Subgroups — #25079784

Order 11008.

660 conjugacy classes of subgroups.

The subgroup lattice has 482 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	#19145902	C₂	1	1	yes	maximal, characteristic
3	#19144918	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134142	C₂	1	2	yes	maximal, complemented
5	#19134128	C₂	1	2	yes	maximal, complemented
6	#19134046	C₂	1	2	yes	maximal, complemented
7	#19134032	C₂	1	2	yes	maximal, complemented
8	C₂×#14582652	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133286	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133273	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583456	C₂²	1	1	yes	characteristic
13	#14583449	C₂²	1	1	yes	characteristic
14	#14583254	—	2	1	no	—
15	#14583254	—	2	1	no	—
16	#14583250	C₂²	1	1	yes	characteristic
17	#14583250	C₂²	1	1	yes	characteristic
18	#14583246	C₂²	1	1	yes	characteristic
19	#14583246	C₂²	1	1	yes	characteristic
20	#14583189	C₂²	1	2	yes	—
21	#14583181	—	2	1	no	—
22	#14583179	C₂²	1	2	yes	—
23	#14583176	—	2	1	no	—
24	#14583133	—	2	2	no	—
25	#14583126	—	2	2	no	—
26	#14583104	C₂²	1	2	yes	—
27	#14583096	—	2	1	no	—
28	#14583094	C₂²	1	2	yes	—
29	#14583091	—	2	1	no	—
30	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
32	#14582896	—	2	1	no	—
33	#14582896	—	2	1	no	—
34	#14582652	C₂²	1	2	yes	—
35	#14582652	C₂²	1	2	yes	—
36	#14582647	C₂²	1	2	yes	—
37	#14582646	C₂²	1	2	yes	—
38	#14582644	C₂²	1	2	yes	—
39	#14582642	C₂²	1	2	yes	—
40	C₂×#131×C₄₃	—	2	1	no	—
41	C₄₃×#532	C₂²	1	1	yes	characteristic
42	C₄₃×#436	—	2	1	no	—
43	C₄₃×#436	C₂²	1	2	yes	—
44	C₈×D₄×C₄₃	—	2	1	no	—
45	C₈×D₄×C₄₃	C₂²	1	2	yes	—
46	C₄₃×#423	C₂²	1	1	yes	characteristic
47	C₄₃×#408	—	2	1	no	—
48	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
49	C₂×#10621898	—	2	1	no	—
50	C₂×#10621883	—	2	2	no	—
51	C₂×#10621882	—	2	2	no	—
52	C₂²×C₄₃⋊C₈	—	2	1	no	—
53	C₂²×C₄₃⋊C₈	—	2	1	no	—
54	#13063325	C₂³	1	1	yes	characteristic
55	#13063325	C₂³	1	1	yes	characteristic
56	#13063325	C₂³	1	1	yes	characteristic
57	#13063322	C₂³	1	1	yes	characteristic
58	#13063317	—	2	1	no	—
59	#13063313	—	2	1	no	—
60	#13063304	—	2	1	no	—
61	#13063304	—	2	1	no	—
62	#13063299	—	2	1	no	—
63	#13063299	—	2	1	no	—
64	C₄×Dic₈₆	—	2	1	no	—
65	C₄×Dic₈₆	—	2	1	no	—
66	C₄×D₁₇₂	—	2	1	no	—
67	C₄×D₁₇₂	—	2	1	no	—
68	#13063284	—	2	1	no	—
69	#13063258	—	2	2	no	—
70	#13063256	—	2	2	no	—
71	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
72	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
73	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
74	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
75	#13063250	—	2	1	no	—
76	#13063250	—	2	1	no	—
77	#13063250	—	2	1	no	—
78	#13063250	—	2	1	no	—
79	#13063248	—	2	2	no	—
80	#13063247	—	2	1	no	—
81	#13063247	—	2	1	no	—
82	#13063247	—	2	1	no	—
83	#13063247	—	2	1	no	—
84	#13063246	—	2	2	no	—
85	#13063246	—	2	2	no	—
86	#13063245	—	2	2	no	—
87	C₂×#41×C₄₃	—	2	1	no	—
88	#131×C₄₃	—	4	4	no	—
89	C₂×M₁₆×C₄₃	—	2	1	no	—
90	C₂×M₁₆×C₄₃	—	2	2	no	—
91	C₂²×C₈×C₄₃	—	2	2	no	—
92	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
94	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
95	#127×C₄₃	D₄	1	1	yes	characteristic
96	#124×C₄₃	—	2	1	no	—
97	#121×C₄₃	—	2	1	no	—
98	#121×C₄₃	D₄	1	2	yes	—
99	C₄×D₄×C₄₃	—	2	1	no	—
100	C₄×D₄×C₄₃	C₂³	1	2	yes	—
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₄₃	—	2	1	no	—
103	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
104	C₂²⋊C₈×C₄₃	—	2	2	no	—
105	C₂²⋊C₈×C₄₃	—	2	2	no	—
106	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
107	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
108	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
110	#41×C₄₃	—	4	2	no	—
111	#41×C₄₃	—	4	2	no	—
112	C₂×Q₈×C₄₃	—	2	1	no	—
113	C₂×D₄×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	2	1	no	—
115	C₂×D₄×C₄₃	—	2	2	no	—
116	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
121	C₂×C₂²⋊D₄₃	—	4	1	no	—
122	#10621898	—	4	2	no	—
123	#10621898	—	4	2	no	—
124	C₂×D₁₇₂	—	2	1	no	—
125	C₂×D₁₇₂	—	2	1	no	—
126	C₂×D₁₇₂	—	2	1	no	—
127	C₂×C₄×D₄₃	—	4	1	no	—
128	C₂×Dic₈₆	—	2	1	no	—
129	C₂×Dic₈₆	—	2	1	no	—
130	C₂×Dic₈₆	—	2	1	no	—
131	M₁₆×C₄₃	—	4	4	no	—
132	M₁₆×C₄₃	—	4	2	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	2	2	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	4	4	no	—
137	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₄₃	—	2	1	no	—
142	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
143	C₂²⋊C₄×C₄₃	—	2	2	no	—
144	C₂²⋊C₄×C₄₃	—	2	2	no	—
145	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₃	#41	1	1	yes	characteristic
148	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
149	C₂²⋊Dic₄₃	—	4	1	no	—
150	#10621883	—	8	2	no	—
151	#10621882	—	8	2	no	—
152	(C₂×D₄₃)⋊C₄	—	4	1	no	—
153	(C₂×D₄₃)⋊C₄	—	4	1	no	—
154	C₄⋊Dic₄₃	—	2	1	no	—
155	C₄⋊Dic₄₃	—	2	1	no	—
156	C₄⋊Dic₄₃	—	2	1	no	—
157	C₄⋊Dic₄₃	—	2	1	no	—
158	C₄⋊Dic₄₃	—	2	1	no	—
159	C₄⋊Dic₄₃	—	2	1	no	—
160	Dic₄₃⋊C₄	—	4	1	no	—
161	Dic₄₃⋊C₄	—	4	1	no	—
162	C₄×Dic₄₃	—	4	1	no	—
163	C₂×C₄₃⋊C₈	—	2	2	no	—
164	C₂×C₄₃⋊C₈	—	2	2	no	—
165	C₂×C₄₃⋊C₈	—	8	1	no	—
166	C₂×C₄₃⋊C₈	—	8	1	no	—
167	C₂³×C₄₃	—	2	2	no	—
168	C₂³×C₄₃	#121	1	1	yes	characteristic
169	C₂²×D₄₃	—	4	1	no	—
170	Q₈×C₄₃	—	4	2	no	—
171	D₄×C₄₃	—	2	2	no	—
172	D₄×C₄₃	—	2	2	no	—
173	D₄×C₄₃	—	4	2	no	—
174	D₄×C₄₃	—	4	4	no	—
175	D₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	4	1	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
183	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
184	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
185	C₂×C₄×C₄₃	#135	1	2	yes	—
186	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
187	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
190	C₂²⋊D₄₃	—	8	2	no	—
191	C₂×Dic₄₃	—	4	1	no	—
192	C₂×Dic₄₃	—	4	1	no	—
193	C₂×Dic₄₃	—	4	1	no	—
194	D₁₇₂	—	4	1	no	—
195	D₁₇₂	—	4	1	no	—
196	D₁₇₂	—	4	1	no	—
197	D₁₇₂	—	4	1	no	—
198	D₁₇₂	—	8	1	no	—
199	C₄×D₄₃	—	8	2	no	—
200	Dic₈₆	—	4	1	no	—
201	Dic₈₆	—	4	1	no	—
202	Dic₈₆	—	4	1	no	—
203	Dic₈₆	—	4	1	no	—
204	Dic₈₆	—	8	1	no	—
205	C₈×C₄₃	—	2	1	no	—
206	C₈×C₄₃	—	2	1	no	—
207	C₈×C₄₃	—	2	1	no	—
208	C₈×C₄₃	—	2	1	no	—
209	C₈×C₄₃	—	4	2	no	—
210	C₄₃⋊C₈	—	4	2	no	—
211	C₄₃⋊C₈	—	4	2	no	—
212	#19201	—	43	1	no	maximal, Sylow
213	C₂²×C₄₃	—	2	1	no	—
214	C₂²×C₄₃	—	2	1	no	—
215	C₂²×C₄₃	—	4	2	no	—
216	C₂²×C₄₃	—	4	2	no	—
217	C₂²×C₄₃	—	4	2	no	—
218	C₂²×C₄₃	#463	1	2	yes	—
219	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
220	C₂×D₄₃	—	8	1	no	—
221	C₂×D₄₃	—	8	1	no	—
222	C₂×D₄₃	—	8	1	no	—
223	C₄×C₄₃	—	2	1	no	—
224	C₄×C₄₃	—	2	1	no	—
225	C₄×C₄₃	—	2	1	no	—
226	C₄×C₄₃	—	4	2	no	—
227	C₄×C₄₃	#463	1	2	yes	—
228	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
229	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₄×C₄₃	#576	1	1	yes	characteristic
231	C₄×C₄₃	#578	1	1	yes	characteristic
232	Dic₄₃	—	8	1	no	—
233	Dic₄₃	—	8	1	no	—
234	Dic₄₃	—	8	1	no	—
235	#3246	—	43	1	no	—
236	#3245	—	43	1	no	—
237	#3131	—	43	1	no	—
238	#2931	D₄₃	1	1	yes	characteristic, complemented
239	#1699	—	43	2	no	—
240	#1697	—	43	2	no	—
241	#1683	—	43	2	no	—
242	#1681	—	43	2	no	—
243	C₂×#335	—	43	1	no	—
244	#1550	—	43	1	no	—
245	#1547	—	43	1	no	—
246	C₂×C₄₃	—	2	2	no	—
247	C₂×C₄₃	—	8	2	no	—
248	C₂×C₄₃	C₂×#463	1	1	yes	characteristic
249	C₂×C₄₃	#3061	1	1	yes	characteristic
250	C₂×C₄₃	#3067	1	1	yes	characteristic
251	D₄₃	—	16	1	no	—
252	C₂×#131	—	2	1	no	—
253	#533	—	43	1	no	—
254	#532	—	43	1	no	—
255	#532	C₂×D₄₃	1	1	yes	characteristic
256	#488	—	86	1	no	—
257	#488	—	86	1	no	—
258	#487	—	43	1	no	—
259	#487	—	43	1	no	—
260	#486	—	43	1	no	—
261	#486	—	43	1	no	—
262	#476	—	43	2	no	—
263	#475	—	86	1	no	—
264	#474	—	43	2	no	—
265	#474	—	86	1	no	—
266	#466	—	86	2	no	—
267	#465	—	86	2	no	—
268	#461	—	43	2	no	—
269	#460	—	86	1	no	—
270	#459	—	43	2	no	—
271	#459	—	86	1	no	—
272	#436	—	2	1	no	—
273	#436	C₂×D₄₃	1	2	yes	—
274	C₈×D₄	—	2	1	no	—
275	C₈×D₄	C₂×D₄₃	1	2	yes	—
276	#423	C₂×D₄₃	1	1	yes	characteristic
277	C₂×C₄⋊C₈	—	43	1	no	—
278	C₂×C₄⋊C₈	—	43	1	no	—
279	#416	—	86	1	no	—
280	#416	—	86	1	no	—
281	#408	—	2	1	no	—
282	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
283	#335	—	43	2	no	—
284	#335	—	43	2	no	—
285	#333	—	43	2	no	—
286	#332	—	43	2	no	—
287	#332	—	43	2	no	—
288	#331	—	43	2	no	—
289	C₄₃	#19201	1	1	yes	characteristic, complemented, Sylow
290	C₂×#41	—	2	1	no	—
291	C₂×#41	—	86	1	no	—
292	C₂×SD₁₆	—	86	2	no	—
293	C₂×D₈	—	86	2	no	—
294	#131	—	4	4	no	—
295	C₂×M₁₆	—	2	1	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	86	1	no	—
299	C₂²×C₈	—	86	1	no	—
300	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
301	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
302	C₄⋊Q₈	—	43	1	no	—
303	C₄⋊Q₈	—	43	1	no	—
304	C₄⋊Q₈	—	43	1	no	—
305	C₄⋊Q₈	D₁₇₂	1	1	yes	characteristic
306	#127	—	43	1	no	—
307	#127	D₁₇₂	1	1	yes	characteristic
308	#125	—	86	1	no	—
309	#124	—	2	1	no	—
310	#124	—	86	1	no	—
311	C₂²⋊Q₈	—	86	1	no	—
312	C₂²⋊Q₈	—	86	1	no	—
313	#121	—	2	1	no	—
314	#121	—	86	1	no	—
315	#121	—	86	1	no	—
316	#121	D₁₇₂	1	2	yes	—
317	C₄×Q₈	—	86	1	no	—
318	C₄×Q₈	—	86	1	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	86	1	no	—
321	C₄×D₄	—	86	1	no	—
322	C₄×D₄	C₂²×D₄₃	1	2	yes	—
323	#117	—	86	1	no	—
324	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
325	#107	—	86	2	no	—
326	#106	—	86	2	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	—	43	2	no	—
329	C₄⋊C₈	—	43	2	no	—
330	C₄⋊C₈	—	86	1	no	—
331	C₄⋊C₈	—	86	1	no	—
332	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
333	#103	—	86	1	no	—
334	#103	—	86	1	no	—
335	#103	—	86	1	no	—
336	#103	—	86	1	no	—
337	#103	—	86	2	no	—
338	#102	—	86	2	no	—
339	#102	—	86	2	no	—
340	#102	—	86	1	no	—
341	#102	—	86	1	no	—
342	#102	—	86	1	no	—
343	#102	—	86	1	no	—
344	#102	—	86	2	no	—
345	C₂²⋊C₈	—	2	2	no	—
346	C₂²⋊C₈	—	2	2	no	—
347	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
348	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
349	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
350	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
351	#41	—	4	2	no	—
352	#41	—	4	2	no	—
353	#41	—	172	2	no	—
354	#41	—	172	2	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	86	1	no	—
357	C₂×Q₈	—	86	1	no	—
358	C₂×Q₈	—	86	1	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	86	1	no	—
363	C₂×D₄	—	86	1	no	—
364	C₂×D₄	—	86	1	no	—
365	C₂×D₄	—	172	1	no	—
366	C₂×D₄	C₂×D₁₇₂	1	2	yes	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	172	1	no	—
369	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
370	C₂²×C₄	#10621898	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
372	SD₁₆	—	344	2	no	—
373	D₈	—	344	2	no	—
374	M₁₆	—	4	4	no	—
375	M₁₆	—	4	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	4	4	no	—
380	C₂×C₈	—	86	2	no	—
381	C₂×C₈	—	86	2	no	—
382	C₂×C₈	—	344	1	no	—
383	C₂×C₈	—	344	1	no	—
384	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
385	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
386	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
387	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	86	1	no	—
390	C₄⋊C₄	—	86	1	no	—
391	C₄⋊C₄	—	86	1	no	—
392	C₄⋊C₄	—	86	1	no	—
393	C₄⋊C₄	—	86	1	no	—
394	C₄⋊C₄	—	86	1	no	—
395	C₄⋊C₄	—	172	1	no	—
396	C₄⋊C₄	—	172	1	no	—
397	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	172	1	no	—
401	C₂²⋊C₄	—	172	1	no	—
402	C₂²⋊C₄	—	172	1	no	—
403	C₄²	—	172	1	no	—
404	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
405	C₄²	#10621898	1	1	yes	characteristic
406	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
407	C₄²	C₂³×D₄₃	1	1	yes	characteristic
408	C₂³	—	2	2	no	—
409	C₂³	—	172	1	no	—
410	C₂³	#13063299	1	1	yes	characteristic
411	Q₈	—	4	2	no	—
412	Q₈	—	344	1	no	—
413	Q₈	—	172	1	no	—
414	Q₈	—	172	1	no	—
415	Q₈	—	172	1	no	—
416	Q₈	—	172	1	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	2	no	—
422	D₄	—	344	1	no	—
423	D₄	—	344	2	no	—
424	D₄	—	172	1	no	—
425	D₄	—	172	1	no	—
426	D₄	—	172	1	no	—
427	D₄	—	172	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	344	2	no	—
435	C₂×C₄	—	172	1	no	—
436	C₂×C₄	—	172	1	no	—
437	C₂×C₄	—	172	1	no	—
438	C₂×C₄	#13063299	1	1	yes	characteristic
439	C₂×C₄	#13063299	1	1	yes	characteristic
440	C₂×C₄	#13063299	1	1	yes	characteristic
441	C₂×C₄	#13063345	1	2	yes	—
442	C₂×C₄	#13063351	1	2	yes	—
443	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
445	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	4	2	no	—
451	C₈	—	172	2	no	—
452	C₈	—	172	2	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	344	1	no	—
459	C₂²	—	344	1	no	—
460	C₂²	—	344	1	no	—
461	C₂²	#14583114	1	2	yes	—
462	C₂²	C₂×#13063299	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	344	1	no	—
468	C₄	—	344	1	no	—
469	C₄	—	344	1	no	—
470	C₄	#14583114	1	2	yes	—
471	C₄	C₂×#13063345	1	1	yes	characteristic
472	C₄	C₂×#13063351	1	1	yes	characteristic
473	C₄	#14583704	1	1	yes	characteristic
474	C₄	#14583716	1	1	yes	characteristic
475	C₂	—	2	2	no	—
476	C₂	—	8	2	no	—
477	C₂	—	688	1	no	—
478	C₂	C₂×#14583114	1	1	yes	characteristic
479	C₂	#19144265	1	1	yes	characteristic
480	C₂	#19144315	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063299
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2931	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19145902	C₂
hypercenter	#2931	D₄₃
hypocenter	C₄₃	#19201
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2931

Complements

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

N	H ≅ G/N	type
1. #19145911	C₂	semidirect
3. #19144918	C₂	semidirect
4. #19134142	C₂	semidirect
5. #19134128	C₂	semidirect
6. #19134046	C₂	semidirect
7. #19134032	C₂	semidirect
8. C₂×#14582652	C₂	semidirect
9. #19133286	C₂	semidirect
10. #19133273	C₂	semidirect
11. C₄₃×#2931	C₂	semidirect
238. #2931	D₄₃	semidirect
289. C₄₃	#19201	semidirect

Maximal subgroups

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

subgroup	index
#19145911	2
#19145902	2
#19144918	2
#19134142	2
#19134128	2
#19134046	2
#19134032	2
C₂×#14582652	2
#19133286	2
#19133273	2
C₄₃×#2931	2
#19201	43