Subgroups — #25004100

Order 11008.

854 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582947	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14582881	C₂	1	1	yes	maximal, characteristic
3	#19143039	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582867	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582663	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582663	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1738	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621898	C₂²	1	1	yes	characteristic
9	C₂²×#10621877	C₂²	1	1	yes	characteristic
10	C₂²×#10621877	C₂²	1	1	yes	characteristic
11	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
12	#14582947	—	2	2	no	—
13	#14582947	—	2	2	no	—
14	C₂×#13063260	—	2	2	no	—
15	#14582881	—	2	2	no	—
16	#14582881	—	2	2	no	—
17	C₂×#13063243	C₄	1	2	yes	—
18	C₂×#13063241	C₄	1	2	yes	—
19	#14582867	—	2	2	no	—
20	#14582867	—	2	2	no	—
21	#14582867	—	2	2	no	—
22	#14582865	—	2	2	no	—
23	#14582862	—	2	2	no	—
24	C₂×(C₂×D₄₃)⋊C₈	—	2	2	no	—
25	#14582663	—	2	2	no	—
26	#14582663	—	2	2	no	—
27	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#341	—	2	2	no	—
31	C₂×#10621898	—	2	1	no	—
32	C₂×#10621898	—	2	1	no	—
33	C₂×#10621898	—	2	1	no	—
34	C₂×#10621898	—	2	1	no	—
35	C₂×#10621898	—	2	1	no	—
36	C₂×#10621898	—	2	1	no	—
37	C₂×#10621898	—	2	1	no	—
38	C₂×#10621898	—	2	1	no	—
39	C₂×#10621898	—	2	1	no	—
40	C₂×#10621898	—	2	1	no	—
41	C₂×#10621898	—	2	1	no	—
42	C₂×#10621898	—	2	1	no	—
43	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₂²⋊D₄₃	Q₈	1	2	yes	—
46	C₂²×C₄×D₄₃	D₄	1	2	yes	—
47	C₂×#10621877	—	2	1	no	—
48	C₂×#10621877	—	2	1	no	—
49	C₂×#10621877	—	2	1	no	—
50	C₂×#10621877	—	2	1	no	—
51	C₂×#10621877	—	2	1	no	—
52	C₂×#10621877	—	2	1	no	—
53	C₂×#10621877	—	2	1	no	—
54	C₂×#10621877	—	2	1	no	—
55	C₂×#10621877	C₂×C₄	1	2	yes	—
56	C₂×#10621877	D₄	1	2	yes	—
57	C₂×#10621877	D₄	1	2	yes	—
58	C₂×#10621877	D₄	1	2	yes	—
59	C₂²×C₄₃⋊C₈	—	2	1	no	—
60	C₂²×C₄₃⋊C₈	—	2	1	no	—
61	C₂²×C₄₃⋊C₈	—	2	1	no	—
62	C₂²×C₄₃⋊C₈	—	2	1	no	—
63	C₂²×C₄₃⋊C₈	—	2	1	no	—
64	C₂²×C₄₃⋊C₈	—	2	1	no	—
65	C₂²×C₄₃⋊C₈	—	2	1	no	—
66	C₂²×C₄₃⋊C₈	—	2	1	no	—
67	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
68	#13063260	—	2	8	no	—
69	#13063243	—	2	4	no	—
70	#13063241	—	2	4	no	—
71	(C₂×D₄₃)⋊C₈	—	2	8	no	—
72	(C₂×D₄₃)⋊C₈	—	2	8	no	—
73	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₄₃	—	2	1	no	—
75	C₂×M₁₆×C₄₃	—	2	1	no	—
76	C₂×M₁₆×C₄₃	—	2	1	no	—
77	C₂×M₁₆×C₄₃	—	2	1	no	—
78	C₂×M₁₆×C₄₃	—	2	1	no	—
79	C₂×M₁₆×C₄₃	—	2	1	no	—
80	C₂×M₁₆×C₄₃	—	2	1	no	—
81	C₂×M₁₆×C₄₃	—	2	1	no	—
82	C₂×M₁₆×C₄₃	—	2	1	no	—
83	C₂×M₁₆×C₄₃	—	2	1	no	—
84	C₂×M₁₆×C₄₃	—	2	1	no	—
85	C₂×M₁₆×C₄₃	—	2	1	no	—
86	C₂×M₁₆×C₄₃	—	2	1	no	—
87	C₂×M₁₆×C₄₃	—	2	1	no	—
88	C₂×M₁₆×C₄₃	—	2	1	no	—
89	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
90	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
91	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
92	C₂²×C₈×C₄₃	—	2	1	no	—
93	C₂²×C₈×C₄₃	—	2	1	no	—
94	C₂²×C₈×C₄₃	—	2	1	no	—
95	C₂⁴×C₄₃	C₂×Q₈	1	1	yes	characteristic
96	C₂³×D₄₃	C₄⋊C₄	1	2	yes	—
97	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
111	C₂×C₂²⋊D₄₃	—	2	2	no	—
112	C₂×C₂²⋊D₄₃	—	2	2	no	—
113	C₂×C₂²⋊D₄₃	—	2	2	no	—
114	C₂×C₂²⋊D₄₃	—	2	2	no	—
115	C₂×C₂²⋊D₄₃	—	2	2	no	—
116	C₂×C₂²⋊D₄₃	—	2	2	no	—
117	C₂²×Dic₄₃	C₄⋊C₄	1	2	yes	—
118	#10621898	—	4	1	no	—
119	#10621898	—	4	1	no	—
120	#10621898	—	4	1	no	—
121	#10621898	—	4	1	no	—
122	#10621898	—	4	1	no	—
123	#10621898	—	4	1	no	—
124	#10621898	—	4	1	no	—
125	#10621898	—	4	1	no	—
126	#10621898	—	4	1	no	—
127	#10621898	—	4	1	no	—
128	#10621898	—	4	1	no	—
129	#10621898	—	4	1	no	—
130	#10621898	—	4	1	no	—
131	#10621898	—	4	1	no	—
132	#10621898	—	4	1	no	—
133	#10621898	—	4	1	no	—
134	C₂×D₁₇₂	—	2	1	no	—
135	C₂×D₁₇₂	—	2	1	no	—
136	C₂×D₁₇₂	—	2	1	no	—
137	C₂×D₁₇₂	—	2	1	no	—
138	C₂×D₁₇₂	—	2	1	no	—
139	C₂×D₁₇₂	—	2	1	no	—
140	C₂×C₄×D₄₃	—	2	2	no	—
141	C₂×C₄×D₄₃	—	2	2	no	—
142	C₂×C₄×D₄₃	—	2	2	no	—
143	C₂×C₄×D₄₃	—	2	2	no	—
144	C₂×C₄×D₄₃	—	2	2	no	—
145	C₂×C₄×D₄₃	—	2	2	no	—
146	C₂×Dic₈₆	—	2	1	no	—
147	C₂×Dic₈₆	—	2	1	no	—
148	C₂×Dic₈₆	—	2	1	no	—
149	C₂×Dic₈₆	—	2	1	no	—
150	C₂×Dic₈₆	—	2	1	no	—
151	C₂×Dic₈₆	—	2	1	no	—
152	M₁₆×C₄₃	—	2	2	no	—
153	M₁₆×C₄₃	—	2	2	no	—
154	M₁₆×C₄₃	—	2	2	no	—
155	M₁₆×C₄₃	—	2	2	no	—
156	M₁₆×C₄₃	—	2	2	no	—
157	M₁₆×C₄₃	—	2	2	no	—
158	M₁₆×C₄₃	—	4	1	no	—
159	M₁₆×C₄₃	—	4	1	no	—
160	M₁₆×C₄₃	—	4	1	no	—
161	M₁₆×C₄₃	—	4	1	no	—
162	M₁₆×C₄₃	—	4	1	no	—
163	M₁₆×C₄₃	—	4	1	no	—
164	C₂×C₈×C₄₃	—	2	2	no	—
165	C₂×C₈×C₄₃	—	2	2	no	—
166	C₂×C₈×C₄₃	—	2	2	no	—
167	C₂×C₈×C₄₃	—	4	1	no	—
168	C₂×C₈×C₄₃	—	4	1	no	—
169	C₂×C₈×C₄₃	—	4	1	no	—
170	C₂×C₈×C₄₃	—	4	1	no	—
171	C₂×C₈×C₄₃	—	4	1	no	—
172	C₂×C₈×C₄₃	—	4	1	no	—
173	#10621877	—	2	2	no	—
174	#10621877	—	2	2	no	—
175	#10621877	—	2	2	no	—
176	#10621877	—	2	2	no	—
177	#10621877	—	2	2	no	—
178	#10621877	—	4	1	no	—
179	#10621877	—	4	1	no	—
180	#10621877	C₂²⋊C₄	1	4	yes	—
181	C₂×C₄₃⋊C₈	—	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	—	2	2	no	—
186	C₂×C₄₃⋊C₈	—	2	2	no	—
187	C₂×C₄₃⋊C₈	—	2	2	no	—
188	C₂×C₄₃⋊C₈	—	4	1	no	—
189	C₂×C₄₃⋊C₈	—	4	1	no	—
190	C₂×C₄₃⋊C₈	—	4	1	no	—
191	C₂×C₄₃⋊C₈	—	4	1	no	—
192	C₂×C₄₃⋊C₈	—	4	1	no	—
193	C₂×C₄₃⋊C₈	—	4	1	no	—
194	C₂³×C₄₃	—	4	2	no	—
195	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
197	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
198	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
200	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
201	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
202	C₂²×D₄₃	—	2	2	no	—
203	C₂²×D₄₃	—	2	2	no	—
204	C₂²×D₄₃	—	2	2	no	—
205	C₂²×D₄₃	—	4	4	no	—
206	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₄₃	#117	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	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
213	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
214	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
215	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
216	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
217	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
218	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
219	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
220	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
221	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
222	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
223	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
224	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
225	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
226	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
227	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
228	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
229	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
230	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
231	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
232	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
233	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
234	C₂²⋊D₄₃	—	4	2	no	—
235	C₂²⋊D₄₃	—	4	2	no	—
236	C₂²⋊D₄₃	—	4	2	no	—
237	C₂²⋊D₄₃	—	4	2	no	—
238	C₂×Dic₄₃	—	2	2	no	—
239	C₂×Dic₄₃	—	2	2	no	—
240	C₂×Dic₄₃	—	2	2	no	—
241	D₁₇₂	—	4	1	no	—
242	D₁₇₂	—	4	1	no	—
243	D₁₇₂	—	4	1	no	—
244	D₁₇₂	—	4	1	no	—
245	C₄×D₄₃	—	4	2	no	—
246	C₄×D₄₃	—	4	2	no	—
247	C₄×D₄₃	—	4	2	no	—
248	C₄×D₄₃	—	4	2	no	—
249	Dic₈₆	—	4	1	no	—
250	Dic₈₆	—	4	1	no	—
251	Dic₈₆	—	4	1	no	—
252	Dic₈₆	—	4	1	no	—
253	C₈×C₄₃	—	4	2	no	—
254	C₈×C₄₃	—	4	2	no	—
255	C₈×C₄₃	—	4	2	no	—
256	C₄₃⋊C₈	—	2	4	no	—
257	C₄₃⋊C₈	—	4	2	no	—
258	C₄₃⋊C₈	—	4	2	no	—
259	#11137	—	43	1	no	maximal, Sylow
260	C₂²×C₄₃	—	2	2	no	—
261	C₂²×C₄₃	—	2	2	no	—
262	C₂²×C₄₃	—	2	2	no	—
263	C₂²×C₄₃	—	4	1	no	—
264	C₂²×C₄₃	—	4	1	no	—
265	C₂²×C₄₃	—	4	1	no	—
266	C₂²×C₄₃	—	4	1	no	—
267	C₂²×C₄₃	#380	1	1	yes	characteristic
268	C₂²×C₄₃	#385	1	1	yes	characteristic
269	C₂²×C₄₃	#385	1	1	yes	characteristic
270	C₂²×C₄₃	#393	1	1	yes	characteristic
271	C₂²×C₄₃	#396	1	1	yes	characteristic
272	C₂²×C₄₃	#396	1	1	yes	characteristic
273	C₂²×C₄₃	#399	1	1	yes	characteristic
274	C₂×D₄₃	—	4	4	no	—
275	C₂×D₄₃	—	4	4	no	—
276	C₂×D₄₃	—	4	2	no	—
277	C₂×D₄₃	—	8	2	no	—
278	C₄×C₄₃	#386	1	1	yes	characteristic
279	C₄×C₄₃	#388	1	1	yes	characteristic
280	C₄×C₄₃	#388	1	1	yes	characteristic
281	C₄×C₄₃	#390	1	1	yes	characteristic
282	C₄×C₄₃	#392	1	1	yes	characteristic
283	C₄×C₄₃	#394	1	1	yes	characteristic
284	C₄×C₄₃	#394	1	1	yes	characteristic
285	C₄×C₄₃	#397	1	1	yes	characteristic
286	Dic₄₃	—	4	2	no	—
287	C₂×#430	—	43	1	no	—
288	C₂×#413	—	43	1	no	—
289	#2879	—	43	1	no	—
290	C₂×#408	—	43	1	no	—
291	#1738	D₄₃	1	1	yes	characteristic, complemented
292	C₂×#341	—	43	1	no	—
293	C₂×#341	—	43	1	no	—
294	C₂×C₄₃	—	2	1	no	—
295	C₂×C₄₃	—	2	1	no	—
296	C₂×C₄₃	—	2	1	no	—
297	C₂×C₄₃	—	2	1	no	—
298	C₂×C₄₃	—	2	1	no	—
299	C₂×C₄₃	—	2	1	no	—
300	C₂×C₄₃	#1439	1	1	yes	characteristic
301	C₂×C₄₃	#1858	1	2	yes	—
302	D₄₃	—	8	2	no	—
303	C₂²×#41	—	43	1	no	—
304	C₂²×M₁₆	—	43	1	no	—
305	C₂²×M₁₆	—	43	1	no	—
306	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
307	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
308	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
309	C₂³×C₈	—	43	1	no	—
310	#430	—	86	2	no	—
311	#430	—	86	2	no	—
312	C₂×#108	—	86	2	no	—
313	#413	—	86	2	no	—
314	#413	—	86	2	no	—
315	C₂×#101	—	43	2	no	—
316	C₂×#100	—	43	2	no	—
317	#408	—	86	2	no	—
318	#408	—	86	2	no	—
319	#408	—	86	2	no	—
320	#408	—	86	2	no	—
321	#407	—	86	2	no	—
322	C₂×C₂²⋊C₈	—	86	2	no	—
323	#341	—	2	2	no	—
324	#341	—	86	2	no	—
325	#341	—	86	2	no	—
326	C₄₃	#11137	1	1	yes	characteristic, complemented, Sylow
327	C₂×#41	—	86	1	no	—
328	C₂×#41	—	86	1	no	—
329	C₂×#41	—	86	1	no	—
330	C₂×#41	—	86	1	no	—
331	C₂×#41	—	86	1	no	—
332	C₂×#41	—	86	1	no	—
333	C₂×#41	—	86	1	no	—
334	C₂×#41	—	86	1	no	—
335	C₂×#41	—	86	1	no	—
336	C₂×#41	—	86	1	no	—
337	C₂×#41	—	86	1	no	—
338	C₂×#41	—	86	1	no	—
339	C₂²×Q₈	—	43	1	no	—
340	C₂²×D₄	—	43	2	no	—
341	C₂²×D₄	—	43	1	no	—
342	C₂³×C₄	—	43	2	no	—
343	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	43	2	no	—
360	C₂×M₁₆	—	43	2	no	—
361	C₂×M₁₆	—	43	2	no	—
362	C₂×M₁₆	—	43	2	no	—
363	C₂×M₁₆	—	86	1	no	—
364	C₂×M₁₆	—	86	1	no	—
365	C₂×M₁₆	—	86	1	no	—
366	C₂×M₁₆	—	86	1	no	—
367	C₂×M₁₆	—	86	1	no	—
368	C₂×M₁₆	—	86	1	no	—
369	C₂×M₁₆	—	86	1	no	—
370	C₂×M₁₆	—	86	1	no	—
371	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
372	C₂×M₁₆	D₁₇₂	1	2	yes	—
373	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	43	2	no	—
378	C₂²×C₈	—	86	1	no	—
379	C₂²×C₈	—	86	1	no	—
380	C₂²×C₈	—	86	1	no	—
381	C₂²×C₈	—	86	1	no	—
382	C₂²×C₈	—	86	1	no	—
383	C₂²×C₈	—	86	1	no	—
384	C₂²×C₈	—	86	1	no	—
385	C₂²×C₈	—	86	1	no	—
386	#108	—	86	8	no	—
387	#101	—	86	4	no	—
388	#100	—	86	4	no	—
389	C₂²⋊C₈	—	86	8	no	—
390	C₂²⋊C₈	—	86	8	no	—
391	C₂⁴	—	43	2	no	—
392	C₂⁴	Q₈×D₄₃	1	1	yes	characteristic
393	#41	—	172	1	no	—
394	#41	—	172	1	no	—
395	#41	—	172	1	no	—
396	#41	—	172	1	no	—
397	#41	—	172	1	no	—
398	#41	—	172	1	no	—
399	#41	—	172	1	no	—
400	#41	—	172	1	no	—
401	#41	—	172	1	no	—
402	#41	—	172	1	no	—
403	#41	—	172	1	no	—
404	#41	—	172	1	no	—
405	#41	—	172	1	no	—
406	#41	—	172	1	no	—
407	#41	—	172	1	no	—
408	#41	—	172	1	no	—
409	C₂×Q₈	—	86	1	no	—
410	C₂×Q₈	—	86	1	no	—
411	C₂×Q₈	—	86	1	no	—
412	C₂×Q₈	—	86	1	no	—
413	C₂×Q₈	—	86	1	no	—
414	C₂×Q₈	—	86	1	no	—
415	C₂×D₄	—	86	2	no	—
416	C₂×D₄	—	86	2	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	1	no	—
422	C₂×D₄	—	86	1	no	—
423	C₂×D₄	—	86	1	no	—
424	C₂×D₄	—	86	1	no	—
425	C₂×D₄	—	86	1	no	—
426	C₂×D₄	—	86	1	no	—
427	C₂²×C₄	—	43	2	no	—
428	C₂²×C₄	—	86	2	no	—
429	C₂²×C₄	—	86	2	no	—
430	C₂²×C₄	—	86	2	no	—
431	C₂²×C₄	—	86	2	no	—
432	C₂²×C₄	—	86	2	no	—
433	C₂²×C₄	—	86	2	no	—
434	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
436	C₂²×C₄	#10621898	1	1	yes	characteristic
437	C₂²×C₄	#10621898	1	1	yes	characteristic
438	C₂²×C₄	#10621898	1	1	yes	characteristic
439	C₂²×C₄	#10621898	1	1	yes	characteristic
440	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
441	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
442	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
443	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
444	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
445	C₂²×C₄	#10621900	1	1	yes	characteristic
446	C₂²×C₄	#10621902	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	4	1	no	—
455	M₁₆	—	4	1	no	—
456	M₁₆	—	4	1	no	—
457	M₁₆	—	4	1	no	—
458	M₁₆	—	4	1	no	—
459	M₁₆	—	4	1	no	—
460	M₁₆	—	43	4	no	—
461	M₁₆	—	86	2	no	—
462	M₁₆	—	86	2	no	—
463	M₁₆	—	86	2	no	—
464	M₁₆	—	86	2	no	—
465	M₁₆	—	86	2	no	—
466	M₁₆	—	172	1	no	—
467	M₁₆	—	172	1	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	4	1	no	—
472	C₂×C₈	—	4	1	no	—
473	C₂×C₈	—	4	1	no	—
474	C₂×C₈	—	4	1	no	—
475	C₂×C₈	—	4	1	no	—
476	C₂×C₈	—	4	1	no	—
477	C₂×C₈	—	86	2	no	—
478	C₂×C₈	—	86	2	no	—
479	C₂×C₈	—	86	2	no	—
480	C₂×C₈	—	86	2	no	—
481	C₂×C₈	—	86	2	no	—
482	C₂×C₈	—	86	2	no	—
483	C₂×C₈	—	86	2	no	—
484	C₂×C₈	—	172	1	no	—
485	C₂×C₈	—	172	1	no	—
486	C₂×C₈	—	172	1	no	—
487	C₂×C₈	—	172	1	no	—
488	C₂×C₈	—	172	1	no	—
489	C₂×C₈	—	172	1	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	86	2	no	—
492	C₂³	—	86	2	no	—
493	C₂³	—	86	2	no	—
494	C₂³	—	172	4	no	—
495	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
496	C₂³	#13063301	1	1	yes	characteristic
497	C₂³	#13063303	1	1	yes	characteristic
498	C₂³	#13063303	1	1	yes	characteristic
499	C₂³	#13063303	1	1	yes	characteristic
500	C₂³	#13063303	1	1	yes	characteristic
501	C₂³	#13063305	1	1	yes	characteristic
502	Q₈	—	172	1	no	—
503	Q₈	—	172	1	no	—
504	Q₈	—	172	1	no	—
505	Q₈	—	172	1	no	—
506	D₄	—	172	2	no	—
507	D₄	—	172	2	no	—
508	D₄	—	172	2	no	—
509	D₄	—	172	2	no	—
510	D₄	—	172	1	no	—
511	D₄	—	172	1	no	—
512	D₄	—	172	1	no	—
513	D₄	—	172	1	no	—
514	C₂×C₄	—	86	2	no	—
515	C₂×C₄	—	86	2	no	—
516	C₂×C₄	—	86	2	no	—
517	C₂×C₄	—	172	2	no	—
518	C₂×C₄	—	172	2	no	—
519	C₂×C₄	—	172	2	no	—
520	C₂×C₄	—	172	2	no	—
521	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
522	C₂×C₄	#13063282	1	1	yes	characteristic
523	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
524	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
525	C₂×C₄	#13063287	1	1	yes	characteristic
526	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
527	C₂×C₄	#13063293	1	1	yes	characteristic
528	C₂×C₄	#13063295	1	1	yes	characteristic
529	C₂×C₄	#13063295	1	1	yes	characteristic
530	C₂×C₄	#13063297	1	1	yes	characteristic
531	C₂×C₄	#13063298	1	1	yes	characteristic
532	C₂×C₄	#13063298	1	1	yes	characteristic
533	C₂×C₄	#13063298	1	1	yes	characteristic
534	C₂×C₄	#13063298	1	1	yes	characteristic
535	C₂×C₄	#13063298	1	1	yes	characteristic
536	C₂×C₄	#13063299	1	1	yes	characteristic
537	C₂×C₄	#13063300	1	1	yes	characteristic
538	C₂×C₄	#13063307	1	1	yes	characteristic
539	C₂×C₄	#13063308	1	1	yes	characteristic
540	C₂×C₄	#13063310	1	1	yes	characteristic
541	C₂×C₄	#13063310	1	1	yes	characteristic
542	C₂×C₄	#13063310	1	1	yes	characteristic
543	C₂×C₄	#13063311	1	1	yes	characteristic
544	C₂×C₄	#13063311	1	1	yes	characteristic
545	C₂×C₄	#13063313	1	1	yes	characteristic
546	C₂×C₄	#13063319	1	1	yes	characteristic
547	C₂×C₄	#13063320	1	1	yes	characteristic
548	C₂×C₄	#13063321	1	1	yes	characteristic
549	C₈	—	4	2	no	—
550	C₈	—	4	2	no	—
551	C₈	—	4	2	no	—
552	C₈	—	86	4	no	—
553	C₈	—	172	2	no	—
554	C₈	—	172	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	344	2	no	—
563	C₂²	—	172	4	no	—
564	C₂²	—	172	4	no	—
565	C₂²	—	172	2	no	—
566	C₂²	#14582758	1	1	yes	characteristic
567	C₂²	#14582770	1	1	yes	characteristic
568	C₂²	#14582773	1	1	yes	characteristic
569	C₂²	#14582812	1	1	yes	characteristic
570	C₂²	#14582821	1	1	yes	characteristic
571	C₂²	#14582823	1	1	yes	characteristic
572	C₂²	#14582834	1	1	yes	characteristic
573	C₄	—	172	2	no	—
574	C₄	#14582777	1	1	yes	characteristic
575	C₄	#14582788	1	1	yes	characteristic
576	C₄	#14582790	1	1	yes	characteristic
577	C₄	#14582799	1	1	yes	characteristic
578	C₄	#14582808	1	1	yes	characteristic
579	C₄	#14582814	1	1	yes	characteristic
580	C₄	#14582817	1	1	yes	characteristic
581	C₄	#14582828	1	1	yes	characteristic
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	344	2	no	—
589	C₂	#19132839	1	1	yes	characteristic
590	C₂	#19134813	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13063293
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₄₃×#1738	C₂
socle	C₂²×C₄₃	#385
prime radical	C₂²×#10621898	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	#1738	D₄₃
hypocenter	C₄₃	#11137
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1738

Complements

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

N	H ≅ G/N	type
1. C₂×#14582947	C₂	semidirect
5. C₂×#14582663	C₂	semidirect
6. C₂×#14582663	C₂	semidirect
7. C₄₃×#1738	C₂	semidirect
291. #1738	D₄₃	semidirect
326. C₄₃	#11137	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582947	2
C₂×#14582881	2
#19143039	2
C₂×#14582867	2
C₂×#14582663	2
C₄₃×#1738	2
#11137	43