Subgroups — #25080163

Order 11008.

722 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	#19145911	C₂	1	1	yes	maximal, characteristic, complemented
2	#19145536	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143542	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134076	C₂	1	2	yes	maximal, complemented
5	#19134064	C₂	1	2	yes	maximal, complemented
6	#19133952	C₂	1	2	yes	maximal, complemented
7	#19133940	C₂	1	2	yes	maximal, complemented
8	#19133347	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133244	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14582643	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3151	C₂	1	1	yes	maximal, characteristic
12	#14583456	C₂²	1	1	yes	characteristic
13	#14583271	—	2	1	no	—
14	#14583245	—	2	1	no	—
15	#14583189	—	2	1	no	—
16	#14583181	C₂²	1	2	yes	complemented
17	#14583126	—	2	2	no	—
18	#14583104	—	2	1	no	—
19	#14583096	C₂²	1	2	yes	—
20	#14583096	C₂²	1	2	yes	—
21	#14583096	C₂²	1	2	yes	complemented
22	#14583050	—	2	2	no	—
23	#14583029	C₂²	1	2	yes	complemented
24	#14583027	—	2	2	no	—
25	C₈×Dic₈₆	C₂²	1	2	yes	complemented
26	#14582952	C₂²	1	1	yes	characteristic
27	#14582927	—	2	1	no	—
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
30	#14582857	—	2	1	no	—
31	#14582652	C₂²	1	2	yes	complemented
32	#14582650	C₂²	1	2	yes	complemented
33	#14582645	C₂²	1	1	yes	characteristic, complemented
34	#14582645	C₂²	1	1	yes	characteristic, complemented
35	#14582643	C₂²	1	2	yes	—
36	#14582643	C₂²	1	2	yes	—
37	#14582643	C₂²	1	1	yes	characteristic, complemented
38	#14582643	C₂²	1	1	yes	characteristic, complemented
39	C₂×AGL(1,ℤ/8)×C₄₃	—	2	1	no	—
40	C₂×AGL(1,ℤ/8)×C₄₃	—	2	1	no	—
41	C₄₃×#532	C₂²	1	1	yes	characteristic
42	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#496	—	2	2	no	—
44	C₄₃×#493	C₂²	1	2	yes	—
45	C₄₃×#492	C₂²	1	2	yes	—
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621883	—	2	2	no	—
48	C₂×#10621883	—	2	2	no	—
49	C₂×#10621883	—	2	2	no	—
50	C₂²×C₄₃⋊C₈	—	2	1	no	—
51	C₂²×C₄₃⋊C₈	—	2	1	no	—
52	#13063325	D₄	1	1	yes	characteristic
53	#13063325	D₄	1	1	yes	characteristic
54	#13063317	—	2	1	no	—
55	#13063304	—	2	1	no	—
56	#13063304	D₄	1	2	yes	—
57	C₄×Dic₈₆	—	2	1	no	—
58	C₄×Dic₈₆	C₂³	1	2	yes	—
59	#13063284	—	2	1	no	—
60	#13063256	—	2	2	no	—
61	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
62	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
63	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
64	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
67	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
68	Dic₄₃⋊C₈	—	2	2	no	—
69	Dic₄₃⋊C₈	—	2	2	no	—
70	#13063248	—	2	2	no	—
71	#13063246	—	2	2	no	—
72	#13063246	—	2	2	no	—
73	#13063246	—	2	2	no	—
74	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
75	#13063235	—	2	2	no	—
76	C₄×C₄₃⋊C₈	—	2	1	no	—
77	C₈×Dic₄₃	—	2	2	no	—
78	C₂×#41×C₄₃	—	2	1	no	—
79	C₂²×D₄×C₄₃	—	2	1	no	—
80	C₂²×D₄×C₄₃	—	2	1	no	—
81	C₂²×D₄×C₄₃	—	2	1	no	—
82	AGL(1,ℤ/8)×C₄₃	—	4	4	no	—
83	AGL(1,ℤ/8)×C₄₃	—	4	4	no	—
84	C₂×SD₁₆×C₄₃	—	2	2	no	—
85	C₂×SD₁₆×C₄₃	—	2	2	no	—
86	C₂×D₈×C₄₃	—	2	2	no	—
87	C₂×D₈×C₄₃	—	2	2	no	—
88	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
89	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
90	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
91	#127×C₄₃	—	2	1	no	—
92	#127×C₄₃	—	2	1	no	—
93	#127×C₄₃	—	2	1	no	—
94	#127×C₄₃	C₂³	1	2	yes	—
95	#127×C₄₃	C₂³	1	1	yes	characteristic
96	#124×C₄₃	—	2	1	no	—
97	#121×C₄₃	—	2	1	no	—
98	#121×C₄₃	—	2	1	no	—
99	C₄×D₄×C₄₃	—	2	1	no	—
100	C₄×D₄×C₄₃	—	2	1	no	—
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	#97×C₄₃	D₄	1	2	yes	—
103	C₄×C₈×C₄₃	C₂³	1	2	yes	—
104	C₂⁴×C₄₃	—	4	1	no	—
105	#41×C₄₃	—	4	2	no	—
106	#41×C₄₃	—	4	2	no	—
107	C₂×Q₈×C₄₃	—	2	1	no	—
108	C₂×D₄×C₄₃	—	2	1	no	—
109	C₂×D₄×C₄₃	—	2	1	no	—
110	C₂×D₄×C₄₃	—	2	2	no	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	1	no	—
113	C₂×D₄×C₄₃	—	2	2	no	—
114	C₂×D₄×C₄₃	—	4	1	no	—
115	C₂×D₄×C₄₃	—	4	1	no	—
116	C₂×D₄×C₄₃	—	4	1	no	—
117	C₂×D₄×C₄₃	—	4	1	no	—
118	C₂×D₄×C₄₃	—	4	2	no	—
119	C₂×D₄×C₄₃	—	4	2	no	—
120	C₂×D₄×C₄₃	—	8	1	no	—
121	C₂×D₄×C₄₃	—	8	1	no	—
122	C₂×D₄×C₄₃	—	8	2	no	—
123	C₂²×C₄×C₄₃	—	4	1	no	—
124	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
127	C₂×Dic₈₆	—	2	1	no	—
128	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
129	SD₁₆×C₄₃	—	4	4	no	—
130	SD₁₆×C₄₃	—	4	4	no	—
131	D₈×C₄₃	—	4	4	no	—
132	D₈×C₄₃	—	4	4	no	—
133	M₁₆×C₄₃	—	2	2	no	—
134	M₁₆×C₄₃	SD₁₆	1	4	yes	complemented
135	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
137	C₄⋊C₄×C₄₃	—	2	1	no	—
138	C₄⋊C₄×C₄₃	—	2	1	no	—
139	C₂²⋊C₄×C₄₃	—	4	1	no	—
140	C₂²⋊C₄×C₄₃	—	4	1	no	—
141	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₄₃	#41	1	1	yes	characteristic
144	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
145	C₂²⋊Dic₄₃	—	2	2	no	—
146	#10621883	—	8	2	no	—
147	#10621883	—	8	2	no	—
148	#10621883	—	8	2	no	—
149	C₄⋊Dic₄₃	—	2	1	no	—
150	C₄⋊Dic₄₃	—	2	1	no	—
151	C₄⋊Dic₄₃	—	2	1	no	—
152	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
153	Dic₄₃⋊C₄	—	2	2	no	—
154	Dic₄₃⋊C₄	—	2	2	no	—
155	C₄×Dic₄₃	—	2	2	no	—
156	C₂×C₄₃⋊C₈	—	2	1	no	—
157	C₂×C₄₃⋊C₈	—	2	1	no	—
158	C₂×C₄₃⋊C₈	—	2	1	no	—
159	C₂×C₄₃⋊C₈	—	2	1	no	—
160	C₂×C₄₃⋊C₈	—	2	2	no	—
161	C₂×C₄₃⋊C₈	—	4	2	no	—
162	C₂×C₄₃⋊C₈	—	8	1	no	—
163	C₂³×C₄₃	—	4	1	no	—
164	C₂³×C₄₃	—	4	2	no	—
165	C₂³×C₄₃	—	8	2	no	—
166	C₂³×C₄₃	—	8	2	no	—
167	C₂³×C₄₃	—	8	2	no	—
168	C₂³×C₄₃	#121	1	1	yes	characteristic
169	Q₈×C₄₃	—	4	1	no	—
170	Q₈×C₄₃	—	4	1	no	—
171	D₄×C₄₃	—	4	1	no	—
172	D₄×C₄₃	—	4	2	no	—
173	D₄×C₄₃	—	4	1	no	—
174	D₄×C₄₃	—	4	2	no	—
175	D₄×C₄₃	—	4	1	no	—
176	D₄×C₄₃	—	4	2	no	—
177	D₄×C₄₃	—	4	2	no	—
178	D₄×C₄₃	—	4	1	no	—
179	D₄×C₄₃	—	8	1	no	—
180	D₄×C₄₃	—	8	2	no	—
181	D₄×C₄₃	—	8	2	no	—
182	D₄×C₄₃	—	8	2	no	—
183	D₄×C₄₃	—	8	2	no	—
184	D₄×C₄₃	—	8	2	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	4	1	no	—
188	C₂×C₄×C₄₃	—	4	1	no	—
189	C₂×C₄×C₄₃	—	8	2	no	—
190	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
191	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
192	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
194	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
195	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
198	C₂×Dic₄₃	—	2	2	no	—
199	C₂×Dic₄₃	—	2	2	no	—
200	Dic₈₆	—	2	2	no	—
201	Dic₈₆	—	2	2	no	—
202	Dic₈₆	—	8	1	no	—
203	C₈×C₄₃	—	2	2	no	—
204	C₈×C₄₃	C₂×SD₁₆	1	4	yes	—
205	C₄₃⋊C₈	—	4	1	no	—
206	C₄₃⋊C₈	—	4	1	no	—
207	C₄₃⋊C₈	—	4	2	no	—
208	C₄₃⋊C₈	—	4	1	no	—
209	C₄₃⋊C₈	—	4	1	no	—
210	#19238	—	43	1	no	maximal, Sylow
211	C₂²×C₄₃	—	2	1	no	—
212	C₂²×C₄₃	—	2	1	no	—
213	C₂²×C₄₃	—	8	2	no	—
214	C₂²×C₄₃	—	8	1	no	—
215	C₂²×C₄₃	—	8	2	no	—
216	C₂²×C₄₃	—	8	1	no	—
217	C₂²×C₄₃	—	8	2	no	—
218	C₂²×C₄₃	—	8	1	no	—
219	C₂²×C₄₃	—	16	4	no	—
220	C₂²×C₄₃	#460	1	2	yes	—
221	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
222	C₄×C₄₃	—	2	1	no	—
223	C₄×C₄₃	—	2	1	no	—
224	C₄×C₄₃	—	2	1	no	—
225	C₄×C₄₃	—	8	1	no	—
226	C₄×C₄₃	#460	1	2	yes	—
227	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
228	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₄×C₄₃	#576	1	1	yes	characteristic
230	C₄×C₄₃	#577	1	1	yes	characteristic
231	Dic₄₃	—	4	2	no	—
232	Dic₄₃	—	4	2	no	—
233	#3246	—	43	1	no	—
234	#3208	—	43	1	no	—
235	#3151	D₄₃	1	1	yes	characteristic
236	#2962	—	43	1	no	—
237	#1688	—	43	2	no	—
238	#1686	—	43	2	no	—
239	#1668	—	43	2	no	—
240	#1666	—	43	2	no	—
241	#1565	—	43	1	no	—
242	#1540	—	43	1	no	—
243	C₂×#331	—	43	1	no	—
244	C₂×C₄₃	—	2	2	no	—
245	C₂×C₄₃	—	16	1	no	—
246	C₂×C₄₃	—	16	2	no	—
247	C₂×C₄₃	C₂×#460	1	1	yes	characteristic
248	C₂×C₄₃	#3062	1	1	yes	characteristic
249	C₂×C₄₃	#3068	1	1	yes	characteristic
250	C₂×AGL(1,ℤ/8)	—	2	1	no	—
251	C₂×AGL(1,ℤ/8)	—	2	1	no	—
252	#533	—	43	1	no	—
253	#532	C₂×D₄₃	1	1	yes	characteristic
254	C₂×#127	C₂×D₄₃	1	1	yes	characteristic
255	#496	—	2	2	no	—
256	#493	C₂×D₄₃	1	2	yes	—
257	#492	—	86	1	no	—
258	#492	C₂×D₄₃	1	2	yes	—
259	#486	—	86	1	no	—
260	#476	—	86	1	no	—
261	#475	—	43	2	no	—
262	#465	—	86	2	no	—
263	#461	—	86	1	no	—
264	#460	—	43	2	no	—
265	#460	—	43	2	no	—
266	#460	—	43	2	no	—
267	#450	—	86	2	no	—
268	#446	—	43	2	no	—
269	#446	—	86	2	no	—
270	C₈×Q₈	—	43	2	no	—
271	#431	—	43	1	no	—
272	#424	—	86	1	no	—
273	C₂×C₄⋊C₈	—	43	1	no	—
274	C₂×C₄⋊C₈	—	43	1	no	—
275	#405	—	86	1	no	—
276	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
277	#335	—	43	2	no	—
278	#334	—	43	2	no	—
279	#332	—	43	1	no	—
280	#332	—	43	1	no	—
281	#331	—	43	2	no	—
282	#331	—	43	2	no	—
283	#331	—	43	1	no	—
284	#331	—	43	1	no	—
285	C₄₃	#19238	1	1	yes	characteristic, complemented, Sylow
286	C₂×#41	—	2	1	no	—
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	—	2	1	no	—
290	AGL(1,ℤ/8)	—	4	4	no	—
291	AGL(1,ℤ/8)	—	4	4	no	—
292	C₂×SD₁₆	—	2	2	no	—
293	C₂×SD₁₆	—	2	2	no	—
294	C₂×SD₁₆	—	86	2	no	—
295	C₂×SD₁₆	—	86	2	no	—
296	C₂×SD₁₆	—	86	2	no	—
297	C₂×D₈	—	2	2	no	—
298	C₂×D₈	—	2	2	no	—
299	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
300	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
301	C₂²×C₈	—	86	1	no	—
302	C₂²×C₈	—	86	1	no	—
303	C₄⋊Q₈	—	43	1	no	—
304	C₄⋊Q₈	—	43	1	no	—
305	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
306	#127	—	2	1	no	—
307	#127	—	2	1	no	—
308	#127	—	2	1	no	—
309	#127	C₂²×D₄₃	1	2	yes	—
310	#127	C₂²×D₄₃	1	1	yes	characteristic
311	#125	—	86	1	no	—
312	#124	—	2	1	no	—
313	C₂²⋊Q₈	—	43	2	no	—
314	C₂²⋊Q₈	—	86	1	no	—
315	#121	—	2	1	no	—
316	#121	—	2	1	no	—
317	C₄×Q₈	—	43	2	no	—
318	C₄×Q₈	—	86	1	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	#117	—	86	1	no	—
322	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
323	#106	—	86	2	no	—
324	C₄⋊C₈	—	43	1	no	—
325	C₄⋊C₈	—	43	1	no	—
326	C₄⋊C₈	—	43	2	no	—
327	C₄⋊C₈	—	43	1	no	—
328	C₄⋊C₈	—	43	1	no	—
329	C₄⋊C₈	—	86	2	no	—
330	C₄⋊C₈	—	86	2	no	—
331	C₄⋊C₈	—	86	1	no	—
332	C₄⋊C₈	—	86	1	no	—
333	#103	—	86	2	no	—
334	#102	—	86	2	no	—
335	#102	—	86	2	no	—
336	#102	—	86	2	no	—
337	C₂²⋊C₈	—	86	1	no	—
338	#97	—	86	2	no	—
339	#97	C₂²⋊D₄₃	1	2	yes	—
340	C₄×C₈	—	86	2	no	—
341	C₄×C₈	—	86	1	no	—
342	C₄×C₈	C₂²×D₄₃	1	2	yes	—
343	C₂⁴	—	4	1	no	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	43	2	no	—
348	C₂×Q₈	—	86	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	4	1	no	—
356	C₂×D₄	—	4	1	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	—	4	1	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	8	1	no	—
362	C₂×D₄	—	8	1	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
366	C₂²×C₄	#10621900	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
368	SD₁₆	—	4	4	no	—
369	SD₁₆	—	4	4	no	—
370	SD₁₆	—	344	2	no	—
371	SD₁₆	—	344	2	no	—
372	SD₁₆	—	344	2	no	—
373	D₈	—	4	4	no	—
374	D₈	—	4	4	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	#10621883	1	4	yes	complemented
377	C₂×C₈	—	86	1	no	—
378	C₂×C₈	—	86	1	no	—
379	C₂×C₈	—	86	2	no	—
380	C₂×C₈	—	86	1	no	—
381	C₂×C₈	—	86	1	no	—
382	C₂×C₈	—	344	1	no	—
383	C₂×C₈	—	172	2	no	—
384	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
385	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	43	2	no	—
389	C₄⋊C₄	—	86	1	no	—
390	C₄⋊C₄	—	86	1	no	—
391	C₄⋊C₄	—	86	2	no	—
392	C₄⋊C₄	—	86	1	no	—
393	C₄⋊C₄	—	86	2	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₂²⋊C₄	—	86	2	no	—
397	C₄²	—	86	2	no	—
398	C₄²	D₄×D₄₃	1	1	yes	characteristic
399	C₄²	#10621900	1	1	yes	characteristic
400	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
401	C₄²	C₂³×D₄₃	1	1	yes	characteristic
402	C₂³	—	4	1	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	8	2	no	—
405	C₂³	—	8	2	no	—
406	C₂³	—	8	2	no	—
407	C₂³	#13063296	1	1	yes	characteristic
408	Q₈	—	4	1	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	86	2	no	—
411	Q₈	—	86	2	no	—
412	Q₈	—	344	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	1	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	1	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	1	no	—
421	D₄	—	8	2	no	—
422	D₄	—	8	1	no	—
423	D₄	—	8	2	no	—
424	D₄	—	8	2	no	—
425	D₄	—	8	2	no	—
426	D₄	—	8	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	—	86	2	no	—
433	C₂×C₄	—	86	2	no	—
434	C₂×C₄	#13063296	1	1	yes	characteristic
435	C₂×C₄	#13063296	1	1	yes	characteristic
436	C₂×C₄	#13063296	1	1	yes	characteristic
437	C₂×C₄	C₂×#10621883	1	2	yes	—
438	C₂×C₄	#13063351	1	2	yes	—
439	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
440	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
441	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	172	1	no	—
444	C₈	—	172	1	no	—
445	C₈	—	172	2	no	—
446	C₈	—	172	1	no	—
447	C₈	—	172	1	no	—
448	C₈	C₂×#10621883	1	4	yes	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	16	4	no	—
458	C₂²	#14583096	1	2	yes	—
459	C₂²	C₂×#13063296	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	8	1	no	—
464	C₄	—	172	2	no	—
465	C₄	—	172	2	no	—
466	C₄	#14583096	1	2	yes	—
467	C₄	C₂²×#10621883	1	1	yes	characteristic
468	C₄	C₂×#13063351	1	1	yes	characteristic
469	C₄	#14583703	1	1	yes	characteristic
470	C₄	#14583709	1	1	yes	characteristic
471	C₂	—	2	2	no	—
472	C₂	—	16	2	no	—
473	C₂	—	16	1	no	—
474	C₂	C₂×#14583096	1	1	yes	characteristic
475	C₂	#19144269	1	1	yes	characteristic
476	C₂	#19144319	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063296
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting, prime radical	C₄₃×#3151	C₂
socle	C₂²×C₄₃	C₂×#121
hypercenter	#3151	D₄₃
hypocenter	C₄₃	#19238
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3151

Complements

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

N	H ≅ G/N	type
1. #19145911	C₂	semidirect
2. #19145536	C₂	semidirect
3. #19143542	C₂	semidirect
4. #19134076	C₂	semidirect
5. #19134064	C₂	semidirect
6. #19133952	C₂	semidirect
7. #19133940	C₂	semidirect
8. #19133347	C₂	semidirect
9. #19133244	C₂	semidirect
10. C₂×#14582643	C₂	semidirect
16. #14583181	C₂²	semidirect
21. #14583096	C₂²	semidirect
23. #14583029	C₂²	semidirect
25. C₈×Dic₈₆	C₂²	semidirect
31. #14582652	C₂²	semidirect
32. #14582650	C₂²	semidirect
33. #14582645	C₂²	semidirect
34. #14582645	C₂²	semidirect
37. #14582643	C₂²	semidirect
38. #14582643	C₂²	semidirect
134. M₁₆×C₄₃	SD₁₆	semidirect
285. C₄₃	#19238	semidirect
376. M₁₆	#10621883	semidirect

Maximal subgroups

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

subgroup	index
#19145911	2
#19145536	2
#19143542	2
#19134076	2
#19134064	2
#19133952	2
#19133940	2
#19133347	2
#19133244	2
C₂×#14582643	2
C₄₃×#3151	2
#19238	43