Subgroups — C₄₃×#29994 #24950011

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#2293	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2086	C₂	1	4	yes	maximal, complemented
4	C₄₃×#2067	C₂	1	4	yes	maximal
5	C₄₃×#1947	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1842	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1802	C₂	1	2	yes	maximal
8	C₂×#125×C₄₃	—	2	1	no	—
9	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×#117×C₄₃	—	2	1	no	—
11	C₂×#107×C₄₃	C₂²	1	4	yes	—
12	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
13	C₂×C₄⋊C₈×C₄₃	C₂²	1	4	yes	—
14	C₂×#102×C₄₃	C₂²	1	4	yes	—
15	C₄₃×#390	C₂²	1	2	yes	—
16	C₄₃×#389	—	2	2	no	—
17	C₄₃×#389	C₂²	1	4	yes	—
18	C₄₃×#389	C₂²	1	2	yes	—
19	C₄₃×#388	—	2	2	no	—
20	C₄₃×#384	C₂²	1	2	yes	—
21	C₄₃×#382	—	2	1	no	—
22	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
24	C₄³×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#340	C₂²	1	4	yes	—
26	C₄₃×#340	C₂²	1	4	yes	—
27	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
28	C₂³×C₄×C₄₃	—	2	1	no	—
29	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
30	#125×C₄₃	—	4	4	no	—
31	C₄×D₄×C₄₃	—	2	2	no	—
32	C₄×D₄×C₄₃	Q₈	1	4	yes	—
33	#117×C₄₃	—	4	4	no	—
34	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
35	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
37	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
39	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
40	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
43	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
44	C₂×C₄²×C₄₃	—	2	1	no	—
45	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₄₃	D₄	1	2	yes	—
47	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
49	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
50	#107×C₄₃	—	4	4	no	—
51	C₄⋊C₈×C₄₃	—	2	4	no	—
52	C₄⋊C₈×C₄₃	—	4	4	no	—
53	#102×C₄₃	—	4	4	no	—
54	#95×C₄₃	—	2	2	no	—
55	#95×C₄₃	—	2	1	no	—
56	#95×C₄₃	—	2	4	no	—
57	C₂⁴×C₄₃	—	2	1	no	—
58	C₂×D₄×C₄₃	—	2	1	no	—
59	C₂×D₄×C₄₃	—	2	2	no	—
60	C₂×D₄×C₄₃	—	2	2	no	—
61	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
62	C₂²×C₄×C₄₃	—	2	4	no	—
63	C₂²×C₄×C₄₃	—	2	1	no	—
64	C₂²×C₄×C₄₃	—	2	2	no	—
65	C₂²×C₄×C₄₃	—	2	4	no	—
66	C₂²×C₄×C₄₃	—	4	2	no	—
67	C₂²×C₄×C₄₃	—	4	2	no	—
68	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
69	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
71	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
73	C₂×C₈×C₄₃	—	2	4	no	—
74	C₂×C₈×C₄₃	—	2	4	no	—
75	C₂×C₈×C₄₃	—	2	4	no	—
76	C₄⋊C₄×C₄₃	—	2	1	no	—
77	C₄⋊C₄×C₄₃	—	2	4	no	—
78	C₄⋊C₄×C₄₃	—	2	2	no	—
79	C₄⋊C₄×C₄₃	—	2	2	no	—
80	C₄⋊C₄×C₄₃	—	2	4	no	—
81	C₄⋊C₄×C₄₃	—	4	4	no	—
82	C₄⋊C₄×C₄₃	—	4	4	no	—
83	C₄⋊C₄×C₄₃	—	4	8	no	—
84	C₄⋊C₄×C₄₃	—	4	4	no	—
85	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
86	C₂²⋊C₄×C₄₃	—	2	4	no	—
87	C₂²⋊C₄×C₄₃	—	4	4	no	—
88	C₂²⋊C₄×C₄₃	—	4	4	no	—
89	C₄²×C₄₃	—	2	2	no	—
90	C₄²×C₄₃	—	2	2	no	—
91	C₄²×C₄₃	—	2	2	no	—
92	C₄²×C₄₃	—	4	2	no	—
93	C₄²×C₄₃	—	4	2	no	—
94	C₄²×C₄₃	D₈	1	4	yes	—
95	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
96	C₄²×C₄₃	#41	1	2	yes	—
97	C₂³×C₄₃	—	2	2	no	—
98	C₂³×C₄₃	—	4	2	no	—
99	C₂³×C₄₃	—	4	1	no	—
100	C₂³×C₄₃	—	4	1	no	—
101	C₂³×C₄₃	—	4	2	no	—
102	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
103	D₄×C₄₃	—	2	4	no	—
104	D₄×C₄₃	—	4	1	no	—
105	D₄×C₄₃	—	4	1	no	—
106	C₂×C₄×C₄₃	—	2	2	no	—
107	C₂×C₄×C₄₃	—	2	2	no	—
108	C₂×C₄×C₄₃	—	2	2	no	—
109	C₂×C₄×C₄₃	—	2	2	no	—
110	C₂×C₄×C₄₃	—	2	2	no	—
111	C₂×C₄×C₄₃	—	2	2	no	—
112	C₂×C₄×C₄₃	—	2	2	no	—
113	C₂×C₄×C₄₃	—	4	1	no	—
114	C₂×C₄×C₄₃	—	4	1	no	—
115	C₂×C₄×C₄₃	—	4	8	no	—
116	C₂×C₄×C₄₃	—	4	4	no	—
117	C₂×C₄×C₄₃	—	4	2	no	—
118	C₂×C₄×C₄₃	—	4	2	no	—
119	C₂×C₄×C₄₃	—	4	4	no	—
120	C₂×C₄×C₄₃	—	4	2	no	—
121	C₂×C₄×C₄₃	—	4	4	no	—
122	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
123	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
124	C₂×C₄×C₄₃	C₂×D₈	1	4	yes	—
125	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
126	C₂×C₄×C₄₃	#137	1	2	yes	—
127	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
128	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
129	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
130	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
131	C₈×C₄₃	—	4	4	no	—
132	#29994	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂²×C₄₃	—	4	2	no	—
134	C₂²×C₄₃	—	4	2	no	—
135	C₂²×C₄₃	—	4	2	no	—
136	C₂²×C₄₃	—	8	2	no	—
137	C₂²×C₄₃	—	8	2	no	—
138	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
139	C₂²×C₄₃	#537	1	2	yes	—
140	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
141	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
142	C₂²×C₄₃	#575	1	2	yes	—
143	C₄×C₄₃	—	2	2	no	—
144	C₄×C₄₃	—	2	4	no	—
145	C₄×C₄₃	—	4	2	no	—
146	C₄×C₄₃	—	4	2	no	—
147	C₄×C₄₃	—	8	2	no	—
148	C₄×C₄₃	—	8	4	no	—
149	C₄×C₄₃	#474	1	4	yes	—
150	C₄×C₄₃	#540	1	1	yes	characteristic
151	C₄×C₄₃	#541	1	1	yes	characteristic
152	C₄×C₄₃	#544	1	2	yes	—
153	#2859	C₂×C₄₃	1	1	yes	characteristic, complemented
154	#2293	C₂×C₄₃	1	1	yes	characteristic
155	#2086	C₂×C₄₃	1	4	yes	complemented
156	#2067	C₂×C₄₃	1	4	yes	—
157	#1947	C₂×C₄₃	1	2	yes	complemented
158	#1842	C₂×C₄₃	1	1	yes	characteristic, complemented
159	#1802	C₂×C₄₃	1	2	yes	—
160	C₂×C₄₃	—	8	2	no	—
161	C₂×C₄₃	#2629	1	1	yes	characteristic
162	C₂×C₄₃	C₂×#474	1	1	yes	characteristic
163	C₂×C₄₃	#3080	1	1	yes	characteristic
164	C₂×C₄₃	#3245	1	2	yes	—
165	C₂×C₄₃	#3252	1	2	yes	—
166	C₂×#125	—	2	1	no	—
167	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
168	C₂×#117	—	2	1	no	—
169	C₂×#107	C₂²×C₄₃	1	4	yes	—
170	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
171	C₂×C₄⋊C₈	C₂²×C₄₃	1	4	yes	—
172	C₂×#102	C₂²×C₄₃	1	4	yes	—
173	#390	C₂²×C₄₃	1	2	yes	—
174	#389	—	2	2	no	—
175	#389	C₂²×C₄₃	1	4	yes	—
176	#389	C₂²×C₄₃	1	2	yes	—
177	#388	—	2	2	no	—
178	#384	C₂²×C₄₃	1	2	yes	—
179	#382	—	2	1	no	—
180	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
181	C₄×C₂²⋊C₄	—	2	1	no	—
182	C₄³	C₂²×C₄₃	1	1	yes	characteristic
183	#340	C₂²×C₄₃	1	4	yes	—
184	#340	C₂²×C₄₃	1	4	yes	—
185	C₄₃	#29994	1	1	yes	characteristic, direct product factor, Sylow
186	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
187	C₂³×C₄	—	2	1	no	—
188	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
189	#125	—	4	4	no	—
190	C₄×D₄	—	2	2	no	—
191	C₄×D₄	Q₈×C₄₃	1	4	yes	—
192	#117	—	4	4	no	—
193	C₂×C₄⋊C₄	—	2	2	no	—
194	C₂×C₄⋊C₄	—	2	2	no	—
195	C₂×C₄⋊C₄	—	2	4	no	—
196	C₂×C₄⋊C₄	—	2	2	no	—
197	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
198	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
199	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
200	C₂×C₂²⋊C₄	—	2	1	no	—
201	C₂×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₂²⋊C₄	—	2	2	no	—
203	C₂×C₄²	—	2	1	no	—
204	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
205	C₂×C₄²	D₄×C₄₃	1	2	yes	—
206	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
207	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
208	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
209	#107	—	4	4	no	—
210	C₄⋊C₈	—	2	4	no	—
211	C₄⋊C₈	—	4	4	no	—
212	#102	—	4	4	no	—
213	#95	—	2	2	no	—
214	#95	—	2	1	no	—
215	#95	—	2	4	no	—
216	C₂⁴	—	2	1	no	—
217	C₂×D₄	—	2	1	no	—
218	C₂×D₄	—	2	2	no	—
219	C₂×D₄	—	2	2	no	—
220	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
221	C₂²×C₄	—	2	1	no	—
222	C₂²×C₄	—	2	4	no	—
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	2	4	no	—
225	C₂²×C₄	—	4	2	no	—
226	C₂²×C₄	—	4	2	no	—
227	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
228	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
229	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
230	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
231	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
232	C₂×C₈	—	2	4	no	—
233	C₂×C₈	—	2	4	no	—
234	C₂×C₈	—	2	4	no	—
235	C₄⋊C₄	—	2	1	no	—
236	C₄⋊C₄	—	2	4	no	—
237	C₄⋊C₄	—	2	2	no	—
238	C₄⋊C₄	—	2	2	no	—
239	C₄⋊C₄	—	2	4	no	—
240	C₄⋊C₄	—	4	4	no	—
241	C₄⋊C₄	—	4	4	no	—
242	C₄⋊C₄	—	4	8	no	—
243	C₄⋊C₄	—	4	4	no	—
244	C₄⋊C₄	C₂×Q₈×C₄₃	1	2	yes	—
245	C₂²⋊C₄	—	2	4	no	—
246	C₂²⋊C₄	—	4	4	no	—
247	C₂²⋊C₄	—	4	4	no	—
248	C₄²	—	2	2	no	—
249	C₄²	—	2	2	no	—
250	C₄²	—	2	2	no	—
251	C₄²	—	4	2	no	—
252	C₄²	—	4	2	no	—
253	C₄²	D₈×C₄₃	1	4	yes	—
254	C₄²	C₂×Q₈×C₄₃	1	2	yes	—
255	C₄²	#41×C₄₃	1	2	yes	—
256	C₂³	—	2	2	no	—
257	C₂³	—	4	2	no	—
258	C₂³	—	4	1	no	—
259	C₂³	—	4	1	no	—
260	C₂³	—	4	2	no	—
261	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
262	D₄	—	2	4	no	—
263	D₄	—	4	1	no	—
264	D₄	—	4	1	no	—
265	C₂×C₄	—	2	2	no	—
266	C₂×C₄	—	2	2	no	—
267	C₂×C₄	—	2	2	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	4	1	no	—
273	C₂×C₄	—	4	1	no	—
274	C₂×C₄	—	4	8	no	—
275	C₂×C₄	—	4	4	no	—
276	C₂×C₄	—	4	2	no	—
277	C₂×C₄	—	4	2	no	—
278	C₂×C₄	—	4	4	no	—
279	C₂×C₄	—	4	2	no	—
280	C₂×C₄	—	4	4	no	—
281	C₂×C₄	C₂²⋊Q₈×C₄₃	1	2	yes	—
282	C₂×C₄	C₂²⋊Q₈×C₄₃	1	2	yes	—
283	C₂×C₄	C₂×D₈×C₄₃	1	4	yes	—
284	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
285	C₂×C₄	#137×C₄₃	1	2	yes	—
286	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
287	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
288	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
289	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
290	C₈	—	4	4	no	—
291	C₂²	—	4	2	no	—
292	C₂²	—	4	2	no	—
293	C₂²	—	4	2	no	—
294	C₂²	—	8	2	no	—
295	C₂²	—	8	2	no	—
296	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
297	C₂²	C₄₃×#537	1	2	yes	—
298	C₂²	C₂²×D₈×C₄₃	1	1	yes	characteristic
299	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
300	C₂²	C₄₃×#575	1	2	yes	—
301	C₄	—	2	4	no	—
302	C₄	—	2	2	no	—
303	C₄	—	4	2	no	—
304	C₄	—	4	2	no	—
305	C₄	—	8	2	no	—
306	C₄	—	8	4	no	—
307	C₄	C₄₃×#474	1	4	yes	—
308	C₄	C₄₃×#540	1	1	yes	characteristic
309	C₄	C₄₃×#541	1	1	yes	characteristic
310	C₄	C₄₃×#544	1	2	yes	—
311	C₂	—	8	2	no	—
312	C₂	C₄₃×#2629	1	1	yes	characteristic
313	C₂	C₂×C₄₃×#474	1	1	yes	characteristic
314	C₂	C₄₃×#3080	1	1	yes	characteristic
315	C₂	C₄₃×#3245	1	2	yes	—
316	C₂	C₄₃×#3252	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×D₄×C₄₃	C₂³
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
1. C₄₃×#2859	C₂	semidirect
3. C₄₃×#2086	C₂	semidirect
5. C₄₃×#1947	C₂	semidirect
6. C₄₃×#1842	C₂	semidirect
132. #29994	C₄₃	direct (N × H)
153. #2859	C₂×C₄₃	semidirect
155. #2086	C₂×C₄₃	semidirect
157. #1947	C₂×C₄₃	semidirect
158. #1842	C₂×C₄₃	semidirect
185. C₄₃	#29994	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#2859	2
C₄₃×#2293	2
C₄₃×#2086	2
C₄₃×#2067	2
C₄₃×#1947	2
C₄₃×#1842	2
C₄₃×#1802	2
#29994	43

Subgroups — C43×#29994 #24950011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29994 #24950011