Subgroups — #25002323

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582662	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582661	C₂	1	2	yes	maximal
4	#19132824	C₂	1	2	yes	maximal
5	C₂×C₄₃×#340	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×Dic₄₃	—	2	4	no	—
10	C₂×C₈×Dic₄₃	C₄	1	4	yes	complemented
11	C₂×C₄₃⋊#95	—	2	2	no	—
12	C₂×C₄₃⋊#95	—	2	2	no	—
13	#14582662	C₄	1	4	yes	complemented
14	#14582661	—	2	4	no	—
15	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
17	C₄₃×#340	C₄	1	4	yes	complemented
18	C₂³×Dic₄₃	—	2	2	no	—
19	C₂³×Dic₄₃	D₄	1	1	yes	characteristic
20	C₂³×Dic₄₃	D₄	1	1	yes	characteristic
21	C₂²×C₄₃⋊C₈	—	2	2	no	—
22	C₂²×C₄₃⋊C₈	—	2	1	no	—
23	C₂²×C₄₃⋊C₈	—	2	1	no	—
24	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
25	C₂²×C₄₃⋊C₈	D₄	1	4	yes	—
26	C₂×C₄⋊Dic₄₃	—	2	2	no	—
27	C₂×C₄⋊Dic₄₃	—	2	2	no	—
28	C₂×C₄⋊Dic₄₃	—	2	2	no	—
29	C₂×C₄⋊Dic₄₃	—	2	2	no	—
30	C₂×C₄⋊Dic₄₃	—	2	2	no	—
31	C₂×C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
32	C₂×C₄×Dic₄₃	—	2	2	no	—
33	C₂×C₄×Dic₄₃	—	2	2	no	—
34	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
35	C₂×C₄×Dic₄₃	Q₈	1	2	yes	—
36	C₈×Dic₄₃	—	2	8	no	—
37	C₄₃⋊#95	—	4	4	no	—
38	C₄₃⋊#95	—	4	4	no	—
39	C₂³×C₄×C₄₃	—	2	2	no	—
40	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₄₃	—	2	2	no	—
42	C₂²×C₈×C₄₃	—	2	2	no	—
43	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
52	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₄₃	—	2	4	no	—
54	C₂²×C₄×C₄₃	—	4	2	no	—
55	C₂²×C₄×C₄₃	—	4	2	no	—
56	C₂²×C₄×C₄₃	—	4	2	no	—
57	C₂²×C₄×C₄₃	—	4	2	no	—
58	C₂²×C₄×C₄₃	—	4	2	no	—
59	C₂²×C₄×C₄₃	—	4	2	no	—
60	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
65	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
66	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
67	C₂²×C₄×C₄₃	#41	1	2	yes	—
68	C₂²×C₄×C₄₃	#41	1	2	yes	—
69	C₂²×C₄×C₄₃	#41	1	2	yes	—
70	C₂²×Dic₄₃	—	2	4	no	—
71	C₂²×Dic₄₃	—	2	2	no	—
72	C₂²×Dic₄₃	—	2	2	no	—
73	C₂²×Dic₄₃	—	2	1	no	—
74	C₂²×Dic₄₃	—	2	2	no	—
75	C₂²×Dic₄₃	—	2	1	no	—
76	C₂²×Dic₄₃	—	4	2	no	—
77	C₂²×Dic₄₃	—	4	2	no	—
78	C₂²×Dic₄₃	—	4	2	no	—
79	C₂²×Dic₄₃	—	4	2	no	—
80	C₂²×Dic₄₃	—	4	2	no	—
81	C₂²×Dic₄₃	—	4	2	no	—
82	C₂²×Dic₄₃	C₄⋊C₄	1	2	yes	—
83	C₂²×Dic₄₃	C₄⋊C₄	1	2	yes	—
84	C₂²×Dic₄₃	D₈	1	2	yes	—
85	C₂²×Dic₄₃	SD₁₆	1	4	yes	—
86	C₂²×Dic₄₃	Q₁₆	1	2	yes	—
87	C₂×C₈×C₄₃	—	2	2	no	—
88	C₂×C₈×C₄₃	—	2	2	no	—
89	C₂×C₈×C₄₃	—	2	4	no	—
90	C₂×C₈×C₄₃	—	2	4	no	—
91	C₂×C₈×C₄₃	C₄²	1	4	yes	—
92	C₄⋊C₄×C₄₃	—	2	4	no	—
93	C₄⋊C₄×C₄₃	—	2	4	no	—
94	C₄⋊C₄×C₄₃	—	4	2	no	—
95	C₄⋊C₄×C₄₃	—	4	2	no	—
96	C₄⋊Dic₄₃	—	2	4	no	—
97	C₄⋊Dic₄₃	—	2	4	no	—
98	C₄⋊Dic₄₃	—	4	2	no	—
99	C₄⋊Dic₄₃	—	4	2	no	—
100	C₄×Dic₄₃	—	2	2	no	—
101	C₄×Dic₄₃	—	2	2	no	—
102	C₄×Dic₄₃	—	2	4	no	—
103	C₂×C₄₃⋊C₈	—	2	2	no	—
104	C₂×C₄₃⋊C₈	—	2	2	no	—
105	C₂×C₄₃⋊C₈	—	2	4	no	—
106	C₂×C₄₃⋊C₈	—	2	4	no	—
107	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	4	yes	—
108	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
109	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
110	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
111	C₂³×C₄₃	#121	1	2	yes	—
112	C₂³×C₄₃	#124	1	2	yes	—
113	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
114	C₂³×C₄₃	C₂×SD₁₆	1	2	yes	—
115	C₂³×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
116	C₂³×C₄₃	#135	1	1	yes	characteristic
117	C₂³×C₄₃	#135	1	2	yes	—
118	C₂³×C₄₃	#135	1	1	yes	characteristic
119	C₂×C₄×C₄₃	—	4	4	no	—
120	C₂×C₄×C₄₃	—	4	4	no	—
121	C₂×C₄×C₄₃	—	4	4	no	—
122	C₂×C₄×C₄₃	—	8	2	no	—
123	C₂×C₄×C₄₃	—	8	2	no	—
124	C₂×C₄×C₄₃	—	8	2	no	—
125	C₂×C₄×C₄₃	—	8	2	no	—
126	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
127	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
129	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
130	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
131	C₂×C₄×C₄₃	#117	1	2	yes	—
132	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
133	C₂×C₄×C₄₃	#117	1	2	yes	—
134	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
135	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
136	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
137	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
138	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
139	C₂×C₄×C₄₃	#123	1	2	yes	—
140	C₂×C₄×C₄₃	#123	1	2	yes	—
141	C₂×C₄×C₄₃	#125	1	2	yes	—
142	C₂×C₄×C₄₃	#126	1	2	yes	—
143	C₂×C₄×C₄₃	#126	1	2	yes	—
144	C₂×Dic₄₃	—	2	2	no	—
145	C₂×Dic₄₃	—	2	2	no	—
146	C₂×Dic₄₃	—	2	2	no	—
147	C₂×Dic₄₃	—	2	2	no	—
148	C₂×Dic₄₃	—	2	4	no	—
149	C₂×Dic₄₃	—	2	4	no	—
150	C₂×Dic₄₃	—	2	4	no	—
151	C₂×Dic₄₃	—	2	4	no	—
152	C₂×Dic₄₃	—	4	4	no	—
153	C₂×Dic₄₃	—	4	4	no	—
154	C₂×Dic₄₃	—	4	4	no	—
155	C₂×Dic₄₃	—	8	2	no	—
156	C₂×Dic₄₃	—	8	2	no	—
157	C₂×Dic₄₃	—	8	2	no	—
158	C₂×Dic₄₃	—	8	2	no	—
159	C₂×Dic₄₃	#106	1	4	yes	—
160	C₂×Dic₄₃	#107	1	4	yes	—
161	C₈×C₄₃	—	2	4	no	—
162	C₄₃⋊C₈	—	2	4	no	—
163	#10820	—	43	1	no	maximal, Sylow
164	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×C₄₃	#380	1	1	yes	characteristic
166	C₂²×C₄₃	#382	1	1	yes	characteristic
167	C₂²×C₄₃	#388	1	2	yes	—
168	C₂²×C₄₃	#388	1	2	yes	—
169	C₂²×C₄₃	C₂×#106	1	1	yes	characteristic
170	C₂²×C₄₃	C₂×#107	1	1	yes	characteristic
171	C₂²×C₄₃	#427	1	1	yes	characteristic
172	C₂²×C₄₃	#427	1	1	yes	characteristic
173	C₂²×C₄₃	C₄×D₈	1	1	yes	characteristic
174	C₂²×C₄₃	C₄×D₈	1	1	yes	characteristic
175	C₂²×C₄₃	C₄×SD₁₆	1	2	yes	—
176	C₂²×C₄₃	C₄×SD₁₆	1	2	yes	—
177	C₂²×C₄₃	C₄×Q₁₆	1	1	yes	characteristic
178	C₂²×C₄₃	C₄×Q₁₆	1	1	yes	characteristic
179	C₂²×C₄₃	#465	1	2	yes	—
180	C₂²×C₄₃	#465	1	2	yes	—
181	C₂²×C₄₃	#466	1	2	yes	—
182	C₂²×C₄₃	#467	1	2	yes	—
183	C₂²×C₄₃	#486	1	2	yes	—
184	C₂²×C₄₃	#487	1	2	yes	—
185	C₂²×C₄₃	#488	1	2	yes	—
186	C₂²×C₄₃	#488	1	2	yes	—
187	C₄×C₄₃	—	8	4	no	—
188	C₄×C₄₃	#376	1	1	yes	characteristic
189	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
190	C₄×C₄₃	#381	1	1	yes	characteristic
191	C₄×C₄₃	#383	1	1	yes	characteristic
192	C₄×C₄₃	#387	1	2	yes	—
193	C₄×C₄₃	#387	1	2	yes	—
194	Dic₄₃	—	2	4	no	—
195	Dic₄₃	—	2	4	no	—
196	Dic₄₃	—	8	4	no	—
197	C₂²×C₄×C₈	—	43	1	no	—
198	C₂×#340	—	43	1	no	—
199	C₂×#340	—	43	2	no	—
200	C₂×#340	D₄₃	1	1	yes	characteristic
201	C₄⋊#95	—	43	2	no	—
202	C₂×C₄₃	#1434	1	1	yes	characteristic
203	C₂×C₄₃	C₄×#106	1	1	yes	characteristic
204	C₂×C₄₃	C₄×#107	1	1	yes	characteristic
205	C₂×C₄₃	#1807	1	1	yes	characteristic
206	C₂×C₄₃	#1808	1	1	yes	characteristic
207	C₂×C₄₃	#1834	1	1	yes	characteristic
208	C₂×C₄₃	#1835	1	1	yes	characteristic
209	C₂×C₄₃	#1933	1	2	yes	—
210	C₂×C₄₃	#1933	1	2	yes	—
211	C₂×C₄₃	#1934	1	2	yes	—
212	C₂×C₄₃	#1934	1	2	yes	—
213	C₂³×C₈	—	43	1	no	—
214	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
215	C₂²×C₄⋊C₄	—	43	2	no	—
216	C₂²×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
217	C₂²×C₄²	—	43	1	no	—
218	C₂×C₄×C₈	—	43	4	no	—
219	C₂×C₄×C₈	—	86	4	no	—
220	C₂×#95	—	86	2	no	—
221	C₂×#95	—	86	2	no	—
222	#340	—	43	4	no	—
223	#340	—	86	4	no	—
224	#340	Dic₄₃	1	4	yes	complemented
225	C₄₃	#10820	1	1	yes	characteristic, complemented, Sylow
226	C₂³×C₄	—	2	2	no	—
227	C₂³×C₄	—	43	1	no	—
228	C₂³×C₄	—	43	1	no	—
229	C₂³×C₄	—	86	2	no	—
230	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	—	43	2	no	—
234	C₂²×C₈	—	43	4	no	—
235	C₂²×C₈	—	86	2	no	—
236	C₂²×C₈	—	86	1	no	—
237	C₂²×C₈	—	86	1	no	—
238	C₂²×C₈	C₄×D₄₃	1	2	yes	—
239	C₂²×C₈	C₄×D₄₃	1	2	yes	—
240	C₂²×C₈	C₂×Dic₄₃	1	2	yes	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	43	4	no	—
247	C₂×C₄⋊C₄	—	86	2	no	—
248	C₂×C₄⋊C₄	—	86	2	no	—
249	C₂×C₄⋊C₄	—	86	2	no	—
250	C₂×C₄⋊C₄	—	86	2	no	—
251	C₂×C₄⋊C₄	—	86	2	no	—
252	C₂×C₄⋊C₄	C₂×Dic₄₃	1	4	yes	—
253	C₂×C₄²	—	43	2	no	—
254	C₂×C₄²	—	43	2	no	—
255	C₂×C₄²	—	86	2	no	—
256	C₂×C₄²	—	86	2	no	—
257	C₄×C₈	—	86	8	no	—
258	#95	—	172	4	no	—
259	#95	—	172	4	no	—
260	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	43	2	no	—
269	C₂²×C₄	—	43	2	no	—
270	C₂²×C₄	—	43	2	no	—
271	C₂²×C₄	—	43	4	no	—
272	C₂²×C₄	—	43	2	no	—
273	C₂²×C₄	—	86	2	no	—
274	C₂²×C₄	—	86	2	no	—
275	C₂²×C₄	—	86	1	no	—
276	C₂²×C₄	—	86	2	no	—
277	C₂²×C₄	—	86	1	no	—
278	C₂²×C₄	—	86	4	no	—
279	C₂²×C₄	—	172	2	no	—
280	C₂²×C₄	—	172	2	no	—
281	C₂²×C₄	—	172	2	no	—
282	C₂²×C₄	—	172	2	no	—
283	C₂²×C₄	—	172	2	no	—
284	C₂²×C₄	—	172	2	no	—
285	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
287	C₂²×C₄	#10621898	1	2	yes	—
288	C₂²×C₄	#10621898	1	2	yes	—
289	C₂²×C₄	D₄×D₄₃	1	2	yes	—
290	C₂²×C₄	#10621900	1	2	yes	—
291	C₂²×C₄	#10621900	1	1	yes	characteristic
292	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
293	C₂²×C₄	#10621902	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	43	4	no	—
300	C₂×C₈	—	86	2	no	—
301	C₂×C₈	—	86	2	no	—
302	C₂×C₈	—	86	4	no	—
303	C₂×C₈	—	86	4	no	—
304	C₂×C₈	C₄×Dic₄₃	1	4	yes	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	86	4	no	—
310	C₄⋊C₄	—	86	4	no	—
311	C₄⋊C₄	—	172	2	no	—
312	C₄⋊C₄	—	172	2	no	—
313	C₄²	—	86	2	no	—
314	C₄²	—	86	2	no	—
315	C₄²	—	86	4	no	—
316	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
317	C₂³	#13063287	1	1	yes	characteristic
318	C₂³	D₄×Dic₄₃	1	1	yes	characteristic
319	C₂³	#13063298	1	2	yes	—
320	C₂³	#13063311	1	2	yes	—
321	C₂³	D₈×D₄₃	1	1	yes	characteristic
322	C₂³	SD₁₆×D₄₃	1	2	yes	—
323	C₂³	Q₁₆×D₄₃	1	1	yes	characteristic
324	C₂³	#13063344	1	1	yes	characteristic
325	C₂³	#13063346	1	2	yes	—
326	C₂³	#13063348	1	1	yes	characteristic
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	—	8	2	no	—
332	C₂×C₄	—	8	2	no	—
333	C₂×C₄	—	8	2	no	—
334	C₂×C₄	—	43	4	no	—
335	C₂×C₄	—	43	4	no	—
336	C₂×C₄	—	86	4	no	—
337	C₂×C₄	—	86	4	no	—
338	C₂×C₄	—	86	4	no	—
339	C₂×C₄	—	86	4	no	—
340	C₂×C₄	—	86	2	no	—
341	C₂×C₄	—	86	2	no	—
342	C₂×C₄	—	86	2	no	—
343	C₂×C₄	—	86	2	no	—
344	C₂×C₄	—	344	2	no	—
345	C₂×C₄	—	344	2	no	—
346	C₂×C₄	—	344	2	no	—
347	C₂×C₄	—	344	2	no	—
348	C₂×C₄	—	172	4	no	—
349	C₂×C₄	—	172	4	no	—
350	C₂×C₄	—	172	4	no	—
351	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
352	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
353	C₂×C₄	#13063281	1	1	yes	characteristic
354	C₂×C₄	#13063282	1	1	yes	characteristic
355	C₂×C₄	#13063282	1	1	yes	characteristic
356	C₂×C₄	#13063282	1	2	yes	—
357	C₂×C₄	#13063283	1	1	yes	characteristic
358	C₂×C₄	#13063284	1	2	yes	—
359	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
360	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
361	C₂×C₄	#13063290	1	1	yes	characteristic
362	C₂×C₄	Q₈×Dic₄₃	1	1	yes	characteristic
363	C₂×C₄	#13063303	1	2	yes	—
364	C₂×C₄	#13063307	1	2	yes	—
365	C₂×C₄	#13063310	1	2	yes	—
366	C₂×C₄	#13063315	1	2	yes	—
367	C₂×C₄	#13063318	1	2	yes	—
368	C₂×C₄	#13063320	1	2	yes	—
369	C₈	—	2	4	no	—
370	C₈	—	86	4	no	—
371	C₂²	C₄⋊C₄×Dic₄₃	1	1	yes	characteristic
372	C₂²	#14582758	1	1	yes	characteristic
373	C₂²	#14582763	1	1	yes	characteristic
374	C₂²	#14582788	1	2	yes	—
375	C₂²	#14582792	1	2	yes	—
376	C₂²	#106×D₄₃	1	1	yes	characteristic
377	C₂²	#107×D₄₃	1	1	yes	characteristic
378	C₂²	#14582934	1	1	yes	characteristic
379	C₂²	#14582936	1	1	yes	characteristic
380	C₂²	#14582981	1	1	yes	characteristic
381	C₂²	D₈×Dic₄₃	1	1	yes	characteristic
382	C₂²	#14582986	1	2	yes	—
383	C₂²	SD₁₆×Dic₄₃	1	2	yes	—
384	C₂²	#14582993	1	1	yes	characteristic
385	C₂²	Q₁₆×Dic₄₃	1	1	yes	characteristic
386	C₂²	#14583127	1	2	yes	—
387	C₂²	#14583131	1	2	yes	—
388	C₂²	#14583134	1	2	yes	—
389	C₂²	#14583139	1	2	yes	—
390	C₂²	#14583244	1	2	yes	—
391	C₂²	#14583248	1	2	yes	—
392	C₂²	#14583252	1	2	yes	—
393	C₂²	#14583255	1	2	yes	—
394	C₄	—	8	4	no	—
395	C₄	—	86	4	no	—
396	C₄	—	86	4	no	—
397	C₄	—	344	4	no	—
398	C₄	#14582745	1	1	yes	characteristic
399	C₄	C₂²⋊C₄×Dic₄₃	1	1	yes	characteristic
400	C₄	#14582761	1	1	yes	characteristic
401	C₄	#14582766	1	1	yes	characteristic
402	C₄	#14582781	1	2	yes	—
403	C₄	#14582785	1	2	yes	—
404	C₂	#19132820	1	1	yes	characteristic
405	C₂	#106×Dic₄₃	1	1	yes	characteristic
406	C₂	#107×Dic₄₃	1	1	yes	characteristic
407	C₂	#19134619	1	1	yes	characteristic
408	C₂	#19134623	1	1	yes	characteristic
409	C₂	#19134721	1	1	yes	characteristic
410	C₂	#19134724	1	1	yes	characteristic
411	C₂	#19135269	1	2	yes	—
412	C₂	#19135273	1	2	yes	—
413	C₂	#19135276	1	2	yes	—
414	C₂	#19135280	1	2	yes	—

	subgroup	G/H
center	C₂⁴	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#340	C₂
socle, prime radical	C₂⁴×C₄₃	C₂×D₄
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#340	D₄₃
hypocenter	C₄₃	#10820
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
10. C₂×C₈×Dic₄₃	C₄	semidirect
13. #14582662	C₄	semidirect
17. C₄₃×#340	C₄	semidirect
224. #340	Dic₄₃	semidirect
225. C₄₃	#10820	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×Dic₄₃	2
C₂×#14582662	2
C₂×#14582661	2
#19132824	2
C₂×C₄₃×#340	2
#10820	43