Subgroups — #19142954

Order 5504.

472 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063315	C₂	1	2	yes	maximal
2	#14582798	C₂	1	1	yes	maximal, characteristic
3	#14582797	C₂	1	1	yes	maximal, characteristic
4	#14582796	C₂	1	2	yes	maximal
5	#14582795	C₂	1	1	yes	maximal, characteristic
6	#14582794	C₂	1	2	yes	maximal
7	#14582768	C₂	1	1	yes	maximal, characteristic
8	#14582768	C₂	1	1	yes	maximal, characteristic
9	#14582763	C₂	1	2	yes	maximal
10	C₄²×Dic₄₃	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#389	C₂	1	1	yes	maximal, characteristic
12	#13063315	—	2	8	no	—
13	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
15	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
17	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
18	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
19	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
20	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
21	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
22	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
28	C₄₃⋊#95	C₂²	1	2	yes	—
29	C₄₃⋊#95	C₂²	1	2	yes	—
30	C₄₃⋊#95	C₂²	1	2	yes	—
31	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
32	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
35	#95×C₄₃	C₂²	1	2	yes	—
36	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
37	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
38	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂²×Dic₄₃	C₂³	1	2	yes	—
42	C₂²×Dic₄₃	C₂³	1	2	yes	—
43	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
44	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
45	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
46	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
47	C₄⋊C₄×C₄₃	—	2	4	no	—
48	C₄⋊C₄×C₄₃	—	2	2	no	—
49	C₄⋊C₄×C₄₃	—	2	2	no	—
50	C₄²×C₄₃	—	2	2	no	—
51	C₄⋊Dic₄₃	—	2	2	no	—
52	C₄⋊Dic₄₃	—	2	2	no	—
53	C₄⋊Dic₄₃	—	2	4	no	—
54	Dic₄₃⋊C₄	—	2	4	no	—
55	Dic₄₃⋊C₄	—	2	4	no	—
56	Dic₄₃⋊C₄	—	2	4	no	—
57	Dic₄₃⋊C₄	—	2	4	no	—
58	Dic₄₃⋊C₄	—	2	4	no	—
59	Dic₄₃⋊C₄	—	2	4	no	—
60	C₄×Dic₄₃	—	2	2	no	—
61	C₄×Dic₄₃	—	2	2	no	—
62	C₄×Dic₄₃	—	2	2	no	—
63	C₄×Dic₄₃	D₄	1	4	yes	—
64	C₄×Dic₄₃	Q₈	1	4	yes	—
65	C₄×Dic₄₃	Q₈	1	4	yes	—
66	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
67	C₂×C₄×C₄₃	—	2	1	no	—
68	C₂×C₄×C₄₃	—	2	1	no	—
69	C₂×C₄×C₄₃	—	2	1	no	—
70	C₂×C₄×C₄₃	—	2	1	no	—
71	C₂×C₄×C₄₃	—	2	2	no	—
72	C₂×C₄×C₄₃	—	2	2	no	—
73	C₂×C₄×C₄₃	—	2	2	no	—
74	C₂×C₄×C₄₃	—	2	2	no	—
75	C₂×C₄×C₄₃	—	2	2	no	—
76	C₂×C₄×C₄₃	—	2	2	no	—
77	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
78	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
79	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
80	C₂×C₄×C₄₃	#41	1	2	yes	—
81	C₂×C₄×C₄₃	#41	1	2	yes	—
82	C₂×Dic₄₃	—	2	1	no	—
83	C₂×Dic₄₃	—	2	1	no	—
84	C₂×Dic₄₃	—	2	1	no	—
85	C₂×Dic₄₃	—	2	1	no	—
86	C₂×Dic₄₃	—	2	2	no	—
87	C₂×Dic₄₃	—	2	2	no	—
88	C₂×Dic₄₃	—	2	2	no	—
89	C₂×Dic₄₃	—	2	2	no	—
90	C₂×Dic₄₃	—	2	2	no	—
91	C₂×Dic₄₃	—	2	2	no	—
92	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
93	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
94	C₂×Dic₄₃	C₂×Q₈	1	2	yes	—
95	C₂×Dic₄₃	C₂×Q₈	1	2	yes	—
96	C₂×Dic₄₃	C₂×Q₈	1	2	yes	—
97	C₂×Dic₄₃	C₂×Q₈	1	2	yes	—
98	C₂×Dic₄₃	#41	1	2	yes	—
99	C₂×Dic₄₃	#41	1	2	yes	—
100	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
101	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
102	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
103	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
104	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
105	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
106	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
107	C₄×C₄₃	—	2	2	no	—
108	C₄×C₄₃	—	2	2	no	—
109	C₄×C₄₃	—	4	2	no	—
110	C₄×C₄₃	—	4	2	no	—
111	C₄×C₄₃	#125	1	4	yes	complemented
112	Dic₄₃	—	2	2	no	—
113	Dic₄₃	—	2	2	no	—
114	Dic₄₃	—	4	2	no	—
115	Dic₄₃	—	4	2	no	—
116	Dic₄₃	#125	1	4	yes	complemented
117	Dic₄₃	C₄⋊Q₈	1	4	yes	—
118	#2859	—	43	1	no	maximal, Sylow
119	C₂×C₄₃	C₂×#125	1	1	yes	characteristic
120	C₂×C₄₃	C₂×#125	1	1	yes	characteristic
121	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
122	C₂×C₄₃	#532	1	1	yes	characteristic
123	C₂×C₄₃	#532	1	1	yes	characteristic
124	C₂×C₄₃	#533	1	1	yes	characteristic
125	C₂×C₄₃	#533	1	1	yes	characteristic
126	C₂×#125	—	43	2	no	—
127	#389	—	43	2	no	—
128	#389	—	43	1	no	—
129	#389	—	43	1	no	—
130	#389	—	43	1	no	—
131	#389	—	43	2	no	—
132	#389	D₄₃	1	1	yes	characteristic
133	#384	—	43	1	no	—
134	#384	—	43	1	no	—
135	#382	—	43	2	no	—
136	C₄³	—	43	1	no	—
137	C₄₃	#2859	1	1	yes	characteristic, complemented, Sylow
138	#125	—	86	8	no	—
139	C₂×C₄⋊C₄	—	43	2	no	—
140	C₂×C₄⋊C₄	—	43	2	no	—
141	C₂×C₄⋊C₄	—	43	2	no	—
142	C₂×C₄⋊C₄	—	43	2	no	—
143	C₂×C₄⋊C₄	—	43	2	no	—
144	C₂×C₄⋊C₄	—	43	2	no	—
145	C₂×C₄⋊C₄	—	43	2	no	—
146	C₂×C₄⋊C₄	—	43	1	no	—
147	C₂×C₄⋊C₄	—	43	1	no	—
148	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
149	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
150	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
151	C₂×C₄²	—	43	1	no	—
152	C₂×C₄²	—	43	1	no	—
153	C₂×C₄²	—	43	1	no	—
154	C₂×C₄²	—	43	1	no	—
155	C₂×C₄²	—	43	1	no	—
156	C₂×C₄²	—	43	1	no	—
157	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
158	#95	—	43	2	no	—
159	#95	—	43	2	no	—
160	#95	—	43	2	no	—
161	#95	C₂×D₄₃	1	2	yes	—
162	C₂²×C₄	—	43	1	no	—
163	C₂²×C₄	—	43	1	no	—
164	C₂²×C₄	—	43	1	no	—
165	C₂²×C₄	—	43	1	no	—
166	C₂²×C₄	—	43	2	no	—
167	C₂²×C₄	—	43	2	no	—
168	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
169	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
170	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
171	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
172	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	2	4	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	86	4	no	—
177	C₄⋊C₄	—	86	4	no	—
178	C₄⋊C₄	—	86	4	no	—
179	C₄⋊C₄	—	86	4	no	—
180	C₄⋊C₄	—	86	4	no	—
181	C₄⋊C₄	—	86	4	no	—
182	C₄⋊C₄	—	86	2	no	—
183	C₄⋊C₄	—	86	4	no	—
184	C₄⋊C₄	—	86	2	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	43	4	no	—
187	C₄²	—	43	4	no	—
188	C₄²	—	43	4	no	—
189	C₄²	—	86	2	no	—
190	C₄²	—	86	2	no	—
191	C₄²	—	86	2	no	—
192	C₂³	C₂³×D₄₃	1	1	yes	characteristic
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	43	2	no	—
204	C₂×C₄	—	43	2	no	—
205	C₂×C₄	—	43	2	no	—
206	C₂×C₄	—	43	2	no	—
207	C₂×C₄	—	43	2	no	—
208	C₂×C₄	—	43	2	no	—
209	C₂×C₄	—	43	2	no	—
210	C₂×C₄	—	43	2	no	—
211	C₂×C₄	—	86	1	no	—
212	C₂×C₄	—	86	1	no	—
213	C₂×C₄	—	86	1	no	—
214	C₂×C₄	—	86	1	no	—
215	C₂×C₄	—	86	2	no	—
216	C₂×C₄	—	86	2	no	—
217	C₂×C₄	—	86	2	no	—
218	C₂×C₄	—	86	2	no	—
219	C₂×C₄	—	86	2	no	—
220	C₂×C₄	—	86	2	no	—
221	C₂×C₄	#10621898	1	2	yes	—
222	C₂×C₄	D₄×D₄₃	1	2	yes	—
223	C₂×C₄	#10621900	1	2	yes	—
224	C₂×C₄	Q₈×D₄₃	1	2	yes	—
225	C₂×C₄	Q₈×D₄₃	1	2	yes	—
226	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
227	C₂²	C₂×Q₈×D₄₃	1	1	yes	characteristic
228	C₂²	C₂×Q₈×D₄₃	1	1	yes	characteristic
229	C₂²	#41×D₄₃	1	1	yes	characteristic
230	C₂²	#41×D₄₃	1	1	yes	characteristic
231	C₂²	C₂×#10621900	1	1	yes	characteristic
232	C₂²	C₂×#10621898	1	1	yes	characteristic
233	C₄	—	2	2	no	—
234	C₄	—	2	2	no	—
235	C₄	—	4	2	no	—
236	C₄	—	4	2	no	—
237	C₄	—	43	4	no	—
238	C₄	—	43	4	no	—
239	C₄	—	86	2	no	—
240	C₄	—	86	2	no	—
241	C₄	—	172	2	no	—
242	C₄	—	172	2	no	—
243	C₄	#13063315	1	4	yes	complemented
244	C₂	#125×D₄₃	1	1	yes	characteristic
245	C₂	C₂×#13063315	1	1	yes	characteristic
246	C₂	C₄⋊Q₈×D₄₃	1	1	yes	characteristic
247	C₂	#14583444	1	1	yes	characteristic
248	C₂	#14583446	1	1	yes	characteristic
249	C₂	#14583451	1	1	yes	characteristic
250	C₂	#14583453	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#389	C₂
hypercenter	#389	D₄₃
hypocenter	C₄₃	#2859
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #389

Complements

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

N	H ≅ G/N	type
111. C₄×C₄₃	#125	semidirect
116. Dic₄₃	#125	semidirect
137. C₄₃	#2859	semidirect
243. C₄	#13063315	semidirect