Subgroups — #25146401

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144971	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583099	C₂	1	1	yes	maximal, characteristic
3	#19143544	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135952	C₂	1	2	yes	maximal, complemented
5	#19135855	C₂	1	2	yes	maximal, complemented
6	#19135497	C₂	1	2	yes	maximal, complemented
7	#19135434	C₂	1	1	yes	maximal, characteristic
8	#19135368	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135256	C₂	1	2	yes	maximal, complemented
10	C₄×#13063244	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10621884	C₂²	1	2	yes	—
13	C₂×#13063322	C₂²	1	1	yes	characteristic
14	#14583265	—	2	2	no	—
15	#14583247	—	2	1	no	—
16	#14583247	—	2	1	no	—
17	#14583099	—	2	1	no	—
18	#14583099	—	2	1	no	—
19	#14583099	—	2	2	no	—
20	#14583030	—	2	1	no	—
21	#14583030	—	2	2	no	—
22	Q₈×C₄₃⋊C₈	—	2	1	no	—
23	C₂×#13063260	C₂²	1	2	yes	—
24	#14582926	C₂²	1	2	yes	—
25	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
26	#14582903	C₂²	1	2	yes	—
27	#14582903	C₂²	1	2	yes	—
28	C₂×#13063245	C₂²	1	2	yes	—
29	C₂×#13063244	C₂²	1	1	yes	characteristic
30	C₂×#13063244	C₂²	1	1	yes	characteristic
31	C₂×#13063241	C₂²	1	2	yes	—
32	C₂×#13063241	C₂²	1	2	yes	—
33	#14582855	C₂²	1	2	yes	—
34	C₄×#10621877	C₂²	1	1	yes	characteristic
35	C₄×#10621877	C₂²	1	1	yes	characteristic
36	#14582668	C₂²	1	1	yes	characteristic
37	#14582668	C₂²	1	1	yes	characteristic
38	#14582663	C₂²	1	2	yes	—
39	C₄₃×#533	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#479	—	2	2	no	—
42	C₄₃×#477	—	2	1	no	—
43	C₄₃×#475	—	2	1	no	—
44	C₄₃×#428	C₂²	1	2	yes	—
45	C₄₃×#423	C₂²	1	1	yes	characteristic
46	C₄₃×#419	C₂²	1	2	yes	—
47	C₂²×D₁₇₂	—	2	1	no	—
48	C₂²×D₁₇₂	—	2	1	no	—
49	C₂²×D₁₇₂	C₂³	1	2	yes	—
50	C₂×#10621884	—	2	4	no	—
51	C₂×#10621884	—	2	2	no	—
52	C₂×#10621884	—	2	2	no	—
53	C₂×#10621884	—	4	2	no	—
54	C₂×#10621877	C₂³	1	1	yes	characteristic
55	C₂×#10621877	C₂³	1	1	yes	characteristic
56	C₂×#10621877	C₂³	1	1	yes	characteristic
57	C₂×#10621877	C₂³	1	1	yes	characteristic
58	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
59	#13063322	—	2	1	no	—
60	#13063322	—	2	1	no	—
61	#13063322	—	2	1	no	—
62	#13063322	—	2	1	no	—
63	#13063260	—	4	2	no	—
64	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
65	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
66	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
67	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
68	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
69	#13063245	—	2	2	no	—
70	#13063245	—	2	2	no	—
71	#13063245	—	2	2	no	—
72	#13063245	—	2	2	no	—
73	#13063245	—	2	2	no	—
74	#13063245	—	2	2	no	—
75	#13063244	—	2	2	no	—
76	#13063244	—	2	2	no	—
77	#13063241	—	2	4	no	—
78	#13063241	—	4	2	no	—
79	#13063236	—	2	1	no	—
80	#13063236	—	2	1	no	—
81	#13063236	—	2	2	no	—
82	C₄×C₄₃⋊C₈	—	2	1	no	—
83	C₄×C₄₃⋊C₈	—	2	1	no	—
84	C₄×C₄₃⋊C₈	—	2	2	no	—
85	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
87	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
88	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
89	#125×C₄₃	D₄	1	2	yes	—
90	C₂²⋊Q₈×C₄₃	—	2	1	no	—
91	C₂²⋊Q₈×C₄₃	—	2	1	no	—
92	C₄×Q₈×C₄₃	—	2	1	no	—
93	C₄×Q₈×C₄₃	—	2	1	no	—
94	C₄×Q₈×C₄₃	—	2	1	no	—
95	C₄×Q₈×C₄₃	—	2	1	no	—
96	C₄×Q₈×C₄₃	—	2	1	no	—
97	C₄×Q₈×C₄₃	—	2	1	no	—
98	#117×C₄₃	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
100	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	—	2	1	no	—
102	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
103	#107×C₄₃	—	2	2	no	—
104	#106×C₄₃	—	2	2	no	—
105	C₄⋊C₈×C₄₃	—	2	1	no	—
106	C₄⋊C₈×C₄₃	—	2	1	no	—
107	#103×C₄₃	—	2	2	no	—
108	#103×C₄₃	—	2	2	no	—
109	C₂³×D₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	2	1	no	—
111	C₂×Q₈×C₄₃	—	2	1	no	—
112	C₂×Q₈×C₄₃	—	2	1	no	—
113	C₂×Q₈×C₄₃	—	2	1	no	—
114	C₂×Q₈×C₄₃	—	2	1	no	—
115	C₂×Q₈×C₄₃	—	2	1	no	—
116	C₂×Q₈×C₄₃	—	2	1	no	—
117	C₂×Q₈×C₄₃	#41	1	2	yes	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	2	1	no	—
120	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
123	C₂×D₁₇₂	—	2	2	no	—
124	C₂×D₁₇₂	—	2	2	no	—
125	C₂×D₁₇₂	—	2	2	no	—
126	C₂×D₁₇₂	—	2	2	no	—
127	C₂×D₁₇₂	—	2	2	no	—
128	C₂×D₁₇₂	—	2	2	no	—
129	C₂×D₁₇₂	—	4	1	no	—
130	C₂×D₁₇₂	—	4	1	no	—
131	C₂×D₁₇₂	—	4	1	no	—
132	C₂×D₁₇₂	—	4	1	no	—
133	C₂×D₁₇₂	—	8	2	no	—
134	C₂×D₁₇₂	—	8	2	no	—
135	M₁₆×C₄₃	—	2	2	no	—
136	M₁₆×C₄₃	—	2	2	no	—
137	C₂×C₈×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	2	1	no	—
141	C₄⋊C₄×C₄₃	—	2	1	no	—
142	C₄⋊C₄×C₄₃	—	2	1	no	—
143	C₄⋊C₄×C₄₃	—	2	1	no	—
144	C₄⋊C₄×C₄₃	—	4	1	no	—
145	C₄⋊C₄×C₄₃	—	4	1	no	—
146	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
148	C₂²⋊C₄×C₄₃	—	2	2	no	—
149	C₄²×C₄₃	—	2	2	no	—
150	C₄²×C₄₃	—	4	1	no	—
151	C₄²×C₄₃	—	4	1	no	—
152	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
156	#10621884	—	4	4	no	—
157	#10621884	—	4	4	no	—
158	#10621877	—	2	1	no	—
159	#10621877	—	2	1	no	—
160	#10621877	—	2	1	no	—
161	#10621877	—	2	1	no	—
162	#10621877	—	2	1	no	—
163	#10621877	—	2	1	no	—
164	#10621877	—	2	1	no	—
165	#10621877	#41	1	2	yes	—
166	C₂×C₄₃⋊C₈	—	2	1	no	—
167	C₂×C₄₃⋊C₈	—	2	2	no	—
168	C₂×C₄₃⋊C₈	—	2	2	no	—
169	C₂×C₄₃⋊C₈	—	2	1	no	—
170	C₂×C₄₃⋊C₈	—	2	1	no	—
171	C₂×C₄₃⋊C₈	—	2	1	no	—
172	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
173	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
174	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂²×D₄₃	—	4	2	no	—
176	C₂²×D₄₃	—	4	2	no	—
177	C₂²×D₄₃	—	4	2	no	—
178	C₂²×D₄₃	—	8	2	no	—
179	C₂²×D₄₃	—	8	2	no	—
180	Q₈×C₄₃	—	2	2	no	—
181	Q₈×C₄₃	—	2	2	no	—
182	Q₈×C₄₃	—	4	1	no	—
183	Q₈×C₄₃	—	4	1	no	—
184	Q₈×C₄₃	—	4	2	no	—
185	Q₈×C₄₃	—	8	1	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	2	2	no	—
190	C₂×C₄×C₄₃	—	4	1	no	—
191	C₂×C₄×C₄₃	—	4	1	no	—
192	C₂×C₄×C₄₃	—	4	1	no	—
193	C₂×C₄×C₄₃	—	4	1	no	—
194	C₂×C₄×C₄₃	—	8	1	no	—
195	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
196	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
197	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
198	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
205	D₁₇₂	—	4	2	no	—
206	D₁₇₂	—	4	2	no	—
207	D₁₇₂	—	4	2	no	—
208	D₁₇₂	—	4	2	no	—
209	D₁₇₂	—	8	2	no	—
210	D₁₇₂	—	8	2	no	—
211	D₁₇₂	—	8	2	no	—
212	D₁₇₂	—	8	2	no	—
213	C₈×C₄₃	—	4	2	no	—
214	C₄₃⋊C₈	—	2	2	no	—
215	C₄₃⋊C₈	—	2	2	no	—
216	C₄₃⋊C₈	—	2	2	no	—
217	C₄₃⋊C₈	—	4	1	no	—
218	C₄₃⋊C₈	—	4	1	no	—
219	C₄₃⋊C₈	—	4	1	no	—
220	#25315	—	43	1	no	maximal, Sylow
221	C₂²×C₄₃	—	2	1	no	—
222	C₂²×C₄₃	—	2	1	no	—
223	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
224	C₂²×C₄₃	#529	1	1	yes	characteristic
225	C₂²×C₄₃	#542	1	1	yes	characteristic
226	C₂×D₄₃	—	8	2	no	—
227	C₂×D₄₃	—	8	2	no	—
228	C₂×D₄₃	—	8	2	no	—
229	C₂×D₄₃	—	16	2	no	—
230	C₂×D₄₃	—	16	2	no	—
231	C₄×C₄₃	—	2	1	no	—
232	C₄×C₄₃	—	2	1	no	—
233	C₄×C₄₃	—	2	1	no	—
234	C₄×C₄₃	—	4	2	no	—
235	C₄×C₄₃	—	4	2	no	—
236	C₄×C₄₃	—	4	2	no	—
237	C₄×C₄₃	—	8	1	no	—
238	C₄×C₄₃	#471	1	2	yes	—
239	C₄×C₄₃	#546	1	1	yes	characteristic
240	C₄×C₄₃	#548	1	1	yes	characteristic
241	C₄×C₄₃	#548	1	1	yes	characteristic
242	C₄×C₄₃	#550	1	1	yes	characteristic
243	#3138	—	43	1	no	—
244	#3078	D₄₃	1	1	yes	characteristic, complemented
245	C₂×#460	—	43	1	no	—
246	#2962	—	43	1	no	—
247	#2063	—	43	2	no	—
248	#2046	—	43	2	no	—
249	#1977	—	43	2	no	—
250	#1965	—	43	1	no	—
251	#1950	—	43	1	no	—
252	#1931	—	43	2	no	—
253	C₄×#101	—	43	1	no	—
254	C₂×C₄₃	—	2	1	no	—
255	C₂×C₄₃	—	2	1	no	—
256	C₂×C₄₃	#2426	1	1	yes	characteristic
257	C₂×C₄₃	C₂×#471	1	1	yes	characteristic
258	C₂×C₄₃	#3068	1	1	yes	characteristic
259	D₄₃	—	16	2	no	—
260	C₂²×SD₁₆	—	43	2	no	—
261	#533	C₂×D₄₃	1	1	yes	characteristic
262	C₂×#127	—	43	1	no	—
263	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
264	#490	—	86	2	no	—
265	#486	—	86	1	no	—
266	#486	—	86	1	no	—
267	#479	—	2	2	no	—
268	#477	—	2	1	no	—
269	#475	—	2	1	no	—
270	#460	—	86	1	no	—
271	#460	—	86	2	no	—
272	#460	—	86	1	no	—
273	#446	—	86	2	no	—
274	#446	—	86	1	no	—
275	C₈×Q₈	—	86	1	no	—
276	C₂×#108	—	43	2	no	—
277	#428	C₂×D₄₃	1	2	yes	—
278	#424	—	43	2	no	—
279	#423	C₂×D₄₃	1	1	yes	characteristic
280	C₂×C₄⋊C₈	—	43	1	no	—
281	#419	C₂×D₄₃	1	2	yes	—
282	#418	—	43	2	no	—
283	#418	—	43	2	no	—
284	C₂×#102	—	43	2	no	—
285	C₂×#101	—	43	1	no	—
286	C₂×#101	—	43	1	no	—
287	C₂×#100	—	43	2	no	—
288	C₂×#100	—	43	2	no	—
289	#405	—	43	2	no	—
290	C₄×M₁₆	—	43	1	no	—
291	C₄×M₁₆	—	43	1	no	—
292	#343	—	43	1	no	—
293	#343	—	43	1	no	—
294	#341	—	43	2	no	—
295	C₄₃	#25315	1	1	yes	characteristic, complemented, Sylow
296	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
297	C₂²×D₄	—	43	2	no	—
298	C₂²×D₄	—	86	1	no	—
299	C₂²×D₄	—	86	1	no	—
300	C₂×SD₁₆	—	86	2	no	—
301	C₂×SD₁₆	—	86	2	no	—
302	C₂×SD₁₆	—	86	4	no	—
303	C₂×SD₁₆	—	172	2	no	—
304	C₂×M₁₆	—	43	1	no	—
305	C₂×M₁₆	—	43	1	no	—
306	C₂×M₁₆	—	43	1	no	—
307	C₂×M₁₆	—	43	1	no	—
308	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
309	C₂²×C₈	—	43	2	no	—
310	C₄⋊Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
311	C₄⋊Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
312	#127	—	86	1	no	—
313	#127	—	86	1	no	—
314	#127	—	86	1	no	—
315	#127	—	86	1	no	—
316	#125	C₂²⋊D₄₃	1	2	yes	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₂²⋊Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	—	2	1	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	2	1	no	—
325	#117	C₂²×D₄₃	1	2	yes	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
330	#108	—	172	2	no	—
331	#107	—	2	2	no	—
332	#106	—	2	2	no	—
333	C₄⋊C₈	—	2	1	no	—
334	C₄⋊C₈	—	2	1	no	—
335	C₄⋊C₈	—	43	1	no	—
336	C₄⋊C₈	—	43	1	no	—
337	C₄⋊C₈	—	43	2	no	—
338	C₄⋊C₈	—	86	2	no	—
339	C₄⋊C₈	—	86	2	no	—
340	#103	—	2	2	no	—
341	#103	—	2	2	no	—
342	#102	—	86	2	no	—
343	#102	—	86	2	no	—
344	#102	—	86	2	no	—
345	#102	—	86	2	no	—
346	#102	—	86	2	no	—
347	#102	—	86	2	no	—
348	#101	—	86	2	no	—
349	#101	—	86	2	no	—
350	#100	—	86	4	no	—
351	#100	—	172	2	no	—
352	#97	—	86	2	no	—
353	#97	—	86	1	no	—
354	#97	—	86	1	no	—
355	C₄×C₈	—	86	2	no	—
356	C₄×C₈	—	86	1	no	—
357	C₄×C₈	—	86	1	no	—
358	C₂⁴	—	86	2	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	#10621902	1	2	yes	—
367	C₂×D₄	—	86	2	no	—
368	C₂×D₄	—	86	2	no	—
369	C₂×D₄	—	86	2	no	—
370	C₂×D₄	—	86	2	no	—
371	C₂×D₄	—	86	2	no	—
372	C₂×D₄	—	86	2	no	—
373	C₂×D₄	—	344	2	no	—
374	C₂×D₄	—	344	2	no	—
375	C₂×D₄	—	172	1	no	—
376	C₂×D₄	—	172	1	no	—
377	C₂×D₄	—	172	1	no	—
378	C₂×D₄	—	172	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	#10621900	1	1	yes	characteristic
382	C₂²×C₄	#10621900	1	1	yes	characteristic
383	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
384	SD₁₆	—	172	4	no	—
385	SD₁₆	—	172	4	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	—	43	2	no	—
389	M₁₆	—	86	1	no	—
390	M₁₆	—	86	1	no	—
391	M₁₆	—	86	1	no	—
392	M₁₆	—	86	1	no	—
393	M₁₆	—	86	1	no	—
394	M₁₆	—	86	1	no	—
395	M₁₆	—	86	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	43	2	no	—
398	C₂×C₈	—	43	2	no	—
399	C₂×C₈	—	86	1	no	—
400	C₂×C₈	—	86	2	no	—
401	C₂×C₈	—	86	2	no	—
402	C₂×C₈	—	86	1	no	—
403	C₂×C₈	—	86	1	no	—
404	C₂×C₈	—	86	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	4	1	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
414	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	4	1	no	—
418	C₄²	—	4	1	no	—
419	C₄²	D₄×D₄₃	1	1	yes	characteristic
420	C₄²	D₄×D₄₃	1	1	yes	characteristic
421	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
422	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
423	C₂³	—	344	2	no	—
424	C₂³	—	344	2	no	—
425	C₂³	—	172	2	no	—
426	C₂³	—	172	2	no	—
427	C₂³	—	172	2	no	—
428	C₂³	C₂×#10621900	1	1	yes	characteristic
429	Q₈	—	2	2	no	—
430	Q₈	—	2	2	no	—
431	Q₈	—	4	1	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	4	2	no	—
434	Q₈	—	8	1	no	—
435	D₄	—	344	2	no	—
436	D₄	—	344	2	no	—
437	D₄	—	344	2	no	—
438	D₄	—	344	2	no	—
439	D₄	—	172	2	no	—
440	D₄	—	172	2	no	—
441	D₄	—	172	2	no	—
442	D₄	—	172	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	8	1	no	—
452	C₂×C₄	#13063297	1	1	yes	characteristic
453	C₂×C₄	#13063297	1	1	yes	characteristic
454	C₂×C₄	#13063297	1	1	yes	characteristic
455	C₂×C₄	#13063297	1	1	yes	characteristic
456	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
457	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
458	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
459	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
460	C₂×C₄	#13063371	1	1	yes	characteristic
461	C₂×C₄	#13063373	1	1	yes	characteristic
462	C₈	—	4	2	no	—
463	C₈	—	86	2	no	—
464	C₈	—	86	2	no	—
465	C₈	—	86	2	no	—
466	C₈	—	172	1	no	—
467	C₈	—	172	1	no	—
468	C₈	—	172	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	344	2	no	—
472	C₂²	—	344	2	no	—
473	C₂²	—	344	2	no	—
474	C₂²	—	688	2	no	—
475	C₂²	—	688	2	no	—
476	C₂²	C₂×#13063297	1	1	yes	characteristic
477	C₂²	#14583435	1	1	yes	characteristic
478	C₂²	#14583522	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	8	1	no	—
486	C₄	#14583164	1	2	yes	—
487	C₄	#14583540	1	1	yes	characteristic
488	C₄	#14583559	1	1	yes	characteristic
489	C₄	#14583560	1	1	yes	characteristic
490	C₄	#14583568	1	1	yes	characteristic
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	688	2	no	—
494	C₂	#19138163	1	1	yes	characteristic
495	C₂	C₂×#14583164	1	1	yes	characteristic
496	C₂	#19144325	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063297
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#3078	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂×#13063322	C₂²
hypercenter	#3078	D₄₃
hypocenter	C₄₃	#25315
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3078

Complements

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

N	H ≅ G/N	type
3. #19143544	C₂	semidirect
4. #19135952	C₂	semidirect
5. #19135855	C₂	semidirect
6. #19135497	C₂	semidirect
8. #19135368	C₂	semidirect
9. #19135256	C₂	semidirect
10. C₄×#13063244	C₂	semidirect
11. C₄₃×#3078	C₂	semidirect
244. #3078	D₄₃	semidirect
295. C₄₃	#25315	semidirect

Maximal subgroups

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

subgroup	index
#19144971	2
C₂×#14583099	2
#19143544	2
#19135952	2
#19135855	2
#19135497	2
#19135434	2
#19135368	2
#19135256	2
C₄×#13063244	2
C₄₃×#3078	2
#25315	43