Subgroups — C₄₃×#29798 #24949815

Order 11008.

942 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×C₄₃×#461	C₂	1	2	yes	maximal
2	C₄₃×#2868	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2293	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2043	C₂	1	4	yes	maximal, complemented
5	C₄₃×#2013	C₂	1	4	yes	maximal
6	C₄₃×#1981	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×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×D₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×#117×C₄₃	—	2	1	no	—
13	C₄₃×#461	—	2	8	no	—
14	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
15	C₂×#103×C₄₃	C₂²	1	4	yes	—
16	C₂×#103×C₄₃	C₂²	1	8	yes	—
17	C₄₃×#390	C₂²	1	2	yes	—
18	C₄₃×#389	C₂²	1	2	yes	—
19	C₄₃×#388	—	2	2	no	—
20	C₄₃×#384	—	2	1	no	—
21	C₄₃×#384	—	2	2	no	—
22	C₄₃×#384	—	2	1	no	—
23	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₄₃	—	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×D₄×C₄₃	C₂³	1	1	yes	characteristic
29	C₂³×C₄×C₄₃	—	2	1	no	—
30	C₂×SD₁₆×C₄₃	—	2	8	no	—
31	C₂×SD₁₆×C₄₃	—	4	8	no	—
32	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
33	C₄⋊Q₈×C₄₃	—	2	4	no	—
34	C₄⋊Q₈×C₄₃	—	2	4	no	—
35	C₄⋊Q₈×C₄₃	—	4	8	no	—
36	C₄×D₄×C₄₃	—	2	2	no	—
37	C₄×D₄×C₄₃	D₄	1	4	yes	—
38	#117×C₄₃	—	4	4	no	—
39	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
42	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
45	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
49	C₂×C₄²×C₄₃	—	2	1	no	—
50	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₄₃	D₄	1	2	yes	—
52	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
54	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
55	C₄⋊C₈×C₄₃	—	2	4	no	—
56	#103×C₄₃	—	2	8	no	—
57	#103×C₄₃	—	4	8	no	—
58	#95×C₄₃	—	2	2	no	—
59	#95×C₄₃	—	2	1	no	—
60	C₂⁴×C₄₃	—	2	1	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×D₄×C₄₃	—	2	1	no	—
66	C₂×D₄×C₄₃	—	2	4	no	—
67	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
68	C₂²×C₄×C₄₃	—	2	4	no	—
69	C₂²×C₄×C₄₃	—	2	1	no	—
70	C₂²×C₄×C₄₃	—	2	2	no	—
71	C₂²×C₄×C₄₃	—	2	4	no	—
72	C₂²×C₄×C₄₃	—	4	2	no	—
73	C₂²×C₄×C₄₃	—	4	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	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
79	SD₁₆×C₄₃	—	4	16	no	—
80	C₂×C₈×C₄₃	—	2	4	no	—
81	C₂×C₈×C₄₃	—	2	8	no	—
82	C₄⋊C₄×C₄₃	—	2	1	no	—
83	C₄⋊C₄×C₄₃	—	2	4	no	—
84	C₄⋊C₄×C₄₃	—	4	8	no	—
85	C₄⋊C₄×C₄₃	—	4	8	no	—
86	C₄⋊C₄×C₄₃	—	4	4	no	—
87	C₄⋊C₄×C₄₃	—	4	4	no	—
88	C₄⋊C₄×C₄₃	—	4	4	no	—
89	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
90	C₂²⋊C₄×C₄₃	—	2	4	no	—
91	C₂²⋊C₄×C₄₃	—	4	4	no	—
92	C₂²⋊C₄×C₄₃	—	4	4	no	—
93	C₄²×C₄₃	—	2	4	no	—
94	C₄²×C₄₃	—	2	2	no	—
95	C₄²×C₄₃	—	2	4	no	—
96	C₄²×C₄₃	—	4	2	no	—
97	C₄²×C₄₃	SD₁₆	1	4	yes	complemented
98	C₄²×C₄₃	C₂×D₄	1	2	yes	—
99	C₄²×C₄₃	#41	1	2	yes	—
100	C₂³×C₄₃	—	2	2	no	—
101	C₂³×C₄₃	—	4	2	no	—
102	C₂³×C₄₃	—	4	1	no	—
103	C₂³×C₄₃	—	4	2	no	—
104	C₂³×C₄₃	—	4	1	no	—
105	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
106	Q₈×C₄₃	—	4	4	no	—
107	Q₈×C₄₃	—	4	4	no	—
108	Q₈×C₄₃	—	4	8	no	—
109	D₄×C₄₃	—	2	4	no	—
110	D₄×C₄₃	—	4	2	no	—
111	C₂×C₄×C₄₃	—	2	2	no	—
112	C₂×C₄×C₄₃	—	2	2	no	—
113	C₂×C₄×C₄₃	—	2	2	no	—
114	C₂×C₄×C₄₃	—	2	2	no	—
115	C₂×C₄×C₄₃	—	2	2	no	—
116	C₂×C₄×C₄₃	—	2	2	no	—
117	C₂×C₄×C₄₃	—	4	1	no	—
118	C₂×C₄×C₄₃	—	4	1	no	—
119	C₂×C₄×C₄₃	—	4	8	no	—
120	C₂×C₄×C₄₃	—	4	4	no	—
121	C₂×C₄×C₄₃	—	4	2	no	—
122	C₂×C₄×C₄₃	—	4	8	no	—
123	C₂×C₄×C₄₃	—	4	2	no	—
124	C₂×C₄×C₄₃	—	4	2	no	—
125	C₂×C₄×C₄₃	#121	1	2	yes	—
126	C₂×C₄×C₄₃	#121	1	2	yes	—
127	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
128	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
129	C₂×C₄×C₄₃	#137	1	4	yes	—
130	C₂×C₄×C₄₃	#137	1	2	yes	—
131	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
133	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
134	C₈×C₄₃	—	4	4	no	—
135	#29798	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂²×C₄₃	—	4	2	no	—
137	C₂²×C₄₃	—	4	2	no	—
138	C₂²×C₄₃	—	4	2	no	—
139	C₂²×C₄₃	—	8	2	no	—
140	C₂²×C₄₃	—	8	2	no	—
141	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
142	C₂²×C₄₃	#535	1	2	yes	—
143	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
144	C₂²×C₄₃	C₂×#137	1	2	yes	—
145	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
146	C₄×C₄₃	—	2	4	no	—
147	C₄×C₄₃	—	2	4	no	—
148	C₄×C₄₃	—	2	2	no	—
149	C₄×C₄₃	—	4	2	no	—
150	C₄×C₄₃	—	8	4	no	—
151	C₄×C₄₃	—	8	2	no	—
152	C₄×C₄₃	#461	1	4	yes	—
153	C₄×C₄₃	#535	1	2	yes	—
154	C₄×C₄₃	#540	1	2	yes	—
155	C₂×#461	C₂×C₄₃	1	2	yes	—
156	#2868	C₂×C₄₃	1	1	yes	characteristic, complemented
157	#2293	C₂×C₄₃	1	1	yes	characteristic
158	#2043	C₂×C₄₃	1	4	yes	complemented
159	#2013	C₂×C₄₃	1	4	yes	—
160	#1981	C₂×C₄₃	1	2	yes	complemented
161	#1831	C₂×C₄₃	1	1	yes	characteristic, complemented
162	C₂×C₄₃	—	8	2	no	—
163	C₂×C₄₃	#2619	1	1	yes	characteristic
164	C₂×C₄₃	C₂×#461	1	1	yes	characteristic
165	C₂×C₄₃	#3039	1	1	yes	characteristic
166	C₂×C₄₃	#3206	1	2	yes	—
167	C₂×C₄₃	#3218	1	2	yes	—
168	C₂²×SD₁₆	C₂²×C₄₃	1	4	yes	—
169	C₂×C₄⋊Q₈	C₂²×C₄₃	1	2	yes	—
170	C₂×C₄⋊Q₈	C₂²×C₄₃	1	4	yes	—
171	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
172	C₂×#117	—	2	1	no	—
173	#461	—	2	8	no	—
174	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
175	C₂×#103	C₂²×C₄₃	1	4	yes	—
176	C₂×#103	C₂²×C₄₃	1	8	yes	—
177	#390	C₂²×C₄₃	1	2	yes	—
178	#389	C₂²×C₄₃	1	2	yes	—
179	#388	—	2	2	no	—
180	#384	—	2	1	no	—
181	#384	—	2	2	no	—
182	#384	—	2	1	no	—
183	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
184	C₄×C₂²⋊C₄	—	2	1	no	—
185	C₄³	C₂²×C₄₃	1	1	yes	characteristic
186	#336	C₂²×C₄₃	1	4	yes	—
187	C₄₃	#29798	1	1	yes	characteristic, direct product factor, Sylow
188	C₂²×Q₈	C₂³×C₄₃	1	4	yes	—
189	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
190	C₂³×C₄	—	2	1	no	—
191	C₂×SD₁₆	—	2	8	no	—
192	C₂×SD₁₆	—	4	8	no	—
193	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
194	C₄⋊Q₈	—	2	4	no	—
195	C₄⋊Q₈	—	2	4	no	—
196	C₄⋊Q₈	—	4	8	no	—
197	C₄×D₄	—	2	2	no	—
198	C₄×D₄	D₄×C₄₃	1	4	yes	—
199	#117	—	4	4	no	—
200	C₂×C₄⋊C₄	—	2	2	no	—
201	C₂×C₄⋊C₄	—	2	4	no	—
202	C₂×C₄⋊C₄	—	2	4	no	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
206	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
207	C₂×C₂²⋊C₄	—	2	1	no	—
208	C₂×C₂²⋊C₄	—	2	2	no	—
209	C₂×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₄²	—	2	1	no	—
211	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
212	C₂×C₄²	D₄×C₄₃	1	2	yes	—
213	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
214	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
215	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
216	C₄⋊C₈	—	2	4	no	—
217	#103	—	2	8	no	—
218	#103	—	4	8	no	—
219	#95	—	2	2	no	—
220	#95	—	2	1	no	—
221	C₂⁴	—	2	1	no	—
222	C₂×Q₈	—	2	4	no	—
223	C₂×Q₈	—	2	4	no	—
224	C₂×Q₈	—	2	8	no	—
225	C₂×Q₈	—	2	8	no	—
226	C₂×D₄	—	2	1	no	—
227	C₂×D₄	—	2	4	no	—
228	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
229	C₂²×C₄	—	2	1	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	4	2	no	—
234	C₂²×C₄	—	4	2	no	—
235	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
236	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
237	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
238	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
239	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
240	SD₁₆	—	4	16	no	—
241	C₂×C₈	—	2	4	no	—
242	C₂×C₈	—	2	8	no	—
243	C₄⋊C₄	—	2	1	no	—
244	C₄⋊C₄	—	2	4	no	—
245	C₄⋊C₄	—	4	8	no	—
246	C₄⋊C₄	—	4	8	no	—
247	C₄⋊C₄	—	4	4	no	—
248	C₄⋊C₄	—	4	4	no	—
249	C₄⋊C₄	—	4	4	no	—
250	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
251	C₂²⋊C₄	—	2	4	no	—
252	C₂²⋊C₄	—	4	4	no	—
253	C₂²⋊C₄	—	4	4	no	—
254	C₄²	—	2	4	no	—
255	C₄²	—	2	2	no	—
256	C₄²	—	2	4	no	—
257	C₄²	—	4	2	no	—
258	C₄²	SD₁₆×C₄₃	1	4	yes	complemented
259	C₄²	C₂×D₄×C₄₃	1	2	yes	—
260	C₄²	#41×C₄₃	1	2	yes	—
261	C₂³	—	2	2	no	—
262	C₂³	—	4	2	no	—
263	C₂³	—	4	1	no	—
264	C₂³	—	4	2	no	—
265	C₂³	—	4	1	no	—
266	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
267	Q₈	—	4	4	no	—
268	Q₈	—	4	4	no	—
269	Q₈	—	4	8	no	—
270	D₄	—	2	4	no	—
271	D₄	—	4	2	no	—
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	4	1	no	—
279	C₂×C₄	—	4	1	no	—
280	C₂×C₄	—	4	8	no	—
281	C₂×C₄	—	4	4	no	—
282	C₂×C₄	—	4	2	no	—
283	C₂×C₄	—	4	8	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	4	2	no	—
286	C₂×C₄	#121×C₄₃	1	2	yes	—
287	C₂×C₄	#121×C₄₃	1	2	yes	—
288	C₂×C₄	C₂×SD₁₆×C₄₃	1	4	yes	—
289	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
290	C₂×C₄	#137×C₄₃	1	4	yes	—
291	C₂×C₄	#137×C₄₃	1	2	yes	—
292	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
293	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
294	C₂×C₄	H(5,𝔽₂)×C₄₃	1	4	yes	—
295	C₈	—	4	4	no	—
296	C₂²	—	4	2	no	—
297	C₂²	—	4	2	no	—
298	C₂²	—	4	2	no	—
299	C₂²	—	8	2	no	—
300	C₂²	—	8	2	no	—
301	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
302	C₂²	C₄₃×#535	1	2	yes	—
303	C₂²	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
304	C₂²	C₂×#137×C₄₃	1	2	yes	—
305	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
306	C₄	—	2	4	no	—
307	C₄	—	2	4	no	—
308	C₄	—	2	2	no	—
309	C₄	—	4	2	no	—
310	C₄	—	8	4	no	—
311	C₄	—	8	2	no	—
312	C₄	C₄₃×#461	1	4	yes	—
313	C₄	C₄₃×#535	1	2	yes	—
314	C₄	C₄₃×#540	1	2	yes	—
315	C₂	—	8	2	no	—
316	C₂	C₄₃×#2619	1	1	yes	characteristic
317	C₂	C₂×C₄₃×#461	1	1	yes	characteristic
318	C₂	C₄₃×#3039	1	1	yes	characteristic
319	C₂	C₄₃×#3206	1	2	yes	—
320	C₂	C₄₃×#3218	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
2. C₄₃×#2868	C₂	semidirect
4. C₄₃×#2043	C₂	semidirect
6. C₄₃×#1981	C₂	semidirect
7. C₄₃×#1831	C₂	semidirect
97. C₄²×C₄₃	SD₁₆	semidirect
135. #29798	C₄₃	direct (N × H)
156. #2868	C₂×C₄₃	semidirect
158. #2043	C₂×C₄₃	semidirect
160. #1981	C₂×C₄₃	semidirect
161. #1831	C₂×C₄₃	semidirect
187. C₄₃	#29798	direct (N × H)
258. C₄²	SD₁₆×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×#461	2
C₄₃×#2868	2
C₄₃×#2293	2
C₄₃×#2043	2
C₄₃×#2013	2
C₄₃×#1981	2
C₄₃×#1831	2
#29798	43

Subgroups — C43×#29798 #24949815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29798 #24949815