Subgroups — #24986847

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143227	C₂	1	1	yes	maximal, characteristic
2	#19143223	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#19132492	C₂	1	1	yes	maximal, characteristic, complemented
5	#19132491	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1301	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₄₃	—	2	1	no	—
9	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
10	#14582955	—	2	1	no	—
11	#14582955	—	2	1	no	—
12	#14582955	C₄	1	2	yes	—
13	#14582953	C₄	1	2	yes	—
14	#14582952	C₂²	1	1	yes	characteristic
15	#14582951	—	2	1	no	—
16	#14582951	C₄	1	2	yes	—
17	#14582950	—	2	1	no	—
18	#14582923	C₂²	1	1	yes	characteristic
19	#14582921	—	2	1	no	—
20	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×Dic₄₃⋊C₈	—	2	1	no	—
22	C₄⋊C₈×D₄₃	—	2	1	no	—
23	C₄⋊C₈×D₄₃	—	2	1	no	—
24	C₄⋊C₈×D₄₃	C₄	1	2	yes	—
25	C₄⋊C₈×D₄₃	C₄	1	2	yes	—
26	#14582862	—	2	1	no	—
27	#14582861	C₄	1	2	yes	—
28	M₁₆×Dic₄₃	—	2	1	no	—
29	C₄×#10621872	—	2	1	no	—
30	C₄₃×#431	C₂²	1	1	yes	characteristic
31	C₄₃×#423	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₄₃	Q₈	1	1	yes	characteristic
36	C₂×#10621877	—	2	1	no	—
37	C₂×#10621872	—	2	2	no	—
38	C₂²×C₄₃⋊C₈	—	2	1	no	—
39	C₂×C₈×D₄₃	—	2	2	no	—
40	C₂×C₈×D₄₃	—	2	2	no	—
41	C₂×C₈×D₄₃	—	4	2	no	—
42	C₂×C₈×D₄₃	—	4	2	no	—
43	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₄₃	Q₈	1	1	yes	characteristic
46	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
47	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
48	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₄₃	D₄	1	1	yes	characteristic
51	C₄²×D₄₃	D₄	1	1	yes	characteristic
52	C₄²×D₄₃	D₄	1	1	yes	characteristic
53	C₄²×D₄₃	D₄	1	1	yes	characteristic
54	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
56	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
57	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
58	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
59	Dic₄₃⋊C₈	—	2	2	no	—
60	Dic₄₃⋊C₈	—	2	2	no	—
61	Dic₄₃⋊C₈	—	2	2	no	—
62	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
63	(C₂×D₄₃)⋊C₈	—	2	2	no	—
64	(C₂×D₄₃)⋊C₈	—	2	2	no	—
65	(C₂×D₄₃)⋊C₈	—	2	2	no	—
66	#13063235	—	2	2	no	—
67	#13063235	—	2	2	no	—
68	C₄×C₄₃⋊C₈	—	2	1	no	—
69	C₈×Dic₄₃	—	2	2	no	—
70	C₂×M₁₆×C₄₃	—	2	1	no	—
71	C₂²×C₈×C₄₃	—	2	1	no	—
72	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₄₃	—	2	1	no	—
74	C₄⋊C₈×C₄₃	—	2	1	no	—
75	C₄⋊C₈×C₄₃	—	2	1	no	—
76	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
77	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
78	C₂²⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
79	C₄×C₈×C₄₃	—	2	1	no	—
80	C₂³×D₄₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
84	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×D₄₃	—	2	1	no	—
88	C₂×C₄×D₄₃	—	2	1	no	—
89	C₂×C₄×D₄₃	—	2	1	no	—
90	C₂×C₄×D₄₃	—	2	1	no	—
91	C₂×C₄×D₄₃	—	2	4	no	—
92	C₂×C₄×D₄₃	—	4	2	no	—
93	C₂×C₄×D₄₃	C₄²	1	1	yes	characteristic
94	C₂×C₄×D₄₃	C₄²	1	1	yes	characteristic
95	C₂×C₄×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
105	M₁₆×C₄₃	—	4	1	no	—
106	M₁₆×C₄₃	—	4	1	no	—
107	C₂×C₈×C₄₃	—	2	2	no	—
108	C₂×C₈×C₄₃	—	2	2	no	—
109	C₂×C₈×C₄₃	—	2	2	no	—
110	C₂×C₈×C₄₃	—	4	1	no	—
111	C₂×C₈×C₄₃	—	4	1	no	—
112	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₄×Dic₄₃	C₄²	1	1	yes	characteristic
117	C₄×Dic₄₃	C₄²	1	1	yes	characteristic
118	C₄×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₄×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₄×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₄×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₄×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₄×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
128	#10621877	—	4	1	no	—
129	#10621877	—	4	1	no	—
130	C₂×C₄₃⋊C₈	—	2	2	no	—
131	C₂×C₄₃⋊C₈	—	2	2	no	—
132	C₂×C₄₃⋊C₈	—	2	2	no	—
133	C₂×C₄₃⋊C₈	—	4	1	no	—
134	C₂×C₄₃⋊C₈	—	4	1	no	—
135	#10621872	—	4	4	no	—
136	C₈×D₄₃	—	4	4	no	—
137	C₈×D₄₃	—	4	4	no	—
138	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂²×D₄₃	—	2	1	no	—
140	C₂²×D₄₃	—	2	1	no	—
141	C₂²×D₄₃	—	2	2	no	—
142	C₂²×D₄₃	—	2	2	no	—
143	C₂²×D₄₃	#95	1	1	yes	characteristic
144	C₂²×D₄₃	#95	1	1	yes	characteristic
145	C₂×C₄×C₄₃	—	2	2	no	—
146	C₂×C₄×C₄₃	—	4	1	no	—
147	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
156	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
157	C₂×Dic₄₃	—	2	1	no	—
158	C₂×Dic₄₃	—	2	1	no	—
159	C₂×Dic₄₃	—	2	2	no	—
160	C₂×Dic₄₃	—	4	1	no	—
161	C₂×Dic₄₃	#95	1	1	yes	characteristic
162	C₂×Dic₄₃	#95	1	1	yes	characteristic
163	C₂×Dic₄₃	#95	1	1	yes	characteristic
164	C₂×Dic₄₃	#95	1	1	yes	characteristic
165	C₂×Dic₄₃	#95	1	1	yes	characteristic
166	C₂×Dic₄₃	#95	1	1	yes	characteristic
167	C₄×D₄₃	—	2	2	no	—
168	C₄×D₄₃	—	2	2	no	—
169	C₄×D₄₃	—	2	2	no	—
170	C₄×D₄₃	—	2	1	no	—
171	C₄×D₄₃	—	2	1	no	—
172	C₄×D₄₃	—	2	1	no	—
173	C₄×D₄₃	—	2	1	no	—
174	C₄×D₄₃	—	2	1	no	—
175	C₄×D₄₃	—	2	1	no	—
176	C₄×D₄₃	—	2	1	no	—
177	C₄×D₄₃	—	2	1	no	—
178	C₄×D₄₃	—	2	2	no	—
179	C₄×D₄₃	—	2	2	no	—
180	C₄×D₄₃	—	4	1	no	—
181	C₄×D₄₃	—	4	1	no	—
182	C₄×D₄₃	#108	1	4	yes	—
183	C₈×C₄₃	—	4	2	no	—
184	C₈×C₄₃	—	4	2	no	—
185	C₈×C₄₃	—	4	2	no	—
186	C₄₃⋊C₈	—	4	2	no	—
187	C₄₃⋊C₈	—	4	2	no	—
188	C₄₃⋊C₈	—	4	2	no	—
189	#8082	—	43	1	no	maximal, Sylow
190	C₂²×C₄₃	—	2	1	no	—
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
193	C₂²×C₄₃	#428	1	1	yes	characteristic
194	C₂²×C₄₃	#428	1	1	yes	characteristic
195	C₂×D₄₃	—	2	4	no	—
196	C₂×D₄₃	—	2	4	no	—
197	C₂×D₄₃	—	2	1	no	—
198	C₂×D₄₃	—	2	1	no	—
199	C₂×D₄₃	—	2	1	no	—
200	C₂×D₄₃	—	2	1	no	—
201	C₂×D₄₃	#341	1	2	yes	—
202	C₂×D₄₃	#344	1	2	yes	—
203	C₄×C₄₃	—	2	1	no	—
204	C₄×C₄₃	—	2	1	no	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	#417	1	1	yes	characteristic
207	C₄×C₄₃	#417	1	1	yes	characteristic
208	C₄×C₄₃	#418	1	1	yes	characteristic
209	C₄×C₄₃	#419	1	1	yes	characteristic
210	C₄×C₄₃	C₂×#108	1	2	yes	—
211	Dic₄₃	—	2	1	no	—
212	Dic₄₃	—	2	1	no	—
213	Dic₄₃	—	2	1	no	—
214	Dic₄₃	—	2	1	no	—
215	Dic₄₃	—	2	1	no	—
216	Dic₄₃	#341	1	2	yes	—
217	#2920	—	43	1	no	—
218	#2920	—	43	1	no	—
219	C₂²×C₄⋊C₈	—	43	1	no	—
220	#1301	—	43	1	no	—
221	#1301	—	43	1	no	—
222	#1301	—	43	1	no	—
223	#1301	D₄₃	1	1	yes	characteristic, complemented
224	C₂×C₄₃	—	2	1	no	—
225	C₂×C₄₃	—	2	1	no	—
226	C₂×C₄₃	#1736	1	1	yes	characteristic
227	C₂×C₄₃	C₂×#341	1	1	yes	characteristic
228	C₂×C₄₃	C₂×#344	1	1	yes	characteristic
229	D₄₃	—	2	2	no	—
230	D₄₃	—	2	2	no	—
231	C₂³×C₈	—	86	1	no	—
232	C₂²×C₄²	—	43	1	no	—
233	#432	—	43	2	no	—
234	#432	—	43	2	no	—
235	#432	—	86	1	no	—
236	#432	—	86	1	no	—
237	#431	—	43	1	no	—
238	#431	—	43	2	no	—
239	#431	—	86	1	no	—
240	#431	—	86	1	no	—
241	#431	C₂×D₄₃	1	1	yes	characteristic
242	#423	—	43	1	no	—
243	#423	—	86	1	no	—
244	#423	C₂×D₄₃	1	1	yes	characteristic
245	C₂×C₄⋊C₈	—	43	1	no	—
246	C₂×C₄⋊C₈	—	43	2	no	—
247	C₂×C₄⋊C₈	—	43	2	no	—
248	C₂×C₄⋊C₈	—	86	1	no	—
249	C₂×C₄⋊C₈	—	86	1	no	—
250	C₂×C₄⋊C₈	—	86	1	no	—
251	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
252	#407	—	43	2	no	—
253	#407	—	86	1	no	—
254	C₄×M₁₆	—	86	1	no	—
255	C₄×M₁₆	—	86	1	no	—
256	C₄₃	#8082	1	1	yes	characteristic, complemented, Sylow
257	C₂³×C₄	—	43	1	no	—
258	C₂³×C₄	—	43	1	no	—
259	C₂³×C₄	—	43	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	86	2	no	—
262	C₂×M₁₆	—	86	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	86	2	no	—
265	C₂²×C₈	—	86	2	no	—
266	C₂²×C₈	—	86	1	no	—
267	C₂²×C₈	—	172	2	no	—
268	C₂²×C₈	—	172	2	no	—
269	C₂×C₄²	—	43	1	no	—
270	C₂×C₄²	—	43	1	no	—
271	C₂×C₄²	—	43	1	no	—
272	C₂×C₄²	—	43	1	no	—
273	C₂×C₄²	—	43	1	no	—
274	C₂×C₄²	—	43	1	no	—
275	C₂×C₄²	—	43	1	no	—
276	C₂×C₄²	—	43	1	no	—
277	C₂×C₄²	—	43	1	no	—
278	C₂×C₄²	—	43	1	no	—
279	C₂×C₄²	—	43	1	no	—
280	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	43	2	no	—
285	C₄⋊C₈	—	43	2	no	—
286	C₄⋊C₈	—	86	2	no	—
287	C₄⋊C₈	—	86	2	no	—
288	C₄⋊C₈	—	86	2	no	—
289	C₄⋊C₈	—	86	1	no	—
290	C₄⋊C₈	—	86	1	no	—
291	C₄⋊C₈	—	86	1	no	—
292	C₄⋊C₈	C₄×D₄₃	1	2	yes	—
293	C₄⋊C₈	C₄×D₄₃	1	2	yes	—
294	C₂²⋊C₈	—	43	2	no	—
295	C₂²⋊C₈	—	86	2	no	—
296	C₂²⋊C₈	—	86	2	no	—
297	C₂²⋊C₈	—	86	2	no	—
298	C₂²⋊C₈	C₄×D₄₃	1	2	yes	—
299	#97	—	86	2	no	—
300	#97	—	86	2	no	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	—	86	2	no	—
303	C₄×C₈	—	86	1	no	—
304	C₂⁴	—	43	1	no	—
305	C₂²×C₄	—	43	1	no	—
306	C₂²×C₄	—	43	1	no	—
307	C₂²×C₄	—	43	1	no	—
308	C₂²×C₄	—	43	1	no	—
309	C₂²×C₄	—	43	1	no	—
310	C₂²×C₄	—	43	1	no	—
311	C₂²×C₄	—	43	1	no	—
312	C₂²×C₄	—	43	1	no	—
313	C₂²×C₄	—	43	1	no	—
314	C₂²×C₄	—	43	1	no	—
315	C₂²×C₄	—	43	1	no	—
316	C₂²×C₄	—	43	1	no	—
317	C₂²×C₄	—	43	1	no	—
318	C₂²×C₄	—	43	1	no	—
319	C₂²×C₄	—	43	1	no	—
320	C₂²×C₄	—	86	4	no	—
321	C₂²×C₄	—	86	1	no	—
322	C₂²×C₄	—	86	1	no	—
323	C₂²×C₄	—	86	1	no	—
324	C₂²×C₄	—	86	1	no	—
325	C₂²×C₄	—	172	2	no	—
326	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
328	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
329	M₁₆	—	4	1	no	—
330	M₁₆	—	4	1	no	—
331	M₁₆	—	172	4	no	—
332	M₁₆	—	172	1	no	—
333	M₁₆	—	172	1	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	86	2	no	—
340	C₂×C₈	—	86	2	no	—
341	C₂×C₈	—	86	2	no	—
342	C₂×C₈	—	172	4	no	—
343	C₂×C₈	—	172	4	no	—
344	C₂×C₈	—	172	1	no	—
345	C₂×C₈	—	172	1	no	—
346	C₄²	—	43	1	no	—
347	C₄²	—	43	1	no	—
348	C₄²	—	43	1	no	—
349	C₄²	—	43	1	no	—
350	C₄²	—	43	1	no	—
351	C₄²	—	43	1	no	—
352	C₄²	—	43	1	no	—
353	C₄²	—	43	1	no	—
354	C₄²	—	43	1	no	—
355	C₄²	—	43	1	no	—
356	C₄²	—	43	1	no	—
357	C₄²	—	43	1	no	—
358	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
359	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
360	C₄²	D₄×D₄₃	1	1	yes	characteristic
361	C₄²	D₄×D₄₃	1	1	yes	characteristic
362	C₂³	—	43	1	no	—
363	C₂³	—	43	1	no	—
364	C₂³	—	86	2	no	—
365	C₂³	—	86	2	no	—
366	C₂³	—	86	1	no	—
367	C₂³	—	86	1	no	—
368	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	43	1	no	—
372	C₂×C₄	—	43	4	no	—
373	C₂×C₄	—	43	1	no	—
374	C₂×C₄	—	43	1	no	—
375	C₂×C₄	—	43	1	no	—
376	C₂×C₄	—	43	1	no	—
377	C₂×C₄	—	43	1	no	—
378	C₂×C₄	—	86	2	no	—
379	C₂×C₄	—	86	2	no	—
380	C₂×C₄	—	86	2	no	—
381	C₂×C₄	—	86	2	no	—
382	C₂×C₄	—	86	2	no	—
383	C₂×C₄	—	86	1	no	—
384	C₂×C₄	—	86	1	no	—
385	C₂×C₄	—	86	1	no	—
386	C₂×C₄	—	86	1	no	—
387	C₂×C₄	—	86	1	no	—
388	C₂×C₄	—	86	1	no	—
389	C₂×C₄	—	86	1	no	—
390	C₂×C₄	—	86	1	no	—
391	C₂×C₄	—	86	1	no	—
392	C₂×C₄	—	86	1	no	—
393	C₂×C₄	—	86	2	no	—
394	C₂×C₄	—	172	1	no	—
395	C₂×C₄	—	172	1	no	—
396	C₂×C₄	—	172	1	no	—
397	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
398	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
399	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
400	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
401	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
402	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
403	C₂×C₄	#13063349	1	1	yes	characteristic
404	C₂×C₄	#13063352	1	1	yes	characteristic
405	C₂×C₄	#13063354	1	1	yes	characteristic
406	C₂×C₄	#13063357	1	1	yes	characteristic
407	C₈	—	4	2	no	—
408	C₈	—	4	2	no	—
409	C₈	—	4	2	no	—
410	C₈	—	172	2	no	—
411	C₈	—	172	2	no	—
412	C₈	—	172	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	43	2	no	—
416	C₂²	—	43	2	no	—
417	C₂²	—	86	4	no	—
418	C₂²	—	86	4	no	—
419	C₂²	—	86	1	no	—
420	C₂²	—	86	1	no	—
421	C₂²	—	86	1	no	—
422	C₂²	—	86	1	no	—
423	C₂²	#95×D₄₃	1	1	yes	characteristic
424	C₂²	#14582938	1	1	yes	characteristic
425	C₂²	#14582940	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	43	2	no	—
430	C₄	—	86	1	no	—
431	C₄	—	86	1	no	—
432	C₄	—	86	1	no	—
433	C₄	—	86	1	no	—
434	C₄	—	86	1	no	—
435	C₄	#14582897	1	1	yes	characteristic
436	C₄	#14582899	1	1	yes	characteristic
437	C₄	#14582902	1	1	yes	characteristic
438	C₄	#14582906	1	1	yes	characteristic
439	C₄	#108×D₄₃	1	2	yes	—
440	C₂	—	2	1	no	—
441	C₂	—	2	1	no	—
442	C₂	—	86	2	no	—
443	C₂	—	86	2	no	—
444	C₂	#19134313	1	1	yes	characteristic
445	C₂	#341×D₄₃	1	1	yes	characteristic
446	C₂	#344×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1301	C₂
socle	C₂²×C₄₃	C₂×#95
prime radical	C₂³×D₄₃	C₄⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1301	D₄₃
hypocenter	C₄₃	#8082
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

Complements

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

N	H ≅ G/N	type
4. #19132492	C₂	semidirect
5. #19132491	C₂	semidirect
6. #19132490	C₂	semidirect
7. C₄₃×#1301	C₂	semidirect
223. #1301	D₄₃	semidirect
256. C₄₃	#8082	semidirect

Maximal subgroups

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

subgroup	index
#19143227	2
#19143223	2
C₂×C₄⋊C₈×D₄₃	2
#19132492	2
#19132491	2
#19132490	2
C₄₃×#1301	2
#8082	43