Subgroups — #24992836

Order 11008.

646 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582977	C₂	1	1	yes	maximal, characteristic, complemented
2	#19135402	C₂	1	1	yes	maximal, characteristic, complemented
3	#19134595	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14582643	C₂	1	1	yes	maximal, characteristic, complemented
5	#19132479	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132429	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#459	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10621877	—	2	1	no	—
9	#14582977	—	2	2	no	—
10	#14582977	—	2	2	no	—
11	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#13063246	—	2	1	no	—
14	C₂×#13063246	—	2	1	no	—
15	C₂×#13063246	—	2	1	no	—
16	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
17	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
18	#14582769	C₂²	1	1	yes	characteristic
19	#14582661	—	2	1	no	—
20	#14582643	—	2	2	no	—
21	C₂²×D₈×C₄₃	—	2	1	no	—
22	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#459	—	2	2	no	—
25	C₄₃×#459	C₄	1	4	yes	complemented
26	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#102×C₄₃	—	2	1	no	—
28	C₂×#10621877	—	2	4	no	—
29	C₂×#10621877	—	4	2	no	—
30	C₂×#10621877	—	4	2	no	—
31	C₂²×C₄₃⋊C₈	—	2	1	no	—
32	C₂²×C₄₃⋊C₈	—	2	1	no	—
33	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
34	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
35	C₂×C₄⋊Dic₄₃	—	2	1	no	—
36	C₂×C₄⋊Dic₄₃	—	2	1	no	—
37	C₂×C₄⋊Dic₄₃	—	2	1	no	—
38	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
39	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
40	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
41	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
42	#13063246	—	4	2	no	—
43	#13063246	—	4	2	no	—
44	#13063246	—	4	2	no	—
45	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
46	C₄×C₄₃⋊C₈	—	2	1	no	—
47	C₄×C₄₃⋊C₈	—	2	1	no	—
48	C₂²×D₄×C₄₃	—	2	1	no	—
49	C₂²×D₄×C₄₃	—	2	1	no	—
50	C₂²×D₄×C₄₃	—	2	1	no	—
51	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	—	2	1	no	—
53	C₂×D₈×C₄₃	—	2	4	no	—
54	C₂×D₈×C₄₃	—	4	2	no	—
55	C₂×D₈×C₄₃	—	4	2	no	—
56	C₂²×C₈×C₄₃	—	2	1	no	—
57	#127×C₄₃	—	2	1	no	—
58	#127×C₄₃	—	2	1	no	—
59	#127×C₄₃	—	2	1	no	—
60	#127×C₄₃	C₂×C₄	1	2	yes	—
61	C₄×D₄×C₄₃	—	2	1	no	—
62	C₄×D₄×C₄₃	—	2	1	no	—
63	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
64	C₄×D₄×C₄₃	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₄₃	—	2	1	no	—
69	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
70	#102×C₄₃	—	2	4	no	—
71	C₂⁴×C₄₃	—	2	1	no	—
72	C₂⁴×C₄₃	—	4	1	no	—
73	C₂×D₄×C₄₃	—	2	1	no	—
74	C₂×D₄×C₄₃	—	2	2	no	—
75	C₂×D₄×C₄₃	—	2	2	no	—
76	C₂×D₄×C₄₃	—	2	2	no	—
77	C₂×D₄×C₄₃	—	2	1	no	—
78	C₂×D₄×C₄₃	—	2	1	no	—
79	C₂×D₄×C₄₃	—	2	1	no	—
80	C₂×D₄×C₄₃	—	2	1	no	—
81	C₂×D₄×C₄₃	—	4	1	no	—
82	C₂×D₄×C₄₃	—	4	1	no	—
83	C₂×D₄×C₄₃	—	4	1	no	—
84	C₂×D₄×C₄₃	—	4	1	no	—
85	C₂×D₄×C₄₃	—	4	1	no	—
86	C₂×D₄×C₄₃	—	4	1	no	—
87	C₂×D₄×C₄₃	—	4	1	no	—
88	C₂×D₄×C₄₃	—	4	1	no	—
89	C₂×D₄×C₄₃	—	4	1	no	—
90	C₂×D₄×C₄₃	—	4	1	no	—
91	C₂×D₄×C₄₃	—	4	1	no	—
92	C₂×D₄×C₄₃	—	8	1	no	—
93	C₂×D₄×C₄₃	—	8	1	no	—
94	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	1	no	—
98	C₂²×C₄×C₄₃	—	4	1	no	—
99	C₂²×C₄×C₄₃	—	4	1	no	—
100	C₂²×C₄×C₄₃	—	4	1	no	—
101	C₂²×C₄×C₄₃	—	4	1	no	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
105	C₂²×Dic₄₃	—	4	1	no	—
106	D₈×C₄₃	—	4	8	no	—
107	C₂×C₈×C₄₃	—	2	2	no	—
108	C₂×C₈×C₄₃	—	4	1	no	—
109	C₂×C₈×C₄₃	—	4	1	no	—
110	C₄⋊C₄×C₄₃	—	2	1	no	—
111	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
112	C₂²⋊C₄×C₄₃	—	2	2	no	—
113	C₂²⋊C₄×C₄₃	—	2	2	no	—
114	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₄₃	#41	1	1	yes	characteristic
118	C₄⋊Dic₄₃	—	4	1	no	—
119	C₄⋊Dic₄₃	—	4	1	no	—
120	C₄⋊Dic₄₃	—	4	1	no	—
121	C₄⋊Dic₄₃	—	4	1	no	—
122	C₄⋊Dic₄₃	—	8	1	no	—
123	#10621877	—	4	8	no	—
124	C₂×C₄₃⋊C₈	—	2	1	no	—
125	C₂×C₄₃⋊C₈	—	2	1	no	—
126	C₂×C₄₃⋊C₈	—	2	1	no	—
127	C₂×C₄₃⋊C₈	—	2	2	no	—
128	C₂×C₄₃⋊C₈	—	2	1	no	—
129	C₂×C₄₃⋊C₈	—	2	1	no	—
130	C₂×C₄₃⋊C₈	—	4	1	no	—
131	C₂×C₄₃⋊C₈	—	4	1	no	—
132	C₂×C₄₃⋊C₈	—	4	1	no	—
133	C₂×C₄₃⋊C₈	—	4	1	no	—
134	C₂×C₄₃⋊C₈	—	4	1	no	—
135	C₂×C₄₃⋊C₈	D₈	1	2	yes	complemented
136	C₂³×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	4	1	no	—
138	C₂³×C₄₃	—	4	1	no	—
139	C₂³×C₄₃	—	4	1	no	—
140	C₂³×C₄₃	—	4	1	no	—
141	C₂³×C₄₃	—	4	1	no	—
142	C₂³×C₄₃	—	4	1	no	—
143	C₂³×C₄₃	—	4	2	no	—
144	C₂³×C₄₃	—	8	1	no	—
145	C₂³×C₄₃	—	8	1	no	—
146	C₂³×C₄₃	—	8	1	no	—
147	C₂³×C₄₃	—	8	1	no	—
148	C₂³×C₄₃	—	8	1	no	—
149	C₂³×C₄₃	—	8	1	no	—
150	C₂³×C₄₃	#121	1	1	yes	characteristic
151	D₄×C₄₃	—	2	2	no	—
152	D₄×C₄₃	—	2	2	no	—
153	D₄×C₄₃	—	4	2	no	—
154	D₄×C₄₃	—	4	2	no	—
155	D₄×C₄₃	—	4	2	no	—
156	D₄×C₄₃	—	4	2	no	—
157	D₄×C₄₃	—	4	1	no	—
158	D₄×C₄₃	—	4	1	no	—
159	D₄×C₄₃	—	8	2	no	—
160	D₄×C₄₃	—	8	2	no	—
161	D₄×C₄₃	—	8	1	no	—
162	D₄×C₄₃	—	8	1	no	—
163	D₄×C₄₃	—	8	1	no	—
164	D₄×C₄₃	—	8	1	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
178	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
179	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
182	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
188	C₂×Dic₄₃	—	8	1	no	—
189	C₂×Dic₄₃	—	8	1	no	—
190	C₂×Dic₄₃	—	8	1	no	—
191	C₈×C₄₃	—	4	2	no	—
192	C₄₃⋊C₈	—	2	2	no	—
193	C₄₃⋊C₈	—	4	2	no	—
194	C₄₃⋊C₈	—	4	1	no	—
195	C₄₃⋊C₈	—	8	1	no	—
196	#9229	—	43	1	no	maximal, Sylow
197	C₂²×C₄₃	—	4	2	no	—
198	C₂²×C₄₃	—	4	2	no	—
199	C₂²×C₄₃	—	4	2	no	—
200	C₂²×C₄₃	—	8	1	no	—
201	C₂²×C₄₃	—	8	1	no	—
202	C₂²×C₄₃	—	8	1	no	—
203	C₂²×C₄₃	—	8	1	no	—
204	C₂²×C₄₃	—	8	2	no	—
205	C₂²×C₄₃	—	8	2	no	—
206	C₂²×C₄₃	—	8	2	no	—
207	C₂²×C₄₃	—	16	1	no	—
208	C₂²×C₄₃	—	16	1	no	—
209	C₂²×C₄₃	—	16	1	no	—
210	C₂²×C₄₃	—	16	1	no	—
211	C₂²×C₄₃	#386	1	1	yes	characteristic
212	C₂²×C₄₃	#459	1	1	yes	characteristic
213	C₂²×C₄₃	#463	1	1	yes	characteristic
214	C₂²×C₄₃	#468	1	1	yes	characteristic
215	C₂²×C₄₃	#469	1	1	yes	characteristic
216	C₂²×C₄₃	#471	1	1	yes	characteristic
217	C₂²×C₄₃	#472	1	1	yes	characteristic
218	C₄×C₄₃	—	2	1	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	4	2	no	—
221	C₄×C₄₃	#417	1	1	yes	characteristic
222	C₄×C₄₃	#418	1	1	yes	characteristic
223	C₄×C₄₃	C₄×D₈	1	1	yes	characteristic
224	C₄×C₄₃	#442	1	1	yes	characteristic
225	C₄×C₄₃	#447	1	1	yes	characteristic
226	C₄×C₄₃	#449	1	1	yes	characteristic
227	C₄×C₄₃	#468	1	1	yes	characteristic
228	C₄×C₄₃	#469	1	1	yes	characteristic
229	Dic₄₃	—	16	1	no	—
230	C₂×#459	D₄₃	1	1	yes	characteristic
231	C₂×#436	—	43	1	no	—
232	#1957	—	43	1	no	—
233	#1802	—	43	1	no	—
234	C₂×#331	—	43	1	no	—
235	#1296	—	43	1	no	—
236	#1277	—	43	1	no	—
237	C₂×C₄₃	—	8	2	no	—
238	C₂×C₄₃	—	16	2	no	—
239	C₂×C₄₃	#1685	1	1	yes	characteristic
240	C₂×C₄₃	#1687	1	1	yes	characteristic
241	C₂×C₄₃	#1697	1	1	yes	characteristic
242	C₂×C₄₃	#1701	1	1	yes	characteristic
243	C₂×C₄₃	#1879	1	1	yes	characteristic
244	C₂×C₄₃	#1895	1	1	yes	characteristic
245	C₂×C₄₃	#1907	1	1	yes	characteristic
246	C₂²×D₈	—	2	1	no	—
247	C₂²×M₁₆	—	86	1	no	—
248	C₂×#127	C₂×D₄₃	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
250	#459	—	2	2	no	—
251	#459	Dic₄₃	1	4	yes	complemented
252	#436	—	86	2	no	—
253	#436	—	86	2	no	—
254	C₂×C₄⋊C₈	—	43	1	no	—
255	C₂×C₄⋊C₈	—	43	1	no	—
256	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
257	C₂×#102	—	2	1	no	—
258	C₂×#102	—	86	1	no	—
259	C₂×#102	—	86	1	no	—
260	C₂×#102	—	86	1	no	—
261	C₂×C₂²⋊C₈	—	86	1	no	—
262	C₂×C₄×C₈	—	43	1	no	—
263	#384	—	43	1	no	—
264	#340	—	86	1	no	—
265	#331	—	86	2	no	—
266	C₄₃	#9229	1	1	yes	characteristic, complemented, Sylow
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
271	C₂³×C₄	—	2	1	no	—
272	C₂×D₈	—	2	4	no	—
273	C₂×D₈	—	4	2	no	—
274	C₂×D₈	—	4	2	no	—
275	C₂×M₁₆	—	86	4	no	—
276	C₂×M₁₆	—	172	2	no	—
277	C₂×M₁₆	—	172	2	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	43	1	no	—
280	C₂²×C₈	—	43	1	no	—
281	C₂²×C₈	—	86	1	no	—
282	C₂²×C₈	—	86	1	no	—
283	#127	—	2	1	no	—
284	#127	—	2	1	no	—
285	#127	—	2	1	no	—
286	#127	C₂×Dic₄₃	1	2	yes	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	C₂×Dic₄₃	1	2	yes	—
290	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
291	C₂×C₄⋊C₄	—	86	1	no	—
292	C₂×C₄⋊C₄	—	86	1	no	—
293	C₂×C₄⋊C₄	—	86	1	no	—
294	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	43	2	no	—
299	C₄⋊C₈	—	86	1	no	—
300	C₄⋊C₈	—	86	1	no	—
301	C₄⋊C₈	—	86	1	no	—
302	C₄⋊C₈	C₂×Dic₄₃	1	2	yes	—
303	#102	—	2	4	no	—
304	#102	—	172	2	no	—
305	#102	—	172	2	no	—
306	#102	—	172	2	no	—
307	C₂²⋊C₈	—	86	4	no	—
308	C₄×C₈	—	86	1	no	—
309	C₄×C₈	—	86	1	no	—
310	C₂⁴	—	2	1	no	—
311	C₂⁴	—	4	1	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	8	1	no	—
332	C₂×D₄	—	8	1	no	—
333	C₂×D₄	C₂²⋊Dic₄₃	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	172	1	no	—
342	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
343	C₂²×C₄	#10621900	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
345	D₈	—	4	8	no	—
346	M₁₆	—	172	8	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	43	2	no	—
351	C₂×C₈	—	86	1	no	—
352	C₂×C₈	—	86	1	no	—
353	C₂×C₈	—	86	1	no	—
354	C₂×C₈	—	86	2	no	—
355	C₂×C₈	—	86	1	no	—
356	C₂×C₈	—	86	1	no	—
357	C₂×C₈	—	172	1	no	—
358	C₂×C₈	—	172	1	no	—
359	C₂×C₈	—	172	1	no	—
360	C₂×C₈	—	172	1	no	—
361	C₂×C₈	—	172	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	344	1	no	—
364	C₄⋊C₄	—	172	1	no	—
365	C₄⋊C₄	—	172	1	no	—
366	C₄⋊C₄	—	172	1	no	—
367	C₄⋊C₄	—	172	1	no	—
368	C₄⋊C₄	C₂²⋊Dic₄₃	1	2	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₄²	D₄×D₄₃	1	1	yes	characteristic
372	C₄²	#10621900	1	1	yes	characteristic
373	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
375	C₂³	—	2	2	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	8	1	no	—
384	C₂³	—	8	1	no	—
385	C₂³	—	8	1	no	—
386	C₂³	—	8	1	no	—
387	C₂³	—	8	1	no	—
388	C₂³	—	8	1	no	—
389	C₂³	#13063297	1	1	yes	characteristic
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	8	2	no	—
399	D₄	—	8	2	no	—
400	D₄	—	8	1	no	—
401	D₄	—	8	1	no	—
402	D₄	—	8	1	no	—
403	D₄	—	8	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	344	1	no	—
414	C₂×C₄	—	344	1	no	—
415	C₂×C₄	—	344	1	no	—
416	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
417	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
418	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
419	C₂×C₄	#13063293	1	1	yes	characteristic
420	C₂×C₄	#13063297	1	1	yes	characteristic
421	C₂×C₄	#13063306	1	1	yes	characteristic
422	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
423	C₂×C₄	#13063344	1	1	yes	characteristic
424	C₂×C₄	#13063349	1	1	yes	characteristic
425	C₂×C₄	#13063349	1	1	yes	characteristic
426	C₂×C₄	#13063350	1	1	yes	characteristic
427	C₂×C₄	#13063351	1	1	yes	characteristic
428	C₂×C₄	#13063351	1	1	yes	characteristic
429	C₂×C₄	#13063355	1	1	yes	characteristic
430	C₈	—	4	2	no	—
431	C₈	—	86	2	no	—
432	C₈	—	344	1	no	—
433	C₈	—	172	1	no	—
434	C₈	—	172	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	1	no	—
441	C₂²	—	8	1	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	16	1	no	—
446	C₂²	—	16	1	no	—
447	C₂²	—	16	1	no	—
448	C₂²	—	16	1	no	—
449	C₂²	#14582779	1	1	yes	characteristic
450	C₂²	#14583092	1	1	yes	characteristic
451	C₂²	#14583112	1	1	yes	characteristic
452	C₂²	#14583143	1	1	yes	characteristic
453	C₂²	#14583150	1	1	yes	characteristic
454	C₂²	#14583160	1	1	yes	characteristic
455	C₂²	#14583167	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	688	1	no	—
460	C₄	#14582900	1	1	yes	characteristic
461	C₄	#14582904	1	1	yes	characteristic
462	C₄	D₈×Dic₄₃	1	1	yes	characteristic
463	C₄	#14583011	1	1	yes	characteristic
464	C₄	#14583031	1	1	yes	characteristic
465	C₄	#14583041	1	1	yes	characteristic
466	C₄	#14583143	1	1	yes	characteristic
467	C₄	#14583150	1	1	yes	characteristic
468	C₂	—	8	2	no	—
469	C₂	—	16	2	no	—
470	C₂	#19134058	1	1	yes	characteristic
471	C₂	#19134072	1	1	yes	characteristic
472	C₂	#19134126	1	1	yes	characteristic
473	C₂	#19134154	1	1	yes	characteristic
474	C₂	#19134945	1	1	yes	characteristic
475	C₂	#19135034	1	1	yes	characteristic
476	C₂	#19135105	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063297
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting, prime radical	C₂×C₄₃×#459	C₂
socle	C₂³×C₄₃	#121
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×#459	D₄₃
hypocenter	C₄₃	#9229
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#459

Complements

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

N	H ≅ G/N	type
1. C₂×#14582977	C₂	semidirect
2. #19135402	C₂	semidirect
3. #19134595	C₂	semidirect
4. C₂×#14582643	C₂	semidirect
5. #19132479	C₂	semidirect
6. #19132429	C₂	semidirect
25. C₄₃×#459	C₄	semidirect
135. C₂×C₄₃⋊C₈	D₈	semidirect
251. #459	Dic₄₃	semidirect
266. C₄₃	#9229	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582977	2
#19135402	2
#19134595	2
C₂×#14582643	2
#19132479	2
#19132429	2
C₂×C₄₃×#459	2
#9229	43