Subgroups — #24987148

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13063240	C₂	1	1	yes	maximal, characteristic
2	#19134371	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×C₂²⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132913	C₂	1	1	yes	maximal, characteristic
5	#19132442	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132442	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#435	C₂	1	1	yes	maximal, characteristic
8	C₂×#13063240	C₄	1	2	yes	—
9	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#13063235	—	2	1	no	—
12	C₂×C₈×Dic₄₃	—	2	1	no	—
13	C₄×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
14	C₄×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	#14582666	C₄	1	2	yes	—
16	#14582653	—	2	1	no	—
17	#14582653	—	2	1	no	—
18	#14582625	C₄	1	2	yes	complemented
19	#14582623	C₄	1	2	yes	complemented
20	C₂²×M₁₆×C₄₃	C₄	1	1	yes	characteristic, complemented
21	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#435	—	2	1	no	—
24	C₄₃×#435	—	2	1	no	—
25	C₄₃×#435	—	2	1	no	—
26	C₄₃×#435	—	2	1	no	—
27	C₂×C₄⋊C₈×C₄₃	C₄	1	1	yes	characteristic, complemented
28	C₂×C₂²⋊C₈×C₄₃	C₄	1	1	yes	characteristic, complemented
29	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#97×C₄₃	C₄	1	1	yes	characteristic, complemented
31	C₂²×C₄₃⋊C₈	—	2	1	no	—
32	C₂²×C₄₃⋊C₈	—	2	1	no	—
33	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
34	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
35	C₂×C₄×Dic₄₃	—	2	1	no	—
36	C₂×C₄×Dic₄₃	—	2	1	no	—
37	#13063240	—	2	4	no	—
38	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
39	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
40	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
41	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
42	#13063235	—	4	2	no	—
43	C₈×Dic₄₃	—	4	2	no	—
44	C₄₃⋊#95	—	2	1	no	—
45	C₄₃⋊#95	—	2	1	no	—
46	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₄₃	—	2	1	no	—
50	C₂×M₁₆×C₄₃	—	2	1	no	—
51	C₂×M₁₆×C₄₃	—	4	2	no	—
52	C₂²×C₈×C₄₃	—	4	2	no	—
53	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
61	C₄×D₄×C₄₃	—	2	1	no	—
62	C₄×D₄×C₄₃	—	2	1	no	—
63	C₄×D₄×C₄₃	—	2	1	no	—
64	C₄×D₄×C₄₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
69	C₄⋊C₈×C₄₃	—	2	1	no	—
70	C₄⋊C₈×C₄₃	—	2	1	no	—
71	C₂²⋊C₈×C₄₃	—	2	1	no	—
72	C₂²⋊C₈×C₄₃	—	2	1	no	—
73	C₂²⋊C₈×C₄₃	—	2	1	no	—
74	C₂²⋊C₈×C₄₃	—	2	1	no	—
75	#97×C₄₃	—	2	1	no	—
76	#97×C₄₃	—	2	1	no	—
77	C₂⁴×C₄₃	C₄²	1	1	yes	characteristic
78	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
79	C₂×D₄×C₄₃	—	2	1	no	—
80	C₂×D₄×C₄₃	—	2	1	no	—
81	C₂×D₄×C₄₃	—	2	2	no	—
82	C₂×D₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	1	no	—
84	C₂²×C₄×C₄₃	—	2	1	no	—
85	C₂²×C₄×C₄₃	—	4	1	no	—
86	C₂²×C₄×C₄₃	—	4	1	no	—
87	C₂²×C₄×C₄₃	—	4	1	no	—
88	C₂²×C₄×C₄₃	—	4	1	no	—
89	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
98	C₂²×Dic₄₃	—	2	2	no	—
99	C₂²×Dic₄₃	—	2	2	no	—
100	M₁₆×C₄₃	—	4	2	no	—
101	M₁₆×C₄₃	—	4	2	no	—
102	C₂×C₈×C₄₃	—	2	2	no	—
103	C₂×C₈×C₄₃	—	2	2	no	—
104	C₂×C₈×C₄₃	—	2	2	no	—
105	C₂×C₈×C₄₃	—	2	1	no	—
106	C₂×C₈×C₄₃	—	2	1	no	—
107	C₂×C₈×C₄₃	—	4	1	no	—
108	C₂×C₈×C₄₃	—	4	1	no	—
109	C₂×C₈×C₄₃	—	4	1	no	—
110	C₂×C₈×C₄₃	—	4	1	no	—
111	C₂×C₈×C₄₃	—	4	1	no	—
112	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₄⋊C₄×C₄₃	—	2	1	no	—
117	C₄⋊C₄×C₄₃	—	2	1	no	—
118	C₂²⋊C₄×C₄₃	—	2	1	no	—
119	C₂²⋊C₄×C₄₃	—	2	1	no	—
120	C₂²⋊C₄×C₄₃	—	2	1	no	—
121	C₂²⋊C₄×C₄₃	—	2	1	no	—
122	C₄²×C₄₃	—	2	1	no	—
123	C₄²×C₄₃	—	2	1	no	—
124	C₂²⋊Dic₄₃	—	2	2	no	—
125	C₂²⋊Dic₄₃	—	2	2	no	—
126	C₂²⋊Dic₄₃	—	2	2	no	—
127	C₂²⋊Dic₄₃	M₁₆	1	4	yes	complemented
128	C₄×Dic₄₃	—	4	1	no	—
129	C₄×Dic₄₃	—	4	1	no	—
130	C₄×Dic₄₃	—	4	1	no	—
131	C₄×Dic₄₃	—	4	1	no	—
132	C₂×C₄₃⋊C₈	—	2	2	no	—
133	C₂×C₄₃⋊C₈	—	2	2	no	—
134	C₂×C₄₃⋊C₈	—	4	1	no	—
135	C₂×C₄₃⋊C₈	—	4	1	no	—
136	C₂×C₄₃⋊C₈	—	4	1	no	—
137	C₂×C₄₃⋊C₈	—	4	1	no	—
138	C₂³×C₄₃	—	2	1	no	—
139	C₂³×C₄₃	—	2	1	no	—
140	C₂³×C₄₃	—	2	1	no	—
141	C₂³×C₄₃	—	4	1	no	—
142	C₂³×C₄₃	—	4	1	no	—
143	C₂³×C₄₃	—	4	1	no	—
144	C₂³×C₄₃	—	4	1	no	—
145	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
146	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
147	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
148	C₂³×C₄₃	C₂×M₁₆	1	2	yes	—
149	C₂³×C₄₃	#131	1	2	yes	—
150	D₄×C₄₃	—	4	2	no	—
151	D₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	—	2	1	no	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	2	1	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
175	C₂×Dic₄₃	—	2	4	no	—
176	C₂×Dic₄₃	—	4	2	no	—
177	C₂×Dic₄₃	—	4	2	no	—
178	C₂×Dic₄₃	—	4	2	no	—
179	C₂×Dic₄₃	—	4	2	no	—
180	C₂×Dic₄₃	—	4	2	no	—
181	C₈×C₄₃	—	2	1	no	—
182	C₈×C₄₃	—	2	1	no	—
183	C₈×C₄₃	—	2	1	no	—
184	C₈×C₄₃	—	4	1	no	—
185	C₈×C₄₃	—	4	1	no	—
186	C₈×C₄₃	#99	1	2	yes	complemented
187	C₄₃⋊C₈	—	4	2	no	—
188	C₄₃⋊C₈	—	4	2	no	—
189	#8161	—	43	1	no	maximal, Sylow
190	C₂²×C₄₃	—	2	1	no	—
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	—	2	1	no	—
194	C₂²×C₄₃	—	2	1	no	—
195	C₂²×C₄₃	—	2	1	no	—
196	C₂²×C₄₃	—	4	2	no	—
197	C₂²×C₄₃	—	4	2	no	—
198	C₂²×C₄₃	—	4	1	no	—
199	C₂²×C₄₃	—	4	1	no	—
200	C₂²×C₄₃	—	4	1	no	—
201	C₂²×C₄₃	—	8	1	no	—
202	C₂²×C₄₃	—	8	1	no	—
203	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
204	C₂²×C₄₃	C₄×M₁₆	1	1	yes	characteristic
205	C₂²×C₄₃	#405	1	1	yes	characteristic
206	C₂²×C₄₃	#435	1	2	yes	—
207	C₂²×C₄₃	#436	1	2	yes	—
208	C₄×C₄₃	—	2	1	no	—
209	C₄×C₄₃	—	2	1	no	—
210	C₄×C₄₃	—	2	1	no	—
211	C₄×C₄₃	—	4	1	no	—
212	C₄×C₄₃	—	4	1	no	—
213	C₄×C₄₃	—	4	1	no	—
214	C₄×C₄₃	C₂×#99	1	1	yes	characteristic
215	C₄×C₄₃	#410	1	1	yes	characteristic
216	Dic₄₃	—	4	4	no	—
217	Dic₄₃	—	8	2	no	—
218	C₂×#435	D₄₃	1	1	yes	characteristic
219	C₄×#99	—	43	1	no	—
220	#1752	—	43	1	no	—
221	C₈×C₂²⋊C₄	—	43	1	no	—
222	#1459	—	43	1	no	—
223	#1282	—	43	1	no	—
224	#1282	—	43	1	no	—
225	C₂×C₄₃	—	2	2	no	—
226	C₂×C₄₃	—	2	2	no	—
227	C₂×C₄₃	—	2	1	no	—
228	C₂×C₄₃	—	2	1	no	—
229	C₂×C₄₃	—	8	1	no	—
230	C₂×C₄₃	#1753	1	1	yes	characteristic
231	C₂×C₄₃	C₄×#99	1	1	yes	characteristic
232	C₂×C₄₃	#1757	1	1	yes	characteristic
233	C₂²×M₁₆	Dic₄₃	1	1	yes	characteristic, complemented
234	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
236	#435	—	2	1	no	—
237	#435	—	2	1	no	—
238	#435	—	2	1	no	—
239	#435	—	2	1	no	—
240	C₂×C₄⋊C₈	Dic₄₃	1	1	yes	characteristic, complemented
241	C₂×#99	—	43	2	no	—
242	C₂×C₂²⋊C₈	—	43	1	no	—
243	C₂×C₂²⋊C₈	—	43	1	no	—
244	C₂×C₂²⋊C₈	Dic₄₃	1	1	yes	characteristic, complemented
245	C₂×C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic
246	C₂×#97	—	86	1	no	—
247	C₂×#97	Dic₄₃	1	1	yes	characteristic, complemented
248	C₂×C₄×C₈	—	86	1	no	—
249	C₄×C₂²⋊C₄	—	43	1	no	—
250	C₄×C₂²⋊C₄	—	43	1	no	—
251	#342	—	43	2	no	—
252	#336	—	86	1	no	—
253	#336	—	86	1	no	—
254	#324	—	43	2	no	—
255	#323	—	43	2	no	—
256	C₄₃	#8161	1	1	yes	characteristic, complemented, Sylow
257	C₂²×D₄	C₄×D₄₃	1	1	yes	characteristic
258	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
259	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	—	4	2	no	—
263	C₂²×C₈	—	4	2	no	—
264	C₂²×C₈	—	86	1	no	—
265	C₂²×C₈	—	86	1	no	—
266	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
267	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
268	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
269	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
270	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
271	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
272	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
273	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	43	2	no	—
280	C₂×C₂²⋊C₄	—	43	2	no	—
281	C₂×C₂²⋊C₄	C₄×D₄₃	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₄×D₄₃	1	1	yes	characteristic
283	C₂×C₄²	—	86	1	no	—
284	C₂×C₄²	—	86	1	no	—
285	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	#99	—	86	4	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	2	1	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	43	2	no	—
294	C₂²⋊C₈	—	43	2	no	—
295	C₂²⋊C₈	—	86	1	no	—
296	C₂²⋊C₈	—	86	1	no	—
297	#97	—	2	1	no	—
298	#97	—	2	1	no	—
299	#97	—	172	2	no	—
300	C₄×C₈	—	172	2	no	—
301	#95	—	86	1	no	—
302	#95	—	86	1	no	—
303	C₂⁴	C₄×Dic₄₃	1	1	yes	characteristic
304	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	86	2	no	—
316	C₂²×C₄	—	86	2	no	—
317	C₂²×C₄	C₄×Dic₄₃	1	1	yes	characteristic
318	C₂²×C₄	C₄×Dic₄₃	1	1	yes	characteristic
319	C₂²×C₄	C₄×Dic₄₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
321	C₂²×C₄	#10621898	1	1	yes	characteristic
322	C₂²×C₄	#10621898	1	1	yes	characteristic
323	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
326	M₁₆	—	4	2	no	—
327	M₁₆	—	4	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	86	2	no	—
339	C₂×C₈	—	86	2	no	—
340	C₂×C₈	—	172	1	no	—
341	C₂×C₈	—	172	1	no	—
342	C₂×C₈	—	172	1	no	—
343	C₂×C₈	—	172	1	no	—
344	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
345	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
346	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
347	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	2	1	no	—
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	43	4	no	—
355	C₂²⋊C₄	—	86	2	no	—
356	C₂²⋊C₄	—	86	2	no	—
357	C₂²⋊C₄	—	86	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	172	1	no	—
361	C₄²	—	172	1	no	—
362	C₄²	—	172	1	no	—
363	C₄²	—	172	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	C₂×C₄×Dic₄₃	1	1	yes	characteristic
372	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
373	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
374	C₂³	M₁₆×D₄₃	1	2	yes	—
375	C₂³	#13063333	1	2	yes	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	86	4	no	—
398	C₂×C₄	—	172	2	no	—
399	C₂×C₄	—	172	2	no	—
400	C₂×C₄	—	172	2	no	—
401	C₂×C₄	—	172	2	no	—
402	C₂×C₄	—	172	2	no	—
403	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
404	C₂×C₄	#13063284	1	1	yes	characteristic
405	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
406	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
407	C₈	—	2	1	no	—
408	C₈	—	2	1	no	—
409	C₈	—	2	1	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	172	2	no	—
413	C₈	—	172	2	no	—
414	C₈	#13063240	1	2	yes	complemented
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	C₄×C₂²⋊Dic₄₃	1	1	yes	characteristic
429	C₂²	M₁₆×Dic₄₃	1	1	yes	characteristic
430	C₂²	#14582857	1	1	yes	characteristic
431	C₂²	#14582968	1	2	yes	—
432	C₂²	#14582975	1	2	yes	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	344	2	no	—
440	C₄	—	172	4	no	—
441	C₄	C₂×#13063240	1	1	yes	characteristic
442	C₄	#14582873	1	1	yes	characteristic
443	C₂	—	2	2	no	—
444	C₂	—	2	2	no	—
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	8	1	no	—
448	C₂	#19134376	1	1	yes	characteristic
449	C₂	C₄×#13063240	1	1	yes	characteristic
450	C₂	#19134395	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₄₃
commutator	C₂³×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#435	C₂
socle	C₂²×C₄₃	C₄×C₂²⋊C₄
prime radical	C₂²×D₄×C₄₃	C₂×C₄
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#435	D₄₃
hypocenter	C₄₃	#8161
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ C₂×#435

Complements

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

N	H ≅ G/N	type
2. #19134371	C₂	semidirect
3. C₈×C₂²⋊Dic₄₃	C₂	semidirect
5. #19132442	C₂	semidirect
6. #19132442	C₂	semidirect
18. #14582625	C₄	semidirect
19. #14582623	C₄	semidirect
20. C₂²×M₁₆×C₄₃	C₄	semidirect
27. C₂×C₄⋊C₈×C₄₃	C₄	semidirect
28. C₂×C₂²⋊C₈×C₄₃	C₄	semidirect
30. C₂×#97×C₄₃	C₄	semidirect
127. C₂²⋊Dic₄₃	M₁₆	semidirect
186. C₈×C₄₃	#99	semidirect
233. C₂²×M₁₆	Dic₄₃	semidirect
240. C₂×C₄⋊C₈	Dic₄₃	semidirect
244. C₂×C₂²⋊C₈	Dic₄₃	semidirect
247. C₂×#97	Dic₄₃	semidirect
256. C₄₃	#8161	semidirect
414. C₈	#13063240	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13063240	2
#19134371	2
C₈×C₂²⋊Dic₄₃	2
#19132913	2
#19132442	2
C₂×C₄₃×#435	2
#8161	43