Subgroups — C₂×#10588581 #11899377

Order 1152.

552 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63464	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₉×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#63371	C₂	1	1	yes	maximal, characteristic, complemented
4	#10588581	C₂	1	8	yes	maximal, direct product factor
5	C₂×#63357	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₆×D₉	C₂	1	2	yes	maximal, complemented
7	C₂×#4901	—	3	1	no	maximal
8	C₂×#3697	C₄	1	1	yes	characteristic
9	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
10	C₂×#3667	C₄	1	1	yes	characteristic
11	#63464	C₄	1	4	yes	—
12	#63464	C₂²	1	4	yes	—
13	C₂×#3663	C₄	1	2	yes	—
14	C₂×C₈×D₉	C₂²	1	2	yes	—
15	C₂×C₉×C₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₉×C₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₉×C₁₆	C₂²	1	4	yes	complemented
18	#63371	C₂²	1	4	yes	complemented
19	C₂×C₉⋊C₁₆	C₂²	1	2	yes	—
20	#63357	C₂²	1	8	yes	complemented
21	C₁₆×D₉	C₂²	1	8	yes	complemented
22	C₂×#901	—	3	1	no	—
23	C₂²×C₃×C₁₆	D₃	1	1	yes	characteristic
24	C₂×#812	—	3	1	no	—
25	#4901	—	3	8	no	—
26	C₂×#798	—	3	2	no	—
27	C₂×D₃×C₁₆	—	3	2	no	—
28	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
29	C₂×#611	C₈	1	2	yes	—
30	#3697	C₈	1	4	yes	—
31	#3697	C₂×C₄	1	4	yes	—
32	C₂×D₃₆	C₈	1	1	yes	characteristic
33	C₂×C₄×D₉	C₂×C₄	1	2	yes	—
34	C₂×Dic₁₈	C₈	1	1	yes	characteristic
35	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₈×C₉	C₂×C₄	1	2	yes	—
37	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
38	C₂×C₈×C₉	C₂³	1	2	yes	—
39	#3667	C₂×C₄	1	4	yes	—
40	C₂×C₉⋊C₈	C₂×C₄	1	2	yes	—
41	#3663	C₂×C₄	1	8	yes	—
42	C₈×D₉	C₂×C₄	1	4	yes	—
43	C₈×D₉	C₂³	1	4	yes	—
44	C₉×C₁₆	C₂³	1	2	yes	—
45	C₉×C₁₆	C₂³	1	2	yes	—
46	C₉⋊C₁₆	C₂³	1	4	yes	—
47	C₂×#504	—	9	1	no	Sylow
48	C₂×#235	—	3	1	no	—
49	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
50	C₂×#208	—	3	1	no	—
51	#901	—	3	4	no	—
52	#901	—	3	4	no	—
53	C₂×ΓL(1,𝔽₂₅)	—	3	2	no	—
54	C₂×D₃×C₈	—	3	2	no	—
55	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic
56	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic
57	C₂×C₃×C₁₆	C₂×D₃	1	4	yes	—
58	#812	—	3	4	no	—
59	C₂×C₃⋊C₁₆	—	3	2	no	—
60	#798	—	3	8	no	—
61	D₃×C₁₆	—	3	8	no	—
62	C₂³×C₉	C₂×C₈	1	1	yes	characteristic
63	C₂²×D₉	C₂×C₈	1	2	yes	—
64	C₂×C₄×C₉	C₂×C₈	1	1	yes	characteristic
65	C₂×C₄×C₉	C₂×C₈	1	2	yes	—
66	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
68	#611	C₂×C₈	1	8	yes	—
69	C₂×Dic₉	C₂×C₈	1	2	yes	—
70	D₃₆	C₂×C₈	1	4	yes	—
71	C₄×D₉	C₂×C₈	1	4	yes	—
72	C₄×D₉	C₂²×C₄	1	4	yes	—
73	Dic₁₈	C₂×C₈	1	4	yes	—
74	C₈×C₉	C₂²×C₄	1	1	yes	characteristic
75	C₈×C₉	C₂²×C₄	1	2	yes	—
76	C₈×C₉	C₂⁴	1	1	yes	characteristic
77	C₉⋊C₈	C₂²×C₄	1	4	yes	—
78	C₂×#131	—	9	1	no	—
79	#504	—	9	8	no	—
80	C₂×M₃₂	—	9	1	no	—
81	C₂×M₃₂	—	9	2	no	—
82	C₂²×C₁₆	—	9	2	no	—
83	C₂²×C₁₆	D₉	1	1	yes	characteristic, complemented
84	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
85	C₂×#67	—	3	2	no	—
86	#235	—	3	4	no	—
87	#235	—	3	4	no	—
88	C₂×D₁₂	—	3	1	no	—
89	C₂×C₄×D₃	—	3	2	no	—
90	C₂×Dic₆	—	3	1	no	—
91	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
92	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
93	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
94	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
95	#208	—	3	4	no	—
96	C₂×C₃⋊C₈	—	3	2	no	—
97	ΓL(1,𝔽₂₅)	—	3	8	no	—
98	D₃×C₈	—	3	4	no	—
99	D₃×C₈	—	3	4	no	—
100	C₃×C₁₆	C₂²×D₃	1	2	yes	—
101	C₃×C₁₆	C₂²×D₃	1	2	yes	—
102	C₃⋊C₁₆	—	3	4	no	—
103	C₂²×C₉	—	2	2	no	—
104	C₂²×C₉	C₂²×C₈	1	2	yes	—
105	C₂²×C₉	C₂²×C₈	1	1	yes	characteristic
106	C₂×D₉	—	2	4	no	—
107	C₂×D₉	C₂²×C₈	1	4	yes	—
108	C₄×C₉	C₂²×C₈	1	2	yes	—
109	C₄×C₉	C₂²×C₈	1	1	yes	characteristic
110	C₄×C₉	C₂³×C₄	1	1	yes	characteristic
111	Dic₉	C₂²×C₈	1	4	yes	—
112	C₂×#41	—	9	1	no	—
113	#131	—	9	4	no	—
114	#131	—	9	4	no	—
115	C₂×M₁₆	—	9	1	no	—
116	C₂×M₁₆	—	9	2	no	—
117	C₂²×C₈	—	9	2	no	—
118	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
119	M₃₂	—	9	4	no	—
120	M₃₂	—	9	8	no	—
121	C₂×C₁₆	—	9	2	no	—
122	C₂×C₁₆	—	9	8	no	—
123	C₂×C₁₆	C₂×D₉	1	1	yes	characteristic
124	C₂×C₁₆	C₂×D₉	1	1	yes	characteristic
125	C₂×C₁₆	C₂×D₉	1	4	yes	complemented
126	C₂³×C₃	D₃×C₈	1	1	yes	characteristic
127	C₂²×D₃	—	3	2	no	—
128	C₂×C₃×C₄	D₃×C₈	1	1	yes	characteristic
129	C₂×C₃×C₄	D₃×C₈	1	2	yes	—
130	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
131	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
132	#67	—	3	8	no	—
133	C₂×Dic₃	—	3	2	no	—
134	D₁₂	—	3	4	no	—
135	C₄×D₃	—	3	4	no	—
136	C₄×D₃	—	3	4	no	—
137	Dic₆	—	3	4	no	—
138	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
139	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
140	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
141	C₃⋊C₈	—	3	4	no	—
142	C₂×C₉	—	2	2	no	—
143	C₂×C₉	#504	1	2	yes	complemented
144	C₂×C₉	C₂³×C₈	1	1	yes	characteristic
145	D₉	—	2	4	no	—
146	#41	—	9	4	no	—
147	#41	—	9	4	no	—
148	C₂×Q₈	—	9	1	no	—
149	C₂×D₄	—	9	2	no	—
150	C₂×D₄	—	9	1	no	—
151	C₂²×C₄	—	9	2	no	—
152	C₂²×C₄	C₄×D₉	1	1	yes	characteristic
153	M₁₆	—	9	4	no	—
154	M₁₆	—	9	8	no	—
155	C₂×C₈	—	9	2	no	—
156	C₂×C₈	—	9	4	no	—
157	C₂×C₈	—	9	4	no	—
158	C₂×C₈	C₄×D₉	1	1	yes	characteristic
159	C₂×C₈	C₄×D₉	1	2	yes	—
160	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
161	C₂×C₈	C₂²×D₉	1	2	yes	—
162	C₁₆	—	9	4	no	—
163	C₁₆	C₂²×D₉	1	2	yes	—
164	C₁₆	C₂²×D₉	1	2	yes	—
165	C₂²×C₃	—	2	2	no	—
166	C₂²×C₃	C₂×D₃×C₈	1	2	yes	—
167	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
168	C₂×D₃	—	3	4	no	—
169	C₂×D₃	—	6	4	no	—
170	C₃×C₄	C₂×D₃×C₈	1	2	yes	—
171	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
172	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
173	Dic₃	—	3	4	no	—
174	C₉	C₂×#504	1	1	yes	characteristic, complemented, Sylow
175	C₂³	—	9	2	no	—
176	C₂³	C₈×D₉	1	1	yes	characteristic
177	Q₈	—	9	4	no	—
178	D₄	—	9	8	no	—
179	D₄	—	9	4	no	—
180	C₂×C₄	—	9	2	no	—
181	C₂×C₄	—	9	4	no	—
182	C₂×C₄	—	9	4	no	—
183	C₂×C₄	C₈×D₉	1	1	yes	characteristic
184	C₂×C₄	C₈×D₉	1	2	yes	—
185	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
186	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
187	C₈	—	9	4	no	—
188	C₈	C₂×C₄×D₉	1	1	yes	characteristic
189	C₈	C₂×C₄×D₉	1	2	yes	—
190	C₈	C₂³×D₉	1	1	yes	characteristic
191	C₂×C₃	—	2	2	no	—
192	C₂×C₃	#4901	1	2	yes	—
193	C₂×C₃	C₂²×D₃×C₈	1	1	yes	characteristic
194	D₃	—	6	4	no	—
195	C₂²	—	2	2	no	—
196	C₂²	—	9	4	no	—
197	C₂²	—	18	4	no	—
198	C₂²	C₂×C₈×D₉	1	2	yes	—
199	C₂²	C₂×C₈×D₉	1	1	yes	characteristic
200	C₄	—	9	4	no	—
201	C₄	C₂×C₈×D₉	1	1	yes	characteristic
202	C₄	C₂×C₈×D₉	1	2	yes	—
203	C₄	C₂²×C₄×D₉	1	1	yes	characteristic
204	C₃	C₂×#4901	1	1	yes	characteristic
205	C₂	—	2	2	no	—
206	C₂	—	18	4	no	—
207	C₂	#10588581	1	2	yes	direct product factor
208	C₂	C₂²×C₈×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×D₉
commutator	C₂×C₉	C₂³×C₈
Frattini	C₃×C₈	C₂³×D₃
Fitting	C₂²×C₉×C₁₆	C₂
socle	C₂²×C₃	C₂×D₃×C₈
prime radical	C₂×#3697	C₄
cosocle	C₈×C₉	C₂⁴
hypercenter	C₂²×C₁₆	D₉
hypocenter	C₉	C₂×#504
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₉×C₁₆	C₂	semidirect
3. C₂×#63371	C₂	semidirect
4. #10588581	C₂	direct (N × H)
5. C₂×#63357	C₂	semidirect
6. C₂×C₁₆×D₉	C₂	semidirect
17. C₂×C₉×C₁₆	C₂²	semidirect
18. #63371	C₂²	semidirect
20. #63357	C₂²	semidirect
21. C₁₆×D₉	C₂²	semidirect
83. C₂²×C₁₆	D₉	semidirect
125. C₂×C₁₆	C₂×D₉	semidirect
143. C₂×C₉	#504	semidirect
174. C₉	C₂×#504	semidirect
207. C₂	#10588581	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×#63464	2
C₂²×C₉×C₁₆	2
C₂×#63371	2
#10588581	2
C₂×#63357	2
C₂×C₁₆×D₉	2
C₂×#4901	3

Subgroups — C2×#10588581 #11899377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588581 #11899377