Subgroups — C₂×#494×D₄₃ #25966001

Order 11008.

3262 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₁₆×D₄₃	C₂	1	4	yes	maximal
2	C₂×C₄⋊Q₈×D₄₃	C₂	1	2	yes	maximal
3	C₂×#14583279	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14583278	C₂	1	2	yes	maximal, complemented
5	C₂×#14583277	C₂	1	4	yes	maximal, complemented
6	#494×D₄₃	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₄×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₈×D₄₃	C₂²	1	4	yes	—
10	C₂²×Dic₁₇₂	C₂²	1	4	yes	—
11	C₂²×#10621885	C₂²	1	8	yes	—
12	C₂×Q₁₆×D₄₃	—	2	32	no	—
13	C₂×Q₁₆×D₄₃	C₂²	1	32	yes	—
14	C₂²×C₈×D₄₃	C₂²	1	2	yes	—
15	C₂×#13063325	C₂²	1	2	yes	—
16	C₂×#13063324	—	2	4	no	—
17	C₂×#13063323	C₂²	1	4	yes	—
18	C₄⋊Q₈×D₄₃	—	2	8	no	—
19	C₄⋊Q₈×D₄₃	C₂²	1	16	yes	—
20	C₂×C₄⋊C₄×D₄₃	—	2	4	no	—
21	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
22	#14583279	C₂²	1	8	yes	complemented
23	#14583278	C₂²	1	16	yes	complemented
24	#14583277	C₂²	1	32	yes	complemented
25	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
27	C₄×C₈×D₄₃	C₂²	1	8	yes	—
28	C₂²×Q₁₆×C₄₃	C₂²	1	4	yes	—
29	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
30	C₄₃×#494	C₂²	1	8	yes	complemented
31	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₂²×Dic₈₆	—	2	4	no	—
33	C₂²×Dic₈₆	C₂³	1	4	yes	—
34	C₂×Q₈×D₄₃	—	2	8	no	—
35	C₂×Q₈×D₄₃	—	2	32	no	—
36	C₂×Q₈×D₄₃	C₂³	1	16	yes	—
37	C₂²×C₄×D₄₃	—	2	4	no	—
38	C₂²×C₄×D₄₃	D₄	1	2	yes	—
39	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
40	C₂×Dic₁₇₂	—	2	16	no	—
41	C₂×Dic₁₇₂	C₂³	1	16	yes	—
42	C₂×#10621885	—	2	32	no	—
43	C₂×#10621885	C₂³	1	32	yes	—
44	Q₁₆×D₄₃	—	2	128	no	—
45	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
46	C₂×C₈×D₄₃	D₄	1	16	yes	—
47	C₂×C₈×D₄₃	C₂³	1	8	yes	—
48	#13063325	—	2	4	no	—
49	#13063325	C₂³	1	8	yes	—
50	#13063324	—	2	32	no	—
51	#13063323	—	2	8	no	—
52	#13063323	C₂³	1	16	yes	—
53	C₂×C₄⋊Dic₄₃	—	2	4	no	—
54	C₂×Dic₄₃⋊C₄	—	2	8	no	—
55	C₄⋊C₄×D₄₃	—	2	32	no	—
56	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
57	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
58	C₄²×D₄₃	D₄	1	4	yes	—
59	C₄²×D₄₃	C₂³	1	4	yes	—
60	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
61	C₈×Dic₄₃	C₂³	1	8	yes	—
62	C₂²×Q₈×C₄₃	C₂³	1	4	yes	—
63	C₂×Q₁₆×C₄₃	—	2	16	no	—
64	C₂×Q₁₆×C₄₃	C₂³	1	16	yes	—
65	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
66	C₄⋊Q₈×C₄₃	—	2	4	no	—
67	C₄⋊Q₈×C₄₃	C₂³	1	8	yes	—
68	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
69	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
70	C₄×C₈×C₄₃	C₂³	1	4	yes	—
71	C₂³×D₄₃	C₂×D₄	1	1	yes	characteristic
72	C₂×Q₈×C₄₃	—	2	4	no	—
73	C₂×Q₈×C₄₃	—	2	16	no	—
74	C₂×Q₈×C₄₃	C₂⁴	1	8	yes	—
75	C₂²×C₄×C₄₃	—	2	4	no	—
76	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
78	C₂²×Dic₄₃	—	2	4	no	—
79	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
81	Q₈×D₄₃	—	2	64	no	—
82	Q₈×D₄₃	—	4	32	no	—
83	C₂×C₄×D₄₃	—	2	16	no	—
84	C₂×C₄×D₄₃	—	4	16	no	—
85	C₂×C₄×D₄₃	Q₁₆	1	16	yes	complemented
86	C₂×C₄×D₄₃	C₂×D₄	1	8	yes	—
87	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
88	C₂×C₄×D₄₃	C₂×D₄	1	8	yes	—
89	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
90	C₂×Dic₈₆	—	2	16	no	—
91	C₂×Dic₈₆	—	2	4	no	—
92	C₂×Dic₈₆	—	2	16	no	—
93	C₂×Dic₈₆	—	4	16	no	—
94	C₂×Dic₈₆	C₂⁴	1	8	yes	—
95	Q₁₆×C₄₃	—	2	32	no	—
96	C₂×C₈×C₄₃	C₂×D₄	1	8	yes	—
97	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
98	C₄⋊C₄×C₄₃	—	2	16	no	—
99	C₄²×C₄₃	C₂×D₄	1	2	yes	—
100	C₄²×C₄₃	C₂⁴	1	2	yes	—
101	#10621885	—	2	64	no	—
102	C₄⋊Dic₄₃	—	2	16	no	—
103	Dic₄₃⋊C₄	—	2	32	no	—
104	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
105	C₄×Dic₄₃	C₂×D₄	1	8	yes	—
106	C₄×Dic₄₃	C₂⁴	1	2	yes	—
107	C₂×C₄₃⋊C₈	C₂×D₄	1	8	yes	—
108	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
109	Dic₁₇₂	—	2	32	no	—
110	C₈×D₄₃	C₂×D₄	1	32	yes	—
111	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
112	C₂²×D₄₃	#127	1	4	yes	—
113	C₂²×D₄₃	C₂×Q₁₆	1	8	yes	—
114	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
115	Q₈×C₄₃	—	2	16	no	—
116	Q₈×C₄₃	—	4	8	no	—
117	C₂×C₄×C₄₃	—	2	8	no	—
118	C₂×C₄×C₄₃	—	4	8	no	—
119	C₂×C₄×C₄₃	C₂×Q₁₆	1	8	yes	complemented
120	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
121	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
122	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
123	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
124	C₂×Dic₄₃	—	2	8	no	—
125	C₂×Dic₄₃	—	4	8	no	—
126	C₂×Dic₄₃	#127	1	4	yes	—
127	C₂×Dic₄₃	C₂×Q₁₆	1	8	yes	complemented
128	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
129	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
130	C₄×D₄₃	—	4	32	no	—
131	C₄×D₄₃	#127	1	8	yes	—
132	C₄×D₄₃	C₂×Q₁₆	1	32	yes	complemented
133	C₄×D₄₃	C₂²×D₄	1	8	yes	—
134	Dic₈₆	—	2	16	no	—
135	Dic₈₆	—	4	8	no	—
136	Dic₈₆	—	4	32	no	—
137	C₈×C₄₃	C₂²×D₄	1	8	yes	—
138	C₄₃⋊C₈	C₂²×D₄	1	8	yes	—
139	C₂²×#494	—	43	1	no	maximal, Sylow
140	C₂²×C₄₃	C₂×#127	1	2	yes	—
141	C₂²×C₄₃	C₂²×Q₁₆	1	4	yes	—
142	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
143	C₂×D₄₃	#494	1	16	yes	direct product factor
144	C₂×D₄₃	C₂×#127	1	4	yes	—
145	C₂×D₄₃	C₂²×Q₁₆	1	8	yes	—
146	C₄×C₄₃	—	4	8	no	—
147	C₄×C₄₃	C₂×#127	1	2	yes	—
148	C₄×C₄₃	C₂²×Q₁₆	1	8	yes	complemented
149	C₄×C₄₃	C₂³×D₄	1	2	yes	—
150	Dic₄₃	—	4	8	no	—
151	Dic₄₃	C₂×#127	1	4	yes	—
152	Dic₄₃	C₂²×Q₁₆	1	8	yes	complemented
153	C₂³×Q₁₆	—	43	4	no	—
154	C₂²×C₄⋊Q₈	—	43	2	no	—
155	C₂×#494	—	43	16	no	—
156	C₂×#494	—	43	1	no	—
157	C₂×#494	—	43	4	no	—
158	C₂×#494	—	43	2	no	—
159	C₂×#494	D₄₃	1	1	yes	characteristic, direct product factor
160	C₂²×C₄×C₈	—	43	1	no	—
161	C₂×C₄₃	C₂×#494	1	4	yes	complemented
162	C₂×C₄₃	C₂²×#127	1	1	yes	characteristic
163	C₂×C₄₃	C₂³×Q₁₆	1	2	yes	—
164	D₄₃	C₂×#494	1	8	yes	direct product factor
165	C₂³×Q₈	—	43	4	no	—
166	C₂²×Q₁₆	—	43	8	no	—
167	C₂²×Q₁₆	—	43	32	no	—
168	C₂²×Q₁₆	—	43	4	no	—
169	C₂²×Q₁₆	—	86	32	no	—
170	C₂²×Q₁₆	C₂×D₄₃	1	4	yes	—
171	C₂³×C₈	—	43	2	no	—
172	C₂×C₄⋊Q₈	—	43	4	no	—
173	C₂×C₄⋊Q₈	—	43	16	no	—
174	C₂×C₄⋊Q₈	—	43	2	no	—
175	C₂×C₄⋊Q₈	—	86	4	no	—
176	C₂×C₄⋊Q₈	—	86	8	no	—
177	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
178	C₂²×C₄⋊C₄	—	86	4	no	—
179	C₂²×C₄²	—	43	1	no	—
180	#494	—	43	32	no	—
181	#494	—	43	16	no	—
182	#494	—	43	8	no	—
183	#494	C₂×D₄₃	1	8	yes	direct product factor
184	C₂×C₄×C₈	—	43	2	no	—
185	C₂×C₄×C₈	—	43	1	no	—
186	C₂×C₄×C₈	—	43	8	no	—
187	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
188	C₄₃	C₂²×#494	1	1	yes	characteristic, complemented, Sylow
189	C₂²×Q₈	—	43	16	no	—
190	C₂²×Q₈	—	43	4	no	—
191	C₂²×Q₈	—	86	4	no	—
192	C₂²×Q₈	—	86	8	no	—
193	C₂²×Q₈	—	86	32	no	—
194	C₂²×Q₈	C₂²×D₄₃	1	4	yes	—
195	C₂³×C₄	—	43	2	no	—
196	C₂³×C₄	—	43	1	no	—
197	C₂³×C₄	—	86	4	no	—
198	C₂×Q₁₆	—	2	16	no	—
199	C₂×Q₁₆	—	43	32	no	—
200	C₂×Q₁₆	—	43	16	no	—
201	C₂×Q₁₆	—	86	128	no	—
202	C₂×Q₁₆	—	86	32	no	—
203	C₂×Q₁₆	—	86	16	no	—
204	C₂×Q₁₆	C₂²×D₄₃	1	16	yes	—
205	C₂²×C₈	—	43	2	no	—
206	C₂²×C₈	—	43	16	no	—
207	C₂²×C₈	—	43	8	no	—
208	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
209	C₄⋊Q₈	—	2	4	no	—
210	C₄⋊Q₈	—	43	16	no	—
211	C₄⋊Q₈	—	43	8	no	—
212	C₄⋊Q₈	—	86	32	no	—
213	C₄⋊Q₈	—	86	8	no	—
214	C₄⋊Q₈	—	86	4	no	—
215	C₄⋊Q₈	C₂²×D₄₃	1	8	yes	—
216	C₂×C₄⋊C₄	—	2	4	no	—
217	C₂×C₄⋊C₄	—	86	32	no	—
218	C₂×C₄⋊C₄	—	86	8	no	—
219	C₂×C₄⋊C₄	—	86	4	no	—
220	C₂×C₄²	—	43	2	no	—
221	C₂×C₄²	—	43	1	no	—
222	C₂×C₄²	—	43	4	no	—
223	C₂×C₄²	—	43	4	no	—
224	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
225	C₄×C₈	—	43	8	no	—
226	C₄×C₈	—	43	4	no	—
227	C₄×C₈	C₂²×D₄₃	1	4	yes	—
228	C₂⁴	—	43	1	no	—
229	C₂×Q₈	—	2	4	no	—
230	C₂×Q₈	—	2	16	no	—
231	C₂×Q₈	—	43	8	no	—
232	C₂×Q₈	—	86	16	no	—
233	C₂×Q₈	—	86	64	no	—
234	C₂×Q₈	—	86	4	no	—
235	C₂×Q₈	—	86	16	no	—
236	C₂×Q₈	—	172	16	no	—
237	C₂×Q₈	—	172	32	no	—
238	C₂×Q₈	C₂³×D₄₃	1	8	yes	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	43	2	no	—
241	C₂²×C₄	—	43	1	no	—
242	C₂²×C₄	—	43	16	no	—
243	C₂²×C₄	—	43	8	no	—
244	C₂²×C₄	—	43	2	no	—
245	C₂²×C₄	—	43	8	no	—
246	C₂²×C₄	—	43	2	no	—
247	C₂²×C₄	—	86	16	no	—
248	C₂²×C₄	—	86	4	no	—
249	C₂²×C₄	—	172	16	no	—
250	C₂²×C₄	D₄×D₄₃	1	2	yes	—
251	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
252	Q₁₆	—	2	32	no	—
253	Q₁₆	—	86	64	no	—
254	Q₁₆	—	86	32	no	—
255	C₂×C₈	—	43	8	no	—
256	C₂×C₈	—	43	4	no	—
257	C₂×C₈	—	43	32	no	—
258	C₂×C₈	D₄×D₄₃	1	8	yes	—
259	C₂×C₈	C₂³×D₄₃	1	4	yes	—
260	C₄⋊C₄	—	2	16	no	—
261	C₄⋊C₄	—	86	32	no	—
262	C₄⋊C₄	—	86	16	no	—
263	C₄²	—	43	2	no	—
264	C₄²	—	43	8	no	—
265	C₄²	—	43	2	no	—
266	C₄²	D₄×D₄₃	1	2	yes	—
267	C₄²	C₂³×D₄₃	1	2	yes	—
268	C₂³	—	43	8	no	—
269	C₂³	—	43	4	no	—
270	C₂³	—	43	2	no	—
271	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
272	Q₈	—	2	16	no	—
273	Q₈	—	4	8	no	—
274	Q₈	—	86	16	no	—
275	Q₈	—	172	32	no	—
276	Q₈	—	172	8	no	—
277	C₂×C₄	—	2	8	no	—
278	C₂×C₄	—	4	8	no	—
279	C₂×C₄	—	43	8	no	—
280	C₂×C₄	—	43	4	no	—
281	C₂×C₄	—	43	4	no	—
282	C₂×C₄	—	43	2	no	—
283	C₂×C₄	—	43	32	no	—
284	C₂×C₄	—	43	8	no	—
285	C₂×C₄	—	43	8	no	—
286	C₂×C₄	—	86	8	no	—
287	C₂×C₄	—	172	32	no	—
288	C₂×C₄	—	172	8	no	—
289	C₂×C₄	Q₁₆×D₄₃	1	8	yes	complemented
290	C₂×C₄	C₂×D₄×D₄₃	1	4	yes	—
291	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
292	C₂×C₄	C₂×D₄×D₄₃	1	4	yes	—
293	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
294	C₈	—	43	8	no	—
295	C₈	C₂×D₄×D₄₃	1	8	yes	—
296	C₂²	—	43	8	no	—
297	C₂²	—	43	16	no	—
298	C₂²	—	43	4	no	—
299	C₂²	#127×D₄₃	1	2	yes	—
300	C₂²	C₂×Q₁₆×D₄₃	1	4	yes	—
301	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
302	C₄	—	4	8	no	—
303	C₄	—	43	8	no	—
304	C₄	—	43	4	no	—
305	C₄	—	172	8	no	—
306	C₄	#127×D₄₃	1	2	yes	—
307	C₄	C₂×Q₁₆×D₄₃	1	8	yes	complemented
308	C₄	C₂²×D₄×D₄₃	1	2	yes	—
309	C₂	—	43	8	no	—
310	C₂	#494×D₄₃	1	4	yes	direct product factor
311	C₂	C₂×#127×D₄₃	1	1	yes	characteristic
312	C₂	C₂²×Q₁₆×D₄₃	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#494	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂³×D₄₃	C₂×D₄
hypercenter	C₂×#494	D₄₃
hypocenter	C₄₃	C₂²×#494
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

Complements

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

N	H ≅ G/N	type
3. C₂×#14583279	C₂	semidirect
4. C₂×#14583278	C₂	semidirect
5. C₂×#14583277	C₂	semidirect
6. #494×D₄₃	C₂	direct (N × H)
8. C₂×C₄₃×#494	C₂	semidirect
22. #14583279	C₂²	semidirect
23. #14583278	C₂²	semidirect
24. #14583277	C₂²	semidirect
30. C₄₃×#494	C₂²	semidirect
85. C₂×C₄×D₄₃	Q₁₆	semidirect
119. C₂×C₄×C₄₃	C₂×Q₁₆	semidirect
127. C₂×Dic₄₃	C₂×Q₁₆	semidirect
132. C₄×D₄₃	C₂×Q₁₆	semidirect
143. C₂×D₄₃	#494	direct (N × H)
148. C₄×C₄₃	C₂²×Q₁₆	semidirect
152. Dic₄₃	C₂²×Q₁₆	semidirect
159. C₂×#494	D₄₃	direct (N × H)
161. C₂×C₄₃	C₂×#494	semidirect
164. D₄₃	C₂×#494	direct (N × H)
183. #494	C₂×D₄₃	direct (N × H)
188. C₄₃	C₂²×#494	semidirect
289. C₂×C₄	Q₁₆×D₄₃	semidirect
307. C₄	C₂×Q₁₆×D₄₃	semidirect
310. C₂	#494×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
C₂²×Q₁₆×D₄₃	2
C₂×C₄⋊Q₈×D₄₃	2
C₂×#14583279	2
C₂×#14583278	2
C₂×#14583277	2
#494×D₄₃	2
C₂×C₄×C₈×D₄₃	2
C₂×C₄₃×#494	2
C₂²×#494	43

Subgroups — C2×#494×D43 #25966001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#494×D₄₃ #25966001