Subgroups — C₄₃×#18374 #24938391

Order 11008.

838 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3502	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#3236	C₂	1	2	yes	maximal
3	C₄₃×#2634	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1617	C₂	1	4	yes	maximal
5	C₄₃×#1611	C₂	1	4	yes	maximal
6	C₄₃×#1515	C₂	1	2	yes	maximal
7	C₄₃×#1467	C₂	1	1	yes	maximal, characteristic
8	Q₈²×C₄₃	—	2	2	no	—
9	C₄₃×#557	—	2	2	no	—
10	C₄₃×#557	—	2	4	no	—
11	C₄₃×#544	—	2	1	no	—
12	C₄₃×#544	C₂²	1	4	yes	—
13	C₄₃×#533	—	2	2	no	—
14	C₄₃×#533	C₂²	1	2	yes	—
15	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#519	—	2	1	no	—
17	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#501	—	2	2	no	—
19	C₄₃×#491	—	2	2	no	—
20	C₄₃×#484	C₂²	1	4	yes	—
21	C₄₃×#483	C₂²	1	4	yes	—
22	C₄₃×#479	—	2	4	no	—
23	C₄₃×#432	C₂²	1	2	yes	—
24	C₄₃×#400	—	2	1	no	—
25	C₄₃×#400	C₂²	1	2	yes	—
26	C₄₃×#398	C₂²	1	2	yes	—
27	C₄₃×#395	—	2	1	no	—
28	C₄₃×#387	—	2	2	no	—
29	C₄₃×#383	C₂²	1	1	yes	characteristic
30	C₄₃×#328	C₂²	1	8	yes	—
31	C₄₃×#324	C₂²	1	4	yes	—
32	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
33	C₄⋊Q₈×C₄₃	—	2	2	no	—
34	C₄⋊Q₈×C₄₃	—	2	2	no	—
35	C₄⋊Q₈×C₄₃	—	2	4	no	—
36	C₄⋊Q₈×C₄₃	—	2	8	no	—
37	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
38	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
39	#125×C₄₃	—	2	4	no	—
40	#125×C₄₃	—	2	4	no	—
41	#125×C₄₃	—	2	8	no	—
42	#125×C₄₃	—	2	2	no	—
43	#125×C₄₃	—	2	2	no	—
44	#125×C₄₃	—	2	2	no	—
45	C₂²⋊Q₈×C₄₃	—	2	2	no	—
46	C₂²⋊Q₈×C₄₃	—	2	4	no	—
47	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
48	C₄×Q₈×C₄₃	—	2	4	no	—
49	C₄×Q₈×C₄₃	—	2	4	no	—
50	C₄×Q₈×C₄₃	—	2	4	no	—
51	C₄×Q₈×C₄₃	—	2	4	no	—
52	C₄×Q₈×C₄₃	—	2	2	no	—
53	C₄×Q₈×C₄₃	—	2	2	no	—
54	C₄×Q₈×C₄₃	—	2	2	no	—
55	C₄×Q₈×C₄₃	D₄	1	4	yes	—
56	#117×C₄₃	—	2	4	no	—
57	#117×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
65	C₂×C₄²×C₄₃	D₄	1	2	yes	—
66	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
67	#107×C₄₃	—	2	4	no	—
68	#106×C₄₃	—	2	4	no	—
69	C₄⋊C₈×C₄₃	—	2	2	no	—
70	#103×C₄₃	—	2	4	no	—
71	#103×C₄₃	—	2	4	no	—
72	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
73	#97×C₄₃	—	2	2	no	—
74	#95×C₄₃	—	2	1	no	—
75	#95×C₄₃	—	2	1	no	—
76	#95×C₄₃	—	2	2	no	—
77	#95×C₄₃	—	2	2	no	—
78	#95×C₄₃	—	2	2	no	—
79	#95×C₄₃	C₂³	1	2	yes	—
80	C₂×Q₈×C₄₃	—	2	4	no	—
81	C₂×Q₈×C₄₃	—	2	2	no	—
82	C₂×Q₈×C₄₃	—	2	2	no	—
83	C₂×Q₈×C₄₃	—	2	4	no	—
84	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
85	C₂²×C₄×C₄₃	—	2	2	no	—
86	C₂²×C₄×C₄₃	—	2	1	no	—
87	C₂²×C₄×C₄₃	—	2	1	no	—
88	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
93	C₂×C₈×C₄₃	—	2	4	no	—
94	C₄⋊C₄×C₄₃	—	2	4	no	—
95	C₄⋊C₄×C₄₃	—	2	4	no	—
96	C₄⋊C₄×C₄₃	—	2	4	no	—
97	C₄⋊C₄×C₄₃	—	2	8	no	—
98	C₄⋊C₄×C₄₃	—	2	2	no	—
99	C₄⋊C₄×C₄₃	—	2	2	no	—
100	C₄⋊C₄×C₄₃	—	2	2	no	—
101	C₄⋊C₄×C₄₃	—	2	2	no	—
102	C₄⋊C₄×C₄₃	—	2	4	no	—
103	C₄⋊C₄×C₄₃	—	2	4	no	—
104	C₄⋊C₄×C₄₃	—	2	4	no	—
105	C₄⋊C₄×C₄₃	—	2	2	no	—
106	C₄⋊C₄×C₄₃	—	2	2	no	—
107	C₄⋊C₄×C₄₃	—	4	1	no	—
108	C₄⋊C₄×C₄₃	—	4	2	no	—
109	C₄⋊C₄×C₄₃	—	4	1	no	—
110	C₄⋊C₄×C₄₃	—	4	4	no	—
111	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
112	C₂²⋊C₄×C₄₃	—	2	4	no	—
113	C₄²×C₄₃	—	2	8	no	—
114	C₄²×C₄₃	—	2	2	no	—
115	C₄²×C₄₃	—	2	2	no	—
116	C₄²×C₄₃	—	2	4	no	—
117	C₄²×C₄₃	C₂×D₄	1	2	yes	—
118	C₄²×C₄₃	C₂×D₄	1	2	yes	—
119	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
120	Q₈×C₄₃	—	2	8	no	—
121	Q₈×C₄₃	—	4	4	no	—
122	Q₈×C₄₃	—	4	4	no	—
123	Q₈×C₄₃	—	8	4	no	—
124	C₂×C₄×C₄₃	—	2	2	no	—
125	C₂×C₄×C₄₃	—	2	2	no	—
126	C₂×C₄×C₄₃	—	2	2	no	—
127	C₂×C₄×C₄₃	—	2	4	no	—
128	C₂×C₄×C₄₃	—	2	4	no	—
129	C₂×C₄×C₄₃	—	2	2	no	—
130	C₂×C₄×C₄₃	—	4	1	no	—
131	C₂×C₄×C₄₃	—	4	1	no	—
132	C₂×C₄×C₄₃	—	4	2	no	—
133	C₂×C₄×C₄₃	—	4	2	no	—
134	C₂×C₄×C₄₃	—	4	2	no	—
135	C₂×C₄×C₄₃	—	4	2	no	—
136	C₂×C₄×C₄₃	—	4	1	no	—
137	C₂×C₄×C₄₃	—	4	1	no	—
138	C₂×C₄×C₄₃	—	4	2	no	—
139	C₂×C₄×C₄₃	—	4	2	no	—
140	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
141	C₂×C₄×C₄₃	#120	1	2	yes	—
142	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
143	C₂×C₄×C₄₃	#137	1	4	yes	—
144	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
145	C₈×C₄₃	—	4	4	no	—
146	#18374	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂²×C₄₃	—	2	1	no	—
148	C₂²×C₄₃	—	2	1	no	—
149	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
150	C₂²×C₄₃	C₂×#137	1	2	yes	—
151	C₄×C₄₃	—	2	2	no	—
152	C₄×C₄₃	—	2	4	no	—
153	C₄×C₄₃	—	2	1	no	—
154	C₄×C₄₃	—	2	1	no	—
155	C₄×C₄₃	—	2	2	no	—
156	C₄×C₄₃	—	4	4	no	—
157	C₄×C₄₃	—	4	2	no	—
158	C₄×C₄₃	—	4	4	no	—
159	C₄×C₄₃	—	8	2	no	—
160	C₄×C₄₃	—	8	1	no	—
161	C₄×C₄₃	—	8	1	no	—
162	#3502	C₂×C₄₃	1	1	yes	characteristic
163	#3236	C₂×C₄₃	1	2	yes	—
164	#2634	C₂×C₄₃	1	1	yes	characteristic
165	#1617	C₂×C₄₃	1	4	yes	—
166	#1611	C₂×C₄₃	1	4	yes	—
167	#1515	C₂×C₄₃	1	2	yes	—
168	#1467	C₂×C₄₃	1	1	yes	characteristic
169	C₂×C₄₃	—	2	2	no	—
170	C₂×C₄₃	#3004	1	1	yes	characteristic
171	C₂×C₄₃	#3020	1	1	yes	characteristic
172	C₂×C₄₃	#3028	1	1	yes	characteristic
173	Q₈²	—	2	2	no	—
174	#557	—	2	2	no	—
175	#557	—	2	4	no	—
176	#544	—	2	1	no	—
177	#544	C₂²×C₄₃	1	4	yes	—
178	#533	—	2	2	no	—
179	#533	C₂²×C₄₃	1	2	yes	—
180	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
181	#519	—	2	1	no	—
182	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
183	#501	—	2	2	no	—
184	#491	—	2	2	no	—
185	#484	C₂²×C₄₃	1	4	yes	—
186	#483	C₂²×C₄₃	1	4	yes	—
187	#479	—	2	4	no	—
188	#432	C₂²×C₄₃	1	2	yes	—
189	#400	—	2	1	no	—
190	#400	C₂²×C₄₃	1	2	yes	—
191	#398	C₂²×C₄₃	1	2	yes	—
192	#395	—	2	1	no	—
193	#387	—	2	2	no	—
194	#383	C₂²×C₄₃	1	1	yes	characteristic
195	#328	C₂²×C₄₃	1	8	yes	—
196	#324	C₂²×C₄₃	1	4	yes	—
197	C₄₃	#18374	1	1	yes	characteristic, direct product factor, Sylow
198	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
199	C₄⋊Q₈	—	2	2	no	—
200	C₄⋊Q₈	—	2	2	no	—
201	C₄⋊Q₈	—	2	4	no	—
202	C₄⋊Q₈	—	2	8	no	—
203	C₄⋊Q₈	D₄×C₄₃	1	2	yes	—
204	C₄⋊Q₈	D₄×C₄₃	1	2	yes	—
205	#125	—	2	4	no	—
206	#125	—	2	4	no	—
207	#125	—	2	8	no	—
208	#125	—	2	2	no	—
209	#125	—	2	2	no	—
210	#125	—	2	2	no	—
211	C₂²⋊Q₈	—	2	2	no	—
212	C₂²⋊Q₈	—	2	4	no	—
213	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
214	C₄×Q₈	—	2	4	no	—
215	C₄×Q₈	—	2	4	no	—
216	C₄×Q₈	—	2	4	no	—
217	C₄×Q₈	—	2	4	no	—
218	C₄×Q₈	—	2	2	no	—
219	C₄×Q₈	—	2	2	no	—
220	C₄×Q₈	—	2	2	no	—
221	C₄×Q₈	D₄×C₄₃	1	4	yes	—
222	#117	—	2	4	no	—
223	#117	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	1	no	—
225	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
231	C₂×C₄²	D₄×C₄₃	1	2	yes	—
232	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
233	#107	—	2	4	no	—
234	#106	—	2	4	no	—
235	C₄⋊C₈	—	2	2	no	—
236	#103	—	2	4	no	—
237	#103	—	2	4	no	—
238	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
239	#97	—	2	2	no	—
240	#95	—	2	1	no	—
241	#95	—	2	1	no	—
242	#95	—	2	2	no	—
243	#95	—	2	2	no	—
244	#95	—	2	2	no	—
245	#95	C₂³×C₄₃	1	2	yes	—
246	C₂×Q₈	—	2	4	no	—
247	C₂×Q₈	—	2	2	no	—
248	C₂×Q₈	—	2	2	no	—
249	C₂×Q₈	—	2	4	no	—
250	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	1	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
255	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
256	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
257	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
258	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
259	C₂×C₈	—	2	4	no	—
260	C₄⋊C₄	—	2	4	no	—
261	C₄⋊C₄	—	2	4	no	—
262	C₄⋊C₄	—	2	4	no	—
263	C₄⋊C₄	—	2	8	no	—
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	—	2	2	no	—
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	—	2	4	no	—
270	C₄⋊C₄	—	2	4	no	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	4	1	no	—
274	C₄⋊C₄	—	4	2	no	—
275	C₄⋊C₄	—	4	1	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
278	C₂²⋊C₄	—	2	4	no	—
279	C₄²	—	2	8	no	—
280	C₄²	—	2	2	no	—
281	C₄²	—	2	2	no	—
282	C₄²	—	2	4	no	—
283	C₄²	C₂×D₄×C₄₃	1	2	yes	—
284	C₄²	C₂×D₄×C₄₃	1	2	yes	—
285	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
286	Q₈	—	2	8	no	—
287	Q₈	—	4	4	no	—
288	Q₈	—	4	4	no	—
289	Q₈	—	8	4	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	4	1	no	—
297	C₂×C₄	—	4	1	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	1	no	—
303	C₂×C₄	—	4	1	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
307	C₂×C₄	#120×C₄₃	1	2	yes	—
308	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
309	C₂×C₄	#137×C₄₃	1	4	yes	—
310	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
311	C₈	—	4	4	no	—
312	C₂²	—	2	1	no	—
313	C₂²	—	2	1	no	—
314	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
315	C₂²	C₂×#137×C₄₃	1	2	yes	—
316	C₄	—	2	2	no	—
317	C₄	—	2	4	no	—
318	C₄	—	2	1	no	—
319	C₄	—	2	1	no	—
320	C₄	—	2	2	no	—
321	C₄	—	4	4	no	—
322	C₄	—	4	2	no	—
323	C₄	—	4	4	no	—
324	C₄	—	8	2	no	—
325	C₄	—	8	1	no	—
326	C₄	—	8	1	no	—
327	C₂	—	2	2	no	—
328	C₂	C₄₃×#3004	1	1	yes	characteristic
329	C₂	C₄₃×#3020	1	1	yes	characteristic
330	C₂	C₄₃×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂³×C₄₃	C₂²×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
146. #18374	C₄₃	direct (N × H)
197. C₄₃	#18374	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×#3502	2
C₄₃×#3236	2
C₄₃×#2634	2
C₄₃×#1617	2
C₄₃×#1611	2
C₄₃×#1515	2
C₄₃×#1467	2
#18374	43

Subgroups — C43×#18374 #24938391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#18374 #24938391