Subgroups — #19147120

Order 5504.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583620	C₂	1	1	yes	maximal, characteristic
2	#14583591	C₂	1	1	yes	maximal, characteristic
3	#14583306	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583239	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583238	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583237	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583232	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583204	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583192	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583137	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583006	C₂	1	1	yes	maximal, characteristic, complemented
12	#14582968	C₂	1	1	yes	maximal, characteristic
13	#14582941	C₂	1	1	yes	maximal, characteristic, complemented
14	#14582934	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
17	#13063324	C₂²	1	1	yes	characteristic
18	#13063320	—	2	1	no	—
19	#13063320	—	2	1	no	—
20	#13063318	—	2	1	no	—
21	#13063316	—	2	1	no	—
22	#13063316	C₂²	1	1	yes	characteristic
23	#13063311	—	2	1	no	—
24	#13063309	—	2	1	no	—
25	#13063301	C₂²	1	1	yes	characteristic
26	#13063301	C₂²	1	1	yes	characteristic
27	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
28	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
29	#13063290	—	2	1	no	—
30	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
31	#13063284	C₂²	1	1	yes	characteristic
32	#13063283	C₂²	1	1	yes	characteristic
33	#13063283	C₂²	1	1	yes	characteristic
34	#13063281	—	2	1	no	—
35	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
36	#13063259	C₂²	1	1	yes	characteristic
37	#13063259	C₂²	1	1	yes	characteristic
38	#13063258	C₂²	1	1	yes	characteristic
39	#13063258	C₂²	1	1	yes	characteristic
40	#13063258	C₂²	1	1	yes	characteristic
41	#13063257	C₂²	1	1	yes	characteristic
42	#13063257	C₂²	1	1	yes	characteristic
43	#13063256	C₂²	1	1	yes	characteristic
44	Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
45	#13063249	C₂²	1	1	yes	characteristic
46	#13063249	C₂²	1	1	yes	characteristic
47	#13063249	C₂²	1	1	yes	characteristic
48	#13063249	C₂²	1	1	yes	characteristic
49	C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
50	(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
51	#13063235	C₂²	1	1	yes	characteristic
52	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
54	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
55	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
56	#106×C₄₃	C₂²	1	1	yes	characteristic
57	#103×C₄₃	C₂²	1	1	yes	characteristic
58	#103×C₄₃	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
60	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
63	C₂²×Dic₄₃	—	2	1	no	—
64	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
65	C₂×Dic₈₆	—	2	1	no	—
66	Q₁₆×C₄₃	—	2	2	no	—
67	M₁₆×C₄₃	—	2	2	no	—
68	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
70	C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
73	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
74	C₂²⋊C₄×C₄₃	—	2	1	no	—
75	C₂²⋊C₄×C₄₃	—	2	1	no	—
76	C₂²⋊Dic₄₃	—	2	1	no	—
77	C₂²⋊Dic₄₃	D₄	1	1	yes	characteristic
78	(C₂×D₄₃)⋊C₄	—	2	1	no	—
79	(C₂×D₄₃)⋊C₄	—	2	1	no	—
80	(C₂×D₄₃)⋊C₄	—	2	1	no	—
81	(C₂×D₄₃)⋊C₄	—	2	1	no	—
82	(C₂×D₄₃)⋊C₄	D₄	1	1	yes	characteristic
83	C₄⋊Dic₄₃	—	2	1	no	—
84	C₄⋊Dic₄₃	—	2	1	no	—
85	C₄⋊Dic₄₃	—	2	1	no	—
86	C₄⋊Dic₄₃	—	2	1	no	—
87	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
88	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
89	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
90	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
91	Dic₄₃⋊C₄	—	2	1	no	—
92	Dic₄₃⋊C₄	—	2	1	no	—
93	Dic₄₃⋊C₄	—	2	1	no	—
94	Dic₄₃⋊C₄	—	2	1	no	—
95	Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
96	C₄×Dic₄₃	—	2	1	no	—
97	C₄×Dic₄₃	—	2	1	no	—
98	C₄×Dic₄₃	—	2	1	no	—
99	C₄×Dic₄₃	—	2	1	no	—
100	C₄×Dic₄₃	—	2	1	no	—
101	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
102	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
103	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
104	C₈×D₄₃	—	2	2	no	—
105	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
107	Q₈×C₄₃	—	2	1	no	—
108	Q₈×C₄₃	—	2	1	no	—
109	Q₈×C₄₃	—	2	1	no	—
110	Q₈×C₄₃	—	2	1	no	—
111	C₂×C₄×C₄₃	—	2	1	no	—
112	C₂×C₄×C₄₃	—	2	1	no	—
113	C₂×C₄×C₄₃	—	2	1	no	—
114	C₂×C₄×C₄₃	—	2	1	no	—
115	C₂×C₄×C₄₃	—	2	1	no	—
116	C₂×C₄×C₄₃	—	2	1	no	—
117	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
119	C₂²⋊D₄₃	—	4	1	no	—
120	C₂×Dic₄₃	—	2	1	no	—
121	C₂×Dic₄₃	—	2	1	no	—
122	C₂×Dic₄₃	—	2	1	no	—
123	C₂×Dic₄₃	—	2	1	no	—
124	C₂×Dic₄₃	—	4	2	no	—
125	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
128	C₄×D₄₃	—	2	1	no	—
129	C₄×D₄₃	—	2	1	no	—
130	Dic₈₆	—	4	2	no	—
131	C₈×C₄₃	—	2	1	no	—
132	C₈×C₄₃	#41	1	2	yes	—
133	C₄₃⋊C₈	—	2	1	no	—
134	C₄₃⋊C₈	—	2	1	no	—
135	C₂²×C₄₃	—	2	1	no	—
136	C₂²×C₄₃	—	2	1	no	—
137	C₂²×C₄₃	—	2	1	no	—
138	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
139	C₂×D₄₃	—	2	1	no	—
140	C₂×D₄₃	—	2	1	no	—
141	C₂×D₄₃	—	2	1	no	—
142	C₄×C₄₃	—	2	1	no	—
143	C₄×C₄₃	—	4	1	no	—
144	C₄×C₄₃	—	4	1	no	—
145	C₄×C₄₃	—	4	1	no	—
146	C₄×C₄₃	—	4	1	no	—
147	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
148	C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
149	Dic₄₃	—	2	1	no	—
150	Dic₄₃	—	2	1	no	—
151	Dic₄₃	—	2	1	no	—
152	Dic₄₃	—	4	1	no	—
153	Dic₄₃	—	4	1	no	—
154	Dic₄₃	—	4	1	no	—
155	Dic₄₃	—	4	1	no	—
156	#3349	—	43	1	no	maximal, Sylow
157	C₂×C₄₃	—	4	1	no	—
158	C₂×C₄₃	#547	1	1	yes	characteristic
159	C₂×C₄₃	#575	1	1	yes	characteristic
160	C₂×C₄₃	#578	1	1	yes	characteristic
161	D₄₃	—	4	1	no	—
162	#556	—	43	1	no	—
163	#552	—	43	1	no	—
164	#501	—	43	1	no	—
165	#485	—	43	1	no	—
166	#485	—	43	1	no	—
167	#485	—	43	1	no	—
168	#484	—	43	1	no	—
169	#479	—	43	1	no	—
170	#477	—	43	1	no	—
171	#470	D₄₃	1	1	yes	characteristic, complemented
172	#467	—	43	1	no	—
173	#441	—	43	1	no	—
174	#435	—	43	1	no	—
175	#428	—	43	1	no	—
176	#427	—	43	1	no	—
177	C₄₃	#3349	1	1	yes	characteristic, complemented, Sylow
178	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
179	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
180	C₂²×C₈	—	43	1	no	—
181	C₄⋊Q₈	—	43	1	no	—
182	#126	—	86	1	no	—
183	#126	—	86	1	no	—
184	#126	—	86	1	no	—
185	#125	—	43	1	no	—
186	#125	—	86	1	no	—
187	#124	—	86	1	no	—
188	#123	—	86	1	no	—
189	C₂²⋊Q₈	—	43	1	no	—
190	C₂²⋊Q₈	—	43	1	no	—
191	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
192	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
193	C₄×Q₈	—	43	1	no	—
194	C₄×Q₈	—	43	1	no	—
195	C₄×Q₈	—	86	1	no	—
196	C₄×D₄	—	43	1	no	—
197	#117	—	43	1	no	—
198	#117	—	43	1	no	—
199	#117	—	43	1	no	—
200	#117	—	86	1	no	—
201	C₂×C₄⋊C₄	—	43	1	no	—
202	#107	—	43	1	no	—
203	#107	—	43	1	no	—
204	#107	—	43	1	no	—
205	#107	—	43	1	no	—
206	#107	—	43	1	no	—
207	#106	—	43	1	no	—
208	#106	—	43	1	no	—
209	#106	—	43	1	no	—
210	#106	C₂×D₄₃	1	1	yes	characteristic
211	C₄⋊C₈	—	43	1	no	—
212	#103	—	43	1	no	—
213	#103	—	43	1	no	—
214	#103	—	43	1	no	—
215	#103	—	43	1	no	—
216	#103	C₂×D₄₃	1	1	yes	characteristic
217	#103	C₂×D₄₃	1	1	yes	characteristic
218	C₂²⋊C₈	—	43	1	no	—
219	C₂²⋊C₈	—	43	1	no	—
220	#97	—	43	1	no	—
221	C₂×Q₈	—	86	1	no	—
222	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
223	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
224	C₂×D₄	—	43	1	no	—
225	C₂²×C₄	—	43	1	no	—
226	C₂²×C₄	—	86	1	no	—
227	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
228	Q₁₆	—	2	2	no	—
229	M₁₆	—	2	2	no	—
230	C₂×C₈	—	43	1	no	—
231	C₂×C₈	—	43	1	no	—
232	C₂×C₈	—	86	2	no	—
233	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
234	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
235	C₄⋊C₄	—	2	1	no	—
236	C₄⋊C₄	—	2	1	no	—
237	C₄⋊C₄	—	43	1	no	—
238	C₄⋊C₄	—	43	1	no	—
239	C₄⋊C₄	—	43	1	no	—
240	C₄⋊C₄	—	43	1	no	—
241	C₄⋊C₄	—	43	1	no	—
242	C₄⋊C₄	—	86	1	no	—
243	C₄⋊C₄	—	86	1	no	—
244	C₄⋊C₄	—	86	1	no	—
245	C₄⋊C₄	—	86	1	no	—
246	C₄⋊C₄	—	86	1	no	—
247	C₄⋊C₄	—	86	1	no	—
248	C₄⋊C₄	—	86	1	no	—
249	C₄⋊C₄	—	86	1	no	—
250	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
251	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
252	C₂²⋊C₄	—	2	1	no	—
253	C₂²⋊C₄	—	2	1	no	—
254	C₂²⋊C₄	—	43	1	no	—
255	C₂²⋊C₄	—	43	1	no	—
256	C₂²⋊C₄	—	86	1	no	—
257	C₂²⋊C₄	—	86	1	no	—
258	C₂²⋊C₄	—	86	1	no	—
259	C₂²⋊C₄	—	86	1	no	—
260	C₂²⋊C₄	—	86	1	no	—
261	C₄²	—	43	1	no	—
262	C₄²	—	86	1	no	—
263	C₄²	—	86	1	no	—
264	C₄²	—	86	1	no	—
265	C₄²	—	86	1	no	—
266	C₄²	—	86	1	no	—
267	C₂³	—	43	1	no	—
268	C₂³	D₄×D₄₃	1	1	yes	characteristic
269	Q₈	—	2	1	no	—
270	Q₈	—	2	1	no	—
271	Q₈	—	2	1	no	—
272	Q₈	—	2	1	no	—
273	Q₈	—	172	2	no	—
274	D₄	—	172	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	43	1	no	—
282	C₂×C₄	—	43	1	no	—
283	C₂×C₄	—	43	1	no	—
284	C₂×C₄	—	86	1	no	—
285	C₂×C₄	—	86	1	no	—
286	C₂×C₄	—	86	1	no	—
287	C₂×C₄	—	86	1	no	—
288	C₂×C₄	—	86	1	no	—
289	C₂×C₄	—	86	1	no	—
290	C₂×C₄	—	172	2	no	—
291	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
292	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
293	C₈	—	2	1	no	—
294	C₈	—	86	1	no	—
295	C₈	—	86	1	no	—
296	C₈	#10621900	1	2	yes	—
297	C₂²	—	2	1	no	—
298	C₂²	—	2	1	no	—
299	C₂²	—	2	1	no	—
300	C₂²	—	86	1	no	—
301	C₂²	—	86	1	no	—
302	C₂²	—	86	1	no	—
303	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
304	C₄	—	2	1	no	—
305	C₄	—	4	1	no	—
306	C₄	—	4	1	no	—
307	C₄	—	4	1	no	—
308	C₄	—	4	1	no	—
309	C₄	—	86	1	no	—
310	C₄	—	86	1	no	—
311	C₄	—	86	1	no	—
312	C₄	—	172	1	no	—
313	C₄	—	172	1	no	—
314	C₄	—	172	1	no	—
315	C₄	—	172	1	no	—
316	C₄	C₂×#10621900	1	1	yes	characteristic
317	C₄	#13063372	1	1	yes	characteristic
318	C₂	—	4	1	no	—
319	C₂	—	172	1	no	—
320	C₂	#14583549	1	1	yes	characteristic
321	C₂	#14583698	1	1	yes	characteristic
322	C₂	#14583715	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#470	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#470	D₄₃
hypocenter	C₄₃	#3349
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #470

Complements

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

N	H ≅ G/N	type
3. #14583306	C₂	semidirect
4. #14583239	C₂	semidirect
5. #14583238	C₂	semidirect
6. #14583237	C₂	semidirect
7. #14583232	C₂	semidirect
8. #14583204	C₂	semidirect
9. #14583192	C₂	semidirect
10. #14583137	C₂	semidirect
11. #14583006	C₂	semidirect
13. #14582941	C₂	semidirect
14. #14582934	C₂	semidirect
15. C₄₃×#470	C₂	semidirect
171. #470	D₄₃	semidirect
177. C₄₃	#3349	semidirect