Subgroups — #25146976

Order 11008.

764 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144989	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14583179	C₂	1	1	yes	maximal, characteristic, complemented
3	#19144059	C₂	1	1	yes	maximal, characteristic
4	#19143341	C₂	1	1	yes	maximal, characteristic, complemented
5	#19136039	C₂	1	2	yes	maximal, complemented
6	#19135887	C₂	1	2	yes	maximal, complemented
7	#19135584	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135370	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135100	C₂	1	2	yes	maximal, complemented
10	#19134658	C₂	1	2	yes	maximal, complemented
11	C₄×#100×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063351	C₂²	1	2	yes	—
13	C₂×#13063333	C₂²	1	2	yes	—
14	#14583449	C₂²	1	1	yes	characteristic
15	C₂×#13063325	C₂²	1	1	yes	characteristic
16	#14583259	—	2	2	no	—
17	#14583250	—	2	1	no	—
18	#14583246	—	2	1	no	—
19	#14583179	—	2	1	no	—
20	#14583179	—	2	2	no	—
21	#14583179	—	2	1	no	—
22	#14583114	—	2	2	no	—
23	#14583104	—	2	1	no	—
24	#14583094	—	2	1	no	—
25	#14582978	—	2	1	no	—
26	#14582972	—	2	2	no	—
27	C₈×D₁₇₂	—	2	1	no	—
28	C₂×#13063260	C₂²	1	2	yes	—
29	C₂×#13063258	C₂²	1	2	yes	—
30	#14582923	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
32	#14582901	C₂²	1	2	yes	—
33	#14582901	C₂²	1	2	yes	—
34	#14582898	C₂²	1	2	yes	—
35	C₂×#13063246	C₂²	1	2	yes	—
36	#14582867	C₂²	1	2	yes	—
37	#14582667	C₂²	1	2	yes	—
38	#14582667	C₂²	1	2	yes	—
39	#14582663	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#100×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×#100×C₄₃	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#343	C₂²	1	1	yes	characteristic
46	C₄₃×#343	C₂²	1	1	yes	characteristic
47	C₂×#10621898	C₂³	1	2	yes	—
48	C₂²×Dic₈₆	—	2	1	no	—
49	#13063351	—	2	4	no	—
50	#13063351	—	4	2	no	—
51	C₂×#10621883	—	2	2	no	—
52	C₂×#10621882	—	2	2	no	—
53	#13063333	—	2	4	no	—
54	#13063333	—	4	2	no	—
55	C₂×#10621877	C₂³	1	2	yes	—
56	C₂×#10621872	—	2	2	no	—
57	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
58	C₂×C₈×D₄₃	—	2	2	no	—
59	#13063325	—	2	1	no	—
60	#13063325	—	2	1	no	—
61	#13063325	—	2	1	no	—
62	#13063325	—	2	1	no	—
63	#13063325	D₄	1	1	yes	characteristic
64	#13063322	D₄	1	1	yes	characteristic
65	#13063313	D₄	1	2	yes	—
66	#13063299	—	2	1	no	—
67	#13063299	—	2	1	no	—
68	C₄×D₁₇₂	—	2	1	no	—
69	C₄×D₁₇₂	—	2	1	no	—
70	C₂×C₄⋊Dic₄₃	—	2	1	no	—
71	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
72	#13063260	—	4	2	no	—
73	#13063258	—	2	2	no	—
74	#13063258	—	2	2	no	—
75	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
76	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
77	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
78	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
79	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
80	#13063250	—	2	2	no	—
81	#13063250	—	2	2	no	—
82	#13063248	—	2	2	no	—
83	#13063247	—	2	2	no	—
84	#13063247	—	2	2	no	—
85	#13063246	—	2	2	no	—
86	#13063246	—	2	2	no	—
87	#13063245	—	2	2	no	—
88	(C₂×D₄₃)⋊C₈	—	2	2	no	—
89	(C₂×D₄₃)⋊C₈	—	2	2	no	—
90	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₄₃	—	2	1	no	—
92	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₄₃	—	2	1	no	—
97	C₄×D₄×C₄₃	—	2	1	no	—
98	C₄×D₄×C₄₃	—	2	1	no	—
99	C₄×D₄×C₄₃	—	2	1	no	—
100	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
102	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
103	#100×C₄₃	—	2	2	no	—
104	#100×C₄₃	—	2	2	no	—
105	#97×C₄₃	—	2	1	no	—
106	#97×C₄₃	—	2	1	no	—
107	C₄×C₈×C₄₃	—	2	1	no	—
108	C₄×C₈×C₄₃	—	2	1	no	—
109	C₂⁴×C₄₃	—	2	1	no	—
110	C₂×D₄×C₄₃	—	2	1	no	—
111	C₂×D₄×C₄₃	—	2	1	no	—
112	C₂×D₄×C₄₃	—	2	1	no	—
113	C₂×D₄×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	2	1	no	—
115	C₂×D₄×C₄₃	#41	1	2	yes	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	4	1	no	—
118	C₂²×C₄×C₄₃	—	4	1	no	—
119	C₂²×C₄×C₄₃	—	8	2	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×C₂²⋊D₄₃	—	2	2	no	—
124	C₂²×Dic₄₃	—	2	2	no	—
125	#10621898	—	2	2	no	—
126	#10621898	—	2	2	no	—
127	#10621898	—	2	2	no	—
128	#10621898	—	2	2	no	—
129	C₂×D₁₇₂	—	2	1	no	—
130	C₂×D₁₇₂	—	2	1	no	—
131	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
132	C₂×C₄×D₄₃	—	2	2	no	—
133	C₂×Dic₈₆	—	4	1	no	—
134	C₂×Dic₈₆	—	4	1	no	—
135	C₂×Dic₈₆	—	8	2	no	—
136	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
137	M₁₆×C₄₃	—	2	1	no	—
138	M₁₆×C₄₃	—	2	1	no	—
139	M₁₆×C₄₃	—	2	1	no	—
140	M₁₆×C₄₃	—	2	1	no	—
141	M₁₆×C₄₃	—	2	1	no	—
142	M₁₆×C₄₃	—	2	1	no	—
143	M₁₆×C₄₃	—	2	1	no	—
144	M₁₆×C₄₃	#41	1	2	yes	—
145	C₂×C₈×C₄₃	—	2	1	no	—
146	C₂×C₈×C₄₃	—	2	1	no	—
147	C₂×C₈×C₄₃	—	2	1	no	—
148	C₂×C₈×C₄₃	—	2	1	no	—
149	C₄⋊C₄×C₄₃	—	2	1	no	—
150	C₄⋊C₄×C₄₃	—	2	1	no	—
151	C₂²⋊C₄×C₄₃	—	4	1	no	—
152	C₂²⋊C₄×C₄₃	—	4	1	no	—
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	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
157	#10621883	—	4	4	no	—
158	#10621882	—	4	4	no	—
159	(C₂×D₄₃)⋊C₄	—	2	2	no	—
160	(C₂×D₄₃)⋊C₄	—	2	2	no	—
161	C₄⋊Dic₄₃	—	2	1	no	—
162	C₄⋊Dic₄₃	—	2	1	no	—
163	C₄⋊Dic₄₃	—	2	2	no	—
164	C₄⋊Dic₄₃	—	2	2	no	—
165	C₄⋊Dic₄₃	—	4	1	no	—
166	C₄⋊Dic₄₃	—	4	1	no	—
167	#10621877	—	2	2	no	—
168	#10621877	—	2	2	no	—
169	C₂×C₄₃⋊C₈	—	2	2	no	—
170	C₂×C₄₃⋊C₈	—	2	2	no	—
171	C₂×C₄₃⋊C₈	—	2	2	no	—
172	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
173	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
174	#10621872	—	4	4	no	—
175	C₈×D₄₃	—	4	4	no	—
176	C₂³×C₄₃	—	2	2	no	—
177	C₂³×C₄₃	—	4	1	no	—
178	C₂³×C₄₃	—	4	1	no	—
179	C₂³×C₄₃	—	8	1	no	—
180	C₂³×C₄₃	—	8	1	no	—
181	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
182	C₂²×D₄₃	—	2	2	no	—
183	D₄×C₄₃	—	2	2	no	—
184	D₄×C₄₃	—	2	2	no	—
185	D₄×C₄₃	—	4	1	no	—
186	D₄×C₄₃	—	4	1	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	4	1	no	—
189	C₂×C₄×C₄₃	—	4	1	no	—
190	C₂×C₄×C₄₃	—	8	2	no	—
191	C₂×C₄×C₄₃	—	8	2	no	—
192	C₂×C₄×C₄₃	—	8	1	no	—
193	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
194	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
195	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
196	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂²⋊D₄₃	—	4	2	no	—
204	C₂²⋊D₄₃	—	4	2	no	—
205	C₂×Dic₄₃	—	2	2	no	—
206	C₂×Dic₄₃	—	4	2	no	—
207	C₂×Dic₄₃	—	8	2	no	—
208	D₁₇₂	—	2	2	no	—
209	D₁₇₂	—	2	2	no	—
210	D₁₇₂	—	4	2	no	—
211	D₁₇₂	—	8	1	no	—
212	C₄×D₄₃	—	4	2	no	—
213	C₄×D₄₃	—	4	2	no	—
214	Dic₈₆	—	2	2	no	—
215	Dic₈₆	—	2	2	no	—
216	Dic₈₆	—	8	2	no	—
217	Dic₈₆	—	8	2	no	—
218	C₈×C₄₃	—	2	2	no	—
219	C₈×C₄₃	—	4	1	no	—
220	C₈×C₄₃	—	4	1	no	—
221	C₈×C₄₃	—	4	1	no	—
222	C₄₃⋊C₈	—	2	2	no	—
223	C₄₃⋊C₈	—	2	2	no	—
224	C₄₃⋊C₈	—	4	2	no	—
225	#25358	—	43	1	no	maximal, Sylow
226	C₂²×C₄₃	—	2	1	no	—
227	C₂²×C₄₃	—	2	1	no	—
228	C₂²×C₄₃	—	4	2	no	—
229	C₂²×C₄₃	—	8	2	no	—
230	C₂²×C₄₃	—	8	2	no	—
231	C₂²×C₄₃	—	8	1	no	—
232	C₂²×C₄₃	—	8	1	no	—
233	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
234	C₂²×C₄₃	#529	1	1	yes	characteristic
235	C₂²×C₄₃	#542	1	1	yes	characteristic
236	C₂×D₄₃	—	4	2	no	—
237	C₂×D₄₃	—	4	2	no	—
238	C₂×D₄₃	—	4	2	no	—
239	C₄×C₄₃	—	2	1	no	—
240	C₄×C₄₃	—	2	1	no	—
241	C₄×C₄₃	—	2	1	no	—
242	C₄×C₄₃	—	8	1	no	—
243	C₄×C₄₃	#472	1	2	yes	—
244	C₄×C₄₃	#546	1	1	yes	characteristic
245	C₄×C₄₃	#546	1	1	yes	characteristic
246	C₄×C₄₃	#547	1	1	yes	characteristic
247	C₄×C₄₃	#548	1	1	yes	characteristic
248	Dic₄₃	—	4	2	no	—
249	Dic₄₃	—	8	2	no	—
250	#3141	—	43	1	no	—
251	C₂×#474	—	43	1	no	—
252	#3036	—	43	1	no	—
253	#2935	—	43	1	no	—
254	#2078	—	43	2	no	—
255	#2051	—	43	2	no	—
256	#1997	—	43	1	no	—
257	#1950	—	43	1	no	—
258	#1907	—	43	2	no	—
259	#1816	—	43	2	no	—
260	C₄×#100	D₄₃	1	1	yes	characteristic, complemented
261	C₂×C₄₃	—	2	1	no	—
262	C₂×C₄₃	—	2	1	no	—
263	C₂×C₄₃	—	8	2	no	—
264	C₂×C₄₃	#2427	1	1	yes	characteristic
265	C₂×C₄₃	C₂×#472	1	1	yes	characteristic
266	C₂×C₄₃	#3069	1	1	yes	characteristic
267	D₄₃	—	8	2	no	—
268	C₂×AGL(1,ℤ/8)	—	43	2	no	—
269	C₂×#131	—	43	2	no	—
270	#532	—	43	1	no	—
271	C₂×C₄⋊Q₈	—	43	1	no	—
272	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
273	#489	—	86	2	no	—
274	#487	—	86	1	no	—
275	#486	—	86	1	no	—
276	#474	—	86	1	no	—
277	#474	—	86	2	no	—
278	#474	—	86	1	no	—
279	#463	—	86	2	no	—
280	#461	—	86	1	no	—
281	#459	—	86	1	no	—
282	#436	—	86	1	no	—
283	#435	—	86	2	no	—
284	C₈×D₄	—	86	1	no	—
285	C₂×#108	—	43	2	no	—
286	C₂×#107	—	43	2	no	—
287	#423	—	43	1	no	—
288	C₂×C₄⋊C₈	—	43	1	no	—
289	#417	—	43	2	no	—
290	#417	—	43	2	no	—
291	#417	—	43	2	no	—
292	C₂×#102	—	43	2	no	—
293	C₂×#100	C₂×D₄₃	1	1	yes	characteristic
294	C₂×#100	C₂×D₄₃	1	1	yes	characteristic
295	#408	—	43	2	no	—
296	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
297	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
298	#343	—	43	2	no	—
299	#343	—	43	2	no	—
300	#343	C₂×D₄₃	1	1	yes	characteristic
301	#343	C₂×D₄₃	1	1	yes	characteristic
302	#341	—	43	2	no	—
303	C₄₃	#25358	1	1	yes	characteristic, complemented, Sylow
304	C₂×#41	—	43	2	no	—
305	C₂²×Q₈	—	86	1	no	—
306	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
307	C₂³×C₄	—	2	1	no	—
308	AGL(1,ℤ/8)	—	86	4	no	—
309	AGL(1,ℤ/8)	—	172	2	no	—
310	C₂×SD₁₆	—	86	2	no	—
311	C₂×D₈	—	86	2	no	—
312	#131	—	86	4	no	—
313	#131	—	172	2	no	—
314	C₂×M₁₆	—	43	2	no	—
315	C₂×M₁₆	—	86	2	no	—
316	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
317	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
318	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
319	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
320	C₂²×C₈	—	43	2	no	—
321	C₂²×C₈	—	86	2	no	—
322	C₄⋊Q₈	—	43	1	no	—
323	C₄⋊Q₈	—	86	1	no	—
324	C₄⋊Q₈	—	86	1	no	—
325	C₄⋊Q₈	—	86	1	no	—
326	C₄⋊Q₈	—	86	1	no	—
327	#127	—	43	1	no	—
328	#124	—	43	2	no	—
329	#121	—	86	1	no	—
330	#121	—	86	1	no	—
331	C₄×D₄	—	2	1	no	—
332	C₄×D₄	—	2	1	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	—	86	1	no	—
336	C₄×D₄	—	86	1	no	—
337	C₂×C₄⋊C₄	—	43	2	no	—
338	C₂×C₄⋊C₄	—	86	1	no	—
339	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
342	#108	—	172	2	no	—
343	#107	—	86	2	no	—
344	#107	—	86	2	no	—
345	C₄⋊C₈	—	43	1	no	—
346	C₄⋊C₈	—	43	2	no	—
347	C₄⋊C₈	—	43	1	no	—
348	C₄⋊C₈	—	86	1	no	—
349	C₄⋊C₈	—	86	1	no	—
350	#103	—	86	2	no	—
351	#103	—	86	2	no	—
352	#103	—	86	2	no	—
353	#102	—	86	2	no	—
354	#102	—	86	2	no	—
355	#102	—	86	2	no	—
356	#102	—	86	2	no	—
357	#102	—	86	2	no	—
358	#100	—	2	2	no	—
359	#100	—	2	2	no	—
360	C₂²⋊C₈	—	86	2	no	—
361	C₂²⋊C₈	—	86	2	no	—
362	#97	—	2	1	no	—
363	#97	—	2	1	no	—
364	C₄×C₈	—	2	1	no	—
365	C₄×C₈	—	2	1	no	—
366	C₂⁴	—	2	1	no	—
367	#41	—	86	2	no	—
368	#41	—	86	2	no	—
369	#41	—	86	2	no	—
370	#41	—	86	2	no	—
371	C₂×Q₈	—	43	2	no	—
372	C₂×Q₈	—	344	2	no	—
373	C₂×Q₈	—	172	1	no	—
374	C₂×Q₈	—	172	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	43	2	no	—
381	C₂×D₄	—	86	2	no	—
382	C₂×D₄	—	86	1	no	—
383	C₂×D₄	—	86	1	no	—
384	C₂×D₄	#10621898	1	2	yes	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	8	2	no	—
389	C₂²×C₄	—	86	2	no	—
390	C₂²×C₄	—	86	2	no	—
391	C₂²×C₄	#10621898	1	1	yes	characteristic
392	C₂²×C₄	#10621898	1	1	yes	characteristic
393	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
394	SD₁₆	—	172	4	no	—
395	D₈	—	172	4	no	—
396	M₁₆	—	2	1	no	—
397	M₁₆	—	2	1	no	—
398	M₁₆	—	2	1	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	2	1	no	—
402	M₁₆	—	2	1	no	—
403	M₁₆	—	86	2	no	—
404	M₁₆	—	86	2	no	—
405	M₁₆	—	172	4	no	—
406	M₁₆	#10621898	1	2	yes	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	43	2	no	—
412	C₂×C₈	—	43	2	no	—
413	C₂×C₈	—	86	2	no	—
414	C₂×C₈	—	86	2	no	—
415	C₂×C₈	—	86	2	no	—
416	C₂×C₈	—	172	4	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	86	1	no	—
420	C₄⋊C₄	—	86	1	no	—
421	C₄⋊C₄	—	86	2	no	—
422	C₄⋊C₄	—	86	2	no	—
423	C₄⋊C₄	—	172	1	no	—
424	C₄⋊C₄	—	172	1	no	—
425	C₂²⋊C₄	—	4	1	no	—
426	C₂²⋊C₄	—	4	1	no	—
427	C₂²⋊C₄	—	86	2	no	—
428	C₂²⋊C₄	—	86	2	no	—
429	C₄²	D₄×D₄₃	1	1	yes	characteristic
430	C₄²	D₄×D₄₃	1	1	yes	characteristic
431	C₄²	D₄×D₄₃	1	1	yes	characteristic
432	C₄²	D₄×D₄₃	1	1	yes	characteristic
433	C₂³	—	2	2	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	8	1	no	—
437	C₂³	—	8	1	no	—
438	C₂³	—	86	2	no	—
439	C₂³	C₂×#10621898	1	1	yes	characteristic
440	Q₈	—	86	2	no	—
441	Q₈	—	86	2	no	—
442	Q₈	—	344	2	no	—
443	Q₈	—	344	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	4	1	no	—
447	D₄	—	4	1	no	—
448	D₄	—	86	2	no	—
449	D₄	—	86	2	no	—
450	D₄	—	344	1	no	—
451	D₄	—	172	2	no	—
452	D₄	—	172	2	no	—
453	D₄	—	172	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	8	2	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	—	8	1	no	—
460	C₂×C₄	—	86	2	no	—
461	C₂×C₄	—	344	2	no	—
462	C₂×C₄	—	172	2	no	—
463	C₂×C₄	—	172	2	no	—
464	C₂×C₄	—	172	2	no	—
465	C₂×C₄	#13063298	1	1	yes	characteristic
466	C₂×C₄	#13063298	1	1	yes	characteristic
467	C₂×C₄	#13063298	1	1	yes	characteristic
468	C₂×C₄	#13063298	1	1	yes	characteristic
469	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
470	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
471	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
472	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
473	C₂×C₄	#13063371	1	1	yes	characteristic
474	C₂×C₄	#13063372	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	4	1	no	—
477	C₈	—	4	1	no	—
478	C₈	—	4	1	no	—
479	C₈	—	86	2	no	—
480	C₈	—	86	2	no	—
481	C₈	—	172	2	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	2	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	172	2	no	—
490	C₂²	—	172	2	no	—
491	C₂²	—	172	2	no	—
492	C₂²	C₂×#13063298	1	1	yes	characteristic
493	C₂²	#14583433	1	1	yes	characteristic
494	C₂²	#14583520	1	1	yes	characteristic
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	8	1	no	—
499	C₄	—	344	2	no	—
500	C₄	—	172	2	no	—
501	C₄	#14583168	1	2	yes	—
502	C₄	#14583545	1	1	yes	characteristic
503	C₄	#14583545	1	1	yes	characteristic
504	C₄	#14583554	1	1	yes	characteristic
505	C₄	#14583558	1	1	yes	characteristic
506	C₂	—	2	1	no	—
507	C₂	—	2	1	no	—
508	C₂	—	8	2	no	—
509	C₂	—	344	2	no	—
510	C₂	#19138172	1	1	yes	characteristic
511	C₂	C₂×#14583168	1	1	yes	characteristic
512	C₂	#19144335	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063298
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×#100×C₄₃	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19144059	C₂
hypercenter	C₄×#100	D₄₃
hypocenter	C₄₃	#25358
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#100

Complements

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

N	H ≅ G/N	type
1. #19144989	C₂	semidirect
2. C₂×#14583179	C₂	semidirect
4. #19143341	C₂	semidirect
5. #19136039	C₂	semidirect
6. #19135887	C₂	semidirect
7. #19135584	C₂	semidirect
8. #19135370	C₂	semidirect
9. #19135100	C₂	semidirect
10. #19134658	C₂	semidirect
11. C₄×#100×C₄₃	C₂	semidirect
260. C₄×#100	D₄₃	semidirect
303. C₄₃	#25358	semidirect

Maximal subgroups

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

subgroup	index
#19144989	2
C₂×#14583179	2
#19144059	2
#19143341	2
#19136039	2
#19135887	2
#19135584	2
#19135370	2
#19135100	2
#19134658	2
C₄×#100×C₄₃	2
#25358	43