Subgroups — #442×Dic₄₃ #25095081

Order 11008.

1326 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583011	C₂	1	1	yes	maximal, characteristic
2	C₂×D₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄×D₄×Dic₄₃	C₂	1	2	yes	maximal, complemented
4	#19134495	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134492	C₂	1	1	yes	maximal, characteristic, complemented
6	#106×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134422	C₂	1	2	yes	maximal, complemented
8	#19134420	C₂	1	2	yes	maximal, complemented
9	#102×Dic₄₃	C₂	1	2	yes	maximal, complemented
10	#97×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#442	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×Dic₄₃	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₃	C₂²	1	2	yes	—
14	C₂²×C₄×Dic₄₃	—	2	2	no	—
15	#14583011	C₄	1	8	yes	complemented
16	D₈×Dic₄₃	C₄	1	8	yes	complemented
17	C₂×#13063259	C₂²	1	1	yes	characteristic
18	C₂×#13063257	C₂²	1	1	yes	characteristic
19	C₂×#13063246	C₂²	1	2	yes	—
20	C₂×#13063246	C₂²	1	2	yes	—
21	C₂×#13063236	C₂²	1	1	yes	characteristic
22	C₂×#13063235	C₂²	1	1	yes	characteristic
23	C₂×#13063235	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
26	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
27	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
28	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
29	C₂²⋊C₄×Dic₄₃	—	2	2	no	—
30	C₂²⋊C₄×Dic₄₃	—	2	2	no	—
31	C₄×C₂²⋊Dic₄₃	—	2	2	no	—
32	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
33	#14582662	C₂²	1	2	yes	—
34	#14582661	C₂²	1	2	yes	—
35	#14582661	C₂²	1	2	yes	—
36	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
38	C₄₃×#442	C₄	1	8	yes	complemented
39	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×#102×C₄₃	C₂²	1	2	yes	—
41	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
42	C₂³×Dic₄₃	—	2	2	no	—
43	C₂³×Dic₄₃	—	2	2	no	—
44	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
46	D₄×Dic₄₃	—	2	4	no	—
47	D₄×Dic₄₃	—	2	4	no	—
48	D₄×Dic₄₃	C₂×C₄	1	8	yes	complemented
49	D₄×Dic₄₃	C₂×C₄	1	8	yes	complemented
50	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
52	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
53	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
54	C₂×C₄×Dic₄₃	—	2	2	no	—
55	C₂×C₄×Dic₄₃	—	2	2	no	—
56	C₂×C₄×Dic₄₃	—	2	2	no	—
57	C₂×C₄×Dic₄₃	—	4	8	no	—
58	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
59	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
60	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
62	#13063259	C₂×C₄	1	4	yes	complemented
63	#13063257	C₂×C₄	1	4	yes	complemented
64	#13063246	C₂×C₄	1	8	yes	complemented
65	#13063246	C₂×C₄	1	8	yes	complemented
66	#13063236	—	2	2	no	—
67	#13063235	—	2	2	no	—
68	#13063235	C₂×C₄	1	4	yes	complemented
69	C₈×Dic₄₃	—	2	2	no	—
70	C₈×Dic₄₃	C₂×C₄	1	4	yes	complemented
71	C₄₃⋊#95	—	2	2	no	—
72	C₄₃⋊#95	—	2	2	no	—
73	C₄₃⋊#95	—	2	2	no	—
74	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₄₃	—	2	2	no	—
76	C₂×D₈×C₄₃	C₂×C₄	1	4	yes	—
77	C₂×D₈×C₄₃	C₂×C₄	1	4	yes	—
78	C₂×D₈×C₄₃	C₂×C₄	1	4	yes	—
79	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
81	C₄×D₄×C₄₃	—	2	4	no	—
82	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	complemented
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
86	#106×C₄₃	C₂×C₄	1	4	yes	complemented
87	#102×C₄₃	C₂×C₄	1	8	yes	complemented
88	#97×C₄₃	C₂×C₄	1	4	yes	complemented
89	C₂⁴×C₄₃	—	2	2	no	—
90	C₂×D₄×C₄₃	—	2	2	no	—
91	C₂×D₄×C₄₃	—	2	2	no	—
92	C₂×D₄×C₄₃	—	2	2	no	—
93	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
94	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
95	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₃	—	2	8	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	4	4	no	—
99	C₂²×C₄×C₄₃	—	4	4	no	—
100	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₄₃	—	2	8	no	—
103	C₂²×Dic₄₃	—	2	8	no	—
104	C₂²×Dic₄₃	—	2	2	no	—
105	C₂²×Dic₄₃	—	2	2	no	—
106	C₂²×Dic₄₃	—	4	4	no	—
107	C₂²×Dic₄₃	—	4	4	no	—
108	C₂²×Dic₄₃	—	4	4	no	—
109	C₂²×Dic₄₃	—	4	4	no	—
110	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
112	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
113	D₈×C₄₃	C₄²	1	16	yes	complemented
114	C₂×C₈×C₄₃	—	2	1	no	—
115	C₂×C₈×C₄₃	—	2	1	no	—
116	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
120	C₄⋊C₄×C₄₃	—	2	2	no	—
121	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
122	C₂²⋊C₄×C₄₃	—	2	8	no	—
123	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
124	C₄²×C₄₃	#41	1	2	yes	—
125	C₂²⋊Dic₄₃	—	2	8	no	—
126	C₂²⋊Dic₄₃	—	2	8	no	—
127	C₄⋊Dic₄₃	—	2	2	no	—
128	C₄⋊Dic₄₃	—	2	2	no	—
129	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
130	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
131	C₄×Dic₄₃	—	2	4	no	—
132	C₄×Dic₄₃	—	4	2	no	—
133	C₄×Dic₄₃	—	4	4	no	—
134	C₄×Dic₄₃	—	4	4	no	—
135	C₄×Dic₄₃	—	4	4	no	—
136	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
137	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
138	C₄×Dic₄₃	#41	1	2	yes	—
139	C₄×Dic₄₃	#41	1	2	yes	—
140	C₂×C₄₃⋊C₈	—	2	1	no	—
141	C₂×C₄₃⋊C₈	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	2	1	no	—
143	C₂×C₄₃⋊C₈	—	2	1	no	—
144	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
146	C₂³×C₄₃	—	2	4	no	—
147	C₂³×C₄₃	—	2	4	no	—
148	C₂³×C₄₃	—	2	4	no	—
149	C₂³×C₄₃	—	4	2	no	—
150	C₂³×C₄₃	—	4	2	no	—
151	C₂³×C₄₃	—	4	2	no	—
152	C₂³×C₄₃	—	4	2	no	—
153	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
154	D₄×C₄₃	—	2	4	no	—
155	D₄×C₄₃	—	2	4	no	—
156	D₄×C₄₃	—	2	4	no	—
157	D₄×C₄₃	C₂×C₄²	1	8	yes	complemented
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	4	no	—
161	C₂×C₄×C₄₃	—	4	16	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
165	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
171	C₂×Dic₄₃	—	2	2	no	—
172	C₂×Dic₄₃	—	2	2	no	—
173	C₂×Dic₄₃	—	2	2	no	—
174	C₂×Dic₄₃	—	2	4	no	—
175	C₂×Dic₄₃	—	2	4	no	—
176	C₂×Dic₄₃	—	4	16	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	C₂×Dic₄₃	—	4	16	no	—
182	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
183	C₂×Dic₄₃	C₄×D₄	1	4	yes	—
184	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
185	C₂×Dic₄₃	AGL(1,ℤ/8)	1	4	yes	—
186	C₈×C₄₃	—	2	2	no	—
187	C₈×C₄₃	C₂×C₄²	1	4	yes	complemented
188	C₄₃⋊C₈	—	2	2	no	—
189	C₄₃⋊C₈	—	2	2	no	—
190	C₄×#442	—	43	1	no	maximal, Sylow
191	C₂²×C₄₃	—	2	8	no	—
192	C₂²×C₄₃	—	4	4	no	—
193	C₂²×C₄₃	—	4	4	no	—
194	C₂²×C₄₃	—	4	4	no	—
195	C₂²×C₄₃	—	4	4	no	—
196	C₂²×C₄₃	—	4	4	no	—
197	C₂²×C₄₃	—	4	4	no	—
198	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
200	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
202	C₂²×C₄₃	#575	1	2	yes	—
203	C₄×C₄₃	—	2	4	no	—
204	C₄×C₄₃	—	4	4	no	—
205	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
206	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
207	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
208	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
209	Dic₄₃	—	2	2	no	—
210	Dic₄₃	—	2	4	no	—
211	Dic₄₃	—	4	4	no	—
212	Dic₄₃	—	4	4	no	—
213	Dic₄₃	#442	1	4	yes	direct product factor
214	C₂×#442	—	43	1	no	—
215	C₂×#442	D₄₃	1	1	yes	characteristic
216	C₂×C₄×D₈	—	43	1	no	—
217	C₄²×D₄	—	43	2	no	—
218	#1776	—	43	1	no	—
219	#1776	—	43	1	no	—
220	C₄×#106	—	43	1	no	—
221	#1762	—	43	2	no	—
222	#1762	—	43	2	no	—
223	C₄×#102	—	43	2	no	—
224	C₄×#97	—	43	1	no	—
225	C₂×C₄₃	—	4	8	no	—
226	C₂×C₄₃	C₄²×D₄	1	1	yes	characteristic
227	C₂×C₄₃	C₂×#442	1	1	yes	characteristic
228	C₂×C₄₃	#2943	1	1	yes	characteristic
229	C₂×C₄₃	C₄×AGL(1,ℤ/8)	1	2	yes	—
230	C₂×C₄₃	C₄×AGL(1,ℤ/8)	1	2	yes	—
231	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
232	C₂×C₄×D₄	—	43	2	no	—
233	C₂×C₄×D₄	—	43	2	no	—
234	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
235	C₂²×C₄²	—	86	2	no	—
236	#442	—	43	8	no	—
237	#442	Dic₄₃	1	8	yes	direct product factor
238	C₄×D₈	—	43	8	no	—
239	C₂×#107	—	43	1	no	—
240	C₂×#106	—	43	1	no	—
241	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
242	C₂×#102	—	43	2	no	—
243	C₂×#102	—	43	2	no	—
244	C₂×#102	C₂×D₄₃	1	2	yes	—
245	C₂×#97	—	43	1	no	—
246	C₂×#97	—	43	1	no	—
247	C₂×#97	—	43	1	no	—
248	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
249	C₂×C₄×C₈	—	43	1	no	—
250	C₂×C₄×C₈	—	43	1	no	—
251	C₄×C₄⋊C₄	—	43	2	no	—
252	C₄×C₄⋊C₄	—	43	2	no	—
253	C₄×C₄⋊C₄	—	43	2	no	—
254	C₄×C₂²⋊C₄	—	86	2	no	—
255	C₄×C₂²⋊C₄	—	86	2	no	—
256	C₄×C₂²⋊C₄	—	86	2	no	—
257	C₄³	—	43	1	no	—
258	#340	—	43	2	no	—
259	#340	—	43	2	no	—
260	#340	—	43	2	no	—
261	C₄₃	C₄×#442	1	1	yes	characteristic, complemented, Sylow
262	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
263	C₂³×C₄	—	2	2	no	—
264	C₂³×C₄	—	86	2	no	—
265	C₂³×C₄	—	86	2	no	—
266	C₂×D₈	C₄×D₄₃	1	4	yes	—
267	C₂×D₈	C₄×D₄₃	1	4	yes	—
268	C₂×D₈	C₂×Dic₄₃	1	4	yes	—
269	C₂²×C₈	—	43	1	no	—
270	C₂²×C₈	—	43	1	no	—
271	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
272	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	43	8	no	—
275	C₄×D₄	—	43	8	no	—
276	C₄×D₄	—	86	4	no	—
277	C₄×D₄	—	86	4	no	—
278	C₄×D₄	C₂×Dic₄₃	1	8	yes	complemented
279	C₂×C₄⋊C₄	—	43	2	no	—
280	C₂×C₄⋊C₄	—	43	2	no	—
281	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	86	2	no	—
284	C₂×C₂²⋊C₄	—	86	2	no	—
285	C₂×C₄²	—	43	1	no	—
286	C₂×C₄²	—	43	1	no	—
287	C₂×C₄²	—	43	2	no	—
288	C₂×C₄²	—	43	2	no	—
289	C₂×C₄²	—	86	2	no	—
290	C₂×C₄²	—	86	2	no	—
291	C₂×C₄²	—	86	2	no	—
292	C₂×C₄²	—	172	8	no	—
293	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
294	#107	—	43	4	no	—
295	#106	—	43	4	no	—
296	#106	C₂×Dic₄₃	1	4	yes	complemented
297	#102	—	43	8	no	—
298	#102	—	43	8	no	—
299	#102	C₂×Dic₄₃	1	8	yes	complemented
300	#97	—	43	4	no	—
301	#97	—	86	2	no	—
302	#97	—	86	2	no	—
303	#97	C₂×Dic₄₃	1	4	yes	complemented
304	C₄×C₈	—	43	4	no	—
305	C₄×C₈	—	86	2	no	—
306	#95	—	86	2	no	—
307	#95	—	86	2	no	—
308	#95	—	86	2	no	—
309	C₂⁴	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	C₂×C₄×D₄₃	1	4	yes	—
314	C₂×D₄	C₂×C₄×D₄₃	1	4	yes	—
315	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	43	1	no	—
321	C₂²×C₄	—	43	1	no	—
322	C₂²×C₄	—	43	2	no	—
323	C₂²×C₄	—	86	8	no	—
324	C₂²×C₄	—	86	8	no	—
325	C₂²×C₄	—	86	2	no	—
326	C₂²×C₄	—	86	2	no	—
327	C₂²×C₄	—	172	4	no	—
328	C₂²×C₄	—	172	4	no	—
329	C₂²×C₄	—	172	4	no	—
330	C₂²×C₄	—	172	4	no	—
331	C₂²×C₄	D₄×D₄₃	1	2	yes	—
332	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
333	D₈	C₄×Dic₄₃	1	16	yes	complemented
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	43	2	no	—
337	C₂×C₈	—	43	2	no	—
338	C₂×C₈	—	86	1	no	—
339	C₂×C₈	—	86	1	no	—
340	C₂×C₈	—	86	1	no	—
341	C₂×C₈	—	86	1	no	—
342	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
343	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
344	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
345	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	43	4	no	—
348	C₄⋊C₄	—	43	4	no	—
349	C₄⋊C₄	—	86	2	no	—
350	C₄⋊C₄	—	86	2	no	—
351	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
352	C₂²⋊C₄	—	2	8	no	—
353	C₂²⋊C₄	—	86	8	no	—
354	C₂²⋊C₄	—	86	8	no	—
355	C₄²	—	43	2	no	—
356	C₄²	—	43	2	no	—
357	C₄²	—	43	2	no	—
358	C₄²	—	43	2	no	—
359	C₄²	—	86	4	no	—
360	C₄²	—	172	2	no	—
361	C₄²	—	172	4	no	—
362	C₄²	—	172	4	no	—
363	C₄²	—	172	4	no	—
364	C₄²	#10621900	1	2	yes	—
365	C₄²	C₂²×Dic₄₃	1	2	yes	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	4	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
374	D₄	—	2	4	no	—
375	D₄	—	2	4	no	—
376	D₄	—	2	4	no	—
377	D₄	C₂×C₄×Dic₄₃	1	8	yes	complemented
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	16	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	43	2	no	—
385	C₂×C₄	—	43	4	no	—
386	C₂×C₄	—	43	2	no	—
387	C₂×C₄	—	43	4	no	—
388	C₂×C₄	—	86	2	no	—
389	C₂×C₄	—	86	2	no	—
390	C₂×C₄	—	86	2	no	—
391	C₂×C₄	—	86	4	no	—
392	C₂×C₄	—	86	4	no	—
393	C₂×C₄	—	172	16	no	—
394	C₂×C₄	—	172	16	no	—
395	C₂×C₄	—	172	2	no	—
396	C₂×C₄	—	172	2	no	—
397	C₂×C₄	—	172	2	no	—
398	C₂×C₄	—	172	2	no	—
399	C₂×C₄	D₄×Dic₄₃	1	4	yes	—
400	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
402	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
403	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
404	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
405	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	86	2	no	—
408	C₈	—	86	2	no	—
409	C₈	C₂×C₄×Dic₄₃	1	4	yes	complemented
410	C₂²	—	2	8	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	4	no	—
417	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
418	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
419	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
420	C₂²	AGL(1,ℤ/8)×D₄₃	1	2	yes	—
421	C₂²	#14583695	1	2	yes	—
422	C₄	—	2	4	no	—
423	C₄	—	4	4	no	—
424	C₄	—	43	4	no	—
425	C₄	—	86	2	no	—
426	C₄	—	86	4	no	—
427	C₄	—	172	4	no	—
428	C₄	—	172	4	no	—
429	C₄	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
430	C₄	C₄×#10621900	1	1	yes	characteristic
431	C₄	C₄×#10621900	1	1	yes	characteristic
432	C₄	#41×Dic₄₃	1	1	yes	characteristic
433	C₂	—	4	8	no	—
434	C₂	C₄×D₄×Dic₄₃	1	1	yes	characteristic
435	C₂	#442×D₄₃	1	1	yes	characteristic
436	C₂	#19143392	1	1	yes	characteristic
437	C₂	AGL(1,ℤ/8)×Dic₄₃	1	2	yes	—
438	C₂	#19143406	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#442	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₈×C₄₃	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#442	D₄₃
hypocenter	C₄₃	C₄×#442
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#442

Complements

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

N	H ≅ G/N	type
3. C₄×D₄×Dic₄₃	C₂	semidirect
4. #19134495	C₂	semidirect
5. #19134492	C₂	semidirect
6. #106×Dic₄₃	C₂	semidirect
7. #19134422	C₂	semidirect
8. #19134420	C₂	semidirect
9. #102×Dic₄₃	C₂	semidirect
10. #97×Dic₄₃	C₂	semidirect
15. #14583011	C₄	semidirect
16. D₈×Dic₄₃	C₄	semidirect
38. C₄₃×#442	C₄	semidirect
48. D₄×Dic₄₃	C₂×C₄	semidirect
49. D₄×Dic₄₃	C₂×C₄	semidirect
62. #13063259	C₂×C₄	semidirect
63. #13063257	C₂×C₄	semidirect
64. #13063246	C₂×C₄	semidirect
65. #13063246	C₂×C₄	semidirect
68. #13063235	C₂×C₄	semidirect
70. C₈×Dic₄₃	C₂×C₄	semidirect
82. C₄×D₄×C₄₃	C₂×C₄	semidirect
86. #106×C₄₃	C₂×C₄	semidirect
87. #102×C₄₃	C₂×C₄	semidirect
88. #97×C₄₃	C₂×C₄	semidirect
113. D₈×C₄₃	C₄²	semidirect
157. D₄×C₄₃	C₂×C₄²	semidirect
187. C₈×C₄₃	C₂×C₄²	semidirect
213. Dic₄₃	#442	direct (N × H)
237. #442	Dic₄₃	direct (N × H)
261. C₄₃	C₄×#442	semidirect
278. C₄×D₄	C₂×Dic₄₃	semidirect
296. #106	C₂×Dic₄₃	semidirect
299. #102	C₂×Dic₄₃	semidirect
303. #97	C₂×Dic₄₃	semidirect
333. D₈	C₄×Dic₄₃	semidirect
377. D₄	C₂×C₄×Dic₄₃	semidirect
409. C₈	C₂×C₄×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583011	2
C₂×D₈×Dic₄₃	2
C₄×D₄×Dic₄₃	2
#19134495	2
#19134492	2
#106×Dic₄₃	2
#19134422	2
#19134420	2
#102×Dic₄₃	2
#97×Dic₄₃	2
C₂×C₄₃×#442	2
C₄×#442	43

Subgroups — #442×Dic43 #25095081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #442×Dic₄₃ #25095081