Subgroups — #25066534

Order 11008.

766 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	#19144595	C₂	1	1	yes	maximal, characteristic
2	#19143308	C₂	1	1	yes	maximal, characteristic, complemented
3	#19133459	C₂	1	4	yes	maximal, complemented
4	#19133417	C₂	1	4	yes	maximal, complemented
5	#19133365	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133020	C₂	1	1	yes	maximal, characteristic, complemented
7	#19132993	C₂	1	1	yes	maximal, characteristic, complemented
8	#19132887	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₈×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13063331	—	2	1	no	—
11	#14583449	C₂²	1	1	yes	characteristic
12	#14583212	C₄	1	2	yes	—
13	#14583179	C₄	1	2	yes	—
14	#14583094	C₄	1	2	yes	—
15	#14583033	C₄	1	2	yes	—
16	C₄×#10621882	C₂²	1	4	yes	—
17	#14582978	—	2	1	no	—
18	#14582978	C₂²	1	2	yes	complemented
19	C₈×D₁₇₂	—	2	1	no	—
20	C₈×D₁₇₂	C₂²	1	2	yes	complemented
21	#14582952	C₂²	1	1	yes	characteristic
22	#14582952	C₂²	1	1	yes	characteristic
23	#14582923	C₂²	1	1	yes	characteristic
24	#14582865	—	2	1	no	—
25	#14582649	C₂²	1	4	yes	complemented
26	D₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
27	#14582626	C₂²	1	4	yes	complemented
28	#14582621	C₂²	1	2	yes	complemented
29	#14582621	C₂²	1	2	yes	complemented
30	C₂³×C₈×C₄₃	—	2	1	no	—
31	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
32	C₈×D₄×C₄₃	—	2	1	no	—
33	C₈×D₄×C₄₃	—	2	1	no	—
34	C₈×D₄×C₄₃	C₂²	1	2	yes	—
35	C₈×D₄×C₄₃	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
38	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#10621898	—	2	1	no	—
40	C₂×#10621882	C₂×C₄	1	4	yes	—
41	#13063331	—	4	4	no	—
42	C₂×#10621877	—	2	1	no	—
43	C₂×#10621872	—	2	2	no	—
44	C₂×C₈×D₄₃	—	2	2	no	—
45	#13063325	C₂×C₄	1	1	yes	characteristic
46	#13063322	C₂×C₄	1	1	yes	characteristic
47	#13063313	—	2	1	no	—
48	#13063299	—	2	1	no	—
49	#13063299	C₂×C₄	1	2	yes	—
50	C₄×D₁₇₂	—	2	1	no	—
51	C₄×D₁₇₂	C₂³	1	2	yes	—
52	#13063258	C₂×C₄	1	4	yes	—
53	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
56	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
57	#13063246	C₂×C₄	1	4	yes	—
58	#13063245	C₂×C₄	1	4	yes	—
59	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
60	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
61	(C₂×D₄₃)⋊C₈	—	2	2	no	—
62	(C₂×D₄₃)⋊C₈	—	2	2	no	—
63	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
64	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
65	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₃	—	2	1	no	—
67	C₂²×C₈×C₄₃	—	2	1	no	—
68	C₂²×C₈×C₄₃	—	2	2	no	—
69	C₂²×C₈×C₄₃	—	2	2	no	—
70	C₂²×C₈×C₄₃	—	4	4	no	—
71	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
72	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
73	C₄×D₄×C₄₃	—	2	1	no	—
74	C₄×D₄×C₄₃	—	2	1	no	—
75	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
76	C₄×D₄×C₄₃	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₄₃	—	2	1	no	—
81	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
82	C₂²⋊C₈×C₄₃	—	2	2	no	—
83	C₂²⋊C₈×C₄₃	—	2	2	no	—
84	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
85	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
86	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₂⁴×C₄₃	—	2	1	no	—
89	C₂×D₄×C₄₃	—	2	4	no	—
90	C₂×D₄×C₄₃	—	2	1	no	—
91	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₄₃	—	2	2	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	1	no	—
95	C₂²×C₄×C₄₃	—	4	2	no	—
96	C₂²×C₄×C₄₃	—	4	2	no	—
97	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
100	C₂×C₂²⋊D₄₃	—	2	2	no	—
101	#10621898	—	4	2	no	—
102	#10621898	—	4	2	no	—
103	C₂×D₁₇₂	—	2	1	no	—
104	C₂×D₁₇₂	—	2	1	no	—
105	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
106	C₂×C₄×D₄₃	—	2	2	no	—
107	C₂×Dic₈₆	—	2	1	no	—
108	C₂×C₈×C₄₃	—	2	2	no	—
109	C₂×C₈×C₄₃	—	2	2	no	—
110	C₂×C₈×C₄₃	—	2	2	no	—
111	C₂×C₈×C₄₃	—	4	4	no	—
112	C₂×C₈×C₄₃	—	4	4	no	—
113	C₂×C₈×C₄₃	—	4	2	no	—
114	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₄⋊C₄×C₄₃	—	2	1	no	—
119	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
120	C₂²⋊C₄×C₄₃	—	2	2	no	—
121	C₂²⋊C₄×C₄₃	—	2	2	no	—
122	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₄₃	#41	1	1	yes	characteristic
125	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
126	#10621882	—	2	8	no	—
127	(C₂×D₄₃)⋊C₄	—	2	2	no	—
128	(C₂×D₄₃)⋊C₄	—	2	2	no	—
129	C₄⋊Dic₄₃	—	2	1	no	—
130	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
131	#10621877	—	4	2	no	—
132	C₂×C₄₃⋊C₈	—	2	2	no	—
133	C₂×C₄₃⋊C₈	—	2	2	no	—
134	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
135	#10621872	—	4	4	no	—
136	C₈×D₄₃	—	4	4	no	—
137	C₂³×C₄₃	—	2	4	no	—
138	C₂³×C₄₃	—	2	2	no	—
139	C₂³×C₄₃	—	4	2	no	—
140	C₂³×C₄₃	—	4	2	no	—
141	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
142	C₂²×D₄₃	—	2	2	no	—
143	D₄×C₄₃	—	2	4	no	—
144	D₄×C₄₃	—	2	2	no	—
145	D₄×C₄₃	#131	1	4	yes	complemented
146	C₂×C₄×C₄₃	—	2	2	no	—
147	C₂×C₄×C₄₃	—	2	2	no	—
148	C₂×C₄×C₄₃	—	4	1	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	—	4	2	no	—
151	C₂×C₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	—	4	4	no	—
153	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
157	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
158	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
161	C₂²⋊D₄₃	—	4	4	no	—
162	C₂×Dic₄₃	—	2	2	no	—
163	D₁₇₂	—	2	4	no	—
164	D₁₇₂	—	4	2	no	—
165	D₁₇₂	—	4	2	no	—
166	C₄×D₄₃	—	4	2	no	—
167	C₄×D₄₃	—	4	2	no	—
168	Dic₈₆	—	4	2	no	—
169	C₈×C₄₃	—	2	1	no	—
170	C₈×C₄₃	—	2	1	no	—
171	C₈×C₄₃	—	2	1	no	—
172	C₈×C₄₃	—	2	1	no	—
173	C₈×C₄₃	—	4	2	no	—
174	C₄₃⋊C₈	—	2	4	no	—
175	C₄₃⋊C₈	—	4	2	no	—
176	C₄₃⋊C₈	—	4	2	no	—
177	#17907	—	43	1	no	maximal, Sylow
178	C₂²×C₄₃	—	2	1	no	—
179	C₂²×C₄₃	—	2	1	no	—
180	C₂²×C₄₃	—	2	4	no	—
181	C₂²×C₄₃	—	4	8	no	—
182	C₂²×C₄₃	—	4	2	no	—
183	C₂²×C₄₃	—	4	2	no	—
184	C₂²×C₄₃	#442	1	2	yes	—
185	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂×D₄₃	—	4	2	no	—
187	C₂×D₄₃	—	4	2	no	—
188	C₂×D₄₃	—	4	2	no	—
189	C₄×C₄₃	—	2	1	no	—
190	C₄×C₄₃	—	2	1	no	—
191	C₄×C₄₃	—	2	1	no	—
192	C₄×C₄₃	—	4	2	no	—
193	C₄×C₄₃	#442	1	2	yes	—
194	C₄×C₄₃	C₂×#131	1	2	yes	—
195	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	Dic₄₃	—	4	2	no	—
198	#3100	—	43	1	no	—
199	#2931	—	43	1	no	—
200	C₂×C₈×D₄	D₄₃	1	1	yes	characteristic, complemented
201	#1586	—	43	4	no	—
202	#1580	—	43	4	no	—
203	#1570	—	43	1	no	—
204	#1486	—	43	1	no	—
205	#1480	—	43	1	no	—
206	#1452	—	43	1	no	—
207	C₂×C₄₃	—	2	2	no	—
208	C₂×C₄₃	—	4	4	no	—
209	C₂×C₄₃	#2929	1	1	yes	characteristic
210	C₂×C₄₃	C₂×#442	1	1	yes	characteristic
211	C₂×C₄₃	#2955	1	1	yes	characteristic
212	D₄₃	—	8	2	no	—
213	C₂×#131	—	86	1	no	—
214	C₂³×C₈	—	2	1	no	—
215	#532	—	43	1	no	—
216	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
217	#480	—	43	2	no	—
218	#474	—	43	2	no	—
219	#459	—	43	2	no	—
220	#447	—	43	2	no	—
221	C₄×D₈	—	43	4	no	—
222	#436	—	43	2	no	—
223	#436	—	86	1	no	—
224	C₈×D₄	—	2	1	no	—
225	C₈×D₄	—	2	1	no	—
226	C₈×D₄	—	43	2	no	—
227	C₈×D₄	—	86	1	no	—
228	C₈×D₄	C₂×D₄₃	1	2	yes	—
229	C₈×D₄	C₂×D₄₃	1	2	yes	—
230	#431	—	43	1	no	—
231	#431	—	43	1	no	—
232	#423	—	43	1	no	—
233	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
234	#408	—	86	1	no	—
235	C₂×C₂²⋊C₈	—	2	1	no	—
236	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
237	#334	—	43	4	no	—
238	D₄⋊C₈	—	43	4	no	—
239	D₄⋊C₈	—	43	4	no	—
240	#322	—	43	2	no	—
241	#322	—	43	2	no	—
242	C₄₃	#17907	1	1	yes	characteristic, complemented, Sylow
243	C₂×#41	—	86	1	no	—
244	C₂²×D₄	C₄×D₄₃	1	1	yes	characteristic
245	C₂³×C₄	—	2	1	no	—
246	C₂×D₈	—	43	4	no	—
247	#131	—	172	4	no	—
248	C₂×M₁₆	—	86	1	no	—
249	C₂×M₁₆	—	86	2	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	4	4	no	—
254	C₂²×C₈	—	86	2	no	—
255	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
256	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
257	C₄⋊Q₈	—	43	1	no	—
258	#127	—	43	1	no	—
259	#124	—	86	1	no	—
260	#121	—	43	2	no	—
261	#121	—	86	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	43	2	no	—
265	C₄×D₄	—	86	1	no	—
266	C₄×D₄	C₄×D₄₃	1	2	yes	—
267	C₄×D₄	C₂²×D₄₃	1	2	yes	—
268	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
271	#107	—	43	4	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	43	2	no	—
274	C₄⋊C₈	—	43	2	no	—
275	C₄⋊C₈	—	86	1	no	—
276	C₄⋊C₈	—	86	1	no	—
277	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
278	#102	—	43	4	no	—
279	#102	—	43	4	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	C₂²⋊C₈	—	2	2	no	—
282	C₂²⋊C₈	—	43	2	no	—
283	C₂²⋊C₈	—	86	1	no	—
284	C₂²⋊C₈	—	86	2	no	—
285	C₂²⋊C₈	—	86	2	no	—
286	C₄×C₈	—	43	2	no	—
287	C₄×C₈	—	43	2	no	—
288	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
289	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
292	C₂⁴	—	2	1	no	—
293	#41	—	172	2	no	—
294	#41	—	172	2	no	—
295	C₂×Q₈	—	86	1	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	43	2	no	—
299	C₂×D₄	—	86	2	no	—
300	C₂×D₄	—	86	1	no	—
301	C₂×D₄	—	86	1	no	—
302	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	86	2	no	—
309	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
310	C₂²×C₄	#10621898	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
312	D₈	—	86	8	no	—
313	M₁₆	—	172	4	no	—
314	M₁₆	—	172	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	4	4	no	—
319	C₂×C₈	—	4	4	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	—	43	4	no	—
322	C₂×C₈	—	86	2	no	—
323	C₂×C₈	—	86	2	no	—
324	C₂×C₈	—	172	4	no	—
325	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
326	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
327	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
328	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	43	2	no	—
331	C₄⋊C₄	—	86	1	no	—
332	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	86	2	no	—
336	C₂²⋊C₄	—	86	2	no	—
337	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
338	C₄²	#10621898	1	1	yes	characteristic
339	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
340	C₄²	C₂³×D₄₃	1	1	yes	characteristic
341	C₂³	—	2	4	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	86	2	no	—
346	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
347	Q₈	—	172	2	no	—
348	D₄	—	2	4	no	—
349	D₄	—	2	2	no	—
350	D₄	—	86	4	no	—
351	D₄	—	172	2	no	—
352	D₄	—	172	4	no	—
353	D₄	—	172	2	no	—
354	D₄	#13063331	1	4	yes	complemented
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	86	2	no	—
363	C₂×C₄	—	172	2	no	—
364	C₂×C₄	—	172	2	no	—
365	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
366	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
367	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
368	C₂×C₄	#13063350	1	2	yes	—
369	C₂×C₄	#13063351	1	2	yes	—
370	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
372	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
373	C₈	—	2	1	no	—
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	4	2	no	—
378	C₈	—	86	4	no	—
379	C₈	—	172	2	no	—
380	C₈	—	172	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	4	8	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	172	2	no	—
388	C₂²	—	172	2	no	—
389	C₂²	—	172	2	no	—
390	C₂²	#14583009	1	2	yes	—
391	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	4	2	no	—
396	C₄	—	172	2	no	—
397	C₄	#14583009	1	2	yes	—
398	C₄	C₂×#13063331	1	2	yes	—
399	C₄	C₂×#13063350	1	1	yes	characteristic
400	C₄	C₂×#13063351	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	4	4	no	—
403	C₂	—	344	2	no	—
404	C₂	#19143289	1	1	yes	characteristic
405	C₂	C₂×#14583009	1	1	yes	characteristic
406	C₂	#19143496	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₈×D₄×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#19144595	C₂
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	C₂×C₈×D₄	D₄₃
hypocenter	C₄₃	#17907
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
2. #19143308	C₂	semidirect
3. #19133459	C₂	semidirect
4. #19133417	C₂	semidirect
5. #19133365	C₂	semidirect
6. #19133020	C₂	semidirect
7. #19132993	C₂	semidirect
8. #19132887	C₂	semidirect
9. C₂×C₈×D₄×C₄₃	C₂	semidirect
18. #14582978	C₂²	semidirect
20. C₈×D₁₇₂	C₂²	semidirect
25. #14582649	C₂²	semidirect
27. #14582626	C₂²	semidirect
28. #14582621	C₂²	semidirect
29. #14582621	C₂²	semidirect
145. D₄×C₄₃	#131	semidirect
200. C₂×C₈×D₄	D₄₃	semidirect
242. C₄₃	#17907	semidirect
354. D₄	#13063331	semidirect

Maximal subgroups

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

subgroup	index
#19144595	2
#19143308	2
#19133459	2
#19133417	2
#19133365	2
#19133020	2
#19132993	2
#19132887	2
C₂×C₈×D₄×C₄₃	2
#17907	43