Subgroups — C₄₃×#12674 #24932691

Order 11008.

358 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×C₄₃×#367	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#366	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#346	C₂	1	1	yes	maximal, characteristic
4	C₄×#107×C₄₃	C₂	1	2	yes	maximal
5	C₄₃×#1380	C₂	1	2	yes	maximal
6	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
7	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
8	C₂×#107×C₄₃	C₂²	1	2	yes	—
9	C₂×#107×C₄₃	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₄×C₄⋊C₄×C₄₃	—	2	2	no	—
12	C₄₃×#367	C₄	1	4	yes	complemented
13	C₄₃×#366	C₄	1	4	yes	complemented
14	C₄₃×#346	C₄	1	4	yes	complemented
15	C₄₃×#340	—	2	2	no	—
16	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
19	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
20	C₂×C₄²×C₄₃	—	4	2	no	—
21	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
22	C₂×C₁₆×C₄₃	—	2	1	no	—
23	C₂×C₁₆×C₄₃	—	2	1	no	—
24	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
25	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
26	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
27	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
28	#107×C₄₃	—	2	2	no	—
29	#107×C₄₃	—	2	2	no	—
30	#107×C₄₃	C₂×C₄	1	4	yes	—
31	#107×C₄₃	C₂×C₄	1	4	yes	—
32	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
33	C₄×C₈×C₄₃	Q₈	1	2	yes	—
34	#95×C₄₃	—	4	2	no	—
35	C₂²×C₄×C₄₃	—	4	2	no	—
36	C₂²×C₄×C₄₃	—	4	2	no	—
37	C₂²×C₄×C₄₃	D₈	1	2	yes	—
38	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₈×C₄₃	—	2	1	no	—
40	C₂×C₈×C₄₃	—	2	1	no	—
41	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
42	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
47	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
48	C₄⋊C₄×C₄₃	—	2	4	no	—
49	C₄⋊C₄×C₄₃	—	2	4	no	—
50	C₄⋊C₄×C₄₃	—	4	2	no	—
51	C₄⋊C₄×C₄₃	—	4	2	no	—
52	C₄²×C₄₃	—	8	4	no	—
53	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
54	C₄²×C₄₃	Q₁₆	1	2	yes	—
55	C₁₆×C₄₃	—	2	2	no	—
56	C₁₆×C₄₃	C₄²	1	4	yes	complemented
57	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
58	C₂×C₄×C₄₃	—	2	2	no	—
59	C₂×C₄×C₄₃	—	2	2	no	—
60	C₂×C₄×C₄₃	—	4	4	no	—
61	C₂×C₄×C₄₃	—	4	4	no	—
62	C₂×C₄×C₄₃	—	8	2	no	—
63	C₂×C₄×C₄₃	—	8	2	no	—
64	C₂×C₄×C₄₃	—	8	2	no	—
65	C₂×C₄×C₄₃	—	8	2	no	—
66	C₂×C₄×C₄₃	#107	1	4	yes	—
67	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
69	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
70	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
71	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
72	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
73	C₈×C₄₃	—	2	2	no	—
74	C₈×C₄₃	C₂×C₄²	1	1	yes	characteristic
75	C₈×C₄₃	#117	1	1	yes	characteristic
76	C₈×C₄₃	C₄×Q₈	1	1	yes	characteristic
77	C₈×C₄₃	C₄×Q₈	1	1	yes	characteristic
78	#12674	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂²×C₄₃	C₂×#107	1	1	yes	characteristic
80	C₂²×C₄₃	C₄×D₈	1	1	yes	characteristic
81	C₂²×C₄₃	C₄×D₈	1	1	yes	characteristic
82	C₂²×C₄₃	#509	1	2	yes	—
83	C₂²×C₄₃	#510	1	2	yes	—
84	C₄×C₄₃	—	2	4	no	—
85	C₄×C₄₃	—	8	4	no	—
86	C₄×C₄₃	—	8	4	no	—
87	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
88	C₄×C₄₃	#427	1	1	yes	characteristic
89	C₄×C₄₃	C₄×Q₁₆	1	1	yes	characteristic
90	C₄×C₄₃	C₄×Q₁₆	1	1	yes	characteristic
91	C₂×#367	C₂×C₄₃	1	1	yes	characteristic
92	C₂×#366	C₂×C₄₃	1	1	yes	characteristic
93	C₂×#346	C₂×C₄₃	1	1	yes	characteristic
94	C₄×#107	C₂×C₄₃	1	2	yes	—
95	#1380	C₂×C₄₃	1	2	yes	—
96	C₂×C₄₃	C₄×#107	1	1	yes	characteristic
97	C₂×C₄₃	#2159	1	2	yes	—
98	C₂×C₄₃	#2175	1	2	yes	—
99	C₂×C₄₃	#2176	1	1	yes	characteristic
100	C₂×C₄₃	#2177	1	1	yes	characteristic
101	C₂²×C₁₆	C₂²×C₄₃	1	1	yes	characteristic
102	C₂²×C₁₆	C₂²×C₄₃	1	1	yes	characteristic
103	C₂×#107	C₂²×C₄₃	1	2	yes	—
104	C₂×#107	C₂²×C₄₃	1	2	yes	—
105	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
106	C₄×C₄⋊C₄	—	2	2	no	—
107	#367	C₄×C₄₃	1	4	yes	complemented
108	#366	C₄×C₄₃	1	4	yes	complemented
109	#346	C₄×C₄₃	1	4	yes	complemented
110	#340	—	2	2	no	—
111	C₄₃	#12674	1	1	yes	characteristic, direct product factor, Sylow
112	C₂²×C₈	D₄×C₄₃	1	1	yes	characteristic
113	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
114	C₂×C₄⋊C₄	—	2	2	no	—
115	C₂×C₄⋊C₄	—	2	2	no	—
116	C₂×C₄²	—	4	2	no	—
117	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
118	C₂×C₁₆	—	2	1	no	—
119	C₂×C₁₆	—	2	1	no	—
120	C₂×C₁₆	C₂×C₄×C₄₃	1	2	yes	—
121	C₂×C₁₆	C₂×C₄×C₄₃	1	2	yes	—
122	C₂×C₁₆	C₂×C₄×C₄₃	1	2	yes	—
123	C₂×C₁₆	C₂×C₄×C₄₃	1	2	yes	—
124	#107	—	2	2	no	—
125	#107	—	2	2	no	—
126	#107	C₂×C₄×C₄₃	1	4	yes	—
127	#107	C₂×C₄×C₄₃	1	4	yes	—
128	C₄×C₈	C₂×C₄×C₄₃	1	2	yes	—
129	C₄×C₈	Q₈×C₄₃	1	2	yes	—
130	#95	—	4	2	no	—
131	C₂²×C₄	—	4	2	no	—
132	C₂²×C₄	—	4	2	no	—
133	C₂²×C₄	D₈×C₄₃	1	2	yes	—
134	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
135	C₂×C₈	—	2	1	no	—
136	C₂×C₈	—	2	1	no	—
137	C₂×C₈	C₄⋊C₄×C₄₃	1	2	yes	—
138	C₂×C₈	C₂²×C₄×C₄₃	1	1	yes	characteristic
139	C₂×C₈	C₂²×C₄×C₄₃	1	1	yes	characteristic
140	C₂×C₈	C₂²×C₄×C₄₃	1	1	yes	characteristic
141	C₂×C₈	C₂×Q₈×C₄₃	1	1	yes	characteristic
142	C₂×C₈	#41×C₄₃	1	1	yes	characteristic
143	C₂×C₈	#41×C₄₃	1	1	yes	characteristic
144	C₄⋊C₄	—	2	4	no	—
145	C₄⋊C₄	—	2	4	no	—
146	C₄⋊C₄	—	4	2	no	—
147	C₄⋊C₄	—	4	2	no	—
148	C₄²	—	8	4	no	—
149	C₄²	C₄⋊C₄×C₄₃	1	2	yes	—
150	C₄²	Q₁₆×C₄₃	1	2	yes	—
151	C₁₆	—	2	2	no	—
152	C₁₆	C₄²×C₄₃	1	4	yes	complemented
153	C₂³	C₂×D₈×C₄₃	1	1	yes	characteristic
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	4	4	no	—
157	C₂×C₄	—	4	4	no	—
158	C₂×C₄	—	8	2	no	—
159	C₂×C₄	—	8	2	no	—
160	C₂×C₄	—	8	2	no	—
161	C₂×C₄	—	8	2	no	—
162	C₂×C₄	#107×C₄₃	1	4	yes	—
163	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
164	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
165	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
166	C₂×C₄	C₂×Q₁₆×C₄₃	1	1	yes	characteristic
167	C₂×C₄	#135×C₄₃	1	1	yes	characteristic
168	C₂×C₄	#135×C₄₃	1	1	yes	characteristic
169	C₈	—	2	2	no	—
170	C₈	C₂×C₄²×C₄₃	1	1	yes	characteristic
171	C₈	#117×C₄₃	1	1	yes	characteristic
172	C₈	C₄×Q₈×C₄₃	1	1	yes	characteristic
173	C₈	C₄×Q₈×C₄₃	1	1	yes	characteristic
174	C₂²	C₂×#107×C₄₃	1	1	yes	characteristic
175	C₂²	C₄×D₈×C₄₃	1	1	yes	characteristic
176	C₂²	C₄×D₈×C₄₃	1	1	yes	characteristic
177	C₂²	C₄₃×#509	1	2	yes	—
178	C₂²	C₄₃×#510	1	2	yes	—
179	C₄	—	2	4	no	—
180	C₄	—	8	4	no	—
181	C₄	—	8	4	no	—
182	C₄	C₄×C₄⋊C₄×C₄₃	1	1	yes	characteristic
183	C₄	C₄₃×#427	1	1	yes	characteristic
184	C₄	C₄×Q₁₆×C₄₃	1	1	yes	characteristic
185	C₄	C₄×Q₁₆×C₄₃	1	1	yes	characteristic
186	C₂	C₄×#107×C₄₃	1	1	yes	characteristic
187	C₂	C₄₃×#2159	1	2	yes	—
188	C₂	C₄₃×#2175	1	2	yes	—
189	C₂	C₄₃×#2176	1	1	yes	characteristic
190	C₂	C₄₃×#2177	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₄₃	C₂×D₈
commutator	C₈	C₂×C₄²×C₄₃
Frattini, cosocle	C₂²×C₈	C₂³×C₄₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ C₂×C₄×C₈×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₄₃×#367	C₄	semidirect
13. C₄₃×#366	C₄	semidirect
14. C₄₃×#346	C₄	semidirect
56. C₁₆×C₄₃	C₄²	semidirect
78. #12674	C₄₃	direct (N × H)
107. #367	C₄×C₄₃	semidirect
108. #366	C₄×C₄₃	semidirect
109. #346	C₄×C₄₃	semidirect
111. C₄₃	#12674	direct (N × H)
152. C₁₆	C₄²×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#367	2
C₂×C₄₃×#366	2
C₂×C₄₃×#346	2
C₄×#107×C₄₃	2
C₄₃×#1380	2
#12674	43

Subgroups — C43×#12674 #24932691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#12674 #24932691