Subgroups — #25103539

Order 11008.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144311	C₂	1	1	yes	maximal, characteristic
2	#19143494	C₂	1	2	yes	maximal, complemented
3	C₂×#14583016	C₂	1	1	yes	maximal, characteristic, complemented
4	#19143017	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135385	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135267	C₂	1	2	yes	maximal, complemented
7	#19135093	C₂	1	2	yes	maximal, complemented
8	#19134646	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134476	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134397	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1976	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583697	C₂²	1	2	yes	—
13	C₂×#13063333	C₂²	1	1	yes	characteristic
14	C₂×#13063332	C₂²	1	2	yes	—
15	C₂×#13063331	C₂²	1	1	yes	characteristic
16	#14583367	C₂²	1	1	yes	characteristic
17	#14583171	C₄	1	2	yes	complemented
18	#14583166	C₄	1	2	yes	complemented
19	#14583159	C₄	1	4	yes	complemented
20	#14583018	—	2	4	no	—
21	#14583016	—	2	1	no	—
22	#14583016	—	2	1	no	—
23	#14583016	—	2	1	no	—
24	#14583016	—	2	1	no	—
25	#14583013	—	2	4	no	—
26	#14582947	C₂²	1	2	yes	—
27	C₂×#13063261	C₂²	1	1	yes	characteristic
28	C₂×#13063261	C₂²	1	1	yes	characteristic
29	#14582917	C₂²	1	2	yes	—
30	C₂×#13063252	C₂²	1	2	yes	—
31	#14582883	C₂²	1	2	yes	—
32	#14582856	—	2	1	no	—
33	#14582855	C₂²	1	2	yes	—
34	#14582855	C₂²	1	1	yes	characteristic
35	#14582853	—	2	1	no	—
36	#14582851	—	2	1	no	—
37	M₁₆×Dic₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
39	C₄×C₈×D₄₃	—	2	1	no	—
40	#14582669	C₂²	1	2	yes	—
41	#14582669	C₂²	1	2	yes	—
42	#14582658	C₂²	1	2	yes	—
43	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#427	C₂²	1	1	yes	characteristic
45	C₄₃×#421	C₂²	1	2	yes	—
46	C₄₃×#410	C₂²	1	2	yes	—
47	C₄₃×#405	C₂²	1	1	yes	characteristic
48	C₂×#10621898	C₂³	1	1	yes	characteristic
49	#13063356	C₂×C₄	1	4	yes	—
50	#13063355	—	2	2	no	—
51	#13063351	C₂×C₄	1	4	yes	—
52	#13063350	—	2	2	no	—
53	#13063345	—	2	4	no	—
54	#13063333	—	2	1	no	—
55	#13063333	—	2	1	no	—
56	#13063333	D₄	1	2	yes	—
57	#13063333	D₄	1	2	yes	—
58	#13063332	—	2	2	no	—
59	#13063332	—	2	2	no	—
60	#13063332	—	2	2	no	—
61	#13063332	—	2	2	no	—
62	#13063331	—	2	1	no	—
63	#13063331	—	2	1	no	—
64	#13063331	C₂×C₄	1	2	yes	—
65	#13063331	C₂×C₄	1	2	yes	—
66	C₂×#10621877	—	2	2	no	—
67	C₂×#10621877	C₂³	1	2	yes	—
68	C₂×#10621877	C₂³	1	1	yes	characteristic
69	C₂×#10621877	C₂³	1	2	yes	—
70	C₂×#10621872	—	2	1	no	—
71	C₂×#10621872	—	2	1	no	—
72	C₂²×C₄₃⋊C₈	—	2	2	no	—
73	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
74	C₂×C₈×D₄₃	—	2	1	no	—
75	C₂×C₈×D₄₃	—	2	1	no	—
76	#13063290	—	2	1	no	—
77	#13063287	—	2	1	no	—
78	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
79	#13063282	—	2	1	no	—
80	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
81	C₄²×D₄₃	—	2	1	no	—
82	#13063261	—	2	1	no	—
83	#13063261	—	2	1	no	—
84	#13063261	C₂×C₄	1	2	yes	complemented
85	#13063261	C₂×C₄	1	2	yes	complemented
86	#13063260	—	2	4	no	—
87	#13063253	—	2	4	no	—
88	#13063252	—	2	2	no	—
89	#13063252	—	2	2	no	—
90	#13063244	C₂×C₄	1	4	yes	complemented
91	#13063242	C₂×C₄	1	4	yes	complemented
92	#13063236	—	2	1	no	—
93	#13063236	—	2	2	no	—
94	#13063235	—	2	1	no	—
95	C₄×C₄₃⋊C₈	—	2	1	no	—
96	C₄×C₄₃⋊C₈	—	2	2	no	—
97	C₈×Dic₄₃	—	2	1	no	—
98	C₈×Dic₄₃	D₄	1	1	yes	characteristic
99	C₈×Dic₄₃	D₄	1	1	yes	characteristic
100	C₈×Dic₄₃	D₄	1	1	yes	characteristic
101	C₈×Dic₄₃	D₄	1	1	yes	characteristic
102	C₂×#41×C₄₃	C₂³	1	2	yes	—
103	#135×C₄₃	—	2	1	no	—
104	#135×C₄₃	—	2	1	no	—
105	#135×C₄₃	—	2	1	no	—
106	#135×C₄₃	—	2	1	no	—
107	C₂×Q₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic, complemented
108	C₂×SD₁₆×C₄₃	C₂×C₄	1	2	yes	complemented
109	C₂×D₈×C₄₃	C₂×C₄	1	1	yes	characteristic, complemented
110	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
112	#117×C₄₃	C₂³	1	2	yes	—
113	#117×C₄₃	C₂³	1	1	yes	characteristic
114	#107×C₄₃	—	2	1	no	—
115	#106×C₄₃	—	2	1	no	—
116	#104×C₄₃	—	2	4	no	—
117	#99×C₄₃	—	2	4	no	—
118	#97×C₄₃	—	2	1	no	—
119	C₄×C₈×C₄₃	—	2	1	no	—
120	#41×C₄₃	—	2	2	no	—
121	#41×C₄₃	—	2	2	no	—
122	#41×C₄₃	—	2	2	no	—
123	#41×C₄₃	—	2	2	no	—
124	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
125	C₂×D₄×C₄₃	—	2	2	no	—
126	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
129	C₂×C₂²⋊D₄₃	—	2	1	no	—
130	C₂²×Dic₄₃	—	2	1	no	—
131	#10621898	—	2	1	no	—
132	#10621898	—	2	1	no	—
133	#10621898	C₂²×C₄	1	2	yes	—
134	#10621898	C₂×D₄	1	2	yes	—
135	C₂×D₁₇₂	#41	1	1	yes	characteristic
136	C₂×C₄×D₄₃	—	2	1	no	—
137	C₂×C₄×D₄₃	—	2	2	no	—
138	C₂×Dic₈₆	#41	1	1	yes	characteristic
139	Q₁₆×C₄₃	—	2	1	no	—
140	Q₁₆×C₄₃	—	2	1	no	—
141	SD₁₆×C₄₃	—	2	2	no	—
142	SD₁₆×C₄₃	—	2	2	no	—
143	D₈×C₄₃	—	2	1	no	—
144	D₈×C₄₃	—	2	1	no	—
145	M₁₆×C₄₃	—	2	1	no	—
146	M₁₆×C₄₃	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₄₃	—	2	1	no	—
148	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
153	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
154	C₄⋊C₄×C₄₃	—	2	1	no	—
155	C₄⋊C₄×C₄₃	—	2	2	no	—
156	C₂²⋊C₄×C₄₃	—	2	2	no	—
157	C₂²⋊C₄×C₄₃	#41	1	2	yes	—
158	C₄²×C₄₃	—	2	1	no	—
159	C₄²×C₄₃	—	2	2	no	—
160	#10621885	—	2	4	no	—
161	#10621884	—	2	4	no	—
162	#10621883	—	2	4	no	—
163	#10621882	—	2	4	no	—
164	(C₂×D₄₃)⋊C₄	—	2	2	no	—
165	Dic₄₃⋊C₄	—	2	2	no	—
166	C₄×Dic₄₃	—	2	2	no	—
167	C₄×Dic₄₃	—	2	1	no	—
168	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
169	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
170	#10621877	—	2	1	no	—
171	#10621877	—	2	2	no	—
172	#10621877	—	2	2	no	—
173	#10621877	—	2	2	no	—
174	#10621877	—	4	2	no	—
175	#10621877	—	4	2	no	—
176	#10621877	C₂²×C₄	1	2	yes	—
177	#10621877	C₂²×C₄	1	4	yes	—
178	C₂×C₄₃⋊C₈	—	2	1	no	—
179	C₂×C₄₃⋊C₈	—	2	2	no	—
180	C₂×C₄₃⋊C₈	—	2	2	no	—
181	C₂×C₄₃⋊C₈	—	4	2	no	—
182	C₂×C₄₃⋊C₈	—	4	2	no	—
183	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
184	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
185	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
186	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
187	C₂×C₄₃⋊C₈	#41	1	1	yes	characteristic
188	C₂×C₄₃⋊C₈	#41	1	1	yes	characteristic
189	#10621872	—	2	2	no	—
190	#10621872	—	2	2	no	—
191	#10621872	—	2	2	no	—
192	#10621872	—	2	2	no	—
193	C₈×D₄₃	—	2	2	no	—
194	C₈×D₄₃	—	2	2	no	—
195	C₈×D₄₃	—	2	2	no	—
196	C₈×D₄₃	—	2	2	no	—
197	C₂³×C₄₃	—	2	2	no	—
198	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
199	C₂²×D₄₃	—	2	1	no	—
200	Q₈×C₄₃	—	2	2	no	—
201	Q₈×C₄₃	—	2	2	no	—
202	D₄×C₄₃	—	2	2	no	—
203	D₄×C₄₃	—	2	2	no	—
204	D₄×C₄₃	—	4	2	no	—
205	D₄×C₄₃	—	4	2	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	4	2	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
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	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
217	C₂²⋊D₄₃	—	2	2	no	—
218	C₂²⋊D₄₃	—	2	2	no	—
219	C₂×Dic₄₃	—	2	1	no	—
220	C₂×Dic₄₃	—	2	1	no	—
221	C₂×Dic₄₃	—	2	1	no	—
222	C₂×Dic₄₃	—	4	2	no	—
223	D₁₇₂	—	2	1	no	—
224	D₁₇₂	C₄×D₄	1	2	yes	—
225	C₄×D₄₃	—	2	2	no	—
226	C₄×D₄₃	—	2	2	no	—
227	C₄×D₄₃	—	4	4	no	—
228	Dic₈₆	—	2	1	no	—
229	Dic₈₆	C₄×D₄	1	2	yes	—
230	C₈×C₄₃	—	2	2	no	—
231	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
232	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
233	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
234	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
235	C₄₃⋊C₈	—	2	2	no	—
236	C₄₃⋊C₈	—	2	4	no	—
237	C₄₃⋊C₈	—	4	2	no	—
238	C₄₃⋊C₈	#121	1	1	yes	characteristic
239	C₄₃⋊C₈	#121	1	1	yes	characteristic
240	C₄₃⋊C₈	#121	1	1	yes	characteristic
241	C₄₃⋊C₈	#121	1	1	yes	characteristic
242	#21558	—	43	1	no	maximal, Sylow
243	C₂²×C₄₃	—	4	1	no	—
244	C₂²×C₄₃	—	4	2	no	—
245	C₂²×C₄₃	—	8	2	no	—
246	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
247	C₂²×C₄₃	#525	1	1	yes	characteristic
248	C₂²×C₄₃	#532	1	1	yes	characteristic
249	C₂×D₄₃	—	2	2	no	—
250	C₂×D₄₃	—	4	2	no	—
251	C₄×C₄₃	—	4	2	no	—
252	C₄×C₄₃	—	4	2	no	—
253	C₄×C₄₃	—	8	2	no	—
254	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
256	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
257	C₄×C₄₃	#529	1	1	yes	characteristic
258	Dic₄₃	—	2	2	no	—
259	Dic₄₃	—	2	2	no	—
260	Dic₄₃	—	4	1	no	—
261	#3067	—	43	1	no	—
262	#2955	—	43	2	no	—
263	C₂×#443	—	43	1	no	—
264	C₄×#131	—	43	1	no	—
265	#1976	D₄₃	1	1	yes	characteristic, complemented
266	#1953	—	43	1	no	—
267	#1932	—	43	2	no	—
268	#1906	—	43	2	no	—
269	#1814	—	43	1	no	—
270	#1772	—	43	1	no	—
271	#1757	—	43	2	no	—
272	C₂×C₄₃	—	2	1	no	—
273	C₂×C₄₃	—	2	1	no	—
274	C₂×C₄₃	—	2	1	no	—
275	C₂×C₄₃	—	8	2	no	—
276	C₂×C₄₃	C₄×#121	1	1	yes	characteristic
277	D₄₃	—	4	2	no	—
278	#575	—	43	2	no	—
279	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
280	C₂×#131	—	43	2	no	—
281	C₂×#131	—	43	1	no	—
282	C₂×#131	—	43	1	no	—
283	C₄×#41	—	43	1	no	—
284	#473	—	43	2	no	—
285	#472	—	43	2	no	—
286	#471	—	43	4	no	—
287	#444	—	86	4	no	—
288	#443	—	86	1	no	—
289	#443	—	86	1	no	—
290	#443	—	86	1	no	—
291	#443	—	86	1	no	—
292	#443	—	86	4	no	—
293	#430	—	43	2	no	—
294	C₂×#108	—	43	1	no	—
295	C₂×#108	—	43	1	no	—
296	#427	C₂×D₄₃	1	1	yes	characteristic
297	#421	—	43	2	no	—
298	#421	C₂×D₄₃	1	2	yes	—
299	C₂×#104	—	43	2	no	—
300	#413	—	43	2	no	—
301	#410	C₂×D₄₃	1	2	yes	—
302	#405	—	43	1	no	—
303	#405	—	43	2	no	—
304	#405	—	86	1	no	—
305	#405	—	86	1	no	—
306	#405	C₂×D₄₃	1	1	yes	characteristic
307	C₄×M₁₆	—	43	1	no	—
308	C₄×M₁₆	—	86	1	no	—
309	C₂×C₄×C₈	—	43	1	no	—
310	C₂×C₄×C₈	—	86	1	no	—
311	#344	—	43	2	no	—
312	#344	—	43	2	no	—
313	#339	—	43	2	no	—
314	C₄₃	#21558	1	1	yes	characteristic, complemented, Sylow
315	C₂×#41	—	43	1	no	—
316	C₂×#41	C₂²×D₄₃	1	2	yes	—
317	#137	—	43	4	no	—
318	#137	—	86	2	no	—
319	AGL(1,ℤ/8)	—	43	4	no	—
320	AGL(1,ℤ/8)	—	86	2	no	—
321	#135	—	2	1	no	—
322	#135	—	2	1	no	—
323	#135	—	2	1	no	—
324	#135	—	2	1	no	—
325	#135	—	86	4	no	—
326	C₂×Q₁₆	C₄×D₄₃	1	1	yes	characteristic, complemented
327	C₂×SD₁₆	C₄×D₄₃	1	2	yes	complemented
328	C₂×D₈	C₄×D₄₃	1	1	yes	characteristic, complemented
329	#131	—	43	2	no	—
330	#131	—	43	2	no	—
331	#131	—	43	2	no	—
332	#131	—	43	2	no	—
333	#131	—	86	1	no	—
334	#131	—	86	1	no	—
335	#131	—	86	2	no	—
336	#131	—	86	2	no	—
337	#131	—	86	2	no	—
338	#131	—	86	2	no	—
339	#131	—	86	1	no	—
340	#131	—	86	1	no	—
341	C₂×M₁₆	—	43	1	no	—
342	C₂×M₁₆	—	43	2	no	—
343	C₂×M₁₆	—	43	2	no	—
344	C₂×M₁₆	—	86	1	no	—
345	C₂×M₁₆	—	86	2	no	—
346	C₂×M₁₆	—	86	1	no	—
347	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
348	C₂²×C₈	—	43	1	no	—
349	C₂²×C₈	—	86	1	no	—
350	C₂²×C₈	—	86	2	no	—
351	C₂²×C₈	—	86	1	no	—
352	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
353	C₄×Q₈	—	86	1	no	—
354	C₄×D₄	—	86	1	no	—
355	C₄×D₄	—	86	2	no	—
356	#117	—	86	1	no	—
357	#117	C₂²×D₄₃	1	2	yes	—
358	#117	C₂²×D₄₃	1	1	yes	characteristic
359	C₂×C₄²	—	43	1	no	—
360	C₂×C₄²	—	86	1	no	—
361	#108	—	43	2	no	—
362	#108	—	43	2	no	—
363	#108	—	86	4	no	—
364	#108	—	86	1	no	—
365	#108	—	86	1	no	—
366	#107	—	2	1	no	—
367	#106	—	2	1	no	—
368	#104	—	2	4	no	—
369	#104	—	86	4	no	—
370	#104	—	86	2	no	—
371	#104	—	86	2	no	—
372	#101	—	43	4	no	—
373	#100	—	43	4	no	—
374	#99	—	2	4	no	—
375	#97	—	2	1	no	—
376	#97	—	86	1	no	—
377	#97	—	86	2	no	—
378	#97	—	86	1	no	—
379	C₄×C₈	—	2	1	no	—
380	C₄×C₈	—	43	1	no	—
381	C₄×C₈	—	43	1	no	—
382	C₄×C₈	—	43	1	no	—
383	C₄×C₈	—	43	1	no	—
384	C₄×C₈	—	86	1	no	—
385	C₄×C₈	—	86	2	no	—
386	C₄×C₈	—	86	1	no	—
387	#41	—	2	2	no	—
388	#41	—	2	2	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	43	2	no	—
392	#41	—	43	2	no	—
393	#41	—	86	1	no	—
394	#41	—	86	1	no	—
395	C₂×Q₈	—	43	1	no	—
396	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	43	1	no	—
399	C₂×D₄	—	86	1	no	—
400	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	86	2	no	—
403	C₂²×C₄	—	86	1	no	—
404	C₂²×C₄	—	86	1	no	—
405	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
406	Q₁₆	—	2	1	no	—
407	Q₁₆	—	2	1	no	—
408	Q₁₆	—	86	4	no	—
409	SD₁₆	—	2	2	no	—
410	SD₁₆	—	2	2	no	—
411	SD₁₆	—	86	4	no	—
412	SD₁₆	—	86	4	no	—
413	D₈	—	2	1	no	—
414	D₈	—	2	1	no	—
415	D₈	—	86	4	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	43	2	no	—
418	M₁₆	—	43	4	no	—
419	M₁₆	—	86	2	no	—
420	M₁₆	—	86	2	no	—
421	M₁₆	—	86	2	no	—
422	M₁₆	—	86	1	no	—
423	M₁₆	—	86	2	no	—
424	M₁₆	—	86	2	no	—
425	M₁₆	—	86	2	no	—
426	M₁₆	—	86	2	no	—
427	M₁₆	—	172	2	no	—
428	M₁₆	—	172	2	no	—
429	M₁₆	D₄×D₄₃	1	2	yes	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	43	1	no	—
432	C₂×C₈	—	43	1	no	—
433	C₂×C₈	—	43	1	no	—
434	C₂×C₈	—	43	1	no	—
435	C₂×C₈	—	43	1	no	—
436	C₂×C₈	—	43	1	no	—
437	C₂×C₈	—	86	2	no	—
438	C₂×C₈	—	86	2	no	—
439	C₂×C₈	—	86	1	no	—
440	C₂×C₈	—	86	2	no	—
441	C₂×C₈	—	86	2	no	—
442	C₂×C₈	—	86	2	no	—
443	C₂×C₈	—	86	2	no	—
444	C₂×C₈	—	172	2	no	—
445	C₂×C₈	—	172	2	no	—
446	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
447	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
448	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
449	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
450	C₂×C₈	#10621900	1	1	yes	characteristic
451	C₂×C₈	#10621900	1	1	yes	characteristic
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	86	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	86	2	no	—
457	C₂²⋊C₄	#10621900	1	2	yes	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	43	1	no	—
461	C₄²	—	43	1	no	—
462	C₄²	—	86	2	no	—
463	C₄²	—	86	1	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	86	1	no	—
466	C₂³	C₂×#10621900	1	1	yes	characteristic
467	Q₈	—	2	2	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	43	2	no	—
470	Q₈	—	86	1	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	43	2	no	—
476	D₄	—	86	2	no	—
477	D₄	—	86	2	no	—
478	D₄	—	86	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	86	1	no	—
485	C₂×C₄	—	86	1	no	—
486	C₂×C₄	—	86	2	no	—
487	C₂×C₄	—	86	2	no	—
488	C₂×C₄	—	86	1	no	—
489	C₂×C₄	—	172	4	no	—
490	C₂×C₄	—	172	2	no	—
491	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
493	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
494	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
495	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
496	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	43	1	no	—
499	C₈	—	43	1	no	—
500	C₈	—	43	1	no	—
501	C₈	—	43	1	no	—
502	C₈	—	86	4	no	—
503	C₈	—	86	2	no	—
504	C₈	—	172	2	no	—
505	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
506	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
507	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
508	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
509	C₂²	—	4	1	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	86	2	no	—
513	C₂²	—	172	2	no	—
514	C₂²	C₄×#10621900	1	1	yes	characteristic
515	C₂²	#14583409	1	1	yes	characteristic
516	C₂²	#14583447	1	1	yes	characteristic
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	8	2	no	—
520	C₄	—	86	2	no	—
521	C₄	—	86	2	no	—
522	C₄	—	172	1	no	—
523	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
524	C₄	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
525	C₄	#121×D₄₃	1	1	yes	characteristic
526	C₄	#14583428	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	8	2	no	—
531	C₂	—	172	2	no	—
532	C₂	#19137111	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1976	C₂
socle	C₂×C₄₃	C₄×#121
prime radical	#19144311	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1976	D₄₃
hypocenter	C₄₃	#21558
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1976

Complements

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

N	H ≅ G/N	type
2. #19143494	C₂	semidirect
3. C₂×#14583016	C₂	semidirect
4. #19143017	C₂	semidirect
5. #19135385	C₂	semidirect
6. #19135267	C₂	semidirect
7. #19135093	C₂	semidirect
8. #19134646	C₂	semidirect
9. #19134476	C₂	semidirect
10. #19134397	C₂	semidirect
11. C₄₃×#1976	C₂	semidirect
17. #14583171	C₄	semidirect
18. #14583166	C₄	semidirect
19. #14583159	C₄	semidirect
84. #13063261	C₂×C₄	semidirect
85. #13063261	C₂×C₄	semidirect
90. #13063244	C₂×C₄	semidirect
91. #13063242	C₂×C₄	semidirect
107. C₂×Q₁₆×C₄₃	C₂×C₄	semidirect
108. C₂×SD₁₆×C₄₃	C₂×C₄	semidirect
109. C₂×D₈×C₄₃	C₂×C₄	semidirect
265. #1976	D₄₃	semidirect
314. C₄₃	#21558	semidirect
326. C₂×Q₁₆	C₄×D₄₃	semidirect
327. C₂×SD₁₆	C₄×D₄₃	semidirect
328. C₂×D₈	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19144311	2
#19143494	2
C₂×#14583016	2
#19143017	2
#19135385	2
#19135267	2
#19135093	2
#19134646	2
#19134476	2
#19134397	2
C₄₃×#1976	2
#21558	43