Subgroups — #19143293

Order 5504.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063331	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583408	C₂	1	1	yes	maximal, characteristic
4	#14582977	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582976	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582974	C₂	1	1	yes	maximal, characteristic, complemented
7	#14582974	C₂	1	1	yes	maximal, characteristic, complemented
8	#14582972	C₂	1	1	yes	maximal, characteristic, complemented
9	#14582970	C₂	1	1	yes	maximal, characteristic, complemented
10	#14582968	C₂	1	1	yes	maximal, characteristic, complemented
11	#14582924	C₂	1	1	yes	maximal, characteristic, complemented
12	#14582864	C₂	1	1	yes	maximal, characteristic, complemented
13	#14582861	C₂	1	1	yes	maximal, characteristic, complemented
14	#14582856	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10621898	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
18	#13063331	—	2	4	no	—
19	C₂×#10621877	C₂²	1	1	yes	characteristic
20	C₂×#10621877	C₂²	1	1	yes	characteristic, complemented
21	C₂×#10621872	C₂²	1	1	yes	characteristic
22	C₂×#10621872	C₂²	1	1	yes	characteristic
23	C₂×#10621872	C₂²	1	1	yes	characteristic
24	C₂×#10621872	C₂²	1	1	yes	characteristic
25	C₂×#10621872	C₂²	1	1	yes	characteristic, complemented
26	M₁₆×D₄₃	—	2	4	no	—
27	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
30	#13063310	C₄	1	1	yes	characteristic
31	#13063307	C₄	1	1	yes	characteristic
32	#13063303	C₄	1	1	yes	characteristic
33	#13063302	C₄	1	1	yes	characteristic
34	#13063298	C₄	1	1	yes	characteristic
35	#13063297	C₄	1	1	yes	characteristic
36	#13063295	C₄	1	1	yes	characteristic
37	#13063293	C₄	1	1	yes	characteristic
38	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
41	#13063282	C₂²	1	1	yes	characteristic
42	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
43	Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
46	C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
47	(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
48	(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
49	(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	#13063235	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
55	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
60	#97×C₄₃	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₄₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊D₄₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₄₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₄₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
70	#10621898	—	2	2	no	—
71	#10621898	—	2	2	no	—
72	C₂×D₁₇₂	C₂×C₄	1	1	yes	characteristic
73	C₂×D₁₇₂	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₄₃	—	2	2	no	—
75	C₂×C₄×D₄₃	—	2	2	no	—
76	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
81	C₂×Dic₈₆	C₂×C₄	1	1	yes	characteristic
82	M₁₆×C₄₃	—	2	2	no	—
83	C₂×C₈×C₄₃	—	2	2	no	—
84	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
91	C₄²×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
99	(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
101	Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
102	Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
103	Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
104	Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
106	#10621877	—	2	2	no	—
107	#10621877	—	2	2	no	—
108	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
109	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
112	#10621872	—	2	2	no	—
113	#10621872	—	2	2	no	—
114	#10621872	—	2	2	no	—
115	#10621872	—	2	2	no	—
116	#10621872	—	2	2	no	—
117	C₈×D₄₃	—	2	2	no	—
118	C₈×D₄₃	—	2	2	no	—
119	C₈×D₄₃	D₄	1	4	yes	complemented
120	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×D₄₃	—	2	2	no	—
123	C₂²×D₄₃	—	4	1	no	—
124	C₂²×D₄₃	—	4	1	no	—
125	C₂²×D₄₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×D₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×D₄₃	C₂²×C₄	1	1	yes	characteristic
128	D₄×C₄₃	—	4	1	no	—
129	C₂×C₄×C₄₃	—	2	1	no	—
130	C₂×C₄×C₄₃	—	2	1	no	—
131	C₂×C₄×C₄₃	—	2	1	no	—
132	C₂×C₄×C₄₃	—	2	1	no	—
133	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
138	C₂²⋊D₄₃	—	2	2	no	—
139	C₂²⋊D₄₃	—	2	2	no	—
140	C₂²⋊D₄₃	—	4	1	no	—
141	C₂²⋊D₄₃	—	4	1	no	—
142	C₂×Dic₄₃	—	2	2	no	—
143	C₂×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
148	D₁₇₂	—	2	2	no	—
149	D₁₇₂	—	4	1	no	—
150	C₄×D₄₃	—	2	2	no	—
151	C₄×D₄₃	—	2	1	no	—
152	C₄×D₄₃	—	2	1	no	—
153	C₄×D₄₃	—	2	1	no	—
154	C₄×D₄₃	—	2	1	no	—
155	C₄×D₄₃	—	2	2	no	—
156	C₄×D₄₃	C₂×D₄	1	2	yes	—
157	C₄×D₄₃	#41	1	2	yes	—
158	Dic₈₆	—	2	2	no	—
159	C₈×C₄₃	—	2	1	no	—
160	C₈×C₄₃	—	2	1	no	—
161	C₈×C₄₃	—	2	1	no	—
162	C₈×C₄₃	C₂×D₄	1	2	yes	—
163	C₄₃⋊C₈	—	2	1	no	—
164	C₄₃⋊C₈	—	2	1	no	—
165	C₄₃⋊C₈	—	2	1	no	—
166	C₄₃⋊C₈	C₂×D₄	1	2	yes	—
167	C₂²×C₄₃	—	2	1	no	—
168	C₂²×C₄₃	—	2	1	no	—
169	C₂²×C₄₃	—	2	1	no	—
170	C₂²×C₄₃	—	2	1	no	—
171	C₂²×C₄₃	—	2	1	no	—
172	C₂²×C₄₃	—	2	1	no	—
173	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×D₄₃	—	2	1	no	—
175	C₂×D₄₃	—	2	1	no	—
176	C₂×D₄₃	—	2	1	no	—
177	C₂×D₄₃	—	2	1	no	—
178	C₂×D₄₃	—	2	1	no	—
179	C₂×D₄₃	—	2	1	no	—
180	C₂×D₄₃	—	2	1	no	—
181	C₂×D₄₃	—	2	1	no	—
182	C₂×D₄₃	—	4	4	no	—
183	C₂×D₄₃	C₄×D₄	1	2	yes	—
184	C₄×C₄₃	—	2	1	no	—
185	C₄×C₄₃	—	2	1	no	—
186	C₄×C₄₃	—	2	1	no	—
187	C₄×C₄₃	—	2	1	no	—
188	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
190	Dic₄₃	—	2	1	no	—
191	Dic₄₃	—	2	1	no	—
192	Dic₄₃	—	2	1	no	—
193	Dic₄₃	—	2	1	no	—
194	Dic₄₃	C₄×D₄	1	2	yes	—
195	#2930	—	43	1	no	maximal, Sylow
196	C₂×C₄₃	—	4	1	no	—
197	C₂×C₄₃	—	4	1	no	—
198	C₂×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂×C₄₃	#568	1	1	yes	characteristic
200	C₂×C₄₃	#568	1	1	yes	characteristic
201	D₄₃	—	2	2	no	—
202	D₄₃	—	4	1	no	—
203	D₄₃	—	4	1	no	—
204	C₂×#131	—	43	1	no	—
205	C₂²×M₁₆	—	43	1	no	—
206	#525	—	43	1	no	—
207	#436	—	43	1	no	—
208	#436	—	43	1	no	—
209	#436	—	43	1	no	—
210	#436	—	43	1	no	—
211	#435	—	43	1	no	—
212	#435	—	43	1	no	—
213	#435	—	43	1	no	—
214	#435	D₄₃	1	1	yes	characteristic, complemented
215	#424	—	43	1	no	—
216	#408	—	43	1	no	—
217	#407	—	43	1	no	—
218	#405	—	43	1	no	—
219	C₄₃	#2930	1	1	yes	characteristic, complemented, Sylow
220	C₂×#41	—	43	1	no	—
221	C₂³×C₄	—	43	1	no	—
222	#131	—	86	4	no	—
223	C₂×M₁₆	—	43	1	no	—
224	C₂×M₁₆	—	43	1	no	—
225	C₂×M₁₆	—	43	1	no	—
226	C₂×M₁₆	—	43	1	no	—
227	C₂×M₁₆	—	43	1	no	—
228	C₂×M₁₆	—	43	1	no	—
229	C₂×M₁₆	—	43	1	no	—
230	C₂×M₁₆	—	86	4	no	—
231	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
232	C₂²×C₈	—	43	1	no	—
233	C₂²×C₈	—	43	1	no	—
234	C₂²×C₈	—	43	1	no	—
235	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
236	#123	—	43	1	no	—
237	#123	—	43	1	no	—
238	C₂²⋊Q₈	—	43	1	no	—
239	C₂²⋊Q₈	—	43	1	no	—
240	#121	—	43	1	no	—
241	#121	—	43	1	no	—
242	#120	—	43	1	no	—
243	#120	—	43	1	no	—
244	C₄×D₄	—	43	1	no	—
245	C₄×D₄	—	43	1	no	—
246	C₄×D₄	—	43	1	no	—
247	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
248	#117	—	43	1	no	—
249	C₄⋊C₈	—	43	1	no	—
250	C₄⋊C₈	—	43	1	no	—
251	C₄⋊C₈	—	43	1	no	—
252	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
253	C₂²⋊C₈	—	43	1	no	—
254	C₂²⋊C₈	—	43	1	no	—
255	C₂²⋊C₈	—	43	1	no	—
256	C₂²⋊C₈	—	43	1	no	—
257	C₂²⋊C₈	—	43	1	no	—
258	C₂²⋊C₈	—	43	1	no	—
259	C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic
260	C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
261	#97	—	43	1	no	—
262	#97	C₂×D₄₃	1	1	yes	characteristic, complemented
263	C₄×C₈	—	43	1	no	—
264	C₄×C₈	—	43	1	no	—
265	C₂⁴	—	43	1	no	—
266	#41	—	86	2	no	—
267	#41	—	86	2	no	—
268	C₂×Q₈	—	43	1	no	—
269	C₂×D₄	—	43	1	no	—
270	C₂×D₄	—	43	1	no	—
271	C₂×D₄	—	43	1	no	—
272	C₂×D₄	—	43	1	no	—
273	C₂×D₄	—	43	1	no	—
274	C₂×D₄	—	43	1	no	—
275	C₂×D₄	C₄×D₄₃	1	1	yes	characteristic
276	C₂²×C₄	—	43	1	no	—
277	C₂²×C₄	—	43	1	no	—
278	C₂²×C₄	—	43	1	no	—
279	C₂²×C₄	—	43	1	no	—
280	C₂²×C₄	—	43	1	no	—
281	C₂²×C₄	—	43	1	no	—
282	C₂²×C₄	—	86	2	no	—
283	C₂²×C₄	—	86	2	no	—
284	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
286	M₁₆	—	2	2	no	—
287	M₁₆	—	86	2	no	—
288	M₁₆	—	86	2	no	—
289	M₁₆	—	86	2	no	—
290	M₁₆	—	86	2	no	—
291	M₁₆	—	86	2	no	—
292	M₁₆	—	86	2	no	—
293	M₁₆	—	86	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	43	1	no	—
296	C₂×C₈	—	43	4	no	—
297	C₂×C₈	—	43	1	no	—
298	C₂×C₈	—	43	1	no	—
299	C₂×C₈	—	43	1	no	—
300	C₂×C₈	—	86	2	no	—
301	C₂×C₈	—	86	2	no	—
302	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
304	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
306	C₄⋊C₄	—	43	1	no	—
307	C₄⋊C₄	—	43	1	no	—
308	C₄⋊C₄	—	43	1	no	—
309	C₄⋊C₄	—	43	1	no	—
310	C₄⋊C₄	—	43	1	no	—
311	C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
312	C₂²⋊C₄	—	43	1	no	—
313	C₂²⋊C₄	—	43	1	no	—
314	C₂²⋊C₄	—	43	1	no	—
315	C₂²⋊C₄	—	43	1	no	—
316	C₂²⋊C₄	—	43	1	no	—
317	C₂²⋊C₄	—	43	1	no	—
318	C₂²⋊C₄	—	43	1	no	—
319	C₂²⋊C₄	—	43	1	no	—
320	C₂²⋊C₄	C₄×D₄₃	1	1	yes	characteristic
321	C₂²⋊C₄	C₄×D₄₃	1	1	yes	characteristic
322	C₄²	—	43	1	no	—
323	C₄²	C₂²×D₄₃	1	1	yes	characteristic
324	C₂³	—	43	1	no	—
325	C₂³	—	43	1	no	—
326	C₂³	—	43	1	no	—
327	C₂³	—	86	2	no	—
328	C₂³	—	172	1	no	—
329	C₂³	—	172	1	no	—
330	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
331	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
332	Q₈	—	86	2	no	—
333	D₄	—	4	1	no	—
334	D₄	—	86	2	no	—
335	D₄	—	86	2	no	—
336	D₄	—	86	2	no	—
337	D₄	—	172	1	no	—
338	D₄	—	172	1	no	—
339	D₄	—	172	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	43	1	no	—
345	C₂×C₄	—	43	2	no	—
346	C₂×C₄	—	43	2	no	—
347	C₂×C₄	—	43	1	no	—
348	C₂×C₄	—	43	1	no	—
349	C₂×C₄	—	43	1	no	—
350	C₂×C₄	—	43	1	no	—
351	C₂×C₄	—	86	2	no	—
352	C₂×C₄	—	86	2	no	—
353	C₂×C₄	—	86	2	no	—
354	C₂×C₄	—	86	1	no	—
355	C₂×C₄	—	86	1	no	—
356	C₂×C₄	—	86	1	no	—
357	C₂×C₄	—	86	1	no	—
358	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
362	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	43	2	no	—
367	C₈	—	86	1	no	—
368	C₈	—	86	1	no	—
369	C₈	—	86	1	no	—
370	C₈	D₄×D₄₃	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	43	2	no	—
378	C₂²	—	86	1	no	—
379	C₂²	—	86	1	no	—
380	C₂²	—	86	1	no	—
381	C₂²	—	86	1	no	—
382	C₂²	—	86	1	no	—
383	C₂²	—	86	1	no	—
384	C₂²	—	86	1	no	—
385	C₂²	—	86	1	no	—
386	C₂²	—	172	4	no	—
387	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	43	2	no	—
393	C₄	—	86	1	no	—
394	C₄	—	86	1	no	—
395	C₄	—	86	1	no	—
396	C₄	—	86	1	no	—
397	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
398	C₄	#41×D₄₃	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	4	1	no	—
401	C₂	—	86	2	no	—
402	C₂	—	172	1	no	—
403	C₂	—	172	1	no	—
404	C₂	C₄×D₄×D₄₃	1	1	yes	characteristic
405	C₂	#14583664	1	1	yes	characteristic
406	C₂	#14583665	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₄
Fitting	C₄₃×#435	C₂
hypercenter	#435	D₄₃
hypocenter	C₄₃	#2930
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×#13063331	C₂	semidirect
2. C₂×M₁₆×D₄₃	C₂	semidirect
4. #14582977	C₂	semidirect
5. #14582976	C₂	semidirect
6. #14582974	C₂	semidirect
7. #14582974	C₂	semidirect
8. #14582972	C₂	semidirect
9. #14582970	C₂	semidirect
10. #14582968	C₂	semidirect
11. #14582924	C₂	semidirect
12. #14582864	C₂	semidirect
13. #14582861	C₂	semidirect
14. #14582856	C₂	semidirect
15. C₄₃×#435	C₂	semidirect
20. C₂×#10621877	C₂²	semidirect
25. C₂×#10621872	C₂²	semidirect
29. C₂×C₈×D₄₃	C₂²	semidirect
42. C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
43. Dic₄₃⋊C₈	C₂²	semidirect
44. Dic₄₃⋊C₈	C₂²	semidirect
46. C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
49. (C₂×D₄₃)⋊C₈	C₂²	semidirect
50. (C₂×D₄₃)⋊C₈	C₂²	semidirect
51. #13063235	C₂²	semidirect
52. C₄×C₄₃⋊C₈	C₂²	semidirect
53. C₈×Dic₄₃	C₂²	semidirect
55. C₂²×C₈×C₄₃	C₂²	semidirect
57. C₄⋊C₈×C₄₃	C₂²	semidirect
59. C₂²⋊C₈×C₄₃	C₂²	semidirect
60. #97×C₄₃	C₂²	semidirect
119. C₈×D₄₃	D₄	semidirect
214. #435	D₄₃	semidirect
219. C₄₃	#2930	semidirect
235. C₂²×C₈	C₂×D₄₃	semidirect
252. C₄⋊C₈	C₂×D₄₃	semidirect
260. C₂²⋊C₈	C₂×D₄₃	semidirect
262. #97	C₂×D₄₃	semidirect