Subgroups — #24984978

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19134575	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582654	C₂	1	1	yes	maximal, characteristic
3	#19132418	C₂	1	4	yes	maximal, complemented
4	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄₃⋊C₈	—	2	1	no	—
6	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
7	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
8	#14582654	—	2	1	no	—
9	#14582654	C₂²	1	2	yes	—
10	#14582654	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
12	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
13	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×#391	—	2	1	no	—
15	C₄₃×#389	—	2	1	no	—
16	C₄₃×#389	C₂²	1	2	yes	—
17	C₄₃×#384	C₄	1	1	yes	characteristic
18	C₄₃×#380	—	2	1	no	—
19	C₄₃×#380	C₄	1	2	yes	—
20	C₂²×C₄₃⋊C₈	—	2	4	no	—
21	C₂²×C₄₃⋊C₈	—	2	2	no	—
22	C₂²×C₄₃⋊C₈	—	2	2	no	—
23	C₂²×C₄₃⋊C₈	—	4	2	no	—
24	C₂²×C₄₃⋊C₈	—	4	2	no	—
25	C₄⋊(C₄₃⋊C₈)	—	4	2	no	—
26	C₂²⋊(C₄₃⋊C₈)	—	4	2	no	—
27	C₂²×Q₈×C₄₃	—	2	1	no	—
28	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
31	C₄⋊Q₈×C₄₃	—	4	2	no	—
32	C₂²⋊Q₈×C₄₃	—	4	2	no	—
33	C₂²⋊Q₈×C₄₃	—	4	2	no	—
34	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
35	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
36	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
37	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
39	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
40	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
41	C₂×C₄²×C₄₃	—	4	2	no	—
42	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
46	#95×C₄₃	—	2	2	no	—
47	#95×C₄₃	—	2	2	no	—
48	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×Q₈×C₄₃	—	4	2	no	—
50	C₂×Q₈×C₄₃	—	4	2	no	—
51	C₂×Q₈×C₄₃	—	4	2	no	—
52	C₂²×C₄×C₄₃	—	2	2	no	—
53	C₂²×C₄×C₄₃	—	2	2	no	—
54	C₂²×C₄×C₄₃	—	2	2	no	—
55	C₂²×C₄×C₄₃	—	2	2	no	—
56	C₂²×C₄×C₄₃	—	2	2	no	—
57	C₂²×C₄×C₄₃	—	2	2	no	—
58	C₂²×C₄×C₄₃	—	4	1	no	—
59	C₂²×C₄×C₄₃	—	4	1	no	—
60	C₂²×C₄×C₄₃	—	4	1	no	—
61	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₃	D₈	1	2	yes	—
65	C₂²×C₄×C₄₃	SD₁₆	1	2	yes	—
66	C₂²×C₄×C₄₃	SD₁₆	1	2	yes	—
67	C₂²×C₄×C₄₃	Q₁₆	1	2	yes	—
68	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
71	C₄⋊C₄×C₄₃	—	2	4	no	—
72	C₄⋊C₄×C₄₃	—	4	2	no	—
73	C₄⋊C₄×C₄₃	—	4	2	no	—
74	C₄⋊C₄×C₄₃	—	4	2	no	—
75	C₄⋊C₄×C₄₃	—	4	2	no	—
76	C₄⋊C₄×C₄₃	—	4	2	no	—
77	C₄⋊C₄×C₄₃	—	4	2	no	—
78	C₂²⋊C₄×C₄₃	—	4	4	no	—
79	C₄²×C₄₃	—	2	2	no	—
80	C₄²×C₄₃	—	2	2	no	—
81	C₄²×C₄₃	—	4	1	no	—
82	C₄²×C₄₃	—	4	1	no	—
83	C₂×C₄₃⋊C₈	—	2	4	no	—
84	C₂×C₄₃⋊C₈	—	4	2	no	—
85	C₂×C₄₃⋊C₈	—	4	8	no	—
86	C₂×C₄₃⋊C₈	—	4	2	no	—
87	C₂×C₄₃⋊C₈	—	4	2	no	—
88	C₂×C₄₃⋊C₈	—	4	2	no	—
89	C₂×C₄₃⋊C₈	—	4	2	no	—
90	C₂³×C₄₃	—	2	1	no	—
91	C₂³×C₄₃	—	2	1	no	—
92	C₂³×C₄₃	—	2	1	no	—
93	C₂³×C₄₃	—	2	1	no	—
94	C₂³×C₄₃	#101	1	2	yes	—
95	C₂³×C₄₃	#102	1	2	yes	—
96	C₂³×C₄₃	#103	1	2	yes	—
97	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	Q₈×C₄₃	—	8	4	no	—
99	C₂×C₄×C₄₃	—	2	1	no	—
100	C₂×C₄×C₄₃	—	2	1	no	—
101	C₂×C₄×C₄₃	—	2	1	no	—
102	C₂×C₄×C₄₃	—	2	1	no	—
103	C₂×C₄×C₄₃	—	2	1	no	—
104	C₂×C₄×C₄₃	—	2	1	no	—
105	C₂×C₄×C₄₃	—	2	1	no	—
106	C₂×C₄×C₄₃	—	2	1	no	—
107	C₂×C₄×C₄₃	—	2	4	no	—
108	C₂×C₄×C₄₃	—	2	4	no	—
109	C₂×C₄×C₄₃	—	2	1	no	—
110	C₂×C₄×C₄₃	—	2	1	no	—
111	C₂×C₄×C₄₃	—	2	1	no	—
112	C₂×C₄×C₄₃	—	4	2	no	—
113	C₂×C₄×C₄₃	—	4	2	no	—
114	C₂×C₄×C₄₃	—	4	4	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	#99	1	2	yes	—
122	C₂×C₄×C₄₃	#102	1	2	yes	—
123	C₂×C₄×C₄₃	#103	1	2	yes	—
124	C₂×C₄×C₄₃	#104	1	2	yes	—
125	C₂×C₄×C₄₃	#131	1	2	yes	—
126	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
127	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
128	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
129	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
130	C₄₃⋊C₈	—	4	4	no	—
131	C₄₃⋊C₈	—	8	2	no	—
132	#7665	—	43	1	no	maximal, Sylow
133	C₂²×C₄₃	—	2	2	no	—
134	C₂²×C₄₃	—	2	2	no	—
135	C₂²×C₄₃	—	2	2	no	—
136	C₂²×C₄₃	—	2	2	no	—
137	C₂²×C₄₃	—	2	2	no	—
138	C₂²×C₄₃	—	2	2	no	—
139	C₂²×C₄₃	#332	1	4	yes	—
140	C₂²×C₄₃	#408	1	1	yes	characteristic
141	C₂²×C₄₃	C₂×#99	1	1	yes	characteristic
142	C₂²×C₄₃	C₂×#101	1	1	yes	characteristic
143	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
144	C₂²×C₄₃	C₂×#103	1	1	yes	characteristic
145	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
146	C₂²×C₄₃	#421	1	1	yes	characteristic
147	C₄×C₄₃	—	2	2	no	—
148	C₄×C₄₃	—	2	1	no	—
149	C₄×C₄₃	—	2	1	no	—
150	C₄×C₄₃	—	2	1	no	—
151	C₄×C₄₃	—	2	2	no	—
152	C₄×C₄₃	—	2	1	no	—
153	C₄×C₄₃	—	4	1	no	—
154	C₄×C₄₃	—	8	2	no	—
155	C₄×C₄₃	—	8	2	no	—
156	C₄×C₄₃	#328	1	4	yes	—
157	#2857	D₄₃	1	1	yes	characteristic
158	#1797	—	43	1	no	—
159	C₂×#336	—	43	1	no	—
160	#1271	—	43	4	no	—
161	C₂×C₄₃	—	2	4	no	—
162	C₂×C₄₃	#1472	1	1	yes	characteristic
163	C₂×C₄₃	#1481	1	1	yes	characteristic
164	C₂×C₄₃	#1492	1	1	yes	characteristic
165	C₂×C₄₃	C₂×#328	1	1	yes	characteristic
166	C₂×C₄₃	#1519	1	1	yes	characteristic
167	C₂×C₄₃	#1531	1	1	yes	characteristic
168	C₂×C₄₃	C₂×#332	1	1	yes	characteristic
169	C₂³×C₈	—	86	1	no	—
170	C₂×C₄⋊Q₈	Dic₄₃	1	1	yes	characteristic
171	C₂×C₂²⋊Q₈	—	2	1	no	—
172	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
173	C₂×C₄⋊C₈	—	86	1	no	—
174	C₂×C₂²⋊C₈	—	86	1	no	—
175	#391	—	2	1	no	—
176	#389	—	2	1	no	—
177	#389	C₂×D₄₃	1	2	yes	—
178	#384	Dic₄₃	1	1	yes	characteristic
179	#380	—	2	1	no	—
180	#380	Dic₄₃	1	2	yes	—
181	#336	—	43	2	no	—
182	#336	—	43	2	no	—
183	#336	—	86	1	no	—
184	C₄₃	#7665	1	1	yes	characteristic, complemented, Sylow
185	C₂²×Q₈	—	2	1	no	—
186	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
187	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
188	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
189	C₂²×C₈	—	86	4	no	—
190	C₂²×C₈	—	86	2	no	—
191	C₂²×C₈	—	86	2	no	—
192	C₂²×C₈	—	172	2	no	—
193	C₂²×C₈	—	172	2	no	—
194	C₄⋊Q₈	—	4	2	no	—
195	C₂²⋊Q₈	—	4	2	no	—
196	C₂²⋊Q₈	—	4	2	no	—
197	C₂×C₄⋊C₄	—	2	1	no	—
198	C₂×C₄⋊C₄	—	2	1	no	—
199	C₂×C₄⋊C₄	—	2	1	no	—
200	C₂×C₄⋊C₄	—	2	2	no	—
201	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
202	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
203	C₂×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₄²	—	4	2	no	—
205	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
206	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
207	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
208	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
209	C₄⋊C₈	—	172	2	no	—
210	C₂²⋊C₈	—	172	2	no	—
211	#95	—	2	2	no	—
212	#95	—	2	2	no	—
213	C₂⁴	C₂²⋊Dic₄₃	1	1	yes	characteristic
214	C₂×Q₈	—	4	2	no	—
215	C₂×Q₈	—	4	2	no	—
216	C₂×Q₈	—	4	2	no	—
217	C₂²×C₄	—	2	2	no	—
218	C₂²×C₄	—	2	2	no	—
219	C₂²×C₄	—	2	2	no	—
220	C₂²×C₄	—	2	2	no	—
221	C₂²×C₄	—	2	2	no	—
222	C₂²×C₄	—	2	2	no	—
223	C₂²×C₄	—	4	1	no	—
224	C₂²×C₄	—	4	1	no	—
225	C₂²×C₄	—	4	1	no	—
226	C₂²×C₄	#10621882	1	2	yes	—
227	C₂²×C₄	#10621883	1	2	yes	—
228	C₂²×C₄	#10621884	1	2	yes	—
229	C₂²×C₄	#10621885	1	2	yes	—
230	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
231	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
232	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
233	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
234	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
235	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
236	C₂×C₈	—	86	4	no	—
237	C₂×C₈	—	172	2	no	—
238	C₂×C₈	—	172	2	no	—
239	C₂×C₈	—	172	2	no	—
240	C₂×C₈	—	172	2	no	—
241	C₂×C₈	—	172	8	no	—
242	C₂×C₈	—	172	2	no	—
243	C₄⋊C₄	—	2	4	no	—
244	C₄⋊C₄	—	4	2	no	—
245	C₄⋊C₄	—	4	2	no	—
246	C₄⋊C₄	—	4	2	no	—
247	C₄⋊C₄	—	4	2	no	—
248	C₄⋊C₄	—	4	2	no	—
249	C₄⋊C₄	—	4	2	no	—
250	C₂²⋊C₄	—	4	4	no	—
251	C₄²	—	2	2	no	—
252	C₄²	—	2	2	no	—
253	C₄²	—	4	1	no	—
254	C₄²	—	4	1	no	—
255	C₂³	—	2	1	no	—
256	C₂³	—	2	1	no	—
257	C₂³	—	2	1	no	—
258	C₂³	—	2	1	no	—
259	C₂³	#13063244	1	2	yes	—
260	C₂³	#13063246	1	2	yes	—
261	C₂³	#13063249	1	2	yes	—
262	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
263	Q₈	—	8	4	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	2	1	no	—
272	C₂×C₄	—	2	4	no	—
273	C₂×C₄	—	2	4	no	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	4	2	no	—
278	C₂×C₄	—	4	2	no	—
279	C₂×C₄	—	4	4	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	#13063240	1	2	yes	—
287	C₂×C₄	#13063246	1	2	yes	—
288	C₂×C₄	#13063249	1	2	yes	—
289	C₂×C₄	#13063252	1	2	yes	—
290	C₂×C₄	#13063332	1	2	yes	—
291	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
292	C₂×C₄	C₂×#10621884	1	1	yes	characteristic
293	C₂×C₄	C₂×#10621883	1	1	yes	characteristic
294	C₂×C₄	C₂×#10621885	1	1	yes	characteristic
295	C₈	—	344	2	no	—
296	C₈	—	172	4	no	—
297	C₂²	—	2	2	no	—
298	C₂²	—	2	2	no	—
299	C₂²	—	2	2	no	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	2	no	—
302	C₂²	—	2	2	no	—
303	C₂²	#14582645	1	4	yes	—
304	C₂²	#14582866	1	1	yes	characteristic
305	C₂²	C₂×#13063240	1	1	yes	characteristic
306	C₂²	C₂×#13063244	1	1	yes	characteristic
307	C₂²	C₂×#13063246	1	1	yes	characteristic
308	C₂²	C₂×#13063249	1	1	yes	characteristic
309	C₂²	C₂×#13063252	1	1	yes	characteristic
310	C₂²	#14582916	1	1	yes	characteristic
311	C₄	—	2	2	no	—
312	C₄	—	2	1	no	—
313	C₄	—	2	1	no	—
314	C₄	—	2	1	no	—
315	C₄	—	2	2	no	—
316	C₄	—	2	1	no	—
317	C₄	—	4	1	no	—
318	C₄	—	8	2	no	—
319	C₄	—	8	2	no	—
320	C₄	#14582636	1	4	yes	—
321	C₂	—	2	4	no	—
322	C₂	#19132959	1	1	yes	characteristic
323	C₂	#19132998	1	1	yes	characteristic
324	C₂	#19133046	1	1	yes	characteristic
325	C₂	C₂×#14582636	1	1	yes	characteristic
326	C₂	#19133163	1	1	yes	characteristic
327	C₂	#19133210	1	1	yes	characteristic
328	C₂	C₂×#14582645	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#2857	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#2857	D₄₃
hypocenter	C₄₃	#7665
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2857

Complements

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

N	H ≅ G/N	type
3. #19132418	C₂	semidirect
184. C₄₃	#7665	semidirect

Maximal subgroups

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

subgroup	index
#19134575	2
C₂×#14582654	2
#19132418	2
C₄₃×#2857	2
#7665	43