Subgroups — C₄₃×#29799 #24949816

Order 11008.

866 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#462	C₂	1	2	yes	maximal
2	C₄₃×#2868	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2295	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2043	C₂	1	4	yes	maximal
5	C₄₃×#2016	C₂	1	4	yes	maximal
6	C₄₃×#1981	C₂	1	2	yes	maximal
7	C₄₃×#1831	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₁₆×C₄₃	C₂²	1	4	yes	—
9	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Q₈×C₄₃	C₂²	1	4	yes	—
11	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₄₃×#462	—	2	8	no	—
13	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
14	C₂×#103×C₄₃	C₂²	1	4	yes	—
15	C₂×#103×C₄₃	C₂²	1	8	yes	—
16	C₄₃×#391	C₂²	1	2	yes	—
17	C₄₃×#389	C₂²	1	2	yes	—
18	C₄₃×#387	—	2	2	no	—
19	C₄₃×#384	—	2	1	no	—
20	C₄₃×#384	—	2	2	no	—
21	C₄₃×#384	—	2	1	no	—
22	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
23	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#376	—	2	1	no	—
25	C₄³×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#336	C₂²	1	4	yes	—
27	C₂²×Q₈×C₄₃	C₂³	1	4	yes	—
28	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
29	C₂×Q₁₆×C₄₃	—	2	8	no	—
30	C₂×Q₁₆×C₄₃	—	4	8	no	—
31	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
32	C₄⋊Q₈×C₄₃	—	2	4	no	—
33	C₄⋊Q₈×C₄₃	—	2	4	no	—
34	C₄⋊Q₈×C₄₃	—	4	8	no	—
35	C₄×Q₈×C₄₃	—	2	2	no	—
36	C₄×Q₈×C₄₃	D₄	1	4	yes	—
37	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
38	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
39	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
40	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
44	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂×C₄²×C₄₃	—	2	1	no	—
46	C₂×C₄²×C₄₃	—	2	1	no	—
47	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₄₃	D₄	1	2	yes	—
49	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
51	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
52	C₄⋊C₈×C₄₃	—	2	4	no	—
53	#103×C₄₃	—	2	8	no	—
54	#103×C₄₃	—	4	8	no	—
55	#95×C₄₃	—	2	2	no	—
56	#95×C₄₃	—	2	2	no	—
57	#95×C₄₃	—	2	2	no	—
58	#95×C₄₃	—	2	1	no	—
59	C₂×Q₈×C₄₃	—	2	1	no	—
60	C₂×Q₈×C₄₃	—	2	4	no	—
61	C₂×Q₈×C₄₃	—	2	4	no	—
62	C₂×Q₈×C₄₃	—	2	4	no	—
63	C₂×Q₈×C₄₃	—	2	8	no	—
64	C₂×Q₈×C₄₃	—	2	8	no	—
65	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₄₃	—	2	1	no	—
67	C₂²×C₄×C₄₃	—	2	1	no	—
68	C₂²×C₄×C₄₃	—	2	2	no	—
69	C₂²×C₄×C₄₃	—	2	4	no	—
70	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
72	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
73	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
75	Q₁₆×C₄₃	—	4	16	no	—
76	C₂×C₈×C₄₃	—	2	4	no	—
77	C₂×C₈×C₄₃	—	2	8	no	—
78	C₄⋊C₄×C₄₃	—	2	4	no	—
79	C₄⋊C₄×C₄₃	—	2	1	no	—
80	C₄⋊C₄×C₄₃	—	2	4	no	—
81	C₄⋊C₄×C₄₃	—	4	8	no	—
82	C₄⋊C₄×C₄₃	—	4	8	no	—
83	C₄⋊C₄×C₄₃	—	4	4	no	—
84	C₄⋊C₄×C₄₃	—	4	4	no	—
85	C₄⋊C₄×C₄₃	—	4	4	no	—
86	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
87	C₄²×C₄₃	—	2	4	no	—
88	C₄²×C₄₃	—	2	4	no	—
89	C₄²×C₄₃	—	2	2	no	—
90	C₄²×C₄₃	—	2	4	no	—
91	C₄²×C₄₃	—	4	2	no	—
92	C₄²×C₄₃	Q₁₆	1	4	yes	complemented
93	C₄²×C₄₃	C₂×D₄	1	2	yes	—
94	C₄²×C₄₃	#41	1	2	yes	—
95	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
96	Q₈×C₄₃	—	2	4	no	—
97	Q₈×C₄₃	—	4	2	no	—
98	Q₈×C₄₃	—	4	4	no	—
99	Q₈×C₄₃	—	4	4	no	—
100	Q₈×C₄₃	—	4	8	no	—
101	C₂×C₄×C₄₃	—	2	2	no	—
102	C₂×C₄×C₄₃	—	2	2	no	—
103	C₂×C₄×C₄₃	—	2	2	no	—
104	C₂×C₄×C₄₃	—	2	2	no	—
105	C₂×C₄×C₄₃	—	2	2	no	—
106	C₂×C₄×C₄₃	—	2	2	no	—
107	C₂×C₄×C₄₃	—	2	2	no	—
108	C₂×C₄×C₄₃	—	4	2	no	—
109	C₂×C₄×C₄₃	—	4	2	no	—
110	C₂×C₄×C₄₃	—	4	4	no	—
111	C₂×C₄×C₄₃	—	4	2	no	—
112	C₂×C₄×C₄₃	—	4	8	no	—
113	C₂×C₄×C₄₃	—	4	2	no	—
114	C₂×C₄×C₄₃	—	4	2	no	—
115	C₂×C₄×C₄₃	#121	1	2	yes	—
116	C₂×C₄×C₄₃	#121	1	2	yes	—
117	C₂×C₄×C₄₃	C₂×Q₁₆	1	4	yes	—
118	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
119	C₂×C₄×C₄₃	#137	1	4	yes	—
120	C₂×C₄×C₄₃	#137	1	2	yes	—
121	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
122	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
123	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
124	C₈×C₄₃	—	4	4	no	—
125	#29799	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
127	C₂²×C₄₃	#535	1	2	yes	—
128	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
129	C₂²×C₄₃	C₂×#137	1	2	yes	—
130	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
131	C₄×C₄₃	—	2	4	no	—
132	C₄×C₄₃	—	2	4	no	—
133	C₄×C₄₃	—	2	2	no	—
134	C₄×C₄₃	—	4	2	no	—
135	C₄×C₄₃	—	4	2	no	—
136	C₄×C₄₃	—	8	4	no	—
137	C₄×C₄₃	—	8	2	no	—
138	C₄×C₄₃	#462	1	4	yes	—
139	C₄×C₄₃	#535	1	2	yes	—
140	C₄×C₄₃	#540	1	2	yes	—
141	C₂×#462	C₂×C₄₃	1	2	yes	—
142	#2868	C₂×C₄₃	1	1	yes	characteristic
143	#2295	C₂×C₄₃	1	1	yes	characteristic
144	#2043	C₂×C₄₃	1	4	yes	—
145	#2016	C₂×C₄₃	1	4	yes	—
146	#1981	C₂×C₄₃	1	2	yes	—
147	#1831	C₂×C₄₃	1	1	yes	characteristic
148	C₂×C₄₃	#2619	1	1	yes	characteristic
149	C₂×C₄₃	C₂×#462	1	1	yes	characteristic
150	C₂×C₄₃	#3039	1	1	yes	characteristic
151	C₂×C₄₃	#3209	1	2	yes	—
152	C₂×C₄₃	#3218	1	2	yes	—
153	C₂²×Q₁₆	C₂²×C₄₃	1	4	yes	—
154	C₂×C₄⋊Q₈	C₂²×C₄₃	1	2	yes	—
155	C₂×C₄⋊Q₈	C₂²×C₄₃	1	4	yes	—
156	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
157	#462	—	2	8	no	—
158	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
159	C₂×#103	C₂²×C₄₃	1	4	yes	—
160	C₂×#103	C₂²×C₄₃	1	8	yes	—
161	#391	C₂²×C₄₃	1	2	yes	—
162	#389	C₂²×C₄₃	1	2	yes	—
163	#387	—	2	2	no	—
164	#384	—	2	1	no	—
165	#384	—	2	2	no	—
166	#384	—	2	1	no	—
167	C₄×C₄⋊C₄	—	2	1	no	—
168	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
169	#376	—	2	1	no	—
170	C₄³	C₂²×C₄₃	1	1	yes	characteristic
171	#336	C₂²×C₄₃	1	4	yes	—
172	C₄₃	#29799	1	1	yes	characteristic, direct product factor, Sylow
173	C₂²×Q₈	C₂³×C₄₃	1	4	yes	—
174	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
175	C₂×Q₁₆	—	2	8	no	—
176	C₂×Q₁₆	—	4	8	no	—
177	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
178	C₄⋊Q₈	—	2	4	no	—
179	C₄⋊Q₈	—	2	4	no	—
180	C₄⋊Q₈	—	4	8	no	—
181	C₄×Q₈	—	2	2	no	—
182	C₄×Q₈	D₄×C₄₃	1	4	yes	—
183	C₂×C₄⋊C₄	—	2	1	no	—
184	C₂×C₄⋊C₄	—	2	4	no	—
185	C₂×C₄⋊C₄	—	2	4	no	—
186	C₂×C₄⋊C₄	—	2	2	no	—
187	C₂×C₄⋊C₄	—	2	2	no	—
188	C₂×C₄⋊C₄	—	2	2	no	—
189	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
190	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
191	C₂×C₄²	—	2	1	no	—
192	C₂×C₄²	—	2	1	no	—
193	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
194	C₂×C₄²	D₄×C₄₃	1	2	yes	—
195	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
196	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
197	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
198	C₄⋊C₈	—	2	4	no	—
199	#103	—	2	8	no	—
200	#103	—	4	8	no	—
201	#95	—	2	2	no	—
202	#95	—	2	2	no	—
203	#95	—	2	2	no	—
204	#95	—	2	1	no	—
205	C₂×Q₈	—	2	1	no	—
206	C₂×Q₈	—	2	4	no	—
207	C₂×Q₈	—	2	4	no	—
208	C₂×Q₈	—	2	4	no	—
209	C₂×Q₈	—	2	8	no	—
210	C₂×Q₈	—	2	8	no	—
211	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
212	C₂²×C₄	—	2	1	no	—
213	C₂²×C₄	—	2	1	no	—
214	C₂²×C₄	—	2	2	no	—
215	C₂²×C₄	—	2	4	no	—
216	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
217	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
218	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
219	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
220	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
221	Q₁₆	—	4	16	no	—
222	C₂×C₈	—	2	4	no	—
223	C₂×C₈	—	2	8	no	—
224	C₄⋊C₄	—	2	4	no	—
225	C₄⋊C₄	—	2	1	no	—
226	C₄⋊C₄	—	2	4	no	—
227	C₄⋊C₄	—	4	8	no	—
228	C₄⋊C₄	—	4	8	no	—
229	C₄⋊C₄	—	4	4	no	—
230	C₄⋊C₄	—	4	4	no	—
231	C₄⋊C₄	—	4	4	no	—
232	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
233	C₄²	—	2	4	no	—
234	C₄²	—	2	4	no	—
235	C₄²	—	2	2	no	—
236	C₄²	—	2	4	no	—
237	C₄²	—	4	2	no	—
238	C₄²	Q₁₆×C₄₃	1	4	yes	complemented
239	C₄²	C₂×D₄×C₄₃	1	2	yes	—
240	C₄²	#41×C₄₃	1	2	yes	—
241	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
242	Q₈	—	2	4	no	—
243	Q₈	—	4	2	no	—
244	Q₈	—	4	4	no	—
245	Q₈	—	4	4	no	—
246	Q₈	—	4	8	no	—
247	C₂×C₄	—	2	2	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	2	2	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	4	2	no	—
255	C₂×C₄	—	4	2	no	—
256	C₂×C₄	—	4	4	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	—	4	8	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	#121×C₄₃	1	2	yes	—
262	C₂×C₄	#121×C₄₃	1	2	yes	—
263	C₂×C₄	C₂×Q₁₆×C₄₃	1	4	yes	—
264	C₂×C₄	C₂×Q₁₆×C₄₃	1	2	yes	—
265	C₂×C₄	#137×C₄₃	1	4	yes	—
266	C₂×C₄	#137×C₄₃	1	2	yes	—
267	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
268	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
269	C₂×C₄	H(5,𝔽₂)×C₄₃	1	4	yes	—
270	C₈	—	4	4	no	—
271	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
272	C₂²	C₄₃×#535	1	2	yes	—
273	C₂²	C₂²×Q₁₆×C₄₃	1	1	yes	characteristic
274	C₂²	C₂×#137×C₄₃	1	2	yes	—
275	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
276	C₄	—	2	4	no	—
277	C₄	—	2	4	no	—
278	C₄	—	2	2	no	—
279	C₄	—	4	2	no	—
280	C₄	—	4	2	no	—
281	C₄	—	8	4	no	—
282	C₄	—	8	2	no	—
283	C₄	C₄₃×#462	1	4	yes	—
284	C₄	C₄₃×#535	1	2	yes	—
285	C₄	C₄₃×#540	1	2	yes	—
286	C₂	C₄₃×#2619	1	1	yes	characteristic
287	C₂	C₂×C₄₃×#462	1	1	yes	characteristic
288	C₂	C₄₃×#3039	1	1	yes	characteristic
289	C₂	C₄₃×#3209	1	2	yes	—
290	C₂	C₄₃×#3218	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄³×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
92. C₄²×C₄₃	Q₁₆	semidirect
125. #29799	C₄₃	direct (N × H)
172. C₄₃	#29799	direct (N × H)
238. C₄²	Q₁₆×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#462	2
C₄₃×#2868	2
C₄₃×#2295	2
C₄₃×#2043	2
C₄₃×#2016	2
C₄₃×#1981	2
C₄₃×#1831	2
#29799	43

Subgroups — C43×#29799 #24949816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29799 #24949816