Subgroups — #25002206

Order 11008.

838 conjugacy classes of subgroups.

The subgroup lattice has 254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582654	C₂	1	2	yes	maximal
2	C₂×#14582654	C₂	1	2	yes	maximal
3	C₂×#14582654	C₂	1	2	yes	maximal
4	C₂×C₄₃×#376	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄₃⋊C₈	C₂²	1	4	yes	—
6	#14582654	—	2	4	no	—
7	#14582654	—	2	4	no	—
8	#14582654	C₄	1	8	yes	complemented
9	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	C₄₃×#376	—	2	4	no	—
13	C₂×#95×C₄₃	C₄	1	4	yes	—
14	C₂²×C₄₃⋊C₈	—	2	4	no	—
15	C₂²×C₄₃⋊C₈	—	2	4	no	—
16	C₂²×C₄₃⋊C₈	—	2	4	no	—
17	C₂²×C₄₃⋊C₈	—	2	4	no	—
18	C₂²×C₄₃⋊C₈	—	2	4	no	—
19	C₂²×C₄₃⋊C₈	—	2	4	no	—
20	C₂²×C₄₃⋊C₈	C₂×C₄	1	8	yes	—
21	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
22	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
23	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂×C₄²×C₄₃	—	2	2	no	—
26	C₂×C₄²×C₄₃	—	2	2	no	—
27	C₂×C₄²×C₄₃	—	2	2	no	—
28	C₂×C₄²×C₄₃	—	2	2	no	—
29	C₂×C₄²×C₄₃	—	2	2	no	—
30	C₂×C₄²×C₄₃	—	2	2	no	—
31	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
32	C₂×C₄²×C₄₃	D₄	1	2	yes	—
33	C₂×C₄²×C₄₃	D₄	1	4	yes	—
34	C₂×C₄²×C₄₃	Q₈	1	2	yes	—
35	#95×C₄₃	—	2	8	no	—
36	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₄₃	—	2	2	no	—
38	C₂²×C₄×C₄₃	—	2	2	no	—
39	C₂²×C₄×C₄₃	—	2	2	no	—
40	C₂²×C₄×C₄₃	—	2	2	no	—
41	C₂²×C₄×C₄₃	—	2	2	no	—
42	C₂²×C₄×C₄₃	—	2	2	no	—
43	C₂²×C₄×C₄₃	—	2	8	no	—
44	C₂²×C₄×C₄₃	—	2	8	no	—
45	C₂²×C₄×C₄₃	—	2	8	no	—
46	C₂²×C₄×C₄₃	C₄²	1	4	yes	—
47	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
48	C₂²×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
49	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
50	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
51	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
53	C₂²×C₄×C₄₃	#41	1	2	yes	—
54	C₂²×C₄×C₄₃	#41	1	2	yes	—
55	C₂²×C₄×C₄₃	#41	1	2	yes	—
56	C₂²×C₄×C₄₃	#41	1	2	yes	—
57	C₄²×C₄₃	—	2	8	no	—
58	C₄²×C₄₃	—	2	4	no	—
59	C₄²×C₄₃	—	2	4	no	—
60	C₄²×C₄₃	—	2	8	no	—
61	C₂×C₄₃⋊C₈	—	2	8	no	—
62	C₂×C₄₃⋊C₈	—	2	8	no	—
63	C₂×C₄₃⋊C₈	—	2	8	no	—
64	C₂×C₄₃⋊C₈	—	4	4	no	—
65	C₂×C₄₃⋊C₈	—	4	4	no	—
66	C₂×C₄₃⋊C₈	—	4	4	no	—
67	C₂×C₄₃⋊C₈	—	4	4	no	—
68	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
69	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₂³×C₄₃	#117	1	1	yes	characteristic
72	C₂³×C₄₃	#117	1	1	yes	characteristic
73	C₂³×C₄₃	#117	1	1	yes	characteristic
74	C₂³×C₄₃	#117	1	1	yes	characteristic
75	C₂³×C₄₃	#131	1	8	yes	—
76	C₂×C₄×C₄₃	—	2	4	no	—
77	C₂×C₄×C₄₃	—	2	4	no	—
78	C₂×C₄×C₄₃	—	2	4	no	—
79	C₂×C₄×C₄₃	—	2	8	no	—
80	C₂×C₄×C₄₃	—	2	8	no	—
81	C₂×C₄×C₄₃	—	2	8	no	—
82	C₂×C₄×C₄₃	—	4	4	no	—
83	C₂×C₄×C₄₃	—	4	4	no	—
84	C₂×C₄×C₄₃	—	4	4	no	—
85	C₂×C₄×C₄₃	—	4	4	no	—
86	C₂×C₄×C₄₃	—	4	4	no	—
87	C₂×C₄×C₄₃	—	4	4	no	—
88	C₂×C₄×C₄₃	#117	1	4	yes	—
89	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
90	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
91	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
92	C₂×C₄×C₄₃	#121	1	2	yes	—
93	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
94	C₂×C₄×C₄₃	#123	1	4	yes	—
95	C₂×C₄×C₄₃	#124	1	2	yes	—
96	C₂×C₄×C₄₃	#125	1	2	yes	—
97	C₂×C₄×C₄₃	#126	1	4	yes	—
98	C₄₃⋊C₈	—	4	8	no	—
99	#10796	—	43	1	no	maximal, Sylow
100	C₂²×C₄₃	#376	1	1	yes	characteristic
101	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
103	C₂²×C₄₃	#380	1	1	yes	characteristic
104	C₂²×C₄₃	#381	1	1	yes	characteristic
105	C₂²×C₄₃	#382	1	1	yes	characteristic
106	C₂²×C₄₃	#383	1	1	yes	characteristic
107	C₂²×C₄₃	#405	1	4	yes	—
108	C₂²×C₄₃	#408	1	4	yes	—
109	C₂²×C₄₃	#424	1	4	yes	—
110	C₂²×C₄₃	#433	1	4	yes	—
111	C₂²×C₄₃	#433	1	4	yes	—
112	C₂²×C₄₃	#433	1	4	yes	—
113	C₂²×C₄₃	#433	1	4	yes	—
114	C₄×C₄₃	—	4	4	no	—
115	C₄×C₄₃	—	4	4	no	—
116	C₄×C₄₃	—	4	4	no	—
117	C₄×C₄₃	#387	1	4	yes	—
118	C₄×C₄₃	#388	1	4	yes	—
119	C₂×#376	D₄₃	1	1	yes	characteristic
120	C₂×#336	—	43	2	no	—
121	C₂×#336	—	43	2	no	—
122	C₂×#336	—	43	2	no	—
123	C₂×C₄₃	#1434	1	1	yes	characteristic
124	C₂×C₄₃	#1746	1	2	yes	—
125	C₂×C₄₃	#1750	1	2	yes	—
126	C₂×C₄₃	#1768	1	2	yes	—
127	C₂×C₄₃	#1798	1	2	yes	—
128	C₂×C₄₃	#1818	1	2	yes	—
129	C₂×C₄₃	#1832	1	2	yes	—
130	C₂×C₄₃	#1840	1	2	yes	—
131	C₂³×C₈	—	43	4	no	—
132	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
133	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
134	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
135	#376	—	2	4	no	—
136	C₂×#95	Dic₄₃	1	4	yes	—
137	#336	—	43	8	no	—
138	#336	—	86	4	no	—
139	#336	—	86	4	no	—
140	C₄₃	#10796	1	1	yes	characteristic, complemented, Sylow
141	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
142	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
143	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
144	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
145	C₂²×C₈	—	43	8	no	—
146	C₂²×C₈	—	86	4	no	—
147	C₂²×C₈	—	86	4	no	—
148	C₂²×C₈	—	86	4	no	—
149	C₂²×C₈	—	86	4	no	—
150	C₂²×C₈	—	86	4	no	—
151	C₂²×C₈	—	86	4	no	—
152	C₂×C₄²	—	2	2	no	—
153	C₂×C₄²	—	2	2	no	—
154	C₂×C₄²	—	2	2	no	—
155	C₂×C₄²	—	2	2	no	—
156	C₂×C₄²	—	2	2	no	—
157	C₂×C₄²	—	2	2	no	—
158	C₂×C₄²	Dic₈₆	1	2	yes	—
159	C₂×C₄²	C₄×D₄₃	1	4	yes	—
160	C₂×C₄²	D₁₇₂	1	2	yes	—
161	C₂×C₄²	C₂²⋊D₄₃	1	4	yes	—
162	#95	—	2	8	no	—
163	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	8	no	—
171	C₂²×C₄	—	2	8	no	—
172	C₂²×C₄	—	2	8	no	—
173	C₂²×C₄	C₄×Dic₄₃	1	4	yes	—
174	C₂²×C₄	C₄⋊Dic₄₃	1	4	yes	—
175	C₂²×C₄	C₂²⋊Dic₄₃	1	4	yes	—
176	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
178	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
179	C₂²×C₄	#10621898	1	2	yes	—
180	C₂²×C₄	#10621898	1	2	yes	—
181	C₂²×C₄	#10621898	1	2	yes	—
182	C₂²×C₄	#10621898	1	2	yes	—
183	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
184	C₂×C₈	—	86	8	no	—
185	C₂×C₈	—	86	8	no	—
186	C₂×C₈	—	86	8	no	—
187	C₂×C₈	—	172	4	no	—
188	C₂×C₈	—	172	4	no	—
189	C₂×C₈	—	172	4	no	—
190	C₂×C₈	—	172	4	no	—
191	C₄²	—	2	8	no	—
192	C₄²	—	2	4	no	—
193	C₄²	—	2	4	no	—
194	C₄²	—	2	8	no	—
195	C₂³	C₂×C₄×Dic₄₃	1	1	yes	characteristic
196	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
197	C₂³	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
198	C₂³	#13063284	1	1	yes	characteristic
199	C₂³	#13063284	1	1	yes	characteristic
200	C₂³	#13063284	1	1	yes	characteristic
201	C₂³	#13063284	1	1	yes	characteristic
202	C₂³	#13063332	1	8	yes	—
203	C₂×C₄	—	2	8	no	—
204	C₂×C₄	—	2	8	no	—
205	C₂×C₄	—	2	8	no	—
206	C₂×C₄	—	2	4	no	—
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	2	4	no	—
209	C₂×C₄	—	4	4	no	—
210	C₂×C₄	—	4	4	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	4	no	—
213	C₂×C₄	—	4	4	no	—
214	C₂×C₄	—	4	4	no	—
215	C₂×C₄	#13063282	1	4	yes	—
216	C₂×C₄	C₄×C₂²⋊D₄₃	1	4	yes	—
217	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
218	C₂×C₄	C₄×Dic₈₆	1	2	yes	—
219	C₂×C₄	#13063299	1	2	yes	—
220	C₂×C₄	#13063304	1	2	yes	—
221	C₂×C₄	#13063308	1	4	yes	—
222	C₂×C₄	#13063313	1	2	yes	—
223	C₂×C₄	#13063317	1	2	yes	—
224	C₂×C₄	#13063319	1	4	yes	—
225	C₈	—	172	8	no	—
226	C₂²	#14582745	1	1	yes	characteristic
227	C₂²	C₄×C₂²⋊Dic₄₃	1	1	yes	characteristic
228	C₂²	C₄×C₄⋊Dic₄₃	1	1	yes	characteristic
229	C₂²	#14582759	1	1	yes	characteristic
230	C₂²	#14582762	1	1	yes	characteristic
231	C₂²	#14582765	1	1	yes	characteristic
232	C₂²	#14582767	1	1	yes	characteristic
233	C₂²	#14582855	1	4	yes	—
234	C₂²	#14582866	1	4	yes	—
235	C₂²	#14582926	1	4	yes	—
236	C₂²	#14582960	1	4	yes	—
237	C₂²	#14582960	1	4	yes	—
238	C₂²	#14582960	1	4	yes	—
239	C₂²	#14582960	1	4	yes	—
240	C₄	—	4	4	no	—
241	C₄	—	4	4	no	—
242	C₄	—	4	4	no	—
243	C₄	#14582783	1	4	yes	—
244	C₄	#14582790	1	4	yes	—
245	C₂	#19132822	1	1	yes	characteristic
246	C₂	#19134347	1	2	yes	—
247	C₂	#19134361	1	2	yes	—
248	C₂	#19134452	1	2	yes	—
249	C₂	#19134579	1	2	yes	—
250	C₂	#19134666	1	2	yes	—
251	C₂	#19134715	1	2	yes	—
252	C₂	#19134740	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₄₃
commutator	C₂³×C₄₃	C₂×C₄²
Fitting	C₂×C₄₃×#376	C₂
socle, prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#376	D₄₃
hypocenter	C₄₃	#10796
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#376

Complements

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

N	H ≅ G/N	type
8. #14582654	C₄	semidirect
140. C₄₃	#10796	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582654	2
C₂×C₄₃×#376	2
#10796	43