Subgroups — C₂×#10588604 #11858240

Order 1152.

864 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	C₂²×C₄²×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#3667	C₂	1	2	yes	maximal
3	#10588604	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄⋊(C₉⋊C₈)	C₂	1	4	yes	maximal, complemented
5	C₂×#4924	—	3	1	no	maximal
6	C₂³×C₄×C₉	C₄	1	2	yes	—
7	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₉	C₄	1	1	yes	characteristic
9	C₂×C₄²×C₉	C₄	1	4	yes	—
10	C₂×C₄²×C₉	C₄	1	1	yes	characteristic
11	C₂×C₄²×C₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₉	C₂²	1	4	yes	—
13	C₂×#3667	—	2	8	no	—
14	C₂×#3667	C₂²	1	8	yes	—
15	C₂²×C₉⋊C₈	C₂²	1	4	yes	—
16	C₄⋊(C₉⋊C₈)	C₂²	1	16	yes	complemented
17	C₂²×C₃×C₄²	D₃	1	1	yes	characteristic
18	C₂²×#208	—	3	2	no	—
19	#4924	—	3	8	no	—
20	C₂×C₄⋊(C₃⋊C₈)	—	3	4	no	—
21	C₂⁴×C₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₉	—	2	8	no	—
23	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₉	C₂×C₄	1	8	yes	—
25	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
28	C₂²×C₄×C₉	D₄	1	4	yes	—
29	C₂²×C₄×C₉	Q₈	1	4	yes	—
30	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₉	C₂³	1	2	yes	—
32	C₄²×C₉	C₂×C₄	1	4	yes	—
33	C₄²×C₉	C₂×C₄	1	4	yes	—
34	C₄²×C₉	C₂×C₄	1	4	yes	—
35	C₄²×C₉	C₂³	1	4	yes	—
36	#3667	—	2	16	no	—
37	C₂×C₉⋊C₈	—	2	8	no	—
38	C₂×C₉⋊C₈	C₂³	1	8	yes	—
39	C₂×#423	—	9	1	no	Sylow
40	C₂³×C₃×C₄	Dic₃	1	2	yes	—
41	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
42	C₂×C₃×C₄²	Dic₃	1	1	yes	characteristic
43	C₂×C₃×C₄²	Dic₃	1	4	yes	—
44	C₂×C₃×C₄²	Dic₃	1	1	yes	characteristic
45	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
46	C₂×C₃×C₄²	C₂×D₃	1	4	yes	—
47	C₂×#208	—	3	8	no	—
48	C₂×#208	—	6	8	no	—
49	C₂²×C₃⋊C₈	—	3	4	no	—
50	C₄⋊(C₃⋊C₈)	—	3	16	no	—
51	C₂³×C₉	—	2	4	no	—
52	C₂³×C₉	C₄⋊C₄	1	4	yes	—
53	C₂³×C₉	C₂²×C₄	1	2	yes	—
54	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₄×C₉	—	2	4	no	—
56	C₂×C₄×C₉	—	2	16	no	—
57	C₂×C₄×C₉	C₄⋊C₄	1	8	yes	—
58	C₂×C₄×C₉	C₄⋊C₄	1	4	yes	—
59	C₂×C₄×C₉	M₁₆	1	8	yes	complemented
60	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
61	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
63	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
64	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
65	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
66	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
67	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
68	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
69	C₉⋊C₈	—	2	8	no	—
70	C₂²×M₁₆	—	9	2	no	—
71	C₂²×C₄²	D₉	1	1	yes	characteristic
72	#423	—	9	8	no	—
73	C₂×C₄⋊C₈	—	9	4	no	—
74	C₂⁴×C₃	C₂×Dic₃	1	1	yes	characteristic
75	C₂²×C₃×C₄	—	2	8	no	—
76	C₂²×C₃×C₄	Dic₆	1	4	yes	—
77	C₂²×C₃×C₄	D₁₂	1	4	yes	—
78	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
79	C₂²×C₃×C₄	C₂×Dic₃	1	8	yes	—
80	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
81	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
82	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
83	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
84	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
85	C₃×C₄²	C₂×Dic₃	1	4	yes	—
86	C₃×C₄²	C₂×Dic₃	1	4	yes	—
87	C₃×C₄²	C₂×Dic₃	1	4	yes	—
88	C₃×C₄²	C₂²×D₃	1	4	yes	—
89	#208	—	6	16	no	—
90	C₂×C₃⋊C₈	—	3	8	no	—
91	C₂×C₃⋊C₈	—	6	8	no	—
92	C₂²×C₉	—	2	4	no	—
93	C₂²×C₉	—	2	8	no	—
94	C₂²×C₉	C₂×C₄⋊C₄	1	4	yes	—
95	C₂²×C₉	C₂×C₄⋊C₄	1	2	yes	—
96	C₂²×C₉	C₂×M₁₆	1	4	yes	—
97	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
98	C₄×C₉	—	2	4	no	—
99	C₄×C₉	C₂×C₄⋊C₄	1	2	yes	—
100	C₄×C₉	C₂×C₄⋊C₄	1	4	yes	—
101	C₄×C₉	C₂×M₁₆	1	8	yes	complemented
102	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
103	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
104	C₂³×C₄	Dic₉	1	2	yes	—
105	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
106	C₂×M₁₆	—	9	8	no	—
107	C₂×M₁₆	—	18	8	no	—
108	C₂²×C₈	—	9	4	no	—
109	C₂×C₄²	Dic₉	1	1	yes	characteristic
110	C₂×C₄²	Dic₉	1	4	yes	—
111	C₂×C₄²	Dic₉	1	1	yes	characteristic
112	C₂×C₄²	C₂×D₉	1	4	yes	—
113	C₂×C₄²	C₂×D₉	1	2	yes	—
114	C₄⋊C₈	—	9	16	no	—
115	C₂³×C₃	—	2	4	no	—
116	C₂³×C₃	C₄⋊Dic₃	1	4	yes	—
117	C₂³×C₃	C₂²×Dic₃	1	2	yes	—
118	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
119	C₂×C₃×C₄	—	2	4	no	—
120	C₂×C₃×C₄	—	2	16	no	—
121	C₂×C₃×C₄	#208	1	8	yes	—
122	C₂×C₃×C₄	C₄⋊Dic₃	1	8	yes	—
123	C₂×C₃×C₄	C₄⋊Dic₃	1	4	yes	—
124	C₂×C₃×C₄	C₂×Dic₆	1	4	yes	—
125	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
126	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
127	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
128	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
129	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
130	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
131	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
132	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
133	C₃⋊C₈	—	6	8	no	—
134	C₂×C₉	—	2	4	no	—
135	C₂×C₉	#423	1	4	yes	complemented
136	C₂×C₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₉	C₂²×M₁₆	1	2	yes	—
138	C₂⁴	C₂×Dic₉	1	1	yes	characteristic
139	C₂²×C₄	—	2	8	no	—
140	C₂²×C₄	Dic₁₈	1	4	yes	—
141	C₂²×C₄	D₃₆	1	4	yes	—
142	C₂²×C₄	C₂×Dic₉	1	2	yes	—
143	C₂²×C₄	C₂×Dic₉	1	8	yes	—
144	C₂²×C₄	C₂×Dic₉	1	2	yes	—
145	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
146	C₂²×C₄	C₂×Dic₉	1	2	yes	—
147	C₂²×C₄	C₂²×D₉	1	2	yes	—
148	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
149	M₁₆	—	18	16	no	—
150	C₂×C₈	—	9	8	no	—
151	C₂×C₈	—	18	8	no	—
152	C₄²	C₂×Dic₉	1	4	yes	—
153	C₄²	C₂×Dic₉	1	4	yes	—
154	C₄²	C₂×Dic₉	1	4	yes	—
155	C₄²	C₂²×D₉	1	4	yes	—
156	C₂²×C₃	—	2	8	no	—
157	C₂²×C₃	—	2	4	no	—
158	C₂²×C₃	C₂×#208	1	4	yes	—
159	C₂²×C₃	C₂×C₄⋊Dic₃	1	4	yes	—
160	C₂²×C₃	C₂×C₄⋊Dic₃	1	2	yes	—
161	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
162	C₃×C₄	—	2	4	no	—
163	C₃×C₄	C₂×#208	1	8	yes	—
164	C₃×C₄	C₂×C₄⋊Dic₃	1	2	yes	—
165	C₃×C₄	C₂×C₄⋊Dic₃	1	4	yes	—
166	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
167	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
168	C₉	C₂×#423	1	1	yes	characteristic, complemented, Sylow
169	C₂³	—	2	4	no	—
170	C₂³	C₄⋊Dic₉	1	4	yes	—
171	C₂³	C₂²×Dic₉	1	2	yes	—
172	C₂³	C₂²×Dic₉	1	1	yes	characteristic
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	2	16	no	—
175	C₂×C₄	#3667	1	8	yes	complemented
176	C₂×C₄	C₄⋊Dic₉	1	8	yes	—
177	C₂×C₄	C₄⋊Dic₉	1	4	yes	—
178	C₂×C₄	C₂×Dic₁₈	1	4	yes	—
179	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
180	C₂×C₄	C₂×D₃₆	1	2	yes	—
181	C₂×C₄	C₂×D₃₆	1	4	yes	—
182	C₂×C₄	C₂²×Dic₉	1	4	yes	—
183	C₂×C₄	C₂²×Dic₉	1	4	yes	—
184	C₂×C₄	C₂²×Dic₉	1	2	yes	—
185	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
186	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
187	C₈	—	18	8	no	—
188	C₂×C₃	—	2	4	no	—
189	C₂×C₃	#4924	1	4	yes	—
190	C₂×C₃	C₂²×#208	1	2	yes	—
191	C₂×C₃	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
192	C₂²	—	2	4	no	—
193	C₂²	—	2	8	no	—
194	C₂²	C₂×#3667	1	4	yes	—
195	C₂²	C₂×C₄⋊Dic₉	1	4	yes	—
196	C₂²	C₂×C₄⋊Dic₉	1	2	yes	—
197	C₂²	C₂³×Dic₉	1	1	yes	characteristic
198	C₄	—	2	4	no	—
199	C₄	C₂×#3667	1	8	yes	complemented
200	C₄	C₂×C₄⋊Dic₉	1	4	yes	—
201	C₄	C₂×C₄⋊Dic₉	1	2	yes	—
202	C₄	C₂²×Dic₁₈	1	1	yes	characteristic
203	C₄	C₂²×D₃₆	1	1	yes	characteristic
204	C₃	C₂×#4924	1	1	yes	characteristic
205	C₂	—	2	4	no	—
206	C₂	#10588604	1	4	yes	direct product factor
207	C₂	C₂²×#3667	1	2	yes	—
208	C₂	C₂²×C₄⋊Dic₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂²×C₄²×C₉	C₂
socle	C₂³×C₃	C₂²×Dic₃
prime radical	C₂⁴×C₃	C₂×Dic₃
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂²×C₄²	D₉
hypocenter	C₉	C₂×#423
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
3. #10588604	C₂	direct (N × H)
4. C₂×C₄⋊(C₉⋊C₈)	C₂	semidirect
16. C₄⋊(C₉⋊C₈)	C₂²	semidirect
59. C₂×C₄×C₉	M₁₆	semidirect
101. C₄×C₉	C₂×M₁₆	semidirect
135. C₂×C₉	#423	semidirect
168. C₉	C₂×#423	semidirect
175. C₂×C₄	#3667	semidirect
199. C₄	C₂×#3667	semidirect
206. C₂	#10588604	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×C₄²×C₉	2
C₂²×#3667	2
#10588604	2
C₂×C₄⋊(C₉⋊C₈)	2
C₂×#4924	3

Subgroups — C2×#10588604 #11858240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588604 #11858240