Subgroups — #25002429

Order 11008.

774 conjugacy classes of subgroups.

The subgroup lattice has 192 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	C₂×#14582664	C₂	1	4	yes	maximal
3	C₂²×#97×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10621877	C₂²	1	4	yes	—
5	#14582923	—	2	4	no	—
6	#14582923	C₄	1	8	yes	—
7	C₂×C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
8	#14582664	—	2	8	no	—
9	C₂³×C₈×C₄₃	C₂²	1	2	yes	—
10	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×#97×C₄₃	—	2	4	no	—
12	C₂×#97×C₄₃	C₄	1	4	yes	—
13	C₂×#10621877	—	2	4	no	—
14	C₂×#10621877	—	2	8	no	—
15	C₂×#10621877	—	2	8	no	—
16	C₂×#10621877	C₂×C₄	1	8	yes	—
17	C₂²×C₄₃⋊C₈	—	2	4	no	—
18	C₄⋊(C₄₃⋊C₈)	—	2	16	no	—
19	C₂³×C₄×C₄₃	Q₈	1	2	yes	—
20	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
21	C₂²×C₈×C₄₃	—	2	4	no	—
22	C₂²×C₈×C₄₃	—	2	4	no	—
23	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
24	C₂²×C₈×C₄₃	D₄	1	4	yes	—
25	C₂²×C₈×C₄₃	Q₈	1	4	yes	—
26	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
27	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₄₃	D₄	1	2	yes	—
29	C₂×C₄²×C₄₃	D₄	1	4	yes	—
30	#97×C₄₃	—	2	8	no	—
31	C₂⁴×C₄₃	C₂×Q₈	1	1	yes	characteristic
32	C₂²×C₄×C₄₃	—	4	4	no	—
33	C₂²×C₄×C₄₃	C₄⋊C₄	1	8	yes	—
34	C₂²×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
35	C₂²×C₄×C₄₃	C₂²×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	C₂×D₄	1	2	yes	—
39	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
40	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
41	C₂²×C₄×C₄₃	#41	1	4	yes	—
42	C₂×C₈×C₄₃	—	2	4	no	—
43	C₂×C₈×C₄₃	—	2	4	no	—
44	C₂×C₈×C₄₃	—	2	8	no	—
45	C₂×C₈×C₄₃	—	2	8	no	—
46	C₂×C₈×C₄₃	C₄⋊C₄	1	8	yes	—
47	C₄²×C₄₃	C₄²	1	4	yes	—
48	C₄²×C₄₃	C₂²⋊C₄	1	8	yes	—
49	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
50	#10621877	—	2	16	no	—
51	#10621877	—	4	8	no	—
52	C₂×C₄₃⋊C₈	—	2	8	no	—
53	C₂×C₄₃⋊C₈	—	4	4	no	—
54	C₂×C₄₃⋊C₈	—	4	4	no	—
55	C₂³×C₄₃	—	2	4	no	—
56	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
57	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂³×C₄₃	#125	1	2	yes	—
59	C₂³×C₄₃	C₄⋊Q₈	1	2	yes	—
60	C₂×C₄×C₄₃	—	2	8	no	—
61	C₂×C₄×C₄₃	—	4	8	no	—
62	C₂×C₄×C₄₃	#95	1	8	yes	—
63	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
64	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
65	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
67	C₂×C₄×C₄₃	#117	1	2	yes	—
68	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
69	C₂×C₄×C₄₃	C₄×Q₈	1	4	yes	—
70	C₂×C₄×C₄₃	#121	1	4	yes	—
71	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
72	C₂×C₄×C₄₃	#124	1	2	yes	—
73	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
74	C₂×C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
75	C₈×C₄₃	—	2	8	no	—
76	C₄₃⋊C₈	—	4	8	no	—
77	#10845	—	43	1	no	maximal, Sylow
78	C₂²×C₄₃	—	2	4	no	—
79	C₂²×C₄₃	—	2	4	no	—
80	C₂²×C₄₃	—	2	4	no	—
81	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
82	C₂²×C₄₃	#382	1	1	yes	characteristic
83	C₂²×C₄₃	#384	1	1	yes	characteristic
84	C₂²×C₄₃	#389	1	4	yes	—
85	C₂²×C₄₃	#430	1	4	yes	—
86	C₄×C₄₃	—	2	8	no	—
87	C₄×C₄₃	C₄×C₄⋊C₄	1	2	yes	—
88	C₄×C₄₃	#380	1	2	yes	—
89	C₄×C₄₃	#390	1	2	yes	—
90	C₄×C₄₃	#391	1	2	yes	—
91	C₂×#423	—	43	2	no	—
92	C₂²×#97	D₄₃	1	1	yes	characteristic
93	C₂×#341	—	43	4	no	—
94	C₂×C₄₃	—	2	4	no	—
95	C₂×C₄₃	C₄⋊#95	1	1	yes	characteristic
96	C₂×C₄₃	#1738	1	2	yes	—
97	C₂×C₄₃	#1838	1	2	yes	—
98	C₂×C₄₃	#1849	1	2	yes	—
99	C₂²×M₁₆	—	43	4	no	—
100	C₂³×C₈	C₂×D₄₃	1	2	yes	—
101	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
102	#423	—	43	8	no	—
103	#423	—	86	4	no	—
104	C₂×C₄⋊C₈	—	86	4	no	—
105	C₂×#97	—	2	4	no	—
106	C₂×#97	Dic₄₃	1	4	yes	—
107	#341	—	86	8	no	—
108	C₄₃	#10845	1	1	yes	characteristic, complemented, Sylow
109	C₂³×C₄	Dic₈₆	1	2	yes	—
110	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
111	C₂×M₁₆	—	43	8	no	—
112	C₂×M₁₆	—	86	4	no	—
113	C₂×M₁₆	—	86	8	no	—
114	C₂×M₁₆	—	86	8	no	—
115	C₂²×C₈	—	2	4	no	—
116	C₂²×C₈	—	2	4	no	—
117	C₂²×C₈	—	86	4	no	—
118	C₂²×C₈	Dic₈₆	1	4	yes	—
119	C₂²×C₈	D₁₇₂	1	4	yes	—
120	C₂²×C₈	C₂×Dic₄₃	1	4	yes	—
121	C₂×C₄²	C₄×D₄₃	1	4	yes	—
122	C₂×C₄²	D₁₇₂	1	2	yes	—
123	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
124	C₂×C₄²	C₂²⋊D₄₃	1	4	yes	—
125	C₄⋊C₈	—	86	16	no	—
126	#97	—	2	8	no	—
127	C₂⁴	C₂×Dic₈₆	1	1	yes	characteristic
128	C₂²×C₄	—	4	4	no	—
129	C₂²×C₄	Dic₄₃⋊C₄	1	8	yes	—
130	C₂²×C₄	C₄⋊Dic₄₃	1	4	yes	—
131	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
132	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
133	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
134	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
135	C₂²×C₄	#10621898	1	4	yes	—
136	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
137	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
138	M₁₆	—	86	16	no	—
139	M₁₆	—	172	8	no	—
140	C₂×C₈	—	2	4	no	—
141	C₂×C₈	—	2	4	no	—
142	C₂×C₈	—	2	8	no	—
143	C₂×C₈	—	2	8	no	—
144	C₂×C₈	—	86	8	no	—
145	C₂×C₈	—	172	4	no	—
146	C₂×C₈	—	172	4	no	—
147	C₂×C₈	C₄⋊Dic₄₃	1	8	yes	—
148	C₄²	C₄×Dic₄₃	1	4	yes	—
149	C₄²	(C₂×D₄₃)⋊C₄	1	8	yes	—
150	C₄²	C₂²⋊Dic₄₃	1	4	yes	—
151	C₂³	—	2	4	no	—
152	C₂³	C₂×Dic₄₃⋊C₄	1	2	yes	—
153	C₂³	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
154	C₂³	#13063317	1	2	yes	—
155	C₂³	#13063325	1	2	yes	—
156	C₂×C₄	—	2	8	no	—
157	C₂×C₄	—	4	8	no	—
158	C₂×C₄	C₄₃⋊#95	1	8	yes	—
159	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
160	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
161	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
162	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
163	C₂×C₄	#13063284	1	2	yes	—
164	C₂×C₄	C₄×D₁₇₂	1	4	yes	—
165	C₂×C₄	C₄×Dic₈₆	1	4	yes	—
166	C₂×C₄	#13063299	1	4	yes	—
167	C₂×C₄	#13063304	1	4	yes	—
168	C₂×C₄	#13063313	1	2	yes	—
169	C₂×C₄	#13063322	1	1	yes	characteristic
170	C₂×C₄	#13063325	1	1	yes	characteristic
171	C₈	—	2	8	no	—
172	C₈	—	172	8	no	—
173	C₂²	—	2	4	no	—
174	C₂²	—	2	4	no	—
175	C₂²	—	2	4	no	—
176	C₂²	C₂×C₄₃⋊#95	1	1	yes	characteristic
177	C₂²	#14582765	1	1	yes	characteristic
178	C₂²	#14582769	1	1	yes	characteristic
179	C₂²	#14582797	1	4	yes	—
180	C₂²	#14582948	1	4	yes	—
181	C₄	—	2	8	no	—
182	C₄	C₄×C₄⋊Dic₄₃	1	2	yes	—
183	C₄	#14582759	1	2	yes	—
184	C₄	#14582801	1	2	yes	—
185	C₄	#14582805	1	2	yes	—
186	C₂	—	2	4	no	—
187	C₂	#19132825	1	1	yes	characteristic
188	C₂	#19134322	1	2	yes	—
189	C₂	#19134736	1	2	yes	—
190	C₂	#19134770	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂²×#97×C₄₃	C₂
socle	C₂³×C₄₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₄₃	C₂×Q₈
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂²×#97	D₄₃
hypocenter	C₄₃	#10845
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
108. C₄₃	#10845	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
C₂×#14582664	2
C₂²×#97×C₄₃	2
#10845	43