Subgroups — #25079449

Order 11008.

766 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145045	C₂	1	1	yes	maximal, characteristic
2	#19144626	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134077	C₂	1	2	yes	maximal, complemented
5	#19134065	C₂	1	2	yes	maximal, complemented
6	#19133953	C₂	1	2	yes	maximal, complemented
7	#19133941	C₂	1	2	yes	maximal, complemented
8	#19133345	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133270	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133263	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063351	—	2	1	no	—
13	C₂×#13063351	—	2	1	no	—
14	#14583449	C₂²	1	1	yes	characteristic
15	#14583286	—	2	2	no	—
16	#14583275	C₂²	1	2	yes	—
17	#14583271	C₂²	1	2	yes	—
18	#14583217	—	2	1	no	—
19	#14583184	C₂²	1	1	yes	characteristic, complemented
20	#14583184	C₂²	1	1	yes	characteristic, complemented
21	#14583099	C₂²	1	1	yes	characteristic, complemented
22	#14583099	C₂²	1	1	yes	characteristic, complemented
23	#14583038	—	2	1	no	—
24	#14583030	—	2	2	no	—
25	#14583030	C₂²	1	2	yes	complemented
26	Q₈×C₄₃⋊C₈	C₂²	1	2	yes	complemented
27	C₄×#10621884	—	2	1	no	—
28	C₄×#10621884	—	2	1	no	—
29	#14582952	C₂²	1	1	yes	characteristic
30	#14582923	—	2	1	no	—
31	#14582923	C₂²	1	1	yes	characteristic
32	C₄×#10621877	—	2	1	no	—
33	C₄×#10621877	C₂²	1	1	yes	characteristic
34	#14582651	C₂²	1	2	yes	complemented
35	#14582649	C₂²	1	2	yes	complemented
36	#14582644	C₂²	1	2	yes	complemented
37	#14582643	C₂²	1	2	yes	—
38	#14582643	C₂²	1	2	yes	—
39	#14582642	C₂²	1	2	yes	complemented
40	C₂²×SD₁₆×C₄₃	—	2	1	no	—
41	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#460	—	2	1	no	—
44	C₄₃×#460	—	2	1	no	—
45	C₄₃×#460	C₂²	1	2	yes	—
46	C₄₃×#460	C₂²	1	2	yes	—
47	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
48	C₂×#102×C₄₃	—	2	1	no	—
49	C₂×#10621898	—	2	1	no	—
50	#13063351	—	4	4	no	—
51	#13063351	—	4	4	no	—
52	C₂×#10621883	—	2	2	no	—
53	C₂×#10621883	—	2	2	no	—
54	C₂×#10621884	—	2	1	no	—
55	C₂×#10621884	—	2	1	no	—
56	C₂×#10621882	—	2	2	no	—
57	C₂×#10621882	—	2	2	no	—
58	C₂×#10621877	—	2	1	no	—
59	C₂×#10621877	D₄	1	1	yes	characteristic
60	C₂×#10621877	D₄	1	1	yes	characteristic
61	#13063325	C₂³	1	1	yes	characteristic
62	#13063322	C₂³	1	1	yes	characteristic
63	#13063313	—	2	1	no	—
64	#13063299	—	2	1	no	—
65	#13063299	—	2	1	no	—
66	C₄×D₁₇₂	—	2	1	no	—
67	C₄×D₁₇₂	—	2	1	no	—
68	#13063256	—	2	1	no	—
69	#13063256	—	2	1	no	—
70	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
71	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
72	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
73	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
74	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
75	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
76	#13063249	—	2	1	no	—
77	#13063249	—	2	1	no	—
78	#13063245	—	2	1	no	—
79	#13063245	—	2	1	no	—
80	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
81	#13063236	—	2	2	no	—
82	#13063236	D₄	1	2	yes	—
83	C₄×C₄₃⋊C₈	—	2	1	no	—
84	C₄×C₄₃⋊C₈	—	2	2	no	—
85	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
86	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
87	C₂²×D₄×C₄₃	—	2	1	no	—
88	C₂²×D₄×C₄₃	—	2	1	no	—
89	C₂²×D₄×C₄₃	—	2	1	no	—
90	C₂×SD₁₆×C₄₃	—	2	2	no	—
91	C₂×SD₁₆×C₄₃	—	2	2	no	—
92	C₂×SD₁₆×C₄₃	—	4	4	no	—
93	C₂²×C₈×C₄₃	—	2	1	no	—
94	#127×C₄₃	—	2	1	no	—
95	#127×C₄₃	—	2	1	no	—
96	#127×C₄₃	—	2	1	no	—
97	#127×C₄₃	C₂³	1	2	yes	—
98	C₄×Q₈×C₄₃	—	2	1	no	—
99	C₄×Q₈×C₄₃	—	2	1	no	—
100	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
101	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
102	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
103	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
105	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₄₃	—	2	1	no	—
107	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₄₃	—	2	1	no	—
109	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
110	#102×C₄₃	—	2	2	no	—
111	#102×C₄₃	—	2	2	no	—
112	C₂⁴×C₄₃	—	4	1	no	—
113	C₂×Q₈×C₄₃	—	2	1	no	—
114	C₂×Q₈×C₄₃	—	2	2	no	—
115	C₂×Q₈×C₄₃	—	4	1	no	—
116	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂×D₄×C₄₃	—	2	2	no	—
119	C₂×D₄×C₄₃	—	2	2	no	—
120	C₂×D₄×C₄₃	—	2	2	no	—
121	C₂×D₄×C₄₃	—	4	1	no	—
122	C₂×D₄×C₄₃	—	4	1	no	—
123	C₂×D₄×C₄₃	—	4	1	no	—
124	C₂×D₄×C₄₃	—	4	2	no	—
125	C₂×D₄×C₄₃	—	4	2	no	—
126	C₂×D₄×C₄₃	—	4	2	no	—
127	C₂×D₄×C₄₃	—	4	2	no	—
128	C₂×D₄×C₄₃	—	8	2	no	—
129	C₂²×C₄×C₄₃	—	2	1	no	—
130	C₂²×C₄×C₄₃	—	2	1	no	—
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
134	C₂×C₂²⋊D₄₃	—	4	1	no	—
135	#10621898	—	4	2	no	—
136	#10621898	—	4	2	no	—
137	C₂×D₁₇₂	—	2	1	no	—
138	C₂×D₁₇₂	—	2	1	no	—
139	C₂×D₁₇₂	—	2	1	no	—
140	C₂×C₄×D₄₃	—	4	1	no	—
141	C₂×Dic₈₆	—	2	1	no	—
142	SD₁₆×C₄₃	—	4	4	no	—
143	SD₁₆×C₄₃	—	4	4	no	—
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₂×C₈×C₄₃	—	4	2	no	—
146	C₄⋊C₄×C₄₃	—	2	1	no	—
147	C₄⋊C₄×C₄₃	—	2	1	no	—
148	C₄⋊C₄×C₄₃	—	2	1	no	—
149	C₄⋊C₄×C₄₃	—	2	1	no	—
150	C₄⋊C₄×C₄₃	—	2	1	no	—
151	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
152	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₄₃	—	2	1	no	—
154	C₄²×C₄₃	—	2	1	no	—
155	C₄²×C₄₃	—	2	1	no	—
156	C₄²×C₄₃	—	2	1	no	—
157	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₄₃	#41	1	1	yes	characteristic
160	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
161	#10621884	—	4	2	no	—
162	#10621884	—	4	2	no	—
163	#10621883	—	4	4	no	—
164	#10621883	—	4	4	no	—
165	#10621882	—	4	4	no	—
166	#10621882	—	4	4	no	—
167	(C₂×D₄₃)⋊C₄	—	4	1	no	—
168	(C₂×D₄₃)⋊C₄	—	4	1	no	—
169	C₄⋊Dic₄₃	—	2	1	no	—
170	C₄⋊Dic₄₃	—	2	1	no	—
171	#10621877	—	2	2	no	—
172	#10621877	—	4	2	no	—
173	#10621877	SD₁₆	1	4	yes	complemented
174	C₂×C₄₃⋊C₈	—	2	2	no	—
175	C₂×C₄₃⋊C₈	—	2	1	no	—
176	C₂×C₄₃⋊C₈	—	2	1	no	—
177	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
178	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
179	C₂³×C₄₃	—	4	2	no	—
180	C₂³×C₄₃	—	8	2	no	—
181	C₂³×C₄₃	—	8	2	no	—
182	C₂³×C₄₃	—	8	2	no	—
183	C₂³×C₄₃	#121	1	1	yes	characteristic
184	C₂²×D₄₃	—	4	1	no	—
185	Q₈×C₄₃	—	2	1	no	—
186	Q₈×C₄₃	—	2	1	no	—
187	Q₈×C₄₃	—	2	1	no	—
188	Q₈×C₄₃	—	4	2	no	—
189	Q₈×C₄₃	AGL(1,ℤ/8)	1	2	yes	complemented
190	D₄×C₄₃	—	4	2	no	—
191	D₄×C₄₃	—	4	2	no	—
192	D₄×C₄₃	—	4	2	no	—
193	D₄×C₄₃	—	4	2	no	—
194	D₄×C₄₃	—	8	2	no	—
195	D₄×C₄₃	—	8	2	no	—
196	D₄×C₄₃	—	8	2	no	—
197	D₄×C₄₃	—	8	2	no	—
198	C₂×C₄×C₄₃	—	2	1	no	—
199	C₂×C₄×C₄₃	—	2	1	no	—
200	C₂×C₄×C₄₃	—	2	1	no	—
201	C₂×C₄×C₄₃	—	2	1	no	—
202	C₂×C₄×C₄₃	—	2	1	no	—
203	C₂×C₄×C₄₃	—	2	1	no	—
204	C₂×C₄×C₄₃	—	4	1	no	—
205	C₂×C₄×C₄₃	—	4	2	no	—
206	C₂×C₄×C₄₃	—	8	1	no	—
207	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
208	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
209	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
211	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
212	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
215	C₂²⋊D₄₃	—	8	2	no	—
216	C₂×Dic₄₃	—	4	1	no	—
217	D₁₇₂	—	4	1	no	—
218	D₁₇₂	—	4	1	no	—
219	D₁₇₂	—	4	1	no	—
220	D₁₇₂	—	4	1	no	—
221	D₁₇₂	—	8	1	no	—
222	C₄×D₄₃	—	8	2	no	—
223	Dic₈₆	—	4	1	no	—
224	Dic₈₆	—	4	1	no	—
225	C₈×C₄₃	—	4	2	no	—
226	C₄₃⋊C₈	—	2	2	no	—
227	C₄₃⋊C₈	—	4	2	no	—
228	C₄₃⋊C₈	—	4	1	no	—
229	C₄₃⋊C₈	—	4	1	no	—
230	C₄₃⋊C₈	C₂×SD₁₆	1	4	yes	complemented
231	#19170	—	43	1	no	maximal, Sylow
232	C₂²×C₄₃	—	2	1	no	—
233	C₂²×C₄₃	—	2	1	no	—
234	C₂²×C₄₃	—	8	2	no	—
235	C₂²×C₄₃	—	8	2	no	—
236	C₂²×C₄₃	—	8	2	no	—
237	C₂²×C₄₃	—	16	4	no	—
238	C₂²×C₄₃	#460	1	2	yes	—
239	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
240	C₂×D₄₃	—	8	1	no	—
241	C₂×D₄₃	—	8	1	no	—
242	C₂×D₄₃	—	8	1	no	—
243	C₄×C₄₃	—	2	1	no	—
244	C₄×C₄₃	—	2	2	no	—
245	C₄×C₄₃	—	2	1	no	—
246	C₄×C₄₃	—	2	1	no	—
247	C₄×C₄₃	—	4	1	no	—
248	C₄×C₄₃	—	4	1	no	—
249	C₄×C₄₃	—	4	1	no	—
250	C₄×C₄₃	#460	1	2	yes	—
251	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
252	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
254	C₄×C₄₃	#575	1	1	yes	characteristic
255	Dic₄₃	—	8	1	no	—
256	#3151	—	43	1	no	—
257	#3103	—	43	1	no	—
258	C₂×#460	D₄₃	1	1	yes	characteristic, complemented
259	Q₈×M₁₆	—	43	1	no	—
260	#1688	—	43	2	no	—
261	#1686	—	43	2	no	—
262	#1668	—	43	2	no	—
263	#1666	—	43	2	no	—
264	#1565	—	43	1	no	—
265	#1547	—	43	1	no	—
266	#1545	—	43	1	no	—
267	C₂×C₄₃	—	2	2	no	—
268	C₂×C₄₃	—	16	2	no	—
269	C₂×C₄₃	C₂×#460	1	1	yes	characteristic
270	C₂×C₄₃	#3055	1	1	yes	characteristic
271	C₂×C₄₃	#3068	1	1	yes	characteristic
272	D₄₃	—	16	1	no	—
273	C₂×AGL(1,ℤ/8)	—	86	1	no	—
274	C₂×AGL(1,ℤ/8)	—	86	1	no	—
275	C₂²×SD₁₆	—	2	1	no	—
276	#532	—	43	1	no	—
277	C₂×#127	C₂×D₄₃	1	1	yes	characteristic
278	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
279	#496	—	86	2	no	—
280	#493	—	43	2	no	—
281	#492	—	43	2	no	—
282	#481	—	86	1	no	—
283	#475	—	43	1	no	—
284	#475	—	43	1	no	—
285	#460	—	2	1	no	—
286	#460	—	2	1	no	—
287	#460	—	43	1	no	—
288	#460	—	43	1	no	—
289	#460	C₂×D₄₃	1	2	yes	—
290	#460	C₂×D₄₃	1	2	yes	—
291	#448	—	86	1	no	—
292	#446	—	43	2	no	—
293	#446	—	86	2	no	—
294	C₈×Q₈	—	43	2	no	—
295	C₄×SD₁₆	—	86	1	no	—
296	C₄×SD₁₆	—	86	1	no	—
297	#431	—	43	1	no	—
298	#423	—	43	1	no	—
299	#423	—	86	1	no	—
300	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
301	C₂×#102	—	2	1	no	—
302	C₄×M₁₆	—	43	1	no	—
303	C₄×M₁₆	—	86	1	no	—
304	#335	—	43	2	no	—
305	#334	—	43	2	no	—
306	#332	—	43	2	no	—
307	#331	—	43	2	no	—
308	#331	—	43	2	no	—
309	#331	—	43	2	no	—
310	C₄₃	#19170	1	1	yes	characteristic, complemented, Sylow
311	C₂×#41	—	86	1	no	—
312	C₂²×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	—	2	1	no	—
316	AGL(1,ℤ/8)	—	172	4	no	—
317	AGL(1,ℤ/8)	—	172	4	no	—
318	C₂×SD₁₆	—	2	2	no	—
319	C₂×SD₁₆	—	2	2	no	—
320	C₂×SD₁₆	—	4	4	no	—
321	C₂×SD₁₆	—	86	2	no	—
322	C₂×SD₁₆	—	86	2	no	—
323	C₂×SD₁₆	—	86	1	no	—
324	C₂×SD₁₆	—	86	1	no	—
325	C₂×D₈	—	86	2	no	—
326	C₂×D₈	—	86	2	no	—
327	C₂×M₁₆	—	43	1	no	—
328	C₂×M₁₆	—	43	1	no	—
329	C₂×M₁₆	—	86	1	no	—
330	C₂²×C₈	—	2	1	no	—
331	C₄⋊Q₈	—	43	1	no	—
332	#127	—	2	1	no	—
333	#127	—	2	1	no	—
334	#127	—	2	1	no	—
335	#127	—	43	1	no	—
336	#127	C₂²×D₄₃	1	2	yes	—
337	#124	—	86	1	no	—
338	#121	—	86	1	no	—
339	#121	—	86	1	no	—
340	C₄×Q₈	—	2	1	no	—
341	C₄×Q₈	—	2	1	no	—
342	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
343	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
344	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
345	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
346	C₄×D₄	—	86	1	no	—
347	C₄×D₄	—	86	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
352	#106	—	86	1	no	—
353	#106	—	86	1	no	—
354	C₄⋊C₈	—	2	1	no	—
355	C₄⋊C₈	—	43	2	no	—
356	C₄⋊C₈	—	43	1	no	—
357	C₄⋊C₈	—	43	1	no	—
358	C₄⋊C₈	—	86	2	no	—
359	C₄⋊C₈	—	86	2	no	—
360	C₄⋊C₈	—	86	1	no	—
361	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
362	#103	—	86	1	no	—
363	#103	—	86	1	no	—
364	#102	—	2	2	no	—
365	#102	—	2	2	no	—
366	#102	—	86	1	no	—
367	#102	—	86	1	no	—
368	C₂²⋊C₈	—	86	1	no	—
369	#97	—	43	2	no	—
370	#97	—	86	2	no	—
371	C₄×C₈	—	43	2	no	—
372	C₄×C₈	—	86	2	no	—
373	C₄×C₈	—	86	1	no	—
374	C₂⁴	—	4	1	no	—
375	#41	—	172	2	no	—
376	#41	—	172	2	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	4	1	no	—
380	C₂×Q₈	—	86	1	no	—
381	C₂×Q₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
382	C₂×Q₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	—	4	1	no	—
389	C₂×D₄	—	4	1	no	—
390	C₂×D₄	—	4	1	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	8	2	no	—
394	C₂×D₄	—	86	1	no	—
395	C₂×D₄	—	86	1	no	—
396	C₂×D₄	—	86	1	no	—
397	C₂×D₄	—	172	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	172	1	no	—
401	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
402	C₂²×C₄	#10621900	1	1	yes	characteristic
403	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
404	SD₁₆	—	4	4	no	—
405	SD₁₆	—	4	4	no	—
406	SD₁₆	—	172	4	no	—
407	SD₁₆	—	172	4	no	—
408	SD₁₆	—	172	2	no	—
409	SD₁₆	—	172	2	no	—
410	D₈	—	172	4	no	—
411	D₈	—	172	4	no	—
412	M₁₆	—	43	4	no	—
413	M₁₆	—	86	2	no	—
414	M₁₆	—	172	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	4	2	no	—
417	C₂×C₈	—	43	2	no	—
418	C₂×C₈	—	43	2	no	—
419	C₂×C₈	—	86	2	no	—
420	C₂×C₈	—	86	1	no	—
421	C₂×C₈	—	86	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	86	1	no	—
428	C₄⋊C₄	—	86	1	no	—
429	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
430	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
431	C₂²⋊C₄	—	172	1	no	—
432	C₂²⋊C₄	—	172	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₄²	D₄×D₄₃	1	1	yes	characteristic
438	C₄²	#10621900	1	1	yes	characteristic
439	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
440	C₄²	C₂³×D₄₃	1	1	yes	characteristic
441	C₂³	—	4	2	no	—
442	C₂³	—	8	2	no	—
443	C₂³	—	8	2	no	—
444	C₂³	—	8	2	no	—
445	C₂³	—	172	1	no	—
446	C₂³	#13063297	1	1	yes	characteristic
447	Q₈	—	2	1	no	—
448	Q₈	—	2	1	no	—
449	Q₈	—	2	1	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	172	1	no	—
452	Q₈	—	172	1	no	—
453	Q₈	#13063351	1	2	yes	complemented
454	D₄	—	4	2	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	8	2	no	—
459	D₄	—	8	2	no	—
460	D₄	—	8	2	no	—
461	D₄	—	8	2	no	—
462	D₄	—	344	1	no	—
463	D₄	—	344	2	no	—
464	D₄	—	172	1	no	—
465	D₄	—	172	1	no	—
466	D₄	—	172	1	no	—
467	D₄	—	172	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	8	1	no	—
477	C₂×C₄	—	344	2	no	—
478	C₂×C₄	—	172	1	no	—
479	C₂×C₄	#13063297	1	1	yes	characteristic
480	C₂×C₄	#13063297	1	1	yes	characteristic
481	C₂×C₄	#13063297	1	1	yes	characteristic
482	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
483	C₂×C₄	#13063352	1	2	yes	—
484	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
486	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
487	C₈	—	4	2	no	—
488	C₈	—	43	4	no	—
489	C₈	—	86	2	no	—
490	C₈	—	172	1	no	—
491	C₈	—	172	2	no	—
492	C₈	—	172	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	16	4	no	—
499	C₂²	—	344	1	no	—
500	C₂²	—	344	1	no	—
501	C₂²	—	344	1	no	—
502	C₂²	#14583097	1	2	yes	—
503	C₂²	C₂×#13063297	1	1	yes	characteristic
504	C₄	—	2	1	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	1	no	—
511	C₄	—	344	1	no	—
512	C₄	#14583097	1	2	yes	—
513	C₄	C₂×SD₁₆×D₄₃	1	1	yes	characteristic
514	C₄	C₂×#13063351	1	1	yes	characteristic
515	C₄	C₂×#13063352	1	1	yes	characteristic
516	C₄	#14583697	1	1	yes	characteristic
517	C₂	—	2	2	no	—
518	C₂	—	16	2	no	—
519	C₂	—	688	1	no	—
520	C₂	C₂×#14583097	1	1	yes	characteristic
521	C₂	#19144210	1	1	yes	characteristic
522	C₂	#19144320	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063297
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#460	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19145045	C₂
hypercenter	C₂×#460	D₄₃
hypocenter	C₄₃	#19170
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#460

Complements

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

N	H ≅ G/N	type
2. #19144626	C₂	semidirect
3. Q₈×#10621877	C₂	semidirect
4. #19134077	C₂	semidirect
5. #19134065	C₂	semidirect
6. #19133953	C₂	semidirect
7. #19133941	C₂	semidirect
8. #19133345	C₂	semidirect
9. #19133270	C₂	semidirect
10. #19133263	C₂	semidirect
11. C₂×C₄₃×#460	C₂	semidirect
19. #14583184	C₂²	semidirect
20. #14583184	C₂²	semidirect
21. #14583099	C₂²	semidirect
22. #14583099	C₂²	semidirect
25. #14583030	C₂²	semidirect
26. Q₈×C₄₃⋊C₈	C₂²	semidirect
34. #14582651	C₂²	semidirect
35. #14582649	C₂²	semidirect
36. #14582644	C₂²	semidirect
39. #14582642	C₂²	semidirect
173. #10621877	SD₁₆	semidirect
189. Q₈×C₄₃	AGL(1,ℤ/8)	semidirect
230. C₄₃⋊C₈	C₂×SD₁₆	semidirect
258. C₂×#460	D₄₃	semidirect
310. C₄₃	#19170	semidirect
453. Q₈	#13063351	semidirect

Maximal subgroups

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

subgroup	index
#19145045	2
#19144626	2
Q₈×#10621877	2
#19134077	2
#19134065	2
#19133953	2
#19133941	2
#19133345	2
#19133270	2
#19133263	2
C₂×C₄₃×#460	2
#19170	43