Subgroups — C₄₃×#29948 #24949965

Order 11008.

608 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2629	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2314	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2101	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2083	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2076	C₂	1	2	yes	maximal
6	C₄₃×#2075	C₂	1	2	yes	maximal
7	C₄₃×#1989	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1947	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1798	C₂	1	1	yes	maximal, characteristic
10	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×#107×C₄₃	C₂²	1	2	yes	—
13	C₂×#107×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#398	—	2	2	no	—
18	C₄₃×#396	—	2	2	no	—
19	C₄₃×#389	C₂²	1	2	yes	—
20	C₄₃×#388	—	2	2	no	—
21	C₄₃×#387	—	2	2	no	—
22	C₄₃×#384	C₂²	1	1	yes	characteristic
23	C₄₃×#384	C₂²	1	1	yes	characteristic
24	C₄₃×#382	C₂²	1	1	yes	characteristic
25	C₄₃×#380	C₂²	1	2	yes	—
26	C₄₃×#380	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
28	C₄₃×#340	C₂²	1	2	yes	—
29	C₄₃×#340	C₂²	1	2	yes	—
30	C₄₃×#340	C₂²	1	2	yes	—
31	C₄₃×#340	C₂²	1	2	yes	—
32	C₄₃×#340	C₂²	1	2	yes	—
33	C₄₃×#340	C₂²	1	2	yes	—
34	C₄₃×#336	C₂²	1	2	yes	—
35	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
37	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
38	#125×C₄₃	—	2	4	no	—
39	#117×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	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
46	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
47	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
48	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
49	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
51	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
52	C₂×C₄²×C₄₃	—	2	2	no	—
53	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
55	#107×C₄₃	—	4	2	no	—
56	#107×C₄₃	—	4	2	no	—
57	C₄⋊C₈×C₄₃	—	2	4	no	—
58	C₂²⋊C₈×C₄₃	—	4	1	no	—
59	C₂²⋊C₈×C₄₃	—	4	1	no	—
60	#95×C₄₃	—	2	2	no	—
61	#95×C₄₃	—	2	2	no	—
62	#95×C₄₃	—	2	2	no	—
63	#95×C₄₃	—	2	2	no	—
64	#95×C₄₃	—	2	2	no	—
65	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₃	—	2	2	no	—
67	C₂²×C₄×C₄₃	—	2	1	no	—
68	C₂²×C₄×C₄₃	—	2	2	no	—
69	C₂²×C₄×C₄₃	—	2	1	no	—
70	C₂²×C₄×C₄₃	—	2	2	no	—
71	C₂²×C₄×C₄₃	—	2	2	no	—
72	C₂²×C₄×C₄₃	—	2	2	no	—
73	C₂²×C₄×C₄₃	—	2	2	no	—
74	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
78	C₂×C₈×C₄₃	—	2	2	no	—
79	C₂×C₈×C₄₃	—	2	2	no	—
80	C₂×C₈×C₄₃	—	2	2	no	—
81	C₂×C₈×C₄₃	—	2	2	no	—
82	C₂×C₈×C₄₃	—	2	2	no	—
83	C₂×C₈×C₄₃	—	2	2	no	—
84	C₄⋊C₄×C₄₃	—	2	4	no	—
85	C₄⋊C₄×C₄₃	—	2	4	no	—
86	C₄⋊C₄×C₄₃	—	2	2	no	—
87	C₄⋊C₄×C₄₃	—	2	2	no	—
88	C₄⋊C₄×C₄₃	—	2	4	no	—
89	C₄⋊C₄×C₄₃	—	2	2	no	—
90	C₄⋊C₄×C₄₃	—	2	2	no	—
91	C₄⋊C₄×C₄₃	—	4	4	no	—
92	C₄⋊C₄×C₄₃	—	8	2	no	—
93	C₄⋊C₄×C₄₃	—	8	2	no	—
94	C₄⋊C₄×C₄₃	—	8	2	no	—
95	C₂²⋊C₄×C₄₃	—	2	4	no	—
96	C₂²⋊C₄×C₄₃	—	8	2	no	—
97	C₂²⋊C₄×C₄₃	—	8	2	no	—
98	C₄²×C₄₃	—	2	2	no	—
99	C₄²×C₄₃	—	8	2	no	—
100	C₄²×C₄₃	#41	1	4	yes	—
101	C₂³×C₄₃	—	2	1	no	—
102	C₂³×C₄₃	—	2	1	no	—
103	C₂³×C₄₃	—	2	1	no	—
104	C₂³×C₄₃	—	2	2	no	—
105	C₂³×C₄₃	—	2	2	no	—
106	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
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	1	no	—
111	C₂×C₄×C₄₃	—	2	1	no	—
112	C₂×C₄×C₄₃	—	2	1	no	—
113	C₂×C₄×C₄₃	—	2	2	no	—
114	C₂×C₄×C₄₃	—	2	2	no	—
115	C₂×C₄×C₄₃	—	4	2	no	—
116	C₂×C₄×C₄₃	—	4	2	no	—
117	C₂×C₄×C₄₃	—	4	2	no	—
118	C₂×C₄×C₄₃	—	4	2	no	—
119	C₂×C₄×C₄₃	—	4	2	no	—
120	C₂×C₄×C₄₃	—	4	2	no	—
121	C₂×C₄×C₄₃	—	4	2	no	—
122	C₂×C₄×C₄₃	—	4	2	no	—
123	C₂×C₄×C₄₃	—	4	2	no	—
124	C₂×C₄×C₄₃	—	4	2	no	—
125	C₂×C₄×C₄₃	—	4	2	no	—
126	C₂×C₄×C₄₃	—	4	2	no	—
127	C₂×C₄×C₄₃	—	4	2	no	—
128	C₂×C₄×C₄₃	—	4	2	no	—
129	C₂×C₄×C₄₃	#123	1	4	yes	—
130	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
131	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
132	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
133	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
134	C₈×C₄₃	—	4	2	no	—
135	C₈×C₄₃	—	4	2	no	—
136	#29948	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂²×C₄₃	—	4	2	no	—
138	C₂²×C₄₃	—	4	1	no	—
139	C₂²×C₄₃	—	4	2	no	—
140	C₂²×C₄₃	—	4	1	no	—
141	C₂²×C₄₃	—	4	1	no	—
142	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
143	C₂²×C₄₃	#536	1	1	yes	characteristic
144	C₂²×C₄₃	#537	1	1	yes	characteristic
145	C₂²×C₄₃	#576	1	2	yes	—
146	C₂²×C₄₃	#578	1	2	yes	—
147	C₄×C₄₃	—	2	4	no	—
148	C₄×C₄₃	—	4	2	no	—
149	C₄×C₄₃	—	4	1	no	—
150	C₄×C₄₃	—	8	2	no	—
151	C₄×C₄₃	—	8	2	no	—
152	C₄×C₄₃	—	8	2	no	—
153	C₄×C₄₃	—	8	2	no	—
154	C₄×C₄₃	#541	1	2	yes	—
155	C₄×C₄₃	#542	1	2	yes	—
156	#2629	C₂×C₄₃	1	1	yes	characteristic
157	#2314	C₂×C₄₃	1	1	yes	characteristic
158	#2101	C₂×C₄₃	1	2	yes	complemented
159	#2083	C₂×C₄₃	1	2	yes	complemented
160	#2076	C₂×C₄₃	1	2	yes	—
161	#2075	C₂×C₄₃	1	2	yes	—
162	#1989	C₂×C₄₃	1	2	yes	complemented
163	#1947	C₂×C₄₃	1	2	yes	complemented
164	#1798	C₂×C₄₃	1	1	yes	characteristic
165	C₂×C₄₃	—	8	1	no	—
166	C₂×C₄₃	#2625	1	1	yes	characteristic
167	C₂×C₄₃	#3098	1	2	yes	—
168	C₂×C₄₃	#3243	1	2	yes	—
169	C₂×C₄₃	#3259	1	1	yes	characteristic
170	C₂×C₄₃	#3261	1	1	yes	characteristic
171	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
172	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
173	C₂×#107	C₂²×C₄₃	1	2	yes	—
174	C₂×#107	C₂²×C₄₃	1	2	yes	—
175	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
176	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
177	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
178	#398	—	2	2	no	—
179	#396	—	2	2	no	—
180	#389	C₂²×C₄₃	1	2	yes	—
181	#388	—	2	2	no	—
182	#387	—	2	2	no	—
183	#384	C₂²×C₄₃	1	1	yes	characteristic
184	#384	C₂²×C₄₃	1	1	yes	characteristic
185	#382	C₂²×C₄₃	1	1	yes	characteristic
186	#380	C₂²×C₄₃	1	2	yes	—
187	#380	C₂²×C₄₃	1	2	yes	—
188	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
189	#340	C₂²×C₄₃	1	2	yes	—
190	#340	C₂²×C₄₃	1	2	yes	—
191	#340	C₂²×C₄₃	1	2	yes	—
192	#340	C₂²×C₄₃	1	2	yes	—
193	#340	C₂²×C₄₃	1	2	yes	—
194	#340	C₂²×C₄₃	1	2	yes	—
195	#336	C₂²×C₄₃	1	2	yes	—
196	C₄₃	#29948	1	1	yes	characteristic, direct product factor, Sylow
197	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
198	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
199	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
200	#125	—	2	4	no	—
201	#117	—	2	4	no	—
202	C₂×C₄⋊C₄	—	2	2	no	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	2	2	no	—
206	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
207	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
208	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
209	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
210	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
211	C₂×C₂²⋊C₄	—	2	2	no	—
212	C₂×C₂²⋊C₄	—	2	2	no	—
213	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
214	C₂×C₄²	—	2	2	no	—
215	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
216	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
217	#107	—	4	2	no	—
218	#107	—	4	2	no	—
219	C₄⋊C₈	—	2	4	no	—
220	C₂²⋊C₈	—	4	1	no	—
221	C₂²⋊C₈	—	4	1	no	—
222	#95	—	2	2	no	—
223	#95	—	2	2	no	—
224	#95	—	2	2	no	—
225	#95	—	2	2	no	—
226	#95	—	2	2	no	—
227	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
228	C₂²×C₄	—	2	2	no	—
229	C₂²×C₄	—	2	1	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	2	1	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
237	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
238	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
239	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
240	C₂×C₈	—	2	2	no	—
241	C₂×C₈	—	2	2	no	—
242	C₂×C₈	—	2	2	no	—
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	2	no	—
246	C₄⋊C₄	—	2	4	no	—
247	C₄⋊C₄	—	2	4	no	—
248	C₄⋊C₄	—	2	2	no	—
249	C₄⋊C₄	—	2	2	no	—
250	C₄⋊C₄	—	2	4	no	—
251	C₄⋊C₄	—	2	2	no	—
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	—	4	4	no	—
254	C₄⋊C₄	—	8	2	no	—
255	C₄⋊C₄	—	8	2	no	—
256	C₄⋊C₄	—	8	2	no	—
257	C₂²⋊C₄	—	2	4	no	—
258	C₂²⋊C₄	—	8	2	no	—
259	C₂²⋊C₄	—	8	2	no	—
260	C₄²	—	2	2	no	—
261	C₄²	—	8	2	no	—
262	C₄²	#41×C₄₃	1	4	yes	—
263	C₂³	—	2	1	no	—
264	C₂³	—	2	1	no	—
265	C₂³	—	2	1	no	—
266	C₂³	—	2	2	no	—
267	C₂³	—	2	2	no	—
268	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	1	no	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	4	2	no	—
278	C₂×C₄	—	4	2	no	—
279	C₂×C₄	—	4	2	no	—
280	C₂×C₄	—	4	2	no	—
281	C₂×C₄	—	4	2	no	—
282	C₂×C₄	—	4	2	no	—
283	C₂×C₄	—	4	2	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	4	2	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	—	4	2	no	—
288	C₂×C₄	—	4	2	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	4	2	no	—
291	C₂×C₄	#123×C₄₃	1	4	yes	—
292	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
293	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
294	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
295	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
296	C₈	—	4	2	no	—
297	C₈	—	4	2	no	—
298	C₂²	—	4	2	no	—
299	C₂²	—	4	1	no	—
300	C₂²	—	4	2	no	—
301	C₂²	—	4	1	no	—
302	C₂²	—	4	1	no	—
303	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
304	C₂²	C₄₃×#536	1	1	yes	characteristic
305	C₂²	C₄₃×#537	1	1	yes	characteristic
306	C₂²	C₄₃×#576	1	2	yes	—
307	C₂²	C₄₃×#578	1	2	yes	—
308	C₄	—	2	4	no	—
309	C₄	—	4	2	no	—
310	C₄	—	4	1	no	—
311	C₄	—	8	2	no	—
312	C₄	—	8	2	no	—
313	C₄	—	8	2	no	—
314	C₄	—	8	2	no	—
315	C₄	C₄₃×#541	1	2	yes	—
316	C₄	C₄₃×#542	1	2	yes	—
317	C₂	—	8	1	no	—
318	C₂	C₄₃×#2625	1	1	yes	characteristic
319	C₂	C₄₃×#3098	1	2	yes	—
320	C₂	C₄₃×#3243	1	2	yes	—
321	C₂	C₄₃×#3259	1	1	yes	characteristic
322	C₂	C₄₃×#3261	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂⁴×C₄₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₃×#2101	C₂	semidirect
4. C₄₃×#2083	C₂	semidirect
7. C₄₃×#1989	C₂	semidirect
8. C₄₃×#1947	C₂	semidirect
136. #29948	C₄₃	direct (N × H)
158. #2101	C₂×C₄₃	semidirect
159. #2083	C₂×C₄₃	semidirect
162. #1989	C₂×C₄₃	semidirect
163. #1947	C₂×C₄₃	semidirect
196. C₄₃	#29948	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×#2629	2
C₄₃×#2314	2
C₄₃×#2101	2
C₄₃×#2083	2
C₄₃×#2076	2
C₄₃×#2075	2
C₄₃×#1989	2
C₄₃×#1947	2
C₄₃×#1798	2
#29948	43

Subgroups — C43×#29948 #24949965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29948 #24949965