Subgroups — #25095652

Order 11008.

826 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583027	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583023	C₂	1	1	yes	maximal, characteristic
3	#19137071	C₂	1	1	yes	maximal, characteristic
4	#19134466	C₂	1	1	yes	maximal, characteristic
5	#19134463	C₂	1	1	yes	maximal, characteristic
6	C₄⋊C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₈×Dic₄₃⋊C₄	C₂	1	1	yes	maximal, characteristic
8	#19134456	C₂	1	1	yes	maximal, characteristic
9	#19134455	C₂	1	1	yes	maximal, characteristic
10	#19134454	C₂	1	1	yes	maximal, characteristic
11	C₄×Dic₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
12	#19134348	C₂	1	1	yes	maximal, characteristic
13	#19134345	C₂	1	1	yes	maximal, characteristic
14	#19134339	C₂	1	1	yes	maximal, characteristic
15	C₄₃×#1771	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
17	#14583027	C₄	1	8	yes	complemented
18	#14583023	C₄	1	8	yes	complemented
19	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×#13063235	C₂²	1	1	yes	characteristic
25	C₂×#13063235	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
33	#14582803	C₄	1	2	yes	—
34	#14582794	C₄	1	2	yes	—
35	#14582784	C₄	1	2	yes	—
36	#14582780	C₄	1	2	yes	—
37	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
39	#14582745	C₂²	1	1	yes	characteristic
40	#14582745	C₂²	1	1	yes	characteristic
41	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
42	#14582654	C₂²	1	1	yes	characteristic
43	#14582654	C₂²	1	1	yes	characteristic
44	#14582653	C₂²	1	1	yes	characteristic
45	#14582653	C₂²	1	1	yes	characteristic
46	#14582653	C₂²	1	1	yes	characteristic
47	#14582653	C₂²	1	1	yes	characteristic
48	#14582653	C₂²	1	1	yes	characteristic
49	#14582653	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
51	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
52	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
55	C₄₃×#336	C₂²	1	1	yes	characteristic
56	C₄₃×#336	C₂²	1	1	yes	characteristic
57	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
62	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
63	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
64	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
65	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
70	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
74	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
75	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
76	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
77	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
78	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
79	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
80	#13063235	—	4	1	no	—
81	#13063235	C₂×C₄	1	4	yes	—
82	C₄×C₄₃⋊C₈	—	4	1	no	—
83	C₄×C₄₃⋊C₈	—	4	1	no	—
84	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
85	C₈×Dic₄₃	—	4	1	no	—
86	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
87	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
88	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
89	C₄₃⋊#95	C₂×C₄	1	2	yes	—
90	C₄₃⋊#95	C₂×C₄	1	2	yes	—
91	C₄₃⋊#95	C₂×C₄	1	2	yes	—
92	C₄₃⋊#95	C₂×C₄	1	2	yes	—
93	C₄₃⋊#95	C₂×C₄	1	2	yes	—
94	C₄₃⋊#95	C₂×C₄	1	2	yes	—
95	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
100	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
104	#97×C₄₃	—	4	1	no	—
105	#97×C₄₃	C₂×C₄	1	4	yes	—
106	C₄×C₈×C₄₃	—	4	1	no	—
107	#95×C₄₃	C₂×C₄	1	2	yes	—
108	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
114	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
115	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×Dic₈₆	—	2	4	no	—
120	C₂×Dic₈₆	C₄²	1	4	yes	—
121	C₂×C₈×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	—	2	1	no	—
123	C₂×C₈×C₄₃	—	2	1	no	—
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	—	2	1	no	—
126	C₂×C₈×C₄₃	—	2	1	no	—
127	C₂×C₈×C₄₃	—	2	1	no	—
128	C₂×C₈×C₄₃	—	2	1	no	—
129	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₄₃	—	2	4	no	—
134	C₄²×C₄₃	—	2	1	no	—
135	C₄²×C₄₃	—	2	1	no	—
136	C₄²×C₄₃	—	2	1	no	—
137	C₄²×C₄₃	—	2	1	no	—
138	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
139	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
140	C₄⋊Dic₄₃	C₄²	1	4	yes	—
141	Dic₄₃⋊C₄	—	2	4	no	—
142	Dic₄₃⋊C₄	—	2	4	no	—
143	Dic₄₃⋊C₄	C₄²	1	4	yes	—
144	Dic₄₃⋊C₄	C₄²	1	4	yes	—
145	C₄×Dic₄₃	—	2	4	no	—
146	C₄×Dic₄₃	—	2	1	no	—
147	C₄×Dic₄₃	—	2	1	no	—
148	C₄×Dic₄₃	—	2	1	no	—
149	C₄×Dic₄₃	—	2	1	no	—
150	C₄×Dic₄₃	—	2	4	no	—
151	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
152	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
153	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
154	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
155	C₂×C₄₃⋊C₈	—	2	1	no	—
156	C₂×C₄₃⋊C₈	—	2	1	no	—
157	C₂×C₄₃⋊C₈	—	2	1	no	—
158	C₂×C₄₃⋊C₈	—	2	1	no	—
159	C₂×C₄₃⋊C₈	—	2	1	no	—
160	C₂×C₄₃⋊C₈	—	2	1	no	—
161	C₂×C₄₃⋊C₈	—	2	1	no	—
162	C₂×C₄₃⋊C₈	—	2	1	no	—
163	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
164	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
165	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
166	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
167	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
176	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
177	C₂×C₄×C₄₃	#131	1	4	yes	—
178	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
182	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
183	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
184	C₂×Dic₄₃	—	2	2	no	—
185	C₂×Dic₄₃	—	2	2	no	—
186	C₂×Dic₄₃	—	2	2	no	—
187	C₂×Dic₄₃	—	2	2	no	—
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	2	2	no	—
190	C₂×Dic₄₃	—	2	2	no	—
191	C₂×Dic₄₃	—	2	2	no	—
192	C₂×Dic₄₃	—	2	2	no	—
193	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
194	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
195	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
196	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
197	C₂×Dic₄₃	#131	1	4	yes	—
198	Dic₈₆	—	2	8	no	—
199	C₈×C₄₃	—	2	2	no	—
200	C₈×C₄₃	—	2	2	no	—
201	C₈×C₄₃	—	2	2	no	—
202	C₈×C₄₃	—	2	2	no	—
203	C₄₃⋊C₈	—	2	2	no	—
204	C₄₃⋊C₈	—	2	2	no	—
205	C₄₃⋊C₈	—	2	2	no	—
206	C₄₃⋊C₈	—	2	2	no	—
207	#20571	—	43	1	no	maximal, Sylow
208	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
209	C₂²×C₄₃	#519	1	1	yes	characteristic
210	C₂²×C₄₃	#520	1	1	yes	characteristic
211	C₂²×C₄₃	C₂×#131	1	2	yes	—
212	C₂²×C₄₃	C₂×#131	1	2	yes	—
213	C₄×C₄₃	—	2	2	no	—
214	C₄×C₄₃	—	2	2	no	—
215	C₄×C₄₃	—	2	4	no	—
216	C₄×C₄₃	—	4	2	no	—
217	C₄×C₄₃	#519	1	1	yes	characteristic
218	C₄×C₄₃	#519	1	1	yes	characteristic
219	C₄×C₄₃	#520	1	1	yes	characteristic
220	C₄×C₄₃	#520	1	1	yes	characteristic
221	Dic₄₃	—	2	2	no	—
222	Dic₄₃	—	2	2	no	—
223	Dic₄₃	—	2	2	no	—
224	Dic₄₃	—	4	2	no	—
225	Dic₄₃	—	4	2	no	—
226	Dic₄₃	#405	1	4	yes	—
227	C₂×#446	—	43	1	no	—
228	C₂×C₈×Q₈	—	43	1	no	—
229	#2295	—	43	1	no	—
230	#1771	—	43	1	no	—
231	#1771	D₄₃	1	1	yes	characteristic
232	#1770	—	43	1	no	—
233	C₈×C₄⋊C₄	—	43	1	no	—
234	C₈×C₄⋊C₄	—	43	1	no	—
235	C₈×C₄⋊C₄	—	43	1	no	—
236	#1768	—	43	1	no	—
237	#1768	—	43	1	no	—
238	C₄×C₄⋊C₈	—	43	1	no	—
239	#1746	—	43	1	no	—
240	#1746	—	43	1	no	—
241	#1744	—	43	1	no	—
242	C₂×C₄₃	#2276	1	1	yes	characteristic
243	C₂×C₄₃	C₂×#405	1	1	yes	characteristic
244	C₂×C₄₃	C₄×#131	1	1	yes	characteristic
245	C₂×C₄₃	#2986	1	2	yes	—
246	C₂×C₄₃	#2994	1	2	yes	—
247	C₂×C₄×Q₈	—	43	1	no	—
248	#446	—	43	8	no	—
249	C₈×Q₈	—	43	8	no	—
250	C₂×C₄⋊C₈	—	43	1	no	—
251	C₂×C₄⋊C₈	—	43	1	no	—
252	C₂×C₄⋊C₈	—	43	1	no	—
253	C₂×C₄⋊C₈	—	43	1	no	—
254	C₂×C₄⋊C₈	—	43	1	no	—
255	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
256	C₂×#97	—	43	1	no	—
257	C₂×#97	—	43	1	no	—
258	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
259	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
260	C₂×C₄×C₈	—	43	1	no	—
261	C₂×C₄×C₈	—	43	1	no	—
262	C₂×C₄×C₈	—	43	1	no	—
263	C₂×C₄×C₈	—	43	1	no	—
264	C₂×C₄×C₈	—	43	1	no	—
265	C₂×C₄×C₈	—	43	1	no	—
266	C₂×C₄×C₈	—	43	1	no	—
267	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
268	#391	—	43	2	no	—
269	#389	—	43	2	no	—
270	#387	—	43	2	no	—
271	#387	—	43	2	no	—
272	C₄×C₄⋊C₄	—	43	1	no	—
273	C₄×C₄⋊C₄	—	43	1	no	—
274	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
275	#376	—	43	1	no	—
276	#376	—	43	1	no	—
277	C₄³	—	43	1	no	—
278	#336	—	43	1	no	—
279	#336	—	43	1	no	—
280	#336	—	43	1	no	—
281	#336	—	43	1	no	—
282	#336	—	43	1	no	—
283	#336	—	43	1	no	—
284	#336	—	43	1	no	—
285	#336	—	43	1	no	—
286	#336	C₂×D₄₃	1	1	yes	characteristic
287	#336	C₂×D₄₃	1	1	yes	characteristic
288	C₄₃	#20571	1	1	yes	characteristic, complemented, Sylow
289	C₂²×Q₈	—	43	1	no	—
290	C₂²×C₈	—	43	1	no	—
291	C₂²×C₈	—	43	1	no	—
292	C₂²×C₈	—	43	1	no	—
293	C₂²×C₈	—	43	1	no	—
294	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
295	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
296	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
297	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
298	C₄×Q₈	—	43	4	no	—
299	C₄×Q₈	—	43	4	no	—
300	C₂×C₄⋊C₄	—	43	1	no	—
301	C₂×C₄⋊C₄	—	43	1	no	—
302	C₂×C₄⋊C₄	—	43	1	no	—
303	C₂×C₄⋊C₄	—	43	2	no	—
304	C₂×C₄⋊C₄	—	43	2	no	—
305	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
306	C₂×C₄²	—	43	1	no	—
307	C₂×C₄²	—	43	1	no	—
308	C₂×C₄²	—	43	2	no	—
309	C₂×C₄²	—	43	2	no	—
310	C₂×C₄²	—	43	1	no	—
311	C₂×C₄²	—	43	1	no	—
312	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
313	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
314	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
315	C₄⋊C₈	—	43	4	no	—
316	C₄⋊C₈	—	43	4	no	—
317	C₄⋊C₈	—	43	4	no	—
318	C₄⋊C₈	—	43	4	no	—
319	C₄⋊C₈	—	43	4	no	—
320	C₄⋊C₈	C₄×D₄₃	1	4	yes	—
321	#97	—	4	1	no	—
322	#97	—	43	4	no	—
323	#97	—	172	1	no	—
324	#97	C₄×D₄₃	1	4	yes	—
325	C₄×C₈	—	4	1	no	—
326	C₄×C₈	—	43	4	no	—
327	C₄×C₈	—	43	4	no	—
328	C₄×C₈	—	43	4	no	—
329	C₄×C₈	—	43	4	no	—
330	C₄×C₈	—	172	1	no	—
331	C₄×C₈	—	172	1	no	—
332	C₄×C₈	—	172	1	no	—
333	#95	—	43	2	no	—
334	#95	—	43	2	no	—
335	#95	—	43	2	no	—
336	#95	—	43	2	no	—
337	#95	—	43	2	no	—
338	#95	—	43	2	no	—
339	#95	C₄×D₄₃	1	2	yes	—
340	C₂×Q₈	—	43	4	no	—
341	C₂×Q₈	—	86	4	no	—
342	C₂²×C₄	—	43	1	no	—
343	C₂²×C₄	—	43	1	no	—
344	C₂²×C₄	—	43	1	no	—
345	C₂²×C₄	—	43	1	no	—
346	C₂²×C₄	—	43	2	no	—
347	C₂²×C₄	—	43	2	no	—
348	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
349	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
352	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	43	2	no	—
362	C₂×C₈	—	43	2	no	—
363	C₂×C₈	—	43	2	no	—
364	C₂×C₈	—	43	2	no	—
365	C₂×C₈	—	86	1	no	—
366	C₂×C₈	—	86	1	no	—
367	C₂×C₈	—	86	1	no	—
368	C₂×C₈	—	86	1	no	—
369	C₂×C₈	—	86	1	no	—
370	C₂×C₈	—	86	1	no	—
371	C₂×C₈	—	86	1	no	—
372	C₂×C₈	—	86	1	no	—
373	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
374	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
375	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
376	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	43	4	no	—
379	C₄⋊C₄	—	43	4	no	—
380	C₄⋊C₄	—	43	4	no	—
381	C₄⋊C₄	—	86	4	no	—
382	C₄⋊C₄	—	86	4	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	43	2	no	—
388	C₄²	—	43	2	no	—
389	C₄²	—	43	2	no	—
390	C₄²	—	43	2	no	—
391	C₄²	—	86	4	no	—
392	C₄²	—	86	4	no	—
393	C₄²	—	86	1	no	—
394	C₄²	—	86	1	no	—
395	C₄²	—	86	1	no	—
396	C₄²	—	86	1	no	—
397	C₄²	C₂×C₄×D₄₃	1	2	yes	—
398	C₄²	C₂×C₄×D₄₃	1	2	yes	—
399	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
400	Q₈	—	86	8	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	43	2	no	—
409	C₂×C₄	—	43	4	no	—
410	C₂×C₄	—	43	2	no	—
411	C₂×C₄	—	43	2	no	—
412	C₂×C₄	—	43	2	no	—
413	C₂×C₄	—	86	2	no	—
414	C₂×C₄	—	86	2	no	—
415	C₂×C₄	—	86	2	no	—
416	C₂×C₄	—	86	2	no	—
417	C₂×C₄	—	86	2	no	—
418	C₂×C₄	—	86	2	no	—
419	C₂×C₄	—	86	2	no	—
420	C₂×C₄	—	86	2	no	—
421	C₂×C₄	—	86	2	no	—
422	C₂×C₄	C₄²×D₄₃	1	2	yes	—
423	C₂×C₄	C₄²×D₄₃	1	2	yes	—
424	C₂×C₄	#13063333	1	4	yes	—
425	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
427	C₂×C₄	#13063370	1	1	yes	characteristic
428	C₂×C₄	#13063372	1	1	yes	characteristic
429	C₂×C₄	#13063372	1	1	yes	characteristic
430	C₂×C₄	#13063373	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	86	2	no	—
436	C₈	—	86	2	no	—
437	C₈	—	86	2	no	—
438	C₈	—	86	2	no	—
439	C₂²	C₂×C₄²×D₄₃	1	1	yes	characteristic
440	C₂²	#14583375	1	1	yes	characteristic
441	C₂²	#14583378	1	1	yes	characteristic
442	C₂²	#131×D₄₃	1	2	yes	—
443	C₂²	C₂×#13063333	1	2	yes	—
444	C₄	—	2	4	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	43	4	no	—
449	C₄	—	86	2	no	—
450	C₄	—	86	2	no	—
451	C₄	—	86	2	no	—
452	C₄	—	172	2	no	—
453	C₄	—	172	2	no	—
454	C₄	#14583375	1	1	yes	characteristic
455	C₄	#14583376	1	1	yes	characteristic
456	C₄	#14583378	1	1	yes	characteristic
457	C₄	#14583380	1	1	yes	characteristic
458	C₂	#19136959	1	1	yes	characteristic
459	C₂	#405×D₄₃	1	1	yes	characteristic
460	C₂	C₄×#13063333	1	1	yes	characteristic
461	C₂	#19143693	1	2	yes	—
462	C₂	#19143748	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂²×C₄²
Fitting	C₄₃×#1771	C₂
socle, prime radical	C₂³×C₄₃	C₂³×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1771	D₄₃
hypocenter	C₄₃	#20571
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1771

Complements

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

N	H ≅ G/N	type
17. #14583027	C₄	semidirect
18. #14583023	C₄	semidirect
288. C₄₃	#20571	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583027	2
C₂×#14583023	2
#19137071	2
#19134466	2
#19134463	2
C₄⋊C₄×C₄₃⋊C₈	2
C₈×Dic₄₃⋊C₄	2
#19134456	2
#19134455	2
#19134454	2
C₄×Dic₄₃⋊C₈	2
#19134348	2
#19134345	2
#19134339	2
C₄₃×#1771	2
#20571	43