Subgroups — #25249168

Order 11008.

830 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583300	C₂	1	4	yes	maximal
2	#19142956	C₂	1	2	yes	maximal
3	#19134758	C₂	1	4	yes	maximal
4	#19134755	C₂	1	1	yes	maximal, characteristic
5	#19134751	C₂	1	2	yes	maximal
6	C₄×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1845	C₂	1	1	yes	maximal, characteristic
8	C₂×#13063316	C₂²	1	4	yes	—
9	#14583300	—	2	16	no	—
10	C₂×#13063259	C₂²	1	4	yes	—
11	C₂×#13063256	C₂²	1	8	yes	—
12	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
14	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
15	#14582798	—	2	4	no	—
16	#14582795	—	2	4	no	—
17	#14582769	C₂²	1	2	yes	—
18	#14582764	C₂²	1	4	yes	—
19	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
20	C₂×#107×C₄₃	C₂²	1	4	yes	—
21	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#384	C₂²	1	2	yes	—
23	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
24	#13063316	—	2	16	no	—
25	C₂×C₄⋊Dic₄₃	—	2	4	no	—
26	C₂×C₄⋊Dic₄₃	—	2	4	no	—
27	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
28	C₂×Dic₄₃⋊C₄	—	2	4	no	—
29	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
30	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
31	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
32	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
33	#13063259	—	2	8	no	—
34	#13063256	—	2	16	no	—
35	C₄×C₄₃⋊C₈	Q₈	1	4	yes	—
36	C₈×Dic₄₃	D₄	1	8	yes	—
37	C₈×Dic₄₃	Q₈	1	8	yes	—
38	C₄₃⋊#95	—	2	8	no	—
39	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
40	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
42	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
43	#107×C₄₃	—	2	8	no	—
44	C₄×C₈×C₄₃	Q₈	1	4	yes	—
45	C₂²×C₄×C₄₃	—	2	4	no	—
46	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
47	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
48	C₂²×Dic₄₃	—	2	4	no	—
49	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
51	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
52	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
53	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
54	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
55	C₄⋊C₄×C₄₃	—	2	8	no	—
56	C₄⋊C₄×C₄₃	—	4	8	no	—
57	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
58	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
59	C₄⋊Dic₄₃	—	2	8	no	—
60	C₄⋊Dic₄₃	—	4	8	no	—
61	C₄⋊Dic₄₃	—	4	8	no	—
62	Dic₄₃⋊C₄	—	4	8	no	—
63	C₄×Dic₄₃	—	2	4	no	—
64	C₄×Dic₄₃	—	2	4	no	—
65	C₄×Dic₄₃	C₂×D₄	1	4	yes	—
66	C₄×Dic₄₃	C₂×Q₈	1	4	yes	—
67	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
68	C₂×C₄₃⋊C₈	C₂×Q₈	1	4	yes	—
69	C₂×C₄₃⋊C₈	C₂×Q₈	1	4	yes	—
70	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
71	C₂×C₄×C₄₃	—	4	4	no	—
72	C₂×C₄×C₄₃	—	4	8	no	—
73	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
74	C₂×C₄×C₄₃	#135	1	4	yes	—
75	C₂×C₄×C₄₃	#135	1	4	yes	—
76	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
77	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
78	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
79	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
80	C₂×Dic₄₃	—	2	2	no	—
81	C₂×Dic₄₃	—	2	2	no	—
82	C₂×Dic₄₃	—	2	2	no	—
83	C₂×Dic₄₃	—	2	2	no	—
84	C₂×Dic₄₃	—	4	4	no	—
85	C₂×Dic₄₃	—	4	8	no	—
86	C₂×Dic₄₃	#127	1	2	yes	—
87	C₂×Dic₄₃	#127	1	2	yes	—
88	C₂×Dic₄₃	C₄⋊Q₈	1	4	yes	—
89	C₈×C₄₃	C₄⋊Q₈	1	8	yes	—
90	C₄₃⋊C₈	C₄⋊Q₈	1	8	yes	—
91	#33311	—	43	1	no	maximal, Sylow
92	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
93	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
94	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
95	C₂²×C₄₃	C₂×#135	1	2	yes	—
96	C₂²×C₄₃	C₂×#135	1	2	yes	—
97	C₄×C₄₃	—	8	4	no	—
98	C₄×C₄₃	#499	1	8	yes	complemented
99	C₄×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
100	C₄×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
101	Dic₄₃	—	2	2	no	—
102	Dic₄₃	—	2	2	no	—
103	Dic₄₃	—	2	4	no	—
104	Dic₄₃	—	8	4	no	—
105	C₂×#499	—	43	4	no	—
106	#2859	—	43	2	no	—
107	#1846	—	43	4	no	—
108	#1845	—	43	1	no	—
109	#1845	D₄₃	1	1	yes	characteristic
110	#1844	—	43	2	no	—
111	C₄²×C₈	—	43	1	no	—
112	C₂×C₄₃	#2868	1	1	yes	characteristic
113	C₂×C₄₃	#3147	1	1	yes	characteristic
114	C₂×C₄₃	#3147	1	1	yes	characteristic
115	C₂×C₄₃	C₂×#499	1	2	yes	—
116	C₂×C₄₃	#3160	1	2	yes	—
117	C₂×#125	—	43	4	no	—
118	#499	—	86	16	no	—
119	C₂×#107	—	43	4	no	—
120	C₂×#107	C₂×D₄₃	1	4	yes	—
121	C₂×#106	—	43	8	no	—
122	C₂×C₄×C₈	—	43	2	no	—
123	C₂×C₄×C₈	—	43	2	no	—
124	C₂×C₄×C₈	—	43	1	no	—
125	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
126	#389	—	86	4	no	—
127	#389	—	86	4	no	—
128	#384	—	43	2	no	—
129	#384	C₂×D₄₃	1	2	yes	—
130	#382	—	43	4	no	—
131	C₄³	—	43	1	no	—
132	C₄₃	#33311	1	1	yes	characteristic, complemented, Sylow
133	C₂²×C₈	—	43	2	no	—
134	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
135	#125	—	86	16	no	—
136	C₂×C₄⋊C₄	—	2	4	no	—
137	C₂×C₄⋊C₄	—	43	4	no	—
138	C₂×C₄⋊C₄	—	86	4	no	—
139	C₂×C₄⋊C₄	—	86	4	no	—
140	C₂×C₄⋊C₄	—	86	4	no	—
141	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
142	C₂×C₄²	—	43	1	no	—
143	C₂×C₄²	—	43	1	no	—
144	C₂×C₄²	—	43	2	no	—
145	C₂×C₄²	—	43	2	no	—
146	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
147	#107	—	2	8	no	—
148	#107	—	86	8	no	—
149	#106	—	86	16	no	—
150	C₄×C₈	—	43	8	no	—
151	C₄×C₈	—	43	8	no	—
152	C₄×C₈	—	43	4	no	—
153	C₄×C₈	Dic₈₆	1	4	yes	—
154	#95	—	86	8	no	—
155	C₂²×C₄	—	2	4	no	—
156	C₂²×C₄	—	43	2	no	—
157	C₂²×C₄	—	43	1	no	—
158	C₂²×C₄	—	43	1	no	—
159	C₂²×C₄	—	86	4	no	—
160	C₂²×C₄	D₄×D₄₃	1	2	yes	—
161	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
162	C₂×C₈	—	43	4	no	—
163	C₂×C₈	—	43	4	no	—
164	C₂×C₈	—	43	4	no	—
165	C₂×C₈	C₂×Dic₈₆	1	4	yes	—
166	C₂×C₈	D₄×D₄₃	1	4	yes	—
167	C₂×C₈	Q₈×D₄₃	1	4	yes	—
168	C₄⋊C₄	—	2	8	no	—
169	C₄⋊C₄	—	4	8	no	—
170	C₄⋊C₄	—	86	8	no	—
171	C₄⋊C₄	—	172	8	no	—
172	C₄⋊C₄	—	172	8	no	—
173	C₄⋊C₄	—	172	8	no	—
174	C₄²	—	43	4	no	—
175	C₄²	—	43	4	no	—
176	C₄²	—	86	4	no	—
177	C₄²	—	86	4	no	—
178	C₄²	C₂×Dic₈₆	1	2	yes	—
179	C₄²	Q₈×D₄₃	1	2	yes	—
180	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
181	C₂×C₄	—	4	8	no	—
182	C₂×C₄	—	4	4	no	—
183	C₂×C₄	—	43	2	no	—
184	C₂×C₄	—	43	2	no	—
185	C₂×C₄	—	43	4	no	—
186	C₂×C₄	—	86	2	no	—
187	C₂×C₄	—	86	2	no	—
188	C₂×C₄	—	86	2	no	—
189	C₂×C₄	—	86	2	no	—
190	C₂×C₄	—	172	8	no	—
191	C₂×C₄	—	172	4	no	—
192	C₂×C₄	#13063324	1	4	yes	—
193	C₂×C₄	#13063344	1	4	yes	—
194	C₂×C₄	#13063348	1	4	yes	—
195	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
196	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
197	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
198	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
199	C₈	—	43	8	no	—
200	C₈	#13063324	1	8	yes	—
201	C₂²	#127×D₄₃	1	1	yes	characteristic
202	C₂²	C₄⋊Q₈×D₄₃	1	1	yes	characteristic
203	C₂²	C₂×#13063324	1	1	yes	characteristic
204	C₂²	C₂×#13063344	1	2	yes	—
205	C₂²	C₂×#13063348	1	2	yes	—
206	C₄	—	8	4	no	—
207	C₄	—	86	2	no	—
208	C₄	—	86	2	no	—
209	C₄	—	86	4	no	—
210	C₄	—	344	4	no	—
211	C₄	#14583300	1	8	yes	complemented
212	C₄	C₄⋊Q₈×D₄₃	1	2	yes	—
213	C₄	C₂×#13063324	1	2	yes	—
214	C₂	#19142992	1	1	yes	characteristic
215	C₂	#19145022	1	1	yes	characteristic
216	C₂	#19145024	1	1	yes	characteristic
217	C₂	C₂×#14583300	1	2	yes	—
218	C₂	#19145106	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1845	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
hypercenter	#1845	D₄₃
hypocenter	C₄₃	#33311
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

Complements

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

N	H ≅ G/N	type
98. C₄×C₄₃	#499	semidirect
132. C₄₃	#33311	semidirect
211. C₄	#14583300	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583300	2
#19142956	2
#19134758	2
#19134755	2
#19134751	2
C₄×C₈×Dic₄₃	2
C₄₃×#1845	2
#33311	43