Subgroups — #24989952

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13063283	C₂	1	1	yes	maximal, characteristic
2	#19134572	C₂	1	1	yes	maximal, characteristic
3	C₄×(C₂×D₄₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#19132436	C₂	1	1	yes	maximal, characteristic, complemented
5	#19132435	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13063283	C₄	1	1	yes	characteristic
9	C₂×#13063283	C₄	1	1	yes	characteristic
10	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
13	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
14	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×Dic₄₃	C₄	1	1	yes	characteristic
16	C₄⋊C₄×Dic₄₃	C₄	1	1	yes	characteristic
17	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
18	C₄×(C₂×D₄₃)⋊C₄	—	2	1	no	—
19	#14582746	—	2	1	no	—
20	#14582744	—	2	1	no	—
21	C₄²×Dic₄₃	—	2	1	no	—
22	#14582653	—	2	1	no	—
23	#14582653	—	2	1	no	—
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
30	C₂²×C₄₃⋊C₈	—	2	1	no	—
31	C₂²×C₄₃⋊C₈	—	2	1	no	—
32	#13063283	—	2	2	no	—
33	#13063283	—	2	2	no	—
34	#13063283	—	2	2	no	—
35	#13063283	C₈	1	4	yes	complemented
36	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
38	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
39	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
40	C₂×C₄×Dic₄₃	—	2	1	no	—
41	C₂×C₄×Dic₄₃	—	2	1	no	—
42	C₂×C₄×Dic₄₃	—	2	1	no	—
43	C₂×C₄×Dic₄₃	—	2	1	no	—
44	C₂×C₄×Dic₄₃	—	2	1	no	—
45	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
48	C₄²×D₄₃	—	2	1	no	—
49	C₄²×D₄₃	—	2	1	no	—
50	C₄²×D₄₃	—	2	1	no	—
51	C₄²×D₄₃	—	2	1	no	—
52	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
54	(C₂×D₄₃)⋊C₈	—	2	4	no	—
55	(C₂×D₄₃)⋊C₈	—	4	2	no	—
56	C₄×C₄₃⋊C₈	—	2	1	no	—
57	C₄×C₄₃⋊C₈	—	2	1	no	—
58	C₄₃⋊#95	—	2	1	no	—
59	C₄₃⋊#95	—	2	1	no	—
60	C₄₃⋊#95	—	2	1	no	—
61	C₂²×C₈×C₄₃	—	2	1	no	—
62	C₂²×C₈×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₃	—	2	1	no	—
66	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₄₃	—	2	1	no	—
68	C₄⋊C₈×C₄₃	—	2	1	no	—
69	C₄×C₈×C₄₃	—	2	1	no	—
70	C₄×C₈×C₄₃	—	2	1	no	—
71	#95×C₄₃	—	2	1	no	—
72	C₂³×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₃	—	2	1	no	—
74	C₂²×C₄×C₄₃	—	2	1	no	—
75	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×Dic₄₃	—	2	1	no	—
79	C₂²×Dic₄₃	—	2	1	no	—
80	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₄₃	—	2	1	no	—
84	C₂×C₄×D₄₃	—	2	1	no	—
85	C₂×C₄×D₄₃	—	2	1	no	—
86	C₂×C₄×D₄₃	—	2	1	no	—
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	1	no	—
92	C₂×C₄×D₄₃	—	2	1	no	—
93	C₂×C₄×D₄₃	—	2	1	no	—
94	C₂×C₄×D₄₃	—	2	1	no	—
95	C₂×C₄×D₄₃	—	2	2	no	—
96	C₂×C₄×D₄₃	—	4	1	no	—
97	C₂×C₄×D₄₃	C₂×C₈	1	2	yes	—
98	C₂×C₄×D₄₃	M₁₆	1	2	yes	—
99	C₂×C₈×C₄₃	—	2	2	no	—
100	C₂×C₈×C₄₃	—	4	1	no	—
101	C₂×C₈×C₄₃	—	4	1	no	—
102	C₂×C₈×C₄₃	—	4	1	no	—
103	C₂×C₈×C₄₃	—	4	1	no	—
104	C₂×C₈×C₄₃	—	4	1	no	—
105	C₄⋊C₄×C₄₃	—	2	1	no	—
106	C₄⋊C₄×C₄₃	—	2	1	no	—
107	C₄⋊C₄×C₄₃	C₂×C₈	1	2	yes	—
108	C₄⋊C₄×C₄₃	M₁₆	1	2	yes	—
109	C₄²×C₄₃	—	4	1	no	—
110	C₄²×C₄₃	—	4	1	no	—
111	C₄²×C₄₃	#41	1	1	yes	characteristic
112	C₄²×C₄₃	#41	1	1	yes	characteristic
113	C₄²×C₄₃	#41	1	1	yes	characteristic
114	C₄²×C₄₃	#41	1	1	yes	characteristic
115	(C₂×D₄₃)⋊C₄	—	2	4	no	—
116	(C₂×D₄₃)⋊C₄	—	2	4	no	—
117	C₄⋊Dic₄₃	—	2	1	no	—
118	C₄⋊Dic₄₃	—	2	1	no	—
119	C₄⋊Dic₄₃	C₂×C₈	1	2	yes	—
120	C₄⋊Dic₄₃	M₁₆	1	2	yes	—
121	C₄×Dic₄₃	—	2	4	no	—
122	C₄×Dic₄₃	—	2	1	no	—
123	C₄×Dic₄₃	—	2	1	no	—
124	C₄×Dic₄₃	—	2	1	no	—
125	C₄×Dic₄₃	—	2	1	no	—
126	C₄×Dic₄₃	—	2	1	no	—
127	C₄×Dic₄₃	—	2	1	no	—
128	C₄×Dic₄₃	—	2	4	no	—
129	C₄×Dic₄₃	—	4	2	no	—
130	C₄×Dic₄₃	—	4	1	no	—
131	C₄×Dic₄₃	—	4	1	no	—
132	C₄×Dic₄₃	—	4	2	no	—
133	C₂×C₄₃⋊C₈	—	2	2	no	—
134	C₂×C₄₃⋊C₈	—	4	1	no	—
135	C₂×C₄₃⋊C₈	—	4	1	no	—
136	C₂×C₄₃⋊C₈	—	4	1	no	—
137	C₂×C₄₃⋊C₈	—	4	1	no	—
138	C₂×C₄₃⋊C₈	—	4	1	no	—
139	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×D₄₃	—	2	1	no	—
141	C₂²×D₄₃	—	2	1	no	—
142	C₂²×D₄₃	—	2	1	no	—
143	C₂²×D₄₃	—	2	1	no	—
144	C₂²×D₄₃	—	2	1	no	—
145	C₂²×D₄₃	—	2	1	no	—
146	C₂²×D₄₃	C₂²⋊C₈	1	2	yes	—
147	C₂×C₄×C₄₃	—	2	1	no	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	—	4	1	no	—
153	C₂×C₄×C₄₃	—	4	1	no	—
154	C₂×C₄×C₄₃	—	4	1	no	—
155	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
156	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
157	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
158	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
159	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
165	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
166	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
167	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
169	C₂×Dic₄₃	—	2	1	no	—
170	C₂×Dic₄₃	—	2	1	no	—
171	C₂×Dic₄₃	—	2	1	no	—
172	C₂×Dic₄₃	—	2	1	no	—
173	C₂×Dic₄₃	—	2	1	no	—
174	C₂×Dic₄₃	—	2	2	no	—
175	C₂×Dic₄₃	—	2	2	no	—
176	C₂×Dic₄₃	—	2	1	no	—
177	C₂×Dic₄₃	—	2	1	no	—
178	C₂×Dic₄₃	—	4	1	no	—
179	C₂×Dic₄₃	—	4	1	no	—
180	C₂×Dic₄₃	—	4	1	no	—
181	C₂×Dic₄₃	—	4	1	no	—
182	C₂×Dic₄₃	C₂²⋊C₈	1	2	yes	—
183	C₂×Dic₄₃	#104	1	2	yes	—
184	C₄×D₄₃	—	2	2	no	—
185	C₄×D₄₃	—	2	2	no	—
186	C₄×D₄₃	—	2	2	no	—
187	C₄×D₄₃	—	2	2	no	—
188	C₄×D₄₃	—	4	2	no	—
189	C₄×D₄₃	—	4	2	no	—
190	C₄×D₄₃	—	4	1	no	—
191	C₄×D₄₃	—	4	1	no	—
192	C₄×D₄₃	—	4	1	no	—
193	C₄×D₄₃	—	4	1	no	—
194	C₈×C₄₃	—	4	2	no	—
195	C₈×C₄₃	—	8	1	no	—
196	C₄₃⋊C₈	—	4	2	no	—
197	C₄₃⋊C₈	—	8	1	no	—
198	#8708	—	43	1	no	maximal, Sylow
199	C₂²×C₄₃	#381	1	1	yes	characteristic
200	C₂²×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
201	C₂²×C₄₃	#407	1	1	yes	characteristic
202	C₂²×C₄₃	#416	1	1	yes	characteristic
203	C₂²×C₄₃	#417	1	1	yes	characteristic
204	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
205	C₂²×C₄₃	#421	1	1	yes	characteristic
206	C₂×D₄₃	—	2	2	no	—
207	C₂×D₄₃	—	2	2	no	—
208	C₂×D₄₃	—	2	2	no	—
209	C₂×D₄₃	—	4	1	no	—
210	C₂×D₄₃	—	4	1	no	—
211	C₂×D₄₃	—	4	1	no	—
212	C₂×D₄₃	—	4	1	no	—
213	C₄×C₄₃	—	2	1	no	—
214	C₄×C₄₃	—	2	1	no	—
215	C₄×C₄₃	—	4	2	no	—
216	C₄×C₄₃	—	4	2	no	—
217	C₄×C₄₃	#431	1	1	yes	characteristic
218	C₄×C₄₃	#431	1	1	yes	characteristic
219	C₄×C₄₃	#432	1	1	yes	characteristic
220	C₄×C₄₃	#432	1	1	yes	characteristic
221	C₄×C₄₃	#482	1	1	yes	characteristic
222	C₄×C₄₃	#482	1	1	yes	characteristic
223	C₄×C₄₃	#485	1	1	yes	characteristic
224	C₄×C₄₃	#485	1	1	yes	characteristic
225	Dic₄₃	—	2	2	no	—
226	Dic₄₃	—	2	2	no	—
227	Dic₄₃	—	4	1	no	—
228	Dic₄₃	—	4	2	no	—
229	Dic₄₃	—	4	2	no	—
230	C₄×#117	—	43	1	no	—
231	#1797	—	43	1	no	—
232	C₄×C₂²⋊C₈	—	43	1	no	—
233	#1279	—	43	1	no	—
234	#1279	—	43	1	no	—
235	#1279	—	43	1	no	—
236	#1279	D₄₃	1	1	yes	characteristic, complemented
237	C₂×C₄₃	#1476	1	1	yes	characteristic
238	C₂×C₄₃	#1477	1	1	yes	characteristic
239	C₂×C₄₃	#1488	1	1	yes	characteristic
240	C₂×C₄₃	#1489	1	1	yes	characteristic
241	C₂×C₄₃	#1817	1	1	yes	characteristic
242	C₂×C₄₃	#1825	1	1	yes	characteristic
243	C₂×C₄₃	#1826	1	1	yes	characteristic
244	D₄₃	—	4	2	no	—
245	C₂×#117	—	43	1	no	—
246	C₂×#117	—	43	1	no	—
247	C₂²×C₄²	—	43	1	no	—
248	C₂×C₄⋊C₈	—	43	1	no	—
249	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
250	C₂×C₂²⋊C₈	—	86	1	no	—
251	C₂×C₂²⋊C₈	—	86	1	no	—
252	C₂×C₄×C₈	—	43	1	no	—
253	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
254	C₄×C₄⋊C₄	—	43	1	no	—
255	C₄×C₄⋊C₄	—	43	1	no	—
256	C₄×C₄⋊C₄	—	43	1	no	—
257	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
258	C₄×C₂²⋊C₄	—	86	1	no	—
259	C₄×C₂²⋊C₄	—	86	1	no	—
260	#376	—	86	1	no	—
261	C₄³	—	86	1	no	—
262	#336	—	86	1	no	—
263	#336	—	86	1	no	—
264	C₄₃	#8708	1	1	yes	characteristic, complemented, Sylow
265	C₂³×C₄	—	43	1	no	—
266	C₂³×C₄	—	43	1	no	—
267	C₂³×C₄	—	43	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	86	1	no	—
271	C₂²×C₈	—	86	1	no	—
272	#117	—	43	4	no	—
273	#117	—	86	2	no	—
274	#117	—	86	2	no	—
275	#117	—	86	2	no	—
276	C₂×C₄⋊C₄	—	43	1	no	—
277	C₂×C₄⋊C₄	—	43	1	no	—
278	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	—	86	1	no	—
281	C₂×C₂²⋊C₄	—	86	1	no	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	43	1	no	—
284	C₂×C₄²	—	43	1	no	—
285	C₂×C₄²	—	43	1	no	—
286	C₂×C₄²	—	86	1	no	—
287	C₂×C₄²	—	86	1	no	—
288	C₂×C₄²	—	86	1	no	—
289	C₂×C₄²	—	86	1	no	—
290	C₂×C₄²	—	86	1	no	—
291	C₂×C₄²	—	86	1	no	—
292	C₂×C₄²	—	86	1	no	—
293	C₂×C₄²	—	86	1	no	—
294	C₂×C₄²	—	86	1	no	—
295	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	86	1	no	—
299	C₄⋊C₈	—	86	1	no	—
300	C₂²⋊C₈	—	86	4	no	—
301	C₂²⋊C₈	—	172	2	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	—	2	1	no	—
304	C₄×C₈	—	86	1	no	—
305	C₄×C₈	—	86	1	no	—
306	#95	—	2	1	no	—
307	#95	—	86	1	no	—
308	#95	—	86	1	no	—
309	#95	—	86	1	no	—
310	C₂⁴	—	43	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	43	1	no	—
314	C₂²×C₄	—	43	1	no	—
315	C₂²×C₄	—	43	2	no	—
316	C₂²×C₄	—	43	2	no	—
317	C₂²×C₄	—	43	1	no	—
318	C₂²×C₄	—	86	2	no	—
319	C₂²×C₄	—	86	1	no	—
320	C₂²×C₄	—	86	1	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	—	86	1	no	—
326	C₂²×C₄	—	86	1	no	—
327	C₂²×C₄	—	86	1	no	—
328	C₂²×C₄	—	86	1	no	—
329	C₂²×C₄	—	86	1	no	—
330	C₂²×C₄	—	86	1	no	—
331	C₂²×C₄	—	86	1	no	—
332	C₂²×C₄	—	86	1	no	—
333	C₂²×C₄	—	172	1	no	—
334	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
336	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	86	2	no	—
344	C₂×C₈	—	172	1	no	—
345	C₂×C₈	—	172	1	no	—
346	C₂×C₈	—	172	1	no	—
347	C₂×C₈	—	172	1	no	—
348	C₂×C₈	—	172	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	43	2	no	—
352	C₄⋊C₄	—	43	2	no	—
353	C₄⋊C₄	—	86	1	no	—
354	C₄⋊C₄	—	86	1	no	—
355	C₄⋊C₄	C₈×D₄₃	1	2	yes	—
356	C₄⋊C₄	#10621872	1	2	yes	—
357	C₂²⋊C₄	—	86	4	no	—
358	C₂²⋊C₄	—	86	4	no	—
359	C₄²	—	4	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	—	86	4	no	—
362	C₄²	—	86	4	no	—
363	C₄²	—	86	1	no	—
364	C₄²	—	86	1	no	—
365	C₄²	—	86	1	no	—
366	C₄²	—	86	1	no	—
367	C₄²	—	86	1	no	—
368	C₄²	—	86	1	no	—
369	C₄²	—	172	2	no	—
370	C₄²	—	172	2	no	—
371	C₄²	—	172	1	no	—
372	C₄²	—	172	1	no	—
373	C₄²	#10621898	1	1	yes	characteristic
374	C₄²	#10621898	1	1	yes	characteristic
375	C₄²	#10621900	1	1	yes	characteristic
376	C₄²	#10621902	1	1	yes	characteristic
377	C₂³	—	43	2	no	—
378	C₂³	—	86	1	no	—
379	C₂³	—	86	1	no	—
380	C₂³	—	86	1	no	—
381	C₂³	—	86	1	no	—
382	C₂³	—	86	1	no	—
383	C₂³	—	86	1	no	—
384	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	43	2	no	—
394	C₂×C₄	—	43	2	no	—
395	C₂×C₄	—	86	1	no	—
396	C₂×C₄	—	86	1	no	—
397	C₂×C₄	—	86	1	no	—
398	C₂×C₄	—	86	1	no	—
399	C₂×C₄	—	86	2	no	—
400	C₂×C₄	—	86	2	no	—
401	C₂×C₄	—	86	2	no	—
402	C₂×C₄	—	86	2	no	—
403	C₂×C₄	—	86	2	no	—
404	C₂×C₄	—	86	2	no	—
405	C₂×C₄	—	86	1	no	—
406	C₂×C₄	—	86	1	no	—
407	C₂×C₄	—	86	1	no	—
408	C₂×C₄	—	172	2	no	—
409	C₂×C₄	—	172	2	no	—
410	C₂×C₄	—	172	1	no	—
411	C₂×C₄	—	172	1	no	—
412	C₂×C₄	—	172	1	no	—
413	C₂×C₄	—	172	1	no	—
414	C₂×C₄	—	172	1	no	—
415	C₂×C₄	—	172	1	no	—
416	C₂×C₄	—	172	1	no	—
417	C₂×C₄	—	172	1	no	—
418	C₂×C₄	#13063282	1	1	yes	characteristic
419	C₂×C₄	#13063283	1	1	yes	characteristic
420	C₂×C₄	#13063307	1	1	yes	characteristic
421	C₂×C₄	#13063307	1	1	yes	characteristic
422	C₂×C₄	#13063310	1	1	yes	characteristic
423	C₂×C₄	#13063310	1	1	yes	characteristic
424	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
425	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
426	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
427	C₂×C₄	C₂×#10621872	1	1	yes	characteristic
428	C₂×C₄	#13063346	1	1	yes	characteristic
429	C₂×C₄	#13063348	1	1	yes	characteristic
430	C₂×C₄	#13063349	1	1	yes	characteristic
431	C₂×C₄	#13063354	1	1	yes	characteristic
432	C₈	—	4	2	no	—
433	C₈	—	8	1	no	—
434	C₈	—	344	1	no	—
435	C₈	—	172	2	no	—
436	C₂²	—	86	2	no	—
437	C₂²	—	86	2	no	—
438	C₂²	—	86	2	no	—
439	C₂²	—	172	1	no	—
440	C₂²	—	172	1	no	—
441	C₂²	—	172	1	no	—
442	C₂²	—	172	1	no	—
443	C₂²	#14582761	1	1	yes	characteristic
444	C₂²	C₂²⋊C₈×D₄₃	1	1	yes	characteristic
445	C₂²	#14582861	1	1	yes	characteristic
446	C₂²	#14582894	1	1	yes	characteristic
447	C₂²	#14582897	1	1	yes	characteristic
448	C₂²	#104×D₄₃	1	1	yes	characteristic
449	C₂²	#14582914	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	86	2	no	—
455	C₄	—	86	2	no	—
456	C₄	—	172	2	no	—
457	C₄	—	172	2	no	—
458	C₄	—	172	1	no	—
459	C₄	#14582950	1	1	yes	characteristic
460	C₄	#14582951	1	1	yes	characteristic
461	C₄	#14582954	1	1	yes	characteristic
462	C₄	#14582955	1	1	yes	characteristic
463	C₄	#14583222	1	1	yes	characteristic
464	C₄	#14583226	1	1	yes	characteristic
465	C₄	#14583239	1	1	yes	characteristic
466	C₄	#14583243	1	1	yes	characteristic
467	C₂	—	172	2	no	—
468	C₂	#19132976	1	1	yes	characteristic
469	C₂	#19132979	1	1	yes	characteristic
470	C₂	#19133028	1	1	yes	characteristic
471	C₂	#19133031	1	1	yes	characteristic
472	C₂	#19134662	1	1	yes	characteristic
473	C₂	#19134689	1	1	yes	characteristic
474	C₂	#19134693	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1279	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1279	D₄₃
hypocenter	C₄₃	#8708
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. #19132436	C₂	semidirect
5. #19132435	C₂	semidirect
6. #19132434	C₂	semidirect
7. C₄₃×#1279	C₂	semidirect
35. #13063283	C₈	semidirect
236. #1279	D₄₃	semidirect
264. C₄₃	#8708	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13063283	2
#19134572	2
C₄×(C₂×D₄₃)⋊C₈	2
#19132436	2
#19132435	2
#19132434	2
C₄₃×#1279	2
#8708	43