Subgroups — Q₈×Q₁₆×D₄₃ #25977042

Order 11008.

1830 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈²×D₄₃	C₂	1	2	yes	maximal
2	Q₈×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₁₆×Dic₈₆	C₂	1	3	yes	maximal, complemented
4	#19147478	C₂	1	3	yes	maximal, complemented
5	Q₈×#10621885	C₂	1	2	yes	maximal, complemented
6	#19147476	C₂	1	6	yes	maximal, complemented
7	#500×D₄₃	C₂	1	3	yes	maximal
8	#477×D₄₃	C₂	1	6	yes	maximal
9	C₈×Q₈×D₄₃	C₂	1	1	yes	maximal, characteristic
10	C₄×Q₁₆×D₄₃	C₂	1	3	yes	maximal
11	Q₈×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₄₃	C₂²	1	1	yes	characteristic
13	Q₈×Dic₈₆	—	2	2	no	—
14	Q₈×Dic₈₆	C₂²	1	6	yes	—
15	Q₈×Dic₈₆	C₂²	1	2	yes	—
16	#14583629	—	2	6	no	—
17	#14583629	C₂²	1	6	yes	—
18	C₄⋊Q₈×D₄₃	—	2	6	no	—
19	C₄⋊Q₈×D₄₃	C₂²	1	6	yes	—
20	C₄×Q₈×D₄₃	—	2	2	no	—
21	C₄×Q₈×D₄₃	C₂²	1	6	yes	—
22	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
23	#14583304	C₂²	1	3	yes	—
24	#14583303	C₂²	1	6	yes	—
25	#14583303	C₂²	1	6	yes	—
26	#14583302	C₂²	1	6	yes	—
27	#14583195	C₂²	1	6	yes	—
28	#14583194	C₂²	1	6	yes	—
29	#14583193	C₂²	1	12	yes	—
30	#14583192	C₂²	1	12	yes	—
31	#14583191	C₂²	1	6	yes	—
32	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
33	C₈×Dic₈₆	C₂²	1	3	yes	—
34	#14583023	C₂²	1	3	yes	—
35	C₄×Dic₁₇₂	C₂²	1	3	yes	—
36	Q₁₆×Dic₄₃	C₂²	1	3	yes	—
37	#14582993	C₂²	1	3	yes	—
38	C₄×#10621885	C₂²	1	6	yes	—
39	#14582991	C₂²	1	6	yes	—
40	#107×D₄₃	C₂²	1	3	yes	—
41	#107×D₄₃	C₂²	1	6	yes	—
42	C₄⋊C₈×D₄₃	C₂²	1	3	yes	—
43	#103×D₄₃	C₂²	1	6	yes	—
44	C₄×C₈×D₄₃	C₂²	1	3	yes	—
45	Q₈²×C₄₃	C₂²	1	2	yes	—
46	C₄₃×#500	C₂²	1	3	yes	—
47	C₄₃×#477	C₂²	1	6	yes	—
48	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic
49	C₄×Q₁₆×C₄₃	C₂²	1	3	yes	—
50	C₂×Q₈×D₄₃	—	2	6	no	—
51	C₂×Q₈×D₄₃	D₄	1	1	yes	characteristic
52	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
53	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
54	C₂×#10621885	C₂³	1	2	yes	—
55	Q₁₆×D₄₃	Q₈	1	8	yes	direct product factor
56	C₂×C₈×D₄₃	C₂³	1	3	yes	—
57	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
58	#13063325	—	2	6	no	—
59	#13063325	C₂³	1	6	yes	—
60	#13063324	—	2	6	no	—
61	#13063324	—	2	6	no	—
62	#13063324	—	2	12	no	—
63	#13063324	—	2	6	no	—
64	#13063324	C₂³	1	12	yes	—
65	#13063323	—	2	12	no	—
66	#13063323	—	2	6	no	—
67	Q₈×Dic₄₃	—	2	2	no	—
68	Q₈×Dic₄₃	D₄	1	1	yes	characteristic
69	Q₈×Dic₄₃	C₂³	1	6	yes	—
70	C₄×Dic₈₆	—	2	6	no	—
71	C₄×Dic₈₆	—	2	6	no	—
72	C₄×Dic₈₆	C₂³	1	6	yes	—
73	C₄×Dic₈₆	C₂³	1	3	yes	—
74	#13063290	—	2	6	no	—
75	#13063290	—	2	6	no	—
76	#13063290	D₄	1	3	yes	—
77	#13063290	C₂³	1	6	yes	—
78	C₄⋊C₄×D₄₃	—	2	6	no	—
79	C₄⋊C₄×D₄₃	—	2	6	no	—
80	C₄⋊C₄×D₄₃	D₄	1	3	yes	—
81	C₄⋊C₄×D₄₃	C₂³	1	6	yes	—
82	C₄²×D₄₃	—	2	6	no	—
83	C₄²×D₄₃	C₂³	1	3	yes	—
84	#13063259	C₂³	1	3	yes	—
85	#13063259	C₂³	1	6	yes	—
86	#13063258	C₂³	1	6	yes	—
87	#13063258	C₂³	1	12	yes	—
88	C₄⋊(C₄₃⋊C₈)	C₂³	1	3	yes	—
89	Dic₄₃⋊C₈	C₂³	1	6	yes	—
90	#13063250	C₂³	1	6	yes	—
91	#13063249	C₂³	1	6	yes	—
92	#13063248	C₂³	1	6	yes	—
93	C₄×C₄₃⋊C₈	C₂³	1	3	yes	—
94	C₈×Dic₄₃	C₂³	1	3	yes	—
95	C₈×Dic₄₃	C₂³	1	3	yes	—
96	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
97	C₄⋊Q₈×C₄₃	—	2	6	no	—
98	C₄⋊Q₈×C₄₃	C₂³	1	6	yes	—
99	C₄×Q₈×C₄₃	—	2	2	no	—
100	C₄×Q₈×C₄₃	C₂³	1	6	yes	—
101	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
102	#107×C₄₃	C₂³	1	3	yes	—
103	#107×C₄₃	C₂³	1	6	yes	—
104	C₄⋊C₈×C₄₃	C₂³	1	3	yes	—
105	#103×C₄₃	C₂³	1	6	yes	—
106	C₄×C₈×C₄₃	C₂³	1	3	yes	—
107	C₂×Q₈×C₄₃	—	2	6	no	—
108	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
110	Q₈×D₄₃	—	2	4	no	—
111	Q₈×D₄₃	—	8	12	no	—
112	Q₈×D₄₃	Q₁₆	1	8	yes	direct product factor
113	Q₈×D₄₃	C₂×Q₈	1	8	yes	—
114	C₂×C₄×D₄₃	—	2	2	no	—
115	C₂×C₄×D₄₃	—	2	6	no	—
116	C₂×C₄×D₄₃	C₂×D₄	1	3	yes	—
117	C₂×C₄×D₄₃	C₂×D₄	1	3	yes	—
118	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
119	C₂×Dic₈₆	—	2	2	no	—
120	C₂×Dic₈₆	—	2	6	no	—
121	C₂×Dic₈₆	—	2	12	no	—
122	C₂×Dic₈₆	C₂×D₄	1	3	yes	—
123	C₂×Dic₈₆	C₂⁴	1	2	yes	—
124	Q₁₆×C₄₃	C₂×Q₈	1	4	yes	complemented
125	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
126	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
127	C₄⋊C₄×C₄₃	—	2	6	no	—
128	C₄⋊C₄×C₄₃	—	2	6	no	—
129	C₄⋊C₄×C₄₃	C₂×D₄	1	3	yes	—
130	C₄⋊C₄×C₄₃	C₂⁴	1	6	yes	—
131	C₄²×C₄₃	—	2	6	no	—
132	C₄²×C₄₃	C₂⁴	1	3	yes	—
133	#10621885	C₂×Q₈	1	8	yes	complemented
134	C₄⋊Dic₄₃	—	2	6	no	—
135	C₄⋊Dic₄₃	—	2	6	no	—
136	C₄⋊Dic₄₃	C₂×D₄	1	3	yes	—
137	C₄⋊Dic₄₃	C₂⁴	1	6	yes	—
138	Dic₄₃⋊C₄	—	2	6	no	—
139	Dic₄₃⋊C₄	—	2	12	no	—
140	Dic₄₃⋊C₄	—	2	6	no	—
141	Dic₄₃⋊C₄	—	2	6	no	—
142	Dic₄₃⋊C₄	C₂×D₄	1	6	yes	—
143	C₄×Dic₄₃	—	2	6	no	—
144	C₄×Dic₄₃	—	2	6	no	—
145	C₄×Dic₄₃	—	2	6	no	—
146	C₄×Dic₄₃	C₂×D₄	1	3	yes	—
147	C₄×Dic₄₃	C₂×D₄	1	3	yes	—
148	C₄×Dic₄₃	C₂⁴	1	3	yes	—
149	C₂×C₄₃⋊C₈	C₂⁴	1	3	yes	—
150	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
151	Dic₁₇₂	C₂×Q₈	1	4	yes	complemented
152	C₈×D₄₃	—	2	6	no	—
153	C₈×D₄₃	C₂×Q₈	1	4	yes	—
154	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₄₃	—	2	2	no	—
156	Q₈×C₄₃	—	8	6	no	—
157	Q₈×C₄₃	C₂×Q₁₆	1	4	yes	complemented
158	Q₈×C₄₃	C₂²×Q₈	1	4	yes	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	6	no	—
161	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
162	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
163	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
164	C₂×Dic₄₃	—	2	2	no	—
165	C₂×Dic₄₃	—	2	6	no	—
166	C₂×Dic₄₃	C₂²×D₄	1	3	yes	—
167	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×Dic₄₃	C₂²×D₄	1	3	yes	—
169	C₄×D₄₃	—	2	8	no	—
170	C₄×D₄₃	—	2	6	no	—
171	C₄×D₄₃	—	4	12	no	—
172	C₄×D₄₃	C₂×Q₁₆	1	12	yes	—
173	C₄×D₄₃	C₂²×Q₈	1	2	yes	—
174	C₄×D₄₃	2₋¹⁺⁴	1	2	yes	—
175	Dic₈₆	—	2	2	no	—
176	Dic₈₆	—	2	8	no	—
177	Dic₈₆	—	8	12	no	—
178	Dic₈₆	—	8	6	no	—
179	Dic₈₆	C₂×Q₁₆	1	12	yes	complemented
180	Dic₈₆	C₂²×Q₈	1	4	yes	—
181	C₈×C₄₃	—	2	3	no	—
182	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
183	C₄₃⋊C₈	—	2	3	no	—
184	C₄₃⋊C₈	C₂²×Q₈	1	2	yes	—
185	C₂×Q₈×Q₁₆	—	43	1	no	maximal, Sylow
186	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
187	C₂×D₄₃	D₄×Q₈	1	2	yes	—
188	C₂×D₄₃	C₂²×Q₁₆	1	2	yes	—
189	C₂×D₄₃	#576	1	2	yes	—
190	C₄×C₄₃	—	2	4	no	—
191	C₄×C₄₃	—	2	3	no	—
192	C₄×C₄₃	—	4	6	no	—
193	C₄×C₄₃	C₂²×Q₁₆	1	6	yes	—
194	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
195	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
196	Dic₄₃	—	2	4	no	—
197	Dic₄₃	—	2	3	no	—
198	Dic₄₃	—	4	6	no	—
199	Dic₄₃	D₄×Q₈	1	2	yes	—
200	Dic₄₃	C₂²×Q₁₆	1	6	yes	—
201	C₂×Q₈²	—	43	2	no	—
202	Q₈×Q₁₆	—	43	3	no	—
203	Q₈×Q₁₆	—	43	6	no	—
204	Q₈×Q₁₆	—	43	1	no	—
205	Q₈×Q₁₆	—	43	3	no	—
206	Q₈×Q₁₆	—	43	2	no	—
207	Q₈×Q₁₆	D₄₃	1	1	yes	characteristic, direct product factor
208	C₂×#500	—	43	3	no	—
209	C₂×#477	—	43	6	no	—
210	C₂×C₈×Q₈	—	43	1	no	—
211	C₂×C₄×Q₁₆	—	43	3	no	—
212	C₂×C₄₃	C₂×D₄×Q₈	1	1	yes	characteristic
213	C₂×C₄₃	C₂³×Q₁₆	1	1	yes	characteristic
214	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
215	D₄₃	Q₈×Q₁₆	1	4	yes	direct product factor
216	C₂²×Q₁₆	—	43	1	no	—
217	Q₈²	—	43	6	no	—
218	Q₈²	—	43	6	no	—
219	Q₈²	—	43	2	no	—
220	Q₈²	—	86	2	no	—
221	Q₈²	—	86	6	no	—
222	Q₈²	C₂×D₄₃	1	2	yes	—
223	C₂×C₄⋊Q₈	—	43	6	no	—
224	C₂×C₄⋊Q₈	—	86	6	no	—
225	C₂×C₄×Q₈	—	43	1	no	—
226	C₂×C₄×Q₈	—	43	6	no	—
227	C₂×C₄×Q₈	—	86	2	no	—
228	#500	—	43	6	no	—
229	#500	—	43	6	no	—
230	#500	—	43	6	no	—
231	#500	—	43	3	no	—
232	#500	C₂×D₄₃	1	3	yes	—
233	#477	—	43	6	no	—
234	#477	—	43	6	no	—
235	#477	—	43	12	no	—
236	#477	—	43	6	no	—
237	#477	—	43	12	no	—
238	#477	C₂×D₄₃	1	6	yes	—
239	C₈×Q₈	—	43	1	no	—
240	C₈×Q₈	—	43	3	no	—
241	C₈×Q₈	—	43	3	no	—
242	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic
243	C₄×Q₁₆	—	43	3	no	—
244	C₄×Q₁₆	—	43	6	no	—
245	C₄×Q₁₆	—	43	3	no	—
246	C₄×Q₁₆	—	43	6	no	—
247	C₄×Q₁₆	—	43	3	no	—
248	C₄×Q₁₆	C₂×D₄₃	1	3	yes	—
249	C₂×#107	—	43	6	no	—
250	C₂×#107	—	43	3	no	—
251	C₂×C₄⋊C₈	—	43	3	no	—
252	C₂×#103	—	43	6	no	—
253	C₂×C₄×C₈	—	43	3	no	—
254	C₄₃	C₂×Q₈×Q₁₆	1	1	yes	characteristic, complemented, Sylow
255	C₂²×Q₈	—	43	1	no	—
256	C₂²×Q₈	—	43	2	no	—
257	C₂²×Q₈	—	86	6	no	—
258	C₂×Q₁₆	—	43	2	no	—
259	C₂×Q₁₆	—	43	8	no	—
260	C₂×Q₁₆	—	43	1	no	—
261	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
262	C₂²×C₈	—	43	1	no	—
263	C₂²×C₈	—	43	3	no	—
264	C₄⋊Q₈	—	2	6	no	—
265	C₄⋊Q₈	—	43	12	no	—
266	C₄⋊Q₈	—	43	6	no	—
267	C₄⋊Q₈	—	86	6	no	—
268	C₄⋊Q₈	—	86	6	no	—
269	C₄⋊Q₈	—	86	6	no	—
270	C₄⋊Q₈	—	86	12	no	—
271	C₄⋊Q₈	—	86	6	no	—
272	C₄⋊Q₈	—	86	12	no	—
273	C₄⋊Q₈	—	86	6	no	—
274	C₄⋊Q₈	C₂²×D₄₃	1	6	yes	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	—	43	1	no	—
277	C₄×Q₈	—	43	3	no	—
278	C₄×Q₈	—	43	3	no	—
279	C₄×Q₈	—	43	6	no	—
280	C₄×Q₈	—	43	6	no	—
281	C₄×Q₈	—	43	6	no	—
282	C₄×Q₈	—	86	6	no	—
283	C₄×Q₈	—	86	6	no	—
284	C₄×Q₈	—	86	6	no	—
285	C₄×Q₈	—	86	6	no	—
286	C₄×Q₈	—	86	2	no	—
287	C₄×Q₈	C₂²×D₄₃	1	6	yes	—
288	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	—	43	3	no	—
290	C₂×C₄⋊C₄	—	43	6	no	—
291	C₂×C₄⋊C₄	—	86	6	no	—
292	C₂×C₄⋊C₄	—	86	6	no	—
293	C₂×C₄²	—	43	3	no	—
294	C₂×C₄²	—	86	6	no	—
295	#107	—	43	3	no	—
296	#107	—	43	6	no	—
297	#107	—	43	6	no	—
298	#107	—	43	12	no	—
299	#107	C₂²×D₄₃	1	3	yes	—
300	#107	C₂²×D₄₃	1	6	yes	—
301	C₄⋊C₈	—	43	6	no	—
302	C₄⋊C₈	—	43	3	no	—
303	C₄⋊C₈	C₂²×D₄₃	1	3	yes	—
304	#103	—	43	6	no	—
305	#103	—	43	6	no	—
306	#103	—	43	6	no	—
307	#103	C₂²×D₄₃	1	6	yes	—
308	C₄×C₈	—	43	3	no	—
309	C₄×C₈	—	43	3	no	—
310	C₄×C₈	—	43	3	no	—
311	C₄×C₈	C₂²×D₄₃	1	3	yes	—
312	C₂×Q₈	—	2	6	no	—
313	C₂×Q₈	—	43	8	no	—
314	C₂×Q₈	—	43	3	no	—
315	C₂×Q₈	—	43	8	no	—
316	C₂×Q₈	—	43	2	no	—
317	C₂×Q₈	—	86	2	no	—
318	C₂×Q₈	—	86	12	no	—
319	C₂×Q₈	—	86	4	no	—
320	C₂×Q₈	—	86	6	no	—
321	C₂×Q₈	—	344	12	no	—
322	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
323	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
324	C₂²×C₄	—	43	3	no	—
325	C₂²×C₄	—	43	1	no	—
326	C₂²×C₄	—	43	3	no	—
327	C₂²×C₄	—	86	2	no	—
328	C₂²×C₄	—	86	6	no	—
329	Q₁₆	—	43	8	no	—
330	Q₁₆	—	43	4	no	—
331	Q₁₆	Q₈×D₄₃	1	4	yes	direct product factor
332	C₂×C₈	—	43	1	no	—
333	C₂×C₈	—	43	4	no	—
334	C₂×C₈	—	43	3	no	—
335	C₂×C₈	—	86	6	no	—
336	C₂×C₈	C₂³×D₄₃	1	3	yes	—
337	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
338	C₄⋊C₄	—	2	6	no	—
339	C₄⋊C₄	—	2	6	no	—
340	C₄⋊C₄	—	43	6	no	—
341	C₄⋊C₄	—	43	3	no	—
342	C₄⋊C₄	—	43	6	no	—
343	C₄⋊C₄	—	86	6	no	—
344	C₄⋊C₄	—	86	6	no	—
345	C₄⋊C₄	—	86	6	no	—
346	C₄⋊C₄	—	86	12	no	—
347	C₄⋊C₄	—	86	6	no	—
348	C₄⋊C₄	—	86	6	no	—
349	C₄⋊C₄	D₄×D₄₃	1	3	yes	—
350	C₄⋊C₄	C₂³×D₄₃	1	6	yes	—
351	C₄²	—	2	6	no	—
352	C₄²	—	43	3	no	—
353	C₄²	—	43	3	no	—
354	C₄²	—	43	3	no	—
355	C₄²	—	86	6	no	—
356	C₄²	—	86	6	no	—
357	C₄²	—	86	6	no	—
358	C₄²	C₂³×D₄₃	1	3	yes	—
359	C₂³	—	43	1	no	—
360	Q₈	—	2	2	no	—
361	Q₈	—	8	6	no	—
362	Q₈	—	43	12	no	—
363	Q₈	—	43	4	no	—
364	Q₈	—	86	8	no	—
365	Q₈	—	86	2	no	—
366	Q₈	—	344	6	no	—
367	Q₈	—	344	12	no	—
368	Q₈	Q₁₆×D₄₃	1	4	yes	direct product factor
369	Q₈	C₂×Q₈×D₄₃	1	4	yes	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	43	1	no	—
373	C₂×C₄	—	43	3	no	—
374	C₂×C₄	—	43	12	no	—
375	C₂×C₄	—	43	2	no	—
376	C₂×C₄	—	43	2	no	—
377	C₂×C₄	—	43	3	no	—
378	C₂×C₄	—	86	6	no	—
379	C₂×C₄	—	86	8	no	—
380	C₂×C₄	—	86	2	no	—
381	C₂×C₄	—	86	6	no	—
382	C₂×C₄	—	172	12	no	—
383	C₂×C₄	C₂×D₄×D₄₃	1	3	yes	—
384	C₂×C₄	C₂×D₄×D₄₃	1	3	yes	—
385	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
386	C₈	—	2	3	no	—
387	C₈	—	43	2	no	—
388	C₈	—	86	3	no	—
389	C₈	C₂×Q₈×D₄₃	1	2	yes	—
390	C₂²	—	43	2	no	—
391	C₂²	—	43	2	no	—
392	C₂²	—	43	2	no	—
393	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
394	C₄	—	2	3	no	—
395	C₄	—	2	4	no	—
396	C₄	—	4	6	no	—
397	C₄	—	43	6	no	—
398	C₄	—	43	2	no	—
399	C₄	—	86	3	no	—
400	C₄	—	86	4	no	—
401	C₄	—	172	6	no	—
402	C₄	C₂×Q₁₆×D₄₃	1	6	yes	—
403	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
404	C₄	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
405	C₂	—	43	4	no	—
406	C₂	D₄×Q₈×D₄₃	1	1	yes	characteristic
407	C₂	C₂²×Q₁₆×D₄₃	1	1	yes	characteristic
408	C₂	#576×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	Q₈×Q₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂²×D₄₃	C₂²×D₄
hypercenter	Q₈×Q₁₆	D₄₃
hypocenter	C₄₃	C₂×Q₈×Q₁₆
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ Q₈×Q₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×Dic₁₇₂	C₂	semidirect
3. Q₁₆×Dic₈₆	C₂	semidirect
4. #19147478	C₂	semidirect
5. Q₈×#10621885	C₂	semidirect
6. #19147476	C₂	semidirect
11. Q₈×Q₁₆×C₄₃	C₂	semidirect
55. Q₁₆×D₄₃	Q₈	direct (N × H)
112. Q₈×D₄₃	Q₁₆	direct (N × H)
124. Q₁₆×C₄₃	C₂×Q₈	semidirect
133. #10621885	C₂×Q₈	semidirect
151. Dic₁₇₂	C₂×Q₈	semidirect
157. Q₈×C₄₃	C₂×Q₁₆	semidirect
179. Dic₈₆	C₂×Q₁₆	semidirect
207. Q₈×Q₁₆	D₄₃	direct (N × H)
215. D₄₃	Q₈×Q₁₆	direct (N × H)
254. C₄₃	C₂×Q₈×Q₁₆	semidirect
331. Q₁₆	Q₈×D₄₃	direct (N × H)
368. Q₈	Q₁₆×D₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈²×D₄₃	2
Q₈×Dic₁₇₂	2
Q₁₆×Dic₈₆	2
#19147478	2
Q₈×#10621885	2
#19147476	2
#500×D₄₃	2
#477×D₄₃	2
C₈×Q₈×D₄₃	2
C₄×Q₁₆×D₄₃	2
Q₈×Q₁₆×C₄₃	2
C₂×Q₈×Q₁₆	43

Subgroups — Q8×Q16×D43 #25977042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×Q₁₆×D₄₃ #25977042