Subgroups — #25100167

Order 11008.

844 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582946	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582946	C₂	1	1	yes	maximal, characteristic
3	#430×D₄₃	C₂	1	2	yes	maximal
4	#19143011	C₂	1	1	yes	maximal, characteristic
5	#19135386	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135385	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135384	C₂	1	2	yes	maximal, complemented
8	#19135383	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135382	C₂	1	2	yes	maximal, complemented
10	#344×D₄₃	C₂	1	2	yes	maximal
11	C₄₃×#1953	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10621872	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×D₄₃	C₂²	1	2	yes	—
14	C₂×M₁₆×D₄₃	C₂²	1	2	yes	—
15	C₂×M₁₆×D₄₃	C₂²	1	1	yes	characteristic
16	#117×D₄₃	C₂²	1	1	yes	characteristic
17	#14582948	C₂²	1	2	yes	—
18	#14582947	C₂²	1	2	yes	—
19	#14582947	C₂²	1	2	yes	—
20	#14582946	—	2	1	no	—
21	#14582946	—	2	1	no	—
22	#14582946	—	2	1	no	—
23	#14582946	—	2	1	no	—
24	#14582946	—	2	4	no	—
25	#14582946	C₄	1	8	yes	complemented
26	C₂×#13063261	C₂²	1	1	yes	characteristic
27	C₂×#13063261	C₂²	1	1	yes	characteristic
28	C₂×#13063260	C₂²	1	2	yes	—
29	C₂×#13063260	C₂²	1	2	yes	—
30	#108×D₄₃	—	2	4	no	—
31	#14582857	C₂²	1	1	yes	characteristic
32	#14582856	—	2	1	no	—
33	#14582855	C₂²	1	1	yes	characteristic
34	#14582854	C₂²	1	1	yes	characteristic
35	#14582853	—	2	1	no	—
36	#14582851	—	2	1	no	—
37	C₄×#10621872	—	2	1	no	—
38	#14582671	C₂²	1	2	yes	—
39	#14582670	C₂²	1	2	yes	—
40	#14582669	C₂²	1	2	yes	—
41	C₄₃×#430	C₂²	1	2	yes	—
42	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
43	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#405	C₂²	1	1	yes	characteristic
45	C₄₃×#344	C₂²	1	2	yes	—
46	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
47	C₂×#10621877	C₂³	1	2	yes	—
48	C₂×#10621877	C₂³	1	2	yes	—
49	C₂×#10621877	C₂³	1	1	yes	characteristic
50	C₂×#10621872	—	2	1	no	—
51	C₂×#10621872	—	2	2	no	—
52	C₂×#10621872	—	2	2	no	—
53	C₂×#10621872	C₂×C₄	1	4	yes	—
54	C₂×#10621872	D₄	1	1	yes	characteristic
55	C₂×#10621872	D₄	1	1	yes	characteristic
56	C₂×#10621872	D₄	1	1	yes	characteristic
57	C₂×#10621872	D₄	1	1	yes	characteristic
58	C₂×#10621872	Q₈	1	4	yes	—
59	M₁₆×D₄₃	—	2	2	no	—
60	M₁₆×D₄₃	—	2	2	no	—
61	M₁₆×D₄₃	—	2	2	no	—
62	M₁₆×D₄₃	—	2	2	no	—
63	M₁₆×D₄₃	—	2	2	no	—
64	M₁₆×D₄₃	—	2	2	no	—
65	M₁₆×D₄₃	—	2	2	no	—
66	M₁₆×D₄₃	C₂×C₄	1	4	yes	—
67	M₁₆×D₄₃	C₂×C₄	1	4	yes	—
68	M₁₆×D₄₃	D₄	1	4	yes	—
69	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×C₈×D₄₃	—	2	1	no	—
71	C₂×C₈×D₄₃	—	2	2	no	—
72	C₂×C₈×D₄₃	—	2	2	no	—
73	#13063284	C₂³	1	1	yes	characteristic
74	#13063283	—	2	1	no	—
75	#13063282	—	2	1	no	—
76	#13063281	Q₈	1	2	yes	—
77	C₄⋊C₄×D₄₃	—	2	1	no	—
78	C₂²⋊C₄×D₄₃	Q₈	1	2	yes	—
79	C₄²×D₄₃	—	2	1	no	—
80	#13063261	—	2	1	no	—
81	#13063261	—	2	1	no	—
82	#13063261	—	2	4	no	—
83	#13063261	C₂×C₄	1	4	yes	complemented
84	#13063260	—	2	4	no	—
85	#13063260	—	2	4	no	—
86	#13063260	—	2	2	no	—
87	#13063260	—	2	2	no	—
88	#13063260	C₂×C₄	1	8	yes	complemented
89	#13063236	—	2	1	no	—
90	#13063235	—	2	1	no	—
91	#13063235	—	2	1	no	—
92	C₄×C₄₃⋊C₈	—	2	1	no	—
93	C₈×Dic₄₃	—	2	1	no	—
94	C₈×Dic₄₃	—	2	1	no	—
95	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
96	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
97	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
99	#117×C₄₃	C₂³	1	1	yes	characteristic
100	#108×C₄₃	—	2	4	no	—
101	#108×C₄₃	—	2	1	no	—
102	#108×C₄₃	—	2	1	no	—
103	#108×C₄₃	C₂×C₄	1	4	yes	complemented
104	#97×C₄₃	—	2	1	no	—
105	C₄×C₈×C₄₃	—	2	1	no	—
106	C₂³×D₄₃	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
108	C₂²×Dic₄₃	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₄×D₄₃	—	2	2	no	—
110	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
111	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
114	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
115	C₂×C₄×D₄₃	#41	1	2	yes	—
116	C₂×C₄×D₄₃	#41	1	1	yes	characteristic
117	C₂×C₄×D₄₃	#41	1	1	yes	characteristic
118	M₁₆×C₄₃	—	2	2	no	—
119	M₁₆×C₄₃	—	2	1	no	—
120	M₁₆×C₄₃	—	2	2	no	—
121	M₁₆×C₄₃	—	2	2	no	—
122	M₁₆×C₄₃	C₂²×C₄	1	4	yes	—
123	M₁₆×C₄₃	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₂²⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
133	C₄²×C₄₃	—	2	1	no	—
134	C₂²⋊Dic₄₃	C₂×Q₈	1	2	yes	—
135	(C₂×D₄₃)⋊C₄	—	2	2	no	—
136	C₄⋊Dic₄₃	—	2	1	no	—
137	Dic₄₃⋊C₄	—	2	2	no	—
138	C₄×Dic₄₃	—	2	1	no	—
139	C₄×Dic₄₃	—	2	2	no	—
140	#10621877	—	2	2	no	—
141	#10621877	—	2	1	no	—
142	#10621877	—	2	2	no	—
143	#10621877	—	2	2	no	—
144	#10621877	C₂²×C₄	1	4	yes	—
145	#10621877	C₂×D₄	1	2	yes	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	C₂×C₄₃⋊C₈	—	2	2	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
153	#10621872	—	2	4	no	—
154	#10621872	—	2	4	no	—
155	#10621872	—	2	4	no	—
156	#10621872	—	4	2	no	—
157	#10621872	—	4	2	no	—
158	#10621872	C₄⋊C₄	1	4	yes	—
159	#10621872	C₄⋊C₄	1	4	yes	—
160	#10621872	C₄⋊C₄	1	4	yes	—
161	#10621872	C₄⋊C₄	1	4	yes	—
162	C₈×D₄₃	—	2	4	no	—
163	C₈×D₄₃	—	2	4	no	—
164	C₈×D₄₃	—	2	4	no	—
165	C₈×D₄₃	—	4	2	no	—
166	C₈×D₄₃	—	4	2	no	—
167	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
168	C₂²×D₄₃	—	8	1	no	—
169	C₂²×D₄₃	C₄×Q₈	1	2	yes	—
170	C₂²×D₄₃	C₂²⋊Q₈	1	1	yes	characteristic
171	C₂²×D₄₃	C₂²⋊Q₈	1	1	yes	characteristic
172	C₂²×D₄₃	C₄⋊Q₈	1	2	yes	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
180	C₂×Dic₄₃	—	2	2	no	—
181	C₂×Dic₄₃	C₄×Q₈	1	2	yes	—
182	C₂×Dic₄₃	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂×Dic₄₃	C₂²⋊Q₈	1	1	yes	characteristic
184	C₂×Dic₄₃	C₄⋊Q₈	1	2	yes	—
185	C₄×D₄₃	—	8	2	no	—
186	C₄×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
187	C₄×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
188	C₄×D₄₃	C₄×D₄	1	2	yes	—
189	C₄×D₄₃	C₄×D₄	1	2	yes	—
190	C₄×D₄₃	#121	1	2	yes	—
191	C₄×D₄₃	#121	1	2	yes	—
192	C₄×D₄₃	#125	1	2	yes	—
193	C₄×D₄₃	#125	1	2	yes	—
194	C₈×C₄₃	—	2	4	no	—
195	C₈×C₄₃	—	2	2	no	—
196	C₈×C₄₃	—	4	2	no	—
197	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
198	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
199	C₄₃⋊C₈	—	2	4	no	—
200	C₄₃⋊C₈	—	2	2	no	—
201	C₄₃⋊C₈	—	4	2	no	—
202	C₄₃⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
203	C₄₃⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
204	#21184	—	43	1	no	maximal, Sylow
205	C₂²×C₄₃	—	4	1	no	—
206	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
207	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
208	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
209	C₂×D₄₃	—	4	2	no	—
210	C₂×D₄₃	—	4	1	no	—
211	C₂×D₄₃	—	4	1	no	—
212	C₂×D₄₃	—	4	2	no	—
213	C₂×D₄₃	#389	1	2	yes	—
214	C₂×D₄₃	#389	1	2	yes	—
215	C₄×C₄₃	—	4	2	no	—
216	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
217	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
218	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
219	C₄×C₄₃	C₂×#125	1	1	yes	characteristic
220	Dic₄₃	—	4	2	no	—
221	Dic₄₃	#389	1	2	yes	—
222	Dic₄₃	#389	1	2	yes	—
223	C₂×#430	—	43	1	no	—
224	C₂×#430	—	43	1	no	—
225	C₂×#430	—	43	2	no	—
226	#2873	—	43	1	no	—
227	#1953	—	43	2	no	—
228	#1953	—	43	1	no	—
229	#1953	—	43	1	no	—
230	#1953	—	43	1	no	—
231	#1953	—	43	2	no	—
232	#1953	D₄₃	1	1	yes	characteristic, complemented
233	C₂×#344	—	43	2	no	—
234	C₂×C₄₃	—	2	1	no	—
235	C₂×C₄₃	—	2	1	no	—
236	C₂×C₄₃	—	2	1	no	—
237	C₂×C₄₃	C₂×#389	1	1	yes	characteristic
238	D₄₃	—	2	2	no	—
239	D₄₃	—	2	2	no	—
240	C₂²×M₁₆	—	43	1	no	—
241	C₂²×M₁₆	—	43	1	no	—
242	C₂²×M₁₆	—	43	2	no	—
243	C₂²×M₁₆	—	43	2	no	—
244	C₂×#117	—	43	1	no	—
245	#430	—	43	8	no	—
246	#430	—	43	2	no	—
247	#430	—	43	2	no	—
248	#430	—	43	2	no	—
249	#430	—	86	4	no	—
250	#430	—	86	1	no	—
251	#430	—	86	1	no	—
252	#430	—	86	1	no	—
253	#430	—	86	1	no	—
254	#430	C₂×D₄₃	1	2	yes	—
255	C₂×#108	—	43	2	no	—
256	C₂×#108	—	43	1	no	—
257	C₂×#108	—	43	2	no	—
258	C₂×#108	—	43	1	no	—
259	C₂×#108	—	86	4	no	—
260	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
261	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
262	#405	—	43	1	no	—
263	#405	—	43	1	no	—
264	#405	—	43	1	no	—
265	#405	—	86	1	no	—
266	#405	—	86	1	no	—
267	#405	C₂×D₄₃	1	1	yes	characteristic
268	C₄×M₁₆	—	86	1	no	—
269	C₄×M₁₆	—	86	1	no	—
270	#344	—	43	2	no	—
271	#344	—	43	2	no	—
272	#344	—	43	2	no	—
273	#344	C₂×D₄₃	1	2	yes	—
274	C₄₃	#21184	1	1	yes	characteristic, complemented, Sylow
275	C₂³×C₄	—	43	1	no	—
276	C₂×M₁₆	—	43	4	no	—
277	C₂×M₁₆	—	43	1	no	—
278	C₂×M₁₆	—	43	1	no	—
279	C₂×M₁₆	—	43	1	no	—
280	C₂×M₁₆	—	43	1	no	—
281	C₂×M₁₆	—	43	4	no	—
282	C₂×M₁₆	—	43	2	no	—
283	C₂×M₁₆	—	43	1	no	—
284	C₂×M₁₆	—	43	4	no	—
285	C₂×M₁₆	—	43	4	no	—
286	C₂×M₁₆	—	43	4	no	—
287	C₂×M₁₆	—	43	2	no	—
288	C₂×M₁₆	—	86	1	no	—
289	C₂×M₁₆	—	86	2	no	—
290	C₂×M₁₆	—	86	2	no	—
291	C₂×M₁₆	—	86	2	no	—
292	C₂×M₁₆	—	86	2	no	—
293	C₂×M₁₆	—	86	2	no	—
294	C₂×M₁₆	—	86	2	no	—
295	C₂×M₁₆	—	86	2	no	—
296	C₂×M₁₆	—	86	2	no	—
297	C₂×M₁₆	—	86	2	no	—
298	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
299	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
300	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
301	C₂²×C₈	—	43	1	no	—
302	C₂²×C₈	—	86	1	no	—
303	C₂²×C₈	—	86	2	no	—
304	C₂²×C₈	—	86	2	no	—
305	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
306	#117	—	43	1	no	—
307	#117	—	43	2	no	—
308	#117	—	86	1	no	—
309	#117	—	86	1	no	—
310	#117	C₂²×D₄₃	1	1	yes	characteristic
311	C₂×C₄⋊C₄	—	86	1	no	—
312	C₂×C₂²⋊C₄	—	43	2	no	—
313	C₂×C₄²	—	86	1	no	—
314	#108	—	2	4	no	—
315	#108	—	2	1	no	—
316	#108	—	2	1	no	—
317	#108	—	43	8	no	—
318	#108	—	43	4	no	—
319	#108	—	86	4	no	—
320	#108	—	86	2	no	—
321	#108	—	86	2	no	—
322	#108	—	86	4	no	—
323	#108	—	86	4	no	—
324	#108	—	86	1	no	—
325	#108	—	86	1	no	—
326	#108	C₄×D₄₃	1	4	yes	complemented
327	#97	—	2	1	no	—
328	#97	—	86	1	no	—
329	#97	—	86	1	no	—
330	#97	—	86	1	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	86	1	no	—
333	C₄×C₈	—	86	1	no	—
334	C₄×C₈	—	86	1	no	—
335	C₂⁴	—	43	1	no	—
336	C₂²×C₄	—	43	1	no	—
337	C₂²×C₄	—	43	2	no	—
338	C₂²×C₄	—	43	1	no	—
339	C₂²×C₄	—	43	1	no	—
340	C₂²×C₄	—	43	2	no	—
341	C₂²×C₄	—	43	2	no	—
342	C₂²×C₄	—	43	1	no	—
343	C₂²×C₄	—	43	1	no	—
344	C₂²×C₄	—	43	2	no	—
345	C₂²×C₄	—	86	2	no	—
346	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	1	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	43	4	no	—
352	M₁₆	—	43	4	no	—
353	M₁₆	—	43	4	no	—
354	M₁₆	—	43	4	no	—
355	M₁₆	—	43	4	no	—
356	M₁₆	—	43	2	no	—
357	M₁₆	—	86	4	no	—
358	M₁₆	—	86	4	no	—
359	M₁₆	—	86	4	no	—
360	M₁₆	—	86	2	no	—
361	M₁₆	—	86	1	no	—
362	M₁₆	—	86	2	no	—
363	M₁₆	—	86	2	no	—
364	M₁₆	—	172	2	no	—
365	M₁₆	—	172	2	no	—
366	M₁₆	C₂×C₄×D₄₃	1	4	yes	—
367	M₁₆	D₄×D₄₃	1	2	yes	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	43	2	no	—
372	C₂×C₈	—	43	1	no	—
373	C₂×C₈	—	43	1	no	—
374	C₂×C₈	—	43	2	no	—
375	C₂×C₈	—	86	4	no	—
376	C₂×C₈	—	86	4	no	—
377	C₂×C₈	—	86	4	no	—
378	C₂×C₈	—	86	1	no	—
379	C₂×C₈	—	86	2	no	—
380	C₂×C₈	—	86	2	no	—
381	C₂×C₈	—	172	2	no	—
382	C₂×C₈	—	172	2	no	—
383	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
384	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
385	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
386	C₂×C₈	Q₈×D₄₃	1	2	yes	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	86	2	no	—
389	C₄⋊C₄	—	86	1	no	—
390	C₂²⋊C₄	—	43	2	no	—
391	C₂²⋊C₄	—	86	2	no	—
392	C₂²⋊C₄	Q₈×D₄₃	1	2	yes	—
393	C₄²	—	2	1	no	—
394	C₄²	—	86	2	no	—
395	C₄²	—	86	1	no	—
396	C₂³	—	43	2	no	—
397	C₂³	—	43	1	no	—
398	C₂³	—	43	1	no	—
399	C₂³	—	43	2	no	—
400	C₂³	—	344	1	no	—
401	C₂³	C₂×Q₈×D₄₃	1	1	yes	characteristic
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	43	2	no	—
404	C₂×C₄	—	43	1	no	—
405	C₂×C₄	—	43	1	no	—
406	C₂×C₄	—	43	2	no	—
407	C₂×C₄	—	43	2	no	—
408	C₂×C₄	—	43	2	no	—
409	C₂×C₄	—	43	2	no	—
410	C₂×C₄	—	43	2	no	—
411	C₂×C₄	—	43	2	no	—
412	C₂×C₄	—	43	2	no	—
413	C₂×C₄	—	43	2	no	—
414	C₂×C₄	—	43	2	no	—
415	C₂×C₄	—	86	2	no	—
416	C₂×C₄	—	344	2	no	—
417	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
418	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
419	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
420	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
421	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
422	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	2	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	43	2	no	—
427	C₈	—	43	2	no	—
428	C₈	—	86	4	no	—
429	C₈	—	86	2	no	—
430	C₈	—	172	2	no	—
431	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
432	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
433	C₂²	—	4	1	no	—
434	C₂²	—	43	2	no	—
435	C₂²	—	43	2	no	—
436	C₂²	—	172	1	no	—
437	C₂²	—	172	1	no	—
438	C₂²	—	172	2	no	—
439	C₂²	—	172	2	no	—
440	C₂²	C₄×Q₈×D₄₃	1	1	yes	characteristic
441	C₂²	C₂²⋊Q₈×D₄₃	1	1	yes	characteristic
442	C₂²	C₄⋊Q₈×D₄₃	1	1	yes	characteristic
443	C₄	—	4	2	no	—
444	C₄	—	43	2	no	—
445	C₄	—	43	2	no	—
446	C₄	—	172	2	no	—
447	C₄	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
448	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
449	C₄	#121×D₄₃	1	1	yes	characteristic
450	C₄	#125×D₄₃	1	1	yes	characteristic
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	86	2	no	—
455	C₂	—	86	2	no	—
456	C₂	#389×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1953	C₂
socle	C₂×C₄₃	C₂×#389
prime radical	C₂³×D₄₃	C₂×Q₈
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1953	D₄₃
hypocenter	C₄₃	#21184
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1953

Complements

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

N	H ≅ G/N	type
5. #19135386	C₂	semidirect
6. #19135385	C₂	semidirect
7. #19135384	C₂	semidirect
8. #19135383	C₂	semidirect
9. #19135382	C₂	semidirect
11. C₄₃×#1953	C₂	semidirect
25. #14582946	C₄	semidirect
83. #13063261	C₂×C₄	semidirect
88. #13063260	C₂×C₄	semidirect
103. #108×C₄₃	C₂×C₄	semidirect
232. #1953	D₄₃	semidirect
274. C₄₃	#21184	semidirect
326. #108	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582946	2
#430×D₄₃	2
#19143011	2
#19135386	2
#19135385	2
#19135384	2
#19135383	2
#19135382	2
#344×D₄₃	2
C₄₃×#1953	2
#21184	43