Subgroups — #25147608

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145054	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583173	C₂	1	2	yes	maximal, complemented
3	#19144067	C₂	1	1	yes	maximal, characteristic
4	C₂×#14583109	C₂	1	1	yes	maximal, characteristic, complemented
5	#19143341	C₂	1	1	yes	maximal, characteristic
6	#19135897	C₂	1	2	yes	maximal, complemented
7	#19135715	C₂	1	2	yes	maximal, complemented
8	#19135439	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135370	C₂	1	1	yes	maximal, characteristic, complemented
10	#19135111	C₂	1	2	yes	maximal, complemented
11	C₄×#101×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063358	C₂²	1	2	yes	—
13	C₂×#13063358	C₂²	1	2	yes	—
14	C₂×#13063356	C₂²	1	2	yes	—
15	C₂²×#10621885	C₂²	1	2	yes	—
16	C₂×#13063333	C₂²	1	2	yes	—
17	#14583449	C₂²	1	1	yes	characteristic
18	C₂×#13063325	C₂²	1	1	yes	characteristic
19	#14583293	—	2	2	no	—
20	#14583279	—	2	1	no	—
21	#14583272	—	2	1	no	—
22	#14583173	—	2	8	no	—
23	#14583121	—	2	2	no	—
24	#14583109	—	2	1	no	—
25	#14583109	—	2	1	no	—
26	#14583109	—	2	2	no	—
27	#14583109	—	2	1	no	—
28	#14583099	—	2	1	no	—
29	#14582978	—	2	1	no	—
30	#14582972	—	2	2	no	—
31	C₈×D₁₇₂	—	2	1	no	—
32	C₂×#13063260	C₂²	1	2	yes	—
33	#14582923	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
35	#14582898	C₂²	1	2	yes	—
36	C₂×#13063248	C₂²	1	2	yes	—
37	C₂×#13063243	C₂²	1	2	yes	—
38	C₂×#13063243	C₂²	1	2	yes	—
39	#14582867	C₂²	1	2	yes	—
40	#14582663	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×#101×C₄₃	C₂²	1	1	yes	characteristic
43	C₂×#101×C₄₃	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
46	C₄₃×#343	C₂²	1	1	yes	characteristic
47	C₄₃×#343	C₂²	1	1	yes	characteristic
48	C₂×#10621898	C₂³	1	2	yes	—
49	C₂²×Dic₈₆	C₂³	1	2	yes	—
50	#13063358	—	2	4	no	—
51	#13063358	—	2	4	no	—
52	#13063358	—	4	2	no	—
53	#13063358	—	4	2	no	—
54	#13063356	—	2	4	no	—
55	#13063356	—	4	2	no	—
56	C₂×Dic₁₇₂	—	2	2	no	—
57	C₂×Dic₁₇₂	—	2	2	no	—
58	C₂×#10621885	—	2	4	no	—
59	C₂×#10621885	—	2	2	no	—
60	C₂×#10621885	—	2	2	no	—
61	C₂×#10621885	—	2	2	no	—
62	C₂×#10621885	—	4	2	no	—
63	C₂×#10621873	—	2	2	no	—
64	C₂×#10621873	—	2	2	no	—
65	C₂×#10621884	—	2	2	no	—
66	#13063333	—	2	4	no	—
67	#13063333	—	4	2	no	—
68	C₂×#10621877	C₂³	1	2	yes	—
69	C₂×#10621872	—	2	2	no	—
70	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
71	C₂×C₈×D₄₃	—	2	2	no	—
72	#13063325	—	2	1	no	—
73	#13063325	—	2	1	no	—
74	#13063325	—	2	1	no	—
75	#13063325	—	2	1	no	—
76	#13063325	D₄	1	1	yes	characteristic
77	#13063322	D₄	1	1	yes	characteristic
78	#13063313	D₄	1	2	yes	—
79	#13063299	—	2	1	no	—
80	#13063299	—	2	1	no	—
81	C₄×D₁₇₂	—	2	1	no	—
82	C₄×D₁₇₂	—	2	1	no	—
83	C₂×C₄⋊Dic₄₃	—	2	1	no	—
84	C₂×C₄⋊Dic₄₃	—	2	1	no	—
85	#13063260	—	2	4	no	—
86	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
87	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
88	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
89	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
90	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
91	#13063248	—	2	2	no	—
92	#13063248	—	2	2	no	—
93	#13063248	—	2	2	no	—
94	#13063245	—	2	2	no	—
95	#13063243	—	2	4	no	—
96	#13063243	—	4	2	no	—
97	(C₂×D₄₃)⋊C₈	—	2	2	no	—
98	(C₂×D₄₃)⋊C₈	—	2	2	no	—
99	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
104	C₄×Q₈×C₄₃	—	2	1	no	—
105	C₄×Q₈×C₄₃	—	2	1	no	—
106	C₄×Q₈×C₄₃	—	2	1	no	—
107	C₄×Q₈×C₄₃	—	2	1	no	—
108	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
109	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₄₃	—	2	1	no	—
111	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
112	#101×C₄₃	—	2	2	no	—
113	#101×C₄₃	D₄	1	4	yes	complemented
114	#97×C₄₃	—	2	1	no	—
115	#97×C₄₃	—	2	1	no	—
116	C₄×C₈×C₄₃	—	2	1	no	—
117	C₄×C₈×C₄₃	—	2	1	no	—
118	C₂×Q₈×C₄₃	—	2	1	no	—
119	C₂×Q₈×C₄₃	—	2	1	no	—
120	C₂×Q₈×C₄₃	—	2	1	no	—
121	C₂×Q₈×C₄₃	—	2	1	no	—
122	C₂×Q₈×C₄₃	—	2	1	no	—
123	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₃	—	2	1	no	—
125	C₂²×C₄×C₄₃	—	2	1	no	—
126	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
129	C₂×C₂²⋊D₄₃	—	2	2	no	—
130	C₂²×Dic₄₃	—	2	2	no	—
131	#10621898	—	2	2	no	—
132	#10621898	—	2	2	no	—
133	#10621898	—	2	2	no	—
134	#10621898	—	2	2	no	—
135	C₂×D₁₇₂	—	2	1	no	—
136	C₂×D₁₇₂	—	2	1	no	—
137	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
138	C₂×C₄×D₄₃	—	2	2	no	—
139	C₂×Dic₈₆	—	2	2	no	—
140	C₂×Dic₈₆	—	2	2	no	—
141	C₂×Dic₈₆	—	2	2	no	—
142	C₂×Dic₈₆	—	2	2	no	—
143	C₂×Dic₈₆	—	2	2	no	—
144	C₂×Dic₈₆	—	2	2	no	—
145	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
146	M₁₆×C₄₃	—	2	1	no	—
147	M₁₆×C₄₃	—	2	1	no	—
148	M₁₆×C₄₃	—	2	1	no	—
149	M₁₆×C₄₃	—	2	1	no	—
150	M₁₆×C₄₃	—	2	1	no	—
151	M₁₆×C₄₃	C₂×D₄	1	2	yes	—
152	M₁₆×C₄₃	C₂×D₄	1	2	yes	—
153	M₁₆×C₄₃	#41	1	2	yes	—
154	C₂×C₈×C₄₃	—	2	1	no	—
155	C₂×C₈×C₄₃	—	2	1	no	—
156	C₂×C₈×C₄₃	—	2	1	no	—
157	C₂×C₈×C₄₃	—	2	1	no	—
158	C₄⋊C₄×C₄₃	—	2	1	no	—
159	C₄⋊C₄×C₄₃	—	2	1	no	—
160	C₄⋊C₄×C₄₃	—	4	1	no	—
161	C₄⋊C₄×C₄₃	—	4	1	no	—
162	C₄²×C₄₃	—	4	1	no	—
163	C₄²×C₄₃	—	4	1	no	—
164	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
168	#10621885	—	4	4	no	—
169	#10621885	—	4	4	no	—
170	#10621885	—	4	4	no	—
171	#10621884	—	4	4	no	—
172	(C₂×D₄₃)⋊C₄	—	2	2	no	—
173	(C₂×D₄₃)⋊C₄	—	2	2	no	—
174	C₄⋊Dic₄₃	—	2	1	no	—
175	C₄⋊Dic₄₃	—	2	1	no	—
176	C₄⋊Dic₄₃	—	4	1	no	—
177	C₄⋊Dic₄₃	—	4	1	no	—
178	C₄⋊Dic₄₃	—	4	1	no	—
179	C₄⋊Dic₄₃	—	4	1	no	—
180	#10621877	—	2	2	no	—
181	#10621877	—	2	2	no	—
182	C₂×C₄₃⋊C₈	—	2	2	no	—
183	C₂×C₄₃⋊C₈	—	2	2	no	—
184	C₂×C₄₃⋊C₈	—	2	2	no	—
185	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
186	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
187	Dic₁₇₂	—	4	4	no	—
188	Dic₁₇₂	—	4	4	no	—
189	#10621873	—	4	4	no	—
190	#10621873	—	4	4	no	—
191	#10621872	—	4	4	no	—
192	C₈×D₄₃	—	4	4	no	—
193	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
194	C₂²×D₄₃	—	2	2	no	—
195	Q₈×C₄₃	—	2	2	no	—
196	Q₈×C₄₃	—	2	2	no	—
197	Q₈×C₄₃	—	4	1	no	—
198	Q₈×C₄₃	—	4	1	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	2	2	no	—
201	C₂×C₄×C₄₃	—	4	1	no	—
202	C₂×C₄×C₄₃	—	4	1	no	—
203	C₂×C₄×C₄₃	—	4	1	no	—
204	C₂×C₄×C₄₃	—	4	1	no	—
205	C₂×C₄×C₄₃	—	8	1	no	—
206	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂²⋊D₄₃	—	4	2	no	—
217	C₂²⋊D₄₃	—	4	2	no	—
218	C₂×Dic₄₃	—	2	2	no	—
219	C₂×Dic₄₃	—	4	2	no	—
220	C₂×Dic₄₃	—	4	2	no	—
221	C₂×Dic₄₃	—	4	2	no	—
222	D₁₇₂	—	2	2	no	—
223	D₁₇₂	—	2	2	no	—
224	D₁₇₂	—	4	2	no	—
225	D₁₇₂	—	8	1	no	—
226	C₄×D₄₃	—	4	2	no	—
227	C₄×D₄₃	—	4	2	no	—
228	Dic₈₆	—	2	2	no	—
229	Dic₈₆	—	2	2	no	—
230	Dic₈₆	—	4	2	no	—
231	Dic₈₆	—	4	2	no	—
232	Dic₈₆	—	4	2	no	—
233	Dic₈₆	—	4	2	no	—
234	C₈×C₄₃	—	2	2	no	—
235	C₈×C₄₃	—	2	2	no	—
236	C₈×C₄₃	—	2	2	no	—
237	C₈×C₄₃	—	4	1	no	—
238	C₄₃⋊C₈	—	2	2	no	—
239	C₄₃⋊C₈	—	2	2	no	—
240	C₄₃⋊C₈	—	4	2	no	—
241	#25406	—	43	1	no	maximal, Sylow
242	C₂²×C₄₃	—	2	1	no	—
243	C₂²×C₄₃	—	2	1	no	—
244	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
245	C₂²×C₄₃	#532	1	1	yes	characteristic
246	C₂²×C₄₃	#540	1	1	yes	characteristic
247	C₂×D₄₃	—	4	2	no	—
248	C₂×D₄₃	—	4	2	no	—
249	C₂×D₄₃	—	4	2	no	—
250	C₄×C₄₃	—	2	1	no	—
251	C₄×C₄₃	—	2	1	no	—
252	C₄×C₄₃	—	2	1	no	—
253	C₄×C₄₃	—	4	2	no	—
254	C₄×C₄₃	—	8	1	no	—
255	C₄×C₄₃	#473	1	2	yes	complemented
256	C₄×C₄₃	D₄²	1	1	yes	characteristic
257	C₄×C₄₃	D₄²	1	1	yes	characteristic
258	C₄×C₄₃	#546	1	1	yes	characteristic
259	C₄×C₄₃	#550	1	1	yes	characteristic
260	Dic₄₃	—	4	2	no	—
261	Dic₄₃	—	8	2	no	—
262	#3152	—	43	1	no	—
263	C₂×#473	—	43	2	no	—
264	#3037	—	43	1	no	—
265	C₂×#462	—	43	1	no	—
266	#2935	—	43	1	no	—
267	#2052	—	43	2	no	—
268	#2020	—	43	2	no	—
269	#1966	—	43	1	no	—
270	#1950	—	43	1	no	—
271	#1908	—	43	2	no	—
272	C₄×#101	D₄₃	1	1	yes	characteristic, complemented
273	C₂×C₄₃	—	2	1	no	—
274	C₂×C₄₃	—	2	1	no	—
275	C₂×C₄₃	#2428	1	1	yes	characteristic
276	C₂×C₄₃	C₂×#473	1	1	yes	characteristic
277	C₂×C₄₃	#3069	1	1	yes	characteristic
278	D₄₃	—	8	2	no	—
279	C₂×#137	—	43	2	no	—
280	C₂×#137	—	43	2	no	—
281	C₂×#137	—	43	2	no	—
282	C₂²×Q₁₆	—	43	2	no	—
283	C₂×#131	—	43	2	no	—
284	#532	—	43	1	no	—
285	C₂×C₄⋊Q₈	—	43	1	no	—
286	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
287	#497	—	86	2	no	—
288	#494	—	86	1	no	—
289	#492	—	86	1	no	—
290	#473	—	86	8	no	—
291	#464	—	86	2	no	—
292	#462	—	86	1	no	—
293	#462	—	86	2	no	—
294	#462	—	86	1	no	—
295	#462	—	86	1	no	—
296	#460	—	86	1	no	—
297	#436	—	86	1	no	—
298	#435	—	86	2	no	—
299	C₈×D₄	—	86	1	no	—
300	C₂×#108	—	43	2	no	—
301	#423	—	43	1	no	—
302	C₂×C₄⋊C₈	—	43	1	no	—
303	#417	—	43	2	no	—
304	C₂×#103	—	43	2	no	—
305	C₂×#101	—	43	2	no	—
306	C₂×#101	—	43	2	no	—
307	C₂×#101	C₂×D₄₃	1	1	yes	characteristic
308	C₂×#101	C₂×D₄₃	1	1	yes	characteristic
309	#408	—	43	2	no	—
310	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
311	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
312	#343	C₂×D₄₃	1	1	yes	characteristic
313	#343	C₂×D₄₃	1	1	yes	characteristic
314	#341	—	43	2	no	—
315	C₄₃	#25406	1	1	yes	characteristic, complemented, Sylow
316	C₂×#41	—	43	2	no	—
317	C₂²×Q₈	—	43	2	no	—
318	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
319	#137	—	86	4	no	—
320	#137	—	86	4	no	—
321	#137	—	86	4	no	—
322	#137	—	172	2	no	—
323	#137	—	172	2	no	—
324	#137	—	172	2	no	—
325	C₂×Q₁₆	—	86	2	no	—
326	C₂×Q₁₆	—	86	2	no	—
327	C₂×Q₁₆	—	86	2	no	—
328	C₂×Q₁₆	—	86	2	no	—
329	C₂×Q₁₆	—	86	2	no	—
330	C₂×Q₁₆	—	86	4	no	—
331	C₂×Q₁₆	—	172	2	no	—
332	C₂×SD₁₆	—	86	2	no	—
333	C₂×SD₁₆	—	86	2	no	—
334	C₂×SD₁₆	—	86	2	no	—
335	#131	—	86	4	no	—
336	#131	—	172	2	no	—
337	C₂×M₁₆	—	43	2	no	—
338	C₂×M₁₆	—	86	2	no	—
339	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
340	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
341	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
342	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
343	C₂²×C₈	—	43	2	no	—
344	C₂²×C₈	—	86	2	no	—
345	C₄⋊Q₈	—	43	1	no	—
346	C₄⋊Q₈	—	86	1	no	—
347	C₄⋊Q₈	—	86	1	no	—
348	C₄⋊Q₈	—	86	1	no	—
349	C₄⋊Q₈	—	86	1	no	—
350	#127	—	43	1	no	—
351	#124	—	43	2	no	—
352	#121	—	86	1	no	—
353	#121	—	86	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×D₄	—	86	1	no	—
359	C₄×D₄	—	86	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	86	1	no	—
362	C₂×C₄⋊C₄	—	86	1	no	—
363	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
366	#108	—	86	4	no	—
367	C₄⋊C₈	—	43	1	no	—
368	C₄⋊C₈	—	43	2	no	—
369	C₄⋊C₈	—	43	1	no	—
370	C₄⋊C₈	—	86	1	no	—
371	C₄⋊C₈	—	86	1	no	—
372	#103	—	86	2	no	—
373	#103	—	86	2	no	—
374	#103	—	86	2	no	—
375	#102	—	86	2	no	—
376	#101	—	2	2	no	—
377	#101	—	86	4	no	—
378	#101	—	172	2	no	—
379	#101	D₁₇₂	1	4	yes	complemented
380	C₂²⋊C₈	—	86	2	no	—
381	C₂²⋊C₈	—	86	2	no	—
382	#97	—	2	1	no	—
383	#97	—	2	1	no	—
384	C₄×C₈	—	2	1	no	—
385	C₄×C₈	—	2	1	no	—
386	#41	—	86	2	no	—
387	#41	—	86	2	no	—
388	#41	—	86	2	no	—
389	#41	—	86	2	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	43	2	no	—
396	C₂×Q₈	—	86	2	no	—
397	C₂×Q₈	—	86	2	no	—
398	C₂×Q₈	—	86	2	no	—
399	C₂×Q₈	—	86	2	no	—
400	C₂×Q₈	—	86	2	no	—
401	C₂×Q₈	—	86	2	no	—
402	C₂×Q₈	C₂×D₁₇₂	1	2	yes	—
403	C₂×D₄	—	43	2	no	—
404	C₂×D₄	—	86	2	no	—
405	C₂×D₄	—	86	1	no	—
406	C₂×D₄	—	86	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	86	2	no	—
410	C₂²×C₄	—	86	2	no	—
411	C₂²×C₄	#10621898	1	1	yes	characteristic
412	C₂²×C₄	#10621898	1	1	yes	characteristic
413	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
414	Q₁₆	—	172	4	no	—
415	Q₁₆	—	172	4	no	—
416	Q₁₆	—	172	4	no	—
417	Q₁₆	—	172	4	no	—
418	Q₁₆	—	172	4	no	—
419	SD₁₆	—	172	4	no	—
420	SD₁₆	—	172	4	no	—
421	SD₁₆	—	172	4	no	—
422	M₁₆	—	2	1	no	—
423	M₁₆	—	2	1	no	—
424	M₁₆	—	2	1	no	—
425	M₁₆	—	2	1	no	—
426	M₁₆	—	2	1	no	—
427	M₁₆	—	86	2	no	—
428	M₁₆	—	86	2	no	—
429	M₁₆	—	172	4	no	—
430	M₁₆	C₂×D₁₇₂	1	2	yes	—
431	M₁₆	C₂×D₁₇₂	1	2	yes	—
432	M₁₆	#10621898	1	2	yes	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	43	2	no	—
438	C₂×C₈	—	43	2	no	—
439	C₂×C₈	—	86	2	no	—
440	C₂×C₈	—	86	2	no	—
441	C₂×C₈	—	86	2	no	—
442	C₂×C₈	—	172	4	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₄⋊C₄	—	4	1	no	—
447	C₄⋊C₄	—	86	1	no	—
448	C₄⋊C₄	—	86	1	no	—
449	C₄⋊C₄	—	172	1	no	—
450	C₄⋊C₄	—	172	1	no	—
451	C₄⋊C₄	—	172	1	no	—
452	C₄⋊C₄	—	172	1	no	—
453	C₂²⋊C₄	—	86	2	no	—
454	C₂²⋊C₄	—	86	2	no	—
455	C₄²	—	4	1	no	—
456	C₄²	—	4	1	no	—
457	C₄²	D₄×D₄₃	1	1	yes	characteristic
458	C₄²	D₄×D₄₃	1	1	yes	characteristic
459	C₄²	D₄×D₄₃	1	1	yes	characteristic
460	C₄²	D₄×D₄₃	1	1	yes	characteristic
461	C₂³	—	86	2	no	—
462	C₂³	C₂×#10621898	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	86	2	no	—
468	Q₈	—	86	2	no	—
469	Q₈	—	172	2	no	—
470	Q₈	—	172	2	no	—
471	Q₈	—	172	2	no	—
472	Q₈	—	172	2	no	—
473	D₄	—	86	2	no	—
474	D₄	—	86	2	no	—
475	D₄	—	344	1	no	—
476	D₄	—	172	2	no	—
477	D₄	—	172	2	no	—
478	D₄	—	172	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	8	1	no	—
486	C₂×C₄	—	86	2	no	—
487	C₂×C₄	—	172	2	no	—
488	C₂×C₄	—	172	2	no	—
489	C₂×C₄	—	172	2	no	—
490	C₂×C₄	—	172	2	no	—
491	C₂×C₄	—	172	2	no	—
492	C₂×C₄	#13063298	1	1	yes	characteristic
493	C₂×C₄	#13063298	1	1	yes	characteristic
494	C₂×C₄	#13063298	1	1	yes	characteristic
495	C₂×C₄	#13063298	1	1	yes	characteristic
496	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
497	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
499	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
500	C₂×C₄	#13063371	1	1	yes	characteristic
501	C₂×C₄	#13063371	1	1	yes	characteristic
502	C₈	—	2	2	no	—
503	C₈	—	2	2	no	—
504	C₈	—	2	2	no	—
505	C₈	—	4	1	no	—
506	C₈	—	86	2	no	—
507	C₈	—	86	2	no	—
508	C₈	—	172	2	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	172	2	no	—
512	C₂²	—	172	2	no	—
513	C₂²	—	172	2	no	—
514	C₂²	C₂×#13063298	1	1	yes	characteristic
515	C₂²	#14583449	1	1	yes	characteristic
516	C₂²	#14583504	1	1	yes	characteristic
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	8	1	no	—
522	C₄	—	344	2	no	—
523	C₄	—	172	2	no	—
524	C₄	#14583173	1	2	yes	complemented
525	C₄	D₄×D₁₇₂	1	1	yes	characteristic
526	C₄	D₄×D₁₇₂	1	1	yes	characteristic
527	C₄	#14583545	1	1	yes	characteristic
528	C₄	#14583570	1	1	yes	characteristic
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	344	2	no	—
532	C₂	#19138183	1	1	yes	characteristic
533	C₂	C₂×#14583173	1	1	yes	characteristic
534	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×#101×C₄₃	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#14583449	C₂²
hypercenter	C₄×#101	D₄₃
hypocenter	C₄₃	#25406
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#101

Complements

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

N	H ≅ G/N	type
2. C₂×#14583173	C₂	semidirect
4. C₂×#14583109	C₂	semidirect
6. #19135897	C₂	semidirect
7. #19135715	C₂	semidirect
8. #19135439	C₂	semidirect
9. #19135370	C₂	semidirect
10. #19135111	C₂	semidirect
11. C₄×#101×C₄₃	C₂	semidirect
113. #101×C₄₃	D₄	semidirect
255. C₄×C₄₃	#473	semidirect
272. C₄×#101	D₄₃	semidirect
315. C₄₃	#25406	semidirect
379. #101	D₁₇₂	semidirect
524. C₄	#14583173	semidirect

Maximal subgroups

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

subgroup	index
#19145054	2
C₂×#14583173	2
#19144067	2
C₂×#14583109	2
#19143341	2
#19135897	2
#19135715	2
#19135439	2
#19135370	2
#19135111	2
C₄×#101×C₄₃	2
#25406	43