Subgroups — #25103043

Order 11008.

922 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144052	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583017	C₂	1	2	yes	maximal, complemented
3	#19143308	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#13063331	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135513	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135371	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135244	C₂	1	2	yes	maximal, complemented
8	#19134921	C₂	1	2	yes	maximal, complemented
9	#19134616	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134432	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	2	yes	—
13	C₂×#13063331	C₂²	1	2	yes	—
14	C₂×#13063331	C₂²	1	1	yes	characteristic
15	C₂×#13063331	C₂²	1	1	yes	characteristic
16	#14583449	C₂²	1	1	yes	characteristic
17	C₄×#10621898	C₂²	1	1	yes	characteristic
18	#14583122	C₄	1	2	yes	complemented
19	#14583115	C₄	1	2	yes	complemented
20	#14583110	C₄	1	1	yes	characteristic, complemented
21	#14583105	C₄	1	1	yes	characteristic, complemented
22	#14583100	C₄	1	1	yes	characteristic, complemented
23	#14583095	C₄	1	1	yes	characteristic, complemented
24	#14583017	—	2	8	no	—
25	#14582978	—	2	1	no	—
26	#14582978	—	2	1	no	—
27	C₈×D₁₇₂	—	2	1	no	—
28	C₈×D₁₇₂	—	2	1	no	—
29	C₂×#13063261	C₂²	1	2	yes	—
30	#14582923	C₂²	1	1	yes	characteristic
31	C₂×#13063253	C₂²	1	2	yes	—
32	C₂×#13063253	C₂²	1	2	yes	—
33	C₂×#13063253	C₂²	1	2	yes	—
34	#14582896	C₂²	1	2	yes	—
35	#14582865	C₂²	1	2	yes	—
36	#14582854	C₂²	1	1	yes	characteristic
37	#14582854	C₂²	1	1	yes	characteristic
38	#14582853	—	2	1	no	—
39	#14582853	—	2	1	no	—
40	C₄×#10621877	C₂²	1	1	yes	characteristic
41	C₄×#10621872	—	2	1	no	—
42	C₄×C₈×D₄₃	—	2	1	no	—
43	#14582664	C₂²	1	2	yes	—
44	#14582659	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
49	C₄₃×#336	C₂²	1	2	yes	—
50	C₂×#10621898	C₂³	1	2	yes	—
51	C₂×#10621898	C₂³	1	1	yes	characteristic
52	#13063347	—	2	4	no	—
53	#13063347	—	2	4	no	—
54	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
55	C₂×#10621873	C₂×C₄	1	2	yes	—
56	C₂×#10621873	C₂×C₄	1	2	yes	—
57	C₂×D₃₄₄	C₂×C₄	1	2	yes	—
58	#13063331	—	2	2	no	—
59	#13063331	—	2	2	no	—
60	#13063331	—	2	2	no	—
61	#13063331	—	2	4	no	—
62	#13063331	—	2	4	no	—
63	#13063331	D₄	1	4	yes	complemented
64	C₂×#10621877	C₂³	1	2	yes	—
65	C₂×#10621877	C₂³	1	1	yes	characteristic
66	C₂×#10621877	C₂³	1	1	yes	characteristic
67	C₂×#10621872	—	2	1	no	—
68	C₂×#10621872	—	2	1	no	—
69	C₂×#10621872	—	2	2	no	—
70	C₂×C₈×D₄₃	—	2	1	no	—
71	C₂×C₈×D₄₃	—	2	1	no	—
72	C₂×C₈×D₄₃	—	2	2	no	—
73	#13063325	C₂×C₄	1	1	yes	characteristic
74	#13063322	C₂×C₄	1	1	yes	characteristic
75	#13063313	C₂×C₄	1	2	yes	—
76	#13063299	—	2	1	no	—
77	#13063299	—	2	1	no	—
78	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
80	C₄×D₁₇₂	—	2	1	no	—
81	C₄×D₁₇₂	—	2	1	no	—
82	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
83	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
84	C₄×C₂²⋊D₄₃	—	2	1	no	—
85	C₄×C₂²⋊D₄₃	—	2	1	no	—
86	#13063284	C₂³	1	1	yes	characteristic
87	#13063282	—	2	1	no	—
88	C₄²×D₄₃	—	2	1	no	—
89	#13063261	—	2	4	no	—
90	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
91	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
92	#13063253	—	2	4	no	—
93	#13063253	—	2	4	no	—
94	#13063253	—	2	4	no	—
95	#13063250	C₂×C₄	1	2	yes	—
96	#13063250	C₂×C₄	1	2	yes	—
97	#13063247	C₂×C₄	1	2	yes	—
98	#13063247	C₂×C₄	1	2	yes	—
99	(C₂×D₄₃)⋊C₈	—	2	2	no	—
100	(C₂×D₄₃)⋊C₈	—	2	2	no	—
101	#13063236	—	2	1	no	—
102	#13063235	—	2	1	no	—
103	#13063235	—	2	1	no	—
104	C₄×C₄₃⋊C₈	—	2	1	no	—
105	C₈×Dic₄₃	—	2	1	no	—
106	C₈×Dic₄₃	—	2	1	no	—
107	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
111	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
112	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
114	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
115	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
116	C₄×C₈×C₄₃	—	2	4	no	—
117	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
118	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
119	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
120	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
121	#95×C₄₃	—	2	1	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
126	C₂×C₂²⋊D₄₃	—	2	1	no	—
127	C₂×C₂²⋊D₄₃	—	2	2	no	—
128	#10621898	—	2	1	no	—
129	#10621898	—	2	1	no	—
130	#10621898	—	2	2	no	—
131	#10621898	—	2	2	no	—
132	#10621898	—	2	2	no	—
133	#10621898	—	2	2	no	—
134	#10621898	C₂×D₄	1	2	yes	—
135	#10621898	#41	1	2	yes	—
136	C₂×D₁₇₂	—	2	1	no	—
137	C₂×D₁₇₂	—	2	1	no	—
138	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
139	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×D₄₃	—	2	1	no	—
141	C₂×C₄×D₄₃	—	2	1	no	—
142	C₂×C₄×D₄₃	—	2	1	no	—
143	C₂×C₄×D₄₃	—	2	2	no	—
144	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
145	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₄₃	—	2	2	no	—
147	C₂×C₈×C₄₃	—	2	1	no	—
148	C₂×C₈×C₄₃	—	2	1	no	—
149	C₂×C₈×C₄₃	—	2	2	no	—
150	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₄₃	#41	1	2	yes	—
158	C₄⋊C₄×C₄₃	—	2	4	no	—
159	C₄²×C₄₃	—	2	2	no	—
160	C₄²×C₄₃	—	2	2	no	—
161	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
165	C₂²⋊Dic₄₃	—	2	1	no	—
166	(C₂×D₄₃)⋊C₄	—	2	1	no	—
167	(C₂×D₄₃)⋊C₄	—	2	1	no	—
168	(C₂×D₄₃)⋊C₄	—	2	2	no	—
169	(C₂×D₄₃)⋊C₄	—	2	2	no	—
170	C₄⋊Dic₄₃	—	2	1	no	—
171	C₄⋊Dic₄₃	—	2	1	no	—
172	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
173	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
174	Dic₄₃⋊C₄	—	2	1	no	—
175	Dic₄₃⋊C₄	—	2	1	no	—
176	C₄×Dic₄₃	—	2	1	no	—
177	C₄×Dic₄₃	—	2	1	no	—
178	C₄×Dic₄₃	—	2	1	no	—
179	#10621877	—	2	1	no	—
180	#10621877	—	2	1	no	—
181	#10621877	—	2	2	no	—
182	#10621877	—	2	2	no	—
183	#10621877	C₂×D₄	1	2	yes	—
184	#10621877	#41	1	2	yes	—
185	C₂×C₄₃⋊C₈	—	2	1	no	—
186	C₂×C₄₃⋊C₈	—	2	1	no	—
187	C₂×C₄₃⋊C₈	—	2	2	no	—
188	Dic₁₇₂	—	2	4	no	—
189	D₃₄₄	—	2	4	no	—
190	#10621873	—	2	4	no	—
191	#10621873	—	2	4	no	—
192	#10621872	—	2	4	no	—
193	#10621872	—	2	4	no	—
194	#10621872	—	4	4	no	—
195	C₈×D₄₃	—	2	4	no	—
196	C₈×D₄₃	—	2	4	no	—
197	C₈×D₄₃	—	4	4	no	—
198	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
199	C₂²×D₄₃	—	2	1	no	—
200	C₂²×D₄₃	—	2	2	no	—
201	C₂×C₄×C₄₃	—	2	2	no	—
202	C₂×C₄×C₄₃	—	2	4	no	—
203	C₂×C₄×C₄₃	—	4	1	no	—
204	C₂×C₄×C₄₃	—	4	2	no	—
205	C₂×C₄×C₄₃	—	4	2	no	—
206	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂³×C₄	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	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
216	C₂²⋊D₄₃	—	2	2	no	—
217	C₂²⋊D₄₃	—	2	2	no	—
218	C₂²⋊D₄₃	—	4	2	no	—
219	C₂²⋊D₄₃	—	4	2	no	—
220	C₂×Dic₄₃	—	2	1	no	—
221	C₂×Dic₄₃	—	2	1	no	—
222	C₂×Dic₄₃	—	2	1	no	—
223	C₂×Dic₄₃	—	2	2	no	—
224	D₁₇₂	—	2	2	no	—
225	D₁₇₂	—	2	1	no	—
226	D₁₇₂	—	2	2	no	—
227	D₁₇₂	—	4	2	no	—
228	D₁₇₂	—	4	2	no	—
229	D₁₇₂	C₄×D₄	1	2	yes	—
230	C₄×D₄₃	—	2	2	no	—
231	C₄×D₄₃	—	2	2	no	—
232	C₄×D₄₃	—	4	2	no	—
233	C₄×D₄₃	—	4	2	no	—
234	C₄×D₄₃	—	4	2	no	—
235	C₄×D₄₃	—	4	2	no	—
236	Dic₈₆	—	2	1	no	—
237	Dic₈₆	—	2	2	no	—
238	Dic₈₆	—	2	2	no	—
239	Dic₈₆	C₄×D₄	1	2	yes	—
240	C₈×C₄₃	—	2	2	no	—
241	C₈×C₄₃	—	2	2	no	—
242	C₈×C₄₃	—	2	1	no	—
243	C₈×C₄₃	—	2	1	no	—
244	C₈×C₄₃	#121	1	2	yes	—
245	C₈×C₄₃	#121	1	2	yes	—
246	C₄₃⋊C₈	—	2	2	no	—
247	C₄₃⋊C₈	—	2	2	no	—
248	C₄₃⋊C₈	—	4	2	no	—
249	#21517	—	43	1	no	maximal, Sylow
250	C₂²×C₄₃	—	2	1	no	—
251	C₂²×C₄₃	—	2	1	no	—
252	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₄₃	#529	1	1	yes	characteristic
254	C₂²×C₄₃	#532	1	1	yes	characteristic
255	C₂×D₄₃	—	2	2	no	—
256	C₂×D₄₃	—	4	1	no	—
257	C₂×D₄₃	—	4	1	no	—
258	C₂×D₄₃	—	4	2	no	—
259	C₂×D₄₃	—	4	2	no	—
260	C₂×D₄₃	—	4	2	no	—
261	C₄×C₄₃	—	2	1	no	—
262	C₄×C₄₃	—	2	1	no	—
263	C₄×C₄₃	—	2	1	no	—
264	C₄×C₄₃	—	4	4	no	—
265	C₄×C₄₃	#443	1	2	yes	complemented
266	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
267	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
268	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
269	C₄×C₄₃	#525	1	1	yes	characteristic
270	Dic₄₃	—	2	2	no	—
271	Dic₄₃	—	4	1	no	—
272	Dic₄₃	—	4	1	no	—
273	Dic₄₃	—	4	2	no	—
274	#3035	—	43	1	no	—
275	C₂×#443	—	43	2	no	—
276	#2931	—	43	1	no	—
277	C₄×#131	—	43	1	no	—
278	#1980	—	43	1	no	—
279	#1950	—	43	1	no	—
280	#1929	—	43	2	no	—
281	#1876	—	43	2	no	—
282	#1806	—	43	1	no	—
283	C₈×C₄⋊C₄	D₄₃	1	1	yes	characteristic, complemented
284	#1764	—	43	2	no	—
285	C₂×C₄₃	—	2	1	no	—
286	C₂×C₄₃	—	2	1	no	—
287	C₂×C₄₃	C₄×#121	1	1	yes	characteristic
288	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
289	C₂×C₄₃	#2955	1	1	yes	characteristic
290	D₄₃	—	4	2	no	—
291	D₄₃	—	8	2	no	—
292	C₂×#135	—	43	2	no	—
293	C₂×#131	—	43	1	no	—
294	C₂×#131	—	43	1	no	—
295	C₂×#131	—	43	2	no	—
296	#532	—	43	1	no	—
297	C₄×#41	—	43	1	no	—
298	#464	—	43	2	no	—
299	#463	—	43	2	no	—
300	#462	—	43	1	no	—
301	#461	—	43	1	no	—
302	#460	—	43	1	no	—
303	#459	—	43	1	no	—
304	#443	—	86	8	no	—
305	#436	—	86	1	no	—
306	#436	—	86	1	no	—
307	C₈×D₄	—	86	1	no	—
308	C₈×D₄	—	86	1	no	—
309	C₂×#108	—	43	2	no	—
310	#423	—	43	1	no	—
311	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
312	C₂×#104	—	43	2	no	—
313	C₂×#104	—	43	2	no	—
314	C₂×#104	—	43	2	no	—
315	#416	—	43	2	no	—
316	#408	—	43	2	no	—
317	#405	—	43	1	no	—
318	#405	—	43	1	no	—
319	#405	—	86	1	no	—
320	#405	—	86	1	no	—
321	C₄×M₁₆	—	43	1	no	—
322	C₄×M₁₆	—	86	1	no	—
323	C₂×C₄×C₈	—	86	1	no	—
324	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
325	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
326	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
327	#341	—	43	2	no	—
328	#339	—	43	2	no	—
329	#336	C₂×D₄₃	1	2	yes	—
330	C₄₃	#21517	1	1	yes	characteristic, complemented, Sylow
331	C₂×#41	—	43	1	no	—
332	C₂×#41	—	43	2	no	—
333	#135	—	86	4	no	—
334	#135	—	86	4	no	—
335	C₂×Q₁₆	—	43	2	no	—
336	C₂×SD₁₆	—	43	2	no	—
337	C₂×SD₁₆	—	43	2	no	—
338	C₂×D₈	—	43	2	no	—
339	#131	—	43	4	no	—
340	#131	—	86	2	no	—
341	#131	—	86	2	no	—
342	#131	—	86	2	no	—
343	#131	—	86	4	no	—
344	#131	—	86	4	no	—
345	C₂×M₁₆	—	43	1	no	—
346	C₂×M₁₆	—	43	1	no	—
347	C₂×M₁₆	—	43	2	no	—
348	C₂×M₁₆	—	86	1	no	—
349	C₂×M₁₆	—	86	1	no	—
350	C₂×M₁₆	—	86	2	no	—
351	C₂²×C₈	—	86	1	no	—
352	C₂²×C₈	—	86	1	no	—
353	C₂²×C₈	—	86	2	no	—
354	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
355	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
356	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
357	C₄⋊Q₈	—	43	1	no	—
358	#127	—	43	1	no	—
359	#124	—	43	2	no	—
360	#121	—	86	1	no	—
361	#121	—	86	1	no	—
362	C₄×Q₈	—	43	1	no	—
363	C₄×Q₈	—	43	1	no	—
364	C₄×D₄	—	43	1	no	—
365	C₄×D₄	—	43	1	no	—
366	C₄×D₄	—	86	1	no	—
367	C₄×D₄	—	86	1	no	—
368	C₄×D₄	—	86	1	no	—
369	C₄×D₄	—	86	1	no	—
370	#117	—	43	1	no	—
371	#117	—	86	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄²	—	86	1	no	—
374	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
375	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
376	#108	—	86	4	no	—
377	C₄⋊C₈	—	86	1	no	—
378	C₄⋊C₈	—	86	1	no	—
379	C₄⋊C₈	C₄×D₄₃	1	1	yes	characteristic
380	C₄⋊C₈	C₄×D₄₃	1	1	yes	characteristic
381	C₄⋊C₈	C₄×D₄₃	1	2	yes	—
382	#104	—	86	4	no	—
383	#104	—	86	4	no	—
384	#104	—	86	4	no	—
385	#103	—	43	2	no	—
386	#103	—	43	2	no	—
387	#102	—	43	2	no	—
388	#102	—	43	2	no	—
389	C₂²⋊C₈	—	86	2	no	—
390	C₂²⋊C₈	—	86	2	no	—
391	#97	—	86	1	no	—
392	#97	—	86	1	no	—
393	#97	—	86	1	no	—
394	C₄×C₈	—	2	4	no	—
395	C₄×C₈	—	86	1	no	—
396	C₄×C₈	—	86	1	no	—
397	C₄×C₈	—	86	1	no	—
398	C₄×C₈	D₁₇₂	1	1	yes	characteristic
399	C₄×C₈	D₁₇₂	1	1	yes	characteristic
400	C₄×C₈	D₁₇₂	1	1	yes	characteristic
401	C₄×C₈	D₁₇₂	1	1	yes	characteristic
402	#95	—	2	1	no	—
403	#41	—	43	2	no	—
404	#41	—	43	2	no	—
405	#41	—	86	1	no	—
406	#41	—	86	1	no	—
407	#41	—	86	2	no	—
408	#41	—	86	2	no	—
409	#41	—	86	2	no	—
410	#41	—	86	2	no	—
411	C₂×Q₈	—	43	1	no	—
412	C₂×Q₈	—	43	2	no	—
413	C₂×D₄	—	43	1	no	—
414	C₂×D₄	—	43	2	no	—
415	C₂×D₄	—	86	1	no	—
416	C₂×D₄	—	86	2	no	—
417	C₂×D₄	—	86	1	no	—
418	C₂×D₄	—	86	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	86	1	no	—
421	C₂²×C₄	—	86	1	no	—
422	C₂²×C₄	—	86	1	no	—
423	C₂²×C₄	—	86	2	no	—
424	C₂²×C₄	#10621898	1	1	yes	characteristic
425	C₂²×C₄	#10621898	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
427	Q₁₆	—	86	4	no	—
428	SD₁₆	—	86	4	no	—
429	SD₁₆	—	86	4	no	—
430	D₈	—	86	4	no	—
431	M₁₆	—	43	2	no	—
432	M₁₆	—	43	2	no	—
433	M₁₆	—	86	4	no	—
434	M₁₆	—	86	1	no	—
435	M₁₆	—	86	1	no	—
436	M₁₆	—	86	4	no	—
437	M₁₆	—	86	2	no	—
438	M₁₆	—	86	2	no	—
439	M₁₆	—	172	4	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	86	4	no	—
445	C₂×C₈	—	86	1	no	—
446	C₂×C₈	—	86	1	no	—
447	C₂×C₈	—	86	4	no	—
448	C₂×C₈	—	86	2	no	—
449	C₂×C₈	—	172	4	no	—
450	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
451	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
452	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
453	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
454	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
455	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
456	C₂×C₈	D₄×D₄₃	1	2	yes	—
457	C₂×C₈	#10621902	1	2	yes	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	43	1	no	—
460	C₄⋊C₄	—	43	1	no	—
461	C₄⋊C₄	—	86	1	no	—
462	C₄⋊C₄	—	86	1	no	—
463	C₄⋊C₄	—	86	1	no	—
464	C₄⋊C₄	—	86	1	no	—
465	C₂²⋊C₄	—	86	1	no	—
466	C₂²⋊C₄	—	86	1	no	—
467	C₂²⋊C₄	—	86	1	no	—
468	C₂²⋊C₄	—	86	2	no	—
469	C₂²⋊C₄	—	86	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	86	1	no	—
473	C₄²	—	86	1	no	—
474	C₄²	—	86	1	no	—
475	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
476	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
477	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
478	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
479	C₂³	—	86	1	no	—
480	C₂³	—	86	2	no	—
481	C₂³	C₂×#10621898	1	1	yes	characteristic
482	Q₈	—	43	2	no	—
483	Q₈	—	86	1	no	—
484	Q₈	—	86	2	no	—
485	Q₈	—	86	2	no	—
486	D₄	—	43	2	no	—
487	D₄	—	86	2	no	—
488	D₄	—	86	2	no	—
489	D₄	—	86	2	no	—
490	D₄	—	86	1	no	—
491	D₄	—	86	2	no	—
492	D₄	—	172	2	no	—
493	D₄	—	172	2	no	—
494	D₄	—	172	2	no	—
495	D₄	—	172	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	86	1	no	—
502	C₂×C₄	—	86	2	no	—
503	C₂×C₄	—	86	2	no	—
504	C₂×C₄	—	86	1	no	—
505	C₂×C₄	—	86	1	no	—
506	C₂×C₄	—	86	2	no	—
507	C₂×C₄	—	172	2	no	—
508	C₂×C₄	—	172	2	no	—
509	C₂×C₄	—	172	2	no	—
510	C₂×C₄	—	172	2	no	—
511	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
512	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
513	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
514	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
516	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
518	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
519	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
520	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
521	C₈	—	2	2	no	—
522	C₈	—	2	2	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	86	2	no	—
526	C₈	—	86	2	no	—
527	C₈	—	172	2	no	—
528	C₈	#13063300	1	2	yes	—
529	C₈	#13063300	1	2	yes	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	86	2	no	—
533	C₂²	—	172	2	no	—
534	C₂²	—	172	2	no	—
535	C₂²	—	172	2	no	—
536	C₂²	—	172	1	no	—
537	C₂²	—	172	1	no	—
538	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
539	C₂²	#14583436	1	1	yes	characteristic
540	C₂²	#14583446	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	4	4	no	—
545	C₄	—	86	2	no	—
546	C₄	—	172	1	no	—
547	C₄	—	172	1	no	—
548	C₄	—	172	2	no	—
549	C₄	#14583017	1	2	yes	complemented
550	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
551	C₄	C₄×#10621902	1	1	yes	characteristic
552	C₄	C₂×#13063300	1	1	yes	characteristic
553	C₄	#14583411	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	344	2	no	—
557	C₂	—	172	2	no	—
558	C₂	C₄×#13063300	1	1	yes	characteristic
559	C₂	C₂×#14583017	1	1	yes	characteristic
560	C₂	#19143499	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₈×C₄⋊C₄×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#19144052	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₄₃
hypocenter	C₄₃	#21517
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#14583017	C₂	semidirect
3. #19143308	C₂	semidirect
4. C₄×#13063331	C₂	semidirect
5. #19135513	C₂	semidirect
6. #19135371	C₂	semidirect
7. #19135244	C₂	semidirect
8. #19134921	C₂	semidirect
9. #19134616	C₂	semidirect
10. #19134432	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₃	C₂	semidirect
18. #14583122	C₄	semidirect
19. #14583115	C₄	semidirect
20. #14583110	C₄	semidirect
21. #14583105	C₄	semidirect
22. #14583100	C₄	semidirect
23. #14583095	C₄	semidirect
63. #13063331	D₄	semidirect
265. C₄×C₄₃	#443	semidirect
283. C₈×C₄⋊C₄	D₄₃	semidirect
330. C₄₃	#21517	semidirect
549. C₄	#14583017	semidirect

Maximal subgroups

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

subgroup	index
#19144052	2
C₂×#14583017	2
#19143308	2
C₄×#13063331	2
#19135513	2
#19135371	2
#19135244	2
#19134921	2
#19134616	2
#19134432	2
C₈×C₄⋊C₄×C₄₃	2
#21517	43