Subgroups — C₂×C₄₃×#1417 #24933636

Order 11008.

294 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#508	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#368	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1417	C₂	1	4	yes	maximal, direct product factor
5	C₂×#135×C₄₃	—	2	1	no	—
6	C₄₃×#508	—	2	1	no	—
7	C₄₃×#508	—	2	1	no	—
8	C₄₃×#508	C₄	1	2	yes	—
9	C₄₃×#508	C₂²	1	2	yes	—
10	C₂×Q₃₂×C₄₃	C₄	1	1	yes	characteristic
11	C₂×SD₃₂×C₄₃	—	2	1	no	—
12	C₂×D₁₆×C₄₃	C₄	1	1	yes	characteristic
13	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#108×C₄₃	—	2	1	no	—
15	C₂×C₃₂×C₄₃	—	2	1	no	—
16	C₂×C₃₂×C₄₃	—	2	1	no	—
17	C₂×C₃₂×C₄₃	C₂²	1	2	yes	complemented
18	C₄₃×#368	—	2	1	no	—
19	C₄₃×#368	C₂²	1	2	yes	complemented
20	C₂×#41×C₄₃	—	4	1	no	—
21	#135×C₄₃	—	2	2	no	—
22	#135×C₄₃	—	2	2	no	—
23	#135×C₄₃	—	4	1	no	—
24	#135×C₄₃	—	4	1	no	—
25	C₂×Q₁₆×C₄₃	—	2	1	no	—
26	C₂×SD₁₆×C₄₃	—	4	1	no	—
27	C₂×D₈×C₄₃	—	2	1	no	—
28	C₂×M₁₆×C₄₃	—	4	1	no	—
29	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
30	Q₃₂×C₄₃	—	2	1	no	—
31	Q₃₂×C₄₃	C₂×C₄	1	2	yes	—
32	SD₃₂×C₄₃	—	2	2	no	—
33	SD₃₂×C₄₃	—	2	2	no	—
34	D₁₆×C₄₃	—	2	1	no	—
35	D₁₆×C₄₃	C₂×C₄	1	2	yes	—
36	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
39	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
40	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
41	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
42	#108×C₄₃	—	2	2	no	—
43	#108×C₄₃	—	4	1	no	—
44	C₃₂×C₄₃	—	2	2	no	—
45	#41×C₄₃	—	4	2	no	—
46	#41×C₄₃	—	4	2	no	—
47	#41×C₄₃	—	8	1	no	—
48	#41×C₄₃	—	8	1	no	—
49	C₂×Q₈×C₄₃	—	4	1	no	—
50	C₂×D₄×C₄₃	—	4	1	no	—
51	C₂×D₄×C₄₃	—	8	1	no	—
52	C₂²×C₄×C₄₃	—	8	1	no	—
53	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
54	Q₁₆×C₄₃	—	2	2	no	—
55	Q₁₆×C₄₃	—	4	1	no	—
56	SD₁₆×C₄₃	—	4	2	no	—
57	SD₁₆×C₄₃	—	4	2	no	—
58	D₈×C₄₃	—	2	2	no	—
59	D₈×C₄₃	—	4	1	no	—
60	M₁₆×C₄₃	—	4	2	no	—
61	M₁₆×C₄₃	—	8	1	no	—
62	C₂×C₈×C₄₃	—	8	1	no	—
63	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
66	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
67	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
68	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
69	C₁₆×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₁₆×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₁₆×C₄₃	C₂²×C₄	1	1	yes	characteristic
72	C₁₆×C₄₃	C₂×D₄	1	1	yes	characteristic
73	C₂³×C₄₃	—	8	1	no	—
74	C₂³×C₄₃	SD₃₂	1	1	yes	characteristic
75	Q₈×C₄₃	—	4	2	no	—
76	Q₈×C₄₃	—	8	1	no	—
77	D₄×C₄₃	—	4	2	no	—
78	D₄×C₄₃	—	8	2	no	—
79	D₄×C₄₃	—	8	2	no	—
80	D₄×C₄₃	—	8	1	no	—
81	C₂×C₄×C₄₃	—	8	1	no	—
82	C₂×C₄×C₄₃	—	8	2	no	—
83	C₂×C₄×C₄₃	—	8	2	no	—
84	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
85	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
86	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
87	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
88	C₂×C₄×C₄₃	SD₃₂	1	1	yes	characteristic
89	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
90	C₈×C₄₃	—	8	2	no	—
91	C₈×C₄₃	#102	1	1	yes	characteristic
92	C₈×C₄₃	#102	1	1	yes	characteristic
93	C₈×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₈×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
95	C₂×#1417	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂²×C₄₃	—	2	2	no	—
97	C₂²×C₄₃	—	8	2	no	—
98	C₂²×C₄₃	—	16	2	no	—
99	C₂²×C₄₃	#357	1	1	yes	characteristic
100	C₂²×C₄₃	#357	1	1	yes	characteristic
101	C₂²×C₄₃	C₂×SD₃₂	1	1	yes	characteristic
102	C₄×C₄₃	—	8	2	no	—
103	C₄×C₄₃	#357	1	1	yes	characteristic
104	C₄×C₄₃	#357	1	1	yes	characteristic
105	C₄×C₄₃	C₂×#102	1	1	yes	characteristic
106	C₄×C₄₃	C₂×D₁₆	1	1	yes	characteristic
107	C₂×#508	C₂×C₄₃	1	1	yes	characteristic
108	C₂²×C₃₂	C₂×C₄₃	1	1	yes	characteristic, complemented
109	C₂×#368	C₂×C₄₃	1	1	yes	characteristic, complemented
110	#1417	C₂×C₄₃	1	4	yes	direct product factor
111	C₂×C₄₃	—	2	1	no	—
112	C₂×C₄₃	—	2	1	no	—
113	C₂×C₄₃	—	16	2	no	—
114	C₂×C₄₃	#1417	1	2	yes	direct product factor
115	C₂×C₄₃	C₂×#357	1	1	yes	characteristic
116	C₂×#135	—	2	1	no	—
117	#508	—	2	1	no	—
118	#508	—	2	1	no	—
119	#508	C₄×C₄₃	1	2	yes	—
120	#508	C₂²×C₄₃	1	2	yes	—
121	C₂×Q₃₂	C₄×C₄₃	1	1	yes	characteristic
122	C₂×SD₃₂	—	2	1	no	—
123	C₂×D₁₆	C₄×C₄₃	1	1	yes	characteristic
124	C₂²×C₁₆	C₂²×C₄₃	1	1	yes	characteristic
125	C₂×#108	—	2	1	no	—
126	C₂×C₃₂	—	2	1	no	—
127	C₂×C₃₂	—	2	1	no	—
128	C₂×C₃₂	C₂²×C₄₃	1	2	yes	complemented
129	#368	—	2	1	no	—
130	#368	C₂²×C₄₃	1	2	yes	complemented
131	C₄₃	C₂×#1417	1	1	yes	characteristic, direct product factor, Sylow
132	C₂×#41	—	4	1	no	—
133	#135	—	2	2	no	—
134	#135	—	2	2	no	—
135	#135	—	4	1	no	—
136	#135	—	4	1	no	—
137	C₂×Q₁₆	—	2	1	no	—
138	C₂×SD₁₆	—	4	1	no	—
139	C₂×D₈	—	2	1	no	—
140	C₂×M₁₆	—	4	1	no	—
141	C₂²×C₈	D₄×C₄₃	1	1	yes	characteristic
142	Q₃₂	—	2	1	no	—
143	Q₃₂	C₂×C₄×C₄₃	1	2	yes	—
144	SD₃₂	—	2	2	no	—
145	SD₃₂	—	2	2	no	—
146	D₁₆	—	2	1	no	—
147	D₁₆	C₂×C₄×C₄₃	1	2	yes	—
148	C₂×C₁₆	C₂×C₄×C₄₃	1	1	yes	characteristic
149	C₂×C₁₆	C₂×C₄×C₄₃	1	1	yes	characteristic
150	C₂×C₁₆	D₄×C₄₃	1	1	yes	characteristic
151	C₂×C₁₆	D₄×C₄₃	1	1	yes	characteristic
152	C₂×C₁₆	D₄×C₄₃	1	1	yes	characteristic
153	C₂×C₁₆	C₂³×C₄₃	1	1	yes	characteristic
154	#108	—	2	2	no	—
155	#108	—	4	1	no	—
156	C₃₂	—	2	2	no	—
157	#41	—	4	2	no	—
158	#41	—	4	2	no	—
159	#41	—	8	1	no	—
160	#41	—	8	1	no	—
161	C₂×Q₈	—	4	1	no	—
162	C₂×D₄	—	4	1	no	—
163	C₂×D₄	—	8	1	no	—
164	C₂²×C₄	—	8	1	no	—
165	C₂²×C₄	D₈×C₄₃	1	1	yes	characteristic
166	Q₁₆	—	2	2	no	—
167	Q₁₆	—	4	1	no	—
168	SD₁₆	—	4	2	no	—
169	SD₁₆	—	4	2	no	—
170	D₈	—	2	2	no	—
171	D₈	—	4	1	no	—
172	M₁₆	—	4	2	no	—
173	M₁₆	—	8	1	no	—
174	C₂×C₈	—	8	1	no	—
175	C₂×C₈	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
176	C₂×C₈	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
177	C₂×C₈	D₈×C₄₃	1	1	yes	characteristic
178	C₂×C₈	SD₁₆×C₄₃	1	1	yes	characteristic
179	C₂×C₈	SD₁₆×C₄₃	1	1	yes	characteristic
180	C₂×C₈	C₂×D₄×C₄₃	1	1	yes	characteristic
181	C₁₆	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
182	C₁₆	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
183	C₁₆	C₂²×C₄×C₄₃	1	1	yes	characteristic
184	C₁₆	C₂×D₄×C₄₃	1	1	yes	characteristic
185	C₂³	—	8	1	no	—
186	C₂³	SD₃₂×C₄₃	1	1	yes	characteristic
187	Q₈	—	4	2	no	—
188	Q₈	—	8	1	no	—
189	D₄	—	4	2	no	—
190	D₄	—	8	2	no	—
191	D₄	—	8	2	no	—
192	D₄	—	8	1	no	—
193	C₂×C₄	—	8	1	no	—
194	C₂×C₄	—	8	2	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	#102×C₄₃	1	1	yes	characteristic
197	C₂×C₄	#102×C₄₃	1	1	yes	characteristic
198	C₂×C₄	D₁₆×C₄₃	1	1	yes	characteristic
199	C₂×C₄	D₁₆×C₄₃	1	1	yes	characteristic
200	C₂×C₄	SD₃₂×C₄₃	1	1	yes	characteristic
201	C₂×C₄	C₂×D₈×C₄₃	1	1	yes	characteristic
202	C₈	—	8	2	no	—
203	C₈	#102×C₄₃	1	1	yes	characteristic
204	C₈	#102×C₄₃	1	1	yes	characteristic
205	C₈	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
206	C₈	C₂×SD₁₆×C₄₃	1	1	yes	characteristic
207	C₂²	—	2	2	no	—
208	C₂²	—	8	2	no	—
209	C₂²	—	16	2	no	—
210	C₂²	C₄₃×#357	1	1	yes	characteristic
211	C₂²	C₄₃×#357	1	1	yes	characteristic
212	C₂²	C₂×SD₃₂×C₄₃	1	1	yes	characteristic
213	C₄	—	8	2	no	—
214	C₄	C₄₃×#357	1	1	yes	characteristic
215	C₄	C₄₃×#357	1	1	yes	characteristic
216	C₄	C₂×#102×C₄₃	1	1	yes	characteristic
217	C₄	C₂×D₁₆×C₄₃	1	1	yes	characteristic
218	C₂	—	2	1	no	—
219	C₂	—	2	1	no	—
220	C₂	—	16	2	no	—
221	C₂	C₄₃×#1417	1	2	yes	direct product factor
222	C₂	C₂×C₄₃×#357	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₃	D₁₆
commutator	C₁₆	C₂²×C₄×C₄₃
Frattini, cosocle	C₂×C₁₆	C₂³×C₄₃
socle	C₂²×C₄₃	#357
prime radical	C₂×C₄₃×#508	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂²×C₄×C₄₃ ◁ C₂²×C₈×C₄₃ ◁ C₂²×C₁₆×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃₂×C₄₃	C₂	semidirect
3. C₂×C₄₃×#368	C₂	semidirect
4. C₄₃×#1417	C₂	direct (N × H)
17. C₂×C₃₂×C₄₃	C₂²	semidirect
19. C₄₃×#368	C₂²	semidirect
95. C₂×#1417	C₄₃	direct (N × H)
108. C₂²×C₃₂	C₂×C₄₃	semidirect
109. C₂×#368	C₂×C₄₃	semidirect
110. #1417	C₂×C₄₃	direct (N × H)
114. C₂×C₄₃	#1417	direct (N × H)
128. C₂×C₃₂	C₂²×C₄₃	semidirect
130. #368	C₂²×C₄₃	semidirect
131. C₄₃	C₂×#1417	direct (N × H)
221. C₂	C₄₃×#1417	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#508	2
C₂²×C₃₂×C₄₃	2
C₂×C₄₃×#368	2
C₄₃×#1417	2
C₂×#1417	43

Subgroups — C2×C43×#1417 #24933636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1417 #24933636