Subgroups — #25063296

Order 11008.

1306 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583449	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582923	C₂	1	1	yes	maximal, characteristic, complemented
3	#19133047	C₂	1	4	yes	maximal, complemented
4	#19133021	C₂	1	4	yes	maximal, complemented
5	#19132995	C₂	1	4	yes	maximal, complemented
6	C₂×C₄₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#10621898	—	2	1	no	—
8	C₂²×#10621877	—	2	1	no	—
9	#14583449	—	2	1	no	—
10	#14583449	—	2	1	no	—
11	#14583449	—	2	1	no	—
12	#14583449	—	2	1	no	—
13	#14583449	C₄	1	2	yes	—
14	#14583449	C₄	1	2	yes	—
15	#14583449	C₂²	1	2	yes	—
16	#14583449	C₂²	1	2	yes	—
17	C₂×#13063325	C₄	1	1	yes	characteristic
18	C₂×#13063322	C₄	1	1	yes	characteristic
19	C₂×#13063313	—	2	1	no	—
20	C₂×#13063299	—	2	1	no	—
21	C₂×#13063299	C₄	1	2	yes	—
22	C₂×C₄×D₁₇₂	—	2	1	no	—
23	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
24	#14582923	—	2	1	no	—
25	#14582923	—	2	1	no	—
26	#14582923	C₂²	1	2	yes	—
27	#14582923	C₂²	1	2	yes	complemented
28	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
29	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
30	#14582628	C₂²	1	16	yes	complemented
31	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#431	—	2	1	no	—
33	C₄₃×#431	—	2	1	no	—
34	C₄₃×#431	C₂²	1	2	yes	—
35	C₄₃×#431	C₂²	1	2	yes	complemented
36	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
37	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
38	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	complemented
39	C₂×#10621898	—	2	2	no	—
40	C₂×#10621898	—	2	2	no	—
41	C₂×#10621898	—	2	2	no	—
42	C₂×#10621898	—	2	2	no	—
43	C₂×#10621898	—	4	4	no	—
44	C₂×#10621898	—	4	4	no	—
45	C₂²×Dic₈₆	—	2	1	no	—
46	C₂²×D₁₇₂	—	2	1	no	—
47	C₂²×D₁₇₂	—	2	1	no	—
48	C₂²×D₁₇₂	C₂×C₄	1	2	yes	—
49	C₂²×C₂²⋊D₄₃	—	2	2	no	—
50	C₂²×C₄×D₄₃	—	2	2	no	—
51	C₂×#10621877	—	2	2	no	—
52	C₂×#10621877	—	2	2	no	—
53	C₂×#10621877	—	4	4	no	—
54	C₂²×C₄₃⋊C₈	—	2	2	no	—
55	#13063325	—	2	1	no	—
56	#13063325	—	2	1	no	—
57	#13063325	C₂×C₄	1	2	yes	—
58	#13063325	C₂×C₄	1	2	yes	—
59	#13063322	—	2	1	no	—
60	#13063322	—	2	1	no	—
61	#13063322	C₂×C₄	1	2	yes	—
62	#13063322	C₂×C₄	1	2	yes	—
63	#13063313	—	2	2	no	—
64	#13063313	—	2	2	no	—
65	#13063313	—	2	2	no	—
66	#13063313	—	2	2	no	—
67	#13063299	—	2	2	no	—
68	#13063299	—	2	2	no	—
69	#13063299	—	2	2	no	—
70	#13063299	—	2	2	no	—
71	#13063299	—	2	2	no	—
72	#13063299	—	2	2	no	—
73	#13063299	C₂×C₄	1	4	yes	—
74	#13063299	C₂×C₄	1	4	yes	—
75	C₄×D₁₇₂	—	2	2	no	—
76	C₄×D₁₇₂	—	2	2	no	—
77	C₄×D₁₇₂	—	2	2	no	—
78	C₄×D₁₇₂	—	2	2	no	—
79	C₄×D₁₇₂	—	2	2	no	—
80	C₄×D₁₇₂	—	2	2	no	—
81	C₄×D₁₇₂	C₂×C₄	1	4	yes	—
82	C₄×D₁₇₂	C₂³	1	4	yes	—
83	C₂×C₄⋊Dic₄₃	—	2	1	no	—
84	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
85	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
86	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
87	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
88	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
89	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
90	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
91	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
92	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
94	C₂²×C₈×C₄₃	—	2	2	no	—
95	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
107	C₄⋊C₈×C₄₃	—	2	2	no	—
108	C₄⋊C₈×C₄₃	—	2	2	no	—
109	C₂²⋊C₈×C₄₃	—	2	2	no	—
110	C₂²⋊C₈×C₄₃	—	2	2	no	—
111	C₄×C₈×C₄₃	—	2	2	no	—
112	C₄×C₈×C₄₃	C₂³	1	4	yes	—
113	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂³×D₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	4	2	no	—
116	C₂²×C₄×C₄₃	—	4	2	no	—
117	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	D₈	1	4	yes	—
127	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	—
128	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₂²⋊D₄₃	—	2	4	no	—
138	C₂×C₂²⋊D₄₃	—	2	4	no	—
139	C₂×C₂²⋊D₄₃	—	4	8	no	—
140	C₂²×Dic₄₃	—	2	2	no	—
141	#10621898	—	4	8	no	—
142	#10621898	—	4	8	no	—
143	#10621898	—	4	4	no	—
144	#10621898	—	4	4	no	—
145	#10621898	—	4	4	no	—
146	#10621898	—	4	4	no	—
147	C₂×D₁₇₂	—	2	2	no	—
148	C₂×D₁₇₂	—	2	2	no	—
149	C₂×D₁₇₂	—	2	2	no	—
150	C₂×D₁₇₂	—	2	2	no	—
151	C₂×D₁₇₂	—	2	2	no	—
152	C₂×D₁₇₂	—	4	4	no	—
153	C₂×D₁₇₂	—	4	4	no	—
154	C₂×D₁₇₂	—	4	4	no	—
155	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
156	C₂×C₄×D₄₃	—	2	4	no	—
157	C₂×C₄×D₄₃	—	2	4	no	—
158	C₂×C₄×D₄₃	—	4	4	no	—
159	C₂×C₄×D₄₃	—	4	4	no	—
160	C₂×Dic₈₆	—	2	2	no	—
161	C₂×Dic₈₆	—	2	2	no	—
162	C₂×Dic₈₆	—	4	4	no	—
163	C₂×C₈×C₄₃	—	2	4	no	—
164	C₂×C₈×C₄₃	—	4	4	no	—
165	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
166	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
181	(C₂×D₄₃)⋊C₄	—	2	4	no	—
182	(C₂×D₄₃)⋊C₄	—	2	4	no	—
183	(C₂×D₄₃)⋊C₄	—	2	4	no	—
184	(C₂×D₄₃)⋊C₄	—	2	4	no	—
185	C₄⋊Dic₄₃	—	2	2	no	—
186	C₄⋊Dic₄₃	—	2	2	no	—
187	C₄⋊Dic₄₃	—	2	2	no	—
188	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
189	#10621877	—	4	4	no	—
190	#10621877	—	4	4	no	—
191	C₂×C₄₃⋊C₈	—	2	4	no	—
192	C₂×C₄₃⋊C₈	—	4	4	no	—
193	C₂³×C₄₃	—	4	1	no	—
194	C₂³×C₄₃	—	4	1	no	—
195	C₂³×C₄₃	#102	1	4	yes	—
196	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×D₄₃	—	2	4	no	—
200	C₂²×D₄₃	—	4	4	no	—
201	C₂²×D₄₃	—	4	4	no	—
202	C₂²×D₄₃	—	4	4	no	—
203	C₂×C₄×C₄₃	—	2	2	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	2	2	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	2	2	no	—
209	C₂×C₄×C₄₃	—	4	1	no	—
210	C₂×C₄×C₄₃	—	4	1	no	—
211	C₂×C₄×C₄₃	—	4	1	no	—
212	C₂×C₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	—	4	1	no	—
214	C₂×C₄×C₄₃	—	4	1	no	—
215	C₂×C₄×C₄₃	#102	1	4	yes	—
216	C₂×C₄×C₄₃	#102	1	4	yes	—
217	C₂×C₄×C₄₃	#102	1	4	yes	—
218	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
228	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
229	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
230	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
231	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
232	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
233	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
236	C₂²⋊D₄₃	—	4	8	no	—
237	C₂²⋊D₄₃	—	4	8	no	—
238	C₂×Dic₄₃	—	2	4	no	—
239	C₂×Dic₄₃	—	4	4	no	—
240	D₁₇₂	—	2	8	no	—
241	D₁₇₂	—	4	4	no	—
242	D₁₇₂	—	4	4	no	—
243	D₁₇₂	—	4	4	no	—
244	D₁₇₂	—	4	4	no	—
245	D₁₇₂	—	4	4	no	—
246	C₄×D₄₃	—	4	4	no	—
247	C₄×D₄₃	—	4	4	no	—
248	C₄×D₄₃	—	4	8	no	—
249	Dic₈₆	—	4	4	no	—
250	Dic₈₆	—	4	4	no	—
251	C₈×C₄₃	—	4	4	no	—
252	C₄₃⋊C₈	—	4	4	no	—
253	#17485	—	43	1	no	maximal, Sylow
254	C₂²×C₄₃	—	2	1	no	—
255	C₂²×C₄₃	—	2	1	no	—
256	C₂²×C₄₃	—	2	1	no	—
257	C₂²×C₄₃	—	2	1	no	—
258	C₂²×C₄₃	—	2	1	no	—
259	C₂²×C₄₃	—	2	1	no	—
260	C₂²×C₄₃	—	4	4	no	—
261	C₂²×C₄₃	C₂×#102	1	2	yes	—
262	C₂²×C₄₃	C₂×#102	1	2	yes	—
263	C₂²×C₄₃	C₂×#102	1	2	yes	—
264	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×D₄₃	—	4	4	no	—
266	C₂×D₄₃	—	4	4	no	—
267	C₂×D₄₃	—	4	4	no	—
268	C₂×D₄₃	—	8	8	no	—
269	C₄×C₄₃	—	2	1	no	—
270	C₄×C₄₃	—	2	1	no	—
271	C₄×C₄₃	—	2	1	no	—
272	C₄×C₄₃	—	2	1	no	—
273	C₄×C₄₃	—	2	1	no	—
274	C₄×C₄₃	—	2	1	no	—
275	C₄×C₄₃	C₂×#102	1	2	yes	—
276	C₄×C₄₃	C₂×#102	1	2	yes	—
277	C₄×C₄₃	C₂×#102	1	2	yes	—
278	C₄×C₄₃	#421	1	2	yes	—
279	C₄×C₄₃	#568	1	2	yes	—
280	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
281	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
282	Dic₄₃	—	4	4	no	—
283	C₂×#532	—	43	1	no	—
284	C₂×#431	D₄₃	1	1	yes	characteristic, complemented
285	C₂×#423	—	43	1	no	—
286	#1492	—	43	4	no	—
287	#1486	—	43	4	no	—
288	#1480	—	43	4	no	—
289	C₂×C₄₃	—	2	2	no	—
290	C₂×C₄₃	—	2	2	no	—
291	C₂×C₄₃	—	2	2	no	—
292	C₂×C₄₃	#2879	1	1	yes	characteristic
293	C₂×C₄₃	C₂²×#102	1	1	yes	characteristic
294	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
295	D₄₃	—	8	4	no	—
296	C₂²×#41	—	86	1	no	—
297	C₂²×M₁₆	—	86	1	no	—
298	#532	—	43	2	no	—
299	#532	—	43	2	no	—
300	#532	—	43	2	no	—
301	#532	—	43	2	no	—
302	#532	—	86	1	no	—
303	#532	—	86	1	no	—
304	#532	—	86	1	no	—
305	#532	—	86	1	no	—
306	C₂×C₄⋊Q₈	—	43	1	no	—
307	C₂×#127	—	43	1	no	—
308	C₂×#124	—	86	1	no	—
309	C₂×#121	—	43	2	no	—
310	C₂×#121	—	86	1	no	—
311	C₂×C₄×D₄	—	43	2	no	—
312	C₂×C₄×D₄	—	86	1	no	—
313	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
314	#431	—	2	1	no	—
315	#431	—	2	1	no	—
316	#431	C₂×D₄₃	1	2	yes	—
317	#431	C₂×D₄₃	1	2	yes	complemented
318	#423	—	43	2	no	—
319	#423	—	43	2	no	—
320	#423	—	86	1	no	—
321	#423	—	86	1	no	—
322	C₂×C₄⋊C₈	—	2	1	no	—
323	C₂×C₄⋊C₈	—	43	2	no	—
324	C₂×C₄⋊C₈	—	86	1	no	—
325	C₂×C₂²⋊C₈	—	2	1	no	—
326	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	complemented
327	D₄⋊C₈	—	43	16	no	—
328	C₄₃	#17485	1	1	yes	characteristic, complemented, Sylow
329	C₂×#41	—	86	2	no	—
330	C₂×#41	—	86	2	no	—
331	C₂×#41	—	86	2	no	—
332	C₂×#41	—	86	2	no	—
333	C₂×#41	—	172	4	no	—
334	C₂×#41	—	172	4	no	—
335	C₂²×Q₈	—	86	1	no	—
336	C₂²×D₄	—	43	2	no	—
337	C₂²×D₄	—	86	2	no	—
338	C₂²×D₄	—	86	1	no	—
339	C₂²×D₄	—	86	1	no	—
340	C₂³×C₄	—	86	2	no	—
341	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
342	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
343	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
344	C₂×M₁₆	—	86	2	no	—
345	C₂×M₁₆	—	86	2	no	—
346	C₂×M₁₆	—	172	4	no	—
347	C₂²×C₈	—	2	2	no	—
348	C₂²×C₈	—	86	2	no	—
349	C₄⋊Q₈	—	43	2	no	—
350	C₄⋊Q₈	—	43	2	no	—
351	C₄⋊Q₈	—	86	1	no	—
352	C₄⋊Q₈	—	86	1	no	—
353	#127	—	43	2	no	—
354	#127	—	43	2	no	—
355	#127	—	86	1	no	—
356	#127	—	86	1	no	—
357	#124	—	86	2	no	—
358	#124	—	86	2	no	—
359	#124	—	86	2	no	—
360	#124	—	86	2	no	—
361	#121	—	43	4	no	—
362	#121	—	43	4	no	—
363	#121	—	86	2	no	—
364	#121	—	86	2	no	—
365	#121	—	86	2	no	—
366	#121	—	86	2	no	—
367	#121	—	86	2	no	—
368	#121	—	86	2	no	—
369	C₄×D₄	—	43	4	no	—
370	C₄×D₄	—	43	4	no	—
371	C₄×D₄	—	86	2	no	—
372	C₄×D₄	—	86	2	no	—
373	C₄×D₄	—	86	2	no	—
374	C₄×D₄	—	86	2	no	—
375	C₄×D₄	—	86	2	no	—
376	C₄×D₄	—	86	2	no	—
377	C₂×C₄⋊C₄	—	43	2	no	—
378	C₂×C₄⋊C₄	—	86	1	no	—
379	C₂×C₂²⋊C₄	—	86	2	no	—
380	C₂×C₂²⋊C₄	—	86	2	no	—
381	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
382	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
383	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
384	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
385	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
386	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
387	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
388	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
389	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
390	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
391	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
392	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
393	C₄⋊C₈	—	2	2	no	—
394	C₄⋊C₈	—	2	2	no	—
395	C₄⋊C₈	—	43	4	no	—
396	C₄⋊C₈	—	86	2	no	—
397	C₄⋊C₈	—	86	2	no	—
398	C₄⋊C₈	—	86	2	no	—
399	C₂²⋊C₈	—	2	2	no	—
400	C₂²⋊C₈	—	2	2	no	—
401	C₄×C₈	—	2	2	no	—
402	C₄×C₈	C₂²×D₄₃	1	4	yes	—
403	C₂⁴	—	86	2	no	—
404	C₂⁴	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
405	#41	—	172	8	no	—
406	#41	—	172	8	no	—
407	#41	—	172	4	no	—
408	#41	—	172	4	no	—
409	#41	—	172	4	no	—
410	#41	—	172	4	no	—
411	C₂×Q₈	—	86	2	no	—
412	C₂×Q₈	—	86	2	no	—
413	C₂×Q₈	—	172	4	no	—
414	C₂×D₄	—	43	4	no	—
415	C₂×D₄	—	86	4	no	—
416	C₂×D₄	—	86	4	no	—
417	C₂×D₄	—	86	2	no	—
418	C₂×D₄	—	86	2	no	—
419	C₂×D₄	—	86	2	no	—
420	C₂×D₄	—	86	2	no	—
421	C₂×D₄	—	86	2	no	—
422	C₂×D₄	—	172	4	no	—
423	C₂×D₄	—	172	4	no	—
424	C₂×D₄	—	172	8	no	—
425	C₂×D₄	—	172	4	no	—
426	C₂²×C₄	—	4	2	no	—
427	C₂²×C₄	—	4	2	no	—
428	C₂²×C₄	—	86	2	no	—
429	C₂²×C₄	—	86	4	no	—
430	C₂²×C₄	—	86	4	no	—
431	C₂²×C₄	—	172	4	no	—
432	C₂²×C₄	—	172	4	no	—
433	C₂²×C₄	#10621873	1	4	yes	—
434	C₂²×C₄	D₃₄₄	1	4	yes	—
435	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
436	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
437	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
438	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
439	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
440	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
441	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
442	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
443	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
450	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
452	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
453	M₁₆	—	172	4	no	—
454	M₁₆	—	172	4	no	—
455	C₂×C₈	—	2	4	no	—
456	C₂×C₈	—	4	4	no	—
457	C₂×C₈	—	86	4	no	—
458	C₂×C₈	—	172	4	no	—
459	C₄⋊C₄	—	43	4	no	—
460	C₄⋊C₄	—	86	2	no	—
461	C₄⋊C₄	—	86	2	no	—
462	C₄⋊C₄	—	86	2	no	—
463	C₂²⋊C₄	—	86	4	no	—
464	C₂²⋊C₄	—	86	4	no	—
465	C₂²⋊C₄	—	86	4	no	—
466	C₂²⋊C₄	—	86	4	no	—
467	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
468	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
469	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
470	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
471	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
472	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
473	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
474	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
475	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
476	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
477	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
478	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
479	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
480	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
481	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
482	C₄²	C₂³×D₄₃	1	1	yes	characteristic
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	86	4	no	—
486	C₂³	—	172	4	no	—
487	C₂³	—	172	4	no	—
488	C₂³	—	172	4	no	—
489	C₂³	#13063247	1	4	yes	—
490	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
491	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
492	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
493	Q₈	—	172	4	no	—
494	Q₈	—	172	4	no	—
495	D₄	—	86	8	no	—
496	D₄	—	172	4	no	—
497	D₄	—	172	4	no	—
498	D₄	—	172	8	no	—
499	D₄	—	172	8	no	—
500	D₄	—	172	4	no	—
501	D₄	—	172	4	no	—
502	D₄	—	172	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	86	4	no	—
516	C₂×C₄	—	172	4	no	—
517	C₂×C₄	—	172	8	no	—
518	C₂×C₄	—	172	4	no	—
519	C₂×C₄	—	172	4	no	—
520	C₂×C₄	#13063247	1	4	yes	—
521	C₂×C₄	#13063247	1	4	yes	—
522	C₂×C₄	#13063247	1	4	yes	—
523	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
524	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
525	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
526	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
527	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
528	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
529	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
530	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
531	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
532	C₂×C₄	C₂×D₃₄₄	1	2	yes	—
533	C₂×C₄	C₂×D₃₄₄	1	2	yes	—
534	C₂×C₄	C₂×D₃₄₄	1	2	yes	—
535	C₂×C₄	C₂×#10621873	1	2	yes	—
536	C₂×C₄	C₂×#10621873	1	2	yes	—
537	C₂×C₄	C₂×#10621873	1	2	yes	—
538	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
539	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
541	C₈	—	4	4	no	—
542	C₈	—	172	4	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	344	8	no	—
551	C₂²	—	172	4	no	—
552	C₂²	—	172	4	no	—
553	C₂²	—	172	4	no	—
554	C₂²	C₂×#13063247	1	2	yes	—
555	C₂²	C₂×#13063247	1	2	yes	—
556	C₂²	C₂×#13063247	1	2	yes	—
557	C₂²	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	172	4	no	—
565	C₄	C₂×#13063247	1	2	yes	—
566	C₄	C₂×#13063247	1	2	yes	—
567	C₄	C₂×#13063247	1	2	yes	—
568	C₄	#14582917	1	2	yes	—
569	C₄	#14583665	1	2	yes	—
570	C₄	C₂²×D₃₄₄	1	1	yes	characteristic
571	C₄	C₂²×#10621873	1	1	yes	characteristic
572	C₂	—	2	2	no	—
573	C₂	—	2	2	no	—
574	C₂	—	2	2	no	—
575	C₂	—	344	4	no	—
576	C₂	#19143039	1	1	yes	characteristic
577	C₂	C₂²×#13063247	1	1	yes	characteristic
578	C₂	C₂×#14582917	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#431	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	C₂×#14583449	C₂
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	C₂×#431	D₄₃
hypocenter	C₄₃	#17485
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
2. C₂×#14582923	C₂	semidirect
3. #19133047	C₂	semidirect
4. #19133021	C₂	semidirect
5. #19132995	C₂	semidirect
6. C₂×C₄₃×#431	C₂	semidirect
27. #14582923	C₂²	semidirect
29. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
30. #14582628	C₂²	semidirect
35. C₄₃×#431	C₂²	semidirect
38. C₂×C₄×C₈×C₄₃	C₂²	semidirect
284. C₂×#431	D₄₃	semidirect
317. #431	C₂×D₄₃	semidirect
326. C₂×C₄×C₈	C₂×D₄₃	semidirect
328. C₄₃	#17485	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583449	2
C₂×#14582923	2
#19133047	2
#19133021	2
#19132995	2
C₂×C₄₃×#431	2
#17485	43