Subgroups — C₂×#14583509 #19147961

Order 5504.

1004 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583509	C₂	1	16	yes	maximal, direct product factor
2	C₂×#13063323	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13063318	C₂	1	2	yes	maximal
4	C₂×#13063318	C₂	1	2	yes	maximal
5	C₂×#13063316	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13063316	C₂	1	2	yes	maximal, complemented
7	C₂×#13063315	C₂	1	2	yes	maximal, complemented
8	C₂×#13063304	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13063290	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#13063284	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂²⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
13	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
14	#13063323	C₂²	1	8	yes	complemented
15	#13063318	C₂²	1	16	yes	—
16	#13063318	C₂²	1	16	yes	—
17	#13063316	C₂²	1	8	yes	complemented
18	#13063316	C₂²	1	16	yes	complemented
19	#13063315	C₂²	1	16	yes	complemented
20	#13063304	C₂²	1	8	yes	—
21	Q₈×Dic₄₃	C₂²	1	8	yes	complemented
22	#13063290	C₂²	1	8	yes	complemented
23	#13063284	C₂²	1	8	yes	—
24	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
28	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
29	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
30	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
31	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
32	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
33	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
34	C₂×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
37	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
40	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
41	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
43	C₂²⋊Q₈×C₄₃	C₂²	1	8	yes	—
44	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
46	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
47	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
48	C₂×Q₈×C₄₃	—	2	4	no	—
49	C₂×Q₈×C₄₃	C₂³	1	4	yes	—
50	C₂²×C₄×C₄₃	—	2	4	no	—
51	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
52	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
53	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
55	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
56	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
57	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
58	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
59	C₂²×Dic₄₃	C₂³	1	2	yes	—
60	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
61	C₂²×Dic₄₃	C₂³	1	2	yes	—
62	C₂×Dic₈₆	—	2	4	no	—
63	C₂×Dic₈₆	C₂³	1	4	yes	—
64	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
65	C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
66	C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
67	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
68	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
69	C₂²⋊Dic₄₃	C₂³	1	8	yes	—
70	C₄⋊Dic₄₃	C₂³	1	4	yes	—
71	C₄⋊Dic₄₃	C₂³	1	4	yes	—
72	C₄⋊Dic₄₃	C₂³	1	4	yes	—
73	C₄⋊Dic₄₃	C₂³	1	8	yes	—
74	C₄⋊Dic₄₃	C₂³	1	8	yes	—
75	Dic₄₃⋊C₄	C₂³	1	8	yes	—
76	Dic₄₃⋊C₄	C₂³	1	8	yes	—
77	Dic₄₃⋊C₄	C₂³	1	8	yes	—
78	Dic₄₃⋊C₄	C₂³	1	8	yes	—
79	Dic₄₃⋊C₄	C₂³	1	8	yes	—
80	C₄×Dic₄₃	C₂³	1	4	yes	—
81	C₄×Dic₄₃	C₂³	1	4	yes	—
82	C₄×Dic₄₃	C₂³	1	8	yes	—
83	C₄×Dic₄₃	C₂³	1	8	yes	—
84	C₂³×C₄₃	—	2	2	no	—
85	C₂³×C₄₃	—	2	2	no	—
86	C₂³×C₄₃	—	2	2	no	—
87	C₂³×C₄₃	C₂⁴	1	2	yes	—
88	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
89	Q₈×C₄₃	—	2	8	no	—
90	C₂×C₄×C₄₃	—	2	2	no	—
91	C₂×C₄×C₄₃	—	2	4	no	—
92	C₂×C₄×C₄₃	—	2	4	no	—
93	C₂×C₄×C₄₃	—	2	8	no	—
94	C₂×C₄×C₄₃	#41	1	4	yes	—
95	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
96	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
97	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
98	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
99	C₂×Dic₄₃	—	2	4	no	—
100	C₂×Dic₄₃	—	2	2	no	—
101	C₂×Dic₄₃	—	2	2	no	—
102	C₂×Dic₄₃	—	2	2	no	—
103	C₂×Dic₄₃	—	2	2	no	—
104	C₂×Dic₄₃	—	2	4	no	—
105	C₂×Dic₄₃	C₂⁴	1	2	yes	—
106	C₂×Dic₄₃	C₂⁴	1	2	yes	—
107	C₂×Dic₄₃	C₂⁴	1	2	yes	—
108	C₂×Dic₄₃	C₂⁴	1	4	yes	—
109	C₂×Dic₄₃	C₂⁴	1	2	yes	—
110	C₂×Dic₄₃	C₂⁴	1	4	yes	—
111	Dic₈₆	—	2	8	no	—
112	C₂²×C₄₃	—	2	2	no	—
113	C₂²×C₄₃	—	2	2	no	—
114	C₂²×C₄₃	—	2	2	no	—
115	C₂²×C₄₃	—	4	4	no	—
116	C₂²×C₄₃	C₂×#41	1	2	yes	—
117	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
118	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
119	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
120	C₄×C₄₃	—	2	2	no	—
121	C₄×C₄₃	—	2	4	no	—
122	C₄×C₄₃	—	2	4	no	—
123	C₄×C₄₃	C₂×#41	1	4	yes	—
124	Dic₄₃	—	2	4	no	—
125	Dic₄₃	—	2	2	no	—
126	Dic₄₃	—	2	2	no	—
127	Dic₄₃	—	2	2	no	—
128	Dic₄₃	—	2	2	no	—
129	Dic₄₃	—	2	4	no	—
130	C₂×#541	—	43	1	no	maximal, Sylow
131	C₂×C₄₃	—	4	2	no	—
132	C₂×C₄₃	#541	1	4	yes	complemented
133	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
134	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
135	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
136	#541	—	43	16	no	—
137	C₂×C₄⋊Q₈	—	43	1	no	—
138	C₂×#126	—	43	2	no	—
139	C₂×#126	—	43	2	no	—
140	C₂×#125	—	43	2	no	—
141	C₂×#125	—	43	1	no	—
142	C₂×#125	—	43	2	no	—
143	C₂×C₂²⋊Q₈	—	43	1	no	—
144	C₂×C₂²⋊Q₈	D₄₃	1	1	yes	characteristic
145	C₂×C₄×Q₈	—	43	1	no	—
146	C₂×C₄×Q₈	—	43	1	no	—
147	C₂×#117	—	43	1	no	—
148	C₄₃	C₂×#541	1	1	yes	characteristic, complemented, Sylow
149	C₂²×Q₈	—	43	1	no	—
150	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
151	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
152	C₄⋊Q₈	—	43	8	no	—
153	#126	—	43	16	no	—
154	#126	—	43	16	no	—
155	#125	—	43	16	no	—
156	#125	—	43	8	no	—
157	#125	—	43	16	no	—
158	C₂²⋊Q₈	—	43	8	no	—
159	C₂²⋊Q₈	C₂×D₄₃	1	8	yes	—
160	C₄×Q₈	—	43	8	no	—
161	C₄×Q₈	—	43	8	no	—
162	#117	—	43	8	no	—
163	C₂×C₄⋊C₄	—	43	1	no	—
164	C₂×C₄⋊C₄	—	43	1	no	—
165	C₂×C₄⋊C₄	—	43	1	no	—
166	C₂×C₄⋊C₄	—	43	2	no	—
167	C₂×C₄⋊C₄	—	43	2	no	—
168	C₂×C₄⋊C₄	—	43	2	no	—
169	C₂×C₄⋊C₄	—	43	2	no	—
170	C₂×C₄⋊C₄	—	43	2	no	—
171	C₂×C₄⋊C₄	—	43	2	no	—
172	C₂×C₄⋊C₄	—	43	2	no	—
173	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
174	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
175	C₂×C₂²⋊C₄	—	43	1	no	—
176	C₂×C₂²⋊C₄	—	43	1	no	—
177	C₂×C₂²⋊C₄	—	43	2	no	—
178	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
179	C₂×C₄²	—	43	1	no	—
180	C₂×C₄²	—	43	1	no	—
181	C₂×C₄²	—	43	2	no	—
182	C₂×C₄²	—	43	2	no	—
183	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
184	C₂×Q₈	—	2	4	no	—
185	C₂×Q₈	—	43	4	no	—
186	C₂×Q₈	—	86	4	no	—
187	C₂×Q₈	C₂²×D₄₃	1	4	yes	—
188	C₂²×C₄	—	2	4	no	—
189	C₂²×C₄	—	43	1	no	—
190	C₂²×C₄	—	43	1	no	—
191	C₂²×C₄	—	43	1	no	—
192	C₂²×C₄	—	43	1	no	—
193	C₂²×C₄	—	43	2	no	—
194	C₂²×C₄	—	43	2	no	—
195	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
196	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
197	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
198	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
199	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
200	C₄⋊C₄	—	43	4	no	—
201	C₄⋊C₄	—	43	4	no	—
202	C₄⋊C₄	—	43	4	no	—
203	C₄⋊C₄	—	43	8	no	—
204	C₄⋊C₄	—	43	8	no	—
205	C₄⋊C₄	—	43	8	no	—
206	C₄⋊C₄	—	43	8	no	—
207	C₄⋊C₄	—	43	8	no	—
208	C₄⋊C₄	—	43	8	no	—
209	C₄⋊C₄	—	43	8	no	—
210	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
211	C₄⋊C₄	C₂²×D₄₃	1	8	yes	—
212	C₂²⋊C₄	—	43	4	no	—
213	C₂²⋊C₄	—	43	4	no	—
214	C₂²⋊C₄	—	43	8	no	—
215	C₂²⋊C₄	C₂²×D₄₃	1	8	yes	—
216	C₄²	—	43	4	no	—
217	C₄²	—	43	4	no	—
218	C₄²	—	43	8	no	—
219	C₄²	—	43	8	no	—
220	C₂³	—	2	2	no	—
221	C₂³	—	2	2	no	—
222	C₂³	—	2	2	no	—
223	C₂³	C₂³×D₄₃	1	2	yes	—
224	C₂³	C₂³×D₄₃	1	1	yes	characteristic
225	Q₈	—	2	8	no	—
226	Q₈	—	86	8	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	4	no	—
229	C₂×C₄	—	2	4	no	—
230	C₂×C₄	—	2	8	no	—
231	C₂×C₄	—	43	2	no	—
232	C₂×C₄	—	43	2	no	—
233	C₂×C₄	—	43	2	no	—
234	C₂×C₄	—	43	2	no	—
235	C₂×C₄	—	43	4	no	—
236	C₂×C₄	—	43	4	no	—
237	C₂×C₄	—	86	4	no	—
238	C₂×C₄	—	86	2	no	—
239	C₂×C₄	—	86	2	no	—
240	C₂×C₄	—	86	2	no	—
241	C₂×C₄	—	86	2	no	—
242	C₂×C₄	—	86	4	no	—
243	C₂×C₄	#10621900	1	4	yes	—
244	C₂×C₄	C₂³×D₄₃	1	4	yes	—
245	C₂×C₄	C₂³×D₄₃	1	4	yes	—
246	C₂×C₄	C₂³×D₄₃	1	2	yes	—
247	C₂×C₄	C₂³×D₄₃	1	2	yes	—
248	C₂²	—	2	2	no	—
249	C₂²	—	2	2	no	—
250	C₂²	—	2	2	no	—
251	C₂²	—	4	4	no	—
252	C₂²	C₂×#10621900	1	2	yes	—
253	C₂²	#13063372	1	2	yes	—
254	C₂²	#13063373	1	2	yes	—
255	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
256	C₄	—	2	2	no	—
257	C₄	—	2	4	no	—
258	C₄	—	2	4	no	—
259	C₄	—	86	4	no	—
260	C₄	—	86	2	no	—
261	C₄	—	86	2	no	—
262	C₄	—	86	2	no	—
263	C₄	—	86	2	no	—
264	C₄	—	86	4	no	—
265	C₄	C₂×#10621900	1	4	yes	—
266	C₂	—	4	2	no	—
267	C₂	#14583509	1	4	yes	direct product factor
268	C₂	C₂²×#10621900	1	1	yes	characteristic
269	C₂	C₂×#13063372	1	1	yes	characteristic
270	C₂	C₂×#13063373	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁵
Frattini	C₂²	C₂⁴×D₄₃
Fitting	C₂×C₂²⋊Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₂×C₂²⋊Q₈	D₄₃
hypocenter	C₄₃	C₂×#541
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #14583509	C₂	direct (N × H)
2. C₂×#13063323	C₂	semidirect
5. C₂×#13063316	C₂	semidirect
6. C₂×#13063316	C₂	semidirect
7. C₂×#13063315	C₂	semidirect
9. C₂×Q₈×Dic₄₃	C₂	semidirect
10. C₂×#13063290	C₂	semidirect
14. #13063323	C₂²	semidirect
17. #13063316	C₂²	semidirect
18. #13063316	C₂²	semidirect
19. #13063315	C₂²	semidirect
21. Q₈×Dic₄₃	C₂²	semidirect
22. #13063290	C₂²	semidirect
132. C₂×C₄₃	#541	semidirect
148. C₄₃	C₂×#541	semidirect
267. C₂	#14583509	direct (N × H)

Subgroups — C2×#14583509 #19147961

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583509 #19147961