Subgroups — #25096748

Order 11008.

1158 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582923	C₂	1	2	yes	maximal
2	#19134712	C₂	1	8	yes	maximal, complemented
3	#19134289	C₂	1	4	yes	maximal
4	C₂×C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10621877	C₂²	1	4	yes	—
6	#14582923	—	2	8	no	—
7	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	8	yes	—
8	#14582654	C₂²	1	16	yes	—
9	C₂²×C₄²×C₄₃	C₄	1	4	yes	—
10	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
11	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	C₄³×C₄₃	C₄	1	2	yes	—
13	C₄³×C₄₃	C₄	1	2	yes	—
14	C₄³×C₄₃	C₂²	1	4	yes	—
15	C₂×#10621877	—	2	8	no	—
16	C₂×#10621877	—	2	16	no	—
17	C₂²×C₄₃⋊C₈	C₂³	1	8	yes	—
18	C₄⋊(C₄₃⋊C₈)	—	2	16	no	—
19	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
20	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
21	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂×C₄²×C₄₃	—	2	8	no	—
23	C₂×C₄²×C₄₃	—	2	16	no	—
24	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
25	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
26	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
27	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
30	C₂×C₄²×C₄₃	D₄	1	4	yes	—
31	C₂×C₄²×C₄₃	Q₈	1	4	yes	—
32	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
33	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
34	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₄₃	—	2	16	no	—
36	C₂²×C₄×C₄₃	—	2	8	no	—
37	C₂²×C₄×C₄₃	—	2	8	no	—
38	C₂²×C₄×C₄₃	C₄⋊C₄	1	8	yes	—
39	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
40	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
41	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
43	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
44	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
45	C₂²×C₄×C₄₃	#41	1	8	yes	—
46	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
47	C₄²×C₄₃	—	2	8	no	—
48	C₄²×C₄₃	—	2	16	no	—
49	C₄²×C₄₃	—	2	8	no	—
50	C₄²×C₄₃	—	2	8	no	—
51	C₄²×C₄₃	C₄⋊C₄	1	4	yes	—
52	C₄²×C₄₃	C₄⋊C₄	1	4	yes	—
53	C₄²×C₄₃	M₁₆	1	16	yes	complemented
54	C₄²×C₄₃	C₂×D₄	1	4	yes	—
55	C₄²×C₄₃	C₂×Q₈	1	4	yes	—
56	#10621877	—	4	16	no	—
57	C₂×C₄₃⋊C₈	—	2	8	no	—
58	C₂×C₄₃⋊C₈	—	2	16	no	—
59	C₂³×C₄₃	—	2	4	no	—
60	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
61	C₂³×C₄₃	#117	1	4	yes	—
62	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
63	C₂×C₄×C₄₃	—	2	32	no	—
64	C₂×C₄×C₄₃	—	2	8	no	—
65	C₂×C₄×C₄₃	—	2	4	no	—
66	C₂×C₄×C₄₃	—	2	8	no	—
67	C₂×C₄×C₄₃	—	2	16	no	—
68	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
69	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
70	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
71	C₂×C₄×C₄₃	#117	1	4	yes	—
72	C₂×C₄×C₄₃	#124	1	8	yes	—
73	C₂×C₄×C₄₃	#125	1	8	yes	—
74	C₂×C₄×C₄₃	C₂×M₁₆	1	16	yes	—
75	C₂×C₄×C₄₃	C₂×M₁₆	1	8	yes	—
76	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
77	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
78	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
79	C₄₃⋊C₈	—	4	8	no	—
80	#20752	—	43	1	no	maximal, Sylow
81	C₂²×C₄₃	—	2	4	no	—
82	C₂²×C₄₃	—	2	8	no	—
83	C₂²×C₄₃	#382	1	4	yes	—
84	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄₃	C₂×#117	1	2	yes	—
86	C₂²×C₄₃	C₂²×M₁₆	1	4	yes	—
87	C₄×C₄₃	—	2	4	no	—
88	C₄×C₄₃	—	2	16	no	—
89	C₄×C₄₃	#382	1	4	yes	—
90	C₄×C₄₃	#423	1	8	yes	—
91	C₄×C₄₃	C₂×#124	1	2	yes	—
92	C₄×C₄₃	C₂×#125	1	2	yes	—
93	C₂×#423	—	43	2	no	—
94	C₂×C₄³	D₄₃	1	1	yes	characteristic
95	#1831	—	43	8	no	—
96	#1728	—	43	4	no	—
97	C₂×C₄₃	—	2	4	no	—
98	C₂×C₄₃	C₂×#382	1	1	yes	characteristic
99	C₂×C₄₃	C₂×#423	1	2	yes	—
100	C₂×C₄₃	#2920	1	4	yes	—
101	C₂²×M₁₆	—	43	4	no	—
102	C₂²×C₄²	Dic₄₃	1	4	yes	—
103	C₂²×C₄²	C₂×D₄₃	1	2	yes	—
104	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
105	#423	—	86	8	no	—
106	C₂×C₄⋊C₈	—	43	8	no	—
107	C₄³	Dic₄₃	1	2	yes	—
108	C₄³	Dic₄₃	1	2	yes	—
109	C₄³	C₂×D₄₃	1	4	yes	—
110	#336	—	43	16	no	—
111	C₄₃	#20752	1	1	yes	characteristic, complemented, Sylow
112	C₂³×C₄	C₂×Dic₄₃	1	4	yes	—
113	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
114	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
115	C₂×M₁₆	—	86	8	no	—
116	C₂×M₁₆	—	86	16	no	—
117	C₂²×C₈	—	43	8	no	—
118	C₂×C₄²	—	2	8	no	—
119	C₂×C₄²	—	2	16	no	—
120	C₂×C₄²	Dic₈₆	1	4	yes	—
121	C₂×C₄²	D₁₇₂	1	4	yes	—
122	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
123	C₂×C₄²	C₂×Dic₄₃	1	8	yes	—
124	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
125	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
126	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
127	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
128	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
129	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
130	C₄⋊C₈	—	86	16	no	—
131	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
132	C₂²×C₄	—	2	8	no	—
133	C₂²×C₄	—	2	16	no	—
134	C₂²×C₄	—	2	8	no	—
135	C₂²×C₄	C₄⋊Dic₄₃	1	8	yes	—
136	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
137	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
138	C₂²×C₄	#10621898	1	8	yes	—
139	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
140	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
141	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
142	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
143	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
144	M₁₆	—	172	16	no	—
145	C₂×C₈	—	86	8	no	—
146	C₂×C₈	—	86	16	no	—
147	C₄²	—	2	8	no	—
148	C₄²	—	2	16	no	—
149	C₄²	—	2	8	no	—
150	C₄²	—	2	8	no	—
151	C₄²	#10621877	1	16	yes	complemented
152	C₄²	C₄⋊Dic₄₃	1	4	yes	—
153	C₄²	C₄⋊Dic₄₃	1	4	yes	—
154	C₄²	C₂×Dic₈₆	1	4	yes	—
155	C₄²	C₂×D₁₇₂	1	4	yes	—
156	C₂³	—	2	4	no	—
157	C₂³	C₂×C₄⋊Dic₄₃	1	2	yes	—
158	C₂³	#13063284	1	4	yes	—
159	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
160	C₂×C₄	—	2	32	no	—
161	C₂×C₄	—	2	8	no	—
162	C₂×C₄	—	2	8	no	—
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	—	2	16	no	—
165	C₂×C₄	C₂×C₄⋊Dic₄₃	1	4	yes	—
166	C₂×C₄	C₂×C₄⋊Dic₄₃	1	4	yes	—
167	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
168	C₂×C₄	#13063284	1	4	yes	—
169	C₂×C₄	#13063313	1	8	yes	—
170	C₂×C₄	#13063317	1	8	yes	—
171	C₂×C₄	C₂×#10621877	1	16	yes	—
172	C₂×C₄	C₂×#10621877	1	8	yes	—
173	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
174	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
175	C₂×C₄	C₂×#10621898	1	4	yes	—
176	C₈	—	172	8	no	—
177	C₂²	—	2	8	no	—
178	C₂²	—	2	4	no	—
179	C₂²	#14582765	1	4	yes	—
180	C₂²	C₂²×C₄⋊Dic₄₃	1	1	yes	characteristic
181	C₂²	C₂×#13063284	1	2	yes	—
182	C₂²	C₂²×#10621877	1	4	yes	—
183	C₄	—	2	16	no	—
184	C₄	—	2	4	no	—
185	C₄	#14582765	1	4	yes	—
186	C₄	#14582923	1	8	yes	—
187	C₄	C₂×#13063313	1	2	yes	—
188	C₄	C₂×#13063317	1	2	yes	—
189	C₂	—	2	4	no	—
190	C₂	C₂×#14582765	1	1	yes	characteristic
191	C₂	C₂×#14582923	1	2	yes	—
192	C₂	#19143228	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₂×C₄³×C₄₃	C₂
prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×C₄³	D₄₃
hypocenter	C₄₃	#20752
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
2. #19134712	C₂	semidirect
53. C₄²×C₄₃	M₁₆	semidirect
111. C₄₃	#20752	semidirect
151. C₄²	#10621877	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582923	2
#19134712	2
#19134289	2
C₂×C₄³×C₄₃	2
#20752	43