Subgroups — #25249844

Order 11008.

642 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19147697	C₂	1	2	yes	maximal, complemented
2	#19143499	C₂	1	1	yes	maximal, characteristic
3	#19136436	C₂	1	4	yes	maximal, complemented
4	#19136431	C₂	1	4	yes	maximal, complemented
5	C₂×#14582684	C₂	1	2	yes	maximal, complemented
6	#19136192	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2153	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583699	C₄	1	1	yes	characteristic
9	C₂×#13063331	C₂²	1	2	yes	—
10	#14583317	C₂²	1	8	yes	complemented
11	#14583315	—	2	4	no	—
12	C₂×#13063265	C₂²	1	1	yes	characteristic
13	M₃₂×D₄₃	—	2	4	no	—
14	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
15	#14583022	C₄	1	4	yes	—
16	#14583017	C₂²	1	4	yes	—
17	#14582948	C₄	1	1	yes	characteristic
18	#14582917	C₄	1	2	yes	—
19	#14582684	C₂²	1	4	yes	complemented
20	#14582684	C₂²	1	4	yes	complemented
21	#14582675	C₂²	1	2	yes	complemented
22	C₄×C₄₃⋊C₁₆	C₂²	1	2	yes	complemented
23	C₂×M₃₂×C₄₃	C₂²	1	2	yes	—
24	C₄₃×#405	C₂²	1	1	yes	characteristic
25	C₄₃×#364	C₂²	1	4	yes	complemented
26	C₂×#10621898	C₂×C₄	1	2	yes	—
27	#13063358	C₈	1	4	yes	—
28	#13063353	C₈	1	4	yes	—
29	#13063347	C₂×C₄	1	4	yes	—
30	#13063331	—	2	2	no	—
31	#13063331	—	2	2	no	—
32	#13063331	C₂×C₄	1	4	yes	—
33	#13063331	C₂³	1	4	yes	—
34	C₂×#10621877	C₂×C₄	1	2	yes	—
35	C₂×#10621872	—	2	2	no	—
36	C₂×C₈×D₄₃	—	2	2	no	—
37	#13063265	D₄	1	4	yes	—
38	#13063264	—	2	8	no	—
39	C₂×C₄₃⋊C₁₆	—	2	2	no	—
40	C₂×C₄₃⋊C₁₆	C₂³	1	1	yes	characteristic
41	C₂×C₄₃⋊C₁₆	C₂³	1	1	yes	characteristic
42	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
43	C₁₆×D₄₃	—	2	8	no	—
44	#13063261	C₂×C₄	1	4	yes	—
45	#13063253	C₂×C₄	1	8	yes	—
46	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
48	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
49	M₃₂×C₄₃	—	2	2	no	—
50	M₃₂×C₄₃	C₂³	1	4	yes	—
51	C₂×C₁₆×C₄₃	—	2	2	no	—
52	#97×C₄₃	C₂×C₄	1	2	yes	—
53	C₄×C₈×C₄₃	C₂³	1	2	yes	—
54	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₂²⋊D₄₃	—	2	2	no	—
56	#10621898	—	2	2	no	—
57	#10621898	—	2	2	no	—
58	#10621898	C₂×C₈	1	4	yes	—
59	#10621898	C₂²×C₄	1	4	yes	—
60	C₂×D₁₇₂	C₂×C₈	1	2	yes	—
61	C₂×C₄×D₄₃	—	2	2	no	—
62	C₂×Dic₈₆	C₂×C₈	1	2	yes	—
63	M₁₆×C₄₃	C₂×C₈	1	4	yes	—
64	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
66	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
67	C₂×C₈×C₄₃	#41	1	2	yes	—
68	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
69	C₄⋊C₄×C₄₃	—	2	1	no	—
70	C₂²⋊C₄×C₄₃	—	2	1	no	—
71	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
72	#10621877	—	2	2	no	—
73	#10621877	C₂²×C₄	1	4	yes	—
74	C₂×C₄₃⋊C₈	—	2	2	no	—
75	Dic₁₇₂	C₂×C₈	1	4	yes	—
76	D₃₄₄	C₂×C₈	1	4	yes	—
77	#10621873	C₂×C₈	1	8	yes	—
78	#10621872	—	2	4	no	—
79	#10621872	—	2	4	no	—
80	C₈×D₄₃	—	2	4	no	—
81	C₈×D₄₃	—	2	4	no	—
82	C₁₆×C₄₃	—	2	4	no	—
83	C₄₃⋊C₁₆	—	2	1	no	—
84	C₄₃⋊C₁₆	—	2	1	no	—
85	C₄₃⋊C₁₆	C₂×D₄	1	4	yes	—
86	C₂³×C₄₃	#131	1	1	yes	characteristic
87	C₂²×D₄₃	—	2	2	no	—
88	C₂×C₄×C₄₃	—	2	2	no	—
89	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
90	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
91	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
92	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
93	C₂²⋊D₄₃	—	2	4	no	—
94	C₂²⋊D₄₃	—	2	4	no	—
95	C₂×Dic₄₃	—	2	2	no	—
96	D₁₇₂	—	2	2	no	—
97	D₁₇₂	C₂²×C₈	1	4	yes	—
98	C₄×D₄₃	—	2	4	no	—
99	C₄×D₄₃	—	2	4	no	—
100	Dic₈₆	—	2	2	no	—
101	Dic₈₆	C₂²×C₈	1	4	yes	—
102	C₈×C₄₃	C₄×D₄	1	2	yes	—
103	C₈×C₄₃	C₂²×C₈	1	4	yes	—
104	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
105	C₈×C₄₃	C₂×#41	1	1	yes	characteristic
106	C₄₃⋊C₈	—	2	4	no	—
107	#33442	—	43	1	no	maximal, Sylow
108	C₂²×C₄₃	—	4	1	no	—
109	C₂²×C₄₃	C₈×D₄	1	2	yes	—
110	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
111	C₂×D₄₃	—	2	4	no	—
112	C₂×D₄₃	—	8	2	no	—
113	C₄×C₄₃	—	4	2	no	—
114	C₄×C₄₃	C₈×D₄	1	2	yes	—
115	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
116	C₄×C₄₃	C₂³×C₈	1	1	yes	characteristic
117	Dic₄₃	—	2	4	no	—
118	#3407	—	43	2	no	—
119	#2955	—	43	1	no	—
120	#2171	—	43	4	no	—
121	#2170	—	43	4	no	—
122	#2153	D₄₃	1	1	yes	characteristic, complemented
123	C₂×#350	—	43	2	no	—
124	#2108	—	43	1	no	—
125	C₂×C₄₃	—	2	1	no	—
126	C₂×C₄₃	—	2	2	no	—
127	C₂×C₄₃	C₂×C₈×D₄	1	1	yes	characteristic
128	D₄₃	—	4	4	no	—
129	#575	—	43	1	no	—
130	C₂×#131	—	43	2	no	—
131	#504	—	43	8	no	—
132	#504	—	86	4	no	—
133	C₂×M₃₂	—	43	1	no	—
134	C₂×M₃₂	—	86	4	no	—
135	C₂×M₃₂	C₂×D₄₃	1	2	yes	—
136	C₂²×C₁₆	—	43	1	no	—
137	#444	—	43	4	no	—
138	#443	—	43	4	no	—
139	#430	—	43	1	no	—
140	#421	—	43	2	no	—
141	#405	C₂×D₄₃	1	1	yes	characteristic
142	#364	C₂×D₄₃	1	4	yes	complemented
143	#350	—	43	4	no	—
144	#350	—	43	4	no	—
145	#346	—	43	2	no	—
146	C₄×C₁₆	—	43	2	no	—
147	C₄₃	#33442	1	1	yes	characteristic, complemented, Sylow
148	C₂×#41	—	43	2	no	—
149	#137	—	43	4	no	—
150	AGL(1,ℤ/8)	—	43	4	no	—
151	#135	—	43	4	no	—
152	#131	—	43	4	no	—
153	#131	—	43	4	no	—
154	#131	—	86	2	no	—
155	#131	—	86	2	no	—
156	C₂×M₁₆	—	43	2	no	—
157	C₂×M₁₆	—	86	2	no	—
158	C₂×M₁₆	C₄×D₄₃	1	1	yes	characteristic
159	C₂²×C₈	—	86	2	no	—
160	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
161	#117	C₄×D₄₃	1	1	yes	characteristic
162	M₃₂	—	2	2	no	—
163	M₃₂	—	43	4	no	—
164	M₃₂	—	86	8	no	—
165	M₃₂	C₂²×D₄₃	1	4	yes	—
166	C₂×C₁₆	—	2	2	no	—
167	C₂×C₁₆	—	43	2	no	—
168	C₂×C₁₆	—	43	1	no	—
169	C₂×C₁₆	—	43	1	no	—
170	C₂×C₁₆	—	86	8	no	—
171	C₂×C₁₆	—	86	2	no	—
172	#108	—	43	4	no	—
173	#104	—	43	8	no	—
174	#97	C₄×D₄₃	1	2	yes	—
175	C₄×C₈	C₂²×D₄₃	1	2	yes	—
176	#41	—	43	4	no	—
177	#41	—	43	4	no	—
178	#41	—	86	2	no	—
179	#41	—	86	2	no	—
180	C₂×Q₈	—	43	2	no	—
181	C₂×D₄	—	43	2	no	—
182	C₂×D₄	—	86	2	no	—
183	C₂²×C₄	—	86	2	no	—
184	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
185	Q₁₆	—	43	4	no	—
186	SD₁₆	—	43	8	no	—
187	D₈	—	43	4	no	—
188	M₁₆	—	43	4	no	—
189	M₁₆	—	86	2	no	—
190	M₁₆	—	86	4	no	—
191	M₁₆	—	86	4	no	—
192	M₁₆	C₈×D₄₃	1	4	yes	—
193	C₂×C₈	—	86	2	no	—
194	C₂×C₈	—	86	4	no	—
195	C₂×C₈	—	86	4	no	—
196	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
197	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
198	C₂×C₈	D₄×D₄₃	1	2	yes	—
199	C₂×C₈	#10621902	1	2	yes	—
200	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
201	C₄⋊C₄	—	2	1	no	—
202	C₂²⋊C₄	—	2	1	no	—
203	C₄²	C₂×C₄×D₄₃	1	2	yes	—
204	C₁₆	—	2	4	no	—
205	C₁₆	—	43	4	no	—
206	C₁₆	—	86	1	no	—
207	C₁₆	—	86	1	no	—
208	C₂³	—	86	2	no	—
209	C₂³	#13063333	1	1	yes	characteristic
210	Q₈	—	43	4	no	—
211	Q₈	—	86	2	no	—
212	D₄	—	43	4	no	—
213	D₄	—	86	4	no	—
214	D₄	—	86	4	no	—
215	D₄	—	86	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	86	2	no	—
218	C₂×C₄	—	86	4	no	—
219	C₂×C₄	—	86	4	no	—
220	C₂×C₄	#13063287	1	2	yes	—
221	C₂×C₄	C₂×C₈×D₄₃	1	2	yes	—
222	C₂×C₄	#13063333	1	1	yes	characteristic
223	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
224	C₈	—	86	4	no	—
225	C₈	#13063287	1	2	yes	—
226	C₈	C₂×C₈×D₄₃	1	4	yes	—
227	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
228	C₈	C₂×#10621902	1	1	yes	characteristic
229	C₂²	—	4	1	no	—
230	C₂²	—	86	4	no	—
231	C₂²	—	344	2	no	—
232	C₂²	#14582964	1	2	yes	—
233	C₂²	C₂×#13063333	1	1	yes	characteristic
234	C₄	—	4	2	no	—
235	C₄	—	86	4	no	—
236	C₄	#14582964	1	2	yes	—
237	C₄	C₂×#13063287	1	1	yes	characteristic
238	C₄	C₂²×C₈×D₄₃	1	1	yes	characteristic
239	C₂	—	2	1	no	—
240	C₂	—	2	2	no	—
241	C₂	—	172	4	no	—
242	C₂	C₂×#14582964	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₄₃
commutator	C₄×C₄₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₄₃×#2153	C₂
socle	C₂×C₄₃	C₂×C₈×D₄
prime radical	#14583699	C₄
cosocle	C₂×C₈×C₄₃	C₂⁴
hypercenter	#2153	D₄₃
hypocenter	C₄₃	#33442
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2153

Complements

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

N	H ≅ G/N	type
1. #19147697	C₂	semidirect
3. #19136436	C₂	semidirect
4. #19136431	C₂	semidirect
5. C₂×#14582684	C₂	semidirect
6. #19136192	C₂	semidirect
7. C₄₃×#2153	C₂	semidirect
10. #14583317	C₂²	semidirect
19. #14582684	C₂²	semidirect
20. #14582684	C₂²	semidirect
21. #14582675	C₂²	semidirect
22. C₄×C₄₃⋊C₁₆	C₂²	semidirect
25. C₄₃×#364	C₂²	semidirect
122. #2153	D₄₃	semidirect
142. #364	C₂×D₄₃	semidirect
147. C₄₃	#33442	semidirect

Maximal subgroups

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

subgroup	index
#19147697	2
#19143499	2
#19136436	2
#19136431	2
C₂×#14582684	2
#19136192	2
C₄₃×#2153	2
#33442	43