Subgroups — #24985986

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582952	C₂	1	2	yes	maximal
2	C₄₃⋊#1273	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
4	#14582952	—	2	4	no	—
5	#14582952	—	2	4	no	—
6	C₂×C₄⋊(C₄₃⋊C₈)	C₄	1	4	yes	—
7	C₂×C₂²⋊(C₄₃⋊C₈)	C₄	1	4	yes	—
8	C₂×C₄×C₄₃⋊C₈	C₂²	1	4	yes	—
9	C₂²×M₁₆×C₄₃	C₄	1	2	yes	—
10	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	C₄×M₁₆×C₄₃	—	2	4	no	—
12	C₂×#97×C₄₃	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₄₃⋊C₈	C₂×C₄	1	8	yes	—
15	C₄⋊(C₄₃⋊C₈)	—	2	8	no	—
16	C₂²⋊(C₄₃⋊C₈)	—	2	8	no	—
17	C₄×C₄₃⋊C₈	—	2	4	no	—
18	C₄×C₄₃⋊C₈	—	2	4	no	—
19	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
20	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂×M₁₆×C₄₃	—	2	4	no	—
22	C₂×M₁₆×C₄₃	—	2	8	no	—
23	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₄₃	D₄	1	2	yes	—
27	C₂×C₄²×C₄₃	D₄	1	4	yes	—
28	C₂×C₄²×C₄₃	Q₈	1	2	yes	—
29	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
30	#97×C₄₃	—	2	4	no	—
31	C₄×C₈×C₄₃	—	2	4	no	—
32	C₂⁴×C₄₃	C₄²	1	1	yes	characteristic
33	C₂²×C₄×C₄₃	—	2	4	no	—
34	C₂²×C₄×C₄₃	—	2	8	no	—
35	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
36	C₂²×C₄×C₄₃	C₄²	1	2	yes	—
37	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
38	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
40	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
41	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
42	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
43	M₁₆×C₄₃	—	2	16	no	—
44	C₂×C₈×C₄₃	—	2	4	no	—
45	C₂×C₈×C₄₃	—	2	4	no	—
46	C₂×C₈×C₄₃	M₁₆	1	8	yes	—
47	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
48	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
49	C₄²×C₄₃	C₄⋊C₄	1	4	yes	—
50	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
51	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
52	C₄²×C₄₃	C₂×D₄	1	2	yes	—
53	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
54	C₂×C₄₃⋊C₈	—	2	8	no	—
55	C₂×C₄₃⋊C₈	—	2	16	no	—
56	C₂³×C₄₃	—	2	2	no	—
57	C₂³×C₄₃	—	2	4	no	—
58	C₂³×C₄₃	#95	1	2	yes	—
59	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
60	C₂×C₄×C₄₃	—	2	2	no	—
61	C₂×C₄×C₄₃	—	2	4	no	—
62	C₂×C₄×C₄₃	—	2	4	no	—
63	C₂×C₄×C₄₃	—	2	8	no	—
64	C₂×C₄×C₄₃	—	2	4	no	—
65	C₂×C₄×C₄₃	—	2	8	no	—
66	C₂×C₄×C₄₃	#95	1	2	yes	—
67	C₂×C₄×C₄₃	#95	1	4	yes	—
68	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
69	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
71	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₄₃	C₂×M₁₆	1	4	yes	—
73	C₂×C₄×C₄₃	#131	1	8	yes	—
74	C₈×C₄₃	—	2	8	no	—
75	C₄₃⋊C₈	—	4	8	no	—
76	#7850	—	43	1	no	maximal, Sylow
77	C₂²×C₄₃	—	2	2	no	—
78	C₂²×C₄₃	—	2	4	no	—
79	C₂²×C₄₃	—	4	4	no	—
80	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
81	C₂²×C₄₃	C₄×M₁₆	1	2	yes	—
82	C₂²×C₄₃	#405	1	4	yes	—
83	C₄×C₄₃	—	2	2	no	—
84	C₄×C₄₃	—	2	4	no	—
85	C₄×C₄₃	#407	1	2	yes	—
86	C₄×C₄₃	#408	1	4	yes	—
87	C₄×C₄₃	#423	1	2	yes	—
88	C₄×C₄₃	#424	1	4	yes	—
89	C₂×#431	—	43	2	no	—
90	C₂×C₄×M₁₆	D₄₃	1	1	yes	characteristic
91	#1273	—	43	4	no	—
92	C₂×C₄₃	—	4	2	no	—
93	C₂×C₄₃	#1453	1	4	yes	—
94	C₂×C₄₃	#1728	1	1	yes	characteristic
95	C₂×C₄₃	#1729	1	2	yes	—
96	C₂²×M₁₆	Dic₄₃	1	2	yes	—
97	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
98	#431	—	86	4	no	—
99	#431	—	86	4	no	—
100	C₂×C₄⋊C₈	—	43	4	no	—
101	C₂×C₂²⋊C₈	—	43	4	no	—
102	C₄×M₁₆	—	2	4	no	—
103	C₂×#97	Dic₄₃	1	2	yes	—
104	C₂×C₄×C₈	—	43	4	no	—
105	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
106	C₄₃	#7850	1	1	yes	characteristic, complemented, Sylow
107	C₂³×C₄	C₄×D₄₃	1	2	yes	—
108	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
109	C₂×M₁₆	—	2	4	no	—
110	C₂×M₁₆	—	2	8	no	—
111	C₂²×C₈	—	43	8	no	—
112	C₂²×C₈	C₂×Dic₄₃	1	4	yes	—
113	C₂×C₄²	Dic₈₆	1	2	yes	—
114	C₂×C₄²	C₄×D₄₃	1	2	yes	—
115	C₂×C₄²	D₁₇₂	1	2	yes	—
116	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
117	C₂×C₄²	C₂²⋊D₄₃	1	4	yes	—
118	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
119	C₄⋊C₈	—	86	8	no	—
120	C₂²⋊C₈	—	86	8	no	—
121	#97	—	2	4	no	—
122	C₄×C₈	—	2	4	no	—
123	C₄×C₈	—	86	4	no	—
124	C₄×C₈	—	86	4	no	—
125	C₂⁴	C₄×Dic₄₃	1	1	yes	characteristic
126	C₂²×C₄	—	2	4	no	—
127	C₂²×C₄	—	2	8	no	—
128	C₂²×C₄	C₄×Dic₄₃	1	1	yes	characteristic
129	C₂²×C₄	C₄×Dic₄₃	1	2	yes	—
130	C₂²×C₄	Dic₄₃⋊C₄	1	4	yes	—
131	C₂²×C₄	C₄⋊Dic₄₃	1	2	yes	—
132	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
133	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
134	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
135	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
136	M₁₆	—	2	16	no	—
137	C₂×C₈	—	2	4	no	—
138	C₂×C₈	—	2	4	no	—
139	C₂×C₈	—	86	8	no	—
140	C₂×C₈	—	86	16	no	—
141	C₂×C₈	#10621877	1	8	yes	—
142	C₄²	Dic₄₃⋊C₄	1	4	yes	—
143	C₄²	C₄⋊Dic₄₃	1	2	yes	—
144	C₄²	(C₂×D₄₃)⋊C₄	1	4	yes	—
145	C₄²	C₂²⋊Dic₄₃	1	2	yes	—
146	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
147	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
148	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
149	C₂³	—	2	2	no	—
150	C₂³	—	2	4	no	—
151	C₂³	C₄₃⋊#95	1	2	yes	—
152	C₂³	C₂×C₄×Dic₄₃	1	1	yes	characteristic
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	4	no	—
155	C₂×C₄	—	2	4	no	—
156	C₂×C₄	—	2	8	no	—
157	C₂×C₄	—	2	4	no	—
158	C₂×C₄	—	2	8	no	—
159	C₂×C₄	C₄₃⋊#95	1	2	yes	—
160	C₂×C₄	C₄₃⋊#95	1	4	yes	—
161	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
162	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
163	C₂×C₄	C₂×Dic₄₃⋊C₄	1	2	yes	—
164	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
165	C₂×C₄	C₂×#10621877	1	4	yes	—
166	C₂×C₄	#13063333	1	8	yes	—
167	C₈	—	2	8	no	—
168	C₈	—	172	8	no	—
169	C₂²	—	2	2	no	—
170	C₂²	—	2	4	no	—
171	C₂²	—	4	4	no	—
172	C₂²	C₂×C₄₃⋊#95	1	1	yes	characteristic
173	C₂²	C₄×#10621877	1	2	yes	—
174	C₂²	#14582857	1	4	yes	—
175	C₄	—	2	2	no	—
176	C₄	—	2	4	no	—
177	C₄	#14582863	1	2	yes	—
178	C₄	#14582867	1	4	yes	—
179	C₄	#14582923	1	2	yes	—
180	C₄	#14582927	1	4	yes	—
181	C₂	—	4	2	no	—
182	C₂	#19132892	1	4	yes	—
183	C₂	#19134289	1	1	yes	characteristic
184	C₂	#19134293	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₄₃
commutator, socle	C₂³×C₄₃	C₂×C₄²
Fitting	C₂×C₄×M₁₆×C₄₃	C₂
prime radical	C₂⁴×C₄₃	C₄²
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×C₄×M₁₆	D₄₃
hypocenter	C₄₃	#7850
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₄₃⋊#1273	C₂	semidirect
106. C₄₃	#7850	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582952	2
C₄₃⋊#1273	2
C₂×C₄×M₁₆×C₄₃	2
#7850	43