Subgroups — #25095666

Order 11008.

898 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583028	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583027	C₂	1	1	yes	maximal, characteristic
3	C₄×#13063290	C₂	1	1	yes	maximal, characteristic
4	#19134471	C₂	1	1	yes	maximal, characteristic
5	#19134470	C₂	1	1	yes	maximal, characteristic
6	#19134468	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	#19134449	C₂	1	1	yes	maximal, characteristic
10	C₄⋊C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
11	C₄×Dic₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
12	#19134343	C₂	1	1	yes	maximal, characteristic
13	#19134342	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	C₂×#13063290	C₄	1	2	yes	—
18	#14583028	C₄	1	8	yes	complemented
19	#14583027	C₄	1	8	yes	complemented
20	C₂×C₄⋊(C₄₃⋊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×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×#13063236	C₂²	1	1	yes	characteristic
26	C₂×#13063236	C₂²	1	1	yes	characteristic
27	C₂×#13063235	C₂²	1	1	yes	characteristic
28	C₂×#13063235	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₄₃⋊C₈	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	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
34	C₄⋊C₄×Dic₄₃	C₄	1	2	yes	—
35	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
37	#14582750	C₄	1	2	yes	—
38	#14582750	C₄	1	2	yes	—
39	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
40	C₄²×Dic₄₃	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	#13063290	—	2	8	no	—
65	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
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×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
73	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
74	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
75	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
76	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
80	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
81	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
82	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
83	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
84	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
85	#13063236	—	4	1	no	—
86	#13063236	C₂×C₄	1	4	yes	—
87	#13063235	C₂×C₄	1	4	yes	—
88	#13063235	C₂×C₄	1	4	yes	—
89	C₄×C₄₃⋊C₈	—	4	1	no	—
90	C₈×Dic₄₃	—	4	1	no	—
91	C₈×Dic₄₃	—	4	1	no	—
92	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
93	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
94	C₄₃⋊#95	C₂×C₄	1	2	yes	—
95	C₄₃⋊#95	C₂×C₄	1	2	yes	—
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	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
105	#97×C₄₃	—	4	1	no	—
106	#97×C₄₃	C₂×C₄	1	4	yes	—
107	C₄×C₈×C₄₃	—	4	1	no	—
108	#95×C₄₃	C₂×C₄	1	2	yes	—
109	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
114	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
118	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
119	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×Dic₈₆	—	2	4	no	—
121	C₂×Dic₈₆	C₄²	1	4	yes	—
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	—	2	1	no	—
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	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
134	C₄⋊C₄×C₄₃	—	2	4	no	—
135	C₄²×C₄₃	—	2	1	no	—
136	C₄²×C₄₃	—	2	1	no	—
137	C₄²×C₄₃	—	2	1	no	—
138	C₄²×C₄₃	—	2	1	no	—
139	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
140	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
141	C₄⋊Dic₄₃	C₄²	1	4	yes	—
142	Dic₄₃⋊C₄	—	2	4	no	—
143	Dic₄₃⋊C₄	C₄²	1	4	yes	—
144	Dic₄₃⋊C₄	C₄²	1	4	yes	—
145	Dic₄₃⋊C₄	M₁₆	1	8	yes	—
146	C₄×Dic₄₃	—	2	4	no	—
147	C₄×Dic₄₃	—	2	1	no	—
148	C₄×Dic₄₃	—	2	1	no	—
149	C₄×Dic₄₃	—	2	1	no	—
150	C₄×Dic₄₃	—	2	1	no	—
151	C₄×Dic₄₃	—	2	4	no	—
152	C₄×Dic₄₃	—	2	4	no	—
153	C₄×Dic₄₃	—	2	4	no	—
154	C₄×Dic₄₃	—	2	4	no	—
155	C₄×Dic₄₃	—	2	4	no	—
156	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
157	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
158	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
159	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
164	C₂×C₄₃⋊C₈	—	2	1	no	—
165	C₂×C₄₃⋊C₈	—	2	1	no	—
166	C₂×C₄₃⋊C₈	—	2	1	no	—
167	C₂×C₄₃⋊C₈	—	2	1	no	—
168	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
170	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
171	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
172	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
181	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
182	C₂×C₄×C₄₃	C₂×M₁₆	1	4	yes	—
183	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
187	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
188	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
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	—	2	2	no	—
194	C₂×Dic₄₃	—	2	2	no	—
195	C₂×Dic₄₃	—	2	2	no	—
196	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
197	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
198	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
199	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
200	C₂×Dic₄₃	C₂×M₁₆	1	4	yes	—
201	C₂×Dic₄₃	C₂×M₁₆	1	4	yes	—
202	C₂×Dic₄₃	#131	1	4	yes	—
203	Dic₈₆	—	2	8	no	—
204	C₈×C₄₃	—	2	2	no	—
205	C₈×C₄₃	—	2	2	no	—
206	C₈×C₄₃	—	2	2	no	—
207	C₈×C₄₃	—	2	2	no	—
208	C₄₃⋊C₈	—	2	2	no	—
209	C₄₃⋊C₈	—	2	2	no	—
210	C₄₃⋊C₈	—	2	2	no	—
211	C₄₃⋊C₈	—	2	2	no	—
212	#20573	—	43	1	no	maximal, Sylow
213	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
214	C₂²×C₄₃	#519	1	1	yes	characteristic
215	C₂²×C₄₃	#520	1	1	yes	characteristic
216	C₂²×C₄₃	C₂²×M₁₆	1	2	yes	—
217	C₂²×C₄₃	C₂×#131	1	2	yes	—
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	2	2	no	—
220	C₄×C₄₃	—	2	4	no	—
221	C₄×C₄₃	—	4	2	no	—
222	C₄×C₄₃	#519	1	1	yes	characteristic
223	C₄×C₄₃	#519	1	1	yes	characteristic
224	C₄×C₄₃	#520	1	1	yes	characteristic
225	C₄×C₄₃	#520	1	1	yes	characteristic
226	Dic₄₃	—	2	2	no	—
227	Dic₄₃	—	2	2	no	—
228	Dic₄₃	—	2	2	no	—
229	Dic₄₃	—	2	4	no	—
230	Dic₄₃	—	2	4	no	—
231	Dic₄₃	C₄×M₁₆	1	4	yes	—
232	C₂×#446	—	43	1	no	—
233	C₂×#446	—	43	1	no	—
234	C₄²×Q₈	—	43	1	no	—
235	#1771	—	43	1	no	—
236	#1771	—	43	1	no	—
237	#1771	—	43	1	no	—
238	#1771	D₄₃	1	1	yes	characteristic
239	C₈×C₄⋊C₄	—	43	1	no	—
240	C₈×C₄⋊C₄	—	43	1	no	—
241	#1767	—	43	1	no	—
242	C₄×C₄⋊C₈	—	43	1	no	—
243	C₄×C₄⋊C₈	—	43	1	no	—
244	#1745	—	43	1	no	—
245	#1745	—	43	1	no	—
246	#1744	—	43	1	no	—
247	C₂×C₄₃	#2276	1	1	yes	characteristic
248	C₂×C₄₃	C₂×C₄×M₁₆	1	1	yes	characteristic
249	C₂×C₄₃	C₄×#131	1	1	yes	characteristic
250	C₂×C₄₃	#2984	1	2	yes	—
251	C₂×C₄₃	#2990	1	2	yes	—
252	C₂×C₄×Q₈	—	43	2	no	—
253	C₂×C₄×Q₈	—	43	1	no	—
254	#446	—	43	8	no	—
255	#446	—	43	8	no	—
256	C₂×C₄⋊C₈	—	43	1	no	—
257	C₂×C₄⋊C₈	—	43	1	no	—
258	C₂×C₄⋊C₈	—	43	1	no	—
259	C₂×C₄⋊C₈	—	43	1	no	—
260	C₂×C₄⋊C₈	—	43	1	no	—
261	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
262	C₂×#97	—	43	1	no	—
263	C₂×#97	—	43	1	no	—
264	C₂×#97	—	43	1	no	—
265	C₂×#97	—	43	1	no	—
266	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
267	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
268	C₂×C₄×C₈	—	43	1	no	—
269	C₂×C₄×C₈	—	43	1	no	—
270	C₂×C₄×C₈	—	43	1	no	—
271	C₂×C₄×C₈	—	43	1	no	—
272	C₂×C₄×C₈	—	43	1	no	—
273	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
274	C₄×C₄⋊C₄	—	43	2	no	—
275	C₄×C₄⋊C₄	—	43	1	no	—
276	C₄×C₄⋊C₄	—	43	1	no	—
277	C₄×C₄⋊C₄	—	43	2	no	—
278	C₄×C₄⋊C₄	—	43	2	no	—
279	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
280	C₄³	—	43	1	no	—
281	C₄³	—	43	1	no	—
282	C₄³	—	43	1	no	—
283	#336	—	43	1	no	—
284	#336	—	43	1	no	—
285	#336	—	43	1	no	—
286	#336	—	43	1	no	—
287	#336	—	43	1	no	—
288	#336	—	43	1	no	—
289	#336	—	43	1	no	—
290	#336	—	43	1	no	—
291	#336	C₂×D₄₃	1	1	yes	characteristic
292	#336	C₂×D₄₃	1	1	yes	characteristic
293	C₄₃	#20573	1	1	yes	characteristic, complemented, Sylow
294	C₂²×Q₈	—	43	1	no	—
295	C₂²×C₈	—	43	1	no	—
296	C₂²×C₈	—	43	1	no	—
297	C₂²×C₈	—	43	1	no	—
298	C₂²×C₈	—	43	1	no	—
299	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
300	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
301	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
302	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
303	C₄×Q₈	—	43	4	no	—
304	C₄×Q₈	—	43	4	no	—
305	C₄×Q₈	—	86	8	no	—
306	C₂×C₄⋊C₄	—	43	1	no	—
307	C₂×C₄⋊C₄	—	43	1	no	—
308	C₂×C₄⋊C₄	—	43	2	no	—
309	C₂×C₄⋊C₄	—	43	1	no	—
310	C₂×C₄⋊C₄	—	43	2	no	—
311	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
312	C₂×C₄²	—	43	1	no	—
313	C₂×C₄²	—	43	1	no	—
314	C₂×C₄²	—	43	2	no	—
315	C₂×C₄²	—	43	2	no	—
316	C₂×C₄²	—	43	2	no	—
317	C₂×C₄²	—	43	2	no	—
318	C₂×C₄²	—	43	2	no	—
319	C₂×C₄²	—	43	2	no	—
320	C₂×C₄²	—	43	1	no	—
321	C₂×C₄²	—	43	1	no	—
322	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
323	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
324	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
325	C₄⋊C₈	—	43	4	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	C₄×D₄₃	1	4	yes	—
331	#97	—	4	1	no	—
332	#97	—	43	4	no	—
333	#97	—	43	4	no	—
334	#97	—	43	4	no	—
335	#97	—	172	1	no	—
336	#97	C₄×D₄₃	1	4	yes	—
337	C₄×C₈	—	4	1	no	—
338	C₄×C₈	—	43	4	no	—
339	C₄×C₈	—	43	4	no	—
340	C₄×C₈	—	172	1	no	—
341	C₄×C₈	—	172	1	no	—
342	C₄×C₈	—	172	1	no	—
343	#95	—	43	2	no	—
344	#95	—	43	2	no	—
345	#95	C₄×D₄₃	1	2	yes	—
346	C₂×Q₈	—	43	4	no	—
347	C₂×Q₈	—	86	4	no	—
348	C₂²×C₄	—	43	1	no	—
349	C₂²×C₄	—	43	1	no	—
350	C₂²×C₄	—	43	1	no	—
351	C₂²×C₄	—	43	2	no	—
352	C₂²×C₄	—	43	2	no	—
353	C₂²×C₄	—	43	1	no	—
354	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
355	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
358	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	43	2	no	—
368	C₂×C₈	—	43	2	no	—
369	C₂×C₈	—	43	2	no	—
370	C₂×C₈	—	43	2	no	—
371	C₂×C₈	—	86	1	no	—
372	C₂×C₈	—	86	1	no	—
373	C₂×C₈	—	86	1	no	—
374	C₂×C₈	—	86	1	no	—
375	C₂×C₈	—	86	1	no	—
376	C₂×C₈	—	86	1	no	—
377	C₂×C₈	—	86	1	no	—
378	C₂×C₈	—	86	1	no	—
379	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
380	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
381	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
382	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	43	4	no	—
385	C₄⋊C₄	—	43	4	no	—
386	C₄⋊C₄	—	43	4	no	—
387	C₄⋊C₄	—	43	8	no	—
388	C₄⋊C₄	—	86	4	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	43	2	no	—
394	C₄²	—	43	2	no	—
395	C₄²	—	43	2	no	—
396	C₄²	—	43	2	no	—
397	C₄²	—	86	4	no	—
398	C₄²	—	86	4	no	—
399	C₄²	—	86	4	no	—
400	C₄²	—	86	4	no	—
401	C₄²	—	86	4	no	—
402	C₄²	—	86	4	no	—
403	C₄²	—	86	1	no	—
404	C₄²	—	86	1	no	—
405	C₄²	—	86	1	no	—
406	C₄²	—	86	1	no	—
407	C₄²	C₂×C₄×D₄₃	1	2	yes	—
408	C₄²	C₂×C₄×D₄₃	1	2	yes	—
409	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
410	Q₈	—	86	8	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	43	2	no	—
419	C₂×C₄	—	43	4	no	—
420	C₂×C₄	—	43	2	no	—
421	C₂×C₄	—	43	2	no	—
422	C₂×C₄	—	43	2	no	—
423	C₂×C₄	—	43	4	no	—
424	C₂×C₄	—	43	4	no	—
425	C₂×C₄	—	86	2	no	—
426	C₂×C₄	—	86	2	no	—
427	C₂×C₄	—	86	2	no	—
428	C₂×C₄	—	86	2	no	—
429	C₂×C₄	—	86	2	no	—
430	C₂×C₄	—	86	2	no	—
431	C₂×C₄	—	86	2	no	—
432	C₂×C₄	C₄²×D₄₃	1	2	yes	—
433	C₂×C₄	C₄²×D₄₃	1	2	yes	—
434	C₂×C₄	M₁₆×D₄₃	1	4	yes	—
435	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
436	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
437	C₂×C₄	#13063370	1	1	yes	characteristic
438	C₂×C₄	#13063372	1	1	yes	characteristic
439	C₂×C₄	#13063372	1	1	yes	characteristic
440	C₂×C₄	#13063373	1	1	yes	characteristic
441	C₈	—	2	2	no	—
442	C₈	—	2	2	no	—
443	C₈	—	2	2	no	—
444	C₈	—	2	2	no	—
445	C₈	—	86	2	no	—
446	C₈	—	86	2	no	—
447	C₈	—	86	2	no	—
448	C₈	—	86	2	no	—
449	C₂²	C₂×C₄²×D₄₃	1	1	yes	characteristic
450	C₂²	#14583375	1	1	yes	characteristic
451	C₂²	#14583378	1	1	yes	characteristic
452	C₂²	C₂×M₁₆×D₄₃	1	2	yes	—
453	C₂²	#131×D₄₃	1	2	yes	—
454	C₄	—	2	4	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	43	4	no	—
459	C₄	—	86	4	no	—
460	C₄	—	86	4	no	—
461	C₄	—	86	2	no	—
462	C₄	—	86	2	no	—
463	C₄	—	86	2	no	—
464	C₄	#14583375	1	1	yes	characteristic
465	C₄	#14583376	1	1	yes	characteristic
466	C₄	#14583378	1	1	yes	characteristic
467	C₄	#14583380	1	1	yes	characteristic
468	C₂	#19136959	1	1	yes	characteristic
469	C₂	C₄×M₁₆×D₄₃	1	1	yes	characteristic
470	C₂	#19143017	1	1	yes	characteristic
471	C₂	#19143681	1	2	yes	—
472	C₂	#19143715	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	#20573
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
18. #14583028	C₄	semidirect
19. #14583027	C₄	semidirect
293. C₄₃	#20573	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583028	2
C₂×#14583027	2
C₄×#13063290	2
#19134471	2
#19134470	2
#19134468	2
C₈×Dic₄₃⋊C₄	2
#19134456	2
#19134449	2
C₄⋊C₈×Dic₄₃	2
C₄×Dic₄₃⋊C₈	2
#19134343	2
#19134342	2
#19134339	2
C₄₃×#1771	2
#20573	43