Subgroups — #24983803

Order 11008.

226 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	#19136351	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582652	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1848	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063265	—	2	1	no	—
5	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
6	C₄⋊(C₄₃⋊C₁₆)	—	2	1	no	—
7	C₄⋊(C₄₃⋊C₁₆)	C₄	1	2	yes	—
8	#14582652	—	2	1	no	—
9	#14582652	C₄	1	2	yes	—
10	C₂×#108×C₄₃	—	2	1	no	—
11	C₂×#108×C₄₃	C₄	1	2	yes	—
12	C₄₃×#423	—	2	1	no	—
13	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄₃⋊C₈	—	4	1	no	—
15	#13063265	—	4	1	no	—
16	#13063265	—	4	1	no	—
17	C₂×C₄₃⋊C₁₆	—	2	2	no	—
18	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
19	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
20	C₂×M₁₆×C₄₃	—	2	2	no	—
21	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
24	#108×C₄₃	—	4	2	no	—
25	#108×C₄₃	—	4	1	no	—
26	#108×C₄₃	—	4	1	no	—
27	C₄⋊C₈×C₄₃	—	4	1	no	—
28	C₄⋊C₈×C₄₃	—	4	1	no	—
29	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
30	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
32	C₄×C₈×C₄₃	Q₈	1	1	yes	characteristic
33	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂²×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
35	C₂²×C₄×C₄₃	Q₁₆	1	1	yes	characteristic
36	M₁₆×C₄₃	—	4	2	no	—
37	M₁₆×C₄₃	—	4	2	no	—
38	C₂×C₈×C₄₃	—	2	1	no	—
39	C₂×C₈×C₄₃	—	2	1	no	—
40	C₂×C₈×C₄₃	—	4	2	no	—
41	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
42	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
46	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
47	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
48	C₂×C₈×C₄₃	Q₁₆	1	1	yes	characteristic
49	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
50	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
51	C₄²×C₄₃	D₈	1	1	yes	characteristic
52	C₄²×C₄₃	SD₁₆	1	1	yes	characteristic
53	C₂×C₄₃⋊C₈	—	4	2	no	—
54	C₂×C₄₃⋊C₈	—	8	2	no	—
55	C₄₃⋊C₁₆	—	4	2	no	—
56	C₂³×C₄₃	#103	1	1	yes	characteristic
57	C₂×C₄×C₄₃	—	2	1	no	—
58	C₂×C₄×C₄₃	—	2	1	no	—
59	C₂×C₄×C₄₃	—	4	1	no	—
60	C₂×C₄×C₄₃	#95	1	1	yes	characteristic
61	C₂×C₄×C₄₃	#100	1	1	yes	characteristic
62	C₂×C₄×C₄₃	#101	1	1	yes	characteristic
63	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
64	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
65	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
66	C₂×C₄×C₄₃	#103	1	1	yes	characteristic
67	C₂×C₄×C₄₃	#103	1	1	yes	characteristic
68	C₂×C₄×C₄₃	#106	1	1	yes	characteristic
69	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
70	C₈×C₄₃	—	2	1	no	—
71	C₈×C₄₃	—	2	1	no	—
72	C₈×C₄₃	—	8	2	no	—
73	C₈×C₄₃	#102	1	1	yes	characteristic
74	C₈×C₄₃	#103	1	1	yes	characteristic
75	C₈×C₄₃	#106	1	1	yes	characteristic
76	C₈×C₄₃	#107	1	1	yes	characteristic
77	C₄₃⋊C₈	—	8	2	no	—
78	#7281	—	43	1	no	maximal, Sylow
79	C₂²×C₄₃	—	2	1	no	—
80	C₂²×C₄₃	—	2	1	no	—
81	C₂²×C₄₃	#332	1	1	yes	characteristic
82	C₂²×C₄₃	#333	1	1	yes	characteristic
83	C₂²×C₄₃	#340	1	1	yes	characteristic
84	C₄×C₄₃	—	2	1	no	—
85	C₄×C₄₃	—	2	1	no	—
86	C₄×C₄₃	—	2	1	no	—
87	C₄×C₄₃	#331	1	1	yes	characteristic
88	C₄×C₄₃	#332	1	1	yes	characteristic
89	C₄×C₄₃	#340	1	1	yes	characteristic
90	C₄×C₄₃	#343	1	1	yes	characteristic
91	C₄×C₄₃	#361	1	1	yes	characteristic
92	C₄×C₄₃	#362	1	1	yes	characteristic
93	#2150	—	43	1	no	—
94	#1848	D₄₃	1	1	yes	characteristic
95	C₂×#335	—	43	1	no	—
96	C₂×C₄₃	—	2	1	no	—
97	C₂×C₄₃	—	2	1	no	—
98	C₂×C₄₃	#1296	1	1	yes	characteristic
99	C₂×C₄₃	#1385	1	1	yes	characteristic
100	C₂×C₄₃	#1387	1	1	yes	characteristic
101	C₂×M₃₂	—	86	1	no	—
102	C₂×#108	—	2	1	no	—
103	C₂×#108	Dic₄₃	1	2	yes	—
104	#423	—	2	1	no	—
105	C₂×C₄⋊C₈	—	86	1	no	—
106	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
107	C₄⋊C₁₆	—	43	2	no	—
108	C₄⋊C₁₆	—	86	1	no	—
109	#335	—	43	2	no	—
110	#335	—	86	1	no	—
111	C₄₃	#7281	1	1	yes	characteristic, complemented, Sylow
112	C₂×M₁₆	—	2	2	no	—
113	C₂²×C₈	—	172	1	no	—
114	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
115	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
116	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
117	M₃₂	—	172	1	no	—
118	M₃₂	—	172	1	no	—
119	C₂×C₁₆	—	86	2	no	—
120	#108	—	4	2	no	—
121	#108	—	4	1	no	—
122	#108	—	4	1	no	—
123	C₄⋊C₈	—	4	1	no	—
124	C₄⋊C₈	—	4	1	no	—
125	C₄⋊C₈	—	86	2	no	—
126	C₄⋊C₈	—	172	1	no	—
127	C₄×C₈	Dic₈₆	1	1	yes	characteristic
128	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
129	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
130	C₄×C₈	D₁₇₂	1	1	yes	characteristic
131	C₂²×C₄	#10621884	1	1	yes	characteristic
132	C₂²×C₄	#10621885	1	1	yes	characteristic
133	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
134	M₁₆	—	4	2	no	—
135	M₁₆	—	4	2	no	—
136	C₂×C₈	—	2	1	no	—
137	C₂×C₈	—	2	1	no	—
138	C₂×C₈	—	4	2	no	—
139	C₂×C₈	—	344	2	no	—
140	C₂×C₈	—	172	2	no	—
141	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
142	C₂×C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
143	C₂×C₈	C₄⋊Dic₄₃	1	1	yes	characteristic
144	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
145	C₂×C₈	#10621882	1	1	yes	characteristic
146	C₂×C₈	#10621883	1	1	yes	characteristic
147	C₂×C₈	#10621884	1	1	yes	characteristic
148	C₂×C₈	#10621885	1	1	yes	characteristic
149	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
150	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
151	C₄²	#10621882	1	1	yes	characteristic
152	C₄²	#10621883	1	1	yes	characteristic
153	C₁₆	—	172	2	no	—
154	C₂³	#13063249	1	1	yes	characteristic
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	1	no	—
157	C₂×C₄	—	4	1	no	—
158	C₂×C₄	C₄₃⋊#95	1	1	yes	characteristic
159	C₂×C₄	#13063242	1	1	yes	characteristic
160	C₂×C₄	#13063244	1	1	yes	characteristic
161	C₂×C₄	#13063245	1	1	yes	characteristic
162	C₂×C₄	#13063246	1	1	yes	characteristic
163	C₂×C₄	#13063246	1	1	yes	characteristic
164	C₂×C₄	#13063248	1	1	yes	characteristic
165	C₂×C₄	#13063249	1	1	yes	characteristic
166	C₂×C₄	#13063256	1	1	yes	characteristic
167	C₂×C₄	#13063258	1	1	yes	characteristic
168	C₈	—	2	1	no	—
169	C₈	—	2	1	no	—
170	C₈	—	8	2	no	—
171	C₈	—	344	2	no	—
172	C₈	#13063245	1	1	yes	characteristic
173	C₈	#13063248	1	1	yes	characteristic
174	C₈	#13063256	1	1	yes	characteristic
175	C₈	#13063258	1	1	yes	characteristic
176	C₂²	—	2	1	no	—
177	C₂²	—	2	1	no	—
178	C₂²	#14582645	1	1	yes	characteristic
179	C₂²	#14582648	1	1	yes	characteristic
180	C₂²	#14582661	1	1	yes	characteristic
181	C₄	—	2	1	no	—
182	C₄	—	2	1	no	—
183	C₄	—	2	1	no	—
184	C₄	#14582643	1	1	yes	characteristic
185	C₄	#14582645	1	1	yes	characteristic
186	C₄	#14582661	1	1	yes	characteristic
187	C₄	#14582668	1	1	yes	characteristic
188	C₄	#14582711	1	1	yes	characteristic
189	C₄	#14582714	1	1	yes	characteristic
190	C₂	—	2	1	no	—
191	C₂	—	2	1	no	—
192	C₂	#19132478	1	1	yes	characteristic
193	C₂	#19132698	1	1	yes	characteristic
194	C₂	#19132705	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14582661
commutator	C₂×C₈×C₄₃	C₄²
Frattini	C₂×C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#1848	C₂
socle	C₂²×C₄₃	#340
prime radical	C₂³×C₄₃	#103
cosocle	C₂×C₄×C₈×C₄₃	C₂²
hypercenter	#1848	D₄₃
hypocenter	C₄₃	#7281
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1848

Complements

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

N	H ≅ G/N	type
111. C₄₃	#7281	semidirect

Maximal subgroups

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

subgroup	index
#19136351	2
C₂×#14582652	2
C₄₃×#1848	2
#7281	43