Subgroups — #25097046

Order 11008.

1070 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582940	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582938	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582934	C₂	1	1	yes	maximal, characteristic
4	C₂×#107×D₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582856	C₂	1	1	yes	maximal, characteristic
6	#19137220	C₂	1	1	yes	maximal, characteristic
7	#19137216	C₂	1	1	yes	maximal, characteristic
8	#19134763	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134762	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134760	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134757	C₂	1	1	yes	maximal, characteristic, complemented
12	#19134756	C₂	1	1	yes	maximal, characteristic, complemented
13	#19134754	C₂	1	1	yes	maximal, characteristic, complemented
14	#19134753	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1847	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10621872	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
18	C₂×#13063283	C₂²	1	1	yes	characteristic
19	C₂×#13063283	C₂²	1	1	yes	characteristic
20	C₂×#13063282	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic
23	#14582940	—	2	4	no	—
24	#14582938	—	2	4	no	—
25	#14582934	—	2	4	no	—
26	C₂×#13063259	C₂²	1	1	yes	characteristic
27	C₂×#13063259	C₂²	1	1	yes	characteristic
28	C₂×#13063258	C₂²	1	1	yes	characteristic
29	C₂×#13063258	C₂²	1	1	yes	characteristic
30	C₂×#13063258	C₂²	1	1	yes	characteristic
31	C₂×#13063258	C₂²	1	1	yes	characteristic
32	C₂×#13063258	C₂²	1	1	yes	characteristic
33	C₂×#13063258	C₂²	1	1	yes	characteristic
34	#107×D₄₃	—	2	4	no	—
35	C₂×#13063257	C₂²	1	1	yes	characteristic
36	C₂×#13063257	C₂²	1	1	yes	characteristic
37	C₂×#13063256	C₂²	1	1	yes	characteristic
38	C₂×#13063256	C₂²	1	1	yes	characteristic
39	#14582856	C₄	1	8	yes	complemented
40	C₂×#13063235	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
43	#14582796	—	2	2	no	—
44	#14582794	—	2	2	no	—
45	#14582773	—	2	2	no	—
46	#14582770	—	2	2	no	—
47	#14582769	C₂²	1	1	yes	characteristic
48	#14582768	C₂²	1	1	yes	characteristic
49	#14582768	C₂²	1	1	yes	characteristic
50	#14582765	C₂²	1	1	yes	characteristic
51	#14582764	C₂²	1	1	yes	characteristic
52	#14582764	C₂²	1	1	yes	characteristic
53	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
54	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
55	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
56	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
57	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
58	C₄₃×#384	C₂²	1	1	yes	characteristic
59	C₄₃×#382	C₂²	1	1	yes	characteristic
60	C₂²×C₄×D₄₃	—	2	1	no	—
61	C₂²×C₄×D₄₃	—	2	1	no	—
62	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
63	C₂×#10621872	C₂×C₄	1	4	yes	—
64	C₂×#10621872	D₄	1	4	yes	—
65	C₂×#10621872	Q₈	1	4	yes	—
66	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₄₃	C₂×C₄	1	4	yes	—
69	C₂×C₈×D₄₃	D₄	1	4	yes	—
70	C₂×C₈×D₄₃	Q₈	1	4	yes	—
71	#13063283	—	2	2	no	—
72	#13063283	—	2	2	no	—
73	#13063283	—	2	2	no	—
74	#13063283	—	2	2	no	—
75	#13063282	C₂×C₄	1	4	yes	—
76	#13063282	Q₈	1	4	yes	—
77	C₂×C₄⋊Dic₄₃	—	2	2	no	—
78	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
82	C₂×Dic₄₃⋊C₄	—	2	1	no	—
83	C₂×Dic₄₃⋊C₄	—	2	1	no	—
84	C₂×Dic₄₃⋊C₄	—	2	2	no	—
85	C₂×Dic₄₃⋊C₄	—	2	2	no	—
86	C₂×Dic₄₃⋊C₄	D₄	1	2	yes	—
87	C₄⋊C₄×D₄₃	—	2	2	no	—
88	C₄⋊C₄×D₄₃	—	2	2	no	—
89	C₄⋊C₄×D₄₃	—	2	2	no	—
90	C₄⋊C₄×D₄₃	—	2	2	no	—
91	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
92	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
93	C₂×(C₂×D₄₃)⋊C₄	D₄	1	2	yes	—
94	C₂×C₄×Dic₄₃	—	2	1	no	—
95	C₂×C₄×Dic₄₃	—	2	1	no	—
96	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
97	#13063259	—	2	2	no	—
98	#13063259	—	2	2	no	—
99	#13063258	—	2	2	no	—
100	#13063258	—	2	2	no	—
101	#13063258	—	2	2	no	—
102	#13063258	—	2	2	no	—
103	#13063258	—	2	2	no	—
104	#13063258	—	2	2	no	—
105	#13063257	—	2	2	no	—
106	#13063257	—	2	2	no	—
107	#13063256	—	2	2	no	—
108	#13063256	—	2	2	no	—
109	#13063235	C₂×C₄	1	4	yes	complemented
110	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	complemented
111	C₈×Dic₄₃	C₂×C₄	1	4	yes	complemented
112	C₄₃⋊#95	—	2	2	no	—
113	C₄₃⋊#95	—	2	2	no	—
114	C₄₃⋊#95	—	2	2	no	—
115	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
118	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
123	#107×C₄₃	—	2	2	no	—
124	#107×C₄₃	—	2	2	no	—
125	#106×C₄₃	—	2	2	no	—
126	#106×C₄₃	—	2	2	no	—
127	#97×C₄₃	C₂×C₄	1	4	yes	complemented
128	#95×C₄₃	—	2	2	no	—
129	C₂³×D₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	—	2	1	no	—
131	C₂²×C₄×C₄₃	—	2	1	no	—
132	C₂²×C₄×C₄₃	—	2	1	no	—
133	C₂²×C₄×C₄₃	—	2	1	no	—
134	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
136	C₂²×Dic₄₃	—	2	1	no	—
137	C₂²×Dic₄₃	—	2	1	no	—
138	C₂²×Dic₄₃	—	2	1	no	—
139	C₂²×Dic₄₃	—	2	1	no	—
140	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
141	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×D₄₃	—	4	2	no	—
143	C₂×C₄×D₄₃	—	4	2	no	—
144	C₂×C₄×D₄₃	—	8	2	no	—
145	C₂×C₄×D₄₃	—	8	2	no	—
146	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
147	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
148	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
149	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
150	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
151	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
152	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
157	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
158	C₄⋊C₄×C₄₃	—	2	1	no	—
159	C₄⋊C₄×C₄₃	—	2	1	no	—
160	C₄⋊C₄×C₄₃	—	2	1	no	—
161	C₄⋊C₄×C₄₃	—	2	1	no	—
162	C₄⋊C₄×C₄₃	—	2	1	no	—
163	C₄⋊C₄×C₄₃	—	2	1	no	—
164	C₄⋊C₄×C₄₃	—	2	1	no	—
165	C₄⋊C₄×C₄₃	—	2	1	no	—
166	C₄⋊C₄×C₄₃	—	8	2	no	—
167	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
168	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
169	(C₂×D₄₃)⋊C₄	—	4	2	no	—
170	(C₂×D₄₃)⋊C₄	—	4	2	no	—
171	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	8	yes	—
172	C₄⋊Dic₄₃	—	2	1	no	—
173	C₄⋊Dic₄₃	—	2	1	no	—
174	C₄⋊Dic₄₃	—	2	1	no	—
175	C₄⋊Dic₄₃	—	2	1	no	—
176	C₄⋊Dic₄₃	—	2	1	no	—
177	C₄⋊Dic₄₃	—	2	1	no	—
178	C₄⋊Dic₄₃	—	2	1	no	—
179	C₄⋊Dic₄₃	—	2	1	no	—
180	C₄⋊Dic₄₃	—	8	2	no	—
181	Dic₄₃⋊C₄	—	4	2	no	—
182	Dic₄₃⋊C₄	—	4	2	no	—
183	Dic₄₃⋊C₄	—	8	2	no	—
184	Dic₄₃⋊C₄	—	8	2	no	—
185	Dic₄₃⋊C₄	C₄⋊C₄	1	8	yes	—
186	C₄×Dic₄₃	—	4	2	no	—
187	C₄×Dic₄₃	—	4	2	no	—
188	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
189	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
190	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
191	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
192	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
193	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
194	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
195	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
196	#10621872	C₄⋊C₄	1	16	yes	complemented
197	C₈×D₄₃	C₄⋊C₄	1	16	yes	complemented
198	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	C₂²×D₄₃	—	2	2	no	—
200	C₂²×D₄₃	—	2	2	no	—
201	C₂²×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
202	C₂²×D₄₃	#127	1	2	yes	—
203	C₂²×D₄₃	C₄⋊Q₈	1	2	yes	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	2	2	no	—
206	C₂×C₄×C₄₃	—	4	1	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	—	4	1	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	2	no	—
213	C₂×C₄×C₄₃	—	4	2	no	—
214	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
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	C₂²×Q₈	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂²×Q₈	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	C₂×Dic₄₃	—	4	2	no	—
228	C₂×Dic₄₃	—	4	2	no	—
229	C₂×Dic₄₃	—	4	2	no	—
230	C₂×Dic₄₃	—	4	2	no	—
231	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
232	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
233	C₂×Dic₄₃	#127	1	2	yes	—
234	C₂×Dic₄₃	C₄⋊Q₈	1	2	yes	—
235	C₄×D₄₃	—	8	4	no	—
236	C₄×D₄₃	—	8	4	no	—
237	C₄×D₄₃	C₂×C₄⋊C₄	1	4	yes	—
238	C₄×D₄₃	C₂×C₄⋊C₄	1	4	yes	—
239	C₄×D₄₃	C₄⋊Q₈	1	4	yes	—
240	C₄×D₄₃	C₄⋊Q₈	1	4	yes	—
241	C₈×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
242	C₈×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
243	C₄₃⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
244	C₄₃⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
245	#20803	—	43	1	no	maximal, Sylow
246	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
247	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
248	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
249	C₂²×C₄₃	#576	1	2	yes	—
250	C₂²×C₄₃	#578	1	2	yes	—
251	C₂×D₄₃	—	2	2	no	—
252	C₂×D₄₃	—	2	2	no	—
253	C₂×D₄₃	—	2	4	no	—
254	C₂×D₄₃	—	2	4	no	—
255	C₂×D₄₃	#384	1	4	yes	—
256	C₄×C₄₃	—	2	4	no	—
257	C₄×C₄₃	—	8	1	no	—
258	C₄×C₄₃	—	8	1	no	—
259	C₄×C₄₃	—	8	1	no	—
260	C₄×C₄₃	—	8	1	no	—
261	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
262	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
263	C₄×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
264	C₄×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
265	Dic₄₃	—	2	4	no	—
266	Dic₄₃	—	8	1	no	—
267	Dic₄₃	—	8	1	no	—
268	Dic₄₃	—	8	1	no	—
269	Dic₄₃	—	8	1	no	—
270	Dic₄₃	#384	1	4	yes	—
271	C₂×#428	—	43	1	no	—
272	C₂×#428	—	43	1	no	—
273	C₂×#427	—	43	1	no	—
274	C₂²×#107	—	43	1	no	—
275	C₂×#405	—	43	1	no	—
276	#2317	—	43	1	no	—
277	#2317	—	43	1	no	—
278	#1847	—	43	1	no	—
279	#1847	—	43	1	no	—
280	#1847	—	43	1	no	—
281	#1847	D₄₃	1	1	yes	characteristic, complemented
282	#1846	—	43	1	no	—
283	#1846	—	43	1	no	—
284	#1845	—	43	1	no	—
285	#1845	—	43	1	no	—
286	C₂×C₄₃	C₂×#384	1	1	yes	characteristic
287	C₂×C₄₃	#2913	1	2	yes	—
288	C₂×C₄₃	#3155	1	1	yes	characteristic
289	C₂×C₄₃	#3156	1	1	yes	characteristic
290	C₂×C₄₃	#3164	1	2	yes	—
291	D₄₃	—	2	4	no	—
292	C₂²×M₁₆	—	43	1	no	—
293	C₂³×C₈	—	43	1	no	—
294	C₂×#117	—	43	1	no	—
295	C₂×#117	—	43	1	no	—
296	C₂×#117	—	43	1	no	—
297	C₂²×C₄⋊C₄	—	43	1	no	—
298	C₂²×C₄⋊C₄	—	43	1	no	—
299	#428	—	86	4	no	—
300	#428	—	86	4	no	—
301	#427	—	86	4	no	—
302	C₂×#107	—	43	1	no	—
303	C₂×#107	—	43	1	no	—
304	C₂×#107	—	43	1	no	—
305	C₂×#107	—	43	1	no	—
306	C₂×#107	—	43	1	no	—
307	C₂×#107	—	43	1	no	—
308	C₂×#107	—	43	1	no	—
309	C₂×#107	—	43	1	no	—
310	C₂×#107	—	86	4	no	—
311	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
312	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
313	C₂×#106	—	43	1	no	—
314	C₂×#106	—	43	1	no	—
315	C₂×#106	—	43	1	no	—
316	C₂×#106	—	43	1	no	—
317	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
318	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
319	#405	—	43	8	no	—
320	C₂×#97	—	43	1	no	—
321	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
322	C₂×C₄×C₈	—	43	1	no	—
323	C₂×C₄×C₈	—	43	1	no	—
324	#389	—	86	2	no	—
325	#389	—	86	2	no	—
326	#385	—	86	2	no	—
327	#385	—	86	2	no	—
328	#384	—	43	1	no	—
329	#384	—	43	1	no	—
330	#384	—	43	1	no	—
331	#384	C₂×D₄₃	1	1	yes	characteristic
332	#382	—	43	1	no	—
333	#382	—	43	1	no	—
334	#382	—	43	1	no	—
335	#382	C₂×D₄₃	1	1	yes	characteristic
336	C₄₃	#20803	1	1	yes	characteristic, complemented, Sylow
337	C₂³×C₄	—	43	1	no	—
338	C₂³×C₄	—	86	1	no	—
339	C₂³×C₄	—	86	1	no	—
340	C₂×M₁₆	—	43	4	no	—
341	C₂×M₁₆	—	43	4	no	—
342	C₂×M₁₆	—	43	4	no	—
343	C₂²×C₈	—	43	1	no	—
344	C₂²×C₈	—	43	1	no	—
345	C₂²×C₈	—	43	4	no	—
346	C₂²×C₈	—	43	4	no	—
347	C₂²×C₈	—	43	4	no	—
348	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
349	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
350	#117	—	43	4	no	—
351	#117	—	43	4	no	—
352	#117	—	86	2	no	—
353	#117	—	86	2	no	—
354	#117	—	86	2	no	—
355	#117	—	86	2	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	43	2	no	—
358	C₂×C₄⋊C₄	—	43	1	no	—
359	C₂×C₄⋊C₄	—	43	1	no	—
360	C₂×C₄⋊C₄	—	43	1	no	—
361	C₂×C₄⋊C₄	—	43	1	no	—
362	C₂×C₄⋊C₄	—	86	2	no	—
363	C₂×C₄⋊C₄	—	86	2	no	—
364	C₂×C₄⋊C₄	—	86	2	no	—
365	C₂×C₄⋊C₄	—	86	2	no	—
366	C₂×C₄⋊C₄	—	86	2	no	—
367	C₂×C₄⋊C₄	—	86	2	no	—
368	C₂×C₄⋊C₄	—	86	2	no	—
369	C₂×C₄⋊C₄	—	86	1	no	—
370	C₂×C₄⋊C₄	—	86	1	no	—
371	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	—	43	2	no	—
376	C₂×C₂²⋊C₄	—	86	1	no	—
377	C₂×C₂²⋊C₄	—	86	1	no	—
378	C₂×C₄²	—	43	1	no	—
379	C₂×C₄²	—	86	1	no	—
380	C₂×C₄²	—	86	1	no	—
381	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
382	#107	—	2	2	no	—
383	#107	—	2	2	no	—
384	#107	—	86	2	no	—
385	#107	—	86	2	no	—
386	#107	—	86	2	no	—
387	#107	—	86	2	no	—
388	#107	—	86	2	no	—
389	#107	—	86	2	no	—
390	#107	—	86	2	no	—
391	#107	—	86	2	no	—
392	#106	—	2	2	no	—
393	#106	—	2	2	no	—
394	#106	—	86	2	no	—
395	#106	—	86	2	no	—
396	#106	—	86	2	no	—
397	#106	—	86	2	no	—
398	#97	—	43	4	no	—
399	#97	C₄×D₄₃	1	4	yes	complemented
400	C₄×C₈	—	43	4	no	—
401	C₄×C₈	—	43	4	no	—
402	#95	—	2	2	no	—
403	#95	—	86	2	no	—
404	#95	—	86	2	no	—
405	#95	—	86	2	no	—
406	C₂⁴	—	43	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	43	1	no	—
412	C₂²×C₄	—	43	2	no	—
413	C₂²×C₄	—	43	2	no	—
414	C₂²×C₄	—	43	2	no	—
415	C₂²×C₄	—	43	2	no	—
416	C₂²×C₄	—	43	2	no	—
417	C₂²×C₄	—	43	2	no	—
418	C₂²×C₄	—	43	2	no	—
419	C₂²×C₄	—	86	1	no	—
420	C₂²×C₄	—	86	1	no	—
421	C₂²×C₄	—	86	1	no	—
422	C₂²×C₄	—	86	1	no	—
423	C₂²×C₄	—	344	2	no	—
424	C₂²×C₄	—	344	2	no	—
425	C₂²×C₄	—	172	2	no	—
426	C₂²×C₄	—	172	2	no	—
427	C₂²×C₄	D₄×D₄₃	1	2	yes	—
428	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
429	M₁₆	—	43	16	no	—
430	C₂×C₈	—	43	2	no	—
431	C₂×C₈	—	43	2	no	—
432	C₂×C₈	—	43	2	no	—
433	C₂×C₈	—	43	2	no	—
434	C₂×C₈	—	43	2	no	—
435	C₂×C₈	—	43	2	no	—
436	C₂×C₈	—	43	16	no	—
437	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
438	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
439	C₂×C₈	D₄×D₄₃	1	2	yes	—
440	C₂×C₈	D₄×D₄₃	1	2	yes	—
441	C₂×C₈	Q₈×D₄₃	1	2	yes	—
442	C₂×C₈	Q₈×D₄₃	1	2	yes	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	8	2	no	—
452	C₄⋊C₄	—	43	8	no	—
453	C₄⋊C₄	—	86	1	no	—
454	C₄⋊C₄	—	86	1	no	—
455	C₄⋊C₄	—	86	1	no	—
456	C₄⋊C₄	—	86	1	no	—
457	C₄⋊C₄	—	86	1	no	—
458	C₄⋊C₄	—	86	1	no	—
459	C₄⋊C₄	—	86	1	no	—
460	C₄⋊C₄	—	86	1	no	—
461	C₄⋊C₄	—	344	2	no	—
462	C₄⋊C₄	—	344	2	no	—
463	C₄⋊C₄	—	344	2	no	—
464	C₄⋊C₄	—	172	2	no	—
465	C₄⋊C₄	—	172	2	no	—
466	C₂²⋊C₄	—	43	8	no	—
467	C₂²⋊C₄	—	172	2	no	—
468	C₂²⋊C₄	—	172	2	no	—
469	C₄²	—	43	2	no	—
470	C₄²	—	43	2	no	—
471	C₄²	—	172	2	no	—
472	C₄²	—	172	2	no	—
473	C₄²	C₂×C₄×D₄₃	1	2	yes	—
474	C₄²	Q₈×D₄₃	1	2	yes	—
475	C₂³	—	43	2	no	—
476	C₂³	—	43	2	no	—
477	C₂³	—	43	2	no	—
478	C₂³	—	86	2	no	—
479	C₂³	—	86	2	no	—
480	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	43	2	no	—
492	C₂×C₄	—	43	2	no	—
493	C₂×C₄	—	43	2	no	—
494	C₂×C₄	—	43	4	no	—
495	C₂×C₄	—	43	4	no	—
496	C₂×C₄	—	43	4	no	—
497	C₂×C₄	—	43	4	no	—
498	C₂×C₄	—	43	4	no	—
499	C₂×C₄	—	86	2	no	—
500	C₂×C₄	—	86	2	no	—
501	C₂×C₄	—	344	4	no	—
502	C₂×C₄	—	344	4	no	—
503	C₂×C₄	—	172	1	no	—
504	C₂×C₄	—	172	1	no	—
505	C₂×C₄	—	172	1	no	—
506	C₂×C₄	—	172	1	no	—
507	C₂×C₄	—	172	2	no	—
508	C₂×C₄	—	172	2	no	—
509	C₂×C₄	—	172	2	no	—
510	C₂×C₄	—	172	2	no	—
511	C₂×C₄	C₄⋊C₄×D₄₃	1	4	yes	—
512	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
513	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
514	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
515	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
516	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
517	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
518	C₈	—	43	4	no	—
519	C₈	—	43	4	no	—
520	C₈	C₄⋊C₄×D₄₃	1	4	yes	—
521	C₈	C₄⋊C₄×D₄₃	1	4	yes	—
522	C₂²	—	43	4	no	—
523	C₂²	—	86	4	no	—
524	C₂²	—	86	2	no	—
525	C₂²	—	86	2	no	—
526	C₂²	—	86	4	no	—
527	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
528	C₂²	#127×D₄₃	1	1	yes	characteristic
529	C₂²	C₄⋊Q₈×D₄₃	1	1	yes	characteristic
530	C₂²	#14583703	1	2	yes	—
531	C₂²	#14583715	1	2	yes	—
532	C₄	—	2	4	no	—
533	C₄	—	8	1	no	—
534	C₄	—	8	1	no	—
535	C₄	—	8	1	no	—
536	C₄	—	8	1	no	—
537	C₄	—	43	4	no	—
538	C₄	—	86	4	no	—
539	C₄	—	344	1	no	—
540	C₄	—	344	1	no	—
541	C₄	—	344	1	no	—
542	C₄	—	344	1	no	—
543	C₄	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
544	C₄	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
545	C₄	C₄⋊Q₈×D₄₃	1	1	yes	characteristic
546	C₄	C₄⋊Q₈×D₄₃	1	1	yes	characteristic
547	C₂	—	86	4	no	—
548	C₂	#384×D₄₃	1	1	yes	characteristic
549	C₂	#19143194	1	2	yes	—
550	C₂	#19145079	1	1	yes	characteristic
551	C₂	#19145087	1	1	yes	characteristic
552	C₂	#19145130	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1847	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂³×D₄₃	C₂×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1847	D₄₃
hypocenter	C₄₃	#20803
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1847

Complements

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

N	H ≅ G/N	type
8. #19134763	C₂	semidirect
9. #19134762	C₂	semidirect
10. #19134760	C₂	semidirect
11. #19134757	C₂	semidirect
12. #19134756	C₂	semidirect
13. #19134754	C₂	semidirect
14. #19134753	C₂	semidirect
15. C₄₃×#1847	C₂	semidirect
39. #14582856	C₄	semidirect
109. #13063235	C₂×C₄	semidirect
110. C₄×C₄₃⋊C₈	C₂×C₄	semidirect
111. C₈×Dic₄₃	C₂×C₄	semidirect
127. #97×C₄₃	C₂×C₄	semidirect
196. #10621872	C₄⋊C₄	semidirect
197. C₈×D₄₃	C₄⋊C₄	semidirect
281. #1847	D₄₃	semidirect
336. C₄₃	#20803	semidirect
399. #97	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582940	2
C₂×#14582938	2
C₂×#14582934	2
C₂×#107×D₄₃	2
C₂×#14582856	2
#19137220	2
#19137216	2
#19134763	2
#19134762	2
#19134760	2
#19134757	2
#19134756	2
#19134754	2
#19134753	2
C₄₃×#1847	2
#20803	43