	2	2	no	—
137	#10621877	—	2	2	no	—
138	#10621877	—	2	2	no	—
139	C₂×C₄₃⋊C₈	—	2	1	no	—
140	C₂×C₄₃⋊C₈	—	2	1	no	—
141	C₂×C₄₃⋊C₈	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	2	1	no	—
143	C₂×C₄₃⋊C₈	—	2	2	no	—
144	C₂×C₄₃⋊C₈	—	2	2	no	—
145	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
147	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
148	C₂³×C₄₃	—	2	1	no	—
149	C₂³×C₄₃	—	2	1	no	—
150	C₂³×C₄₃	—	4	1	no	—
151	C₂³×C₄₃	—	4	1	no	—
152	C₂³×C₄₃	C₄×D₄	1	2	yes	—
153	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	2	1	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	4	4	no	—
165	C₂×C₄×C₄₃	—	8	2	no	—
166	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
173	C₂×Dic₄₃	—	2	2	no	—
174	C₂×Dic₄₃	—	4	1	no	—
175	C₂×Dic₄₃	—	4	1	no	—
176	C₂×Dic₄₃	—	4	1	no	—
177	C₂×Dic₄₃	—	4	1	no	—
178	C₂×Dic₄₃	—	4	1	no	—
179	C₈×C₄₃	—	2	2	no	—
180	C₈×C₄₃	#117	1	2	yes	—
181	C₈×C₄₃	#117	1	2	yes	—
182	C₄₃⋊C₈	—	2	1	no	—
183	C₄₃⋊C₈	—	2	1	no	—
184	C₄₃⋊C₈	—	2	2	no	—
185	C₄₃⋊C₈	—	4	2	no	—
186	C₄₃⋊C₈	—	4	2	no	—
187	#22608	—	43	1	no	maximal, Sylow
188	C₂²×C₄₃	—	2	1	no	—
189	C₂²×C₄₃	—	2	1	no	—
190	C₂²×C₄₃	—	2	2	no	—
191	C₂²×C₄₃	—	2	2	no	—
192	C₂²×C₄₃	—	2	2	no	—
193	C₂²×C₄₃	—	8	1	no	—
194	C₂²×C₄₃	—	8	1	no	—
195	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂²×C₄₃	#552	1	1	yes	characteristic
197	C₂²×C₄₃	#552	1	1	yes	characteristic
198	C₄×C₄₃	—	2	2	no	—
199	C₄×C₄₃	—	4	2	no	—
200	C₄×C₄₃	—	4	2	no	—
201	C₄×C₄₃	—	4	2	no	—
202	C₄×C₄₃	—	4	2	no	—
203	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
204	C₄×C₄₃	#519	1	1	yes	characteristic
205	C₄×C₄₃	#547	1	1	yes	characteristic
206	C₄×C₄₃	#547	1	1	yes	characteristic
207	Dic₄₃	—	4	2	no	—
208	Dic₄₃	—	8	1	no	—
209	#2924	—	43	2	no	—
210	#2911	D₄₃	1	1	yes	characteristic
211	#1946	—	43	1	no	—
212	#1945	—	43	1	no	—
213	#1922	—	43	2	no	—
214	#1922	—	43	2	no	—
215	#1826	—	43	2	no	—
216	#1811	—	43	1	no	—
217	#1773	—	43	1	no	—
218	#1772	—	43	1	no	—
219	#1753	—	43	1	no	—
220	C₂×C₄₃	—	2	1	no	—
221	C₂×C₄₃	—	2	1	no	—
222	C₂×C₄₃	—	4	2	no	—
223	C₂×C₄₃	#2344	1	1	yes	characteristic
224	C₂×C₄₃	#2955	1	1	yes	characteristic
225	C₂×C₄₃	#2956	1	1	yes	characteristic
226	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
227	C₂×#117	C₂×D₄₃	1	2	yes	—
228	#433	—	86	2	no	—
229	#433	—	86	2	no	—
230	#432	—	86	2	no	—
231	#431	—	86	2	no	—
232	C₂×#108	—	43	1	no	—
233	C₂×#108	—	43	1	no	—
234	#428	Dic₄₃	1	2	yes	complemented
235	#428	Dic₄₃	1	2	yes	complemented
236	#428	Dic₄₃	1	2	yes	complemented
237	#428	Dic₄₃	1	2	yes	complemented
238	#427	C₂×D₄₃	1	2	yes	—
239	#427	C₂×D₄₃	1	1	yes	characteristic
240	#427	C₂×D₄₃	1	1	yes	characteristic
241	#424	—	43	2	no	—
242	#424	—	43	2	no	—
243	#407	—	43	2	no	—
244	C₂×C₂²⋊C₈	—	43	1	no	—
245	#405	—	43	2	no	—
246	#405	—	43	2	no	—
247	C₂×#97	—	43	1	no	—
248	C₂×C₄×C₈	—	43	1	no	—
249	C₄×C₂²⋊C₄	—	43	1	no	—
250	#341	—	43	2	no	—
251	#339	—	43	2	no	—
252	#339	—	43	2	no	—
253	#339	—	43	2	no	—
254	#339	—	43	2	no	—
255	#336	—	43	1	no	—
256	#336	—	43	1	no	—
257	C₄₃	#22608	1	1	yes	characteristic, complemented, Sylow
258	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	43	2	no	—
262	C₂×M₁₆	—	43	2	no	—
263	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
264	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
265	C₂²×C₈	—	43	1	no	—
266	C₂²×C₈	—	43	1	no	—
267	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
269	#117	—	2	2	no	—
270	#117	—	2	2	no	—
271	#117	C₂×Dic₄₃	1	2	yes	—
272	#117	C₂×Dic₄₃	1	2	yes	—
273	#117	C₂²×D₄₃	1	2	yes	—
274	#117	C₂²×D₄₃	1	2	yes	—
275	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
276	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	86	1	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	—	43	1	no	—
281	C₂×C₄²	—	43	1	no	—
282	#108	—	86	2	no	—
283	#108	—	86	2	no	—
284	#107	C₂×Dic₄₃	1	2	yes	—
285	#107	C₂×Dic₄₃	1	2	yes	—
286	#107	C₂×Dic₄₃	1	1	yes	characteristic
287	#107	C₂×Dic₄₃	1	1	yes	characteristic
288	#107	C₂×Dic₄₃	1	1	yes	characteristic
289	#107	C₂×Dic₄₃	1	1	yes	characteristic
290	#106	C₂×Dic₄₃	1	2	yes	—
291	#106	C₂×Dic₄₃	1	2	yes	—
292	#106	C₂×Dic₄₃	1	2	yes	—
293	#106	C₂×Dic₄₃	1	2	yes	—
294	C₄⋊C₈	—	86	2	no	—
295	C₄⋊C₈	—	86	2	no	—
296	C₄⋊C₈	—	86	2	no	—
297	C₄⋊C₈	—	86	2	no	—
298	C₂²⋊C₈	—	43	2	no	—
299	C₂²⋊C₈	—	43	2	no	—
300	C₂²⋊C₈	—	86	2	no	—
301	C₂²⋊C₈	—	86	2	no	—
302	#97	—	86	2	no	—
303	#97	—	86	2	no	—
304	#97	—	86	2	no	—
305	C₄×C₈	—	86	2	no	—
306	C₄×C₈	—	86	2	no	—
307	C₄×C₈	—	86	2	no	—
308	#95	—	86	1	no	—
309	C₂⁴	#10621900	1	1	yes	characteristic
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	86	1	no	—
317	C₂²×C₄	—	86	1	no	—
318	C₂²×C₄	D₄×D₄₃	1	2	yes	—
319	C₂²×C₄	#10621900	1	1	yes	characteristic
320	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
321	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
322	M₁₆	—	2	4	no	—
323	M₁₆	—	2	4	no	—
324	M₁₆	—	86	2	no	—
325	M₁₆	—	86	2	no	—
326	M₁₆	—	86	2	no	—
327	M₁₆	—	86	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	43	1	no	—
331	C₂×C₈	—	43	2	no	—
332	C₂×C₈	—	43	1	no	—
333	C₂×C₈	—	86	1	no	—
334	C₂×C₈	—	86	1	no	—
335	C₂×C₈	—	86	1	no	—
336	C₂×C₈	—	86	1	no	—
337	C₂×C₈	—	86	2	no	—
338	C₂×C₈	—	86	2	no	—
339	C₂×C₈	#10621898	1	2	yes	—
340	C₂×C₈	#10621898	1	2	yes	—
341	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
342	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
343	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
347	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
348	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
349	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	172	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	86	1	no	—
360	C₄²	—	86	1	no	—
361	C₄²	—	86	1	no	—
362	C₄²	—	86	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	D₄×Dic₄₃	1	2	yes	—
368	C₂³	C₂×#10621900	1	1	yes	characteristic
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	—	86	2	no	—
382	C₂×C₄	—	172	1	no	—
383	C₂×C₄	—	172	1	no	—
384	C₂×C₄	—	172	1	no	—
385	C₂×C₄	—	172	1	no	—
386	C₂×C₄	—	172	1	no	—
387	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
388	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
389	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
390	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
391	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
392	C₂×C₄	#13063373	1	1	yes	characteristic
393	C₂×C₄	#13063373	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	86	1	no	—
396	C₈	—	86	2	no	—
397	C₈	—	86	1	no	—
398	C₈	—	172	2	no	—
399	C₈	—	172	2	no	—
400	C₈	#13063284	1	2	yes	—
401	C₈	#13063284	1	2	yes	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
410	C₂²	#14583584	1	1	yes	characteristic
411	C₂²	#14583584	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	344	1	no	—
418	C₄	—	172	2	no	—
419	C₄	C₂×#13063284	1	1	yes	characteristic
420	C₄	#14583377	1	1	yes	characteristic
421	C₄	#14583550	1	1	yes	characteristic
422	C₄	#14583550	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	4	2	no	—
426	C₂	#19137464	1	1	yes	characteristic
427	C₂	#19143498	1	1	yes	characteristic
428	C₂	#19143505	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	C₄₃×#2911	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂⁴×C₄₃	#41
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#2911	D₄₃
hypocenter	C₄₃	#22608
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #2911

Complements

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

N	H ≅ G/N	type
2. #19135349	C₂	semidirect
3. #19135344	C₂	semidirect
4. #19135196	C₂	semidirect
5. #19135196	C₂	semidirect
8. #19134481	C₂	semidirect
9. #19134476	C₂	semidirect
36. C₄₃×#428	C₄	semidirect
37. C₄₃×#428	C₄	semidirect
38. C₄₃×#428	C₄	semidirect
39. C₄₃×#428	C₄	semidirect
234. #428	Dic₄₃	semidirect
235. #428	Dic₄₃	semidirect
236. #428	Dic₄₃	semidirect
237. #428	Dic₄₃	semidirect
257. C₄₃	#22608	semidirect

Maximal subgroups

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

subgroup	index
#19143253	2
#19135349	2
#19135344	2
#19135196	2
#19134694	2
#19134637	2
#19134481	2
#19134476	2
#19134376	2
C₄₃×#2911	2
#22608	43