Subgroups — C₄₃×#13955 #24933972

Order 11008.

1342 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#382	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1442	C₂	1	4	yes	maximal
5	C₄₃×C₄⋊#95	C₂	1	4	yes	maximal
6	C₄₃×#1434	C₂	1	4	yes	maximal
7	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
10	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
11	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
12	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
13	C₄₃×#382	—	2	4	no	—
14	C₄×C₄⋊C₄×C₄₃	—	2	4	no	—
15	C₄×C₄⋊C₄×C₄₃	C₄	1	8	yes	complemented
16	C₂×#95×C₄₃	C₂²	1	2	yes	—
17	C₂×#95×C₄₃	C₂²	1	2	yes	—
18	C₂×#95×C₄₃	C₂²	1	8	yes	—
19	C₂×#95×C₄₃	C₂²	1	2	yes	—
20	C₂×#95×C₄₃	C₂²	1	8	yes	—
21	C₂×#95×C₄₃	C₂²	1	2	yes	—
22	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
23	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
24	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
25	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
26	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
27	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
29	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
30	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
31	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
32	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
33	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
34	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
35	C₂×C₄²×C₄₃	—	2	4	no	—
36	C₂×C₄²×C₄₃	—	2	8	no	—
37	C₂×C₄²×C₄₃	—	4	4	no	—
38	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
39	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
40	C₂×C₄²×C₄₃	D₄	1	4	yes	—
41	C₂×C₄²×C₄₃	Q₈	1	4	yes	—
42	#95×C₄₃	—	2	4	no	—
43	#95×C₄₃	—	2	4	no	—
44	#95×C₄₃	—	2	4	no	—
45	#95×C₄₃	—	2	16	no	—
46	#95×C₄₃	—	4	8	no	—
47	#95×C₄₃	C₂×C₄	1	8	yes	—
48	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
49	C₂²×C₄×C₄₃	—	2	4	no	—
50	C₂²×C₄×C₄₃	—	2	4	no	—
51	C₂²×C₄×C₄₃	—	2	4	no	—
52	C₂²×C₄×C₄₃	—	2	8	no	—
53	C₂²×C₄×C₄₃	—	2	4	no	—
54	C₂²×C₄×C₄₃	—	2	4	no	—
55	C₂²×C₄×C₄₃	—	2	4	no	—
56	C₂²×C₄×C₄₃	—	2	4	no	—
57	C₂²×C₄×C₄₃	—	2	4	no	—
58	C₂²×C₄×C₄₃	—	2	8	no	—
59	C₂²×C₄×C₄₃	—	2	8	no	—
60	C₂²×C₄×C₄₃	—	2	2	no	—
61	C₂²×C₄×C₄₃	—	2	4	no	—
62	C₂²×C₄×C₄₃	—	2	8	no	—
63	C₂²×C₄×C₄₃	—	2	4	no	—
64	C₂²×C₄×C₄₃	—	2	2	no	—
65	C₂²×C₄×C₄₃	—	2	4	no	—
66	C₂²×C₄×C₄₃	—	2	4	no	—
67	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
68	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
69	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
70	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
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	2	yes	—
74	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
75	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
76	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
77	C₂²×C₄×C₄₃	#41	1	8	yes	—
78	C₂²×C₄×C₄₃	#41	1	4	yes	—
79	C₂²×C₄×C₄₃	#41	1	4	yes	—
80	C₄⋊C₄×C₄₃	—	2	16	no	—
81	C₄⋊C₄×C₄₃	—	2	16	no	—
82	C₄⋊C₄×C₄₃	—	4	8	no	—
83	C₄²×C₄₃	—	4	8	no	—
84	C₄²×C₄₃	—	4	8	no	—
85	C₄²×C₄₃	C₄⋊C₄	1	16	yes	—
86	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
87	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
88	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
89	C₂³×C₄₃	C₂×#41	1	2	yes	—
90	C₂³×C₄₃	C₂×#41	1	2	yes	—
91	C₂³×C₄₃	C₂×#41	1	4	yes	—
92	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
93	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
94	C₂×C₄×C₄₃	—	2	4	no	—
95	C₂×C₄×C₄₃	—	2	2	no	—
96	C₂×C₄×C₄₃	—	2	2	no	—
97	C₂×C₄×C₄₃	—	2	4	no	—
98	C₂×C₄×C₄₃	—	2	4	no	—
99	C₂×C₄×C₄₃	—	2	4	no	—
100	C₂×C₄×C₄₃	—	2	4	no	—
101	C₂×C₄×C₄₃	—	2	8	no	—
102	C₂×C₄×C₄₃	—	2	8	no	—
103	C₂×C₄×C₄₃	—	2	8	no	—
104	C₂×C₄×C₄₃	—	2	8	no	—
105	C₂×C₄×C₄₃	—	2	8	no	—
106	C₂×C₄×C₄₃	—	2	8	no	—
107	C₂×C₄×C₄₃	—	4	4	no	—
108	C₂×C₄×C₄₃	—	4	4	no	—
109	C₂×C₄×C₄₃	—	4	4	no	—
110	C₂×C₄×C₄₃	—	4	4	no	—
111	C₂×C₄×C₄₃	—	4	8	no	—
112	C₂×C₄×C₄₃	—	4	8	no	—
113	C₂×C₄×C₄₃	—	4	4	no	—
114	C₂×C₄×C₄₃	—	4	4	no	—
115	C₂×C₄×C₄₃	—	4	4	no	—
116	C₂×C₄×C₄₃	—	4	8	no	—
117	C₂×C₄×C₄₃	—	4	8	no	—
118	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
119	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
120	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
121	C₂×C₄×C₄₃	#117	1	8	yes	—
122	C₂×C₄×C₄₃	#124	1	4	yes	—
123	C₂×C₄×C₄₃	#124	1	4	yes	—
124	C₂×C₄×C₄₃	#125	1	8	yes	—
125	#13955	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
127	C₂²×C₄₃	C₂×#117	1	2	yes	—
128	C₂²×C₄₃	C₄×#41	1	2	yes	—
129	C₂²×C₄₃	#518	1	1	yes	characteristic
130	C₂²×C₄₃	#519	1	1	yes	characteristic
131	C₂²×C₄₃	#525	1	2	yes	—
132	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
133	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
134	C₂²×C₄₃	C₂×#125	1	2	yes	—
135	C₂²×C₄₃	#533	1	2	yes	—
136	C₂²×C₄₃	#537	1	2	yes	—
137	C₂²×C₄₃	#544	1	2	yes	—
138	C₂²×C₄₃	#552	1	4	yes	—
139	C₂²×C₄₃	#553	1	4	yes	—
140	C₂²×C₄₃	#556	1	4	yes	—
141	C₂²×C₄₃	#559	1	4	yes	—
142	C₄×C₄₃	—	2	4	no	—
143	C₄×C₄₃	—	2	4	no	—
144	C₄×C₄₃	—	4	8	no	—
145	C₄×C₄₃	—	4	8	no	—
146	C₄×C₄₃	—	8	4	no	—
147	C₄×C₄₃	#382	1	8	yes	—
148	C₂×#382	C₂×C₄₃	1	1	yes	characteristic
149	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
150	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
151	#1442	C₂×C₄₃	1	4	yes	—
152	C₄⋊#95	C₂×C₄₃	1	4	yes	—
153	#1434	C₂×C₄₃	1	4	yes	—
154	C₂×C₄₃	C₂×#382	1	1	yes	characteristic
155	C₂×C₄₃	#2296	1	1	yes	characteristic
156	C₂×C₄₃	#2316	1	1	yes	characteristic
157	C₂×C₄₃	#2356	1	2	yes	—
158	C₂×C₄₃	#2357	1	2	yes	—
159	C₂×C₄₃	#2562	1	2	yes	—
160	C₂×C₄₃	#2570	1	4	yes	—
161	C₂×C₄₃	#2592	1	2	yes	—
162	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
163	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
164	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
165	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
166	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
167	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
168	#382	—	2	4	no	—
169	C₄×C₄⋊C₄	—	2	4	no	—
170	C₄×C₄⋊C₄	C₄×C₄₃	1	8	yes	complemented
171	C₂×#95	C₂²×C₄₃	1	2	yes	—
172	C₂×#95	C₂²×C₄₃	1	2	yes	—
173	C₂×#95	C₂²×C₄₃	1	8	yes	—
174	C₂×#95	C₂²×C₄₃	1	2	yes	—
175	C₂×#95	C₂²×C₄₃	1	8	yes	—
176	C₂×#95	C₂²×C₄₃	1	2	yes	—
177	C₄₃	#13955	1	1	yes	characteristic, direct product factor, Sylow
178	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
179	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
180	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
181	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
182	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
183	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
184	C₂×C₄⋊C₄	—	2	4	no	—
185	C₂×C₄⋊C₄	—	2	8	no	—
186	C₂×C₄⋊C₄	—	2	4	no	—
187	C₂×C₄⋊C₄	—	2	4	no	—
188	C₂×C₄⋊C₄	—	2	4	no	—
189	C₂×C₄⋊C₄	—	2	8	no	—
190	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
191	C₂×C₄²	—	2	4	no	—
192	C₂×C₄²	—	2	8	no	—
193	C₂×C₄²	—	4	4	no	—
194	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	—
195	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
196	C₂×C₄²	D₄×C₄₃	1	4	yes	—
197	C₂×C₄²	Q₈×C₄₃	1	4	yes	—
198	#95	—	2	4	no	—
199	#95	—	2	4	no	—
200	#95	—	2	4	no	—
201	#95	—	2	16	no	—
202	#95	—	4	8	no	—
203	#95	C₂×C₄×C₄₃	1	8	yes	—
204	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
205	C₂²×C₄	—	2	4	no	—
206	C₂²×C₄	—	2	2	no	—
207	C₂²×C₄	—	2	2	no	—
208	C₂²×C₄	—	2	4	no	—
209	C₂²×C₄	—	2	8	no	—
210	C₂²×C₄	—	2	4	no	—
211	C₂²×C₄	—	2	4	no	—
212	C₂²×C₄	—	2	4	no	—
213	C₂²×C₄	—	2	4	no	—
214	C₂²×C₄	—	2	4	no	—
215	C₂²×C₄	—	2	4	no	—
216	C₂²×C₄	—	2	8	no	—
217	C₂²×C₄	—	2	4	no	—
218	C₂²×C₄	—	2	4	no	—
219	C₂²×C₄	—	2	8	no	—
220	C₂²×C₄	—	2	8	no	—
221	C₂²×C₄	—	2	4	no	—
222	C₂²×C₄	—	2	4	no	—
223	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
224	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
225	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
226	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
227	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
228	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
229	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
230	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
231	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
232	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
233	C₂²×C₄	#41×C₄₃	1	8	yes	—
234	C₂²×C₄	#41×C₄₃	1	4	yes	—
235	C₂²×C₄	#41×C₄₃	1	4	yes	—
236	C₄⋊C₄	—	2	16	no	—
237	C₄⋊C₄	—	2	16	no	—
238	C₄⋊C₄	—	4	8	no	—
239	C₄²	—	4	8	no	—
240	C₄²	—	4	8	no	—
241	C₄²	C₄⋊C₄×C₄₃	1	16	yes	—
242	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
243	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
244	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
245	C₂³	C₂×#41×C₄₃	1	2	yes	—
246	C₂³	C₂×#41×C₄₃	1	2	yes	—
247	C₂³	C₂×#41×C₄₃	1	4	yes	—
248	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
249	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
250	C₂×C₄	—	2	4	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	4	no	—
254	C₂×C₄	—	2	4	no	—
255	C₂×C₄	—	2	4	no	—
256	C₂×C₄	—	2	4	no	—
257	C₂×C₄	—	2	8	no	—
258	C₂×C₄	—	2	8	no	—
259	C₂×C₄	—	2	8	no	—
260	C₂×C₄	—	2	8	no	—
261	C₂×C₄	—	2	8	no	—
262	C₂×C₄	—	2	8	no	—
263	C₂×C₄	—	4	4	no	—
264	C₂×C₄	—	4	4	no	—
265	C₂×C₄	—	4	4	no	—
266	C₂×C₄	—	4	8	no	—
267	C₂×C₄	—	4	4	no	—
268	C₂×C₄	—	4	8	no	—
269	C₂×C₄	—	4	4	no	—
270	C₂×C₄	—	4	4	no	—
271	C₂×C₄	—	4	4	no	—
272	C₂×C₄	—	4	8	no	—
273	C₂×C₄	—	4	8	no	—
274	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
275	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
276	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
277	C₂×C₄	#117×C₄₃	1	8	yes	—
278	C₂×C₄	#124×C₄₃	1	4	yes	—
279	C₂×C₄	#124×C₄₃	1	4	yes	—
280	C₂×C₄	#125×C₄₃	1	8	yes	—
281	C₂²	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
282	C₂²	C₂×#117×C₄₃	1	2	yes	—
283	C₂²	C₄×#41×C₄₃	1	2	yes	—
284	C₂²	C₄₃×#518	1	1	yes	characteristic
285	C₂²	C₄₃×#519	1	1	yes	characteristic
286	C₂²	C₄₃×#525	1	2	yes	—
287	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
288	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
289	C₂²	C₂×#125×C₄₃	1	2	yes	—
290	C₂²	C₄₃×#533	1	2	yes	—
291	C₂²	C₄₃×#537	1	2	yes	—
292	C₂²	C₄₃×#544	1	2	yes	—
293	C₂²	C₄₃×#552	1	4	yes	—
294	C₂²	C₄₃×#553	1	4	yes	—
295	C₂²	C₄₃×#556	1	4	yes	—
296	C₂²	C₄₃×#559	1	4	yes	—
297	C₄	—	2	4	no	—
298	C₄	—	2	4	no	—
299	C₄	—	4	8	no	—
300	C₄	—	4	8	no	—
301	C₄	—	8	4	no	—
302	C₄	C₄₃×#382	1	8	yes	—
303	C₂	C₂×C₄₃×#382	1	1	yes	characteristic
304	C₂	C₄₃×#2296	1	1	yes	characteristic
305	C₂	C₄₃×#2316	1	1	yes	characteristic
306	C₂	C₄₃×#2356	1	2	yes	—
307	C₂	C₄₃×#2357	1	2	yes	—
308	C₂	C₄₃×#2562	1	2	yes	—
309	C₂	C₄₃×#2570	1	4	yes	—
310	C₂	C₄₃×#2592	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
15. C₄×C₄⋊C₄×C₄₃	C₄	semidirect
125. #13955	C₄₃	direct (N × H)
170. C₄×C₄⋊C₄	C₄×C₄₃	semidirect
177. C₄₃	#13955	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#382	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₄₃×#1442	2
C₄₃×C₄⋊#95	2
C₄₃×#1434	2
#13955	43

Subgroups — C43×#13955 #24933972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#13955 #24933972