Subgroups — #19147127

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	#14583619	C₂	1	1	yes	maximal, characteristic
2	#14583589	C₂	1	1	yes	maximal, characteristic
3	#14583308	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583241	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583241	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583241	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583235	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583207	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583195	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583157	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583140	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583007	C₂	1	1	yes	maximal, characteristic, complemented
13	#14582941	C₂	1	1	yes	maximal, characteristic, complemented
14	#14582937	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#435	C₂	1	1	yes	maximal, characteristic
16	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
17	#13063325	C₂²	1	1	yes	characteristic
18	#13063318	—	2	1	no	—
19	#13063318	—	2	1	no	—
20	#13063318	—	2	1	no	—
21	#13063317	C₂²	1	1	yes	characteristic
22	#13063315	—	2	1	no	—
23	#13063312	—	2	1	no	—
24	#13063306	—	2	1	no	—
25	#13063304	C₂²	1	1	yes	characteristic
26	#13063304	C₂²	1	1	yes	characteristic
27	#13063304	C₂²	1	1	yes	characteristic
28	#13063304	C₂²	1	1	yes	characteristic
29	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
30	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
31	#13063290	—	2	1	no	—
32	#13063284	C₂²	1	1	yes	characteristic
33	#13063284	C₂²	1	1	yes	characteristic
34	#13063284	C₂²	1	1	yes	characteristic
35	#13063281	—	2	1	no	—
36	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
37	#13063259	C₂²	1	1	yes	characteristic
38	#13063259	C₂²	1	1	yes	characteristic
39	#13063259	C₂²	1	1	yes	characteristic
40	#13063259	C₂²	1	1	yes	characteristic
41	#13063259	C₂²	1	1	yes	characteristic
42	#13063257	C₂²	1	1	yes	characteristic
43	#13063257	C₂²	1	1	yes	characteristic
44	#13063257	C₂²	1	1	yes	characteristic
45	#13063257	C₂²	1	1	yes	characteristic
46	#13063250	C₂²	1	1	yes	characteristic
47	#13063250	C₂²	1	1	yes	characteristic
48	#13063250	C₂²	1	1	yes	characteristic
49	#13063250	C₂²	1	1	yes	characteristic
50	#13063250	C₂²	1	1	yes	characteristic
51	#13063250	C₂²	1	1	yes	characteristic
52	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
53	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
55	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
56	C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
57	C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
58	#97×C₄₃	C₂²	1	1	yes	characteristic
59	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
60	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂²×Dic₄₃	—	2	1	no	—
63	C₂×Dic₈₆	—	2	1	no	—
64	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
65	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
66	M₁₆×C₄₃	—	2	2	no	—
67	C₂×C₈×C₄₃	—	2	2	no	—
68	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
71	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
72	C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
73	C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
74	C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
75	C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	C₂²⋊Dic₄₃	—	2	1	no	—
77	C₂²⋊Dic₄₃	—	2	1	no	—
78	C₂²⋊Dic₄₃	—	2	1	no	—
79	C₂²⋊Dic₄₃	—	2	1	no	—
80	C₂²⋊Dic₄₃	—	2	1	no	—
81	C₂²⋊Dic₄₃	—	2	1	no	—
82	C₂²⋊Dic₄₃	—	2	1	no	—
83	C₄⋊Dic₄₃	—	2	1	no	—
84	C₄⋊Dic₄₃	—	2	1	no	—
85	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
86	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
96	Dic₄₃⋊C₄	—	2	1	no	—
97	Dic₄₃⋊C₄	—	2	1	no	—
98	Dic₄₃⋊C₄	—	2	1	no	—
99	C₄×Dic₄₃	—	2	1	no	—
100	C₄×Dic₄₃	—	2	1	no	—
101	C₄×Dic₄₃	—	2	1	no	—
102	C₄×Dic₄₃	—	2	1	no	—
103	C₄×Dic₄₃	—	2	1	no	—
104	Dic₁₇₂	—	2	2	no	—
105	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
107	D₄×C₄₃	—	4	1	no	—
108	C₂×C₄×C₄₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
113	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
117	C₂×Dic₄₃	—	2	1	no	—
118	C₂×Dic₄₃	—	2	1	no	—
119	C₂×Dic₄₃	—	2	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	—	2	1	no	—
125	C₂×Dic₄₃	—	4	2	no	—
126	Dic₈₆	—	2	1	no	—
127	Dic₈₆	—	2	1	no	—
128	Dic₈₆	—	2	1	no	—
129	Dic₈₆	—	2	1	no	—
130	Dic₈₆	—	4	2	no	—
131	C₈×C₄₃	—	2	1	no	—
132	C₈×C₄₃	—	2	1	no	—
133	C₈×C₄₃	—	2	1	no	—
134	C₈×C₄₃	#41	1	2	yes	—
135	C₂²×C₄₃	—	2	1	no	—
136	C₂²×C₄₃	—	2	1	no	—
137	C₂²×C₄₃	—	2	1	no	—
138	C₂²×C₄₃	—	2	1	no	—
139	C₂²×C₄₃	—	2	1	no	—
140	C₂²×C₄₃	—	2	1	no	—
141	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
142	C₄×C₄₃	—	2	1	no	—
143	C₄×C₄₃	—	2	1	no	—
144	C₄×C₄₃	—	2	1	no	—
145	C₄×C₄₃	—	2	1	no	—
146	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
147	C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
148	Dic₄₃	—	4	1	no	—
149	Dic₄₃	—	4	1	no	—
150	Dic₄₃	—	4	1	no	—
151	Dic₄₃	—	4	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	—	4	1	no	—
159	C₂×C₄₃	#547	1	1	yes	characteristic
160	C₂×C₄₃	#575	1	1	yes	characteristic
161	C₂×C₄₃	#578	1	1	yes	characteristic
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	—	43	1	no	—
172	#467	—	43	1	no	—
173	#441	—	43	1	no	—
174	#435	D₄₃	1	1	yes	characteristic
175	#428	—	43	1	no	—
176	#427	—	43	1	no	—
177	C₄₃	#3349	1	1	yes	characteristic, complemented, Sylow
178	C₂×Q₁₆	—	43	1	no	—
179	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
180	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
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	—	43	1	no	—
192	C₂²⋊Q₈	—	43	1	no	—
193	C₄×Q₈	—	43	1	no	—
194	C₄×Q₈	—	43	1	no	—
195	C₄×Q₈	—	86	1	no	—
196	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
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	—	43	1	no	—
211	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
212	#103	—	43	1	no	—
213	#103	—	43	1	no	—
214	#103	—	43	1	no	—
215	#103	—	43	1	no	—
216	#103	—	43	1	no	—
217	#103	—	43	1	no	—
218	C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic
219	C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic
220	#97	C₂×D₄₃	1	1	yes	characteristic
221	C₂×Q₈	—	43	1	no	—
222	C₂×Q₈	—	43	1	no	—
223	C₂×Q₈	—	86	1	no	—
224	C₂×D₄	D₁₇₂	1	1	yes	characteristic
225	C₂²×C₄	—	86	1	no	—
226	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
227	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
228	Q₁₆	—	86	2	no	—
229	M₁₆	—	2	2	no	—
230	C₂×C₈	—	2	2	no	—
231	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
232	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
233	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
234	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
235	C₄⋊C₄	—	43	1	no	—
236	C₄⋊C₄	—	43	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	—	86	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	—	86	1	no	—
251	C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
252	C₂²⋊C₄	—	86	1	no	—
253	C₂²⋊C₄	—	86	1	no	—
254	C₂²⋊C₄	—	86	1	no	—
255	C₂²⋊C₄	—	86	1	no	—
256	C₂²⋊C₄	—	86	1	no	—
257	C₂²⋊C₄	—	86	1	no	—
258	C₂²⋊C₄	—	86	1	no	—
259	C₂²⋊C₄	D₁₇₂	1	1	yes	characteristic
260	C₂²⋊C₄	D₁₇₂	1	1	yes	characteristic
261	C₄²	—	86	1	no	—
262	C₄²	—	86	1	no	—
263	C₄²	—	86	1	no	—
264	C₄²	—	86	1	no	—
265	C₄²	—	86	1	no	—
266	C₄²	C₂²×D₄₃	1	1	yes	characteristic
267	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
268	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
269	Q₈	—	86	1	no	—
270	Q₈	—	86	1	no	—
271	Q₈	—	86	1	no	—
272	Q₈	—	86	1	no	—
273	Q₈	—	172	2	no	—
274	D₄	—	4	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	—	86	1	no	—
280	C₂×C₄	—	86	1	no	—
281	C₂×C₄	—	86	1	no	—
282	C₂×C₄	—	86	1	no	—
283	C₂×C₄	—	86	1	no	—
284	C₂×C₄	—	86	1	no	—
285	C₂×C₄	—	86	1	no	—
286	C₂×C₄	—	86	1	no	—
287	C₂×C₄	—	172	2	no	—
288	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
289	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
290	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
291	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
292	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
293	C₈	—	2	1	no	—
294	C₈	—	2	1	no	—
295	C₈	—	2	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	—	2	1	no	—
301	C₂²	—	2	1	no	—
302	C₂²	—	2	1	no	—
303	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
304	C₄	—	2	1	no	—
305	C₄	—	2	1	no	—
306	C₄	—	2	1	no	—
307	C₄	—	2	1	no	—
308	C₄	—	172	1	no	—
309	C₄	—	172	1	no	—
310	C₄	—	172	1	no	—
311	C₄	—	172	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	—	4	1	no	—
320	C₂	#14583553	1	1	yes	characteristic
321	C₂	#14583699	1	1	yes	characteristic
322	C₂	#14583716	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#435	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#435	D₄₃
hypocenter	C₄₃	#3349
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #435

Complements

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

N	H ≅ G/N	type
3. #14583308	C₂	semidirect
4. #14583241	C₂	semidirect
5. #14583241	C₂	semidirect
6. #14583241	C₂	semidirect
7. #14583235	C₂	semidirect
8. #14583207	C₂	semidirect
9. #14583195	C₂	semidirect
10. #14583157	C₂	semidirect
11. #14583140	C₂	semidirect
12. #14583007	C₂	semidirect
13. #14582941	C₂	semidirect
14. #14582937	C₂	semidirect
177. C₄₃	#3349	semidirect