Subgroups — C₂×#19136192 #25249232

Order 11008.

854 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×#13063265	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#19136192	C₂	1	8	yes	maximal, direct product factor
4	C₂×#14582675	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×C₄₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic
7	C₂×#13063265	C₄	1	8	yes	complemented
8	C₂×#13063265	C₂²	1	4	yes	—
9	C₂²×C₄₃⋊C₁₆	C₄	1	8	yes	complemented
10	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₄₃⋊C₁₆	C₂²	1	2	yes	—
13	C₂²×C₄₃⋊C₁₆	C₂²	1	4	yes	—
14	#14582675	C₂²	1	8	yes	complemented
15	C₄×C₄₃⋊C₁₆	C₂²	1	8	yes	complemented
16	C₂²×M₁₆×C₄₃	C₄	1	1	yes	characteristic
17	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₃	C₄	1	1	yes	characteristic
19	C₄₃×#405	C₄	1	4	yes	—
20	C₄₃×#405	C₂²	1	4	yes	—
21	C₂×#97×C₄₃	C₄	1	2	yes	—
22	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
23	#13063265	C₂×C₄	1	16	yes	complemented
24	C₂×C₄₃⋊C₁₆	C₂×C₄	1	4	yes	—
25	C₂×C₄₃⋊C₁₆	C₂×C₄	1	4	yes	—
26	C₂×C₄₃⋊C₁₆	C₂×C₄	1	8	yes	—
27	C₂×C₄₃⋊C₁₆	C₂×C₄	1	16	yes	complemented
28	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
29	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
30	C₂×C₄₃⋊C₁₆	C₂³	1	4	yes	—
31	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
32	C₂×M₁₆×C₄₃	C₈	1	8	yes	—
33	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
35	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
36	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
41	#117×C₄₃	C₈	1	4	yes	—
42	#117×C₄₃	C₂×C₄	1	4	yes	—
43	C₂×C₄⋊C₄×C₄₃	C₈	1	2	yes	—
44	C₂×C₂²⋊C₄×C₄₃	C₈	1	2	yes	—
45	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
46	#97×C₄₃	C₂×C₄	1	8	yes	—
47	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
48	C₄×C₈×C₄₃	C₂³	1	4	yes	—
49	C₂⁴×C₄₃	C₂×C₈	1	1	yes	characteristic
50	C₂²×C₄×C₄₃	C₄²	1	4	yes	—
51	C₂²×C₄×C₄₃	C₂×C₈	1	4	yes	—
52	C₂²×C₄×C₄₃	C₂×C₈	1	4	yes	—
53	C₂²×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
54	C₂²×C₄×C₄₃	C₂×C₈	1	2	yes	—
55	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
57	M₁₆×C₄₃	C₂×C₈	1	16	yes	—
58	C₂×C₈×C₄₃	C₄²	1	4	yes	—
59	C₂×C₈×C₄₃	C₄²	1	8	yes	—
60	C₂×C₈×C₄₃	C₂×C₈	1	8	yes	—
61	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
62	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
63	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
64	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
65	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
67	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
68	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
69	C₄⋊C₄×C₄₃	C₂×C₈	1	8	yes	—
70	C₂²⋊C₄×C₄₃	C₂×C₈	1	8	yes	—
71	C₄²×C₄₃	C₂×C₈	1	4	yes	—
72	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
73	C₄₃⋊C₁₆	C₂²×C₄	1	4	yes	—
74	C₄₃⋊C₁₆	C₂²×C₄	1	4	yes	—
75	C₄₃⋊C₁₆	C₂²×C₄	1	8	yes	—
76	C₂³×C₄₃	—	2	4	no	—
77	C₂³×C₄₃	C₄×C₈	1	4	yes	—
78	C₂³×C₄₃	C₂²×C₈	1	2	yes	—
79	C₂³×C₄₃	C₂²×C₈	1	1	yes	characteristic
80	C₂×C₄×C₄₃	—	2	8	no	—
81	C₂×C₄×C₄₃	C₄×C₈	1	8	yes	—
82	C₂×C₄×C₄₃	C₄×C₈	1	4	yes	—
83	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
84	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
85	C₂×C₄×C₄₃	C₂²×C₈	1	8	yes	—
86	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
87	C₂×C₄×C₄₃	C₂²×C₈	1	4	yes	—
88	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
89	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
90	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
91	C₈×C₄₃	C₂×C₄²	1	2	yes	—
92	C₈×C₄₃	C₂×C₄²	1	4	yes	—
93	C₈×C₄₃	C₂²×C₈	1	8	yes	—
94	C₈×C₄₃	C₂³×C₄	1	1	yes	characteristic
95	C₈×C₄₃	C₂³×C₄	1	1	yes	characteristic
96	C₂×#2108	—	43	1	no	maximal, Sylow
97	C₂²×C₄₃	—	2	8	no	—
98	C₂²×C₄₃	—	2	4	no	—
99	C₂²×C₄₃	C₂×C₄×C₈	1	4	yes	—
100	C₂²×C₄₃	C₂×C₄×C₈	1	2	yes	—
101	C₂²×C₄₃	#504	1	4	yes	—
102	C₂²×C₄₃	C₂³×C₈	1	1	yes	characteristic
103	C₄×C₄₃	—	2	8	no	—
104	C₄×C₄₃	C₂×C₄×C₈	1	2	yes	—
105	C₄×C₄₃	C₂×C₄×C₈	1	4	yes	—
106	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
107	C₄×C₄₃	C₂³×C₈	1	1	yes	characteristic
108	C₂²×M₃₂	—	43	1	no	—
109	C₂³×C₁₆	—	43	1	no	—
110	C₂×#405	D₄₃	1	1	yes	characteristic
111	#2108	—	43	8	no	—
112	C₂×#346	—	43	2	no	—
113	C₂×C₄×C₁₆	—	43	2	no	—
114	C₂×C₄₃	—	2	4	no	—
115	C₂×C₄₃	#2108	1	4	yes	complemented
116	C₂×C₄₃	C₂²×C₄×C₈	1	1	yes	characteristic
117	C₂×C₄₃	C₂×#504	1	2	yes	—
118	C₂²×M₁₆	Dic₄₃	1	1	yes	characteristic
119	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
120	C₂×#117	Dic₄₃	1	1	yes	characteristic
121	C₂×M₃₂	—	43	4	no	—
122	C₂×M₃₂	—	43	8	no	—
123	C₂²×C₁₆	—	43	4	no	—
124	C₂²×C₁₆	—	43	1	no	—
125	C₂²×C₁₆	—	43	2	no	—
126	C₂²×C₁₆	—	43	1	no	—
127	C₂²×C₁₆	—	43	8	no	—
128	#405	Dic₄₃	1	4	yes	—
129	#405	C₂×D₄₃	1	4	yes	—
130	C₂×#97	Dic₄₃	1	2	yes	—
131	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
132	#346	—	43	8	no	—
133	C₄×C₁₆	—	43	8	no	—
134	C₄₃	C₂×#2108	1	1	yes	characteristic, complemented, Sylow
135	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
136	C₂×M₁₆	C₄₃⋊C₈	1	8	yes	—
137	C₂×M₁₆	C₂×Dic₄₃	1	4	yes	—
138	C₂²×C₈	C₄×D₄₃	1	4	yes	—
139	C₂²×C₈	C₄×D₄₃	1	4	yes	—
140	C₂²×C₈	C₂×Dic₄₃	1	2	yes	—
141	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
142	C₂²×C₈	C₂×Dic₄₃	1	2	yes	—
143	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
144	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
145	#117	C₄₃⋊C₈	1	4	yes	—
146	#117	C₂×Dic₄₃	1	4	yes	—
147	C₂×C₄⋊C₄	C₄₃⋊C₈	1	2	yes	—
148	C₂×C₂²⋊C₄	C₄₃⋊C₈	1	2	yes	—
149	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
150	M₃₂	—	43	16	no	—
151	C₂×C₁₆	—	43	4	no	—
152	C₂×C₁₆	—	43	4	no	—
153	C₂×C₁₆	—	43	8	no	—
154	C₂×C₁₆	—	43	16	no	—
155	C₂×C₁₆	—	43	2	no	—
156	C₂×C₁₆	—	43	4	no	—
157	C₂×C₁₆	—	43	2	no	—
158	#97	C₂×Dic₄₃	1	8	yes	—
159	C₄×C₈	C₂×Dic₄₃	1	4	yes	—
160	C₄×C₈	C₂²×D₄₃	1	4	yes	—
161	C₂⁴	C₂×C₄₃⋊C₈	1	1	yes	characteristic
162	C₂²×C₄	C₂×C₄₃⋊C₈	1	4	yes	—
163	C₂²×C₄	C₂×C₄₃⋊C₈	1	1	yes	characteristic
164	C₂²×C₄	C₂×C₄₃⋊C₈	1	2	yes	—
165	C₂²×C₄	C₂×C₄₃⋊C₈	1	4	yes	—
166	C₂²×C₄	C₄×Dic₄₃	1	4	yes	—
167	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
168	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
169	M₁₆	C₂×C₄₃⋊C₈	1	16	yes	—
170	C₂×C₈	C₂×C₄₃⋊C₈	1	8	yes	—
171	C₂×C₈	C₄×Dic₄₃	1	4	yes	—
172	C₂×C₈	C₄×Dic₄₃	1	8	yes	—
173	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
174	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
175	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
176	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
177	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
178	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
179	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
180	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
181	C₄⋊C₄	C₂×C₄₃⋊C₈	1	8	yes	—
182	C₂²⋊C₄	C₂×C₄₃⋊C₈	1	8	yes	—
183	C₄²	C₂×C₄₃⋊C₈	1	4	yes	—
184	C₄²	C₂²×Dic₄₃	1	4	yes	—
185	C₁₆	—	43	4	no	—
186	C₁₆	—	43	4	no	—
187	C₁₆	—	43	8	no	—
188	C₂³	—	2	4	no	—
189	C₂³	C₄×C₄₃⋊C₈	1	4	yes	—
190	C₂³	C₂²×C₄₃⋊C₈	1	2	yes	—
191	C₂³	C₂²×C₄₃⋊C₈	1	1	yes	characteristic
192	C₂×C₄	—	2	8	no	—
193	C₂×C₄	C₄×C₄₃⋊C₈	1	8	yes	—
194	C₂×C₄	C₄×C₄₃⋊C₈	1	4	yes	—
195	C₂×C₄	C₂×C₄×Dic₄₃	1	4	yes	—
196	C₂×C₄	C₂×C₄×Dic₄₃	1	2	yes	—
197	C₂×C₄	C₂²×C₄₃⋊C₈	1	8	yes	—
198	C₂×C₄	C₂²×C₄₃⋊C₈	1	1	yes	characteristic
199	C₂×C₄	C₂²×C₄₃⋊C₈	1	2	yes	—
200	C₂×C₄	C₂²×C₄₃⋊C₈	1	2	yes	—
201	C₂×C₄	C₂²×C₄₃⋊C₈	1	4	yes	—
202	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
203	C₈	C₂×C₄×Dic₄₃	1	4	yes	—
204	C₈	C₂×C₄×Dic₄₃	1	2	yes	—
205	C₈	C₂²×C₄₃⋊C₈	1	8	yes	—
206	C₈	C₂²×C₄×D₄₃	1	1	yes	characteristic
207	C₈	C₂²×C₄×D₄₃	1	1	yes	characteristic
208	C₂²	—	2	4	no	—
209	C₂²	—	2	8	no	—
210	C₂²	C₂×C₄×C₄₃⋊C₈	1	4	yes	—
211	C₂²	C₂×C₄×C₄₃⋊C₈	1	2	yes	—
212	C₂²	#14583316	1	4	yes	—
213	C₂²	C₂³×C₄₃⋊C₈	1	1	yes	characteristic
214	C₄	—	2	8	no	—
215	C₄	C₂×C₄×C₄₃⋊C₈	1	2	yes	—
216	C₄	C₂×C₄×C₄₃⋊C₈	1	4	yes	—
217	C₄	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
218	C₄	C₂³×C₄₃⋊C₈	1	1	yes	characteristic
219	C₂	—	2	4	no	—
220	C₂	#19136192	1	4	yes	direct product factor
221	C₂	C₂²×C₄×C₄₃⋊C₈	1	1	yes	characteristic
222	C₂	C₂×#14583316	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂²×D₄₃
commutator	C₂×C₄₃	C₂²×C₄×C₈
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₂×C₄₃×#405	C₂
socle	C₂³×C₄₃	C₂²×C₈
prime radical	C₂⁴×C₄₃	C₂×C₈
cosocle	C₂×C₈×C₄₃	C₂⁴
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	C₂×#2108
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
3. #19136192	C₂	direct (N × H)
4. C₂×#14582675	C₂	semidirect
5. C₂×C₄×C₄₃⋊C₁₆	C₂	semidirect
7. C₂×#13063265	C₄	semidirect
9. C₂²×C₄₃⋊C₁₆	C₄	semidirect
14. #14582675	C₂²	semidirect
15. C₄×C₄₃⋊C₁₆	C₂²	semidirect
23. #13063265	C₂×C₄	semidirect
27. C₂×C₄₃⋊C₁₆	C₂×C₄	semidirect
115. C₂×C₄₃	#2108	semidirect
134. C₄₃	C₂×#2108	semidirect
220. C₂	#19136192	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×#13063265	2
C₂³×C₄₃⋊C₁₆	2
#19136192	2
C₂×#14582675	2
C₂×C₄×C₄₃⋊C₁₆	2
C₂×C₄₃×#405	2
C₂×#2108	43

Subgroups — C2×#19136192 #25249232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19136192 #25249232