Subgroups — #24995894

Order 11008.

506 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19135548	C₂	1	2	yes	maximal
2	#19134462	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582650	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582645	C₂	1	2	yes	maximal
5	C₂×C₄₃×#494	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
8	C₂×#13063235	—	2	1	no	—
9	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
10	#14582661	—	2	4	no	—
11	#14582653	—	2	1	no	—
12	#14582650	—	2	2	no	—
13	#14582645	—	2	4	no	—
14	C₂²×Q₁₆×C₄₃	—	2	1	no	—
15	C₂²×Q₁₆×C₄₃	—	2	1	no	—
16	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
17	C₄₃×#494	—	2	2	no	—
18	C₄₃×#494	C₄	1	4	yes	complemented
19	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄₃⋊C₈	—	2	1	no	—
21	C₂²×C₄₃⋊C₈	—	2	2	no	—
22	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
23	C₂×C₄×Dic₄₃	—	2	1	no	—
24	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
25	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
26	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
27	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
28	#13063235	—	4	2	no	—
29	C₄₃⋊#95	—	2	1	no	—
30	C₂²×Q₈×C₄₃	—	2	2	no	—
31	C₂×Q₁₆×C₄₃	—	2	4	no	—
32	C₂×Q₁₆×C₄₃	—	2	4	no	—
33	C₂×Q₁₆×C₄₃	—	4	2	no	—
34	C₂×Q₁₆×C₄₃	—	4	2	no	—
35	C₂×Q₁₆×C₄₃	—	4	2	no	—
36	C₂×Q₁₆×C₄₃	—	4	2	no	—
37	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
39	C₄⋊Q₈×C₄₃	—	2	2	no	—
40	C₄⋊Q₈×C₄₃	—	2	2	no	—
41	C₄⋊Q₈×C₄₃	—	2	2	no	—
42	C₄⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
43	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
45	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
46	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
47	C₄×C₈×C₄₃	D₄	1	2	yes	—
48	C₂×Q₈×C₄₃	—	2	4	no	—
49	C₂×Q₈×C₄₃	—	4	2	no	—
50	C₂×Q₈×C₄₃	—	4	2	no	—
51	C₂×Q₈×C₄₃	—	4	2	no	—
52	C₂×Q₈×C₄₃	—	4	2	no	—
53	C₂×Q₈×C₄₃	—	4	2	no	—
54	C₂²×C₄×C₄₃	—	4	2	no	—
55	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
58	C₂²×Dic₄₃	—	2	2	no	—
59	Q₁₆×C₄₃	—	4	8	no	—
60	Q₁₆×C₄₃	—	4	8	no	—
61	C₂×C₈×C₄₃	—	2	1	no	—
62	C₂×C₈×C₄₃	—	2	1	no	—
63	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
64	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
65	C₂×C₈×C₄₃	D₈	1	2	yes	—
66	C₂×C₈×C₄₃	SD₁₆	1	2	yes	—
67	C₄⋊C₄×C₄₃	—	2	4	no	—
68	C₄⋊C₄×C₄₃	—	2	4	no	—
69	C₄⋊C₄×C₄₃	—	4	2	no	—
70	C₄⋊C₄×C₄₃	—	4	2	no	—
71	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₄₃	#41	1	1	yes	characteristic
75	C₄⋊Dic₄₃	—	2	4	no	—
76	C₄×Dic₄₃	—	4	1	no	—
77	C₄×Dic₄₃	—	4	1	no	—
78	C₂×C₄₃⋊C₈	—	2	2	no	—
79	C₂×C₄₃⋊C₈	—	4	1	no	—
80	C₂×C₄₃⋊C₈	—	4	1	no	—
81	C₂×C₄₃⋊C₈	—	4	2	no	—
82	C₂×C₄₃⋊C₈	—	4	4	no	—
83	C₂³×C₄₃	#121	1	1	yes	characteristic
84	Q₈×C₄₃	—	4	4	no	—
85	Q₈×C₄₃	—	4	4	no	—
86	Q₈×C₄₃	—	8	2	no	—
87	Q₈×C₄₃	—	8	2	no	—
88	C₂×C₄×C₄₃	—	2	2	no	—
89	C₂×C₄×C₄₃	—	4	4	no	—
90	C₂×C₄×C₄₃	—	8	2	no	—
91	C₂×C₄×C₄₃	—	8	2	no	—
92	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
95	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
96	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
97	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
98	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
99	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
100	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
101	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
102	C₂×C₄×C₄₃	#137	1	4	yes	—
103	C₂×Dic₄₃	—	4	2	no	—
104	C₂×Dic₄₃	—	4	2	no	—
105	C₂×Dic₄₃	—	4	2	no	—
106	C₈×C₄₃	—	2	2	no	—
107	C₈×C₄₃	#102	1	4	yes	—
108	C₄₃⋊C₈	—	4	2	no	—
109	C₄₃⋊C₈	—	8	2	no	—
110	#9742	—	43	1	no	maximal, Sylow
111	C₂²×C₄₃	#390	1	1	yes	characteristic
112	C₂²×C₄₃	#459	1	1	yes	characteristic
113	C₂²×C₄₃	#460	1	1	yes	characteristic
114	C₂²×C₄₃	#470	1	2	yes	—
115	C₂²×C₄₃	#473	1	2	yes	—
116	C₄×C₄₃	—	2	1	no	—
117	C₄×C₄₃	—	2	1	no	—
118	C₄×C₄₃	—	8	4	no	—
119	C₄×C₄₃	C₂×#102	1	1	yes	characteristic
120	C₄×C₄₃	#418	1	1	yes	characteristic
121	C₄×C₄₃	#441	1	2	yes	—
122	C₄×C₄₃	#459	1	1	yes	characteristic
123	C₄×C₄₃	#460	1	1	yes	characteristic
124	C₄×C₄₃	#497	1	2	yes	—
125	Dic₄₃	—	8	2	no	—
126	C₂×#494	D₄₃	1	1	yes	characteristic
127	#1988	—	43	2	no	—
128	#1770	—	43	1	no	—
129	C₂×#334	—	43	1	no	—
130	C₂×#332	—	43	2	no	—
131	C₂×C₄₃	#1689	1	2	yes	—
132	C₂×C₄₃	#1690	1	2	yes	—
133	C₂×C₄₃	#1971	1	1	yes	characteristic
134	C₂×C₄₃	#1979	1	1	yes	characteristic
135	C₂×C₄₃	#1982	1	1	yes	characteristic
136	C₂²×Q₁₆	—	2	1	no	—
137	C₂²×Q₁₆	—	2	1	no	—
138	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
139	#494	—	2	2	no	—
140	#494	Dic₄₃	1	4	yes	complemented
141	C₂×C₄⋊C₈	—	43	1	no	—
142	C₂×C₄⋊C₈	—	43	2	no	—
143	C₂×#97	—	86	1	no	—
144	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
145	C₄×C₄⋊C₄	—	43	1	no	—
146	#340	—	86	4	no	—
147	#336	—	86	1	no	—
148	#334	—	86	2	no	—
149	#332	—	86	4	no	—
150	C₄₃	#9742	1	1	yes	characteristic, complemented, Sylow
151	C₂²×Q₈	—	2	2	no	—
152	C₂×Q₁₆	—	2	4	no	—
153	C₂×Q₁₆	—	2	4	no	—
154	C₂×Q₁₆	—	4	2	no	—
155	C₂×Q₁₆	—	4	2	no	—
156	C₂×Q₁₆	—	4	2	no	—
157	C₂×Q₁₆	—	4	2	no	—
158	C₂²×C₈	—	86	1	no	—
159	C₂²×C₈	—	86	2	no	—
160	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
161	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
162	C₄⋊Q₈	—	2	2	no	—
163	C₄⋊Q₈	—	2	2	no	—
164	C₄⋊Q₈	—	2	2	no	—
165	C₄⋊Q₈	C₂×Dic₄₃	1	4	yes	—
166	C₂×C₄⋊C₄	—	2	2	no	—
167	C₂×C₄⋊C₄	—	2	2	no	—
168	C₂×C₄⋊C₄	—	43	2	no	—
169	C₂×C₄²	—	86	1	no	—
170	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
171	C₄⋊C₈	—	43	2	no	—
172	C₄⋊C₈	—	86	2	no	—
173	C₄⋊C₈	—	86	1	no	—
174	C₄⋊C₈	—	86	2	no	—
175	#97	—	172	2	no	—
176	C₄×C₈	C₂×Dic₄₃	1	2	yes	—
177	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
178	#95	—	86	1	no	—
179	C₂×Q₈	—	2	4	no	—
180	C₂×Q₈	—	4	2	no	—
181	C₂×Q₈	—	4	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	2	no	—
185	C₂²×C₄	—	4	2	no	—
186	C₂²×C₄	—	86	2	no	—
187	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
188	C₂²×C₄	#10621900	1	1	yes	characteristic
189	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
190	Q₁₆	—	4	8	no	—
191	Q₁₆	—	4	8	no	—
192	C₂×C₈	—	2	1	no	—
193	C₂×C₈	—	2	1	no	—
194	C₂×C₈	—	86	2	no	—
195	C₂×C₈	—	172	2	no	—
196	C₂×C₈	—	172	4	no	—
197	C₂×C₈	—	172	1	no	—
198	C₂×C₈	—	172	1	no	—
199	C₂×C₈	#10621882	1	2	yes	—
200	C₂×C₈	#10621883	1	2	yes	—
201	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
202	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
203	C₄⋊C₄	—	2	4	no	—
204	C₄⋊C₄	—	2	4	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₄⋊C₄	—	86	4	no	—
208	C₄²	—	172	1	no	—
209	C₄²	—	172	1	no	—
210	C₄²	D₄×D₄₃	1	1	yes	characteristic
211	C₄²	#10621900	1	1	yes	characteristic
212	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
213	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
214	C₂³	#13063296	1	1	yes	characteristic
215	Q₈	—	4	4	no	—
216	Q₈	—	4	4	no	—
217	Q₈	—	8	2	no	—
218	Q₈	—	8	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	8	2	no	—
222	C₂×C₄	—	8	2	no	—
223	C₂×C₄	—	172	2	no	—
224	C₂×C₄	—	172	2	no	—
225	C₂×C₄	—	172	2	no	—
226	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
227	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
228	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
229	C₂×C₄	#13063296	1	1	yes	characteristic
230	C₂×C₄	#13063312	1	1	yes	characteristic
231	C₂×C₄	#13063321	1	1	yes	characteristic
232	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
233	C₂×C₄	C₂×#10621883	1	1	yes	characteristic
234	C₂×C₄	#13063351	1	1	yes	characteristic
235	C₂×C₄	#13063351	1	1	yes	characteristic
236	C₂×C₄	#13063357	1	4	yes	—
237	C₈	—	2	2	no	—
238	C₈	—	344	2	no	—
239	C₈	—	172	2	no	—
240	C₈	#13063246	1	4	yes	—
241	C₂²	#14582802	1	1	yes	characteristic
242	C₂²	#14583091	1	1	yes	characteristic
243	C₂²	#14583096	1	1	yes	characteristic
244	C₂²	#14583154	1	2	yes	—
245	C₂²	#14583171	1	2	yes	—
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	8	4	no	—
249	C₄	—	344	2	no	—
250	C₄	C₂×#13063246	1	1	yes	characteristic
251	C₄	#14582904	1	1	yes	characteristic
252	C₄	#14583006	1	2	yes	—
253	C₄	#14583091	1	1	yes	characteristic
254	C₄	#14583096	1	1	yes	characteristic
255	C₄	#14583292	1	2	yes	—
256	C₂	#19134081	1	2	yes	—
257	C₂	#19134086	1	2	yes	—
258	C₂	#19135467	1	1	yes	characteristic
259	C₂	#19135511	1	1	yes	characteristic
260	C₂	#19135523	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063296
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#494	C₂
socle, prime radical	C₂³×C₄₃	#121
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×#494	D₄₃
hypocenter	C₄₃	#9742
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

Complements

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

N	H ≅ G/N	type
18. C₄₃×#494	C₄	semidirect
140. #494	Dic₄₃	semidirect
150. C₄₃	#9742	semidirect

Maximal subgroups

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

subgroup	index
#19135548	2
#19134462	2
C₂×#14582650	2
C₂×#14582645	2
C₂×C₄₃×#494	2
#9742	43