Subgroups — C₄₃×#14282 #24934299

Order 11008.

1630 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#382	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#376	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1446	C₂	1	4	yes	maximal
5	C₄₃×#1445	C₂	1	4	yes	maximal
6	C₄₃×C₄⋊#95	C₂	1	4	yes	maximal
7	C₂³×Q₈×C₄₃	C₂²	1	2	yes	—
8	C₂×C₄⋊Q₈×C₄₃	—	2	4	no	—
9	C₂×C₄⋊Q₈×C₄₃	—	2	4	no	—
10	C₂×C₄⋊Q₈×C₄₃	C₄	1	8	yes	complemented
11	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#382	—	2	4	no	—
17	C₄₃×#376	—	2	4	no	—
18	C₂×#95×C₄₃	C₂²	1	2	yes	—
19	C₂×#95×C₄₃	C₂²	1	2	yes	—
20	C₂×#95×C₄₃	C₂²	1	2	yes	—
21	C₂×#95×C₄₃	C₂²	1	2	yes	—
22	C₂×#95×C₄₃	C₂²	1	16	yes	—
23	C₂²×Q₈×C₄₃	—	2	4	no	—
24	C₂²×Q₈×C₄₃	—	2	4	no	—
25	C₂²×Q₈×C₄₃	—	4	8	no	—
26	C₂²×Q₈×C₄₃	C₂×C₄	1	8	yes	—
27	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
28	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
29	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
30	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
33	C₄⋊Q₈×C₄₃	—	2	32	no	—
34	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
35	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
36	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
37	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
38	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
39	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
40	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
41	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
42	C₂×C₄²×C₄₃	—	2	4	no	—
43	C₂×C₄²×C₄₃	—	2	4	no	—
44	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₄₃	D₄	1	4	yes	—
46	C₂×C₄²×C₄₃	D₄	1	4	yes	—
47	C₂×C₄²×C₄₃	Q₈	1	8	yes	complemented
48	#95×C₄₃	—	2	4	no	—
49	#95×C₄₃	—	2	4	no	—
50	#95×C₄₃	—	2	4	no	—
51	#95×C₄₃	—	2	4	no	—
52	#95×C₄₃	—	4	16	no	—
53	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
54	C₂×Q₈×C₄₃	—	2	16	no	—
55	C₂×Q₈×C₄₃	—	4	16	no	—
56	C₂×Q₈×C₄₃	—	4	16	no	—
57	C₂×Q₈×C₄₃	—	4	16	no	—
58	C₂²×C₄×C₄₃	—	2	4	no	—
59	C₂²×C₄×C₄₃	—	2	4	no	—
60	C₂²×C₄×C₄₃	—	2	4	no	—
61	C₂²×C₄×C₄₃	—	2	4	no	—
62	C₂²×C₄×C₄₃	—	2	4	no	—
63	C₂²×C₄×C₄₃	—	2	8	no	—
64	C₂²×C₄×C₄₃	—	2	4	no	—
65	C₂²×C₄×C₄₃	—	2	8	no	—
66	C₂²×C₄×C₄₃	—	2	16	no	—
67	C₂²×C₄×C₄₃	—	2	8	no	—
68	C₂²×C₄×C₄₃	—	2	4	no	—
69	C₂²×C₄×C₄₃	—	2	8	no	—
70	C₂²×C₄×C₄₃	—	2	8	no	—
71	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
72	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
73	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
74	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
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	2	yes	—
78	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
80	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₄₃	C₂×Q₈	1	8	yes	—
82	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
83	C₂²×C₄×C₄₃	#41	1	4	yes	—
84	C₄⋊C₄×C₄₃	—	2	16	no	—
85	C₄⋊C₄×C₄₃	—	2	16	no	—
86	C₄⋊C₄×C₄₃	—	4	8	no	—
87	C₄²×C₄₃	—	2	16	no	—
88	C₄²×C₄₃	C₂²⋊C₄	1	16	yes	—
89	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
90	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
91	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
92	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
93	C₂³×C₄₃	C₂×#41	1	2	yes	—
94	C₂³×C₄₃	H(5,𝔽₂)	1	4	yes	—
95	C₂³×C₄₃	2₋¹⁺⁴	1	4	yes	—
96	Q₈×C₄₃	—	4	32	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	4	no	—
102	C₂×C₄×C₄₃	—	2	4	no	—
103	C₂×C₄×C₄₃	—	2	8	no	—
104	C₂×C₄×C₄₃	—	2	16	no	—
105	C₂×C₄×C₄₃	—	2	8	no	—
106	C₂×C₄×C₄₃	—	2	16	no	—
107	C₂×C₄×C₄₃	—	4	4	no	—
108	C₂×C₄×C₄₃	—	4	8	no	—
109	C₂×C₄×C₄₃	—	4	8	no	—
110	C₂×C₄×C₄₃	—	4	4	no	—
111	C₂×C₄×C₄₃	—	4	8	no	—
112	C₂×C₄×C₄₃	—	4	4	no	—
113	C₂×C₄×C₄₃	—	4	4	no	—
114	C₂×C₄×C₄₃	—	4	4	no	—
115	C₂×C₄×C₄₃	—	4	16	no	—
116	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
117	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
118	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
119	C₂×C₄×C₄₃	C₄×Q₈	1	8	yes	—
120	C₂×C₄×C₄₃	C₂²⋊Q₈	1	8	yes	—
121	C₂×C₄×C₄₃	#124	1	4	yes	—
122	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
123	#14282	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
126	C₂²×C₄₃	#518	1	2	yes	—
127	C₂²×C₄₃	#519	1	2	yes	—
128	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
129	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
130	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
131	C₂²×C₄₃	#535	1	2	yes	—
132	C₂²×C₄₃	#535	1	2	yes	—
133	C₂²×C₄₃	#536	1	2	yes	—
134	C₂²×C₄₃	#536	1	2	yes	—
135	C₂²×C₄₃	#542	1	8	yes	—
136	C₂²×C₄₃	#544	1	8	yes	—
137	C₄×C₄₃	—	2	4	no	—
138	C₄×C₄₃	—	2	4	no	—
139	C₄×C₄₃	—	4	8	no	—
140	C₄×C₄₃	—	4	8	no	—
141	C₄×C₄₃	—	8	4	no	—
142	C₄×C₄₃	#391	1	8	yes	—
143	C₂²×C₄⋊Q₈	C₂×C₄₃	1	1	yes	characteristic
144	C₂×#382	C₂×C₄₃	1	1	yes	characteristic
145	C₂×#376	C₂×C₄₃	1	1	yes	characteristic
146	#1446	C₂×C₄₃	1	4	yes	—
147	#1445	C₂×C₄₃	1	4	yes	—
148	C₄⋊#95	C₂×C₄₃	1	4	yes	—
149	C₂×C₄₃	C₂×#391	1	1	yes	characteristic
150	C₂×C₄₃	#2309	1	1	yes	characteristic
151	C₂×C₄₃	#2310	1	1	yes	characteristic
152	C₂×C₄₃	#2331	1	4	yes	—
153	C₂×C₄₃	#2628	1	4	yes	—
154	C₂×C₄₃	#2640	1	2	yes	—
155	C₂×C₄₃	#2660	1	2	yes	—
156	C₂³×Q₈	C₂²×C₄₃	1	2	yes	—
157	C₂×C₄⋊Q₈	—	2	4	no	—
158	C₂×C₄⋊Q₈	—	2	4	no	—
159	C₂×C₄⋊Q₈	C₄×C₄₃	1	8	yes	complemented
160	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
161	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
162	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
163	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
164	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
165	#382	—	2	4	no	—
166	#376	—	2	4	no	—
167	C₂×#95	C₂²×C₄₃	1	2	yes	—
168	C₂×#95	C₂²×C₄₃	1	2	yes	—
169	C₂×#95	C₂²×C₄₃	1	2	yes	—
170	C₂×#95	C₂²×C₄₃	1	2	yes	—
171	C₂×#95	C₂²×C₄₃	1	16	yes	—
172	C₄₃	#14282	1	1	yes	characteristic, direct product factor, Sylow
173	C₂²×Q₈	—	2	4	no	—
174	C₂²×Q₈	—	2	4	no	—
175	C₂²×Q₈	—	4	8	no	—
176	C₂²×Q₈	C₂×C₄×C₄₃	1	8	yes	—
177	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
178	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
179	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
180	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
181	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
182	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
183	C₄⋊Q₈	—	2	32	no	—
184	C₂×C₄⋊C₄	—	2	4	no	—
185	C₂×C₄⋊C₄	—	2	4	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×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
192	C₂×C₄²	—	2	4	no	—
193	C₂×C₄²	—	2	4	no	—
194	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
195	C₂×C₄²	D₄×C₄₃	1	4	yes	—
196	C₂×C₄²	D₄×C₄₃	1	4	yes	—
197	C₂×C₄²	Q₈×C₄₃	1	8	yes	complemented
198	#95	—	2	4	no	—
199	#95	—	2	4	no	—
200	#95	—	2	4	no	—
201	#95	—	2	4	no	—
202	#95	—	4	16	no	—
203	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
204	C₂×Q₈	—	2	16	no	—
205	C₂×Q₈	—	4	16	no	—
206	C₂×Q₈	—	4	16	no	—
207	C₂×Q₈	—	4	16	no	—
208	C₂²×C₄	—	2	4	no	—
209	C₂²×C₄	—	2	4	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	8	no	—
215	C₂²×C₄	—	2	16	no	—
216	C₂²×C₄	—	2	8	no	—
217	C₂²×C₄	—	2	4	no	—
218	C₂²×C₄	—	2	8	no	—
219	C₂²×C₄	—	2	8	no	—
220	C₂²×C₄	—	2	8	no	—
221	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
222	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
223	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
224	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
225	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
226	C₂²×C₄	C₂×D₄×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×D₄×C₄₃	1	2	yes	—
231	C₂²×C₄	C₂×Q₈×C₄₃	1	8	yes	—
232	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
233	C₂²×C₄	#41×C₄₃	1	4	yes	—
234	C₄⋊C₄	—	2	16	no	—
235	C₄⋊C₄	—	2	16	no	—
236	C₄⋊C₄	—	4	8	no	—
237	C₄²	—	2	16	no	—
238	C₄²	C₂²⋊C₄×C₄₃	1	16	yes	—
239	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
240	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
241	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
242	C₂³	C₂²×Q₈×C₄₃	1	2	yes	—
243	C₂³	C₂×#41×C₄₃	1	2	yes	—
244	C₂³	H(5,𝔽₂)×C₄₃	1	4	yes	—
245	C₂³	2₋¹⁺⁴×C₄₃	1	4	yes	—
246	Q₈	—	4	32	no	—
247	C₂×C₄	—	2	4	no	—
248	C₂×C₄	—	2	4	no	—
249	C₂×C₄	—	2	4	no	—
250	C₂×C₄	—	2	4	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	2	4	no	—
253	C₂×C₄	—	2	8	no	—
254	C₂×C₄	—	2	16	no	—
255	C₂×C₄	—	2	8	no	—
256	C₂×C₄	—	2	16	no	—
257	C₂×C₄	—	4	8	no	—
258	C₂×C₄	—	4	8	no	—
259	C₂×C₄	—	4	4	no	—
260	C₂×C₄	—	4	4	no	—
261	C₂×C₄	—	4	8	no	—
262	C₂×C₄	—	4	4	no	—
263	C₂×C₄	—	4	4	no	—
264	C₂×C₄	—	4	4	no	—
265	C₂×C₄	—	4	16	no	—
266	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
267	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
268	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
269	C₂×C₄	C₄×Q₈×C₄₃	1	8	yes	—
270	C₂×C₄	C₂²⋊Q₈×C₄₃	1	8	yes	—
271	C₂×C₄	#124×C₄₃	1	4	yes	—
272	C₂×C₄	C₄⋊Q₈×C₄₃	1	4	yes	—
273	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
274	C₂²	C₂×C₄×Q₈×C₄₃	1	2	yes	—
275	C₂²	C₄₃×#518	1	2	yes	—
276	C₂²	C₄₃×#519	1	2	yes	—
277	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	2	yes	—
278	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
279	C₂²	C₂×C₄⋊Q₈×C₄₃	1	1	yes	characteristic
280	C₂²	C₄₃×#535	1	2	yes	—
281	C₂²	C₄₃×#535	1	2	yes	—
282	C₂²	C₄₃×#536	1	2	yes	—
283	C₂²	C₄₃×#536	1	2	yes	—
284	C₂²	C₄₃×#542	1	8	yes	—
285	C₂²	C₄₃×#544	1	8	yes	—
286	C₄	—	2	4	no	—
287	C₄	—	2	4	no	—
288	C₄	—	4	8	no	—
289	C₄	—	4	8	no	—
290	C₄	—	8	4	no	—
291	C₄	C₄₃×#391	1	8	yes	—
292	C₂	C₂×C₄₃×#391	1	1	yes	characteristic
293	C₂	C₄₃×#2309	1	1	yes	characteristic
294	C₂	C₄₃×#2310	1	1	yes	characteristic
295	C₂	C₄₃×#2331	1	4	yes	—
296	C₂	C₄₃×#2628	1	4	yes	—
297	C₂	C₄₃×#2640	1	2	yes	—
298	C₂	C₄₃×#2660	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
10. C₂×C₄⋊Q₈×C₄₃	C₄	semidirect
47. C₂×C₄²×C₄₃	Q₈	semidirect
123. #14282	C₄₃	direct (N × H)
159. C₂×C₄⋊Q₈	C₄×C₄₃	semidirect
172. C₄₃	#14282	direct (N × H)
197. C₂×C₄²	Q₈×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₄₃	2
C₂×C₄₃×#382	2
C₂×C₄₃×#376	2
C₄₃×#1446	2
C₄₃×#1445	2
C₄₃×C₄⋊#95	2
#14282	43

Subgroups — C43×#14282 #24934299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#14282 #24934299