Subgroups — C₂×#19136376 #25249623

Order 11008.

694 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	C₂²×C₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582936	C₂	1	2	yes	maximal
3	#19136376	C₂	1	8	yes	maximal, direct product factor
4	C₂×#14582726	C₂	1	2	yes	maximal, complemented
5	C₂×#14582725	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₃×#366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
8	C₂×#13063283	—	2	2	no	—
9	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×D₄₃	C₄	1	8	yes	complemented
11	C₂×C₁₆×D₄₃	C₂²	1	4	yes	—
12	#14582936	—	2	4	no	—
13	#14582936	C₂²	1	8	yes	—
14	C₂×#13063259	C₂²	1	2	yes	—
15	C₂×#13063256	—	2	2	no	—
16	#14582726	C₂²	1	8	yes	complemented
17	#14582725	C₂²	1	4	yes	complemented
18	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#107×C₄₃	C₂²	1	2	yes	—
20	C₄₃×#366	C₂²	1	4	yes	complemented
21	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
22	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
23	C₂×C₈×D₄₃	C₂×C₄	1	4	yes	—
24	C₂×C₈×D₄₃	D₄	1	2	yes	—
25	C₂×C₈×D₄₃	Q₈	1	4	yes	—
26	C₂×C₈×D₄₃	C₂³	1	2	yes	—
27	#13063283	—	2	8	no	—
28	#13063283	—	4	4	no	—
29	C₂×C₄⋊Dic₄₃	—	2	2	no	—
30	C₂×(C₂×D₄₃)⋊C₄	—	4	2	no	—
31	C₂×C₄×Dic₄₃	—	4	2	no	—
32	C₂×C₄₃⋊C₁₆	C₂×C₄	1	4	yes	—
33	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
34	C₁₆×D₄₃	C₂×C₄	1	16	yes	complemented
35	#13063259	—	2	2	no	—
36	#13063259	C₂³	1	4	yes	—
37	#13063256	—	2	8	no	—
38	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
40	C₂×C₁₆×C₄₃	C₂×C₄	1	4	yes	—
41	C₂×C₁₆×C₄₃	C₂³	1	2	yes	—
42	#107×C₄₃	—	2	2	no	—
43	#107×C₄₃	C₂³	1	4	yes	—
44	C₂³×D₄₃	D₈	1	1	yes	characteristic
45	C₂²×C₄×C₄₃	—	4	2	no	—
46	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×Dic₄₃	—	4	2	no	—
48	C₂²×Dic₄₃	D₈	1	1	yes	characteristic
49	C₂×C₄×D₄₃	C₄⋊C₄	1	4	yes	—
50	C₂×C₄×D₄₃	D₈	1	2	yes	—
51	C₂×C₄×D₄₃	Q₁₆	1	4	yes	—
52	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
53	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
54	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
56	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
57	C₄⋊C₄×C₄₃	—	2	4	no	—
58	C₄⋊C₄×C₄₃	—	4	2	no	—
59	(C₂×D₄₃)⋊C₄	—	4	8	no	—
60	C₄⋊Dic₄₃	—	2	4	no	—
61	C₄⋊Dic₄₃	—	4	2	no	—
62	C₄×Dic₄₃	—	4	8	no	—
63	C₂×C₄₃⋊C₈	C₄⋊C₄	1	4	yes	—
64	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
65	C₈×D₄₃	C₄⋊C₄	1	8	yes	—
66	C₈×D₄₃	C₂²×C₄	1	4	yes	—
67	C₈×D₄₃	C₂×Q₈	1	4	yes	—
68	C₁₆×C₄₃	C₂²×C₄	1	4	yes	—
69	C₄₃⋊C₁₆	C₂²×C₄	1	4	yes	—
70	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
71	C₂²×D₄₃	—	2	2	no	—
72	C₂²×D₄₃	—	2	2	no	—
73	C₂²×D₄₃	#107	1	4	yes	—
74	C₂²×D₄₃	C₂×D₈	1	2	yes	—
75	C₂×C₄×C₄₃	—	4	4	no	—
76	C₂×C₄×C₄₃	—	8	4	no	—
77	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
78	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
79	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
80	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
81	C₂×Dic₄₃	—	4	4	no	—
82	C₂×Dic₄₃	—	8	4	no	—
83	C₂×Dic₄₃	#107	1	4	yes	—
84	C₂×Dic₄₃	C₂×D₈	1	2	yes	—
85	C₄×D₄₃	#107	1	8	yes	—
86	C₄×D₄₃	C₂×C₄⋊C₄	1	4	yes	—
87	C₄×D₄₃	C₂×Q₁₆	1	4	yes	—
88	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
89	C₈×C₄₃	C₂³×C₄	1	1	yes	characteristic
90	C₈×C₄₃	C₂²×Q₈	1	1	yes	characteristic
91	C₄₃⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
92	C₂×#2158	—	43	1	no	maximal, Sylow
93	C₂²×C₄₃	C₂×#107	1	2	yes	—
94	C₂²×C₄₃	#508	1	2	yes	—
95	C₂²×C₄₃	#508	1	2	yes	—
96	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
97	C₂×D₄₃	—	2	2	no	—
98	C₂×D₄₃	—	2	2	no	—
99	C₂×D₄₃	—	2	8	no	—
100	C₂×D₄₃	C₂×#107	1	4	yes	—
101	C₄×C₄₃	—	8	4	no	—
102	C₄×C₄₃	C₂×#107	1	2	yes	—
103	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
104	C₄×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
105	Dic₄₃	—	8	4	no	—
106	Dic₄₃	C₂×#107	1	4	yes	—
107	C₂³×C₁₆	—	43	1	no	—
108	C₂×#427	—	43	2	no	—
109	#2158	—	43	8	no	—
110	C₂×#367	—	43	2	no	—
111	C₂×#366	—	43	1	no	—
112	C₂×#366	D₄₃	1	1	yes	characteristic, complemented
113	C₂×C₄₃	#2158	1	4	yes	complemented
114	C₂×C₄₃	C₂²×#107	1	1	yes	characteristic
115	C₂×C₄₃	C₂×#508	1	1	yes	characteristic
116	C₂×C₄₃	C₂×#508	1	1	yes	characteristic
117	D₄₃	—	2	4	no	—
118	C₂³×C₈	—	43	1	no	—
119	C₂×#117	—	86	2	no	—
120	C₂²×C₁₆	—	43	1	no	—
121	C₂²×C₁₆	—	43	4	no	—
122	C₂²×C₁₆	—	43	8	no	—
123	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
124	#427	—	43	8	no	—
125	#427	—	86	4	no	—
126	C₂×#107	—	43	2	no	—
127	C₂×#107	C₂×D₄₃	1	2	yes	—
128	C₂×#106	—	86	2	no	—
129	#367	—	43	8	no	—
130	#366	—	43	4	no	—
131	#366	C₂×D₄₃	1	4	yes	complemented
132	C₄₃	C₂×#2158	1	1	yes	characteristic, complemented, Sylow
133	C₂³×C₄	—	43	1	no	—
134	C₂²×C₈	—	43	1	no	—
135	C₂²×C₈	—	43	4	no	—
136	C₂²×C₈	—	43	2	no	—
137	C₂²×C₈	—	43	4	no	—
138	C₂²×C₈	—	43	2	no	—
139	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
140	#117	—	86	8	no	—
141	#117	—	172	4	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	86	2	no	—
144	C₂×C₂²⋊C₄	—	172	2	no	—
145	C₂×C₄²	—	172	2	no	—
146	C₂×C₁₆	—	43	4	no	—
147	C₂×C₁₆	—	43	2	no	—
148	C₂×C₁₆	—	43	16	no	—
149	C₂×C₁₆	C₄×D₄₃	1	4	yes	—
150	C₂×C₁₆	C₂²×D₄₃	1	2	yes	—
151	#107	—	2	2	no	—
152	#107	—	43	4	no	—
153	#107	—	86	2	no	—
154	#107	C₂²×D₄₃	1	4	yes	—
155	#106	—	86	8	no	—
156	C₂⁴	—	43	1	no	—
157	C₂²×C₄	—	4	2	no	—
158	C₂²×C₄	—	43	1	no	—
159	C₂²×C₄	—	43	4	no	—
160	C₂²×C₄	—	43	2	no	—
161	C₂²×C₄	—	43	4	no	—
162	C₂²×C₄	—	43	2	no	—
163	C₂²×C₄	—	172	2	no	—
164	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
165	C₂×C₈	—	43	4	no	—
166	C₂×C₈	—	43	2	no	—
167	C₂×C₈	—	43	8	no	—
168	C₂×C₈	—	43	4	no	—
169	C₂×C₈	—	43	4	no	—
170	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
171	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
172	C₂×C₈	Q₈×D₄₃	1	2	yes	—
173	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
174	C₄⋊C₄	—	2	4	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	86	4	no	—
177	C₄⋊C₄	—	172	2	no	—
178	C₂²⋊C₄	—	172	8	no	—
179	C₄²	—	172	8	no	—
180	C₁₆	—	43	4	no	—
181	C₁₆	C₂×C₄×D₄₃	1	4	yes	—
182	C₂³	—	43	2	no	—
183	C₂³	—	43	4	no	—
184	C₂³	—	86	2	no	—
185	C₂³	—	86	2	no	—
186	C₂³	D₈×D₄₃	1	1	yes	characteristic
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	—	8	4	no	—
189	C₂×C₄	—	43	2	no	—
190	C₂×C₄	—	43	4	no	—
191	C₂×C₄	—	43	4	no	—
192	C₂×C₄	—	43	4	no	—
193	C₂×C₄	—	43	8	no	—
194	C₂×C₄	—	344	4	no	—
195	C₂×C₄	—	172	4	no	—
196	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
197	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
198	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
199	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
200	C₈	—	43	4	no	—
201	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
202	C₈	C₂²×C₄×D₄₃	1	1	yes	characteristic
203	C₈	C₂×Q₈×D₄₃	1	1	yes	characteristic
204	C₂²	—	43	4	no	—
205	C₂²	—	86	8	no	—
206	C₂²	—	86	2	no	—
207	C₂²	—	86	2	no	—
208	C₂²	#107×D₄₃	1	2	yes	—
209	C₂²	#14583328	1	2	yes	—
210	C₂²	#14583332	1	2	yes	—
211	C₂²	C₂×D₈×D₄₃	1	1	yes	characteristic
212	C₄	—	8	4	no	—
213	C₄	—	43	4	no	—
214	C₄	—	344	4	no	—
215	C₄	#107×D₄₃	1	2	yes	—
216	C₄	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
217	C₄	C₂×Q₁₆×D₄₃	1	1	yes	characteristic
218	C₂	—	86	4	no	—
219	C₂	#19136376	1	4	yes	direct product factor
220	C₂	C₂×#107×D₄₃	1	1	yes	characteristic
221	C₂	C₂×#14583328	1	1	yes	characteristic
222	C₂	C₂×#14583332	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₈×D₄₃
commutator	C₈×C₄₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₂×C₄₃×#366	C₂
socle	C₂³×C₄₃	C₂×D₈
prime radical	C₂³×D₄₃	D₈
cosocle	C₂×C₈×C₄₃	C₂⁴
hypercenter	C₂×#366	D₄₃
hypocenter	C₄₃	C₂×#2158
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

Complements

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

N	H ≅ G/N	type
3. #19136376	C₂	direct (N × H)
4. C₂×#14582726	C₂	semidirect
5. C₂×#14582725	C₂	semidirect
6. C₂×C₄₃×#366	C₂	semidirect
10. C₂×C₁₆×D₄₃	C₄	semidirect
16. #14582726	C₂²	semidirect
17. #14582725	C₂²	semidirect
20. C₄₃×#366	C₂²	semidirect
34. C₁₆×D₄₃	C₂×C₄	semidirect
112. C₂×#366	D₄₃	semidirect
113. C₂×C₄₃	#2158	semidirect
131. #366	C₂×D₄₃	semidirect
132. C₄₃	C₂×#2158	semidirect
219. C₂	#19136376	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₆×D₄₃	2
C₂×#14582936	2
#19136376	2
C₂×#14582726	2
C₂×#14582725	2
C₂×C₄₃×#366	2
C₂×#2158	43

Subgroups — C2×#19136376 #25249623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19136376 #25249623