Subgroups — #25062935

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143684	C₂	1	2	yes	maximal
2	#19132951	C₂	1	6	yes	maximal
3	#19132939	C₂	1	3	yes	maximal
4	#19132919	C₂	1	3	yes	maximal
5	C₂×C₄₃×#557	C₂	1	1	yes	maximal, characteristic
6	#14583030	—	2	6	no	—
7	Q₈×C₄₃⋊C₈	—	2	2	no	—
8	#14582956	C₂²	1	6	yes	—
9	#14582952	C₂²	1	6	yes	—
10	#14582625	C₂²	1	3	yes	—
11	#14582625	C₂²	1	6	yes	—
12	#14582625	C₂²	1	6	yes	—
13	#14582625	C₂²	1	1	yes	characteristic
14	C₄₃×#557	—	2	2	no	—
15	C₄₃×#557	—	2	6	no	—
16	C₂×C₄⋊Q₈×C₄₃	C₄	1	3	yes	—
17	C₂×#125×C₄₃	C₄	1	3	yes	—
18	C₂×#125×C₄₃	C₂²	1	3	yes	—
19	C₂×C₄×Q₈×C₄₃	C₄	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₄₃	C₄	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₄₃	C₂²	1	3	yes	—
22	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₄⋊(C₄₃⋊C₈)	—	2	6	no	—
24	C₄⋊(C₄₃⋊C₈)	—	2	6	no	—
25	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
26	C₂²⋊(C₄₃⋊C₈)	C₂³	1	6	yes	—
27	#13063236	—	2	6	no	—
28	C₄×C₄₃⋊C₈	—	2	6	no	—
29	C₂²×Q₈×C₄₃	C₂×C₄	1	3	yes	—
30	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
31	C₄⋊Q₈×C₄₃	—	2	6	no	—
32	C₄⋊Q₈×C₄₃	—	2	6	no	—
33	#125×C₄₃	—	2	6	no	—
34	#125×C₄₃	—	2	6	no	—
35	#125×C₄₃	—	2	6	no	—
36	#125×C₄₃	—	2	6	no	—
37	C₄×Q₈×C₄₃	—	2	3	no	—
38	C₄×Q₈×C₄₃	—	2	1	no	—
39	C₄×Q₈×C₄₃	—	2	3	no	—
40	C₄×Q₈×C₄₃	—	2	1	no	—
41	C₄×Q₈×C₄₃	—	2	6	no	—
42	C₄×Q₈×C₄₃	—	2	6	no	—
43	C₄×Q₈×C₄₃	D₄	1	2	yes	—
44	C₄×Q₈×C₄₃	D₄	1	6	yes	—
45	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	3	yes	—
46	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	3	yes	—
47	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	3	yes	—
48	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	6	yes	—
49	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	3	yes	—
50	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
52	C₂×C₄²×C₄₃	C₂×C₄	1	3	yes	—
53	C₂×C₄²×C₄₃	C₂×C₄	1	3	yes	—
54	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
55	C₂×Q₈×C₄₃	—	2	4	no	—
56	C₂×Q₈×C₄₃	—	2	6	no	—
57	C₂×Q₈×C₄₃	—	2	6	no	—
58	C₂×Q₈×C₄₃	—	4	3	no	—
59	C₂×Q₈×C₄₃	C₂²⋊C₄	1	3	yes	—
60	C₂×Q₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₃	C₂²×C₄	1	3	yes	—
62	C₂²×C₄×C₄₃	C₂²×C₄	1	3	yes	—
63	C₂²×C₄×C₄₃	C₂²×C₄	1	3	yes	—
64	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₃	C₂²×C₄	1	3	yes	—
67	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
68	C₄⋊C₄×C₄₃	—	2	6	no	—
69	C₄⋊C₄×C₄₃	—	2	3	no	—
70	C₄⋊C₄×C₄₃	—	2	3	no	—
71	C₄⋊C₄×C₄₃	—	2	3	no	—
72	C₄⋊C₄×C₄₃	—	2	3	no	—
73	C₄⋊C₄×C₄₃	—	2	12	no	—
74	C₄⋊C₄×C₄₃	—	2	2	no	—
75	C₄⋊C₄×C₄₃	—	2	6	no	—
76	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	6	yes	—
77	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	6	yes	—
78	C₄²×C₄₃	—	2	3	no	—
79	C₄²×C₄₃	—	2	3	no	—
80	C₄²×C₄₃	—	2	3	no	—
81	C₄²×C₄₃	—	2	3	no	—
82	C₄²×C₄₃	C₂×D₄	1	6	yes	—
83	C₄²×C₄₃	C₂×D₄	1	6	yes	—
84	C₂×C₄₃⋊C₈	—	2	2	no	—
85	C₂×C₄₃⋊C₈	—	2	6	no	—
86	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
87	Q₈×C₄₃	—	2	6	no	—
88	Q₈×C₄₃	—	4	12	no	—
89	Q₈×C₄₃	#101	1	4	yes	—
90	C₂×C₄×C₄₃	—	2	1	no	—
91	C₂×C₄×C₄₃	—	2	3	no	—
92	C₂×C₄×C₄₃	—	2	3	no	—
93	C₂×C₄×C₄₃	—	2	1	no	—
94	C₂×C₄×C₄₃	—	2	6	no	—
95	C₂×C₄×C₄₃	—	2	1	no	—
96	C₂×C₄×C₄₃	—	2	3	no	—
97	C₂×C₄×C₄₃	—	2	3	no	—
98	C₂×C₄×C₄₃	—	2	3	no	—
99	C₂×C₄×C₄₃	—	2	3	no	—
100	C₂×C₄×C₄₃	—	4	1	no	—
101	C₂×C₄×C₄₃	—	4	1	no	—
102	C₂×C₄×C₄₃	—	4	3	no	—
103	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	3	yes	—
104	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	6	yes	—
105	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	3	yes	—
106	C₂×C₄×C₄₃	#131	1	2	yes	—
107	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
108	C₄₃⋊C₈	—	4	2	no	—
109	C₄₃⋊C₈	—	4	6	no	—
110	#17430	—	43	1	no	maximal, Sylow
111	C₂²×C₄₃	—	2	1	no	—
112	C₂²×C₄₃	—	2	1	no	—
113	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
115	C₂²×C₄₃	#568	1	1	yes	characteristic
116	C₄×C₄₃	—	2	6	no	—
117	C₄×C₄₃	—	2	2	no	—
118	C₄×C₄₃	—	2	2	no	—
119	C₄×C₄₃	—	2	3	no	—
120	C₄×C₄₃	—	4	3	no	—
121	C₄×C₄₃	—	4	1	no	—
122	C₄×C₄₃	—	4	3	no	—
123	C₄×C₄₃	C₂×#101	1	6	yes	—
124	C₂×#557	D₄₃	1	1	yes	characteristic
125	#2984	—	43	2	no	—
126	#1470	—	43	6	no	—
127	#1467	—	43	3	no	—
128	#1461	—	43	3	no	—
129	C₂×C₄₃	—	2	1	no	—
130	C₂×C₄₃	—	2	1	no	—
131	C₂×C₄₃	#2880	1	1	yes	characteristic
132	C₂×C₄₃	#2884	1	1	yes	characteristic
133	C₂×C₄₃	C₂²×#101	1	1	yes	characteristic
134	#557	—	2	2	no	—
135	#557	—	2	6	no	—
136	C₂×C₄⋊Q₈	Dic₄₃	1	3	yes	—
137	C₂×#125	Dic₄₃	1	3	yes	—
138	C₂×#125	C₂×D₄₃	1	3	yes	—
139	C₂×C₄×Q₈	Dic₄₃	1	1	yes	characteristic
140	C₂×C₄×Q₈	Dic₄₃	1	1	yes	characteristic
141	C₂×C₄×Q₈	C₂×D₄₃	1	3	yes	—
142	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
143	#446	—	86	6	no	—
144	C₈×Q₈	—	86	2	no	—
145	#432	—	43	6	no	—
146	#431	—	43	6	no	—
147	#324	—	43	1	no	—
148	#324	—	43	3	no	—
149	#324	—	43	6	no	—
150	#324	—	43	6	no	—
151	C₄₃	#17430	1	1	yes	characteristic, complemented, Sylow
152	C₂²×Q₈	C₂×Dic₄₃	1	3	yes	—
153	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
154	C₄⋊Q₈	—	2	6	no	—
155	C₄⋊Q₈	—	2	6	no	—
156	#125	—	2	6	no	—
157	#125	—	2	6	no	—
158	#125	—	2	6	no	—
159	#125	—	2	6	no	—
160	C₄×Q₈	—	2	3	no	—
161	C₄×Q₈	—	2	1	no	—
162	C₄×Q₈	—	2	3	no	—
163	C₄×Q₈	—	2	1	no	—
164	C₄×Q₈	—	2	6	no	—
165	C₄×Q₈	—	2	6	no	—
166	C₄×Q₈	C₂²⋊D₄₃	1	2	yes	—
167	C₄×Q₈	C₂²⋊D₄₃	1	6	yes	—
168	C₂×C₄⋊C₄	C₂×Dic₄₃	1	3	yes	—
169	C₂×C₄⋊C₄	C₂×Dic₄₃	1	3	yes	—
170	C₂×C₄⋊C₄	C₂×Dic₄₃	1	3	yes	—
171	C₂×C₄⋊C₄	C₂×Dic₄₃	1	6	yes	—
172	C₂×C₄⋊C₄	C₂×Dic₄₃	1	3	yes	—
173	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
174	C₂×C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
175	C₂×C₄²	C₂×Dic₄₃	1	3	yes	—
176	C₂×C₄²	C₂×Dic₄₃	1	3	yes	—
177	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
178	C₄⋊C₈	—	86	6	no	—
179	C₄⋊C₈	—	86	6	no	—
180	C₂²⋊C₈	—	43	2	no	—
181	C₂²⋊C₈	—	43	6	no	—
182	#97	—	86	6	no	—
183	C₄×C₈	—	86	6	no	—
184	C₂×Q₈	—	2	4	no	—
185	C₂×Q₈	—	2	6	no	—
186	C₂×Q₈	—	2	6	no	—
187	C₂×Q₈	—	4	3	no	—
188	C₂×Q₈	C₂²⋊Dic₄₃	1	3	yes	—
189	C₂×Q₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
190	C₂²×C₄	C₂²×Dic₄₃	1	3	yes	—
191	C₂²×C₄	C₂²×Dic₄₃	1	3	yes	—
192	C₂²×C₄	C₂²×Dic₄₃	1	3	yes	—
193	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
194	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
195	C₂²×C₄	C₂²×Dic₄₃	1	3	yes	—
196	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
197	C₂×C₈	—	86	2	no	—
198	C₂×C₈	—	86	6	no	—
199	C₄⋊C₄	—	2	6	no	—
200	C₄⋊C₄	—	2	3	no	—
201	C₄⋊C₄	—	2	3	no	—
202	C₄⋊C₄	—	2	3	no	—
203	C₄⋊C₄	—	2	3	no	—
204	C₄⋊C₄	—	2	12	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	2	6	no	—
207	C₄⋊C₄	C₂²⋊Dic₄₃	1	6	yes	—
208	C₄⋊C₄	C₂²⋊Dic₄₃	1	6	yes	—
209	C₄²	—	2	3	no	—
210	C₄²	—	2	3	no	—
211	C₄²	—	2	3	no	—
212	C₄²	—	2	3	no	—
213	C₄²	C₂×C₂²⋊D₄₃	1	6	yes	—
214	C₄²	C₂×C₂²⋊D₄₃	1	6	yes	—
215	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
216	Q₈	—	2	6	no	—
217	Q₈	—	4	12	no	—
218	Q₈	#13063244	1	4	yes	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	3	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	3	no	—
223	C₂×C₄	—	2	6	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	3	no	—
226	C₂×C₄	—	2	3	no	—
227	C₂×C₄	—	2	3	no	—
228	C₂×C₄	—	2	3	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	4	1	no	—
231	C₂×C₄	—	4	3	no	—
232	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	3	yes	—
233	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	6	yes	—
234	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	3	yes	—
235	C₂×C₄	#13063332	1	2	yes	—
236	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
237	C₈	—	172	2	no	—
238	C₈	—	172	6	no	—
239	C₂²	—	2	1	no	—
240	C₂²	—	2	1	no	—
241	C₂²	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
242	C₂²	C₂×#13063332	1	1	yes	characteristic
243	C₂²	#14583666	1	1	yes	characteristic
244	C₄	—	2	6	no	—
245	C₄	—	2	2	no	—
246	C₄	—	2	2	no	—
247	C₄	—	2	3	no	—
248	C₄	—	4	3	no	—
249	C₄	—	4	1	no	—
250	C₄	—	4	3	no	—
251	C₄	C₂×#13063244	1	6	yes	—
252	C₂	—	2	1	no	—
253	C₂	—	2	1	no	—
254	C₂	#19143044	1	1	yes	characteristic
255	C₂	#19143059	1	1	yes	characteristic
256	C₂	C₂²×#13063244	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₃
commutator, prime radical	C₂³×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#557	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#557	D₄₃
hypocenter	C₄₃	#17430
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄×Q₈ ◁ C₂×#557

Complements

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

N	H ≅ G/N	type
151. C₄₃	#17430	semidirect

Maximal subgroups

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

subgroup	index
#19143684	2
#19132951	2
#19132939	2
#19132919	2
C₂×C₄₃×#557	2
#17430	43