Subgroups — #24989454

Order 11008.

478 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582950	C₂	1	1	yes	maximal, characteristic
2	#19134572	C₂	1	2	yes	maximal
3	C₂×#14582650	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132429	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₃×#335	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
7	#14582950	—	2	2	no	—
8	#14582950	—	2	2	no	—
9	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
10	C₂×Dic₄₃⋊C₈	C₄	1	1	yes	characteristic
11	C₂×Dic₄₃⋊C₈	C₄	1	1	yes	characteristic
12	C₂×(C₂×D₄₃)⋊C₈	—	2	2	no	—
13	C₂×(C₂×D₄₃)⋊C₈	C₄	1	1	yes	characteristic
14	C₂×(C₂×D₄₃)⋊C₈	C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	#14582653	—	2	2	no	—
17	#14582650	—	2	2	no	—
18	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#335	—	2	2	no	—
21	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
23	C₂²×C₄×D₄₃	Q₈	1	1	yes	characteristic
24	C₂²×C₄₃⋊C₈	—	2	2	no	—
25	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
29	C₂×C₄×Dic₄₃	Q₈	1	1	yes	characteristic
30	C₄²×D₄₃	—	2	1	no	—
31	C₄²×D₄₃	—	2	1	no	—
32	C₄²×D₄₃	—	2	1	no	—
33	C₄²×D₄₃	—	2	1	no	—
34	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
35	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
36	Dic₄₃⋊C₈	—	2	2	no	—
37	Dic₄₃⋊C₈	—	2	2	no	—
38	(C₂×D₄₃)⋊C₈	—	2	2	no	—
39	(C₂×D₄₃)⋊C₈	—	2	2	no	—
40	(C₂×D₄₃)⋊C₈	—	4	4	no	—
41	C₄×C₄₃⋊C₈	—	2	1	no	—
42	C₄×C₄₃⋊C₈	—	2	1	no	—
43	C₂²×C₈×C₄₃	—	2	2	no	—
44	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
47	C₄⋊C₈×C₄₃	—	2	2	no	—
48	C₄⋊C₈×C₄₃	—	2	2	no	—
49	C₄×C₈×C₄₃	D₄	1	2	yes	—
50	C₄×C₈×C₄₃	D₄	1	2	yes	—
51	C₂³×D₄₃	C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
55	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
57	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₄×D₄₃	—	2	1	no	—
59	C₂×C₄×D₄₃	—	2	1	no	—
60	C₂×C₄×D₄₃	—	2	2	no	—
61	C₂×C₄×D₄₃	—	2	1	no	—
62	C₂×C₄×D₄₃	—	2	1	no	—
63	C₂×C₄×D₄₃	—	2	1	no	—
64	C₂×C₄×D₄₃	—	2	1	no	—
65	C₂×C₄×D₄₃	—	2	2	no	—
66	C₂×C₄×D₄₃	—	2	2	no	—
67	C₂×C₄×D₄₃	—	2	2	no	—
68	C₂×C₄×D₄₃	—	2	2	no	—
69	C₂×C₄×D₄₃	—	2	2	no	—
70	C₂×C₈×C₄₃	—	2	2	no	—
71	C₂×C₈×C₄₃	—	2	2	no	—
72	C₂×C₈×C₄₃	—	4	2	no	—
73	C₂×C₈×C₄₃	—	4	2	no	—
74	C₂×C₈×C₄₃	—	4	2	no	—
75	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
76	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
77	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₄₃	#41	1	1	yes	characteristic
80	C₄²×C₄₃	#41	1	1	yes	characteristic
81	C₄×Dic₄₃	—	2	1	no	—
82	C₄×Dic₄₃	—	2	1	no	—
83	C₄×Dic₄₃	—	2	1	no	—
84	C₄×Dic₄₃	—	2	1	no	—
85	C₄×Dic₄₃	—	2	1	no	—
86	C₄×Dic₄₃	—	2	1	no	—
87	C₂×C₄₃⋊C₈	—	2	1	no	—
88	C₂×C₄₃⋊C₈	—	2	1	no	—
89	C₂×C₄₃⋊C₈	—	2	2	no	—
90	C₂×C₄₃⋊C₈	—	2	2	no	—
91	C₂×C₄₃⋊C₈	—	4	2	no	—
92	C₂×C₄₃⋊C₈	—	4	2	no	—
93	C₂×C₄₃⋊C₈	—	4	2	no	—
94	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
95	C₂²×D₄₃	—	2	1	no	—
96	C₂²×D₄₃	—	2	2	no	—
97	C₂²×D₄₃	—	2	2	no	—
98	C₂²×D₄₃	—	2	1	no	—
99	C₂²×D₄₃	#108	1	2	yes	—
100	C₂×C₄×C₄₃	—	2	1	no	—
101	C₂×C₄×C₄₃	—	2	1	no	—
102	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
104	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
105	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
106	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
107	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
108	C₂×C₄×C₄₃	#131	1	2	yes	—
109	C₂×C₄×C₄₃	#131	1	2	yes	—
110	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
111	C₂×C₄×C₄₃	#137	1	2	yes	—
112	C₂×Dic₄₃	—	2	1	no	—
113	C₂×Dic₄₃	—	2	1	no	—
114	C₂×Dic₄₃	—	2	1	no	—
115	C₂×Dic₄₃	—	2	1	no	—
116	C₂×Dic₄₃	—	2	2	no	—
117	C₂×Dic₄₃	—	2	2	no	—
118	C₂×Dic₄₃	#108	1	2	yes	—
119	C₄×D₄₃	—	2	4	no	—
120	C₄×D₄₃	—	2	4	no	—
121	C₄×D₄₃	—	4	1	no	—
122	C₄×D₄₃	—	4	1	no	—
123	C₄×D₄₃	—	4	2	no	—
124	C₄×D₄₃	—	4	2	no	—
125	C₄×D₄₃	—	4	1	no	—
126	C₄×D₄₃	—	4	1	no	—
127	C₈×C₄₃	—	2	2	no	—
128	C₈×C₄₃	—	2	2	no	—
129	C₈×C₄₃	—	8	2	no	—
130	C₄₃⋊C₈	—	4	1	no	—
131	C₄₃⋊C₈	—	4	1	no	—
132	C₄₃⋊C₈	—	8	2	no	—
133	#8600	—	43	1	no	maximal, Sylow
134	C₂²×C₄₃	#380	1	1	yes	characteristic
135	C₂²×C₄₃	#424	1	2	yes	—
136	C₂²×C₄₃	#428	1	2	yes	—
137	C₂²×C₄₃	C₂×#108	1	1	yes	characteristic
138	C₂²×C₄₃	C₂×#108	1	1	yes	characteristic
139	C₂×D₄₃	—	2	2	no	—
140	C₂×D₄₃	—	2	4	no	—
141	C₂×D₄₃	—	4	1	no	—
142	C₂×D₄₃	—	4	1	no	—
143	C₂×D₄₃	—	4	2	no	—
144	C₄×C₄₃	—	2	1	no	—
145	C₄×C₄₃	—	2	1	no	—
146	C₄×C₄₃	#408	1	1	yes	characteristic
147	C₄×C₄₃	#408	1	1	yes	characteristic
148	C₄×C₄₃	#433	1	2	yes	—
149	C₄×C₄₃	#468	1	2	yes	—
150	C₄×C₄₃	#469	1	1	yes	characteristic
151	C₄×C₄₃	#470	1	1	yes	characteristic
152	Dic₄₃	—	2	2	no	—
153	Dic₄₃	—	4	1	no	—
154	Dic₄₃	—	4	1	no	—
155	C₂×#431	—	43	1	no	—
156	#1797	—	43	2	no	—
157	C₂×#335	D₄₃	1	1	yes	characteristic, complemented
158	C₂×#334	—	43	1	no	—
159	#1277	—	43	2	no	—
160	C₂×C₄₃	#1573	1	2	yes	—
161	C₂×C₄₃	#1574	1	2	yes	—
162	C₂×C₄₃	#1798	1	1	yes	characteristic
163	C₂×C₄₃	#1809	1	1	yes	characteristic
164	C₂×C₄₃	#1810	1	1	yes	characteristic
165	D₄₃	—	4	2	no	—
166	C₂²×C₄²	—	43	1	no	—
167	#431	—	86	2	no	—
168	#431	—	86	2	no	—
169	C₂×C₄⋊C₈	—	43	1	no	—
170	C₂×C₄⋊C₈	—	43	1	no	—
171	C₂×C₄⋊C₈	—	43	2	no	—
172	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
173	C₂×C₂²⋊C₈	—	43	1	no	—
174	C₂×C₂²⋊C₈	—	43	1	no	—
175	C₂×C₂²⋊C₈	—	86	2	no	—
176	C₂×C₄×C₈	—	43	1	no	—
177	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
178	#336	—	86	2	no	—
179	#335	—	2	2	no	—
180	#334	—	86	2	no	—
181	C₄₃	#8600	1	1	yes	characteristic, complemented, Sylow
182	C₂³×C₄	—	43	1	no	—
183	C₂³×C₄	—	43	1	no	—
184	C₂³×C₄	—	43	1	no	—
185	C₂²×C₈	—	2	2	no	—
186	C₂²×C₈	—	43	1	no	—
187	C₂²×C₈	—	43	1	no	—
188	C₂²×C₈	—	86	2	no	—
189	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
190	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
191	C₂×C₄²	—	43	1	no	—
192	C₂×C₄²	—	43	1	no	—
193	C₂×C₄²	—	43	1	no	—
194	C₂×C₄²	—	86	1	no	—
195	C₂×C₄²	—	86	1	no	—
196	C₂×C₄²	—	86	1	no	—
197	C₂×C₄²	—	86	1	no	—
198	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
199	C₄⋊C₈	—	2	2	no	—
200	C₄⋊C₈	—	2	2	no	—
201	C₄⋊C₈	—	86	2	no	—
202	C₄⋊C₈	—	86	2	no	—
203	C₄⋊C₈	—	86	2	no	—
204	C₄⋊C₈	—	86	2	no	—
205	C₂²⋊C₈	—	86	2	no	—
206	C₂²⋊C₈	—	86	2	no	—
207	C₂²⋊C₈	—	172	4	no	—
208	C₄×C₈	—	86	1	no	—
209	C₄×C₈	—	86	1	no	—
210	C₄×C₈	D₁₇₂	1	2	yes	—
211	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
212	C₂⁴	—	43	1	no	—
213	C₂²×C₄	—	43	1	no	—
214	C₂²×C₄	—	43	1	no	—
215	C₂²×C₄	—	43	1	no	—
216	C₂²×C₄	—	86	2	no	—
217	C₂²×C₄	—	86	2	no	—
218	C₂²×C₄	—	86	1	no	—
219	C₂²×C₄	—	86	1	no	—
220	C₂²×C₄	—	86	1	no	—
221	C₂²×C₄	—	86	1	no	—
222	C₂²×C₄	—	86	1	no	—
223	C₂²×C₄	—	86	1	no	—
224	C₂²×C₄	—	86	2	no	—
225	C₂²×C₄	—	86	2	no	—
226	C₂²×C₄	—	86	2	no	—
227	C₂²×C₄	—	86	2	no	—
228	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
229	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
230	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
231	C₂×C₈	—	2	2	no	—
232	C₂×C₈	—	2	2	no	—
233	C₂×C₈	—	4	2	no	—
234	C₂×C₈	—	4	2	no	—
235	C₂×C₈	—	4	2	no	—
236	C₂×C₈	—	86	1	no	—
237	C₂×C₈	—	86	1	no	—
238	C₂×C₈	—	86	2	no	—
239	C₂×C₈	—	86	2	no	—
240	C₂×C₈	—	172	2	no	—
241	C₂×C₈	—	172	2	no	—
242	C₂×C₈	—	172	2	no	—
243	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
244	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
245	C₄²	—	86	1	no	—
246	C₄²	—	86	1	no	—
247	C₄²	—	86	1	no	—
248	C₄²	—	86	1	no	—
249	C₄²	—	86	1	no	—
250	C₄²	—	86	1	no	—
251	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
252	C₄²	#10621900	1	1	yes	characteristic
253	C₄²	#10621902	1	1	yes	characteristic
254	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
255	C₂³	—	43	2	no	—
256	C₂³	—	86	2	no	—
257	C₂³	—	86	2	no	—
258	C₂³	—	86	1	no	—
259	C₂³	—	86	1	no	—
260	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	43	2	no	—
264	C₂×C₄	—	86	4	no	—
265	C₂×C₄	—	86	4	no	—
266	C₂×C₄	—	86	1	no	—
267	C₂×C₄	—	86	1	no	—
268	C₂×C₄	—	86	2	no	—
269	C₂×C₄	—	86	2	no	—
270	C₂×C₄	—	86	1	no	—
271	C₂×C₄	—	86	1	no	—
272	C₂×C₄	—	172	1	no	—
273	C₂×C₄	—	172	1	no	—
274	C₂×C₄	—	172	2	no	—
275	C₂×C₄	—	172	1	no	—
276	C₂×C₄	—	172	1	no	—
277	C₂×C₄	—	172	2	no	—
278	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
279	C₂×C₄	#13063283	1	1	yes	characteristic
280	C₂×C₄	#13063296	1	1	yes	characteristic
281	C₂×C₄	#13063300	1	1	yes	characteristic
282	C₂×C₄	#13063301	1	1	yes	characteristic
283	C₂×C₄	#13063305	1	1	yes	characteristic
284	C₂×C₄	#13063331	1	2	yes	—
285	C₂×C₄	#13063333	1	2	yes	—
286	C₂×C₄	#13063349	1	2	yes	—
287	C₂×C₄	#13063357	1	2	yes	—
288	C₈	—	2	2	no	—
289	C₈	—	2	2	no	—
290	C₈	—	8	2	no	—
291	C₈	—	344	2	no	—
292	C₈	—	172	1	no	—
293	C₈	—	172	1	no	—
294	C₂²	—	86	2	no	—
295	C₂²	—	86	4	no	—
296	C₂²	—	172	1	no	—
297	C₂²	—	172	1	no	—
298	C₂²	—	172	2	no	—
299	C₂²	#14582756	1	1	yes	characteristic
300	C₂²	#14582924	1	2	yes	—
301	C₂²	#14582940	1	2	yes	—
302	C₂²	#108×D₄₃	1	1	yes	characteristic
303	C₂²	#108×D₄₃	1	1	yes	characteristic
304	C₄	—	2	1	no	—
305	C₄	—	2	1	no	—
306	C₄	—	86	2	no	—
307	C₄	—	172	1	no	—
308	C₄	—	172	1	no	—
309	C₄	#14582865	1	1	yes	characteristic
310	C₄	#14582867	1	1	yes	characteristic
311	C₄	#14582959	1	2	yes	—
312	C₄	#14583146	1	2	yes	—
313	C₄	#14583149	1	1	yes	characteristic
314	C₄	#14583154	1	1	yes	characteristic
315	C₂	—	172	2	no	—
316	C₂	#19133379	1	2	yes	—
317	C₂	#19133385	1	2	yes	—
318	C₂	#19134576	1	1	yes	characteristic
319	C₂	#19134629	1	1	yes	characteristic
320	C₂	#19134630	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#335	C₂
socle	C₂³×C₄₃	C₂×C₄⋊C₄
prime radical	C₂³×D₄₃	C₄⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×#335	D₄₃
hypocenter	C₄₃	#8600
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
3. C₂×#14582650	C₂	semidirect
4. #19132429	C₂	semidirect
5. C₂×C₄₃×#335	C₂	semidirect
157. C₂×#335	D₄₃	semidirect
181. C₄₃	#8600	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582950	2
#19134572	2
C₂×#14582650	2
#19132429	2
C₂×C₄₃×#335	2
#8600	43