Subgroups — #24990263

Order 11008.

378 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19134747	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063236	C₂	1	1	yes	maximal, characteristic
3	#19132429	C₂	1	4	yes	maximal
4	C₄₃×#1831	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
6	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
7	C₂×#13063236	C₄	1	2	yes	—
8	C₂×#13063236	C₄	1	1	yes	characteristic
9	C₂×#13063236	C₄	1	1	yes	characteristic
10	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
11	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
12	C₄³×C₄₃	C₂²	1	1	yes	characteristic
13	C₄₃×#336	—	2	2	no	—
14	C₂²×C₄₃⋊C₈	—	2	2	no	—
15	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
16	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
17	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
18	C₄⋊(C₄₃⋊C₈)	—	4	4	no	—
19	#13063236	—	2	2	no	—
20	#13063236	—	2	4	no	—
21	#13063236	C₈	1	4	yes	complemented
22	C₄×C₄₃⋊C₈	—	2	2	no	—
23	C₄×C₄₃⋊C₈	—	2	2	no	—
24	C₂²×C₈×C₄₃	—	2	2	no	—
25	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₄₃	D₄	1	2	yes	—
28	C₂×C₄²×C₄₃	Q₈	1	2	yes	—
29	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
30	C₄⋊C₈×C₄₃	—	2	4	no	—
31	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
32	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
33	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₈×C₄₃	—	4	2	no	—
37	C₂×C₈×C₄₃	—	4	2	no	—
38	C₂×C₈×C₄₃	—	4	2	no	—
39	C₄²×C₄₃	—	2	2	no	—
40	C₄²×C₄₃	—	2	2	no	—
41	C₄²×C₄₃	—	2	2	no	—
42	C₄²×C₄₃	—	4	2	no	—
43	C₄²×C₄₃	C₂×C₈	1	2	yes	—
44	C₄²×C₄₃	M₁₆	1	2	yes	—
45	C₄²×C₄₃	#41	1	2	yes	—
46	C₄²×C₄₃	#41	1	2	yes	—
47	C₂×C₄₃⋊C₈	—	2	2	no	—
48	C₂×C₄₃⋊C₈	—	2	2	no	—
49	C₂×C₄₃⋊C₈	—	2	2	no	—
50	C₂×C₄₃⋊C₈	—	2	2	no	—
51	C₂×C₄₃⋊C₈	—	4	2	no	—
52	C₂×C₄₃⋊C₈	—	4	4	no	—
53	C₂×C₄₃⋊C₈	C₂×C₈	1	4	yes	—
54	C₂×C₄₃⋊C₈	M₁₆	1	4	yes	—
55	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₄×C₄₃	—	2	2	no	—
57	C₂×C₄×C₄₃	—	2	2	no	—
58	C₂×C₄×C₄₃	—	2	2	no	—
59	C₂×C₄×C₄₃	—	2	2	no	—
60	C₂×C₄×C₄₃	—	2	2	no	—
61	C₂×C₄×C₄₃	—	2	2	no	—
62	C₂×C₄×C₄₃	C₄⋊C₈	1	4	yes	—
63	C₂×C₄×C₄₃	#117	1	2	yes	—
64	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
65	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
66	C₂×C₄×C₄₃	#125	1	2	yes	—
67	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
68	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
69	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
70	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
71	C₂×C₄×C₄₃	#137	1	2	yes	—
72	C₈×C₄₃	—	8	2	no	—
73	C₄₃⋊C₈	—	2	4	no	—
74	C₄₃⋊C₈	—	2	4	no	—
75	C₄₃⋊C₈	—	8	2	no	—
76	#8786	—	43	1	no	maximal, Sylow
77	C₂²×C₄₃	#382	1	1	yes	characteristic
78	C₂²×C₄₃	C₂×C₄⋊C₈	1	1	yes	characteristic
79	C₂²×C₄₃	#423	1	1	yes	characteristic
80	C₂²×C₄₃	#428	1	2	yes	—
81	C₂²×C₄₃	#430	1	2	yes	—
82	C₄×C₄₃	—	2	4	no	—
83	C₄×C₄₃	—	2	2	no	—
84	C₄×C₄₃	—	4	2	no	—
85	C₄×C₄₃	#431	1	2	yes	—
86	C₄×C₄₃	#432	1	2	yes	—
87	C₄×C₄₃	#489	1	2	yes	—
88	C₄×C₄₃	#490	1	1	yes	characteristic
89	C₄×C₄₃	#491	1	1	yes	characteristic
90	#1842	—	43	1	no	—
91	#1831	D₄₃	1	1	yes	characteristic
92	C₄×#97	—	43	1	no	—
93	#1277	—	43	4	no	—
94	C₂×C₄₃	#1565	1	2	yes	—
95	C₂×C₄₃	#1569	1	2	yes	—
96	C₂×C₄₃	#1831	1	1	yes	characteristic
97	C₂×C₄₃	#1836	1	1	yes	characteristic
98	C₂×C₄₃	#1838	1	1	yes	characteristic
99	C₂×C₄⋊C₈	—	43	2	no	—
100	C₂×C₄⋊C₈	—	86	2	no	—
101	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
102	C₂×#97	—	43	1	no	—
103	C₂×#97	—	43	2	no	—
104	C₂×#97	—	43	1	no	—
105	C₂×C₄×C₈	—	43	2	no	—
106	C₄³	C₂×D₄₃	1	1	yes	characteristic
107	#336	—	2	2	no	—
108	C₄₃	#8786	1	1	yes	characteristic, complemented, Sylow
109	C₂²×C₈	—	2	2	no	—
110	C₂²×C₈	—	43	2	no	—
111	C₂²×C₈	—	43	2	no	—
112	C₂²×C₈	—	86	2	no	—
113	C₂×C₄²	Dic₈₆	1	2	yes	—
114	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
115	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
116	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
117	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
118	C₄⋊C₈	—	2	4	no	—
119	C₄⋊C₈	—	86	4	no	—
120	C₄⋊C₈	—	172	4	no	—
121	#97	—	43	4	no	—
122	#97	—	86	4	no	—
123	#97	—	86	2	no	—
124	C₄×C₈	—	86	2	no	—
125	C₄×C₈	—	86	2	no	—
126	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
127	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
128	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
129	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
130	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
131	C₂×C₈	—	4	2	no	—
132	C₂×C₈	—	4	2	no	—
133	C₂×C₈	—	4	2	no	—
134	C₂×C₈	—	43	4	no	—
135	C₂×C₈	—	43	4	no	—
136	C₂×C₈	—	86	2	no	—
137	C₂×C₈	—	86	2	no	—
138	C₂×C₈	—	86	2	no	—
139	C₂×C₈	—	86	2	no	—
140	C₂×C₈	—	172	2	no	—
141	C₂×C₈	—	172	4	no	—
142	C₄²	—	2	2	no	—
143	C₄²	—	2	2	no	—
144	C₄²	—	2	2	no	—
145	C₄²	—	4	2	no	—
146	C₄²	C₈×D₄₃	1	2	yes	—
147	C₄²	#10621872	1	2	yes	—
148	C₄²	#10621900	1	2	yes	—
149	C₄²	#10621902	1	2	yes	—
150	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	Dic₄₃⋊C₈	1	4	yes	—
158	C₂×C₄	#13063283	1	2	yes	—
159	C₂×C₄	#13063312	1	1	yes	characteristic
160	C₂×C₄	#13063314	1	1	yes	characteristic
161	C₂×C₄	#13063316	1	2	yes	—
162	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
163	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
164	C₂×C₄	C₂×#10621872	1	1	yes	characteristic
165	C₂×C₄	#13063350	1	2	yes	—
166	C₂×C₄	#13063355	1	2	yes	—
167	C₈	—	8	2	no	—
168	C₈	—	86	4	no	—
169	C₈	—	86	4	no	—
170	C₈	—	344	2	no	—
171	C₂²	#14582764	1	1	yes	characteristic
172	C₂²	C₂×Dic₄₃⋊C₈	1	1	yes	characteristic
173	C₂²	#14582922	1	1	yes	characteristic
174	C₂²	#14582942	1	2	yes	—
175	C₂²	#14582947	1	2	yes	—
176	C₄	—	2	2	no	—
177	C₄	—	2	4	no	—
178	C₄	—	4	2	no	—
179	C₄	#14582951	1	2	yes	—
180	C₄	#14582955	1	2	yes	—
181	C₄	#14583258	1	2	yes	—
182	C₄	#14583265	1	1	yes	characteristic
183	C₄	#14583269	1	1	yes	characteristic
184	C₂	#19133348	1	2	yes	—
185	C₂	#19133363	1	2	yes	—
186	C₂	#19134711	1	1	yes	characteristic
187	C₂	#19134728	1	1	yes	characteristic
188	C₂	#19134735	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1831	C₂
socle, prime radical	C₂³×C₄₃	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1831	D₄₃
hypocenter	C₄₃	#8786
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

Complements

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

N	H ≅ G/N	type
21. #13063236	C₈	semidirect
108. C₄₃	#8786	semidirect

Maximal subgroups

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

subgroup	index
#19134747	2
C₄×#13063236	2
#19132429	2
C₄₃×#1831	2
#8786	43