Subgroups — #25119144

Order 11008.

892 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583016	C₂	1	1	yes	maximal, characteristic, complemented
2	#19143322	C₂	1	2	yes	maximal, complemented
3	C₂²×#13063261	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135484	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135344	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135245	C₂	1	2	yes	maximal, complemented
7	#19134898	C₂	1	2	yes	maximal, complemented
8	#19134872	C₂	1	2	yes	maximal, complemented
9	#19134476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₂²⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3050	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063332	C₂²	1	2	yes	—
13	C₂²×#10621877	C₂²	1	2	yes	—
14	#14583016	—	2	4	no	—
15	#14582977	—	2	2	no	—
16	#14582971	—	2	2	no	—
17	#14582971	—	2	2	no	—
18	D₄×C₄₃⋊C₈	—	2	2	no	—
19	C₂×#13063261	—	2	4	no	—
20	C₂×#13063261	C₂²	1	2	yes	—
21	C₂×#13063261	C₂²	1	1	yes	characteristic
22	C₂×#13063261	C₂²	1	1	yes	characteristic
23	#14582926	C₂²	1	2	yes	—
24	C₂×#13063252	C₂²	1	2	yes	—
25	C₂×#13063252	C₂²	1	2	yes	—
26	#14582866	C₂²	1	2	yes	—
27	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
28	#14582855	C₂²	1	2	yes	—
29	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
31	C₄×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
32	#14582658	C₂²	1	2	yes	—
33	#14582658	C₂²	1	2	yes	—
34	#14582653	C₂²	1	1	yes	characteristic
35	#14582653	C₂²	1	1	yes	characteristic
36	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
37	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₄₃×#525	C₂²	1	2	yes	—
39	C₄₃×#467	C₄	1	1	yes	characteristic, complemented
40	C₄₃×#467	C₄	1	1	yes	characteristic, complemented
41	C₄₃×#466	C₄	1	1	yes	characteristic, complemented
42	C₄₃×#466	C₄	1	1	yes	characteristic, complemented
43	C₄₃×#465	C₄	1	2	yes	complemented
44	C₄₃×#465	C₄	1	2	yes	complemented
45	C₄₃×#427	C₂²	1	1	yes	characteristic
46	C₄₃×#416	C₂²	1	2	yes	—
47	#13063332	—	2	4	no	—
48	#13063332	—	4	2	no	—
49	C₂×#10621877	—	2	2	no	—
50	C₂×#10621877	—	2	2	no	—
51	C₂×#10621877	—	2	4	no	—
52	C₂×#10621877	—	4	2	no	—
53	C₂×#10621877	C₂³	1	2	yes	—
54	C₂×#10621877	C₂³	1	2	yes	—
55	C₂²×C₄₃⋊C₈	—	2	2	no	—
56	C₂²×C₄₃⋊C₈	—	2	2	no	—
57	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
60	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
62	#13063261	—	2	2	no	—
63	#13063261	—	2	4	no	—
64	#13063261	D₄	1	4	yes	complemented
65	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
66	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
67	#13063252	—	2	4	no	—
68	#13063252	—	4	2	no	—
69	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
70	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
71	C₂²⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
72	C₂²⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
73	C₂²⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
74	C₂²⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
75	#13063236	—	2	2	no	—
76	C₄×C₄₃⋊C₈	—	2	2	no	—
77	C₈×Dic₄₃	—	2	2	no	—
78	C₈×Dic₄₃	—	2	2	no	—
79	C₄₃⋊#95	—	2	1	no	—
80	C₂×#41×C₄₃	C₂³	1	2	yes	—
81	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
82	#135×C₄₃	—	2	2	no	—
83	#135×C₄₃	—	2	2	no	—
84	C₂×Q₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
85	C₂×SD₁₆×C₄₃	C₂×C₄	1	2	yes	—
86	C₂×D₈×C₄₃	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₄₃	—	2	2	no	—
88	C₂²×C₈×C₄₃	—	2	2	no	—
89	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
91	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
92	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
95	#123×C₄₃	—	2	2	no	—
96	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
97	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
98	#121×C₄₃	C₂×C₄	1	2	yes	—
99	#121×C₄₃	C₂×C₄	1	2	yes	—
100	#120×C₄₃	—	2	2	no	—
101	C₄×D₄×C₄₃	—	2	2	no	—
102	C₄×D₄×C₄₃	—	2	2	no	—
103	#117×C₄₃	C₂³	1	2	yes	—
104	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
105	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
106	#106×C₄₃	C₂×C₄	1	2	yes	—
107	#103×C₄₃	C₂×C₄	1	2	yes	—
108	#103×C₄₃	C₂×C₄	1	2	yes	—
109	#102×C₄₃	C₂×C₄	1	2	yes	—
110	#102×C₄₃	C₂×C₄	1	2	yes	—
111	C₂⁴×C₄₃	#41	1	1	yes	characteristic
112	#41×C₄₃	—	2	2	no	—
113	#41×C₄₃	—	2	2	no	—
114	#41×C₄₃	—	2	2	no	—
115	#41×C₄₃	—	2	2	no	—
116	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
117	C₂×D₄×C₄₃	—	2	2	no	—
118	C₂×D₄×C₄₃	—	2	2	no	—
119	C₂×D₄×C₄₃	—	2	2	no	—
120	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₄₃	—	2	1	no	—
122	C₂²×C₄×C₄₃	—	2	1	no	—
123	C₂²×C₄×C₄₃	—	2	1	no	—
124	C₂²×C₄×C₄₃	—	2	1	no	—
125	C₂²×C₄×C₄₃	—	2	2	no	—
126	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
132	C₂²×Dic₄₃	—	2	1	no	—
133	C₂²×Dic₄₃	—	2	1	no	—
134	Q₁₆×C₄₃	—	2	2	no	—
135	SD₁₆×C₄₃	—	2	4	no	—
136	D₈×C₄₃	—	2	2	no	—
137	C₂×C₈×C₄₃	—	2	1	no	—
138	C₂×C₈×C₄₃	—	2	1	no	—
139	C₂×C₈×C₄₃	—	2	2	no	—
140	C₂×C₈×C₄₃	—	2	2	no	—
141	C₂×C₈×C₄₃	—	2	2	no	—
142	C₂×C₈×C₄₃	—	2	2	no	—
143	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₄₃	#41	1	2	yes	—
149	C₄⋊C₄×C₄₃	—	2	2	no	—
150	C₄⋊C₄×C₄₃	—	2	2	no	—
151	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
152	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
153	C₂²⋊C₄×C₄₃	—	2	2	no	—
154	C₂²⋊C₄×C₄₃	—	2	2	no	—
155	C₂²⋊C₄×C₄₃	—	2	2	no	—
156	C₂²⋊C₄×C₄₃	—	2	2	no	—
157	C₂²⋊C₄×C₄₃	—	2	2	no	—
158	C₄²×C₄₃	—	2	2	no	—
159	C₂²⋊Dic₄₃	—	2	4	no	—
160	C₄×Dic₄₃	—	2	1	no	—
161	C₄×Dic₄₃	—	2	1	no	—
162	C₄×Dic₄₃	—	2	1	no	—
163	C₄×Dic₄₃	—	2	1	no	—
164	#10621877	—	2	2	no	—
165	#10621877	—	2	2	no	—
166	#10621877	—	2	2	no	—
167	#10621877	—	4	4	no	—
168	#10621877	—	4	4	no	—
169	#10621877	C₂×D₄	1	4	yes	—
170	C₂×C₄₃⋊C₈	—	2	1	no	—
171	C₂×C₄₃⋊C₈	—	2	2	no	—
172	C₂×C₄₃⋊C₈	—	2	1	no	—
173	C₂×C₄₃⋊C₈	—	2	1	no	—
174	C₂×C₄₃⋊C₈	—	2	1	no	—
175	C₂×C₄₃⋊C₈	—	2	2	no	—
176	C₂×C₄₃⋊C₈	—	4	4	no	—
177	C₂×C₄₃⋊C₈	—	4	4	no	—
178	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
179	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
180	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
181	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
182	C₂³×C₄₃	—	2	1	no	—
183	C₂³×C₄₃	—	2	1	no	—
184	C₂³×C₄₃	—	2	2	no	—
185	C₂³×C₄₃	—	2	2	no	—
186	C₂³×C₄₃	—	4	1	no	—
187	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
188	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
189	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
190	Q₈×C₄₃	—	2	2	no	—
191	Q₈×C₄₃	—	2	2	no	—
192	D₄×C₄₃	—	2	2	no	—
193	D₄×C₄₃	—	2	2	no	—
194	D₄×C₄₃	—	4	2	no	—
195	D₄×C₄₃	—	4	2	no	—
196	D₄×C₄₃	—	4	4	no	—
197	D₄×C₄₃	—	8	2	no	—
198	C₂×C₄×C₄₃	—	2	1	no	—
199	C₂×C₄×C₄₃	—	2	1	no	—
200	C₂×C₄×C₄₃	—	2	1	no	—
201	C₂×C₄×C₄₃	—	2	1	no	—
202	C₂×C₄×C₄₃	—	2	1	no	—
203	C₂×C₄×C₄₃	—	2	1	no	—
204	C₂×C₄×C₄₃	—	2	1	no	—
205	C₂×C₄×C₄₃	—	2	1	no	—
206	C₂×C₄×C₄₃	—	2	1	no	—
207	C₂×C₄×C₄₃	—	2	1	no	—
208	C₂×C₄×C₄₃	—	2	2	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	2	2	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	2	no	—
213	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
220	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
221	C₂×Dic₄₃	—	2	2	no	—
222	C₂×Dic₄₃	—	2	2	no	—
223	C₂×Dic₄₃	—	4	1	no	—
224	C₂×Dic₄₃	—	4	1	no	—
225	C₂×Dic₄₃	—	4	1	no	—
226	C₂×Dic₄₃	—	4	1	no	—
227	C₈×C₄₃	—	2	1	no	—
228	C₈×C₄₃	—	2	1	no	—
229	C₈×C₄₃	C₄×D₄	1	2	yes	—
230	C₈×C₄₃	C₄×D₄	1	2	yes	—
231	C₄₃⋊C₈	—	2	1	no	—
232	C₄₃⋊C₈	—	2	1	no	—
233	C₄₃⋊C₈	—	2	4	no	—
234	C₄₃⋊C₈	—	2	1	no	—
235	C₄₃⋊C₈	—	2	1	no	—
236	C₄₃⋊C₈	—	4	2	no	—
237	#23018	—	43	1	no	maximal, Sylow
238	C₂²×C₄₃	—	2	1	no	—
239	C₂²×C₄₃	—	2	1	no	—
240	C₂²×C₄₃	—	2	1	no	—
241	C₂²×C₄₃	—	2	1	no	—
242	C₂²×C₄₃	—	2	1	no	—
243	C₂²×C₄₃	—	2	1	no	—
244	C₂²×C₄₃	—	2	1	no	—
245	C₂²×C₄₃	—	4	2	no	—
246	C₂²×C₄₃	—	4	2	no	—
247	C₂²×C₄₃	—	4	2	no	—
248	C₂²×C₄₃	—	4	2	no	—
249	C₂²×C₄₃	—	4	2	no	—
250	C₂²×C₄₃	#443	1	2	yes	complemented
251	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂²×C₄₃	#548	1	1	yes	characteristic
253	C₂²×C₄₃	#553	1	1	yes	characteristic
254	C₄×C₄₃	—	2	1	no	—
255	C₄×C₄₃	—	2	1	no	—
256	C₄×C₄₃	—	4	2	no	—
257	C₄×C₄₃	—	4	2	no	—
258	C₄×C₄₃	—	4	2	no	—
259	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
260	C₄×C₄₃	#520	1	1	yes	characteristic
261	C₄×C₄₃	D₄²	1	1	yes	characteristic
262	C₄×C₄₃	#547	1	1	yes	characteristic
263	Dic₄₃	—	4	2	no	—
264	Dic₄₃	—	4	2	no	—
265	#3050	D₄₃	1	1	yes	characteristic
266	C₂×#443	—	43	1	no	—
267	#2933	—	43	2	no	—
268	C₂²×#108	—	43	1	no	—
269	#1974	—	43	1	no	—
270	#1945	—	43	1	no	—
271	#1929	—	43	2	no	—
272	#1871	—	43	2	no	—
273	#1866	—	43	2	no	—
274	#1772	—	43	1	no	—
275	C₈×C₂²⋊C₄	—	43	1	no	—
276	C₂×C₄₃	—	2	1	no	—
277	C₂×C₄₃	—	2	1	no	—
278	C₂×C₄₃	—	2	2	no	—
279	C₂×C₄₃	—	4	1	no	—
280	C₂×C₄₃	—	8	2	no	—
281	C₂×C₄₃	#2361	1	1	yes	characteristic
282	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
283	C₂×C₄₃	#2957	1	1	yes	characteristic
284	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
285	C₂×#131	—	43	2	no	—
286	C₂²×M₁₆	—	43	2	no	—
287	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
288	#525	C₂×D₄₃	1	2	yes	—
289	#467	Dic₄₃	1	1	yes	characteristic, complemented
290	#467	Dic₄₃	1	1	yes	characteristic, complemented
291	#466	Dic₄₃	1	1	yes	characteristic, complemented
292	#466	Dic₄₃	1	1	yes	characteristic, complemented
293	#465	Dic₄₃	1	2	yes	complemented
294	#465	Dic₄₃	1	2	yes	complemented
295	#443	—	86	4	no	—
296	#436	—	86	2	no	—
297	#435	—	86	2	no	—
298	#435	—	86	2	no	—
299	C₈×D₄	—	86	2	no	—
300	C₂×#108	—	43	1	no	—
301	C₂×#108	—	43	2	no	—
302	C₂×#108	—	43	1	no	—
303	C₂×#108	—	86	4	no	—
304	#427	C₂×D₄₃	1	1	yes	characteristic
305	#424	—	43	2	no	—
306	C₂×#104	—	43	2	no	—
307	C₂×#104	—	43	2	no	—
308	#416	C₂×D₄₃	1	2	yes	—
309	#408	—	43	2	no	—
310	C₂×C₂²⋊C₈	—	43	1	no	—
311	#405	—	43	2	no	—
312	C₂×C₄×C₈	—	43	1	no	—
313	C₂×C₄×C₈	—	43	1	no	—
314	C₄×C₂²⋊C₄	—	43	1	no	—
315	#339	—	43	2	no	—
316	#339	—	43	2	no	—
317	#336	—	43	1	no	—
318	#336	—	43	1	no	—
319	C₄₃	#23018	1	1	yes	characteristic, complemented, Sylow
320	C₂×#41	C₂²×D₄₃	1	2	yes	—
321	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
322	#135	—	2	2	no	—
323	#135	—	2	2	no	—
324	C₂×Q₁₆	C₂×Dic₄₃	1	1	yes	characteristic
325	C₂×SD₁₆	C₂×Dic₄₃	1	2	yes	—
326	C₂×D₈	C₂×Dic₄₃	1	1	yes	characteristic
327	#131	—	86	4	no	—
328	#131	—	172	2	no	—
329	C₂×M₁₆	—	43	2	no	—
330	C₂×M₁₆	—	43	2	no	—
331	C₂×M₁₆	—	86	2	no	—
332	C₂×M₁₆	—	86	2	no	—
333	C₂×M₁₆	—	86	4	no	—
334	C₂×M₁₆	—	172	2	no	—
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	43	1	no	—
338	C₂²×C₈	—	43	1	no	—
339	C₂²×C₈	—	86	2	no	—
340	C₂²×C₈	—	86	2	no	—
341	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
342	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
343	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
344	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
346	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
347	#123	—	2	2	no	—
348	C₂²⋊Q₈	C₂×Dic₄₃	1	2	yes	—
349	C₂²⋊Q₈	C₂×Dic₄₃	1	2	yes	—
350	#121	C₂×Dic₄₃	1	2	yes	—
351	#121	C₂×Dic₄₃	1	2	yes	—
352	#120	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	#117	C₂²×D₄₃	1	2	yes	—
356	C₂×C₂²⋊C₄	—	86	1	no	—
357	C₂×C₄²	—	43	1	no	—
358	C₂×C₄²	—	43	1	no	—
359	#108	—	43	4	no	—
360	#108	—	86	4	no	—
361	#108	—	86	2	no	—
362	#107	C₂×Dic₄₃	1	1	yes	characteristic
363	#107	C₂×Dic₄₃	1	1	yes	characteristic
364	#106	C₂×Dic₄₃	1	2	yes	—
365	C₄⋊C₈	—	86	2	no	—
366	C₄⋊C₈	—	86	2	no	—
367	#104	—	86	4	no	—
368	#104	—	172	2	no	—
369	#103	C₂×Dic₄₃	1	2	yes	—
370	#103	C₂×Dic₄₃	1	2	yes	—
371	#102	C₂×Dic₄₃	1	2	yes	—
372	#102	C₂×Dic₄₃	1	2	yes	—
373	C₂²⋊C₈	—	43	1	no	—
374	C₂²⋊C₈	—	43	1	no	—
375	C₂²⋊C₈	—	43	1	no	—
376	C₂²⋊C₈	—	43	1	no	—
377	C₂²⋊C₈	—	86	2	no	—
378	C₂²⋊C₈	—	86	2	no	—
379	#97	—	86	2	no	—
380	C₄×C₈	—	86	2	no	—
381	C₄×C₈	—	86	2	no	—
382	C₄×C₈	—	86	2	no	—
383	#95	—	86	1	no	—
384	C₂⁴	#10621900	1	1	yes	characteristic
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	2	2	no	—
388	#41	—	2	2	no	—
389	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	86	1	no	—
400	C₂²×C₄	—	86	1	no	—
401	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
402	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
403	C₂²×C₄	#10621900	1	1	yes	characteristic
404	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
405	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
406	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
407	Q₁₆	—	2	2	no	—
408	SD₁₆	—	2	4	no	—
409	D₈	—	2	2	no	—
410	M₁₆	—	43	4	no	—
411	M₁₆	—	86	2	no	—
412	M₁₆	—	86	2	no	—
413	M₁₆	—	86	2	no	—
414	M₁₆	—	172	4	no	—
415	M₁₆	—	172	4	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	43	1	no	—
423	C₂×C₈	—	43	1	no	—
424	C₂×C₈	—	43	1	no	—
425	C₂×C₈	—	43	1	no	—
426	C₂×C₈	—	86	1	no	—
427	C₂×C₈	—	86	2	no	—
428	C₂×C₈	—	86	1	no	—
429	C₂×C₈	—	86	1	no	—
430	C₂×C₈	—	86	1	no	—
431	C₂×C₈	—	86	2	no	—
432	C₂×C₈	—	172	4	no	—
433	C₂×C₈	—	172	4	no	—
434	C₂×C₈	D₄×D₄₃	1	2	yes	—
435	C₂×C₈	#10621900	1	2	yes	—
436	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
437	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
438	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
439	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
443	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	86	4	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	86	1	no	—
452	C₄²	—	86	1	no	—
453	C₄²	—	86	1	no	—
454	C₄²	—	86	1	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	4	1	no	—
460	C₂³	D₄×Dic₄₃	1	1	yes	characteristic
461	C₂³	D₄×Dic₄₃	1	1	yes	characteristic
462	C₂³	C₂×#10621900	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	4	no	—
470	D₄	—	8	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	86	2	no	—
487	C₂×C₄	—	86	2	no	—
488	C₂×C₄	—	172	1	no	—
489	C₂×C₄	—	172	1	no	—
490	C₂×C₄	—	172	1	no	—
491	C₂×C₄	—	172	1	no	—
492	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
493	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
494	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
495	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
496	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
497	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
498	C₂×C₄	#13063371	1	1	yes	characteristic
499	C₂×C₄	#13063372	1	1	yes	characteristic
500	C₈	—	2	1	no	—
501	C₈	—	2	1	no	—
502	C₈	—	86	1	no	—
503	C₈	—	86	1	no	—
504	C₈	—	86	4	no	—
505	C₈	—	86	1	no	—
506	C₈	—	86	1	no	—
507	C₈	—	172	2	no	—
508	C₈	D₄×Dic₄₃	1	2	yes	—
509	C₈	D₄×Dic₄₃	1	2	yes	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	#14583016	1	2	yes	complemented
523	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
524	C₂²	#14583555	1	1	yes	characteristic
525	C₂²	#14583601	1	1	yes	characteristic
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	172	2	no	—
532	C₄	—	172	2	no	—
533	C₄	C₂×D₄×Dic₄₃	1	1	yes	characteristic
534	C₄	#14583382	1	1	yes	characteristic
535	C₄	#14583533	1	1	yes	characteristic
536	C₄	#14583549	1	1	yes	characteristic
537	C₂	—	2	1	no	—
538	C₂	—	2	1	no	—
539	C₂	—	2	2	no	—
540	C₂	—	4	1	no	—
541	C₂	—	8	2	no	—
542	C₂	#19137615	1	1	yes	characteristic
543	C₂	C₂×#14583016	1	1	yes	characteristic
544	C₂	#19143512	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting, prime radical	C₄₃×#3050	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#3050	D₄₃
hypocenter	C₄₃	#23018
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3050

Complements

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

N	H ≅ G/N	type
1. C₂×#14583016	C₂	semidirect
2. #19143322	C₂	semidirect
3. C₂²×#13063261	C₂	semidirect
4. #19135484	C₂	semidirect
5. #19135344	C₂	semidirect
6. #19135245	C₂	semidirect
7. #19134898	C₂	semidirect
8. #19134872	C₂	semidirect
9. #19134476	C₂	semidirect
10. C₈×C₂²⋊Dic₄₃	C₂	semidirect
39. C₄₃×#467	C₄	semidirect
40. C₄₃×#467	C₄	semidirect
41. C₄₃×#466	C₄	semidirect
42. C₄₃×#466	C₄	semidirect
43. C₄₃×#465	C₄	semidirect
44. C₄₃×#465	C₄	semidirect
64. #13063261	D₄	semidirect
250. C₂²×C₄₃	#443	semidirect
289. #467	Dic₄₃	semidirect
290. #467	Dic₄₃	semidirect
291. #466	Dic₄₃	semidirect
292. #466	Dic₄₃	semidirect
293. #465	Dic₄₃	semidirect
294. #465	Dic₄₃	semidirect
319. C₄₃	#23018	semidirect
522. C₂²	#14583016	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583016	2
#19143322	2
C₂²×#13063261	2
#19135484	2
#19135344	2
#19135245	2
#19134898	2
#19134872	2
#19134476	2
C₈×C₂²⋊Dic₄₃	2
C₄₃×#3050	2
#23018	43