Subgroups — #25960992

Order 11008.

1882 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#533×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#19143547	C₂	1	4	yes	maximal, complemented
3	Q₈×#10621872	C₂	1	4	yes	maximal, complemented
4	#19143543	C₂	1	4	yes	maximal, complemented
5	#19143537	C₂	1	4	yes	maximal, complemented
6	#19143534	C₂	1	2	yes	maximal, complemented
7	#19143533	C₂	1	2	yes	maximal, complemented
8	#19143530	C₂	1	1	yes	maximal, characteristic, complemented
9	#19143529	C₂	1	1	yes	maximal, characteristic, complemented
10	#19143525	C₂	1	1	yes	maximal, characteristic, complemented
11	#19143156	C₂	1	2	yes	maximal
12	#423×D₄₃	C₂	1	1	yes	maximal, characteristic
13	#19143011	C₂	1	2	yes	maximal
14	C₂×C₄×#10621872	C₂	1	1	yes	maximal, characteristic
15	C₄₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10621872	C₂²	1	1	yes	characteristic
17	C₂²×#10621872	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×D₄₃	C₂²	1	2	yes	—
19	#14583456	C₂²	1	1	yes	characteristic
20	#14583455	C₄	1	2	yes	—
21	#14583454	C₄	1	2	yes	—
22	#14583453	C₂²	1	4	yes	—
23	#14583452	C₂²	1	2	yes	—
24	#14583451	C₄	1	4	yes	—
25	C₄⋊Q₈×D₄₃	C₄	1	2	yes	—
26	#125×D₄₃	C₄	1	2	yes	—
27	C₂²⋊Q₈×D₄₃	C₄	1	4	yes	—
28	C₄×Q₈×D₄₃	C₂²	1	4	yes	—
29	#117×D₄₃	C₂²	1	2	yes	—
30	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
31	#14583030	C₂²	1	4	yes	complemented
32	#14583029	C₂²	1	4	yes	complemented
33	#14583029	C₂²	1	8	yes	complemented
34	#14583028	C₂²	1	8	yes	complemented
35	#14583027	C₂²	1	8	yes	complemented
36	#14583026	C₂²	1	4	yes	complemented
37	#14583026	C₂²	1	8	yes	complemented
38	Q₈×C₄₃⋊C₈	C₂²	1	4	yes	complemented
39	C₈×Dic₈₆	C₂²	1	4	yes	complemented
40	#14583023	C₂²	1	4	yes	complemented
41	#14582927	C₂²	1	2	yes	—
42	#14582926	C₂²	1	2	yes	—
43	#14582925	C₂²	1	2	yes	—
44	#14582924	C₂²	1	8	yes	—
45	#14582923	C₂²	1	1	yes	characteristic
46	#14582922	C₂²	1	2	yes	—
47	#14582921	C₂²	1	4	yes	—
48	#14582921	C₂²	1	8	yes	—
49	C₄⋊C₈×D₄₃	C₂²	1	4	yes	—
50	#14582857	C₂²	1	2	yes	—
51	#14582856	C₂²	1	4	yes	—
52	#14582855	C₂²	1	2	yes	—
53	#14582854	C₂²	1	2	yes	—
54	#14582853	C₂²	1	4	yes	—
55	#14582851	C₂²	1	4	yes	—
56	C₄×#10621872	C₂²	1	2	yes	—
57	C₄×#10621872	C₂²	1	2	yes	—
58	C₄×#10621872	C₂²	1	2	yes	—
59	C₄×#10621872	C₂²	1	2	yes	—
60	C₄×#10621872	C₂²	1	4	yes	—
61	C₂×#13063235	C₂²	1	1	yes	characteristic
62	C₂×#13063235	C₂²	1	1	yes	characteristic
63	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
64	C₄₃×#533	C₂²	1	1	yes	characteristic
65	C₄₃×#446	C₂²	1	4	yes	complemented
66	C₈×Q₈×C₄₃	C₂²	1	4	yes	complemented
67	C₄₃×#424	C₂²	1	2	yes	—
68	C₄₃×#423	C₂²	1	1	yes	characteristic
69	C₄₃×#405	C₂²	1	2	yes	—
70	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
71	C₂×Q₈×D₄₃	C₂×C₄	1	4	yes	—
72	C₂²×C₄×D₄₃	C₂×C₄	1	2	yes	—
73	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
74	C₂×#10621877	C₂³	1	2	yes	—
75	C₂×#10621872	—	2	4	no	—
76	C₂×#10621872	Q₈	1	8	yes	complemented
77	C₂×#10621872	C₂³	1	2	yes	—
78	C₂×#10621872	C₂³	1	2	yes	—
79	C₂×#10621872	C₂³	1	4	yes	—
80	C₂×#10621872	C₂³	1	1	yes	characteristic
81	C₂×#10621872	C₂³	1	1	yes	characteristic
82	C₂×#10621872	C₂³	1	1	yes	characteristic
83	C₂×#10621872	C₂³	1	1	yes	characteristic
84	M₁₆×D₄₃	—	2	8	no	—
85	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₈×D₄₃	C₂³	1	4	yes	—
88	#13063325	C₂×C₄	1	2	yes	—
89	#13063324	C₂×C₄	1	4	yes	—
90	#13063324	C₂×C₄	1	4	yes	—
91	#13063323	C₂×C₄	1	4	yes	—
92	#13063317	C₂×C₄	1	2	yes	—
93	#13063316	C₂×C₄	1	4	yes	—
94	#13063315	C₂×C₄	1	8	yes	—
95	#13063305	C₂×C₄	1	4	yes	—
96	#13063304	C₂×C₄	1	4	yes	—
97	#13063303	C₂×C₄	1	8	yes	—
98	#13063302	C₂×C₄	1	8	yes	—
99	#13063301	C₂×C₄	1	4	yes	—
100	Q₈×Dic₄₃	C₂×C₄	1	4	yes	—
101	C₄×Dic₈₆	C₂³	1	8	yes	—
102	C₄×Dic₈₆	C₂³	1	4	yes	—
103	#13063290	C₂×C₄	1	4	yes	—
104	#13063290	C₂×C₄	1	8	yes	—
105	#13063284	C₂³	1	2	yes	—
106	#13063283	C₂×C₄	1	4	yes	—
107	#13063282	C₂³	1	4	yes	—
108	#13063281	C₂×C₄	1	4	yes	—
109	C₄⋊C₄×D₄₃	C₂×C₄	1	4	yes	—
110	C₄⋊C₄×D₄₃	C₂×C₄	1	8	yes	—
111	C₄⋊C₄×D₄₃	C₂×C₄	1	4	yes	—
112	C₂²⋊C₄×D₄₃	C₂×C₄	1	4	yes	—
113	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
114	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
115	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
116	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
117	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
118	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
119	C₄²×D₄₃	C₂³	1	2	yes	—
120	C₄²×D₄₃	C₂³	1	2	yes	—
121	C₄²×D₄₃	C₂³	1	4	yes	—
122	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
123	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
124	Dic₄₃⋊C₈	C₂³	1	8	yes	—
125	Dic₄₃⋊C₈	C₂³	1	8	yes	—
126	Dic₄₃⋊C₈	C₂³	1	8	yes	—
127	#13063236	C₂³	1	4	yes	—
128	#13063235	C₂³	1	2	yes	—
129	#13063235	C₂³	1	2	yes	—
130	#13063235	C₂³	1	2	yes	—
131	#13063235	C₂³	1	2	yes	—
132	#13063235	C₂³	1	4	yes	—
133	#13063235	C₂³	1	4	yes	—
134	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
135	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
136	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
137	C₈×Dic₄₃	C₂³	1	4	yes	—
138	C₈×Dic₄₃	C₂³	1	4	yes	—
139	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
140	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
143	#125×C₄₃	C₂×C₄	1	2	yes	—
144	C₂²⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
145	C₄×Q₈×C₄₃	C₂³	1	4	yes	—
146	#117×C₄₃	C₂³	1	2	yes	—
147	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
148	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
149	C₄⋊C₈×C₄₃	C₂³	1	8	yes	—
150	#97×C₄₃	C₂³	1	4	yes	—
151	C₄×C₈×C₄₃	C₂³	1	2	yes	—
152	C₄×C₈×C₄₃	C₂³	1	2	yes	—
153	C₄×C₈×C₄₃	C₂³	1	4	yes	—
154	C₂³×D₄₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
156	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
158	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
159	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
160	Q₈×D₄₃	—	4	8	no	—
161	C₂×C₄×D₄₃	—	4	4	no	—
162	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
163	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
164	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
165	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
166	C₂×C₄×D₄₃	C₂²×C₄	1	8	yes	—
167	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₄₃	C₂×Q₈	1	4	yes	—
170	C₂×C₄×D₄₃	#41	1	4	yes	—
171	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
173	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
174	C₂×Dic₈₆	C₂²×C₄	1	8	yes	—
175	M₁₆×C₄₃	—	2	4	no	—
176	C₂×C₈×C₄₃	—	2	2	no	—
177	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	complemented
178	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
179	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
180	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
181	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
182	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
183	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
184	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
185	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
186	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
188	C₄²×C₄₃	C₂⁴	1	2	yes	—
189	C₄²×C₄₃	C₂⁴	1	4	yes	—
190	C₂²⋊Dic₄₃	C₂²×C₄	1	4	yes	—
191	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	8	yes	—
192	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
193	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
194	C₄⋊Dic₄₃	C₂²×C₄	1	8	yes	—
195	Dic₄₃⋊C₄	C₂²×C₄	1	8	yes	—
196	Dic₄₃⋊C₄	C₂²×C₄	1	8	yes	—
197	Dic₄₃⋊C₄	C₂²×C₄	1	8	yes	—
198	Dic₄₃⋊C₄	C₂²×C₄	1	8	yes	—
199	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
201	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
202	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
203	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
204	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
205	C₄×Dic₄₃	C₂²×C₄	1	8	yes	—
206	C₄×Dic₄₃	C₂⁴	1	4	yes	—
207	C₄×Dic₄₃	C₂⁴	1	2	yes	—
208	#10621877	—	2	4	no	—
209	C₂×C₄₃⋊C₈	—	2	2	no	—
210	C₂×C₄₃⋊C₈	C₂×Q₈	1	4	yes	complemented
211	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
212	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
213	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
214	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
215	#10621872	—	2	8	no	—
216	#10621872	—	2	4	no	—
217	#10621872	—	2	4	no	—
218	#10621872	C₂×Q₈	1	4	yes	—
219	#10621872	C₂×Q₈	1	4	yes	—
220	#10621872	C₂×Q₈	1	4	yes	complemented
221	#10621872	C₂×Q₈	1	4	yes	complemented
222	C₈×D₄₃	—	2	8	no	—
223	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
224	C₂²×D₄₃	—	4	2	no	—
225	C₂²×D₄₃	C₄×Q₈	1	4	yes	—
226	C₂²×D₄₃	C₂³×C₄	1	1	yes	characteristic
227	C₂²×D₄₃	C₂³×C₄	1	1	yes	characteristic
228	Q₈×C₄₃	—	2	8	no	—
229	C₂×C₄×C₄₃	—	2	4	no	—
230	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
231	C₂×C₄×C₄₃	C₂³×C₄	1	8	yes	—
232	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
234	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
235	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
236	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
237	C₂×Dic₄₃	—	4	2	no	—
238	C₂×Dic₄₃	C₄×Q₈	1	4	yes	—
239	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
240	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
241	C₂×Dic₄₃	C₂³×C₄	1	8	yes	—
242	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
243	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
244	C₄×D₄₃	—	2	4	no	—
245	C₄×D₄₃	—	2	4	no	—
246	C₄×D₄₃	—	4	2	no	—
247	C₄×D₄₃	—	4	2	no	—
248	C₄×D₄₃	—	4	8	no	—
249	C₄×D₄₃	C₄×Q₈	1	4	yes	—
250	C₄×D₄₃	C₄×Q₈	1	4	yes	—
251	C₄×D₄₃	C₂²×Q₈	1	2	yes	—
252	C₄×D₄₃	C₂²×Q₈	1	2	yes	—
253	C₄×D₄₃	C₂×#41	1	2	yes	—
254	C₄×D₄₃	C₂×#41	1	2	yes	—
255	Dic₈₆	—	2	8	no	—
256	Dic₈₆	—	4	8	no	—
257	C₈×C₄₃	—	2	4	no	—
258	C₈×C₄₃	—	2	2	no	—
259	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
260	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
261	C₄₃⋊C₈	—	2	4	no	—
262	C₄₃⋊C₈	—	2	2	no	—
263	C₄₃⋊C₈	C₂²×Q₈	1	2	yes	—
264	C₄₃⋊C₈	C₂²×Q₈	1	2	yes	—
265	#60192	—	43	1	no	maximal, Sylow
266	C₂²×C₄₃	—	2	2	no	—
267	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
268	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
269	C₂×D₄₃	—	2	2	no	—
270	C₂×D₄₃	—	2	2	no	—
271	C₂×D₄₃	—	4	4	no	—
272	C₂×D₄₃	C₂×C₄×Q₈	1	2	yes	—
273	C₂×D₄₃	C₂×C₄×Q₈	1	2	yes	—
274	C₄×C₄₃	—	2	8	no	—
275	C₄×C₄₃	—	2	2	no	—
276	C₄×C₄₃	C₂×C₄×Q₈	1	2	yes	—
277	C₄×C₄₃	#568	1	4	yes	—
278	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
279	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
280	Dic₄₃	—	2	8	no	—
281	Dic₄₃	—	2	2	no	—
282	Dic₄₃	—	2	2	no	—
283	Dic₄₃	C₂×C₄×Q₈	1	2	yes	—
284	Dic₄₃	C₂×C₄×Q₈	1	2	yes	—
285	C₂×#533	—	43	1	no	—
286	Q₈×M₁₆	—	43	4	no	—
287	Q₈×M₁₆	—	43	4	no	—
288	#2962	—	43	4	no	—
289	#2962	—	43	4	no	—
290	#2961	—	43	2	no	—
291	#2961	—	43	2	no	—
292	#2960	—	43	1	no	—
293	#2960	—	43	1	no	—
294	#2960	—	43	1	no	—
295	#2960	D₄₃	1	1	yes	characteristic, complemented
296	#2905	—	43	2	no	—
297	C₂×#423	—	43	1	no	—
298	#2873	—	43	2	no	—
299	C₂×C₄×M₁₆	—	43	1	no	—
300	C₂×C₄₃	—	2	2	no	—
301	C₂×C₄₃	C₂²×C₄×Q₈	1	1	yes	characteristic
302	C₂×C₄₃	C₂×#568	1	2	yes	—
303	D₄₃	—	2	2	no	—
304	D₄₃	—	2	2	no	—
305	C₂²×M₁₆	—	43	2	no	—
306	C₂²×M₁₆	—	43	1	no	—
307	C₂²×M₁₆	—	43	1	no	—
308	#533	—	43	2	no	—
309	#533	—	43	2	no	—
310	#533	—	43	4	no	—
311	#533	—	43	4	no	—
312	#533	—	43	2	no	—
313	#533	—	43	1	no	—
314	#533	C₂×D₄₃	1	1	yes	characteristic
315	C₂×C₄⋊Q₈	—	43	2	no	—
316	C₂×#125	—	43	2	no	—
317	C₂×C₂²⋊Q₈	—	43	4	no	—
318	C₂×C₄×Q₈	—	43	4	no	—
319	C₂×#117	—	43	2	no	—
320	C₂²×C₄²	—	43	1	no	—
321	#446	—	43	4	no	—
322	#446	—	43	4	no	—
323	#446	—	43	8	no	—
324	#446	—	43	8	no	—
325	#446	—	43	8	no	—
326	#446	—	43	4	no	—
327	#446	—	43	8	no	—
328	#446	C₂×D₄₃	1	4	yes	complemented
329	C₈×Q₈	—	43	4	no	—
330	C₈×Q₈	—	43	4	no	—
331	C₈×Q₈	—	43	4	no	—
332	C₈×Q₈	C₂×D₄₃	1	4	yes	complemented
333	#424	—	43	2	no	—
334	#424	—	43	2	no	—
335	#424	—	43	2	no	—
336	#424	—	43	8	no	—
337	#424	C₂×D₄₃	1	2	yes	—
338	#423	—	43	2	no	—
339	#423	—	43	1	no	—
340	#423	—	43	4	no	—
341	#423	—	43	8	no	—
342	#423	C₂×D₄₃	1	1	yes	characteristic
343	C₂×C₄⋊C₈	—	43	4	no	—
344	#405	—	43	2	no	—
345	#405	—	43	2	no	—
346	#405	—	43	2	no	—
347	#405	—	43	4	no	—
348	#405	—	43	4	no	—
349	#405	C₂×D₄₃	1	2	yes	—
350	C₄×M₁₆	—	43	4	no	—
351	C₄×M₁₆	—	43	2	no	—
352	C₄×M₁₆	—	43	2	no	—
353	C₄×M₁₆	—	43	2	no	—
354	C₄×M₁₆	—	43	2	no	—
355	C₄×M₁₆	—	43	4	no	—
356	C₂×#97	—	43	1	no	—
357	C₂×#97	—	43	1	no	—
358	C₂×C₄×C₈	—	43	1	no	—
359	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
360	C₄₃	#60192	1	1	yes	characteristic, complemented, Sylow
361	C₂²×Q₈	—	43	4	no	—
362	C₂³×C₄	—	43	1	no	—
363	C₂³×C₄	—	43	2	no	—
364	C₂×M₁₆	—	43	2	no	—
365	C₂×M₁₆	—	43	8	no	—
366	C₂×M₁₆	—	43	1	no	—
367	C₂×M₁₆	—	43	1	no	—
368	C₂×M₁₆	—	43	1	no	—
369	C₂×M₁₆	—	43	1	no	—
370	C₂×M₁₆	—	43	4	no	—
371	C₂×M₁₆	—	43	2	no	—
372	C₂×M₁₆	—	43	2	no	—
373	C₂×M₁₆	—	86	4	no	—
374	C₂×M₁₆	—	86	8	no	—
375	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
376	C₂²×C₈	—	43	1	no	—
377	C₂²×C₈	—	43	1	no	—
378	C₂²×C₈	—	43	4	no	—
379	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
380	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
381	C₄⋊Q₈	—	43	4	no	—
382	C₄⋊Q₈	—	43	4	no	—
383	C₄⋊Q₈	—	43	4	no	—
384	C₄⋊Q₈	—	43	2	no	—
385	C₄⋊Q₈	C₄×D₄₃	1	2	yes	—
386	#125	—	43	8	no	—
387	#125	—	43	4	no	—
388	#125	—	43	2	no	—
389	#125	C₄×D₄₃	1	2	yes	—
390	C₂²⋊Q₈	—	43	4	no	—
391	C₂²⋊Q₈	—	43	4	no	—
392	C₂²⋊Q₈	—	43	8	no	—
393	C₂²⋊Q₈	—	43	4	no	—
394	C₂²⋊Q₈	—	43	8	no	—
395	C₂²⋊Q₈	C₄×D₄₃	1	4	yes	—
396	C₄×Q₈	—	43	4	no	—
397	C₄×Q₈	—	43	4	no	—
398	C₄×Q₈	—	43	8	no	—
399	C₄×Q₈	—	43	4	no	—
400	C₄×Q₈	—	43	8	no	—
401	C₄×Q₈	C₂²×D₄₃	1	4	yes	—
402	#117	—	43	2	no	—
403	#117	—	43	4	no	—
404	#117	—	43	4	no	—
405	#117	—	43	4	no	—
406	#117	C₂²×D₄₃	1	2	yes	—
407	C₂×C₄⋊C₄	—	43	4	no	—
408	C₂×C₄⋊C₄	—	43	8	no	—
409	C₂×C₄⋊C₄	—	43	4	no	—
410	C₂×C₂²⋊C₄	—	43	4	no	—
411	C₂×C₄²	—	43	2	no	—
412	C₂×C₄²	—	43	1	no	—
413	C₂×C₄²	—	43	1	no	—
414	C₂×C₄²	—	43	1	no	—
415	C₂×C₄²	—	43	1	no	—
416	C₂×C₄²	—	43	1	no	—
417	C₂×C₄²	—	43	4	no	—
418	C₂×C₄²	—	43	2	no	—
419	C₂×C₄²	—	43	2	no	—
420	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
421	C₄⋊C₈	—	43	8	no	—
422	C₄⋊C₈	—	43	8	no	—
423	C₄⋊C₈	—	43	8	no	—
424	C₄⋊C₈	—	43	4	no	—
425	C₄⋊C₈	—	43	8	no	—
426	C₄⋊C₈	C₂²×D₄₃	1	4	yes	—
427	C₄⋊C₈	C₂²×D₄₃	1	8	yes	—
428	#97	—	43	2	no	—
429	#97	—	43	2	no	—
430	#97	—	43	2	no	—
431	#97	—	43	2	no	—
432	#97	—	43	4	no	—
433	#97	—	43	4	no	—
434	#97	—	43	4	no	—
435	#97	C₂²×D₄₃	1	4	yes	—
436	C₄×C₈	—	43	4	no	—
437	C₄×C₈	—	43	4	no	—
438	C₄×C₈	—	43	2	no	—
439	C₄×C₈	—	43	2	no	—
440	C₄×C₈	—	43	4	no	—
441	C₄×C₈	C₂²×D₄₃	1	2	yes	—
442	C₄×C₈	C₂²×D₄₃	1	2	yes	—
443	C₄×C₈	C₂²×D₄₃	1	4	yes	—
444	C₂⁴	—	43	1	no	—
445	C₂×Q₈	—	43	4	no	—
446	C₂×Q₈	—	43	8	no	—
447	C₂×Q₈	—	172	8	no	—
448	C₂×Q₈	C₂×C₄×D₄₃	1	4	yes	—
449	C₂²×C₄	—	43	1	no	—
450	C₂²×C₄	—	43	1	no	—
451	C₂²×C₄	—	43	1	no	—
452	C₂²×C₄	—	43	4	no	—
453	C₂²×C₄	—	43	4	no	—
454	C₂²×C₄	—	43	1	no	—
455	C₂²×C₄	—	43	1	no	—
456	C₂²×C₄	—	43	2	no	—
457	C₂²×C₄	—	43	2	no	—
458	C₂²×C₄	—	43	2	no	—
459	C₂²×C₄	—	43	2	no	—
460	C₂²×C₄	—	43	2	no	—
461	C₂²×C₄	—	43	8	no	—
462	C₂²×C₄	—	172	4	no	—
463	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
464	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
465	M₁₆	—	2	4	no	—
466	M₁₆	—	43	4	no	—
467	M₁₆	—	43	4	no	—
468	M₁₆	—	43	4	no	—
469	M₁₆	—	43	4	no	—
470	M₁₆	—	86	4	no	—
471	M₁₆	—	86	4	no	—
472	M₁₆	—	86	8	no	—
473	M₁₆	—	86	4	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	43	4	no	—
476	C₂×C₈	—	43	1	no	—
477	C₂×C₈	—	43	1	no	—
478	C₂×C₈	—	43	4	no	—
479	C₂×C₈	—	43	2	no	—
480	C₂×C₈	—	86	8	no	—
481	C₂×C₈	—	86	2	no	—
482	C₂×C₈	Q₈×D₄₃	1	4	yes	complemented
483	C₂×C₈	C₂³×D₄₃	1	4	yes	—
484	C₂×C₈	C₂³×D₄₃	1	2	yes	—
485	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
486	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
487	C₄⋊C₄	—	43	8	no	—
488	C₄⋊C₄	—	43	4	no	—
489	C₄⋊C₄	—	43	8	no	—
490	C₄⋊C₄	—	43	8	no	—
491	C₄⋊C₄	—	43	8	no	—
492	C₄⋊C₄	—	43	8	no	—
493	C₄⋊C₄	—	43	4	no	—
494	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
495	C₄⋊C₄	C₂×C₄×D₄₃	1	8	yes	—
496	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
497	C₂²⋊C₄	—	43	4	no	—
498	C₂²⋊C₄	—	43	8	no	—
499	C₂²⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
500	C₄²	—	43	2	no	—
501	C₄²	—	43	2	no	—
502	C₄²	—	43	2	no	—
503	C₄²	—	43	1	no	—
504	C₄²	—	43	2	no	—
505	C₄²	—	43	1	no	—
506	C₄²	—	43	8	no	—
507	C₄²	—	43	4	no	—
508	C₄²	—	43	2	no	—
509	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
510	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
511	C₄²	C₂³×D₄₃	1	2	yes	—
512	C₄²	C₂³×D₄₃	1	4	yes	—
513	C₂³	—	43	1	no	—
514	C₂³	—	43	1	no	—
515	C₂³	—	43	4	no	—
516	C₂³	—	172	2	no	—
517	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
518	Q₈	—	2	8	no	—
519	Q₈	—	86	8	no	—
520	Q₈	—	172	8	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	43	4	no	—
523	C₂×C₄	—	43	1	no	—
524	C₂×C₄	—	43	1	no	—
525	C₂×C₄	—	43	4	no	—
526	C₂×C₄	—	43	4	no	—
527	C₂×C₄	—	43	2	no	—
528	C₂×C₄	—	43	2	no	—
529	C₂×C₄	—	43	2	no	—
530	C₂×C₄	—	43	2	no	—
531	C₂×C₄	—	43	2	no	—
532	C₂×C₄	—	43	2	no	—
533	C₂×C₄	—	43	8	no	—
534	C₂×C₄	—	86	4	no	—
535	C₂×C₄	—	86	4	no	—
536	C₂×C₄	—	172	2	no	—
537	C₂×C₄	—	172	2	no	—
538	C₂×C₄	—	172	8	no	—
539	C₂×C₄	—	172	2	no	—
540	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
541	C₂×C₄	C₂²×C₄×D₄₃	1	8	yes	—
542	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
543	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
544	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
545	C₂×C₄	#41×D₄₃	1	2	yes	—
546	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
547	C₈	—	2	2	no	—
548	C₈	—	2	4	no	—
549	C₈	—	43	2	no	—
550	C₈	—	43	2	no	—
551	C₈	—	86	4	no	—
552	C₈	—	86	2	no	—
553	C₈	C₂×Q₈×D₄₃	1	2	yes	—
554	C₈	C₂×Q₈×D₄₃	1	2	yes	—
555	C₂²	—	2	2	no	—
556	C₂²	—	43	2	no	—
557	C₂²	—	43	2	no	—
558	C₂²	—	86	2	no	—
559	C₂²	—	86	2	no	—
560	C₂²	—	172	4	no	—
561	C₂²	C₄×Q₈×D₄₃	1	2	yes	—
562	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
563	C₄	—	2	2	no	—
564	C₄	—	2	8	no	—
565	C₄	—	43	2	no	—
566	C₄	—	43	2	no	—
567	C₄	—	86	2	no	—
568	C₄	—	86	2	no	—
569	C₄	—	86	8	no	—
570	C₄	C₄×Q₈×D₄₃	1	2	yes	—
571	C₄	#14583664	1	4	yes	—
572	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
573	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
574	C₂	—	2	2	no	—
575	C₂	—	86	2	no	—
576	C₂	—	86	2	no	—
577	C₂	C₂×C₄×Q₈×D₄₃	1	1	yes	characteristic
578	C₂	C₂×#14583664	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁴×C₄
Fitting	C₄₃×#2960	C₂
prime radical	C₂³×D₄₃	C₂²×C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	#2960	D₄₃
hypocenter	C₄₃	#60192
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #2960

Complements

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

N	H ≅ G/N	type
2. #19143547	C₂	semidirect
3. Q₈×#10621872	C₂	semidirect
4. #19143543	C₂	semidirect
5. #19143537	C₂	semidirect
6. #19143534	C₂	semidirect
7. #19143533	C₂	semidirect
8. #19143530	C₂	semidirect
9. #19143529	C₂	semidirect
10. #19143525	C₂	semidirect
15. C₄₃×#2960	C₂	semidirect
31. #14583030	C₂²	semidirect
32. #14583029	C₂²	semidirect
33. #14583029	C₂²	semidirect
34. #14583028	C₂²	semidirect
35. #14583027	C₂²	semidirect
36. #14583026	C₂²	semidirect
37. #14583026	C₂²	semidirect
38. Q₈×C₄₃⋊C₈	C₂²	semidirect
39. C₈×Dic₈₆	C₂²	semidirect
40. #14583023	C₂²	semidirect
65. C₄₃×#446	C₂²	semidirect
66. C₈×Q₈×C₄₃	C₂²	semidirect
76. C₂×#10621872	Q₈	semidirect
177. C₂×C₈×C₄₃	C₂×Q₈	semidirect
210. C₂×C₄₃⋊C₈	C₂×Q₈	semidirect
220. #10621872	C₂×Q₈	semidirect
221. #10621872	C₂×Q₈	semidirect
295. #2960	D₄₃	semidirect
328. #446	C₂×D₄₃	semidirect
332. C₈×Q₈	C₂×D₄₃	semidirect
360. C₄₃	#60192	semidirect
482. C₂×C₈	Q₈×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#533×D₄₃	2
#19143547	2
Q₈×#10621872	2
#19143543	2
#19143537	2
#19143534	2
#19143533	2
#19143530	2
#19143529	2
#19143525	2
#19143156	2
#423×D₄₃	2
#19143011	2
C₂×C₄×#10621872	2
C₄₃×#2960	2
#60192	43