Subgroups — #25004013

Order 11008.

930 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063261	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13063252	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582866	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582658	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134292	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582653	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#416	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10621877	C₂²	1	1	yes	characteristic
9	C₂²×#10621877	C₂²	1	1	yes	characteristic
10	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
12	C₂×#13063261	—	2	2	no	—
13	C₂×#13063261	—	2	2	no	—
14	C₂×#13063261	—	2	2	no	—
15	C₂×#13063252	—	2	2	no	—
16	C₂×#13063252	—	2	2	no	—
17	C₂×#13063252	—	2	2	no	—
18	#14582866	—	2	2	no	—
19	#14582866	—	2	2	no	—
20	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
21	#14582658	—	2	2	no	—
22	#14582654	—	2	2	no	—
23	#14582653	—	2	2	no	—
24	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
25	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#416	—	2	2	no	—
28	C₄₃×#416	—	2	2	no	—
29	C₂×#103×C₄₃	C₄	1	1	yes	characteristic, complemented
30	C₂×#103×C₄₃	C₄	1	1	yes	characteristic, complemented
31	C₂×#102×C₄₃	C₄	1	1	yes	characteristic, complemented
32	C₂×#102×C₄₃	C₄	1	1	yes	characteristic, complemented
33	C₂³×Dic₄₃	—	2	1	no	—
34	C₂×#10621877	—	2	1	no	—
35	C₂×#10621877	—	2	1	no	—
36	C₂×#10621877	—	2	1	no	—
37	C₂×#10621877	—	2	1	no	—
38	C₂×#10621877	—	2	1	no	—
39	C₂×#10621877	—	2	1	no	—
40	C₂×#10621877	—	2	1	no	—
41	C₂×#10621877	—	2	1	no	—
42	C₂×#10621877	—	2	1	no	—
43	C₂×#10621877	—	2	1	no	—
44	C₂×#10621877	D₄	1	2	yes	—
45	C₂×#10621877	D₄	1	2	yes	—
46	C₂²×C₄₃⋊C₈	—	2	1	no	—
47	C₂²×C₄₃⋊C₈	—	2	1	no	—
48	C₂²×C₄₃⋊C₈	—	2	1	no	—
49	C₂²×C₄₃⋊C₈	—	2	1	no	—
50	C₂²×C₄₃⋊C₈	—	2	1	no	—
51	C₂²×C₄₃⋊C₈	—	2	1	no	—
52	C₂²×C₄₃⋊C₈	—	2	1	no	—
53	C₂²×C₄₃⋊C₈	—	2	1	no	—
54	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
55	C₂×C₄×Dic₄₃	—	2	1	no	—
56	C₂×C₄×Dic₄₃	—	2	1	no	—
57	C₂×C₄×Dic₄₃	—	2	1	no	—
58	C₂×C₄×Dic₄₃	—	2	1	no	—
59	C₂×C₄×Dic₄₃	—	2	1	no	—
60	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
61	#13063261	—	2	8	no	—
62	#13063252	—	2	8	no	—
63	C₂²⋊(C₄₃⋊C₈)	—	2	8	no	—
64	C₂×#41×C₄₃	—	2	1	no	—
65	C₂×#41×C₄₃	—	2	1	no	—
66	C₂×#41×C₄₃	—	2	1	no	—
67	C₂×#41×C₄₃	—	2	1	no	—
68	C₂×#41×C₄₃	—	2	1	no	—
69	C₂×#41×C₄₃	—	2	1	no	—
70	C₂×#41×C₄₃	—	2	1	no	—
71	C₂×#41×C₄₃	—	2	1	no	—
72	C₂×#41×C₄₃	—	2	1	no	—
73	C₂×#41×C₄₃	—	2	1	no	—
74	C₂×#41×C₄₃	D₄	1	2	yes	—
75	C₂×#41×C₄₃	Q₈	1	2	yes	—
76	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
77	C₂²×D₄×C₄₃	—	2	1	no	—
78	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₄₃	—	2	1	no	—
80	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₃	—	2	1	no	—
82	C₂²×C₈×C₄₃	—	2	1	no	—
83	C₂²×C₈×C₄₃	—	2	1	no	—
84	C₂²×C₈×C₄₃	—	2	1	no	—
85	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₄₃	D₄	1	2	yes	—
88	C₂²×C₈×C₄₃	D₄	1	2	yes	—
89	#117×C₄₃	—	2	1	no	—
90	#117×C₄₃	—	2	1	no	—
91	#117×C₄₃	—	2	1	no	—
92	#117×C₄₃	—	2	1	no	—
93	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₄²×C₄₃	—	2	1	no	—
97	#103×C₄₃	—	2	2	no	—
98	#103×C₄₃	—	2	2	no	—
99	#102×C₄₃	—	2	2	no	—
100	#102×C₄₃	—	2	2	no	—
101	C₂⁴×C₄₃	—	2	1	no	—
102	C₂⁴×C₄₃	#41	1	1	yes	characteristic
103	#41×C₄₃	—	2	2	no	—
104	#41×C₄₃	—	2	2	no	—
105	#41×C₄₃	—	2	2	no	—
106	#41×C₄₃	—	2	2	no	—
107	#41×C₄₃	—	2	2	no	—
108	#41×C₄₃	—	2	2	no	—
109	#41×C₄₃	—	2	2	no	—
110	#41×C₄₃	—	2	2	no	—
111	#41×C₄₃	—	4	1	no	—
112	#41×C₄₃	—	4	1	no	—
113	#41×C₄₃	—	4	1	no	—
114	#41×C₄₃	—	4	1	no	—
115	#41×C₄₃	—	4	1	no	—
116	#41×C₄₃	—	4	1	no	—
117	#41×C₄₃	—	4	1	no	—
118	#41×C₄₃	—	4	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	—	2	1	no	—
124	C₂×Q₈×C₄₃	C₄⋊C₄	1	2	yes	—
125	C₂×D₄×C₄₃	—	2	1	no	—
126	C₂×D₄×C₄₃	—	2	2	no	—
127	C₂×D₄×C₄₃	—	2	2	no	—
128	C₂×D₄×C₄₃	—	2	1	no	—
129	C₂×D₄×C₄₃	—	2	1	no	—
130	C₂×D₄×C₄₃	—	2	1	no	—
131	C₂×D₄×C₄₃	—	2	1	no	—
132	C₂×D₄×C₄₃	—	4	1	no	—
133	C₂×D₄×C₄₃	—	4	1	no	—
134	C₂×D₄×C₄₃	—	4	1	no	—
135	C₂×D₄×C₄₃	—	4	1	no	—
136	C₂×D₄×C₄₃	C₄⋊C₄	1	2	yes	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	2	2	no	—
139	C₂²×C₄×C₄₃	—	2	1	no	—
140	C₂²×C₄×C₄₃	—	2	1	no	—
141	C₂²×C₄×C₄₃	—	2	1	no	—
142	C₂²×C₄×C₄₃	—	4	1	no	—
143	C₂²×C₄×C₄₃	—	4	1	no	—
144	C₂²×C₄×C₄₃	—	4	1	no	—
145	C₂²×C₄×C₄₃	—	4	1	no	—
146	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
155	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
156	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
157	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
158	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
159	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
160	C₂²×Dic₄₃	—	2	4	no	—
161	C₂²×Dic₄₃	—	2	2	no	—
162	C₂²×Dic₄₃	—	4	2	no	—
163	C₂²×Dic₄₃	—	4	1	no	—
164	C₂²×Dic₄₃	—	4	1	no	—
165	C₂×C₈×C₄₃	—	2	1	no	—
166	C₂×C₈×C₄₃	—	2	1	no	—
167	C₂×C₈×C₄₃	—	2	1	no	—
168	C₂×C₈×C₄₃	—	2	1	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₂×C₈×C₄₃	—	2	2	no	—
171	C₂×C₈×C₄₃	—	2	2	no	—
172	C₂×C₈×C₄₃	—	2	2	no	—
173	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
174	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
175	C₄⋊C₄×C₄₃	—	2	1	no	—
176	C₄⋊C₄×C₄₃	—	2	1	no	—
177	C₄⋊C₄×C₄₃	—	2	1	no	—
178	C₄⋊C₄×C₄₃	—	2	1	no	—
179	C₂²⋊C₄×C₄₃	—	4	1	no	—
180	C₂²⋊C₄×C₄₃	—	4	1	no	—
181	C₄²×C₄₃	—	4	1	no	—
182	C₄²×C₄₃	—	4	1	no	—
183	C₄×Dic₄₃	—	2	2	no	—
184	C₄×Dic₄₃	—	2	2	no	—
185	C₄×Dic₄₃	—	4	1	no	—
186	C₄×Dic₄₃	—	4	1	no	—
187	#10621877	—	2	2	no	—
188	#10621877	—	2	2	no	—
189	#10621877	—	2	2	no	—
190	#10621877	—	2	2	no	—
191	#10621877	—	4	1	no	—
192	#10621877	—	4	1	no	—
193	#10621877	—	4	1	no	—
194	#10621877	—	4	1	no	—
195	C₂×C₄₃⋊C₈	—	2	2	no	—
196	C₂×C₄₃⋊C₈	—	2	2	no	—
197	C₂×C₄₃⋊C₈	—	2	2	no	—
198	C₂×C₄₃⋊C₈	—	2	2	no	—
199	C₂×C₄₃⋊C₈	—	2	2	no	—
200	C₂×C₄₃⋊C₈	—	4	1	no	—
201	C₂×C₄₃⋊C₈	—	4	1	no	—
202	C₂×C₄₃⋊C₈	—	4	1	no	—
203	C₂×C₄₃⋊C₈	—	4	1	no	—
204	C₂×C₄₃⋊C₈	—	4	1	no	—
205	C₂×C₄₃⋊C₈	—	4	1	no	—
206	C₂×C₄₃⋊C₈	—	4	1	no	—
207	C₂×C₄₃⋊C₈	—	4	1	no	—
208	C₂³×C₄₃	—	2	2	no	—
209	C₂³×C₄₃	—	2	2	no	—
210	C₂³×C₄₃	—	2	2	no	—
211	C₂³×C₄₃	—	4	1	no	—
212	C₂³×C₄₃	—	4	1	no	—
213	C₂³×C₄₃	—	4	2	no	—
214	C₂³×C₄₃	—	4	2	no	—
215	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
216	C₂³×C₄₃	#121	1	1	yes	characteristic
217	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
218	C₂³×C₄₃	#123	1	1	yes	characteristic
219	C₂³×C₄₃	#124	1	1	yes	characteristic
220	C₂³×C₄₃	#124	1	1	yes	characteristic
221	C₂³×C₄₃	#126	1	1	yes	characteristic
222	Q₈×C₄₃	—	2	2	no	—
223	Q₈×C₄₃	—	2	2	no	—
224	Q₈×C₄₃	—	4	1	no	—
225	Q₈×C₄₃	—	4	1	no	—
226	D₄×C₄₃	—	2	2	no	—
227	D₄×C₄₃	—	2	2	no	—
228	D₄×C₄₃	—	4	2	no	—
229	D₄×C₄₃	—	4	2	no	—
230	D₄×C₄₃	—	4	2	no	—
231	D₄×C₄₃	—	4	2	no	—
232	D₄×C₄₃	—	4	1	no	—
233	D₄×C₄₃	—	4	1	no	—
234	C₂×C₄×C₄₃	—	2	2	no	—
235	C₂×C₄×C₄₃	—	4	1	no	—
236	C₂×C₄×C₄₃	—	4	1	no	—
237	C₂×C₄×C₄₃	—	4	2	no	—
238	C₂×C₄×C₄₃	—	4	2	no	—
239	C₂×C₄×C₄₃	—	4	2	no	—
240	C₂×C₄×C₄₃	—	4	2	no	—
241	C₂×C₄×C₄₃	—	4	1	no	—
242	C₂×C₄×C₄₃	—	4	1	no	—
243	C₂×C₄×C₄₃	—	4	2	no	—
244	C₂×C₄×C₄₃	—	4	2	no	—
245	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
252	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
253	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
254	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
255	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
256	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
257	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
258	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
259	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
260	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
261	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
262	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
263	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
267	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
268	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
269	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
270	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
271	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
272	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
273	C₂×Dic₄₃	—	2	4	no	—
274	C₂×Dic₄₃	—	4	4	no	—
275	C₂×Dic₄₃	—	4	4	no	—
276	C₂×Dic₄₃	—	4	2	no	—
277	C₂×Dic₄₃	—	4	2	no	—
278	C₈×C₄₃	—	2	2	no	—
279	C₈×C₄₃	—	2	2	no	—
280	C₄₃⋊C₈	—	4	2	no	—
281	C₄₃⋊C₈	—	4	2	no	—
282	C₄₃⋊C₈	—	4	2	no	—
283	#11125	—	43	1	no	maximal, Sylow
284	C₂²×C₄₃	—	2	2	no	—
285	C₂²×C₄₃	—	2	2	no	—
286	C₂²×C₄₃	—	2	2	no	—
287	C₂²×C₄₃	—	2	2	no	—
288	C₂²×C₄₃	—	2	1	no	—
289	C₂²×C₄₃	—	2	1	no	—
290	C₂²×C₄₃	—	2	1	no	—
291	C₂²×C₄₃	—	2	1	no	—
292	C₂²×C₄₃	—	4	4	no	—
293	C₂²×C₄₃	—	4	2	no	—
294	C₂²×C₄₃	—	8	2	no	—
295	C₂²×C₄₃	—	8	1	no	—
296	C₂²×C₄₃	—	8	1	no	—
297	C₂²×C₄₃	#385	1	1	yes	characteristic
298	C₂²×C₄₃	#388	1	1	yes	characteristic
299	C₂²×C₄₃	#390	1	1	yes	characteristic
300	C₂²×C₄₃	#393	1	1	yes	characteristic
301	C₂²×C₄₃	#394	1	1	yes	characteristic
302	C₂²×C₄₃	#396	1	1	yes	characteristic
303	C₂²×C₄₃	#397	1	1	yes	characteristic
304	C₂²×C₄₃	#443	1	2	yes	—
305	C₂²×C₄₃	#444	1	2	yes	—
306	C₄×C₄₃	—	4	2	no	—
307	C₄×C₄₃	—	8	1	no	—
308	C₄×C₄₃	—	8	1	no	—
309	C₄×C₄₃	#380	1	1	yes	characteristic
310	C₄×C₄₃	#385	1	1	yes	characteristic
311	C₄×C₄₃	#386	1	1	yes	characteristic
312	C₄×C₄₃	#388	1	1	yes	characteristic
313	C₄×C₄₃	#392	1	1	yes	characteristic
314	C₄×C₄₃	#394	1	1	yes	characteristic
315	C₄×C₄₃	#396	1	1	yes	characteristic
316	C₄×C₄₃	#399	1	1	yes	characteristic
317	Dic₄₃	—	4	4	no	—
318	C₂²×#108	—	43	1	no	—
319	C₂²×#104	—	43	1	no	—
320	C₂×#416	D₄₃	1	1	yes	characteristic
321	C₂×#408	—	43	1	no	—
322	C₂×#339	—	43	1	no	—
323	#1729	—	43	1	no	—
324	C₂×#336	—	43	1	no	—
325	C₂×C₄₃	—	2	1	no	—
326	C₂×C₄₃	—	2	1	no	—
327	C₂×C₄₃	—	2	1	no	—
328	C₂×C₄₃	—	2	1	no	—
329	C₂×C₄₃	—	8	2	no	—
330	C₂×C₄₃	#1439	1	1	yes	characteristic
331	C₂×C₄₃	#1866	1	2	yes	—
332	C₂×C₄₃	#1929	1	2	yes	—
333	C₂×C₄₃	#1974	1	1	yes	characteristic
334	C₂×C₄₃	#1975	1	1	yes	characteristic
335	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
336	C₂²×M₁₆	—	43	1	no	—
337	C₂²×M₁₆	—	43	1	no	—
338	C₂³×C₈	—	43	1	no	—
339	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
340	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
341	C₂²×C₄²	—	43	1	no	—
342	C₂×#108	—	86	2	no	—
343	C₂×#108	—	86	2	no	—
344	C₂×#108	—	86	2	no	—
345	C₂×#104	—	86	2	no	—
346	C₂×#104	—	86	2	no	—
347	C₂×#104	—	86	2	no	—
348	#416	—	2	2	no	—
349	#416	—	2	2	no	—
350	C₂×#103	Dic₄₃	1	1	yes	characteristic, complemented
351	C₂×#103	Dic₄₃	1	1	yes	characteristic, complemented
352	C₂×#102	Dic₄₃	1	1	yes	characteristic, complemented
353	C₂×#102	Dic₄₃	1	1	yes	characteristic, complemented
354	#408	—	86	2	no	—
355	#408	—	86	2	no	—
356	C₂×C₂²⋊C₈	—	86	2	no	—
357	#339	—	86	2	no	—
358	#336	—	86	2	no	—
359	#336	—	86	2	no	—
360	C₄₃	#11125	1	1	yes	characteristic, complemented, Sylow
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	Dic₈₆	1	2	yes	—
372	C₂×#41	D₁₇₂	1	2	yes	—
373	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
374	C₂²×D₄	—	2	1	no	—
375	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
376	C₂³×C₄	—	2	1	no	—
377	C₂³×C₄	—	86	1	no	—
378	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
379	C₂×M₁₆	—	43	2	no	—
380	C₂×M₁₆	—	43	2	no	—
381	C₂×M₁₆	—	86	1	no	—
382	C₂×M₁₆	—	86	1	no	—
383	C₂×M₁₆	—	86	1	no	—
384	C₂×M₁₆	—	86	1	no	—
385	C₂×M₁₆	—	86	1	no	—
386	C₂×M₁₆	—	86	1	no	—
387	C₂×M₁₆	—	86	1	no	—
388	C₂×M₁₆	—	86	1	no	—
389	C₂×M₁₆	—	86	1	no	—
390	C₂×M₁₆	—	86	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	2	1	no	—
395	C₂²×C₈	—	43	2	no	—
396	C₂²×C₈	—	86	1	no	—
397	C₂²×C₈	—	86	1	no	—
398	C₂²×C₈	—	86	1	no	—
399	C₂²×C₈	—	86	1	no	—
400	C₂²×C₈	—	86	1	no	—
401	C₂²×C₈	—	86	1	no	—
402	C₂²×C₈	—	86	1	no	—
403	C₂²×C₈	—	86	1	no	—
404	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
405	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
406	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
407	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
408	#117	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	—	43	2	no	—
417	C₂×C₄²	—	86	1	no	—
418	C₂×C₄²	—	86	1	no	—
419	C₂×C₄²	—	86	1	no	—
420	C₂×C₄²	—	86	1	no	—
421	C₂×C₄²	—	86	1	no	—
422	#108	—	86	8	no	—
423	#104	—	86	8	no	—
424	#103	—	2	2	no	—
425	#103	—	2	2	no	—
426	#102	—	2	2	no	—
427	#102	—	2	2	no	—
428	C₂²⋊C₈	—	86	8	no	—
429	C₂⁴	—	2	1	no	—
430	C₂⁴	#10621900	1	1	yes	characteristic
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	#41	—	2	2	no	—
437	#41	—	2	2	no	—
438	#41	—	2	2	no	—
439	#41	—	4	1	no	—
440	#41	—	4	1	no	—
441	#41	—	4	1	no	—
442	#41	—	4	1	no	—
443	#41	—	4	1	no	—
444	#41	—	4	1	no	—
445	#41	—	4	1	no	—
446	#41	—	4	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	C₄⋊Dic₄₃	1	2	yes	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	4	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	C₄⋊Dic₄₃	1	2	yes	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	4	1	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	C₂²×C₄	—	86	4	no	—
475	C₂²×C₄	—	86	2	no	—
476	C₂²×C₄	—	172	2	no	—
477	C₂²×C₄	—	172	1	no	—
478	C₂²×C₄	—	172	1	no	—
479	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
481	C₂²×C₄	#10621898	1	1	yes	characteristic
482	C₂²×C₄	#10621898	1	1	yes	characteristic
483	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
484	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
485	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
486	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
487	C₂²×C₄	#10621900	1	1	yes	characteristic
488	C₂²×C₄	#10621900	1	1	yes	characteristic
489	C₂²×C₄	#10621900	1	1	yes	characteristic
490	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
491	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
492	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
493	M₁₆	—	86	2	no	—
494	M₁₆	—	86	2	no	—
495	M₁₆	—	86	2	no	—
496	M₁₆	—	86	2	no	—
497	M₁₆	—	172	1	no	—
498	M₁₆	—	172	1	no	—
499	M₁₆	—	172	1	no	—
500	M₁₆	—	172	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	86	2	no	—
510	C₂×C₈	—	86	2	no	—
511	C₂×C₈	—	86	2	no	—
512	C₂×C₈	—	86	2	no	—
513	C₂×C₈	—	86	2	no	—
514	C₂×C₈	—	172	1	no	—
515	C₂×C₈	—	172	1	no	—
516	C₂×C₈	—	172	1	no	—
517	C₂×C₈	—	172	1	no	—
518	C₂×C₈	—	172	1	no	—
519	C₂×C₈	—	172	1	no	—
520	C₂×C₈	—	172	1	no	—
521	C₂×C₈	—	172	1	no	—
522	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
523	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₂²⋊C₄	—	4	1	no	—
530	C₄²	—	4	1	no	—
531	C₄²	—	4	1	no	—
532	C₄²	—	86	2	no	—
533	C₄²	—	86	2	no	—
534	C₄²	—	172	1	no	—
535	C₄²	—	172	1	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	2	no	—
542	C₂³	—	4	2	no	—
543	C₂³	D₄×Dic₄₃	1	1	yes	characteristic
544	C₂³	#13063296	1	1	yes	characteristic
545	C₂³	#13063302	1	1	yes	characteristic
546	C₂³	#13063309	1	1	yes	characteristic
547	C₂³	#13063311	1	1	yes	characteristic
548	C₂³	#13063312	1	1	yes	characteristic
549	C₂³	#13063318	1	1	yes	characteristic
550	Q₈	—	2	2	no	—
551	Q₈	—	2	2	no	—
552	Q₈	—	4	1	no	—
553	Q₈	—	4	1	no	—
554	D₄	—	2	2	no	—
555	D₄	—	2	2	no	—
556	D₄	—	4	2	no	—
557	D₄	—	4	2	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	2	no	—
560	D₄	—	4	1	no	—
561	D₄	—	4	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	86	4	no	—
574	C₂×C₄	—	172	2	no	—
575	C₂×C₄	—	172	4	no	—
576	C₂×C₄	—	172	4	no	—
577	C₂×C₄	—	172	2	no	—
578	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
579	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
580	C₂×C₄	#13063284	1	1	yes	characteristic
581	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
582	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
583	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
584	C₂×C₄	#13063293	1	1	yes	characteristic
585	C₂×C₄	#13063295	1	1	yes	characteristic
586	C₂×C₄	#13063295	1	1	yes	characteristic
587	C₂×C₄	#13063296	1	1	yes	characteristic
588	C₂×C₄	#13063297	1	1	yes	characteristic
589	C₂×C₄	#13063297	1	1	yes	characteristic
590	C₂×C₄	#13063298	1	1	yes	characteristic
591	C₂×C₄	#13063298	1	1	yes	characteristic
592	C₂×C₄	#13063299	1	1	yes	characteristic
593	C₂×C₄	#13063299	1	1	yes	characteristic
594	C₂×C₄	#13063302	1	1	yes	characteristic
595	C₂×C₄	#13063302	1	1	yes	characteristic
596	C₂×C₄	#13063302	1	1	yes	characteristic
597	C₂×C₄	#13063304	1	1	yes	characteristic
598	C₂×C₄	#13063304	1	1	yes	characteristic
599	C₂×C₄	#13063306	1	1	yes	characteristic
600	C₂×C₄	#13063307	1	1	yes	characteristic
601	C₂×C₄	#13063307	1	1	yes	characteristic
602	C₂×C₄	#13063309	1	1	yes	characteristic
603	C₂×C₄	#13063311	1	1	yes	characteristic
604	C₂×C₄	#13063318	1	1	yes	characteristic
605	C₂×C₄	#13063321	1	1	yes	characteristic
606	C₈	—	2	2	no	—
607	C₈	—	2	2	no	—
608	C₈	—	172	2	no	—
609	C₈	—	172	2	no	—
610	C₈	—	172	2	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	4	4	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	2	no	—
623	C₂²	—	8	1	no	—
624	C₂²	#14582774	1	1	yes	characteristic
625	C₂²	#14582792	1	1	yes	characteristic
626	C₂²	#14582802	1	1	yes	characteristic
627	C₂²	#14582811	1	1	yes	characteristic
628	C₂²	#14582815	1	1	yes	characteristic
629	C₂²	#14582822	1	1	yes	characteristic
630	C₂²	#14582824	1	1	yes	characteristic
631	C₂²	#14583016	1	2	yes	—
632	C₂²	#14583021	1	2	yes	—
633	C₄	—	4	2	no	—
634	C₄	—	8	1	no	—
635	C₄	—	8	1	no	—
636	C₄	—	172	4	no	—
637	C₄	#14582759	1	1	yes	characteristic
638	C₄	#14582774	1	1	yes	characteristic
639	C₄	#14582779	1	1	yes	characteristic
640	C₄	#14582792	1	1	yes	characteristic
641	C₄	#14582808	1	1	yes	characteristic
642	C₄	#14582815	1	1	yes	characteristic
643	C₄	#14582822	1	1	yes	characteristic
644	C₄	#14582835	1	1	yes	characteristic
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	8	2	no	—
650	C₂	#19132840	1	1	yes	characteristic
651	C₂	#19134872	1	2	yes	—
652	C₂	#19135245	1	2	yes	—
653	C₂	#19135484	1	1	yes	characteristic
654	C₂	#19135489	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#416	C₂
socle	C₂³×C₄₃	C₄×D₄
prime radical	C₂²×#41×C₄₃	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#416	D₄₃
hypocenter	C₄₃	#11125
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#416

Complements

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

N	H ≅ G/N	type
1. C₂²×#13063261	C₂	semidirect
4. C₂×#14582658	C₂	semidirect
5. #19134292	C₂	semidirect
6. C₂×#14582653	C₂	semidirect
29. C₂×#103×C₄₃	C₄	semidirect
30. C₂×#103×C₄₃	C₄	semidirect
31. C₂×#102×C₄₃	C₄	semidirect
32. C₂×#102×C₄₃	C₄	semidirect
350. C₂×#103	Dic₄₃	semidirect
351. C₂×#103	Dic₄₃	semidirect
352. C₂×#102	Dic₄₃	semidirect
353. C₂×#102	Dic₄₃	semidirect
360. C₄₃	#11125	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13063261	2
C₂²×#13063252	2
C₂×#14582866	2
C₂×#14582658	2
#19134292	2
C₂×#14582653	2
C₂×C₄₃×#416	2
#11125	43