Subgroups — #24987849

Order 11008.

430 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13063257	C₂	1	1	yes	maximal, characteristic
2	#19134460	C₂	1	2	yes	maximal
3	C₂×#14582620	C₂	1	1	yes	maximal, characteristic
4	#19132434	C₂	1	2	yes	maximal
5	C₂×C₄₃×#335	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063257	C₄	1	2	yes	—
7	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×Dic₄₃	—	2	2	no	—
10	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
11	#14582662	C₄	1	2	yes	—
12	#14582653	—	2	2	no	—
13	#14582620	C₄	1	4	yes	complemented
14	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#335	C₄	1	4	yes	complemented
17	C₂²×C₄₃⋊C₈	—	2	1	no	—
18	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
19	C₂×C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
20	C₂×C₄×Dic₄₃	—	2	2	no	—
21	#13063257	C₈	1	8	yes	complemented
22	C₄×C₄₃⋊C₈	—	2	1	no	—
23	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
24	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
25	C₄×C₄₃⋊C₈	Q₈	1	2	yes	—
26	C₈×Dic₄₃	—	4	4	no	—
27	C₄₃⋊#95	—	2	2	no	—
28	C₂²×C₈×C₄₃	—	2	2	no	—
29	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
32	C₄⋊C₈×C₄₃	—	2	2	no	—
33	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
34	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
36	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
39	C₂²×Dic₄₃	—	2	4	no	—
40	C₂×C₈×C₄₃	—	2	2	no	—
41	C₂×C₈×C₄₃	—	2	4	no	—
42	C₂×C₈×C₄₃	—	4	2	no	—
43	C₂×C₈×C₄₃	—	4	2	no	—
44	C₂×C₈×C₄₃	C₄²	1	2	yes	—
45	C₂×C₈×C₄₃	C₄²	1	2	yes	—
46	C₂×C₈×C₄₃	C₂×C₈	1	4	yes	—
47	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
48	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
49	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
50	C₄²×C₄₃	#41	1	1	yes	characteristic
51	C₄⋊Dic₄₃	—	2	4	no	—
52	C₄⋊Dic₄₃	C₂×C₈	1	8	yes	—
53	C₄×Dic₄₃	—	4	2	no	—
54	C₄×Dic₄₃	—	4	2	no	—
55	C₂×C₄₃⋊C₈	—	2	2	no	—
56	C₂×C₄₃⋊C₈	—	2	2	no	—
57	C₂×C₄₃⋊C₈	—	2	2	no	—
58	C₂×C₄₃⋊C₈	—	4	2	no	—
59	C₂×C₄₃⋊C₈	C₄⋊C₄	1	4	yes	—
60	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
61	C₂×C₄×C₄₃	—	2	2	no	—
62	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
63	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
65	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
66	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
67	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
68	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
69	C₂×C₄×C₄₃	#131	1	2	yes	—
70	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
71	C₂×C₄×C₄₃	#137	1	2	yes	—
72	C₂×Dic₄₃	—	2	8	no	—
73	C₂×Dic₄₃	—	4	4	no	—
74	C₂×Dic₄₃	—	4	4	no	—
75	C₈×C₄₃	—	2	2	no	—
76	C₈×C₄₃	—	4	4	no	—
77	C₈×C₄₃	C₄×C₈	1	4	yes	complemented
78	C₄₃⋊C₈	—	2	4	no	—
79	C₄₃⋊C₈	—	4	2	no	—
80	#8285	—	43	1	no	maximal, Sylow
81	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄₃	C₈×D₄	1	2	yes	—
83	C₂²×C₄₃	#440	1	2	yes	—
84	C₂²×C₄₃	#444	1	2	yes	—
85	C₄×C₄₃	—	2	1	no	—
86	C₄×C₄₃	—	2	1	no	—
87	C₄×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
88	C₄×C₄₃	#405	1	1	yes	characteristic
89	C₄×C₄₃	#428	1	2	yes	—
90	C₄×C₄₃	#441	1	1	yes	characteristic
91	C₄×C₄₃	#442	1	1	yes	characteristic
92	C₄×C₄₃	C₈×Q₈	1	2	yes	—
93	Dic₄₃	—	4	8	no	—
94	C₄×#106	—	43	1	no	—
95	C₈×C₄⋊C₄	—	43	2	no	—
96	C₂×#335	D₄₃	1	1	yes	characteristic
97	C₂×#322	—	43	1	no	—
98	#1279	—	43	2	no	—
99	C₂×C₄₃	SD₁₆⋊C₈	1	4	yes	—
100	C₂×C₄₃	C₈×C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄₃	#1773	1	1	yes	characteristic
102	C₂×C₄₃	#1776	1	1	yes	characteristic
103	C₂×#106	—	43	2	no	—
104	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
105	C₂×C₄×C₈	—	43	1	no	—
106	C₂×C₄×C₈	—	43	1	no	—
107	C₂×C₄×C₈	—	86	2	no	—
108	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
109	C₄×C₄⋊C₄	—	43	2	no	—
110	#340	—	43	2	no	—
111	#336	—	86	2	no	—
112	#335	Dic₄₃	1	4	yes	complemented
113	#322	—	43	4	no	—
114	C₄₃	#8285	1	1	yes	characteristic, complemented, Sylow
115	C₂²×C₈	—	2	2	no	—
116	C₂²×C₈	—	43	2	no	—
117	C₂²×C₈	—	86	1	no	—
118	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
119	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
120	C₂×C₄⋊C₄	—	43	4	no	—
121	C₂×C₄²	—	86	2	no	—
122	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
123	#106	—	43	8	no	—
124	C₄⋊C₈	—	2	2	no	—
125	C₄⋊C₈	C₂×Dic₄₃	1	4	yes	—
126	C₄×C₈	—	43	2	no	—
127	C₄×C₈	—	43	2	no	—
128	C₄×C₈	—	43	2	no	—
129	C₄×C₈	—	86	1	no	—
130	C₄×C₈	—	172	4	no	—
131	C₄×C₈	C₄×D₄₃	1	2	yes	—
132	C₄×C₈	C₂×Dic₄₃	1	2	yes	—
133	#95	—	86	2	no	—
134	C₂²×C₄	—	86	4	no	—
135	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
136	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
137	C₂²×C₄	#10621902	1	1	yes	characteristic
138	C₂×C₈	—	2	2	no	—
139	C₂×C₈	—	2	4	no	—
140	C₂×C₈	—	4	2	no	—
141	C₂×C₈	—	4	2	no	—
142	C₂×C₈	—	43	4	no	—
143	C₂×C₈	—	86	2	no	—
144	C₂×C₈	—	86	2	no	—
145	C₂×C₈	—	86	2	no	—
146	C₂×C₈	—	172	2	no	—
147	C₂×C₈	C₈×D₄₃	1	4	yes	—
148	C₂×C₈	C₄×Dic₄₃	1	2	yes	—
149	C₂×C₈	C₄×Dic₄₃	1	2	yes	—
150	C₄⋊C₄	—	43	8	no	—
151	C₄⋊C₄	—	86	4	no	—
152	C₄²	—	172	2	no	—
153	C₄²	—	172	2	no	—
154	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
155	C₄²	#10621900	1	1	yes	characteristic
156	C₄²	Q₈×D₄₃	1	1	yes	characteristic
157	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
158	C₂³	#13063287	1	1	yes	characteristic
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	86	8	no	—
161	C₂×C₄	—	172	4	no	—
162	C₂×C₄	—	172	4	no	—
163	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
164	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
165	C₂×C₄	#13063283	1	1	yes	characteristic
166	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
167	C₂×C₄	#13063290	1	1	yes	characteristic
168	C₂×C₄	Q₈×Dic₄₃	1	1	yes	characteristic
169	C₂×C₄	C₂×C₈×D₄₃	1	2	yes	—
170	C₂×C₄	#13063333	1	2	yes	—
171	C₂×C₄	#13063349	1	2	yes	—
172	C₂×C₄	#13063357	1	2	yes	—
173	C₈	—	2	2	no	—
174	C₈	—	4	4	no	—
175	C₈	—	86	4	no	—
176	C₈	—	172	2	no	—
177	C₈	C₈×Dic₄₃	1	4	yes	complemented
178	C₂²	C₄⋊C₄×Dic₄₃	1	1	yes	characteristic
179	C₂²	#14582964	1	2	yes	—
180	C₂²	#14582998	1	2	yes	—
181	C₂²	#14583020	1	2	yes	—
182	C₄	—	2	1	no	—
183	C₄	—	2	1	no	—
184	C₄	—	172	8	no	—
185	C₄	C₂×C₈×Dic₄₃	1	1	yes	characteristic
186	C₄	#14582857	1	1	yes	characteristic
187	C₄	#14582940	1	2	yes	—
188	C₄	#14583006	1	1	yes	characteristic
189	C₄	#14583011	1	1	yes	characteristic
190	C₄	#14583023	1	2	yes	—
191	C₂	#19133406	1	4	yes	—
192	C₂	#19134460	1	1	yes	characteristic
193	C₂	#19134482	1	1	yes	characteristic
194	C₂	#19134494	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₄×C₄₃	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#335	C₂
socle, prime radical	C₂³×C₄₃	C₄×D₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×#335	D₄₃
hypocenter	C₄₃	#8285
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
13. #14582620	C₄	semidirect
16. C₄₃×#335	C₄	semidirect
21. #13063257	C₈	semidirect
77. C₈×C₄₃	C₄×C₈	semidirect
112. #335	Dic₄₃	semidirect
114. C₄₃	#8285	semidirect
177. C₈	C₈×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13063257	2
#19134460	2
C₂×#14582620	2
#19132434	2
C₂×C₄₃×#335	2
#8285	43