Subgroups — #25961160

Order 11008.

1878 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19147980	C₂	1	1	yes	maximal, characteristic
2	#19143599	C₂	1	4	yes	maximal, complemented
3	#19143595	C₂	1	4	yes	maximal, complemented
4	#19143589	C₂	1	4	yes	maximal, complemented
5	#19143585	C₂	1	4	yes	maximal, complemented
6	#19143533	C₂	1	1	yes	maximal, characteristic, complemented
7	#19143527	C₂	1	1	yes	maximal, characteristic, complemented
8	#19143311	C₂	1	1	yes	maximal, characteristic, complemented
9	#19143305	C₂	1	1	yes	maximal, characteristic, complemented
10	#19143300	C₂	1	1	yes	maximal, characteristic, complemented
11	#19143296	C₂	1	1	yes	maximal, characteristic, complemented
12	#19143291	C₂	1	1	yes	maximal, characteristic, complemented
13	#19143287	C₂	1	1	yes	maximal, characteristic, complemented
14	#19143240	C₂	1	1	yes	maximal, characteristic, complemented
15	#19143239	C₂	1	1	yes	maximal, characteristic, complemented
16	#19143231	C₂	1	1	yes	maximal, characteristic, complemented
17	#19143020	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14582856	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13063331	C₂²	1	1	yes	characteristic
21	C₂×#13063331	C₂²	1	1	yes	characteristic
22	C₂²×#10621872	C₂²	1	1	yes	characteristic
23	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
24	#14583521	C₄	1	2	yes	—
25	#14583514	C₄	1	2	yes	—
26	#14583507	C₄	1	2	yes	—
27	#14583500	C₄	1	2	yes	—
28	#14583491	C₄	1	4	yes	—
29	#14583482	C₄	1	4	yes	—
30	#14583452	C₂²	1	1	yes	characteristic
31	#14583445	C₂²	1	1	yes	characteristic
32	#14583433	C₂²	1	4	yes	—
33	#14583427	C₂²	1	4	yes	—
34	#14583411	C₂²	1	1	yes	characteristic
35	#14583406	C₂²	1	1	yes	characteristic
36	C₄×#10621898	C₂²	1	1	yes	characteristic
37	C₂×#13063282	C₂²	1	1	yes	characteristic
38	#14583029	C₂²	1	4	yes	complemented
39	#14583027	C₂²	1	4	yes	complemented
40	#14583027	C₂²	1	4	yes	complemented
41	C₈×Dic₈₆	C₂²	1	4	yes	complemented
42	#14582978	C₂²	1	4	yes	—
43	#14582975	C₂²	1	4	yes	—
44	#14582975	C₂²	1	4	yes	complemented
45	#14582972	C₂²	1	4	yes	—
46	#14582972	C₂²	1	4	yes	—
47	#14582970	C₂²	1	4	yes	—
48	#14582970	C₂²	1	4	yes	complemented
49	#14582968	C₂²	1	4	yes	—
50	#14582968	C₂²	1	4	yes	complemented
51	C₈×D₁₇₂	C₂²	1	4	yes	—
52	C₈×C₂²⋊D₄₃	C₂²	1	4	yes	—
53	C₈×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
54	#14582961	C₂²	1	4	yes	—
55	#14582961	C₂²	1	4	yes	complemented
56	#14582960	C₂²	1	4	yes	complemented
57	#14582958	C₂²	1	4	yes	—
58	#14582952	C₂²	1	4	yes	complemented
59	#14582950	C₂²	1	4	yes	complemented
60	#14582927	C₂²	1	1	yes	characteristic
61	#14582927	C₂²	1	1	yes	characteristic
62	#14582926	C₂²	1	1	yes	characteristic
63	#14582926	C₂²	1	1	yes	characteristic
64	#14582922	C₂²	1	1	yes	characteristic
65	#14582922	C₂²	1	1	yes	characteristic
66	#14582867	C₂²	1	1	yes	characteristic
67	#14582867	C₂²	1	1	yes	characteristic
68	#14582866	C₂²	1	1	yes	characteristic
69	#14582866	C₂²	1	1	yes	characteristic
70	#14582862	C₂²	1	1	yes	characteristic
71	#14582862	C₂²	1	1	yes	characteristic
72	#14582856	C₂²	1	2	yes	—
73	#14582856	C₂²	1	2	yes	—
74	#14582856	C₂²	1	2	yes	—
75	#14582856	C₂²	1	2	yes	—
76	#14582856	C₂²	1	2	yes	complemented
77	#14582856	C₂²	1	2	yes	complemented
78	#14582854	C₂²	1	1	yes	characteristic
79	#14582854	C₂²	1	1	yes	characteristic
80	C₄×#10621877	C₂²	1	1	yes	characteristic
81	#14582851	C₂²	1	2	yes	complemented
82	C₂×#13063235	C₂²	1	1	yes	characteristic
83	#97×D₄₃	C₂²	1	2	yes	complemented
84	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
85	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
86	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
87	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
88	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
89	C₄₃×#405	C₂²	1	1	yes	characteristic
90	C₄₃×#405	C₂²	1	1	yes	characteristic
91	C₄₃×#405	C₂²	1	2	yes	complemented
92	C₄₃×#405	C₂²	1	2	yes	complemented
93	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₄₃	C₂²	1	2	yes	complemented
95	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
96	C₂×#97×C₄₃	C₂²	1	2	yes	complemented
97	C₂×#10621898	C₂³	1	1	yes	characteristic
98	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
99	#13063331	—	2	4	no	—
100	#13063331	—	2	4	no	—
101	C₂×#10621877	C₂³	1	1	yes	characteristic
102	C₂×#10621877	C₂³	1	1	yes	characteristic
103	C₂×#10621872	—	2	4	no	—
104	C₂×#10621872	C₂³	1	2	yes	—
105	C₂×#10621872	C₂³	1	2	yes	—
106	C₂×#10621872	C₂³	1	2	yes	—
107	C₂×#10621872	C₂³	1	2	yes	—
108	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
109	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₈×D₄₃	—	2	4	no	—
111	C₂×C₈×D₄₃	C₂³	1	2	yes	—
112	C₂×C₈×D₄₃	C₂³	1	2	yes	—
113	C₂×C₈×D₄₃	C₂³	1	2	yes	—
114	C₂×C₈×D₄₃	C₂³	1	2	yes	—
115	#13063324	C₂×C₄	1	2	yes	—
116	#13063323	C₂×C₄	1	1	yes	characteristic
117	#13063321	C₂×C₄	1	1	yes	characteristic
118	#13063320	C₂×C₄	1	4	yes	—
119	#13063319	C₂×C₄	1	4	yes	—
120	#13063319	C₂×C₄	1	4	yes	—
121	#13063318	C₂×C₄	1	4	yes	—
122	#13063317	C₂×C₄	1	4	yes	—
123	#13063316	C₂×C₄	1	2	yes	—
124	#13063315	C₂×C₄	1	4	yes	—
125	#13063314	C₂×C₄	1	1	yes	characteristic
126	#13063313	C₂×C₄	1	4	yes	—
127	#13063312	C₂×C₄	1	1	yes	characteristic
128	#13063311	C₂×C₄	1	4	yes	—
129	#13063310	C₂×C₄	1	4	yes	—
130	#13063309	C₂×C₄	1	2	yes	—
131	#13063308	C₂×C₄	1	4	yes	—
132	#13063308	C₂×C₄	1	4	yes	—
133	#13063307	C₂×C₄	1	4	yes	—
134	#13063306	C₂×C₄	1	2	yes	—
135	#13063305	C₂×C₄	1	2	yes	—
136	#13063304	C₂×C₄	1	4	yes	—
137	#13063303	C₂×C₄	1	4	yes	—
138	#13063302	C₂×C₄	1	4	yes	—
139	#13063301	C₂×C₄	1	2	yes	—
140	#13063300	C₂×C₄	1	2	yes	—
141	#13063299	C₂×C₄	1	4	yes	—
142	#13063298	C₂×C₄	1	4	yes	—
143	#13063297	C₂×C₄	1	4	yes	—
144	#13063296	C₂×C₄	1	2	yes	—
145	#13063295	C₂×C₄	1	2	yes	—
146	#13063293	C₂×C₄	1	2	yes	—
147	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
148	C₄×Dic₈₆	C₂³	1	4	yes	—
149	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
150	C₄×D₁₇₂	C₂³	1	4	yes	—
151	C₄×C₂²⋊D₄₃	C₂×C₄	1	4	yes	—
152	C₄×C₂²⋊D₄₃	C₂³	1	4	yes	—
153	C₄×C₂²⋊D₄₃	C₂³	1	4	yes	—
154	#13063284	C₂³	1	1	yes	characteristic
155	#13063282	C₂×C₄	1	2	yes	—
156	#13063282	C₂×C₄	1	2	yes	—
157	#13063282	C₂³	1	2	yes	—
158	#13063282	C₂³	1	2	yes	—
159	#13063282	C₂³	1	2	yes	—
160	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
161	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
162	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
163	C₄²×D₄₃	C₂³	1	2	yes	—
164	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
165	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
166	Dic₄₃⋊C₈	C₂³	1	4	yes	—
167	Dic₄₃⋊C₈	C₂³	1	4	yes	—
168	Dic₄₃⋊C₈	C₂³	1	4	yes	—
169	Dic₄₃⋊C₈	C₂³	1	4	yes	—
170	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
171	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
172	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
173	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
174	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
175	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
176	#13063236	C₂³	1	2	yes	—
177	#13063235	C₂³	1	2	yes	—
178	#13063235	C₂³	1	2	yes	—
179	#13063235	C₂³	1	2	yes	—
180	#13063235	C₂³	1	2	yes	—
181	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
182	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
183	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
184	C₈×Dic₄₃	C₂³	1	2	yes	—
185	C₈×Dic₄₃	C₂³	1	2	yes	—
186	C₈×Dic₄₃	C₂³	1	2	yes	—
187	C₈×Dic₄₃	C₂³	1	2	yes	—
188	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
189	#131×C₄₃	—	2	4	no	—
190	#131×C₄₃	—	2	4	no	—
191	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
192	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
193	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
194	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
195	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
196	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
197	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
198	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
199	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
200	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
201	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
202	#117×C₄₃	C₂³	1	1	yes	characteristic
203	#117×C₄₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
206	#97×C₄₃	C₂³	1	1	yes	characteristic
207	#97×C₄₃	C₂³	1	1	yes	characteristic
208	#97×C₄₃	C₂³	1	1	yes	characteristic
209	#97×C₄₃	C₂³	1	1	yes	characteristic
210	#97×C₄₃	C₂³	1	2	yes	—
211	#97×C₄₃	C₂³	1	2	yes	—
212	#97×C₄₃	C₂³	1	2	yes	—
213	C₄×C₈×C₄₃	C₂³	1	2	yes	—
214	C₄×C₈×C₄₃	C₂³	1	2	yes	—
215	C₄×C₈×C₄₃	C₂³	1	2	yes	—
216	C₂³×D₄₃	C₂²×C₄	1	1	yes	characteristic
217	#41×C₄₃	—	2	2	no	—
218	#41×C₄₃	—	2	2	no	—
219	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
220	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
221	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
222	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
223	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
224	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
226	C₂×C₂²⋊D₄₃	C₂²×C₄	1	2	yes	—
227	C₂×C₂²⋊D₄₃	C₂²×C₄	1	4	yes	—
228	C₂×C₂²⋊D₄₃	C₂²×C₄	1	4	yes	—
229	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
230	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
231	#10621898	—	2	2	no	—
232	#10621898	—	2	2	no	—
233	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
234	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
235	C₂×C₄×D₄₃	—	2	2	no	—
236	C₂×C₄×D₄₃	—	2	2	no	—
237	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
238	C₂×C₄×D₄₃	C₂²×C₄	1	4	yes	—
239	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
240	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
241	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
242	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
243	M₁₆×C₄₃	—	2	2	no	—
244	M₁₆×C₄₃	—	2	2	no	—
245	M₁₆×C₄₃	—	2	4	no	—
246	M₁₆×C₄₃	—	2	4	no	—
247	C₂×C₈×C₄₃	—	2	4	no	—
248	C₂×C₈×C₄₃	—	2	4	no	—
249	C₂×C₈×C₄₃	#41	1	4	yes	—
250	C₂×C₈×C₄₃	#41	1	4	yes	—
251	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
252	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
253	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
257	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
258	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
259	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
260	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
261	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
262	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
263	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
264	C₄²×C₄₃	C₂⁴	1	2	yes	—
265	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
266	C₂²⋊Dic₄₃	C₂²×C₄	1	2	yes	—
267	C₂²⋊Dic₄₃	C₂²×C₄	1	4	yes	—
268	C₂²⋊Dic₄₃	C₂²×C₄	1	4	yes	—
269	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
270	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
271	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
272	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
273	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
274	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
275	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
276	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
277	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
278	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
279	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
280	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
281	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
282	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
283	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
284	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
285	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
286	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
287	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
288	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
289	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
290	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
291	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
292	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
293	C₄×Dic₄₃	C₂⁴	1	2	yes	—
294	C₄×Dic₄₃	C₂⁴	1	2	yes	—
295	#10621877	—	2	2	no	—
296	#10621877	—	2	2	no	—
297	C₂×C₄₃⋊C₈	—	2	2	no	—
298	C₂×C₄₃⋊C₈	—	2	2	no	—
299	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
300	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
301	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
302	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
303	#10621872	—	2	4	no	—
304	#10621872	—	2	4	no	—
305	#10621872	—	2	4	no	—
306	#10621872	—	2	4	no	—
307	C₈×D₄₃	—	2	4	no	—
308	C₈×D₄₃	—	2	4	no	—
309	C₈×D₄₃	—	2	4	no	—
310	C₈×D₄₃	—	2	4	no	—
311	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
312	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
313	C₂²×D₄₃	—	2	2	no	—
314	C₂²×D₄₃	—	4	2	no	—
315	C₂²×D₄₃	C₂³×C₄	1	2	yes	—
316	C₂²×D₄₃	C₂³×C₄	1	2	yes	—
317	Q₈×C₄₃	—	2	2	no	—
318	D₄×C₄₃	—	2	4	no	—
319	D₄×C₄₃	—	2	2	no	—
320	C₂×C₄×C₄₃	—	2	2	no	—
321	C₂×C₄×C₄₃	—	2	2	no	—
322	C₂×C₄×C₄₃	—	4	4	no	—
323	C₂×C₄×C₄₃	—	4	2	no	—
324	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
325	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
326	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
327	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
328	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
329	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
330	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
331	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
332	C₂²⋊D₄₃	—	2	4	no	—
333	C₂²⋊D₄₃	—	4	4	no	—
334	C₂²⋊D₄₃	—	4	4	no	—
335	C₂×Dic₄₃	—	2	2	no	—
336	C₂×Dic₄₃	—	4	2	no	—
337	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
338	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
339	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
340	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
341	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
342	D₁₇₂	—	2	2	no	—
343	D₁₇₂	—	4	4	no	—
344	C₄×D₄₃	—	2	4	no	—
345	C₄×D₄₃	—	2	2	no	—
346	C₄×D₄₃	—	2	2	no	—
347	C₄×D₄₃	—	2	2	no	—
348	C₄×D₄₃	—	2	2	no	—
349	C₄×D₄₃	—	4	4	no	—
350	Dic₈₆	—	2	2	no	—
351	Dic₈₆	—	4	4	no	—
352	C₈×C₄₃	—	2	2	no	—
353	C₈×C₄₃	—	2	2	no	—
354	C₈×C₄₃	C₂×#41	1	2	yes	—
355	C₈×C₄₃	C₂×#41	1	2	yes	—
356	C₈×C₄₃	C₂×#41	1	2	yes	—
357	C₈×C₄₃	C₂×#41	1	2	yes	—
358	C₄₃⋊C₈	—	2	2	no	—
359	C₄₃⋊C₈	—	2	2	no	—
360	C₄₃⋊C₈	—	2	2	no	—
361	C₄₃⋊C₈	—	2	2	no	—
362	#60209	—	43	1	no	maximal, Sylow
363	C₂²×C₄₃	—	2	2	no	—
364	C₂²×C₄₃	—	2	2	no	—
365	C₂²×C₄₃	—	2	4	no	—
366	C₂²×C₄₃	C₄×#41	1	2	yes	—
367	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
368	C₂×D₄₃	—	2	2	no	—
369	C₂×D₄₃	—	2	2	no	—
370	C₂×D₄₃	—	2	2	no	—
371	C₂×D₄₃	—	2	2	no	—
372	C₂×D₄₃	—	2	4	no	—
373	C₂×D₄₃	—	4	4	no	—
374	C₄×C₄₃	—	2	2	no	—
375	C₄×C₄₃	—	2	4	no	—
376	C₄×C₄₃	—	2	2	no	—
377	C₄×C₄₃	—	2	2	no	—
378	C₄×C₄₃	C₄×#41	1	2	yes	—
379	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
380	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
381	Dic₄₃	—	2	2	no	—
382	Dic₄₃	—	2	2	no	—
383	Dic₄₃	—	2	2	no	—
384	Dic₄₃	—	2	4	no	—
385	Dic₄₃	—	2	2	no	—
386	#3455	—	43	1	no	—
387	#2969	—	43	4	no	—
388	#2969	—	43	4	no	—
389	#2968	—	43	4	no	—
390	#2968	—	43	4	no	—
391	#2961	—	43	1	no	—
392	#2960	—	43	1	no	—
393	#2932	—	43	1	no	—
394	#2931	—	43	1	no	—
395	#2930	—	43	1	no	—
396	#2930	—	43	1	no	—
397	#2929	—	43	1	no	—
398	#2929	—	43	1	no	—
399	#2922	—	43	1	no	—
400	#2922	—	43	1	no	—
401	#2921	—	43	1	no	—
402	#2875	—	43	1	no	—
403	#2875	D₄₃	1	1	yes	characteristic, complemented
404	C₂×#405	—	43	1	no	—
405	C₂×C₄₃	—	2	2	no	—
406	C₂×C₄₃	—	4	2	no	—
407	C₂×C₄₃	C₂×C₄×#41	1	1	yes	characteristic
408	C₂×C₄₃	#3573	1	2	yes	—
409	D₄₃	—	4	2	no	—
410	D₄₃	—	4	2	no	—
411	C₂×#131	—	43	1	no	—
412	C₂×#131	—	43	1	no	—
413	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
414	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
415	C₂²×M₁₆	—	43	1	no	—
416	C₂³×C₈	—	43	1	no	—
417	#542	—	43	2	no	—
418	#542	—	43	2	no	—
419	#541	—	43	2	no	—
420	#540	—	43	2	no	—
421	#539	—	43	4	no	—
422	#538	—	43	4	no	—
423	#533	—	43	1	no	—
424	#532	—	43	1	no	—
425	#529	—	43	4	no	—
426	#529	—	43	4	no	—
427	#525	—	43	1	no	—
428	#525	—	43	1	no	—
429	C₄×#41	—	43	1	no	—
430	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
431	C₂×#117	—	43	1	no	—
432	#446	—	43	4	no	—
433	#446	—	43	4	no	—
434	#446	—	43	4	no	—
435	C₈×Q₈	—	43	4	no	—
436	#436	—	43	4	no	—
437	#436	—	43	4	no	—
438	#436	—	43	4	no	—
439	#435	—	43	4	no	—
440	#435	—	43	4	no	—
441	#435	—	43	4	no	—
442	#435	—	43	4	no	—
443	#435	—	43	4	no	—
444	#435	—	43	4	no	—
445	C₈×D₄	—	43	4	no	—
446	C₈×D₄	—	43	4	no	—
447	C₈×D₄	—	43	4	no	—
448	#433	—	43	4	no	—
449	#433	—	43	4	no	—
450	#433	—	43	4	no	—
451	#433	—	43	4	no	—
452	#431	—	43	4	no	—
453	#431	—	43	4	no	—
454	#424	—	43	1	no	—
455	#424	—	43	1	no	—
456	#424	—	43	1	no	—
457	#424	—	43	1	no	—
458	#423	—	43	1	no	—
459	#423	—	43	1	no	—
460	#408	—	43	1	no	—
461	#408	—	43	1	no	—
462	#408	—	43	1	no	—
463	#408	—	43	1	no	—
464	#407	—	43	1	no	—
465	#407	—	43	1	no	—
466	#405	—	43	1	no	—
467	#405	—	43	1	no	—
468	#405	—	43	2	no	—
469	#405	—	43	2	no	—
470	#405	—	43	2	no	—
471	#405	—	43	2	no	—
472	#405	—	43	2	no	—
473	#405	—	43	2	no	—
474	#405	C₂×D₄₃	1	1	yes	characteristic
475	#405	C₂×D₄₃	1	1	yes	characteristic
476	#405	C₂×D₄₃	1	2	yes	complemented
477	#405	C₂×D₄₃	1	2	yes	complemented
478	C₄×M₁₆	—	43	1	no	—
479	C₄×M₁₆	—	43	2	no	—
480	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
481	C₄×M₁₆	C₂×D₄₃	1	2	yes	complemented
482	C₂×#97	—	43	1	no	—
483	C₂×#97	—	43	2	no	—
484	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
485	C₂×#97	C₂×D₄₃	1	2	yes	complemented
486	C₂×C₄×C₈	—	43	1	no	—
487	C₂×C₄×C₈	—	43	1	no	—
488	C₄₃	#60209	1	1	yes	characteristic, complemented, Sylow
489	C₂×#41	—	43	1	no	—
490	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
491	C₂³×C₄	—	43	1	no	—
492	#131	—	2	4	no	—
493	#131	—	2	4	no	—
494	#131	—	86	4	no	—
495	#131	—	86	4	no	—
496	C₂×M₁₆	—	43	1	no	—
497	C₂×M₁₆	—	43	1	no	—
498	C₂×M₁₆	—	43	2	no	—
499	C₂×M₁₆	—	43	2	no	—
500	C₂×M₁₆	—	43	2	no	—
501	C₂×M₁₆	—	43	2	no	—
502	C₂×M₁₆	—	86	4	no	—
503	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
504	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
505	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
506	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
507	C₂²×C₈	—	43	1	no	—
508	C₂²×C₈	—	43	1	no	—
509	C₂²×C₈	—	43	2	no	—
510	C₂²×C₈	—	43	2	no	—
511	C₂²×C₈	—	43	2	no	—
512	C₂²×C₈	—	43	2	no	—
513	C₂²×C₈	—	86	4	no	—
514	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
515	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
516	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
517	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
518	C₄⋊Q₈	—	43	1	no	—
519	C₄⋊Q₈	—	43	2	no	—
520	#127	—	43	1	no	—
521	#126	—	43	4	no	—
522	#126	—	43	4	no	—
523	#126	—	43	4	no	—
524	#126	—	43	4	no	—
525	#125	—	43	4	no	—
526	#125	—	43	2	no	—
527	#125	—	43	4	no	—
528	#124	—	43	1	no	—
529	#124	—	43	1	no	—
530	#124	—	43	4	no	—
531	#124	—	43	4	no	—
532	#123	—	43	2	no	—
533	#123	—	43	4	no	—
534	#123	—	43	4	no	—
535	#123	—	43	4	no	—
536	#123	—	43	2	no	—
537	#123	—	43	4	no	—
538	C₂²⋊Q₈	—	43	2	no	—
539	C₂²⋊Q₈	—	43	4	no	—
540	C₂²⋊Q₈	—	43	2	no	—
541	C₂²⋊Q₈	—	43	4	no	—
542	C₂²⋊Q₈	—	43	4	no	—
543	#121	—	43	2	no	—
544	#121	—	43	4	no	—
545	#121	—	43	4	no	—
546	#121	—	43	2	no	—
547	#121	—	43	4	no	—
548	#120	—	43	2	no	—
549	#120	—	43	2	no	—
550	C₄×Q₈	—	43	2	no	—
551	C₄×Q₈	—	43	4	no	—
552	C₄×Q₈	C₄×D₄₃	1	2	yes	—
553	C₄×D₄	—	43	4	no	—
554	C₄×D₄	—	43	4	no	—
555	C₄×D₄	—	43	4	no	—
556	C₄×D₄	—	43	2	no	—
557	C₄×D₄	—	43	4	no	—
558	C₄×D₄	C₄×D₄₃	1	4	yes	—
559	C₄×D₄	C₄×D₄₃	1	2	yes	—
560	#117	—	43	1	no	—
561	#117	—	43	2	no	—
562	#117	—	43	2	no	—
563	#117	—	43	2	no	—
564	#117	—	43	2	no	—
565	#117	—	43	2	no	—
566	#117	C₂²×D₄₃	1	1	yes	characteristic
567	#117	C₂²×D₄₃	1	2	yes	—
568	C₂×C₄⋊C₄	—	43	2	no	—
569	C₂×C₂²⋊C₄	—	43	2	no	—
570	C₂×C₄²	—	43	1	no	—
571	C₂×C₄²	—	43	2	no	—
572	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
573	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
574	C₄⋊C₈	—	43	4	no	—
575	C₄⋊C₈	—	43	4	no	—
576	C₄⋊C₈	—	43	4	no	—
577	C₄⋊C₈	—	43	4	no	—
578	C₄⋊C₈	—	43	4	no	—
579	C₄⋊C₈	—	43	4	no	—
580	C₂²⋊C₈	—	43	4	no	—
581	C₂²⋊C₈	—	43	4	no	—
582	C₂²⋊C₈	—	43	4	no	—
583	C₂²⋊C₈	—	43	4	no	—
584	C₂²⋊C₈	—	43	4	no	—
585	C₂²⋊C₈	—	43	4	no	—
586	#97	—	43	2	no	—
587	#97	—	43	2	no	—
588	#97	—	43	2	no	—
589	#97	—	43	2	no	—
590	#97	—	43	2	no	—
591	#97	C₂²×D₄₃	1	1	yes	characteristic
592	#97	C₂²×D₄₃	1	1	yes	characteristic
593	#97	C₂²×D₄₃	1	1	yes	characteristic
594	#97	C₂²×D₄₃	1	1	yes	characteristic
595	#97	C₂²×D₄₃	1	2	yes	—
596	#97	C₂²×D₄₃	1	2	yes	—
597	#97	C₂²×D₄₃	1	2	yes	—
598	C₄×C₈	—	43	2	no	—
599	C₄×C₈	—	43	2	no	—
600	C₄×C₈	—	43	2	no	—
601	C₄×C₈	—	43	2	no	—
602	C₄×C₈	—	43	2	no	—
603	C₄×C₈	—	43	2	no	—
604	C₄×C₈	—	43	2	no	—
605	C₄×C₈	C₂²×D₄₃	1	2	yes	—
606	C₄×C₈	C₂²×D₄₃	1	2	yes	—
607	C₄×C₈	C₂²×D₄₃	1	2	yes	—
608	C₂⁴	—	43	1	no	—
609	#41	—	2	2	no	—
610	#41	—	2	2	no	—
611	#41	—	86	2	no	—
612	#41	—	86	2	no	—
613	C₂×Q₈	—	43	1	no	—
614	C₂×Q₈	—	43	4	no	—
615	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
616	C₂×D₄	—	43	2	no	—
617	C₂×D₄	—	43	4	no	—
618	C₂×D₄	—	43	4	no	—
619	C₂×D₄	—	43	1	no	—
620	C₂×D₄	—	43	4	no	—
621	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
622	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
623	C₂²×C₄	—	43	1	no	—
624	C₂²×C₄	—	43	2	no	—
625	C₂²×C₄	—	43	2	no	—
626	C₂²×C₄	—	43	2	no	—
627	C₂²×C₄	—	43	2	no	—
628	C₂²×C₄	—	43	4	no	—
629	C₂²×C₄	—	86	2	no	—
630	C₂²×C₄	—	86	2	no	—
631	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
632	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
633	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
634	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
635	M₁₆	—	2	2	no	—
636	M₁₆	—	2	2	no	—
637	M₁₆	—	2	4	no	—
638	M₁₆	—	2	4	no	—
639	M₁₆	—	86	2	no	—
640	M₁₆	—	86	2	no	—
641	M₁₆	—	86	4	no	—
642	M₁₆	—	86	4	no	—
643	M₁₆	—	86	4	no	—
644	M₁₆	—	86	4	no	—
645	C₂×C₈	—	2	4	no	—
646	C₂×C₈	—	2	4	no	—
647	C₂×C₈	—	43	2	no	—
648	C₂×C₈	—	43	2	no	—
649	C₂×C₈	—	43	2	no	—
650	C₂×C₈	—	43	2	no	—
651	C₂×C₈	—	86	2	no	—
652	C₂×C₈	—	86	2	no	—
653	C₂×C₈	—	86	4	no	—
654	C₂×C₈	—	86	4	no	—
655	C₂×C₈	—	86	4	no	—
656	C₂×C₈	—	86	4	no	—
657	C₂×C₈	#10621898	1	4	yes	—
658	C₂×C₈	#10621898	1	4	yes	—
659	C₂×C₈	C₂³×D₄₃	1	2	yes	—
660	C₂×C₈	C₂³×D₄₃	1	2	yes	—
661	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
662	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
663	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
664	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
665	C₄⋊C₄	—	43	2	no	—
666	C₄⋊C₄	—	43	2	no	—
667	C₄⋊C₄	—	43	2	no	—
668	C₄⋊C₄	—	43	2	no	—
669	C₄⋊C₄	—	43	2	no	—
670	C₄⋊C₄	—	43	4	no	—
671	C₄⋊C₄	—	43	4	no	—
672	C₄⋊C₄	—	43	4	no	—
673	C₄⋊C₄	—	43	4	no	—
674	C₄⋊C₄	—	43	4	no	—
675	C₄⋊C₄	—	43	4	no	—
676	C₄⋊C₄	—	43	4	no	—
677	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
678	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
679	C₂²⋊C₄	—	43	2	no	—
680	C₂²⋊C₄	—	43	4	no	—
681	C₂²⋊C₄	—	43	4	no	—
682	C₂²⋊C₄	—	43	2	no	—
683	C₂²⋊C₄	—	43	2	no	—
684	C₂²⋊C₄	—	43	2	no	—
685	C₂²⋊C₄	—	43	2	no	—
686	C₂²⋊C₄	—	43	4	no	—
687	C₂²⋊C₄	—	43	4	no	—
688	C₂²⋊C₄	—	43	4	no	—
689	C₂²⋊C₄	—	43	4	no	—
690	C₂²⋊C₄	—	43	4	no	—
691	C₂²⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
692	C₂²⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
693	C₄²	—	43	1	no	—
694	C₄²	—	43	1	no	—
695	C₄²	—	43	4	no	—
696	C₄²	—	43	2	no	—
697	C₄²	—	43	2	no	—
698	C₄²	C₂×C₄×D₄₃	1	2	yes	—
699	C₄²	C₂×C₄×D₄₃	1	4	yes	—
700	C₄²	C₂³×D₄₃	1	1	yes	characteristic
701	C₄²	C₂³×D₄₃	1	1	yes	characteristic
702	C₄²	C₂³×D₄₃	1	2	yes	—
703	C₂³	—	43	2	no	—
704	C₂³	—	43	2	no	—
705	C₂³	—	86	2	no	—
706	C₂³	—	172	2	no	—
707	C₂³	C₂²×C₄×D₄₃	1	2	yes	—
708	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
709	Q₈	—	2	2	no	—
710	Q₈	—	86	2	no	—
711	Q₈	—	172	4	no	—
712	D₄	—	2	4	no	—
713	D₄	—	2	2	no	—
714	D₄	—	86	4	no	—
715	D₄	—	86	2	no	—
716	D₄	—	172	4	no	—
717	D₄	—	172	4	no	—
718	D₄	—	172	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	—	43	2	no	—
724	C₂×C₄	—	43	4	no	—
725	C₂×C₄	—	43	2	no	—
726	C₂×C₄	—	43	2	no	—
727	C₂×C₄	—	43	2	no	—
728	C₂×C₄	—	86	2	no	—
729	C₂×C₄	—	86	4	no	—
730	C₂×C₄	—	86	2	no	—
731	C₂×C₄	—	86	2	no	—
732	C₂×C₄	—	86	2	no	—
733	C₂×C₄	—	86	2	no	—
734	C₂×C₄	—	172	4	no	—
735	C₂×C₄	—	172	2	no	—
736	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
737	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
738	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
739	C₂×C₄	C₂²×C₄×D₄₃	1	4	yes	—
740	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
741	C₂×C₄	C₂×#10621898	1	2	yes	—
742	C₂×C₄	C₂×#10621898	1	2	yes	—
743	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
744	C₈	—	2	2	no	—
745	C₈	—	2	2	no	—
746	C₈	—	86	2	no	—
747	C₈	—	86	2	no	—
748	C₈	—	86	2	no	—
749	C₈	—	86	2	no	—
750	C₈	C₂×#10621898	1	2	yes	—
751	C₈	C₂×#10621898	1	2	yes	—
752	C₈	C₂×#10621898	1	2	yes	—
753	C₈	C₂×#10621898	1	2	yes	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	86	4	no	—
758	C₂²	—	86	2	no	—
759	C₂²	—	86	2	no	—
760	C₂²	—	86	2	no	—
761	C₂²	—	86	2	no	—
762	C₂²	—	172	4	no	—
763	C₂²	C₄×#10621898	1	2	yes	—
764	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	2	4	no	—
768	C₄	—	2	2	no	—
769	C₄	—	86	2	no	—
770	C₄	—	86	4	no	—
771	C₄	—	86	2	no	—
772	C₄	—	86	2	no	—
773	C₄	—	86	2	no	—
774	C₄	C₄×#10621898	1	2	yes	—
775	C₄	C₂²×#10621898	1	1	yes	characteristic
776	C₄	C₂²×#10621898	1	1	yes	characteristic
777	C₂	—	2	2	no	—
778	C₂	—	4	2	no	—
779	C₂	—	172	2	no	—
780	C₂	—	172	2	no	—
781	C₂	C₂×C₄×#10621898	1	1	yes	characteristic
782	C₂	#19149308	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁴×C₄
Fitting	C₄₃×#2875	C₂
prime radical	#19147980	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	#2875	D₄₃
hypocenter	C₄₃	#60209
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #2875

Complements

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

N	H ≅ G/N	type
2. #19143599	C₂	semidirect
3. #19143595	C₂	semidirect
4. #19143589	C₂	semidirect
5. #19143585	C₂	semidirect
6. #19143533	C₂	semidirect
7. #19143527	C₂	semidirect
8. #19143311	C₂	semidirect
9. #19143305	C₂	semidirect
10. #19143300	C₂	semidirect
11. #19143296	C₂	semidirect
12. #19143291	C₂	semidirect
13. #19143287	C₂	semidirect
14. #19143240	C₂	semidirect
15. #19143239	C₂	semidirect
16. #19143231	C₂	semidirect
17. #19143020	C₂	semidirect
18. C₂×#14582856	C₂	semidirect
19. C₄₃×#2875	C₂	semidirect
38. #14583029	C₂²	semidirect
39. #14583027	C₂²	semidirect
40. #14583027	C₂²	semidirect
41. C₈×Dic₈₆	C₂²	semidirect
44. #14582975	C₂²	semidirect
48. #14582970	C₂²	semidirect
50. #14582968	C₂²	semidirect
53. C₈×C₂²⋊D₄₃	C₂²	semidirect
55. #14582961	C₂²	semidirect
56. #14582960	C₂²	semidirect
58. #14582952	C₂²	semidirect
59. #14582950	C₂²	semidirect
76. #14582856	C₂²	semidirect
77. #14582856	C₂²	semidirect
81. #14582851	C₂²	semidirect
83. #97×D₄₃	C₂²	semidirect
91. C₄₃×#405	C₂²	semidirect
92. C₄₃×#405	C₂²	semidirect
94. C₄×M₁₆×C₄₃	C₂²	semidirect
96. C₂×#97×C₄₃	C₂²	semidirect
403. #2875	D₄₃	semidirect
476. #405	C₂×D₄₃	semidirect
477. #405	C₂×D₄₃	semidirect
481. C₄×M₁₆	C₂×D₄₃	semidirect
485. C₂×#97	C₂×D₄₃	semidirect
488. C₄₃	#60209	semidirect

Maximal subgroups

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

subgroup	index
#19147980	2
#19143599	2
#19143595	2
#19143589	2
#19143585	2
#19143533	2
#19143527	2
#19143311	2
#19143305	2
#19143300	2
#19143296	2
#19143291	2
#19143287	2
#19143240	2
#19143239	2
#19143231	2
#19143020	2
C₂×#14582856	2
C₄₃×#2875	2
#60209	43